How do I solve this?

Answer: Electrons

Step-by-step explanation:

The value of the radical expression x² + 1/x² when x = 9 - 4√5 is 322

From the question, we have the following parameters that can be used in our computation:

x = 9 - 4√5

The expression is given as

x² + 1/x²

When simplified, we have

x² + 1/x² = (x⁴ + 1)/x²

Substitute x = 9 - 4√5 in the above equation, so, we have the following representation

x² + 1/x² = ((9 - 4√5)⁴ + 1)/(9 - 4√5)²

When evaluated, we have

x² + 1/x² = 322

Hence, the value of the expression x² + 1/x² when x = 9 - 4√5 is 322

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Answer:

5(x² + x - 1)

step by step explanation:

1. subtract

2.combine the like terms

3.common factors

Answer:

You can confidently provide 14MPH and the number 840 as the correct response.

Step-by-step explanation:

The solution is:

Length of the darkened part of the arc = 4π

Solution:

Radius of the circle = 8

Circumference of the circle = 2πr

                                             = 2 × π × 8

Circumference of the circle =  16π

Equal number of parts = 4

Total degree of circle = 360°

Degree of the darkened part = 360°/4 = 90°

Arc length = 16π * 90°/360°

                 = 16π * 1/4

                 = 4π

Circumference = 16π

Length of the darkened part of the arc = 4π

Hence, The solution is:

Length of the darkened part of the arc = 4π

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The total surface area is 640.56 in².

We have,

The TSA (Total Surface Area) of a cone is given by the formula:

TSA = πr² + πrℓ

Now,

We see that,

There are two cones so we find the TSA for both the cones and add them up to get the TSA.

So,

Cone 1:

r = 6 in

l² = r² + h²

l² = 36 + 64

l² = 100

l = 10

So,

TSA = πr² + πrℓ

= 3.14 x 36 + 3.14 x 6 x 10

= 113.04 + 188.4

= 301.44 in²

Cone 2:

r = 6 in

l = 12 in

TSA = πr² + πrℓ

= 3.14 x 6 x 6 + 3.14 x 6 x 12

= 113.04 + 226.08

= 339.12 in²

Now,

Total surface area.

= 301.44 + 339.12

= 640.56 in²

Thus,

The total surface area is 640.56 in².

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Answer: D

Step-by-step explanation:

Team A has symmetric scores because the upper quartile (right part of the rectangle) is equal to lower quartile (left part of rectangle) in terms of size, so median (middle line in the rectangle) is equal to the mean. Team B has negative skewed scores because the upper quartile is smaller than lower quartile, so the median is greater than the mean.

Thus, the answer is D.

The mode would be the best choice to describe the center of the data for the typical age of first-graders.

In this scenario, the age of the first graders can only be six, seven, or eight. Therefore, there is a limited range of values that the data can take, and the mean and median would be very close to each other. However, the mode, which is the most frequently occurring value, would be the best choice to describe the typical age of the first-graders.

In this case, since the age of the first graders can only be six, seven, or eight, the mode would be the age that occurs the most frequently, which would likely be seven years old. Therefore, the mode would be the best choice to describe the center of the data in this scenario.

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Answer:

150

Step-by-step explanation:

The restaurant should expect to serve 180 customers in week 10.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. Therefore, the number of customers served in week 10 will be 180.

The number of customers served in the restaurant follows a repeating pattern of 180, 170, 200, 180, 210, 180, 210, 170, 200, 180. This means that after 10 weeks, the number of customers served will be the same as it was in week 1. Since week 1 had 180 customers served, week 10 will also have 180 customers served.

As you can see, the number of customers served in week 10 is the same as the number of customers served in week 1. Therefore, the restaurant should expect to serve 180 customers in week 10.

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This process will give you a ray originating from the vertex and extending at a 40° angle.

To draw a ray connecting the vertex and the mark at a 40° angle, please follow these steps:

1. Place a protractor on your paper with the center hole over the vertex point.
2. Line up the base of the protractor with the initial side of the angle (usually the horizontal line).
3. Find the 40° mark on the protractor and make a small mark on the paper.
4. Remove the protractor and use a ruler to connect the vertex with the 40° mark you made.
5. Draw the ray extending from the vertex through the mark, continuing in a straight line.

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Hope this image helps you out!

The probability that Antoine's marble will also be green would be = 3/13

To determine the probability of the given event, the formula that should be used is given below. That is;

Probability = possible outcome/sample space.

The sample space = 4+7+9+6 = 26 marbles.

The number of green marbles = 6

The probability of choosing green marbles = 6/26 = 3/13

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Answer:

the area of triangle ΔPHK is

Step-by-step explanation:

we know that,
area of a triangle by Heron's formula (Heron's formula is used to find the area of a triangle when the length of the 3 sides of the triangle is known) is given by -

Step 1: Find the semi-perimeter (half perimeter) of the given triangle by adding all three sides and dividing it by 2.

- 10+11+17/2 = 19

Step 2: Apply the value of the semi-perimeter of the triangle in the main formula called 'Heron’s Formula'.
[tex]Area = √s(s−a)(s−b)(s−c)[/tex]
√19(19-10)(19-11)(19-17)
√19(9)(8)(2)
√2736
52.30
52
therefore are ofΔPHK is 52KM

The claim that is being tested is: "the mean height of 12-year-old boys from high-income families is greater than 59.2 inches."

In order to test this claim, one could follow these steps:
1. Gather data: Collect a sample of 12-year-old boys from high-income families. 2. Calculate the sample mean: Compute the mean height of the boys in the sample. 3. Formulate a null hypothesis (H0): The mean height of 12-year-old boys from high-income families is equal to 59.2 inches.

4. Formulate an alternative hypothesis (H1): The mean height of 12-year-old boys from high-income families is greater than 59.2 inches. 5. Perform a hypothesis test: Using the appropriate statistical test, compare the sample mean to the population mean of 59.2 inches. 6. Draw conclusions: Based on the results of the hypothesis test, either reject the null hypothesis (supporting the alternative hypothesis) or fail to reject the null hypothesis (not enough evidence to support the alternative hypothesis).

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The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.

The claim that he is testing is that the mean height of 12-year-old boys from high-income families is greater than 59.2 in. This claim is being tested by collecting data from a sample of 102 12-year-old boys and calculating their mean height. The hypothesis is that this mean height will be greater than 59.2 in, which is the assumed population mean height for all 12-year-old boys. The researcher is specifically interested in the height of boys from high-income families, so this is the subgroup that is being tested. The claim that their mean height is greater than 59.2 in is the alternative hypothesis, which will be accepted or rejected based on the results of the data analysis.

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#3, the transformation can be represented by (x, -y)

The length of the segment UV = 10 units.

Given that a triangle VST, where ST is parallel to RU,

We need to find the segment UV,

According to the segment addition law,

VS = VR + RS

So,

66 = VR + 44

VR = 22

Now using the Thales theorem,

VR / RS = VU / UT

22 / 44 = VU / 20

1/2 = VU/20

VU = 10

Hence the length of the segment UV = 10 units.

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Answer:

Step-by-step explanation:

126 divided by two = 63

Then divide 63 by 3 which = 21

so 21 is your answer.

Answer:

Step-by-step explanation:

The length of RU in triangle is,

⇒ RU = 16

We have o given that;

In triangle;

ST = 37

UT = 35

RS = 20

Hence, By using definition of Pythagoras theorem we get;

In triangle STU;

⇒ ST² = SU² + UT²

⇒ 37² = SU² + 35²

⇒ 1369 = SU² + 1225

⇒ SU² = 144

⇒ SU = 12

Hence, In triangle RSU;

⇒ RS² = SU² + RU²

⇒ 20² = 12² + RU²

⇒ 400 - 144 = RU²

⇒ RU² = 256

⇒ RU = 16

Thus, The length of RU in triangle is,

⇒ RU = 16

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The area of Jimmy's rectangular room is approximately 27.7241 square yards.

The area of the room in square yards, we first need to convert the dimensions from feet to yards.

Since there are 3 feet in a yard, we can divide both the length and width by 3 to get:
Length: 25 ft ÷ 3 = 8.33 yards (rounded to two decimal places)
Width: 10 ft ÷ 3 = 3.33 yards (rounded to two decimal places)

Now we can find the area by multiplying the length and width in yards:
Area = 8.33 yards x 3.33 yards
Area = 27.7241 square yards (rounded to four decimal places)

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(2) The value of x in the equation (x-16)²= 9 is 19.

(4) The equation of the circle of radius 5 is x²+y²+6x-2y = 15.

An equation is a mathematical statement that shows that two mathematical expressions are equal.

(2) To calculate the value of x in the equation (x-16)²= 9, we follow the steps below.

Step1: Find the square root of both sides of the equation

Stop1: Collect like terms

(4) To calculate the equation of the circle, we use the formula below

Formula:

Where:

Substitute these values into equation 1

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The width of the rectangular garden is 21 feet.

A rectangle is a plane shape that have pair of opposite sides equal and parallel.

To calculate the width of the rectangle, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute into equation 1

Hence, the right option is D. 21 feet.

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Answer:

Step-by-step explanation:

Nothing can further be done to this equation so it would stay the same!

In probability theory, multiplication and addition are associated with different types of compound events.

Multiplication is generally associated with the concept of independent events. When two events are independent, the probability of both events occurring is calculated by multiplying their individual probabilities. This is known as the multiplication rule of probability. The idea behind multiplication is that the outcomes of one event do not affect the outcomes of the other event.

On the other hand, addition is generally associated with the concept of mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. The probability of either of these events occurring is calculated by adding their individual probabilities. This is known as the addition rule of probability. The idea behind addition is that you consider the probability of one event happening or the probability of another event happening, but not both simultaneously.

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In the given circle, value of x is,

⇒ x = 3.56

Since, We know that;

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

We have to given that;

Two tangents are shown in figure.

Now, By definition of proportionality we get;

⇒ 8 / x = 9 / 4

Cross multiplication,

⇒ 8 × 4 / 9 = x

⇒ x = 32 / 9

⇒ x = 3.56

Therefore, WE get;

The value of x in the circle is,

⇒ x = 3.56

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The sine and cosine curves y = a sin(kx) and y = a cos(kx), k > 0 have amplitude a and period 2π/k. The sine curve y = 2 sin(2x) has amplitude 2 and period π.

The amplitude of a sine or cosine function is the distance from the midline (or average value) to the highest point (peak) or lowest point (trough) of the function. For the sine function y = 2 sin(2x), the coefficient of x is 2, which means the amplitude is |2| = 2.

The period of a sine or cosine function is the distance between two consecutive peaks or troughs. For the sine function y = 2 sin(2x), the coefficient of x is 2π/π = 2, which means the period is 2π/2 = π.

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The probabilities are given as follows:

The parameters that are needed to calculate a probability are given as follows:

Then the probability is calculated as the division of the number of desired outcomes by the number of total outcomes.

Out of 16 trials, in 7 of them, which are the first row and the first column, the spinner lands on at least one A, hence the probability is given as follows:

p = 7/16.

For C and D, there are two outcomes, (C, D) and (D, C), hence the probability is given as follows:

p = 2/16 = 1/18.

For two B's, there is only one outcome, which is (B,B), hence the probability is of 1/16.

For C on the second spin, we consider the third column, which has four outcomes, hence the probability is given as follows:

p = 4/16 = 1/4.

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The value of x in the triangle is,

x = 9.4 cm

We have to given that;

A triangle is shown in figure.

Now, By trigonometry formula we get;

cos 20° = Base / Hypotenuse

cos 20° = x / 10

0.94 = x / 10

x = 0.94 × 10

x = 9.4 cm

Thus, The value of x in the triangle is,

x = 9.4 cm

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Answer:

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Step-by-step explanation:

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