Janet's savings in January is $800
What is word problem?A word problem in math is a math question written as one sentence or more. This statements are interpreted into mathematical equation or expression.
Represent Mary's savings by x and Janet's savings by y
7/4 = x/y
40/100 × x = 40x/100 = 2x/5
New savings for Mary =
x -2x/5 = 5x - 2x)/5 = 3x/5
50/100 × y = y/2
New savings for Janet =
y + y/2 = 3y/2
3y/2 + 3x/5 = 2040
15y + 6x = 20400
7y = 4x
y = 4/7x
Substitute (4/7)x for y
15( 4/7) x + 6x = 20400
(60/7 )x + 6x = 20400
60x + 42x = 142800
102x = 142800
x = 142800/102
x = $ 1400
y = 4/7 × 1400
y = $800
Therefore, the savings for Janet in January is $800.
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Which of the lines or segments below is tangent to circle P?
A) <—>
ZM
B)——
EX
C)——
LE
D)<—>
TX
Answer:
A) Line ZM is tangent to circle P.
3rd Grade Math Question
Answer:
∠ 1 = 110° , ∠ 2 = 70°
Step-by-step explanation:
∠ 1 and ∠ 2 lie on a straight line and sum to 180° , that is
6x + 20 + 4x + 10 = 180
10x + 30 = 180 ( subtract 30 from both sides )
10x = 150 ( divide both sides by 10 )
x = 15
Then
∠ 1 = 6x + 20 = 6(15) + 20 = 90 + 20 = 110°
∠ 2 = 4x + 10 = 4(15) + 10 = 60 + 10 = 70°
Graphing Linear Inequalities and Systems of Linear Inequalities in Real-World Situations - Item 50373Question 2 of 7
A coffee shop orders at most $ 3 , 500 worth of coffee and tea. The shop needs to make a profit of at least $ 1 , 900 on the order. The possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea:
6 c + 13 t ≤ 3 , 500
3 . 50 c + 4 t ≥ 1 , 900
Which graph's shaded region represents the possible combinations of coffee and tea for this order?
Material Cost per
Pound Profit per
Pound
Coffee $6.00 $3.50
Tea $13.00 $4.00
CLEAR CHECK
A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space above both lines is shaded.
A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space between the 2 lines after they cross near the 500 mark is shaded.
A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space between the 2 lines between the Y-axis and where they cross near the 500 mark is shaded.
A graph with X-axis labeled c and points labeled 100 to 600, and Y-axis labeled t, with points labeled 100 to 600. 1 line starts just under 300 on the Y-axis and goes to the right of the X-axis. Another line starts at about 450 on the Y-axis and goes to just past the 500 on the X-axis. The space below both lines is shaded.
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Answer:
695,512
Step-by-step explanation:
no explanation just x
Jolly Goods Limited specialized in hand-made christmas ornaments. these ornaments go through three processes: cutting, assembling and finishing. two days ago, the company received an unexpected order for 2,000 ornaments. both the cutting and assembling depatments have the capacity to fulfill the order and would have to work at 100% capacity to complete it. due to the amount of detailed work required to produce each ornament, the finishing department does not have enough time to meet the deadline. the company as a whole is working at 85% of capacity. as a result, the company is concerned that it will be unable to accept the order.
Jolly Goods Limited may not be able to accept the order for 2,000 ornaments due to the limited capacity of the finishing department. While the cutting and assembling departments have the capacity to fulfill the order by working at 100% capacity, the finishing department cannot complete the required work within the given deadline. The company as a whole is operating at 85% of capacity, which suggests that the finishing department is already working close to its maximum capacity.
Jolly Goods Limited specializes in hand-made Christmas ornaments and has three processes: cutting, assembling, and finishing. The company received an unexpected order for 2,000 ornaments. To determine if the order can be accepted, we need to assess the capacity of each department and their ability to meet the demand.The cutting and assembling departments have the capacity to fulfill the order since they can work at 100% capacity. This means that they have the resources and time required to complete the cutting and assembling processes for 2,000 ornaments.However, the finishing department does not have enough time to meet the deadline. The detailed work involved in the finishing process takes longer than the available time. As a result, the finishing department is operating at a limited capacity and cannot handle the additional workload of the unexpected order.The overall capacity of the company is operating at 85%. This indicates that the company's resources are already allocated to other orders and projects. Working at 100% capacity in the cutting and assembling departments means that there is limited room to accommodate the additional workload in the finishing department.Therefore, based on the limited capacity of the finishing department and the company as a whole, Jolly Goods Limited may not be able to accept the order for 2,000 ornaments.For more such questions on Jolly Goods Limited, click on:
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find the inverse of each equation
The inverse of the equation is determined as [tex]y = \log_{6}(-3x)[/tex].
option D is the correct answer.
What is the inverse of the equation?The inverse of the equation is calculated by applying the following method;
The given equation;
y = - 6ˣ/3
The inverse of the equation is calculated as;
multiply through by 3
[tex]-3x = 6^y[/tex]
Take the logarithm of both sides of the equation with base -6:
[tex]\log_{6}(-3x) = y[/tex]
Finally, replace y with x to obtain the inverse equation as follows;
[tex]y = \log_{6}(-3x)[/tex]
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Given rhombus LMNO below. If m
The measure of angle LOP is given as follows:
m < LOP = 52º.
How to obtain the angle measure?The segment OP bisects the angle O of the rhombus into two smaller angles, which are NOP and LOP.
.
A bisection means that the larger angle is divided into two smaller angles of equal measure.
The measure of angle NOP is given as follows:
m < NOP = 52º.
Hence the measure of angle LOP is given as follows:
m < LOP = 52º.
Missing InformationThe final sentence is to find the measure of angle LOP.
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Tasha used the pattern in the table to find the value of 4 Superscript negative 4.
Powers of 4
Value
4 squared
16
4 Superscript 1
4
4 Superscript 0
1
4 Superscript negative 1
One-fourth
4 Superscript negative 2
StartFraction 1 Over 16 EndFraction
She used these steps.
Step 1 Find a pattern in the table.
The pattern is to divide the previous value by 4 when the exponent decreases by 1.
Step 2 Find the value of 4 Superscript negative 3.
4 Superscript negative 3 = StartFraction 1 Over 16 EndFraction divided by 4 = StartFraction 1 Over 16 EndFraction times one-fourth = StartFraction 1 Over 64 EndFraction
Step 3 Find the value of 4 Superscript negative 4.
4 Superscript negative 4 = StartFraction 1 Over 64 EndFraction divided by 4 = StartFraction 1 Over 64 EndFraction times one-fourth = StartFraction 1 Over 256 EndFraction
Step 4 Rewrite the value for 4 Superscript negative 4.
StartFraction 1 Over 256 EndFraction = negative StartFraction 1 Over 4 Superscript negative 4 EndFraction
The value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.
In the given table, Tasha observed a pattern in the powers of 4. When the exponent decreases by 1, the previous value is divided by 4. Using this pattern, she determined the values for 4 squared, 4 Superscript 1, 4 Superscript 0, 4 Superscript negative 1, and 4 Superscript negative 2.
To find the value of 4 Superscript negative 3, she divided the previous value (StartFraction 1 Over 16 EndFraction) by 4, resulting in StartFraction 1 Over 64 EndFraction.
Similarly, for 4 Superscript negative 4, she divided the previous value (StartFraction 1 Over 64 EndFraction) by 4, yielding StartFraction 1 Over 256 EndFraction.
Finally, to rewrite the value for 4 Superscript negative 4, she expressed it as negative StartFraction 1 Over 4 Superscript negative 4 EndFraction.
Therefore, the value of 4 Superscript negative 4 is negative StartFraction 1 Over 4 Superscript negative 4 EndFraction, which simplifies to StartFraction 1 Over 256 EndFraction
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what would be your first step in completely factoring 6a^2-15a+6
The completely factoring form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
To completely factor the expression 6a^2 - 15a + 6, the first step is to check if there is a common factor among the coefficients (6, -15, and 6) and the terms (a^2, a, and 1).
In this case, we can see that the common factor among the coefficients is 3, so we can factor out 3:
3(2a^2 - 5a + 2)
Now we need to factor the quadratic expression inside the parentheses further. We are looking for two binomials that, when multiplied, give us 2a^2 - 5a + 2. The factors of 2a^2 are 2a and a, and the factors of 2 are 2 and 1. We need to find two numbers that multiply to give 2 and add up to -5.
The numbers -2 and -1 fit this criteria, so we can rewrite the expression as:
3(2a - 1)(a - 2)
Therefore, the completely factored form of 6a^2 - 15a + 6 is 3(2a - 1)(a - 2).
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A train consists of a locomotive and two carriages. The mass of the locomotive is 5600 kg and the mass brakes. The train comes to rest after travelling 360 m. The resistance forces throughout this motion are of each carriage is 3200 kg. The train is moving at a speed of 40 km h¹ when the driver applies the constant, 700 N on the locomotive and 400 N on each carriage. a Find the force in the coupling between the first carriage and the locomotive. b Is this force a tension or a thrust?
a) The force in the coupling between the first carriage and the locomotive can be found by analyzing the net force acting on the train. It is determined to be 100 N.
b) The force in the coupling between the first carriage and the locomotive is a tension force.
a) To find the force in the coupling between the first carriage and the locomotive, we need to analyze the forces acting on the train.
The forces acting on the train are:
The driving force applied by the locomotive: 700 N
The resistance force of each carriage: 400 N (assuming equal resistance forces for both carriages)
The force in the coupling between the first carriage and the locomotive (unknown)
Since the train comes to rest, the net force acting on the train must be zero. We can set up the equation for the net force as:
Net force = Driving force - Resistance force - Force in coupling = 0
Substituting the given values:
700 N - 2(400 N) - Force in coupling = 0
Simplifying the equation:
700 N - 800 N - Force in coupling = 0
-100 N - Force in coupling = 0
Therefore, the force in the coupling between the first carriage and the locomotive is 100 N (opposite in direction to the driving force).
b) The force in the coupling between the first carriage and the locomotive is a tension force. Tension forces act along a string, cable, or any stretched connection. In this case, the coupling acts as a connection between the locomotive and the first carriage, so the force in the coupling is a tension force.
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6. The diagram shows two points A and B. B is 40m East and then 55m South. Work out the bearing of B from A.
Answer:
X=68m
Step-by-step explanation:
X²=40²+55²
X²=1600+3025
X²=4625
X=(4625)½
X=68m.
A car that averages 22 miles per gallon emits 4.3 metric tons of carbon dioxide per year. A passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. How much less carbon dioxide does a commuter who takes a bus emit in a year compared to a commuter who drives everyday?
13.5 metric tons
2.1 metric tons
5.1 metric tons
3.99 metric tons
The answer is 3.99 metric tons.
To calculate the difference in carbon dioxide emissions between a commuter who takes a bus and one who drives a car every day, we need to compare the emissions of each mode of transportation per person.
The car averages 22 miles per gallon, which means it emits 4.3 metric tons of carbon dioxide per year. However, we don't know the number of passengers in the car.
The passenger bus emits 9.2 metric tons of carbon dioxide per year and can carry 30 people at a time. To find the emissions per person, we divide the total emissions by the number of passengers. In this case, each person on the bus emits 9.2 / 30 = 0.3067 metric tons of carbon dioxide per year.
To determine the difference in emissions, we subtract the emissions per person for the bus from the emissions per person for the car. Therefore, the difference is 4.3 - 0.3067 = 3.9933 metric tons of carbon dioxide per year.
Rounding this value to two decimal places, we get 3.99 metric tons.
Therefore, the answer is 3.99 metric tons.
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which is true regarding the sequence below?
5,2,-3,-10,-19
Answer: Its going down by odd numbers
Step-by-step explanation:
5-2=3, 2-(-3)= 5, then it would go on 7, 9, 11, 13...
Answer:
The difference between the numbers does not follow a common pattern; hence, the sequence is not arithmetic.
Step-by-step explanation:
Let's take the 1st two digits, 5 and 2
The difference between the numbers, 5-2 = 3
Following this pattern,
2-(-3) = 5
-3-(-10) = 7 and,
-10-(-19) = 9.
We can see that the differences are 3, 5, 7 and 9 and therefore we can prove that there is no common difference between the numbers.
Hence the sequence does not follow an arithmetic pattern as there is no common difference
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Decide whether you have enough information to find the measures of x and y. If you do, find the angle
If you don't, write "Not Enough Info" (NEI)
which expression is equivalent to the given expression assume the denominatior does not equal zero 14x4y5/7xry2
The expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.
This expression can be simplified as follows: Simplifying the expression 14x^4y^5/7xr^y^2First, we can write the given expression as shown below:14 x 4 * y^5 / (7 * x * r * y^2) = 2 * 7 * x^3 * y^3 / 7 * r * x * y^2 = 2x^2y/rr.
Now, the numerator and the denominator have x, y, and r, and we can cancel them out as shown below:2x^2y/rr = 2xy * x * x / rr * y * y / y * y = 2x^3y^3/r.
Therefore, the expression equivalent to the given expression 14x^4y^5/7xr^y^2 is 2x^3y^3/r.
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A bag contains red marbles, blue marbles and green marbles only. The ratio of the number of each marble is Red:Green:Blue=12:5:2. There are 112 more red marbles than green marbles. Work out the number of blue marbles
Answer:
There are 14 blue marbles in the bag.
Step-by-step explanation:
Let's call the number of green marbles "x". Then we know that the number of red marbles is 112 more than x, or x+112. We can use the ratio to find the number of blue marbles.
First, we need to find the total number of parts in the ratio. That's 12+5+2=19.
Next, we can use the ratio to set up an equation. The number of blue marbles is 2/19 of the total number of marbles. We can write this as:
2/19 (x + x + 112 + blue) = blue
Simplifying this equation, we get:
2x + 224 = 17blue
Now we can solve for blue:
blue = (2x + 224)/17
We know that blue is a whole number, so we need to find a value of x that makes the numerator of this fraction divisible by 17. After some trial and error, we find that x=3 works:
blue = (2(3) + 224)/17 = 14
Therefore, there are 14 blue marbles in the bag.
Which of the following is the best use for the sign chart when graphing
rational functions?
OA. To check whether F(x) is a straight or curved line for values of x
B. To check whether F(x) has a positive or negative slope
OC. To check whether F(x) reaches a maximum or a minimum
OD. To check whether F(x) is positive or negative for values of x
The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x.
A sign chart, also known as an interval chart, is a tool used to determine the sign (positive or negative) of a function over different intervals. When graphing rational functions, it is essential to identify the intervals where the function is positive or negative.
By constructing a sign chart for the rational function, you can analyze the behavior of the function and determine its sign over different intervals. This information is crucial for sketching an accurate graph of the rational function.
The sign chart helps identify intervals where the function is positive (above the x-axis) or negative (below the x-axis), which directly impacts the shape and position of the graph. It provides information about the regions where the function is increasing or decreasing.
The best use for a sign chart when graphing rational functions is Option D: To check whether F(x) is positive or negative for values of x. Options A, B, and C are not the best uses for a sign chart when graphing rational functions. Checking whether the function is a straight or curved line (Option A), the slope (Option B).
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Help with question in picture
The factoring of the polynomials gives;
1) Option C
2) Option A
3) Option B
4) Option C
5) Option A
6) Option B
7) Option C
8) Option C
9) Option B
10) Option B
How is a polynomial factored?1) 9x - 9
9(x - 1)
2) [tex]3x^2 - 9x[/tex]
3x(x - 3)
3) [tex]36x^2 - 1[/tex]
By the difference of two squares;
(6x + 1) ( 6x - 1)
4) [tex]x^2 - 4[/tex]
By the difference of two squares;
(x + 2) (x - 2)
5)
[tex]x^2 + 12x + 36\\x^2 + 6x + 6x + 36[/tex]
x(x + 6) + 6(x + 6)
(x + 6) (x + 6)
[tex](x + 6)^2[/tex]
6)
[tex]25x^2 - 20x + 4\\5x^2 + 2(5x) -2 + (-2)^2\\(5x - 2)^2[/tex]
7) [tex]x^2 - 3x - 54[/tex]
(x + 6) (x - 9)
8) [tex]2x^2 + 9x + 18 x+ 81\\ 2x^2 + 18 x + 9x + 81[/tex]
2x(x + 9) + 9 (x + 9)
(2x + 9) (x + 9)
9)
[tex]9y^2 + 18y + 8\\9y^2 + 12y + 6y + 8[/tex]
3y(3y + 4) + 2y(3y +4)
(3y + 2) (3y + 4)
10)
[tex]20z^2 - 3z - 9\\20z^2 - 15z + 12z - 9[/tex]
5z(4z - 3) + 3(4z - 3)
(5z - 3) (4z + 3)
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maths homework struggling
Answer:
Θ = 23.9°
Step-by-step explanation:
Use inverse tangent in a calculator.
tan Θ = 23/52
tan Θ = 0.4423
tan^-1 0.4423 = 23.9°
he class is trying to determine who will take care of the class hamster for the weekend. In order to win the chance, you must flip heads on a coin and then spin an even number on a spinner with 9 equal sections labeled from 1 - 9. What is the probability of winning the chance to take care of the hamster?
Answer:
2/9
Step-by-step explanation:
Coin
A coin has 1 side heads and 1 side tails.
total number of possible outcomes = 2
desired outcome: heads
number of desired outcomes = 1
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(heads) = 1/2
Spinner
The spinner has 9 sections of equal size.
possible outcomes: the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9
total number of possible outcomes = 9
desired outcome: even number
number of desired outcomes = 4
p(event) = (number of desired outcomes)/(total number of possible outcomes)
p(even number) = 4/9
Combined probability
The coin and spinner are independent events. The overall probability of independent events is the product of the individual probabilities.
p(heads then even) = 1/2 × 4/9 = 4/18 = 2/9
Answer: 2/9
F(x) = 2x + 3 and g(x) = -4x - 27 find the intersection
Answer: (-5, -7)
Step-by-step explanation: To find the intersection of two functions, you need to set them equal to each other and solve for x.
In this case, we have:
2x + 3 = -4x - 27
Adding 4x to both sides, we get:
6x + 3 = -27
Subtracting 3 from both sides, we get:
6x = -30
Dividing both sides by 6, we get:
x = -5
Now that we have the value of x, we can find the corresponding value of y by plugging it into either of the original equations. Let's use f(x) = 2x + 3:
f(-5) = 2(-5) + 3 = -7
Therefore, the intersection of the two functions is (-5, -7).
Which graph best represents the solution to the following pair of equations?
y = 4x + 2
y = x + 5
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair 1, 6.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair 2, negative7.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair negative 1, negative 6.
A graph is plotted with values ranging from negative 10 to 10 on both x axis and y axis at increments of 1. Two lines having equations y is equal to 4 times x plus 2 and y is equal to x plus 5 are plotted. These 2 lines intersect at the ordered pair negative 2, 7.
The given pair of equations is y = 4x + 2 and y = x + 5, and we are to determine which of the given graphs represents their solution. The first equation is in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. Comparing this with the given equation, we see that its slope is 4 and y-intercept is 2.
The second equation is also in slope-intercept form, y = mx + b. Comparing it with the given equation, we see that its slope is 1 and y-intercept is 5.Since we have two lines, we need to find their point of intersection. Substituting y = 4x + 2 into y = x + 5, we have4x + 2 = x + 5Simplifying the equation, we get3x = 3, which gives x = 1.
Substituting this value of x into either of the equations, say y = 4x + 2, we have y = 4(1) + 2 = 6. Hence, the point of intersection is (1, 6). Now, let's examine the given graphs and see which one has (1, 6) as a point of intersection:
Graph 1: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 1 is not the solution.
Graph 2: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 2 is not the solution.
Graph 3: The line y = 4x + 2 passes through (-1, -2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2.
Hence, these two lines cannot intersect at (1, 6). Graph 3 is not the solution.Graph 4: The line y = 4x + 2 passes through (0, 2) and has a slope of 4, which means it will be steeper than the line y = x + 5. The line y = x + 5 passes through (0, 5) and has a slope of 1, which means it will be flatter than the line y = 4x + 2. Hence, these two lines cannot intersect at (1, 6). Graph 4 is not the solution.
Therefore, none of the given graphs represents the solution to the pair of equations.
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Please help!! I don’t understand what to do
Answer:
y = x^2 + 6x +7
y=-x+1
Step-by-step explanation:
To answer this question, we need to find the equation for the line and for the parabola. So, let's do just that!
Line:
The line has a slope of -1 and and y-intercept of 1. This means that the equation for the line is y=-x+1.
Parabola:
To find the vertex form of a parabola, we must first find the vertex form of a parabola. The vertex form of a parabola is y=a(x-h)^2+k, where the vertex is (h,k). Since the vertex of the parabola is (-3,-2), h=-3 and k=-2. Let's plug these values into the vertex form of a parabola.
y=a(x-h)^2+k
y=a(x-(-3))^2+(-2)
y=a(x+3)^2-2
We're not done yet, though, as we still need to find the value of a. To do this, we will take one of the points on the parabola and plug it into the equation. I will be using the point (-1,2).
y=a(x+3)^2-2 [Plug in x and y values]
2=a((-1)+3)^2-2 [Simplify]
2=a(2)^2-2 [Simplify]
2=4a-2 [Add 2 to both sides]
4=4a [Divide both sides by 4]
a=1
Now, we know that the equation of our parabola in vertex form is y=(x+3)^2-2. This isn't what the problem is asking for, though. Instead, they want the standard form of the parabola. To do this, we will need to expand y=(x+3)^2-2.
y=(x+3)^2-2
y=x^2 + 6x + 9 -2
y = x^2 + 6x +7
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A merchant uses the rule: selling price equals cost plus 10% of cost. This is a function. _-_-_Why?_-_-_
_-_-_Why?_-_-_
_-_-_Why?_-_-_
I don't need the equasion, I need to know how it's a function.
The rule used by the merchant is a function because it establishes a relationship between the cost of an item and its selling price
What is a function?A function is simply described as a mathematical rule, law or expression that shows the relationship between two variables.
These two variables are known as;
The dependent variablesThe independent variablesFrom the information given, we have that;
Function assigns a unique selling price for every cost input
Input: cost
Output: selling price = cost + 10% of cost Formula: SP = C + 0.1C.
By following this rule, consistent selling prices can be determined efficiently based on cos
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If a school room is 32 metres long and 11 metres wide, how many boy will it accommodate allowing 8sq. metres to each boy? A. 56 boys B. 54 boys C. 44 boys D. 36 boys E. 34 boys
Answer:
[tex]\huge\boxed{\sf 44\ boys}[/tex]
Step-by-step explanation:
Area of rectangle:= Length × Width
Given data:Length = 32 m
Width = 11 m
Solution:Area of school room:
= Length × Width
= 32 × 11
= 352 m²
Number of boys to accommodate 8 sq. meters:= 352 / 8
= 44 boys[tex]\rule[225]{225}{2}[/tex]
Please help!!!! I will give points to correct answer !!!
The equation that shows the Pythagorean identity is true for θ = 270° and is in the form sin²θ + cos²θ = 1 is option B. 0² + (-1)² = 1
The Pythagorean identity is a fundamental trigonometric identity that relates the sine and cosine functions. It states that for any angle θ, the sum of the squares of the sine and cosine of that angle is equal to 1: sin²θ + cos²θ = 1.
We are given θ = 270° and we need to select the equation that satisfies the Pythagorean identity in the given form.
Let's evaluate each option:
A. 0² + 1² = 1
In this case, sin²θ = 0² = 0 and cos²θ = 1² = 1. Adding them together, we get 0 + 1 = 1, which satisfies the Pythagorean identity.
B. 0² + (−1)² = 1
Here, sin²θ = 0² = 0 and cos²θ = (−1)² = 1. Adding them, we have 0 + 1 = 1, which satisfies the Pythagorean identity.
C. (−1)² + 0² - 1
In this equation, sin²θ = (−1)² = 1 and co
s²θ = 0² = 0. However, the equation does not satisfy the Pythagorean identity because 1 + 0 - 1 ≠ 1.
D. 1² + 0² = 1
For this option, sin²θ = 1² = 1 and cos²θ = 0² = 0. Adding them together, we get 1 + 0 = 1, which satisfies the Pythagorean identity.
Based on our evaluation, options A and B both satisfy the Pythagorean identity for θ = 270°. Therefore, either A or B can be selected as the correct equation.The correct answer is b.
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The Question was Incomplete, Find the full content below :
Which equation shows that the Pythagorean identity is true for θ = 270°?
Select the equation that is in the form sin²θ+ cos²θ = 1.
A. 0² + 1² = 1
B. 0² + (−1)² = 1
C. (-1)² + 0² - 1
D. 1² + 0² = 1
PLEASE ANSWER AND FILL IN THE BOX IF NEEDED
Answer:
A. p(t) = 16 -5t +2t²
Step-by-step explanation:
You want the interpolating polynomial for points (1, 13), (2, 14), and (3, 19).
Quadratic regressionThe given system of equations can be solved by your favorite method to find ...
a₀ = 16a₁ = -5a₂ = 2The interpolating polynomial is p(t) = 16 -5t +2t².
__
Additional comment
The points and the polynomial are graphed in the second attachment.
<95141404393>
The interpolating polynomial is (a) p(t) = 13 - 2.5t +1.5t²
How to determine the interpolating polynomialFrom the question, we have the following parameters that can be used in our computation:
Points = (1, 13), (2, 14), and (3, 19).
Using the general form of the quadratic formula, we have
a + b + c = 12
4a + 2b + c = 14
9a + 3b + c = 19
Subtract the equations to eliminate c
So, we have
3a + b = 2
5a + b = 5
Subtract the equations to eliminate b
So, we have
2a = 3
So, we have
a = 1.5
Next, we have
3a + b = 2
3(1.5) + b = 2
Evaluate
b = -2.5
Lastly, we have
4a + 2b + c = 14
4(1.5) + 2(-2.5) + c = 14
Evaluate
c = 13
So, the equation is p(t) = 13 - 2.5t +1.5t²
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The recipe for your gummy candy makes 2,000 grams, and looks like this:
5 packages of gelatin - for the gummy texture.
2 cup citric acid - for flavor
4 cup corn syrup - for flavor
2 cup of water
OR
5 Gel + 2 Ca + 4 Cs + 2Cw → 2000 Gu
The store manager that is responsible for ordering ingredients is taking a few weeks off for vacation now that they are vaccinated and coronavirus related restrictions are rolling back (hurray!). They want to know if they need to order more ingredients before they leave.
The current stock of supplies is:
32 packets of gelatin
64 cups of citric acid (4 gallons)
24,000Gu*2Ca2000Gu
64 cups of corn syrup (4 gallons)
The Problem:
The manager is going to be leaving for 2 weeks(12 work days), so you will need to make 24,000 grams of gummies while they are gone. How many of each ingredient does the manager need to order before they leave?
The manager should order 120 packages of gelatin, 240 cups of citric acid, and 480 cups of corn syrup before leaving for vacation to ensure there are enough ingredients to make 24,000 grams of gummies.
To make 24,000 grams of gummies while the manager is away, the manager needs to order the following ingredients:
Gelatin: The recipe calls for 5 packages of gelatin to make 2000 grams of gummies. Therefore, to make 24,000 grams, the manager needs to order 120 packages of gelatin (5 packages x 24).
Citric acid: The recipe requires 2 cups of citric acid to make 2000 grams of gummies. Since 24,000 grams are needed, the manager should order 240 cups of citric acid (2 cups x 120).
Corn syrup: The recipe calls for 4 cups of corn syrup to make 2000 grams of gummies. To make 24,000 grams, the manager needs to order 480 cups of corn syrup (4 cups x 120).
Water: The recipe states that 2 cups of water are required, and it remains the same regardless of the number of gummies being made. Therefore, no additional water needs to be ordered.
In summary, the manager should order 120 packages of gelatin, 240 cups of citric acid, and 480 cups of corn syrup before leaving for vacation to ensure there are enough ingredients to make 24,000 grams of gummies.
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A manufacturer determines that x units of a particular item will be sold when the price is p left parenthesis x right parenthesis equals 9000 space e to the power of negative 0.1 x end exponent dollars per unit. What is the approximate revenue in dollars, which is obtained from selling the 7th unit of this product?
The approximate revenue obtained from selling the 7th unit of this product is $24,387.93.
To find the revenue from selling the 7th unit, we first need to determine the price at which the 7th unit will be sold. We can do this by substituting x = 7 in the given price function:
p(7) = 9000e^(-0.1*7) = 9000e^(-0.7) = 3483.99
Therefore, the price at which the 7th unit will be sold is approximately $3,483.99.
Now we can calculate the revenue obtained from the sale of the 7th unit as the product of the price and the quantity:
Revenue = 7 * 3483.99 = $24,387.93
Thus, the approximate revenue obtained from selling the 7th unit of this product is $24,387.93.
It is important to note that the given price function is an example of an exponential decay function, which is often used to model situations where the demand for a product decreases as the price increases. In this case, the function shows that as the price increases, the quantity demanded decreases at an accelerating rate (-0.1 is the rate of decay). The revenue function can be derived as the product of the price and the quantity, and the revenue can be maximized by finding the price that will result in the highest quantity of units sold. However, in this problem, we were given the quantity and asked to find the revenue, so we simply used the price function to determine the price of the 7th unit and multiplied it by 7 to find the revenue.
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Using the Empirical Rule, approximate the following percentages for Parts A - E.
The distribution of weights of newborn babies in one region is bell-shaped with a mean of 3000 grams and standard deviation of 500 grams. For all questions below, show all relevant work.
Part A :Approximately, what percentage of newborn babies weigh more than 3000 grams?
Part B : Approximately, what percentage of newborn babies weigh more than 2000 grams?
Part C : Approximately, what percentage of newborn babies weigh less than 4000 grams?
Part D : Approximately, what percentage of newborn babies weigh between 2000 and 4000 grams?
Part E : What is the range of birth weights that would contain the middle 68% of newborn babies' weights?
Part A: Approximately 50% of newborn babies weigh more than 3000 grams. Part B: Approximately 84.13% of newborn babies weigh more than 2000 grams. Part C: Approximately 84.13% of newborn babies weigh less than 4000 grams. Part D: Approximately 68% of newborn babies weigh between 2000 and 4000 grams. Part E: The range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.
1: Calculate the Z-scores for the given weights using the formula: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.
For Part A:
Z = (3000 - 3000) / 500 = 0
Using the Z-table, we find that the percentage of babies weighing more than 3000 grams is approximately 50%.
For Part B:
Z = (2000 - 3000) / 500 = -2
Using the Z-table, we find that the percentage of babies weighing more than 2000 grams is approximately 97.72%. Since we want the percentage of babies weighing more than 2000 grams, we subtract this value from 100% to get approximately 2.28%.
For Part C:
Z = (4000 - 3000) / 500 = 2
Using the Z-table, we find that the percentage of babies weighing less than 4000 grams is approximately 97.72%.
For Part D:
To find the percentage of babies weighing between 2000 and 4000 grams, we subtract the percentage of babies weighing more than 2000 grams from the percentage of babies weighing less than 4000 grams.
Approximately 97.72% - 2.28% = 95.44%
For Part E:
Since the Empirical Rule states that approximately 68% of the data falls within one standard deviation of the mean, we need to find the weights that correspond to the boundaries of this range.
The lower boundary would be the mean minus one standard deviation: 3000 - 500 = 2500 grams.
The upper boundary would be the mean plus one standard deviation: 3000 + 500 = 3500 grams.
Therefore, the range of birth weights that would contain the middle 68% of newborn babies' weights is from 2500 grams to 3500 grams.
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Solve for x: 3x + 7 = 22.
Answer:
x = 5
Step-by-step explanation:
3x + 7 = 22 <-- Subtract 7 on both sides
3x = 15 <-- Divide both sides by 3 to isolate x
x = 5
The value of x is:
x = 5
Work/explanation:
The objective of this problem is to solve 3x + 7 = 22 by isolating x.
I begin by subtracting 7 from each side:
3x = 22 - 7
3x = 15
Next, I divide each side by 3:
x = 5
Hence, the value of x is 5.
