WILL GIVE BRAINLIEST

Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.

1
one half
3
one third

AND GIVE EXPLANATION

Answer: 20

Step-by-step explanation: Opposite sides of a parallelogram are congruent

In forecasting, there should be a correlation between the independent and dependent variables. This correlation can be high or low but should not be greater than 1 as it would indicate a problem with the data.

A high correlation would mean that the variables are strongly related, whereas a low correlation would mean that there is little to no relationship between the variables. A correlation close to zero would indicate that the variables are not related at all. The goal is to find a correlation that is strong enough to make accurate predictions but not so strong that it suggests a problem with the data.

A high correlation indicates a strong relationship between the variables, which is beneficial for making accurate predictions. A correlation close to zero represents a low correlation, which is not desirable as it suggests a weak relationship between the variables.

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a.) The fraction of the students that said science would be = 8/15

b.) When represented on a pie chart the degree that will show science would be = 192°

The total number of students in the class = 4+8+3= 15

The total number of students that are for science = 8

The fraction of students for science = 8/15

When represented on a pie chart the percentage of science would be = 8/15 × 360/1

= 2880/15

= 192°

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The value of angle R is 28.03( nearest hundredth)

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.

The two legs of the right angled triangle are opposite sides and adjascent while he third side is hypotenuse.

sin(tetha) = opp/hyp

cos(tetha) = adj/hyp

tan(tetha) = opp/adj

Here, using angle R, opp = 8cm , adj = 15cm and hyp = 17cm

Therefore sin(R) = 8/17

sin(R) = 0.47

R = sin^-1( 0.47)

R = 28.03( nearest hundredth)

therefore the value of angle R is 28.03°

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In this case, Time (together) = 600 flowers / 500 flowers/hour, which simplifies to Time (together) = 1.2 hours. So, it would take Tim and Samara 1.2 hours to plant 600 flowers together.

Tim and Samara are volunteering to plant flowers in the community garden. It takes Tim 2 hours to plant 600 flowers, so his rate is 600 flowers/2 hours = 300 flowers/hour. It takes Samara 3 hours to plant 600 flowers, so her rate is 600 flowers/3 hours = 200 flowers/hour.

When they work together, their combined rate is the sum of their individual rates: 300 flowers/hour (Tim) + 200 flowers/hour (Samara) = 500 flowers/hour (combined). To determine how long it would take them to plant 600 flowers together, we can use the equation:

Time (together) = Total flowers / Combined rate
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7. The probability of picking a black retriever and then a brown hound is D, 15/144

8. The probability of picking a blue marble first, changing it, and then selecting another blue marble is C, 9/25.

7. Since the first puppy is replaced back in the box, the probability of picking a black retriever on the first draw is 5/12 (since there are 5 black retrievers out of 12 total puppies).

The probability of picking a brown hound on the second draw is 3/12 (since there are 3 brown hounds left out of 12 total puppies, assuming one black retriever has already been selected and replaced in the box).

Therefore, the probability of picking a black retriever and then a brown hound is:

(5/12) x (3/12) = 15/144 = 5/48.

So the probability of picking a black retriever and then a brown hound is 5/48.

8. Since the blue marble is replaced after the first draw, the probability of picking a blue marble on both the first and second draws is the same, which is 3/5.

Therefore, the probability of picking a blue marble the first time, replacing it, and then picking another blue marble is:

(3/5) x (3/5) = 9/25

So the probability of picking a blue marble the first time, replacing it, and then picking another blue marble is 9/25.

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Answer:

Step-by-step explanation:
Hello! Since this is a right triangle, the three things we would be able use to solve for x and y are tangent, cosine, and sine.

The first thing we could do is solve for x (it doesn't matter what you do first, though). The side measuring 6 is opposite from the 90 degree angle, meaning it is the hypotenuse. The side measuring x is opposite from the 60 degree angle, meaning it is the opposite side from the 60 degree angle. The side measuring y forms the 60 degree angle and is not the hypotenuse, meaning it is the adjacent side to the angle measuring 60 degrees. Now that we know this, here are some formulas:

Sine = Opposite/Hypotenuse
Cosine = Adjacent/Hypotenuse
Tangent = Opposite/Adjacent

Since we know that x is the opposite side and 6 (our known value) is the hypotenuse, what is the only formula using the opposite side and hypotenuse? Sine!

Sine = Opposite/Hypotenuse
Sine (60) = x/6
Sine (60) x 6 = x

Here is something to help you remember this: SOH--CAH--TOA

Sine-Opp-Adj--Cosine-Adj-Hyp--Tangent-Opp-Adj.

Solve for sine 60 degrees on your calculator by pressing the button saying sin and then typing the number (60).

((the square root of three)/2) x 6 = x
3 x the square root of three = x.

So, x = 3(the square root of three).

C and d both have options saying that x = 3(square root of three), so we will have to solve for y to find the right answer.

y is the adjacent side to 60 degrees, and now we can either use x or 6 to solve for this problem. I will use 6, the hypotenuse. We will need to use adjacent/hypotenuse = cosine (__)

cosine (__) = adjacent/hypotenuse
cosine (60) = y/6
cosine (60) x 6 = y

Solve for cosine 60 on your calculator by pressing sin and then 60.

1/2 x 6 = y
3 = y.

y = 3 and x = 3(the square root of three)

So the answer is d.

The answer in the form of polynomial is:

x² + 2/(x-1) = x + 3 + 1/(x-1)

An expression that consists of variables, constants, and exponents and that is combined using mathematical operations such as addition, subtraction, multiplication, and division (no division operation by a variable) is referred to as a polynomial.

To write x² + 2/(x-1) in the form of p(x) + k/(x-1), we need to perform partial fraction decomposition:

x² + 2/(x-1) = (Ax + B)/(x-1) + Cx + D

Multiplying both sides by (x-1), we get:

x² + 2 = (Ax + B) + (Cx + D)(x-1)

Expanding the right-hand side, we get:

x² + 2 = Ax + B + Cx² - Cx + Dx - D

Matching coefficients on both sides, we get the following system of equations:

C = 1

D - B = 2

A - C = 0

-B + D = 0

Solving for A, B, C, and D, we get:

A = 1

B = -1

C = 1

D = 1

Therefore, we have:

x² + 2/(x-1) = (x-1)/x-1 + x + 1

                   = x + 2 + 1/(x-1)

Hence, the answer is:

x² + 2/(x-1) = x + 3 + 1/(x-1)

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Student had $24. 00. Each pack of pencils costs $2.40.

Let the cost of each pack of glue sticks be x and the cost of each pack of pencils be y. Then we can set up a system of two equations

14x + 5y = 24 (total cost of 14 packs of glue sticks and 5 packs of pencils is $24)

y = (24 - 14x)/5 (solve for y in terms of x)

Substituting the second equation into the first equation, we get

14x + 5[(24 - 14x)/5] = 24

Simplifying and solving for x, we get

14x + 24 - 14x = 120

x = 6

So each pack of glue sticks costs $6. To find the cost of each pack of pencils, we can substitute x = 6 into the second equation

y = (24 - 14(6))/5

y = 2.4

Therefore, pack of pencils costs $2.40. We can check our answer by verifying that the total cost is indeed $24

14(6) + 5(2.4) = 84 + 12 = 96

96/4 = 24

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The number of gallons of paint the hotel will need to buy is (b) 10 gallons

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

The composite figure of a pool

The surface area is calculated as

Surface Area = Rectangular Prism + Half Cylinder - Common Area

Using the above as a guide, we have the following:

Surface Area = 2 * (10 * 10 + 10 * 50 + 50 * 10) + 22/7 * 2.5 * (2.5 + 4) - 5 * 4

Evaluate

Surface Area = 2231

For the number of gallons, we have

Gallons = 2231/200

Evaluate

Gallons = 11.2

The closest to this is 10

Hence, the number of gallons is 10

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To solve this problem, we need to use some trigonometry. We can use the tangent function to find the length of the magma below sea level.

Let's define the following variables:

• x: the length of magma below sea level (what we want to find)

• y: the total length of magma (which we don't know)

• θ: the angle of elevation, which is 40°

We can set up a right triangle with the hypotenuse representing the total length of magma (y), the opposite side representing the length of magma below sea level (x), and the adjacent side representing the distance from the volcano to the point where the magma rises above sea level (which we don't need to calculate).

Using the tangent function, we can write:

tan(θ) = x / y

Rearranging this equation, we get:

x = y * tan(θ)

Now we just need to plug in the values we know:

• θ = 40°

• y = 15 kilometers (since the magma reservoir is located 15 kilometers beneath the Chijiwa Bay)

Using a calculator, we can evaluate tan(40°) to be approximately 0.8391.

Plugging in these values, we get:

X = 15km*0.8391, X = 12.5865km

Therefore, the length of magma below sea level is approximately 12.5865 kilometers



The graph of the function x + 5y = 6 is added as an attachment

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

x+5y=6

Express the equation properly

So, we have

x + 5y = 6

The above expression is a an equation of a linear function

Make y the subject

So, we have

y = -x/5 + 6/5

So, we have

Next, we plot the graph using a graphing tool

To plot the graph, we enter the equation in a graphing tool and attach the display

See attachment for the graph of the function

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Answer:

SIf Caden's burrito stand uses 7/8 of a bag of tortillas each day, then in one day, the stand will use 1 bag of tortillas after (1 / 7/8) = 8/7 days.

Therefore, 7 7/8 bags of tortillas will last for (7 7/8) x (8/7) = 8 days.

So, 7 7/8 bags of tortillas will last for 8 days at Caden's burrito stand.

Answer: 225 cm^3

Step-by-step explanation: To find the volume of the composite object, we need to find the sum of the volumes of the cylinder and the cone.

Volume of cylinder = pi * r^2 * h = 3 * 3^2 * 7 = 189 cubic units

Volume of cone = 1/3 * pi * r^2 * h = 1/3 * 3 * 3^2 * 4 = 36 cubic units

Total volume of composite object = volume of cylinder + volume of cone = 189 + 36 = 225 cubic units.

Therefore, the volume of the composite object is 225 cm^3.

Answer: 135 cm³

Step-by-step explanation:

You have 2 shapes.  Find volume for both and add them

V(cone) = [tex]\frac{\pi r^{2} h}{3}[/tex]            r=3        h=3       [tex]\pi[/tex]=3

            =[tex]\frac{3(3^{2})3 }{3}[/tex]

            =27

V(sphere)= [tex]\frac{4}{3 }\pi r^{3}[/tex]         r=3    [tex]\pi[/tex]=3

               = [tex]\frac{4}{3 }(3) 3^{3}[/tex]

               =108

Add the 2 volumes

V=27+108 = 135 cm³

For a normal distribution of SAT, scores of students particular high school over the last 8 years. The actual SAT score is equals the 224.213.

A normalized value called z-score can be associated to every data, (x) which is normally distributed. The z-score formula is an extremely used way of comparing data sets which are normally distributed. We have a study of students which is conducted from a particular high school over the last 8 yrs. In case of SAT scores

Mean of score, μ = 1019

Standard deviations of score, σ = 201

The scores on sat test are normally distributed. In case of ACT score, Mean of score = 20

Standard deviations of score = 5.1

Now, if a student got sat score that is the 27-percentile. We have to determine actual sat score. Probability value for varible, p value = 0.27

So, using normal distribution table or P value to Z-score calculator value of 27th percentile corresponds to a z-score of 0.613. Using Z-score formula,

[tex]z = \frac{ X - \mu}{ \sigma}[/tex]

so, [tex] 0.613= \frac{ X - 1019}{ 201}[/tex]

Solve the expression,

=> 201 × 0.613 = X - 101

=> X= 101 + 123.213

=> X = 224.213

Therefore, a score of 224.213 corresponds to the 27th percentile .

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Answer:

Yes, the 3-4-5 triangle and the 1.5, 2, 2.5 triangles are both working right triangles.

Step-by-step explanation:

I am assuming that the triangle we are given below is 1.5, 2, 2.5, and not necessarily a Pythagorean triple (we are asked to check if it is). We can check if this triangle meets the Pythagorean Theorem, which states that:

a^2+b^2=c^2

Where a and b are both the legs of the triangle and c is the hypotenuse (longest side). Now we can simply plug in 1.5, 2, and 2.5 and see if we get a working Pythagorean triple (if so, then the equation will be true).

(1.5)^2+2^2= 2.25 + 4= 6.25

and

(2.5)^2=6.25

This works! Giving that:

(1.5)^2+2^2=(2.5)^2 in the form of: a^2 + b^2=c^2

Now for the second part of the problem, how can we figure out if a 3,4, and 5 triangle is also a working Pythagorean triple by using our existing knowledge about the 1.5, 2, 2.5? Well, the 3, 4, and 5 triangle is also the right triangle! This is because every number in the set "1.5, 2, 2.5" is simply multiplied by 2, which is alike to scaled triangles. We can see so like this:

1.5*2=3

2*2=4

2.5*2=5

It is scaled up from the 1.5, 2, and 2.5 triangles! Now lets double check our work and see if we are correct.

3^2+4^2=9+16=25

5^2=25

Thus,

(3)^2+(4)^2=(5)^2

So, yes, the 3, 4, and 5, triangles and the 1.5, 2, 2.5, triangles are both working Pythagorean triples, we were able to prove this by scaling up and existing triple to find new ones. Have a great day!

Answer:

Slope

Step-by-step explanation:

I pretty sure it is slope because I did this question beginning of the year and I know this by heart it is slope

The value of the variable x are;

31. x = 1

32. x = 2

33. x = -3

34. x = 5

35.  x= 17

From the information given, we have to know that;

We then have;

m<2 and m< 7 are corresponding angles

Then,

2x = 8x - 6

collect the like terms

x = 1

m<1 = m< 8; corresponding angles

3x - 2 = 5x - 4

collect the like terms

x = 1

m<2 = m<5

6x + 4 = 8x + 10

collect the like terms

x = -3

m<1 = m< 6

2x - 5 = x

collect the like terms

x = 5

m<3 + m< 4 = 180

3x + 6 + 7x + 4 = 180

collect the terms

10x = 170

x = 17

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The polynomial with a factor of x + 1 is f(x) = x³ + 3x² + 3x + 1

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

Factor =  (x + 1)

The above factor is a linear factor

Since, we need at least two factors to make a polynomial, we can use the following equation

f(x) = (x + 1)³

When expanded, we have

f(x) = x³ + 3x² + 3x + 1

Hence, a polynomial with a factor of x + 1 is f(x) = x³ + 3x² + 3x + 1

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The p-value for the hypothesis test is approximately 0.65.

To find the p-value for the hypothesis test, we need to determine the test statistic and the corresponding probability.

First, we need to state the null and alternative hypotheses:

Null Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is equal to the mean number of alcoholic drinks for U.S. college students in general, which is 4.73.

Alternative Hypothesis: The mean number of alcoholic drinks for college students at the liberal arts college is not equal to the mean number of alcoholic drinks for U.S. college students in general.

Next, we need to determine the test statistic, which is calculated as follows:

t = (sample mean - hypothesized mean) / (standard deviation / sqrt(sample size))

t = (4.45 - 4.73) / (3.92 / sqrt(70))
t = -0.28 / 0.47
t = -0.596

Using a t-distribution table with 69 degrees of freedom (70 - 1), we find the corresponding two-tailed probability to be 0.553.

Therefore, the p-value for the hypothesis test is 0.553. This means that if we assume the null hypothesis is true, there is a 55.3% chance of observing a sample mean of 4.45 drinks per week or more extreme. Since this p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that the mean number of alcoholic drinks for college students at the liberal arts college differs from the mean number of alcoholic drinks for U.S. college students in general.
To find the p-value for the hypothesis test, we first need to set up the null and alternative hypotheses:

Null hypothesis (H₀): The mean number of alcoholic drinks for college students at this liberal arts college is equal to the national mean (µ = 4.73).
Alternative hypothesis (H₁): The mean number of alcoholic drinks for college students at this liberal arts college is different from the national mean (µ ≠ 4.73).

Next, we'll perform a t-test, since we have a sample mean, standard deviation, and sample size, but not the population standard deviation.

First, calculate the t-statistic:
t = (sample mean - population mean) / (sample standard deviation / √sample size)
t = (4.45 - 4.73) / (3.92 / √70)
t ≈ -0.46

Now, we need to find the degrees of freedom (df) for the t-distribution:
df = sample size - 1
df = 70 - 1 = 69

Using a t-table or t-distribution calculator, we can find the p-value for a two-tailed test (since we're testing for a difference, not specifically greater or lesser) with t ≈ -0.46 and df = 69. The p-value is approximately 0.65.

Your answer: The p-value for the hypothesis test is approximately 0.65.

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The new average waiting time in the queue as per the mentioned informations would be calculated to be 2 minutes.

To calculate the new average waiting time in the queue, we need to use Little's Law, which states that the average number of customers in a queuing system is equal to the average arrival rate of customers multiplied by the average time a customer spends in the system:

L = λW

where L is the average number of customers in the system, λ is the arrival rate, and W is the average time a customer spends in the system.

Assuming that the arrival rate of customers remains the same, the only thing that changes when we replace Tim Gonzales with John Thunderbolt is the average time a customer spends in the system, which includes both the time spent waiting in the queue and the time spent being served.

Let's call the average time a customer spends in the system with Tim Gonzales WT and the average time a customer spends in the system with John Thunderbolt WJ

The average time a customer spends in the system with Tim Gonzales is equal to the average waiting time plus the average service time:

WT = W + 6

where 6 is the average service time for Tim Gonzales (we assume that it takes him 6 minutes to serve a customer on average).

The average time a customer spends in the system with John Thunderbolt is equal to the average waiting time plus the average service time:

WJ = W + 4

where 4 is the average service time for John Thunderbolt (we assume that it takes him 4 minutes to serve a customer on average).

We want to find the new average waiting time in the queue, which is just the difference between the average time a customer spends in the system with Tim Gonzales and the average time a customer spends in the system with John Thunderbolt:

W = WT- WJ

Substituting the expressions for WTand WJ, we get:

W = (W + 6) - (W + 4) = 2

Therefore, the new average waiting time in the queue would be 2 minutes.

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Answer:

69

Step-by-step explanation:

27 + 18 + 13 + 11 = 69

Therefore, the sum of 27, 18, 13, and 11 is 69

Your welcome

Answer:

The answer to your problem is, 69

Step-by-step explanation:

First lets split the problem into the following:

27 + 18      13 + 11

First we are going to do, 27 + 18

27 + 18 = 45. Done

Next we are going to do, 13 + 11

13 + 11 = 24. Done

Add them, 24 + 45

24 + 45 = 69

Thus the answer to your problem is, 69

The variance of the bedroom areas in the five-bedroom house is 864, and the standard deviation is approximately 29.39 square feet.


Mean: (100 + 100 + 120 + 120 + 180) / 5 = 620 / 5 = 124
Squared differences: (24^2, 24^2, 4^2, 4^2, 56^2) = (576, 576, 16, 16, 3136)
Mean of squared differences: (576 + 576 + 16 + 16 + 3136) / 5 = 4320 / 5 = 864
Variance: 864
Standard deviation: √864 ≈ 29.39


Hence, The variance of the bedroom areas in the five-bedroom house is 864, and the standard deviation is approximately 29.39 square feet.

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The election of 2000 demonstrated that a poll may not be reliable if the sample size is too small (option d).

The factor that can impact the reliability of a poll is bias. If the sample is biased, it may not accurately represent the larger population, leading to skewed results. Bias can occur in several ways, such as selecting a sample that is not representative of the larger population, asking leading questions, or using a sampling method that favors a particular group.

In the 2000 election, both of these factors contributed to the unreliability of the polls. The race was extremely close, with the outcome depending on the results in a few key states. Pollsters struggled to accurately predict the outcome of the election, with some predicting a win for Al Gore and others predicting a win for George W. Bush.

Additionally, the sample sizes and methods used by pollsters were called into question. Some pollsters used small sample sizes, while others were accused of bias in their sampling methods. The combination of these factors led to unreliable poll results and uncertainty about the outcome of the election.

Hence the correct option is (d).

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The value of -3(U x V) is 366. None of the options is correct.

What is dot product?

A pair of vectors' dot product is the result of adding the products of each corresponding component. It is equal to their product of magnitudes times the cosine of the angle at which they are separated. The magnitude square of a vector is its dot product with itself.

The given vectors are U=-6i-10j and V = 7i + 8j.

The formula of dot product is

A = x₁i + y₁j and  B = x₂i + y₂j

A.B = x₁x₂ + y₁y₂.

Apply the formula:

U.V = (-6×7) + (-10×8)

=-42 - 80

= - 122

Now calculate -3(U . V):

-3(U . V) = -3×(- 122)

-3(U . V) = 366

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Check the picture below.

[tex]\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=\sqrt{c^2 - a^2} \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{10400}\qquad \leftarrow 6400+4000\\ a=\stackrel{adjacent}{4000}\\ o=\stackrel{opposite}{SP} \end{cases} \\\\\\ SP=\sqrt{ 10400^2 - 4000^2}\implies SP=\sqrt{ 108160000 - 16000000 } \\\\\\ SP=\sqrt{ 92160000 }\implies SP=9600~mi[/tex]

The statements regarding the triangles can be completed with the following:

The converse Pythagoras theorem states that a triangle is a right triangle if the square of its longest side equals the sum of its squares on the other two sides.

The converse Pythagoras theorem can be used to determine whether a triangle is acute, right, or obtuse by comparing the sum of its two sides to the square of its third side.

Proof: If the square of the longest side in a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right-angled traingle.

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