Penn volunteered a total of 96 hours
over the last 12 weeks. He
volunteered the same number of
hours each week.
How many hours did Penn volunteer
in one week? Write an equation
and solve the problem.
Equation:
Answer:

The inequality is solved and the number is x ≥ 12

Given data ,

Let the number be represented as x

Now , sum of three times a number and -4 is at least twice the number plus 8

And , 3x - 4 ≥ 2x + 8

To solve for "x", we can start by isolating the "x" term on one side of the inequality

3x - 4 ≥ 2x + 8

Subtract 2x from both sides , we get

3x - 2x - 4 ≥ 2x - 2x + 8

x - 4 ≥ 8

Add 4 to both sides , we get

x - 4 + 4 ≥ 8 + 4

x ≥ 12

Hence , the inequality is x ≥ 12

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The proof that Daniel and Edward receive money in the ratio of their ages is shown below.

A ratio expresses the number of times one number contains another. For example, if a dish of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, while the orange-to-total fruit ratio is 8:14.

Given that Daniel and Edward receive money in the ratio of their ages. And the age of Daniel and Edward is 8 years and 12 years, respectively. Therefore, it can be written as,

Ratio of Ages

=Age of Daniel: Age of Edward

= 8 years : 12 years =

= 2 : 3

Ratio of the amount received by them

= Amount received by Daniel: Amount received by Edward

= $30 : $45

= 2 : 3

Since, Ratio of Ages = Ratio of the amount received by them.
Therefore, it can be concluded that Daniel and Edward receive money in the ratio of their ages.

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The complete question is:
Daniel is 8 years old and Edward is 12 years old. Their parents give them money in the ratio of their ages. If Daniella receives $30, then Show that Edward receives $45.

A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). Therefore, p-value given is 0.0062.

A hypothesis is a put forth explanation of a phenomenon (plural: hypotheses). A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientific hypotheses are typically based on prior observations that cannot be adequately explained by the current body of knowledge.

H:p<=0.8

Ha: p>0.8

alpha=0.01 P{reject H:H is true}

critical value z>2.326

z=(0.9-0.8)/sqrt (0.8*0.2/100); sqrt of 0.0016=.04

z=(0.1/.04)=2.5

probability z> 2.5 is 0.0062

check with one sample proportion test on calculator, z=2.5

Reject H

p-value given is 0.0062

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The test statistic is z₀ = 2.65 and the P-value is 0.004. The null hypothesis is rejected at the 5% level of significance, and we conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8.

To test the hypothesis using the P-value approach, we can follow these

Check whether the sample size is large enough for the normal approximation to the binomial distribution. The requirements are satisfied if np₀ >= 10 and n(1-p₀) >= 10,

where p₀ is the hypothesized proportion under the null hypothesis. In this case, p₀ = 0.8, n = 125, so np₀ = 100 and n(1-p₀) = 25, both of which are greater than 10.

The null hypothesis is H₀: p = 0.8 (the true proportion is 0.8).

The alternative hypothesis is H₁: p > 0.8 (the true proportion is greater than 0.8).

Under the null hypothesis, the test statistic follows a standard normal distribution.

The test statistic is calculated as:

z₀ = (x - np₀) / sqrt(np₀(1-p₀))

where x is the number of successes in the sample.

Plugging in the values, we get:

z₀ = (105 - 1250.8) / √(1250.8 x 0.2)

z₀ = 2.65

Calculate the P-value.

The P-value is the probability of observing a test statistic as extreme or more extreme than the one calculated from the sample, assuming the null hypothesis is true.

Since this is a right-tailed test (H₁: p > 0.8), we calculate the area to the right of the test statistic.

Using a standard normal table or calculator, we find that the area to the right of z₀= 2.65 is 0.004.

Therefore, the P-value is 0.004.

Make a decision and interpret the results.

Using a significance level of α = 0.05, we compare the P-value to α.

Since the P-value (0.004) is less than α (0.05), we reject the null hypothesis.

We conclude that there is sufficient evidence to suggest that the true proportion is greater than 0.8 at a 5% level of significance.

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x at the vertex would help Charlie to find out how long it takes his basketball to reach the highest point.

When a quadratic function is in vertex form, the vertex (h, k) represents the highest or lowest point of the parabola.

In this case, the time it takes for the basketball to reach the highest point can be found by finding the x-value of the vertex of the function that represents the height of the basketball over time.

Therefore, option (A) x at the vertex would help Charlie to find the time at which the basketball reaches the highest point.

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The area of the triangle is 2√2 square units.

This is a right triangle, and the base (the side opposite the right angle) has a length of 2√2.

We can use the Pythagorean theorem to find the length of the other two sides:

x² + x²  = (2√2)²

2x²  = 8

x²  = 4

x = 2

So the two other sides have a length of 2.

Now we can use the formula for the area of a triangle:

Area = (1/2) × base × height

In this case, the base is 2√2 and the height is 2, so we have:

Area = (1/2)×2√2 ×2

Area = 2√2

Therefore, the area of the triangle is 2√2 square units.

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The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.

Here, we have,

given that,

the value represented by the digit 8 in the number 8,342

and, the value represented by the digit 8 in the number 284.

now, we have to find that how many times greater is the value.

so, we have to differentiate the value represented by the digit 8 in the number 8,342 with the value represented by the digit 8 in the number 284.

so, we get,

the value represented by the digit 8 in the number 8,342  is 8000

and, the value represented by the digit 8 in the number 284 is 80

so, difference between them is:

8000 - 80

=7980

Hence, The solution is, 7980 times greater is the value represented by the digit 8 in the number 8,342 than the value represented by the digit 8 in the number 284.

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The correct option is A which is federal tax.

The type of tax that funds military defence in the United States is the federal income tax. This is a tax levied by the federal government on individuals, businesses, and other entities based on their income. A portion of this tax revenue is allocated towards funding the military, including salaries for personnel, equipment, and operations.

It's important to note that not all of the federal income tax revenue is earmarked for military defence. The federal government uses this revenue to fund a variety of programs and services, including healthcare, education, infrastructure, and more. The allocation of funds towards military defence is determined by Congress and can vary from year to year based on national security needs.

Other taxes, such as state income tax, local income tax, and FICA tax (which funds Social Security and Medicare), do not directly fund military defence. However, all taxpayers contribute to the national defence in some way, as the federal government relies on a variety of revenue sources to fund its operations and programs, including military defence.

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The expression that uses the commutative property to make it easier to evaluate is (-1/3)  × (-9) × 2/5.

The commutative property is derived from the word "commute" which implies moving around or swapping numbers. The commutative property involves moving the numbers around while the result still remains the same.

Mathematically, if switching the arrangement of the operands does not alter the result of the arithmetic operation then that certain arithmetic operation is commutative.

From the given information, the commutative property that can be used for (-1/3) × 2/5 × (-9) to make it easier to solve is (-1/3)  × (-9) × 2/5.

This is because the commutative property follows the analogy:

In addition, it will be easier to solve (-1/3) × (-9) first, then multiply it with 2/5.

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The value of x is 17.

Given that, two parallel lines cut by a transversal, forming one interior angle has a measure of 75 degrees; the alternate interior angle has a measure of 4x + 7 degrees.

Since, we know that, the alternate interior angles between parallel lines are equal so,

4x+7 = 75

4x = 68

x = 17

Hence the value of x is 17.

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The upper bound of the volume of water left in the fish tank is 20 liters.

In the given statement is :

A fish tank contains 60 liters of water, rounded to 1 significant figure. 40 liters of water, rounded to 1 significant figure, are removed from the tank.

Work out the upper bound of the volume of water left in the fish tank.

Now, According to the question:

Initial water in tank = 60 liters

Amount of water removed = 40 liters

Hence, To calculate the upper bound of the volume of water left in the fish tank;

= 60 - 40

= 20 liters

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As the class sizes range from 22 to 34 students, the answer must be 30,

Let the number of girls in the class "3x" and the number of boys "7x".

Then the total number of students in the class is:

Total students = 3x + 7x = 10x

We don't know the value of "x" yet, but we do know that the total number of students is between 22 and 34.

So we can set up an inequality:

22 ≤ 10x ≤ 34

Divide both sides of the inequality by 10:

2.2 ≤ x ≤ 3.4

Therefore, x can be either 3 or 4.

If x = 3, then the total number of students is:

Total students = 3x + 7x = 30

If x = 4, then the total number of students is:

Total students = 3x + 7x = 40

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The total number of students in Ms. Morales's class is either 20 or 30, depending on the value of x.

Let the ratio of boys to girls in Ms. Morales's class be 3x:7x, where 3x represents the number of boys and 7x represents the number of girls.

The total number of students in the class is equal to the sum of the number of boys and the number of girls, which is 3x + 7x = 10x.

We don't know the value of x, but we do know that the class size is between 22 and 34 students.

Therefore, we can set up an inequality based on the total number of students:

22 ≤ 10x ≤ 34

Dividing all parts of the inequality by 10, we get:

2.2 ≤ x ≤ 3.4

Since x represents a whole number of students, the possible values for x are 3 (if there are 30 students in the class) or 2 (if there are 20 students in the class).

If x = 3, then the total number of students is:

10x = 10(3) = 30

If x = 2, then the total number of students is:

10x = 10(2) = 20

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The equation represents circle A is (x + 1)² + (y + 1)² = 25. (option d)

To represent a circle on a coordinate plane, we use an equation called the equation of the circle. This equation is derived from the distance formula, which you might have learned in your geometry class. The equation of a circle with center (a, b) and radius r is given by:

(x - a)² + (y - b)² = r²

In this question, the center of the circle is given as A (1, 1). So, the equation of the circle will be of the form:

(x - 1)² + (y - 1)² = r²

To find the value of r, we can use the fact that point B (5, 4) lies on the edge of the circle. The distance between the center of the circle (1, 1) and point B (5, 4) is equal to the radius of the circle. Using the distance formula, we can find the distance between these two points:

r = √((5 - 1)² + (4 - 1)²) = √(16 + 9) = √(25) = 5

So, the equation of the circle can be written as:

(x - 1)² + (y - 1)² = 5²

Simplifying this equation, we get:

(x - 1)² + (y - 1)² = 25

Therefore, the correct answer is option d) (x + 1)² + (y + 1)² = 25.

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Answer:

C

Step-by-step explanation:

Look at the picture

Answer: 11

Step-by-step explanation:

-3 x 11 = -33

The maximum height of the ball can reach is 49 feet high.

We know that the height is modeled by the quadratic equation:

h(t) = -16t² + 56t

Remember that for the general quadratic equation is written as:

y = ax² + bx +c

The vertex is at the value x of:

x = -b/2a

The maximum height is at the vertex, which in this case is at the value:

t = -56/(2*-16)

t = 1.75

Evaluating  the height equation in that time, we get:

h = -16*(1.75)² + 56*1.75

h = 49

The maximum height that the ball can reach is 49ft

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Answer:

[tex]m = \frac{ - 9 - 7}{3 - ( - 3)} = \frac{ - 16}{6} = - \frac{8}{3} [/tex]

[tex]7 = - \frac{8}{3} ( - 3) + b[/tex]

[tex]7 = 8 + b[/tex]

[tex]b = - 1[/tex]

[tex]y = - \frac{8}{3} x - 1[/tex]

The y-intercept is -1.

Answer:

D) 4

Step-by-step explanation:

Since g(x) is the inverse of f(x), g(f(x))=x. Therefore, we need to find the value of x such that f(x) = 1. Looking at the table, we can see that f(4) = 1, so g(1) = 4.

Therefore, the correct answer is (D) 4.

The measures of the angles are 33°, 105° and 42°

We can call the top angle P, the bottom left angle Q, and the bottom right angle R. We are also given that angle P is (x - 9) degrees, angle Q is (x + 63)  degrees, and angle R is x degrees.

Now, we can use the fact that the sum of the angles in a triangle is 180 degrees to set up an equation:

Angle P + Angle Q + Angle R = 180

To find Angle, we can use the fact that the sum of the angles in a straight line is 180 degrees. We can see that Angle and Angle A are on a straight line, so we have:

(x – 9) + ( x + 63) +  x = 180

=> 3x + 54 = 180

=> 3x = 126

=> x = 42

We can now use this value to find the measures of the angles.

Angle P is (x -9) degrees, so Angle P = 42 - 9 = 33 degrees.

Angle Q is (x + 63) degrees, so Angle Q = 42 + 63 = 105 degrees.

Angle R is x degrees, so Angle R = 42 degrees.

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The graph of g(x) is on the image at the end, and the correct option for the transformation is B.

We define a horizontal dilation of scale factor k as:

g(x) = f(k*x)

if k > 1, we have a stretch.

if  0 < k < 1, we have a shink of scale factor 1/k

Here we have:

g(x) = f (5x) = 5x - 4

We can notice that k = 5, then we have a stretch, thus, the correct option is B.

The graph of function g(x) can be seen in the image at the end.,

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Answer:

The answer is (d) 10 lbs.

Step-by-step explanation:

Let's start by using the weighted average formula:

weighted average price = (price of first item x weight of first item + price of second item x weight of second item) / total weight

Let x be the number of pounds of walnuts needed.

The total weight of the mixture is x + 8 pounds.

The price of the walnuts is $0.80 per pound, and the price of the cashews is $1.25 per pound.

We want the mixture to cost $1.00 per pound.

Using the formula, we get:

1.00 = (0.80x + 1.25(8)) / (x + 8)

Simplifying, we get:

1.00(x + 8) = 0.80x + 10

1.00x + 8.00 = 0.80x + 10.00

0.20x = 2.00

x = 10

Therefore, Jordan needs to mix 10 pounds of walnuts with 8 pounds of cashews to make a mixture that costs $1.00 per pound.

Answer:480 minutes

Step-by-step explanation:

119-47=72

72/3=24

24*20=480

The volumes of smaller container and larger container are 10.6 in³ and 166.22 in³ respectively.

Given that are two containers in a conical shape and cylindrical shape,

Volume of conical shape = 1/3 × π × radius² × height

= 1/3 × 3.14 × 1.5² × 4.5

= 10.6 in³

Volume of cylindrical shape = π × radius² × height

= 3.14 × 2.75² × 7

= 166.22 in²

When we pour water from smaller container to larger container = 10.6 / 166.22 × 100 = 6.4 % of larger container will be filled.

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Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.

For test the claim that half of all teens have made new friends online, we can use a hypothesis test.

Null hypothesis:

The proportion of teens who have made new friends online is equal to 0.5.

Alternative hypothesis:

The proportion of teens who have made new friends online is not equal to 0.5.

We will use a one-sample proportion test with a significance level of 0.01.

For calculate the test statistic, we can use the formula:

z = (p - P₀) / sqrt(P₀ * (1 - P₀) / n)

where p is the sample proportion, P₀ is the hypothesized proportion (0.5), and n is the sample size.

Using the given information, we have:

p = 0.57

P₀ = 0.5

n = 1060

Plugging these values into the formula, we get:

z = (0.57 - 0.5) / sqrt(0.5 x 0.5 / 1060)

z = 4.39

Hence, Using a standard normal distribution table or calculator, we can find the p-value associated with z = 4.39 to be less than 0.0001.

Since the p-value is less than the significance level of 0.01, we reject the null hypothesis and conclude that there is sufficient evidence to suggest that more than half of all teens have made new friends online.

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The measure of arc and angle in the given circle are as follow,

Measure of arc CA = 144°

Measure of arc AD  = 98°

Measure of ∠C = 90°

In the circle ,

Center of the circle = Q

m∠ABC = 72°

Measure of arc CD = 46°

Measure of arc CA

Measure of ∠ABC = 72°

In a circle angle at the center is double of angle at the circumference of the circle in the same arc.

Measure of ∠CQA = 2 ×∠ABC

                               =  2× 72°

                               = 144°

measure of arc CA = measure of ∠CQA

                                = 144°

Measure of arc AD ,

m ∠AQD + m ∠CQD = m ∠CQA

⇒m ∠AQD  = 144° - 46°

⇒m ∠AQD  =  98°

⇒ Measure of arc AD  = 98°

Measure of angle C = ( 1/2) times of measure of BQD

                                 = ( 1/2) × 180°

                                 = 90°

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