9. The cost of delivering packages is $1.70 per package. The fixed cost to run the
delivery truck is $84 per day. If the company charges $7.70 per package delivered, how many
packages must be delivered a day to break even?

The statements which true about the race are: Stuart finishes the race 1 s after Peter finishes the race; and, Stuart is given a 40 yd head start and loses the race. The correct answers are option B and E.

Although part of your question is missing, you might be referring to this full question: The graph shows the results of a race between Peter and Stuart. Both boys begin the race at the same time. Which statements are true about the race? Select each correct answer.

A. Stuart runs a longer race than Peter.

B. Stuart finishes the race 1 s after Peter finishes the race.

C. Stuart runs the race at a faster rate than Peter.

D. Peter is given a 40 yd head start and wins the race.

E. Stuart is given a 40 yd head start and loses the race.

F. Peter runs the race at an approximate rate of 4.6 yd/s.

As can be seen on the Graph attached:

So, the justification for each statement:

A. Stuart runs a longer race than Peter.

This statement is false, because Peter runs a longer race than Stuart. Peter > Stuart = 100 > 60.

B. Stuart finishes the race 1 s after Peter finishes the race

This statement is true, because Stuart finished the race in 13 secs and Peter finished the race in 12 secs. Peter – Stuart = 13 – 12 = 1. Thus, Stuart finishes the race 1 s after Peter finishes the race.

C. Stuart runs the race at a faster rate than Peter.

This statement is false, because Stuart’s speed = 60 / 13 = 4.62 yard/sec, while Peter’s speed = 100 / 12 = 8.33 yard/sec. Thus, Peter runs the race at a faster rate than Stuart.

D. Peter is given a 40 yd head start and wins the race.

This statement is false, because Peter wins the race but Peter is not given a 40 yd head start.

E. Stuart is given a 40 yd head start and loses the race.

This statement is true, because Stuart loses the race and Stuart is given a 40 yd head start.

F. Peter runs the race at an approximate rate of 4.6 yd/s.

This statement is false, because Stuart runs the race at an approximate rate of 4.6 yd/s, while Peter runs the race at an approximate rate of 8.3 yd/s.

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Answer:

The p-value of the test is 0.9918 > 0.05, which means that we fail to reject \(H_0\), as we do not have enough evidence to say that defect rate of machine is smaller than 3%.

Step-by-step explanation:

The null and alternate hypothesis are:

H0:p≥0.03

Ha:p<0.03

The test statistic is:

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

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.03 is tested at the null hypothesis:

This means that \(\mu = 0.03, \sigma = \sqrt{0.03*0.97}\)

28 out of 600 items produced by the machine were found defective.

This means that \(n = 600, X = \frac{28}{600} = 0.0467\)

Value of the test-statistic:

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

\(z = \frac{0.0467 - 0.03}{\frac{\sqrt{0.03*0.97}}{\sqrt{600}}}\)

\(z = 2.4\)

P-value of the test:

The p-value of the test is the probability of finding a sample proportion below 0.0467, which is the p-value of z = 2.4.

Looking at the z-table, z = 2.4 has a p-value of 0.9918.

The p-value of the test is 0.9918 > 0.05, which means that we fail to reject \(H_0\), as we do not have enough evidence to say that defect rate of machine is smaller than 3%.

Answer:

It is 3 15/28.

Step-by-step explanation:

To solve this problem, we first need to add the whole numbers: 2 + 1 = 3. Next, we need to add the fractions. To do this, we need to find a common denominator for the fractions 2/7 and 1/4. A common denominator for these two fractions is 28, so we can convert the fractions to equivalent fractions with a denominator of 28: 2/7 is equivalent to 8/28 and 1/4 is equivalent to 7/28. With the fractions written in this form, we can add them to get 8/28 + 7/28 = 15/28.

Finally, we need to add the whole number 3 and the fraction 15/28 to get our final answer. To do this, we need to convert the fraction 15/28 to a mixed number. We can do this by dividing 15 by 28 to get a quotient of 0 and a remainder of 15. This means that the mixed number equivalent of 15/28 is 0 + 15/28. Therefore, our final answer is 3 + 0 + 15/28 = 3 + 15/28 = 3 15/28. This is the simplest form of the mixed number, so our final answer is 3 15/28.

Answer:

B

Step-by-step explanation:

given scale is 1 inch represents 7.5 feet

then we require to calculate how many 7.5 feet there are in each dimension.

to obtain this divide each dimension by 7.5, that is

13 ÷ 7.5 ≈ 1.73 ( to 2 decimal places )

26 ÷ 7.5 ≈ 3.47 ( to 2 decimal places )

then dimensions are approximately 1.73 inches by 3.47 inches

Answer: 0.771 you are welcome

The volume of the solid to be 1/3 cubic units.

Volume is a physical quantity that refers to the amount of three-dimensional space occupied by an object or a substance.

Now, we can integrate the areas of the square cross-sections over the interval of y-values that correspond to the region enclosed by the two curves. The limits of integration will be y = 0 (the x-axis) and y = 1, since these are the y-values that define the region.

The integral that represents the volume of the solid is given by:

V = ∫[0,1] (1 - x²)² dy

We can simplify this expression by expanding the square and then integrating:

V = ∫[0,1] (1 - 2x² + x⁴) dy

= ∫[0,1] (1 - 2y + y²) dy

= [y - y²/2 + y³/3] evaluated from 0 to 1

= 1/3

Therefore, the volume of the solid is 1/3 cubic units.

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Complete Question:

Find the volume of the solid whose base is the region enclosed by y=x² and y=1, and the cross sections perpendicular to the y-axis are squares.

Answer:

Step-by-step explanation:

(1\2, 4) = (0.5, 4)

Answer:

c is correct

Step-by-step explanation:

The equation that represents this fraction is 1 ÷ 6 =1/6. Therefore, option C is the correct answer.

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given that, a cake is cut into 6 equal-sized pieces. Each piece is one sixth of the whole.

The equation is 1 ÷ 6 =1/6

Therefore, option C is the correct answer.

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Answer:

the answer is 122

Step-by-step explanation:

Answer:

60°

Step-by-step explanation:

Alternate angle theorem applies here as the triangle in between will have an upper angle of 60 therefore x will be 60 as well.

Answer:

  2x^2 -4x +5 +8/(4x -1)

Step-by-step explanation:

You want to divide 8x^3-18x^2+24x+3 by 4x-1 using polynomial long division.

Polynomial long division is similar to numerical long division, except that the quotient term is always the ratio of the leading dividend term to the leading divisor term.

As with numerical long division, the dividend at each step is reduced by the product of the quotient term and the divisor.

When the dividend is of lower degree than the divisor, the division is finished. That dividend is the remainder.

The attachment shows the division in detail. Your result is ...

  q(x) +r(x)/b(x) = (2x^2-4x+5) +(8)/(4x-1)

Answer:

790

Step-by-step explanation:

7098uuilu4645

a) Probability of occurrence of evant A is equals to the 7/10.

P(not getting a white or a blue shirt), P(Aᶜ ) is equals the 3/10.

Probability of occurrence of evant B is equal to the 1/2.

b) The events A and B are not mutually exclusive

c) Mike's preference is to getting a white shirt with his size L.

We have a probabality based problem. Probability is defined as chance of occurrence of an event or result. It can be calculate as favourable outcomes divided by total possible outcomes. There is total number of avaliabile shirts = 20 i.e., total possible outcomes = 20

Mike is interested in getting a white or a blue shirt in size L. Let us consider two events :

A : Getting a white or a blue shirt

B: Getting a shirt in size L

a) Number of favourable outcomes to getting white or a blue shirt = 9 white or 5 blues

Probability ( Getting a white or a blue shirt) , P(A)

= 9/20 + 5/20 + 0 = 14/20 = 7/10

P(not Getting a white or a blue shirt), P(Aᶜ )

= 1 - P(A) = 1 - 7/10 = 3/10

ii) The number of favourable outcomes for event B, n(B) = 10

So, Probability of getting a shirt in size L, P(B)

= 10/20 = 1/2

b) Mutually exclusive events are defined as the events that can't happen at the same time. In other words AnB = 0 . Here, we see there is total 14 shirts which are in white or blue colors and 10 are in size L , So there is possibility that shirt is white or blue in colour and in size L , i.e, An B ≠0

So, events A and B are not mutually exclusive.

c) Event ,n( A u B )= n(A) + n(B) - n(A n B)

On the basis of all details, we conclude that Mike's preference is to choose white shirt with size L .

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Solution

The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

We have to given that;

The table below shows the ratios of boxed donuts to the cost.

Donuts    A       4        5     C

Cost    13.80  27.60   B   55.20

Now, By definition of ratio, we get;

⇒ A / 13.80 = 4 / 27.60

⇒ A = 13.80 × 4 / 27.60

⇒ A = 2.00

And,

⇒ 4 / 27.60 = 5 / B

⇒ B = 5 × 27.60 / 4

⇒ B = 34.5

⇒ 4 / 27.60 = C / 55.20

⇒ C = 55.20 × 4 / 27.60

⇒ C = 8

Thus, The table with correct values of A, B and C is,

⇒ Donuts   2        4        5        8

    Cost     13.80 27.60 34.50 55.20

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Answer:

a

Step-by-step explanation:

i took the test :)

Answer:

140

Step-by-step explanation:

First we would find the unit rate of students per seventh. So we would do 40 divided by 2 which gives us 20. So per 1/7 we have 20 students. Which we can then say 7 x 20 = 140. So in total there are 140 students

Hope this helped

The tables which shows a proportional relationship between x and y are table 3 and table 4.

Using ratio to find the proportional relationship

Table 1

x : y = 8 : 8

= 1 : 1

x : y = 12 : 10

= 6 : 5

Not proportional

Table 2:

x : y = 2 : 3

x : y = 3 : 8

Not proportional

Table 3:

x : y = 5 : 3

x : y = 10 : 6

= 5 : 3

Proportional

Table 4:

x : y = 4 : 1

x : y = 16 : 4

= 4 : 1

Proportional

Ultimately, table 3 and table 4 shoes a proportional relationship between x and y.

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To find the common roots between two functions, we need to find the roots (or solutions) of each function individually and then identify the shared solutions.

For the function f(x) = x^2 + x - 6, we can find the roots by setting the function equal to zero and solving for x:

x^2 + x - 6 = 0

To factorize this quadratic equation, we need to find two numbers that multiply to -6 and add up to 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2:

(x + 3)(x - 2) = 0

Setting each factor equal to zero:

x + 3 = 0 or x - 2 = 0

Solving for x in each equation:

x = -3 or x = 2

Therefore, the function f(x) = x^2 + x - 6 has two roots: x = -3 and x = 2.

To find the common roots between this function and another function, we would need to know the second function. If you provide the second function, I can help determine if there are any shared roots.

Answer:

3/4

Step-by-step explanation:

0.75

multiply the numerator and denominator by 100.

0.75 x 100 / 1 x 100 = 75/100

75/100

Simplify 75/100

=> 3/4

hope this helps!! p.s. i really need brainliest :)

Then, multiply this result by 100 to get the percentage. In this case, 120 is 80% of 150.

To use a double number line diagram to find what percent 120 is of 150, you need to create a diagram with two parallel lines. On the top line, mark 150 at one end and 100 at the other.

On the bottom line, mark 120 at one end and leave the other end blank. Then, draw diagonal lines connecting 120 on the bottom line to 150 on the top line and 100 on the top line to the blank end of the bottom line.

This creates two triangles. The height of the triangle with 120 is the percentage you're looking for.

To find this percentage, divide the length of the diagonal line connecting 120 and 150 by the length of the diagonal line connecting 100 and the blank end of the bottom line.

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The value of x in the polygon will be 13.25 degrees.

The value of x is 10.

We can find the value of x by plugging in the number of sides of the regular polygon into the formula x = (n-2)*15° - 1.

The sum of the interior angles of a regular polygon with n sides is (n-2) x 180 degrees.

Sum of angles = (24-2) x 180 = 22 x 180 = 3960 degrees

Since all the angles in a regular polygon are congruent, we can divide the sum of the angles by the number of angles to find the measure of one angle:

Measure of one angle = 3960/24 = 165 degrees

165 = 12x + 6

159 = 12x

x = 13.25

Therefore, the value of x is 13.25 degrees.

Each of the triangles in our decomposition has one angle equal to (17x+2)°, so the sum of all the angles in the triangles is 43 × (17x+2)° = 731x+86°.

Therefore, we have:

731x+86° = 7380°

Solving for x, we get:

731x = 7294°

x = 10

Therefore, the value of x is 10.

The equation that can be used to find the value of x is:

(9x+48)° + (15x-24)° = (n-2)*180°

24x + 24 = (n-2)*180°

Dividing both sides by 24, we get:

x + 1 = (n-2)*15°

Subtracting 1 from both sides, we get:

x = (n-2)*15° - 1

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To prove that line segment a is parallel to line segment d, based on the given information, we can utilize the properties of perpendicular and parallel lines.

Given that a is perpendicular to b and b is perpendicular to c, we know that angles formed between a and b, as well as between b and c, are right angles. Let's denote these angles as ∠1 and ∠2, respectively.

Now, since c is parallel to d, we can conclude that the corresponding angles ∠2 and ∠3, formed between c and d, are congruent.Considering the fact that ∠2 is a right angle, it can be inferred that ∠3 is also a right angle.

By transitivity, if ∠1 is a right angle and ∠3 is a right angle, then ∠1 and ∠3 are congruent.Since corresponding angles are congruent, and ∠1 and ∠3 are congruent, we can deduce that line segment a is parallel to line segment d.

Thus, we have successfully proven that a is parallel to d based on the given information and the properties of perpendicular and parallel lines.

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Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer: 4b

Explanation:

From the information given,

the book case has 4 shelves. If there are b books on each shelf, an expression for the total number of books is

4 * b

= 4b

Answer: where is the answer choices

Step-by-step explanation: