a particular fruit's weights are normally distributed, with a mean of 744 grams and a standard deviation of 37 grams. if you pick 20 fruit at random, what is the probability that their mean weight will be between 752 grams and 766 grams.

The monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

To calculate the monthly mortgage payment, we can use the formula for calculating the fixed monthly payment for a fully amortizing loan. The formula is: M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

M = Monthly mortgage payment

P = Principal balance

r = Monthly interest rate (annual interest rate divided by 12 and converted to a decimal)

n = Total number of monthly payments (loan term multiplied by 12)

Plugging in the given values into the formula:

P = $100,000

r = 0.05/12 (5% annual interest rate divided by 12 months)

n = 30 years * 12 (loan term converted to months)

M = 100,000 * (0.004166667 * (1 + 0.004166667)^(3012)) / ((1 + 0.004166667)^(3012) - 1)

M ≈ $536.82

Therefore, the monthly mortgage payment for a $100,000 loan with a 5% annual interest rate and a 30-year fully amortizing term is approximately $536.82.

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The experimental probability the next 4 customers will order a salad is 12.96%

The experimental probability of the next 4 customers ordering a salad can be calculated by multiplying the individual probabilities of each customer ordering a salad.

Given that 60% of customers typically order a salad, the probability of a customer ordering a salad is 0.6, or 60% expressed as a decimal.

To find the probability of all 4 customers ordering a salad, we multiply the probabilities together:

P(4 customers ordering a salad) = 0.6 * 0.6 * 0.6 * 0.6 = 0.6^4 = 0.1296

Therefore, the experimental probability of the next 4 customers ordering a salad is 0.1296, or 12.96% expressed as a percentage.

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We need to find the derivative of the given function. There are various derivative formulas. Let's use some of the common derivative formulas.

(i) Derivative of inverse function:

\((d/dx)(sin⁻¹x) = 1 / √(1−x²)(d/dx)(cos⁻¹x) = −1 / √(1−x²)(d/dx)(tan⁻¹x) = 1 / (1+x²)\)

(ii) Derivative of f\((x)g(x) = f(x)g′(x) + g(x)f′(x)\)

(iii) Derivative of xⁿ = n x^(n−1)

Using the above formulas,

\(Let y = cos⁻¹x + x√(1−x²)⇒ y = u + v\)

We can use the product rule of differentiation here.

Let f\((x) = x and g(x) = √(1−x²)d/dx(x√(1−x²)) = f(x)g′(x)\) \(+ g(x)f′(x)= x(d/dx(√\)\((1−x²))) + (√(1−x²))(d/dx(x))= x(−1 / 2)(1−x²)^(-1 / 2)(−2x) + √(1−x²)(1)= x² / √(1−x²) + √(1−x²)⇒ dv/dx = x² / √(1−x²) + √(1−x²)\)

Substitute the values of du/dx and dv/dx in equation (1).dy/dx = du/dx + dv/dx=\(−1 / √(1−x²) + x² / √(1−x²) + √(1−x²)= (x²+1) / √(1−\)x²)Therefore, the value of dy/dx i\(s (x²+1) / √(1−x\)²).

The correct option is, dy/dx \(= (x²+1) / √(1−x²).\)

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Answer:

86

Step-by-step explanation:

First, we find the area of each individual polygon:

Starting with C for the half circle:

\(C=\pi r^2\\C=\pi (3)^2\\C= 20\\\)

Since it's a half circle, we divide the final product by 2:

\(C=20/2\\C=10\)

Next, the trapezoid:

\(A=\frac{a+b}{2} h\\A=\frac{13+6}{2} (8)\\A=76\)

Last, since we combined the triangle with the trapezoid, we add all the areas we've found to find the area of the entire shape:

\(76+10= 86\)

Hope this helped! Have a good day.

The slope of the linear equation is; 0.5

The y-intercept of the Linear Equation is: 4.75

Yes the equation is proportional

The equation we are given is expressed as;

y = ¹/₂x + 4³/₄

When x = 0,

y = ¹/₂(0) + 4³/₄

y = 4.75

When x = 1,

y = ¹/₂(1) + 4³/₄

y = 5.25

When x = 2,

y = ¹/₂(2) + 4³/₄

y = 5.75

When x = 3,

y = ¹/₂(3) + 4³/₄

y = 6.25

If we go on and on till x = 10, we will see the constant difference in y for every change in x is 0.5

Thus, slope = 0.5

y-intercept = 4.75

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Answer:

8 2/3 per mile

Step-by-step explanation:

130 / 15 = 8 2/3

Hope that helps!

Answer:

(a) The exponential function representing the number of people who had watched the video \(t\) hours after the initial observation is \(n(t) = 129\cdot 1.3^{\frac{t}{3} }\).

(b) As \(n(120) < 5\times 10^{6}\), we conclude that this video is not going "viral".

Step-by-step explanation:

Statement is incomplete. The complete statement is:

An internet analytics company measured the number of people watching a video posted on a social media platform. The company found 129 people had watched the video and that the number of people who had watched it was increasing by 30% every 3 hours.

(a) Write an exponential function for the number of people A who had watched the video n hours after the initial observation.

(b) A video is said to go "viral" if the number of people who have watched the video exceeds 5 million within 5 days (120 hours). Would this video be considered to have gone viral?

(a) From the statement of the problem we get the following relationship:

\(\frac{n_{i+1}}{n_{i}}= r^{[(i+1)-i]}\) (Eq. 1)

Where:

\(n_{i}\) - i-th number of people watching a video, dimensionless.

\(n_{i+1}\) - (i+1)-th number of people watching a video, dimensionless.

\(r\) - Increase ratio, dimensionless.

For Induction Theorem, we get the following relatioship for \(i = 0\):

\(\frac{n_{1}}{n_{o}} = r^{1-0}\) (Eq. 2)

For \(i = m\), the following relationship is constructed:

\(\left(\frac{n_{1}}{n_{o}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+1}}{n_{m}} \right) = r^{m}\)

\(\frac{n_{m+1}}{n_{o}} = r^{m}\)(Eq. 3)

And for \(i = m+1\), we have the following expression:

\(\left(\frac{n_{1}}{n_{0}} \right)\cdot \left(\frac{n_{2}}{n_{1}} \right)\cdot ...\cdot \left(\frac{n_{m+2}}{n_{m}} \right) = r^{m+1}\)

\(\frac{n_{m+2}}{n_{0}} = r^{m+1}\)(Eq. 4)

If we multiply (Eq. 3) by the (m+1)-th ratio based on (Eq. 1):

\(\left(\frac{n_{m+1}}{n_{o}}\right)\cdot \left(\frac{n_{m+2}}{n_{m+1}} \right) = r^{m} \cdot r\)

\(\frac{n_{m+2}}{n_{o}} = r^{m+1}\)

Which is (Eq. 4) and the exponential function is represented by:

\(n_{i+1} = n_{o}\cdot r^{i}\), \(i\in \mathbb{N}_{O}\) (Eq. 5)

As the number of people is increased at constant rate every 3 hours, we get that \(i\) is:

\(i = \frac{t}{3}\), \(t \in \mathbb{R}\), \(t \geq 0\) (Eq. 6)

Where \(t\) is the time, measured in hours.

Then, the exponential function is:

\(n(t) = n_{o}\cdot r^{\frac{t}{3} }\) (Eq. 7)

Where \(n_{o}\) is the initial number of people watching the video, dimensionless.

If we know that \(n_{o} = 129\) and \(r = 1.3\), then the exponential function representing the number of people who had watched the video \(t\) hours after the initial observation is:

\(n(t) = 129\cdot 1.3^{\frac{t}{3} }\)

(b) If we know that \(t = 120\,h\), then we evaluate the exponential function:

\(n (120) = 129\cdot 1.3^{\frac{120}{3} }\)

\(n(120) = 4.659\times 10^{6}\)

As \(n(120) < 5\times 10^{6}\), we conclude that this video is not going "viral".

The sample size that would be required for the width of 99% is 2653.

The number of subjects involved in a sample size is referred to as the sample size in market research. A set of people chosen from the general community who are thought to be a representative sample size for that particular study is referred to as the sample size.

The following details are given:

Margin of error, E = 0.025; Significance Level, = 0.01

The proportion p is estimated to be p = 0.53.

The significance level with a critical value of 0.01 is 2.58.

The smallest sample size needed to estimate the population proportion p within the necessary margin of error is determined using the formula shown below:

n >= p*(1-p)*(zc/E)2 n = 0.53 *(1 - 0.53*)2 n = 2652.97 *(1-p)*(2.58/0.025)2

As a result, we determine that n = 2653 is the minimal sample size needed to satisfy the criteria that

n >= 2652.97 and that it must be an integer value.

Sample size is 2653.

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The generating function for the sequence {an} is given by a(x) = (1 + 2x) / (1 - x - 6x^2). It captures the terms of the sequence {an} as coefficients of the powers of x.

To find the generating function of the sequence {an}, we can use the properties of generating functions and solve the given recurrence relation.

The given recurrence relation is: an = an-1 + 6an-2

We are also given the initial conditions: a0 = 1 and a1 = 3.

To find the generating function, we define the generating function A(x) as:

a(x) = a0 + a1x + a2x² + a3x³ + ...

Multiplying the recurrence relation by x^n and summing over all values of n, we get:

∑(an × xⁿ) = ∑(an-1 × xⁿ) + 6∑(an-2 × xⁿ)

Now, let's express each summation in terms of the generating function a(x):

a(x) - a0 - a1x = x(A(x) - a0) + 6x²ᵃ⁽ˣ⁾

Simplifying and rearranging the terms, we have:

a(x)(1 - x - 6x²) = a0 + (a1 - a0)x

Using the given initial conditions, we have:

a(x)(1 - x - 6x²) = 1 + 2x

Now, we can solve for A(x) by dividing both sides by (1 - x - 6x^2²):

a(x) = (1 + 2x) / (1 - x - 6x²)

Therefore, the generating function for the given sequence is a(x) = (1 + 2x) / (1 - x - 6x²).

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Answer:

Hey I am very sorry but I can only provide the answers I can’t show my work On this thing..

Step-by-step explanation:

First image x+15\(\leq\)22

Answer: x\(\leq\)7

Second Image -4x\(\leq\)16

Answer: x\(\geq\)-4

Third Image -2x+7<-41

Answer: x>24

Fourth Image

Answer: x<-25

Finaly Image 4n+2(n+1)>n+52

Answer: n>10

I am really sorry that I couldn’t show my work I just have the answers. Good luck man.

Answer:

Choice B

------------------------

Choice D

------------------------

Choice B

------------------------

Choice A

------------------------

Choice D

Answer: FINAL IMAGE OF L IS 6 AND 7

Step-by-step explanation:

Answer:(1,-2)

Step-by-step explanation:

Therefore, we can see that the UK has a higher population density than Spain.

In mathematics, "square" usually refers to the operation of multiplying a number by itself. When we square a number, we write it as that number raised to the power of 2, or we can use the symbol "^2" to indicate that we are squaring the number.

For example, the square of 3 is. \(3^2\), which is equal to 9. Similarly, the square of -5 is. \((-5) ^2\), which is equal to 25. In general, we can square any real number (positive, negative, or zero) to get a non-negative result.

We can also use the term "square" to refer to a geometric shape that has four equal sides and four right angles, such as a square on a checkerboard or a piece of paper.

by the question.

For the UK:

\(Population density = Population /Area\)

\(= 66,000,000 /95,000\)

\(= 694.74 people per square mile\)

For Spain:

\(Population density = Population / Area\)

\(= 47,000,000 / 195,000\)

\(= 241.03 people per square mile\)

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Answer:

24 is correct answer

Step-by-step explanation:

its a 5:15 ratio, you are finding 8:x

8/5=1.6-> 1.6 x a5 = 24

Answer:

24 plates

Step-by-step explanation:

If she can wash 15 dishes in 5 minutes you just need to figure out how many dished she can washe in 1 minute. so you are gonna divide 15 by 5 and get 3 because 3 times 5 equals 15. so then that means she can wash 3 plates in 1 minute. so if she washed 15 in 5 in 6 minutes she can wash 18 and in 7 minutes she can wash 21 and in 8 minutes she can wash 24. Your just adding 3 to the 15 for every minute.

Answer:

Linear. y = x also equals y = 1x, and you can put a line on a graph using this equation, hence the name linear.

Answer:

The expression of density of the material with a density of 6 pound per pint in grams per liter (g/L) is 5756.75 g/L

Step-by-step explanation:

The density of the material is 6 pounds per pint of volume

The given conversion factors are;

1 pint (pt) = 2 cups (cups)

1 cup (cup) = 8 fluid ounces (fl oz)

Therefore;

2 cups (cups) = 2 × 8 fluid ounces = 16 fl oz

Also given;

1 fluid ounce = 29.574 mililiters (mL)

16 fl oz = 16 × 29.574 mL = 473.184 mL

1 liter (L) = 1000 mililiters (mL)

∴ 1 mL = 1/1000 L = 0.001 L

473.184 mL = 473.184 ×  0.001 L = 0.473184 L

1 pound (lb) = 0.454 kilograms (kg)

6 lb = 6 × 0.454 kg = 2.724 kg

1 kg = 1000 grams (g)

2.724 kg = 2.724 ×  1000 grams (g) = 2724 g

Therefore, with 6 lb = 2724 g and 1 pt = 0.473184 L, the density, d, of the material in grams per liter that has a density of 6 pounds per pint is given as follows;  

d = 2724 g/(0.473184 L)= 5756.75 g/L

The expression of density of the material with a density of 6 pound per pint in grams per liter (g/L) = 5756.75 g/L = 5756.75 g/L.

Answer:

the answer would be 2 * 2 * y √2 * 5* 7 * y

Step-by-step explanation:

The average rate of change of the substance is given as -2.4

When the value of t is ten years, the radioactive substance in grams is given as 6

When t is 0 on the graph, the gram is given as 3o grams

The rate of change would be

6 - 30 / 10 - 0

= -24 / 10

= - 2.4

The average rate of change is not a good measure. This is because what we have here is an exponential decay

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Answer:

The sketch tool to indicate what Edwin is describing as the parabola's "turning point'' is described below in details.

Step-by-step explanation:

We can see in graph that it intersect X axis and it is open upward it means turning point is below X axis, we can find turning point by find maximum value of Y If open downward and minimum value, if open upward here we can find that minimum point is (3, -5). also you can draw axis of symmetry parabola and finds its intersection with turning point can also be named vertex of parabola.

Answer:

A = $90

Step-by-step explanation:

A = P(1 + RT)

A = 50(1 + .08*10)

A = 50(1.8)

A = $90

Answer: It mentions how they  fear the authority government, also I believe u meant "Power of fear"

Step-by-step explanation:

The scatterplot is appropriate for this data set because we’re supposed to be interviewing 10 people and gathering the data on a graph, and putting the data up and down is the most logical.

The scatterplot is ideal for this data set since it makes the most sense to arrange the data vertically on a graph since we are meant to interview 10 people.

a) Since a scatterplot enables us to visually depict the relationship between two variables, it is appropriate for our data set. Given that you said that the data were obtained through interviews with 10 people, a scatterplot offers a logical and transparent method for arranging the data points on a graph.

The points are arranged vertically to indicate one variable and horizontally to represent the other. This makes it simple to see the data points and analyse them for any potential patterns or trends.

b) The following features are important for a scatterplot and contribute to easy data analysis:

With the addition of these components, the scatterplot is made into a complete and efficient tool for visualising and analysing the data, enabling easy interpretation and the extraction of significant insights from the plotted dots.

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Answer: -10,30

Step-by-step explanation: I drew the graph, and it lined with 30 and interCepted -10

The radius of the pool is 9.01 m.

Given,

In the question:

A circular pool is surrounded by a brick walkway 3 m wide.

The area of the walk- way is 198 m^2.

To find the Radius of the pool.

Now, According to the question:

"Area of the circle bounded by the outside edge of the walkway" minus "area of the pool" = "area of the walkway".

Let R = Radius of the pool

Area of the circle bounded by the outside edge of the walkway is:

\(\pi\)(R +3)^2

Area of the pool is:

\(\pi R^2\)

Now, Our equation is:;

\(\pi\)(R +3)^2 - \(\pi R^2\) = 198

\(\pi\)((R+3)^2 - \(R^2\)) = 198

Open the inner bracket :

\(\pi\)(\(R^2+6R+9-R^2\)) = 198

\(\pi\)(6R +9) = 198

6R+9 = 198/\(\pi\)

6R = 198/\(\pi\) - 9

R = (198/\(\pi\) - 9)/6

R = (198/(3.14) - 9)/6

R = (63.057 - 9)/6

R = 54.057/6

R = 9.01 meters

Hence, The radius of the pool is 9.01 m.

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Answer:

Step-by-step explanation:

When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative.

Answer:

your answer will be 0.0001042

Step-by-step explanation:

hope it helps

have a wonderful day

Answer:

She should pay down her student loan and credit card debt.

Step-by-step explanation:

Because the others would result in more debt or overwork and she has a good salary already

The best thing Anastasia can do to improve her creditworthiness is to pay down her student loan and credit card debt.

Option B is the correct answer.

We have,

The best thing Anastasia can do to improve her creditworthiness is to pay down her student loan and credit card debt.

This will lower her credit utilization ratio, which is a significant factor in determining her credit score.

Having a high credit utilization ratio can indicate to lenders that she may be at risk of defaulting on her debts, which could make it more difficult for her to obtain a mortgage or other loans in the future.

Paying down her debts can help improve her credit score and make her a more attractive borrower to potential lenders.

Thus,

The best thing Anastasia can do to improve her creditworthiness is to pay down her student loan and credit card debt.

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The probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%

Assuming that each prize is drawn independently of the others and that any person can win any of the prizes, we can find the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, by using the multiplication principle of probability.

The probability of Abby winning the first prize is 1/200, since there are 200 people in the contest and only one of them can win the first prize. Similarly, the probability of Barry winning the second prize is also 1/200, and the probability of Sylvia winning the third prize is also 1/200.

Since winning more than one prize is allowed, the probability of all three of these events occurring simultaneously is simply the product of their individual probabilities:

P(Abby wins 1st prize AND Barry wins 2nd prize AND Sylvia wins 3rd prize) = (1/200) * (1/200) * (1/200) = 1/8,000,000

Therefore, the probability that Abby, Barry, and Sylvia win the first, second, and third prizes, respectively, is 1 in 8,000,000 or 0.0000125%

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