The table to the right shows the volume discounts offered by a​ company, where x is the volume of a purchase in dollars. Assume that the volume discounts in the table apply to the entire purchase. That​ is, if the volume x satisfies $300≤x<$1,000​, the entire purchase is discounted 4%. Answer ​a) and ​b) below.
$300≤x<$1,000
$1,000≤x<$3,000
$3,000≤x<$5,000
$5,000≤x
4%
5%
6%
10%

Volume Discount
(Excluding tax)
Volume($x)
Discount Amount
Question content area bottom
Part 1
​a) If x is the volume of a purchase before the discount is​ applied, write a piecewise definition for the discounted price​ D(x) of this purchase.
D(x)= x if 0≤x<300 enter your response here if 300≤x<1,000 0.95x if 1,000≤x<3,000 enter your response here if 3,000≤x<5,000 0.90x 5,000≤x

Answer:

1. The margin of error is of 66.96 square feet.

2. The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet

Step-by-step explanation:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 22 - 1 = 21

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 21 degrees of freedom(y-axis) and a confidence level of \(1 - \frac{1 - 0.95}{2} = 0.975\). So we have T = 2.08

The margin of error is:

\(M = T\frac{s}{\sqrt{n}} = 2.08*\frac{151}{\sqrt{22}} = 66.96\)

In which s is the standard deviation of the sample.

The margin of error is of 66.96 square feet.

The lower end of the interval is the sample mean subtracted by M. So it is 1500 - 66.96 = 1433.04 square feet

The upper end of the interval is the sample mean added to M. So it is 1500 + 314 = 1566.96 square feet

The 95% confidence interval estimate for the population mean using the Student's t-distribution is between 1433.04 square feet and 1566.96 square feet

i think 10 more miles.

70/7=10

which means he gets 10 more miles for every gallon of fuel

Solution

Two angles are called supplementary when their measures add up to 180 degrees

Therefore, the answer is

if 40 is the least frequent multiple of two whole numbers. The higher number to lesser number ratio is 4:5. The two digits after that are 8 and 10.

Least Common Multiple is the meaning of the abbreviation LCM.

The lowest number that may be divided by both numbers is known as the least common multiple (LCM) of two numbers.

It can also be computed using two or more numbers.

Finding the LCM of a given collection of numbers can be done in a variety of ways.

Utilizing the prime factorization of each number and then calculating the product of the greatest powers of the shared prime factors is one of the quickest techniques to determine the LCM of two numbers.

In mathematics, the least common multiple is sometimes referred to as LCM or the lowest common multiple.

The smallest number among all numbers is called the least common multiple of two or more numbers.

According to our question-

The number LCM is equal to 40.

4 × 5 × x = 40

20 × x = 40

20x=40

x=2

The larger number is equal to 4 x=4(2)=8.

The smaller value is =5x=5(2)=10.

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Complete question-

The least common multiple of two whole numbers is 40. The ratio of the greater number to the lesser number is 4:5. What are the two numbers?

Answer: 5.49 × 10-4

Step-by-step explanation:

When you move the decimal over move it over to the right by 4 units.

When you move right it is (-) negative. So you get 5.49 x 10-4.

The natural numbers less than or equal to 8 are :

U = {1, 2, 3, 4, 5, 6, 7, 8}

The even factors of 8 are :

B = {2, 4, 8}

Note that the complement of B is the set of elements in U that is NOT in B.

This will be :

B' = {1, 3, 5, 6, 7}

The answer is B. {1, 3, 5, 6, 7}

Answer:

x = 127

Step-by-step explanation:

\( 7 - \sqrt[3]{2 - x} = 12 \)

\( \sqrt[3]{2 - x} = -5 \)

\( (\sqrt[3]{2 - x})^3 = (-5)^3 \)

\( 2 - x = -125 \)

\( -x = -127 \)

\( x = 127 \)

g(x) = -2√x + 8 is the function that has the same range as f(x) = -2√(x - 3) + 8. Both functions have the range of y ≤ 8

The function that has the same range as f(x) = -2√(x - 3) + 8 is g(x) = -2√x + 8. Both functions have the range of y ≤ 8.There are a few steps involved in determining which function has the same range as f(x) = -2√(x - 3) + 8. The range of a function refers to all the possible output values that the function can produce.Let's begin by examining the original function:f(x) = -2√(x - 3) + 8The square root symbol (√) implies that x-3 must be greater than or equal to 0. If x-3 is negative, then the function would produce an imaginary result.

Let's solve for x when f(x) = 0:0 = -2√(x - 3) + 8-8 = -2√(x - 3)4 = √(x - 3)16 = x - 3x = 19This tells us that the x-value that produces an output of 0 is x = 19. To determine the range, we need to find the maximum and minimum output values. We can use a graphing calculator or sketch a graph to determine the shape of the function and the range.The shape of the function suggests that the range is y ≤ 8, which means that the maximum value of the function is 8. This tells us that any function with the same maximum output value of 8 will have the same range as f(x).

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The probability that both players show rock in the first round is 1/9 or 0.1111 (rounded to four decimal places).

In rock, paper, scissors there are three possible outcomes for each player: rock, paper, or scissors. Assuming both players choose randomly and independently of each other, each player has a 1/3 chance of showing rock in the first round.

To find the probability that both players show rock in the first round, we can use the multiplication rule of probability for independent events. The multiplication rule states that the probability of the intersection of two independent events is the product of their probabilities.

Therefore, the probability that both players show rock in the first round can be calculated as follows:

P(both show rock) = P(player 1 shows rock) x P(player 2 shows rock) P(both show rock) = 1/3 x 1/3 P(both show rock) = 1/9

So the probability that both players show rock in the first round is 1/9 or approximately 0.111.

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Answer:

3n+4

Step-by-step explanation:

four more than three times a number.

3n + 4

The function that represents the dotted line of the graph using transformation rules is; f(x - 1) - 4.

For the function f(x) of the given graph,  when we look at the solid line, we see that it has a root at x = -1 which means it has a zero at x = -1.

However, when observing the dashed line, we see that it has a root at x = 0 which means it has a zero at x = 0.

Thus, we can  deduce from transformation rules that the function was moved by 1 unit to the right to get the new function.

Secondly, we observe that the dashed line is also below the function f(x), and we observe further that 4 was subtracted. Therefore, when we use the transformation rules again for subtracting from a function, we get the final function as; f(x - 1) - 4.

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Answer:

Graph A bc it's the only graph that shows that every 3 years his investment doubles.

Answer:

xy(3x+10)(3x-10)

Answer:

A

Step-by-step explanation:

the answer would be a because it is shown more than the others

Answer:

34(8)

Step-by-step explanation:

Twenty standard cartons of octal boxes weigh a total of 1,100 pounds. The weight per carton is 55 pounds.

Given that twenty standard cartons of octal boxes weigh a total of 1,100 pounds. We need to find the weight per carton.

How to find the weight per carton? To find the weight per carton, we need to divide the total weight of twenty standard cartons of octal boxes by 20.Let's assume the weight of each carton be x.

Therefore, the equation can be formed asx * 20 = 1,100 Solving the above equation for x, x = 1,100/20 Therefore, the weight per carton is 55 pounds. So, twenty standard cartons of octal boxes weigh a total of 1,100 pounds.

The weight per carton is 55 pounds.

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The body surface area is given by the equation A = 1.6865 m²

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the body surface area be represented as A

Now , the equation will be

A = ( HW / 3600 )^1/2

A = √( HW / 3600 )   be equation (1)

where H is the height in centimeters and W is the weight in kilograms

Now , the value of H = 160 cm

The value of W = 64 kg

Substituting the values in the equation , we get

A = √ [ ( 160 x 64 ) / 3600 ]

On simplifying the equation , we get

A = √ ( 10240/3600 )

A = √ ( 2.8444 )

A = 1.6865 m²

Therefore , the body surface area is 1.6865 m²

Hence , the equation is A = 1.6865 m²

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Answer:

A

Step-by-step explanation:

area of the triangle is 5 x 2/ 2 which is 5

area of the square is 25

area of the semi circle is 1/2 * 3.14 * 2.5^2 which is 9.8125

9.8125. + 25 + 5 = 39.8125

Answer:

AB = 28 , BC = 17.5 , X = 13.2

Step-by-step explanation:

since the figures are similar then the ratios of corresponding sides are in proportion, that is

\(\frac{AB}{PQ}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{AB}{8}\) = \(\frac{14}{4}\) ( cross- multiply )

4 AB = 8 × 14 = 112 ( divide both sides by 4 )

AB = 28

and

\(\frac{BC}{QR}\) = \(\frac{AD}{PS}\) ( substitute values )

\(\frac{BC}{5}\) = \(\frac{14}{4}\) ( cross- multiply )

4 BC = 5 × 14 = 70 ( divide both sides by 4 )

BC = 17.5

similarly for the 2 similar figures

\(\frac{x}{6}\) = \(\frac{11}{5}\) ( cross- multiply )

5x = 6 × 11 = 66 ( divide both sides by 5 )

x = 13.2

Answer:

\(\overline{AB}=28\)

\(\overline{BC}=17.5\)

\(x=13.2\)

Step-by-step explanation:

If quadrilateral PQRS is similar to quadrilateral ABCD, their corresponding sides are in the same ratio:

\(\overline{PQ} : \overline{AB} = \overline{QR} : \overline{BC} = \overline{RS} : \overline{CD} = \overline{SP}:\overline{DA}\)

From inspection of the two quadrilaterals, the given side lengths are:

\(\overline{PQ} = 8\)

\(\overline{QR} = 5\)

\(\overline{RS} = 6\)

\(\overline{SP} = 4\)

\(\overline{DA} = 14\)

Substitute these into the ratio equation:

\(8 : \overline{AB} = 5 : \overline{BC} = 6 : \overline{CD} = 4:14\)

Solve for AB:

\(8 : \overline{AB} = 4:14\)

   \(\dfrac{8}{\overline{AB}}= \dfrac{4}{14}\)

 \(8 \cdot 14=4 \cdot{\overline{AB}}\)

   \(\overline{AB}=\dfrac{8 \cdot 14}{4}\)

  \(\boxed{\overline{AB}=28}\)

Solve for BC:

\(5 : \overline{BC} = 4:14\)

  \(5 \cdot 14=4 \cdot \overline{BC}\)

    \(\overline{BC}=\dfrac{5 \cdot 14}{4}\)

   \(\boxed{\overline{BC}=17.5}\)

\(\hrulefill\)

Assuming the two figures are similar, their corresponding sides are in the same ratio. Therefore:

\(x:6=11:5\)

   \(\dfrac{x}{6}=\dfrac{11}{5}\)

   \(x=\dfrac{11 \cdot 6}{5}\)

   \(x=\dfrac{66}{5}\)

  \(\boxed{x=13.2}\)

Answer:

The 10-yard line on a football field

Step-by-step explanation:

A geometric line segment is a straight path of points(that is a line) that has two end points (that is a beginning and an end). A 10 yard line on a football field is a line segment because it has two endpoints which is at the beginning of the 10 yard and at the end of the 10 yard.

A scientist's line of vision as he looks into space with a telescope is not a line segment because it extends forever (has no end).

A line of 15 dancers on stage is not a line segment, A light shone into the darkness is not a line segment because it continues forever and also, the hands of a clock is also not a line segment.

The probability of landing on the dark blue target is 2/5.

Probability is the ratio of required to the total possible outcomes of an event.

P(dark blue ) = 40/100

divide through by 20

P(dark blue ) = 2/5

Therefore, the probability of landing on target is 2/5

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The dimension of the largest possible map would be \(6\frac{2}{3}\)   inches by 10 inches.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

We know that 1 feet=12 inches

2 feets = 2 × 12 = 24 inches

3 feets = 3 × 12 = 36 inches

Scale factor = 24 / 36 = 2/3

Longer side of the paper = 10 inches

Using the scale to obtain the length of the shorter side:

2/3 = x/10

Apply cross multiplication

20=3x

x=20/3

x= \(6\frac{2}{3}\) inches

Hence, the dimension of the largest possible map would be \(6\frac{2}{3}\)   inches by 10 inches.

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The distribution is bimodal (a), eight men weigh less than 150 lbs (b), and the percentage of males that weigh more than 230 lbs is 3.17%.

A: Distribution: The distribution can be classified as bimodal, which means there are two peaks in the graph.

B. The number of males that weigh less than 150 lbs can be determined as follows:

110 - 120 lbs = 2 males

130 -140 lbs = 2 males

140 - 150 lbs = 4 males

2 + 2 + 4 = 8 males

C. The percentage of males that weigh more than 230 lbs can be calculated as follows:

63 = 100%

2   = x

x= 2 x 100 / 63

x = 200 / 63 = 3.17%

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Answer:

(0, 14)

Step-by-step explanation:

The point (0, -2) is 8 spaces away from the reflection line of y = 6, so just count 8 spaces up from the reflection line.

:)

Answer:

The inequality is 25+8.50w≥122

We have shown that C is the image of A by dilation with center B and ratio 3.

Now, To show that C is the image of A by dilation with center B and ratio 3, we need to follow these steps:

Firstly, Find the vector AB by subtracting the coordinates of B from the coordinates of A:

AB = A - B = (6 - 3, 4 - 7) = (3, -3)

Multiply the vector AB by the dilation ratio of 3:

3 AB = 3 (3, -3)  = (9, -9)

Add the resulting vector to the coordinates of the center B:

BC = B + 3 AB = (3, 7) + (9, -9)

BC = (12, -2)

Hence, Compare the resulting point BC to the coordinates of C to show that they are the same:

BC = (12, -2) = C

Therefore, we have shown that C is the image of A by dilation with center B and ratio 3.

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The solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

Given the inequality,

    f(x²-2) < f(7x-8) over D₁ = (-∞, 2)

We need to find the values of x that satisfy this inequality.

Since we know that f is increasing over its domain, we can compare the values inside the function to determine the values of x that satisfy the inequality.

First, we can find the values of x that make the expressions inside the function equal:

x² - 2 = 7x - 8

Simplifying, we get:

x² - 7x + 6 = 0

Factoring, we get:

(x - 6)(x - 1) = 0

So the values of x that make the expressions inside the function equal are x = 6 and x = 1.

We can use these values to divide the domain (-∞, 2) into three intervals:

-∞ < x < 1, 1 < x < 6, and 6 < x < 2.

We can choose a test point in each interval and evaluate

f(x² - 2) and f(7x - 8) at that point. If f(x² - 2) < f(7x - 8) for that test point, then the inequality holds for that interval. Otherwise, it does not.

Let's choose -1, 3, and 7 as our test points.

When x = -1, we have:

f((-1)² - 2) = f(-1) < f(7(-1) - 8) = f(-15)

Since f is increasing, we know that f(-1) < f(-15), so the inequality holds for -∞ < x < 1.

When x = 3, we have:

f((3)² - 2) = f(7) < f(7(3) - 8) = f(13)

Since f is increasing, we know that f(7) < f(13), so the inequality holds for 1 < x < 6.

When x = 7, we have:

f((7)² - 2) = f(47) < f(7(7) - 8) = f(41)

Since f is increasing, we know that f(47) < f(41), so the inequality holds for 6 < x < 2.

Therefore, the solution to the inequality f(x²-2) < f(7x-8) over D₁ = (-∞, 2) is:

-∞ < x < 1 or 1 < x < 6 or 6 < x < 2

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Answer:

-7

Step-by-step explanation:

Tiger Woods was 15 under par after the third round of a golf tournament, but was 8 over par for the fourth round. So, his score for the entire tournament was -15 + 8 = -7 (That is, 7 under par).

hi

because it lead to mathematical nonsense

3x-7  = 3x+5

3x-7 -3x-5 = 0

    -7-5 = 0

    -12 =0  

-12 = 0 is just not possible, so 3x-7 = 3x +5  has no solution.