If x = 4 and y = 7, evaluate the - following expression: 20 +2(3y - 4x)​

Answer: 3

Step-by-step explanation:

If the width is 1 and the length is 3 times the width, multiply 3x1 to find the length, and if you multiply the width x length you get 3

(a) The 99% confidence interval for the mean weight of the toxic substance per gram of mold culture is approximately 1.612 to 2.108 milligrams. (b) The correct statement is (A) The population does not need to be normal.

(a) To find the 99% confidence interval for the mean weight of the toxic substance per gram of mold culture, we can use the following steps:

1, Calculate the sample mean (x) of the measurements provided. Add up all the values and divide by the total number of measurements (in this case, 10).

x = (1.2 + 1.5 + 1.6 + 1.6 + 2.0 + 2.0 + 1.8 + 1.8 + 2.2 + 2.2) / 10 ≈ 1.86

2, Calculate the sample standard deviation (s) of the measurements. This measures the variability in the data.

s = √[((1.2 - 1.86)² + (1.5 - 1.86)² + ... + (2.2 - 1.86)²) / (10 - 1)] ≈ 0.302

3, Determine the critical value (z*) corresponding to the desired confidence level of 99%. This value can be obtained from the standard normal distribution table or using statistical software. For a 99% confidence level, the critical value is approximately 2.62.

4, Calculate the margin of error (E) using the formula:

E = z* * (s / √n)

where z* is the critical value, s is the sample standard deviation, and n is the sample size.

E = 2.62 * (0.302 / √10) ≈ 0.248

5, Finally, construct the confidence interval by subtracting and adding the margin of error to the sample mean:

Confidence interval = x ± E = 1.86 ± 0.248

Therefore, the 99% confidence interval for the mean weight of the toxic substance per gram of mold culture is approximately 1.612 to 2.108 milligrams.

(b) The correct statement regarding part (a) is (A) The population does not need to be normal.

The confidence interval for the mean can be calculated without assuming that the population follows a specific distribution, as long as the sample size is large enough (n ≥ 30) or the population is approximately normally distributed.

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Given:

Bird center bar chart is given.

Option D is the final answer.

The value of the midpoint between (1, 2) and (11,12) is,

⇒ (6, 7)\

We have to given that;

To find the midpoint between (1,2) and (11,12).

Since, A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

Now, By definition of midpoint, we get;

The midpoint between (1,2) and (11,12) is,

⇒ (1 + 11)/2, (2 + 12) / 2

⇒ (12/2, 14/2)

⇒ (6, 7)

Thus, The value of the midpoint between (1, 2) and (11,12) is,

⇒ (6, 7)\

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Thus, the equation that connects C and X is C = 100X + 5.33X² and the depth of the well if the cost is 12000 naira is 38.85 meters.

1. Deriving an equation that connects C and X together The cost C of sinking a well X meters deep varies partly as X and partly X². That is,C = kX + pX²,Where k and p are constants to be determined. To determine the value of k and p, we can use the information given that the cost is 5000 naira if the depth is 30m and cost is 8000 naira if the depth is 50m.From the above information, we can get two equations:

5000 = 30k + 30²p8000 = 50k + 50²p

We can use the first equation to get the value of k and substitute it in the second equation.

5000 = 30k + 900p ⇒ k = 166.67 - 10p

Substituting k in the second equation gives:

8000 = 50(166.67 - 10p) + 2500p

Solving the above equation gives:

p = 5.33 And, k = 100.00

Substituting k and p in the cost equation gives:

C = 100X + 5.33X²2. Finding the depth of the well if the cost is 12000 naira

Given that C = 12000, we need to find the value of X.C = 100X + 5.33X² ⇒ 5.33X² + 100X - 12000 = 0

Solving the above quadratic equation using the quadratic formula gives:

X = (-b ± √(b²-4ac))/2a = (-100 ± √(100² - 4×5.33×(-12000)))/2×5.33= (-100 ± 540.71)/10.66= 38.85 or -23.45

'Since the depth can't be negative, the depth of the well is X = 38.85 meters when the cost is 12000 naira.

Thus, the equation that connects C and X is C = 100X + 5.33X² and the depth of the well if the cost is 12000 naira is 38.85 meters.

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For the fourth step shown in the "Reasons"

Note that both angles lie on the same straight line which is line RV.

Angles on a straight line sum up to 180 degrees.

Therefore,

The answer is option B; Definition of a linear pair

2inch = 8feet

1 1/2inch = 6feet

2 3/4 inch = 11 feet

4 7/8 inch = 19.5 feet

According to the given question.

1/4 inch = 1ft

⇒ 1 inch = 4ft

Therefore,

2inches = 2 × 4 feet = 8feet

1 1/2inches

= 3/2 inches

= 3/2 × 4feet

= 6feet

2 3/4 inches

= 11/4 inch

= 11/4 × 4feet

= 11 feet

4 7/8 inch

= 39/8 inch

= 39/8 × 4

= 19.5 feet

Hence,

2inch = 8feet

1 1/2inch = 6feet

2 3/4 inch = 11 feet

4 7/8 inch = 19.5 feet

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Answer:

The answer is 9 (B)

Step-by-step explanation:

I got 9 because you have to plug in answer (7, 9, 11, 8) in each equation than add them both together. I first plugged in 7 for x in the equation 9x-5. I got 58. I plugged in 7 for x in the equation 5x+12 and got 47. When I added both the answers together I got 105. The answer was to low because SU has to be 133. I plugged in 9 for x in both equations then added them both and got 133 for SU. I hope this helps.

Answer:

B

Step-by-step explanation:

Answer:

42/100

Step-by-step explanation:

The required correct answer is,

The area under P2 is 1, the area under P1 depends on the standard deviation of the dataset

i.e., Option d. is correct.

What is density curve ?

A density curve is a curve that illustrates the general shape of a data distribution. It is always above the x-axis; the area beneath it is always equal to one whole; the area beneath shows the percentage of all observations that fall in a given range. It is statistically easier to deal with a smooth curve than a histogram.

The bell-shaped density curve, which symbolizes the normal distribution, is the most well-known.

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2500 cheers were there when there were only 10 fans whose jubilation factor was 20.

factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder. For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12. A positive integer greater than 1, or an algebraic expression, that has only two factors (i.e., itself and 1) is termed prime; a positive integer or an algebraic expression that has more than two factors is termed composite. The prime factors of a number or an algebraic expression are those factors which are prime.

suppose c =K F \(J^{2}\) ( k is a parameter )

According to the question

1000 = k× 100×\(4^{2}\)

k = \(\frac{1000}{1600}\) = 0.625

so 0 = 0.625 F \(J^{2}\) (equation )

when F equal to 10 , J = 20

k= 0.625 × 10 ×\(20^{2}\) = 2500

2500 cheers were there when there were only 10 fans whose jubilation factor was 20.

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The required answer is  P ≈  $1,904.76 in the CD to have $2,000 in 2 years with a 2.5% annual simple interest rate.

To determine how much you must put in the Certificate of Deposit (CD) to have $2,000 in 2 years with an annual interest rate of 2.5% using simple interest, follow these steps:

1. First, recall the simple interest formula: I = P × r × t
where,

I is the interest earned, P is the principal (initial amount) amount, r is the interest rate, and t is the time in years.
we know that the interest rate is 2.5% per year and the time period is 2 years.
2. Rearrange the formula to solve for the principal: P = I / (r × t)

3. Since you want to have $2,000 in 2 years, calculate the interest earned:
  Interest earned (I) = $2,000 - (amount you need to deposit)
 
4. Plug the interest rate, time, and interest earned into the rearranged formula:
  P = (2,000 - P) / (0.025 × 2)

5. Solve for P:
  0.05P = 2,000 - P
  1.05P = 2,000
  P ≈ $1,904.76

You should deposit approximately $1,904.76 in the CD to have $2,000 in 2 years with a 2.5% annual simple interest rate.

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To find the area between the circles x^2 + y^2 = 324 and x^2 - 18x + y^2 = 0 in the first quadrant, we convert the equations to polar coordinates. The limits of integration for θ are from 0 to π/2. The first circle corresponds to r = 18, and the second circle has two possibilities: r = 0 (origin) and r = 18cos(θ). Setting up the integral in polar coordinates, we have A = ∫[0, π/2] ∫[0, r] r dr dθ. Evaluating this integral will give us the desired area.

To evaluate the integral that gives the area lying in the first quadrant between the circles x^2 + y^2 = 324 and x^2 - 18x + y^2 = 0, we can convert the equations to polar coordinates and find the limits of integration.

In polar coordinates, the conversion from Cartesian coordinates is given by:

x = r * cos(θ)

y = r * sin(θ)

First, let's convert the equations of the circles to polar coordinates:

1. For the circle x^2 + y^2 = 324:

Replacing x and y with their polar coordinate equivalents:

r^2 * cos^2(θ) + r^2 * sin^2(θ) = 324

r^2 = 324

Taking the square root of both sides, we get:

r = 18

2. For the circle x^2 - 18x + y^2 = 0:

Replacing x and y with their polar coordinate equivalents:

r^2 * cos^2(θ) - 18r * cos(θ) + r^2 * sin^2(θ) = 0

r^2 - 18r * cos(θ) = 0

r(r - 18cos(θ)) = 0

From this equation, we have two possibilities:

a) r = 0

b) r = 18cos(θ)

Now, to find the limits of integration, we need to determine the values of θ where the curves intersect. Since we are interested in the area in the first quadrant, the limits of θ will be between 0 and π/2.

For r = 0, it represents the origin, which is the point of intersection.

For r = 18cos(θ), we can set this equation equal to 18 to find the value of θ:

18cos(θ) = 18

cos(θ) = 1

θ = 0

Therefore, the limits of integration for θ are from θ = 0 to θ = π/2.

Now, we can set up the integral to calculate the area:

A = ∫[0, π/2] ∫[0, r] r dr dθ

The inner integral integrates with respect to r from 0 to r, and the outer integral integrates with respect to θ from 0 to π/2.

Evaluating this double integral will give us the desired area.

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Range - { 6, 7, 8,9 ,10, 11 } is the domain and range of this relation.

What is domain and range in math?

How are the domain and range determined?

the domain and range of this relation -

Domain - { 1 , 2, 3, 4, 5, 6 }

Range - { 6, 7, 8,9 ,10, 11 }

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Answer:

0.99, 0.2, 12, 40/41

if the 1-41 is a 41 then it is the largest if it is a 40 then it is still the largest.

Dan suzy and aaron share 16 slices of pizza in ratio 1:2:5 aaron get 10 clicks of pizza out of the total.

To break it down further, we can first find the portion size (x) by dividing the total number of slices (16) by the sum of the ratios (1 + 2 + 5 = 8).

So, x = 16 / 8 = 2.

This means that each portion represents 2 slices of pizza.

Next, we can use the ratio to find how many portions each person received. We know that Dan received 1 portion, Suzy received 2 portions, and Aaron received 5 portions. So, to find the number of slices each person received, we just need to multiply their portion size (2 slices) by the number of portions they received.

For Dan, it's 1 portion * 2 slices/portion = 2 slices.

For Suzy, it's 2 portions * 2 slices/portion = 4 slices.

And for Aaron, it's 5 portions * 2 slices/portion = 10 slices.

So, in total, Aaron received 10 slices of pizza.

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According to different units  1 sqaure foot value will be change like

1 square foot (ft²) = 0.09290304 square meters (m²)

What is square foot let's understand?

The square foot is an area measurement unit that is used in both the United States and the United Kingdom. It is also used in Bangladesh, India, Nepal, Pakistan, Ghana, Liberia, Malaysia, Myanmar, Singapore, and Hong Kong to a lesser extent. It is described as the surface of a square with 1-foot sides.

1 square foot (ft²) = 0.09290304 square meters (m²)

1 square foot (ft²) = 144.0000002229 square inches (in²)

1 square foot (ft²) = 0.111111106982 square yards (yd²)

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Answer:

12 bracelets

Step-by-step explanation:

The interpretation of the slope and y-intercept of the equation:

Is option D.

From the equation we read that:

- The slope is: 1/4

- The y-intercept is: y = f(0) = 1/4 * 0 + 50 = 50

To solve the algebraic expression, add or subtract the variables with same power of variable.

The result of the given problem after simplifying is,

\(y=7m+n-6\)

Algebraic expression are the expression which consist the variables, coefficients of variables and constants.

The algebraic expression are used represent the general problem in the mathematical way to solve them.

To solve the algebraic expression, add or subtract the variables with same power of variable.

Given information-

The given numbers are,

\(Q=7m+3n\\R=11-2m\\S=n+5\\T=-3-3n\)

All the four number given in the form of unknown number \(m\) and \(n\).

The result, need to be find is,

\(R-S+T+M\)

Let the result of above expression is \(y\). Thus,

\(y=R-S+T+M\)

Put the values to solve it further,

\(y=(7m+3n)-(11-2m)+(n+5)+(-m-3n)\)

Solve it further by open the bracket as,

\(y=7m+3n-11+2m+n+5-m-3n\\y=7m+2m-m+3n+n-3n-11+5\\y=7m+n-6\)

Hence the result of the given problem after simplifying is,

\(y=7m+n-6\)

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The correct choice is: A. The absolute maximum of f on the given interval is at x = 8.

First, let's find the critical points by taking the derivative of f(x) and setting it equal to zero:

f'(x) = -6x^2 + 72x - 192

Setting f'(x) = 0 and solving for x, we get:

-6x^2 + 72x - 192 = 0

Dividing both sides by -6, we have:

x^2 - 12x + 32 = 0

Factoring the quadratic equation, we get:

(x - 4)(x - 8) = 0

So, the critical points are x = 4 and x = 8.

Next, we evaluate the function at the critical points and the endpoints of the interval:

f(3) = -2(3)^3 + 36(3)^2 - 192(3) = -54 + 324 - 576 = -306

f(4) = -2(4)^3 + 36(4)^2 - 192(4) = -128 + 576 - 768 = -320

f(8) = -2(8)^3 + 36(8)^2 - 192(8) = -1024 + 2304 - 1536 = -256

f(9) = -2(9)^3 + 36(9)^2 - 192(9) = -1458 + 2916 - 1728 = -270

From these evaluations, we can see that the absolute maximum of f(x) on the interval [3, 9] is -256, which occurs at x = 8.

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Answer:

Over the interval [2, 4], the local minimum is –8.

Over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0.

Answer:

b,c and D

Step-by-step explanation:

Over the interval [2, 4], the local minimum is –8.

Over the interval [3, 5], the local minimum is –8.

Over the interval [1, 4], the local maximum is 0.

Answer:

7 days or, more specifically 7.455 days

Step-by-step explanation:

71 miles divided up into groups of 11

71 mi. ÷ 11 mi. at a time

71 ÷ 11 = 6.455

rounds up to 7 days

6 days will it take him to run 712 miles.

The division is the process of repetitive subtraction. It is the inverse of the multiplication operation. It is defined as the act of forming equal groups. While dividing numbers, we break down a larger number into smaller numbers such that the multiplication of those smaller numbers will be equal to the larger number taken.

Given

Emilio has to run 712 miles every week to train for the football team.

If he runs 112 miles every day

Based on the given conditions

= \(\frac{712}{112}\)

= 6.35

≅ 6 days

Thus, 6 days will it take him to run 712 miles.

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Given:

The equation of line d is perpendicular to line c is y=-4/3 x+5.

The equation of line is y=3/4 x-2.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

In the equation of line is y=3/4 x-2, slope=m=3/4

The slope of a line perpendicular to given line is m1=-1/m2

So, the slope of a perpendicular line is -4/3

Substitute m=-4/3 and (x, y)=(6, -3) in y=mx+c, we get

-3=-4/3 (6)+c

⇒ -3=-8+c

⇒ c=5

Now, substitute m=-4/3 and c=5 in y=mx+c, we get

y=-4/3 x+5

Therefore, the equation of line d is perpendicular to line c is y=-4/3 x+5.

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Answer:

326.5

Step-by-step explanation: