Jonathon created a graph that shows the number of exercises he completes in his workout routine.

On a coordinate plane, a graph titled Jonathon's Exercises has number of crunches on the x-axis and push-ups on the y-axis. Points (15, 2), (30, 4), and (45, 6) are plotted.

Which statement summarizes his exercise routine?
Jonathon does 3 crunches for every 2 push-ups.
Jonathon does 2 push-ups for every 3 crunches.
Jonathon does 2 push-ups for every 15 crunches.
Jonathon does 15 push-ups for every 2 crunches.

Answer:

x=7

y=11

z=7

Step-by-step explanation:

x + y + z = 25

y+z= 18

Z= 7

Substitute the third equation into the second

y+z=18

y+7 = 18

y = 18-7

y = 11

Now substitute y=11 and z=7 into the first

x +y+z = 25

x+11+7 = 25

x+18 = 25

x = 25-18

x=7

Answer:

No solution

Step-by-step explanation:

-2(11-12x) = -4(1-6x)

Distribute the -2 and -4:

-22 + 24x = -4 + 24x

Subtract 24x from both sides:

-22 = -4

Since this is a contradiction, there is no solution. The equation is inconsistent.

Answer:

No Solution.

Explanation:

When solving for x, the two values do not equate to each other.

Answer:

5 • 10^-4 I evaluate this by using scientific notation.

The value of the ratio  (3.5 x 10⁵) : (7x10⁸)  is 0.0005.

An expression is a sentence with at least two numbers or variables having mathematical operation. Maths operations can be addition, subtraction, multiplication, division.

For example, 2x+3

To solve (3.5 x 10⁵) : (7x10⁸), we can simplify the expression by dividing the numerical coefficients and dividing the exponents separately.

Dividing the numerical coefficients 3.5 and 7, we get:

3.5 ÷ 7 = 0.5

Dividing the exponents 5 and 8, we get:

10⁵ ÷ 10⁸ = 10⁵⁻⁸

              = 10⁻³

Therefore, the simplified expression is:

0.5 x 10⁻³

We can further simplify this expression by converting 10⁻³ to a decimal:

10⁻³ = 1/1000 = 0.001

So, the final answer is:

(3.5 x 10⁵) : (7x10⁸) = 0.5 x 10⁻³

                              = 0.5 x 0.001

                              = 0.0005

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Answer:

81

Step-by-step explanation:

24% × 337.5 =

(24 ÷ 100) × 337.5 =

(24 × 337.5) ÷ 100 =

8,100 ÷ 100 =

81;

Answer:

The answer would be 1/4. I explained below if you don't get how you get the answer. Good luck!

Step-by-step explanation:

1. Find the LCM of 4 and 10

4, 8, 12, 16, 20

10, 20

The LCM of 4 and 10 is 20.

2. Divide 4 and 10 by 20.

20 ÷ 4 = 5

20 ÷ 10 = 2

3. Multiply the numbers by the answer you got in step 2.

3 x 5 = 15

5 x 2 = 10

4. Put it together.(example:number you got in step 3/20)

15/20

10/20

5. Subtract

15/20 - 10/20 = 5/20

You get the answer of 5/20 or 1/4. I would write 1/4 though.

Answer:

$47.17 is the tax, so the total is $676.17

Step-by-step explanation:

Answer:

The answer would be a) 4-2g

Step-by-step explanation:

Multiplying by one half is like dividing by 2!

8/2 = 4

and

4/2 = 2

It can't be b because you can't add 4g+2

It can't be c because you can't completely remove the 8/4

It can't be d because you didn't actually distribute

Answer:

Step-by-step explanation:

Ronald's walking speed is 3 miles per hour, and he walks for 2 hours, so he covers 3 * 2 = 6 miles. In the next hour, he runs at a speed of 6 miles per hour, covering an additional 6 miles. Therefore, Ronald traveled a total of 6 + 6 = 12 miles.

The angles that have the given tangents, correct to 2 significant figures, are: 45°, 30° and 15°

To find the angles that have the given tangents, we can use the inverse tangent function (tan⁻¹) or the arctan function on a calculator. Remember that the arctan function gives an angle in radians, so we need to convert the result to degrees.

\(\tan \theta = 1.000\ \theta = \tan^{-1}(1.000)\\\\ \theta \simeq 45^{\circ}\)

tan θ = 0.577

θ = tan⁻¹(0.577)

θ ≈ 30°

tan θ = 0.268

θ = tan⁻¹(0.268)

θ ≈ 15°

tan θ = 4

θ = tan⁻¹(4)

θ ≈ 75.96°

θ ≈ 76° (rounded to 3 significant figures)

tan θ = 2.747\\θ = tan⁻¹(2.747)

θ ≈ 70.53°

θ ≈ 71° (rounded to 3 significant figures)

tan θ = 3.732

θ = tan⁻¹(3.732)

θ ≈ 75.89°

θ ≈ 76° (rounded to 3 significant figures)

Therefore, the angles that have the given tangents, correct to 2 significant figures, are:

45°

30°

15°

And the angles that have the given tangents, correct to 3 significant figures, are:

76°

71°

76°

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Answer:

1. 4

2. 39.3700787 (just round it up)

Answer:

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean \(\mu = 0.39\) and standard deviation \(s = 0.0488\)

Step-by-step explanation:

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question:

\(p = 0.39, n = 100\)

Then

\(s = \sqrt{\frac{0.39*0.61}{100}} = 0.0488\)

By the Central Limit Theorem:

The sampling distribution of the sample proportion of adults who have credit card debts of more than $2000 is approximately normally distributed with mean \(\mu = 0.39\) and standard deviation \(s = 0.0488\)

Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

________________________________________________________

Answer:

Distributive property of multiplication

Step-by-step explanation:

The distributive property of multiplication is basically distributing the terms outside the bracket to all the terms inside the bracket. In this case, 4 is multiplied to 5a as well as 3.

Answer: He used 91 pounds of type A coffee

Explanation:

Let x represent the number of pounds of type A coffee used

Let y represent the number of pounds of type B coffee used

This month, Dante made 156 pounds of the blend. This means that

x + y = 156

y = 56 - x

Type A coffee costs Dante $4.30 per pound, and type B coffee costs $5.50 per

pound. This month, the total cost the blend was $748.80. This means that

4.3x + 5.5y = 748.8

We would substitute y = 56 - x into 4.3x + 5.5y = 748.8. We have

4.3x + 5.5(156 - x) = 748.8

4.3x + 858 - 5.5x = 748.8

4.3x - 5.5x = 748.8 - 858

- 1.2x = - 109.2

x = - 109.2/- 1.2

x = 91

He used 91 pounds of type A coffee

Answer:

the problem is 1/7x+1/8?

The expected length of the piece that we are left with after breaking twice is L/4 and the variance Var(X) is 7L^2/144.

In the given question, consider a stick of length 1.

We break it at a point which is chosen randomly and uniformly over its length and keep the piece that contains the left end of the stick.

We then repeat the same process on the piece that we were left with.

We have to find expected length of the piece that we are left with after breaking twice.

In the same setting as Q7, suppose the length of the piece that we are left with after breaking twice is Y.

We also have to calculate the variance Var(Y).

Following Laws are used in the solution

Law of Iterated Expectations: E[X] = E[ E[X|Y] ]

& Law of total variance: Var(X) = E[Var(X|Y)]+Var(E[X|Y])

Now, Y = Length of the stick after we break it the first time

and X = length of the stick after we break it the second time

As both the distribution is uniformly distributed.

Now, E[Y] = L/2 and Var(Y)= l^2/12

E(x|y)[X|Y=y] = y/2 and Var(x|y)[X|Y=y] = y^2/12

As the expectation of uniform distribution over {a,b} is (b-a)/2 and variance is (b-a)^2/12

Using Law of Iterated Expectations

E[X] = E[ E[X|Y] ]

E[X] = E[ y/2 ]

E[X] = \int_{L}^{0}

E[X] = L/4

Now using Law of Total Variance

Var(X) = E[Var(X|Y)]+Var( E[X|Y] )

Var(X) = E[y^2/12]+Var(y/2)

Var(X) = (1/12)*E[Y^2]+(1/4)*Var(Y)

Var(X) = (1*12)*(Var[Y] + (E[Y])^2) + (1/4)*Var(Y)

Var(X) = (1/12)*(L^2/12+L^2/4) + (1/4)*(L^2/12)

Var(X) = 7L^2/144

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Answer:

what is the ?

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

d = r · t  and we know that the distance is the same.

Let x = time it takes Evelyn (in hours, since the rate is mph).

Evelyn's distance is 84x.

Rick's distance is 36·(x+2/3)  since 40 minutes longer is 2/3 of an hour longer

    84x = 36(x+2/3)

    84x = 36x + 24

    48x = 24

    x = 1/2

So it takes Evelyn 1/2 an hour, meaning the distance is 84(1/2) = 42 miles

To confirm this, it would take Rick 42/36 hours or 1 and 1/6 hours.  That's 70 minutes, which is 40 minutes longer than Evelyn's 1/2 hour trip.

The distance is 42 miles.

Answer:

68% rode the bus; 32% walked home

Step-by-step explanation:

Answer:

414π

Step-by-step explanation:

Volume of a cylinder = area of circle/ cross-section x height

Area of cross-section = πr² = 6²π = 36π

36π x 11.5 = 414π

Answer:

1300.61936 cm

Step-by-step explanation:

:))

Answer: 0.00923521

Step-by-step explanation:

Given : The probability U.S households play video or computer games=69%=0.69

here, the probability of each U.S household play video or computer games is fixed as 0.69

Then, the probability of each U.S household not play video or computer games= 1-0.69=0.31

For independent events the probability of their intersection is product of probability of each event.

Now, the probability that none play video/computer games will be :-

\((0.31)^4=0.00923521\)

The calculated volume of the solid figure is 421.08 cubic feet

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

Base area = 38.28 square feet

Height = 11 feet

Using the above as a guide, we have the following:

Volume = Base area * Height

substitute the known values in the above equation, so, we have the following representation

Volume = 38.28  * 11

Evaluate

Volume = 421.08

Hence, the volume of the solid figure is 421.08 cubic feet

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Answer:

572.6

Step-by-step explanation:

400 = 220 \(x^{5}\)

ln(400/220) = 5 ln(x)

ln(x) = .1195

x = \(e^{.1195}\)

x = 1.127

Y = 220\((1.127)^{8}\)

Y= 572.6

If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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The surface area of this figure is determined as 980.5 m².

The total surface area of the figure is the sum of all the area of the six faces and it is calculated as follows;

Area of top face = 12.7 m x 11 m = 139.7 m²

Area of bottom face = 9.5 m x 16 m = 152 m²

Area of far right face = 12.7 m x 14 m = 177.8 m²

Area of far left face = 9.5 m x 14 m = 133 m²

Area of front face = 16 m x 14 m = 224 m²

Area of back face = 11 m x 14 m = 154 m²

Total surface area = 139.7 m² + 152 m² + 177.8 m² + 133 m² + 224 m² + 154 m²

= 980.5 m²

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The reasonable estimate would be 25

We have to solve this using the rule of 3

9 out of 30 members said that they run more than 5 days a week.

We will form the equations

when 9 ran = 30 menbers

when n ran = 84 members

we will then cross multiply

84 x 9 = 30 x n

n = 25.2

When we round this, the reasonable estimate would be 25

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Complete question

Freemont Run Club surveyed a random sample of 30 of their members about their running habits. Of the members surveyed, 9 said that they run more than 5 days a week.

There are 84 Freemont Run Club members.

Based on the data, what is the most reasonable estimate for the number of Freemont Run Club members who run more than 5 days a week?

Answer:

b

Step-by-step explanation:to get the answer you multiply by 4 1x4 =4 3 x 4=12