Multiply: 4x^3√4x² (2^3√32x²-x√2x)

Help me please

Sin(152) can be expressed as sin(28) by subtracting the given angle from 180 degrees, resulting in a new angle within the range of 0 to 360 degrees.

The given angle is 152 degrees. To express it as a function of a different angle, let's consider 180 degrees as the reference angle. Since 152 degrees is less than 180 degrees, we can express it as follows:

θ = 180 - (180 - 152) = 28 degrees.

Now, we can express sin(152) in terms of θ as sin(28). This is because the sine function has periodicity of 360 degrees, and sin(152) and sin(28) will have the same value.

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Answer:

??? what do you mean?

Step-by-step explanation:

the function A_t(t) models the amount in the fund for each twin, where A_t(t) is the amount in dollars and t is the number of years.

If the amount in the fund for the child is split evenly between the twins, then each twin will have an equal share of the fund. Therefore, the function that models the amount in the fund for each twin would be half of the original amount.

The original function is given as A_c(t) = 5000(1.0025)^(12t). To split the amount evenly between the twins, we can divide the original function by 2.

Therefore, the function that models the amount in the fund for each twin would be:

A_t(t) = 0.5 * A_c(t)

Substituting the original function, we get:

A_t(t) = 0.5 * 5000(1.0025)^(12t)

Simplifying the equation:

A_t(t) = 2500(1.0025)^(12t)

So, the function A_t(t) models the amount in the fund for each twin, where A_t(t) is the amount in dollars and t is the number of years.

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We can conclude that under the AAS congruency condition, we can prove that △WXY ≅ △YZX.

Two triangles are said to be congruent if all three corresponding sides and all three corresponding angles have the same size.

You can move, flip, twist, and turn these triangles to produce the same effect.

When relocated, they are parallel to one another.

So, we know that;
Shared side XZ by △WXZ and △YZX.

Right angles exist between WXZ and XZY.

∠XYZ and ∠XYZ have the same values.

Now that we have the parameters, we can infer that XZ is congruent to itself according to the reflexive property of congruence, and as a result, both triangles have a congruent side.

Second, since WXZ and XZY are right angles, it follows that they are equal and hence congruent.

The last piece of information is that XWZ and XYZ are congruent.

In conclusion, the triangles are congruent according to the AAS Congruency since we have two corresponding angles and one corresponding side that are equal but the corresponding side is not with the included angles.

Therefore, we can conclude that under the AAS congruency condition, we can prove that △WXY ≅ △YZX.

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Answer:

Step-by-step explanation:

20x+5y=15

Subtract 20x from both sides.

5y=15−20x

Divide both sides by 5.

__5y_  = _15-20x_____

    5                5

y=  __15-20______

            5

Divide 15−20x by 5.

y=3−4x

The percentage of people who do not like to listen to radio as well as watch the television is 65%.

It is important to note that a percentage is a value or ratio that may be stated as a fraction of 100. If we need to calculate a percentage of a number, we should divide it's entirety and then multiply it by 100.

From the information, 36% like to listen to radio as well as watch the television.

Therefore, the percentage of the people who do not like to listen to radio as well as watch the television will be:

= 1 - 35%

= 65%

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In a survey of a community. 55% of the people like to listen the radio, 65% like to watch the television and 35% like to listen the radio as well as watch the television

Find the percentage of the people who do not like to listen radio as well as watch the television.

In the given research scenario, the dependent variable is the average number of pounds lost.

The dependent variable is the variable that is being measured or observed in an experiment. It is the outcome or response variable that is expected to change as a result of manipulating the independent variable(s). In this case, the independent variable is the type of diet (low-carb or high-carb), and the dependent variable is the average number of pounds lost by the participants.

The researchers are comparing the average weight loss between the two groups: one following a low-carbohydrate diet and the other following a high-carbohydrate diet with the same number of calories. They are interested in determining whether the type of diet has an effect on weight loss. Hence, the dependent variable is the average number of pounds lost, as it is the variable that is expected to vary based on the diet type.

If you would like to represent the dependent variable using LaTeX code, you can use the following snippet:

\(\text{Dependent Variable: Average number of pounds lost}\)

I hope this explanation clarifies the concept of the dependent variable in the given research scenario. Let me know if you have any further questions.

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The ladder reaches approximately 16.97 feet up the side of the house. Rounded to the nearest hundredth, it would be 16.97 feet.

To determine how far up the side of the house the ladder reaches, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the ladder acts as the hypotenuse of a right triangle, with one side being the distance from the base of the ladder to the house (6 feet) and the other side being the vertical distance we want to find. Let's call the vertical distance "x."

Using the Pythagorean theorem, we have:

(6^2) + (x^2) = (18^2)

36 + x^2 = 324

x^2 = 288

Taking the square root of both sides, we get:

x ≈ √288 ≈ 16.97

Therefore, the ladder reaches approximately 16.97 feet up the side of the house. Rounded to the nearest hundredth, it would be 16.97 feet.

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An 18-foot extension ladder is placed 6 feet away from a house.  How far up the side of the house does the ladder reach? (Round to the nearest hundredth).

The answer in standard form is given by 65.7 ×10⁴

A standard form of a number in Maths is basically mentioned for the representation of large numbers or small numbers. We use exponents to represent such numbers in standard form.

Given here:  (6.31 x 10⁵)+(2.6 x 10⁴)

Simplifying the equation further we get

(6.31 x 10⁵)+(2.6 x 10⁴)= 63.1×10⁴+2.6×10⁴

                                    =65.7×10⁴

Hence, The answer in standard form is given by 65.7 ×10⁴

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Answer:

15 cm is the answer

Step-by-step explanation:

Step-by-step explanation:

15 trust me do that math and will see how it adds up

The 99% confidence interval for the mean daily return on this stock is (-2.97, 1.52). The correct answer is Lower limit: - -2.973 - Upper limit: 1.515.

A certain brokerage house wants to estimate the mean daily return on a certain stock.

A random sample of 11 days yields the following return percentages.

-1.36, -2.85, 2.33, 0.46, 0.9, -1.94, -2.19, 1.14, 0.1, -2.2, -1.26.

Confidence level = 99%df

= n - 1

= 11 - 1

= 10α/2

= (1 - confidence level) / 2

= 0.01 / 2

= 0.005

From the t-distribution table with 10 degrees of freedom at α/2 = 0.005, we get t0.005 = 3.169.

Using the formula, the confidence interval is calculated as follows:

CI = X ± t0.005 * s / √n

Here, sample mean X = (-1.36-2.85+2.33+0.46+0.9-1.94-2.19+1.14+0.1-2.2-1.26) / 11

= -0.7290909091

Sample standard deviation s = sqrt([Σ(xi - X)²]/(n - 1))= 1.726805996

Approximately, 99% of the intervals constructed in this manner contain the true population parameter, mean daily return on this stock.

Lower limit: -2.973

Upper limit: 1.515

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Answer:

8cm

Step-by-step explanation:

\(Here,\\\\Area(A)=64\pi cm^{2} \\Radius(r)=?\\\\As\:we\:have,\\\\\hookrightarrow Area=\pi r^{2} \\\\\hookrightarrow \frac{64\pi cm^{2} }{\pi } =r^{2} \\\hookrightarrow 64 cm^{2} =r^{2} \\\\\hookrightarrow \sqrt{64cm^{2} } =r\\\\\hookrightarrow 8cm=r\\\\\hookrightarrow r=8cm\)

Answer:

\(\huge\boxed{\bf{radius_{circle} = 8cm}}\)

Step-by-step explanation:

Given:-

To find:-

Ans:-

\(\sf \to Area_{circle} = \pi*r^2 \)

\(\sf \to 64\cancel{\pi} cm^2 = \cancel{\pi}*r^2 \)

\(\sf \to 64cm^2 = r^2 \)

\(\sf \to r = \sqrt{64cm^2} \)

\(\sf \to r = 8cm \)

therefore \(\tt radius_{circle} \) = 8cm

\(\: \)

\(\huge\colorbox{skyblue}{BlackPain}\)

When a man on top of a building sees a car approaching him and as the car moves 100 ft closer, the angle of depression changes from 15 to 33 degrees, the height of the building is 159.8 feet.

To solve the problem, we can use the tangent function. Let x be the distance between the man and the building, then we have:

tan(15) = h / x ...........(1) and tan(33) = h / (x - 100) ...........(2)

Dividing (2) by (1), we get:

tan(33) / tan(15) = (x - 100) / x

Simplifying the expression, we have:

(x - 100) / x = 2.22

Solving for x, we get:

x = 100 / 1.22 ≈ 81.97

Using equation (1), we can solve for the height of the building:

h = x * tan(15)

h ≈ 159.8

Therefore, the height of the building is approximately 159.8 feet.

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Answer:

Triangle 3: 3, 4 ,5

Step-by-step explanation:

Well, you can easily tell by 3, 4, 5 being a Pythagorean triple.

But you have to use the Pythagorean Theorem to solve this.

So you get the side lengths of the two shortest sides, and you add the squared versions of them together.

So: 3^2+4^2 and if that equals the biggest side:5^2 then it's a right triangle.

Answer:

4x+17=5

Step-by-step explanation:

The product of 4 and a number: Product means multiplication.

Therefore, we have 4 and any variable of your choice.(I used x)

plus 17: +17

Now we have 4x+17

Is: means equal (=)

Now we plug in what we have: 4x+17=5

Hope this helps! :)

The expected value is the long-term average outcome of a random variable. It is calculated by multiplying each possible outcome by its probability and summing them up. In simpler terms, it represents the average value we expect to get over many trials.

The expected value is a concept in probability and statistics that represents the long-term average outcome of a random variable. It is also known as the mean or average. To calculate the expected value, we multiply each possible outcome by its probability and sum them up.

For example, let's say we have a fair six-sided die. The possible outcomes are numbers 1 to 6, each with a probability of 1/6. To find the expected value, we multiply each outcome by its probability:

Summing up these values gives us:

1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6 = 21/6 = 3.5

Therefore, the expected value of rolling a fair six-sided die is 3.5. This means that if we roll the die many times, the average outcome will be close to 3.5.

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The compound interest formula is given by the formula

Where A = Amount after t years

r = rate = 6

t = time = 5

p = $ 25000

For the first year

For the second year

P=26500+25000=51500

For the third year

P=54590 + 25000=79590

For the fourth year

P=84365.4 + 25000=109365.4

For the fifth year

P= 115927.324 + 25000 =140927.324

At the start of the 6th year

P= 149382.962+25000= 174382.96

Answer = $174382.96

Option B is correct

The value of x as the compound interest is approximately 3.923%.

We have,

To find the value of x, we can use the compound interest formula:

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

Where:

A = Final amount

P = Principal amount (initial investment)

r = Annual interest rate (as a decimal)

n = Number of times interest is compounded per year

t = Number of years

Given information:

P = £3500

r = 2% = 0.02 (for the first year)

t = 3 years

A = £3855.76

We can split the calculation into two parts:

The first year and the remaining two years.

For the first year:

A1 = P (1 + r/1)^(1 x 1)

A1 = £3500(1 + 0.02)^1

A1 = £3500(1.02)

A1 = £3570

For the remaining two years:

A2 = A1(1 + x/1)^(1 x 2)

A2 = £3570(1 + x/100)²

Now, we can set up an equation using the given final amount A and solve for x:

£3855.76 = £3570(1 + x/100)²

Dividing both sides by £3570:

1.08 = (1 + x/100)²

Taking the square root of both sides:

√1.08 = 1 + x/100

Simplifying:

1.03923 ≈ 1 + x/100

Subtracting 1 from both sides:

0.03923 ≈ x/100

Multiplying both sides by 100:

3.923 ≈ x

Approximately, x ≈ 3.923

Therefore,

The value of x is approximately 3.923%.

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For a one-tailed dependent samples t-test with 28 participants, the critical value you need to overcome at the p < 0.01 level is 2.478.

1. Identify the degrees of freedom: Since there are 28 participants, the degrees of freedom (df) = 28 - 1 = 27.
2. Determine the significance level: The question specifies a one-tailed test with p < 0.01, which means a significance level (α) of 0.01.
3. Find the critical value: Using a t-distribution table, look for the value that corresponds to df = 27 and α = 0.01. This value is 2.478.

In a one-tailed dependent samples t-test with 28 participants and a significance level of p < 0.01, the degrees of freedom are 27 (28-1). By referring to a t-distribution table and searching for the critical value that matches the given degrees of freedom and significance level, we find the critical value to be 2.478. This value must be overcome to achieve statistical significance.

For a one-tailed dependent samples t-test with 28 participants at the p < 0.01 level, the specific critical value to overcome is 2.478.

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Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book

Answer: £16

Step-by-step explanation:

To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.

75% of x = £12

To solve for x, we can set up the equation:

0.75x = £12

To isolate x, we divide both sides of the equation by 0.75:

x = £12 / 0.75

x = £16

Therefore, the original price of the book was £16.

A special safe from nine syples for three symbol long passcode you may enter a symbol at any number of times so 729 potential passcodes are there.

In this system, you can choose from nine symbols for a three-symbol long passcode, and you may enter a symbol any number of times.

To find the potential passcodes, you simply need to use the formula: (number of choices)^(length of passcode) .

In this case, you have 9 choices for each of the 3 positions in the passcode: 9^3 = 729 So, there are 729 potential passcodes. The correct answer is option C.

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The value of the equation is A = ⁵√32,768 is A = 8

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.

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 data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

A = ⁵√32,768   be equation (1)

On simplifying the equation , we get

A = 8 x 8 x 8 x 8 x 8 = 32,768

So , the 5th root of ( 32,768 ) is 8

Therefore , the value of A = 8

Hence , the equation is A = 8

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Answer:

Step-by-step explanation:

Answer:

A. She could sample an equal number of students in each type of dance class.

Step-by-step explanation:

The answer is A. because all the other ones are not equal, and some are leaned more towards one side.

Hope this helps! :)

Answer:

a

Step-by-step explanation:

test

Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.

I understand that you would like an explanation related to parallel lines in geometry and the final answer should be concise, covering the main point in the last two lines.
In geometry, parallel lines are lines in a plane that never intersect or touch each other at any point. These lines always maintain the same distance from one another. However, if two lines start as parallel but later diverge, it indicates that they are no longer maintaining the same distance from each other. In such a case, the geometry under consideration is non-Euclidean.

Therefore, when two lines begin parallel but later diverge, it implies that the geometry involved is non-Euclidean.

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Answer:

94, 188, 564

Step-by-step explanation:

let x be the first part then the second part is 2x and third part is 3 × 2x = 6x

then

x + 2x + 6x = 846 , that is

9x = 846 ( divide both sides by 9 )

x = 94

2x = 2 × 94 = 188

6x = 6 × 94 = 564

Answer:

B. x² + y² - 4x +8y +11 = 0

Step-by-step explanation:

B. is the only one that represents a circle. Option A forms an oval, option C forms an X, and option D forms a regular function.

hope this helps!

Answer:

Last choice

Step-by-step explanation:

The basic definition of inverse function is both domain and range are swapped.

The domain is defined as set of all x-values while range is defined as set of all y-values.

If we have set of function h = {(1,2), (3,4), (5,6)} then the inverse will be {(2,1), (4,3), (6,5)}. Thus, if set of (x,y) is original function then set of (y,x) will be inverse of set of (x,y).

Henceforth, the inverse of f(x) will be g(x) = {(3,8), (1,4), (-1,0), (-3,-4)}.

Answer:

D. g(x) = {(3, 8), (1, 4), (–1, 0), (–3, –4)}

Step-by-step explanation:

hope this helps:)