Find the volume of the trapezoidal prism following.

Answer:

x = 67°

Step-by-step explanation:

All angles inside a triangle add up to 180 so...

180 - 46 = 134

134 ÷ 2 = 67

Answer:

Orange and pink, I'm not too sure

Answer:

Orange and pink.

Step-by-step explanation:

Because there shapes are same.

If the radius of Jasmine's swimming pool is 4.2 meter, then it's circumference is 26.4 meters.

The "Circumference" of a circle is known as the distance around the boundary of a circle.

The circumference of a circle is given by the formula : 2 × π × radius,

where π (pi) is a mathematical constant approximately equal to 3.14,

We are given that Jasmine's swimming pool has a radius of 4.2 meters.
So, we can calculate the circumference of the pool as :

⇒ Circumference = 2 × 3.14 × 4.2 meters,

⇒ Circumference ≈ 26.4 meters,

Therefore, the circumference of Jasmine's swimming pool is 26.4 meters.

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Answer:

formula 8.334

Step-by-step explanation: formula 8.334 so

The value of each variable is:

x = 11 units

y = 11√2 units

Trigonometry deals with the relationship between the ratios of the sides of a right-angled triangle with its angles.

We can find the value of each variable using trigonometric ratios:

tan 45° = x/11 (tan = opposite/adjacent)

1 = x/11

x = 11 units

sin 45° =  9/y (sine = opposite/hypotenuse)

(√2)/2 = 11/y

y = 11/ (√2)/2

y = 11√2 units

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According to the information provided, it should be noted that the 750 seniors in her school make up the population of interest, and the parameter of interest is the percentage of seniors who intend to attend the prom.

Given,

Additionally, a strictly random sample is required in order to create a confidence interval. Additionally, the sample size should be examined to see if it adequately represents the population.

Using the z critical of 1.645, a 90% confidence interval will be built. The sample proportion in this case will be:

= 36/50 = 0.72

Q = 1 - 0.72 = 0.28

n = 50

As a result, the standard error will be equal to 50 squared times the multiplication of 0.72 and 0.28. This amounts to 0.0635.

For a big sample randomly selected among 750 seniors, the interval on the context suggests that we are 90% confident that the fraction of those who desire to attend the prom falls within the interval.

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Answer:

2x - y - 2 = 0

Step-by-step explanation:

A (1,0)

B (0,-2)

(y-0)/(-2-0) = (x-1)(0-1)

y/-2 = (x-1)/-1

-y/2 = -x + 1

-y = 2(-x+1)

-y = -2x + 2

2x - y - 2 = 0

Answer:

15

Step-by-step explanation:

Pretend a is the number.

We have: 31 + 3a = 76

=> 3a = 76 - 31 = 45

=> a = 45/3

=> a = 15

Answer:

Hi rei its cam

Step-by-step explanation:

The interest rate for the first period is $287.22

To obtain the first period interest, we use simple interest formula;

Simple Interest = Principal * Rate * Time

Given:

Principal = $45,687.23

Annual interest rate = 7.555%

Interest period = Monthly

Convert the annual interest rate to a monthly interest rate.

Monthly interest = Annual interest/ 12 = 7.555/12 = 0.6295%

Interest = Principal * Monthly interest rate * Time

Since it's the first period, the time is 1 month:

Interest = $45,687.23 * 0.62958333% * 1

Interest = $45,687.23 * 0.0062958333

Interest ≈ $287.22

Therefore, the first period interest is $287.22.

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Answer:

\(b = 90\)

\(c=80\)

\(d =100\)

Step-by-step explanation:

Given

See attachment

Required

Find b, c and d

First, we solve for b using:

\(b + 10 + b - 10 = 180\) --- base angles of a parallelogram

Collect like terms

\(b + b =180+10-10\)

\(2b = 180\)

Solve for b

\(b = 180/2\)

\(b = 90\)

Then, we have:

\(d =b + 10\)

\(c = b - 10\) --- opposite angles

So, we have:

\(d =90 + 10\)

\(d =100\)

\(c = 90 - 10\)

\(c=80\)

The x and y-intercepts of the rational function are; (-3, 0) and (0, -3/25).

The vertical asymptotes of the function are; x = ± 5.

The horizontal asymptotes of the function is f(x) = 0.

For x-intercept; let f (x) = 0;

0 = (x + 3) / (x² - 25)

x + 3 = 0; x = -3 or (-3, 0).

For the y-intercept; let x = 0.

f (0) = (0 + 3) / (0² - 25)

= -3/25 or (0, -3/25).

For the vertical asymptotes;

x² - 25 = 0

x² = 25

x = ±5.

For the horizontal asymptote;

Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is; f (x) = 0.

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Answer:

Ximena can use 1 gigabytes of data

Step-by-step explanation:

The first thing you want to do is subtract

51.10 - 44.50 =  5.6

5.6 is the amount of money she will have to spend on data

With each gigabyte costing 4 dollars and only 5 dollars to spend

she can only use one gigabyte

Answer:

V≈50.97m³

Step-by-step explanation:

Diameter

4.6

Using the formulas

V=4

3πr3

d=2r

Solving for V

V=1

6πd3=1

6·π·4.63≈50.96501m³

(I hope this helps.)

Answer: Therefore, the volume of a sphere is \(\textbf {50.96\; m^{3}}\)\(\textbf {50.96\; m^{3}}\)\(\mathbf{50.96\; m^{3}}\)

Step-by-step explanation:

Given,

Diameter, d = 4.6m

\(\mathbf{Radius, r} = \frac{d}{2} \\ \;\;\;\;\;\\\\= \frac{4.6}{2} \\ \,\\= 2.3\, m\\\\\)

Formula for the volume of a sphere will be,

\(V = \frac{4}{3} \pi r^{3}\;\\\\V = \frac{4}{3} \pi (2.3)^{3}\;\\\\\mathbf{V=50.96\; m^{3}}\)

Therefore, the volume of a sphere is \(\textbf {50.96\; m^{3}}\)\(\textbf {50.96\; m^{3}}\)\(\mathbf{50.96\; m^{3}}\)

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The only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given Range is θ ≈ 19.47 degrees.

a) We are given the equation 8 tan θ = 3 cos θ.

Dividing both sides of the equation by cos θ, we have:

8 tan θ / cos θ = 3

Using the identity tan θ = sin θ / cos θ, we can substitute it into the equation:

8 (sin θ / cos θ) / cos θ = 3

Simplifying further, we get:

8 sin θ / cos^2 θ = 3

Now, multiplying both sides of the equation by cos^2 θ, we have:

8 sin θ = 3 cos^2 θ

Using the identity cos^2 θ = 1 - sin^2 θ, we can substitute it into the equation:

8 sin θ = 3(1 - sin^2 θ)

Expanding the equation, we get:

8 sin θ = 3 - 3 sin^2 θ

Rearranging the terms, we have:

3 sin^2 θ + 8 sin θ - 3 = 0

Therefore, we have successfully shown that the equation can be rewritten in the form 3 sin^2 θ + 8 sin θ - 3 = 0.

b) Now, let's solve the equation 3 sin^2 θ + 8 sin θ - 3 = 0.

To solve the quadratic equation, we can use factoring, quadratic formula, or other appropriate methods.

In this case, the equation factors as:

(3 sin θ - 1)(sin θ + 3) = 0

Setting each factor equal to zero, we have two equations:

3 sin θ - 1 = 0    or    sin θ + 3 = 0

For the first equation, solving for sin θ, we get:

3 sin θ = 1

sin θ = 1/3

Taking the inverse sine (sin^-1) of both sides, we find:

θ = sin^-1(1/3) ≈ 19.47 degrees (to 2 decimal places)

For the second equation, solving for sin θ, we have:

sin θ = -3

Since the range of sine is between -1 and 1, there are no solutions for this equation in the given range (0 ≤ θ ≤ 90 degrees).

Therefore, the only solution for the equation 8 tan^2 θ = 3 cos^2 θ in the given range is θ ≈ 19.47 degrees.

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To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

Answer:

41 meters

Step-by-step explanation:

\(\frac{31}{64}\) = \(\frac{19.8}{x}\)

31x = (19.8)(64)

31x = 1267.2  Divide both sides by 31 and round

x = 41

Answer:

It's equal to itself. Here are the two ways to do this problem. ↓

Since 6 is 10% of 60, if we assume that 10% of the class are left handed and there are 27 left handed students, then 27 is 10% of the total amount of students in the class.

To find how many students are there in the class, notice that 27 is 10% of 270.

Therefore, we can estimate that the total amount of students in that class, is:

Answer:

11 + x

Step-by-step explanation:

addition uses the communtitve property meaning the numbers can be swaped and still result in the same answer

Answer:

The maximum profit the florist will earn from selling celebration bouquets is $725.

The florist will break-even after one-dollar decreases when her profit is zero. From the graph, this occurs at x = 10. So the florist will break-even after 10 one-dollar decreases.

The interval of the number of one-dollar decreases for which the florist makes a profit from celebration bouquets is (0, 10). This is because the profit is positive for values of x between 0 and 10, and becomes negative after 10.

Step-by-step explanation:

Answer:

i think the answer is X, because the elements of both X and Y are in X

Answer:

\(\huge\boxed{\sf f^{-1}(x)=5x+10}\)

Step-by-step explanation:

\(\displaystyle f(x)=\frac{x}{5} -2\)

Put f(x) = y

\(\displaystyle y=\frac{x}{5} -2\)

Swap x and y

\(\displaystyle x = \frac{y}{5} -2\)

Now, solve for y

\(\displaystyle x = \frac{y}{5} -2\)

Add 2 to both sides

\(\displaystyle x + 2 =\frac{y}{5}\)

Multiply 5 to both sides

\(5(x+2)=y\)

Distribute

\(5x + 10 =y\)

Put y = f⁻¹(x)

\(\boxed{f^{-1}(x)=5x+10}\)

\(\rule[225]{225}{2}\)

Answer:

C, A, D, B

Step-by-step explanation:

(a) We need to compare the sum of this series to 3/4 and 31/36.  So we just need to find the sum within 1/36.

1 / (n + 1 + 1)² ≤ 1/36

(n + 2)² ≥ 36

n + 2 ≥ 6

n ≥ 4

So we just need to find the partial sum of the terms from n=0 to n=4.

1 − 1/4 + 1/9 − 1/16 + 1/25 ≈ 0.839

We can use this to approximate the actual sum within 1/64.

(b) 1 − 1/7 + 1/49 − 1/343 + ...

We can rearrange this as the difference between two geometric series:

(1 + 1/49 + 1/2401 + ...) − (1/7 + 1/343 + 1/16807)

∑₀°° (1/49)ⁿ − ∑₀°° 1/7 (1/49)ⁿ

1 / (1 − 1/49) − (1/7) / (1 − 1/49)

(6/7) / (48/49)

7/8

So from smallest to largest, the answer is C, A, D, B.

All the values that are input into a function are referred to as the domain of a function. The collection of all potential inputs for a function is its domain.

Think of this box as the f(x) = 2x function. The domain is only the collection of natural numbers when the input values are x = 1,2,3,4,..., and the values that are returned are referred to as the range.

However, f(x) = 2x is typically defined for all real values of x, and as a result, its domain is the set of all real numbers, which is denoted by (R). The general formulas for determining the domain of various types of functions are listed below.

The set of all real numbers, or R, is used here.

Any polynomial function (linear, quadratic, cubic, etc.) has a domain of R.

The domain of a square root function √x is x≥0.

The domain of an exponential function is R.

The domain of the logarithmic function is x>0.

To find the domain of a rational function y = f(x), set the denominator ≠ 0.

To calculate or find the domain consider the case or an example where X = 1, 2, 3, 4, 5, f: X Y, and R = (x,y): y = x+1.

Domain = the values entered.

Domain = X = thus 1, 2, 3, 4, and 5.

Range equals the function's output values, which are 2, 3, 4, 5, and 6.

and the co-domain is equal to Y = 2, 3, 4, 5, and 6.

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x = 15/2

do u need an explanation?

The probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

Since the probability density function is uniform, the probability of the friend being between 10 and 30 minutes late is equal to the area of the rectangle that lies between x = 10 and x = 30, and below the curve of the probability density function.

The height of the rectangle is equal to the maximum value of the probability density function, which is 1/30 since the interval of possible values for x is [0, 30] minutes.

The width of the rectangle is equal to the difference between the upper and lower limits of the interval, which is 30 - 10 = 20 minutes.

Therefore, the probability of the friend being between 10 and 30 minutes late is:

P(10 < x < 30) = (height of rectangle) x (width of rectangle)

= (1/30) x 20

= 2/3

≈ 0.6667

So the probability that the friend is between 10 and 30 minutes late is approximately 0.6667, or 66.67%.

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Answer:

AB=12m<6

BD=23m>7

Step-by-step explanation: