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Which of the following sets of numbers could represent the three sides of a right
triangle?
O {14, 20, 25}
O {64, 72,97}
O {32, 60, 68}
O {45, 59, 75}

The equivalent ratios are: (1, 2), (2, 4), and (3, 6)

The graph can be plotted on a coordinate grid as shown in the diagram attached below.

Recall:

Let x = number of books

y = cost (dollars)

Using any of the ordered pairs from the table, say, (7, 14), find k:

k = y/x = 14/7 = 2

Write the equation by plugging in the value of k into y = kx

y = 2x

Using the equation, y = 2x, find the equivalent ratios when x = 1, x = 2, and x = 3:

When x = 1:

y = 2(1) = 2 --> (1, 2)

When x = 2:

y = 2(2) = 4 ---> (2, 4)

When x = 3:

y = 2(3) = 6 ---> (3, 6)

The graph for the three equivalent ratios, (1, 2), (2, 4), and (3, 6) can be plotted on a coordinate grid as shown in the diagram attached below.

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Answer:

70, 85, 93, 100, 125, and 127

Explanation:

We want to create a data set with 6 different values whose mean is 100.

Let the sum of the 6 numbers = x

What this means is that the 6 numbers must add up to 600.

Let 5 numbers in the data set be:

• 70, 93, 100, 125, and 127

Add the 5 numbers up:

Subtract the sum from 600 to get the 6th number.

Thus, the 6 diffrent values are:

Answer:

C choice.

Step-by-step explanation:

Since line a is given a slope as -4.

Another line which is line b is given that it's perpendicular to line a or we can say that line a is perpendicular to line b.

Perpendicular is defined as:

\( \displaystyle \large{m_1m_2 = - 1}\)

Both slopes multiply and yield -1.

We know that m1 is -4; we want to find m2 which is slope of line b.

\( \displaystyle \large{ - 4m_2 = - 1}\)

Divide both sides by -4.

\( \displaystyle \large{ \frac{ - 4m_2}{ - 4} = \frac{ - 1}{ - 4} } \\ \displaystyle \large{ m _2 = \frac{1}{4} }\)

Therefore, the slope for line b is 1/4.

Thus, the C choice is correct.

Answer: x=3 and y=4

Step-by-step explanation:

Rewrite equations:

x+3y=15;2x−2y=−2

Step: Solve x+3y=15 for x:

x+3y=15

x+3y+−3y=15+−3y(Add -3y to both sides)

x=−3y+15

Step: Substitute−3y+15 for x in 2x−2y=−2:

2x−2y=−2

2(−3y+15)−2y=−2

−8y+30=−2(Simplify both sides of the equation)

−8y+30+−30=−2+−30(Add -30 to both sides)

−8y=−32

−8y over −8 = −32 over −8

(Divide both sides by -8)

y=4

Step: Substitute 4 for y in x=−3y+15:

x=−3y+15

x=(−3)(4)+15

x=3(Simplify both sides of the equation)

Answer: 12 bottles left

Step-by-step explanation:

18-6=12 bottles

Answer:

Johnny will have 7 beer bottles left.

Step-by-step explanation:

Area=2.5

Step-by-step explanation:

area

\(area = length \times width\)

\(area = 10 \times \frac{1}{4} \)

Answer:

34 cm squared

Step-by-step explanation:

You would need to fill in the cut out part of the shape. Find the area of the whole shape minus the area of the cut out shape.

Area of the bigger shape :6*9 =54cm squared

Area of the cut out shape:4*4=20cm squared

Answer:

Answer: 27:8

Step-by-step explanation:

There are 24 + 16 + 14 = 24+16+14= 54

54 marbles in total.

The ratio of total marbles to red marbles is 54 : 16, which simplifies to 27 : 8.

Answer: 27:8

Answer:

\(\displaystyle 1\frac{2}{5}=\frac{7}{5}\)

Step-by-step explanation:

\(\displaystyle a\frac{b}{c}=\frac{ac+b}{c}\\\\1\frac{2}{5}=\frac{(1)(5)+2}{5}=\frac{5+2}{5}=\frac{7}{5}\)

Answer:

the area of triangle

\( \frac{1}{2} \times base \times height \\ → \frac{1}{2} \times 8 \times 7 \\→ 4 \times 7 = 28 {mm}^{2} \)

Step-by-step explanation:

John's savings amount as a function of time is S(t) = $24,000 / 25. Initially, he needs to save $24,000 for a new car. After the first month, he has saved $1,000. The savings amount is directly proportional to the time elapsed. The constant of proportionality is 1/24. Thus, John's savings amount can be determined based on the remaining amount he needs to save.

John's savings amount can be represented as a function of time and is proportional to the amount he still needs to save. Let's denote the amount John needs to save as N(t) at time t, and his savings amount as S(t) at time t. Initially, John needs to save $24,000, so we have N(0) = $24,000.

We know that John has saved $1,000 after the first month, which means S(1) = $1,000. Since his savings amount is proportional to the amount he still needs to save, we can write the proportionality as:

S(t) = k * N(t)

where k is a constant of proportionality.

We need to find the value of k to determine John's savings amount at any given time.

Using the initial values, we can substitute t = 0 and t = 1 into the equation above:

S(0) = k * N(0)  =>  $1,000 = k * $24,000  =>  k = 1/24

Now we have the value of k, and we can write John's savings amount as a function of time:

S(t) = (1/24) * N(t)

Since John's savings amount is proportional to the amount he still needs to save, we can express the amount he still needs to save at time t as:

N(t) = $24,000 - S(t)

Substituting the expression for N(t) into the equation for S(t), we get:

S(t) = (1/24) * ($24,000 - S(t))

Simplifying the equation, we have:

24S(t) = $24,000 - S(t)

25S(t) = $24,000

S(t) = $24,000 / 25

Therefore, John's savings amount at any given time t is S(t) = $24,000 / 25.

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Answer:

The length of x in the simplest radical form with a rational denominator will be:      

Step-by-step explanation:

Given

hypotenuse = 5

angle Ф = 60°

To determine

x = ?

Using the trigonometric ratio

cos Ф = adjacent / hypotenuse

here

Ф = 60°

adjacent of 60° = x

hypotenuse = 5

so substituting Ф = 60°, adjacent = x and hypotenuse = 5 in the equation

cos Ф = adjacent / hypotenuse

so

\(cos\:60^{\circ }\:=\:\frac{x}{5}\)

       \(\frac{\sqrt{3}}{2}=\frac{x}{5}\)

switch sides

         \(\frac{x}{5}=\frac{\sqrt{3}}{2}\)

Multiply both sides by 5

         \(\frac{5x}{5}=\frac{5\sqrt{3}}{2}\)

Simplify

         \(x=\frac{5\sqrt{3}}{2}\)

Therefore, the length of x in the simplest radical form with a rational denominator will be:      

Let's denote the time it takes for the slower pipe to fill the tank on its own as $x$ hours. Then, the faster pipe takes $x-3$ hours to fill the tank on its own. We can use the formula for the rate of work to set up an equation: $r_1 + r_2 = \frac{1}{2}$, where $r_1$ and $r_2$ are the rates of work for each pipe.

We can express the rate of work in terms of the time it takes for each pipe to fill the tank on its own: $r_1 = \frac{1}{x}$ and $r_2 = \frac{1}{x-3}$. Substituting these expressions into the equation above and solving for $x$, we obtain $x=2$. Therefore, the slower pipe takes 2 hours to fill the tank on its own, and the faster pipe takes $2-3=-1$ hour, which doesn't make physical sense. This means there is an error in the problem statement.

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An.swer:

171.68

Step-by-step explanation:

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer:

choice c is correct

Step-by-step explanation:

b^2 -15b +56 = 0

b^2-8b-7b +56 = 0

b(b-8) -7(b-8) = 0

(b-8)(b-7) = 0

b= {8, 7}

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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we have

f(x)=7x-1

g(x)=(1/7)(x+1)

Part 1

Find out (fog)(x)

(fog)(x)=f(g(x))=7(1/7)(x+1)-1=x+1-1=x

therefore

(fog)(x)=x

Part 2

Find out (gof)(x)

(gof)(x)=g(f(x))=(1/7)(7x-1+1)=x

therefore

(gof)(x)=x

Part 3

(fog)(x)=(gof)(x)=x

the answer is Yes

Answer:

2.9661582

Step-by-step explanation:

2.9661582e+16 this is the answer

Answer:

D α H

k = D/H

k = 3.50

Step-by-step explanation:

Amount paid, D is directly proportional to the number of hotdogs, H

D = $3.50 per hot dog

D = $3.50 is directly proportional to 1 hotdog

Hence,

D α H

D = kH

k = proportionality constant

H = 1

3.50 = k

k = 3.50

k = D/H

Answer:

The correct option is a) 1/2

The probability of obtaining a head after obtaining two heads from two tosses of a coin is 1/2.

What is probability?

Probability is a branch of mathematics concerned with the study of random events or occurrences.

Probability is a quantitative measure of the likelihood that a given event will occur.

Probability is usually given as a number between zero and one (0 ≤ P(E) ≤ 1), where,

P(E) = 0, the event is considered impossible, and

when P(E) = 1, the event is considered a certainty.

What is the probability of obtaining a head after obtaining two heads from two tosses of a coin?

After obtaining two heads from two tosses of a coin, the probability of obtaining a head on the next toss is given by:

Sample space, S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}where H is for head and T is for tail.

Therefore, the probability of obtaining a head after obtaining two heads from two tosses of a coin is given by:

P(E) = favorable outcomes/total outcomes

The favorable outcome in this case is {HHH, HHT, HTH, THH, TTH}.

Hence, P(E) = 5/10

                   = 1/2

Therefore, the correct option is a) 1/2.

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2.67 pints of red paint to be added to the paint Mixer in order to achieve the desired 75% red and 25% yellow mixture.

The number of pints of red paint that need to be added to the paint mixer, we need to calculate the amount of paint in the mixer currently and find the difference between that amount and the desired 75% red mixture.

Currently, the paint mixer contains 4 pints of equal amounts of yellow and red paint. Since the yellow and red paint are in equal amounts, we can say that there are 2 pints of red paint in the mixer.

Now, let's calculate the amount of red paint required for the desired mixture. We want the final mixture to be 75% red, which means that 75% of the total mixture should be red.

the total mixture required is X pints. Since 75% of the mixture should be red, we have:

0.75X pints of red paint.

Since the current amount of red paint in the mixer is 2 pints, we can subtract this from the desired amount to find the additional pints of red paint needed:

0.75X - 2 pints.

We want the additional pints of red paint to equal 0, so we set up the equation:

0.75X - 2 = 0.

Solving this equation, we find:

0.75X = 2.

X = 2 / 0.75.

X ≈ 2.67.

Therefore, we need approximately 2.67 pints of red paint to be added to the paint mixer in order to achieve the desired 75% red and 25% yellow mixture.

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Answer:

6.5 miles per day

Step-by-step explanation:

Take the number of miles and divide by the number of days

39 miles/ 6 days

6.5 miles per day

Answer: 6.5 miles per day is correct

Step-by-step explanation:

You would just need to divide 39 by 6 to find the total miles per day. Therefore C: 6.5 is correct!

Answer:

Step-by-step explanation:

Using Law of Cosine

Suppose Angle A is 60 degrees which is between sides b and c.

we need to find the length of side a

a^2 = b^ + c^ - 2bcCos60

a^2 = 4 + 25 - 20Cos60

a^2 = 29 - 20Cos60

a = 4.3588

Step-by-step explanation:

the other answer is correct but missed a few steps in the explanation. so, just to be sure :

yes, we use the law of cosine (or I call it the general Pythagoras for non-right-angled triangles) :

c is the side opposite of the given angle. a, b are the other 2 sides.

c² = a² + b² - 2ab×cos(angle)

in our case

c² = 2² + 5² - 2×2×5×cos(60°) =

= 4 + 25 - 20×0.5 = 29 - 10 = 19

c (the third side) = sqrt(19) = 4.358898944... units

you see how this is connected to the regular Pythagoras in right-angled triangles ?

c² = a² + b² - 2ab×cos(90°)

cos(90°) = 0

and so all that is left is

c² = a² + b²

Answer:

50

Step-by-step explanation:

Answer: 0.2

Step-by-step explanation:

subtract 9.38 - 3.5 = 5.88

distribute the 1.2.

7.56 - 8.4x = 5.88

subtract 5.88 - 7.56 = -1.68

-8.4x = -1.68

divide both sides by -8.4

answer = 0.2