Finding the area of a triangle is straightforward if you know the length of the base and the height of the triangle. But is it possible to find the area of a triangle if you know only the coordinates of its vertices? In this task, you’ll find out. Consider ΔABC, whose vertices are A(2, 1), B(3, 3), and C(1, 6); let line segment AC represent the base of the triangle.

a. Find the equation of the line passing through B and perpendicular to AC

Type your response here:


b. Let the point of intersection of AC with the line you found in part a be point D. Find the coordinates of point D.

Type your response here:


c. Use the distance formula to find the length of the base and the height of ABC

Type your response here:


d. Find the area of ABC

Type your response here:

Answer:

Step-by-step explanation:

let Josh's current age be x.

2+ 25 times his current age= 25x+2

25x+2=77

25x= 77-2

     = 75

x= 75/25

 =3

The answer is 420.

Hope this helps ^^

The points scored by the remaining players on the team is 31 points.

A component or fraction of a whole can be expressed as a percentage by using a number out of 100. Mathematicians frequently use comparison to represent changes in quantities over time or to compare two numbers. For instance, if a student receives an 80 percent on a test, they properly answered 80 of the 100 questions.

For performing a range of mathematical operations, such as determining the percentage rise or decrease of a quantity or computing interest rates on loans or investments, percentages can be expressed as fractions or decimals.

From the given percentages the total percent is:

Total percentage = 15% + 10% + 13% = 38%

Now, from 100 the remaining percentage is: 100% - 38% = 62%

For the remaining players the score is given as:

Remaining points = 50 * (62/100) = 31

Hence, the points scored by the remaining players on the team is 31 points.

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The base case for the given pseudocode algorithm is 150. A base case is an initial and simplest case in an algorithm that does not necessitate further recursion.

It is the condition that aids in the determination of the smallest size of a problem that can be solved without recursion. A base case is a unique and basic condition that is considered to be true in a specific algorithm. A recursive algorithm cannot be used if there is no base case.

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The probability of winning at least once when playing the instant lottery twice is 0.19, or 19%.

To find the probability of winning at least once in the instant lottery when playing twice, we can use the complement rule.

The complement rule states that the probability of an event occurring (in this case, winning at least once) is equal to 1 minus the probability of the event not occurring (in this case, not winning both times).
Determine the probability of not winning in a single game, which is 1 - 0.1 = 0.9.
Calculate the probability of not winning both times, since outcomes are independent, by multiplying the probabilities of not winning each time: 0.9 * 0.9 = 0.81.
Finally, find the probability of winning at least once by subtracting the probability of not winning both times from 1: 1 - 0.81 = 0.19.

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Answer:

11

Step-by-step explanation:

\(3^{2}\) + 2

9 + 2

11

Answer:

the answer is the second to the left :D

Step-by-step explanation:

each number is divided then you solve\

The third scatter plot is correct.

A scatter plot is a set of points plotted on a horizontal and vertical axes. Scatter plots are important in statistics because they can show the extent of correlation, if any, between the values of observed quantities or phenomena (called variables).

According to the given table for bulldogs and condors.

To get the scatter plot we can make coordinates using x-axis as Bulldogs and y-axis as condors.

The coordinates will be

(5, 3), (6,2) , (3, 4), (2, 5), (7, 4), (6, 5), (3, 9), (6, 7), (5, 4) (6, 3).

So, these coordinates are well represented by third scatter plot.

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a) About 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

b) About 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

c) The estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

To answer these questions, we'll use the properties of the normal distribution and the given mean and standard deviation.

(a) To find the percentage of test takers who earn a score less than 500 on the GRE Chemistry test, we need to calculate the cumulative probability up to the score 500.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (500 - 694) / 112

z-score ≈ -1.732

Now, we look up the cumulative probability for a z-score of -1.732 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.0416 or 4.16%.

So, about 4.16% of test takers earn a score less than 500 on the GRE Chemistry test.

(b) To find the proportion of test takers who earn a score greater than or equal to 900, we need to calculate the cumulative probability from 900 to positive infinity.

z-score = (X - mean) / standard deviation

where X is the score we are interested in.

z-score = (900 - 694) / 112

z-score ≈ 1.839

Now, we look up the cumulative probability for a z-score of 1.839 in the standard normal distribution table or use a calculator to find that the cumulative probability is approximately 0.9664 or 96.64%.

So, about 96.64% of test takers earn a score greater than or equal to 900 on the GRE Chemistry test.

(c) To estimate the score at the 99th percentile on the GRE Chemistry test, we need to find the value that separates the lowest 99% of the scores from the highest 1%.

We use the z-score formula to find the z-score corresponding to the 99th percentile:

z-score = invNorm(0.99)

z-score ≈ 2.326

Now, we use the z-score to find the score corresponding to the 99th percentile:

X = mean + (z-score * standard deviation)

X = 694 + (2.326 * 112)

X ≈ 694 + 260.512

X ≈ 954.512

So, the estimated score at the 99th percentile on the GRE Chemistry test is approximately 954.512.

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Answer:

$5.75

Step-by-step explanation:

20=9.75 + 4.5 + c

20-9.75-4.5=c

5.75=c

The constant of variation based on the information is one half.

From the information given, when x is 2, y is 1, when x is 4, y is 2, etc. It should be noted that this is a direct variation.

This will be illustrated as:

y = kx

when y = 1, x = 2.

1 = 2k

Divide both side by 2.

k = 1/2

Therefore, the constant of variation is 1/2.

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Answer:

answer is pp

Step-by-step explanation:

Answer:

4+4=8

7-1=6

Step-by-step explanation:

Try using your fingers

Given the function:

You need to remember that the Inflection Points of a function are where it changes its concavity.

By definition, a function can have more than one inflection point:

1. You need to find:

Remember the following Derivatives Power Rule:

You get:

2. Find the second derivative by derivating the first derivative. This is:

3. Find the third derivative by derivating the second derivative:

4.Find the roots of the second derivative:

- Set up that:

- And solve for "x":

5. Substitute each root into the third derivative and evaluate:

It is less than zero, therefore there is an inflection point in that x-value.

It is positive output value, therefore there is an inflection point in that x-value.

6. Substitute those x-values into the original function and evaluate:

Therefore, the inflections points are:

Hence, the answer is:

There are two inflection points:

Answer:

113.04 cm.

Step-by-step explanation:

Step 1: Formula/explain

To find the area of a circle, multiply the radius by itself twice, then multiply the product pi.

\(a=\pi r^2(3.14*radius*radius)\)

Step 2: Solve

According to the word problem, the circle has a diameter of 12. This means it has a radius of 6.

Now, we plug the numbers into formula.

\(\pi 6^2 (3.14*6*6)=113.04\)

Step 3: Conclude

Therefore, the area of this circle is 113.04 cm.

Answer:

0/5

12/21

-2/5

Step-by-step explanation:

Slope: y2-y1/x2-x1

6. 7-7/20-15=0/5

7. -12-0/-14-7=-12/-21=12/21

8. -2-10/19-(-11)=-12/30=-2/5

The inequality that represents Rita saving money from the second option is 0.059x < 0.49 + 0.019x

"Information available from the question"

In the question:

1. Pay $0. 49, plus an additional $0. 019 per minute.

2. Pay $0. 059 per minute.

Now, According to the question:

How to determine the inequality that represents the statement?

We have the following parameters that can be used in our computation:

1. Pay $0.49, plus an additional $0.019 per minute.

2. Pay $0.059 per minute.

These statements can be represented as

Option 1: y = 0.49 + 0.019x

Option 2: y = 0.059x

Where y is the total amount and x is the number of minutes

When she saves money, we have

Option 2 < Option 1

Substitute the known values in the above equation, so, we have the following representation

0.059x < 0.49 + 0.019x.

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Answer:

C. Step 3

Step-by-step explanation:

Fred lost the negative sign, but everything else was right. He should have gotten -9.

The probability of obtaining tails and the number 5 is 1/12

the probability of obtaining an even number is 1/2

P(heads and prime number)  1/4

Since the events are independent, the probability of obtaining tails and the number 5 is:

P(tails and 5) = P(tails) * P(5) = (1/2) * (1/6) = 1/12

The coin toss outcome is irrelevant, so the probability of obtaining an even number is:

P(even number) = 1/2

The probability of obtaining heads and a prime number is:

P(heads and prime number) = P(heads) * P(prime number) = (1/2) * (1/2) = 1/4

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$473,710.99 (in thousands of dollars) should be deposited each year to ensure that the university will have enough money at the end of the 6th year to pay for the expansion project.

To determine the amount of money that should be deposited each year to ensure that the university will have enough money at the end of the 6th year  to pay for the expansion project, we can use the concept of future value of an annuity.

The future value of an annuity is the accumulated total value of all the payments or deposits made, including the interest earned over the specified period. It represents the amount of money that will be available at a future date, considering the compounding effect of interest.

The formula to calculate the future value of an annuity is:

\(FV = P * [(1 + r)^n - 1] / r\)

Where:

FV is the future value of the annuity,

P is the amount of each payment or deposit,

r is the interest rate per period,

n is the number of payment periods.

In this case, the university plans to deposit a sum of money at the end of each year for five years from now. This means there are five years of deposit.

The future value (FV) is given as $3 million, so FV = $3,000,000.

The annual interest rate (r) is 5.5%, so r = 0.055.

The number of years (n) is 6 years.

We need to solve the formula for P (the amount to be deposited each year).

$3,000,000 = P * [(1 + 0.055)^6 - 1] / 0.055

$3,000,000 = P * [1.348148 - 1] / 0.055

$3,000,000 = P * 0.348148 / 0.055

$3,000,000 = P * 6.33087

P = $3,000,000 / 6.33087

P ≈ $473,710.99

Therefore, $473,710.99 (in thousands of dollars) should be deposited each year to ensure that the university will have enough money at the end of the 6th year to pay for the expansion project.

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The domain and the range of the function are (-∝, ∝) and (0, ∝), respectively

From the question, we have the following parameters that can be used in our computation:

The graph

The above graph is an exponential function

The rule of an function is that

The domain is the set of all real values

In this case, the domain is (-∝, ∝)

For the range, we have

Range = (0, ∝)

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Answer:

9.50 + 0.20e = 12.50

Step-by-step explanation:

you start with the 9.50, base price. Then with every photo you pay 0.20, since we don't know how many it is we put a variable. Then we know that those two combined is 12.50, so yeah.

Answer:

Step-by-step explanation:

Total Cost = base price + 0.20*x   Where x is the number of prints printed.

12.50 = 9.50 + 0.20x                      Subtract 9.50 from both sides.

12.50 - 9.50 = 0.20x

3 = 0.20x                                         Divide by 0.20

3/0.20 = x

x = 15

So he printed 15 prints.

Answer:

\(y=|\frac{1}{4}x|\)

Step-by-step explanation:

Given that

transformed graph of the parent graph y=|x|

The transformed function is shown below:-

We see the graph at y=1 x reaches to 4 i.e, x=4

In the Same manner at y = 1

and x reaches to -4

that is

x=-4

Now, as per the options that are given in the question

The graph would be satisfied these two points would become transformation

\(y=|\frac{1}{4}x|\)

Now,

At x=4

\(y=|\frac{1}{4}x|\)

\(y=|\frac{1}{4}(4)|\)

y = 1

we can say that the point totally satisfied the equation.

So, Option 1 is right that is

\(y=|\frac{1}{4}x|\)

With the help of a diagram we can go through as attached.

The Function for given graph will be \(y=|\frac{1}{4} x|\)

If the graph of f(x) is given, then the graph of \(f(\frac{1}{k} x)\) is stretch by a factor of k.

Here function is given that,   y=|x|

From given graph it is observed that, graph is stretched by a factor of 4.

So that function for given graph will be,

                            \(y=|\frac{1}{4} x|\)

Graph is attached below,

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Answer: 5

Step-by-step explanation:

Answer: 6

Step-by-step explanation:

thank you to the user above for the comment i just entered it and 6 is correct in delta math

To calculate the area of a parallelogram

 ⇒ we must know the formula

     ⇒ Area = base * height

What are we given:

Thus:

   Area = 3ft * 4ft = 12 \(ft^2\)

Hope that helps!

Considering the surface area of the spherical ballon, it will take 7 seconds for the the balloon to fully inflate.

The surface area of a sphere of radius r is given by:

\(S = 4\pi r^2\)

In this problem, the surface area is of \(784\pi\) cm², hence the radius in cm is found as follows:

\(784\pi = 4\pi r^2\)

\(4r^2 = 784\)

\(r^2 = \frac{784}{4}\)

\(r^2 = 196\)

\(r = \sqrt{196}\)

r = 14 cm.

The radius start at 0 cm, inflating at a rate of 2 cm/s, hence it will take 7 seconds for the the balloon to fully inflate, as 14 cm/(2 cm/s) = 7 s.

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Answer:

All

Step-by-step explanation:

The answer is 1, 2, 3

I, II, III

There are 12 identical marbles in a bag, and Suzy is going to select 9 marbles from the bag at random.

The problem asks how many possible outcomes there are.

To begin with, we need to understand the concept of combinations. A combination is a way to select a subset of objects from a larger set, without regard to the order of the objects. For example, if we have four marbles (A, B, C, and D), there are six possible combinations of two marbles: AB, AC, AD, BC, BD, and CD.

In this problem, we have 12 marbles and we are choosing 9 of them. To find the total number of combinations, we can use the formula for combinations:

nCr = n! / r!(n-r)!

where n is the total number of objects, r is the number of objects we are choosing, and ! represents factorial (i.e. multiplying a number by all the positive integers less than it).

So, plugging in our numbers:

12C9 = 12! / 9!(12-9)! = 12! / 9!3! = (121110) / (321) = 220

Therefore, there are 220 possible outcomes if Suzy selects 9 marbles at random from a bag containing 12 identical marbles.

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Answer:

1.6*10^2

Step-by-step explanation:

here is your answer.is it helpful or not,?

Answer:

1.6 X 10^3

Step-by-step explanation:

1,600 is 1.6 X 10^3 in scientific notation because for it to be in scientific notation you need to move the decimal so there is only one whole number. Therefore you would move the decimal three times to the left and 10 would have the exponent positive 3 because if the decimal is being moved to the left, the exponent will be positive.

The final number remaining in this sequence is the number 2.

We start with the first 300 natural numbers written in ascending order. We remove the numbers at odd places, which means we remove all the numbers at positions 1, 3, 5, and so on.

After the first removal, we are left with the numbers at even positions: 2, 4, 6, and so on.

Now, we repeat the process and remove the numbers at odd positions again. We remove numbers at positions 1, 3, 5, and so on from the remaining sequence.

After the second removal, we are left with the numbers at even positions again: 4, 8, 12, and so on.

We can observe that in each removal, the sequence reduces to half its size, and we are left with the numbers at even positions.

Continuing this process, we will eventually reach a point where we have only one number left.

Since we start with 300 numbers, after the first removal, we have 150 numbers. After the second removal, we have 75 numbers. After the third removal, we have 38 numbers. After the fourth removal, we have 19 numbers. After the fifth removal, we have 10 numbers. After the sixth removal, we have 5 numbers. After the seventh removal, we have 3 numbers. After the eighth removal, we have 2 numbers. Finally, after the ninth and last removal, we are left with a single number.

Therefore, the final number remaining in this sequence is the number 2.

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Answer:

x is 1,800 kw energy used and y is $162 so a equation you can use

for every 1,800 kw of energy used you need to spend $162 so the equation would be

f(n)= 1,800 x 162^2

The conclusion is that there is sufficient evidence to support the claim that the percentage of vacant housing units in their district differs from the percentage of vacant housing units in the country.

Given that the total number of a housing units in her country is 550 and the number of vacant housing units in her country is 130.

The Null hypothesis is p₀=13%=0.13, n=550 and x=130

Significance level α=0.05

Claims given: percentage other than 13%

The claim is anyone of the null hypothesis or the alternative hypothesis. The null hypothesis shows that the proportion of the population is equal to the value stated in the claim. If the null hypothesis is a claim, then the alternative hypothesis states the opposite of the null hypothesis.

H₀:p=13%=0.13

Hₐ:p/0.13

I'm interested in testing population proportion claims, so I'll use z-text with proportions.

Conditions: Random sample, 10% condition, pass / fail condition

Sample: I'm happy because the housing units were randomly selected.  10% Condition: We are happy because the sample of 550 homes in your county is less than 10% of the population.

Pass/ fail condition: Satisfied because both np₀ and n(1-p₀) are both at least 10.

np₀=550(0.13)=71.5≥10

n(1-p₀)=550(1-0.13)=478.5≥10

Therefore, we conclude that all the conditions are met.

The sample percentage is the number of successes divided by the sample size.

\(\begin{aligned}\hat{p}&=\frac{x}{n}\\ &=\frac{130}{550}\\ &\approx 0.2364\end\)

Determines the value of the test statistic:

\(\begin{aligned}z&=\frac{\hat{p}-p_0}{\sqrt{\frac{p_0(1-p_0)}{n}}} \\ &=\frac{0.2364-0.13}{\sqrt{\frac{0.13(1-0.13)}{550}}}\\ &=\frac{0.1064}{0.0143}\\&\approx 7.41 \end\)

The P-value is the probability of getting a test statistic value  or a  more extreme value if the null hypothesis is true. Use the normal probability table in the appendix to determine the P-value.

P=P(Z<−7.41 or Z>7.41)

P=2P(Z>7.41)

P=2(0)

P=0

If the P-value is less than the significance level α,  the null hypothesis is rejected.

P<0.05⇒ Reject H₀

Therefore, there is ample evidence to support the claim that the proportion of vacant homes in the area is different from the proportion of vacant homes in the country.

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