Solve for s in terms of p, q, and r.
q= –spr

The expression that can be used to find the temperature after it changes is 85°F + C

Temperature refers to the degree of hotness or coldness of a body at a particular time. It is measured in degree Celsius, degree Fahrenheit an Kelvin.

The instrument used to measure temperature is a thermometer.

let

The change in temperature = 85°F + C

= 85°F + (-11°F)

= 85 - 11

= 74°F

Therefore, the new temperature after a decrease in 11°F is 74°F

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The number of donuts that can be purchased for $10 is 20.

The total cost of Mrs. Goodwin's donut purchase varies directly with the number of donuts purchased. The total cost of 15 donuts was $7.5. We need to find out the number of donuts that can be purchased for $10.

Let the number of donuts, price, and constant of proportionality be represented by the variables "n", "p", and "k", respectively.

The price is directly proportional to the number of donuts purchased.

p ∝ n

We will remove the proportionality sign.

p = k*n

7.5 = k*15

k = 1/2

The equation is p = (1/2)n. We will now calculate the number of donuts that can be purchased for $10.

p = (1/2)n

10 = (1/2)n

n = 10*2

n = 20

Hence, the number of donuts that can be purchased for $10 is 20.

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Step-by-step explanation:

4a)

that means all 4 events happen in combination as one event.

so, we have to multiply the probabilities of all 4 events.

that means

0.63⁴ = 0.15752961... ≈ 0.16

so, there is a 16% chance that all 4 children get sick.

in other words, the probabilty for that is about 0.16.

b)

the probabilty of at least 1 kids getting sick is the opposite of the probability of no kids is getting sick.

the probability of getting sick is 0.63, so the probability of not getting sick is 1 - 0.63 = 0.37.

the probability of no kids getting sick is similar to a)

0.37⁴ = 0.01874161 ≈ 0.02

the probabilty of at least one kid getting sick is the opposite of that :

1 - 0.01874161... = 0.98125839 ≈ 0.98

5)

A u B is the sample space. so, any possible event is either part of A or B or both.

that means

P(A') = 0.35 = 1 - P(A)

P(A) = 1 - 0.35 = 0.65

P(A and B') = P(of every A that is not B) = 0.25.

because P(A) = 0.65

that means that

P(A and B) = P(every A that is also B) =

= 0.65 - 0.25 = 0.4

P(B) = P(A') + P(A and B) = 0.35 + 0.4 = 0.75

FYI

we could have gotten this directly from

P(A and B') = P(of every A that is not B = everything that is only A) = 0.25.

because

P(A and B')' = P(of everything that is not "only A" = everything that is B) = P(B) = 1 - 0.25 = 0.75

The rectangle has its dimensions to be 8.8 units by 12.4 units

From the question, the equation is given as

2x(x + 8) = 110

This equation represents the area of the rectangle

So, we have

2x(x + 8) = 110

Divide by 2

x(x + 8) = 55

Open the brackets

This gives

x² + 8x = 55

Rewrite as

x² + 8x - 55 = 0

Using a graphing calculator, we have the solutions to be

x = -12.4 and x = 4.4

The variable x cannot be negative

So, we have

x = 4.4

In 2x(x + 8) = 110, we have

Length = 2x

Width = x + 8

So, we have

Length = 2 x 4.4

Width = 4.4 + 8

Evaluate

Length = 8.8

Width = 12.4

Hence, the dimensions of the rectangle are 8.8 units by 12.4 units

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x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

What is, axis of symmetry, vertex and x - intercept?

A vertical line that splits the parabola into two equal half is the axis of symmetry. The equation x = - b/2a tells us where the line of symmetry lies. The parabola's vertex, which is a point (x, y), is where it crosses its axis of symmetry.

A line's x-intercept is the location at which the x-axis is crossed.

Consider, the given equation,

[tex]f(x) = \frac{1}{4}(x - 1)(x + 7)[/tex]

Let,

[tex]y = \frac{1}{4}(x - 1)(x + 7)[/tex]             ..(1)

To find x - intercept, plug y = 0 in above equation,

[tex]\frac{1}{4}(x - 1)(x + 7) = 0\\ (x - 1)(x + 7) = 0\\(x - 1) = 0, (x + 7) = 0\\x = 1, x = -7[/tex]

Therefore, x = 1 and x = -7 are the x - intercepts.

Since, the x-coordinate of the vertex is at the midpoint of the x-intercepts.

So,

[tex]x = \frac{-7+1}{2} = \frac{-6}{2} = -3[/tex]

Plug x = -3 in equation (1)

[tex]y = \frac{1}{4}(-4)(4) = -4[/tex]

Therefore, the vertex is, (-3, -4).

The x - coordinate of the vertex is the axis of symmetry.

Therefore, axis of symmetry is x = -3.

Hence, x = 1 and x = -7 are the x - intercepts, the vertex is, (-3, -4), and axis of symmetry is x = -3.

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Answer:

Using formula to calculate the circumference of wheel: c=d/n

where

D is the distance bike travel

n is the number of times rotation

C is the circumference of the wheel

As per the statement:

Lin’s bike travels 100 meters when her wheels rotate 55 times.

here, n = 55 rotation and D = 100 meter.

then by definition:

meter c=100/55=20/11

Therefore, the circumference of her wheel is 1 9/11

Yes, a baseball fit in box A.

Volume is a mathematical term used to describe how much three-dimensional space an item or closed surface occupies. Volume is measured in cubic units like m³, cm³, in³, etc.

Volume is simply the amount of space a three-dimensional solid takes up. These solids can take the form of a cube, cuboid, cone, cylinder, or sphere.

Volume is sometimes referred to as capacity. For instance, a cylindrical jar's volume can be used to calculate how much water it can hold.

Given:

The circumference of a regulation baseball is at least 9 inches but no more than 9.25 inches.

So, the maximum value of Circumference

2πr = 9.5

r= 9.5/ 2 x 3.14

r = 1.472 inch

So, Volume of ball = 4/3 πr³

Volume of ball = 4/3 x 3.14 x (1.472)³

Volume of ball = 13.36 inch³ < 64 inch³

Hence, it will fit inside the box.

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Answer:22.5

Step-by-step explanation:

The change in the amount of seed in the feeder after 7 days is 78.75 ounces.

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one.

For example, if you ran 80 meters in 10 seconds, you ran on average 8 meters in 1 second

To find the rate at which the amount of seed decreases.

11 1/4 ounces = 5 days

Dividing both sides of the equation by 5.

11 1/4 ounces = 1 day

Multiplying 7 on both sides to get the number for 7 days

7 x 11.25 ounces = 7 days

78.75 ounces  = 7 days

If the amount of seed in a bird feeder decreases by 11 1/4 ounces in 5 days, the amount of seed decreases by 78.75 ounces.

The change in the amount of seed in the feeder in 7 days is 78.75 ounces.

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Answer:

12 tables per classroom.

Step-by-step explanation:

We will assume that the teacher uses all of the 4/5 oz of paint.  We can find how many samples of 1/30 oz are contained in the 4/5 oz by dividing:

(4/5)÷(1/30) = (4/5)*(30/1)

(4/5)*(30/1)  = (120/5)

(120/5) = 24 samples of 1/30 oz paint in (4/5) oz total paint.

Each of the 2 Pre-K classrooms have the same number of tables, so we can divide 24 samples by 2 to find the number of tables in each classroom,

*24 samples/2 classrooms) = 12 tables/classroom

The fraction 7/2a+4/a*a can be written as (7 + 8a) / 2a

What is a fraction?

In general, any number of equal pieces is represented by a fraction, which is a portion of the entire. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many pieces of a particular size there are in spoken common English. In other words, a fraction indicates the components of a whole or group of items.

Solution Explained:

First, we simplify the equation

=  [tex]\frac{7}{2a} + \frac{4}{a} X a[/tex]

=  [tex]\frac{7}{2a} + 4[/tex]

= [tex]\frac{7 + 8a}{2a}[/tex]

Therefore, the equation can be written as (7 + 8a) / 2a

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The formula for nth term in the given arithmetic sequence is 10 - 3n

For an nth term in an arithmetic sequence

U(n) = a + (n - 1)d

Where n is the number of terms

a is the first term

d is the common difference

From the sequence above

a = 7

d = 4 - 7 = - 3

The formula for an nth term is

U(n) = 7 + (n - 1)-3

= 7 - 3n + 3

Hence, the formula for nth term is 10-3n

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11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.

Given that,

35 percent of the 80 kids in the group are girls. 9 of the female students selected volleyball as their preferred sport.

We have to find what percentage of the female students chose volleyball.

The total children's are 80.

The 35% are girls.

9 have selected the volleyball

So,

9/80

0.1125

The percent is

11.25%

Therefore, 11.25 percentage of the female students chose volleyball when 35 percent of the 80 kids in the group are girls.

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Answer:75

Step-by-step explanation:

since there are 15 students and they each need 5 plates you just do 15x5 and get 75

Answer:

10 hours

Step-by-step explanation:

since she spent 5 hours writing 10 pages. you just have to multiple by 2 to know how long it will take to write 20 pages

The equation representing the elevation of the loon and the time of the dive is 3x-2y = 0, and the Loon has been diving for 14.67 seconds.

The red throated loon dived down to a distance of 12 feet under the water in 8 seconds.

We can assume that the loon is diving at a constant rate.

The relation between the elevation wise of the loan after 1 second into the dive can be represented by the linear equation which has the slope,

Slope = 12/8

Slope = 3/2

Now as we have the slope of the equation we can write the equation by using the point slope form, with the point, (8,12)

(y - 12)/(x - 8) = 3/2

2y - 24 = 3x - 24

3x - 2y = 0

This is the equation that represent the elevation y of the loan after x seconds.

When the elevation of The Loon is 22 feet,

We can put y = 22,

3x = 2(22)

x = 14.67 seconds.

So, the loon has been diving for 14.67 seconds.

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Answer:

a = 1

Step-by-step explanation:

Given equation,

→ 7(5a - 4) - 1 = 14 - 8

Now the value of a will be,

→ 7(5a - 4) - 1 = 14 - 8

→ 35a - 28 - 1 = 6

→ 35a - 29 = 6

→ 35a = 6 + 29

→ a = 35/35

→ [ a = 1 ]

Hence, the value of a is 1.

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

In everyday speech, the term "probability" refers to the likelihood that a specific event (or group of events) will take place, represented as a number between 0 and 100% or as a linear scale from 0 (impossibility) to 1 (certainty). Statistics is the study of events that follow a probability distribution. Probability is a way to gauge how likely something is to happen. Even while no event can be foreseen with absolute certainty, probability can be used to convey how likely it is that it will happen.

Given,

12 fair dice rolled,

Probability that the product of the numbers on the top faces is prime:

⁶C₅ × (1/6)⁵ × ³C₁/⁶C₁

6 × (1/6)⁵ × 3/6

1/2(1/6)⁴

Probability that the product of the numbers on the top faces is prime is  1/2(1/6)⁴.

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The three consecutive even integers are -2, 0 and 2.

Let the three consecutive even integers be x, x+2 and x+4.

Since the product of the first two is taken, the result is four less than the square of the third one. This will be:

x(x + 2) = (x + 4)² - 4

x² + 2x = x² + 8x + 16 - 4

x² + 2x = x² + 8x + 12

Collect like terms

x² - x² + 2x - 8x - 12

-6x - 12 = 0

-6x = 12.

Divide

x = -12/6

x = -2

x + 2 = -2 + 2 = 0

x + 4 = -2 + 4 = 2

They're -2, 0, and 2.

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By using the property of similar triangles, it can be obtained that

Value of x is 7.2

What are similar triangles?

Two triangles are said to be similar if the corrosponding angles are equal and the corrosponding sides are similar.

The different axioms of similarity are-

SAS axiom, AA axiom, SSS axiom

By the property of similar triangles,

[tex]\frac{9}{9 + 6} = \frac{x}{12}\\x = \frac{9}{15} \times 12\\x = 7.2[/tex]

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Graph will shift in both horizontal and vertical direction by 4 units.

What is straight line?

An unending, one-dimensional figure with no width is a straight line. It consists of an infinite number of points connected on either side of a point. There is no curvature in a straight line. It might be angled, vertical, or horizontal.

What is general equation of a Straight Line?

The general equation of a straight line can be given as ax + by + c = 0, where

What do you mean by function?

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, co-domain, and domain. The usual way to refer to a function is as fn(x), where x is the input.

We have function,

fn(x) = x + 5

when the graph is translated by 4 units, we can write it as;

g(x) = fn(x) + 4

the graph will shift in both horizontal and vertical direction by 4 units as it can be seen in the graph.

Therefore, graph will shift in both horizontal and vertical direction by 4 units.

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Answer:

28

Step-by-step explanation:

mean is when you add all the numbers divide it by the amount of terms

So to find the sum of the terms we just multiply 5 by 4

20 is the sum and since the mean is 8 with 6 terms we multiply those also

8x6

48 and to find the number we subtract 48 by 20

48-20

28

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A system of inequality to represent the maximum amount of flooring needed is c + h ≥ 2000.

A system of inequality to represent the maximum amount of money wants to spend is 4.50c + 8.25h ≥ 10,000.

In order to solve this word problem, we would assign variables to the number of square feet of carpet and the number of square feet of hardwood for the given flooring area, and then translate the word problem into an algebraic inequality as follows:

For the maximum amount of flooring needed, we have:

c + h ≥ 2000

For the maximum amount of money, we have:

4.50c + 8.25h ≥ 10,000.

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The expression that makes v the subject of the formula, W=5+v/v-3 is v= (5 + 3W)/ (W-1).

The concept is the concept of finding the subject of the formula in an expression.

To know the subject of the formula, we will need to perform some simplification:

W=5+v/v-3

then this can be expressed as:

W(v-3) = 5+v

Wv - 3W = 5+v

then we can rearrange the expression as:

Wv - v = 5 + 3W

then we can factorize  the expression as :

v(W-1) = (5 + 3W)

v= (5 + 3W)/ (W-1)

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The length of the shorter piece is 33 inches.

According to the question,

We have the following information:

A 132 ​-inch is cut into two pieces. One piece is three times the length of the other.

Now, let's take the length of the shorter piece to be x inches and the length of another piece will be 3x inches.

Now, we have the following expression:

x+3x = 132

4x = 132

4 is in multiplication on the left hand side. So, it will be in the division on the right hand side.

x = 132/4

x = 33 inches

Hence, the length of the shorter piece is 33 inches.

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Answer is :

The chosen at random is 25 - 44 years old is  = 26 %.  

Probability determines how likely it is that a stated event would

occur. This event would occur. This probability lies between 0 and 1.

The probability that a person chosen at random is at least

15 years = sum of percentages of people at least 15 years old :

14 + 13 + 13 + 15 + 12 + 13 = 80%

the probability that a person chosen at random is 25 - 44 years old :

13% + 13% = 26%

Therefore The probability is 26%.

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There are zero or null real fourth roots of -1.

This means that the square root of the square root of a number is equal to the number's fourth root. Symbolically, the fourth root is also represented by multiplying the radical by 4, creating the number 4. The fourth root of 16, for instance, is 2, which means that 2 2 2 2 = 16. n, also known as the degree of the root, is a positive integer in this situation. The terms "square root" and "cube root" are used to describe roots of degree 2 and 3, respectively. The ordinal numbers fourth root, twentieth root, etc. are used to refer to roots of higher degree. It is a root extraction to calculate the nth root. A integer y such that y2 = x is referred to as the square root of an x in mathematics.

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Answer:

x=-4

Step-by-step explanation:

-3x-18=-6

-3x=12

x=-4

Answer:  x=-4

Step-by-step explanation:

Start off with the equation: -3x-18=-6

Add 18 to both sides: -3x=12

Divide by -3: x=-4

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