Divide and state the quotient in simplest form.

Divide And State The Quotient In Simplest Form.

Answers

Answer 1

The quotient of the two fractions is (x - 5) / (x - 4).

Option D is the correct answer.

We have,

To divide two fractions, we can multiply the first fraction by the reciprocal of the second fraction.

In this case, that means we need to multiply:

(x² - 2x - 15) / (x + 2) x (x + 2) / (x² - x - 12)

Notice that the (x + 2) terms in the numerator and denominator of the first fraction cancel out with the denominator of the second fraction, so we can simplify before multiplying:

(x² - 2x - 15) / 1 x 1 / (x² - x - 12)

Now we can multiply the numerators and the denominators separately:

(x² - 2x - 15) / (x² - x - 12)

To simplify further, we can factor both the numerator and the denominator:

(x - 5)(x + 3) / (x - 4)(x + 3)

Notice that the (x + 3) terms in the numerator and denominator cancel out, leaving:

(x - 5) / (x - 4)

Therefore,

The quotient of the two fractions is (x - 5) / (x - 4).

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Related Questions

I need help i don't know how to do this please

Answers

The size of matrix cM is given as follows:

9 x 10.

What happens when a matrix is multiplied by a constant?

When a matrix is multiplied by a constant, we have that every element in the matrix is multiplied by the constant. Hence, the dimension of the matrix remains constant.

The parameters for this problem are given as follows:

Constant c.Matrix M of dimensions 9 x 10.

Hence the size of matrix cM is given as follows:

9 x 10.

(same size as the original matrix, as we simplify multiply each element in the matrix by the constant, hence the dimensions remain the same).

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find the probability that a randomly selected point within the large square falls in the red shaded square 6 6 15 15 p= enter as a decimal rounded to the nearest hundredth

Answers

The probability that a randomly selected point within the red-shaded square is 0.16

Finding the probability of a point

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

Red square of 6 by 6White square of length 15

The areas of the above shapes are

Red square = 6 * 6 = 36

White square = 15^2 = 225

The probability is then calculated as

P = Red square /White square

So, we have

P = 36/225

Evaluate

P = 0.16

Hence, the calculated value of the probability that the point falls in the red square is 0.16

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3. Find the solution to each equation mentally.
a. 30+ a = 40
b. 500+ b = 200
C. -1+c= -2
d. d +3.567=0

Answers

Answer:

[tex]a. \: 30 + a = 40 \\ a = 40 - 30 \\ a = 10 \\ b. \: 500 + b = 200 \\ b = 200 - 500 \\ b = - 300 \\ c. \: - 1 + c = - 2 \\ c = - 2 + 1 \\ c = - 1 \\ d. \: d +3.567=0 \\ d = 0 - 3.567 \\ d = - 3.567[/tex]

hope it helps:)

A film distribution manager calculates that 9 % of the films released are flops. If the manager is correct, what is the probability that the proportion of flops in a sample of 407 released films would differ from the population proportion by less than 3% ? Round your answer to four decimal places.​

Answers

The probability that the population percentage would differ from the sample proportion of flops in a sample of 407 released films by less than 3% is roughly 0.8354, rounded to four decimal places.

Describe the binomial distribution using an example.

For the trials we are looking at, the probability of receiving a success in a binomial distribution must stay constant. Since there are only two possible outcomes when tossing a coin, for instance, the probability of flipping a coin is 12 or 0.5 for each experiment we conduct.

To determine the likelihood that the sample proportion of flops is within 3% of the population proportion, we need to know the chance that |p - 0.09| 0.03.

We can suppose that the sample proportion's distribution is

approximately normal with mean μ = 0.09 and standard deviation σ = √((0.09)(0.91)/407)

≈ 0.017.

We may calculate the z-scores for the top and lower boundaries of the interval using the conventional normal distribution:

z1 = (0.06 - 0.09) / 0.017 ≈ -1.76

z2 = (0.12 - 0.09) / 0.017 ≈ 1.76

The probability between these two z-scores is represented by the region beneath the standard normal curve:

P(-1.76 < Z < 1.76)

= 0.9177 - 0.0823

= 0.8354

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OAB is a minor sector of the circle below.
Calculate the length of the minor arc AB in terms of pi
Not drawn accurately
AWARDING BRAINLIEST TO FIRST ANSWER

Answers

The Length of the arc in the circle shown is calculated to one decimal place, in terms of pi, as approximately 3.6π cm.

How to Calculate the Length of an Arc?

The length of an arc in a given circle can be calculated by applying the formula as expressed below:

Length of arc (s) = ∅/360 * 2πr, where:

Reference angle = ∅

Radius of the circle = r.

Given the parameters:

Radius (r) = 16 cm

Reference angle (∅) = 40 degrees.

Plug in the values:

Length of the arc (s) = 40/360 * 2 * π * 16

Length of the arc (s) = 3.6π cm

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Answer:

To calculate the length of the minor arc AB in terms of pi, you need to know the measure of the central angle that intercepts the arc and the radius of the circle. Do you have that information?

Step-by-step explanation:

A 28-year-old females pays $163 for a 1 year $200,000 life insurance policy what is the expected value of the policy for the policyholder?​

Answers

Assuming that the policyholder is healthy and has an average life expectancy, we can estimate the expected value of the policy by multiplying the probability of dying during the policy period by the amount that will be paid out in the event of death.

The probability of dying during the policy period can be estimated using actuarial tables, which provide information on life expectancies based on age, gender, and other factors. For a healthy 28-year-old female, the probability of dying during a one-year policy period is very low, likely less than 0.1%.

If we assume a probability of dying of 0.1%, the expected value of the policy would be:

Expected value = 0.001 x $200,000 = $200

This means that, on average, the policyholder can expect to receive $200 in benefits from the policy. However, it's important to note that this is just an estimate and actual benefits may be higher or lower depending on the policyholder's individual circumstances.

For any positive values x and y, f(xy) = f(x) + f(y). f(1/2021) = 1.
Find f(2021).

I will give BRAINLIEST to correct answer.

Answers

If we let x = 1/2021 and y = 2021, we have:

f(1/2021 * 2021) = f(1/2021) + f(2021)

Simplifying the left-hand side gives us:

f(1) = f(1/2021) + f(2021)

Substituting f(1/2021) = 1, we have:

f(1) = 1 + f(2021)

Therefore,

f(2021) = f(1) - 1.

However, we don't know what f(1) is. One way to find it is to let x = y = 1. Then we have:

f(1) = f(1) + f(1),

which implies that f(1) = 0.

Therefore,

f(2021) = f(1) - 1 = -1.

So the answer is -1.

In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems? There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen matters. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen matters. There are 26C5 = 65,780 ways the students can be chosen because the order they are chosen does not matter. There are 26P5 = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.

Answers

"There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter." is correct statement. Therefore, the answer is option C.

The problem asks us to choose 5 students out of a class of 26 to present homework problems. Since the order in which the students present the problems does not matter, we need to use the combination formula. The combination formula is used to calculate the number of ways to choose a subset of k elements from a set of n elements without regard to order, and it is denoted by nCk.

Option A, "There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters," is incorrect because the order in which the students are chosen does not matter.

Option B, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters," is incorrect because we are choosing 5 students out of 26, and the order in which they are chosen does not matter.

Option D, "There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter," is also incorrect because the order in which the students are chosen does not matter.

Therefore, the answer is option C.

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Complete question is:

In a class of 26 students, a teacher chooses a different student to each present five different homework problems. Which statement describes the number of ways the students can be chosen to present the problems?

A) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen matters.

B) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen matters.

C) There are 26C₅ = 65,780 ways the students can be chosen because the order they are chosen does not matter.

D) There are 26P₅ = 7,893,600 ways the students can be chosen because the order they are chosen does not matter.

Elin chose C as the correct answer. Explain how she got her answer.

Answers

Answer:

Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

Step-by-step explanation:

My apologies for the confusion. Let's analyze how Elin arrived at her answer.

According to the given information, car A travels 221.5 km at a given time. Elin interpreted the statement "car B travels 1.2 times the distance car A travels at the same time" to mean that the distance traveled by car B is 1.2 times the distance traveled by car A.

To calculate the distance traveled by car B, Elin multiplied the distance of car A (221.5 km) by 1.2:

Distance of Car B = 1.2 * Distance of Car A

Distance of Car B = 1.2 * 221.5 km

Distance of Car B = 265.8 km

Therefore, Elin concluded that car B travels a distance of 265.8 km during the same time based on her interpretation of the given information.

A swimming pool holds 450, 000 L
of water and has two drainage
pipes.
Pipe A, by itself, can drain the pool
in 150 minutes. Pipe B, by itself, can
drain the pool in 225 minutes.
If you turned on both pipes at the
same time, how many minutes
would it take to drain the pool?

Answers

Using a linear equation, the minutes it would take both pipes to drain the swimming pool that holds 450,000 liters is 90 minutes.

What is a linear equation?

A linear equation is an equation of a straight line written in the form of y = mx +b, where m is the slope.

The quantity of water the swimming pool holds = 450,000 liters

The drainage time of Pipe A working alone = 150 minutes

Drainage rate of Pipe A = 3,000 liters per minute (450,000 ÷ 150)

The drainage time of Pipe B working alone = 225 minutes

Drainage rate of Pipe B = 2,000 liters per minute (450,000 ÷ 225)

The drainage rate of the combined pipes = 5,000 liters per minute (3,000 + 2,000)

Let the number of minutes for both pipes to drain the pool = x

Therefore, the linear equation is 5,000x = 450,000

x = 90 minutes (450,000 ÷ 5,000)

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In cell D7, enter a formula without using a function that multiples the Monthly_Payment (cell D6) by the Term_in_Months (cell D5), and then subtracts the Loan_Amount (cell B8) from the result to determine the total interest.
In cell D8, enter a formula without using a function that adds the Price (cell B6) to the Total_Interest (cell D7) to determine the total cost.

Answers

1. To find the interest we will use = (D6*D5) - B8,  2. To find the total cost we will use = B6 + D7.

Here we are given the financial information of a firm and are required to give an appropriate formula for total interest and total cost

1.

Here we need to multiply D6 and D7 and subtract B8 from the result. We cannot use any function. Hence we will simply write

= (D6*D5) - B8

The bracket is not necessary but can be put s an added satisfaction that the said formula would multiply the cells first and then only will the loan amount would be subtracted.

2.

Similarly, for cell D8, we need to go to the formula bar and write

= B6 + D7

This will add the cells up to give us the total cost.

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Complete Question

In cell D7, enter a formula without using a function that multiples the Monthly_Payment (cell D6) by the Term_in_Months (cell D5), and then subtracts the Loan_Amount (cell B8) from the result to determine the total interest.In cell D8, enter a formula without using a function that adds the Price (cell B6) to the Total_Interest (cell D7) to determine the total cost

(Image Attached)

I know is blurry just pls help

Answers

12 - 2^2 x 2

---Remember: PEMDAS

---In this case exponents are first, then multiplication, then subtraction

12 - 4 x 2

12 - 8

4

Answer: 4

Hope this helps!

Select the correct answer from each drop-down men
menu.
What is the distance and midpoint between points D and E on the number line?
D
E
-4 -3 -2 -1 0 1 2 3 4 5
distance =
midpoint =
Reset
Next

Answers

The midpoint is M = 0.6 and the distance is D = 4.2

Given data ,

The distance between points D and E on the number line

D = 4.2

Now , the first point D = -1.8

And , the point E = 2.4

And , the distance D = 2.4 - 1.8 = 4.2 units

Thus, the midpoint between points D and E on the number line = 0.6

Hence, the distance and midpoint between points D and E on the number line 4.2 and 0.6

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The complete question is attached below :

What is the distance and midpoint between points D and E on the number line?

Write the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) in slope intercept form.

Answers

Answer: y = (9/5)x + 5.

Step-by-step explanation:

The slope of the given line is -5/9. The slope of a line perpendicular to it would be the negative reciprocal of -5/9, which is 9/5. Using the point-slope form of a line, we can write the equation of the line as y - (-4) = (9/5)(x - (-5)). Simplifying this equation gives y + 4 = (9/5)x + 9. Solving for y, we get y = (9/5)x + 5. This is the equation of the line in slope-intercept form.

In summary, the equation of a line perpendicular to y = −5/9x + 4 and that passes through point (-5,-4) is y = (9/5)x + 5.

Jerome buys 4 pints of milk for the baby goats and has pint of milk left from yesterday. If each baby goat gets pint of milk, how many goats can Jerome
feed?

Jerome can feed (blank) baby goats.

Answers

Answer:

5 baby goats

Step-by-step explanation:

4 + 1 = 5 pints total

each baby goat gets 1 pint

Geometry simplifying square roots

Answers

(2/√3) can be rationalized by multiplying both the numerator and the denominator by √3 to get (2√3/3) .

What is mean by Square root and how to find it ?

The square root is the value that gives a prime number multiplied by itself. Four methods  can be used to find the square root: prime factorization, repeated subtraction, long division, and the evaluation method.

In geometry, we often encounter the square root when calculating the size of shapes, such as the length, area or volume of certain geometric shapes. Simplifying square roots can make calculations much easier and more efficient.

Here are some rules for simplifying square roots:

Simplify perfect squares under the radical sign: For example, √9 = 3 and √25 = 5.  Multiplying or dividing a number outside the radical sign: For example, 2√3 can be simplified to √12. Adding or subtracting like terms: For example, 3√2 2√2 = 5√2.

You can rationalize the denominator by multiplying the numerator and denominator by the conjugate of the denominator: For example, (2/√3) can be rationalized by multiplying both the numerator and the denominator by √3 to get (2√3/3) .

Applying these rules, we can simplify the square root and make calculations easier and more accurate in geometric problems..

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CAN SOMEONE PLEASE HELP me with the correct answer!!!!! I need this done please help like please

Answers

answer: 164 degrees

reasoning: circle = 360 degrees
360-115= 245
245-81= (164 degrees)

given that ab is the diameter of a circle o find the missing angle and arc measures show your work look at the photo of the circle

Answers

The given angles are:

M arc CB=64°,M<AOC= 116° ,M arc AD=26°,M arc DFB=154°,M<CDB=32°.

How to solve this

First, we use the property that the measure of a central angle is equal to the measure of the intercepted arc.

Given that <COB = 64°, we know that the measure of arc CB is also 64°.

Next, we use the fact that the measure of an angle made on the circumference is half the measure of the angle made at the center.

We know that the measure of intercepted arc AD is 26°, and since the angle made at the center, <ABD, is 13°, we can calculate that the measure of arc AD is 2 x 13° = 26°.

Using the fact that a semicircle has a measure of 180°, we know that the measure of arc DFB is 180° - 26° = 154°.

Finally, we can use the angle CDB to find the missing angle.

We know that <CDB is an angle made on the circumference and that the measure of arc CB is 64°.

Thus, we can calculate that <CDB = 64°/2 = 32°.

Therefore, the missing angle is 32°.

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a country radio station wants to know what the most popular type of music is so they ask their listeners to call in say their favorite type

Answers

According to the information, if the radio selects listerners randomly, the sample is random. But if they select listerners are selected without random method the sample may be biased.

Is this an example of sample random or not?

If the radio station randomly selected a subset of their listeners and asked them to call in, then the sample would be random. This would help ensure that the sample is representative of the overall population of the radio station's listeners, and would allow for valid conclusions to be drawn about the preferences of the wider population based on the results of the survey.

However, if the radio station did not use a random sampling method, then the sample may be biased and not representative of the overall population of the radio station's listeners. For example, if the radio station only advertised the survey during certain times of day or on certain shows, then the sample may be biased towards listeners who are more likely to be listening during those times or shows. Similarly, if the radio station only advertised the survey on certain social media platforms or websites, then the sample may be biased towards listeners who use those platforms or websites.

Note: This question is incomplete. Here is the complete information:

State whether or not the sample is random. If it is not random, explain why

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Virginia earns $69,500 per year at her job as a speech pathologist, and she is paid every two weeks. Her most recent paycheck included the following deductions: FICA $200.20 Federal income tax $180.65 State income tax $72.00 Health insurance $110.00 Retirement savings $250.00 Considering her deductions, what percentage of her gross pay did Virginia take home? 71.65% 62.34% 69.59% 68.55%

Answers

She takes 69.5% as gross pay at take home,

Hence option (c) is correct.

Given that,

The amount of earning = $69500

From the given table total deduction = 812.85

Since she pay deductions in every two weeks

Therefore,

The gross earning per year = 69500 - 812.85

                                              = $ 48388

There are 365 days in a year

So earing per day = 69500/365 = 4190.411

So gross earing per day =  48388 /365 = 132.569

SO the gross percentage = (132.5/190.5)x100

                                          = 69.5 %

Hence the required percentage is 69.5%

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If the terminal point of 0 is (0, -1), what is tan 0?

A. Undefined
B. 1
C. -1
D. 0

Answers

If the terminal point of θ  is (0, -1) then tanθ is undefined.

The point (0, -1) lies on the negative y-axis.

Since the tangent function is defined as the ratio of the opposite side to the adjacent side of a right triangle, and the adjacent side is zero for any point on the y-axis, the tangent of θ is undefined.

Therefore, if the terminal point of θ  is (0, -1) then tanθ is undefined.

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Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items.

Answers

Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

How to solve for the cost

B = 1/4 * S

S = 2/3 * P

B + S + P = 23.75 - 4.50

Emma spent 23.75 - 4.50 = $19.25 on the brush, sketchbook, and paint set.

Now we have the equation:

B + S + P = 19.25

Substitute the expressions from relationships 1 and 2 into the equation:

(1/4 * S) + S + (3/2 * S) = 19.25

Now combine the terms:

(1/4 * S) + (4/4 * S) + (6/4 * S) = 19.25

(11/4 * S) = 19.25

Now, to solve for S, multiply both sides of the equation by the reciprocal of the fraction (4/11):

S = (4/11) * 19.25

S = 7

The sketchbook cost $7. Now we can find the costs of the brush and the paint set using relationships 1 and 2:

B = 1/4 * S = 1/4 * 7 = 1.75

P = 3/2 * S = 3/2 * 7 = 10.5

Emma bought a brush for $1.75, a sketchbook for $7, and a paint set for $10.5.

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Complete question

Emma brought $23.75 to the art supply store. She bought a brush, a sketchbook, and a paint set. The brush was 1 /4 as much as the sketchbook, and the sketchbook cost 2/ 3 the cost of the paint set. Emma had $4.50 left over after buying these items. What is the total cost for each item

Statistics Help, pls help me
A nationwide award for high school students is given to outstanding students who are sophomores, juniors, or seniors (freshmen are not eligible). Of the award-winners, 65 percent are SENIORS, 23 percent JUNIORS, and 12 percent are SOPHOMORES.

Answers

a) The probability of selecting exactly 3 award-winners before selecting a SENIOR is  0.078875

b)The probability of selecting more than 2 award-winners before selecting a JUNIOR is 0.135437

c)The probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is 0.252744

Define probability

Probability is a measure of the likelihood or chance of an event occurring. It is a numerical value between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain to occur.

(a) The probability of selecting a SENIOR is 0.65, and the probability of not selecting a SENIOR is 0.35.

Since we are selecting award-winners until we select a SENIOR, the first two selections must not be SENIORS, and the third selection must be a SENIOR.

the probability of selecting exactly 3 award-winners before selecting a SENIOR is:

P(not SENIOR) x P(not SENIOR) x P(SENIOR) = 0.35 x 0.35 x 0.65 = 0.078875

(b)Therefore, the probability of selecting more than 2 award-winners before selecting a JUNIOR is:

P(not JUNIOR) x P(not JUNIOR) x P(JUNIOR) = 0.77 x 0.77 x 0.23 = 0.135437

To find the probability of selecting more than 2 award-winners, we can subtract this value from 1, since the only other possibility is selecting exactly 2 award-winners before selecting a JUNIOR:

P(more than 2) = 1 - P(exactly 2) = 1 - (P(not JUNIOR) x P(JUNIOR) x P(not JUNIOR)) = 1 - (0.77 x 0.23 x 0.77) = 0.567911

(c) The probability of selecting a SOPHOMORE is 0.12, and the probability of not selecting a SOPHOMORE is 0.88.

Since we are selecting award-winners until we select a SOPHOMORE, we can keep selecting SENIORS and JUNIORS until we select a SOPHOMORE.

Therefore, the probability of selecting 2 or fewer award-winners before selecting a SOPHOMORE is:

P(SOPHOMORE) + P(not SOPHOMORE) x P(JUNIOR) x P(SOPHOMORE) + P(not SOPHOMORE) x P(not JUNIOR) x P(JUNIOR) x P(SOPHOMORE) = 0.12 + (0.88 x 0.23 x 0.12) + (0.88 x 0.77 x 0.23 x 0.12) = 0.252744

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According to a recent poll, 22% of US adults get an average of 7 or more hours of sleep per night. Assume this is the parameter value for the population. Suppose you select a simple random sample of 50 US adults and find that 10 of them get an average of 7 or more hours of sleep per night. Let p(hat) = the proportion in the sample who get an average of 7 or more hours of sleep per night.

Assuming the polling information is true, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night is ?
answer is .3664

If needed, use the z-table to answer the question.

Answers

assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.

What is probability?

By simply dividing the favorable number of possibilities by the entire number of possible outcomes, the probability of an occurrence can be determined using the probability formula. Because the favorable number of outcomes can never exceed the entire number of outcomes, the chance of an event occurring might range from 0 to 1.

The mean of the sample proportion distribution is given by:

μp(hat) = p = 0.22

The standard deviation of the sample proportion distribution is given by:

σp(hat) = sqrt((p*(1-p))/n) = sqrt((0.22*0.78)/50) = 0.0802

To find the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night, we need to find the z-score corresponding to this value:

z = (0.20 - 0.22) / 0.0802 = -0.2494

Using a standard normal table or calculator, we find that the probability of obtaining a z-score of -0.2494 or less is 0.4019. Therefore, the probability that 20% or less of US adults get an average of 7 or more hours of sleep per night,

Hence assuming the polling information is true, is 0.4019 or approximately 0.3664 when rounded to four decimal places.

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Find the slope of the line that passes through A (3, 7) and B (7, 10).

Answers

Answer:

[tex]m = \frac{10 - 7}{7 - 3} = \frac{3}{4} [/tex]

Answer - slope of the line is 3/4

We know the points (3, 7 ) and (7, 10 )

Slope formula is y2 - y1 over x2 - x1

Fill in the x and y values from given points

10 - 7 over 7 - 3

3 over 4 = 3/4 slope is your answer

The National Academy of Science reported in a 1997 study that 40% of research in mathematics is published by U.S. authors. The mathematics chairperson of a prestigious university wishes to test the claim that this percentage is no longer 40%. He has no indication of whether the percentage has increased or decreased since that time. He surveys a simple random sample of 130 recent articles published by reputable mathematics research journals and finds that 62 of these articles have U.S. authors. Does this evidence support the mathematics chairperson's claim that the percentage is no longer 40%? Use a 0.05 level of significance.

Answers

There is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

How to test for the evidence

To test the claim that the percentage of research in mathematics published by U.S. authors is no longer 40%, we can use a hypothesis test with a 0.05 level of significance.

Let p be the true proportion of mathematics research published by U.S. authors.

The null hypothesis is that p = 0.4, and the alternative hypothesis is that p ≠ 0.4 (two-tailed test).

sample proportion, x/n = 62/130 = 0.477

The test statistic for a two-tailed test is given by:

z = (0.477 - 0.4) / √(0.4 * 0.6 / 130)

= 2.41

Using a z-table, we find that the p-value for a two-tailed test with z = 2.41 is approximately 0.016.

Since  0.016 < 0.05

, we reject the null hypothesis and conclude that there is evidence to suggest that the percentage of mathematics research published by U.S. authors is no longer 40%.

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Piston movement compresses air in this type of air compressor. Medium size compressors Industrial compressors Small compressors Horizontal compressors​

Answers

Piston movement compresses air in Small compressors type of air compressor

Piston movement compresses air in small compressors. Small compressors, also known as portable compressors, are commonly used for home improvement projects, powering tools, and inflating tires or other objects. The piston moves back and forth inside a cylinder, compressing air and increasing its pressure. The compressed air is then stored in a tank until it is needed to power a tool or inflate an object.

Small compressors are generally less powerful than medium or industrial compressors, but they are more affordable, portable, and easier to use for smaller tasks. They can be powered by electricity or gasoline, and they come in a range of sizes and capacities to meet different needs. Overall, piston-driven small compressors are an efficient and cost-effective way to compress air for various applications.

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For the right triangle shown below, find the exact values of:
sin⁡B b)tan⁡A c)cos⁡A

Answers

Answer:

17

Step-by-step explanation:

11+6=17

(a) The exact value of sin B is 6 / 12.53

(b) The exact value of tan A is 11 / 6

(c) The exact value of cos A is 6 / 11

What is the value of  sin (B) , tan (A) and cos (A)?

The value of sin (B), cos (A) and tan (A) is calculated by applying trigonometry ratio as follows;

The trigonometry ratio is simplified as;

SOH CAH TOA;

SOH ----> sin θ = opposite side / hypothenuse side

CAH -----> cos θ = adjacent side / hypothenuse side

TOA ------> tan θ = opposite side / adjacent side

The value of the hypotenuse side of the right triangle is;

L = √ (6² + 11²)

L = 12.53

(a) The exact value of sin B is;

sin B = 6 / 12.53

(b) The exact value of tan A is;

tan A = 11 / 6

(c) The exact value of cos A is;

cos A = 6 / 11

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Solve the equation without using a calculator

[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex]

Answers

Answer:

x = 5 ± √26

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

Convert the given equation as below:

[tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-1)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+10x^9(9x)[/tex][tex](x^2-9x-1)^{10}+99x^{10}=10x^9(x^2-9x-1)+90x^{10}[/tex][tex](x^2-9x-1)^{10}+9x^{10}=10x^9(x^2-9x-1)[/tex][tex](x^2-9x-1)^{10}-9x^9(x^2-9x-1)=x^9(x^2-9x-1)-9x^9x[/tex]

Let's substitute x² - 9x - 1 = t, then the equation is:

[tex]t^9t-9x^9t=x^9t-9x^9x[/tex]

Comparing both sides, we see that x = t, so:

x² - 9x - 1 = xx² - 10x - 1 = 0

Solving this quadratic equation we get:

x = 5 ± √26

Solve by using a system of equations.
A goldsmith has two gold alloys. The first alloy is 30% gold; the second alloy is 80% gold. How many grams of each should be mixed to produce 40 grams of an alloy that is 60% gold?

Answers

Answer:

Let x be the amount of the first alloy (30% gold) to be mixed and y be the amount of the second alloy (80% gold) to be mixed.

We can set up a system of two equations based on the information given:

x + y = 40 (total amount of alloy produced)

0.3x + 0.8y = 0.6(40) (amount of gold in the alloy produced)

Simplifying the second equation, we get:

0.3x + 0.8y = 24

Now we have a system of two equations:

x + y = 40

0.3x + 0.8y = 24

We can solve for x and y by using any method of solving systems of equations. Here, we will use the substitution method.

Solving the first equation for y, we get:

y = 40 - x

Substituting this expression for y into the second equation, we get:

0.3x + 0.8(40 - x) = 24

Simplifying and solving for x, we get:

0.3x + 32 - 0.8x = 24

-0.5x = -8

x = 16

So we need 16 grams of the first alloy and 24 grams of the second alloy to produce 40 grams of an alloy that is 60% gold.

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