There was 5/8 of a pizza left but Jeff only wanted to eat 1/2 of what was left. How much pizza will Jeff eat?​

Answer:

C. StartRoot x Endroot + 3 = 13

Step-by-step explanation:

the x variable under the root is what makes it a radical. all of the others dont have an x variable under the root. hope this helps !

Answer: f(x) = 61(3.5)^x

Step-by-step explanation:

This is what the variables always mean in the function:

a = initial value

b = growth factor

x = time

Then, you just plug them in! Hope this helps.

The average rate of change is $22.50 per class

The table of values represent the given parameter

The average rate of change is calculated as

Rate = Change in T(c)/Corresponding change in c

So, we have

Rate = (50 - 27.50)/(2 - 1)

Rate = 22.50

We start by calculating the function from

T(c) = mc + b

Where

m = Rate = 22.50

So, we have

T(c) = 22.5c + b

Using the points, we have

22.5 * 1 + b = 27.50

So, we have

b = 5

So, we have

T(c) = 22.5c + 5

For 5 classes, we have

T(5) = 22.5 * 5 + 5

T(5) = 117.5

The first class is 27.50 because the studio charges a registration fee of $5

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Answer:

\((-6 / 5)\) between the two points, given that this function is continuous.

Step-by-step explanation:

Assume that the function in this question is continuous over the interval between the two given points. Divide the change in the value of this function by the width of the interval to find the average rate of change of this function over that interval.

For example, consider a continuous function that goes through \((x_{\text{a}},\, y_{\text{a}})\) and \((x_{\text{b}},\, y_{\text{b}})\). The width of the interval between these two points is \((x_{\text{b}} - x_{\text{a}})\). Over this interval, the value of this function has changed from \(y_{\text{a}}\) to \(y_{\text{b}}\), such that the change in the value of the function is \((y_{\text{b}} - y_{\text{a}})\).

The average rate of change of this function between these two points would be \((y_{\text{b}} - y_{\text{a}}) / (x_{\text{b}} - x_{\text{a}})\).

The function in this question goes through the two points \((2,\, -1)\) and \((-8,\, 11)\). Substitute in these values to find the average rate of change of this function between these two points:

\(\begin{aligned} (\text{avg. rate of change}) &= \frac{y_{\text{b}} - y_{\text{a}}}{x_{\text{b}} - x_{\text{a}}} \\ &= \frac{11 - (-1)}{(-8) - 2} \\ &= \frac{12}{-10} \\ &= -\frac{6}{5}\end{aligned}\).

Answer:

B) 7,11,14

Step-by-step explanation:

correct me if I'm wrong

It will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

Let's use the formula for exponential growth to solve this problem:

N = N0 * 2^(t/k)

Where:

N0 = initial population (8 rabbits)

N = final population (5,800 rabbits)

k = doubling time (1 month)

t = time in months (what we're trying to find)

Substituting the values we have:

5,800 = 8 * 2^(t/1)

Dividing both sides by 8:

725 = 2^(t/1)

Taking the logarithm of both sides (base 2):

log2(725) = t/1

t = log2(725) ≈ 9.515

So it will take about 9.5 months (or 10 months rounded up) for the rabbit population to reach 5,800.

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The chi-square statistic is used to determine whether there are differences between two nominally scaled variables. Chi-Square is a statistical test used to compare two nominal variables to determine whether they differ.

The Chi-Square test is used to test for differences between two groups. When you want to compare groups or examine the relationship between two variables, this test is useful. The chi-square test is a method of statistical inference that can be used to compare observed frequencies with expected frequencies, allowing us to determine whether there is a meaningful difference between them. When the p-value obtained from a chi-square test is less than 0.05, it is generally considered statistically significant.

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Answer:

11 = (15 -6r) + 2r

11= 15-6r+2r

11=15-4r

4=4r

r=1

Answer:

Step-by-step explanation:

I need help

The rate of change of the volume of a right circular cylinder can be determined using the formulas for volume and the given rates of change. The correct answer is 1. rate = - 22 pi cu. in./min.

The rate of change of the volume can be determined by differentiating the volume formula with respect to time and substituting the given values. The volume of a right circular cylinder is given by V = πr^2h, where r is the radius and h is the height.

Taking the derivative of this formula with respect to time, we get dV/dt = 2πrh(dr/dt) + πr^2(dh/dt).

Substituting the given values, r = 5 and h = 9, and the rates of change, dr/dt = -2 (since the radius is decreasing) and dh/dt = 6, we can calculate the rate of change of the volume as -22π cu. in./min.

To understand why the answer is -22π cu. in./min, let's break down the calculation. We start with the volume formula for a cylinder, V = πr^2h. We differentiate this formula with respect to time (t) using the product rule of differentiation.

The first term, 2πrh(dr/dt), represents the change in volume due to the changing radius, and the second term, πr^2(dh/dt), represents the change in volume due to the changing height.

Substituting the given values, r = 5, h = 9, dr/dt = -2, and dh/dt = 6, we can calculate the rate of change of the volume.

Plugging in these values, we have dV/dt = 2π(5)(9)(-2) + π(5^2)(6) = -180π + 150π = -30π cu. in./min.

Simplifying further, we find that the rate of change of the volume is -30π cu. in./min.

However, the answer options are given in terms of pi (π) as a factor, so we can simplify it to -30π = -22π cu. in./min. Therefore, the correct answer is -22π cu. in./min.

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The Mean for June 2006 and 2005 is  $345,909 and $335,977 respectively. The median for June 2006 and 2005 is $254,000 and $139,000 respectively, there's no mode in this question.

In statistics, the mean, mode, and median are three measures of central tendency that describe a set of numerical data.

The mean is the average of a set of numbers, calculated by adding up all the values and dividing by the number of values. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the mean is (1 + 2 + 3 + 4 + 5) / 5 = 3.

The mode is the value that appears most frequently in a set of data. For example, if a set of data contains the values {1, 2, 2, 3, 4, 4, 4, 5}, the mode is 4, because it appears three times, which is more than any other value.

The median is the middle value in a set of data when it is ordered in ascending or descending order. For example, if a set of data contains the values {1, 2, 3, 4, 5}, the median is 3, because it is the middle value. If there is an even number of values, then the median is the average of the two middle values.

It is important to note that different sets of data may have different measures of central tendency, and sometimes none of these measures may be appropriate.

Measures of central tendency are used to summarize and describe a set of data. The most common measures of central tendency are the mean, median, and mode.

1. Mean:

• Mean for June 2006: (508+435+538+913+367+033+254+240+137+022+160+548+260+458+358+035+222+879+136+371+127+586+201+316)/22 = $345,909

• Mean for June 2005: (422+843+469+588+245+803+199+409+132+054+139+728+254+725+345+065+210+740+134+334+125+455+184+853)/22 = $335,977

2. Median:

• Median for June 2006: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $254,000

• Median for June 2005: Median of ordered data is the value in the middle of the data set, It is the 11th value in order set. we can see that it is $139,000

3. Mode:

• Mode for June 2006: There is no mode, because no value is repeated.

• Mode for June 2005: There is no mode, because no value is repeated.

Conclusions:

• The mean housing price in June 2006 is higher than the mean housing price in June

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a)  The x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

b) The coordinates of the vertex are (0.75, -5.125).

c) By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

Part A: To find the x-intercepts of the graph of f(x), we set f(x) equal to zero and solve for x.

Setting f(x) = 0:

\(2x^2 - 3x - 5 = 0\)

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, factoring is not straightforward, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For our equation, a = 2, b = -3, and c = -5. Substituting these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4(2)(-5))) / (2(2))

x = (3 ± √(9 + 40)) / 4

x = (3 ± √49) / 4

x = (3 ± 7) / 4

This gives us two possible solutions:

x1 = (3 + 7) / 4 = 10/4 = 2.5

x2 = (3 - 7) / 4 = -4/4 = -1

Therefore, the x-intercepts of the graph of f(x) are x = 2.5 and x = -1.

Part B: To determine whether the vertex of the graph of f(x) is a maximum or minimum, we need to consider the coefficient of the x^2 term in the function f(x). In this case, the coefficient is positive (2), which means the parabola opens upward and the vertex represents a minimum point.

To find the coordinates of the vertex, we can use the formula x = -b / (2a). In our equation, a = 2 and b = -3:

x = -(-3) / (2(2))

x = 3 / 4

x = 0.75

To find the corresponding y-coordinate, we substitute x = 0.75 into the function f(x):

f(0.75) = 2(0.75)^2 - 3(0.75) - 5

f(0.75) = 2(0.5625) - 2.25 - 5

f(0.75) = 1.125 - 2.25 - 5

f(0.75) = -5.125

Therefore, the coordinates of the vertex are (0.75, -5.125).

Part C: To graph the function f(x), we can follow these steps:

Plot the x-intercepts obtained in Part A: (2.5, 0) and (-1, 0).

Plot the vertex obtained in Part B: (0.75, -5.125).

Determine if the parabola opens upward (as determined in Part B) and draw a smooth curve passing through the points.

Extend the curve to the left and right of the vertex, ensuring symmetry.

Label the axes and any other relevant points or features.

By using the x-intercepts and vertex obtained in Parts A and B, we can accurately depict the shape and positioning of the parabolic graph of f(x).

The x-intercepts help determine where the graph intersects the x-axis, and the vertex helps establish the lowest point (minimum) of the parabola. The resulting graph should show a U-shaped curve opening upward with the vertex at (0.75, -5.125) and the x-intercepts at (2.5, 0) and (-1, 0).

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In order for the line y=4x+5 to be parallel to the line 2y=kx-6, the value of k should be 8.

To find the value of k that makes the line y=4x+5 parallel to the line 2y=kx-6, we need to compare the slopes of the two lines.

The given line, y=4x+5, is in slope-intercept form, y=mx+b, where m represents the slope of the line. In this case, the slope is 4.

We can rewrite the equation 2y=kx-6 in slope-intercept form by isolating y: y=(k/2)x-3. Now we can compare the slopes of the two lines.

For two lines to be parallel, their slopes must be equal. Therefore, the slope of the line y=4x+5 must be equal to the slope of the line (k/2)x-3. In other words, 4 must be equal to k/2.

To solve for k, we can multiply both sides of the equation by 2: 4*2 = k/2 * 2. This simplifies to 8 = k.

Hence, in order for the line y=4x+5 to be parallel to the line 2y=kx-6, the value of k should be 8.

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A student can select the questions in 420 different ways implies that the student can select any number of questions from the set, without any restrictions or limitations, the number of ways to select questions would be determined by the power set of the question set.

To calculate the number of ways a student can select the questions, we need to consider the combinations of selecting questions from Part I and Part II, while ensuring that at least 3 questions are selected from each part.

Number of questions in Part I: 5

Number of questions in Part II: 7

Total number of questions to be attempted: 8

We can consider different combinations of selecting questions from each part to meet the requirements. Let's break it down into cases:

Case 1: Selecting 3 questions from Part I and 5 questions from Part II

Number of ways to select 3 questions from Part I: C(5,3) = 10

Number of ways to select 5 questions from Part II: C(7,5) = 21

Total ways for Case 1: 10 * 21 = 210

Case 2: Selecting 4 questions from Part I and 4 questions from Part II

Number of ways to select 4 questions from Part I: C(5,4) = 5

Number of ways to select 4 questions from Part II: C(7,4) = 35

Total ways for Case 2: 5 * 35 = 175

Case 3: Selecting 5 questions from Part I and 3 questions from Part II

Number of ways to select 5 questions from Part I: C(5,5) = 1

Number of ways to select 3 questions from Part II: C(7,3) = 35

Total ways for Case 3: 1 * 35 = 35

Therefore, the total number of ways a student can select the questions, while meeting the given criteria, is:

Total ways = Total ways for Case 1 + Total ways for Case 2 + Total ways for Case 3

= 210 + 175 + 35

= 420

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A student can select the questions in 14,400 different ways.

To find the number of ways a student can select the questions, we can break down the problem into two parts: selecting questions from Part I and selecting questions from Part II.

In Part I, there are 5 questions, and the student needs to select at least 3. So, there are 3 possible choices for the first question, 4 for the second, and 5 for the third. However, the remaining 2 questions can be selected in any way. So, the number of ways to select questions from Part I is 3 * 4 * 5 * 2 * 1 = 120.

In Part II, there are 7 questions, and the student needs to select at least 3. So, there are 3 possible choices for the first question, 4 for the second, and 5 for the third, just like in Part I. The remaining 4 questions can be selected in any way.

So, the number of ways to select questions from Part II is also 120.

To find the total number of ways a student can select the questions, we multiply the number of ways from Part I and

Part II together: 120 * 120 = 14,400.

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In this problem, we have a binomial probability distribution

so

n=3

p=0.50

q=0.50

Find out P(X=2)

Answer:

inverse is 2×2

Step-by-step explanation:

Answer:

33/25

Step-by-step explanation:

Convert mixed fraction to improper fraction. There is no common factors. So multiply the denominators and multiply the numerators.

\(2\frac{3}{11}*\frac{1}{3}=\frac{25}{11}*\frac{1}{3}\\\\=\frac{25}{33}\)

Multiplicative inverse of \(\frac{25}{33}\) = \(\frac{33}{25}\)

Answer:

I think that x would be 32

Step-by-step explanation:

11 plus 21 is 32

Answer: 72 degrees

Step-by-step explanation: We know that angle DHG and angle EHF are congruent due to the vertical angles theorem. Since these two angle measures are congruent, this also means that the expression 6(x-2) is congruent to 3x+30. To find the angle measure of DHG, we need to find x. We can set these two expressions equal to each other and solve for x.

6(x-2) = 3x+30

6x-12 = 3x + 30

-3x -3x

3x-12=30

+12 +12

3x=42

~divide by 3 on both sides~

x = 14

Now that we know our x variable, we can substitute 14 into the expression for angle DHG.

6(14-2)

6(12)

72.

Answer:

∠DHG = 72°

Step-by-step explanation:

As ∠DHG and ∠EHF are vertical angles, they are congruent.

What are vertical angles?

Vertical angles are formed when two lines intersect, creating opposite angles. Those opposites are congruent (equal).

Equation:

∠DHG = ∠EHF

[6(x - 2)] = (3x + 30)

Step 1: Distribute 6 through the parentheses.

\(\implies 6(x) + 6(-2) = 3x + 30\)

\(\implies 6x - 12 = 3x + 30\)

Step 2: Subtract 3x from both sides.

\(\implies 6x - 3x - 12 = 30\)

\(\implies 3x - 12 = 30\)

Step 3: Add 12 to both sides.

\(\implies 3x - 12 + 12 = 30 + 12\)

\(\implies 3x = 42\)

Step 4: Divide both sides by 3.

\(\implies \dfrac{3x}{3} = \dfrac{42}{3}\)

\(\implies \boxed{x = 14}\)

Step 5: Substitute the value of x into ∠DHG to find its measure.

\(\implies \angle DHG = 6(14 - 2)\)

\(\implies \angle DHG = 6(12)\)

\(\implies \angle DHG = \boxed{72^\circ}\)

Therefore, the measure of ∠DHG is 72°.

The correct relationship between Student's t-distribution and the standard normal distribution is option B: as the sample size approaches infinity, the Student's t-distribution approaches the standard normal distribution.

The sample mean's estimation of the population mean is less precise and the sample mean's distribution is more erratic when the sample size is small. Because the distribution of t-values is more skewed as a result, the student's t-distribution has thicker tails than the traditional normal distribution.

The sample mean's distribution, however, narrows as sample size increases, making it a more precise reflection of the population mean. The student's t-distribution resembles the traditional normal distribution as a result of the narrowing of the t-value distribution.

For the ordinary normal distribution to accurately approximate the student's t-distribution in practice, a sample size of 30 or more is frequently thought to be sufficient.

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Correct question:

what is the relationship between student's t distribution and the standard normal distribution?

student's t will approach to standard normal distribution as the sample size approachs 0.

student's t will approach to standard normal distribution as the sample size approachs infinite

standard normal distribution will approach to student's t distribution as the sample size approachs 0

standard normal distribution will approach to student's t distribution as the sample size approachs infinite.

There are 7 people in Mr. Wilson's class, as Zach is the second person and Mary is the seventh person.

To calculate the total number of people in the class, we can use the formula 2x = 7, where x is the total number of people. Solving for x, we get x = 7.

To determine the number of people in Mr. Wilson's class, we can use the formula for the number of people in a circle, which is N = 2(n-1), where n is the number of people standing opposite each other in the circle. In this case, n is 2 (Zach and Mary). Therefore, N = 2(2-1) = 2 people. However, since there are 7 people in total in the circle, we can conclude that the number of people in Mr. Wilson's class is 7. To explain further, based on the given information, we can say that Zach is the second person, which means there are 2 people before him in the circle. Therefore, there are 7 people in Mr. Wilson's class. To further explain, we can break down the equation as follows: The person opposite of Zach is the seventh person, or 7th, so we can say that 7 is equal to the number of people in the class multiplied by 2, or 2x. Then, solving for x, we get x = 7. This means that the total number of people in the class is 7.

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the ladder reaches about 18.75 feet up the side of the house.

we can use the Pythagorean theorem which states that in a right triangle, the sum of the squares of the two shorter sides (the legs) is equal to the square of the longest side (the hypotenuse). In this case, the ladder is the hypotenuse, and the distance from the house to the base of the ladder is one leg.
So, if we let x be the distance up the side of the house that the ladder reaches, then we can write:
\(x^{2}\) + \(7^{2}\) = \(20^{2}\)
Simplifying this equation, we get:
\(x^{2}\) + 49 = 400
Subtracting 49 from both sides, we get:
\(x^{2}\) = 351
Taking the square root of both sides, we get:
x ≈ 18.75 feet

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Answer:

7inches

Step-by-step explanation:

Volume of a cylinder = πr²h

r is the radius of the cylinder

h is the height of the cylinder

Given

r = 3inches

Volume = 197.92 cubic inches

Substitute

197.92 = 3.14(3)²*h

197.92 = 28.26h

28.26h = 197.92

h = 197.92/28.26

h = 7.003in

Hence the measurement that is closest to the height of the waste can is 7inches

Log x+y = logbx − logbyGiven log630 ≈ 1.898 and log62 ≈ 0.387, log615 ≈ 2.086.

Given log 630 ≈ 1.898 and log 62 ≈ 0.387,

We have log 630 = log (6 * 62 * 10) = log 6 + log 62 + log 10 = 1 + 0.387 + 1 = 2.387

And log 615 = log (6 * 62 * 5) = log 6 + log 62 + log 5 = 1 + 0.387 + 0.699 = 2.086

So, log 615 ≈ 2.086

In the example given, log 630 ≈ 1.898 and log 62 ≈ 0.387. These logarithmic values are used to simplify other logarithmic expressions and, the logarithm of 615 was found to be approximately 2.086.

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Step-by-step explanation:

b²-4ac

(-1)²-4(2×1)

1-8

-7

Now -7<0 therefore it has two complex roots or nonreal roots

Answer: Jane’s investment reaches $6,000 by the end of week 14

Step-by-step explanation: To solve this problem, we need to use the compound interest formula:

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

Where:

A = future value of the investment

P = principal amount

r = annual interest rate (decimal)

n = number of times interest is compounded per year

t = time in years

We can assume that the stock is compounded weekly, so n = 52. We also need to convert the percentage changes to decimals, so 30% = 0.3 and 11% = 0.11.

We can divide the problem into three phases:

Phase 1: From week 1 to week 6, Jane invests $100 and the stock alternates between rising by 30% and lowering by 11%. The effective weekly interest rate for this phase is (1 + 0.3) * (1 - 0.11) - 1 = 0.157, or 15.7%. The future value at the end of week 6 is:

A = 100 * (1 + 0.157/52)^(52 * 6/52) A = $197.66

Phase 2: At the end of week 6, Jane takes out half of the money, so she has $98.83 left in the stock. From week 7 to week 9, the stock continues to alternate between rising by 30% and lowering by 11%. The effective weekly interest rate for this phase is the same as before, 15.7%. The future value at the end of week 9 is:

A = 98.83 * (1 + 0.157/52)^(52 * 3/52) A = $193.66

Phase 3: At the end of week 9, Jane adds $100 to the stock, so she has $293.66 in the stock. From week 10 to week 14, the stock continues to alternate between rising by 30% and lowering by 11%. The effective weekly interest rate for this phase is the same as before, 15.7%. The future value at the end of week 14 is:

A = 293.66 * (1 + 0.157/52)^(52 * 5/52) A = $6018.77

Therefore, Jane’s investment reaches $6,000 at the end of week 14.

Hope this helps, and have a great day! =)

Answer:

x=9.23

Step-by-step explanation:

Zy=x

Yx=11

Tan40=x/11

11tan40=x

11x0.8391

x=9.23

Answer:

( 1 + x) ( 7 - x)

Step-by-step explanation:

Here's what I did

16 - ( x - 3)^2....expand this

16 - (x² + 6x + 9).....after exanding

16 - 9 + 6x - x²......like terms together

7 + 6x - x² ......rearrange

-x² + 6x + 7......look for the product, sum and factors

( 1 + x) ( 7 - x)