According to a poll, 80% of Americans report being afflicted by stress. Suppose a random sample of 1,200 Americans is selected. Complete parts (a) through (d) below.
a. What percentage of the sample would we expect to report being afflicted by stress?

We can fill in the blanks as "Equations with fractions and/or decimals can be rewritten as equivalent equations without fractions and/or decimals, and then solve in the usual manner."

The process described above is called clearing the equation of fractions and/or decimals. To clear fractions, you can multiply both sides of the equation by the least common multiple (LCM) of the denominators. To clear decimals, you can multiply both sides of the equation by a power of ten that will shift the decimal point to the right until there are no more decimals.

After clearing the equation of fractions and/or decimals, you can simplify and solve the equation using algebraic techniques, such as combining like terms, distributing, and isolating the variable.

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Part a: x intercepts are (4.414, 0) and (1.586,0) and y intercept = (0, 7).

Part b: From the graph, vertex = (3, -2).

In mathematics, a quadratic equation is a second-degree polynomial with the conventional form ax² + bx + c = 0, where a, b, and c are mathematical coefficients and a 0. Second degree refers to an equation where at least one term has been raised to a power of two. The value of the variable x in a quadratic equation is unknown, so we must discover the answer.

Given quadratic function for the macroeconomic variable

Q(x) = x² − 6x + 7.

Part a: x and y intercept:

x-intercept occurs when the function becomes zero.

Put Q(x) = 0

0 = x² − 6x + 7.

Find the factors:

x² − 6x + 7 = 0

a = 1 , b = -6 , c = 7 using the quadratic formula.

x = [-b ± √(b² - 4ac)]/ 2a

x = [6 ± √(36 - 4*1*7)]/ 2*1

x = 3 ± √2

Now,

x = 3 + √2

x = 4.414

and x = 3 - √2 = 1.586

Thus, x intercepts are (4.414, 0) and (1.586,0)

Y-intercept, when x = 0

Q(x) = 0² − 6(0) + 7.

Q(x) = 7

y intercept = (0, 7)

Part b: using the graphing tool, draw the graph of the given quadratic function.

Mark the points  (4.414, 0),  (1.586,0), and  (0, 7).

From the graph, vertex = (3, -2).

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Answer:

The probability of choosing a bay horse can be calculated by dividing the number of bay horses by the total number of horses:

Probability of choosing a bay horse = number of bay horses / total number of horses

In this case, we know that there are 5 bay horses and a total of 18 horses:

Probability of choosing a bay horse = 5 / 18

Therefore, the probability of choosing a bay horse is 5/18.

Step-by-step explanation:

Answer:

18/5

Step-by-step explanation:

because a/b equals 18/5

The triangle with side lengths √35 , √14 , 7 is a right triangle.

What is the right triangle?

A right-angle triangle is a triangle that has one of its angles 90 degrees. The sum of angles in a right triangle is 180 degrees.

p² + b² = h² ( In a right-angled triangle)

p = perpendicular of the triangle

b = base of the triangle

h = hypotenuse of the triangle

According to the Pythagoras theorem:

p² + b² = h² (In a right-angled triangle)

In Option D

(√35)² + (√14)² = 7²

49 = 49

Pythagoras theorem is followed in this triangle, hence it is a right angled triangle.

Hence, The triangle with side lengths √35, √14, 7 is a right triangle.

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Answer: 12 inches

Step-by-step explanation:

If the dilation is uniform, both height and width will be multiplied by 4.

So the new height = (1 in) × 4 = 4 in

and the new width = (3 in) × 4 = 12 in

Hope it helps!

The area of the parallelogram in the image given in the attachment below is: 48 mm².

A parallelogram is a quadrilateral (a polygon with four sides) that has two pairs of parallel sides. This means that opposite sides of the parallelogram are parallel and have the same length.

To find the area of a parallelogram, the following formula is used:

Area of parallelogram = base * height.

From the image attached below, we have:

base = 4 mm

height = 12 mm

Substitute:

Area of the parallelogram = 4 * 12

Area of parallelogram = 48 mm²

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The rate at which the infected population is growing after 8 days of the outbreak is approximately 1096.57 people per day, as determined by the derivative of the given function with respect to time.

To find the rate at which the infected population is growing after 8 days, we need to take the derivative of the given function I(t) with respect to t:

[tex]dI/dt = 3900(0.0514)e^(0.0514t)[/tex]

At t=8, the rate at which the infected population is growing is:

[tex]dI/dt = 3900(0.0514)e^(0.0514*8) = 1096.57[/tex]

Therefore, the rate at which the infected population is growing after 8 days is approximately 1096.57 people per day.

It is important to note that this rate of growth is an instantaneous rate at t=8, and it will likely change as time passes and the outbreak progresses. Furthermore, the rate of growth of the infected population depends on various factors such as the transmission rate of the virus, the effectiveness of preventive measures, and the availability of healthcare resources.

In conclusion, the rate at which the infected population is growing after 8 days of the outbreak is approximately 1096.57 people per day, as determined by the derivative of the given function with respect to time. This result provides insight into the early stages of a flu outbreak, but further analysis is required to understand the longer-term dynamics of the outbreak and the factors that affect the spread of the disease.

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Answer: 2n

Step-by-step explanation:

[tex]8n^{3}[/tex] = 2*2*2*n*n*n

[tex]16n[/tex] = 2*2*2*2*n

[tex]6n^{2}[/tex] = 2*3*n*n

gcf = 2n

Answer:

There are 18 total pieces of vegetables, so there are 18 possible choices for the first piece, 17 possible choices for the second piece, 16 possible choices for the third piece, and so on, until there is only 1 possible choice for the last piece. Therefore, the total number of different orders we could eat all the vegetables is:

18 x 17 x 16 x 15 x 14 x 13 x 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

which simplifies to:

18! / 0! = 6,402,373,705,728

Therefore, there are 6,402,373,705,728 different orders in which we could eat all the vegetables.

Answer:

There are 6,402,373,705,728 different orders in which we could eat all the vegetables.

Step-by-step explanation:

To find the total number of different orders in which we could eat all the vegetables, we can use the formula for permutations of n objects:

[tex]\sf\qquad\dashrightarrow P(n) = n![/tex]

where:

In this case, we have a total of 18 vegetables (6 carrot sticks + 4 celery sticks + 5 tomatoes + 3 pieces of cauliflower). So we can calculate the permutation of 18 objects:

[tex]\begin{aligned}\sf:\implies P(18)& =\sf 18! \\&=\sf 18 \times 17 \times 16 \times ... \times 3 \times 2 \times 1 \\ &= \boxed{\bold{\:\:6,402,373,705,728\:\:}}\:\:\:\green{\checkmark}\end{aligned}[/tex]

Therefore, there are 6,402,373,705,728 different orders in which we could eat all the vegetables.

The statements that are true include the following:

A. the function is increasing over the interval -8 ≤ x ≤ -2.

B. the function is constant over the interval -2 ≤ x ≤ 2.

A. the function is decreasing over the interval 3 ≤ x ≤ 7.

In Mathematics, a piecewise-defined function can be defined as a type of function that is defined by two (2) or more mathematical expressions over a specific domain.

Generally speaking, the domain of any piecewise-defined function simply refers to the union of all of its sub-domains. By critically observing the graph of the given piecewise-defined function, we can reasonably infer and logically deduce that it is constant over the interval -2 ≤ x ≤ 2, increasing over the interval -8 ≤ x ≤ -2, and decreasing over the interval 3 ≤ x ≤ 7.

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Answer:

Solution: A sequence in which the ratio between two consecutive terms is the same is called a geometric sequence. The geometric sequence given is 4, 8, 16, 32, ... Therefore, the nth term is an =4(2)n-1.

Step-by-step explanation:

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Answer:

The ratio of x/4 to 8/16 can be rewritten in simplest form by first simplifying 8/16 to 1/2. Then, we can multiply both sides of the equation x/4 = 8/16 by 4 to get x alone on one side of the equation. This gives us x = 2.

Rewriting each explicit formula in function form given below:

[tex]g(n) = -3 * (1/2)^(^n^-^1^)[/tex]

[tex]f(n) = 4 * (1/3)^(^n^-^1^)[/tex]

To convert an explicit formula into a function form, one must denote the variable 'n' as its respective input and represent the formula with that of a function.

Listed below are the steps required:

Original formulas:

[tex]g n = -3.(1_2)n- 1g[/tex]

[tex]n = 4.(1_3)n-1[/tex]

In order to transform the original expression to function format, follow these instructions for each individual formula:

- Step 1: Establish both the name of the function and the input parameter it accepts, denoted respectively by 'g', or 'n'.

- Step 2: Alter the specified representation; replace "g n" with "g(n)".

- Step 3: Substitute the hyphen sign '_' with a division symbol '/'.

Subsequently, applying this method specifically on equation g n = -3 * (1_2)n - 1g generates:

[tex]g(n) = -3 * (1/2)^(^n^-^1^)[/tex]

Thus, the rewritten version in function format is displayed as priorly referred:

[tex]g(n) = -3 * (1/2)^(^n^-^1^)[/tex]

To implement the same procedure on another given formula, where it states n = 4 * (1_3)n - 1:

- Step 1: Uncover the variables' identity with regards to the name of the function and the current parameters utilized, therefore establishing a new function label 'f' while preserving the relative input, just like previously conducted during the initial steps.  

- Step 2: Adapt your notation appropriately utilizing the newly established variables mentioned in Step 1.

- Step 3: Substitute the underscore designation '*' present within the term with a forward slash '/'.

As a result, following the process will create the convenient formulation of the certain algebraic formula as f(n) = [tex]4 * (1/3)^(^n^-^1^).[/tex]

Thus, the final draft written in functional form is presented as:

[tex]f(n) = 4 * (1/3)^(^n^-^1^)[/tex]

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Answer:43/50

Step-by-step explanation:

you must divide both the numerator and denominator by 2

86/100 can be simplified to 43/50 by dividing both the numerator and denominator by 2, which is the greatest common factor. 86/100 can also be written as 0.86 or 86%.

Answer:

-84+(-11)= -95

-84 + (-11) = -84 - 11 = -95

By the commutative property, adding a negative number is the same as subtracting that number as a positive; therefore, something + (-11) = something - 11. After changing the equation from -84 + (-11) to -84 - 11, we use regular addition properties, adding the tens place and ones place to get -95.

The solution of the inequalities is x = 11 and y = 9.

The value of x nickels is 0.05x dollars, and the value of y pennies is 0.01y dollars.

The total value of Sebastian's coins will be:

0.05x + 0.01y dollars

Writing the given conditions as a system of inequalities:

Sebastian has at least 20 coins: x + y ≥ 20

The total value of Sebastian's coins is at most $0.65: 0.05x + 0.01y ≤ 0.65

Solving the inequalities, we substitute y ≥ 20 - x into the second inequality:

0.05x + 0.01(20 - x) ≤ 0.65

0.05x + 0.2 - 0.01x ≤ 0.65

0.04x + 0.2 ≤ 0.65

0.04x ≤ 0.45

x ≤ 11.25

The largest possible whole number value for x is 11.

Solving for the value of y from the first inequality:

x + y ≥ 20

11 + y ≥ 20

y ≥ 9

The closest possible whole number value for y is 11

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To write the given equation in logarithmic form, we can use the definition of logarithms. The equation 10^m = w can be rewritten as a logarithm with base 10: log10(w) = m

The general relationship between exponents and logarithms is as follows:

base^(exponent) = result

In logarithmic form, it's written as:

log_base(result) = exponent

For our given equation, 10^m = w, we have:

base = 10

exponent = m

result = w

Applying the general logarithmic relationship, we write:

log10(w) = m

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We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).

For the 100 m race with Mark Chase and Beatrice, the sample space of all the possible ways in which the three runners can win first, second, and third place is:

{M-C-B, M-B-C, C-M-B, C-B-M, B-M-C, B-C-M}

where M stands for Mark, C stands for Chase, and B stands for Beatrice. We have six possible permutations because there are three choices for the first place, two choices for the second place (as one person has already won first place), and one choice left for the third place.

If there were four runners and three positions to be won, the sample space would be:

{A-B-C-D, A-B-D-C, A-C-B-D, A-C-D-B, A-D-B-C, A-D-C-B, B-A-C-D, B-A-D-C, B-C-A-D, B-C-D-A, B-D-A-C, B-D-C-A, C-A-B-D, C-A-D-B, C-B-A-D, C-B-D-A, C-D-A-B, C-D-B-A, D-A-B-C, D-A-C-B, D-B-A-C, D-B-C-A, D-C-A-B, D-C-B-A}

where A, B, C, and D represent the four runners. We have 24 possible permutations because there are four choices for the first place, three choices for the second place (as two people have already won first and second place), and two choices for the third place (as three people have already won first, second, and third place).

Note that in both cases, we assume that all runners are equally skilled and have an equal chance of winning each position. In reality, there may be differences in skill levels, which would affect the probabilities of each possible outcome.

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x < 5 is the value that satisfies the given inequality.

What are inequalities?

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than, or equal to, less than, or less than or equal to.

The occurrence of an unfair and/or unequal distribution of opportunities and resources among the people that make up a society is referred to as inequality.

Here, we have

Given: 6x-20 < 2x

We have to find the value of x that satisfies the given inequality.

Reduce the greatest common factor for both sides of the inequality: 3x - 10 < x

Now, we rearrange unknown terms to the left side of the equation: 3x - x < 10

Combine like terms: 2x < 10

Reduce the greatest common factor for both sides of the inequality: x < 5

Hence, x < 5 is the value that satisfies the given inequality.

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Among the three students the weight of Darren at birth was the lowest with 8.25 pounds.

What is weight?

Weight gauges how much gravity is pulling on a body.

The weight formula is provided by -

w = mg

Since weight is a force, it has the same SI unit as a force, which is Newton (N).

The students from lightest to heaviest weight at birth are -

Darren (8.25 pounds) < Joel (8.34 pounds) < Rebecca (8.388 pounds)

This is because 8.25 is less than 8.34, and 8.34 is less than 8.388. In other words, Darren weighed the least at birth, followed by Joel, and then Rebecca weighed the most.

It's important to note that the differences in weight between the students are relatively small, and all three weights are within a narrow range.

However, when comparing weights, even small differences can be significant.

Therefore, the lowest weight was of Darren (8.25 pounds).

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Answer:

C. DBA, DB, DC, AC, AB

Step-by-step explanation:

the length of the rope is approximately 11.9 feet.

What is right angle triangle?

The term "right-angled triangle" refers to any triangle with an internal angle that is either a right angle or 90 degrees in value. The right triangle or the 90-degree triangle are other names for this triangle because of this. Right triangles have "opposite" and "adjacent" sides, which refer to the sides that are across from and next to respective angles, respectively. When a right triangle is formed, the hypotenuse is its longest side.

We can consider the flagpole, the ground, and the rope as forming a right triangle. The angle between the flagpole and the rope is 90 degrees, and the angle between the rope and the ground is 35 degrees. Therefore, the angle between the flagpole and the ground is 90 - 35 = 55 degrees.

Let's call the length of the rope "r". We can use the trigonometric function tangent to find r:

tan(35°) = opposite/adjacent = r/20

Multiplying both sides by 20, we get:

r = 20 tan(35°)

Using a calculator, we get:

r ≈ 11.9 feet

Therefore, the length of the rope is approximately 11.9 feet.

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Answer:

To solve 5(98) =___(100-2) using the distributive property, we can distribute the 5 to both the 100 and the -2:

5(98) = 5(100 - 2)

Now, we can use the distributive property to simplify the right side:

5(98) = 5(100) - 5(2)

Multiplying, we get:

490 = 500 - 10

Simplifying further, we get:

490 = 490

Therefore, the equation is true, and we have verified the distributive property.

The second graph represents the function f(x) = - (x+3) (x + 1). The solution has been obtained by using the parabola.

What is a parabola?

A parabola is a mirror-symmetrical, nearly U-shaped planar curve in mathematics. It corresponds to a number of seemingly dissimilar mathematical descriptions, all of which can be shown to define the same curves.

We are given a function as f(x) = - (x+3) (x + 1).

Now, on simplifying the equation, we get

⇒ f(x) = - (x+3) (x + 1)

⇒ f(x) = - ([tex]x^{2}[/tex] + x + 3x + 3)

⇒ f(x) = - ([tex]x^{2}[/tex] + 4x + 3)

So, we get a parabola opening downwards.

Hence, the second graph represents the function f(x) = - (x+3) (x + 1).

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Answer:

1100

Step-by-step explanation:

8 = 1000

9 = 1001

10 = 1010

11 = 1011

12 = 1100

hope this helps :)

The cost of painting the entire surface area of the pyramid, including its square base, is approximately $85.44.

What is the cost of painting?

The Great Pyramid of Giza has a square base, so the surface area of the base is simply the area of a square with side length 1.6 meters:

Area of base = (1.6 m)² = 2.56 m²

To find the surface area of the rest of the pyramid, we need to find the area of each of the four triangular faces. Each face is a right triangle with one leg equal to the slant height of the pyramid (which we can find using the Pythagorean theorem) and the other leg equal to half the length of one side of the base.

The slant height can be found using the Pythagorean theorem:

slant height = √((height)² + (1/2 × base)²)

slant height = √((2.4)² + (0.8)²) ≈ 2.53 meters

Then, the area of one triangular face is:

Area of triangular face = (1/2)baseheight

Area of triangular face = (1/2)(1.6 m)(2.53 m) ≈ 2.03 m²

Since there are four triangular faces, the total surface area of the pyramid is:

Total surface area = 4 × (Area of triangular face) + (Area of base)

Total surface area = 4 × (2.03 m²) + 2.56 m²

Total surface area ≈ 10.68 m²

Therefore, the cost of painting the entire surface area of the pyramid at a rate of $8 per square meter is approximately:

Cost = Total surface area × Cost per m²

Cost = 10.68 m² × $8/m²

Cost ≈ $85.44

So, the cost of painting the entire surface area of the pyramid, including its square base, is approximately $85.44.

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Answer:

$15000 was invested in CDs, $50000 was invested in bonds, and $30000 was invested in stocks.

Step-by-step explanation:

Let x be the amount invested in CDs. Then, the amount invested in bonds is x + 35000. The remaining amount invested in stocks is 95000 - (x + x + 35000) = 25000 - x.

The annual income from CDs is 0.0475x dollars. The annual income from bonds is 0.042(x + 35000) dollars. The annual income from stocks is 0.112(25000 - x) dollars.

The total annual income from all three investments is $6845: 0.0475x + 0.042(x + 35000) + 0.112(25000 - x) = 6845

Solving for x gives: x = $15000

Therefore, $15000 was invested in CDs, $50000 was invested in bonds, and $30000 was invested in stocks.