Question 3 of 5
Select the correct answer.
Find the Inverse of the given function.
f-¹ (x) = -7√x + 4
Of-¹(x) = ¹ +4
O f-¹(x) = 42²
O f¹(x) = 7x³ + 4
f(x) = √72-4

The radius of the hemisphere is approximately 28.0 inches to the nearest tenth.

To find the radius of a hemisphere with a volume of 45,729 in³, we'll use the formula for the volume of a sphere, since a hemisphere is half of a sphere. The volume of a sphere (V) is given by:

V = (4/3)πr³

Since we're dealing with a hemisphere, we'll adjust the formula accordingly:

V = (1/2)(4/3)πr³

Given the volume of the hemisphere is 45,729 in³, we can set up the equation:

45,729 = (1/2)(4/3)πr³

Now, we'll solve for r (the radius) to the nearest tenth:

1. Multiply both sides by 2:
91,458 = (4/3)πr³

2. Multiply both sides by 3/4:
68,594 = πr³

3. Divide both sides by π:
21,841 ≈ r³

4. Take the cube root of both sides:
r ≈ 28.0

So, the radius of the hemisphere is approximately 28.0 inches to the nearest tenth.

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f(4) = 3 and f '(4) = 1/4, Given that the tangent line to y = f(x) at (4, 3) passes through the point (0, 2), we can find f(4) and f '(4) using the slope-point formula.

Since the tangent line passes through (4, 3) and (0, 2), we can calculate the slope (m) as:
m = (y2 - y1) / (x2 - x1)
m = (3 - 2) / (4 - 0)
m = 1 / 4

Now, we know that the slope of the tangent line at (4, 3) is equal to the derivative f '(4). Therefore: f '(4) = 1/4
Since the tangent line touches the curve at (4, 3), we have:
f(4) = 3.

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Answer:

Hi there!

The correct answer should be H, ST/EF=WR/CD

Step-by-step explanation:

the formula for the volume of the open-top box in terms of x is: V(x) = (14 - 2x)(11 - 2x)x

To find the formula for the volume of the open-top box formed from a 14-inch by 11-inch piece of cardboard, we need to consider the dimensions of the box after cutting squares from each corner and folding up the sides.

Let "x" represent the side length of the squares cut from each corner. After cutting and folding, the dimensions of the box will be:

- Length: 14 - 2x inches (removing x inches from both ends)
- Width: 11 - 2x inches (removing x inches from both ends)
- Height: x inches (the height is equal to the side length of the squares)

The formula for the volume of a box is given by:

Volume = Length × Width × Height

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The expression is simplified to 10c - 4d

Algebraic expressions are simply described as mathematical expressions that consists of coefficients, terms, variables, constants and variables.

Algebraic expressions are also made up of arithmetic operations, such as;

From the information given, we have the expression as;

3c-9d+7c+5d

Now, collect the like terms, we get;

3c + 7c - 9d + 5d

Add or subtract the like terms

10c - 4d

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The gcd of 630 and 147 can be expressed as 21 = (-3) x 630 + 13 x 147.

Here are the solutions for each pair of numbers:
(a) To find the gcd of 56 and 42, we can use the Euclidean algorithm:
56 = 42 x 1 + 14
42 = 14 x 3 + 0
So the gcd of 56 and 42 is 14. To express 14 as a linear combination of 56 and 42, we can use the extended Euclidean algorithm:
14 = 56 - 42 x 1
= (-1) x 56 + 1 x 42
So the gcd of 56 and 42 can be expressed as 14 = (-1) x 56 + 1 x 42.
(b) To find the gcd of 81 and 60, we can again use the Euclidean algorithm:
81 = 60 x 1 + 21
60 = 21 x 2 + 18
21 = 18 x 1 + 3
18 = 3 x 6 + 0
So the gcd of 81 and 60 is 3. To express 3 as a linear combination of 81 and 60, we can use the extended Euclidean algorithm:
3 = 21 - 18 x 1
= 21 - (60 - 21 x 2) x 1
= (-1) x 60 + 3 x 21
= (-1) x 60 + 3 x (81 - 60 x 1)
So the gcd of 81 and 60 can be expressed as 3 = (-1) x 60 + 3 x 81.
(c) To find the gcd of 259 and 77, we can use the Euclidean algorithm:
259 = 77 x 3 + 28
77 = 28 x 2 + 21
28 = 21 x 1 + 7
21 = 7 x 3 + 0
So the gcd of 259 and 77 is 7. To express 7 as a linear combination of 259 and 77, we can use the extended Euclidean algorithm:
7 = 28 - 21 x 1
= 28 - (77 - 28 x 2) x 1
= 3 x 28 - 77 x 1
= 3 x (259 - 77 x 3) - 77 x 1
So the gcd of 259 and 77 can be expressed as 7 = 3 x 259 - 10 x 77.
(d) To find the gcd of 72 and 42, we can use the Euclidean algorithm:
72 = 42 x 1 + 30
42 = 30 x 1 + 12
30 = 12 x 2 + 6
12 = 6 x 2 + 0
So the gcd of 72 and 42 is 6. To express 6 as a linear combination of 72 and 42, we can use the extended Euclidean algorithm:
6 = 42 - 30 x 1
= 42 - (72 - 42 x 1) x 1
= (-1) x 72 + 2 x 42
So the gcd of 72 and 42 can be expressed as 6 = (-1) x 72 + 2 x 42.
(e) To find the gcd of 80 and 61, we can use the Euclidean algorithm:
80 = 61 x 1 + 19
61 = 19 x 3 + 4
19 = 4 x 4 + 3
4 = 3 x 1 + 1
3 = 1 x 3 + 0
So the gcd of 80 and 61 is 1. To express 1 as a linear combination of 80 and 61, we can use the extended Euclidean algorithm:
1 = 19 - 4 x 3
= 19 - (61 - 19 x 3) x 3
= 10 x 19 - 3 x 61
= 10 x (80 - 61 x 1) - 3 x 61
So the gcd of 80 and 61 can be expressed as 1 = 10 x 80 - 13 x 61.
(f) To find the gcd of 630 and 147, we can use the Euclidean algorithm:
630 = 147 x 4 + 42
147 = 42 x 3 + 21
42 = 21 x 2 + 0
So the gcd of 630 and 147 is 21. To express 21 as a linear combination of 630 and 147, we can use the extended Euclidean algorithm:
21 = 147 - 42 x 3
= 147 - (630 - 147 x 4) x 3
= (-3) x 630 + 13 x 147

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The vertex form of the function is y = (x + 2)² - 9

The vertex is (-2 , -9)

We have,

The vertex form of the quadratic equation y = ax² + bx + c is

y = a(x - h)² + k, where

(h , k) are the coordinates of the vertex point

a, b, c are constant where a is the leading coefficient of the function (coefficient of x²) , b is the coefficient of x and c is the y-intercept

h = -b/2a

k is the value of y when x = h

∵ y = x² +4x-5

∵ y = ax² + bx + c

∴ a = 1 , b = 4 , c  = -5

∵ h = -b/2a

∴ h = -4/2

∴ h = -2

To find k substitute y by k and x by -2 in the equation above

∵ k is the value of y when x = h

∵ h = -2

∴ k = (-2)² + 4(-2) - 5 = -9

∵ The vertex form of the quadratic equation is y = a(x - h)² + k

∵ a = 1 , h = -2 , k = -9

∴ y = (1)(x - (-2))² + (-9)

∴ y = (x + 2)² - 9

∵ (h , k) are the coordinates of the vertex point

∵ h = -2 and k = -9

∴ The vertex is (-2 , -9)

The vertex form of the function is  y = (x + 2)² - 9

The vertex is (-2 , -9)

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The sample space for rolling a fair seven-sided die is.

Probability theory defines sample space as the complete set consisting of all possible outcomes which can be produced by some random experiment or process.

It is commonly represented by the letter S, and it forms the base for different probability calculations.

In this case, the experiment is rolling of die assuming the die is labelled such that each face has the numbers as 1, 2, 3, 4, 5, 6, and 7 then the sample space would be

S = {1, 2, 3, 4, 5, 6, 7}

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When a cone is sliced in such a way that the plane passes through the cylinder in a slanted direction without going through the base or the vertex, the resulting cross section is an ellipse.

The plane intersects the curved surface of the cone in a non-perpendicular manner, which results in a curved shape that is neither a circle nor a triangle.

An ellipse is a geometric shape that resembles a flattened circle, with two focal points rather than a single center. It is a common cross section that is observed in a variety of natural and man-made structures, from planetary orbits to satellite dishes and reflectors.

In the case of a cone, the resulting ellipse will be wider or narrower depending on the angle of the slicing plane, with a more oblong shape resulting from a steeper angle. This cross section is important in engineering and architecture, as it can be used to create structures with specific geometric properties, such as efficient reflectors or precise satellite dishes.

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The slope intercept form of the equation for each line is y = -1/3 -x.

When any equation is represented in the y = mx +c form, it is called the slope intercept form of the equation.

Here, m is slope and c is constant.

To find the slope intercept form of the equation,

(4, -2) and (-5, 3)

The slope intercept form of the equation is y = -(3/4)x + 3.

Therefore, the slope of the line is;

m = Δy/Δx

m = 5/-9

When we simplify it, then we get the;

3 - y= -5/9(-5-x)

y = -25/9-3 -x

y = -3/9 -x

y = -1/3 -x

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The initial monthly payment on the mortgage loan is $971.35.

To find the initial monthly payment, we can use the formula for calculating the monthly payment on a mortgage loan:

PV = PMT/i[1 - {1/(1+i)ⁿ]

where:

PMT = monthly payment

PV = principal (loan amount)

i = monthly interest rate (annual rate divided by 12)

n = total number of payments (the number of years multiplied by 12)

For the initial fixed period of five years, the interest rate is 4.25%.

So the monthly interest rate is 4.25%/12 = 0.00354.

The total number of payments is 30 years x 12 months/year = 360.

Plugging in the values, we get:

M = 197500 [ 0.00354(1 + 0.00354)³⁶⁰ ] / [ (1 + 0.00354)³⁶⁰ – 1]

M ≈ $971.350054812

M = $971.35

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In this study, participants were randomly assigned to read an article printed in either 14-point or 16-point font size. The article was presented in one of three font styles: Arial, Times New Roman, or Cambria. After reading the article, participants answered several questions aimed at measuring their memory recall.

The study you are referring to involved participants who were randomly assigned to read an article printed in either 14-point or 16-point font in one of three different font styles: Arial, Times New Roman, or Cambria. After reading the article, participants were then asked to answer several questions that were designed to measure their memory recall. This study was likely conducted to explore the impact of font size and style on memory recall, as previous research has suggested that factors such as font type, size, and spacing can have a significant impact on reading comprehension and recall. By randomly assigning participants to different font conditions, the study aimed to control for potential confounding variables and isolate the specific effects of font size and style on memory recall.
In this study, participants were randomly assigned to read an article printed in either 14-point or 16-point font size. The article was presented in one of three font styles: Arial, Times New Roman, or Cambria. After reading the article, participants answered several questions aimed at measuring their memory recall.

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The best type of scale to assess how happy UNC students are on a 7-point scale (1 not very happy to 7 extremely happy) is an ordinal scale.

Ordinal scales are used to measure variables that have an inherent order or ranking, such as the level of happiness in this case. However, the differences between the categories are not necessarily equal or measurable, which rules out the use of an interval or ratio scale. A nominal scale, on the other hand, is used for variables that are categorical and cannot be ranked or ordered, which is not appropriate for this scenario.

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Answer: 365.76 or 365.8

Step-by-step explanation: 1yd = 0.9144m        d(m) = d(yd) × 0.9144

The inequality that is not equivalent to others is D -x<3

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

A -x>-3

B x <3

C x+1 <4

D -x<3

When the expressions are solved, we have

A x < 3

B x <3

C x <3

D x > 3

Hence, the odd option is D -x<3

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Applying the Pythagorean Theorem, the diagonal distance is calculated as: 65 cm.

In order to find the diagonal distance between A and C in the image given, recall the Pythagorean Theorem which states that the sum of the square of each leg's length of a right triangle is equal to the square of its hypotenuse.

In this case, the diagonal is the hypotenuse, therefore:

Diagonal distance = √(60² + 25²)

Diagonal distance = 65 cm

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The probability of Event 1 is 5/36 and the probability of Event 2 is 1/2.

The probability of each of the given events is determined by comparing the outcomes of the rolling of two dies:

There are 6 * 6 = 36 possible outcomes

Event 1: The sum is greater than 8.

There are 5 outcomes where the sum is greater than 8.

P(Event 1) = 5/36

Event 2: The sum is divisible by 2.

There are 18 possible outcomes where the sum is divisible by 2.

The probability of this event will be:

P(Event 2) = 18/36

P(Event 2) = 1/2

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A random number generated from this density using the given us value of 0.127 is approximately 1.068.

To generate a random number from this density using the given us value, we first need to calculate the cumulative distribution function (CDF):

F(x) = ∫(0 to x) f(t) dt
    = ∫(0 to x) (2/9)t dt
    = (1/9) x^2

Next, we set the CDF equal to the given us value and solve for x:

us = F(x) = (1/9) x^2
0.127 = (1/9) x^2
x^2 = 1.139
x = sqrt(1.139) ≈ 1.068

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The purpose is to demonstrate the ability to predict and measure the frequency response of a nontrivial signal in a system of circuits connected in series. The first step is to derive the governing equation (LCCDE) of the system and verify its stability.

1. To derive the governing equation (LCCDE) of the given circuits in the system, you need to first identify the circuit elements (resistors, capacitors, and inductors) and write the equations for each element according to Kirchhoff's voltage and current laws. Then, combine these equations to form the LCCDE. Stability can be verified by analyzing the characteristic equation and ensuring that all poles have negative real parts.

2. To find the overall frequency response H(jω), you can convert the LCCDE into the frequency domain using the Laplace or Fourier transform, and then simplify the expression. Once you have H(jω), you can plot it as a Bode plot by graphing the magnitude and phase as a function of frequency on a logarithmic scale.

3. To derive the output of the system y2(t), first obtain the CTFS of the given square wave input x(t). Then, use the CTFT to find the output of the system by multiplying the input spectrum with the overall frequency response H(jω) and performing the inverse Fourier transform. When T = 1/1000 s, you can plot the input and output over one cycle as a function of time by calculating the time-domain expressions for x(t) and y2(t) and plotting them within the given interval.

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The statement that is not true about qualitative data is: "We can obtain the mean and variance for qualitative data".

The statement "we can calculate relative frequency for qualitative data for each category in the data" is true. Relative frequency is the proportion of each category in the data, and we can calculate it for qualitative data by dividing the frequency of each category by the total number of observations.

The statement "qualitative data cannot be summarized using a frequency table" is false. A frequency table is a common method for summarizing qualitative data. It displays the frequency of each category in a table format, making it easier to compare and analyze the different categories.

The statement "we can obtain the mean and variance for qualitative data" is false. Mean and variance are measures of central tendency and variability that require numerical data. Qualitative data, being non-numerical, cannot be measured using these statistical measures.

The statement "bar charts and pie charts are usually used to describe qualitative data" is true. Bar charts and pie charts are graphical representations that are commonly used to visually display the distribution of qualitative data. These charts can show the relative frequency or proportion of each category in the data.

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The surface area of a rectangular prism of dimensions 4 cm, 5 cm and 6 cm is given as follows:

S = 148 cm².

The surface area of a rectangular prism of height h, width w and length l is given by:

S = 2(hw + lw + lh).

This means that the area of each rectangular face of the prism is calculated, and then the surface area is given by the sum of all these areas.

The dimensions for this problem are given as follows:

4 cm, 5 cm and 6 cm.

Hence the surface area of the prism is given as follows:

S = 2(4 x 5 + 4 x 6 + 5 x 6)

S = 148 cm².

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The significance level is set at 5%, and the probability of the result is 92.2%, which is greater than the significance level. The result is not statistically significant, and we cannot reject the null hypothesis.

The probability of the treatment group’s mean being lower than the control group’s mean by 15 points or more is calculated as follows:

Frequency of means -15 or less = 10 + 18 + 50

Frequency of means -15 or less = 78

Probability(-15 or less) = 78/ 1000

Probability(-15 or less) = 0.078

Probability(more than -15) = 1 - Probability(-15 or less)

Substituting the value:

Probability(more than -15) = 1 - 0.078

Probability(more than -15) = 0.922

Probability(more than -15) = 92.2%

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The complete sentence:

If you want to get from Boston to New York in exactly 5 hours, you must drive at a constant speed of 43 mph.

The distance from Boston to New York is approximately 215 miles.

To travel this distance in 5 hours, you need to divide the distance by the time:

Apply the division operation:

215 divided by 5 can be expressed as,

215 miles ÷ 5 hours = 43 miles per hour.

So, you need to drive at a constant speed of 43 miles per hour to get from Boston to New York in exactly 5 hours.

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To maximize her chance of winning, Carol should choose a number that is close to either 0 or 1.

If Carol chooses a number close to 0, then Bob's number will have to be very close to 0 in order for him to win, giving Alice a disadvantage. Similarly, if Carol chooses a number close to 1, then Alice's number will have to be very close to 1 in order for her to win, giving Bob a disadvantage. Therefore, Carol should choose a number very close to either 0 or 1.
To maximize Carol's chance of winning, she should choose a number that maximizes the probability of being between Alice's and Bob's numbers. Since Alice is choosing uniformly between 0 and 1, Carol should choose a number in the middle of the range of possible numbers for Bob.

Bob's range is between 1/2 and 2/3. The middle of this range is the average of these two values: (1/2 + 2/3)/2 = (3/6 + 4/6)/2 = 7/12. Therefore, Carol should choose the number 7/12 to maximize her chance of winning.

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The recursion that models the dynamics of drug concentration is: ct+1 = (1 - k) * ct + a.

This equation describes how the drug concentration in the bloodstream changes over time. At each time step, the concentration of the drug in the bloodstream is updated by adding the concentration of the drug that is administered (a) and subtracting the fraction of the drug that is metabolized (k * ct). This updated concentration is then used as the starting concentration for the next time step.

The value of k is typically a constant that is specific to the drug being administered and the metabolic rate of the patient. The value of a can vary depending on the dosage and frequency of drug administration. The recursion can be used to model the concentration of the drug over time, which is important for determining the effectiveness and potential side effects of the drug.

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The set of conditions results in a unique triangle is option 4.

The unique triangle :-

If you are given two angles and the length of a side between the angles, then you have a unique triangle.

From the options given,

The fourth option is having a 6-inch side between the angle 45° and 90°

Therefore, it is following the rule of ASA. therefore, giving a unique triangle.

Hence, the set of conditions results in a unique triangle is option 4.

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Answer:

The house will be worth $287,163 in 5 years.

Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the final amount (the value of the house in 5 years)

P = the initial amount (the value of the house when it was bought)

r = the annual interest rate (5%)

n = the number of times the interest is compounded in a year (we will assume it is compounded annually, so n = 1)

t = the number of years (5)

Plugging in the values, we get:

A = 225,000(1 + 0.05/1)^(1*5)

A = 225,000(1.05)^5

A = 225,000(1.27628)

A = $287,163.00

Therefore, the house will be worth approximately $287,163 in 5 years, rounded to the nearest dollar.

Answer:

$287.2 (After I round it)

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The full answer is 1101000. So, 104 in base 10 is equivalent to 1101000 in base 2.  When converting 104 from base 10 to base 2 using repeated division by 2.

The quotient obtained from the third division is as follows:

1. 104 ÷ 2 = 52 (remainder: 0)
2. 52 ÷ 2 = 26 (remainder: 0)
3. 26 ÷ 2 = 13 (remainder: 0)

After the third division, the quotient is 13. The full answer for converting 104 to base 2 will require a few more divisions:

4. 13 ÷ 2 = 6 (remainder: 1)
5. 6 ÷ 2 = 3 (remainder: 0)
6. 3 ÷ 2 = 1 (remainder: 1)
7. 1 ÷ 2 = 0 (remainder: 1)

Reading the remainder from bottom to top, the full answer is 1101000. So, 104 in base 10 is equivalent to 1101000 in base 2.

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