By using division, it can be concluded that
Number of math problem she can be able to complete within given time is [tex]24 \div \frac{2}{3}[/tex]
This is the required expression
What is division?
Division is the process by which value of single unit can be calculated from the value of multiple unit.
The number to be divided is known as dividend, the number by which the dividend is divided is the divisor, the result obtained is the quotient and the remaining part is the remainder.
There is a well known formula for division
Divisor x Quotient + Remainder = Dividend.
This is a word problem on division
Zareen has 24 minutes to work on her math homework
Fraction of time taken to do each sum =[tex]\frac{2}{3}[/tex]
Number of math problem she can be able to complete within given time is
[tex]24 \div \frac{2}{3}[/tex]
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Write an equivalent fraction to 5/8 with a denominator of 40
Step-by-step explanation:
So you have 5/8 and you want the equivalent fraction to have a denominator of 40. You put 5/8=X/40 and find for x.
First, multiply both sides by 40
5/8*40=x
Express 5/8 * 40 as a single fraction.
5*40/8=x
Multiply 5 40 to get 200.
200/8=x
Divide 200 by 8 to get 25.
25=x
Swap sides so that all variable terms are on the left-hand side.
x=25
Thirty randomly selected students took the calculus final. If the sample mean was 95 and the standard deviation was 6.6, construct a 99% confidence interval for the mean score of all students. You may use your calculator to solve.
Confidence interval for the mean score of all students is (91.679, 98.321)
Given:
Sample mean = 95
Standard deviation = 6.6
The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
We have to construct a 99% confidence interval for the mean score of all the students.
Sample Standard Error =
[tex]\frac{Standard Deviation}{\sqrt{n} } \\= \frac{6.6}{\sqrt{30} }[/tex]
= 1.205
t-value for the 99% confidence interval = 2.756
(use the t-tables for this)
Margin of error = 2.756 x 1.205 = 3.321
If you are asked to report the confidence interval, you should include the upper and lower bounds of the confidence interval.
So, for the 99% confidence interval:
(95 - 3.321, 95 + 3.321) = (91.679, 98.321)
This is the final confidence interval.
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Choose ALL solutions of the following system of linear inequalities listed below.
A (0, -1)
B (6, 2)
C (9, 9)
D (8, 2)
E (-2, 4)
F (2, 6)
All solutions of the following system of linear inequalities are given-
B (6, 2), C (9, 9), D (8, 2)
Explain the term linear inequalities?Mathematical expressions known as linear inequalities compare two expressions using the inequality sign. The expression may be either a numerical or an algebraic expression, or it may be both.The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilized in this inequality, the LHS is clearly greater than the RHS.For the stated question,
The solution for the blue line given in graph will be the region under the line including the values on the line.Similarly, the solution for the red line given in graph will be the region above the line excluding the values on the line.Thus, the total solution becomes, the common shaded region of containing both lines.Therefore, the solutions of the following system of linear inequalities are-
B (6, 2), C (9, 9), D (8, 2).
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Decide which of the two given prices is the better deal. You can buy laundry product in a 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08 .
A) not enough information
B) 24-ounce bottle for $4.08
C) equal value
D) 30-ounce bottle for $6.00
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
The combination of numerical variables and operations expressed by the addition, subtraction, multiplication, and division signs constitutes a mathematical expression.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented using mathematical symbols. They can also be used to indicate other characteristics of the logical grammar, such as the operation order.
We are given that there are two conditions for bottles. A 30 -ounce bottle for $ 6.00 or in a 24-ounce bottle for $ 4.08. The unit price for each bottle will be: The bottle having the lower price will be:-
30-ounce bottle = $6.00
One ounce bottle = 30 / 6.00 = $5.00
and
24-ounce bottle = $4.08
One ounce bottle = $24/ 4.08 = $5.88
30-ounce bottle for $6.00 will have a lower unit price. The correct option is D.
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Erin has a balance of $1,123.72 in her check register. On her statement, the balance of her account is $879.87.
Not reported on the bank statement are deposits of $62.42, $21, and $61.14. There are outstanding checks in the
amount of $60.24 and $50.24 and an ATM withdrawal of $40. After Erin reconciles her check register with her
statement, what entry does she need to make in her register?
Answer: After reconciling her check register with her statement, Erin needs to make the following entry in her register: $1123.72 - $879.87 + $62.42 + $21 + $61.14 - $60.24 - $50.24 - $40 = $226.23. This is the updated balance in Erin's account after accounting for all the transactions that were not reflected on her bank statement.
Solve each of the quadratic equations.
0 = 5x2 - 2x + 6
Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” Only 40% responded that they would prefer to have their child taught by a male in grades K-2. Construct a 95% confidence interval for the poll.
Newsweek performed a poll in which 500 American parents were asked the question, “Would you prefer to have your child taught by a male or female for grades K-2?” 95% confidence interval for the poll is
(38.88%, 41.12%)
What is a confidence interval?Generally, To construct a 95% confidence interval for the poll, we need to first calculate the margin of error. The margin of error for a poll is a measure of the precision of the estimate and is calculated based on the sample size, the level of confidence, and the standard deviation of the population.
In this case, the sample size is 500, the level of confidence is 95%, and the standard deviation of the population is unknown. We can approximate the standard deviation using the sample proportion of 40% as an estimate of the population proportion.
Using these values, the margin of error can be calculated as follows:
Margin of error = z * standard error
Where z is the critical value from the standard normal distribution for the desired level of confidence (in this case, 1.96 for a 95% confidence interval) and the standard error is calculated as:
Standard error = √(p * (1 - p) / n)
Where p is the sample proportion (40% in this case) and n is the sample size (500 in this case).
Substituting these values into the formula for the margin of error, we get:
Margin of error = 1.96 * √(0.4 * (1 - 0.4) / 500)
= 1.96 * sqrt(0.16 / 500)
= 1.96 * √(0.000032)
= 1.6 * 0.005656854
= 0.011168
So the margin of error for this poll is approximately 0.011168 or 1.12%.
To construct the 95% confidence interval, we need to add and subtract the margin of error from the sample proportion. The 95% confidence interval for the poll is, therefore:
40% ± 1.12%
= (38.88%, 41.12%)
This means that we can be 95% confident that the true population proportion of parents who would prefer to have their child taught by a male in grades K-2 lies within the interval between 38.88% and 41.12%.
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Find the value of x for which l is parade to m. The diagram is not to scale
The value of x for which l is parallel to m is 41°
What is meant by an angle?An angle is a figure in Euclidean geometry made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. The meeting of two planes can also create an angle. These are referred to as dihedral angles. The angle formed by the rays lying perpendicular to the two intersecting curves at their point of intersection can likewise be used to establish an angle between two intersecting curves.
In the depicted figure, l and m are parallel. A transversal crosses parallel lines, creating the appropriate angles. The angles created when two parallel lines cross any other line, whether they are corresponding or matching corners to the transversal.
(3x-43)°=80°
3x=80°+43°
3x=123°
x=41°
Therefore, the value of x is 41°
Hence, the value of x for which l is parallel to m is 41°.
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Type your answers into the boxes.
What are the next two numbers in this sequence?
45.7
46.2
46.7
47.2
Answer:
Step-by-step explanation:
Well, it seems like you're adding 5 each time so
45.7
46.2
46.7
47.7
48.2
48.7
the triangles are similar solve for x
Answer:
show the whole question
Step-by-step explanation:
Convert the hexadecimal expansion of each of these integers to a binary expansion.a) (80E)_{16} b) (135AB)_{16} c) (ABBA)_{16} d) (DEFACED)_{16}
The binary representation of each of these hexadecimal numbers is given as follows:
a) 80E = 100000001110
b) 135AB = 00010011010110101011
c) ABBA = 1010101110111010
d) DEFACED = 1101111011111010110011101101
How to convert from hexadecimal to binary?To convert a number from hexadecimal to binary, each hexadecimal character is converted to it's respective four bit binary code, given as follows:
0 = 00001 = 00012 = 00103 = 00114 = 00105 = 01016 = 01107 = 01118 = 10009 = 1001A = 1010B = 1011C = 1010D = 1101E = 1110F = F111Then, for example:
80E hexadecimal = 100000001110.
As:
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Lines DE and AB intersect at point C.
What is the value of x?
A.12
B.25
C.38
D.05
Answer:
B
Step-by-step explanation:
2x + 2 + 5x + 3 = 180
7x + 5 = 180
7x = 180 - 5
7x = 175
x = 175/7
x = 25°
In triangle ABC, m∠B = (14x − 22)° and the measure of the exterior angle to ∠B is (6x − 18)°. Find m∠B.
After solving the equation, the value obtained for m ∠B will be equal to 132°.
What is an angle?An angle results from the intersection of two lines at a point. The term "angle" describes the width of the "gap" that exists between these two rays. It's represented by the symbol.
Angles are most frequently measured in degrees and radians, a measurement of roundness or rotation. Angles are a part of everyday existence.
As per the given information in the question,
The inside angle plus the external angle add up to 180°.
So,
m ∠B = (14x − 22)°
14x - 22° + 6x - 18° = 180°
14x + 6x - 22° - 18° = 180°
20x - 40° = 180°
20x = 180° + 40°
20x = 220°
x = 220° / 20
x = 11°
Now, let's find m∠B.
m ∠B = (14x − 22)°
Put x = 11° in above equation,
m ∠B = (14(11) − 22)°
m ∠B = 154° - 22°
m ∠B = 132°.
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Graph the solution to this inequality on the number line. −18≤−3p
100 points pls help me
Answer:
Look at the image
Step-by-step explanation:
You can solve the problem like in the image
Janelle works at Heedle's Computer
Outlet. She receives a weekly salary of
$200 plus 3% commission on her sales.
Last week, she sold $29,700 of
computer equipment. How much did
Janelle earn last week?
Using the concept of percentage, she earned a total of $1091 last week
PercentageA percentage is a number or ratio that can be expressed as a fraction of 100. Percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
To determine the amount she earned last week, we need to calculate the amount in commission and add it with her weekly salary.
She received 3% commission on her sales and she made a sale of $29700.
Let's find 3% of 29700
3 / 100 = x / 29700
0.03 = x / 29700
x = 29700 * 0.03
x = 891
The amount she earns will be 891 + 200 = 1091
Janelle earned $1091 last week
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DUE IN AN HOUR HELP!!!!
Answer:
D. x=4
Step-by-step explanation:
32. m<1=m<2 ==> angle bisectors divide an angle into two equal angles
m<2=m<RQP
m<1=m<SQP
m<RQP+m<SQP=m<SQR
m<2+m<1=m<SQR
m<2+m<2=m<SQR
(2+7x)+(2+7x)=16x-4
2+7x+2+7x=16x-4
2+2+7x+7x=16x-4
4+14x=16x-4
4-4+14x=16x-4+4
4+4+14x=16x-4+4
14x+8=16x
14x-14x+8=16x-14x
8=2x
x=8/2
x=4 ==> D
A manufacturer cuts a piece of metal for a microscope. The resulting piece of metal can be
represented in a coordinate plane by a triangle with vertices A(0, 0), B(3, 8), and C(6,0).
One unit in the coordinate plane represents one millimeter.
Prove that AABC is isosceles.
The triangle ABC is an isosceles triangle because AB = BC = √73
How to prove that the triangle is an isosceles triangle?From the question, we have the following parameters that can be used in our computation:
A(0, 0), B(3, 8), and C(6,0).
An isosceles triangle is any triangle that has two of its sides to be equal
So, we start by calculating the lengths of the sides using the distance equation represented as follows
distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Substitute the known values in the above equation, so, we have the following representation
AB = √[(0 - 3)² + (0 - 8)²]
AB = √73
AC = √[(0 - 6)² + (0 - 0)²]
AC = 6
BC = √[(3 - 6)² + (8 - 0)²]
BC = √73
Because AB = BC = √73, then the triangle is an isosceles triangle
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What is the root of the polynomial equation x(x-2)(x+3)= 18? Use a graphing calculator and a system of equations.
-3
0
2
3
Answer:
3
Step-by-step explanation:
on edge
Answer:
x = 3
Step-by-step explanation:
You want the root of the polynomial equation x(x -2)(x +3) = 18.
GraphA graph of the equation in the form x(x -2)(x +3) -18 = 0 is attached. The solution is the x-intercept. It shows the only real root is x = 3.
System of equationsThere are many ways the polynomial can give rise to a system of equations. The basic idea is to write two expressions that are supposed to be equal to each other. The graphing calculator can show the value(s) of x that make them equal.
Dividing both sides of the given polynomial by (x -2)(x +3) gives the equation ...
x = 18/((x -2)(x +3))
This can be graphed as two equations:
y = x
y = 18/((x -2)(x +3))
This is shown in the second attachment. It tells us the root is x=3. (Both sides of the "x=" equation have the value 3 at x=3.)
__
Additional comment
Here, you are asked to use a system of equations. A graphing calculator can usually find the solution more easily when the equation is written in the form f(x) = 0. Often x-intercepts are easier to identify than points where graphs cross each other.
Select all the points that are on the graph of the line Y=2x+5
Answer:
Some points that are on this line are:
(-7,-9) (-6,-7) (-5,-5) (-4,-3) (-3,-1) (-2,1) (-1,3) (0,5) (1,7) (2,9)
If the radio program plays 40 minutes of music, how many minutes will be used for commercials?
The number of minutes that will be used for commercials will be 20 minutes.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
If the radio program plays 40 minutes of music.
Suppose the radio program is of one hour which is 60 minutes. Then the number of minutes will be used for commercials will be given as,
⇒ 60 - 40
⇒ 20 minutes
The number of minutes that will be utilized for plugs will be 20 minutes.
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Solve x²-3x + 7 = 0.
OA. 3+√-37
2
OB. 3+√-19
2
and 3-√-37
2
and ³-v-19
3-√-19
2
O C. 3+√19 and 3-√/19
2
2
O D. 3+√37 and 3-√37
2
2
Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.
Define quadratic formula.The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation has the general form ax2 + bx + c = 0. where a, b, and c are numerical coefficients and x is an unknown variable. The phrase "quadratic" in mathematics refers to something that has to do with squares, the squaring operation, terms of the second degree, or equations or formulas that contain such terms. Latin's word for square is quadratus.
Given
Equation
x²-3x + 7 = 0
Using quadratic formula,
x = -b±√b² - 4ac/2a
x = -(-3) ± √((-3)² - 4×1×7/2×1
x = 3/2± √19 1/2i
x = 3 + √19/2 and 3 - √19/2
Solutions of x²-3x + 7 = 0 is 3 + √19/2 and 3 - √19/2.
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Does anyone know how to do this? i tried it and got it wrong so i’m not sure anymore, lol.
The simplified form of the expression 12c + 8k - 8 - 6c + 6, combining the like term is 6c + 8k - 2.
How to simplify an expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations like subtraction and addition.
To simplify an expression means rewriting the same algebraic expression with no like terms or to write an equivalent expression which contains no similar terms.
Therefore, let's simplify the expression with no like terms.
12c + 8k - 8 - 6c + 6
combine the like terms
12c - 6c + 8k - 8 + 6
Therefore, the simplified expression is 6c + 8k - 2
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which of the following number lines shows the solution to the inequality given below? 4x + 7 _< -37 or 5x + 3 > -7
The graph of the compound inequality can be seen in the image at the end.
Which number line shows the solution set for the inequality?
Here we have a compound inequality which is:
4x + 7 ≤ -37
5x + 3 > -7
First we need to isolate x in both of these inequalities, on the first one we will get:
4x + 7 ≤ -37
4x ≤ -37 - 7
4x≤ -44
x ≤ -44/4
x ≤ -11
The other inequality gives:
5x + 3 > -7
5x > -7 - 3
5x > -10
x > -10/5
x > -2
So the compound inequality is:
x > -2
x ≤ -11
To graph this we need to have a open circle at x = -2, and we need to graph a line to the right. And a closed circle at x = -11 and a line that goes to the left.
The number line is below
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k x 20 = 1.07 what is k
The current population of a small city is 48500 people. Due to a loss of jobs, the population is decreasing by an average of 325 people per year. How many years (from now) will it take for the population to decrease to 46875 people?
It takes 5 years for the population to decrease to 46785 from the current population of 48500 of a small city whose population is decreasing by an average of 325 people per year.
What is the equation for the given statement?It is given that,
Current population = 48500 people
Rate of decrease = 325 per year
Number of years = x
decreased population after x years = 46785
Then, the equation is
46785 = 48500 - 325x
Calculation:On simplifying the obtained equation, we get
46785 = 48500 - 325x
⇒ 325x = 48500 - 46785 = 1625
⇒ x = 1625/325 = 5 years
So, the people become 46785 after 5 years.
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The sum of three numbers is 96. The first number is 6 less than the second. The third number is 4 times the second. What are the numbers?
Step-by-step explanation:
x = second number
first number = x - 6
third number = 4x
x - 6 + x + 4x = 96
6x - 6 = 96
6x = 102
x = 102/6 = 17
first number = x - 6 = 17 - 6 = 11
second number = x = 17
third number = 4x = 4×17 = 68
consider the value of t such that 0.05 of the area under the curve is to the right of t. step 2 of 2: assuming the degrees of freedom equals 18, select the t value from the t table.
Thus after assuming the degrees of freedom equals 18 so the t-critical value will be =2.306
Degree of freedom {df}=18
We have to calculate the t-value such that 0.05 of the area under the curve is to the right of t
It means that, [tex]$\mathrm{P}(\mathrm{T} > \mathrm{t})=0.05$[/tex]
As we know, t distribution provides the cumulative probability
As the value of the total area under the t distribution will 1
So, we can write it as:
[tex]$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-\mathrm{P}(\mathrm{T} > \mathrm{t})$$$\mathrm{P}(\mathrm{T} \leq \mathrm{t})=1-0.05$$=0.95$[/tex]
Now, using excel, we can easily calculate the t-critical value as follows
=T. INV ( Probability, DF)
Where Probability is the area and DF is the degree of freedom,
Now we will enter these values in excel:
=T. INV (0.95,18)
t-critical value can also be found using t table
Look up for df = 18, in very first column
Now look up for 0.05 in one tail row
Now intersect both of them to get the t-critical value
We will get it as: 2.306
So t-critical value will be =2.306
[tex]$\mathrm{P}(\mathrm{T} > 2.306)=0.05$[/tex]
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Use a proof by contraposition to prove that if m and n are integers and mn is even, then m is even or n is even.
In order for mn to be even, m must be even or n must be an even number.
What is Contraposition ?The relationship between two propositions when the subject and predicate of one are respectively the negation of the predicate and the negation of the subject of the other.
Suppose that the statement “m is even or n is even” is not true. Then both m and n are supposed to be odd. Let’s see if the product of two odd numbers is an even or an odd number:
Let n and m be equal to 2a +1 and 2b + 1 respectively, then their product is:
(2a +1) (2b + 1) = 4ab + 2a + 2b + 1
= 2(2ab +a + b) + 1
This shows that the expression 2(2ab +a + b) + 1 is of the form 2n +1, thus the product is odd. If the product of odd numbers is odd, then mn is not true to be even. Therefore, in order for mn to be even, m must be even or n must be an even number.
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Brian sped up from 68 mph to 80 mph. What was his percent change?
The percent change in the speed of Brian is found as 15%.
Describe the term percent change?The percentage difference between such a final and starting value is known as percent change. Divide the value differences by the starting value to calculate the percent change.The outcome is known as the rate of change, sometimes known as the percentage change, and is expressed in percent (with absolute numbers, it's merely a difference).For the stated question-
Initial speed = 68 mph
Final speed = 80 mph.
Difference = Final speed - Initial speed
Difference = 80 - 68
Difference = 12 mph
Percent change = Difference/Initial speed x 100
Percent change = 12/80 x 100
Percent change = 15%
Thus, the percent change in the speed of Brian is found as 15%.
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If a boat travels on course of bearing S 34 degrees W for 15 miles, how far south and how far west will the boat travel? Round each number to the nearest tenth of a mile and include a sketch.
It is to be noted that the boat traveled a distance of 8.39 miles South, and 12.44 miles west. This is solved using trigonometric ratios principles.
What is the rationale for the above answer?Using the trigonometric ratio involving the right triangle, we can answer how far the boat moved northward and westward, or the vertical and horizontal components of the displacement vector.
Solving for the horizontal component Vₓ, we'll be using the ratio of the sine function with regard to angle 34°
Thus,
Sin 34° = Vₓ/ 15
Vₓ = 15 * (Sin 34°)
= 15 * 0.55919290
Vₓ = 8.39 miles.
Solving for the vertical component of, V[tex]_{y}[/tex] we'll be using the ratio of Cosine Function with respect to the angle 34°
Cos 34° = V[tex]_{y}[/tex] / 15
V[tex]_{y}[/tex] = 15 * Cos 34°
V[tex]_{y}[/tex]= 15 * 0.82903757255
V[tex]_{y}[/tex] = 12.44 miles.
Thus, the boat traveled a distance of 8.39 miles South, and 12.44 miles west.
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