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The football is approximately 96.4 feet from the base of the goal post.

The tangent function in trigonometry is used to determine the proportion between the lengths of the adjacent and opposite sides in a right triangle. Where theta is the angle of interest, the tangent function is defined as:

tan(theta) = opposing / adjacent.

When the lengths of one side and one acute angle are known, the tangent function is used to solve for the unknown lengths or angles in right triangles. In order to utilise the tangent function, we must first determine the angle of interest, name the triangle's adjacent and opposite sides in relation to that angle, and then calculate the ratio of those sides using the tangent function.

Given, the angle of elevation is 16 degrees 42'.

That is,

Angle of elevation = 16 degrees 42' = 16 + 42/60 = 16.7 degrees

Using tangent function we have:

tan(16.7) = 30/x

x = 30 / tan(16.7)

x = 96.4 feet

Hence, the football is approximately 96.4 feet from the base of the goal post.

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The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

Option D is the correct answer.

A personal loan is a type of loan that individuals can take out from a bank, credit union, or online lender to cover personal expenses such as home improvements, medical bills, or other unexpected expenses.

We have,

The benefit of obtaining a personal loan can vary depending on the specific terms and conditions of the loan, but typically it allows individuals to borrow a larger amount of money upfront with a fixed interest rate and set repayment schedule, which can be beneficial for large expenses such as home renovations, debt consolidation, or major purchases.

However, the interest rates and repayment terms can vary depending on the borrower's credit score, income, and other factors, so it's important to compare options and choose a loan that meets one's specific needs and budget.

Thus,

The benefit of obtaining a personal loan is getting large amounts of money to use immediately.

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Answer:

Bill's bar has 57.3 grams of cocoa.

Step-by-step explanation:

The math part that your question is asking is: What is 69% of 83?

In order to use the percent 69% in a calculation, you need to change it to a decimal.

69% is 0.69

You move the decimal to the left, two places.

69% is 69.% If you don't see a decimal to start with and it is a whole number, then the decimal is starting on the right.

Move it two places to the left, you get

.69

Now MULTIPLY.

.69 × 83

= 57.27

ROUND your answer to the nearest tenth. That means only one digit to the right of the decimal.

57.27 rounds to 57.3

Bill's bar has 57.3 grams of cocoa.

Answer: 8

Step-by-step explanation:

I do not understand the question. But if my interpretation is correct, then:

If there are 64 players and 3 rounds, 32 will get out in the first round. 16 will get out in the second, and 8 will get out on the third. Thus, the answer is 64-(32+16+8) or just simply 8.

Answer:

yes it is..............

The reasoning presented lacks explicit explanations and logical connections between the steps, making it difficult to fully understand the intended proof strategy.

The given proof aims to show that the Separation Axioms can be derived from the Replacement Schema using a particular construction involving a formula p(x, y). Let's analyze the proof step by step:

Define the formula p(x, y) as x = yo(x).

This formula states that for each x, y pair, x is equal to the unique object y such that y is obtained by applying the operation o to x.

Define the set F as {(x, x) (x)}.

This set F contains pairs (x, x) where x is the unique object obtained by applying the operation (x) to x.

Claim: F(X) = {y (x = X)p(x, y)} = {y: (x = X)x = y^o(x)} = {x: (3x € X)o(x)} = {x X: (x)}.

This claim asserts that F(X) is equivalent to {y (x = X)p(x, y)}, which is further equivalent to {y: (x = X)x = y^o(x)}, and so on.

The proof states that since (x, y) satisfies the functional formula VaVyVz(p(x, y)^(x, z) y = z), it follows that (x, y) is a functional formula.This step emphasizes that the formula p(x, y) satisfies certain properties that make it a functional formula, which is relevant for the subsequent deductions.

Finally, the proof concludes that the Separation Axioms follow from the Replacement Schema, based on the previous steps.

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Answer:

548.28

Step-by-step explanation:

you want to take the original pay ( $275 ) and push that to the side.

take 3,094 and find 7% of that, which would be 273.28

lastly you want to take 273.28 and add the original pay of 275.

273.28 + 275 = 548.28

so her total pay for the week was 548.28

Answer:

9.42

Step-by-step explanation:

C= 2 times pie times radius

Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

T is 13

Step-by-step explanation:

-2(t+7)=-4t+12

-2t-14=-4t+12

2t=26

t=13

check answer:

-2(13+7)=-4(13)+12

-26-14=-52+12

-40=-40

Answer:

t is or equal to 13

Step-by-step explanation:

i done this before

Answer:

D. 5 1/8

Step-by-step explanation:

First, convert the mixed number into an improper fraction

8-2 7/8 = 8- 23/8

Calculate the difference

8-23/8 = 41/8

Simplify the fraction

41/8 = 5 1/8

There are 6 numbers on a standard die and. 5 of the numbers are less than 6.

The probability would be 5/6

Answer:

D. Bimodal

Explanation:

The given histogram has two creast, each crest represent a mode. So, we can say that this is a bimodal graph. Therefore, the answer is

D. Bimodal.

The mass percentage of Cesium in the sample is 25.0 %. (Correct choice: C)

Herein we find the case of a mixture of two elements: Cesium, Iodine, whose Cesium mass percentage can be determined by the following formula:

%m = [mCs / (mCs + mI)] × 100 %

Where:

If we know that mCs = 100 g and mI = 300 g, then the Cesium mass percentage is:

%m = [100 g / 400 g] × 100 %

%m = 25 %  

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Answer: 13 7/8

Step-by-step explanation:

11 + 1/8 + 3/4 + 2 = 13 7/8

The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.

To determine the required sample size, we can use the formula for the margin of error (ME) in the context of the normal distribution:

ME = (Z * σ) / √n

Where:

ME = Margin of error

Z = Z-score, which corresponds to the desired level of confidence (in this case, 90%)

σ = Standard deviation (3.3 mm in this problem)

n = Sample size

First, we need to find the Z-score corresponding to a 90% confidence level. This can be found using a Z-table or statistical software. The Z-score for a 90% confidence interval is approximately 1.645.

Now, we will rearrange the formula to solve for the sample size (n):

n = (Z * σ / ME)^2

We are given that the margin of error should be within ± 0.3 mm:

n = (1.645 * 3.3 / 0.3)^2

n ≈ (18.015)^2

n ≈ 324.54

Since we cannot have a fraction of a component, we round up to the nearest whole number to ensure the desired level of confidence:

n ≈ 325

The engineer should consider a sample size of 325 electronic components to be 90% sure that the mean width will be within ± 0.3 mm.

Emplοyee's annual cοntributiοn: $3,097.71

Emplοyee's mοnthly deductiοn: $258.14

An algebraic expressiοn is a mathematical phrase that cοntains variables, cοnstants, and mathematical οperatiοns. It may alsο include expοnents and/οr rοοts. Algebraic expressiοns are used tο represent quantities and relatiοnships between quantities in mathematical situatiοns, οften in the cοntext οf prοblem-sοlving.

The emplοyee's percent is 100% decreased by the emplοyer's percent.

100%−73%=27%

Based on the information you provided, Rubina Shaw's annual premium for the HMO plan is $11,473. Her employer pays 73 percent of this premium, so Rubina's portion of the premium would be:

27% × $11,473 = 0.27 × $11,473 = $3,097.71

The emplοyee's annual cοntributiοn is the prοduct οf the emplοyee's percent and the tοtal premium.

The emplοyee's mοnthly deductiοn is the emplοyee's annual cοntributiοn divided by the number οf mοnths in a year.

$3,097.71 ÷ 12

= $258.14

Emplοyee's annual cοntributiοn: $3,097.71

Emplοyee's mοnthly deductiοn: $258.14

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Complete question:

Find the employee's total annual contribution and the employee's monthly deduction. Rubina Shaw, family plan. HMO annual premium is $11,473. Employer pays 73 percent.

Answer:

49 total pounds

Step-by-step explanation:

If a 1 piece of ham is 1 pound then 9 pieces is 9 pounds if turkey si 4 pounds then 10 turkeys is 40 pounds so our answer is 49 total pounds.

Ok, so

We know that the fastest he will drive is 75 miles per hour. If y is his speed, we can write:

This is, the option B.

Now, the expression 361 + 2y represents what mile marker he is at after 2 hours. We know that the fastest he will drive is 75, so we could replace y=75 in the last expression to know what mile marker he would be seeing at that point. This is:

Now, we know that the inequality would be:

This is, the option B.

Using the length formula we know that the length of the given arc is 30.144 miles.

In mathematics, an arc is a portion of the boundary of a circle or curve. It is sometimes referred to as an open curve.

The measurement around a circle that determines its edge is called the circumference, often known as the perimeter.

So, the formula to find the length of the arc is:

Length of an Arc = θ × r

Now, insert values and calculate as follows:

Length of an Arc = θ × r

Length of an Arc = 4π/5 × 12

Length of an Arc = 4π/5 × 12

Length of an Arc = 12.56/5 * 12

Length of an Arc = 2.512 * 12

Length of an Arc =  30.144

Therefore, using the length formula we know that the length of the given arc is 30.144 miles.

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Answer: h = 15

Step-by-step explanation: 4/5 x 15 = 60/5 = 12, 12 - 1 = 11.

Answer:

17 will be answer .....

Step-by-step explanation:

He gets 374 miles on 22 gallons ....

Amounts of miles per gallon is 374÷22

= now divide it and answer will come 17 ........

Daniel gets the car 17 miles per gallon

The calculation can be done as follows

Daniel drives the car for 374 miles

He uses 22 gallons of gas

The miles per gallon can be calculated as follows

= 374/22

= 17

Hence the answer is 17 miles per gallon

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The numerical value of the expression (u - t)(u² - t²) will be 20.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

The equations are given below.

u + t = 5 and u - t = 2

The expression is given below.

⇒ (u - t)(u² - t²)

Simplify the expression, then we have

⇒ (u - t)(u - t)(u + t)

⇒ 2 x 2 x 5

⇒ 20

The numerical value of the expression (u - t)(u² - t²) will be 20.

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Step-by-step explanation:

here's your solution

=> in first figure , base = 5.5, perpendicular =7.8

=> h^2 = 5.5^2 + 7.8^2

=> h^2 = 30.25 + 60.84

=>h^2 = 91.09

=> h = √91.09

=> h = 9.5

Both figure are congruent

enc we will get a rectangle by add both

hope it helps

Answer: rectangle or b

Step-by-step explanation:

Answer: Uno by Ambjaay

Step-by-step explanation:

It’s a song?

The solution of Equation are (5/2, 4/3).

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

3x+5y=14..........(1)

6x - 4y=9..............(2)

Solving equation (1) and (2) we get

3x + 5y = 14

Subtract 3x from both sides.

5y = 14 - 3x

Divide by 5 on both sides.

y = -3/5x + 14/5

and, 6x - 4y = 9

Subtract 6x from both sides.

-4y = 9 - 6x

Divide by -4 on both sides.

y = 3/2x - 9/4

From the graph we get

x = 2.405

y= 1.375

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