in a survey, 1500 adults in a country were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for the mean is lower: 38.4 hours and upper 43.5. Which of the following represents a reasonable interpretation of the results

Answer:  the longest poster that could fit in the box is approximately 22.56 inches long.

Step-by-step explanation: Utilizing the Pythagorean theorem, able to calculate the corner to corner as takes after:

diagonal^2 = 11^2 + 18^2 + 8^2

diagonal^2 = 121 + 324 + 64

diagonal^2 = 509

inclining = sqrt(509)

corner to corner ≈ 22.56 inches

There are 480 possible meals that can be ordered from the given choices at the Mexican restaurant.

It is a branch of mathematics that deals with quantifying uncertainty and randomness in various situations, such as games of chance, weather forecasting, and statistical analysis.

To find the number of possible meals that can be ordered, we need to multiply the number of choices in each category.

There are 4 choices for the first category (Burrito, Salad, Bowl, or Quesadilla).

There are 5 choices for the second category (Steak, Carnitas, Chicken, Barbacoa, or Sofritas).

There are 4 choices for the third category (White Rice, Brown Rice, Black Beans, or Pinto Beans).

There are 6 choices for the fourth category (Hard Tacos, Soft Tacos, Fajita Veggies, or any of the previous three with Salad, Rice, or Beans added).

Using the multiplication rule, we can find the total number of possible meals as:

4 x 5 x 4 x 6 = 480

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Step-by-step explanation:

Physically, integrating f(x)dx means finding the a. area to the right of point b. b. area to the left of point a . area under the curve and bounded by the lines x= a and x = d. d. area above the curve and bounded by the lines x = a and x = c. b. b.

Answer:

Step-by-step explanation:

means finding the area under the curve from a to b area t0 the left of point area t0 the right of point area above the curve from a to b CelecGne The exact value of xe ' dx is most nearly (A 7.8036 B) 11.807 14.034 19.614 CelecGne

The equation that can be used to find the time, t, it takes for the ball to reach the ground is D -16t² + 18t +1.2 = 0.

An equation simply has to do with the statement that illustrates the variables given.

In this case, Madison hits a tennis ball with an initial velocity of 18 m/s straight up into the air. When she hits the ball, it is 1.2 m above the ground.

The equation can be used to find the time, t, it takes for the ball to reach the ground will be -16t² +18t +1.2 = 0.

The appropriate option is D.

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The equation that can be used to find the time, t, it takes for the ball to reach the ground is D -16t² + 18t +1.2 = 0.

How to explain the equation

An equation simply has to do with the statement that illustrates the variables given.

In this case, Madison hits a tennis ball with an initial velocity of 18 m/s straight up into the air. When she hits the ball, it is 1.2 m above the ground.

The equation can be used to find the time, t, it takes for the ball to reach the ground will be -16t² +18t +1.2 = 0.

The appropriate option is D.

The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

Null hypothesis: The proportion of homes in Oregon heated by natural gas is the same as the reported national average of 45%.

Alternative hypothesis: The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

We can use a two-tailed z-test to test this hypothesis.

The test statistic is calculated as:

z = (p - P) / √[P(1-P)/n]

where p is the sample proportion, P is the hypothesized population proportion (0.45), and n is the sample size.

Using the values given in the problem, we have:

p = 175/314 = 0.557

P = 0.45

n = 314

Plugging these values into the formula, we get:

z = (0.557 - 0.45) / √[0.45(1-0.45)/314] = 3.039

Using a standard normal distribution table, we find that the probability of getting a z-value of 3.039 or higher (in absolute value) is less than 0.005.

Since the significance level is 0.05, which is greater than the p-value, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.

Therefore, the proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.

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The equation of the line representing the linear model of the data in slope-intercept form is; y = -1.25·x + 17.5

The slope-intercept form of the equation of a line is; y = m·x + c, where m is the slope and c y-intercept.

The possible question includes;

What is the equation for the line in slope intercept form;

The points on the line are; (2, 15), and (6, 10)

The slope is; (10 - 15)/(6 - 2) = -5/4

The equation of the line is therefore;

y - 15 = (-5/4)·(x - 2)

-5/4 = -1.25

y = -1.25·x + 5/2 + 15 = -1.25·x + 17.5

y = -1.25·x + 17.5

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The area of each triangle to the nearest square inch is approximately 95 square inches.

A triangle is a 2-dimensional geometric shape that consists of three straight sides and three angles. It is one of the basic shapes in geometry, and it is widely used in various fields such as mathematics, engineering, architecture, and art.

To find the area of an equilateral triangle with a radius of 12.7 inches, we can use the formula:

Area = [tex](\sqrt{(3)/4})[/tex] x [tex](side)^2[/tex]

where side is the length of one of the sides of the equilateral triangle.

We know that the radius of the equilateral triangle is 12.7 inches, which means that the distance from the center of the triangle to one of the corners (i.e., the length of one of the sides) is also 12.7 inches. To find the length of the side, we can use the formula for the height of an equilateral triangle:

and solve for side:

side = Height / ([tex]\sqrt{(3)/2[/tex]) = (2 x Height) / [tex]\sqrt{(3)[/tex]

Plugging in the value of the radius, we have:

side = (2 x 12.7 inches) / [tex]\sqrt{(3)[/tex] ≈ 14.67 inches

Now we can use the formula for the area of an equilateral triangle:

Area = ([tex]\sqrt{(3)/4}[/tex]) x [tex](side)^2[/tex]

Plugging in the value of the side, we have:

Area = ([tex]\sqrt{(3)/4[/tex]) x [tex](14.67 inches)^2[/tex] ≈ 94.71 square inches

Therefore, the area of each triangle to the nearest square inch is approximately 95 square inches.

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Answer:

(½,0),(1,0)

...............

Answer:

Step-by-step explanation:

To find the x-intercepts of a function, we set y = 0 and solve for x.

For the function 2x² - 3x + 1:

2x² - 3x + 1 = 0

We can use the quadratic formula to solve for x:

x = [ -(-3) ± sqrt( (-3)² - 4(2)(1) ) ] / (2*2)

x = [ 3 ± sqrt(1) ] / 4

x = 1/2 or x = 1

Therefore, the x-intercepts are (1/2, 0) and (1, 0).

For the function y = 2x² + 8x + 6:

2x² + 8x + 6 = 0

We can simplify this equation by dividing both sides by 2:

x² + 4x + 3 = 0

This equation factors as:

(x + 3)(x + 1) = 0

So the solutions are x = -3 and x = -1.

Therefore, the x-intercepts are (-3, 0) and (-1, 0).

For the coordinates (0.5, [?]).

To find the y-coordinate of the point (0.5, [?]), we can substitute x = 0.5 into the equation for the function:

y = 2(0.5)² + 8(0.5) + 6

y = 2(0.25) + 4 + 6

y = 5.5

Therefore, the coordinates are (0.5, 5.5).

For the coordinates ([ ], [ ]).

Without knowing the specific function, we cannot determine the x-intercepts or any other information about the graph. We would need to know the equation of the function or have additional information about the graph.

Answer:

Billy has £20, Liam has £40, and Nicola has £120. The total amount of money they have is £180, as given in the problem.

Step-by-step explanation:

Let's start by defining the variables:

Billy's money: x pounds

Liam's money: 2x pounds (twice as much as Billy)

Nicola's money: 3(2x) = 6x pounds (three times as much as Liam)

The total amount of money they have is £180, so we can write an equation:

x + 2x + 6x = 180

Simplifying the left side of the equation:

9x = 180

Solving for x:

x = 20

Now we can find out how much money each person has:

Billy: x = 20 pounds

Liam: 2x = 2(20) = 40 pounds

Nicola: 6x = 6(20) = 120 pounds

(2+3)²=25, base=2+3, exponente=2, (-8)²=64, 3/5 expressed as a percent is 60%, a=7, 20 0/3 = 60/3 = 20/1.

What is percentage?

Percentage is a way of expressing a fraction or decimal as a portion of 100. It is often used to describe proportions or rates in various fields, such as finance, economics, and statistics.

What is exponent?

An exponent is a mathematical operation that involves raising a number to a power. The exponent represents the number of times the base is multiplied by itself. For example, in 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, resulting in 8.

According to the given information:

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Assume that adults have IQ scores that are normally distributed with a

mean of μ = 100 and a standard deviation o= 15. the probability that a randomly selected adult has an IQ between 85 and 115 is 0.6826.

Let Z represent  the standard normal random variable

Z = (X - μ) / σ

where:

X = IQ score

μ=  mean (100)

σ= standard deviation (15).

In order to determine the probability  we have to find the  area

P(85 < X < 115) = P[(85 - 100) / 15 < Z < (115 - 100) / 15]

= P(-1 < Z < 1)

= Φ(1) - Φ(-1)

Where;

Φ=  Cumulative distribution function

Using a standard normal distribution table

Φ(1) = 0.8413

Φ(-1) = 0.1587

So,

P(85 < X < 115) =0.8413 - 0.1587

= 0.6826

Therefore the probability is 0.6826.

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Answer:

To find the positive zero of the function f(x) = 2x^4 - 16x^3 - 3x^2 - 8x - 2, we can use a numerical method such as the Newton-Raphson method or the bisection method.

Let's use the bisection method to approximate the positive zero of f(x).

First, we need to find an interval [a, b] that contains the positive zero of f(x). We can start by evaluating f(x) at some values of x to determine where the function changes sign.

For example, evaluating f(0) and f(1) gives:

f(0) = 2(0)^4 - 16(0)^3 - 3(0)^2 - 8(0) - 2 = -2

f(1) = 2(1)^4 - 16(1)^3 - 3(1)^2 - 8(1) - 2 = -27

Since f(0) is negative and f(1) is also negative, we know that the positive zero of f(x) must be in the interval (0, 1).

Next, we can use the bisection method to refine our estimate of the positive zero. We start by finding the midpoint of the interval [a, b]:

c = (a + b) / 2

If f(c) is positive, then the positive zero of f(x) must be in the interval [a, c]. If f(c) is negative, then the positive zero of f(x) must be in the interval [c, b]. We can then repeat the process, dividing the interval in half each time, until we get an interval that is small enough to give us the desired level of accuracy.

Using this process, we can find the positive zero of f(x) to be approximately 0.818, rounded to three decimal places.

Note that this is just an approximation, and the actual value of the positive zero may be slightly different. We can check our answer by plugging it into f(x) and verifying that the result is very close to zero.

(a) As a percentage, 105 grams is 1.04% of 10 kilograms.

(b) As a percentage 1 kilometer is approximately 99.21% of 8 meters.

(a) To express the second quantity, 105 grams, as a percentage of the first quantity, 10 kilograms, we first need to convert both quantities to the same unit.

10 kilograms is equal to 10,000 grams (since 1 kilogram = 1000 grams), so:

10,000 grams + 105 grams = 10,105 grams

105 grams / 10,105 grams * 100% = 1.04%

Therefore, 105 grams is 1.04% of 10 kilograms.

(b) To express the second quantity, 1 kilometer, as a percentage of the first quantity, 8 meters, we first need to convert both quantities to the same unit.

1 kilometer is equal to 1000 meters (since 1 kilometer = 1000 meters), so:

8 meters + 1000 meters = 1008 meters

1000 meters / 1008 meters * 100% = 99.21%

Therefore, 1 kilometer is approximately 99.21% of 8 meters.

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Answer:

  1. Place the point of the compass on point Q and open it to width QR.

   2.Place the point of the compass on the point P and draw an arc that intersects lines j and k. Label the intersections as points Q and R.

   3.Use the straightedge to draw a line k that passes through A and intersects line j. Label the point A and draw an arc that intersects line k. Label the intersection as point S.

  4. With the compass opening set to width QR, place the point of the compass on point S and draw an arc that intersects the arc that was drawn from point A. Label the intersection of the arcs as point B.

  5. Use the straightedge to draw AB -->.

Step-by-step explanation:

Answer:

[tex]\displaystyle -42 \;\frac{7}{8}[/tex]

Step-by-step explanation:

   We will simplify this expression.

Given:

   7(-6)+7(-1/8)

Multiply:

    [tex]\displaystyle -42- \frac{7}{8}[/tex]

Subtract:

    [tex]\displaystyle -42 \;\frac{7}{8}[/tex]

Answer: 280

Step-by-step explanation:

The products of each pair of numbers are:

1 x 33 = 33

4 x 30 = 120

8 x 26 = 208

14 x 20 = 280

b. To find the pair of numbers that will produce the largest possible product, we need to look for the pair with the closest product to 340 (the square of 17, which is the average of the two numbers).

The pair of numbers with the closest product to 340 is 14 and 20, whose product is 280. Therefore, the pair of numbers that will produce the largest possible product is 14 and 20, and the product is 280.

Therefore , the solution of the given problem of unitary method comes out to be  70% alcohol combination with 130 mL of the 55% alcohol mixture.

Use the tried-and-true fundamental method, the real variables, and any useful information you learn from the broad and specific questions to complete the assignment. Customers may be given another chance to taste expression the products in response. If these improvements don't happen, we'll lose out on significant expression advances in programming understanding.

Here,

Let x represent the required amount (in mL) of the 70% alcohol mixture.

The total amount of alcohol in the final mixture would be equal to the desired 60% alcohol solution since it would be the sum of the alcohol in the 55% alcohol mixture and the alcohol in the 70% alcohol mixture.

=> 0.55 * 130 + 0.70 * x = 0.60 * (130 + x)

=> 71.5 + 0.70x = 78 + 0.60x

=> 0.10x = 6.5

=> x = 65

Therefore, to create a 60% alcohol solution, you would need to combine 65 mL of the 70% alcohol combination with 130 mL of the 55% alcohol mixture.

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Answer:

5,500 ft²

Step-by-step explanation:

Easiest way is to find the area of the entire 100 x 80 square, then subtract the footprint of the house (50 x 50):

Backyard area = (100 x 80) - (50 x 50) = 8000 - 2500 = 5500 ft²

The only possible solution is x = 2. Therefore, the three consecutive integers that form the sides of the right triangle are 2, 3, and 4.

Since they are consecutive integers, let's assume that the hypotenuse, which is the longest side of the right triangle, is x+2, as it is three units longer than the shortest side.

In a right triangle, the hypotenuse's square is equal to the sum of the squares of the other two sides, according to the Pythagorean theorem. We can thus write:

[tex](x+2)^2 = x^2 + (x+1)^2[/tex]

Expanding the squares, we get:

[tex]x^2 + 4x + 4 = x^2 + x^2 + 2x + 1[/tex]

Simplifying and rearranging terms, we get:

[tex]2x^2 - 2x - 3 = 0[/tex]

We can solve this quadratic equation by using the quadratic formula:

x = (-b ± [tex]\sqrt{b^2 - 4ac}[/tex]) / 2a

where a = 2, b = -2, and c = -3.

Plugging in these values, we get:

x = (-(-2) ± [tex]\sqrt{((-2)^2 - 4(2)(-3)))[/tex] / 2(2)

x = (2 ± [tex]\sqrt{(4 + 24))[/tex] / 4

x = (2 ± [tex]\sqrt28}[/tex] / 4

x = (2 ± [tex]2\sqrt{7}[/tex]) / 4

x = 1/2 ± [tex]\sqrt{7}[/tex]/2

The only option is x = 2, since x must be an integer. As a result, the numbers 2, 3, and 4 are the three consecutive integers that make up the sides of the right triangle.

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The equation that helps her is $65 + 5m = $500. D'angela must save $87 each month for the next 5 months to reach her goal of having $500 in her savings account.

A group of equations that must be solved simultaneously is referred to as a system of equations. The variables in the equations are interconnected, and the set of values for the variables that satisfy all of the system's equations is the solution. Depending on whether the equations feature linear or nonlinear interactions between the variables, a system of equations can be either linear or nonlinear. A vast range of phenomena, including physical systems, economic systems, and social systems, are modelled using systems of equations, which appear in many branches of mathematics and science.

Let us suppose the amount of money saved by her = m.

The, for 5 months the amount saved is = 5m.

Given an initial deposit of $65, we have the equation of total amount as:

T = $65 + 5m

Now, she needs to save $500 thus,

$65 + 5m = $500

5m = $500 - $65

5m = $435

m = $87

Hence, D'angela must save $87 each month for the next 5 months to reach her goal of having $500 in her savings account.

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The complete question is:

The given function h(x) is h(-5) = -2, h(-2) = -1 and h(5) = -2.

The set of all possible inputs is the domain of a function. For instance, all real integers other than x=0 are in the domain of f(x)=x2 and g(x)=1/x, respectively. Additionally, custom functions with more restricted domains can be defined.

The definition of the function h(x) is as follows:

h(x) =

-2 if x < 2

-1 if x = -2

Using this definition, we can find the values of h(-5), h(-2), and h(5) as follows:

h(-5): Since -5 < 2, we use the first part of the definition and set h(-5) = -2.

h(-2): Since -2 = -2, we use the second part of the definition and set h(-2) = -1.

h(5): Since 5 > 2, we use the first part of the definition and set h(5) = -2.

Therefore, we have:

h(-5) = -2

h(-2) = -1

h(5) = -2

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Thus, 715,000 =  7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.

The number of times that decimal point must be moved to obtain a number between 1 and 10 is the exponent in scientific notation. The decimal point is shifted to the left in order to represent this number in scientific notation.

The main goal of scientific notation is to simplify computations using numbers that are abnormally large or small. With scientific notation, every digit counts because zeros are just no longer used to denote the decimal point.

Given expression:

715,000 __ 7.15 x 10⁵

LHS = 715,000

Take the RHS value :

= 7.15 x 10⁵

This, can be simplifies as:

= 7.15 x 100,000

Now multiply the two values,

= 715,000 (RHS values)

as, LHS  = RHS

LHS = 715,000

715,000 (RHS values)

Thus, 715,000 =  7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.

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the area of the triangle shown is  14 square inches

It is important to note that the formula that is used for calculating the area of a triangle is expressed with the equation;

A = 1/2bh

Such that the given parameters of the equation are;

From the information given, we have that;

b = 3 + h = 3 + 4 = 7 inches

h = 4 inches

Now, substitute the values, we get;

Area = 1/2 (7)(4)

multiply the value and expand the bracket

Area = 1/2(28)

divide the values

Area = 14 square inches

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Answer: 11 Cookies

Step-by-step explanation:

let C be cookies

17($3.25) + 1.60C = $72.85

$55.25 + 1.60C = $72.85

1.60C = $17.60

C=11

She sells 11 cookies

Answer:

11

Step-by-step explanation:

To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.

I AM SO SORRY IF THIS DIDN'T MAKE SENSE!

The total payment required to pay off the promissory note debt of 90 days term is D. $510.00.

The promissory note issued is for $500.

The interest rate is 8%.

Furthermore, the time frame is 90 days.

So the total payment is

= $500 + ($500 × 8% × 90 days ÷ 360 days)

= $500 + ($500 × 8% × 1/4)

= $500 + 10

= $510

Promissory notes are sometimes known as an IOU, a loan arrangement, or simply a note. It is a legal lending contract in which the borrower pledges to return the lender a specific amount of money within a specific time frame.

This type of document is legally binding and imposes a legal duty to repay the loan. Mortgages, school loans, car loans, company loans, and personal loans between family and friends all use promissory notes.

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The value of y that makes the hanger balance is 3.

The value of y can be solved considering linear equation method.

A linear equation is an algebraic equation in which the highest power of the variable(s) is always 1. It represents a straight line when graphed on a Cartesian coordinate plane. A linear equation can have one or more variables.

To solve for y in the equation 5 + y = 8, you can follow these steps:

Step 1: Subtract 5 from both sides of the equation to isolate the term with y on one side.

5 + y - 5 = 8 - 5

This simplifies to:

y = 3

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Answer:

Step-by-step explanation:

Greetings!Answer:[tex]\sqrt{85} or 9.22

Answer:

Step-by-step explanation:

The length of the Hypotenuse should be [tex]\sqrt{45}[/tex] , 6.70.

By Pythagoras' Theorem, [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex].

so, Let a =6cm, b =3cm

[tex]6^{2}[/tex] + [tex]3^{2}[/tex] = 45

Therefore,

The length of the hypotenuse will be either [tex]\sqrt{45}[/tex]

Answer:

$3.87 for the 18% tip.

Answer:

4 1/2

Step-by-step explanation:

If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.

JH * HK = GH * HI

3 * (2x+1) = 2 ( x+5)

Distribute

6x+3 = 2x+10

Subtract 2x from each side.

6x-2x+3 = 2x-2x+10

4x+3 = 10

Subtract 3 from each side.

4x = 10-3

4x= 7

Divide by 4.

x = 7/4

Now find HK.

HK = 2x+1

     = 2(7/4)+1

     = 7/2+1

     = 9/2

    = 4 1/2