Bobby drove 10 miles, and
his car used up 5 gallons of
gas. How many miles can
he drive with 16 gallons of
gas?

Answer:

(8+7)x2

Step-by-step explanation:

a)The mean of the sampling distribution is equal to the population mean, so it is 6.04 thousand dollars.

b)Standard deviation \(= 26.5 / \sqrt(15) = 6.830\) thousand dollars.

the probability that the mean daily commissions received is between \(\$561,116\)and \(\$697,016\) is approximately \(99.77\% - 0.01\% = 99.76\%.\)

To solve the given questions, we'll use the properties of the normal distribution.

1. Sampling Distribution:

a) Mean of the sampling distribution of the sample mean daily commissions received:

The mean of the sampling distribution is equal to the population mean, so it is 6.04 thousand dollars.

b) Standard deviation of the sampling distribution of the sample mean daily commissions received:

The standard deviation of the sampling distribution is equal to the population standard deviation divided by the square root of the sample size:

Standard deviation\(= 26.5 / \sqrt(15) = 6.830\) thousand dollars.

2. Probability Calculations:

a) Probability that the mean daily commissions received is more than $581,652:

We'll calculate the z-score using the formula\(\[ z = \frac{{(\$581,652 - \$604)}}{{\left(\frac{{6.830}}{{\sqrt{15}}}\right)}} \approx -3.161 \]\)

Using a standard normal distribution table, we find that the probability is approximately 0.0008, or 0.08%.

b) Probability that the mean daily commissions received is between $561,116 and $697,016:

We'll calculate the z-scores for both values and find the probabilities associated with those z-scores:

\(z_1 = ($561,116 - $604) / (6.830 / \sqrt(15)) = -3.907\)

\(z2 = ($697,016 - $604) / (6.830 / \sqrt(15)) = 2.870\)

Using the standard normal distribution table, we find the probability associated with z1 as approximately 0.0001, or 0.01%, and the probability associated with z2 as approximately 0.9977, or 99.77%.

Therefore, the probability that the mean daily commissions received is between $561,116 and $697,016 is approximately 99.77% - 0.01% = 99.76%.

3. Maximum average daily commissions receivable from the lowest 7.5% volume trading days:

We'll find the z-score corresponding to the lowest 7.5%:

Using a standard normal distribution table, we find the z-score corresponding to the lowest 7.5% as approximately -1.15.

Now we'll find the corresponding value in the original scale:

\(\[ z = \frac{{(x - \mu)}}{\sigma} \]\)

\(-1.15 = (x - 99.7) / 2.9\)

\(x - 99.7 = -1.15 * 2.9\)

\(x - 99.7 = -3.335\)

\(x = 96.365\)

Rounding to the nearest thousand dollars, the maximum average daily commissions receivable is approximately \(\$96,000.\)

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1. a) Mean = $6.04 thousand dollars
  b) Standard deviation = $6.823 thousand dollars
2. a) Probability = 100%
  b) Probability = 100%
3. Maximum average daily commissions receivable = $98,000

1. To determine the mean and standard deviation of the sampling distribution of the sample mean daily commissions received (in thousand dollars), we can use the following formulas:

a) Mean of the sampling distribution = Mean of the population = $6.04
b) Standard deviation of the sampling distribution = Standard deviation of the population / Square root of the sample size

= \(\frac{\$26.5}{\sqrt{15}} = \$6.823\)

2. To find the probabilities, we need to use the z-score formula:

a) To find the probability that the mean daily commissions received is more than $581,652, we first need to find the z-score.

The z-score formula is given by:

\(z = \frac{x - \mu}{\frac{\sigma}{\sqrt{n}}}\),

where x is the value we want to find the probability for, μ is the mean of the population, σ is the standard deviation of the population, and n is the sample size.

z = \(\frac{\$581,652 - \$6.04}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z = 21518.78

Using a standard normal distribution table or a calculator, we find that the probability is approximately 1.

b) To find the probability that the mean daily commissions received is between $561,116 and $697,016, we need to find the z-scores for both values.

z₁ = \(\frac{(\$561,116 - \$6.04)}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z₁ = 20618.03

z₂ = \(\frac{\$697,016 - \$6.04}{\left(\frac{\$26.5}{\sqrt{15}}\right)}\)

z₂ = 25618.23

Using the standard normal distribution table or a calculator, we find that the probability is approximately 1.

3. To find the maximum average daily commissions receivable from the lowest 7.5% volume trading days, we need to find the z-score that corresponds to a cumulative probability of 0.075.

Using the z-score formula and rearranging it to solve for x, we have: \(x = z \cdot \left(\frac{\sigma}{\sqrt{n}}\right) + \mu\)

First, we find the z-score using the standard normal distribution table or a calculator. For a cumulative probability of 0.075, the z-score is approximately -1.405.

Then, we plug in the values to find x:

x = \(-1.405 \cdot \left(\frac{$2.9}{\sqrt{29}}\right) + $99.7\)

x = $98.324

Rounding to the nearest thousand dollars, the maximum average daily commissions receivable from the lowest 7.5% volume trading days is $98,000.

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Answer:

17

Step-by-step explanation:

17

A. Greater than its adjacent interior angle. The measure of an exterior angle of a triangle is always C. greater than either remote interior angle.

An exterior angle is formed by extending one side of a triangle. In a triangle, the exterior angle is equal to the sum of the two remote interior angles (the two angles that are not adjacent to the exterior angle).

Therefore, the exterior angle will always be greater than either one of the remote interior angles.

The exterior angle theorem states that when two sides of a triangle are adjacent, the resulting exterior angle is equal to the sum of the degrees of the two interior angles of the triangle. This theorem can be used to find the measure of an unknown angle in a triangle.

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Answer:

c² - 11c + 30

Step-by-step explanation:

(c - 5)(c - 6)

each term in the second factor is multiplied by each term in the first factor , that is

c(c - 6) - 5(c - 6) ← distribute parenthesis

= c² - 6c - 5c + 30 ← collect like terms

= c² - 11c + 30

The answer is:

\(\sf{c^2-11c+30}\)

Work/explanation:

Remember that to multiply binomials, we use FOIL:

F = first

O = outside

I = inside

L = last

Now multiply.

The first terms are c and c.

\(\sf{(c-5)(c-6)}\)

\(\sf{c^2}\)

Next, we multiply c times -6

\(\sf{-6c}\)

Then, we multiply -5 times c

\(\sf{-5c}\)

Finally, we multiply -5 times -6

\(\sf{-30}\)

Put the terms together

\(\sf{c^2-6c-5c+30}\)

Combine like terms

\(\sf{c^2-11c+30}\)

Answer: 6

Step-by-step explanation:42/7=6

The length of CE is 7cm

To determine the length, we need to consider the properties of a rectangle, we have;

From the information given, we have that;

AB = 7cm

AD = 17cm

Then, line CE = line AB

But line AB = 7cm

CE = 7cm

Hence, the length is 7cm

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The equation for a cosecant function with vertical asymptotes found at x = nπ such that n is an integer is `y = csc(x - nπ)`.

The cosecant function is the reciprocal of the sine function. The cosecant of a particular angle in a right triangle is the ratio of the hypotenuse to the side opposite the angle.

The cosecant function is written as follows: `csc(x) = 1/sin(x)`

Asymptotes are straight lines or curves that a graph approaches but never touches.

As a result, the graph of a curve gets closer and closer to the asymptote as it moves further away from the origin, but it never touches it.

For a function to have vertical asymptotes at `x = nπ`, the denominator of the function should equal zero. In the cosecant function, the denominator is equal to `sin(x - nπ)`.

Therefore, the vertical asymptotes are where `sin(x - nπ) = 0`.

The general form of the cosecant function is `y = A csc(B(x - C)) + D`.

The constants A, B, C, and D are used to alter the form of the graph of the cosecant function.

They can be used to alter the amplitude, period, phase shift, and vertical displacement of the graph, respectively.

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Answer:

  B.  The height of the mural

Step-by-step explanation:

You want to know what (36 3/8)/(12 1/8) represents in the scenario that a mural with area 36 3/8 m² is 12 1/8 m long.

The area of a rectangle is the product of length and height:

  A = LH

Dividing by length gives ...

  A/L = H

The ratio of area to length is the height of the mural, choice B.

<95141404393>

this is the correct answer

ANSWER

EXPLANATION

If the units to represent are all of the same magnitude - like 0.009 and 0.003, we can divide the axis as if we were dividing it for whole units (from 0 to 10) but each mark will represent the whole unit divided by, in this case, 100:

• instead of 1, 0.001

• instead of 2, 0.002

and so on.

If we have also larger units,for example 10, 11, this could be rather difficult to graph, because all the small units will have to lie between 0 and 1 and the difference will be barely noticeable because of the difference in the magnitude of the units.

\(\red{\bold{Answer:}}\)

z1 Multiplied by z1 = z(1 + 1) = z2

\(\color{skyblue}{\boxed{\tt{Final\:Answer}}}\)

= (3•2³x3y2z²)

Looking at the function, there are two sections of the graph, one on the interval [-1, 1) and the other on the interval [1, ∞). On the first interval, the function corresponds to a quadratic function. The endpoints are (-1, 1) and (1, 1), so the function should be:

On the other hand, the second section of the graph is a horizontal parabola, so the function corresponds to a square root function. It passes through the points (1, 1), (4, 2), and (9, 3), so the function should be:

Then, the piecewise function is:

the length of the stringer for the staircase of 6 steps is 199.74 cm.

The sum of the squares of the two sides (a and b) equals to the square of the hypotenuse (c). In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

According to the question,

Each step is 28 cm long that is the length of one step of the staircase. And 18 cm high which is the height of the step at 90-degree angle thus forming a right-angle triangle and the stringer acts as a hypotenuse. Therefore, we can use Pythagoras theorem to find the length of the stringer of one step.

Length=a=28 inch

Breadth=b=18 inch

Applying the Pythagoras theorem, we get

28²+18²= (length of the stringer)²

28²+18²= = 1108  

Now, √1108 = 33.29

to find the length of 6 steps multiply 33.29 with 6

33.29*6 = 199.74

Therefore, the length of the stringer for the staircase of 6 steps is 199.74 cm.

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Answer:

199.7 cm

Step-by-step explanation:

The number of children and adults in swimming pool is 398 and 224.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form;

Ax + B = 0.

We are given that;

Number of people swimming=613

Price of children=$1.75

Price of adults= $2.25

Total= $1184.75

Let, number of children be x

Number of adults be y

Now, the equations will be

x+y=613....1

1.75x+2.25y=1184.75....2

On solving both the equations

X=389, y=224

Therefore, the solution of linear equation will be 389 and 224.

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The complete question is;

on a certain hot Summer's Day 613 people use the public swimming pool the daily prices are $1.75 for children $2.25 for adults the receipts for admission totaled $1184.75 how many children and how many adults when I am at the public for that day​

Answer:

1. For the statement "There are three times as many carrots as potatoes," the algebraic equation would be: c = 3p. This equation represents that the number of carrots (c) is three times the number of potatoes (p).

2. For the statement "There are ten more potatoes than carrots," the algebraic equation would be: p = c + 10. This equation represents that the number of potatoes (p) is equal to the number of carrots (c) plus ten.

3. For the statement "Fifteen is 12 less than three times a number, n," the algebraic equation would be: 3n - 12 = 15. This equation represents that three times the number (3n) minus 12 is equal to 15.

4. For the statement "The difference of 8 and a number n is 5," the algebraic equation would be: 8 - n = 5. This equation represents that 8 minus the number (n) is equal to 5.

5. For the question "A notebook costs $5. How many notebooks can you buy with d dollars?" the algebraic expression would be: d/5. This expression represents the division of the amount of money (d) by the cost of a notebook ($5).

6. For the statement "A rose costs $4 more than a carnation. If a rose costs d dollars, how much does a carnation cost?" the algebraic expression would be: d - 4. This expression represents the subtraction of $4 from the cost of a rose (d) to find the cost of a carnation.

7. For the question "Twenty-four crayons were shared equally among a small group of students in a kindergarten classroom. Let k = the number of kindergarten students in that group. How many crayons did each student receive?" the algebraic expression would be: 24/k. This expression represents the division of the total number of crayons (24) by the number of students in the group (k).

8. For the statement "Each kindergarten student in a small group was given twenty-four crayons. There were k kindergarten students in that group. How many crayons were given to that group of students?" the algebraic expression would be: 24 * k. This expression represents the multiplication of 24 crayons by the number of kindergarten students in the group (k).

9. For the question "Eleven students from one class and x students from another class joined together at recess to form 4 equal-sized teams. How many students were on each team?" the algebraic expression would be: (11 + x)/4. This expression represents the addition of the number of students from the two classes (11 + x) divided by the number of teams (4).

10. For the statement "There were x students in one class who were organized into four equal-sized groups, named Groups A, B, C, and D. Then one student left Group B. How many students remained in Group B?" the algebraic expression would be: (x/4) - 1. This expression represents the division of the number of students in the class (x) by the number of groups (4), and then subtracting one to account for the student who left Group B.

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Answer:

8m

Step-by-step explanation:

Find the volume of the sphere first :

V sphere = \(\frac{4}{3}\) π 6^3 = 902.51

Then use the volume of the sphere to find the height :

Formula = V/π\(r^{2}\)

902.51/π(6)^2 = 8.004 (rounded is 8)

hope this helped :)

Answer:

8 m

Step-by-step explanation:

Given,

Volume of sphere = Volume of cylinder

Radius ( r ) = 6 m

Formula : -

Volume of sphere = 4/3 πr³

Note : -

The value of π is 3.14

Volume of sphere

= 4/3 x 3.14 x 6³

= 4/3 x 3.14 x 6 x 6 x 6

= 904.32 m³

Hence,

The volume of sphere is 904.32 m³.

Since,

Volume of sphere = Volume of cylinder

So,

Volume of cylinder = 904.32 m³

Formula : -

Volume of cylinder = πr²h

πr²h = 904.32

3.14 x 6 x 6 x h = 904.32

113.04 x h = 904.32

Divide 113.04 on both sides,

h = 904.32 / 113.04

h = 8 m

Answer:

x, 4 y, 3, z2

Step-by-step explanation:

We have the expression:

We have to evaluate it for m = 3 and n = -5.

To do that we replace the variables with its values and calculate:

Answer: the value of the expression is -78.

Answer:

For a green and a blue  P1 = 8/11 * 3/10 = (80 * 33) / 110^2 = .218

For a blue and a green  P2 = 3/11 * 8/10 = (30 * 88) / 110^2 = .218

The probabilities are the same

The probability that Sid takes one counter of each color green and blue from the 11 counters in a bag is 48/121.

When two events P(A) and P(B) occurs one time in an event of which occurs two times. Then the probability of occurring exactly one time both events is,

\(P=P(A)\times P(B)+P(B)\times P(A)\)

There are 11 counters in a bag. In which,

Sid takes at random two counters from the bag. Probability that Sid takes green counter is,

\(P(A)=\dfrac{8}{11}\)

The probability that Sid takes blue counter is,

\(P(A)=\dfrac{3}{11}\)

The probability that Sid takes one counter of each color is,

\(P=\dfrac{8}{11}\times\dfrac{3}{11}+\dfrac{3}{11}\times\dfrac{8}{11}\\P=\dfrac{24}{121}+\dfrac{24}{121}\\P=\dfrac{48}{121}\)

Thus, the probability that Sid takes one counter of each color green and blue from the 11 counters in a bag is 48/121.

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The correct statement regarding the rate of change of the functions is given as follows:

The amount of wood required has a constant rate of change, but the amount of glass does not.

The rate of change of a function is obtained as the change in the output of the function divided by the change in the input of the function.

For the wood function, we have that when x is increased by one, the output of the function W(x) is increased by 10, hence the rate of change is constant.

For the glass function, we have that:

Hence the rate of change is not constant, and then the second statement is the correct statement.

The table is given by the image shown at the end of the answer.

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The equation of sphere is x² + 10x + y² - 4y + z² - 12z + 41 = 81.

The collection of all points that are distanced from the centre by a certain amount, or radius, is referred to as a sphere in three dimensions. The shape of a sphere is spherical and symmetrical.

The distances between each surface point and the centre are equal throughout the three dimensions of the solid. It has a surface area and a volume based on its radius. The formula for a sphere's volume is V = 4/3 r3, where r is the radius and V is its volume. Half of a sphere's diameter makes up its radius.

The equation of a sphere with center (x0, y0, z0) and radius r is given by:

(x - x0)² + (y - y0)² + (z - z0)² = r²

So, for a sphere with center (-5, 2, 6) and radius 9, the equation would be:

(x + 5)² + (y - 2)² + (z - 6)² = 9²

which simplifies to:

x² + 10x + y² - 4y + z² - 12z + 41 = 81.

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The information needed to find how much money Mark earned per hour mowing lawns, is the hours that Mark worked to earn that $32

The test of significance difference in average serotonin levels for the two groups of patients suggests that the antidepressant medication has an effect on serotonin levels in the brain.

In statistical hypothesis testing, a statistically significant difference is a result that is unlikely to occur by chance alone. In other words, it suggests that there is a real difference between two groups or conditions being compared, rather than the difference being due to random variation or error.

In this case, the two groups of patients being compared are those who received the antidepressant medication and those who did not. The average serotonin levels were measured for both groups, and the statistical analysis showed that there is a significant difference between the two groups.

However, further analysis and study would be necessary to determine the magnitude and clinical significance of this effect, as well as to rule out any other potential factors that may have influenced the results.

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Tate and Nathan will leave $ 19.48 to the server to cover up the bill and the tip when they go out to dinner at Red Robin.

As given in the question,

Since Tate and Nathan both order burgers for $12.49 each,

Total amount payable is

$12.49 + $12.49= $24.98.

Now 18% tip is equal to

18% of $24.98

(18/100) × 24.98

= $4.4964

= $4.50 (rounded to nearest cent).

Total gross amount payable (including 18% tip) is

24.98 + 4.50 = $29.48.

Now subtracting the birthday coupon for $10.00 off,

the net amount payable in the bill is

29.48 - 10.00

= $ 19.48

= 19.48 cents

Therefore, after using the coupon, they will leave the server $19.48 to cover the bill and the tip.

The complete question is:

Tate and Nathan go out to dinner at Red Robin They both order burgers for $12.49 each. Tate has a birthday coupon for $10.00 off, but the boys want to leave an 18% tip before subtracting the cour

After using the coupon, how much money will they leave the server to cover the bill and the tip? Round to the nearest cent.

a. $14.49

b. $2768

c. $4.79

d.$19.48

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Let's denote this probability as p, where p represents the probability of a single calculator failing. Therefore, the probability of both calculators failing is given by \(p^2\).

If the failure rate of the second calculator is the same and independent of the first, we can assume that the probability of failure for each calculator remains constant. To determine the probability of both calculators failing, we need to multiply the probabilities of each calculator failing independently. Since the events are independent, we can multiply the individual probabilities together.

Probability of both calculators failing = Probability of first calculator failing * Probability of second calculator failing

= p * p

= \(p^2\)

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