For the following function, find the slope of the graph and the y-intercept. Then sketch the graph. y=4x+3 The slope is

If a random sample of 60 computers, the mean repair cost was $150 with a population standard deviation of $36, the 99% confidence interval for the population mean is ($138, $162). Correct option is B.

To construct a confidence interval for the population mean, we can use the formula:

Confidence Interval = sample mean ± margin of error

The margin of error is calculated using the formula:

Margin of Error = z * (population standard deviation / sqrt(sample size))

Given that the sample mean repair cost is $150, the population standard deviation is $36, and the sample size is 60, we can proceed with calculating the confidence interval.

First, we need to determine the critical value, z, for a 99% confidence level. Since the sample size is large (n > 30), we can use the standard normal distribution. For a 99% confidence level, the z-value is approximately 2.576.

Next, we calculate the margin of error:

Margin of Error = 2.576 * (36 / sqrt(60)) ≈ 12

Finally, we construct the confidence interval:

Confidence Interval = $150 ± $12

The 99% confidence interval for the population mean is ($138, $162).

Correct option is B.

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Answer:

Aubrey is correct because the area of the new parallelogram is 12 (6) = 72 square inches. The original area is 18 square inches. Since 4 (18) = 72, the new parallelogram has 4 times the area of the original.

Step-by-step explanation:

A parallelogram with a base of 6 inches and height of 3 inches. A side has a length of 5 inches.

Aubrey is correct because the area of the new parallelogram is 12 (6) = 72 square inches. The original area is 18 square inches. Since 4 (18) = 72, the new parallelogram has 4 times the area of the original.

Aubrey is correct because the area of the new parallelogram is 10 (7) = 70 square inches. The original area is 18 square inches. Since 4 (18) = 72, it is about 4 times larger than the original.

Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 18 square inches so the new parallelogram will have an area of 2 (18) = 36, or two times more than the original.

Aubrey is incorrect because if one doubles each dimension, then the area will automatically be doubled as well. The original area is 30 square inches so the new parallelogram will have an area of 2 (30) = 60, or 2 times more than the original.

Workings

Area of a parallelogram=base×height

Original parallelogram

Base=6 inches

Height=3 inches

Area=base×height

=6×3

=18 square inches

New parallelogram with doubled dimensions

Base=6 inches doubled=12 inches

Height=3 inches doubled=6 inches

Area=base×height

=12×6

=72 square inches

New area=4 times original area

New area=4×18

New area=72 square inches

Answer:
the answer is A

Step-by-step explanation:

i wan to make this easy and fast

Answer: Y= -5x+4

Step-by-step explanation:

Answer:

E.

Step-by-step explanation:

E gets prio rather than D & F, so E is the first letter. after that, D has more prio than F. so the answer is EDF.

The minimum electric rate in cents per kwh for which the 12-year total cost will be less for the first freezer is 8.61 cents

Let x =  minimum electric rate (Cents/kWh)

Total months in 12 years is 12*12 = 144 m

1st freezer

Total cost over 12 years is

623.95 (cost) + (90 kWh/m)*(144 m)(x/100 $/kWh)

= 623.95 + 129.6x

2nd freezer

Total cost over 12 years is

500 + 100*144*(x/100)

= 500 + 144x

For the 1st freezer to cost less over 12 years,

623.95 + 129.6x < 500 + 144x

123.95 < 14.4x

8.61 < x

The minimum rate is 8.61 cents per kWh

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Answer:

NULL ; TRUE

Step-by-step explanation:

The sampling distribution is on the assumption that the null hypothesis is true .

The null hypothesis is a general statement that states that there

is no relationship between two phenomenon's under

consideration or that there is no association between two groups.

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The sampling distribution is based on the assumption that the null hypothesis is TRUE.  

A null hypothesis is a general statement that something is. There is no relationship between the two phenomena under or consider that there is no relationship between the two groups.  

The sampling distribution is based on the assumption that the null hypothesis is TRUE.

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The cardioid is recognized as a particular instance of an epicycloid and is formed by (x2 + y2 + an x)2 = a2(x2 + y2).

A two-dimensional plane figure called a cardioid features a heart-shaped curvature. The Greek word "cardioid," which meaning "heart," is the source of the word "cardioid." Thus, it is referred to as a heart-shaped curve.

The polar pattern of a cardioid microphone gives it its name. It is classified as a directional microphone since only noises from the front and sides may be picked up by it, and the direction has an impact on the sound image that is recorded.

here the explanation:-

The equation for the heart is (x2 + (9/4)*(y2 + z2 -1)3 - (x2*(z3) -(9/200)*(y2*(z3)).

The cardioid is recognized as a particular instance of an epicycloid and is formed by (x2 + y2 + an x)2 = a2(x2 + y2).

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The length of side CD is equal to 11 units.

Given coordinates of rectangle are A(-7,-5), B(-7,6),C(-4,6) ,D(-4,-5)

We are require to find the length of side CD.

Rectangle is a two dimensional figure whose two opposite sides are equal to each other. Distance between two coordinates is the equal to length of a side.

We know that the distance means how far two points are located.

Coordinates of  A(-7,-5), B(-7,6),C(-4,6) ,D(-4,-5).

Distance=\(\sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} }\) where (\(x_{1} ,y_{2} )(x_{2} ,y_{2} )\) are the coordinates of two ends of a line.

CD=\(\sqrt{(-5-6)^{2} +(-4+4)^{2} }\)

=\(\sqrt{11^{2}+0^{2} }\)

=\(\sqrt{121}\)

=11 units.

Hence the length of side CD is 11 units.

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Question is wrong as it should be :

Coordinates of rectangle A(-7,-5), B(-7,6),C(-4,6) ,D(-4,-5) and find the length of CD.

Answer:

Infinitely many

Step-by-step explanation:

I did it on edge 2020

Answer:

Step-by-step explanation:

Exponent rule:

\(\boxed{(a^{m})^{n}=a^{m*n}}\)

\((x^{\frac{2}{5}})^{10} = x^{\frac{2}{5}*10} \\\\\\\)

           \(=x^{2*2}\\\\=x^{4}\)

To find the median of a set of numbers, we need to first put the numbers in order from least to greatest. In this case, the ages of the Carnegie children are 3, 9, 18, and 24 years old. Since there are 4 numbers in this set, the median is the average of the middle two numbers, which are 9 and 18. The median of the ages of the Carnegie children is (9 + 18) / 2 = 27 / 2 = 13.5 years old.

To find the mean of a set of numbers, we need to add the numbers together and then divide the sum by the number of numbers in the set. In this case, the sum of the ages of the Carnegie children is 3 + 9 + 18 + 24 = 54 years old. Since there are 4 children, the mean age is 54 years / 4 children = 13.5 years old. Therefore, the mean of the ages of the Carnegie children is 13.5 years old.

Answer:

Median: 13.5

Mean: 13.5

Step-by-step explanation:

To get the median, take the middle value. Since there are two middle values, add them together and divide them by two.

To get the mean, add all the values together and divide the sum by the number of values. In this instance, mean and median are the same.

Solution:

Given:

Account 2 details:

Assume a year is 365 days;

Using the compound interest formula to get the amount;

Hence, substituting the values;

Therefore, the balance in account 2 will be $9633.55

Answer:

A

Step-by-step explanation:

22 successes out of a group of 40 means 22/40 were good. Now, simplify 22/40. Both can be divided by 2.

22/2 = 11

40/2 = 20

Now you have 11/20. Put this in decimal form and you have 0.55

Option A answer is 0.55

The proportion of a sample is the ratio of the number of successes or defeats to the total size of the sample, it is used for understanding which trend is more followed and also has many uses in the real world.

The size of the sample is 40.

There are 22 successes in the sample.

To find the proportion of success we have to find the ratio of 22 and 40 which is 11:20, and in numerical terms 0.55

Hence option A is correct, the proportion is 0.55

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Answer:

the answer is 2

Step-by-step explanation:

The equation which represent the three squares which is divided into the 5 fifths is,

\(15 \times \dfrac{1}{5} = 3\)

A fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

\(\dfrac{a}{b}\)

Here (a) is the numerator and (b) is the denominator.

A multiple of a fraction is the number which is n times of the original function.

The model represents,

\(3 \div 1/5\)

Here, the total number of square are given is 3. These three square are then divided into the one fifth.

Thus, we get total 3 times of 5 one fifth which is equal to the entire 3 squares

.

Thus, the equation can be written for this condition as,

\(15 \times \dfrac{1}{5} = 3\)

Hence, the equation which represent the three squares which is divided into the 5 fifths is,

\(15 \times \dfrac{1}{5} = 3\)

Option B is the correct option.

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The relationship between the line segments formed on each transversal is

given by the three parallel lines theorem.

Reasons:

The question is a four part question, with part A being to construct three parallel lines and two transversals to intersect the parallel lines

The equation of the parallel lines are;

y = x, and y = x + 1

The point of intersection of transversal 1 and the parallel lines y, and z

(0.2, 0.2), and (0.3, 0.8)

The length of segment AB = √((0.3 - 0.2)² + (0.8 - 0.2)²) = 0.1·√(37)

The point of intersection of transversal 1 and the parallel lines x, and y

(0.3, 0.8), and (0.4, 1.4)

The length of segment CB = √((0.4 - 0.3)² + (1.4 - 0.8)²) = 0.1·√(37)

The ratio of the lengths of the line segments formed by the transversal 1, AB:CB is found as  follows;

\(\displaystyle \frac{AB}{CB} = \mathbf{\frac{0.1 \cdot \sqrt{37} }{0.1 \cdot \sqrt{37}}} = 1\)

The point of intersection of transversal 2 and the parallel lines y and z are;

(0.8, 0.8), and (0.7, 1.2)

The length of segment EF = √((0.7 - 0.8)² + (1.2 - 0.8)²) = 0.1·√(17)

The point of intersection of transversal 2 and the parallel lines x and y are;

(0.7, 1.2), and (0.6, 1.6)

The length of segment DE = √((0.6 - 0.7)² + (1.6 - 1.2)²) = 0.1·√17

The ratio of the lengths of the line segments formed by the transversal 2, EF:DE is found as  follows;

\(\displaystyle \frac{EF}{DE} =\frac{0.1 \cdot \sqrt{17} }{0.1 \cdot \sqrt{17}} = 1\)

Therefore:

The ratio of the lengths of the two line segments formed on each transversal are equal.

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Answer:

if I can't explain in one line, then I will include the steps in the explanation.

Step-by-step explanation(Q3):

\(3^2-\left(5-3\right)^3+6\\5-3=2\\3^2-2^3+6\\3^2=9\\9-2^3+6\\2^3=8\\9-8+6\\9-8=1\\1+6\\1+6=7\\=7\)

Hope it helps!

Answer:-12\(x^{2}\)-9x-4584671418

Step-by-step explanation:

Answer:

A. It is in standard form because the exponents are in order from highest to lowest

Step-by-step explanation:

On edg 2021

The area of the complex figure is 1863 m².

What is area?

Area is a measure of the size or extent of a two-dimensional surface or shape, such as a square, circle, or rectangle. It is the amount of space inside the boundaries of a shape, usually measured in square units such as square meters (m²), square feet (ft²), or square centimeters (cm²).

The area of give figure :

= area of two rectangles + area of middle rectangle

we know that area of rectangle is length* breadth

so, area of give two rectangles = 2 × length × breadth

                                                  = 2 × 31 × 23

                                                   = 1426m²

similarly, area of the middle rectangle  = length × breadth

                                                                =  (69-23-23) × (31-12)

                                                                = 23 × 19

                                                                = 437 m²

∴ The area of give figure= 1426m²+437 m²

                                        = 1863 m²

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1. For the triple integral ∫∫∫ f(x, y, z) dV with f(x, y, z) = x and Σ being the part of the plane x + 4y + z = 10 in the first octant, the limits of integration are 0 ≤ x ≤ 10, 0 ≤ y ≤ (10 - x)/4, and 0 ≤ z ≤ 10 - x - 4y.

2. For the triple integral ∫∫∫ f(x, y, z) dV with f(x, y, z) = y² and Σ being the part of the plane z = x for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 4, the limits of integration are 0 ≤ x ≤ 2, 0 ≤ y ≤ 4, and 0 ≤ z ≤ x.

1. To evaluate ∫∫∫ f(x, y, z) dV, where f(x, y, z) = x and Σ is the part of the plane x + 4y + z = 10 in the first octant:

We need to find the limits of integration for x, y, and z within the given region Σ. In the first octant, the region is bounded by the planes x = 0, y = 0, and z = 0. Additionally, the plane x + 4y + z = 10 intersects the first octant, giving us the limits: 0 ≤ x ≤ 10, 0 ≤ y ≤ (10 - x)/4, and 0 ≤ z ≤ 10 - x - 4y. Integrating f(x, y, z) = x over these limits will yield the desired result.

2. For ∫∫∫ f(x, y, z) dV, where f(x, y, z) = y² and Σ is the part of the plane z = x for 0 ≤ x ≤ 2 and 0 ≤ y ≤ 4:

The given region Σ lies between the planes z = 0 and z = x. To evaluate the triple integral, we need to determine the limits of integration for x, y, and z. In this case, the limits are: 0 ≤ x ≤ 2, 0 ≤ y ≤ 4, and 0 ≤ z ≤ x. Integrating f(x, y, z) = y² over these limits will give us the final result.

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Here to solve the probability of this sum, it is difficult to say that the probability without no information.

(a)The probability that the team wins the debate with a junior giving the closing argument is 0.083.

(b) To design a simulation to estimate the probability that a sophomore is never selected to give the closing argument in the next 3 debates, one could randomly assign a closing argument speaker for each debate using a table of random digits. The table would have two columns: one for sophomores and one for juniors and seniors. The probability of a sophomore being selected would be 20%, and the probability of a junior or senior being selected would be 80%. The simulation would be run for 3 debates and the number of times a sophomore is never selected would be recorded. This process would be repeated a number of times to estimate the probability of a sophomore never being selected. (e) Based on the dot plot, it appears that there is some evidence that the sophomores were purposely ignored, as there are several simulated sets of 5 debates where a sophomore was not selected to give the closing argument. However, without more information, it is difficult to say for certain if this is enough evidence to support the claim that the sophomores were purposely ignored.

A larger sample size or a more detailed analysis of the simulation results may be needed to make a more convincing determination.

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f(x) dx = 23 and 30, g(x) dx = 7 and 15 are the correct options.

We are given that:

∫f(x) dx = 10       ........(i)

∫[g(x) - 2f(x)] dx = -12    ......(ii)

∫f(x) dx = 17    ..........(iii)

∫g(x) dx = 7    ..........(iv)

∫f(x) dx = 30    ........(v)

∫f(x) dx = 23    ........(vi)

2∫g(x) dx = 16   ......(vii)

5∫g(x) dx = 75  ........(viii)

On solving the above equations, we get,

f(x) = 10   ......from (i)

f(x) = -1  ..........from (ii)

f(x) = 17  .........from (iii)

g(x) = 7   ..........from (iv)

f(x) = 30   .........from (v)

f(x) = 23   .........from (vi)

g(x) = 8  ...........from (vii)

g(x) = 15   .........from (viii)

Therefore, f(x) dx = 23 and 30, g(x) dx = 7 and 15 are the correct options.

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The amount of caffeine C in a pregnant woman's body t hours after consuming is 94 × \(0.944^t\)

"Consuming" refers to the act of ingesting or taking in a substance, usually food or drink, into one's body. In the context of the problem given, consuming refers specifically to the act of drinking or ingesting a 16-oz. cup of iced tea that contains a certain amount of caffeine.

The amount of caffeine C in a pregnant woman's body t hours after consuming a 16-oz. cup of iced tea can be calculated using the formula:

C = Co × \((1 - 0.056)^{t}\)

where Co is the initial amount of caffeine consumed (in milligrams) and t is the time elapsed (in hours).

In this case, Co = 94 mg (the amount of caffeine in the 16-oz. cup of iced tea). Therefore, the amount of caffeine in a pregnant woman's body t hours after consuming the iced tea is:

C = 94 × \((1 - 0.056)^t\)

Simplifying the expression, we get:

C = 94 × \(0.944^t\)

So, for example, if 2 hours have elapsed since the woman consumed the iced tea, the amount of caffeine in her body would be:

C = 94 × 0.944² = 82.6 mg

Therefore, The amount of caffeine C in a pregnant woman's body t hours after consuming is 94 × \(0.944^t\)

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Answer:

54 60

----- = ------

x 100

goal is 90 dollars

Step-by-step explanation:

cross multiply then divide

Answer: 60

Step-by-step explanation:

See

Hence

m<COB=60°

Answer:

x-y+2z=3

Step-by-step explanation:

EZ

Answer:

4.25

Step-by-step explanation:

she has a total of 20 dollars and she wats to buy ice cream each at 3.15 for a total of 5 people including her self.

so 3.15(5) is 15.75

then subtract 15.75 from 20

20 - 15.75 = 4.25

Answer:

48

Step-by-step explanation:

91+41+?=180

91+41=132

180-132=48

Since H is the midpoint of the line GI

that means it divides the line into two equal sides

GH = HI

4x = 2x + 6

4x - 2x = 6

2x = 6

x = 3

Hence proved.

H is the midpoint of GI (given)

GH = 4x (given)

HI = 2x + 6 (given)

GH = HI (H is the midpoint)

4x = 2x + 6 (proven)

x = 3 (given)

4(3) = 2(3) + 6 (x = 3)

12 = 6 + 6

12 = 12