Which is the best reason why 2/5 is the exact quotient for 1/4 divided by 5/7

Which Is The Best Reason Why 2/5 Is The Exact Quotient For 1/4 Divided By 5/7

Answers

Answer 1

The best reason why 2/5 is the exact quotient for 1/4 divided by 5/8 is: ²/₅ * ⁵/₈ = ¹/₄

How to divide fractions?

To divide fractions, firstly, you need to turn the 2nd fraction upside down. For example, 3/8 divided by 3/4 would be 3/8 divided by 4/3. After you have flipped the second fraction, you multiply them - 3*4 = 12. 8*3 = 24 so the answer would be 12/24. Which then could be cancelled down to 1/2.

Now, from the given question, we can say that:

1/4 ÷ 5/8

Now, from the earlier step in dividing fractions, the next step is to turn the 2nd fraction upside down and multiply by the first to get:

¹/₄ * ⁸/₅ = ²/₅

Rearranging, we have:

²/₅ * ⁵/₈ = ¹/₄

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Complete question is:

Which is the best reason why 2/5 is the exact quotient for 1/4 divided by 5/8


Related Questions

if x = 6 units and h = 5 units whats the area of the triangle

Answers

Answer: 15 square units

Step-by-step explanation:

Area of a triangle is 1/2bh

x = b = 6

H=5

1/2(6)(5)

1/2(30)

Area = 15 square units

3. Han thinks that since the arc length in circle A is longer, its central angle is larger. Do
you agree with Han? Show or explain your reasoning.

Answers

Yes , Han is correct as the a circle with a longer arc length has a larger central angle

Given data ,

Let the arc length of the circle A = 6π units

Let the radius of the circle A = 15 units

Let the arc length of circle B = 2π units

Let the radius of the circle B = 5 units

Now , The length of an arc in a circle is determined by both the radius of the circle and the central angle that subtends the arc. The formula for calculating the length of an arc in a circle is given by:

Arc length = (Central angle / 360 degrees) x (2πr)

Though two circles' radii differ, they may nevertheless have distinct arc lengths even though their centre angles are the same. Similar to this, if the radii of two circles are adjusted properly, two circles with differing central angles can nevertheless have the same arc length.

Hence , the central angle is solved

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A contractor can by two types of wood. she got 45 expensive wood and 60 cheap wood for the same total price. if the 45 expensive wood cost $3.00 more than the 60 cheap wood, then which equation below shows the correct relationship between the 2 types of wood that she purchased. Also (x =price of the 60 cheap wood)

A.45(x+3)=60x

B.45(x-3)=60x

C.60(x-3)=45x

D.60(x+3)=45x

Answers

The correct answer is,

C. 60(x - 3) = 45x.

This equation is based on the information that the 45 expensive wood costs $3.00 more than the 60 cheap wood. In other words, if the price of the 60 cheap wood is x, the price of the 45 expensive wood is x + 3.

Since,  Algebra involves working with numbers, equations, and variables to solve real-world problems and understand abstract relationships.

Now, To solve this equation, we must use algebra and solve for x.

First, we multiply both sides of the equation by 4/5. This gives us:

48x + 36 = 45x

-36 = 3x

Finally, we divide left side of the equation by 3, giving us the final solution:

x = -12

Therefore, the price of the 60 cheap wood is $12, and the price of the 45 expensive wood is $15.

that is, 60 (x - 3) = 45x

This equation shows the correct relationship between the two types of wood that the contractor purchased.

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Determining Whether an Integer Satisfies an Inequality
Apr 29, 2:07:45 PM
Which of the following values are solutions to the inequality -10 + 3x ≥-4?
None
O II only
I and II
O II and III
I. 8
II. 2
OI only
O III only
O I and III
O I, II and III
III. 6
Submit Answer

Answers

All three values (I, II, and III) are solutions to the inequality, so the correct answer is "I, II and III."

How to solve

To solve the inequality -10 + 3x ≥ -4, we can follow these steps:

Add 10 to both sides of the inequality:

3x ≥ 6

Divide both sides by 3:

x ≥ 2

Now, let's check which of the given values satisfies the inequality:

I. 8:

x ≥ 2, and 8 ≥ 2, so 8 is a solution.

II. 2:

x ≥ 2, and 2 ≥ 2, so 2 is also a solution.

III. 6:

x ≥ 2, and 6 ≥ 2, so 6 is a solution as well.

All three quantities (I, II, and III) fulfill the requirements of the inequality; hence, the right you have to select is "I, II and III."

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HELP ASAP ASAP PLS PLS I NEED DONE NOW AND BRAINLIEST
The box plot shows the number of jumping jacks completed in a workout class by the class members.

A box plot uses a number line from 14 to 54, with tick marks every one unit. The box extends from 27 to 45 on the number line. A line in the box is at 37. The lines outside the box end at 16 and 52. The graph is Jumping Jacks Completed, and the line is labeled Number of Jumping Jacks.

Which of the following lists the range and IQR for this data?

The range is 18, and the IQR is 36.
The range is 36, and the IQR is 37.
The range is 36, and the IQR is 18.
The range is 18, and the IQR is 37.

Answers

The range of the data is the difference between the maximum and minimum values. In this case, the maximum value is 52 and the minimum value is 16, so the range is 52 - 16 = 36.

The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1). The box in the box plot represents the middle 50% of the data, so Q1 is the 25th percentile and Q3 is the 75th percentile. From the box plot, we can see that Q1 is at 27, Q3 is at 45, and the median (which is also the 50th percentile) is at 37. Therefore, the IQR is 45 - 27 = 18.

So, the correct answer is: The range is 36, and the IQR is 18.

The range is the difference between the maximum and minimum values in the data set. From the box plot, we can see that the maximum value is 52 and the minimum value is 16, so the range is:

Range = Maximum value - Minimum value

Range = 52 - 16

Range = 36

The IQR (interquartile range) is the difference between the first and third quartiles of the data set, which is represented by the length of the box in the box plot. From the box plot, we can see that the length of the box is:

Box length = Upper quartile - Lower quartile

Box length = 45 - 27

Box length = 18

Therefore, the range is 36, and the IQR is 18.

So the correct answer is:

The range is 36, and the IQR is 18.

CAN SOMEONE HELP WITH THIS PROBLEM?

Answers

The value of the infinite series expression [tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] is -30.

Given information:

[tex]\sum^{124}_{i = 1}a_i = -10[/tex]  and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].

The required series form can be rearranged as,

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) &= 29\sum^{124}_{i = 1}a_i - 13\sum^{124}_{i = 1}b_i[/tex]

Substitute the provided values of [tex]\sum^{124}_{i = 1}a_i = -10[/tex]  and [tex]\sum^{124}_{i = 1} b_i = -20[/tex].

We get,

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = 29(-10) - 13(-20)

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -290+ 260

[tex]\sum^{124}_{i = 1}(29a_i - 13b_i) \\[/tex] = -30.

As a result, the required value is -30.

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Find the area of the shaded region

Answers

Answer:

Area= 69π or 216.77 square units.

Step-by-step explanation:

1. Find the area of the white circle.

Remember that the formula for the area of a circle is the following:

[tex]A=\pi r^{2}[/tex]; where "r" is the radius of the circle.

Hence, the area of the white circle is:

[tex]A_{WC} =\pi (10)^{2} =100\pi[/tex]

2. Find the area of the red circle.

Here you can use the same formula, just need to change the value of the radius:

[tex]A_{RC} =\pi (13)^{2} =169\pi[/tex]

3. Find the difference between the 2 areas.

[tex]A_{RC} -A_{WC} =169\pi -100\pi =69\pi[/tex]

4. Express the final result.

The area of the shaded region is 69π or 216.77 square units, approximately.

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for the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. x|y
2|5
6|15
18|45

Answers

Yes , y varies directly with x as a proportion of k = 2.5

Given data ,

Let the values of x = { 2 , 6 , 18 }

Let the values of y = { 5 , 15 , 45 }

Now , the proportion equation is y = kx

On simplifying , we get

k = 5/2

k = 2.5

Therefore , the proportionality constant is k = 2.5

Hence , the proportion is y = 2.5 ( x )

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Your class hopes to collect at least 325 cans of food for the annual food drive. there were 135 cans donated the first week and 89 more the second week.

A. Write an inequality that describes this situation. Let c represent the number of cans of food that must be collected by the end of the third week for your class to meet or surpass its goal.
B. How many cans are needed to meet or surpass the goal

Answers

a.) [tex]135 + 89 + \text{C} \geq 325[/tex]

[tex]224 + \text{C} \geq 325[/tex]

b.) [tex]224 + \text{C} \geq 325[/tex]

[tex]\text{C} \geq 325 - 224[/tex]

[tex]\text{C} \geq 101[/tex]

The exponential function

Answers

Answer:

All real numbers

find 5.79 x 3.3.Then, use an estimate to check for reasonableness.

Answers

5.79 x 3.3 = 19.107

An estimate for 5.79 x 3.3 can be obtained by rounding the factors to 6 and 3, respectively, and multiplying them to obtain 18. Since the actual product is greater than 18, it is reasonable to conclude that the result of 5.79 x 3.3 is reasonable.

What is the 3D shape that would form if the following

Answers

Answer:

These are all the 3D shapes ;cone, cylinders, cuboid,cubes, sphere, rectangular prism, pyramid

A group of researchers wanted to know whether having a flexible start time for when workers began work impacted the number of minutes they spent commuting. To examine this, they had one group of workers leave home at 7am one morning and the next week let them choose the time they wanted to leave home to get to work. The minutes are given below. Conduct the steps of hypothesis testing on these data.

Data table: The number of minutes spent commuting for six subjects when they left a 7am vs leaving at a flexible time
Subject Leaving at 7am Leaving at a flexible time
1 24 20
2 18 17
3 30 30
4 24 25
5 20 12
6 15 5

Answers

The necessary information to carry out the hypothesis are given below.

How to carry out the hypothesis

For carrying out a hypothesis examination on the information, we need to do the following steps:

Step 1: Express the null and alternative hypotheses

Step 2: Pick the pertinent measure of value and significance level

Step 3: Compute the test statistic

Step 4: Estimate the p-value

Step 5: Draw a conclusion and interpret the results

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Pls help
The shape below contains a triangle and a semi-
circle.
Round your responses to two decimal places.

Answers

perimeter of the shape

167.37 units

Area of the shape

40.24 square units

How to find the perimeter of the shape

The shape is a composed of two simpler parts which consists of, namely:

The right triangle and the semi circle

Therefore, the perimeter of the shape includes perimeter of semicircle and the perimeter triangle

To complete the perimeter of the triangle we add two sides of the triangle. the opposite and the adjacent of the right triangle is given so we solve for the hypotenuse.

The hypotenuse of the triangle = [tex]\sqrt{ 7^2 + 6^2}[/tex] = 9.22 units

perimeter of the shape

= perimeter of triangle side + perimeter of semicircle side

= (9.22 + 6) + (3.142 * 3.5)

= 167.37 units

Area of the shape

= area of triangle + area of semicircle

= 1/2 x 7 x 6 + 1/2 x 3.142 x 3.5^2

= 21 + 19.24

= 40.24 square units

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PLEASE HELP
Parts a, b, c, d, and e

Answers

The values of the composite functions are f(g(2)) = 5.5, h(f⁻¹(5)) = 1, x = 5 for f(h(x)) = 7, R(4) = 4 and k(x) = 2

Evaluating the composite functions

From the question, we have the following parameters that can be used in our computation:

The functions f(x), g(x) and h(x)

Solving the composite functions, we have

f(g(2)) = f(3) i.e. g(2) = 3

This gives

f(g(2)) = 5.5

Next, we have

h(f⁻¹(5))

Here, we have

f⁻¹(5) = 4

So, we have

h(f⁻¹(5)) = h(4)

Evaluate

h(f⁻¹(5)) = 1

Next, we have

f(h(x)) = 7

From the graph, we have

f(0) = 7

This means that

h(x) = 0

From the table, we have

h(5) = 0

This means that

x = 5 for f(h(x)) = 7

Evaluating R(x) at x = 4. we have

R(x) = 2f(x) - 3g(x) + h(x)

This means that

R(4) = 2f(4) - 3g(4) + h(4)

So, we have

R(4) = 2 * 9 - 3 * 5 + 1

R(4) = 4

Evaluating k(x) at x = 5. we have

k(x) = h⁻¹(g(f⁻¹(x)))

This means that

k(x) = h⁻¹(g(f⁻¹(5)))

From the graph, f⁻¹(5) = 4

So, we have

k(x) = h⁻¹(g(4))

Next, we have

g(4) = 5

So, we have

k(x) = h⁻¹(5)

From the table, we have

h⁻¹(5) = 2

This means that

k(x) = 2

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Suppose we have data about a three-stock financial market that satisfies the single-index model as below: (the standard deviation of the market-index portfolio is 18%)

Capitalization Beta Excess Return Std Dev
A $3,000 0.15 10% 40%
B $2,000 0.95 2% 30%
C $1,500 1.7 17% 50%
What is the mean excess return of the value-weighted index portfolio?

Express your answer in percent and round it to 2 decimal places. For example, if your answer is 0.25456, then please write down 25.46 (without the percent sign).

Answers

The mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

To calculate the mean excess return of the value-weighted index portfolio, we need to first calculate the total market capitalization of the three stocks:

Total Market Cap = $3,000 + $2,000 + $1,500 = $6,500

Next, we can calculate the weight of each stock in the index portfolio as follows:

Weight of Stock A = $3,000 / $6,500 = 0.4615

Weight of Stock B = $2,000 / $6,500 = 0.3077

Weight of Stock C = $1,500 / $6,500 = 0.2308

The capitalization-weighted beta of the portfolio can then be calculated as the sum of the product of each stock's weight and its beta:

Beta of Index Portfolio = (0.4615 x 0.15) + (0.3077 x 0.95) + (0.2308 x 1.7) = 1.081

The mean excess return of the index portfolio can be calculated using the single-index model as:

Mean Excess Return = Beta of Index Portfolio x Standard Deviation of Market-Index Portfolio

= 1.081 x 18%

= 19.458%

Finally, we need to adjust for the risk-free rate to obtain the actual mean return of the index portfolio. If the risk-free rate is 2%, then the mean return of the index portfolio would be:

Mean Return = Mean Excess Return + Risk-Free Rate

= 19.458% + 2%

= 21.458%

Therefore, the mean excess return of the value-weighted index portfolio is 19.458%, and the mean return of the index portfolio, adjusted for the risk-free rate, is 21.458%.

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PLEASE HELP





the pattern for representing a triangular number​

Answers

The pattern that can be used to represent a triangular number is T(n) = 1 + 2 + 3 + ... + n.

What is a triangular number ?

A number that can take the form of an equilateral triangle is called a triangular number. By definition, it represents the sum of positive integers up to n consecutive natural numbers. The pattern for such a calculation is expressed as follows:

T(n) = 1 + 2 + 3 + ... + n.

Triangular numbers exhibit many engaging properties and are applicable across various mathematical and real-world contexts.

In conclusion, the pattern used to represent a triangular number is T (n) = 1 + 2 + 3 + ... + n.

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HELP ASAP I NEED DONE RESLLY FAST AND BRSINKIEST
An image of a right rectangular prism is shown.

A rectangular prism with dimensions of 4.5 centimeters by 6 centimeters by 4 centimeters.

What is the surface area of the prism?

138 cm2
169 cm2
31 cm2
69 cm2

Answers

Answer:

2((4.5)(6) + (4.5)(4) + (6)(4))

= 2(27 + 18 + 24) = 2(69) = 138 square cm

help me pleaseeeeeeee​
brainliest for 1st answer

Answers

Answer:

A

Step-by-step explanation:

sqrt 5 ( 4pi - 2pi) =   2 pi sqrt 5  for the numerator

then     2 pi sqrt (5)  / 3 sqrt (5)      the sqrt (5) 's cancel out and you have

          2pi / 3

can someone help me on number 1 through 4.

Answers

The values are expressed as;

1. radius = 13cm

2. Diameter = 27.2cm

3. Diameter = 24m

4.  Radius = 24. 5m

How to determine the values

It is important to note the formula for calculating the circumference and area of a circle.

The formula for calculating area of a circle is expressed as;

A = πr²

Such that the parameters are given as;

A is the area of the circler is the radius of the circle

Also, the formula for circumference is expressed as;

C = 2πr

To determine the formula for diameter is expressed as;

Diameter = 2Radius

1. Substitute the values

r = d/2

r = 26/2

r = 13cm

2. If r= 13.6m

d= 2(13.6)

d = 27.2m

3. If r = 12m

d = 2(12)

d = 24m

4. If d = 49m

Then, r = 49/2 = 24. 5m

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5x^2-8x+12=3x+10
solve quadratic by factoring

Answers

On solving the "equation" written as "5x² - 8x + 12 = 3x + 10" by using "factoring-method" , the "solutions" are x = 1/5 and x = 2.

To solve "5x² - 8x + 12 = 3x + 10" by using the "factoring-method", it should first be rearranged in "standard-form", where one side of the equation is = 0,

First, we combine the constant terms on the right side of the quadratic:

⇒ 5x² - 8x + 2 = 3x,

⇒ 5x² - 11x + 2 = 0,  Now, we factor the quadratic expression on the left side of the equation as :

⇒ 5x² - 10x -x + 2 = 0,

⇒ 5x(x - 2) -1(x - 2) = 0,

⇒ (5x - 1)×(x - 2) = 0

By applying the zero product property, we know that either "5x - 1 = 0" or "x - 2 = 0";

⇒ 5x - 1 = 0 , We get x = 1/5,

⇒ x - 2 = 0, We get x = 2;

Therefore, the solution are x = 2, and x = 1/5.

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The given question is incomplete, the complete question is

Solve the quadratic-equation "5x² - 8x + 12 = 3x + 10" by factoring.

El profesor de educación física tenía 12 balones y ahora tiene 96 por cuanto se multiplicó la cantidad de los balones

Answers

Se multiplico por 8

12 x 8 = 96

A pyramid has a square base with an area of 144 ft. Mark each statement as true or false and correct any false statements.

T/F? - The length of one side of the pyramids base can be found using the equation s^2=144.

T/F? - The Length of one side of the pyramids base is 72 feet.

Answers

A = s^2, where A is the area and s is the length of one side of the square gives the area of a square base. The correct option is true

If s^2 = 144, then s = √144 = 12 feet. The correct option is false

What is pyramid ?

A pyramid is a polyhedron that is created by joining an apex and a polygonal base. A triangle known as a lateral face is formed by each base edge and apex.

Therefore, s^2 = 144 is a valid equation to find the length of one side of the base. The correct option is true

Therefore, one side of the pyramid's base is 12 feet, not 72 feet.

The correct option is false

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8. A graph represents the proportional relationship between the number of pages printed, y, and the time in minutes, x. If there is a point on the graph at (4, 720), how many pages can be printed in half a minute?​

Answers

The number of pages that can be printed in half a minute is 90 pages

How many pages can be printed in half a minute?​

From the question, we have the following parameters that can be used in our computation:

The graph represents a  proportional relationship

Where

x = minutes

y = pages

When the time is half a minute, we have

x = 0.5

So, we have the following ordered pair

(0.5, y)

From the question. we have

(4, 720)

So, we have

(0.5, y) = (4, 720)

Express as an equation

So, we have

y/0.5 = 720/4

This gives

y = 0.5 * 720/4

Evaluate

y = 90

Hence, the number of pages is 90


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The cone below has a volume of 264 m³ and a radius of 6 m. Calculate the size of the angle between the slant height and the base to 1 dp.​

Answers

The angle between the slant height and the base of the cone is 30.2°.

How to solve for angle of a cone

Recall the formula of the volume of a cone:

V = (1/3)πr²h

where

V = volume,

r = radius,

h = height.

To get the h, we use the volume formula and substitute:

264 = (1/3)π(6²)h

Make h the subject of the formula and simplify:

h = (3/π)(264/36) = 8.8

Therefore, h = 8.8 m.

Now, we find the slant height using the Pythagorean theorem:

s² = r² + h²

Plugging in the values, we get:

s² = 6² + 8.8² = 102.64

s = √(6² + 8.8²)

s = 10.13

To find the angle between the slant height and the base, we use trigonometry:

tan θ = r / s

r = radius of the base

s = slant height

Plugging in the values, we get:

tan θ = 6 / 10.13

tan θ = 0.5925

Find the arctan of θ

θ = tan⁻¹(0.5925)

θ = 30.2°

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ANSWER ASAPPP I NEED IT!

Answers

Answer:a

Step-by-step explanation:

Answer:

Step-by-step explanation:

It is a A

please help i need this done

Answers

The value of f(j) when

1. j = -1 is 11

2. j = 0 is 10

3. j = 1 is 11

4 . j = 2 is 14

What is a function?

A function is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.

For example, here j is a variable and f(j) is the function of 'j'.

f(j) = j²+10

Therefore , when j = -1

f(j) = -1)² + 10

f(j) = 1+10 = 11

When j = 0

f(j) = 0²+10

= 0+10 = 10

when j = 1

f(j) = 1²+10

= 1+10 = 11

When j= 2

f(j) = 2²+10

= 4+10

= 14

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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°

Answers

The statements that are always true are:

i. m∠5 + m∠6 = 180°

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

What is a triangle?

A triangle is a shape which is bounded by just three sides, thus it has three internal angles whose measures add up to 180°. The internal angle of a triangle is the measure of the angle formed within the two lines forming the edge. While the exterior angles are angles that exist outside the boundary of the triangle when its sides are extended.

From the given question and information, the statements that are always true regarding the diagram are:

i. m∠5 + m∠6 =180°  

ii. m∠2 + m∠3 = m∠6

iii. m∠2 + m∠3 + m∠5 = 180°

The required diagram is attached to this answer as a guide

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Find the area of square ABCD shown below. Round to the nearest tenth if necessary.
O
D
y
O
A
B
square units

Answers

The area of the square given in the diagram is: 25 square units.

What is the area of the square?

Pythagoras Theorem is defined as the way in which we find the missing length of a right angled triangle.

The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).

Pythagoras is in the form of;

a² + b² = c²

Using Pythagoras theorem, we can find the length of a side of the square:

AB = √(3² + 4²)

AB = √(9 + 16)

AB = √25

AB = 5

Area of a square is given by the formula:

A = side * side

Thus:

A = 5 * 5

A = 25

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Answers

The correct statements regarding the scatter plot are given as follows:

The line of best fit gives the best approximation between the SAT score and the GPA.The line of best fit can be used to predict the GPA based on the SAT score.A reasonable prediction of GPA for a SAT score of 2100 is a GPA of 3.5.

What is the scatter plot?

The scatter plot, as shown by the image given in the problem is a series of points of the data-set in the following format:

(SAT score, GPA).

There is a positive association between the data, as the line of best fit, which gives the best approximation between the SAT score and the GPA, and can be used to predict the GPA based on the SAT score, is increasing.

For a SAT score of 1700, an expected GPA is of about 3.1, considering the intersection of y = 3.1 with the line of fit when x = 1700.

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