A rectangle has a length of 8m and a width of 3m. If a similar rectangle has
a length of 22m , what is its width?

Answer:

(No rounding done.)

1. 10

2. 14.1421

3. 8

4. 6.9282

Step-by-step explanation:

To find 1, you need to use tangent. Let's say the missing side is x. You need to use tan(45) = x/10 to be able to solve. If you don't know how to do that, you just need to multiply by 10 on both sides, that way the 10 cancels out and all you get is x. Tan(45) multiplied by 10 is 10.

Now, find 2 with sine. The equation is sin(45) = 10/x. First, you need to multiply both sides by x so you get 10 alone. Now, divide both sides by sin(45) to cancel out the left side and get the answer to 2. 10/sin(45) = 14.1421 (I don't know if you need to round).

To find 3, you need to use cosine. The equation would be cos(60) = 4/x. Again, multiply both sides by x to get 4 alone. Next, divide both sides by cos(60). 4/cos(60) is 8.

To find 4, you need to use sine again. The equation is sin(60) = x/8. Multiply both sides by 8, and there's your answer. 6.9282.

The calculated t-value (4.14) is greater than the critical t-value (2.447), we can reject the null hypothesis and conclude that obese patients consume significantly more calories than their normal-weight siblings at a .05 level of significance.

To test whether obese patients consume significantly more calories than their normal-weight siblings, we can perform a paired t-test at a significance level of .05.

First, we need to calculate the differences in calorie intake between each sibling pair:

Sibling Pair Obese Patient Calorie Intake (cal) Normal-Weight   Sibling   Calorie Intake (cal) Difference

  1 2,450 1,500 950

  2 3,500 1,800 1,700

  3 3,000 2,100 900

  4 2,700 2,000 700

  5 2,800 1,900 900

 6 3,400 2,000 1,400

 7 3,000 2,000 1,000

Next, we need to calculate the mean difference and standard deviation of the differences:

Mean difference = (950 + 1,700 + 900 + 700 + 900 + 1,400 + 1,000) / 7 = 1,014.29

Standard deviation of differences = 382.46

Using these values, we can calculate the t-value:

t = (mean difference - 0) / (standard deviation of differences / \(\sqrt{n}\))

where n is the number of sibling pairs (in this case, n = 7).

t = (1,014.29 - 0) / (382.46 / \(\sqrt{7}\)) = 4.14

Finally, we can compare the t-value to the critical t-value at a .05 level of significance with 6 degrees of freedom (n-1):

t_critical = 2.447

We may rule out the null hypothesis and reach the conclusion that obese individuals consume considerably more calories than their normal-weight siblings at a.05 level of significance because the estimated t-value (4.14) is higher than the critical t-value (2.447).

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Answer:

Down Here ↓↓↓↓↓↓↓

Step-by-step explanation:

Hello!

This is all the information we need to fill up the blank spots:

Two angles whose sum is 180° are supplementary angles.

Vertical angles are formed by the opposite angles when two lines intersect.

Vertical angles are congruent/equal/equal in measure.

A linear pair of angles form adjacent angles, and the sum of their measures is 180°.

Adjacent angles share a common vertex and side.

Answer:

0.15m+25=c

replace c with 71.50

the third one

25+0.15m=71.8

Answer:

the answer is c. 25 + 0.15m = 71.8

Step-by-step explanation:

25 is the initial fee, or the down payment.

.15 represents the cost of a mile

m represents the number of miles driven

so, 25 + .15m = 71.8 (because $71.80 is the total bill)

A quadratic function's graph being wide or narrow is determined or depended on a-term:

\( \large{y = a {x}^{2} + bx + c}\)

If |a| has a lot of value, for example a = 2 or a = 100. The graph will get narrower if increasing the value of |a|. On the other hand, If |a| has small value, for example a = 1/2 or a = 1/10000. The graph would be wide.

Also it does not matter if a-term is negative or not since a-term being positive or negative determines if a parabola is upward or downward. Only |a| determines how narrow/wide the graph is.

From the question, it is clear that the parabola y = 2x^2 is the narrowest graph since it has the highest |a| value out of all choices.

Answer

Answer:

x = 58 degrees

Step-by-step explanation:

Using the SOH CAH TOA trigonometry identity

hypotenuse =99

adjacent = 52

angle of elevation  = x

cos theta = adj/hyp

cos x = 52/99

x = arccos (52/99)

x = arccos(0.5253)

x = 58 degrees ( to the nearest degree)

Answer:

Yes it is a proportional relationship

Step-by-step explanation:

You can see a clear pattern, every time time goes up by a minute earning go up by 6. There is no random numbers without pattern. So it’s proportional.

Answer:

Yes it is a proportional relationship.

Step-by-step explanation:

It is because You can see a clear pattern, every time time goes up by a minute earning go up by 6. There is no random numbers without pattern. So it’s proportional.

a) The radius of the sphere is given as follows: 27.13 ft.

b) The surface area can be checked as follows: S = 4 x 3.14 x 27.13² = 9244.

The surface area for a sphere of radius r is given by the equation presented as follows:

S = 4πr².

The surface area for this problem is given as follows:

9244 ft².

Hence the radius is given as follows:

\(r = \sqrt{\frac{9244}{4 \times 3.14}}\)

r = 27.13 ft.

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Answer:

the answer is B) 24.

Step-by-step explanation:

To find the lateral surface area of the triangular prism, we need to find the perimeter of the base and then multiply it by the height of the prism.

Looking at the net, we can see that the base is a triangle with sides of length 3 cm, 4 cm, and 5 cm. So the perimeter of the base is:

3 cm + 4 cm + 5 cm = 12 cm

The height of the prism is given as 2 cm. Therefore, the lateral surface area is:

12 cm x 2 cm = 24 cm²

So the answer is B) 24.

IF THIS HELPED, CAN YOU PLEASE GIVE 5⭐? thank you

Answer: 80.28 square feet

Step-by-step explanation:

\(2(6.1\cdot 3+3\cdot 2.4+2.4 \cdot 6.1)=80.28\)

Answer:

30244

Step-by-step explanation:

Answer:

3/10

Step-by-step explanation:

\(\frac{1}{2} \ of \ \frac{3}{5} = \frac{1}{2} \times \frac{3}{5} = \frac{3}{10}\)

Answer:

3/10

Step-by-step explanation:

Answer: I believe the answer is 2,3, and 4. If not, then it is just 2 and 4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

1 is 45. 14 is 90

Step-by-step explanation:

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

We have,

To solve the integral ∫ (log(1 + x²) / (x + 1)²) dx, we can use the method of substitution.

Let's substitute u = x + 1, which implies du = dx. Making this substitution, the integral becomes:

∫ (log(1 + (u-1)²) / u²) du.

Expanding the numerator, we have:

∫ (log(1 + u² - 2u + 1) / u²) du

= ∫ (log(u² - 2u + 2) / u²) du.

Now, let's split the logarithm using the properties of logarithms:

∫ (log(u² - 2u + 2) - log(u²)) / u² du

= ∫ (log(u² - 2u + 2) / u²) du - ∫ (log(u²) / u²) du.

We can simplify the second integral:

∫ (log(u²) / u²) du = ∫ (2 log(u) / u²) du.

Using the power rule for integration, we can integrate both terms:

∫ (log(u² - 2u + 2) / u²) du = log(u² - 2u + 2) / u - 2 ∫ (log(u) / u³) du.

Now, let's focus on the second integral:

∫ (log(u) / u³) du.

This integral does not have a simple closed-form solution in terms of elementary functions.

It can be expressed in terms of a special function called the logarithmic integral, denoted as Li(x).

Therefore,

The final result of the integral is:

∫ (log(1 + x²) / (x + 1)²) dx = log(x + 1) - 2 (log(x + 1) / x) - 2Li(x) + C,

where Li(x) is the logarithmic integral function and C is the constant of integration.

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9514 1404 393

Answer:

  -√3

Step-by-step explanation:

We note that this matches the form for the tangent of the difference of two angles:

  tan(α-β) = (tan(α) -tan(β))/(1 +tan(α)tan(βb))

Here, we have α = 25π/24 and β = 3π/8. Then the angle difference is ...

  α -β = π(25/24 -3/8) = π(2/3)

The value you seek is ...

  tan(2π/3) = -√3

Answer:

For a circle of radius R, the perimeter is:

P = 2*pi*R

Where pi = 3.14

If we have a section of this circle, defined by an angle θ, the length of that arc is calculated as:

L = (θ/360°)*2*pi*R

In this case, we have a unit circle, so the radius is 1 unit, and we have a section defined by an angle of 57°.

Then the total distance traveled will be equal to the length of the arc, which is:

L = (57°/360°)*2*3.14*(1 unit) = 0.99 units

Then the correct option is a.

(as we want to find the total distance, the starting point does not matter, so the total distance traveled in a section of 57° would be the same in any point of the circle, this means that the fact that we should start at the point (1,0) has no effect in this question)

Answer: 26129.6

Step-by-step explanation:

6721 x 381 = 2560701

14 + 84 = 98

2560701  / 98 = 26129.6

The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $\(2.40\) for each game played.

To calculate the Expected Value for the player, we can multiply the probability of winning by the amount won, and subtract the probability of losing by the amount paid.

Expected Value = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Paid)

Given the following information:

Probability of winning \(= 0.13\)

Amount won = $15

Probability of losing \(= 0.87\)

Amount paid = $5

Plugging these values into the formula:

Expected Value \(= (0.13 \times $15) - (0.87 times $5)\)

Expected Value \(= $1.95 - $4.35\)

Expected Value = \(-$2.40\)

If a person plays this game a very large number of times over the years, we expect them to come out financially behind, as the Expected Value is negative. This indicates that, on average, the player will lose money over time by playing this game repeatedly.

Therefore, The Expected Value for the player is -$2.40, which is negative. This means that on average, the player can expect to lose $2.40 for each game played.

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Answer:

The correct answer is E. Neither the frequency nor the wavelength is affected. Explanation: The wave frequency does not affect the speed of that wave. An increase in frequency of a wave causes a decrease in wavelength while the wave speed remains the constant. The speed of the waves is significantly higher at higher tensions.

Step-by-step explanation:

Answer:

e is the amount of people

Step-by-step explanation:

4 x so let’s say you have two x you have 50% of the people that said yes.

The product is 42 and the sum is -13.

Answer:

product is 42, and sum is -13

Step-by-step explanation:

Product:  -6   x   -7 = +42    multiplication, negative  x negative is positive

Sum:       -6   +   -7   =  -13   adding numbers , all same sign, keep the sign

The another example that supports Hilary's conjecture are, 26² - 21²

In mathematics, subtraction is an operation which means taking away a few portions of the group or few things from a whole part.

For example, if we take 4 pencils out of 10 then remaining pencils are 6

so this process is called subtraction.

Given that,

Hilary was examining the differences between perfect squares of numbers separated by 5.
The differences always have the digit 5 in the ones place.

Another example that supports Hilary's conjecture is:

= 26² - 21²

= 676 - 441

= 235

As we can see, the difference between the perfect squares of 26 and 21 is 235,

which ends in the digit 5 in the ones place, confirming Hilary's conjecture that the differences between perfect squares of numbers separated by 5 always have the digit 5 in the ones place.

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The answer choice which would be the MOST difficult to adjust if you were looking to reduce your expenses is:

This refers to the reduction of costs by making a plan to which a person would base his financial decisions.

With this in mind, we can see that if a person wants to reduce expenses, then making adjustments on a loan payment for a car would be the most difficult because he has to make periodic payments for the car.

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In a case whereby Darren says that more students hands are 4 2/4 inches longer than 4 and 5 1/4 inches combined, he is wrong

\(4\frac{2}{4}\) that was given in the question can be seen as mixed fraction, we can expressed this as improper fraction so that it will be easier to handle.

\(4\frac{2}{4} = \frac{16+4}{2}\)

=\(\frac{18}{4}\)

Then \(4 + 5\frac{1}{4} = \frac{16}{4} +\frac{20+1}{4} \\\\=\frac{37}{4}\)

Then after expressing the given fractions as improper fraction we can now compare them so that e will know may be Darren is right or wrong, then here we can see that \(\frac{18}{4}\) is less than \(\frac{37}{4}\) Hence, Darren is wrong.

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Answer:

Step-by-step explanation:

THE ANSWER TO YOUR QUESTION IS C.

Answer:

b. DC = 29 and DE = 44.5

Step-by-step explanation:

Given:

AB = 29

BD = 89

Required:

DC and DE

Solution:

Recall: diagonals of a parallelogram bisect each other into equal segments. Also, pairs of parallel sides are equal.

✔️DC = AB = 29 (parallel sides of parallelogram)

DC = 29

✔️DE = ½(DB) (diagonals bisect each other into equal parts)

Substitute

DE = ½(89)

DE = 44.5

he net income for the year is $16,550.

Calculation of the net income for the year:Retained earnings equation is:Beginning Retained Earnings + Net Income − Dividends = Ending Retained EarningsWhere, Beginning Retained Earnings = $0 (not given)Ending Retained Earnings = $16,550 (calculated from balance sheet)Dividends = $0 (not given)

Therefore,Net Income = Ending Retained Earnings - Beginning Retained Earnings + Dividends= $16,550 - $0 + $0= $16,550 Balance Sheet of Cole Valley Book Store as of December 31, current year:Current assets Cash on hand and in bank = $69,250 Amounts due from customers from sales of books = $43,500 Total current assets = $112,750 Property, plant, and equipment Unused portion of store and office equipment = $72,500

Total assets = $185,250Liabilities Amounts owed to publishers for books purchased = $12,400 One-year note payable to a local bank = $3,200 Total liabilities = $15,600 Stock holders' Equity Common stock, 5,600 shares at $71,500 = $400,400 Retained earnings, beginning = $0Net income = $16,550 Retained earnings, ending = $16,550 Total stockholders' equity = $416,950Total liabilities and stockholders' equity = $185,250 + $15,600 + $416,950= $617,800

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