Write in Polar form: rcos 8 + i sin 8). (0 < < 27 and round to 3 decimal places) - 8 + 61 T = 0

Answer:

8+16+2=28

Step-by-step explanation:

The congruent 10 - labeled color spinner isn't attached and could not be found.

However, we could solve the problem hypothetically.

Answer:

Kindly check explanation

Step-by-step explanation:

The events here are independent events :

Probability = required outcome / Total possible outcomes

Total possible outcomes = number of divisions on spinner = 10

Required outcome = number of specified color

Therefore, Probability that first spin lands on yellow :

Number of yellow divisions on spinner / total number of divisions

Let number of yellow divisions = 3

Therefore. Probability that first spin lands in yellow = 3 / 10

Probability that second spin lands on green :

Number of green divisions on spinner / total number of divisions

Let number of green divisions = 2

Therefore. Probability that first spin lands on green = 2 / 10

P(first) * P(second)

3/10 * 2/10 = 3/10 * 1/5 = 3/50

Recall ; this is an hypothetical situation and not the original problem.

The probability that the first spin will land on yellow and the second spin will land on green is; 2/5

The spinner is missing but from online search, it is discovered that from the 10 congruent sections labeled, the colors are as follows;

Yellow - 2 sections

Green - 2 sections

Red - 3 sections

Blue - 3 sections

Thus, probability of getting yellow on first spin is;

P(yellow on first spin) = 2/10

Probability of getting green on second spin is;

P(green on second spin) = 2/10

Thus, probability that the first spin will land on yellow and the second spin will land on green is;

P(1st on yellow and 2nd on green) = 2/10 + 2/10

P(1st on yellow and 2nd on green) = 2/5

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Answer:

5

Step-by-step explanation:

1200cm3 = 12cm * 20cm * Xcm

1200/12 = 100 = 20*X

100/20 = 5 = X

Answer

https://zoom.us/j/99385592884?pwd=ajVOcXZSbGcyT3N3N0kxQm5Zek81Zz09er:

Step-by-step explanation:

Answer:

17 hours and 28 min

Step-by-step explanation:

12 in all:

{2, 4, 36, 6, 8, 10, 12, 16, 18, 20, 24, 30}

Answer:

Step-by-step explanation:

a. The work done on the ball by gravity while descending from its maximum height to the ground is 415.08 ft-lb.

b. The work done on the ball on its descent if it is caught 6 feet above the ground is also 415.08 ft-lb.

a. To find the work done on the ball by gravity while descending from its maximum height to the ground, we need to calculate the change in gravitational potential energy.

The maximum height of the ball can be found by setting h(t) equal to zero and solving for t:

\(\[h(t) = 6 + 8t - 1672 = 0\]\)

Solving this equation, we find:

\(\[8t = 1666\]\[t = \frac{1666}{8} = 208.25\text{ seconds}\]\)

Therefore, the time taken by the ball to reach the ground from its maximum height is 208.25 seconds.

The gravitational potential energy at the maximum height is given by the formula:

\(\[PE_{\text{max}} = mgh_{\text{max}}\]\)

where:

- m is the mass of the ball (0.2 pounds),

- g is the acceleration due to gravity \((32.2 ft/s\(^2\))\),

- \(\(h_{\text{max}}\)\)is the maximum height of the ball.

Substituting the given values, we have:

\(\[PE_{\text{max}} = 0.2 \times 32.2 \times h_{\text{max}}\]\)

The work done by gravity while the ball descends from its maximum height to the ground is equal to the change in potential energy, which can be calculated as:

\(\[W = PE_{\text{max}} - PE_{\text{ground}}\]\)

Since the ball is descending, the potential energy at the ground is zero. Therefore:

\(\[W = PE_{\text{max}} - 0 = PE_{\text{max}}\]\)

Plugging in the known values, we get:

\(\[W = 0.2 \times 32.2 \times h_{\text{max}}\]\)

To find \(\(h_{\text{max}}\)\), we substitute t = 208.25 into the height equation:

\(\[h(t) = 6 + 8t - 1672 = 6 + 8 \times 208.25 - 1672 = 64.5\text{ feet}\]\)

Finally, substituting\(\(h_{\text{max}} = 64.5\)\) into the work equation:

\(\[W = 0.2 \times 32.2 \times 64.5 = \boxed{415.08\text{ ft-lb}}\]\)

b. To find the work done on the ball on its descent if it is caught 6 feet above the ground, we need to consider the change in gravitational potential energy from the maximum height to the catching point.

The catching point is 6 feet above the ground, so the ball will travel a distance of \(\(h_{\text{max}} - 6\)\) during its descent.

The work done by gravity in this case is given by:

\(\[W = PE_{\text{max}} - PE_{\text{catch}}\]\)

The potential energy at the catching point is:

\(\[PE_{\text{catch}} = mgh_{\text{catch}}\]\)

Substituting the given values, we have:

\(\[PE_{\text{catch}} = 0.2 \times 32.2 \times h_{\text{catch}}\]\\\)

Since the work done on the ball is equal to the change in potential energy, we can calculate it as:

\(\[W = PE_{\text{max}} - PE_{\text{catch}}\]\)

Substituting the known values, we get:

\(\[W = 0.2 \times 32.2 \times (h_{\text{max}} - 6)\]\)

From part a, we know that \(\(h_{\text{max}} = 64.5\)\). Substituting this value, we have:

\(\[W = 0.2 \times 32.2 \times (64.5 - 6) = \boxed{415.08\text{ ft-lb}}\]\)

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Answer:

25/2.54 = 9.84251968

9.84 inches

The volume of the given figure is 288 cubic units.

Given a prism with the base dimension of 8×12 units and the height of 3 units.

From the general formula of the volume of the prism,

The volume of a prism is the product of the area of the base and the height of the prism. Prism volume (V) = B × h,

where, B is the area of the base and h is the height of the prism. = l × w × h,

where l, w, and h are the length, width, and height of the rectangular prism.

In our case,

l = 12

w =8

h =3

Volume of the prism = 12 *8 * 3

Volume of the prism = 288

Therefore, the volume of the prism will be 288 cubic units.

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The area of the region R is 0.302 square inches and the volume of the region formed is 0.309 cubic units

Given that we have

Region R between y - y³ = 0 and x = 0

When plotted, we have the shape of the region to be semi ellipse with the following dimensions

a = 0.5 and b = 0.384

The area is then calculated as

Area = 1/2πab

So, we have

Area = 1/2 * 22/7 * 0.5 * 0.384

Evaluate

Area = 0.302 square inches

When rotated, the resulting shape is a ellipsoid with the following dimensions

a = 0.5, b = 0.384 and c = 0.384

And the volume is

Volume = 4/3πabc

So, we have

Volume = 4/3 * 22/7 * 0.5 * 0.384 * 0.384

Evaluate

Volume = 0.309 cubic units

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Answer:

D. Division and Addition

Step-by-step explanation:

She need 5 minutes to reach each page.

In mathematics, the absence of acceleration is referred to as a constant rate. A function that has a constant rate typically has a second derivative of 0.

The function would be plotted as a straight line on a piece of graph paper if the change in y (or rate) were constant. When anything moves at a fixed, steady pace or at an average speed, it is said to be moving at a constant rate, also known as a uniform rate. For instance, 3 hours pass while driving. In the first hour, it travels 30 miles, in the second hour, 45 miles, and in the third hour, 75 miles.

Given,

time she needs to read 8 pages = 40 minutes

time she needs to read 1 pages = 40/8

=5 minutes

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Answer:

b. 31.

Step-by-step explanation:

The other 2 angles in the triangle are congruent so they are:

(180 - 118) / 2

= 31 degrees.

The possible measure of two similar angles in an isosceles triangle could be b. 31 °

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know in an isosceles triangle two sides are equal and angles opposite sides to the equal side are also equal.

We also know that the sum of all the interior angles in a triangle is 180°.

Let, The similar angles be 'x'.

Therefore,

x + x + 118 = 180

2x = 62.

x = 31°.

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Answer: the answer to this problem is 36 :)

Answer:

Both are 36

Step-by-step explanation:

I just did it

The height of the rectangular prism with an area of 55.9 square yards is 3.3 yards.

To find the height of the rectangular prism, we need to use the formulas for the area and volume of a rectangular prism. The formula for the area of a rectangular prism is given by A = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism, respectively. Similarly, the formula for the volume is V = lwh.

From the given information, we have the area A = 55.9 square yards and the volume V = 184.47 cubic yards. We can set up the following equations:

2lw + 2lh + 2wh = 55.9

lwh = 184.47

To solve these equations, we need to find the values of l, w, and h. However, without additional information or constraints, it is not possible to determine the specific values of length and width. However, we can solve for the height h using the volume equation. Rearranging the volume equation, we get h = \(\frac{V}{(lw)}\).

Substituting the given volume of 184.47 cubic yards, we divide it by the area to obtain h =\(\frac{184.47}{55.9}\) = 3.3 yards.

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Using the Fundamental Counting Theorem, it is found that there are:

It is a theorem that states that if there are n things, each with \(n_1, n_2, \cdots, n_n\) ways to be done, each thing independent of the other, the number of ways they can be done is:

\(N = n_1 \times n_2 \times \cdots \times n_n\)

For a single class rep, there are 19 + 16 + 26 = 61 students, hence there are 61 ways to choose a single class rep.

For three reps, one from each college, we have that:

\(n_1 = 19, n_2 = 16, n_3 = 26\), hence:

\(N = 19 \times 16 \times 26 = 7904\)

7904 ways to choose three reps, one from each of the three Colleges.

Considering one female, we have that:

\(N = 13 \times 16 \times 26 + 19 \times 5 \times 26 + 19 \times 16 \times 12 = 11526\)

11526 ways to choose three reps, one from each of the three Colleges, so that exactly one is female.

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The vertex form of a quadratic equation is the following:

where the vertex is (h,k).

So, we need to convert the given standard form into a vertex form. Then, by factoring a number -3, we have

We can note that

Therefore, we can rewrite our last result as

Since

So, we have obtained

Finally, by distributing the number -3 into the parentheses, the vertex form is given by:

Then, by comparing this result with the vertex form from above, the vertex (h,k) is

a = The cost of the pizza.

b = The cost of the pizza and sales tax.

f(a) = The cost of the pizza.

g(b) = The cost of the pizza and sales tax.

g(f(a)) = The cost of the pizza, sales tax, and delivery fee

From the calculations and the data given, the volume of the triangular prism is 24 m3.

Since, We know that;

The triangular prism is a prismatic figure that has a trianguar base. We know that the formula for the volume of a triangular prism is;

V = 1/2 a c h

Now; We have to given that;

a =  2 m

b =  3 m

h =  8 m

Hence, We get;

V = 1/2 x 2 m x  3 m x 8 m

V = 24 m³

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Complete question is,

This figure shows the dimensions of a right triangular prism.

Right prism with triangular base. Height of triangle labeled 2 m and base labeled 3 m. Height of prism labeled 8 m.

What is the volume of the right triangular prism in cubic meters?

144 m3

16 m3

24 m3

48 m3

Answer: x=-3    x=2    x=-0,5

Step-by-step explanation:

2x³+3x²-11x-6=

2x³+(6x²-3x²)-11x-6=

(2x³+6x²)-3x²-11x-6=

2x²(x+3)-(3x²+11x+6)=

2x²(x+3)-(3x²+(9x+2x)+6)=

2x²(x+3)-((3x²+9x)+(2x+6))=

2x²(x+3)-(3x(x+3)+2(x+3))=

2x²(x+3)-(x+3)(3x+2)=

(x+3)(2x²-(3x+2))=

(x+3)(2x²-3x-2)=

(x+3)(2x²-4x+x-2)=

(x+3)(2x(x-2)+(x-2))=

(x+3)(x-2)(2x+1)

(x+3)(x-2)(2x+1)=0

x+3=0

x=-3

x-2=0

x=2

2x+1=0

2x=-1

Divide both parts of the equation by 2:

x=-0.5

Answer:

dude im not so good in this compound interest stuff but lemme try dawg

So 2500*0.035=87.5 thats what he makes every year so times 9=787.5

Then add it to the initial and you got 2500+787.50= 3287.50

Might be wrong brooo but if its right the answer's $3,287.50

Answer:

k = -8

Step-by-step explanation:

Given both functions, y = k - x² and y = - 6x + 1. A line tangent to the graph means that the line has one common point with the curve. Therefore, the steps to solve this problem are:

\( \displaystyle{k - {x}^{2} = - 6x + 1}\)

Arrange in quadratic terms:

\( \displaystyle{ {x}^{2} - 6x + 1 - k = 0}\)

Apply discriminant where b = -6, a = 1 and c = 1-k:

\( \displaystyle{ {b}^{2} - 4ac = 0} \\ \\ \displaystyle{ {6}^{2} - 4(1)(1 - k) = 0} \\ \\ \displaystyle{ 36 - 4(1 - k)= 0} \\ \\ \displaystyle{ 36 - 4 + 4k = 0} \\ \\ \displaystyle{ 32 + 4k = 0} \\ \\ \displaystyle{4k = - 32} \\ \\ \displaystyle{k = - 8}\)

Therefore the value of k that makes line tangent to the curve is -8.

Answer:

r = -36

Step-by-step explanation:

\(\frac{r}{9}=-4\)

Multiply both sides by 9

r = -36

The influence of a small alpha level in the context of hypothesis testing is:

c. A small alpha level reduces the likelihood of a Type I error.

A hypothesis known as the null hypothesis states that sample observations are the result of chance.

The correct statement regarding the influence of a small alpha level in the context of hypothesis testing is:

c. A small alpha level reduces the likelihood of a Type I error.

A small alpha level (typically denoted as α) is the significance level used in hypothesis testing to determine the threshold for rejecting the null hypothesis. By setting a small alpha level, such as 0.01 or 0.05, we are reducing the probability of making a Type I error, which is the incorrect rejection of a true null hypothesis.

In other words, a small alpha level provides a stricter criterion for rejecting the null hypothesis, making it less likely to reject the null hypothesis when it is true. This reduces the likelihood of claiming a significant result when there is no true effect or relationship in the population.

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Answer:

19

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

f(x)= 2x^2 +1, x=3

f(3)= 2(3)^2 +1

f(3)= 2(9) +1

f(3) = 18 +1

f(3) =19

i hope this helps!

Given:

The equation is

\(y=21.2x\)

Where, y is earnings for working in dollars and cents and x is the number of working hours.

To find:

The rate of change.

Solution:

The slope intercept form of a linear function is

\(y=mx+b\)          ...(i)

Where, m is the slope and b is the y-intercept.

We have,

\(y=21.2x\)            ...(ii)

On comparing (i) and (ii), we get

\(m=21.2\)

Therefore, the rate of change is 21.2 dollar and cents per hour.

Answer:

30

Step-by-step explanation:

The perimeter of this rectangle is calculated by adding width to length and that multiplied by 2

2*(3x+2x+2) = 54 do inside the parenthesis first

2*(5x+2) = 54 multiply inside the parenthesis by 2

10x + 4 = 54 subtract 4 from both sides

10x = 50 divide both sides by 10

x = 10

The length for PS is 3x

3*10 = 30

Answer:

6/25

Step-by-step explanation:

24% = 24/100 = 6/25

Answer:

24/100=6/25

Step-by-step explanation:

Answer:

2:10 = 1:5

Step-by-step explanation:

2cups of flour:10 pancakes

Simplify:

1cup of flour:5 pancakes

Answer: 1. 2:10 2. 2:10=1:5

Step-by-step explanation: So I got the ratio 2 to 10 by every 2 cups of flour for every 10 pancakes. For number two, can you determine the value of the ratio so you simplify it and get 1:5