Quincy was stuck inside for an hour during a storm. He spent 20 minutes reading, 18 minutes
eating lunch, 12 minutes watching television, and 10 minutes drawing.
Match the following ratios to what they describe.
Description
The ratio of time inside to time eating lunch
The ratio of time eating lunch to time watching television
The ratio of time reading to time drawing
Ratio
2:1
10:3
3:2

The students will have 316 yards of the courtyard

The number of yards left for the students can be calculated as follows;

A school dedicated 50% of the courtyard area for students to start a garden

= 50/100

= 0.5

The number of yards is 632, the number of yards left for the students can be calculated as follows

= 0.5 × 632

= 316

Hence 316 yards are left for the students

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Step-by-step explanation:

GOOD RIGHT?

Answer:

1. 5/12 in exact form and 0.416 in decimal form

2. 26/3 in exact form and 8.6 in decimal form and 8 2/3 in mixed number form.

On each "6" there's a - on top!

The side length of the square in centimeters is 13 centimeters

The area of a shape is the amount of space on the shape

The equation of the area of the square is given as

p² = 169

The area of a square is the product of its length

This means that we simply take the square root of both sides of the equation to determine the side length

Next, we take the square root of both sides of the equation

So, we have

√p² = √169

Evaluate the square roots

So, we have

p = 13

Hence, the side length of the square in centimeters is 13 centimeters

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The addition of the fractions means that the value when combined is 1.

It should be noted that based on the information given, we simply have to add the fractions that are given and this will be:

= 1/2 + 1/3 + 1/6

= 3/6 + 2/6 + 1/6

= 6/6

= 1

Therefore, the addition of the fractions means that the value when combined is 1.

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The equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)

Expressions are mathematical statements that are represented by variables, coefficients and operators

Rational expressions are expressions that are represented by the quotient of two polynomials or radicals.

This means that, a rational expression is represented by a fraction whose numerator and denominator are polynomials or radicals

The expression is given as

(64x^2/3)^-1/3

Evaluate the product of the exponents

So, we have

(64x^2/3)^-1/3 = 64^-1/3 * x^(2/3*-1/3)

Evaluate the product of the exponents

So, we have

(64x^2/3)^-1/3 = 64^-1/3 * x^-1/9

Evaluate the exponent

So, we have

(64x^2/3)^-1/3 = 1/4 * x^-1/9

Evaluate the product

So, we have

(64x^2/3)^-1/3 = 1/4x^-1/9

Rewrite as

(64x^2/3)^-1/3 = 1/(4x^1/9)

Hence, the equivalent expression of (64x^2/3)^-1/3 is 1/(4x^1/9)

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Answer:

w = 0.9

Step-by-step explanation:

What I did is I subtracted 2.7 from 3.7 bc it was the least number and that gave me 1 so that left me with 0.43 = w - 0.47. Then I added 0.47 to 0.43 and that gives me 0.9 which would be the answer

If you don't understand how I got it I can try to explain a little better, but hopefully, you understand:)

The number of T-shirts bought by the Brandywine Dance Team is 24.

The number of the T-shirts that the Brandywine Dance Team purchased is determined using basic mathematical operations of division, subtraction, addition, and multiplication.

First, the cost of the equipment is subtracted from the total cost spent by the team.  The remainder refers to the cost of the T-shirts.  Since one T-shirt costs $12, the total quantity of T-shirts bought is 24.

The total amount spent = $644

The cost of the equipment = $356

The remainder after the equipment = $288 ($644 - $356)

Unit cost of T-shirts = $12

The number of T-shirts bought = 24 ($288/$12)

Thus, the Brandywine Dance Team bought 24 T-shirts.

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How many T-shirts were purchased by the Team?

The scale of the drawing is 1 inch represents 300 feet .

A scale drawing is a smaller image of a larger diagram or object in terms of dimensions. The scale drawing is usually reduced at a constant dimension.

In order to determine the scale of the drawing, divide the base of the actual Federal triangle by the base of the drawing.

Scale of the drawing = original dimensions / dimensions of the scale drawing

3000 / 10 = 300

1 inch represents 300 feet

1 inch : 300 feet

The scale of a drawing is usually written in this format - one a colon (:), the result of the division of the original dimension and the dimension of the scale.

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Yes..............................

Answer (y2 -y1) / (x2 - x1)

hope this helps

Answer:

(y2 -y1) / (x2 - x1)

Step-by-step explanation:

Use that formula. The answer should be -3/0 which doesn't make sense. Are you sure you have your x values correct? Since in that case, it would be a straight line and the equation for that would be x = 6 since it is a straight line up with no y-intercept.

Answer:

A function is a mathematical relation that maps a value in a set of input numbers to a value in a set of output numbers. Some functions can map multiple values in one set to one value in the other set.

Step-by-step explanation:

The value of [tex]f^{-1}(x)[/tex] is [tex]\frac{x}{\sqrt[3]{2} }[/tex]  when f(x) = 16  is [tex]x=2^\frac{11}{3}[/tex] .

We have given a function [tex]f(x)=x\sqrt[3]{2}[/tex].        ....(1)

 Let y = f(x)

         [tex]y=x\sqrt[3]{2} \\\\x=\frac{y}{\sqrt[3]{2} }[/tex]                         ......(2)

Swap the values of x and y, then the inverse is then

         [tex]y=\frac{x}{\sqrt[3]{2} }[/tex]

        [tex]f^{-1}(x)=y[/tex]                             ...(3)

Comparing equation (2) and (3) , we get

      [tex]f^{-1}(x)=\frac{x}{\sqrt[3]{2} }[/tex]

It is given that f(x) = 16 on comparing it with equation (1) , we get

              [tex]x\sqrt[3]{2}=16\\x=\frac{2^4}{2^\frac{1}{3} } \\x=2^{4-\frac{1}{3} }\\x=2^\frac{11}{3}[/tex]

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A. The ratio of the number of boys to the number of girls is; 115:92

B. The same ratio using another form is; 115 to 92

C. The ratio of the number of boys to the number of adults is; 115:28

D. The same ratio using another form is; 115 to 28

We are told that there are 115 boys, 92 girls, and 28 adults. Thus;

Number of boys = 115

Number of girls = 92

Number of Adults = 28

Now, we want to find some ratios and they are;

A) The ratio of boys to the number of girls = 115 : 92

B) Now, when we have a ratio of a:b, in words, it simply means a to b. Thus, our ratio of boys to girls here can be expressed as;

115 to 92

C) The ratio of the number of boys to the number of adults is;

115:28

D) Similar to answer B above, the ratio of the number of boys to the number of adults can also be expressed as; 115 to 28

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Answer:

It has 2 angles right and acute

the answer is 71 miles far

Answer:

4.6

Step-by-step explanation:

1. Multiply the whole number by the denominator

4 x 5 = 20

2. Add the result of step 1 to the numerator

20 + 3 = 23

3. Divide the result of step 2 by the denominator

23 ÷ 5 = 4.6

Answer:

-5, 1/2, -0.45, -0.05 would be the solution

Yes , the given function is an inverse function which is given by [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]  .

We have given a function [tex]f(x)=\frac{2x^2}{5} +1[/tex].        ....(1)

 Let y = f(x)

     [tex]y=\frac{2x^2}{5} +1\\y-1=\frac{2x^2}{5} \\\\\frac{5(y-1)}{2} =x^2\\\\\sqrt{\frac{5(y-1)}{2} } =x[/tex]                         ......(2)

Swap the values of x and y, then the inverse is then

         [tex]x=f^{-1}(y)[/tex]                           ...(3)

Comparing equation (2) and (3) , we get

   [tex]f^{-1}(y)=\sqrt{\frac{5(y-1)}{2} }[/tex]

We can check that this is really an inverse function or not

Putting in [tex]x=\sqrt{\frac{5(y-1)}{2} }[/tex]    equation (1) , we get

[tex]f(f^{-1}(y))=\frac{2(\sqrt{\frac{5(y-1)}{2} })^2}{5} +1\\\\\y=\frac{2\frac{5(y-1)}{2} }{5} +1\\\\y=\frac{5(y-1)}{5} +1\\\\y=y-1+1\\\\y=y[/tex]

As LHS = RHS  which means inverse function is correct .

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Answer:

9 hours

Step-by-step explanation:

605 miles/11 hours = 55miles/hour

495 miles (time) = 495 / 55 =9
So, 9 hours

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{4}~,~\stackrel{y_1}{6})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{3}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 1 +4}{2}~~~ ,~~~ \cfrac{ 3 +6}{2} \right) \implies \left(\cfrac{ 5 }{2}~~~ ,~~~ \cfrac{ 9 }{2} \right)\implies \left(2\frac{1}{2}~~,~~4\frac{1}{2} \right)[/tex]

Answer:

C

Step-by-step explanation:

The radicands have at least one prime-factor that is not in common.

The equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6

From the question, we are to determine the equation of the line that is perpendicular to the given equation.

A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line.

That is,

If m₁ is the slope of one of the lines

and m₂ is the slope of the other line

Then,

m₁ = -1/m₂

First, we will determine the slope of the given line

The equation of the given line is

y = 3x - 9

Compare the equation to the general form of the equation of a straight line

y = mx + b

Where m is the slope

and b is the y-intercept

By comparison,

m = 3

∴ The slope of the given line is 3

Thus,

The slope of the line that is perpendicular to this line is -1/3

Now,

To determine the equation this line,

We have that the line passes through the point (3, 1)

Using the point-slope form of the equation of a straight line,

y - y₁ = m(x - x₁)

m = -1/3

x₁ = 3

y₁ = 1

Putting the parameters into the equation,

y - 1 = -1/3(x - 3)

Expressing the equation in standard form

3(y -1) = -1(x - 3)

3y - 3 = -x + 3

3y + x = 3 + 3

x + 3y = 6

Hence, the equation of the line perpendicular to the given line and that passes through the point is x + 3y = 6

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The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

According to the given question:

Each block of horizontal  is 1/8 hr = 7.5 min

Each block of vertical is 10 km/hr

Time                     Velocity  (km/hr)

0 Min  ( 0 hr)               0

15 Min (1/4 hr)           50

45 Min (3/4 hr)           50

60 MIn  ( 1 hr)           100

90 Min  ( 3/2 hr)        100

120 Min ( 2hr)             0

The acceleration in first 15 minutes = (1/4 hr)  =  (50 - 0)/(1/4 - 0)  = 50/(1/4)

= 200  km/h²

The distance between the two cities =

= (1/2)(0 + 50)(1/4 - 0)  + 50 * (3/4 - 1/4)  + (1/2)(50 + 100)(1 - 3/4)  + 100 * (3/2 - 1) + (1/2)(100 + 0)(2 - 3/2)

=  25/4  + 25 + 75/4   + 50 + 25

= 125

Distance between two cities = 125 km

Average Speed of train during the journey = 125/2  = 62.5  km/hr

Therefore,

The acceleration in first 15 minutes = 200  km/h²

The distance between the two cities = 125 km

Average Speed of train during the journey =  62.5  km/hr

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