please answer giving BRAINLIEST

Answer:

Step-by-step explanation:

Explanation:

The circle of the center given center and a radius goes by the following pattern: (x - h)² + (y - k)² = r² in which (h, k) is the center and "r" is the radius.

Since the center (9, -16) is already given, this mean that h = 9 and k = -16.

In addition, radius r = 2. Plugging these values to the pattern above, we get: (x - 9)² + (y - (-16))² = 2²

Simplifying the equation above, we get:

(x - 9)² + (y + 16)² = 4

Answer:

In standard form, the equation of the circle is (x - 9)² + (y + 16)² = 4

In general form, we can eliminate the exponents by applying its property. We get:

(x² - 18x + 81) + (y² + 32y + 256) = 4

x² - 18x + 81 + y² + 32y + 256 = 4

Rearrange.

x² + y² - 18x + 32y + 81 + 256 - 4 = 0

x² + y² - 18x + 32y + 333 = 0

In general form, the equation of the circle is x² + y² - 18x + 32y + 333 = 0.

when the discriminant is = 0

Answer:

To solve this problem, we will use the following steps:

Step 1: Let's assume that the larger number is x and the smaller number is y, we know that the difference between the two numbers is 9, so we can write the equation: x-y = 9

Step 2: We know that Four times the larger number plus one-half the smaller is 45, so we can write the equation: 4x + 0.5y = 45

Step 3: Now we have two equations with two unknowns, we can solve for one of the unknowns by isolating it in one of the equations.

x-y = 9

x = y+9

Step 4: Now we can substitute the value of x in the second equation

4(y+9) + 0.5y = 45

4y + 36 + 0.5y = 45

4.5y + 36 = 45

4.5y = 9

y=2

Step 5: We can substitute the value of y in one of the equation, to find the value of x

x-2 = 9

x = 11

Final Answer: The two numbers are 11 and 2.

Answer:

150

Step-by-step explanation:

Collected bills: 18 * 10= 180

1/6 of 180 = 30

180-30=150

Answer:

15 ten dollar bills, 150 dollars

Step-by-step explanation:

1/6 of 18 is 3, so he gave 3 bills to the theater and kept the other 15 for himself

Answers:

Perpendicular Line:  \(\text{y} = \frac{1}{7}\text{x}+\frac{17}{7}\)

Parallel Line:  \(\text{y} = -7\text{x}+31\)

==================================================

Explanation:

The given equation is y = -7x+7 and it's in the form y = mx+b

Perpendicular lines will have a negative reciprocal slope, so we'll flip the fraction and the sign to go from -7 to 1/7 as the perpendicular slope.

The product of the original slope -7 and perpendicular slope 1/7 results in -1.

Let's now turn to point-slope form.

We'll plug in the perpendicular slope along with the coordinates of the point (4,3) to get the following result.

\(\text{y} - \text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y} - 3 = \frac{1}{7}(\text{x}-4)\\\\\text{y} - 3 = \frac{1}{7}\text{x}-\frac{1}{7}(4)\\\\\text{y} - 3 = \frac{1}{7}\text{x}-\frac{4}{7}\\\\\)

\(\text{y} = \frac{1}{7}\text{x}-\frac{4}{7}+3\\\\\text{y} = \frac{1}{7}\text{x}-\frac{4}{7}+\frac{21}{7}\\\\\text{y} = \frac{1}{7}\text{x}+\frac{-4+21}{7}\\\\\text{y} = \frac{1}{7}\text{x}+\frac{17}{7}\\\\\)

This is the equation of the perpendicular line that passes through (4,3)

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

Parallel lines have equal slopes but different y intercepts.

Therefore, the slope of each line is m = -7

Once again we'll use point-slope form. The coordinates of (4,3) are used again, but we'll use a different m value compared to earlier.

\(\text{y} - \text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y} - 3 = -7(\text{x}-4)\\\\\text{y} - 3 = -7\text{x}+28\\\\\text{y} = -7\text{x}+28+3\\\\\text{y} = -7\text{x}+31\\\\\)

This is the equation of the parallel line passing through (4,3)

Marcel can set a goal of purchasing the house in 5 years. The timeframe Factor enables Marcel to work towards his financial goal within a specified period.

Marcel's financial goal is to purchase a house. To make Marcel's financial goal of purchasing a house a specific goal, he can identify the following factors:

Specificity: Marcel should specify the type of house he wants to purchase. This includes the size of the house, the number of rooms, the location, the neighborhood, and the amenities he wants in the house. For instance, Marcel can specify that he wants to purchase a 3-bedroom bungalow house located in a suburban area.

Measurability: Marcel should identify how much money he needs to purchase the house. This means that he should set a financial target that he wants to achieve to be able to purchase the house. For instance, Marcel can set a target of saving $100,000 in 3 years to purchase the house. The measurability factor enables Marcel to track his progress toward achieving his financial goal.

Attainability: Marcel should set a financial goal that is achievable based on his income and financial situation. For instance, if Marcel's current income cannot enable him to save $100,000 in 3 years, he can adjust his financial goal to suit his financial situation.

Realistic: Marcel should set a realistic financial goal that he can achieve given his resources and time frame. For instance, Marcel should not set a financial goal that is too high that he cannot achieve it or too low that it does not challenge him.

Time-bound: Marcel should set a timeframe within which he wants to achieve his financial goal. This means that Marcel should set a specific date by which he wants to purchase the house.

For instance, Marcel can set a goal of purchasing the house in 5 years. The timeframe factor enables Marcel to work towards his financial goal within a specified period.

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The amount remaining after 6, 3, and 1 years following 2, 7, and 4 would be 8, 4, and 0, respectively.

Amount is a quantity or measure of something, such as a number of items, money, or time. It is often used to refer to an amount of money or a measure of quantity, such as an amount of goods or services. Amount is often used as a noun and can also be used as a verb, as in "to amount to something."

Six years after 2, 7, and 4, the remaining numbers would be 8, 4, and 5. Three years after 2, 7, and 4, the remaining numbers would be 5, 1, and 0. One year after 2, 7, and 4, the remaining numbers would be 3, 8, and 5.

Therefore, the amount remaining after 6, 3, and 1 years following 2, 7, and 4 would be 8, 4, and 0, respectively.

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Complete questions as follows-

How much will remain 6,3,1 years after 2,7 and 4 years.

1.) The probability that the sample mean will be greater than 48 minutes is 0.9332.

2.) The probability of the sample mean being between 44 and 49 minutes is 0.6687.

3.) The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean.

To solve this problem, we can use the Central Limit Theorem (CLT), which states that the distribution of sample means tends to be approximately normally distributed, regardless of the shape of the original population, when the sample size is large enough.

1.) Probability of sample mean > 48 minutes:

To calculate this probability, we need to standardize the sample mean using the formula: z = (x - μ) / (σ / √n), where x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

In this case, the population mean (μ) is 45 minutes, the population standard deviation (σ) is 12 minutes, and the sample size (n) is 36. We want to find the probability of the sample mean being greater than 48 minutes.

Calculating the z-score:

z = (48 - 45) / (12 / √36) = 3 / 2 = 1.5

Using a standard normal distribution table or calculator, we find that the probability corresponding to a z-score of 1.5 is approximately 0.9332. Therefore, the probability that the sample mean will be greater than 48 minutes is approximately 0.9332.

2.) Probability of sample mean between 44 and 49 minutes:

To calculate this probability, we need to find the z-scores for both 44 and 49 minutes and then calculate the area between those z-scores.

Calculating the z-scores:

For 44 minutes:

z1 = (44 - 45) / (12 / √36) = -1 / 2 = -0.5

For 49 minutes:

z2 = (49 - 45) / (12 / √36) = 4 / 2 = 2

Using the standard normal distribution table or calculator, we find the probabilities corresponding to z1 and z2:

P(z < -0.5) ≈ 0.3085

P(z < 2) ≈ 0.9772

The probability of the sample mean being between 44 and 49 minutes is approximately P(-0.5 < z < 2) = P(z < 2) - P(z < -0.5) ≈ 0.9772 - 0.3085 = 0.6687.

3.)Conclusion from 100 samples with a mean of 65 minutes:

If 100 samples were collected, and the sample mean was 65 minutes, we would need to assess whether this value is significantly different from the population mean of 45 minutes.

To make this assessment, we can calculate the z-score for the sample mean of 65 minutes:

z = (65 - 45) / (12 / √36) = 20 / 2 = 10

The z-score of 10 indicates that the sample mean of 65 minutes is 10 standard deviations above the population mean. This is an extremely large deviation, suggesting that the sample mean of 65 minutes is highly unlikely to occur by chance.

Given this, we can conclude that the sample mean of 65 minutes is significantly different from the population mean. It may indicate that there is a systematic difference in the delivery times between the sample and the population, possibly due to factors such as increased demand, traffic, or other external variables

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The equation of the parallel line will be y = (2/3)x - 8/3.

Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.

The equation of the line is given below.

y - 4 = 2/3 (x - 3)

The equation of the line that is parallel to the given line will be written as,

y = (2/3)x + c

The equation of the line that passes through (1, -2), then we have

- 2= (2/3)(1) + c

- 2 = 2 /3 + c

c = - 8 / 3

Then the equation of the parallel line will be y = (2/3)x - 8/3.

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It would take approximately 17.12 years for the amount to reach Birr 56,398.43 with a deposit of Birr 500 at the end of each six-month period, compounded semi-annually at an interest rate of 6%.

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = Final amount

P = Principal amount (initial deposit)

r = Annual interest rate (in decimal form)

n = Number of compounding periods per year

t = Number of years

In this case, the principal amount is Birr 500, the annual interest rate is 6% (or 0.06), and the interest is compounded semi-annually, so there are 2 compounding periods per year.

We need to find the number of years (t) it takes for the amount to reach Birr 56,398.43.

Let's substitute the given values into the formula and solve for t:

56,398.43 = 500(1 + 0.06/2)^(2t)

Divide both sides by 500:

112.79686 = (1 + 0.03)^(2t)

Take the natural logarithm of both sides to eliminate the exponent:

ln(112.79686) = ln(1.03)^(2t)

Using the property of logarithms, we can bring down the exponent:

ln(112.79686) = 2t * ln(1.03)

Now, divide both sides by 2 * ln(1.03):

t = ln(112.79686) / (2 * ln(1.03))

Using a calculator, we find t ≈ 17.12.

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Step-by-step explanation:

The four pairs of corresponding angles are

The two pairs of alternate angles are

Hope it will help :)❤

Answer:

0.01596

Step-by-step explanation:

A scientist claims that 8% of the viruses are airborne

Given that:

The population proportion p = 8%

The sample size = 477

We can calculate the standard deviation of the population proportion by using the formula:

\(\sigma_p = \sqrt{\dfrac{p(1-p)}{n}}\)

\(\sigma_p = \sqrt{\dfrac{0.8(1-0.8)}{477}}\)

\(\sigma_p = \sqrt{\dfrac{0.0736}{477}}\)

\(\sigma_p = 0.02098\)

The required probability can be calculated as:

\(P(| \hat p - p| > 0.03) = P(\hat p - p< -0.03 \ or \ \hat p - p > 0.03)\)

\(= P \bigg ( \dfrac{\hat p -p }{\sqrt{\dfrac{p(1-p)}{n}}} < -\dfrac{0.03}{0.0124} \bigg ) + P \bigg ( \dfrac{\hat p -p }{\sqrt{\dfrac{p(1-p)}{n}}} >\dfrac{0.03}{0.0124} \bigg )\)

= P(Z < -2.41) + P(Z > 2.41)

= P(Z < -2.41) + P(Z < -2.41)

= 2P( Z< - 2.41)

From the  Z-tables;

\(P(| \hat p - p| > 0.03)\) = 2 ( 0.00798

\(P(| \hat p - p| > 0.03)\) = 0.01596

Thus, the required probability = 0.01596

Answer:

44 sq. cm

Step-by-step explanation:

I promise it's right, I did the math.

The number of words that Toni can type in 3 minutes is 270 words per minute.

We are given 180 words in 2 minutes. This means;

Toni can type 180/2 = 90 words per minute (90wpm).

Using the above same ratio/rate, it means that in 3 minutes, Toni would be able to type:

90 * 3 = 270 words per minute.

Thus, we conclude that the number of words that Toni can type in 3 minutes is 270 words per minute.

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The answer to the question is 1/3.

There are three possible outcomes: 5, 6, or 7.

Out of these three outcomes, only two satisfy the condition of being odd or greater than 6: 7.

Therefore, the probability of picking a card that is odd or greater than 6 is 1/3, or approximately 0.333 or 33.3%.

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Answer:

composition,

function composition,

composite function

Step-by-step explanation:

(f ° g)(x) = f(g(x))

So we would work on this by putting all of g(x) into the x in the f(x).

i think its d

Step-by-step explanation:

Answer: The answer is A.

Step-by-step explanation:

If you go on Demos and use the graphing calculator you can see.  

You will need 7.104 feet of lumber. (rounded to three decimal places)

There are four basic arithmetic operations in mathematics: addition, subtraction, multiplication, and division.

Among these four procedures, division is one of the most important in our everyday tasks. It is the division of a large group into equal smaller groups.

To find out how many feet of lumber you need, you need to add up the length of all the pieces and then divide by the number of inches in a foot (12).

First, we'll add up the length of all the pieces:

11 (1/4) + 11 (1/4) + 12 (1/2) + 12 (1/2) + 28 (1/8) + 28 (1/8)

= 85 (1/4) inches

Next, we'll convert this total length to feet by dividing by 12:

85 1/4 inches ÷ 12 inches/foot = 7.104 feet

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In a hypothetical situation, an incorrect dosage calculation due to an error in metric system to Imperial System conversion could lead to potential harm to the patient. To avoid such errors, it is crucial to ensure accurate and precise conversions between the metric and Imperial systems. As a nurse, I will double-check my calculations, use reliable conversion charts or tools, and consult with colleagues or supervisors when in doubt. Additionally, ongoing education and training on dosage calculations and metric system conversions will be important to maintain proficiency and prevent errors in the future.

~~~Harsha~~~

The probability that the next person will purchase one or more costumes can be found by dividing the number of visitors who purchased one or more costumes by the total number of visitors.

The total number of visitors is 105 + 41 + 8 = 154.

The number of visitors who purchased one or more costumes is 41 + 8 = 49.

So the probability that the next person will purchase one or more costumes is 49/154, which is approximately 0.32 to the nearest hundredth.

The appropriate percentage of the cities in NYC will be:

Bronx = 16.88%

Brooklyn = 30.72%

Manhattan = 19.43%

Queens = 27.26%

Staten Island = 5.71%

NYC has a total population of 8,244,910 people.

Bronx has a population of 1,392,002, the percent of the total NYC population will be:

= 1,392,002 / 8,244,910 × 100

= 16.88%

Broklyn has a population of 2,532,645, its percent of the total NYC population will be:

= 2532645 / 8244910 × 100

= 30.72%

Manhattan has a population of 1,601,948, its percent of the total NYC population will be:

= 1601948 / 8244910 × 100

= 19.43%

Queens has a population of 2,247,848, its percent of the total NYC population will be:

= 2,247,848 / 8244910 × 100

= 27.26%

Staten Island has a population of 470,467, its percent of the total NYC population will be:

= 470467 / 8244910 × 100

= 5.71%

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The rate of change of the depth of water in the tank when the tank is half

filled can be found using chain rule of differentiation.

When the tank is half filled, the depth of the water is changing at  1.213 ×

10⁻² ft.³/hour.

Reasons:

The given parameter are;

Height of the conical tank, h = 8 feet

Diameter of the conical tank, d = 10 feet

Rate at which water is being pumped into the tank, = 3/5 ft.³/hr.

Required:

The rate at which the depth of the water in the tank is changing when the

tank is half full.

Solution:

The radius of the tank, r = d ÷ 2

∴ r = 10 ft. ÷ 2 = 5 ft.

Using similar triangles, we have;

\(\dfrac{r}{h} = \dfrac{5}{8}\)

The volume of the tank is therefore;

\(V = \mathbf{\dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}\)

\(r = \dfrac{5}{8} \times h\)

Therefore;

\(V = \dfrac{1}{3} \cdot \pi \cdot \left( \dfrac{5}{8} \times h\right)^2 \cdot h = \dfrac{25 \cdot h^3 \cdot \pi}{192}\)

By chain rule of differentiation, we have;

\(\dfrac{dV}{dt} = \mathbf{\dfrac{dV}{dh} \cdot \dfrac{dh}{dt}}\)

\(\dfrac{dV}{dh}=\dfrac{d}{h} \left( \dfrac{25 \cdot h^3 \cdot \pi}{192} \right) = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64}}\)

\(\dfrac{dV}{dt} = \dfrac{3}{5} \ ft.^3/hour\)

Which gives;

\(\dfrac{3}{5} = \mathbf{\dfrac{25 \cdot h^2 \cdot \pi}{64} \times \dfrac{dh}{dt}}\)

When the tank is half filled, we have;

\(V_{1/2} = \dfrac{1}{2} \times \dfrac{1}{3} \times \pi \times 5^2 \times 8 =\mathbf{ \dfrac{25 \cdot h^3 \cdot \pi}{ 192}}\)

Solving gives;

h³ = 256

h = ∛256

\(\dfrac{3}{5} \times \dfrac{64}{25 \cdot h^2 \cdot \pi} = \dfrac{dh}{dt}\)

Which gives;

\(\dfrac{dh}{dt} = \dfrac{3}{5} \times \dfrac{64}{25 \cdot (\sqrt[3]{256}) ^2 \cdot \pi} \approx \mathbf{1.213\times 10^{-2}}\)

When the tank is half filled, the depth of the water is changing at  1.213 × 10⁻² ft.³/hour.

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The members in Jasmine's dance troupe is an illustration equivalent expressions.

The number of members in Jasmine's dance troupe is 62

Assume the number of dancers is n.

One third of the rest is:

\(\mathbf{x = \frac{1}{3}(n - 2)}\)

When she called three more, we have:

\(\mathbf{x = \frac{1}{3}(n - 2) + 3}\)

Expand

\(\mathbf{x = \frac{n}{3} - \frac{2}{3} + 3}\)

\(\mathbf{x = \frac{n}{3} + \frac{-2 + 9}{3}}\)

\(\mathbf{x = \frac{n}{3} + \frac{7}{3}}\)

The remaining dancers (r) are:

\(\mathbf{r = n- \frac{n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{3n - n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{2n}{3} - \frac{7}{3}}\)

\(\mathbf{r = \frac{2n - 7}{3}}\)

When two-fifth of the remaining dancers are added, we have:

\(\mathbf{x = \frac{n}{3} + \frac{7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)

\(\mathbf{x = \frac{n+7}{3} + \frac{2}{5}(\frac{2n - 7}{3})}\)

\(\mathbf{x = \frac{n+7}{3} + \frac{4n - 14}{15}}\)

Take LCM

\(\mathbf{x = \frac{5n + 35 + 4n - 14}{15}}\)

\(\mathbf{x = \frac{9n + 21}{15}}\)

\(\mathbf{x = \frac{3n + 7}{5}}\)

When she called one more dancer, we have:

\(\mathbf{x = \frac{3n + 7}{5} + 1}\)

\(\mathbf{x = \frac{3n + 7+5}{5}}\)

\(\mathbf{x = \frac{3n + 12}{5}}\)

The remaining of the dancer is:

\(\mathbf{r = n - \frac{3n + 12}{5}}\)

\(\mathbf{r = \frac{5n - 3n + 12}{5}}\)

\(\mathbf{r = \frac{2n + 12}{5}}\)

When three-fourth are added, we have:

\(\mathbf{x = \frac{3n + 12}{5} +\frac{3}{4} \times \frac{2n + 12}{5}}\)

\(\mathbf{x = \frac{3n + 12}{5} + \frac{6n + 36}{20}}\)

Take LCM

\(\mathbf{x = \frac{12n + 48+6n + 36}{20}}\)

\(\mathbf{x = \frac{18n +84}{20}}\)

When the last two members are added, we have:

\(\mathbf{n = \frac{18n +84}{20} + 2}\)

\(\mathbf{n = \frac{18n +84+40}{20} }\)

\(\mathbf{n = \frac{18n +124}{20} }\)

Multiply through by 20

\(\mathbf{20n = 18n +124}\)

Collect like terms

\(\mathbf{20n - 18n =124}\)

\(\mathbf{2n =124}\\\)

Divide both sides by 2

\(\mathbf{n =62}\)

Hence, the number of members in Jasmine's dance troupe is 62

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The polar form of the rectangular coordinates (-√√2, -√2) is (2√(1 + √2), 15π/28)

To convert the rectangular coordinates (-√√2, -√2) into polar form, we first need to find the value of r (the radius) and θ (the angle).

r = √((-√√2)^2 + (-√2)^2) = √(2 + 2√2) = 2√(1 + √2)

To find the value of θ, we can use the following formula:

θ = atan(y/x)

where atan is the inverse tangent function, and (x, y) are the rectangular coordinates.

θ = atan(-√2/(-√√2)) = atan(√2) = π/4 radians

However, we need to express the angle in terms of 7 over the interval 0 ≤ θ < 2π/7, with a positive value of r.

To do this, we can add a multiple of 2π/7 to the value of θ until we get an angle in the desired interval.

θ = π/4 + 2π/7 = (7π + 8π)/28 = 15π/28 radians

So the polar form of the rectangular coordinates (-√√2, -√2) is:

(2√(1 + √2), 15π/28)

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Answer:

b = 1.31

Step-by-step explanation:

Step 1: Add 1.93 to both sides.

Step 2: Divide both sides by 9.13.

Step 3: Round to the nearest hundredth.

Therefore, b = 1.31.

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Answer:

b = 1.31

Step-by-step explanation:

9.13b - 1.93 = 10.05(Move 1.93 to the other side to isolate b which changes the sign to positive)

9.13b = 10.05 + 1.93

9.13b = 11.98

Divide by 9.13 to get b

\(\frac{9.13b}{9.13} = \frac{11.98}{9.13} \\\)

b = 1.31

The most appropriate for this measurement will be finding the perimeter of your bedroom to hang lights. Then the correct option is D.

It is the measure of distance between the two points and is known as length. The length is measured in meters generally.

You complete a project and record measurements in feet.

The type of project that would be most appropriate for this measurement will be finding the perimeter of your bedroom to hang lights.

Since, if the error occurs, then the error will increase in finding the area and volume.

Then the correct option is D.

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Answer:

120

Step-by-step explanation:

(+2) x (-5) x (+4) x (-3)
= (-10) x (-12)
= (-)(-) (10 x 12)
= + 120

Answer:

36/(9-4)=7.2

Step-by-step explanation:

You first have to subtract 4 from 9, because it is in the parentheses. The answer is 5, so you have 36/5, which equals 7.2

Answer:

36/5

Step-by-step explanation:

\(\frac{36}{9-4}\\\\\)

Subtract the numbers

\(9-4=5\\\\=\frac{36}{5}\)