f(x) = 2(x – 4)² + 3 compare to the graph of g(x) = x^2

The null hypothesis is: null is 1.32
The alternative hypothesis is: null is greater than 1.32
The test statistic is: a. 4.065
The critical value is: a. qt(p=0.975, df=49) = 2.009

In this scenario, the null hypothesis (H0) is that the average number of people an infected child infects is equal to the average number of people an infected adult infects, which is 1.32. The alternative hypothesis (H1) is that an infected child infects more people than an infected adult, so the average is greater than 1.32.

To calculate the test statistic, we use the t-test formula: (sample mean - population mean) / (sample standard deviation / sqrt(sample size)). In this case, it would be (1.55 - 1.32) / (0.8 / sqrt(50)), resulting in a test statistic of 4.065.

To find the critical value, we use the t-distribution table with a significance level of 0.05 and degrees of freedom equal to the sample size minus 1 (50 - 1 = 49). The critical value is found by looking up the value of qt(p=0.975, df=49), which is 2.009.

Since the test statistic (4.065) is greater than the critical value (2.009), we reject the null hypothesis in favor of the alternative hypothesis. This means that there is significant evidence to suggest that, on average, an infected child in school infects more people than an infected working adult does.

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Answer:

15.7 ft

Step-by-step explanation:

circumference = pi * diameter

c = 3.14 * 5 ft

c = 15.7 ft

Answer: 15.7 ft

Answer:

5 / 37

Step-by-step explanation:

Solution:-

- An archer stall game was played to receive a prize to pierce an arrow through a polka dot balloon.

- There are three types of balloons clustered together. The distribution of each balloon is given as such:

                 Type                        Number

                 Solid                             15

                 Striped                          17

                 Polka Dot                      5

- The probability of an arrow piercing through a polka dot balloon can be determined from the basic definition of probability of an event.

- Define event ( A ) : The number of Polka dots balloon popped

- Then, the probability of event ( A ) would be defined as:

    p ( A ) =  [ Number of polka dots balloons available ] / [ Total balloons ]

- We have 5 polka dots balloons among the cluster. The cluster comprises of balloons of all types with their specific distribution as expressed above. Hence:

                  p ( A ) = [ 5 ] / [ 15 + 17 + 5 ]

                  p ( A ) = [ 5 ] / [ 37 ]

- The probabbility that an arrow pops a polka dot balloon is 5 / 37.

Note: If we are given more than 1 arrow or multiple tries, then we must remember that the probability of event ( A ) changes after every popped balloon ( irrespective of type ). Hence, the probability of popping polka dot balloon is dependent event over number of trials. Except if you miss an arrow and none of the balloons is popped, only then the p ( A ) remains same for the next trial.

Answer:

The round birthday cake has 4241 calories.  Do not touch.  Mine.

Step-by-step explanation:

See attached image.  A calorie density is calculated for the sheet cake (calories/in^3) and used to find the calories in the birthday cake.

Answer:

c) 2.2 feet

Step-by-step explanation:

1) Iris' puppy is 2 1/5 feet long. Which

decimal represents Iris' puppy's length?

c) 2.2 feet

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

The value is evaluated to 5 1/4

A fraction can be described as the part of a whole value, variable or element.

The different types of fractions are;

From the information given, we have that;

1 + (-2/3) - (-m)

If the value of m = 9/2, let's substitute the value, we have;

1 - 2/8 - ( 9/2)

expand the bracket

1 - 2/8 + 9/2

Find the LCM

8 - 2 +  36 /8

42/8

5 1/4

Hence, the value is 5 1/4

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The given curve is y = x³ − 2x and it has to be rotated about the x-axis to find the area of the surface. The formula to find the surface area of a curve obtained by rotating about the x-axis is given by:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx
$$Differentiating the curve with respect to x, we get:$$
y = x^3 - 2x
$$$$
\frac{dy}{dx} = 3x^2 - 2$$Now, squaring it, we get:$$
\left(\frac{dy}{dx}\right)^2 = 9x^4 - 12x^2 + 4$$$$
1 + \left(\frac{dy}{dx}\right)^2 = 1 + 9x^4 - 12x^2 + 4$$$$
= 9x^4 - 12x^2 + 5$$Putting the values in the formula, we get:$$
A = 2\pi \int_a^b y \sqrt{1 + \left(\frac{dy}{dx}\right)^2} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 12x^2 + 5} dx$$Simplifying it further, we get:$$
A = 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{(3x^2 - 1)^2 + 4} dx$$$$
= 2\pi \int_{-1}^2 (x^3 - 2x) \sqrt{9x^4 - 6x^2 + 5} dx$$Now, substituting $9x^4 - 6x^2 + 5 = t^2$, we get:$$(18x^3 - 12x)dx = tdt$$$$
(3x^2 - 2)dx = \frac{tdt}{3}$$When $x = -1$, $t = \sqrt{20}$ and when $x = 2$, $t = 5\sqrt{5}$Substituting the values in the formula, we get:$$
A = 2\pi \int_{\sqrt{20}}^{5\sqrt{5}} \frac{t^2}{27} dt$$$$
= \frac{28\pi}{27} \left[ t^3 \right]_{\sqrt{20}}^{5\sqrt{5}}$$$$
= \frac{28\pi}{27} \left[ 125\sqrt{5} - 20\sqrt{20} - 5\sqrt{5} + 2\sqrt{20} \right]$$$$
= \frac{28\pi}{27} \left[ 120\sqrt{5} - 18\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 9\sqrt{20} \right]$$$$
= \frac{56\pi}{27} \left[ 30\sqrt{5} - 18\sqrt{5} \right]$$$$
= \frac{56\pi}{27} \cdot 12\sqrt{5}$$$$
= \boxed{224\sqrt{5}\pi/3}$$Therefore, the area of the surface obtained by rotating the curve $y = x^3 - 2x$ about the x-axis is $\boxed{224\sqrt{5}\pi/3}$.

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The total area of the regions between the curves is 1.134π square units

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

x = ∛y

We have the interval to be

0 ≤ y ≤ 1

The area of the regions between the curves is then calculated using

\(A =2\pi \int\limits^a_b {f(x) * \sqrt{1 + (dy/dx)^2} } \, dx\)

From x = ∛y, we have

y = x³

Differentiate

dy/dx = 3x²

So, the area becomes

\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + (3x^2)^2} } \, dx\)

Expand

\(A =2\pi \int\limits^1_0 {x^3 * \sqrt{1 + 9x^4 } \, dx\)

Integrate

\(A =2\pi \frac{(9x^4 + 1)^{\frac{3}{2}}}{54}|\limits^1_0\)

Expand

\(A = 2\pi [\frac{(9(1)^4 + 1)^{\frac{3}{2}}}{54} - \frac{(9(0)^4 + 1)^{\frac{3}{2}}}{54}]\)

This gives

A = 2π * 0.5671

Evaluate the products

A = 1.1342π

Approximate

A = 1.134π

Hence, the total area of the regions between the curves is 1.134π square units

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The statement is False. The expression evaluates to 2.0, not 2.5.

The expression (double) (10 / 4) involves several steps of evaluation. Let's break it down to understand the process.

Integer Division: The division operation 10 / 4 is performed first. In integer division, the result is the quotient of the division without any decimal places. In this case, 10 / 4 equals 2, as the fractional part is truncated.

Type Casting: The expression (double) is a type cast that converts the result of the division to a double data type. However, the type casting occurs after the integer division has already taken place. So, the result of the type casting will not affect the value obtained in the integer division.

As a result, the expression (double) (10 / 4) evaluates to 2.0, not 2.5. The value 2.0 is a double representation of the integer 2. The type casting only affects the data type of the value, not its actual numerical value.

Therefore, the statement "The following expression will evaluate to 2.5: (double) (10 / 4)" is false. The expression evaluates to 2.0.

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True. The expression (double) (10 / 4) will evaluate to 2.5.

To evaluate the given expression, we need to follow the order of operations. First, we have the casting operation, which involves converting the result of the division to a double data type. Then, we have the division operation, which involves dividing 10 by 4.

Let's break down the steps:

Therefore, the expression (double) (10 / 4) will evaluate to 2.5.

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The measure of the minor arc is a. 62°.The correct option is a. 62°.

To determine the measure of minor arc AC, we need to consider the measure of angle ABC.

Given that angle ABC is 62°, we can conclude that the measure of minor arc AC is also 62°.

This is because the measure of an arc is equal to the measure of its corresponding central angle.

In this case, minor arc AC corresponds to angle ABC, so they have the same measure.

Therefore, option a. 62° is the appropriate response.

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Answer:

-25.00% decrease, quite a deal

Answer:

Step-by-step explanation:

$28 = 100%

$7 = 25%

$21 = 75%

so, therefore

% change = 100% - 75%

= 25%

Step-by-step explanation:

you know how functions work ?

the variable (or variables) in the findings expression is a placeholder for actual values.

when we have an actual value, we put that into the place of the variable and then simply calculate.

x = 5

therefore, the functional calculation is

y = 3×5 - 7 = 15 - 7 = 8

keep in mind the priorities of mathematical operations :

1. brackets

2. exponents

3. multiplications and divisions

4. additions and subtractions

therefore, we need to calculate "3×5" before we deal with the "- 7" part.

Answer:

Step-by-step explanation:

y=8

Answer:

uh, this is very confusing....is there anyway that you could word it differently?

Answer:

(x-3) times (x+1)

The exact value of x, a right triangle with two sides of 25, is given as follows:

\(x = 25\sqrt{2}\)

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The angle of 45º has the same measure for the sine and the cosine, hence the two sides of the triangle have a length of 25.

Then the hypotenuse x is obtained as follows:

x² = 25² + 25²

\(x = \sqrt{2 \times 25^2}\)

\(x = 25\sqrt{2}\)

The triangle in this problem has a side length of 25 and an angle of 45º, while x is the hypotenuse.

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Answer:

-5x+18/x+2

Step-by-step explanation:

I'm pretty sure it's the answer

Answer:

A. an = -51+12(n-1)

Step-by-step explanation:

edge quiz

The solution is, the explicit rule for the arithmetic sequence is

a n = -51 + ( n - 1 ) · 12 .

An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The nth term of AP : a_n = a + (n – 1) × d

here, we have,

given that,

a 2 = -39

a 2 = a 1 + 12

- 39 = a 1 + 12

a 1 = - 39 - 12

a 1 = - 51 ( first term )

The common difference is : d = 12

The explicit rule for the arithmetic sequence:

a n = a1 + ( n - 1 ) d

a n = -51 + ( n - 1 ) · 12

Hence, The solution is, the explicit rule for the arithmetic sequence is

a n = -51 + ( n - 1 ) · 12 .

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Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

Answer:

12 packages with 2 toothbrushes and 3 soaps each

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

y = 1/3 x

1 = (1/3) (3)

1 = 3/3

1 = 1

The interpretation of the slope is On average, for every additional year of age, bone density loss increases by approximately 0.41. (option a)

To calculate the least squares regression line, the data points are first plotted on a scatter plot. The line of best fit is then drawn through the data points such that the sum of the squared distances between the line and the data points is minimized. The slope of this line can be calculated using the following formula:

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

where n is the number of data points, Σ represents the sum of the values, x represents age, y represents bone density loss, and xy represents the product of x and y.

Using this formula, the slope for this data set can be calculated to be approximately 0.41. This means that, on average, for every additional year of age, bone density loss increases by approximately 0.41. In other words, the slope indicates a positive relationship between age and bone density loss, with bone density loss increasing as age increases.

Therefore, the correct answer is (a) On average, for every additional year of age, bone density loss increases by approximately 0.41.

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Complete Question:

Osteoporosis is a condition in which bone density decreases, often resulting in broken bones. Bone density usually peaks at age 30 and decreases thereafter. To understand more about the condition, a random sample of women aged 50 and over were recruited. Each woman's bone loss was recorded and the date is shown in this file. Create a scatter plot of these two variables, with age as the x variable and bone density loss as the y variable. Calculate the least squares regression line. What is your interpretation of the slope?

a. On average, for every additional year of age, bone density loss increases by approx 0.41.

b. On average, for every additional one point of bone density loss, age increases by approx 0.41.

c. On average, for every additional year of age, bone density loss increases by approx 6.9.

d. none of the above

The net income for Griffin's Goat Farm, Inc., was \(\$184,340\).

The operating cash flow (OCF) for Kerber's Tennis Shop, we can use the following formula:

\(OCF = EBIT + Depreciation - Taxes + \triangle Working Capital\)

where EBIT is earnings before interest and taxes.

Calculate EBIT by subtracting interest expense from operating income:

EBIT = Operating Income - Interest Expense

We do not have the information for operating income, but we can use the fact that interest expense was. \(\$165,000\) to calculate EBIT.

EBIT = Interest Expense / (1 - Tax Rate)

= \(\$165,000 / (1 - 0)\)

= \(\$165,000\)

Calculate the change in working capital (Δ Working Capital). We are told that the company reduced its net working capital investment by \(\$69,000\), which means that working capital increased by  \(\$69,000\).

Therefore:

\(\triangle Working Capital = \$69,000\)

Now, we can calculate OCF:

OCF = EBIT + Depreciation - Taxes + Δ Working Capital

=\(\$165,000 + 0 - 0 +\ $69,000\)

=\(\$234,000\)

Therefore, the firm’s 2018 operating cash flow (OCF) was \(\$234,000\) .

To calculate the net income for Griffin's Goat Farm, we can use the following formula:

Net Income = EBIT - Interest Expense - Taxes

where EBIT is earnings before interest and taxes. We can calculate EBIT as:

EBIT = Sales - Costs - Depreciation

= \(\$686,000 - \$332,000 - \$65,000\)

=\(\$289,000\)

Next, we need to calculate taxes. We are given a tax rate of 24%, so:

Taxes = Tax Rate x (EBIT - Depreciation)

= \(0.24 \times (\$289,000 - \$65,000)= \$56,160\)

Now, we can calculate net income:

Net Income = EBIT - Interest Expense - Taxes

= \(\$289,000 - \$48,500 - \$56,160= \$184,340\)

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To determine the number of female students in the sample who had a positive opinion of campus housing, we need to examine the data provided in the two-way table. The table likely contains information on both gender and opinion of campus housing, allowing us to identify the count of female students with a positive opinion.

1. Look for the row or column in the two-way table that corresponds to the variable "gender" or "female students."

2. Within that row or column, locate the cell or intersection that represents the category "positive opinion of campus housing."

3. Identify the number in that cell, which represents the count of female students who had a positive opinion of campus housing.

4. Based on the given information, retrieve the specific count of female students with a positive opinion from the table, and that will be the answer to the question.

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Answer:

For the first one, I believe you would need to use a rotation matrix; to rotate 90º counterclockwise, the matrices would look like ; you would then multiply those out. A reflection across the x-axis would be changing the sign of f(x) (from negative to positive or positive to negative), a reflection across the y-axis would be changing the sign of x, translation a units to the right would be subtracting a from x, translation b units up would be adding b to x. Rotation of 180º about the origin would be the same format as the first matrix, except it would be cos180 and cos0 on the top and sin180 sin0 on the bottom. Reflection across the y-axis would be changing the sign of x again.

OR

1. We know that, 'Translation shifts the figure in any direction'.

As, the function f(x) is translated 'a' units to the right, the new form of function is f(x-a).

Again, the function is translated 'b' units up, the final form of the function is f(x-a)+b.

2 and 3. We know that, ' Reflection flips the image over a line'.

As the function g(x) is reflected over y-axis, the new form of the function is g(-x).

As the function h(x) is reflected over x-axis, the new form of the function is -h(x).

4 , 5 and 6. We know that, 'Rotation turns the image around a point to a certain degree'.

Let us assume the function to be a point (x,y).

As the function is rotated by 90° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{90}R

90

(x,y) = ( -y,x ).

As the function is rotated by 180° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{180}R

180

(x,y) = ( -x,-y ).

As the function is rotated by 2700° counterclockwise about the origin, the new function becomes ( y,-x ) i.e. R_{270}R

270

(x,

Step-by-step explanation:hopes this helps lol?

Answer:

5n - 7

Step-by-step explanation:

The product of five and a number is 5n

Seven less than the product of five and a number means 5n - 7

There's a pretty simple formula to follow: count of multiples \(*\) average of the multiple.

To find the average, we take the smallest multiple of 4 which is in the range of 1 and 150 which is 4 of course. And the largest would be 148 since that's the only number in the range. So now average them: \(\frac{4 + 148}{2} = \frac{152}{2} = 76\)

Now we find the count of the multiples which is in the range of 1 to 150. To do that, we use this formula:

\(\frac{\text{largest multiple} - \text{smallest multiple}}{n} \\\)

Here, \(n\) is 4 so this would be:

\(\frac{148-4}{4} = \frac{144}{4} = 36\)

This would give you the exclusive count of all the numbers, but we want the inclusive count so, we simple add 1 so the count would be \(37\)

Now following the 1st formula we get: \(37 * 76 = 2812\)

So the answer would be 2812! :D

And here's the check too:

The acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

To find the acceleration of the particle at \(t = 2\) seconds, we need to differentiate the position function twice with respect to time. First, let's differentiate the position function \(s(t)\) once to find the velocity function \(v(t)\). Using the chain rule, we have:

\(\(v(t) = \frac{d}{dt}[(4t+1)^{3/2}]\)\)

To simplify the differentiation, we can rewrite the function as\(\(v(t) = (4t+1)^{3/2}\)\) . Applying the power rule, the derivative becomes:

\(\(v(t) = \frac{3}{2}(4t+1)^{1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(v(t) = 6(4t+1)^{1/2}\)\)

Next, we differentiate the velocity function \(v(t)\) to find the acceleration function \(a(t)\):

\(\(a(t) = \frac{d}{dt}[6(4t+1)^{1/2}]\)\)

Using the power rule again, we get:

\(\(a(t) = 6 \cdot \frac{1}{2}(4t+1)^{-1/2} \cdot 4\)\)

Simplifying further, we have:

\(\(a(t) = 12(4t+1)^{-1/2}\)\)

Now we can find the acceleration at \(t = 2\) seconds by substituting \(t = 2\) into the acceleration function:

\(\(a(2) = 12(4 \cdot 2 + 1)^{-1/2}\)\)

\(\(a(2) = 12(9)^{-1/2}\)\)

Simplifying the expression, we have:

\(\(a(2) = \frac{12}{3} = 4\) cm/s²\)

Therefore, the acceleration of the particle at \(t = 2\) seconds is \(4\) cm/s².

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Answer:

I need to se picture of the shape

70.8 mins - 90 mins = 19.2  minutes