In 5th year, Anisa and Keith have the same amount of stock value. Anisa bought $100 worth of stock and gained $25 per year. Kevin bought $400 worth of stock and lost $35 per year.
Define equation.In mathematics, an equation is a relationship between two expressions that is expressed as an equality on each side of the equal to sign. An equation would be 3y = 16, for instance.
Given
1. For Anisa
For our problem, we know that she will make $25 annually, thus if x denotes the number of years in which she will make this gain 25x. She made a $100 initial deposit, which is also known as y. The following equation can be used to link the quantities if we assume that the stock value will remain constant throughout time:
y = 25x + 100
2. For Kevin
He is currently losing $35 annually. Let the x years be represented. He will lose -35 times year because we know that losses are represented by a minus sign. We now know that her initial investment y in our situation was $400. The following equation can be used to link the quantities if we assume that the stock value will remain constant throughout time:
y = -35x + 400
On year 5th
For Anisa
y = 25(5) + 100
y = 125 + 100
y = 225
For Kevin
y = -35x + 400
y = -35(5) + 400
y = -175 + 400
y = 225
In 5th year, Anisa and Keith have the same amount of stock value.
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I NEED HELP ON THIS QUESTION!!
Answer:
B
Step-by-step explanation:
Determine the equation of the line given by the table and compare with given options.
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (7, 19) ← 2 ordered pairs from the table
m = [tex]\frac{19-9}{7-2}[/tex] = [tex]\frac{10}{5}[/tex] = 2 , then
y = 2x + c ← is the partial equation of the line
to find c substitute any ordered pair from the table into the partial equation.
using (6, 17 ), that is x = 6, y = 17 , then
17 = 12 + c ⇒ c = 17 - 12 = 5
y = 2x + 5 ← equation of line from table, with y- intercept c = 5
thus the function with a y- intercept greater than the table line is B
Brian started cleaning at 3:33 PM and finished at 4:21 PM. How long did it take him.
Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes
How did we figure this out?First, we are figuring out what is given we are counting numbers or we can add to get to 4:21 PM.
Counting numbers:
[tex]\boxed{3:33=3:34=3:35=3:36=3:37=3:38=3:39=3:40 }[/tex]
Add the numbers:
[tex]\boxed{3:33+7=3:40+10=3:50+10=4:00+21=4:21}[/tex]
If we add the numbers it would be faster.
Therefore, when we add we get are answer.
Therefore, Brian started cleaning at 3:33 PM and finished at 4:21 PM. The correct answer is 48 minutes
Answer:
48
Step-by-step explanation:
Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21. At
the same store Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29. Heather bought
1lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23. Write the system of equations to determine how
much a pound of apples costs, a pound of oranges costs and a pound of bananas costs?. Equation 1:
Equation 2:
Equation 3:
0
The system of equations is:
3a + 2r + 7b = 21
2a + 6r + b = 29
a + 4r + 5b = 23
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
a = price of apples
r = price of oranges (I used r instead of letter o since o can be confused with zero)
b = price of bananas
Sally went to the grocery store and bought 3 lbs. of apples, 2 lbs. of oranges, and 7 lbs. of bananas for $21.
3a + 2r + 7b = 21
Kevin bought 2 lbs. of apples, 6 lbs. of oranges and 1 lb. of bananas for $29.
2a + 6r + b = 29
Heather bought 1 lb. of apples, 4 lbs. of oranges and 5 lbs. of bananas for $23.
a + 4r + 5b = 23
The system of equations is:
3a + 2r + 7b = 21
2a + 6r + b = 29
a + 4r + 5b = 23
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Find the 7th term in the
sequence
-1, -3, -9,...
Hint: Write a formula to help you.
1st term. Common Ratio(desired term - 1)
PLEASE HELP IM IN A RUSH PLEASEEEEEEEEEEEEEEEEEEE
Lainey is sliding down a water slide that is 322 feet long at a rate of 46 feet per second. How long will it take Lainey to travel from the top to the bottom of the slide?
A.
-7 seconds
B.
-276 seconds
C.
276 seconds
D.
7 seconds
During the rebuilding after World War II, we were short of tractors. The machine and tractor stations would lend each other equipment as needed. Three machine and tractor stations were neighbors. The first lent the second and third as many tractors as they each already had. A few months later, the second lent the first and third as many as they each had. Still later, the third lent the first and second as many as they each already had. Each station now had 24 tractors.
How many tractors did each station originally have?
The number of tractors lent by the first, second and third stations results in a system of three simultaneous equations which indicates;
The first originally station had 39 tractors, the second station had 21 tractors and the third station originally had 12 tractors
What are simultaneous equations?Simultaneous equations are a set of two or more equations that have common variables.
Let x represent the number of tractors at the first station, let y represent the number of tractors at the second tractor station, and let z, represent the number of tractors at the third tractor station
According to the details in the question, after the first transaction, we get
Number of tractors at the first station = x - y - z
Number of tractors at the second station = y + y = 2·y
Number of tractors at the third station = z + z = 2·z
After the second transaction, we get;
Number of tractors at the first station = 2·x - 2·y - 2·z
Number of tractors at the second station = 2·y - (x - y - z) - 2·z = 3·y - x - z
Number of tractors at the third station = 2·z + 2·z = 4·z
After the third transaction, we get;
Number of tractors at the first station = 2 × (2·x - 2·y - 2·z) = 4·x - 4·y - 4·z
Number of tractors at the second tractor station = 6·y - 2·x - 2·z
Number of tractors at the third tractor station = 4·z - (2·x - 2·y - 2·z) - (3·y - x - z) = 7·z - x - y
The three equations after the third transaction are therefore;
4·x - 4·y - 4·z = 24...(1)
6·y - 2·x - 2·z = 24...(2)
7·z - x - y = 24...(3)
Multiplying equation (2) by 2 and subtracting equation (1) from the result we get;
12·y - 4·x - 4·z - (4·x - 4·y - 4·z) = 16·y - 8·x = 48 - 24 = 24
16·y - 8·x = 24...(4)
Multiplying equation (3) by 2 and multiplying equation (2) by 7, then adding both results, we get;
14·z - 2·x - 2·y = 48
42·y - 14·x - 14·z = 168
42·y - 14·x - 14·z + (14·z - 2·x - 2·y) = 48 + 168
40·y - 16·x = 216...(5)
Multiplying equation (4) by 2 and then subtracting the result from equation (5), we get;
40·y - 16·x - (32·y - 16·x) = 216 - 48 = 168
8·y = 168
y = 168/8 = 21
The number of tractors initially at the second station, y = 21
16·y - 8·x = 24, therefore, 16 × 21 - 8·x = 24
8·x = 16 × 21 - 24 = 312
x = 312 ÷ 8 = 39
The number of tractors initially at the first station, x = 39
7·z - x - y = 24, therefore, 7·z - 39 - 21 = 24
7·z = 24 + 39 + 21 = 84
z = 84/7 = 12
The number of tractors initially at the third station, z = 12
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Calculate total pressure experienced by a diver working 15m below suraface of sea(10N/kg,density of water1g/cm3 and atmospheric pressure =100000N/m3
The total pressure experienced by a diver working 15m below surface of sea is 150000 Pa.
What is Pressure?Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.
We need to find the total pressure experienced by a diver working 15m below surface of sea.
P = h·ρ·g
P = pressure
h = depth = 15 m
ρ = density = 1g/cm³=1000kg/m³
g = acceleration due to gravity = 10 m/s²
Substitute the values in the formula of total pressure.
P=1000×15×10
P=150000Pa
Hence, 150000Pa is the total pressure experienced by a diver working 15m below surface of sea.
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I NEED HELP NEOW PLS
Step-by-step explanation:
SWT + TWU =180º therefore SWU must be a line. Aka SWU is linear. So SWT and TWU must be a linear pair.
SWT + SWT = 180º therefore 2SWT=180º deviding both sies by 2 we get SWT = 90º Therefore SWT is replacing TWU. SWT is substituted into TWU. So substitution.
SU | TV basically means the line that passes through both points S and U is perpendicular to the line that passes through both points T and V. Therefore it is the Defenition of perpendicular lines.
If this helped please rate the answer.
64 divided by blank equals 8
Answer: 8
Step-by-step explanation:
8 times 8 is 64
Based on Ben's work shown, how would he respond?
The point IS a solution to the system. Only one of the equations resulted in an
identity.
The point is NOT a solution to the system. Both equations resulted in identities.
The point is NOT a solution to the system. Only one of the equations resulted in
an identity.
The point IS a solution to the system. Both equations resulted in identities.
Correct option: (A) The point IS a solution to the system. Only one of the equations resulted in an identity.
What is an identity equation?An equality that is true regardless of the values selected for its variables is called an identity. They are used to rearrange or simplify algebraic formulas. The two halves of an identity are, by definition, interchangeable, and we are always free to switch one for the other.
An identity is an equation that, regardless of the values used, is always true. Since 2x + 3x will always equal 5, regardless of the value of, this statement is an identity. The example might be written as 2x+ 3x = 5x since identities can be represented with the symbol "≡"
2x + y = 4
now, putting the values in the equation (6,-8)
2(6) + (-8) = 4
or, 12 - 8 = 4
or, 4 ≡ 4
This equation, point IS a solution to the system.
x + 3y = - 20
or, 6 + 3(-8) = -20
or, 6 - 24 = -20
or, - 18 ≠ - 20
So, for this equation the result is not identity.
Thus, option A is the correct answer.
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Triangle ABC is transformed to obtain triangle A′B′C′:
A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 4, negative 4, B at 12,negative 4, C at 8, negative 12. Triangle A prime B prime C prime has A prime at ordered pair negative1, 1, B prime at negative 3, 1 C prime at negative 2, 3.
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime, because Triangle A prime B prime C prime is obtained by dilating Triangle ABC. By a scale factor of 1 over 4 and then rotating it about the origin by 180 degrees. The correct answer is B.
What is dilation?Dilation is a transformation that is used while resizing an object. The structures can be made longer or shorter via dilation. This transformation produces a picture that retains the original shape. There is, however, a significant fluctuation in the form. During a dilatation, the starting shape should be elongated or compressed.
All the coordinates of A'B'C' are -1/4 times those of ABC.
The dilation factor is 1/4, and rotation by 180° is indicated.
A'(-1, -1) = (-1/4) × A(4, -4)
= A(4x-1/4, -4x-1/4)
= (-1, -1)
B'(-3, 1) = (-1/4) × B(12, -4)
= B(12x-1/4, -4x-1/4)
= (-3, 1)
C'(-2, 3) = (-1/4) × C(8, -12)
= C(8x-1/4, -12x-1/4)
= (-2, 3)
Both coordinates are invalidated by a 180° rotation. In either sequence, it is the same as reflection across the x-axis and reflection across the y-axis.
Therefore, triangle A′B′C′ is obtained by dilating Triangle ABC by a scale factor of 1 over 4 and then rotating it about the origin by 180°.
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The complete question is:
Triangle ABC is transformed to obtain triangle A′B′C′:
A coordinate grid is labeled from negative 12 to 0 to 12 on both x- and y-axes at increments of 1. Triangle ABC has A at ordered pair 4, negative 4, B at 12,negative 4, C at 8, negative 12. Triangle A prime B prime C prime has A prime at ordered pair negative1, 1, B prime at negative 3, 1 C prime at negative 2, 3.
Which statement is correct for Triangle ABC. and Triangle A prime B prime C prime.?
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 6. and then rotating it about the origin by 90 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 4. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 180 degrees
Triangle ABC is similar to triangle A prime B prime C prime., because Triangle A prime B prime C prime. is obtained by dilating Triangle ABC. by a scale factor of 1 over 3. and then rotating it about the origin by 90 degrees
in a linear programming model, the constraints may be non-linear, but the objective function must be linear. true false
It is true that the objective function and the restrictions in a linear programming problem must be linear functions of the choice variables.
What is Linear Programming Model ?The method of choosing the best result from a linear function is known as linear programming. Making a few straightforward assumptions is the easiest way to accomplish linear optimization. As the goal function, the linear function is referred to. Real-life relationships can be quite challenging. However, such interactions can be represented using linear programming, which facilitates analysis of such relationships.
When the need of a mathematical model are represented by linear relationships as, the optimal result can also be obtained using a technique known as the linear programming (LP), sometimes known as linear optimization. A particular type of mathematical programming is linear programming.
Formally speaking, linear programming is the method for optimizing a linear objective function under the restrictions of the linear equality and linear inequality. Convex polytopes, a set defined as the total intersection of a finite number of half spaces, each of which is determined by the linear inequality, make up viable region.
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Simplify. Write your answer as a proper or improper fraction in simplest form.
imagine you compare the effectiveness of four different types of stimulants to keep you awake while revising statistics using a one-way anova. the null hypothesis would be that all four treatments have the same effect on the mean time kept awake. how would you interpret the alternative hypothesis?
The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.
If the one-way ANOVA test rejects the null hypothesis, it means that there is a significant difference in the mean time kept awake among the four treatments. This means that at least one of the treatments is more effective in keeping you awake than the others. It is important to note that the alternative hypothesis does not specify which of the treatments is more effective, only that at least one is different from the others. To determine which treatment is more effective, you would need to conduct additional tests, such as post-hoc tests.
The alternative hypothesis in this case would be that at least one of the four treatments has a different effect on the mean time kept awake compared to the others.
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graph the line y=3x-4
Answer:
See attached image
Step-by-step explanation:
You can graph lines on a website called desmos graphing calculator!
Answer:
Step-by-step explanation:
you replace x with anything you want I will do 0. Then the the first point is (0,-4). Now I am gonna replace x with something else like 4. The second point is (4,8), now connect the two points and you got a line.
in a study, a researcher finds that as a increases, b also increases. the analysis shows that the strength of the relationship is 0.78. what type of linear relationship is this?
The type of linear relationship is positive.
Correlation is a statistical measure that expresses the extent to which two variables are linearly related (meaning they change together at a constant rate). It's a common tool for describing simple relationships without making a statement about cause and effect. The correlation coefficient is a statistical measure of the strength of a linear relationship between two variables. Its values can range from -1 to 1. A coefficient of 1 shows a perfect positive correlation, or a direct relationship. A correlation coefficient of 0 means there is no linear relationship.
The type of linear relationship is positive.
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HELP with 4 and 6 please
Answer:
4.) a.) 2.01 b.) 404.01
6.) a.) 152.17 b.) 18412.17 c.) 153.14 d.) 18565.60
Step-by-step explanation:
To solve, use the exponential growth formula [tex]A_t=A_0(1+\frac{r}{p})^t[/tex] where
[tex]A_t[/tex] = Amount as a function of time
[tex]A_0[/tex] = Original amount
[tex]r[/tex] = rate
[tex]p[/tex] = period
[tex]t[/tex] = time
For question 4, let
[tex]A_0=400\\r=0.06\\p=12\\t=2[/tex]
So,
[tex]A_t=400(1+\frac{0.06}{12})^2\\A_t=400(\frac{201}{200})^2\\A_t=400(1.01)\\A_t=404.01[/tex]
So, the second-period interest would be 404.01-402=2.01
Question 6 can be solved using the same formula, but let
[tex]A_0=18260\\r=0.025\\p=\frac{12}{4}=3\\t_1=1\\t_2=2[/tex]
So,
[tex]A_t=18260(1+\frac{0.025}{3})^1\\A_t=18260(\frac{121}{120})^1\\A_t=18412.17[/tex]
The first-period interest would be 18412.17-18260=152.17
For the second-period, use [tex]t_2[/tex]:
[tex]A_t=18260(1+\frac{0.025}{3})^2\\A_t=18260(\frac{121}{120})^2\\A_t=18260(1.02)\\A_t=18565.60[/tex]
The second-period interest would be 18565.60-18412.17=153.43
What is the percent decrease from 100 to 82
Percent decrease from 100 to 82 is 18% decrease.
Calculating the % decrease from 100 to 82,
[tex]\frac{82-100}{100}[/tex]×100%
[tex]\frac{-18}{100}[/tex]×100%
on simplifying we get,
-18%
here, negative sign indicates that there is a decrease of percentage.
Hence, we get 18% decrease from 100 to 82.
How to calculate Percent decrease?
Do the % growth and reduction calculations. By dividing the new number by the initial value, the percentage is computed.
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. three football teams are taking part in a tournament. each team plays each other team once. for a win the team scores 3 points, the other team 0 points. for a draw both teams get 1 point each. which number of points is impossible, for any team to reach at the end of this tournament?
To get a number point 1 is impossible for any of the team to reach at the end of the described tournament.
As given in the question,
Total number of footballs teams = 3
Each team plays once with other team
Let three teams are Team1, Team2, and Team3
Team1 plays with Team2 and Team3
Team2 will play with Team3
Winning points = 3
Losing team points = 0
Withdraw teams points = 1
To reach in finals suppose Team1 plays with Team2 and Team3 and win
Points of team1 = 3 + 3
= 6points
As team plays once with other team , Team1 is out of the game.
Team2 and Team3 play with each other
To reach at the end of the tournament one team has to win let it be Team2
Points of Team2 = 3
Points of Team3 = 0
No withdraw game is possible to reach into finale.
Therefore, point 1 is impossible for any team to reach at the end of the tournament.
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An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tall platform. The equation for the object's height s at time t seconds after launch is s(t)= -4.9t^2 + 19.6t + 58.8, where s is in meters. How high will the object be after 3 seconds
73.5 ft
98.49 ft
161.7 ft
333.69 ft
The first option is true since the item achieved its maximum height of 73.5 feet.
What does a quadratic equation's vertex form mean?x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem. The answer could be simple or complicated.
This quadratic equation, which has the form y=a(x-h)2 + k, is referred to as being in vertex form. It is so named because the vertex point (peak point) lies on the graph of this equation (h,k)
We may deduce from the facts above that
-4.9 t2 + 19.6 t + 58.8 = 0
The equation will logically fit into the square upon completion.
y = a(x-h)^2 + k
where h will be the time it takes to get to a height of k.
-[tex]4.9t^{2}[/tex] + 19.6t + 58.8 = 0
-[tex]4.9t^{2}[/tex] + 19.6t = - 58.8
-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8
Now take half the linear term, square it, and add it to both sides.
-4.9( [tex]t^{2}[/tex] - 4t ) = -58.8
-4.9( [tex]t^{2}[/tex] - 4t + 4 ) = -58.8 + 19.6
-4.9 [tex](t-2)^{2}[/tex] = - 78.8
s(t) = -4.9 [tex](t-2)^{2}[/tex] + 78.8
now we have t = 3sec
s(t) = 73.5ft
The object reached its maximum height of 73.5 ft, the first choice is correct.
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solve the system if possible by using cramer's rule. if cramer's rule does not apply, solve the system by using another method. write all numbers as integers or simplified fractions.
Using the Cramer's Rule, the solution of the given system of equation is (-17/11, 48/11)
The given system of equations are
10x+4y=2
-6x+2y=18
Solving the equations by using Cramer's rule.
We know that, the solution of a system of linear equations in two unknowns
a(1)x+b(1)y = c(1)
a(2)x+b(2)y = c(2)
is given by ∆x=∆1, and ∆y=∆2.
where,
[tex]\Delta=\text{det}\left [ \begin{matrix} a(1)&b(1) \\ a(2) & b(2)\end{matrix} \right ], \Delta(1)=\text{det}\left [ \begin{matrix} c(1)&b(1) \\ c(2) & b(2)\end{matrix} \right ]\text{ and }\Delta(2)=\text{det}\left [ \begin{matrix} a(1)&c(1) \\ a(2) & c(2)\end{matrix} \right ][/tex]
Since the given equations are;
10x+4y=2
-6x+2y=18
Now,
[tex]\Delta=\text{det}\left [ \begin{matrix} 10&4 \\ -6 & 2\end{matrix} \right ][/tex]
∆ = [(10×2)-(-6×4)]
∆ = 20+24
∆ = 44
[tex]\Delta(1)=\text{det}\left [ \begin{matrix} 2&4 \\ 18 & 2\end{matrix} \right ][/tex]
∆(1) = [(2×2)-(18×4)]
∆(1) = 4-72
∆(1) = -68
[tex]\Delta(2)=\text{det}\left [ \begin{matrix} 10&2 \\ -6 & 18\end{matrix} \right ][/tex]
∆(2) = [(10×18)-(-6×2)]
∆(2) = 180+12
∆(2) = 192
By Cramer's Rule,
∆x = ∆(1)
44 × x = -68
x = -68/44
x = -17/11
Now,
∆y = ∆(2)
44 × y = 192
y = 192/44
y = 48/11
Hence, the solution of the given system of equation is (-17/11, 48/11).
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The right question is:
Solve the system if possible by using Cramer's rule. If Cramer's rule does not apply, solve the system by using another method. Write all numbers as integers or simplified fractions.
10x+4y=2
-6x+2y=18
Geometry Suppose that a pizza must fit into a box with a
base that is 12 in. long and 12 in. wide. You can use the
quadratic function A Tr² to find the area of a pizza in
terms of its radius.
a. What values of r make sense for the function?
b. What values of A make sense for the function?
c. Graph the function. Round values of A to the
nearest tenth.
Question 39
The value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
How to determine the Radius of the circle?You should understand that the pizza is fit inside the square box making all circumference of the circle to touch all the sides of the square box
The quadratic function reads
A= πr²
Where A= Area of circle,
π = 22/7
and r= radius of the circle
A= (22/7)*6
Width of the box is 12
Therefore 12/2 = r=6
A= (22*6*6)/7
A=113.1 in²
In conclusion, he value of (a) r that make sense is 6 in. and (b) the value of A that make sense is 113.1 in²
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Find the angle the line 3v = 2x + 6 makes with the x-axis.
The angle that the line 3y = 2x + 6 makes with the [x] axis is (θ) = 33°69'.
What is a function? What is equation modelling? What is a mathematical equation and expression?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the functionEquation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.
Given is the equation -
3y = 2x + 6
The given equation is -
3y = 2x + 6
y = (2/3)x + (6/3)
y = (2/3)x + 2
Slope of the line -
m = 2/3.
We know slope is also given by -
m = tan(θ)
So -
tan(θ) = 2/3
(θ) = tan⁻¹(2/3)
(θ) = 33°69'
Therefore, the angle that the line makes with the [x] axis is (θ) = 33°69'.
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A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 liter of a 3.5% salt water solution. He defines x as the amount of 2% solution and writes this equation:
0.2x + 0.7(x – 1) = 0.35(1)
He solves the equation and determines that x is about 1.17 liters. He interprets this as needing 1.17 liters of 2% solution to make 1 liter of 3.5% solution.
What errors did the student make? Check all that apply.
Errors student make is the % values in the equation were wrongly written and Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.
Define equation.There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value of a given data set are called equation.
Given
A student has a 2% salt water solution and a 7% salt water solution. To best imitate salt water at a local beach, he needs 1 liter of a 3.5% salt water solution. He defines x as the amount of 2% solution and writes this equation:
0.2x + 0.7(x – 1) = 0.35(1)
He requires 1 litre of a 3.5% salt water solution to accurately mimic the salt water at a nearby beach.
He constructs the following equation, where x is the volume of the 2% solution:
0.2x + 0.7(x - 1) = 0.35(1)
After resolving the equation, he ascertains that x is around 1.17 litres.
Errors student make:
A) The % values in the equation were wrongly written.
B) Instead of writing x - 1 for the amount of the 7% solution, write 1 - x.
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the mean recurrence interval (mri) of an earthquake in the 8.0-9.0 magnitude range in the los angeles area is approximately 1,500 years. based on this, what is the probability of an earthquake in this magnitude range sometime in the next 30 years?
Using the Poisson distribution, the probability of an earthquake in the 0.8-0.9 magnitude range sometime in the next 30 years is
1 - 1.9287 x 10⁻²².
It is given that mean recurrence of an earthquake is the 8.0-9.0 magnitude is approximately 1500 years.
We have to find the probability of an earthquake in this magnitude range sometime in the next 30 years.
Since, an occurrence of an earthquake is a rare event, we can use Poisson distribution here.
Poisson distribution gives the probability of occurrence of any event in a given time interval.
Let the average number of event per year in 30 years of period is λ.
[tex]\lambda = \frac{1500}{30}[/tex]
λ = 50
Let, the occurrence of an earthquake is a random variable x.
Then the probability that at least an earthquake occur in next 30 years is calculated as:
P(x ≥ 1) = 1 - P(x<1)
P(x ≥ 1) = 1- P(x=0) -----(1)
PDF of Poisson distribution with parameter λ is given as:
[tex]P(X = x) = \dfrac{e^{-\lambda}{\lambda}^x}{x!}[/tex]
So, in this case
[tex]P(x=0)= \dfrac{e^{-50}{(50)}^0}{0!}[/tex]
[tex]P(x=0)= \dfrac{1.9287 \times 10^{-22}}{1}[/tex]
[tex]P(x=0)={1.9287 \times 10^{-22}[/tex]
Substitute this value in equation (1)
P(x ≥ 1) = 1 - 1.9287 x 10⁻²²
Hence, the probability of an earthquake in next 30 years is
1 - 1.9287 x 10⁻²².
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or A parabola opening up or down has vertex (0, – 2) and passes through (4, – 1). Write its equation in vertex form. Simplify any fractions.
The vertex (0,2) of the parabola's vertex shape, which can expand upward or downward, equals (x - 0)² + 2.
What is parabola?
Any point on a parabola is at an equal distance from both the focus, a fixed point, and the directrix, a fixed straight line. A parabola is a U-shaped plane curve.
What is a vertex form of an equation?
An equation's conventional vertex form is written as:
f(x) = (x-h)² + k where;
(h, k) is the vertex
Vertex (0,2) should be replaced in the equation's vertex form.
f(x) = (x - 0)² + 2
As a result, vertex (0,2) of the parabola with an opening up or down is equal to (x - 0)² + 2.
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Jocelyn has a points card for a movie theater.
She receives 25 rewards points just for signing up.
• She earns 12.5 points for each visit to the movie theater.
She needs at least 170 points for a free movie ticket.
Write and solve an inequality which can be used to determine v, the
number of visits Jocelyn can make to earn her first free movie ticket.
Answer:
12 visits.
Step-by-step explanation:
Jocelyn receives a flat 25 reward point, and 12.5 points for each visit. She wants to redeem a free movie ticket that costs 170 points.
Set the equation. Let "each visit" be denoted by the variable, x:
12.5 per visit + a flat 25 reward point ≥ Free movie ticket that costs 170 points.
12.5x + 25 ≥ 170
Isolate the variable, x. Note that what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, subtract 25 from both sides of the equation:
12.5x + 25 ≥ 170
12.5x + 25 (-25) ≥ 170 (-25)
12.5x ≥ 170 - 25
12.5x ≥ 145
Next, divide 12.5 from both sides of the equation:
(12.5x)/12.5 ≥ (145)/12.5
x ≥ 145/12.5
x ≥ 11.6
x ≥ 11.6 is your answer. Therefore, Jocelyn would have to make 12 trips to earn her first free movie ticket.
~
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Number 7. There is no answer key, no need to explain , just need the answer.
Priya is comparing two functions: f(x)=10⋅x2 and g(x)=3⋅2x to find out which one has greater output values as x gets very large.
She notices that f(1)=10 and f(2)=40. However, g(1)=6 and g(2)=12. She concludes that as x continues to grow, the values of f will be greater than the values of g.
Explain or show why Priya’s conclusion is incorrect.
Explanation of why Priya's conclusion is correct.
What is a function?
An association between a number of inputs and outputs is called a function. Exactly one output is connected to each input in a function, which is an association of inputs. Every function has a range, co-domain, and domain.
Given the functions;
Simplifying,
f(x)=10x² and
g(x)=6x
The coefficient of variable x :
10 and 6,
where 10> 6.
And the value of x:
x² > x, for all x.
As x continues to grow, the values of f will be greater than the values of g.
Therefore, Priya's conclusion is correct.
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Which fraction has a value that's equal to ⅞? A. 2½4 B.1⅝ c. 4%4 D. 5⅝
The improper fraction 7/8 has no value in the options given
Conversion of Improper FractionTo do this, we must divide the dividend by the divisor in order to change an improper fraction to a mixed number. After division, the acquired quotient becomes the whole numerals, the remainder becomes the new numerator, and the denominator remains the same, resulting in a mixed number.
To convert 7/8 into decimal number;
7/8 = 0.875
2 1/2 = 2.5
1 5/8 = 1.625
4% = 0.04
5 5/8 = 5.625
In the given options, none of them has a value of 7/8
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