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.

If we want to provide a 99% confidence interval for the mean of a population, the confidence coefficient will be 0.99. This means that there is a 99% probability that the true population mean falls within the calculated interval.

The confidence coefficient for a confidence interval represents the level of confidence we have in our estimate.

In the case of a 99% confidence interval, the confidence coefficient is 0.99. This means that we are 99% confident that the true population mean falls within the calculated interval. The confidence coefficient is derived from the desired level of confidence, which is typically expressed as a percentage.

A higher confidence level corresponds to a larger confidence coefficient. In practical terms, a 99% confidence interval indicates that if we were to repeat the sampling process multiple times and construct 99% confidence intervals, approximately 99% of those intervals would contain the true population mean.

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Answer:

52degrees

Step-by-step explanation:

Let the measure of the largest angle be x

middle angle be y

smallest angle be z

Since the sum of angle in a triangle is 180 degrees, hence;

x + y + z = 180 .... 1

If the measure of the largest angle is 32 less than 3 times the smallest angle, then;

x = 3z - 32

3z = x+ 32

z = x+32/3 ..... 2

If he measure of the middle angle is 8 more than half the measure of the largest angle, then;

y = x/2 + 8 .... 3

Substitute 2 and 3 into 1;

x + x/2 + 8 + (x+32)/3 = 180

multiply through by 6

6x + 3x + 48 + 2(x+32) = 1080

9x + 48 + 2x + 64 = 1080

11x + 112 = 1080

11x = 1080-112

11x = 968

x = 968/11

x = 88 degrees

Get the middle angle y;

Since y = x/2 + 8

y = 88/2 + 8

y = 44 + 8

y = 52 degrees

Hence the measure of the middle angle is 52degrees

The angles in a triangle add up to 180 degrees.

The middle angle is 52 degrees

Let the largest, middle angle and the smallest angle be x, y and z

From the question, we have:

\(\mathbf{x = 3z -32}\)

\(\mathbf{y = 8 + \frac 12x}\)

Make z in \(\mathbf{x = 3z -32}\)

\(\mathbf{z =\frac{x + 32}{3}}\)

The angles in a triangle add up to 180 degrees.

So, we have:

\(\mathbf{x + y + z = 180}\)

Substitute the expressions for y and z in   \(\mathbf{x + y + z = 180}\)

\(\mathbf{x + 8 + \frac 12x + \frac{x+32}{3} = 180}\)

Multiply through by 6

\(\mathbf{6x + 3x + 48 + 2(x+32) = 1080}\)

\(\mathbf{9x + 48 + 2(x+32) = 1080}\)

Open brackets  

\(\mathbf{9x + 48 + 2x + 64 = 1080}\)

Evaluate like terms

\(\mathbf{11x + 112 = 1080}\)

Subtract 112 from both sides

\(\mathbf{11x = 968}\)

Divide both sides by 11

\(\mathbf{x = 88}\)

Substitute 88 for x in \(\mathbf{y = 8 + \frac 12x}\)

\(\mathbf{y = 8 + \frac{88}2}\)

\(\mathbf{y = 8 + 44}\)

\(\mathbf{y = 52^o}\)

Hence, the middle angle is 52 degrees

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Answer:

-1 1/5

Hope this helped!

Also I would really appreciate it if you made me the brainliest! :D

The conditional expectation E(X | Y = y) for all y is:

E(X | Y = y) = (y + 1) / 2.

To find the conditional expectation E(X | Y = y), we need to calculate the expected value of X given that the sum of the two dice is y.

Let's consider all possible values of y from 2 to 12 (the possible sums of rolling two dice):

For y = 2:

The only possible combination is (1, 1). In this case, X can only take the value 1. Therefore, E(X | Y = 2) = 1.

For y = 3:

The possible combinations are (1, 2) and (2, 1). In both cases, the value of X is 1. Therefore, E(X | Y = 3) = 1.

For y = 4:

The possible combinations are (1, 3), (2, 2), and (3, 1). In these cases, the value of X can be 1, 2, or 3. Taking the average, we have E(X | Y = 4) = (1 + 2 + 3) / 3 = 2.

Similarly, we can calculate the conditional expectations for y = 5, 6, 7, 8, 9, 10, 11, and 12:

For y = 5: E(X | Y = 5) = (1 + 2 + 3 + 4) / 4 = 2.5

For y = 6: E(X | Y = 6) = (1 + 2 + 3 + 4 + 5) / 5 = 3

For y = 7: E(X | Y = 7) = (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5

For y = 8: E(X | Y = 8) = (2 + 3 + 4 + 5 + 6) / 5 = 4

For y = 9: E(X | Y = 9) = (3 + 4 + 5 + 6) / 4 = 4.5

For y = 10: E(X | Y = 10) = (4 + 5 + 6) / 3 = 5

For y = 11: E(X | Y = 11) = (5 + 6) / 2 = 5.5

For y = 12: E(X | Y = 12) = 6

In summary, the conditional expectation E(X | Y = y) for all y is given by:

E(X | Y = 2) = 1

E(X | Y = 3) = 1

E(X | Y = 4) = 2

E(X | Y = 5) = 2.5

E(X | Y = 6) = 3

E(X | Y = 7) = 3.5

E(X | Y = 8) = 4

E(X | Y = 9) = 4.5

E(X | Y = 10) = 5

E(X | Y = 11) = 5.5

E(X | Y = 12) = 6

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Complete question :

At a farm, four employees harvest 48 pounds of food over a certain numbers of hours. Each employee works the numbered of hours shown. Employee A: 6 hours employee B: 4 hours employee C: 6 hours employee D: 8 hours The number of pounds of food harvested by each employee is proportional to the number of hours worked. Fill in the table with the amount of food, in pounds, each employee harvested.

Answer:

A = 12 lbs ;

B = 8 lbs

C = 12 lbs

D = 16 lbs

Step-by-step explanation:

Total hours worked :

(A + B + C + D)

(6 + 4 + 6 + 8) hours = 24 hours

Total pounds of food = 48 pounds

Pounds harvested per hour = 48 pounds / 24 hours = 2 pounds per hour

Amount of food harvested by each employee :

A = 6 * 2 = 12 pounds

B = 4 * 2 = 8 pounds

C = 6 * 2 = 12 pounds

D = 8 * 2 = 16 pounds

The distance from the center of a circle to its edge or any point on the boundary is the radius.

The radius is half of the length of the diameter.

The radius can be represented as d/2, where d is the diameter.

The diameter represents the line or length that divides the circle equally at the center, from one edge to the other.

Thus, we can state categorically that the radius is the length from the center of a circle to its boundary.

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Answer:

Time when Jessie starts doing her he: 4:30

Time talked to complete the hw : 40minutes

Time Jessie finishes the hw: 5:10

A quotient is any number before a specified variable in a given equation.

i. The division equation required is \(\frac{3}{4}\)x

ii. The quotient is \(\frac{3}{4}\) (0.75)

Fraction is a mathematical expression which consists of a numerator and denominator. Some types are proper fraction, improper fraction and mixed fraction.

In any given algebraic equation, the number that exists before a stated alphabet is termed quotient.

For example, given: 4x + 1

Thus the quotient of x is 4.

Considering the given question, let the tomato sauce be represented by x.

So that 6 quarts of tomato sauce was divided into 8 jars equally. This implies that;

6x ÷ 8 = \(\frac{6}{8}\)x

          = \(\frac{3}{4}\)x

Thus,

i. the division equation that can be used to model the situation = \(\frac{3}{4}\)x

ii. the quotient = \(\frac{3}{4}\)

                         = 0.75

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Answer:

yes

Step-by-step explanation:

51 divided by 25

The correct option is 'The domain of both functions is all real numbers'.

According to statement

Here, functions are f(x) = 5x and g(x) =5x

Since the domain of f(x) is, D= { x : x belongs to all real numbers.}

Therefore, Domain of f(x) is all real numbers.

Since f(x) and g(x) have the same value,

Therefore, Domain of g(x) is also the set of real numbers.

Now, range of f(x) is , R=  { 5x : x belongs to all real numbers.}

Therefore, Range of f(x) is all real numbers.

Range of g(x) is also all real numbers.

So, we can say by the above explanation, only option (1) is correct.

DISCLAIMER: The question was incomplete. Please find the full content below.

QUESTION

Keshawn is asked to compare and contrast the domain and range for the two functions.

f(x) = 5x

g(x) = 5x

Which statements could he include in his explanation? Check all that apply.

1. The domain of both functions is all real numbers.

2. The domain of f(x) is x > 5.

3. The domain of g(x) is x > 5.

4. The range of both functions is y > 5.

5. The range of f(x) is y > 0.

6. The range of g(x) is y > 0.

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Answer:

The area's are the same

Step-by-step explanation:

Both base's areas are 30.

Answer:

B) 3b. 10b

Step-by-step explanation:

B) 3b. 10b = (3x10)(bxb) = 30b²

By using the ASA Congruence Theorem, Delta PQR is congruent to Delta TSR.

We can prove this by using the fact that triangle PQR and triangle TSR are both right triangles and that R is the midpoint of overline PT and overline PQ is congruent to overline TS. Since R is the midpoint of overline PT, it follows that overline PR is congruent to overline TR (by the midpoint theorem).

Since PQR is a right triangle, and R is the right angle, it follows that angle PQR is congruent to angle TSR (by the definition of a right angle). Since overline PQ is congruent to overline TS, it follows that angle PQS is congruent to angle TSR (by the definition of congruence). Together, these congruences imply that triangle PQR is congruent to triangle TSR by the ASA congruence theorem.

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Answer: 9,2 pulgadas²

(a) The cost of 1 kg of turnips is £71.95, and

(b) The cost of 1 kg of mushrooms is £89.50.

To solve this problem, let's assign variables to the unknowns.

Let the cost of 1 kg of mushrooms be 'm' and the cost of 1 kg of turnips be 't'.

According to the given information:

Equation 1: 2m + 2.5t = 8.55

Equation 2: 3m + 4t = 13.10

We can solve these equations simultaneously to find the values of 'm' and 't'.

To eliminate the decimals, let's multiply both sides of Equation 1 by 10 and Equation 2 by 20:

20m + 25t = 85.50

60m + 80t = 262.00

Now, let's multiply Equation 1 by 12 and subtract Equation 2 multiplied by 5:

240m + 300t - (60m + 80t) = 1026.00 - 1310.00

180m + 220t = -284.00

We have a new equation:

180m + 220t = -284.00 ---(3)

Next, let's multiply Equation 1 by 18 and subtract Equation 2 multiplied by 4:

36m + 45t - (60m + 80t) = 154.35 - 524.00

-24m - 35t = -369.65

We have another new equation:

-24m - 35t = -369.65 ---(4)

Now, we have a system of linear equations with two variables. Let's solve this system by eliminating one variable.

Multiply Equation 3 by 35 and Equation 4 by 220:

6300m + 7700t = -9940.00 ---(5)

-5280m - 7700t = -81323.00 ---(6)

Adding Equations 5 and 6, we eliminate 't':

1020m = -91263.00

m = -91263.00/1020

m = -89.50

Substituting the value of 'm' back into Equation 3:

180(-89.50) + 220t = -284.00

-16110 + 220t = -284.00

220t = -284.00 + 16110

220t = 15826.00

t = 15826.00/220

t = 71.95.

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Answer:

2 Liters

Step-by-step explanation:

.25 liters=1/8 fish aquarium

.25x8=2

The domain of the function is given as 0<t<3, which means that the time elapsed is between 0 and 3 hours. Mia's distance from the river after 2 hours of driving is 30 miles.

The given function is:

d(t) = 40|t-1.25|

Here, t represents the time elapsed in hours and d represents the distance from the river in miles.

To find Mia's distance from the river, we need to plug in values of t into the function.

For example, if t=2, then:

d(2) = 40|2-1.25|

d(2) = 40|0.75|

d(2) = 30

So Mia's distance from the river after 2 hours of driving is 30 miles.

Similarly, we can find Mia's distance from the river at other points in time.

To graph the function, we can plot points by choosing different values of t and finding the corresponding values of d. We can then connect these points to get a graph of the function.

Graph of the function d(t) = 40|t-1.25|

The graph shows that Mia starts at a distance of 40 miles from the river and then approaches it until she reaches the other side of the river, where her distance from the river is again 40 miles. The graph is symmetric about t=1.25, which means that Mia spends the same amount of time on either side of the river.

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Answer:

1,460

Step-by-step explanation:

the probability that a positive integer less than 100 picked at random has all distinct digits is 90.

He has 99 positive integers less than 100.

The integers that do not have all distinct digits have the same digit twice.

11, 22, 33, 44, 55, 66, 77, 88, 99

There are 9 integers that do not have distinct digits, therefore there are 99-9 integers that do.

Probability is without a doubt how probable something is to show up. whenever we are uncertain about the final results of an occasion, we can talk about the possibilities of sure outcomes and how probable they are. The analysis of events governed by opportunity is referred to as records.

A chain of moves in which the results are usually unsure. The tossing of a coin, selecting a card from a deck of playing cards, throwing a cube. occasion. it is a single final results of an experiment. Getting a Heads whilst tossing a coin is an event.

Simple probability is the calculation of an outcome or the chance of an event ever taking place. coverage companies use possibility statistics to determine the possibilities of having to pay out a declare. A simple chance is calculated by way of dividing a particular outcome through all of the feasible outcomes.

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Answer:

84

Step-by-step explanation:

7x5x4x3= 84

At the 0.1 level of significance, the conclusion we come up with is to reject the null hypothesis.

we are given that a random sample of 150 people was taken. 98 of the people in the sample favored the candidate, were it to determine whether or not the proportion of the population in favor of candidate a is significantly more than 57%.So we need to find the test statistic, which is 1.98  determined from the z score, here the rejection region is the number more than 1.28, and 1.98 is greater than 1.28, so it is better to simply reject the null hypothesis.

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Answer: x=20

Step-by-step explanation:

If im wrong, sorry

The angles of a triangle add up to 180 degrees.

(3x+5)+(2x+17)+(2x+18)=180

add the ones alike

3x + 2x + 2x=7x

5+17+18=40

so, 7x+40=180

we need to get the variable by itself so we take away 40 first by subtracting it from both sides of the equal sign

7x=140

we take away 7 from x by dividing it- opposite of multiplication is division

x=20

Answer:

x = 20

Step-by-step explanation:

3x+5° + 2x+18° + 2x+17° = 180° (sum of interior angles in a triangle is 180°)

collect like terms

3x + 2x + 2x + 5° + 18° + 17° = 180°

7x + 40° = 180°

solving for x

x = (180 - 40)/7

x = 140/7

x = 20

The shortest distance that gecko covers is 22.4 feet.

According to the statement

we have given that the some data and from that we have to ind the height that gecko does not jump.

So, for this purpose,

For the gecko to walk the shortest distance, it has to go straight from where it is to the ceiling, diagonally from the ceiling to the wall where the fly is and straight from the corner of the ceiling to where the fly is.

straight from where it is to the ceiling: 1 feet

diagonally from the ceiling to the wall where the fly:

it is a right triangle hypotenuse what we want, leg 12 and 8.

(see picture attached):

h² = 12² + 8²   And

h = √208  

h = 14.4 feet

straight from the corner of the ceiling to where the fly is: 7 feet.

1 + 14.4 + 7 = 22.4

It is the shortest distance.

So, The shortest distance that gecko covers is 22.4 feet.

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Answer:

Step-by-step explanation:From the issue, we may deduce that:

x + y = 50 She desires to produce 50 ounces of the combination (because to this).

(0.35x) + (0.60y) = 0.55(x+y) (because we're calculating the amount of salt in each solution and the combination contains 55% salt)

We may take the first equation and replace it in the second equation:

(0.35x) + (0.60y) = 0.55(50) (50)

0.35x + 0.60y = 27.5 when x is substituted.

A system of two equations with two variables is now available:

x + y = 50\s0.35x + 0.60y = 27.5

To determine one of the variables in terms of the other, we may utilize the first equation. Let's figure out y:

y = 50 - x

We now change y in the second equation to the following expression:

0.35x + 0.60(50-x) = 27.5

Finding the value of x:

0.35x + 30 - 0.6x = 27.5

0.25x= -2.5

x= -10

Since the number of ounces cannot be negative, the answer is illogical. As a result, you should double-check your calculations or determine if the issue statement contains a mistake.

To get the answer, you can also try an alternative approach like substitution or elimination. Then, double-check your calculations.

\(\large\bf{\underline{We\:have\:to\:find:-}}\)

\(\large\bf{\underline{To \:find\:the\:value\:of\:x}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(⟹4x + 12 = 8\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(⟹4x = 8 - 12\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(⟹4x = - 4\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(⟹x = \frac{ - 4}{4} \)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(⟹x = - 1\)

\(\large\bf{\underline{Putting\:the\:value\:of\:x\:in\:2x+7}}\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(=2x + 7\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(=2( - 1) + 7\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(= - 2 + 7\)

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\(= 5\)

__________________________________________

\(\large\bf{\underline{Hence}}\)

\(\huge{2x + 7}\)

\(\huge{=5}\)

56/120

Step-by-step explanation:

The body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

To express the body mass of the man's two children in terms of their father's body mass, we can use the given ratios.

Let the body mass of the man be x kg.

The first child's body mass is five-sixths of their father's body mass:

Body mass of the first child = (5/6) * x

= 5x/6 kg.

The second child's body mass is four-fifths of their father's body mass:

Body mass of the second child = (4/5) * x

= 4x/5 kg.

Therefore, the body masses of the two children in terms of their father's body mass, x, are:

First child's body mass = 5x/6 kg

Second child's body mass = 4x/5 kg

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All the real values of p such that 2(x - 4)(x - 2p) has a minimum value of -18 over all real values of x is p = 1 and p = -5.

Given that:

2(x + 4)(x - 2p)

It is required to find the values of p such that this expression has a minimum value of -18.

Expand the given expression.

2(x² + 4x - 2px - 8p)

2(x² + (4 - 2p)x - 8p)

2x² + (8 - 4p)x - 16p

The minimum value of the function can be found by first, setting the derivative equal to 0.

Differentiating,

4x + (8 - 4p) = 0

4x = 4p - 8

x = p - 2

Substitute x = p - 2 to the function 2(x + 4)(x - 2p).

When the value of the function is -18,

2(p - 2 + 4)(p - 2 - 2p) = -18

2(p + 2)(-p - 2) = -18

(p + 2)(-p - 2) = -9

(p + 2)² = 9

p + 2 = ±3

When p + 2 = 3, p = 1.

When p + 2 = -3, p = -5.

Hence the p values are 1 and -5.

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Using the order of operations, the expression can be simplified as  

9 + 1.34 + 62.88 = 73.22

The order of operations instructs us on how to solve steps in multi-step expressions. Any operations contained within parenthesis or brackets are first solved. After that, we handle any exponents. Third, we perform all division and multiplication operations from left to right. Fourth, all addition and subtraction problems are solved from left to right.

Remember PEMDAS when simplifying multi-step expressions, i.e.:

P (Parentheses)

E (Exponents, Powers and Square Roots)

MD (Multiplication and Division, left-to-right)

AS (Addition and Subtraction, left-to-right)

The expression given in the problem is:  9 + 1.34 + 1 2 (3.50 +1.74)

Apply the above operation order:

Step 1: solve the addition inside the parenthesis

9 + 1.34 + 1 2 (3.50 +1.74)  =  9 + 1.34 + 1 2 (5.24)

Step 2: Multiply the result by 12

9 + 1.34 + 1 2 (5.24) = 9 + 1.34 + 62.88

Step 3: Apply addition from left to right

9 + 1.34 + 62.88 = 73.22

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The total number of oranges in the basket is 95.

A ratio or value that may be stated as a fraction of 100 is called a percentage. And it is represented by the symbol '%'.

Given:

Of a basket of oranges,

20% of them are defective and 76 are in good condition.

Let x be the total number of oranges.

That means 80% = 76 oranges are in good condition.

20% in decimal form is 0.2.

Applying the percentage formula,

(1 - 0.2)x = 76

0.8x = 76

x = 95

And 20% of 95 = 19

Therefore, the total = 95.

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The reasonable domain for this function is 0 < x < 50

The domain of a function is defined as the set of all the possible input values that are valid for the given function.

The range of a function is defined as the set of all the possible output values that are valid for the given function.

Given;

A = 50W - W2

The area of a rectangle cannot be negative;

The practical domain of A is determined when;

50W-W^2>0

Taking common factor W

W(50-W)>0

Since W must be positive W>0

50-W>0

Or equivalently

50>w

W<50

The total interval is

0<W<50

Therefore, the domain of the function will be 0 < x < 50

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