(Pythagorean Theorem MC)
Determine which set of side measurements could be used to form a right triangle.
O 9, 11, 13
O 6, 12, 17
O√8, 5, √17
O√√2. √7.9
Question 3(Multiple Choice Worth 2 points)
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Question 1 (Answered)
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pls helpppp

If the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

The equation is

y = -x

The slope intercept form

y = mx+b

Where m is the slope of the line

Comparing the slope intercept form and the given equation

Slope of the line m = -1

The line is passing through the points (-8,2)

The point slope form of the line

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute the values in the equation

y-2 = -1(x-(-8))

y-2 = -1(x+8)

y-2 = -x-8

y = -x-8+2

y = -x-6

Hence, if the equation y = -x, then the equation of the line that is parallel to the given line and passes through the point (-8,2) is y = -x-6

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A cat food manufacturer uses fish and beef by-products.

Let the number of ounces of fish = x

Let the number of ounces of beef = y

The fish contains 12 g of protein and 3 g of fat per ounce.

fish = 12x + 3y

The beef contains 6 g of protein and 9 g of fat per ounce.

Each can of cat food must contain at least 60 g of protein and 45 g of fat.

so,

Beside the above inequalities both of x and y must be greater than 0

so, the system of inequalities will be:

The following figure represents the solution of the system:

As shown in the graph, the vertices are:

( 0 , 10 ) , (3 , 4 ) , ( 15 , 0 )

Two or more expressions with an Equal sign is called as Equation. x=-3 for function f(x)=−13.

Two or more expressions with an Equal sign is called as Equation.

We know that f(x) = -13. This means that:

f(x)= -13 = 2x-7

-13= 2x-7

Now we all need to do is solve this equation. First add 7 to both sides

-13 + 7= 2x

-6=2x

Divide by 2 on both sides.

-6 ÷ 2= x

x= -3

Hence x=-3 for function f(x)=−13.

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Answer:

x = 42

see below for the angle measures.

Step-by-step explanation:

The angle marked 2x - 9 is sort of outside the triangle. It is called an exterior angle. The other two angles are called remote interior angles. "Remote" means that they are away from the exterior angle. When you have this set up, the two remote angles added together EQUAL the exterior one.

x+5 + 28 = 2x - 9

x + 33 = 2x - 9

Subtract x.

33 = x - 9

Add 9.

42 = x

So x = 42° which if you put that back into the expressions you can find the measures of the one remote interior angle (the other we know is 28°) and the exterior angle.

remote int angle:

x+5

= 42 + 5

= 47°

Exterior angle:

2x - 9

= 2(42) - 9

= 84 - 9

= 75°

(You can also then find the completely unmarked angle which is 180°- 75° which is 105°)

The correct option regarding the discounts is given as follows:

Store Z has the best sale price of $28.

The discount can be a percentage or an amount off, and the calculations are explained as follows:

Considering the discount plans and the original price of $35, the discounted prices in this problem are as follows:

Hence the correct statement is given as follows:

Store Z has the best sale price of $28.

The complete problem is:

Leo wants to buy some shoes. He found the shoes at three different stores for a price of $35. The stores are each having a sale:

Which statement about the sale price of these shoes is true?

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Answer:x=

−1/4y+ −3/4

Step-by-step explanation

P(B) such that a and b are mutually exclusive is 0.23

A group of potential results from a specific experiment is an event. Events that do not take place at the same time are said to be mutually exclusive. For instance, if a coin is tossed, the outcome will either be head or tail; we cannot obtain both outcomes. Since they do not occur at the same time, such occurrences are also known as disjunct events.

Given: P(A) =0.28

P(AUB) = 0.51

We know,

P(AUB) = P(A) + P(B) - P(A∩B)

Since A and B are mutually exclusive events, they cannot happen together.

So, P(A∩B) = 0

Then,

P(AUB) = P(A) + P(B)

0.51 = 0.28+ P(B)

P(B) = 0.51 - 0.28 = 0.23.

Hence, P(B) = 0.23

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Answer:

Step-by-step explanation:

We know that:

Apply it to the given to get:

The probability that the experiment results in 9 or more successes = 0.0676

A binomial distribution is given by,

P(X = x) = ⁿCₓ pˣ (1-p)ⁿ⁻ˣ  ,

where p is the probability of success and x is the random variable for success in n trials.

A binomial experiment has only two outcomes- success or failure.

Here, the number of trials, n = 10

Probability of success = 0.63

The probability for 9 or more success = P( X = 9, 10)

                                                               = P (X = 9) + P(X = 10)

So P( X = 9) =  ¹⁰C₉ (0.63)⁹ (1-0.63)¹⁰⁻⁹

                   = 10 x 0.0156 x 0.37

                   = 0.05772

and P(X = 10) = ¹⁰C₁₀ (0.63)¹⁰(1-0.63)¹⁰⁻¹⁰

                     = 1 x 0.009849 x 1

                     =  0.009849

Hence probability for 9 or more success = 0.05772 + 0.009849

                                                                    = 0.067569

                                                                    = 0.0676

The question is incomplete. Find the complete question below:

A binomial experiment with probability of success 0.63 and 10 trials is conducted. What is the probability that the experiment results in 9 or more successes? Do not round your intermediate computations, and round your answer to three decimal places. (If necessary, consult a list of formulas.)

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1. Find the slope of the line that goes through donuts 1-12.

take the points

(1, 1.05) and (2, 2.10)

m=(2.10-1.05)/(2-1)

m=1.05/1

m=1.05

Find the slope of the line that goes from donuts 13-25

take the points

(14,14.05) and (15, 15.10)

m=(15.10-14.05)/(15-14)

m=1.05/1

m=1.05

so

The slope is the same

2. What if we only buy in amounts of baker's dozens? Is there a line for those? What points are on this line? What is the slope?

the points are

(13,13.00) and (24,24.55)

m=(24.55-13.00)/(24-13)

m=11.55/11

m=1.05

the equation in point slope form is

m=1.05

(x1,y1)=13,13)

y-13=(1.05)(x-13)

y-13=1.05x-13.65

y=1.05x-0.65

For x=30 donuts

y=1.05(30)-0.65

y=30.85

therefore

Do you save $0.65

Answer:

6 units

Step-by-step explanation:

count the units between the two points

The solutions to the quadratic equation using completing the square method are  x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.

Given the quadratic equation in the question;

To solve using  completing the square method, first add 21 to both sides

x² + 5x - 21 = 0

x² + 5x - 21 + 21 = 0 + 21

x² + 5x = 21

Next, create a trinomial square on the left side of the equation, determine the value that is equal to the square of half of b which is 5.

( b/2 )² = ( 5/2 )²

Now, add ( 5/2 )²  to both sides of the equation

x² + 5x + ( 5/2 )² = 21 + ( 5/2 )²

Simplify

x² + 5x + 25/4 = 21 + 25/4

Add 21 and 25/4

x² + 5x + 25/4 = 109/4

Factor the perfect trinomial.

x² + 5x + 25/4 = 109/4

( x + 5/2 )² = 109/4

Solve for x by taking the square root of both sides.

x + 5/2 = ±√( 109/4 )

x = -5/2 ±√( 109/4 )

x = ±(√109)/2 -5/2

x = -(√109)/2 - 5/2, (√109)/2 -5/2

Therefore, the solutions to are x = -(√109)/2 - 5/2 and x = (√109)/2 -5/2.

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The slope of the line = rise of the line / run of the line = 2/2 = 1.

The slope (m) of a line can be determined by finding the ratio of the rise of the line to the run of the line, which is, the change in y over the change in x.

Referring to the image attached below, the blue line in the given graph shows the rise of the line while the red line shows the run of the line.

Therefore:

Rise of the line = 2 units

Run of the line = 2 units

Slope of the line (m) = rise/run = 2 units/2 units

Slope of the line (m) = 1

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The identified scale factor of the triangles is 71 / 37.

Scale factor is the ratio of corresponding sides on two similar figures.

The triangles are similar. Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.

Therefore, let's identify the scale factor of the triangles.

The triangle on the right is a scale copy of the triangle on the left.

Hence,

scale factor = 71 / 37 = 71 / 37

Therefore, the scaled factor of the triangles in fraction form is 71 / 37

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a) 10 men are selected at random, the probability their average height is above 72 inches is 0.0122.

b) Exactly one man is selected at random, the probability his average height is above 72 inches is 0.0122.

c) The 80th percentile for the average height of 10 men is 0.0097%.

d) The probability the average height of 10 men is between 70 and 71 inches is 0.13607.

Mean = 69.7 inches

Standard Deviation = 2.8 inches

a) Using normal distribution,

P(Y > 72) = P(Y - mean > 72 - mean)

P(Y > 72) = P((Y - mean ÷ SD) > (72 - mean ÷ SD))

P(Y > 72) = P(Z > (72 - mean ÷ SD))

P(Y > 72) = P(Z > (72 - 69.7 ÷ 2.8))

P(Y > 72) = P(Z > 2.25)

P(Y > 72) = 1 - P(Z  ≤ 2.25)

P(Y > 72) = 0.0122

b) P(man's height is above 72 inches) = 0.0122

c) (80 × 0.0122) ÷ 100

= 0.0097%

d) P( 70 > Y > 71) = P(70 - mean > Y - mean > 71 - mean)

P( 70 > Y > 71) = P((70 - mean ÷ SD) > (Y - mean ÷ SD) > (71 - mean ÷ SD))

P( 70 > Y > 71) = P((70 - mean ÷ SD) > Z > (71 - mean ÷ SD))

P( 70 > Y > 71) = P((70 - 69.7 ÷ 2.8) > Z > (71 - 69.7 ÷ 2.8))

P( 70 > Y > 71) = P(0.107 > Z > 0.464)

P( 70 > Y > 71) = 0.13607

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We need to make h the subject of formula:

A parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is the population mean.

The population mean can be determined by dividing the total number of values in the given data/population by the sum of all values in the data/population. The whole sum of the numbers is referred to as summation. The μ sign stands for the population mean.

The average calculated from the entire group, distribution, or population is known as the population mean. It is calculated by dividing the sum of all population variables by the total population of variables. Here, μ exists the population mean. ∑X exists the sum of all the observations in the population.

The population mean is a quantity that expresses the population's overall degree of individual variation, which is often unknown.

Therefore, the correct answer is option c) the population mean.

The complete question is:

a parameter that represents the amount of spread of individuals in the entire population of interest, which is typically unknown is group of answer choices the (true) standard error.

a) the sample standard deviation.

b) the estimated standard error.

c) the population mean.

d) the population standard deviation.

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Answer:

HERE YOU GO HOPE IT HELPS

The value of x for the given triangle is 30°.

According to the question,

We have the following information:

We have a triangle.

Three angles of the triangle are x°, 65° and (x+55)°.

We know that the sum of all the three angles of a triangle is 180°.

So, the sum of these angles will be 180°.

Now, adding three angles:

x° + 65° + (x+55)° = 180°

(2x+120)° = 180°

2x = 180-120

2x = 60

x = 60/2 (2 was in the multiplication on the left hand side. So, it is in the division on the left hand side.)

x = 30°

Hence, the value of x in the angles of the given triangle is 30°.

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Total 150 miles Jan drove than Ian.

Set the time Ian traveled as I, and set Han's speed as H.

Therefore, Jan's speed is H+5.

We get the following equation for how much Han is ahead of Ian;

H + 5I = 70.

The expression for how much Jan is ahead of Ian is; 2 (H + 5) + 10I

This simplifies to: 2H + 10 + 10I

However, this is just 2(H + 5I) + 10

Substitute, from the first equation, H + 5I as 70

Therefore, the answer is 140 + 10, which is 150.

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A person must score at least 129.24 to be in the top 10%.

Using the z-table, find the z-score that corresponds to the 90% probability.

probability = 0.90

z-score = 1.2825

For a normally distributed set of data, given the mean and standard deviation, the probability can be determined by solving the z-score and using the z-table.

The z-score can be calculated using the formula below.

z-score = (x – μ) / σ

where x = individual data value

μ = mean

σ = standard deviation

Plug in the values and find the score to be in the top 10%, x.

z-score = (x – μ) / σ

1.2825 = (x – 110) / 15

x – 110 = 19.2377

x = 129.24

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The Interquartile range i.e 1.5 (IQR) is used to identify outliers in a set of data which is the correct answer would be option (A).

We may build up a "fence" outside of Q1 and Q3 by using the Interquartile range (IQR) method of spotting outliers. Outliers are values that fall outside of this range.

To construct this barrier, we take 1.5 times the IQR, deduct it from Q1, and add it to Q3. This provides us with the lowest and maximum fence posts against which we will compare each observation.

Outliers are observations that are greater than 1.5 IQR below or above Q1. Minitab's default strategy for identifying outliers is this.

Therefore, the Interquartile range (IQR) is used to identify outliers in a set of data.

Hence, the correct answer would be option (A).

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The probability of the marksman hitting the long-range target in 5 shots is 0.1429.

The geometric distribution is a Bernoulli experiment that predicts the likelihood of the first success after a certain number of failures. Negative-binomial and binomial distributions are two different forms of Bernoulli trials.

P = 0.268

x = 5

Use the geometric probability mass function below to calculate the probability:

P(X = x) = [tex](1 - P)^{(x-1)}[/tex]× P

P(X = x) = [tex](1 - 0.268)^{(3-1)}[/tex]× 0.268

P(X = x) = 0.1429

The probability that it takes 5 shots for the marksman to hit the long-range target is 0.1429.

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We will have the following:

So, the volume is 486 ft^3.

Answer:

82

Step-by-step explanation:

Since x=7, you would put that value into the equation. i.e put that value, of 7, instead of x.

x² + 6x - 9

Answer:

16°F

Step-by-step explanation:

The temperature is −4°F. What will the temperature be if the temperature rises 20°F?

-4 + 20 = 16

so:

16°F

We are to determin if the following sequence are arithmetic and also fin their common difference if they are arithmetic.

(1) -3, -9, -27, -81, ................

This sequence is not an arithmetic sequence because theere is no common difference.

-9 - -3 = -27 - -9

-9 + 3 = -27 + 9

-6 ≠ -18

Therefore is not an arithmetic sequcence.

(2) 13, 17, 21, 25, ......................

This sequence is an arithmetic sequence.

It has a commdon difference of 4

17 - 13 = 21 - 17

4 = 4

Therefore, the sequence is an arithmetic sequence.

(3) -6, -2, 2, 6, .........................

This sequence is an arithmetic sequence.

It has a common difference of 4

-2 - -6 = 2 - -2

-2 + 6 = 2 + 2

4 = 4

Therefore, the sequence is an arithmetic sequence

Answer:

35000

Step-by-step explanation:

So the number is 34582

now look at the hundreds

if it is 5 or over then we add a thousand to and subtract what ever the lower than thosand

and in this case it is 5 so we round UP

and now we have 35000

The answer is 35,000.

To round to the nearest thousand, we look at the last three digits. If these digits are 500 or greater, then we round the thousands digit up, and if they are less than 500, then we round down, keeping the thousand's digit the same.

Since in this case the last three digit consists of 582 which is greater than 500 so we round the thousands digit up i.e. from 4 to 5 in this case.

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SOLUTION

Let the first even integer be 'a'.

Let the second integer be (a + 2) since the second is a consecutive even integer.

Half of the smaller (i.e. a) is equal to two more than the larger (i.e. a + 2). In other words:

Evaluate for a

Simplify

Multiply all through by 2

Collect like terms

Hence, the smaller even integer is

The point-slope equation of this line is y - 7 = -7(x + 5).

Mathematically, the point-slope form of a line is given by this equation:

y - y₁ = m(x - x₁)

Where:

Next, we would determine the slope of this line by using this formula:

Slope, m = Δy/Δx

Slope, m = (y₂ - y₁)/(x₂ - x₁)

Substituting the given parameters into the formula, we have;

Slope, m = (0 - 7)/(-4 + 5)

Slope, m = -7/1

Slope, m = -7

At point (-5, 7), the point-slope equation of the line is given by:

y - y₁ = m(x - x₁)

y - 7 = -7(x - (-5))

y - 7 = -7(x + 5)

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Complete Question:

Complete the point-slope equation of the line through (-5, 7) and (-4, 0). Use exact numbers.