Use a trigonometric ratio to determine the value of x for each the triangle. Round your answer to the nearest hundredth.

Answer:

Carl buys 132.475 liters of water.

Step-by-step explanation:

Since Carl buys seven 5-gallon jugs of water multiply 7 by 5 to know how many gallons of water Carl bought in total.

7(5) = 35 Gallons

Now that you have the total amount of gallons of water Carl bought you have to convert 35 gallons to liters given that 1 gallon = 3.785 liters by multiplying 35 by 3.785.

35(3.785) = 132.475

So Carl bought 132.475 liters of water.

Though that is the answer based on what is given a gallon is actually equal to 3.78541 liters so the exact answer would be 132.489 liters of water.

Answer:

C. 7°F

Step-by-step explanation:

Let \(s_a = \sin(ax)\) and \(c_a = \cos(ax)\), so the integrand is

\(\dfrac{{s_1}^{2k+1} {c_1}^k + {s_1}^k {c_1}^{2k+1}}{{s_1}^{3k+3} + {c_1}^{3k+3}}\)

Factorize everything and recall the identities

2 s₁ c₁ = s₂

c₁² = (1 + c₂)/2

s₁² = (1 - c₂)/2

\(= \dfrac{{s_1}^k {c_1}^k \left({s_1}^{k+1} + {c_1}^{k+1}\right)}{\left({s_1}^{k+1} + {c_1}^{k+1}\right) \left({s_1}^{2k+2} - {s_1}^{k+1} {c_1}^{k+1} + {c_1}^{2k+2}\right)}\)

\(= \dfrac{\left(s_1c_1\right)^k}{\left({s_1}^2\right)^{k+1} - \left(s_1 c_1)^{k+1} + \left({c_1}^2\right)^{k+1}}\)

\(= \dfrac{\left(\frac{s_2}2\right)^k}{\left(\frac{1-c_2}2\right)^{k+1} - \left(\frac{s_2}2\right)^{k+1} + \left(\frac{1+c_2}2\right)^{k+1}}\)

\(= 2 \times \dfrac{{s_2}^k}{(1-c_2)^{k+1} - {s_2}^{k+1} + (1+c_2)^{k+1}}\)

After simplifying, substitute y = 2x. Then

\(\displaystyle \int_0^{\frac\pi4} \frac{\sin^{2k+1}(x) \cos^k(x) + \sin^k(x) \cos^{2k+1}(x)}{\sin^{3k+3}(x) + \cos^{3k+3}(x)} \, dx \\\\\\ = 2 \int_0^{\frac\pi4} \frac{\sin^k(2x)}{(1-\cos(2x))^{k+1} - \sin^{k+1}(2x) + (1 + \cos(2x))^{k+1}} \, dx\\\\\\ = \int_0^{\frac\pi2} \frac{\sin^k(y)}{(1-\cos(y))^{k+1} - \sin^{k+1}(y) + (1+\cos(y))^{k+1}} \, dy\)

Now substitute t = tan(y/2). Under this change of variable, we have

dt = 1/2 sec²(y/2) dy   ⇒   dy = 2/(1 + t²) dt

sin(y) = 2 sin(y/2) cos(y/2) = 2t/(1 + t²)

cos(y) = cos²(y/2) - sin²(y/2) = (1 - t²)/(1 + t²)

Making these replacements and simplifying the integrand reduces it significantly to

\(\displaystyle \int_0^1 \frac{t^k}{t^{2k+2} - t^{k+1} + 1} \, dt\)

Substitute once more with z = tᵏ⁺¹ and dz = (k + 1) tᵏ dt to reduce it to the trivial

\(\displaystyle \frac1{k+1} \int_0^1 \frac{dz}{z^2-z+1} = \frac{2\pi}{3\sqrt3 (k+1)}\)

Then Ω(n) is simply

\(\displaystyle \Omega(n) = \sum_{k=2}^{n-1} \frac{2\pi}{3\sqrt3(k+1)} = \frac{2\pi}{3\sqrt3} \sum_{k=3}^n \frac1k = \frac{2\pi}{3\sqrt3} \left(H_n - \frac32\right)\)

where Hₙ denotes the n-th harmonic number,

\(H_n = \displaystyle \sum_{k=1}^n \frac1k\)

It's known that

\(\displaystyle \lim_{n\to\infty} (H_n - \ln(n)) = \gamma\)

where γ ≈ 0.577216 (the Euler-Mascheroni constant). Then

\(\displaystyle \lim_{n\to\infty} \frac{\Omega(n)}n = \frac{2\pi}{3\sqrt3} \lim_{n\to\infty} \frac{(H_n - \ln(n)) + \ln(n) - \frac32}{n} = \boxed{\frac{2\gamma\pi}{3\sqrt3}} \approx 0.687969\)

Answer:

A and E

Step-by-step explanation:

B and D is unchangeable, species of bears and types of vegetables that existed in the world never changed.

C only consist of one data, temperature of Chicago at noon yesterday only.

Using Pascal's triangle and the difference quotient formula, we expand (x + h)^2 and simplify the expression to (2hx + h^2) / h. As h approaches 0, the term h becomes negligible, and we are left with 2x, which represents the derivative of x^2.

To use Pascal's triangle to find x^2 using the difference quotient formula, we can follow these steps:

1. Write the second row of Pascal's triangle: 1, 1.

2. Use the coefficients in the row as the binomial coefficients for (x + h)^2. In this case, we have (1x + 1h)^2.

3. Expand (x + h)^2 using the binomial theorem: x^2 + 2hx + h^2.

4. Apply the difference quotient formula: f(x + h) - f(x) / h.

5. Substitute the expanded expression into the formula: [(x + h)^2 - x^2] / h.

6. Simplify the numerator: (x^2 + 2hx + h^2 - x^2) / h.

7. Cancel out the x^2 terms in the numerator: (2hx + h^2) / h.

8. Divide both terms in the numerator by h: 2x + h.

9. As h approaches 0, the term h becomes negligible, and we are left with the derivative of x^2, which is 2x.

For more such questions on triangle

https://brainly.com/question/28470545

#SPJ8

Answer:

It is the same thing except for subtracting -4x and 9x, you subtract -4 and 9 and just add x at the end

When we solve for x in the expression 4(x + 8) - 4 = 34 - 2x, the result obtained is 11

From the question given above, the following data were obtained:

The value of x in the given expression can be obtained as illustrated below:

4(x + 4) - 4 = 34 + 2x

Clearing bracket, we have

4x + 16 - 4 = 34 + 2x

4x + 12 = 34 + 2x

Collect like terms

4x - 2x = 34 - 12

2x = 22

Divide both sides by 2

x = 22 / 2

= 11

Thus, the value of x in the expression is 11

Learn more about linear equation:

https://brainly.com/question/28735218

#SPJ1

Complete question:

I don’t know the answer:

Solve for x in the expression 4(x + 8) - 4 = 34 - 2x

Answer:

Step-by-step explanation: 0.15 and 0.2 are the slope of the line on the graph. The graph of the equation reading y = 0.20x + 25 would show a steeper line bc the bigger the slope the steeper the line.

Answer:

the answer for 500×4-8/2 is 1996

Answer:

64°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180°

let the third angle be x , then

x + 90° + 26° = 180°

x + 116° = 180° ( subtract 116° from both sides )

x = 64°

the other angle is 64°

Answer:A topic sentence is used to bring

to a paragraph.

Step-by-step explanation:

A topic sentence is used to bring

to a paragraph.

Answer:

the total monthly lease payment is $383.31 rounded to the nearest cent.

Step-by-step explanation:

To calculate the total monthly lease payment, we need to add the sales tax to the base monthly payment.

Sales tax = 8.25% of base monthly payment

Sales tax = 0.0825 x $354.12 = $29.19

Total monthly lease payment = Base monthly payment + Sales tax

Total monthly lease payment = $354.12 + $29.19 = $383.31

Therefore, the total monthly lease payment is $383.31 rounded to the nearest cent.

When teaching an 8th grade lesson on problem solving, Sylvia begins by utilizing a short video clip. Sylvia uses this video clip as a discrepant event because students attached with science it would look like magic for them.

A discrepant occurrence is an unexpected, counterintuitive result that differs from what an observer would typically anticipate. Oobleck is a classic illustration of a discrepant event.

Most kids (who have never seen it before) wouldn't anticipate that it would have both solid and liquid qualities. They didn't anticipate it to spread out right away once the "ball" was placed on the table instead of rolling into a ball and taking shape.

The main factor is that pupils will develop an obsession with science. They will see this as "magic," and they will be very interested in learning how it worked. After that, they'll be prepared to "amaze" their friends with both the "trick" and their subsequently displayed "smarts."

To learn more about a discrepant event link is here

brainly.com/question/13651668

#SPJ4

Answer:

25 degrees

Step-by-step explanation:

If its 15 when hes about to leave and -10 when he first checked it shou. be 25

Answer:

answer is 25

Step-by-step explanation:

...........

Answer:

34

Step-by-step explanation:

40 * 0.85 = 34

34 questions answered correctly

Hey there,

85% = \(\frac{85}{100}\) = 0,85

0,85 x 40 = 34

The student answered 34 questions correctly.

:)

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

Let's assign variables to represent the statements:

q: The aquarium is full of fish.

r: There are penguins.

The compound statement "If there are penguins and the aquarium is full of fish, then this is an octopus" can be written in symbolic form as: r ∧ q → o

∧ represents the logical operator "and" which connects the statements r and q.

→ represents the logical operator "implies" or "if...then".

o represents the statement "this is an octopus".

Learn more about compound statement on

https://brainly.com/question/28794655

#SPJ1

Answer:

1.8 or 9/5

Step-by-step explanation:

4\(\frac{1}{2}\) ÷ \(2\frac{1}{2}\)

Change into improper fractions

\(\frac{9}{2}\)÷\(\frac{5}{2\\}\)

Flip the second fraction and then multiply

\(\frac{9}{2}\)×\(\frac{2}{5}\)=\(\frac{18}{10}\)

18/10 is 1.8 as a decimal and 9/5 simplified

Answer: 1-4/5 dozens of muffins.

Step-by-step explanation;

Step One. Turn the fractions into decimals to make it easier; 4-1/2 will be 4.5 and 2-1/2 will be 2.5.

Step Two. Apply the rule of three, using the variable x to represent the number of muffins Garnet can make; 2.5/1 = 4.5/x.

Step Three. Solve for x by cross multiplying; x = 1.8. So Garnet can make 1.8 dozens of muffins with 4.5 cups of flour.

Step Four. Convert the decimal into a fraction; 1.8 in a fraction form is 9/5, or 1-4/5.

The number 100 would land in column 2

Given that we have the array of numbers

The length of each row in the array is 7

Dividing 100 by 7, we have

100/7 = 14 Remainder 2

This means that

Column = 2

In (a), we have

100/7 = 14 Remainder 2

This means that

Row = 14

Here, we have

The length of each row in the array is 6

Dividing 100 by 6, we have

100/6 = 16 Remainder 3

So, the location of 100 in rows of 6 numbers is row 16 and column 3

Let the length of each row in the array be n

Dividing 100 by n, we have

100/n = q Remainder r

This means that the location of 100 in rows of n numbers is row q and column r

Read more about numbers at

https://brainly.com/question/20372424

#SPJ1

Answer:

b

Step-by-step explanation:

Answer:

Refer to the step-by-step explanation.

Step-by-step explanation:

Come up with a monomial expression and solve it.

A monomial expression is an algebraic expression that consists of a single term. It is an expression that can contain variables, constants, and non-negative integer exponents, but there should be no addition or subtraction between different terms.

Here are a few examples of an monomial expression:

\(\hrulefill\)

Let's work with the monomial expression, 3x²y³z.

To solve this expression, I assume you would like to evaluate it for specific values of the variables x, y, and z. So let x=3, y=2, and z=1.

Plug these values into the expression:

3x²y³z

=> 3(3)²(2)³(1)

=> 3(9)(8)(1)

=> 27(8)(1)

=> 216(1)

=> 216

Thus, the expression is solved.

Answer:

\(x = \frac{26 + 8 \sqrt{10} }{9} \)

or

\(x = \frac{26 - 8 \sqrt{10} }{9} \)

Step-by-step explanation:

I apologise for my messy explanation.

The solution of the expression will be;

⇒ x = 5.7

or ⇒ x = 0.07

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Now,

Since, The expression is,

⇒ log ₂ (3x + 2) - log ₄ (x) = 3

Solve as;

⇒ log ₂ (3x + 2) - 1/2 log ₂ (x) = 3

⇒ log ₂ (3x + 2) - log ₂ √(x) = 3

⇒ log ₂ (3x + 2) / (√x) = 3

⇒ (3x + 2) / √x = 2³

⇒ (3x + 2) / √x = 8

⇒ (3x + 2) = 8√x

Taking square both side, we get;

⇒ (3x + 2)² = (8√x)²

⇒ 9x² + 12x + 4 = 64x

⇒ 9x² + 12x - 64x + 4 = 0

⇒ 9x² - 52x + 4 = 0

By applying quadratic formula, we get;

⇒ x = - (- 52) ± √ (-52)² - 4×9×4 / 2×9

⇒ x = 52 ± √ 2704 - 144 / 18

⇒ x = 52 ± √2560 / 18

⇒ x = 52 ± 50.6 / 18

This gives two solution as;

⇒ x = (52 + 50.6) / 18

⇒ x = 102.6/18

⇒ x = 5.7

And, We get;

⇒ x = 52 - 50.6 / 18

⇒ x = 1.4 / 18

⇒ x = 0.07

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Step-by-step explanation:

5.|12 - r| > 15

|12 - r| > 15/5

|12 - r| > 3

12 - r < -3 or 12 - r > 3

-r < -3 - 12 or -r > 3 - 12

-r < -15 or -r > -9

r > 15 or r < 9

The probability that the third largest observation in the sample is less than 0.7 is  0.2401 =  24.01%.

The sample size n = 5,

Therefore the order statistics will be represented as X₁, X₂, X₃, X₄, and X₅.

Probability that X₃ is less than 0.7:

Since X₃ is the third largest observation =  (X₁ and X₂) < 0.7.

The probability that X₃ is less than 0.7 is (0.7)² = 0.49.

.

The probability that both X₁ and X₂ are less than or equal to 0.7 is (0.7)² = 0.49 because in a continuous uniform distribution, the probability of any single observation being less than 0.7 is 0.7 - 0 = 0.7.

We then get the product of both cases:

Probability = 0.49 * 0.49 = 0.2401

Learn more about Probability at:

https://brainly.com/question/24756209

#SPJ1

Answer:

hope this will help you more

Answer:

$41269.983

rounded:

$41,269.98

Step-by-step explanation:

well you begin with the equation a=p(1+r/n)\(^{nt}\)

so 30,000(1+0.08/12)to the power of 4 times 12

when you plug all of that in a calculator your receive $41269.983

The inequality on the graph is the third option:

(2/5)*x - 3/2 ≥ y

Let's analyse the graph if the inequality.

We can see that there is a solid linear equation with a positive slope, and the shaded area is below that line, then the inequality is of the form:

y ≤ linear equation.

We know that the symbol "≤" must be used because of the solid line.

We also can see that when x = 0, y takes a velue between -1 and -2.

With that in mind the correct option is the third one:

(4/5)*x - 2y ≥ 3

Isolating y we get:

(4/5)*x - 3 ≥ 2y

(2/5)*x - 3/2 ≥ y

Changing the order:

y ≤ (2/5)*x - 3/2

That is the graphed inequality.

Learn more about inequalities:

https://brainly.com/question/24372553

#SPJ1