The perimeter if a rectangle is 84 inches. The length is 12 inches less than twice the width. Find the length and width of the rectangle.

Add up the 3 items for subtotal.

Then take that subtotal and multiply by 0.20 (which is the same as 20%). That's your tip.

Add subtotal + tip and there's your total bill.

See attached screenshot.

Hope you have a good afternoon : )

Let the original number of rara coins that Jerry had back then be x.

now if he sold 50 rare coins, the coins left will be x - 50

Answer:

x<6

Step-by-step explanation:

The height of the tree and its shadow, and the height of the person and its shadow, at the same time of the day, form two similar right triangles:

Since both triangles are similar, then the corresponding sides are at the same ratio so that:

From this expression, you can determine the height of the tree, just multiply both sides of the equal sign by 5:

The height of the tree is 15 feet.

Answer:

2x -5=-30

2x= 5 -30

2x= 25

x= 25/2

x= 12.5

A parametrization for a circle of radius 6 with center (-4,-2,-5) in a plane parallel to the xy plane:  x = -4 + 6cos(t) : y = -2 + 6sin(t) ; z = -5

The plane is parallel to the xy plane, its normal vector will be (0,0,1). We can use this normal vector and the center of the circle to find the equation of the plane:

0(x+4) + 0(y+2) + 1(z+5) = 0
z = -5

Now we need to find a parametrization for the circle. We can do this by using the equation of the circle in standard form:

(x+4)^2 + (y+2)^2 = 36

We can rewrite this equation in terms of x and y:

x^2 + 8x + 16 + y^2 + 4y + 4 = 36
x^2 + 8x + y^2 + 4y - 16 = 0

Completing the square, we get:

(x+4)^2 - 16 + (y+2)^2 - 4 - 16 = 0
(x+4)^2 + (y+2)^2 = 36

This is the equation of a circle with center (-4,-2) and radius 6. To write our parameterization, we can use the fact that the x component includes a positive cosine. We can choose our parameter t to be the angle in radians that the point on the circle makes with the positive x-axis. Then our parameterization is:

x = -4 + 6cos(t)
y = -2 + 6sin(t)
z = -5

This parameterization traces out the circle as t varies from 0 to 2π.

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Answer:

its A

Step-by-step explanation:

asymptotes:=-1 and hole:x=4

When Pablo and five of his friends share 16 ounces of blueberries equally, each will get 2.67 ounces, using division operation.

Division operation is one of the four basic mathematical operations.

The other three include addition, subtraction, and multiplication.

The division operation involves the dividend (the numerator) divided by the divisor (the denominator) using the division operand (÷) to get a result known as the quotient.

The total quantity of blueberries to be share by 6 friends = 16 ounces

The number of friends sharing the quantity = 6 (Pablo and five friends)

The share of each friend = 2.67 ounces (16 ÷ 6)

Thus, based on division operation, each friend gets 2.67 ounces.

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Step-by-step explanation:

The square root of a fraction is the square root of the numerator over the square root of the denominator. In this case, 1/4. The square root of 1/16 = 1/4 Ans.

The square root of 1/16 is 1/4.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

√(1/16)

This can be written as,

= √1 / √16

= 1 / 4

Thus,

1/4 is the square root of 1/16.

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The 99% confidence interval for the population standard deviation of body temperature is (0.61°F, 0.80°F). Since the entire interval is below 1.80°F, it is safe to conclude that the population standard deviation is less than 1.80°F.

To construct a confidence interval estimate of the standard deviation of body temperature, we can use the formula:

s/sqrt(n-1) * sqrt((n-1)/chi-square(alpha/2, n-1)) < σ < s/sqrt(n-1) * sqrt((n-1)/chi-square(1-alpha/2, n-1))

where s is the sample standard deviation, n is the sample size, α is the significance level (1- confidence level), and chi-square is the chi-square distribution function.

Plugging in the values given, we get:

0.69/sqrt(107-1) * sqrt((107-1)/chi-square(0.01/2, 107-1)) < σ < 0.69/sqrt(107-1) * sqrt((107-1)/chi-square(1-0.01/2, 107-1))

0.69/10.344 * sqrt(106/71.605) < σ < 0.69/10.344 * sqrt(106/146.577)

0.177 < σ < 0.233

Therefore, we can say with 99% confidence that the population standard deviation of body temperature is between 0.177 and 0.233.

As for whether it is safe to conclude that the population standard deviation is less than 1.80°F, we can see that the confidence interval we calculated does not include this value. However, we cannot definitively say that the population standard deviation is less than 1.80°F without further evidence or a wider confidence interval.

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Answer:

6 feet

Step-by-step explanation:

C. 6 feet

Length of Side g is 6 feet

Trigonometric functions defined as the functions which show the relationship between angle and sides of a right-angled triangle.

Given,

∠F = 49°

Length of side f = 7 feet

∠G = 40°

length of side g = ?

According Sine rule,

\(\frac{\sin E}{e}=\frac{\sin F}{f}=\frac{\sin G}{g}\)

\(\frac{\sin 49}{7}=\frac{\sin 40}{g}\)

\({g}=7(\frac{\sin 40}{sin 49})\)

g = 5.96 ≈ 6

Hence, length of side g is 6 feet.

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The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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The equation of the tangent line to the function y=f(x)=(x+1)^2e^x/4 at x=0 is y = 2x + 1.

The function given is, y=f(x) = (x + 1)²e^(x/4).

We have to find the equation of the tangent line to the function at x = 0.

The slope of the tangent line is given by the derivative of the function f'(x) at x = 0.

f(x) = (x + 1)²e^(x/4)

Taking the derivative of f(x) using the product rule, we get

f'(x) = (2(x + 1)e^(x/4) + (x + 1)²(1/4)e^(x/4))

=> f'(0) = 2

The slope of the tangent line is 2 and it passes through (0, f(0)).

To find the y-intercept of the tangent line, we need to evaluate f(0).

f(0) = (0 + 1)²e^(0/4)

= 1

The equation of the tangent line is given by

y = mx + b, where m is the slope and b is the y-intercept.

Substituting the values, we gety = 2x + 1

Therefore, the equation of the tangent line to the function y=f(x)=(x+1)^2e^x/4 at x=0 is y = 2x + 1.

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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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Given a Math exam with 7 short answer questions and Peter intending to answer three of them, there are a total of 35 different combinations of short answer questions he can choose.

To determine the number of combinations, we can use the concept of combinations in combinatorics. The formula for combinations is given by:

C(n, r) = n! / (r! * (n - r)!)

Where:

C(n, r) represents the number of combinations of choosing r items from a set of n items.

n! denotes the factorial of n, which is the product of all positive integers up to n.

In this case, Peter wants to answer three out of the seven questions, so we can calculate it as:

C(7, 3) = 7! / (3! * (7 - 3)!) = 7! / (3! * 4!)

Simplifying further:

7! = 7 * 6 * 5 * 4 * 3 * 2 * 1

3! = 3 * 2 * 1

4! = 4 * 3 * 2 * 1

C(7, 3) = (7 * 6 * 5 * 4 * 3 * 2 * 1) / [(3 * 2 * 1) * (4 * 3 * 2 * 1)]

After canceling out common terms, we get:

C(7, 3) = 7 * 6 * 5 / (3 * 2 * 1) = 35

Therefore, there are 35 different combinations of short answer questions Peter can choose to answer.

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Answer:

?????

Step-by-step explanation:

Evaluating Georgianna's claim using a hypothesis test.The claim is that the average child takes less than 5 years of piano lessons. Therefore, we use a one-tailed hypothesis test with a null hypothesis asH0: µ ≥ 5 versus the alternative hypothesis Ha: µ < 5.

Level of significance is not given, hence we can assume it to be 0.05. Calculating the test statistic as follows:$$t=\frac{\overline{x}-\mu }{s/\sqrt{n}}$$Substituting the given values in the above equation, we get$$t=\frac{4.6-5}{2.2/\sqrt{20}}$$So, t = -1.69, for a one-tailed test (left-tailed) and the degrees of freedom are n-1 = 19. Using the t-distribution table with α = 0.05 and 19 degrees of freedom, the critical value is -1.73, hence, -1.69 falls within the non-rejection region. Therefore, we cannot reject the null hypothesis. There is not enough evidence to support Georgianna's claim.b. Constructing a 95% confidence interval for the number of years students in this city take piano lessons, and interpret it in the context of the data.

The formula for confidence interval for a population mean is Interpretation: We can be 95% confident that the average number of years students in this city take piano lessons falls between 4.01 and 5.19 years.c. Explaining if the results from the hypothesis test and the confidence interval agreeYes, the results from the hypothesis test and the confidence interval agree because we cannot reject the null hypothesis in the hypothesis test. This means that the null hypothesis, H0: µ ≥ 5 is plausible. Further, the 95% confidence interval for the mean number of years students take piano lessons lies completely above the value of 5 years, which is Georgianna's claim. This is in line with the hypothesis test result. Thus, we can conclude that there is no sufficient evidence to support Georgianna's claim.

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Therefore, the approximate change of the function f(x, y) when x changes from 0 to 0.39 and y changes from 0 to 0.39 is approximately 7.02.

To find the approximate change of the function f(x, y) = 2e^(6x+3y) when x changes from 0 to 0.39 and y changes from 0 to 0.39, we can use the total differential.

The total differential of f(x, y) is given by:

df = (∂f/∂x)dx + (∂f/∂y)dy

Taking partial derivatives of f(x, y) with respect to x and y, we have:

\(∂f/∂x = 12e^{(6x+3y)}\\∂f/∂y = 6e^{(6x+3y)}\)

Substituting the given values of x and y, we get:

\(∂f/∂x = 12e^{(6(0)+3(0)) }\)

= 12

\(∂f/∂y = 6e^{(6(0)+3(0))}\)

= 6

Now we can calculate the approximate change using the total differential:

df ≈ (∂f/∂x)dx + (∂f/∂y)dy

≈ 12(0.39 - 0) + 6(0.39 - 0)

≈ 4.68 + 2.34

≈ 7.02

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The differential equation to be solved is Nxy - 0.5ye-0.1x for osx54 with y(0) = 6.5 dx. This can be solved using Euler's method in MATLAB.

Follow the steps below.

Step 1: Create a function file - The differential equation needs to be defined in a function file first. Let's create a function file named "odefun.m".function dydx = odefun(x,y)

dydx = N*x*y - 0.5*y*exp(-0.1*x);

where N is a constant value that needs to be defined.

Step 2: Define the given values - Define the given values such as N, initial value y(0), and step size dx.

N = ...; %

Define N herey 0 = 6.5; %

Define initial value of y here. dx = ...; %

Define step size here

Step 3: Use Euler's method to solve the differential equation - Now, use Euler's method to solve the differential equation using a for loop. The MATLAB code is as follows: x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); %

Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end

Step 4: Plot the solution - Finally, plot the solution using the MATLAB command plot(x,y).

The complete MATLAB code is given below:

N = ...; %

Define N here y0 = 6.5; %

Define initial value of y here dx = ...; %

Define step size here x = 0:dx:54; %

Define range of x values here y = zeros(size(x)); % Initialize y as a vector of zeros y(1) = y0; %

Assign initial value of y to y(1) for i = 1: length(x)-1 dydx = odefun(x(i),y(i)); y(i+1) = y(i) + dydx*dx; end plot(x,y)

The plot of the solution will be displayed.

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Answer:

24 miles

Step-by-step explanation:

20×6=120minutes

120 minutes equals two hours

4×6=24miles

hope this helps!!

brainlest??

The data includes a concave mirror with a radius of curvature of +31.5 cm and magnification of m = 3.40. The formula for magnification is m = v/u, and the focal length is f = r/2. Substituting the values, we get u = v/m, and using the mirror formula, the distance of the object from the mirror is 10.15 cm.

Given data: Radius of curvature of a concave mirror, r = +31.5 cm Magnification produced by the mirror, m = 3.40

We know that the formula for magnification is given by:

m = v/u where, v = the distance of the image from the mirror u = the distance of the object from the mirror We also know that the formula for the focal length of the mirror is given by :

f = r/2where,f = focal length of the mirror

Using the mirror formula:1/f = 1/v - 1/u

We know that a concave mirror has a positive focal length, so we can replace f with r/2.

We can now simplify the equation to get:1/(r/2) = 1/v - 1/u2/r = 1/v - 1/u

Also, from the given data, we have :m = v/u

Substituting the value of v/u in terms of m, we get: u/v = 1/m

So, u = v/m Substituting the value of u in terms of v/m in the previous equation, we get:2/r = 1/v - m/v Substituting the given values of r and m in the above equation, we get:2/31.5 = 1/v - 3.4/v Solving for v, we get: v = 22.6 cm Now that we know the distance of the image from the mirror, we can use the mirror formula to find the distance of the object from the mirror.1/f = 1/v - 1/u

Substituting the given values of r and v, we get:1/(31.5/2) = 1/22.6 - 1/u Solving for u, we get :u = 10.15 cm

Therefore, the distance of the mirror from the face is 10.15 cm. The units are centimeters (cm).Answer: 10.15 cm.

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The given statement is True. A discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable.

A Discrete probability distribution is a statistical term used to describe the probability distribution of a random variable that can take on a finite or countably infinite number of distinct outcomes. In other words, a discrete random variable is one that can only take on a specific set of values, while a continuous random variable can take on any value within a specified range.Examples of discrete random variables include the number of children in a family, the number of accidents that occur in a given day, and the number of red cars that pass through an intersection in an hour. A discrete probability distribution is a way of describing the probabilities associated with each of these possible outcomes.In summary, a discrete probability distribution can be expressed in a graph, table, or formula, as long as it gives the probability associated with each value of the discrete random variable. This is because a discrete random variable can only take on a specific set of values, making it easy to calculate the probabilities associated with each outcome.

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The volume of the given figure is 5760 \(cm^{3}\).

According to the question,

We have the following information:

We have a figure where two cuboids are joined together. So, the volume of the figure will be the sum of the volume of these cuboids.

We know that the following formula is used to find the value of cuboid:

Volume of cuboid = Length*breadth*height

Volume of larger cuboid = 40*8*12

Volume of larger cuboid = 3840 \(cm^{3}\)

Volume of smaller cuboid = 20*8*12

Volume of smaller cuboid = 1920 \(cm^{3}\)

Volume of the figure = 3840+1920

Volume of the figure =  5760 \(cm^{3}\)

Hence, the correct option is B (the second option).

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Answer:

5760

Step-by-step explanation:

The original activity of the sample can be calculated using the equation A=A0e^(-kt), where A0 is the initial activity, k is the decay constant, and t is the elapsed time.

1. Identify the given values: Half-life (t1/2) = 3.8 days, Activity level (A) = 0.17 bq/L, and Elapsed time (t) = 5.0 days.

2. Calculate the decay constant (k) using the equation k = ln(2)/t1/2.

k = ln(2)/3.8 days

k = 0.1815

3. Calculate the original activity (A0) using the equation A0 = A/e^(-kt).

A0 = 0.17 bq/L/e^(-0.1815)

A0 = 0.21 bq/L

Therefore, the original activity of the sample was 0.21 bq/L.

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The function with a greater stretch factor is the function graphed and the value is 3 times greater

The function with a greater stretch factor is the function which has a greater number multiplying the function

The given equation is a(x) = 1/3 x³ while the function graphed is b(x) = x³+ 2

The stretch factor is determined by the coefficients which are

a(x): 1/3 and b(x): 1

comparing this numbers

= b(x) / a(x)

= 1 / 1/3

= 3

this shows that b(x) which is 1 is greater by 3 times.

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The Interquartile Range (IQR) rule is a commonly used quantitative rule to determine univariate outliers and deleting a case may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

The Interquartile Range (IQR) rule is a commonly used method for identifying outliers in a univariate data set. It is calculated as the difference between the 75th percentile (Q3) and the 25th percentile (Q1). Outliers are considered to be any values that fall outside of the range Q1 - 1.5 * IQR to Q3 + 1.5 * IQR. This range encompasses approximately 75% of the data, with outliers being any values that fall outside of this range.

In some cases, deleting a case or participant may be justified if it is a result of a measurement error, data entry error, or if it significantly skews the results.

This decision should be made carefully and only after careful consideration of the implications, as removing data can affect the validity of the results and the conclusions that can be drawn from the analysis. In some cases, it may be better to keep the outlier and consider it a potential error or to conduct further analysis to determine if there is a valid reason for the outlier.

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Answer:

x = - 15

Step-by-step explanation:

Given

\(\frac{x}{5}\) = 5 + \(\frac{x-9}{3}\)

Multiply through by 15 ( the LCM of 5 and 3 ) to clear the fractions

3x = 75 + 5(x - 9) ← distribute and simplify right side

3x = 75 + 5x - 45

3x = 5x + 30 ( subtract 5x from both sides )

- 2x = 30 ( divide both sides by - 2 )

x = - 15

As a check

substitute x = - 15 into the equation and if both sides are equal then it is the solution.

left side = \(\frac{-15}{5}\) = - 3

right side = 5 + \(\frac{-15-9}{3}\) = 5 + \(\frac{-24}{3}\) = 5 - 8 = - 3

Thus x = - 15 is the solution

The time that she should leave so she will be late only 4% of the time is given as follows:

7:41 am.

We first must use the z-score formula, as follows:

\(Z = \frac{X - \mu}{\sigma}\)

In which:

The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, and can be positive(above the mean) or negative(below the mean).

The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure represented by X in the distribution.

The mean and the standard deviation for this problem are given as follows:

\(\mu = 15, \sigma = 2\)

The 96th percentile of times is X when Z = 1.75, hence:

1.75 = (X - 15)/2

X - 15 = 2 x 1.75

Z = 18.5.

Hence she should leave her home at 7:41 am, which is 19 minutes (rounded up) before 8 am.

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