If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y=mx+b. To do so, substitute the value of the slope and the values of x and y using coordinates of the given point, the determine the value of b.
Using the above technique, find the equation of the line containing the points (-2,8) and (4,-1)
The equation of the line is ?

We are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

To find the confidence interval, we can use the formula:

CI = p ± zsqrt(p(1-p)/n)

Where:

CI: Confidence Interval

p: Proportion of students who correctly identified the flavor (sample proportion)

z: Z-score corresponding to the desired confidence level (95% confidence level corresponds to z=1.96)

n: Sample size

Plugging in the values we have:

p = 78/154 = 0.5065

z = 1.96

n = 154

CI = 0.5065 ± 1.96sqrt(0.5065(1-0.5065)/154)

CI = 0.5065 ± 0.0783

CI = (0.4282, 0.5848)

Therefore, we are 95% confident that the true proportion of healthy students who could correctly identify a Skittles flavor blindly lies within the interval (0.4282, 0.5848).

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Answer:

x=155

Step-by-step explanation:

since its a straight line, it has to equal 180 in total.

SQR is 25, so to find PQS you subtract 180-25

Which equals 155

The set of all bounded real functions does not form a vector space with the usual function addition and scalar multiplication.

To determine if a set of objects forms a vector space, we need to check if it satisfies the vector space axioms. These axioms include properties such as closure under addition and scalar multiplication, existence of additive identity and inverses, and distributive properties.

In the case of the set of all bounded real functions, it does not satisfy the closure property under scalar multiplication. To demonstrate this, consider a bounded real function f(x) that is bounded by M, and let c be a scalar.

When we multiply the function f(x) by a scalar c, the resulting function cf(x) may not remain bounded. If c is non-zero and large enough, cf(x) can exceed any bound M, violating the condition of boundedness.

For example, consider the bounded function f(x) = 1, which is bounded by M = 1. If we multiply this function by a scalar c = 2, the resulting function cf(x) = 2 is unbounded and violates the condition of boundedness.

Since the set of all bounded real functions fails to satisfy the closure property under scalar multiplication, it does not form a vector space with the usual function addition and scalar multiplication.

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To calculate the annual payment required to pay off a five-year, $25,000 loan at an interest rate of 3.50 percent EAR, we can use the formula for calculating the equal annual payment for an amortizing loan.

The formula is: A = (P * r) / (1 - (1 + r)^(-n))

Where: A is the annual payment,

P is the loan principal ($25,000 in this case),

r is the annual interest rate in decimal form (0.035),

n is the number of years (5 in this case).

Substituting the given values into the formula, we have:

A = (25,000 * 0.035) / (1 - (1 + 0.035)^(-5))

Simplifying the equation, we can calculate the annual payment:

A = 6,208.61

Therefore, the annual payment required to pay off the five-year, $25,000 loan at an interest rate of 3.50 percent EAR is $6,208.61.

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The values x = 1 and y = 2 can serve as counterexamples to statements that are proven false by substituting these values. The counterexample disproves the statement by showing that it is not universally true.

To determine which statements x = 1 and y = 2 serve as counterexamples for, we need to evaluate each statement by substituting these values into them. If substituting these values into a statement results in a false or contradictory statement, then x = 1 and y = 2 can be considered a counterexample.

By substituting x = 1 and y = 2 into each statement, we can assess their validity. If the statement holds true, it is not a counterexample. However, if the statement becomes false when substituting these values, then x = 1 and y = 2 can be considered a counterexample for that particular statement.

It is important to evaluate each statement individually to determine whether x = 1 and y = 2 contradict the statement. If they do, then x = 1 and y = 2 can be identified as a valid counterexample for that specific statement.

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There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

Finding the roots of the polynomial will allow you to solve it. P(x) = 0 is obtained by setting each factor to 0 and then calculating x. The polynomial equation can be solved by factoring. For every factor, a value of 0 should be used. 2x4 = 0; (x - 6) = 0; (x + 1) = 0 the answer to x, please.

It's important to note this even if there are only two genuine roots. The final two roots of this equation, which contain the integer I, are not real because I appears in both of them.

There are an equal number of roots as long as there are x powers. As a result of the four xs, the polynomial in this situation has four roots.

The complete question is,

Calculate the overall number of roots for each polynomial function using the factored form. f (x) = (x + 2)(x - 1) (x - 1) (x - 1) [x - (4 + 3i)] [x - (4 - 3i)].

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Answer:

-2

Step-by-step explanation:

The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

What is Probability ?

probability can be defined as the ratio of the number of favourable outcomes and the total number of outcomes.

We are given with an exponential distribution with

λ=0.01386.

The probability distribution function is:

F(x)=λ * e power (−λx)

Cumulative distribution function is

F(x) = 1- e power (−λx)

The mean of the exponential distribution function

E(X) = 1 / λ

= 1/0.01386

= 72.15

Hence, E(X) = 72.15

The variance of the exponential distribution function

V(X) = 1 / λ ^{2}

= 1/0.01386*0.01386

= 5205.63

V(X) = 5205.63

Probability that the distance is at most 100m

P(X <= 100 ) = F (100)

= 1- e power (−λx)

= 1 - e power (-0.01386*100)

= 1- e power (-1.386)

= 1-0.25007

= 0.749926

Therefore, P(X<=100) = 0.749926

probability that the distance is at most 200m

P ( X<= 200) = F(200)

=1-e power (−λx)

=1-e power (-0.01386*200)

= 1 - e power (-2.772)

= 1-0.06253

= 0.9375

P(X<= 200) = 0.9375

Probability that the distance is between 100 and 200m

P(100<= X <= 200) = F(200) - F(100)

= 0.9375-0.7499

=01876

P(100 <= X <= 200) = 0.1876

Probability that the distance exceeds the mean distance by more than 2 standard deviation.

P( X + P>μ+2σ) = P(X>72.15+2√5205.63)

= P(X > 72.15 +144.3)

P(X>216.45)

= 1-P(X<= 216.45)

1 - (1- e power (-0.01386*216.45)

=  e power (-2.9999)

= 0.04979

P( X + P>μ+2σ) = 0.04979

Hence , The probability that the distance is at most 100m is 0.749926 and at most 200 m is 0.9375 between 100 and 200 m is 0.1876 and the probability that distance exceeds the mean distance by more than 2 standard deviations is 0.04979

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Answer:

Choice C

Step-by-step explanation:

This is like a matching question. Here's what I mean by this. We know Triangle BCA and Triange JKL are congruent. So, what we have to do is match the side lengths together.

So the first side of BCA matches with JKL, the second side of BCA matches with JKL, the third side of BCA matches with JKL.

So first side:

BC is congruent  to JK

So second side:

CA is congruent  to KL

So third side:

JL is congruent  to BA

The third side is one of our answer choices.

That answer choice is C.

Answer:

c

Step-by-step explanation:

The value of the probability of choosing a green lollipop and a purple lollipop is, 8 / 45

We have to given that;

One bag contains 3 red lollipops and 2 green lollipops.

And, The other bag contains four purple lollipops and five blue lollipops.

Hence, The probability of choosing a green lollipop is,

P₁ = 2 / 5

And, The probability of choosing a purple lollipop is,

P₂ = 4 / 9

Thus, The value of the probability of choosing a green lollipop and a purple lollipop is,

P = P₁ ×  P₂

P = 2/5 × 4/9

P = 8/45

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Answer:

X = 0

Y = 3.25

Step-by-step explanation:

Hope this helps. Pls give brainliest.

Answer:

x = 0

y = 3.25

Step-by-step explanation:

You can do elimination. Multiply (9x + 4y = 13) by 2

4x - 8y = -26

18x + 8y = 26

22x = 0

x = 0

4(0) - 8y = -26

-8y = -26

y = 3.25

8/1 is the answer!

hope this helps

Answer:

8/1

Step-by-step explanation:

The total value of Jerry’s stock at the end of this time period based on the information about the average will be $26.

From the information, Jerry owns 20 shares of stock valued at $23 each. One day, the price of the stock rose$2. It fell $1 on each of the next three days. The stock price rose$4 on the next day.

This will be:

= $23 + $2 - 3($1) + $4

= $23 + $2 - $3 + $4

= $26

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Answer:

$45,262  

multiply 45000*6.5%

Step-by-step explanation:

Answer:

$2762.5

Step-by-step explanation:

6.5%×42,500=2762.5

$2762.5 is the sales tax being charged.

$45,262.5 is the total price.

Answer:

\(3x^{2} + 3x +12\)

Hope that helps!

Step-by-step explanation:

Consider using 3D printing technology to create the spherical fountain. This would allow for precise and customizable designs, and could potentially be more cost-effective than traditional manufacturing methods for complex shapes.

Use a mathematical formula to design the fountain. Here are the steps to design a spherical fountain:

Determine the desired size of the fountain. This will be the diameter of the sphere. Let's say your client wants a fountain with a diameter of 6 feet.

Calculate the radius of the sphere by dividing the diameter by 2. In this case, the radius is 3 feet.

Use the formula for the surface area of a sphere to determine the surface area of the fountain. The formula is: SA = 4π\(r^2\), where r is the radius of the sphere and π is a mathematical constant (approximately 3.14). In this case, the surface area is:

SA = 4π\((3)^2\)

SA = 4π(9)

SA = 36π

SA ≈ 113.1 square feet

Use the desired water flow rate to determine the volume of water that will flow through the fountain per minute. Let's say your client wants a flow rate of 50 gallons per minute.

Use the formula for the volume of a sphere to determine the volume of the fountain. The formula is: V = (4/3)π\(r^3\). In this case, the volume is:

Calculate the amount of time it will take for the fountain to cycle through all of its water. This is known as the turnover time, and it is important to maintain water quality. The turnover time is calculated by dividing the volume of water in the fountain by the flow rate. In this case, the turnover time is:

Use these calculations to design the fountain, taking into account any necessary adjustments for the manufacturer's limitations.

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Full Question: Your client wants you to design a spherical fountain for a new garden bed. It is hard to find a manufacturer that can create perfect curved surfaces. You will need to modify the sphere to a series of cylindrical slabs with gradually decreasing radii.

Answer:

12:8

Step-by-step explanation:

8+4=12

and there are 8 red roses

So, the answer is 12:8

1) Rounding those number to 4 significant digits

a. 431,801 = 431,800

b. 10,235.0 = 10240

c. 1.0348 = 1.035

d. 0.004384010 = 0.0040

e. 0.00078100 =0.0008

f. 0.0098641​ =0.009

The criteria are rounding up to those numbers greater than or equal to 5, and considering the how low is the number or how great it is.

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer: $11,500

.............................

Answer:120,000

Step-by-step explanation:

10,000 is how much she make times that by how many months are in a year its 12 months and you get your out come.

The probability of exactly nine letters being inserted correctly out of ten letters in envelopes is approximately 0.00000028, indicating a very low likelihood of this specific outcome.

Given that Santa has written 10 letters and gives them to each of his elves to insert into their corresponding envelope. We need to find the probability that exactly nine letters were inserted in the proper envelope.

There are 10 letters and they are supposed to be inserted into their corresponding envelopes.

Let us say the letter 1 is supposed to be in the envelope 1 and so on. And the elves have to insert each letter into their correct envelopes.

The probability of the first letter being inserted into the correct envelope is 10 since there is only one way to insert it in the correct envelope out of ten envelopes.

The probability of the second letter being inserted into the correct envelope is 1/2, since there are only two choices of envelopes left, and one of them is the correct envelope.

The probability of the third letter being inserted into the correct envelope is 1/3, since there are only three choices of envelopes left, and one of them is the correct envelope.

The probability of the last letter being inserted into the correct envelope is 1/10, since there are ten choices of envelopes left, and one of them is the correct envelope.

The probability that exactly nine letters are in the proper envelope and one is not in the correct envelope is

10/10! = 1/362880 = 0.0000028.

Hence, the required probability is 0.0000028 or 1/362880.

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The growth of yeast cultures in a medium typically exhibits logarithmic growth.

In logarithmic growth, the population size increases exponentially over time, meaning that the growth rate is proportional to the current population size.

This results in a characteristic J-shaped curve when the population size is plotted against time.

During the early stages of yeast culture growth, there is a lag phase where the population adjusts to the new environment and begins to adapt and reproduce.

Following this phase, yeast cells enter the exponential or logarithmic growth phase, where the population size increases rapidly.

The growth rate is high during this phase as each yeast cell divides and produces new cells, leading to a doubling of the population within a specific time frame.

Logarithmic growth eventually reaches a stationary phase, where the growth rate slows down, and the population stabilizes.

This occurs when the available nutrients in the medium start to become limited or when waste products accumulate, creating an unfavorable environment for further growth.

Therefore, the growth of yeast cultures in a medium shows logarithmic growth.

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Thereforef(x)= \(0.25^{2} -2\),and f(x)= \(3^{2} -2\) are the functions with domain (-(-∞,∞),) and range ((-∞,-2,).

The link between two or more variables stated in equal form is called a function.

Every x value in a function must match a matching y value. The domain and range of the function, respectively, are determined by the values of x and y.

Four functions have been provided to us, and we must identify the ones with domains of (-∞,∞)  , and ranges of (∞ -2), respectively.

By using f(x)= \(0.25^{2} +2\)

f(x)=1-2

=-1

f(1)=0.25-2

=-1.75

f(2)=0.50-2

=-1.50

f(-2)=1/0.50-2

=1-1/0.50

=0

Because the value of the function grows from -2 as the value of x increases, this function has a domain of (-,) and a range of (-2,).

By using f(x)=

Since the aforementioned function is the antithesis of the first function, it operates in an antithetical manner.

By using f(x)= \(3^{2} -2\)

f(0)=1-2

=-1

f(1)=3-2

=1

f(-2)=1/9-2

=(1-18)/9

=-17/9

=-1.8

Because the value of grows from -2 as the value of x increases, this function likewise has a domain (-∞,∞) and range (-∞,-2).

The behavior of the next function is the reverse of that of the third function, as a result.

Thereforef(x)= \(0.25^{2} -2\),)and f(x)= \(3^{2} -2\) are the functions with domain (-(-∞,∞),) and range ((-∞,-2,).

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Answer: (-2,1)

Step-by-step explanation:

The point (1,2) is in quadrant 1.

When rotated 90 degrees counter clockwise, it moves to quadrant 2.

The new point becomes (-2,1)

Answer:

Step-by-step explanation:

9/100 i believe as you would multiply 3/10 by 3/10 due to the fact the marble is being replaced so the probability of getting a red marble the second time will be more unlikely. If I'm right please thank me or give me brainly. Hope this helps :)

The probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.

What is Probability?

It is a branch of mathematics that deals with the occurrence of a random event.

The probability of drawing a red marble on the first draw is 3/10, since there are 3 red marbles out of a total of 10 marbles.

Since the first marble is replaced before the second draw, the probability of drawing a red marble on the second draw is also 3/10.

To find the probability of drawing two red marbles in a row, we multiply the probabilities of the individual events, since they are independent:

P(drawing two red marbles) = P(red on first draw) × P(red on second draw)

P(drawing two red marbles) = (3/10) × (3/10)

= 9/100

Therefore, the probability of drawing two red marbles, if the first marble is replaced after it is drawn, is 9/100.

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We have the following:

We must calculate the value of z

a.

x, is the value to evalute (0.8 - 1)

m, is the mean (0.88)

s, is the standard deviation (0.3)

n, is the sample size (36)

Therefore, the probability is 0.258 or 25.8%

b.

x, is the value to evalute (0.8 - 1)

m, is the mean (0.88)

s, is the standard deviation (0.3)

n, is the sample size (36)

replacing:

Therefore, the probability is 0.937 or 93.7%

Answer:

21 sections

Step-by-step explanation:

the wood is 21 feet long therefore there can be 21 sections of 1ft long wood

209 went to the first game.

192+17=209

Happy to help.