Vhat is the equation of the line that is parallel to the
given line and passes through the point (2, 3)?
O x + 2y = 4
O x + 2y = 8
O 2x + y = 4
O 2x + y = 8

The probability of observing such an extreme result by chance alone is 0.0124.

To find the P-value for a two-tailed test of hypothesis, we need to first determine the significance level (alpha) of the test. Let's assume a significance level of 0.05, which is a common choice.

Since this is a two-tailed test, we need to find the probability of observing a test statistic as extreme or more extreme than 2.5 in either direction. We can find this probability using a standard normal distribution table or a calculator.

Using a standard normal distribution table, we can find that the probability of observing a z-score of 2.5 or greater is 0.0062. The probability of observing a z-score of -2.5 or smaller is also 0.0062. Therefore, the P-value for the two-tailed test of hypothesis is:

P-value = 2 * 0.0062

P-value = 0.0124

This means that if the true proportion of business students who have personal computers at home differs from 30%, with a significance level of 0.05, and we obtain a test statistic of 2.5, then the probability of observing such an extreme result by chance alone is 0.0124.

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The required area of the lune is (D) √3/4 - π/24.

The measurement that expresses the size of a region on a flat or curved surface is termed area.

Surface refers to the area of a surface or the boundary of a tri structure, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

So,

The lune's area is equal to the smaller semicircle's area minus the segment's area.

The area of the segment is equal to the sum of the areas of the sector and the triangle formed by the intersection points and the larger semicircle's center.

Additionally, because all of the sides are one unit, the triangle thus constructed is an equilateral triangle.

Area of the lune = π * 1/8 (60/360 * π * 1² - √3/4 * 1²)

Area of the lune = π/8 - π/6 + √3/4

= √3/4 - π/24

Therefore, the required area of the lune is (D) √3/4 - π/24.

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Answer:

Yes

Step-by-step explanation:

It is reflective

Answer: c

Step-by-step explanation:

\(============================\)

First, let's use the Slope Formula to find the slope:

\(\pmb{\displaystyle\frac{y2-y1}{x2-x1} }\)

\(\pmb{\displaystyle\frac{4-1}{3-0} }\)

\(\pmb{\displaystyle\frac{3}{3}}\)

Which simplifies to

\(\pmb{1}\)

So the slope is 1.

Now, here's a point that the line passes through:

(0, 1)

Write the equation in point-slope form:

\(\pmb{y-y1=m(x-x1)}\)

y-1=1(x-0)

================================================

Hope everything is clear; if you need any more clarification/explanation, kindly let me know, and I will comment and/or edit my answer :)

Answer:

first one y: -3, 0, 3, 6, 12

second one y:5, 2, 0, 2, 5

Step-by-step explanation:

for the first one the equation is y=3x

so when it goes as x:-1, 0, 1, 2, 4

so you should multiply each number by 3 as the equation does

(just replace each number by x in the equation)

so y: -3, 0, 3, 6, 12

next one: equation is y=\(x^{2}\)+1

so do the same as up there: replace x with every number

x:-2, -1, 0, 1, 2

so y will be

y:5, 2, 0, 2, 5

Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

Answer:

D

Step-by-step explanation:

3 | 1   5   - 8   6

   ↓   3    24   48

   ----------------------

    1   8   16    54 ← Remainder

Answer:

Step-by-step explanation:

they are prime to eachother.

There is only one common factor .i.e.,1

45=1×3×3×5

272=1×2×2×2×2×17

Answer:

someone deleted ur ans from y question can you please write it again

thank you.

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

The reference angle for the angle with the measure 2x/3 is 54⁰

You should understand that a reference angle is the acute angle to a given angle.

The given angle is 2x/3

We should understand that since the angle has the variable x

= x + 2x/3 = 90⁰

Simplifying the fraction to have

(3x+2x)/3 = 90

Cross and multiply we have 5x=270⁰

Making x the subject

x= 270/5

x=54⁰

Therefore, the reference angle with the measure 2x/3 is = 54⁰

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\(frequency = \frac{24 \: osc}{60 \: sec} = 0.4 \: osc \: per \: sec\)

\(period = \frac{1}{frequency} = \frac{1}{0.4} = 2.5 \: sec \: per \: osc\)

\(t = 2\pi \sqrt{ \frac{l}{g} } \\ 2.5 = 2\pi \sqrt{ \frac{l}{9.8} } \\ \frac{2.5}{2\pi} = \sqrt{ \frac{l}{9.8} } \\ ( \frac{2.5}{2\pi} ) {}^{2} = \frac{l}{9.8}\)

\(l = ( \frac{2.5}{2\pi} ) {}^{2} \times 9.8 = 1.55148 \: meters\)

To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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The construction of the frequency distribution is as follows:

Tax             Frequency

0-0.49                 4

0.50-0.99           9  

1.0-1.49               5

1.50-1.99             4

2.0-2.49             3

2.50-2.99          3

3.0-3.49             1

3.50-3.99           1

4.0-4.49            0

A frequency distribution is a graphical or tabular representation of a list of values in such a way that it displays the number of observations or outcomes within a given interval.

2.87   0.61    1.17     1.03    2.19    0.44    

0.82   2.55  0.29   0.36   0.82   0.82    

1.57    3.43  0.83    3.79   2.23   2.26    

1.69    1.53   1.48    1.68    1.23    0.68    

0.12    1.46   2.99   0.73   0.57   0.93

Thus, the frequency distribution is stated in tabular form, just as it can be stated graphically.

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Answer:

70 cases will be needed, and with 70 cases, there will be 4 water bottles left over.

Step-by-step explanation:

844 / 12 = 70.333

0.333 = 4 bottles

The function values are:

f(-1) = -9

f(1) = -5

We have,

From the graph,

We have the coordinates as:

(-1, -9) (2, 0), (-4, 0), and (1, -5)

Now,

The coordinates mean (x, y).

x is the x-axis and y is the function value.

f(x) = y

So,

We can have,

When x = -1, y = -9 or f(-1) = -9

And,

When x = 1, y = -5 or f(1) = -5

Thus,

The function values are:

f(-1) = -9

f(1) = -5

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Answer:

$81.06

A P E X :)

Average and mean absolute deviation of pumpkins grown in Cedartown: 668.5; 60.4

Average and mean absolute deviation of pumpkins grown in Baytown: 628.5; 40.2

The average distance of each point from the mean of a data is the absolute mean deviation.

Mean and mean absolute deviation of pumpkins grown in Cedartown:

611, 753, 575, 685.5, 718

Average/Mean = (611 + 753 + 575 + 685.5 + 718)0/5

Average/mean = 3342.5/5 = 668.5

Mean absolute deviation = [(611 - 668.5) + ( 753 - 668.5) + ( 575 - 668.5) + ( 685.5 - 668.5) + ( 718 - 668.5)] / 5

Mean absolute deviation = [(57.5) + (84.5) + (93.5) + (17) + (49.5)]/5 = 302/5

Mean Absolute Deviation = 60.4

Mean and mean absolute deviation of pumpkins grown in Baytown:

584, 622, 713.5, 579, 644

Average/Mean = (584 + 622 + 713.5 + 579 + 644)/5

Average/mean = 3142.5/5 = 628.5

Mean absolute deviation = [(584 - 628.5) + ( 622 - 628.5) + ( 713.5 - 628.5) + ( 579 - 628.5) + ( 644 - 628.5)] / 5

Mean absolute deviation = [(44.5) + (6.5) + (85) + (49.5) + (15.5)]/5 = 201/5

Mean Absolute Deviation = 40.2

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Using commutative and associative properties of addition, the solution for given expression is -5.

What is commutative and associative property?

The associative and commutative characteristics are universal principles that apply to addition and multiplication. The associative property states that rearranging the numbers will get the same result, while the commutative property states that rearranging the numbers will yield the same result.

These properties tell that one can add in any order, the result will always be the same.

We are given an expression as 8+(-8-5).

So, in this instead of adding from left to right, we can see that the 8 + (-8) will be zero and only -5 will be left as an answer.

Hence, the solution for given expression is -5.

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Answer:

C

Step-by-step explanation:

you can see the proportion is right because you get 5 cucumbers for 2 dollars. for double cucumbers times by two which equals 4 dollars. Times 5 by three because it's 3 times bigger meaning it has to equal 6 dollars and finally times 2 by 4 making 20 cucumbers cost 8 dollars.

Answer:

it is the same 4.3

Step-by-step explanation:

this numbers didn't add one number when you round(0,1,2.3.4)

this numbers(5,6,7,8,9), you add one number when you add

4.3 (the three is the tenth)and no number after it so its stell the same

The rounding number of 4.3 when rounded to the nearest tenth is 4.3

Here,

The number is 4.3

We have to find the rounding number of 4.3 nearest tenth.

What is Rounding number?

A method of approximating a number to its nearest place value is called Rounding of Numbers.

Now,

The number is 4.3

To round the decimal number to its nearest tenth, look at the hundredth place.

But here is no any number on hundredth number, hence no change occur for rounding 4.3 to the nearest tenth.

So, The rounding number of 4.3 when rounded to the nearest tenth is same as the number 4.3

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The distributive property for the multiplication states that:

(1) Choosing:

• a = (x + 3),

• b = 4x²,

• c = 5.

We have:

(2) Applying the distributive property for the multiplication, we have:

(3) Replacing a = (x + 3), b = 4x² and c = 5, we get:

(A)

Answer:

(2,6)

Step-by-step explanation:

Option:B

The triangle is rotated 90 degree clockwise around the point (0,0). The point is (-6,2) is made to rotate. The image so formed is at the point (2,6).

Answer:

y = 5

Step-by-step explanation:

y + 6 = –3y + 26

y + 3y + 6 = 26

4y + 6 = 26

4y = 26 - 6

4y = 20

y = 5

I hope this helps!

The final answer for the surface area of the prism is 32 m^2 + 16h m^2.

To find the surface area of the prism, we need to calculate the area of each face and sum them up.

The prism has two identical square faces and four rectangular faces. The square face has a side length of 4 m. The area of one square face is given by:

Area of square face = side length^2 = 4^2 = 16 m^2

Since there are two square faces, the total area of the square faces is:

Total area of square faces = \(2 * 16 = 32 m^2\)

The rectangular faces have a length equal to the side length of the square face (4 m) and a width equal to the height of the prism. Let's assume the height of the prism is h. The area of one rectangular face is given by:

Area of rectangular face = length * width = \(4 * h = 4h m^2\)

Since there are four rectangular faces, the total area of the rectangular faces is:

Total area of rectangular faces = \(4 * 4h = 16h m^2\)

Therefore, the surface area of the prism is the sum of the areas of the square and rectangular faces:

Surface area of prism = Total area of square faces + Total area of rectangular faces

                          = \(32 m^2 + 16h m^2\)

                          = \(32 m^2 + 16h m^2\)

The answer for the surface area of the prism is 32 m^2 + 16h m^2.

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Answer:

The proportion of the sample that does not have a two-year or four-year college degree is 0.7355.

Step-by-step explanation:

Sample of 310 people.

186(only high school) + 42(only some college) did not have have a two-year or four-year college degree.

So

\(p = \frac{186+42}{310} = 0.7355\)

The proportion of the sample that does not have a two-year or four-year college degree is 0.7355.

The solution to the equations is (-4/45, -2/9)

The system of equations is given as

-0.5x = 0.2y

-0.3x + 0.15y = -0.06

Divide both sides of -0.5x = 0.2y by -0.5

So, we have

x = -0.4y

Substitute x = -0.4y in -0.3x + 0.15y = -0.06

So, we have

-0.3 x -0.4y + 0.15y = -0.06

Evaluate the products

0.12y + 0.15y = -0.06

Evaluate the like terms

0.27y = -0.06

So, we have

y = -0.06/0.27

Simplify

y = -2/9

Recall that

x = -0.4y

So, we have

x = -0.4 * 2/9

Evaluate

x = -4/45

Hence, the solution is (-4/45, -2/9)

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Possible question

Solve by using any method. Write your answer as an ordered pair.

-0.5x = 0.2y

-0.3x + 0.15y = -0.06

The growth constant is 1.0986 and the trout population will increase to 14600 after 2.1 years. The result is obtained by using the logistic equation.

The increase of population can be found by using the logistic equation. It is

\(P(t) = \frac{K}{1 + Ae^{-kt} }\)

Where

Sunset Lake is stocked with the rainbow trout. We have

Find the growth constant k and time t when P(t) = 14600!

A = (K - P₀)/P₀

A = (28000 - 2800)/2800

A = 25200/2800

A = 9

After 1 year, we have 7000 rainbow trout. The growth constant is

\(7000 = \frac{28000}{1 + 9e^{-k(1)} }\)

\(1 + 9e^{-k} = 4\)

\(9e^{-k} = 3\)

\(e^{-k} = \frac{1}{3}\)

k = - ln (1/3)

k = 1.0986

Use k value to find the time when the population will increase to 14600!

\(14600 = \frac{28000}{1 + 9e^{-1.0986t} }\)

\(1.9178 = 1 + 9e^{-1.0986t}\)

\(0.9178 = 9e^{-1.0986t}\)

\(\frac{0.9178 }{9} = e^{-1.0986t}\)

\(t = \frac{ln \: 0.10198}{-1.0986}\)

t = 2.078

t ≈ 2.1 years

It is in another 1.1 years after t = 1.

Hence, the growth constant k is 1.0986 the population will increase to 14600 when t is 2.1 years.

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The amount natalya will spend constructing the patio with concrete and brick is $4320, the correct option is D.

We are given that;

The concrete portion of the patio cost=$3 per square

To construct and the brick portion of the patio cost= $6 per square

Now,

The area of a rectangle is given by length times width. The concrete portion of the patio is a rectangle with length 6 cm and width 3 cm. Using the scale, we can convert these to feet:

6 cm = 6 x 4 ft = 24 ft 3 cm = 3 x 4 ft = 12 ft

Therefore, the area of the concrete portion is:

24 ft x 12 ft = 288 ft^2

The brick portion of the patio consists of two identical rectangles with lenth 3 cm and width 6 cm. Using the scale, we can convert these to feet:

3 cm = 3 x 4 ft = 12 ft 6 cm = 6 x 4 ft = 24 ft

Therefore, the area of one brick rectangle is:

12 ft x 24 ft = 288 ft^2

Since there are two brick rectangles, the total area of the brick portion is:

2 x 288 ft^2 = 576 ft^2

Now we can multiply the areas by their costs per square foot to get the costs of each portion:

Concrete cost = $3 x 288 ft^2 = $864 Brick cost = $6 x 576 ft^2 = $3456

The total cost of constructing the patio is the sum of the costs of each portion:

Total cost = $864 + $3456 = $4320

Therefore, by area the answer will be $4320.

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