Name an angle complementary to ∠HZJ. Be sure to use the three-letter naming convention.

To determine how long it will take Mary Corens to repay her student loan, we can divide the total loan amount of $15,000 by the annual repayment amount of $1,800. The result will give us the number of years it will take her to repay the loan.

it will take Mary approximately 8 years to repay the loan.

By dividing the total loan amount of $15,000 by the annual repayment amount of $1,800, we can calculate the number of years needed to repay the loan.

Loan amount: $15,000

Annual repayment: $1,800

Number of years = Loan amount / Annual repayment

Number of years = $15,000 / $1,800

Number of years ≈ 8.33

Since we are asked to round the answer to the nearest whole number, Mary will take approximately 8 years to repay the loan.

It's important to note that this calculation assumes a constant annual repayment amount of $1,800 throughout the entire loan repayment period. In reality, factors such as interest accrual and varying repayment schedules may affect the actual time it takes to fully repay the loan. Additionally, any changes to the annual repayment amount would also impact the duration of the loan repayment.

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Answer:

√3/3

Step-by-step explanation:

Multiply the numerator and denominator by the conjugate.

Hope this helps!! Please consider marking brainliest! Have a good one!!

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.

If the radical in the denominator is a square root, then you multiply by a square root that will give you a perfect square under the radical when multiplied by the denominator.   If the radical in the denominator is a cube root, then you multiply by a cube root that will give you a perfect cube under the radical when multiplied by the denominator and so forth...

Note that the phrase "perfect square" means that you can take the square root of it.  Just as "perfect cube" means we can take the cube root of the number, and so forth.  

Keep in mind that as long as you multiply the numerator and denominator by the exact same thing, the fractions will be equivalent.

Step 2: Make sure all radicals are simplified.

Some radicals will already be in a simplified form, but make sure you simplify the ones that are not.  If you need a review on this, go to Tutorial 39: Simplifying Radical Expressions.

Step 3: Simplify the fraction if needed.

Be careful.  You cannot cancel out a factor that is on the outside of a radical with one that is on the inside of the radical.  In order to cancel out common factors, they have to be both inside the same radical or be both outside the radical.

\(\huge\sf\underline{\purple{❥}\pink{Q}\orange{U}\blue{E}\red{S}\green{T}\purple{I}\pink{O}\red{N}}\)

\(\huge\sf\underline{\purple{❥}\pink{A}\orange {N}\blue{S}\red{W}\green{E}\purple{R}}\)

\( \frac{1}{ \sqrt{3} } \\ \\(to \: rationalize \: the \: denominator \\ we \: have \: multiply \: \frac{1}{ \sqrt{3} } \: to \: the \:given \: fraction \: \: \: ) \\ = \frac{1}{ \sqrt{3} } \times \frac{1}{ \sqrt{3} } \\ = ( \frac{1}{ \sqrt{3} } ) {}^{2} \\ = \frac{1}{3} \)

HOPE IT HELPS YOU..

The common difference of the arithmetic sequence 2, 7, 12, 17, ... is 5. The fifth term is 22. The nth term is given by the formula an = 2 + 4(n - 1). The 100th term is 497.

The common difference is calculated by subtracting the first term from the second term. In this case, 7 - 2 = 5. The fifth term is calculated by using the formula an = a1 + (n - 1)d, where a1 is the first term, n is the term number, and d is the common difference. In this case, a5 = 2 + (5 - 1)5 = 22. The nth term is also calculated using the same formula. In this case, an = 2 + 4(n - 1). The 100th term is calculated by plugging in n = 100 into the formula, which gives an = 497.

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The product of the Expression is 3/ (a-2).

In mathematics, an expression is a phrase that has at least two numbers or variables and at least one math operation. Addition, subtraction, multiplication, or division are all examples of math operations. An expression's structure is as follows:

(Number/variable, Math Operator, Number/variable) is an expression.

We have,

(2a - 7)/ a x (3a²)/  (2a² -11a + 14)

Now, simplifying the expression as

(2a - 7)/ a x (3a²)/  (2a² -11a + 14)

= (2a - 7)/ a x (3a²)/  (2a² -7a - 4a + 14)

= (2a - 7)/ a x (3a²)/  a (2a -7) -2 (2a- 7)

= (2a - 7)/ a x (3a²)/ (a- 2)(2a-7)

= 3a² / a(a-2)

= 3/ (a-2)

Thus, the product is 3/ (a-2).

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The weather that is most likely to occur where Richard is is rain shower.

Weather is the state of the atmosphere of a particular place over a short period of time. There is low atmospheric pressure, so it is likely that it would rain. This is because when the  atmospheric pressure is low, it is likely that it would rain.

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Answer:

Rain shower is most likely to occur where Richard is. (Option c)

• The air pressure is lower than the normal and that's why it suggests that the rainfall will happen in that place because rainfall generally occurs in the place where the low pressure is formed.

• And,the temperature is above than the freezing point of the water so there are no chances of the snowfall in that place.

• That's why rainfall is the most probable thing that will happen in that place.

Step-by-step explanation:

After six​ months, the​ subjects' symptoms are studied and compared. Answer parts​ are given below.

An assumption or concept is given as a hypothesis for the purpose of debating it and testing if it might be true.

Given:

A pharmaceutical company wants to test the effectiveness of a new allergy drug.

The company identifies 250 females​ 30–35 years old who suffer from severe allergies.

The subjects are randomly assigned into two groups.

One group is given the new allergy drug and the other is given a placebo that looks exactly like the new allergy drug.

After six​ months, the​ subjects' symptoms are studied and compared.

Here, 30-35 year-old girls are used to test the new allergy medication's effects.

(a)

Females between the ages of 30 and 35 who are the test subjects are the experimental units.

The new allergy medication, whose results are being studied, is the remedy.

It's best to choose C.

(b)

A bias may develop if a researcher or patient knows whether subjects received a medication or a placebo.

In this case, choice B is preferable.

(c)

If neither the researcher nor the subject knew whether they were receiving a medicine or a placebo, the study would be considered double-blind.

In this case, choice A is preferable.

Therefore, all the correct choices are given above.

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The complete question is given in the image.

Answer:

Step-by-step explanation:

cat

The length is 50 I think

Hope this helps

The width of the cooling tower at the base of the structure is (D) 40 meters.

Now, calculate the cooling tower's width:

Equation: x2/400 given (y-90)

Calculating the width:

Therefore, the width of the cooling tower at the base of the structure is (D) 40 meters.

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Answer:

Starting on a platform 2 feet above sea level, dive down to a location that is 18 feet below sea level, and then rise 8 feet.

Step-by-step explanation:

Using the 2 + (-20) + 8 to describe movement relative to sea level ;

2 can be taken as the starting point, positive values represents elevation above sea level ;

2 can be taken as 2 feet platform above sea level ;

- 20 represents distance dived from platform, negative signifies elevation below sea level ; the distance dived relative to sea level is (-20 + platform height)

(-20 + 2) = - 18

8 feets means a final elevation of 8 above sea level (positive value).

Answer:

hmmmm

wouldent it be

1/2 1/12

Step-by-step explanation:

Answer:

Its 8/12 and 9/12

Step-by-step explanation:

Answer:

\(w=\frac{h}{m} -\frac{3}{3}\)

I hope this is what you were asking for :)

We need to know about test statistic to solve the problem. The formula we will need to calculate test statistic is  (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Test statistic is a number calculated by a statistical test. It describes how far the observed data is from the null hypothesis of no relationship between variables or no difference among sample groups. The test statistic can be calculated using the sample mean, the population mean and population standard deviation.

test statistic= (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

Therefore the formula to calculate the test statistic will be (sample mean- population mean)/(standard deviation/\(\sqrt{size of sample}\))

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Answer: A

Step-by-step explanation:

We are given the equation C = 270g-3g², where g is the number of goods Sam sells for the company.

The number of goods Sam sold in January is 30, so his commission in January will be:

\(C(30) = 270(30) - 3(30)² = $6,300\)

The number of goods Sam sold in February is 40, so his commission in February will be:

\(C(40) = 270(40) - 3(40)² = $7,200\)

To find out how much additional commission Sam made in February over January, we need to subtract the commission he made in January from the commission he made in February:

Additional commission in February = C(40) - C(30) = $7,200 - $6,300 = $900

Therefore, the additional commission that Sam made in February over January is $900. Hence, the correct option is d) $1,500.

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Once you have computed the expected value, you can mark your guess on the graph by finding the point where the curve is balanced. This is the point where the area to the left of the point is equal to the area to the right of the point.

A probability density function is a function that describes the likelihood of a random variable taking on a certain value. The area under the curve of a probability density function must be equal to 1. The normalizing constant, denoted by k, is a constant that is multiplied by the probability density function to ensure that the area under the curve is equal to 1. In other words, k is the value that makes the integration of the probability density function equal to 1.

To find the value of k, you would need to integrate the probability density function over its entire range and set the result equal to 1. Once you have found k, you can sketch the density function by plotting the function on the y-axis and the possible values of x on the x-axis.

The expected value of a random variable is a measure of the center of its distribution. It represents the average value that the variable would take if it were repeated many times. To compute the expected value of a continuous random variable, you would need to integrate the product of the random variable and its probability density function over its entire range.

Once you have computed the expected value, you can mark your guess on the graph by finding the point where the curve is balanced. This is the point where the area to the left of the point is equal to the area to the right of the point.

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Answer:

96

Step-by-step explanation:

Let's assume that the marks needed in the next exam is \(x\). Then if the average becomes 90,

\(\frac{80 + 93 + 91 + x}{4}= 90\)

Now we can simply solve for \(x\):

⇒ \(\frac{264 + x}{4}= 90\)

⇒ \(264 + x = 360\)            [Multiplying both sides by 4]

⇒ \(x = 360 - 264\)            [Subtracting 264 from both sides]

⇒ \(x = \bf96\)

Therefore, you need to score 96 in your next exam to have an average of 90 on the four exams.

Answer:

y=x-2

Step-by-step explanation:

y-y1=m(x-x1)

y-3=1(x-5)

y-3=x-5

y=x-5+3

y=x-2

Answer:

20 minutes

Step-by-step explanation:

The first point to plot on the mean control chart would be at 1.9 at control chart with both limits.

1. There are four measurements in each sample, as shown in the table.

2. To plot the first point on the mean control chart, we need to calculate the mean of the first sample. Adding up the four measurements from the 10:00 am sample (2.0 + 1.8 + 2.0 + 1.8) gives a total of 7.6. Dividing by the number of measurements in the sample (4) gives a mean of 1.9. Since the mean is within the control limits of 1.8 and 2.2, the first point on the chart would be plotted at 1.9.
1. To determine how many measurements are in each sample, we simply count the number of measurements provided for each time.

10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)

Each sample contains 4 measurements.

2. To plot the first point on a mean control chart, we need to calculate the mean of the first sample (10:00 am).

Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4
Mean = 7.6 / 4
Mean = 1.9

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1. There are 4 measurements in each sample.

2. The first point to plot on the mean control chart would be 1.9, corresponding to the 10:00 am sample.

To determine the number of measurements in each sample, simply count the number of values for each time point.
10:00 am: 4 measurements (2.0, 1.8, 2.0, 1.8)
10:15 am: 4 measurements (2.0, 2.0, 2.0, 2.0)
10:30 am: 4 measurements (1.8, 1.9, 2.1, 2.2)
10:45 am: 4 measurements (2.1, 2.1, 1.9, 1.9)
11:00 am: 4 measurements (1.6, 2.0, 2.2, 1.7)
There are 4 measurements in each sample.
To plot the first point on the mean control chart, calculate the mean of the first sample (10:00 am).
Mean = (2.0 + 1.8 + 2.0 + 1.8) / 4 = 7.6 / 4 = 1.9.

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Answer:what is the graph?

Step-by-step explanation:

The result is not statistically significant.

To test the hypothesis is the mean SAT score is less than 1520 at 5% significance level.

The null hypothesis is

H₀ : μ ≥ 1520

The alternative hypothesis is

Hₐ : μ ≤ 1520

then the test statistic is,

t = (x - μ)/(s/√n)

 = (1501 - 1520)/(53/√20)

t = - 1.603

The t-test statistic is - 1.603.

Degree of freedom n - 1 = 20 - 1 = 19

Hence the t-critical value is -1.792.

The conclusion is that the t value corresponds to sample statistics is not fall in the critical region, so the null hypothesis is not rejected at 5% level of significance. There is insignificance evidence indicates that the mean SAT score is less than 1520.

The result is not statistically significant.

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I) f is continuous at x=2

II) f is differentiable at x=2

These both f (function ) are true

The given limit can be recognized as the definition of the derivative of f at x=2. Specifically, it states that the derivative of f at x=2 is equal to 5.

Using this information, we can make the following conclusions:

I) We cannot say for sure whether f is continuous at x=2 based on the given limit alone. While a function being differentiable at a point implies that it is also continuous at that point, the converse is not necessarily true. Therefore, we would need additional information to determine whether f is continuous at x=2.

II) The given limit implies that f is differentiable at x=2, since the limit exists and is finite. Specifically, we can say that the derivative of f at x=2 exists and is equal to 5.

III) The given limit also implies that the derivative of f is continuous at x=2. This is because the limit defines a continuous function at x=2, and it is well-known that if a function is differentiable at a point, then it is also continuous at that point.

Therefore, the correct answers are II and III.

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Answer:

3 & 1

6 & 2

9 & 3

12 & 4

Step-by-step explanation:

Hope that helps!

Answer:

3/4

Step-by-step explanation:

.74(75%) is equal to 75/100

The greatest common factor is 25, so divide 75 by 25 and 100 by 25.

75/25=3  100/25=4

So, 75/100 simplified is 3/4.

Answer:

3/4 is 75% as a fraction

Step-by-step explanation:

Every percent is over 100.

To convert, you would to 75/100 and divide both top and bottom by 5

\(\frac{75}{100} / \frac{5}{5}\) and you would get 15/20

You answer would be 15/20 UNLESS its asking you to put it in simplest form.

To put it into simplest form, you would divide both sides by 5 again.

The test statistic is 5.7735. This means that the sample provides enough evidence to counter the claim made suggesting that the average service time at the deli counter is different from 5 minutes.

To determine whether the sample provides enough evidence to counter the claim made by the store's management, we need to set up the null and alternative hypotheses and conduct a hypothesis test.

Null Hypothesis (H₀): The average service time at the deli counter is 5 minutes.

Alternative Hypothesis (H₁): The average service time at the deli counter is not equal to 5 minutes.

We will conduct a two-tailed hypothesis test since the alternative hypothesis does not specify a direction.

The significance level (α) is given as 0.01, which indicates that we are willing to accept a 1% chance of making a Type I error (rejecting the null hypothesis when it is true).

To perform the hypothesis test, we can use a t-test since the population standard deviation is unknown. With a sample size of 50, we can assume that the sampling distribution of the sample mean will be approximately normal by the Central Limit Theorem.

We can calculate the test statistic using the formula:

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

In this case, the sample mean is 5.6 minutes, the hypothesized mean is 5 minutes, the sample standard deviation is 1.4 minutes, and the sample size is 50.

Substituting these values into the formula, we get:

t = (5.6 - 5) / (1.4 / \(\sqrt{(50)}\))

Calculating this expression, we find that t ≈ 5.7735.

To determine the critical value for the t-test, we need to consider the degrees of freedom, which is the sample size minus 1 (50 - 1 = 49), and the significance level of 0.01. Using a t-table or a t-distribution calculator, we find that the critical value for a two-tailed test with 49 degrees of freedom at a significance level of 0.01 is approximately ±2.6839.

Since the calculated test statistic (5.7735) is greater than the critical value (2.6839), we have sufficient evidence to reject the null hypothesis. This means that the sample provides enough evidence to counter the claim made by the store's management, suggesting that the average service time at the deli counter is different from 5 minutes.

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Answer:

\(3uq \\ 3 \times 2 \times 6 \\ = 36\)

Answer:

\(36\)

Step-by-step explanation:

\(3uq \\ = 3(2)(6) \\ = 36\)

Answer: the first one. the graph is right side up.

Answer:

fuffufufufufufufufufufufufufufuufufufufufufufufufufufufufufffuffuffuffuufufuf

Step-by-step explanation:

The first and third rectangular prisms have the same volume of 30 cubic units.

The second rectangular prism has a volume of 350 cubic units, and the fourth rectangular prism has a volume of 24 cubic units.

The volume of each of the rectangular prisms can be calculated as follows:

1.   length: 1; width: 10; height: 3

volume = 1 x 10 x 3 = 30

2.  length: 5; width: 10; height: 7

volume = 5 x 10 x 7 = 350

3.   length: 2; width: 5; height: 3

volume = 2 x 5 x 3 = 30

4.   length: 4; width: 2; height: 3

volume = 4 x 2 x 3 = 24

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