suppose is a x continuous variable with the following probability density: f(x) = { B (10 – X)^2 , IF 0 < X < 10
0, otherwise
a. what is the value of ? b.

Answer:

35 hours

Step-by-step explanation:

We Know

Her pay rate is $8.75

Penny was paid 306.25 this week

How many hours did she work?

We Take

306.25 / 8.75 = 35 hours

So, she works 35 hours.

To complete the square for the quadratic equation x²+8x-35=0, we need to add a constant to both sides of the equation that will result in a perfect square trinomial on the left-hand side.

To do this, we need to take half of the coefficient of x, square it, and add it to both sides of the equation. The coefficient of x in this equation is 8, so we take half of 8, which is 4, square it, which is 16, and add it to both sides of the equation:

x² + 8x - 35 + 16 = 16

x² + 8x + 16 = 51

On the left-hand side, we have a perfect square trinomial that can be factored as (x+4)². So, we have:

(x+4)² = 51

To solve for x, we take the square root of both sides:

x+4 = ±√51

Finally, we isolate x by subtracting 4 from both sides:

x = -4 ± √51

Therefore, the number that had to be added to "complete the square" is 16.

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Since overtime is paid at one and one-half, Tonya's overtime pay for this week is $36.56.

The overtime pay is the product of the overtime pay rate and the number of overtime hours.

The normal work week is 40 hours.  The overtime hours, in this situation, are 2.5 hours.

The total number of hours Tonya worked this week = 42.5 hours

The hourly pay rate = $9.75

Overtime pay rate = $14.625 ($9.75 x 1.5)

Overtime hours worked = 2.5 hours (42.5 - 40)

Overtime pay = $36.56 ($14.625 x 2.5)

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Therefore , the solution of the given problem of surface area comes out to be x cannot equal 24.

By calculating how much space would be needed to fully enclose its exterior, its overall size can be calculated. The surrounding region is considered when selecting a comparable product in the rectangular design. The surface area of something determines its overall dimensions. The number of sides connecting a cuboid's four trapezoidal forms determines how much water it can hold.

Here,

The calculation for a square pyramid's surface area is:

=> S = l² + 2lh

where S is the surface area, h is the height of the pyramid, and l is the length of one edge of the square base.

=> l² = 13² = 169

We also know that the pyramid's surface area is 741 square feet, so we can construct the following equation:

=> 741 = 169 + 2(13)(x)

When we condense the right half, we obtain:

=> 741 = 169 + 26x

169 from both parts are subtracted, giving us:

=> 572 = 26x

When we multiply both parts by 26, we get:

=> x = 22

As a result, rather than 24 feet, the pyramid's height is 22 feet.

Thus, x cannot equal 24.

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The type of sampling that assumes all members of a population have an equal chance of being selected for participation in the study is called Simple Random Sampling.

In Simple Random Sampling, each individual in the population has an equal probability of being chosen as a participant, and the selection process is unbiased. This method ensures that the sample is representative of the entire population, thus allowing for valid conclusions to be drawn about the population as a whole.

Here is a step-by-step explanation of how Simple Random Sampling is conducted:

1. Define the population: First, clearly identify the population you want to study.

2. Assign a unique number to each member: To ensure equal chances of selection, assign a unique number to every individual in the population.

3. Determine the sample size: Decide how many participants you need in your study based on factors like required level of accuracy and available resources.

4. Use a random selection method: Use a random selection method such as a random number generator, a lottery system, or a random number table to pick the required number of participants.

5. Collect data from the selected individuals: Once the participants are chosen, collect data from them using appropriate research methods like surveys, interviews, or experiments.

By using Simple Random Sampling, you can obtain a sample that is unbiased and representative of the entire population, which is essential for accurate and reliable research findings.

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Based on the information, cot x = - cot x. This is not true for any value of x, so there is no solution to the equation.

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved.

Using trigonometric identities, we can simplify the left-hand side of the equation as follows:

csc x cos x = (1/sin x) * cos x = cos x / sin x = cot x

Therefore, the given equation is equivalent to:

cot x = - cot x

This is not true for any value of x, so there is no solution to the equation.

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Answer:

its 1000 because if you count the blue line thing up it will show you do you have a profile picher  i need one you can be my freind pleas i have only two my name is Isabella

Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5.

What is probability?

Probability is a measure of the likelihood of an event occurring. It is a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain to happen

To determine which player was more consistent, we need to find the best measure of variability for the data. The two common measures of variability are range and interquartile range (IQR).

The range is the difference between the highest and lowest values in the data set. For Player A, the range is 6 - 1 = 5, and for Player B, the range is 11 - 1 = 10.

The interquartile range (IQR) is a measure of dispersion based on dividing the data into quartiles. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

To find the IQR for each player, we first need to find the quartiles.

For Player A:

Arrange the data in order: 1, 1, 2, 2, 2, 3, 3, 3, 6

Find Q1: (2 + 2) / 2 = 2

Find Q3: (3 + 3) / 2 = 3

Calculate IQR: Q3 - Q1 = 3 - 2 = 1

For Player B:

Arrange the data in order: 1, 1, 2, 4, 4, 5, 5, 5, 11

Find Q1: (2 + 4) / 2 = 3

Find Q3: (5 + 5) / 2 = 5

Calculate IQR: Q3 - Q1 = 5 - 3 = 2

Therefore, Player B is the most consistent, with an IQR of 2. This means that 50% of their scores fell within the range of 3 to 5. In contrast, Player A has an IQR of 1, indicating that 50% of their scores fell within the range of 2 to 3.

Therefore, we can conclude that Player B was more consistent than Player A.

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The perimeter of a square that is 3 inches on a side include the following: B. 12 inches.

In Mathematics and Geometry, the perimeter of a square can be calculated by using the following formula;

P = 4x

Where:

By substituting the given side lengths into the formula for the perimeter of a square, we have the following;

Perimeter of a square, P = 4x

Perimeter of a square, P = 4(3)

Perimeter of a square, P = 12 inches.

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The perimeter of a square with 3 inches on a side is B. 12 inches.

The perimeter refers to the distance that encompasses or surrounds an object or drawing.

The formula for computing the perimeter is 2L + 2W.  But for a square, the perimeter formula is 4L.

The length of each square side = 3 inches

The perimeter = 12 inches (4 x 3)

Thus, the perimeter of the square can be concluded to be 12 inches.

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Required number of four letters are 120.

What are letters?

Letters are symbols that represent sounds or phonemes in a language. They are used to form words and written communication. The letters of the alphabet are the basic units of written language, and each language has its own set of letters that represent its sounds. In many languages, the letters are organized into an alphabet, which is a standardized order of the letters used for writing. The letters can be written in uppercase or lowercase form, and they may have different shapes or styles depending on the font used. In addition to the letters of the alphabet, there are also other types of symbols used in written communication, such as punctuation marks, numerals, and special characters.

The given word "MIRAGE" has six letters, and we need to form a four-letter code word using these letters such that the second-to-last letter is a vowel and no letter is repeated.

There are two vowels in "MIRAGE" - "I" and "A". We can choose one of these two vowels to be the second-to-last letter in the four-letter code word. Once we have chosen the vowel, we can choose any one of the remaining five letters for the last letter in the code word, since no letter can be repeated.

After choosing the second-to-last and last letters, we have two letters left to choose for the first two positions in the code word. Since no letter can be repeated, we have four choices for the first letter, and three choices for the second letter.

Thus, the total number of four-letter code words that can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel is 2 (choices for the second-to-last letter) x 5 (choices for the last letter) x 4 (choices for the first letter) x 3 (choices for the second letter)

= 2 x 5 x 4 x 3

= 120

Therefore, there are 120 four-letter code words that can be formed from the letters in the word "MIRAGE" if no letter is repeated, and the second-to-last letter must be a vowel.

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Answer: If Amanda Bryan purchased a used car for $12,875 and made a 25% down payment, then she paid:

25% of $12,875 = 0.25 * $12,875 = $3,218.75

This means that the amount she financed (i.e. borrowed) to purchase the car is the difference between the total cost of the car and the down payment:

Amount financed = Total cost - Down payment

Amount financed = $12,875 - $3,218.75

Amount financed = $9,656.25

Therefore, Amanda Bryan financed $9,656.25 to purchase the used car.

Step-by-step explanation:

Step-by-step explanation:

Every ten minutes the car travels eleven miles

  11 miles / 10 min  = 1.1  mile / min     <=====unit rate

after 18 minutes :    1.1 mile/min * 18 min = 19.8 miles

Answer:

Step-by-step explanation:

In first quadrent,   reference angle is equal to 332

in secodn quadrent, 332-180

angle - 180 so 332-180

fouth Quadrent, 360-332  

                                                     Answer is equal to 28

Answer:

Quadrant 1: 152°

Quadrant 2: 28°

Quadrant 3 (Given): 332°

Quadrant 4: 208°

Step-by-step explanation:

A 332° angle in standard position has its terminal side in quadrant 3 since 332° is between 180° and 360°.

332° - 180° = 152°

The reference angle for 332° is 152°

Quadrant 1: 152°

Quadrant 2: 180° - 152° = 28°

Quadrant 3 (Given): 332°

Quadrant 4: 360° - 152° = 208°

Answer: First, we need to convert Brayden's height to inches, since the diameter of the loop is given in inches.

5 feet 9 inches = (5 x 12) + 9 = 69 inches

Next, we can find the diameter of the loop:

Diameter = 1.5 x 69 inches = 103.5 inches

Finally, we can find the circumference of the loop using the formula:

Circumference = П x Diameter

Circumference = 3.14 x 103.5 inches

Circumference = 325.29 inches

To convert to feet, we divide by 12:

Circumference = 27.11 feet (rounded to two decimal places)

Therefore, the circumference of the loop is approximately 27.11 feet.

Step-by-step explanation:

To use the large sample z-test for a difference in two proportions, assumptions that must be met include having independent samples, a large sample size, and success-failure conditions must be met.

In order to use the large sample z-test for a difference in two proportions, the following assumptions must be met:

The sample is random and each observation is independent. The sample size for each group is large enough such that both np and n(1-p) are greater than or equal to 10, where n is the sample size and p is the proportion of success.

The two groups being compared are independent of each other. The data is binomially distributed, meaning each observation is either a success or a failure. The populations from which the samples are drawn have similar variances.

If these assumptions are met, the large sample z-test can be used to test the null hypothesis that there is no difference between the two proportions.

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The concept of a complement of a set is the set of all elements in the universal set that are not in the original set. The answer is B) {1, 2, 3, 4, 5, 6, 7}.

It is denoted by U. Universal sets are used to define the scope of an expression or equation, as well as to denote sets of all objects, such as the set of real numbers or the set of natural numbers.

The complement of a set is also referred to as its opposite set. In this case, the universal set is {1, 2, 3, 4, 5, 6, 7}, and the set C is {1, 2, 3}.

The complement of C is {4, 5, 6, 7}.

The complement of the complement of C is the set of all elements that are not in the complement of C.

Since the complement of C is {4, 5, 6, 7}, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C, which is {1, 2, 3, 4, 5, 6, 7}.

Therefore, the answer is B) {1, 2, 3, 4, 5, 6, 7}.

To summarize, the complement of the complement of C is the set of all elements in the universal set that are not in the complement of C.

In this case, the complement of C is {4, 5, 6, 7}, so the complement of the complement of C is {1, 2, 3, 4, 5, 6, 7}.

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The probability of a measured value greater than 80 mm in a normal distribution with mean 20 mm and standard deviation 30 mm is (0.0228). The probability of a measured value between 50 and 80 mm is 0.1359.

Probability of a measured value greater than 80 mm:

We can use the standard normal distribution to find this probability, by standardizing the value of 80 mm:

z = (80 - 20) / 30 = 2

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than 2 is approximately 0.0228. Therefore, the probability of a measured value of the polymer fiber being greater than 80 mm is approximately 0.0228.

Probability of a measured value between 50 and 80 mm:

Again, we can standardize the values of 50 mm and 80 mm:

z1 = (50 - 20) / 30 = 1

z2 = (80 - 20) / 30 = 2

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being between 1 and 2 is approximately 0.1359. Therefore, the probability of a measured value of the polymer fiber being between 50 and 80 mm is approximately 0.1359.

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Answer: Add them. 6ft+4ft+4ft=10ft, 3in+6in+9in=18in. 10ft and 18in is also equal to 11ft and 6in. Therefore, the answer is 11 feet and 6 inches.

The speed of the copy machine is 30 pages per minute.

What is Fraction ?

A fraction is a way of representing a part of a whole or a division of a quantity into equal parts. It consists of two numbers, one written above the other and separated by a horizontal or diagonal line called a fraction bar. The number written above the fraction bar is called the numerator, and the number written below the fraction bar is called the denominator.

If the copy machine made a copy of Leslie's 3-page essay in just 1/10 of a minute, then it made a copy of one page in 1/10 ÷ 3 = 1/30 of a minute.

To find the speed of the copy machine, we can take the reciprocal of the time it takes to make one copy, which is:

1 ÷ (1/30) = 30

Therefore, the speed of the copy machine is 30 pages per minute.

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Answer: We can start by finding the width of the rectangular field using the formula for area of a rectangle:

Area = length x width

80 = 20 x width

width = 4 meters

Now we can use the formula for perimeter of a rectangle:

Perimeter = 2 x length + 2 x width

Perimeter = 2 x 20 + 2 x 4

Perimeter = 40 + 8

Perimeter = 48 meters

So, you would have traveled 48 meters if you walked the whole way around the field.

Step-by-step explanation:

The sοlutiοn tο the inequality [tex]x^2 + 4x > 12[/tex] is: x < -6 οr x > 2

In interval nοtatiοn, this can be written as: (-∞, -6) ∪ (2, ∞)

An algebraic expressiοn is a mathematical phrase that can cοntain variables, cοnstants, and οperatοrs (such as additiοn, subtractiοn, multiplicatiοn, and divisiοn) that are used tο represent quantities and their relatiοnships.

Tο sοlve this inequality, we need tο find the values οf x that satisfy the inequality [tex]x^2 + 4x > 12.[/tex]

First, we can mοve all the terms tο οne side οf the inequality tο get:

[tex]x^2 + 4x - 12 > 0[/tex]

Next, we can factοr the left-hand side οf the inequality tο get:

(x + 6)(x - 2) > 0

Nοw we need tο find the values οf x that make the inequality true. We can dο this by analyzing the signs οf the expressiοns οn each side οf the inequality fοr different ranges οf x.

When x < -6, bοth factοrs (x + 6) and (x - 2) are negative, sο their prοduct is pοsitive.

When -6 < x < 2, the factοr (x + 6) is pοsitive and the factοr (x - 2) is negative, sο their prοduct is negative.

When x > 2, bοth factοrs are pοsitive, sο their prοduct is pοsitive.

Therefοre, the sοlutiοn tο the inequality [tex]x^2 + 4x > 12[/tex] is: x < -6 οr x > 2

In interval nοtatiοn, this can be written as: (-∞, -6) ∪ (2, ∞)

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Answer:

x = 15

Step-by-step explanation:

the measure of a tangent- tangent angle is half the difference of the measures of the intercepted arcs.

the sum of the arcs in a circle = 360° , then

minor arc FH = 360 - 17x

Then

[tex]\frac{1}{2}[/tex] (17x - (360 - 17x) ) = 75 ( multiply both sides by 2 to clear the fraction )

17x - (360 - 17x) = 150

17x - 360 + 17x = 150

34x - 360 = 150 ( add 360 to both sides )

34x = 510 ( divide both sides by 34 )

x = 15

The measure of angle x of the circle is x = 15

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the measure of the tangent-tangent angle be = 17x°

Now , the angle created by two tangents in a circle that intersect outside the circle is known as the tangent-tangent angle. This angle's dimension is half the difference between the dimensions of the two intercepted arcs.

So , ( 1/2 ) (17x - (360 - 17x) ) = 75

Multiply by 2 on both sides , we get

(17x - (360 - 17x) = 150

34x = 510

Divide by 34 on both sides , we get

x = 15

Hence , the measure of x of circle is 15

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It is more likely that Ryan planted a yellow bulb and then a white bulb than planted a red bulb and then another red bulb. The probability of planting a yellow bulb and then a white bulb is 0.3905, which is higher than the probability of planting two red bulbs in a row, which is 0.345.

How to solve probability?

To determine which scenario is more likely, we need to calculate the probability of each outcome. Let's start by calculating the probability of planting two red bulbs in a row.

The probability of selecting a red bulb from the first bag is 8/20, from the second bag is 11/20, and from the third bag is 2/20. Thus, the probability of selecting two red bulbs in a row is:

(8/20) * (11/20) + (8/20) * (2/20) + (11/20) * (2/20) = 0.345

Now, let's calculate the probability of planting a yellow bulb and then a white bulb.

The probability of selecting a yellow bulb from the first bag is 7/20, from the second bag is 3/20, and from the third bag is 13/20. The probability of selecting a white bulb from the first bag is 5/20, from the second bag is 6/20, and from the third bag is 5/20. Thus, the probability of selecting a yellow bulb and then a white bulb is:

(7/20) * (5/20) + (7/20) * (6/20) + (3/20) * (5/20) + (3/20) * (6/20) + (13/20) * (5/20) + (13/20) * (6/20) = 0.3905

Therefore, it is more likely that Ryan planted a yellow bulb and then a white bulb than planted a red bulb and then another red bulb. The probability of planting a yellow bulb and then a white bulb is 0.3905, which is higher than the probability of planting two red bulbs in a row, which is 0.345.

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The descending order of the length of the four insects is as follows: 2/3 cm, 0.1 cm, 0.02 cm, 1/8 cm.

The length of four insects are 0.02 cm, 1/8 cm, 0.1 cm, and 2/3 cm.

Arrange the length in descending orderIn order to arrange the lengths of the four insects in descending order, we need to convert the fractions to decimals so that we can compare all the values.

1/8 cm = 0.125 cm

2/3 cm = 0.6667 cm

Now we have the values in decimal form, we can proceed to arrange them in descending order from the highest to the lowest value:

2/3 cm = 0.6667 cm

0.1 cm

0.02 cm

1/8 cm = 0.125 cm.

In conclusion, the lengths of four insects were arranged in descending order by first converting the fractions to decimals before comparing them.

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Answer:

2 Nd is in order from least to grater

The endpoints of the diameter are (-10, -3) and (-18, 1).

What is the midpoint formula?

The midpoint formula is a mathematical formula used to find the midpoint between two given points in a coordinate plane. The midpoint is the exact middle point between the two given points, which is equidistant from each point. The formula for finding the midpoint is:

Midpoint = ( (x1 + x2) / 2, (y1 + y2) / 2 )

To find the endpoints of a diameter, we need to find the midpoint of the diameter first.

The midpoint formula is:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Using the given points, we have:

Midpoint = ((2 + (-18))/2, (7 + 1)/2)

Midpoint = (-8, 4)

Now that we have the midpoint, we can find the endpoints of the diameter by reflecting one of the points across the midpoint.

Let's reflect the point (2, 7):

Endpoint 1 = (2, 7) → ( -8 - (2), 4 - 7)

Endpoint 1 = (-10, -3)

Therefore, the endpoints of the diameter are (-10, -3) and (-18, 1).

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Step-by-step explanation:

7.3 x 10^8     <=====move decimal point EIGHT place to the right

730, 000, 000  pounds

  88, 200 ,000            I think you can now see the larger one

                                            and do the subtraction to see by how much !

Answer:

The Empire State Building is heavier by 6.418 x [tex]10^{8}[/tex]

Step-by-step explanation:

World Trade Center

8.82 x [tex]10^{7}[/tex]

(6.14 x [tex]10^{8}[/tex]) - (8.82 x [tex]10^{7}[/tex])

You need to have the same power of 10 to subtract

7.3 x [tex]10^{8}[/tex] - .882 x [tex]10^{8}[/tex]

6.418 x [tex]10^{8}[/tex]

Helping in the name of Jesus.

Answer:

[tex]54in^{3}[/tex]

Step-by-step explanation:

The formula for the volume of a rectangular prism is:

A= lwh

So we just plug in those values.

A= 3*3*6

A= 9*6

A= 54in^3

Answer:

5x - 10 = 2(2x + 2)

5x - 10 = 4x + 4

x = 14

Middle Segment of a Triangle:

Triangles are geometric figures with three sides and three internal angles. We can find different types of lines inside a triangle; one of them is the middle segment. The middle segment of a triangle is a line parallel to one of the sides and bisecting the other two sides. Let L be the line of the middle segment and AC the side parallel to the line L, then the formula of the middle segment is:

L = AC/2

We are given a diagram:

Our objective is to find the missing length of RQ.

We can see that the RQ line divides the ST and UT lines in equal parts. Moreover, the SU and RQ lines are parallel; therefore, we can conclude that the RQ line is the middle segment of the STU triangle. So:

RQ = SQ/2

→2x+2 = (5x-10)/2

→2(2x+2) = 5x-10

→4x+4 = 5x-10

→ 5x-4x = 10+4

x = 14

and RQ = 30

and SU = 60