During one season of racing at the Talladega Superspeedway, the mean speed of the cars racing there was found to be 158.9 mph with a standard deviation of 6.7 mph. What speed represents the 30th percentile for speeds of race cars at Talladega? Assume that the racing speeds are normally distributed.

Answer:

slope is 1/3

y-intercept is -4

Step-by-step explanation:

x - 3y = 12

3y = x - 12

y = 1/3x - 4

according to y = mx + b, m is slope and b is y-intercept

slope is 1/3

y-intercept is -4

Two circles intersect at points A and B and have a common external tangent that is tangent to the circles at points T and U, M be the intersection of line AB and TU. If AB = 9 and BM = 3, then TU will be equal to 9.6.

In order to find the length of TU, We can use the Pythagorean theorem to find the length of TU. We know that AB = 9, and BM = 3, so the length of AM must be 6. We can then use the Pythagorean theorem to solve for TU:

TU = √(62 + 92) = √93 = 9.6.

Therefore, the length of TU is 9.6.

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The shipping company will need 2,688 one cubic centimeter blocks to fill the box.

The volume of the box can be calculated as:

Volume = length x width x height

Volume = 14 cm x 12 cm x 16 cm

Volume = 2,688 cubic cm

Since each block is also one cubic cm in volume, we can simply divide the total volume of the box by the volume of one block to find the number of blocks needed to fill the box:

Number of blocks = Volume of box / Volume of one block

Number of blocks = 2,688 cubic cm / 1 cubic cm

Number of blocks = 2,688

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Hence, 1) 6 cm (smallest value), 2) 6 cm, and 3)15.167 cm are the approximate dimensions which will result in a material with the biggest volume (largest value).

A 3D object's surface area is indeed the entire area that all of its faces cover. For instance, the surface area of a cube has been its surface area if we need to determine how much paint is needed to paint it. It's always calculated in square units.

Let the height be y as well as the side length of a square base be x. The rectangular solid's surface area is then determined by:

When we simplify this equation, we obtain:

The rectangular solid's volume is determined by:

V = x² × y = x² × (433.5 - 4x²) / (2x)

When we simplify this equation, we obtain:

V = 216.75x - 2x³

We must determine the value of x that maximizes V in order to determine the dimensions that lead to a solid with the maximum volume. Using V's derivative with x as the base, we can calculate:

dV/dx = 216.75 - 6x²

By setting this to 0 and figuring out x, we obtain:

216.75 - 6x² = 0

x² = 36.125

x ≈ 6.005

When we rewrite the equation for y using this value of x, we obtain:

y ≈ 15.167

Thus, the following dimensions will produce a solid with the largest volume:

1. 6 cm (smallest value)

2. 6 cm

3.15.167 cm (largest value)

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Therefore, Person A is approximately 95.17 miles away from the building.

To find out how far person A is from the building, we'll need to use trigonometry. The diagram below shows the situation.

Given that Person A's angle of elevation to the building is 35 degrees, we'll let angle BAC be 35 degrees.

Similarly, since Person B's angle of elevation is 77 degrees, we'll let angle ABC be 77 degrees. We'll also let AB be x, the distance from Person A to the building, and BC be 8 miles, the distance from Person B to the building.

First, we'll use the tangent function to find the height of the building. In triangle ABC, tan(77) = height/8. Solving for the height, we get:

height = 8tan(77) ≈ 61.23 miles.

Next, we'll use the tangent function again to find x. In triangle ABC, tan(35) = height/x + 8. Solving for x, we get:

x = (height)/(tan(35)) - 8
≈ 103.17 miles - 8
≈ 95.17 miles.
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Answer: Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours

Step-by-step explanation:

     We will use the variables x and y the question provides. We know the time worked by each person added together will equal the combined total time. We can write an equation to show this using addition.

        x + y = 11 hours

     Next, we know that Keilantra ironed 30 per hour, Samantha ironed 15 per hour and that they ironed 240 shirts. We can write another equation to represent this using addition and multiplication.

     30x + 15y = 240

     Next, we will graph these two equations. See attached. The solution is the point of intersection written as (x, y). This is (5, 6) meaning that Kelinatra (x) worked 5 hours and Samantha (y) worked 6 hours.

The distance Mrs. Smith covers is 3520 yards during the duration of the week by Friday morning.

One week has seven days in total.

Mrs. Smith walks half a mile each day after work, she walks a total of

0.5 miles/ day × 7 days/ week = 3.5 miles/ week

Now, if we calculate the distance on Friday morning, she must have walked four times till Friday morning since she has to walk after her work.

Therefore,

0.5 miles/ day × 4 days = 2 miles

To convert miles to yards, we can use the fact that there are 1760 yards in one mile:

2 miles/week × 1760 yards/mile = 3520 yards/week

Therefore, by Friday morning, Mrs. Smith will have walked 3520 yards.

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The amount that each type would be 11.87 lbs of cashews and 15.13 lbs of brazil nuts

1. First, find the total cost of 27 lbs of the mixture: 27 lbs x $6.41/lb = $171.07.
2. Next, find the cost of cashews and brazil nuts in the mixture. Cashews cost $7.70/lb and brazil nuts cost $4.80/lb.
3. Subtract the cost of the brazil nuts from the total cost of the mixture: $171.07 - (27 lbs x $4.80/lb) = $105.27.
4. Divide the cost of the cashews ($105.27) by the cost of one pound of cashews ($7.70): $105.27/$7.70 = 13.66 lbs.
5. Subtract the number of pounds of cashews (13.66) from the total pounds of the mixture (27) to find the number of pounds of brazil nuts: 27 - 13.66 = 15.13 lbs.
6. Therefore, the mixture should contain 11.87 lbs of cashews and 15.13 lbs of brazil nuts.

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The phase angle, in degrees is -135.

A wave that repeats as a function of time and position is referred to as a periodic wave. Amplitude, frequency, wavelength, speed, and energy describe the properties of the wave. The phase angle is used to describe the characteristics of a periodic wave.

In phasors, a wave exhibits twofold characteristics: Magnitude and Phase. The phase angle refers to the angular component of a periodic wave.

The Phase Angle is one of the crucial characteristics of a periodic wave. It is similar to the phrase in many properties. The angular component periodic wave is known as the Phase Angle. It is a complex quantity measured by angular units like radians or degrees. A representation of any pure periodic wave is as follows.

A∠θ, where A is the magnitude and θ represents the Phase Angle of the wave.

A is the magnitude

θ is the phase angle

The expression is, which can be reduced to. Since angles are not unique, they can differ by multiples of 360, the answer is -135 degrees, which is in the range of -180 to 180 degrees.

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Answer:

36

Step-by-step explanation:

PxW=p

30x120=p

3600=p

x100%

$36=p

(overpriced ticket of you ask me lol)

Answer:

Step-by-step explanation:

Let's use the variable "s" to represent the number of slices in each pizza.

The drama club bought 999 large pizzas, and each pizza had s slices. So, the total number of pizza slices is given by the product of 999 and s, which can be written as:

999s = 727272

To solve for s, we can divide both sides of the equation by 999:

s = 727272/999

Using a calculator, we can simplify this fraction to:

s ≈ 728.73

Therefore, each pizza has approximately 728 slices. Note that this is an unusual number of slices for a pizza, so it's possible that the problem is not intended to be taken literally, but rather as a math puzzle or word problem.

Answer:

Each pizza has 729 slices.

Step-by-step explanation:

The probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413. This can be calculated using the formula for probability of a normal distribution:

P(x > 52) = 1 - P(x ≤ 52)

P(x ≤ 52) = (52 - 58) / 6 = -1

P(x > 52) = 1 - P(-1) = 1 - 0.1587 = 0.8413.

Therefore, the probability that the diameter of a selected bearing is greater than 52 millimeters is 0.8413.

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To calculate the product of two random variables that follows the normal distribution with mean 0 and variance 1 by using the covariance formula

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Given that two random variables follow a normal distribution with mean 0 and variance 1.

Let X and Y be two independent normal random variables such that X ~ N(0,1) and Y ~ N(0,1)

Now, The expected value of the product of two random variables is given by;

E[XY] = E[X]E[Y] + Cov(X,Y)

Where E[X] and E[Y] are the means of the two random variables X and Y respectively.

Cov(X, Y) is the covariance between the two random variables, which can be calculated using the formula;

Cov(X,Y) = E[XY] - E[X]E[Y]

Now, E[X] = E[Y] = 0 as both have a mean of 0.

Cov(X, Y) = E[XY] - E[X]E[Y]

⇒ E[XY] = the expected value of the product of X and Y.

As X and Y are independent, their covariance will be zero, which implies;

Cov(X, Y) = E[XY] - E[X]E[Y] = E[XY] - 0 = E[XY]

Thus, we can calculate the product of two random variables that follow a normal distribution with mean 0 and variance 1 using the above formula for covariance.

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Answer:

perimeter=42

Area=90

Step-by-step explanation:

find the length of DEFG:

perimeter=a=b+a+b

28=10+b+10+b

28=20+2b

8=2b

4=b

finding the scale factor:

15/10=3/2

to find the perimeter of WXYZ:

the missing side:

=4x3/2

=6

perimeter=a+b+a+b

perimeter=15+6+15+6

perimeter=42

Area of WXYZ:

Area=bh

Area=15x6

Area=90

The given numbers are in decimal and binary system and the final result of the given operation is [tex](4675.31)_{10}[/tex].

A binary integer (base-2) is converted to an equivalent decimal number using the binary to decimal conversion formula. (base-10). In mathematics, integers are expressed using a number system. It is a method to display numerical data. The four various numeral systems are as follows:

System of Binary Numbers (Base-2)
system of octal numbers (Base-8)
System of Decimal Numbers (Base-10)
System of Hexadecimal Numbers (Base-16).
We are the two numbers:-

[tex](4623.56)_{10} , (110011.11)_{2}[/tex]

these are in decimal and binary system respectively.

now, we will express them in same system ( here we choose decimal system).

[tex](110011.11)_{2} = (2^{5} + 2^{4} + 0 + 0 + 2^{1} + 2^{0} + 2^{-1} + 2^{-2} )_{10} \\= (2^{5}+2^{4}+0*2^{4}+0*2^{3}+2^{1}+2^{0}+2^{-1}+2^{-2})_{10} \\= (32+16+2+1+0.5+0.25)_{10} \\= (51.75)_{10}[/tex]

Now, addition is done below:-

4623.56+51.75= 4675.31.

hence, the final result of the given operation= [tex](4675.31)_{10}[/tex]

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The probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll when a fair die is rolled three times is 1/4.

Probability is the study of random events. It is a measure of the likelihood of an event occurring. Probability can be expressed as a decimal, a fraction, or a percentage. There are two types of probability - empirical probability and theoretical probability.

Empirical probability is calculated by conducting experiments or collecting data. It is calculated using the following formula:

Empirical probability = Number of favourable outcomes/Total number of outcomes

Theoretical probability is calculated using probability formulas. It is calculated using the following formula:

Theoretical probability = Number of favourable outcomes/Total number of possible outcomes

In the given problem, a fair die is rolled three times. We need to find the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll. There are 2 favourable outcomes for the first roll, 2 favourable outcomes for the second roll, and 2 favourable outcomes for the third roll.

Total number of outcomes = 6×6×6 = 216

Number of favourable outcomes = 2×2×2 = 8

Probability = Number of favourable outcomes/Total number of outcomes

Probability = 8/216

Probability = 1/27

Therefore, the probability that it is 1 or 2 on the first roll, 3 or 4 on the second roll, or 5 or 6 on the third roll when a fair die is rolled three times is 1/4.

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A theorem which these transformations reveal include the following: theorem of intersecting secants.

In Mathematics and Geometry, the theorem of intersecting secants states that when two lines intersect outside a given circle, the measure of the angle formed by these intersecting lines is equal to one-half (½) of the difference of the two (2) arcs it intercepts.

By applying the theorem of intersecting secants, the value of any of the angle subtended by the intersecting lines can be calculated by using the following mathematical equation:

m∠a = One-half(y – x).

m∠a = ½(y – x).

Where:

x and y represent the angles formed by the intersecting lines.

Therefore, the theorem of intersecting secants describe these set of transformations.

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Answer: 1

Step-by-step explanation:

because it not zero and not 4

The distance she must climb to reach the peak is greater than 2,663 feet. An inequality to show the remaining distance, d, in feet she must climb to reach the peak is d > 2,663.

Inequlity represents a relationship between two values that is not equal. That is inequlity means no equal and the symbols which used for not equal is ≠ and for comparison are < , > , ≤ , ≥. For example, ax > b etc. We have, Rina is climbing a mountain and mountain height present in above figure. See the figure carefully, the main two points in figure are the following: height of mountain peak

= 12,358 feet

height of base camp = 9,695 feet

we have to write an inequality for the remaining distance, d, in feet. Also, it is specified that she has not reached base camp yet. So, his climbed distance is less than 9,695 feet. Let the remaining distance be 'd feet '. From the above figures, d + base camp height > 12,358

Substract 9695 from both sides

=> d > 12,358 - 9,695

=> d > 2,663

Hence, required inequalty is d > 2,663.

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Complete question:

Rina is climbing a mountain. She has not yet reached base camp. Write an inequality to show the remaining distance, d, in feet she must climb to reach the peak. See tha above figure.

Answer: To solve the equation 16=3x-7/2, you can follow these steps:

Multiply both sides of the equation by 2 to get rid of the fraction:

16 * 2 = (3x - 7/2) * 2

32 = 6x - 7

Add 7 to both sides of the equation to isolate the term with x:

32 + 7 = 6x

39 = 6x

Divide both sides of the equation by 6 to solve for x:

39 / 6 = x

6.5 = x

Therefore, the solution to the equation 16=3x-7/2 is x = 6.5.

Step-by-step explanation:

Answer:

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ㅤㅤ [tex]\large{\blue{\star} \: {\underline{\boxed{\pmb{\tt{x = \dfrac{13}{2}}}}}}}[/tex]

ㅤ

Step-by-step explanation:

ㅤ

[tex]\large{\pmb{\tt{16 = 3x - \dfrac{7}{2}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 + \dfrac{7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{2 \times 16 + 7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{32 + 7}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{39}{2} = 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{39 = 2 \times 3x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{39 = 6x}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{\dfrac{\cancel{39}}{\cancel{6}} = x}}}}[/tex]

ㅤ

[tex]\large{\purple{\boxed{\pmb{\tt{\leadsto{\dfrac{13}{2} = x}}}}}}[/tex]

ㅤ

━━━━━━━━━━━

ㅤ

[tex]\large{\underline{\underline{\sf{Verification:-}}}}[/tex]

ㅤ

• Substituting the value of (x) in the given equation,

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = 3 \times \dfrac{13}{2} - \dfrac{7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39}{2} - \dfrac{7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{39 - 7}{2}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = \dfrac{\cancel{32}}{\cancel{2}}}}}}[/tex]

ㅤ

[tex]\large{\pmb{\tt{\leadsto{16 = 16}}}}[/tex]

ㅤ

As LHS = RHS,

Hence Verified

Answer:

A

Step-by-step explanation:

The planet XYZ traveling about the star ABC in a circular orbit takes 24 hours to make an orbit. Assume that the orbit is a circle with a radius of 83,000,000 mi. The linear speed of XYZ in miles per hour is approximately 1,093,333 miles per hour.

  What is the orbit and what is the linear speed?

           An orbit refers to the path taken by an object, such as a planet, as it circles around another object, such as a star. The speed of the planet is its rate of movement, measured in linear units like miles or kilometers per hour, as it travels around the orbit.

         These are terms that are important to understanding the solution to the problem provided. The linear speed of XYZ in miles per hour is approximate _____ miles per hour. (Round to the nearest integer as needed.)

        The planet XYZ travels around the star ABC in a circular orbit that takes 24 hours to complete. The orbit is a circle with a radius of 83,000,000 miles.

To find the linear speed of XYZ in miles per hour, it is necessary to use the formula for the circumference of a circle.

          Circumference = 2πr Circumference

                                    =2πr Substitute 83,000,000 for r in the formula.

          Circumference = 2π(83,000,000)

           Circumference = 522,000,000 π

     The orbit's circumference is 522,000,000 π miles.

      The distance traveled by XYZ in one hour is the linear speed. The linear speed of XYZ in miles per hour is calculated as follows:

             Speed = Distance/TimeSpeed

                         = Circumference/24Speed

                         = (522,000,000 π)/24

              Speed = 21,750,000 π

    The linear speed of XYZ in miles per hour is 21,750,000 π miles per hour.

To get an approximate answer, π is equal to 3.14.

             Speed ≈ 21,750,000 (3.14)

             Speed ≈ 68,295,000

 The linear speed of XYZ in miles per hour is approximately 68,295,000 miles per hour. Rounded to the nearest integer, the linear speed is approximately 1,093,333 miles per hour.

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Answer:

To determine the position of a particle given the input of energy, we need to know the type of energy input and the initial position and velocity of the particle. Without this information, we cannot determine the position of the particle after 2.5 seconds.

Therefore, the answer is A) cannot be determined.

Step-by-step explanation:

ABOVE

17. The population of interest is U.S. adults (age 18 and over).
18. The sample being used is 1,012 randomly selected U.S. adults (age 18 and over).
19. The population parameter of interest is the percentage of U.S. adults (age 18 and over) who are dissatisfied with the quality of education students receive in kindergarten through grade 12. The correct notation for this parameter is p and the relevant statistic is 53%.
20. The interval estimate for the parameter of interest is 49% - 57%, which indicates that between 49% and 57% of U.S. adults (age 18 and over) are dissatisfied with the quality of education students receive in kindergarten through grade 12.

The coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.

What is proportion ?

A proportion refers to the number or fraction of individuals or items that exhibit a particular characteristic or have a certain attribute, relative to the total number or sample size being considered. It is often expressed as a ratio or percentage.

To test whether the distribution of sales is proportional to the number of facings, we can use the chi-squared goodness of fit test. The null hypothesis for this test is that the observed data follows a specific distribution (in this case, a proportional distribution), while the alternative hypothesis is that the observed data does not follow that distribution.

To conduct the test, we first need to calculate the expected frequency for each category assuming a proportional distribution. We can do this by multiplying the total number of sales (610) by the proportion of facings for each brand:

Starbucks: 610 x 0.3 = 183

Dunkin: 610 x 0.4 = 244

Peet's: 610 x 0.2 = 122

Other: 610 x 0.1 = 61

Next, we calculate the chi-squared statistic using the formula:

χ² = Σ((O - E)² / E)

where O is the observed frequency and E is the expected frequency. The degrees of freedom for this test are (k-1), where k is the number of categories. In this case, k = 4, so the degrees of freedom are 3.

Using the observed and expected frequencies from the table, we get:

χ² = ((130-183)²/183) + ((240-244)²/244) + ((85-122)²/122) + ((155-61)²/61) = 124.36

Looking up the critical value of chi-squared for 3 degrees of freedom and a significance level of 0.05, we get a value of 7.815. Since our calculated χ² value of 124.36 is greater than the critical value of 7.815, we reject the null hypothesis and conclude that the observed distribution of sales is not proportional to the number of facings.

Therefore, the coffee shop owner does not have sufficient evidence to conclude that the distribution of sales is proportional to the number of facings at a 5% level of significance.

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Answer:

Step-by-step explanation:

Using the distance formula:  [tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

    [tex]d=\sqrt{(8-0)^2+(-2-6)^2}[/tex]

        [tex]=\sqrt{64+64} \\[/tex]

        [tex]=\sqrt{128}[/tex]

        [tex]=11.3[/tex]

The another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.

The process of generating random variates from a binomial distribution using the inverse transform method for discrete distribution is done as follows:Step 1: Determine the probability mass function (pmf) of the binomial distribution with parameters n and p. For example, for a binomial distribution with n = 6 and p = 0.4, the pmf is given by:P(X=k) = (6 choose k)(0.4)^k(1-0.4)^(6-k), where k=0,1,2,3,4,5,6Step 2: Calculate the cumulative distribution function (CDF) of the binomial distribution by summing the pmf up to each value of k. The CDF is given by:F(k) = P(X ≤ k) = ΣP(X=i) for i=0 to k, where k=0,1,2,3,4,5,6Step 3: Generate a uniform random variate, U, between 0 and 1. For example, U=0.23456.Step 4: Find the smallest value of k such that F(k) ≥ U. This value of k is the random variate X. For example, if U=0.23456, then F(0)=0.10737, F(1)=0.38223, and F(2)=0.74304. Since F(1) is the smallest value of F(k) that is greater than or equal to U, X=1. Therefore, a random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=1.To find another random variate from the same distribution, repeat steps 3 and 4. For example, U=0.987654, F(0)=0.10737, F(1)=0.38223, F(2)=0.74304, F(3)=0.91892, F(4)=0.98544, and F(5)=0.99856. Since F(3) is the smallest value of F(k) that is greater than or equal to U, X=3. Therefore, another random variate from a binomial distribution with n=6 and p=0.4 has been generated as X=3.

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Based on the information provided, the table that correctly displays the data is table III.

Note: The question is incomplete; below I attach the missing information:

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