A linear function has an x-intercept of 12 and a slope of a. How does this function compare to the linear function that is
represented by the table?
16
OIt has the same slope and the same y-intercept.
O Ithas the same slope and a different y-intercept.
OIthas the same y-intercept and a different slope,

Answer:

F= 1 /4 y+ 9 /4

Step-by-step explanation:

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Answer:

3.78%

Step-by-step explanation:

The formula for compound interest is given by:

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

Thus, we can plug in 8500 for P, 11022 for A(t), 1 for n, and 7 for t to find r:

Step 1:  Plug in the values and simplify:

11022 = 8500 * ( 1 + r/1)^(7 * 1)

11022 = 8500 * (1 + r)^(7)

Step 2:  Divide both sides by 8500:

(11022 = 8500 * (1 + r)^(7)) / 8500

11022/8500 = (1 + r)^(7)

5511/4250 = (1 + r)^(7)

Step 3:  Raise both sides to the 1/7 power (this is the same as taking the 7th root of both sides):

(5511/4250 = (1 + r)^(7))^(1/7)

1.037815641 = 1 + r

Step 4:  Subtract 1 from both sides to find r:

(1.037815641 = 1 + r) - 1

0.0378154607 = r

Step 5:  Multiply 0.0378154607 by 100 to find the interest rate as a percentage:

0.0378154607 * 100

3.78156407 = %

Step 6:  Round to the nearest two decimal places:

3.78

Thus, the interest rate is about 3.78%

a) The (9,009, 10,585) range represents the 99% confidence interval for the mean number of steps taken on an average workday for all New York City employees who wear activity trackers. No, we are unable to determine the likelihood of specific values using the confidence interval. Only inferences about the population mean can be drawn from it.

A 99% confidence interval for the mean needs to be calculated.

Since the population standard deviation is unknown, we must infer it from the sample standard deviation in order to get the critical number using a t-students distribution.

Sample Mean(M) = 9,797

Sample Standard Deviation(s) = 2,313.

Sample Size(N) = 61

When σ is unknown, an estimation of σM is made by dividing s by the square root of N:

S = s/√n

S = 2313/√61

S = 2313/7.8102

S = 296.1512

These sample size's degrees of freedom are:

df = n - 1

df = 61 - 1

df = 60

With 61 degrees of freedom and a 99% confidence interval, the t-value is 2.66.

The Margin of Error calculated as:

MOE = t × S

MOE = 2.66 × 296.1512

MOE = 787.7622

The confidence interval's lower and upper bounds are as follows:

Lower Bound = M - MOE

Lower Bound = 9797 - 787.7622

Lower Bound = 9,009.2378

Lower Bound = 9,009(approx)

Upper Bound = M + MOE

Upper Bound = 9797 + 787.7622

Upper Bound = 10,584.7622

Upper Bound = 10,585(approx)

We have a 95% confidence interval between 9,009 and 10,585 steps as the mean number of steps taken on a normal workday for all New York City employees using activity trackers.

b) The value of 8,500 steps is outside the confidence interval, which indicates that it is a high figure for the average number of steps taken by all New Yorkers using activity trackers.

The confidence interval cannot be used to calculate the likelihood of specific values.

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The complete question is:

Activity trackers are electronic devices that people wear to record physical activity. Researchers wanted to estimate the mean number of steps taken on a typical workday for people working in New York City who wear such trackers. A random sample of 61 people working in New York City who wear an activity tracker was selected. The number of steps taken on a typical workday for each person in the sample was recorded. The mean was 9,797 steps and the standard deviation was 2,313 steps.

a. Construct and interpret a 99 percent confidence interval for the mean number of steps taken on a typical workday for all people working in New York City who wear an activity tracker.

b. A wellness director at a company in New York City wants to investigate whether it is unusual for one person working in the city who wears an activity tracker to record approximately 8,500 steps on a typical workday. Is it appropriate to use the confidence interval found in part (a) to conduct the investigation.

Answer:

let me try this first and then I will help you is it ok

Answer: C

Step-by-step explanation:

Just go 2 units up on the grid and one to the left

Answer:

(3,6)

Step-by-step explanation:

First, find the coordinate of the school. The school is at (4,4).

Coordinates are written as (x,y). x represents the side to side coordinate, and y represents the up down coordinate. so if the house is one unit left of the school, subtract one from the x coordinate to get 3. if the house is two units up from the school, add 2 to the y coordinate to get 6. and there you go!

Answer:

10-x

HOPE THIS HELPS!

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Answer:

The margin of error is multiplied by 1.41, which is 1 divided by the square root of 5.

Step-by-step explanation:

The margin of error is:

\(M = z*\frac{\sigma}{\sqrt{n}}\)

In which z is related to the confidence level, \(\sigma\) is the standard deviation of the population and n is the size of the sample.

The margin of error is inverse proportional to the square root of the sample size.

Then

Sample size n:

\(M = z*\frac{\sigma}{\sqrt{n}}\)

Modified(half the sample size):

\(M_{M} = z*\frac{\sigma}{\sqrt{0.5n}}\)

Ratio

\(\frac{M_{M}}{M} = \frac{z*\frac{\sigma}{\sqrt{0.5n}}}{z*\frac{\sigma}{\sqrt{n}}} = \frac{\sqrt{n}}{\sqrt{0.5n}} = \frac{\sqrt{n}}{\sqrt{0.5}*\sqrt{n}} = \frac{1}{\sqrt{0.5}} = 1.41\)

The margin of error is multiplied by 1.41, which is 1 divided by the square root of 5.

Jordyn will earn $135 in interest if she invests $500 at 2.25% simple interest for 12 months.

To calculate the interest Jordyn will earn, we can use the formula for simple interest:

Interest = Principal × Rate × Time

In this case, the principal is $500, the rate is 2.25% (or 0.0225 as a decimal), and the time is 12 months.

Plugging in these values into the formula, we get:

Interest = $500 × 0.0225 × 12

The rate of 2.25% is expressed as a decimal by dividing it by 100. Multiplying this rate by the principal ($500) and the time in years (12 months/12 = 1 year) gives us the interest earned.

Simplifying the expression, we have:

Interest = $500 × 0.27

Calculating this expression, we find:

Interest = $135

Therefore, if Jordyn invests $500 at a simple interest rate of 2.25% for 12 months, she will earn $135 in interest. This means that after one year, her investment will grow by $135, resulting in a total of $635 ($500 + $135).

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The difference between the prices of both books is: $4,266.67.

Let's call the price of the cheapest book "x". According to the statement, the other book costs twice the price of the cheapest one, that is, "2x". Furthermore, we are told that this second book is worth $200 more than the other.

Therefore, we can establish the following equation:

x + 2x + $200 = $13,000

Add like terms:

3x + $200 = $13,000

We subtract $200 from both sides of the equation:

3x = $12,800

We divide both sides by 3 to solve for "x":

x = $4,266.67

The price of the most expensive book is 2 times the price of the cheapest, that is, 2 * $4,266.67 = $8,533.33.

The difference between the prices of both books is:

$8,533.33 - $4,266.67 = $4,266.67.

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Answer:

1.a 0.10

b 0.10

2. 1696.013

1696.0120

Step-by-step explanation:

The exact value  of \(sin 2x\) is \(4√5/9.\)

Given that \(sec x = 3/2 and csc y = 3\)where x and y are in the 2x = 2 sin x quadrant, we need to find the exact value of sin 2x.

In the first quadrant, we have the following values of the trigonometric ratios:\(cos x = 2/3 and sin y = 3/5\)

Also, we know that sin \(2x = 2 sin x cos x.\)

Now, we need to find sin x.

Having sec x = 3/2, we can use the Pythagorean identity

\(^2x + 1 = sec^2xtan^2x + 1 = (3/2)^2tan^2x + 1 = 9/4tan^2x = 9/4 - 1 = 5/4tan x = ± √(5/4) = ± √5/2\)

As x is in the first quadrant, it lies between 0° and 90°.

Therefore, x cannot be negative.

Hence ,\(tan x = √5/2sin x = tan x cos x = √5/2 * 2/3 = √5/3\)

Now, we can find sin 2x by using the value of sin x and cos x derived above sin \(2x = 2 sin x cos xsin 2x = 2 (√5/3) (2/3)sin 2x = 4√5/9\)

Therefore, the exact value  of sin 2x is 4√5/9.

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Answer:

30) =

36) >

Explanation:

|x| means the absolute value and cannot be negative, so |5| and |-5| are the same.

Answer:

30= 5 > -5                         36=  - 1 3/8 is bigger.

Step-by-step explanation:

the closer the negative number is to 0 the bigger it is. An example -1 is bigger that - 100

Answer:

78.75 or 78 3/4

Step-by-step explanation:

Answer:

well im in 7th sorry i cant help

Step-by-step explanation:

Answer:

6 years

Step-by-step explanation:

if we want to know how much i will get with interest

simple interest amount = principal amount × (rate / m) × n

plus the initial quantity

where m is 12 months per year

and n is the number of months

\(4451=2887(\frac{0.09}{12months/year})(n)+2887\\\\4451=2887[\frac{0.09}{12}(n)+1]\\\\(\frac{0.09}{12}\cdot n)+1=\frac{4451}{2887}\\\\\frac{0.09}{12}\cdot n=1.54-1\\\\n(0.09)=12(0.54)\\\\n=\frac{12(0.54)}{0.09}\\\\n=72.23\longleftarrow months\)

so we need to convert it to years

\(72.23=12(6)+0.019\)

6 years and 0 months

I apologize if there is some mistake in my answer

The probability that all of them are real is 0.01875 or 1.875%

If the diamonds are replaced after each draw:

The probability of drawing a real diamond is 9/14, found by making the numerator the number of real diamonds and adding the total number of diamonds to find the denominator. 5+9 = 14.

To find the probability of all 9 diamonds drawn being real, multiply 9/14 by itself 9 times.  = 387420489/ 20661046784. This creates a probability of 387420489/ 20661046784. This cannot be reduced because there is no common factor. To express as a decimal, divide. 387420489/ 20661046784 = 0.01875. To turn this into a percent, multiply by 100. 0.01875*100 = 1.875

Hence, the probability that all of them are real is 0.01875 or 1.875%

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Answer:

11 22 31 41

Step-by-step explanation:

yes thats it dd

f

d

d

d

d

Answer:

6.polygon ABCD is congruent to polygon EFGH

The value of correct expression are equal to a real number are,

b. (-3i)¹²

d. (4 + 5i)(4 - 5i)

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

All the expressions are,

a. (-4i)¹¹

b. (-3i)¹²

C. (2 + 3i)²

d. (4 + 5i)(4 - 5i)

e. (6 + 8i)(8 + 6i)

Now, We can simplify as;

a. (-4i)¹¹

⇒ (- 4)¹¹ (- i)¹¹

⇒ (- 4)¹¹ (- i)

b. (-3i)¹²

⇒ (- 3)¹² (i)¹²

⇒ (- 3)¹²

C. (2 + 3i)²

⇒ 4 + 9i² + 12i

⇒ 4 - 9 + 12i

⇒ - 5 + 12i

d. (4 + 5i)(4 - 5i)

⇒ 4² - (5i)²

⇒ 16 + 25

⇒ 41

e. (6 + 8i)(8 + 6i)

⇒ 48 + 36i + 64i + 48i²
⇒ 48 + 100i - 48

⇒ 100i

Thus, The value of correct expression are equal to a real number are,

b. (-3i)¹²

d. (4 + 5i)(4 - 5i)

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The phasor form of a sinusoid represents the amplitude and phase angle of the sinusoid in complex number notation. In this case, the phasor form of \(8 sin(20t 57)\) would be 8 ∠57°. The amplitude, 8, is the magnitude of the complex number, and the phase angle, 57°, is the angle of the complex number in the complex plane.

In terms of amplitude and phase angle, a sinusoidal waveform is mathematically represented in phasor form. Electrical engineering frequently employs it to depict AC (alternating current) circuits and signals. A complex number that depicts the magnitude and phase of a sinusoidal waveform is called a phasor. The phase angle is represented by the imaginary component of the phasor, whereas the real part of the phasor represents the waveform's amplitude. Complex algebra can be used to analyse AC circuits using the phasor form, which makes computations simpler and makes it simpler to see how the circuit behaves.

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Answer:

15

Step-by-step explanation:

Opposite sides in a parallelogram are equal.

2x - 5 = x + 10

Subtract x and add 5 on both sides.

2x - x = 10 + 5

Combine like terms.

x = 15

Answer:

\(\boxed{\red {x= 15}}\)

Step-by-step explanation:

We know that opposite sides in a parallelogram are equal.

So, in this sum value of the sides in a parallelogram

\(x + 10 \: \: \: and \: \: \: 2x - 5\)

So now let's create an equation

\(x + 10 = 2x - 5\)

Now let's solve for x

\(x + 10 = 2x - 5 \\ 10 + 5 = 2x - x \\ 15 = x\)

The following statements are true:

1. During the first 10 days the professor's standard deviation was more than 0.

4. It is impossible to tell anything about the professor's standard deviation for the first 10 days.

6. Considering all 11 days, the professor's standard deviation was higher than the standard deviation of the first 10 days.

The standard deviation is a measure of how spread out a set of data is. In this case, the data is the prices of the value meals that the professor orders. If all 10 of the first meals cost $5.39, then the standard deviation would be 0.

This is because there is no variation in the data. However, on the 11th day, the professor orders a meal that costs $4.38. This adds variation to the data, which means that the standard deviation will be greater than 0.

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The value trigonometric rations of sinA = √5/2 and cosA = 1/2.

Given that,

SinA = √3 cosA

Divide both side by cos A

⇒ SinA/cosA = √3

Since we know that,

Tan A = SinA/cosA

Therefore,

   SinA/cosA = √3

⇒          tan A = √3

Squaring both sides, we get

⇒          tan² A = 3

⇒      sec²A - 1 = 3

⇒           sec²A = 4

Taking square root both sides, we get

⇒             secA = 2

⇒           1/cosA = 2

⇒              cosA = 1/2

Now again squaring both sides we get

⇒              cos²A = 1/4

⇒           sin²A - 1 = 1/4

⇒                sin²A = 1/4 + 1

⇒                sin²A = 5/4

Taking square root both sides, we get

⇒                sinA = √5/2

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Answer:

x= 45, y = 90

Step-by-step explanation:

3x + x = 180 (angles in opposite segments are supplementary)

4x = 180

x = 45

y = 2(45) = 90 (angle at centre = 2 times angle at circumference)

The probability that a randomly selected household in the area will be in violation of the local law prohibiting owning more than three pets the number of households that own more than three pets divided by the total number of households in the area.

To calculate the probability, we need to determine the number of households that own more than three pets and the total number of households in the area. Let's assume there are a total of N households in the area.

The number of households that own more than three pets can vary, so we'll denote it as X. Now, to find the probability, we divide X by N. The probability can be written as P(X > 3) = X/N.

However, we don't have specific information about the number of households or the distribution of pet ownership in the area. Without these details, it is not possible to provide an exact probability. To calculate the probability accurately, we would need more information about the population of households in the area, such as the total number of households and the distribution of pet ownership. With this information, we could determine the number of households violating the law and calculate the probability accordingly.

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Answer:

114

Step-by-step explanation:

9(4)=36

9(4)=36

14(3)=42

36+36+42=114

Hope this helped!!

The formula for the volume of a cone is:

V = (1/3)πr²h

where r is the radius of the base, h is the height of the cone, and π is pi.

In this case, the slant height is given as 17 cm, which we can use with the radius to find the height of the cone using the Pythagorean theorem:

h² = s² - r²

h² = 17² - 8²

h² = 225

h = 15

Now that we have the height, we can plug in the values for r and h into the formula for the volume:

V = (1/3)π(8²)(15)

V = (1/3)π(64)(15)

V = (1/3)(960π)

V = 320π

Therefore, the volume of the cone is 320π cubic cm. Answer: 320π.

Answer:

z=0

Step-by-step explanation:

Hope this helps and have a great day!