4. In the diagram below TP and TR are tangents circle centered at O. IfPRT-65°, find ROP. O 65° R.​

By using Law of Sines, the side b and a when A = 37°, B = 49°,c=5, and A = 132", C = 23, b = 10 is b ≈ 4.09 and a ≈ 19.66 respectively.

To use the Law of Sines to solve for the missing side in an oblique triangle, we can use the following formula:

a/sin(A) = b/sin(B) = c/sin(C)

Let's solve each problem using the Law of Sines:

Find side b when A = 37°, B = 49°, c = 5.

We know angle A, angle B, and side c. We need to find side b.

b/sin(B) = c/sin(C)

b/sin(49°) = 5/sin(180° - 37° - 49°)

b/sin(49°) = 5/sin(94°)

Cross-multiplying:

b * sin(94°) = 5 * sin(49°)

b = (5 * sin(49°)) / sin(94°)

b ≈ 4.09

Therefore, side b ≈ 4.09 (rounded to the nearest hundredth).

Find side a when A = 132°, C = 23, b = 10.

We know angle A, angle C, and side b. We need to find side a.

a/sin(A) = b/sin(B)

a/sin(132°) = 10/sin(180° - 132° - 23°)

a/sin(132°) = 10/sin(25°)

Cross-multiplying:

a * sin(25°) = 10 * sin(132°)

a = (10 * sin(132°)) / sin(25°)

a ≈ 19.66

Therefore, side a ≈ 19.66 (rounded to the nearest hundredth).

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Answer:

5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

4×5+3=23

this is the solution

Answer:

I'm sorry I haven't read the book in a long time but here are some tips.

Only talk about the events that susan would know about. Don't talk about john at home and things like that.

Make sure you use words that shows Susan is not happy like hate, stupid, etc. Not sure if you are girl or boy, but make sure you talk about all the little details that girls would think about. Like john getting chocolate on Susans dress. You could also talk more about the coin and what she was going to do with it(you can make something up cuz teachers give points for creativity.)

Sorry I couldn't help more, but I hope you get a good grade! :)

Answer:

the median number of minutes spent on math homework each night is also 40.

the mean number of minutes spent on math homework each night is 40.

The source of bias in the survey embarked upon would stem from that 'many people refuse to respond to telephone surveys.'

The behaviour whereby people refuse to respond to telephone surveys is called non-response bias. It can occur for a variety of reasons, such as people being too busy, not interested in the survey, or not trusting the surveyor. Non-response bias can lead to the survey results being inaccurate, as the people who do respond may not be representative of the population as a whole.

Therefore , the presence of bias would likely stem from the fact that "many people refuse to respond to telephone surveys."

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Answer:

(0,4)

Step-by-step explanation:

read the graph from left to right. As you move right from -4,-16, y increases as x increases. then once you hit zero there is no increase or decrease. Then from zero to 4 the y value is decreasing as x increases.

By using the formula for area and perimeter of rectangle, it is obtained that

Area of rectangle is 663 \(m^2\)

What is area and perimeter of Rectangle?

Area of rectangle is the total space taken by the rectangle.

If the length of the rectangle be l and breadth of rectangle be b

Area of rectangle = \(l \times b\)

Perimeter of rectangle is the length of the boundary of the rectangle.

If the length of the rectangle is l and breadth of the rectangle be b then perimeter of rectangle is

Perimeter of rectangle = \(2(l + b)\)

Here,

Let the breadth of rectangle be b m

Length of rectangle = (b + 38)m

Perimeter of rectangle = 2(b+ 38 + b)

                                      = 2(2b + 38)

By the problem,

                        2(2b + 38) = 128

                           2b + 38 = \(\frac{128}{2}\)

                           2b + 38 = 64

                            2b = 64 - 38

                            2b = 26

                              b = \(\frac{26}{2}\\\)

                              b = 13 m

Length of rectangle = 38 + 13 = 51 m

Area of rectangle = \(51 \times 13\)

                             = 663 \(m^2\)

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The length of third side is in between 33.33 and 132.83.

The theorem that the sum of any two sides of a triangle is greater than or equal to the third side is known as the triangle inequality in Euclidean geometry. The theorem basically states that a straight line defines the shortest distance between two points.

Other metric spaces, or spaces that contain a means of measuring distances, have counterparts to the triangle inequality.

Given two sides of triangle are 33.33 yards and 99-100 yards(say 99.5)

There is a triangle here. Since it is not a right triangle, we must employ triangle inequality to determine the third side's length.

The longer side, 99.5 yards must be shorter than the sum of the other two sides. If the second side is c, then

99.5 < 33.33 + c.

The side c must be longer than 33.33

The side c must be shorter than the sum of the other two sides:

c < 99.5 + 33.33.

c < 132.83

Combining both we will get that

33.33  <  c  <  132.83.

This interval (33.33, 132.83) gives all the lengths the third side of the triangle can have.

Hence the length of third side varies between 33.33 and 132.83.

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Given:

in rectangle ABCD, BE = 3x + 5, AC = 40

To find:

X = ?

Solution:

AC = BD - Diagonal of rectangle are always equal

now BD = 40 units .....( i )

BE = ED, the diagonal of rectangle bisect each other in equal half

now, BD = BE + BD ...( ii )

BD = BE +BE from ..( ii )

40 = 2BE

BE = 20

3x + 5 = 20 ... from given

3x = 15

x= 5

Answer- The value of x is 5 units

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16.8 = 2.4 e

=> e = 16.8/2.4

=> e = 168/24

=> e = 7

Hence, E equal to 7

Answer:

e = 7

Step-by-step explanation:

2.4e is the same as \(2.4*e\), so you simply undo the equation.

\(16.8=2.4*e\)

divide by 2.4 on both sides to isolate the variable.

\(16.8/2.4 = (2.4 *e)/2.4\)

\(7 = e\)

Answer:

Correlation doesn't prove causation because just because two things correlate does not necessarily mean that one causes the other.It's easy to think that just because two things seem related, that one must be the cause of the other. But that can be a foolish and sometimes dangerous assumption

Answer:

4.02 x 10 x 10 x 10 x 10 x 10

Step-by-step explanation:

The part that needs expanding is the exponent. Since it is to the power of 5 there needs to be 5 written out 10's, all multiplied.

4.02 x 10 x 10 x 10 x 10 x 10

Answer:

the answer in expanded form is 402000

the problem in expanded form is 4.02  x 10  x 10  x 10  x 10 = above

Step-by-step explanation:

pls leave a thank you trynna rank up

Answer:

33.33

Percentage Calculator: 120 is what percent of 360? = 33.33.

Answer:

e

Step-by-step explanation:

Answer:11/10

Step-by-step explanation:

Answer:

10x=11

Step-by-step explanation:

............

Answer:

13

Step-by-step explanation:

First find the number of children attending elementary school

= 1349*2

= 2698 children

Now each school can accommodate 220 children so divide the number of children by 220

= \(\frac{2698}{220}\)

= 12.26 which is the closest to 13 in the options so the answer is 13

Answer:

Step-by-step explanation:

Since VW = VX ; Two sides are equal, then it is an isosceles triangle.

An isosceles triangle is a triangle that has 2 equal sides and 2 equal angles.

Given: m∠V = 50° ;

Since interior angles must total 180° the remaining 2 unknown angles must have a sum of 130°.

180° - 50° = 130°

130° / 2 = 65°

m∠W = 65° and m∠X = 65°

(e) The complex number 5+2i in exponential form is (\sqrt{29}e^{i\text{tan}^{-1}\left(\frac{2}{5}\right)}\).
(f) The new period is \(0.31\sqrt{\frac{m}{1.6k}}\) when the spring constant is increased by 60%.

(e) To convert a complex number to exponential form, we need to determine its magnitude and argument. For the complex number 5+2i, the magnitude is given by the formula \(A = \sqrt{{\text{Re}}^2 + {\text{Im}}^2}\) where Re and Im represent the real and imaginary parts, respectively. In this case, the magnitude is \(\sqrt{5^2 + 2^2} = \sqrt{29}\).

The argument, \(\theta\), can be found using the formula \(\theta = \text{tan}^{-1}\left(\frac{{\text{Im}}}{{\text{Re}}}\right)\). For 5+2i, the argument is \(\text{tan}^{-1}\left(\frac{2}{5}\right)\).

Thus, the complex number 5+2i in exponential form is \(Ae^{i\theta} = \sqrt{29}e^{i\text{tan}^{-1}\left(\frac{2}{5}\right)}\).



(f) The period of a spring-mass system is determined by the mass and the spring constant. If the spring constant is increased by 60%, we can calculate the new period using the formula \(T' = T\sqrt{\frac{m}{k'}}\).

Given the original period \(T = 0.31\) seconds and an increase in the spring constant by 60%, we have \(k' = 1.6k\) where \(k\) is the original spring constant.

Substituting the values into the formula, the new period is \(T' = 0.31\sqrt{\frac{m}{1.6k}}\).

Increasing the spring constant causes the spring to become stiffer, resulting in a shorter period. The new period, \(T'\), will be less than the original period \(T\) due to the increased stiffness of the spring.

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Answer:

27/30 and 25/30

Step-by-step explanation:

Do you mean 9/10 and 5/6?

find the least common multiple of the denominators 10 and 6

10 = 10, 20, 30

6 = 6, 12, 18, 24, 30

The least common multiple is 30

So 9/10 x 3/3 = 27/30

and 5/6 x 5/5 = 25/30

The number of beetles at time \(x\) can be expressed using the equation \(B = 800 (1.05)^{x}\)

In mathematics, an equation is a statement that two numbers or values are equal, as in 6 x 4 = 12 x 2. When two or more components of a situation must be taken into account in order to comprehend or describe the entire situation, this is known as an equation. By definition, your example is an equation since an equation is any expression that contains the equals sign. The employment of equal signs by mathematicians makes equations a common occurrence in mathematical work. A set of guidelines for producing a specific outcome is known as a formula. A mathematical expression, such as 6x4=12x2, that states that two amounts or values are equal is known as an equation. In an equation, two or more components must be taken into account simultaneously.

\(x =\) number of months that have passed.

\(N=800x^{0.05t}\)

\(1.05 = 1 + .05\), where \(.05\) is the monthly growth rate

An equation is \(B = 800 (1.05)^{x}\).

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To calculate the cash balance at the end of the period, we need to consider the cash inflows and outflows.

Starting cash balance: $4,520

Cash inflows: $1,654 (receivables collected)

Cash outflows: $1,961 (payments to suppliers) + $500 (cash expenses)

Total cash inflows: $1,654

Total cash outflows: $1,961 + $500 = $2,461

To calculate the cash balance at the end of the period, we subtract the total cash outflows from the starting cash balance and add the total cash inflows:

Cash balance at the end of the period = Starting cash balance + Total cash inflows - Total cash outflows

Cash balance at the end of the period = $4,520 + $1,654 - $2,461

Cash balance at the end of the period = $4,520 - $807

Cash balance at the end of the period = $3,713

Therefore, the cash balance at the end of the period is $3,713.

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Given:

Bananas are $2.40 per pound.

To find:

The graph and unit rate on the graph.

Solution:

Let y be the total cost of x pounds of bananas.

Cost of 1 pound of banana = $2.40

Cost of x pound of bananas = $2.40x

So, the required equation for the given situation is:

\(y=2.4x\)

The graph of \(y=2.4x\) describes the proportional relationship between the two quantities.

The graph of \(y=2.4x\) is a line passing through (0, 0) with a slope of 2.4; the slope 2.4 is the unit rate of each pound of bananas.

Therefore, the correct option is (b).

Answer:

a

Step-by-step explanation:

Answer:

60 inches

Step-by-step explanation:

perimeter =2×l+2×w

=2×18+2×12

=36+24

=60

∴The perimeter=60 inches.

hope it is correct!!!!

The correct statement is: d.  "The impact on the volume if the dimensions are multiplied by 14  the new volume will be 14 times the original volume.      

To determine the impact on the volume when the dimensions of the cone are multiplied by 14, we need to calculate the new volume and compare it to the original volume. Let's denote the original radius as r and the original height as h.

Given:

Original radius (r) = 12 ft

Original height (h) = 24 ft

New radius = 14 * r

New height = 14 * h

The formula for the volume of a cone is V = (1/3) * π * r^2 * h.

Original Volume (V_original) = (1/3) * π * (r^2) * h

= (1/3) * π * (12^2) * 24

≈ 10845.12 cubic feet

New Volume (V_new) = (1/3) * π * ((14 * r)^2) * (14 * h)

= (1/3) * π * (196 * r^2) * (14 * h)

= (1/3) * π * (196 * (12^2)) * (14 * 24)

= (1/3) * π * 196 * 144 * 336

≈ 1086615.36 cubic feet

Comparing the new volume to the original volume:

a. The volume will decrease by 116.

False. The new volume is significantly larger than the original volume, so it does not decrease by 116.

b. The original volume will be divided by 43.

False. Dividing the original volume by 43 does not yield the new volume.

c. The original volume is decreased by approximately 2111.15 units^3.

False. The difference between the new volume and the original volume is much larger than 2111.15 units^3.

d. The new volume will be 14 times the original volume.

True. The new volume is approximately 14 times the original volume.

e. The original volume will be multiplied by 164.

False. Multiplying the original volume by 164 does not yield the new volume.

Therefore, the correct statement is:

d. The new volume will be 14 times the original volume.

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We are given the following equation and we must state the reason behind each of the steps taken to solve it:

In the first step after giving the equation 21 is being substracted from both sides of the equation. Remember that the substraction property of the equality states that any value substracted from one side of the equal sign must also be substracted from the other side. Therefore the reason behind this step is the substraction property.

Then the substractions on each side are performed. In the left side we get 21-21=0 so the constant term dissapears and on the right we obtain 21-15=6. This means that during this step only a simplification was performed.

In the following step a number 2 is multiplied to each side of the equal sign. Remember that the multiplication property of equality states that whatever is multiplied in one side of the equal sign must also be multiplied in the other side. Then the reason behind this step is the multiplication property of equality.

In the final step in the left side the 2 multiplying is simplified with the number 2 dividing and in the right side the product between -6 and 2 is performed. Then this step is also a simplification.

Then the reasons in order are:

- Substraction Property of Equality

- Simplifying

- Multiplication Property of Equality

- Simplifying

Therefore, the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2).

To show that the equation x^3 - 15x + c = 0 has at most one root in the interval (-2, 2), we can use the concept of the Intermediate Value Theorem and Rolle's Theorem.

Let's assume that the equation has two distinct roots, denoted as a and b, in the interval (-2, 2). Without loss of generality, we assume a < b.

Since the function is continuous on the closed interval [-2, 2] and differentiable on the open interval (-2, 2), we can apply Rolle's Theorem. According to Rolle's Theorem, there exists a point c in the open interval (a, b) such that the derivative of the function at c is zero.

Consider the derivative of the function f(x) = x^3 - 15x + c:

f'(x) = 3x^2 - 15

Setting f'(c) = 0, we have:

3c^2 - 15 = 0

c^2 - 5 = 0

c^2 = 5

Taking the square root of both sides, we get:

c = ±√5

Now, let's consider the function values at the endpoints of the interval (-2, 2):

f(-2) = (-2)^3 - 15(-2) + c = -8 + 30 + c = 22 + c

f(2) = (2)^3 - 15(2) + c = 8 - 30 + c = -22 + c

If c = √5, then f(-2) = 22 + √5 and f(2) = -22 + √5.

If c = -√5, then f(-2) = 22 - √5 and f(2) = -22 - √5.

In either case, the function values at the endpoints have different signs. This implies that there exists at least one value, say k, in the interval (-2, 2) such that f(k) = 0, according to the Intermediate Value Theorem.

However, we assumed at the beginning that there are two distinct roots in the interval (-2, 2), denoted as a and b. This contradicts our finding that there is at most one root in the interval. Hence, our assumption of having two distinct roots is false.

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Answer: the max height is 7ft, which takes 2 seconds. It was thrown from 3 ft high.

Step-by-step explanation: To further analyze, graph the equation.

The mean heart rate of the athletes is 68.6.Divide the sum of all the heart rates by the number of athletes (15): 1036/15 = 68.6

The mean heart rate of the athletes is 68.6. Divide the sum of all the heart rates by the number of athletes (15): 1036/15 = 68.6

1. Add up all the heart rates: 58 + 59 + 62 + 62 + 64 + 65 + 66 + 67 + 68 + 69 + 70 + 71 + 72 + 76 + 85 = 1036

2. Divide the sum of all the heart rates by the number of athletes (15): 1036/15 = 68.6

3. The mean heart rate of the athletes is 68.6.

The complete question is :The heart rate of a sample of 15 athletes is shown below after a quick warm up activity. 58, 59, 62, 62, 64, 65, 66, 67, 68, 69, 70, 71, 72, 76, 85. What is the mean heart rate of the athletes?

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