What is the formula for the volume of a rectangular prism?

Answer:

(3, -1).

Step-by-step explanation:

f(x)=x^2-6x+8

Convert to vertex form by completing the square:

f(x) = (x - 3)^2 - 9 + 8

     = (x - 3)^2 -1

So the vertex is at (3, -1).

Answer:

(a)

[tex]W^2+4W-165=0[/tex]

(b)

Width: 11 feet

Length: 15 feet

Step-by-step explanation:

Given:

Width (W) = W ft

Length (L) = (4 + W) ft

Area (A) = 165 ft^2

(a)

The area of a rectangle is equal to the product of its length and width, therefore:

       [tex]A=L\times W[/tex]

      [tex]\text{We replacing}[/tex]

[tex]165=(4+W)\times(W)[/tex]

   [tex]4W+W^2=165[/tex]

[tex]W^2+4W-165=0[/tex]

(b)

We solve the equation by factoring:

        [tex]W^2+4W-165=0[/tex]

       [tex]4W=-11W+15W[/tex]

[tex]W^2-11W+15W-165=0[/tex]

[tex]W(W-11)+15(W-11)=0[/tex]

     [tex](W-11)(W-15)=0[/tex]

    [tex]W-11=0\rightarrow W=11[/tex]

   [tex]W+15=0\rightarrow W=-15[/tex]

The width of the rectangle is equal to 11 feet and the length of the rectangle is equal to 15 feet.

Answer:

45

Step-by-step explanation:

Answer:

45

Step-by-step explanation:

Answer:

The gain is 139.

Step-by-step explanation:

34.95x25= 873.75

29.39x25= 734.75

873.75- 734.75= 139

The test statistic is z = 0.68, and the p-value is approximately 0.2486.

This problem involves testing the hypothesis that the proportion of union workers in the population has increased from 11.5%.

Let p be the true proportion of union workers in the population.

The null hypothesis is H0: p = 0.115, and the alternative hypothesis is Ha: p > 0.115 (one-tailed test, since we are testing for an increase in union membership).

To find the test statistic, we use the formula for a z-test for proportions:

z = ([tex]\bar p[/tex] - p) / [tex]\sqrt{(p(1-p)/n) }[/tex]

where, [tex]\bar p[/tex] is the sample proportion, n is the sample size, and sqrt denotes the square root function.

In this case, [tex]\bar p[/tex] = 36/300 = 0.12, n = 300, and p = 0.115.

Substituting these values into the formula, we get:

z = (0.12 - 0.115) / [tex]\sqrt{(0.115(1-0.115)/300) }[/tex]≈ 0.68

To find the p-value, we need to find the probability of getting a test statistic as extreme or more extreme than 0.68, assuming that the null hypothesis is true (i.e., assuming that p = 0.115).

Since this is a one-tailed test, we need to find the area under the standard normal curve to the right of 0.68:

p-value = P(Z > 0.68) ≈ 0.2486

Using a standard normal distribution table or a calculator, we find that the area to the right of 0.68 is approximately 0.2486.

Therefore, the p-value for the test is approximately 0.2486.

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Question: You may need to use the appropriate appendix table or technology to answer this question. An agency reports that historically 11.5% of workers in a particular country belong to unions. Suppose a sample of 300 workers is collected to determine whether union efforts to organize have increased union membership.                                                                                                                                                                                                       If the sample results show that 36 of the workers belonged to unions, what is the p-value for your hypothesis test? Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = ?

The total health care expenditures in year x would be equal to the product of the percentage of income spent on health care (P(x)) and the income (I(x)) in year x. Therefore, the function H can be expressed as:

H(x) = P(x) * I(x)

This function takes into account both the amount spent on health care as well as the income level, providing a comprehensive representation of health care expenditures.

Step-by-step explanation:

that depends on the result dimension of P(x).

if P(x) delivers the percentage in the form xx.xx%, then

H(x) = I(x) × P(x) / 100

if P(x) delivers the percentage in the form 0.xxxx, then

H(x) = I(x) × P(x)

very basically, the absolute amount of a percentage of a whole is the product between both (and divided by 100).

e.g.

let's say, the whole amount is $64,000.

and we need to know 10% of that.

10% of 64,000 is then

64,000 × 10 / 100 = 6,400

or

64,000 × 0.10 = 6,400

can you see the connection, and why both versions do the same ?

Answer:

1) ABE is NOT SIMILAR to DBC

2) FPG is SIMILAR to FGH (AAA)

3) CAN is SIMILAR to HLV (SAS)

4) QRP is SIMILAR to XYP (SSS)

Step-by-step explanation:

1) ABE is NOT SIMILAR to DBC

Since DC and AE are not parallel

2) FPG is SIMILAR to FGH (AAA)

QPF = 180 - 93

QPF = 87

PQF = 180 - 63 - 87

PQF = 30

PQF = GHF

FGH = 180 - 63 - 30

FGH = 87

FGH = QPF

GFH = PFQ

3) CAN is SIMILAR to HLV (SAS)

63 = [tex]x[/tex] x 42

[tex]x[/tex] = 1.5

51 = [tex]x[/tex] x 34

51 = 1.5 x 34

51 = 51

Hypotenuse of CAN = 1.5 x Hypotenuse of HLV

4) QRP is SIMILAR to XYP (SSS)

10 = [tex]x[/tex] x 8

[tex]x[/tex] = 1.25

(20 + 5) = 1.25 x XY

XY = 20

(24 + 6) = 1.25 x XP

XP = 24

Answer:

you would put a solid circle on the 3 and go to the left, for example:

Step-by-step explanation:

You would want the variable to be on the left, so you would need to see that the 3 is bigger or equal to a.

Answer:find the root of 6

Step-by-step explanation:

The solutions in the interval [0, 2) are:

x = 0 and x = 2π/3.

What is the trigonometric ratio?

The trigonometric functions are real functions that relate an angle of a right-angled triangle to ratios of two side lengths. They are widely used in all sciences that are related to geometry, such as navigation, solid mechanics, celestial mechanics, geodesy, and many others.

Using the identity cos2θ = cos²θ - sin²θ, we can rewrite the equation as:

cos²x - sin²x = cos x

We can then use the Pythagorean identity sin² x + cos² x = 1 to substitute for sin² x:

cos²x - (1 - cos²x) = cos x

Simplifying this equation gives:

2cos² x - cos x - 1 = 0

We can solve for cos x using the quadratic formula:

cos x = [1 ± √(1 + 8)] / 4

cos x = [1 ± √9] / 4

cos x = (1 ± 3) / 4

cos x = 1 or cos x = -1/2

If cos x = 1, then x = 0.

If cos x = -1/2, then x = 2π/3 or x = 4π/3.

However, we need to check that these solutions are in the interval [0, 2). The solution x = 4π/3 is outside this interval, so we discard it.

Therefore, the solutions in the interval [0, 2) are:

x = 0 and x = 2π/3.

In increasing order, the solutions are:

x = 0 and x = 2π/3.

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The answer is 6√5

In 3√5 and 3√5, √5 is multiplied with 3 in both terms,

∴ 3 is the common factor

∴ 3√5+3√5= 3(√5+√5)

                   = 3×2√5

                   = 6√5

Hence the answer is 6√5

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The lower class boundary for the first class is 122.5.

Data was collected for 300 fish from the North Atlantic.

The length of the fish (in mm) is summarized in the GFDT below.

| Length (mm) | Frequency | 123 - 145 | 34 | 146 - 168 | 89 | 169 - 191 | 107 | 192 - 214 | 44 |

The class boundaries for a frequency table are calculated by taking the lower limit of one class and subtracting 0.5

from it to find the lower class boundary, and taking the upper limit of the previous class and adding 0.5 to it to find the

upper class boundary.

For the first class, the lower limit is 123 and the upper limit is 145. So the lower class boundary is:123 - 0.5 = 122.5

Therefore, the lower class boundary for the first class is 122.5.

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Hence, it takes 23 and 4 over 7  in² of paper's surface area to wrap six cylindrical mini muffins.

A cylinder is only a three-dimensional shape in geometry. A cylinder has a cylinder-like form and a top and bottom that are shaped like circles. Both the top and bottom are flat and of the same size. I think the simplest way to visualise a cylinder's shape is to think of a soup can.

Given data:

surface area of total 6 number of cylindrical mini muffins:

S = 6*(π*r²*h)

S = 6* (22/7 * 1² * 1.25)

S = 23.55 in²

S = 23 ⁴/₇ in²

Hence, it takes 23 and 4 over 7  in² of paper's surface area to wrap six cylindrical mini muffins.

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Answer:

1. 480ft

2. 12ft below the ground

Step-by-step explanation:

1. 80 × 60 = 480

2. 0 - 6 + 2 - 8 = -12

After answering the presented question, we can conclude that equation Therefore, the price of each snack is $0.62.

An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.

price of each snack x.

15 × $1.75 = $26.25

cost of snacks for the other fifteen students

$26.25 + 15x = $35.55

15x = $35.55 - $26.25

15x = $9.30

x = $0.62

Therefore, the price of each snack is $0.62.

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Answer:

1789/30

Step-by-step explanation:

To solve the expression

You have to convert the mixed fraction => improper:

(284/5 + 7/6) + 4/3

After that add:

1749/30 + 4/3

Add:

1789/30

The length of the side AC or the height of the smaller equilateral triangle is 3√2 inches.

The length of the side AC is equal to the height of the smaller equilateral triangle.

We know that in an equilateral triangle, all sides are equal, and all angles are 60 degrees.

Let's call the height of the smaller equilateral triangle h, and the length of one side of the smaller triangle x.

We can use the Pythagorean theorem to find the value of h:

(1/2)x^2 + h^2 = x^2

h^2 = x^2 - (1/2)x^2

h^2 = (1/2)x^2

h = sqrt((1/2)x^2)

Now, we also know that the side of the large equilateral triangle is 6 inches, so x = 6 inches.

Substituting this value into the equation for h, we get:

h = √((1/2)(6^2))

h = √(18)

h = 3√2 inches.

Therefore, the height of the smaller equilateral triangle is 3√2 inches.

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The highest observed speed is 85 miles per hour.

Below is a sorted stem-and-leaf diagram for the measured speeds (miles per hour) of 49 randomly chosen vehicles on

highway I-80 in Nebraska.

The stem unit is 5. So, the data range is from 50 to 85.

In the stem-and-leaf diagram below, each stem has ten leaves.

The stem-and-leaf diagram for the speeds of the 49 randomly selected vehicles on highway I-80 in Nebraska is as

follows: Stem | Leaf 5 | 08 6 | 013578 7 | 02346678 8 | 0123

The highest observed speed is 85 miles per hour.

The leaf corresponding to the stem 8 is 3, and it is in the last column of the stem-and-leaf diagram.

So, the highest observed speed is 85 miles per hour.

Therefore, the correct option is the one that reads "85."

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Answer:

The amount of discount is 35% of � x, which is (35/100)� x = 0.35� x. So, the discounted price is � x minus the discount, which is � x - 0.35� x = 0.65� x.

Then, the tax is added to the discounted price, which is 8% of the discounted price, or (8/100)(0.65� x) = 0.052� x.

Therefore, the expression for the total amount that Violet paid at the register is:

0.65� x + 0.052� x = 0.702� x

Answer: 10

Step-by-step explanation:

Adjacent angles in a parallelogram are supplementary (add up to 180), so we know that the unknown angle equals 100°, since the adjacent angle equals 80°.

So, we can set up an equation:

[tex]11x-10=100\\11x=110\\x=10[/tex]

To display this data on a line plot, we need to create a number line with a range of values from 1.4 to 2.0 with intervals of 0.1.

Then, we can plot each data point by hovering over the corresponding number on the number line and clicking and dragging up to the corresponding value.

The line plot will show a visual representation of the data, with each point representing the average time spent on the computer each day by a different student.

The line connecting the points will show the trend of the data and can be used to make inferences about the overall behavior of the students in terms of their computer usage.

In conclusion, the line plot for the given data on the average number of hours different students spend on the computer each day will show the student's weekly computer time and provide insight into their computer usage patterns.

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The true statement is B. This is a function.

In order to be considered a function, each element in the domain must be associated with exactly one element in the range. As long as every element in the domain is mapped to one and only one element in the range, it is a function. Option A is incorrect because a function does not require every element in the range to be associated with an element in the domain. There can be unused elements in the range without affecting the status of a function.

Option C is also incorrect because having elements in the domain mapped onto the same element in the range does not disqualify it from being a function. Multiple elements in the domain can share a single element in the range, and it will still be a function as long as each domain element is paired with only one range element. Finally, option D is incorrect because if an element in the domain has multiple elements in the range associated with it, then it would not be a function. However, the correct statement, option B, already indicates that this is a function, so option D is not true for the given question.

In conclusion, the statement "this is a function" is true, as long as each element in the domain has exactly one associated element in the range. Therefore, the correct option is B.

The question was incomplete, Find the full content below:

consider the following: which statement is true? question 1 options:

A. this is not a function because some of the elements in the range are not associated with any element in the domain.

B. this is a function.

C. this is not a function because some of the elements in the domain are mapped onto the same element in the range.

D. this is not a function because some elements in the domain have multiple elements in the range associated with it.

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In Mathematics, the relationship between two values which are not equal is expressed by inequalities. The equation of inequality for the given graph is y ≥ -1/2x + 2.  

In mathematics, an inequality is a relationship in which two numbers or other mathematical expressions compare unequal. Most commonly used to compare two numbers on the number line based on size. There are different notations used to represent different types of inequalities.

In both the cases a is not equal to b and such relationships are known as strict inequalities. This means that a is either strictly less than or greater than b. Equivalents are excluded whereas in inexact inequalities.

For the given graph:

take run = 1 and rise = -1/2

Thus, the slope will be,

Slope = (⁻¹/₂)/1

Slope = -1/2

Since, the y intercept is 2. Then the equation is y = -1/2x + 2

Take point (1,2) on the graph and apply in the equation:

y = -1/2x + 2

2 = -1/2 (1) + 2

2 = -1/2 + 2

2 = 3/2

As, 2 > 3/2. We can replace the = sign into ≥.

So, the eq inequality equation is y ≥ -1/2x + 2.

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Answer: 3 times

Step-by-step explanation:

Setting up the equation

If the function touches the horizontal axis, that means y=0, or f(x)=0 at that point(s).

So, we set our equation equal to 0

[tex]0=x^4+10x^3+24x^2\\[/tex]

Factor out x^2

[tex]0=x^2(x^2+10x+24)[/tex]

So, either [tex]x^2[/tex] or [tex](x^2+10x+24)[/tex] must equal zero

Factoring

[tex]x^2+10x+24=0\\(x+6)(x+4)=0\\[/tex]

x=-6 or x=-4

from before, [tex]x^2 = 0\\x=0[/tex]

So, f(x) equals zero at 3 places, when x=0, when x=-6, and when x=-4

Super Fast Food typically has more wait time because its box plot shows a larger range, with the minimum at 3 and the maximum at 27, compared to the Fast Chicken box plot with a minimum at 5 and a maximum at 20. Additionally, the median of Super Fast Food is 12, compared to the median of Fast Chicken at 12.5. This suggests that the middle value of the data for Super Fast Food is lower than that of Fast Chicken, indicating that Super Fast Food typically has shorter wait times. Therefore, the correct answer is "Super Fast Food, because it has a larger median."

D) Between 0 and 100.


The best system to measure the likelihood of an event occurring would be option D between 0 and 100. This system allows for a greater level of granularity and precision in the measurement of probability, as it provides a wider range of possible values to represent different levels of likelihood. The other options may not provide enough resolution to accurately capture and distinguish between different probabilities.

Answer:

C)  56

Step-by-step explanation:

2(AE) = BD

AC = BD

2(2x + 6) = 6x - 10

4x + 12 = 6x - 10

-2x = -22

x = -22/-2 = 11

AC = 6(11) - 10 = 56

Therefore, segment BD is congruent to segment CA, as required.

A trapezoid is a quadrilateral with at least one pair of parallel sides. In this case, we are given that AB is parallel to CD. The base angles theorem states that the base angles of an isosceles trapezoid are congruent. Since AB and CD are congruent (as given by the reflective property of congruence), the opposite angles formed by the intersecting lines BA and CD (i.e., ∠BAD and ∠CDA) are congruent as well. This establishes that ABCD is an isosceles trapezoid. An isosceles trapezoid has two pairs of congruent sides: AB = CD and AC = BD. Since BA and CO are congruent (as given), we can conclude that AC and BD are congruent as well (by the isosceles trapezoid definition). Finally, the symmetric property of congruence allows us to state that BD is congruent to CA.

Here,

given that ABCD is a trapezoid and segments BA and CO are congruent:

Statements | Reasons

ABCD is a trapezoid | Given

AB || CD | Definition of a trapezoid

∠BAD ≅ ∠CDA | Base angles theorem

AB ≅ CD | Reflective property of congruence

BA ≅ CO | Given

AC ≅ BD | Isosceles trapezoid definition

BD ≅ CA | Symmetric property of congruence

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