The width of a rectanle is 8n - 8.5 feet and the lenght is 8.5n + 10 feet. Find the perimeter of the rectangle

The surface area of the figure is the amount of area covered by the figure.

The figure is not given, so I will give a general solution.

The method followed by Brad to calculate the surface area of the prism is correct.

However, whether Brad correctly calculates the areas of the rectangular prism and the triangular prism cannot be determined.

So, the conclusion is that:

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Answer:

\( \huge \boxed{f(15) = 152 }\)

Step-by-step explanation:

\(f(x) = 15 {x}^{2} - x + 20\)

To find f(3) , substitute the value of x that's 3 into f(x). That is for every x in f(x) replace it with 3.

We have

\(f(15) = 15( {3})^{2} - 3 + 20 \\ \: \: = 15(9) + 17 \\ = 135 + 17 \: \\ = 152 \: \: \: \: \: \: \: \: \: \: \)

We have the final answer as

\(f(15) = 152 \)

Hope this helps you

The registrants would be able to see the 6 sightseeing tours in 18 ways.

Here it is given that the convention has organized the 6 sightseeing tours on 3 days each.

This implies that the 6 sightseeing tours are available on all three days.

Hence, the registrants would be able to book the tour on any of the one days.

Hence, on day 1

the registrants will be able to tour in  ways

On day 2

the registrants would again be able to tour in 6 ways,

Similarly on day 3, they will again be able to tour in 6 ways.

Since they need to choose either of the days given, the total number of ways to tour will be

no.of ways for day 1  +  no. of ways for day 2  +  no. of d6ays for day 3

= 6  +  6  +  6

= 18 ways

Hence, they can go on a sightseeing tour in 18 ways.

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1) Calculating the P-value assumes that the sample is a random sample:

True. The P-value calculation is based on the assumption that the sample is randomly drawn from the population, ensuring unbiased results.

2) If you reject H0 with a test, you will be making a Type II error: False. If you reject the null hypothesis when it is true, you are making a Type I error, not a Type II error.

3) If you fail to reject H0 with a test, you will be making a Type I error: False. If you fail to reject the null hypothesis when it is false, you are making a Type II error, not a Type I error.

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The correlation coefficient in expected returns between Asset A and Asset B is 0.62 (approx).

Given,

Expected return of Asset A, rA = 10.67%

Standard deviation of expected returns of Asset A, σA = 16.36%

Expected return of Asset B, rB = 16.85%

Standard deviation of expected returns of Asset B, σB = 22.72%

Weightage of Asset A, wA = 75%

Weightage of Asset B, wB = 25%

The standard deviation of the portfolio, σP = 15.89%

Let us calculate the covariance between Asset A and Asset B.

σA = 16.36%

σB = 22.72%

rAB = correlation coefficient between A and B

Based on the given information, the following formula is used to calculate the standard deviation of the portfolio:

σP² = wA² σA² + wB² σB² + 2 wA wB

Cov(A, B)σP² = (0.75²)(16.36²) + (0.25²)(22.72²) + 2(0.75)(0.25)

Cov(A, B)σP² = 268.4911 + 129.562 + 0.747

Cov(A, B)σP² = 398.8008 + Cov(A, B)

Cov(A, B) = σP² - 398.8008

Cov(A, B) = 253.8503

Therefore,

Correlation(A, B) = rAB

= Cov(A, B) / (σA * σB)

rAB = 253.8503 / (16.36 * 22.72)

rAB = 0.619

Hence, Correlation(A,B)= 0.62 (approx).

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Answer:

Cylinder B has a greater volume

Step-by-step explanation:

Volume of a cylinder\(=\pi r^2h\)

Cylinder A

h=5m, r=3m

Volume

\(=3.14 *3^2*5\\=141.3m^3\)

Cylinder B

h=3m, r=5m

Volume

\(=3.14 *5^2*3\\=235.5m^3\)

Cylinder B has a greater volume.

Answer:

9:45

Step-by-step explanation:

if you still estimate you will get it wrong

Answer: x ≠ 5; x≠ 0

\(\frac{4}{x-5}+\frac{1}{x}=\frac{x-1}{x-5}\\\\<=> \frac{4x+x-5}{x(x-5)}=\frac{x(x-1)}{x(x-5)} \\<=> 4x+x-5=x(x-1)\\<=> 5x-5 = x^{2}-x\\<=> x^{2} -6x+5=0\\<=>(x-5)(x-1)=0\\\)

because x≠ 5 => x - 5 ≠ 0

=> x - 1 = 0

⇔ x = 1

Step-by-step explanation:

See attachment for math work and answer.

Reject x = 5.

Answer is x = 1.

Jesse and Filipe are desk workers. In a day, Jesse burns about 480 more calories than Filipe.

A calorie is a unit of energy. The energy that food or drink provides to the body is measured in calories. The number of calories we eat and drink must equal the energy we consume through daily activity for weight maintenance.

A desk job is a job that requires sitting at a desk and working with a computer. It is regarded as a sedentary activity. When it comes to sitting at a desk, some individuals move about and stand more than others.

On average, a sedentary person burns about 1.2-1.4 times their basal metabolic rate (BMR) per day. BMR is the amount of energy (in calories) that the body needs to perform basic functions like breathing, circulating blood, and maintaining organ function while at rest.

So, if we assume that Jesse is more active than Filipe, we can estimate that Jesse burns about 1.4 times their BMR per day, while Filipe burns about 1.2 times their BMR per day.

Let's say that Jesse's BMR is 1800 calories per day, and Filipe's BMR is 1700 calories per day. Then we can estimate:

Jesse burns 1.4 x 1800 = 2520 calories per day

Filipe burns 1.2 x 1700 = 2040 calories per day

The difference in calorie burn between Jesse and Filipe is:

Jesse burns 2520 - 2040 = 480 more calories per day than Filipe

Therefore, Jesse burns about 480 more calories per day than Filipe due to his greater movement and standing.

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Answer:

D. Absolute value parent function

we can know fro the symbol |x| in the question written f(x)= |3|

Answer:

Fruit Juice = 24 litres

Lemonade = 16 litres

Step-by-step explanation:

So, the ratio: \(3:2\) really just means: "for every every 3 litres of fruit punch, there is 2 litres of lemonade.

Or in other words, every 3 litres of fruit punch, the entire mixture of both fruit punch and lemonade will be 5 litres, since there is 3 litres and 2 litres.

So dividing the 40 litres, by this 5 litres, we get 8. So we know there will be "8" of 3 litres of fruit punch, and "8" of 2 litres of lemonade.

Thus there will be 24 litres of fruit punch, and 16 litres of lemonade.

Answer:

2 × 10^5

Step-by-step explanation:

Answer: -125

To solve, we mutiply -25 by 5. We get -125.

Answer: i think its 4

Step-by-step explanation:

Answer:

2 ounces of yellow, six of  blue.

Step-by-step explanation:

If you teacher wants you to simplify put: yellow: 1, blue: 3

If not, put: yellow: 2, blue: 6

Based on the given information, we have the mean concentration of sodium in the drinking water of a water system in Connecticut as 26.4 mg/l and the standard deviation as 6 mg/l.

The water department selects a simple random sample of 32 water specimens over the course of a year. To answer the question using the distributions tool, we need to set the mean and standard deviation parameters on the tool to the expected mean and standard error for the distribution of sample mean concentrations.

The expected mean for the distribution of sample mean concentrations is the same as the mean concentration of sodium in the drinking water, which is 26.4 mg/l.

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The water department in Connecticut is monitoring the concentration of sodium in their drinking water. By calculating the mean and standard error for the distribution of sample means, they can determine the probability of the mean concentration exceeding the notification level of 28 mg/l. If this probability is low, the water department will notify the public and recommend necessary actions.

In this scenario, the water department in Connecticut wants to monitor the concentration of sodium in their drinking water. They have set a notification level of 28 mg/l, meaning that if the mean concentration of sodium across a sample of 32 water specimens exceeds this level, they will notify the public.

To analyze this situation, we can use the distribution of sample means. The mean concentration of sodium in the drinking water of the water system is given as 26.4 mg/l, with a standard deviation of 6 mg/l.

To find the expected mean and standard error for the distribution of sample means, we can use the following formulas:

Expected mean of sample means = population mean

                                                        = 26.4 mg/l
Standard error of sample means = population standard deviation / square root of sample size

Using the given values, the standard error of sample means can be calculated as follows:
Standard error of sample means = 6 mg/l / square root of 32

                                                      ≈ 1.06 mg/l

Now, we can use a distributions tool to find the probability that the mean concentration of sodium in the sample of 32 water specimens exceeds 28 mg/l. We will set the mean parameter on the tool to 26.4 mg/l and the standard deviation parameter to 1.06 mg/l.

By entering these values into the distributions tool, we can find the probability of obtaining a mean concentration greater than 28 mg/l. If this probability is less than a certain threshold (e.g., 0.05), it indicates that the mean concentration exceeding 28 mg/l is unlikely to occur by chance alone. In such cases, the water department would notify the public and recommend that individuals on sodium-restricted diets inform their physicians of the sodium content in their drinking water.

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Answer:

1.5gallons

Step-by-step explanation:

Here,

no. of bottles(a) : 12

no. of cups (b) :a*2

=12*2

=24

Now,

No. of gallons. :24/16

:1.5gallons

.·.A cartoon contains 1.5 gallons of lemon tea.

To represent the final price (Px) of the items purchased, we first apply the 30% holiday sale discount and then the 15% off coupon. Let's find the correct function:

1. Apply the 30% holiday sale: Price becomes 0.7x (as 100% - 30% = 70%)
2. Apply the 15% off coupon: Final price becomes 0.85 * 0.7x (as 100% - 15% = 85%)

Now, multiply 0.85 by 0.7, which equals 0.595.

Therefore, the function representing the final price is Px(x) = 0.595x.

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The measure of the side 'x' is 16.31 m. The correct option is C.

Trigonometry is a branch of mathematics that deals with the study of the relationships between the sides and angles of triangles. It is a fundamental part of geometry that has many practical applications in fields such as physics, engineering, navigation, and surveying.

Given that in a right-angled triangle, the value of side RS is x, angle R is 25° and the side RT is 18 m.

The value of x will be calculated as,

sin65° = x / 18

x = 18 x sin65°

x = 16.31 m

Hence, the correct option is C.

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The approximate size of the cover that Maria will need to buy is 45. 84 square feet

The formula for calculating the circumference of a circle is expressed as;

Circumference = πr²

Where 'r' is the radius of the circle

Now, let's substitute the value of the circumference

24 = 2 × 3. 14 × r

r = 24/6. 28

r = 3. 82 feet

Formula for area = πr²

Substitute value of r

Area = 3. 14 × (3. 82)²

Area = 3. 14 × 14. 59

Area = 45. 84 square feet

Hence, the value is  45. 84 square feet

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Answer:

\((3 \: \: x) \binom{2x}{4} = (20) \\ (3 \times 2x) + (x \times 4) = (20)\\ 6x + 4x = 20 \\ 10x = 20 \\ x = \frac{20}{10} \\ \boxed{x = 2}\)

The 97% confidence interval for a sample of 204 soda cans with a mean of 12.05 ounces and a standard deviation of 0.08 ounces is approximately (12.026, 12.074) ounces.

To find the 97% confidence interval, follow these steps:

1. Identify the sample size (n=204), sample mean (X-bar=12.05), and standard deviation (σ=0.08).
2. Determine the appropriate z-score for a 97% confidence interval, which is 2.17 (from a standard normal distribution table).

3. Calculate the standard error (SE) by dividing the standard deviation by the square root of the sample size: SE = σ/√n = 0.08/√204 ≈ 0.0056.

4. Multiply the z-score by the standard error: 2.17 * 0.0056 ≈ 0.0122.

5. Subtract this product from the sample mean for the lower bound: 12.05 - 0.0122 ≈ 12.026.

6. Add this product to the sample mean for the upper bound: 12.05 + 0.0122 ≈ 12.074.

Thus, the 97% confidence interval is approximately (12.026, 12.074) ounces.

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The proportion percent of people who are 67 years old and who are not in the club will be 25.09 : 74.91.

The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.

As per the data given in the question,

Total people in football club = 193

Total 67-year people in the club = 13

Then, the percentage of 67-year people in the club is,

193 × 13/100

= 25.09%

And, the percentage who are not 67 years old is,

(100 - 25.09)% = 74.91%

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This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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Answer:

x+5=5

Step-by-step explanation:

This is an equation where you are actually solving it. The others are expressions.

Answer:

n = 116.2 ≈ 117  

Option E) 117 is the correct answer.

Step-by-step explanation:

Given the data in the question;

Exceed = 0.1

{ 1 - 0.1 = 0.9 }

normal table value at 0.9 = - 1.285

Normal table;

hence

( y - 400 ) / 40 = -1.285

y - 400  = -51.4

y = 400 - 51.4

y = 348.6

so,

348.6 = ∈(y) = ∈[ ⁿ∑\(_{i=1\) X\(_i\) ]

348.6 = n.∈( X\(_i\)  )

we substitute

348.6 = n × 3

n = 348.6 / 3

n = 116.2 ≈ 117  { roundup since we talking of number of cars i.e sample size }

Option E) 117 is the correct answer.

Let's assume the sum of the scores of the 28 students who took the test yesterday is 28 * 72 = 2016.

We know that the sum of the scores of all 30 students is (28 * 72) + x + y, where x and y are the scores of the two students who took the test this morning.

We also know that the mean of all 30 scores is 73. So we can write an equation:

[(28 * 72) + x + y]/30 = 73

Multiplying both sides by 30, we get:

2016 + x + y = 2190

So, x + y = 174.

We are given that the difference of the two scores is 22, so we can write another equation:

y - x = 22

Solving these two equations simultaneously, we get y = 98 and x = 76.

Therefore, the lower score from this morning is 76.

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Answer: a+c=27,126

Step-by-step explanation:

According to the given figure Mrs Martinez data has greater variability than Mrs Jone's data.

The average may be calculated by dividing the total number of values by the sum of all the numbers. The arithmetic average of a group of two or more data variables is referred to as a mean. Typically, average is referred to as mean or arithmetic mean. The word "mean" is only a way of defining the sample's average.

By adding up each value individually and dividing the result by the total number of observations, the average is obtained. The "middle" value, for which half of such observations are greater and half are less, is used to compute the median.

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