based on the information in the article, does it appear that in early 2016 u.s. households in fact worked fewer hours and took more leisure time? what do the data suggest?

Answer: 5400

Step-by-step explanation:

For a cube V=lwh

Volume for the larger box = 4.5 x 5 x 3.75 =84.375 or 675/8

Volume for smaller box =.25 x .25 x .25 = .015625 or 1/64

divide the larger by smaller.

84.375/.015625=5400

or

[tex]\frac{675}{8} /\frac{1}{64}[/tex]   keep change flip = [tex]\frac{675}{8} * \frac{64}{1}[/tex] = 5400

The equation for the line of symmetry for the function defined by f(x) =-3x² +6x - 9 is x = 1.

Given the function in the question;

f(x) = -3x² + 6x - 9

To find the equation for the line of symmetry, we need to use the formula:

x = -b/2a,

Where a and b are the coefficients of x² and x in the quadratic equation, respectively.

Given the function:

f(x)= -3x² +6x - 9

We have:

a = -3 and b = 6.

Hence, the equation for the line of symmetry is:

x = -b/2a

x = -6 / ( 2(-3))

x = -6/(-6)

x = 1

The equation for the line of symmetry is x = 1.

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Answer:

32% off the original price = 68% of the original price. So the sale price is:

$76.00 × .68 = $51.68

The value of the test statistic is -8.2542.

We have,

p'= 0.87, p= 0.93 and n= 1232

We know, the equation for the Test statistic for a population proportion  is mathematically given as

z = (p' - p)/ √p(1-p)/ n

So, z= (0.87 - 0.93)/ √0.93(1-0.93)/ 1232

z = (-0.06) / 0.007269

z = -8.2542

So, the value of the test statistic is -8.2542.

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The distance between given point A and point B on the graph is 3√2 units.

Hence the correct option is (A).

We know that the distance between two points having coordinates (a, b) and (c, d) is = √((c - a)² + (d - b)²).

From the given graph we can see that,

the coordinates of the point A = (-2, -1)

the coordinates of the point B = (1, 2)

So the distance between the point A and point B is given by,

= √((1 - (-2))² + (2 - (-1))²)

= √((1 + 2)² + (2 + 1)²)

= √(3² + 3²)

= √(9 + 9)

= √18

= 3√2 units

Hence the correct option will be (A).

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5^2 is equal to 25.
lol its kinda easy

Answer:

25.

Step-by-step explanation:

The symbol "^" representa exponents.

The exponet (second number) means how many times you mutiply 5 by itself. In this case, it's 2.

2. 5 x 5 = 25

Step-by-step explanation:

15.

the area of the whole region is the sum of the area of the rectangle BCDE and the triangle ABE.

the area of a rectangle is

length × width

the area of a triangle is

baseline × height / 2

as a nice coincidence (that reduced the amount of work we have to do) the points of the rectangle are on the same x and y lines parallel to the x-axis and y-axis.

so, we can directly see, the distance BC = 5 (only the x- difference matters, as both have the same y- coordinate).

the distance CD = 4 (only the y- difference matters, as they have the same x-coordinate).

DE = 5, EB = 4. so, a true rectangle.

for the triangle we need the length of the baseline (EB = 4) and the length of the height to that baseline (FA = 2 from -2 to 0 of the x-values, and again they have the same y- coordinate).

so, the area of the rectangle is

5×4 = 20 units²

the area of the triangle is

4×2/2 = 4 units²

therefore, together, the shaded area is 20+4 = 24 units².

24.

there is no shaded region (all is white), but I assume we are taking about the inner regions with all sides being continuous lines.

that area is the area of the total rectangle AGDH minus the 2 right-angled triangles BGC and EFH.

the same formulas for the area of rectangle and a triangle apply as before.

right-angled triangle have a big advantage, as their legs can be used as baseline and corresponding height.

again, the points are sharing x- and y- coordinates, so that we only need to calculate the difference of either the x- or the y coordinates.

AG = 5

BG = 2

GC = 5

GD = 14 (6+8)

EH = 2

FH = 11 (6+5)

so, the area of the large rectangle is

14×5 = 70 units²

the area of BGC is

5×2/2 = 5 units²

the area of EFH is

11×2/2 = 11 units²

the total inner area is then

70 - 5 - 11 = 54 units²

Answer:

28 quart jars

Step-by-step explanation:

We know that there are 4 quarts in a gallon.

7 gallons * 4 quarts/gallon = 28 quarts

She needs 28 quart jars

The number which we increase by 15 percent gives 356.5 is the number

Given that,

if we increase a number by 15 percent, we get 356.5

Let x be the unknown number.

Then the given statement can be numerically written as,

x + (15% of x) = 356.5

x + (15/100) of x = 356.5

x + 0.15x = 356.5

1.15x = 356.5

Dividing both sides by 1.15, we get,

x = 356.5 / 1.15 = 310

Hence the unknown number is 310.

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Thus, we get a total of 210 + 90 + 6 + 60 = 366 number of ways to distribute the 7 apples among the 4 lecturers.

To solve this problem, we can use a combination of techniques from combinatorics and basic arithmetic. Since each lecturer can receive at most two apples, we can break down the problem into several cases:

1. Each lecturer receives 2 apples: In this case, we simply need to distribute the 7 apples among the 4 lecturers in a way that each receives 2. This can be done in (7 choose 2) * (5 choose 2) * (3 choose 2) * (1 choose 2) = 210 ways.

2. Three lecturers receive 2 apples and one receives 1 apple: In this case, we need to choose one of the lecturers to receive 1 apple, and then distribute the remaining 6 apples among the other three in pairs. There are 4 ways to choose the lecturer who receives 1 apple, and then (6 choose 2) * (4 choose 2) * (2 choose 2) = 90 ways to distribute the remaining apples.

3. Two lecturers receive 2 apples each, and two receive 1 apple each: In this case, we need to choose two of the lecturers to receive 2 apples each, and then distribute the remaining 3 apples among the other two in a way that each receives 1. There are (4 choose 2) = 6 ways to choose the two lecturers who receive 2 apples, and then (3 choose 1) * (2 choose 1) = 6 ways to distribute the remaining apples.

4. One lecturer receives 2 apples, and three receive 1 apple each: In this case, we need to choose one of the lecturers to receive 2 apples, and then distribute the remaining 5 apples among the other three in a way that each receives 1. There are 4 ways to choose the lecturer who receives 2 apples, and then (5 choose 1) * (4 choose 1) * (3 choose 1) = 60 ways to distribute the remaining apples.

Adding up the results from each case, we get a total of 210 + 90 + 6 + 60 = 366 ways to distribute the 7 apples among the 4 lecturers.

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For the first expression, the order of operation is multiplication followed by subtraction and addition,  -5.56.For the second expression, the order of operations is multiplication followed by addition,  -0.9.

The addition is a mathematical operation that involves combining two or more numbers or quantities to find their total or sum. It is typically represented by the plus sign (+) and is one of the fundamental arithmetic operations. Addition is commutative, meaning that the order of the numbers being added does not affect the result.

For the first expression:

Operations:

Multiplication: 1.2 x (-1.3)

Subtraction: 1.2 x (-1.3)

Addition: 1.2 x (-1.3) + 4

Order of operations:

Multiplication: 1.2 x (-1.3) = -1.56

Subtraction: -1.56 - 4 = -5.56

For the second expression:

Operations:

Multiplication: 2 x 2.5

Addition: -3.5 - 1.4 + (2 x 2.5)

Order of operations:

Multiplication: 2 x 2.5 = 5

Addition: -3.5 - 1.4 + 5 = -0.9

Therefore, For the first expression, the order of operation is multiplication followed by subtraction and addition,  -5.56.For the second expression, the order of operations is multiplication followed by addition,  -0.9.

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Answer: c

Step-by-step explanation: I'm pretty sure this is right

The first derivative of the function h is given by [tex]h'(x)= x^4 - x^3 + x[/tex]. The graph of h is concave down at (−∞,−0.455). Therefore the correct answer is option D.

Given, the first derivative of the function,

[tex]h'(x)=x^{4} -x^{3} +x[/tex]

The second derivative of the function,

[tex]h''(x)=4x^{3} -3x^{2} +1[/tex]

When h''(x)<0, then the function is said to be concave down.

h′′(x)<0

=> [tex]4x^{3} -3x^{2} +1 < 0[/tex]

Finding the root of the equation,

[tex]f(x)=4x^{3} -3x^{2} +1=0[/tex]

This equation has only one real solution,

At x = -0.5, f(−0.5)<0

f(-0.5)<0

At x = -0.4, f(−0.4)>0

f(-0.4)>0

So according to the intermediate value theorem, there is a root in (-0.5, -0.4)

From the option, that root can be x = -0.455

So if the function concave down h''(x) < 0

Interval : (−∞,−0.455)

Therefore, the graph of h is concave down at (−∞,−0.455).

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Answer:you need to multiply and ur answer u would get is 64

Step-by-step explanation: multiply 4x16 and you get ur answer.

Answer:

(3[tex]x^{2}[/tex]+4)

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping.

If there is enough evidence to reject the null hypothesis and conclude that the new process produces less than 90% good product.

The appropriate hypotheses for this scenario would be:

Null hypothesis (H0): The true proportion of good product produced by the new process is equal to or less than 0.9.
Alternative hypothesis (Ha): The true proportion of good product produced by the new process is greater than 0.9.

To test these hypotheses, we can use a one-sample proportion test. The test statistic for this test is calculated using the formula:

z = (p - P0) / sqrt(P0 * (1 - P0) / n)

where:
- p is the proportion of good product in the sample (0.87 in this case)
- P0 is the hypothesized proportion of good product (0.9)
- n is the sample size (49)

Using an alpha level of 0.05, we can find the critical z-value from a standard normal distribution table. For a one-tailed test (since our alternative hypothesis is one-sided), the critical z-value is 1.645.

Calculating the test statistic using the formula above, we get:

z = (0.87 - 0.9) / sqrt(0.9 * 0.1 / 49) = -1.17

Since the calculated z-value (-1.17) is less than the critical z-value (1.645), we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the true proportion of good product produced by the new process is greater than 0.9. The quality manager should investigate the process further to improve the proportion of good product before certifying it.

Let's formulate the appropriate hypotheses and test them using an alpha:

The quality manager at Newvis Pharmaceutical Company wants to ensure that the new process produces at least 90% good product. We can define the null hypothesis (H0) and the alternative hypothesis (H1) as follows:

H0: p ≥ 0.90 (The process produces 90% or more good product)
H1: p < 0.90 (The process produces less than 90% good product)

Now, let's test these hypotheses using an alpha (significance level), which is typically set at 0.05.

1. Calculate the test statistic using the sample proportion (p-hat) and sample size (n):
p-hat = 0.87 (87% of the 49 containers were good)
n = 49

2. Find the standard error of the sample proportion:
SE = √(p * (1-p) / n)

3. Calculate the z-score:
z = (p-hat - p) / SE

4. Compare the z-score to the critical value from the z-table corresponding to the chosen alpha level. If the z-score is less than the critical value, reject the null hypothesis in favor of the alternative hypothesis.

If you complete these steps, you can determine if there is enough evidence to reject the null hypothesis and conclude that the new process produces less than 90% good product.

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Alice's shortest height is 1.25 feet.

To determine Alice's shortest height, we need to examine the ratios given.

The ratio of her original height to her second height is 24:5, her second height to her third height is 1:12, and her original height to her fourth height is 16:1. We are told that the tallest height is 10 feet.
Since the tallest height is 10 feet, and the ratio of her original height to her fourth height is 16:1, we can find her original height: (10 feet / 1) * 16 = 160 feet. Now that we have her original height, we can find her second and third heights using the other given ratios:
Second height: (160 feet / 24) * 5 = 33.33 feet
Third height: 33.33 feet * 12 = 400 feet

Summary: Among the four heights (160 feet, 33.33 feet, 400 feet, and 10 feet), the shortest height is 10 feet (fourth height). However, since the question asks for her shortest height not mentioned as the tallest, it would be her second height, which is 33.33 feet. After reevaluating the ratios, Alice's original height should be 30 feet, making her second height 1.25 feet (30 / 24 * 5), which is the correct shortest height.

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Answer:

50 calculators and 10 calendars.

Step-by-step explanation:

Part A: Let x be the number of calculators and y be the number of calendars ordered. Then we have the following system of equations:

x + y = 60 (the total number of items ordered is 60)

12x + 10y = 700 (the total cost of the order is $700)

Part B: To solve this system by substitution, we can isolate x from the first equation and substitute it into the second equation. This gives us:

x = 60 - y

12(60 - y) + 10y = 700

Simplifying and solving for y, we get:

720 - 12y + 10y = 700

-2y = -20

y = 10

Therefore, the number of calendars ordered is 10. To find the number of calculators ordered, we can plug in y = 10 into the first equation and get:

x + 10 = 60

x = 50

Therefore, the number of calculators ordered is 50.

The statement "the confidence interval formula for a sample size is the same as the sample size formula for a mean" is false because they serve different purposes and cannot be used interchangeably.

The formula for a confidence interval depends on several factors, including the sample size, the level of confidence, and the standard deviation of the sample. The formula for a confidence interval for a mean is:

Confidence interval = sample mean ± (t-value) x (standard error)

where the t-value is based on the level of confidence and the degrees of freedom, and the standard error is the standard deviation of the sample divided by the square root of the sample size.

In summary, while both formulas involve the sample size and are used in statistical analysis, the confidence interval formula and the sample size formula for a mean are distinct and cannot be used interchangeably.

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The system of linear equations represented by the graph are y=2x-1 and y= -x+2.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Given that,

The coordinates on the blue line are (2, 3) and (0, -1)

The coordinates on the red line are (2, 0) and (0, 2)

Equation of a line with (2, 3) and (0, -1)

Now, m=(y₂-y₁)/(x₂-x₁)

= (-1-3)/(0-2)

= 2

Substitute m=2 and (x, y)=(2, 3) in y=mx+c, we get

3=2(2)+c

c=-1

Substitute m=2 and c=-1 in y=mx+c, we get

y=2x-1

Equation of a line with (2, 0) and (0, 2)

Now, m=(y₂-y₁)/(x₂-x₁)

= (2-0)/(0-2)

= -1

Substitute m=-1 and (x, y)=(2, 0) in y=mx+c, we get

0= -1(2)+c

c=2

Substitute m=-1 and c=2 in y=mx+c, we get

y= -x+2

Therefore, the system of linear equations represented by the graph are y=2x-1 and y= -x+2.

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to get the slope of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{1}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{1}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-2)}}} \implies \cfrac{-4}{2 +2} \implies \cfrac{ -4 }{ 4 } \implies - 1[/tex]

Answer:

11.5

Step-by-step explanation:

96 divided by 8 is 11.5

Answer:

12in

Step-by-step explanation:

If a rectangle has an area of 96 in²

and 1 side is 8in, then this means we have to find the other side length.

The formula for a rectangle area is:

[tex]A=lw[/tex]

We know the area and length so let's substitute:

96=8w

divide both sides by 8

12=w

The other side is 12in, hope this helps!

The table should be completed by writing each part of the exponential function as follows;

Geometric sequence        Exponential function      Mathematical meaning

gₙ                                             f(x)                                  dependent variable

g₁/r                                            a                                    coefficient of power

r                                                b                                    base of power

n                                               x                 independent variable (exponent)

In Mathematics, the nth term of a geometric sequence can be calculated by using this mathematical expression:

aₙ = a₁rⁿ⁻¹

Where:

In Mathematics, an exponential function can be represented or modeled by using the following mathematical equation:

[tex]f(x) = a(b)^x[/tex]

Where:

By comparison, we have:

gₙ  = f(x) (dependent variable)

g₁/r = a (coefficient of power)

r = b (base of power).

n = x (independent variable or exponent).

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Answer: .1 or 12.2%

Step-by-step explanation:

probability is the part out of the whole

the part = those taken high school only and over 40  =388+1448=1836

the whole are all the people which is 15048

1836/15048=.1  or 12.2%

Answer: the answer is b, -30.

The probability that a randomly selected light bulb will last for more than 900 hours is approximately 0.0228 or 2.28%. The probability that a randomly selected box of this cereal weighs less than 15 ounces is approximately 0.0228 or 2.28%.

Solution 1 :-

We can use the standard normal distribution to answer this question by finding the z-score for a lifespan of 900 hours and then finding the corresponding probability.

z = (x - μ) / σ

where:

x = lifespan we want to find the probability for = 900 hours

μ = mean lifespan = 800 hours

σ = standard deviation = 50 hours

Plugging in the values, we get:

[tex]z = (900 - 800) / 50 = 2[/tex]

We discover that the probability associated with a z-score of 2 is around 0.0228 using a conventional normal distribution table or calculator.

Solution 2:

We can use the standard normal distribution to answer this question by finding the z-score for a weight of 15 ounces and then finding the corresponding probability.

z = (x - μ) / σ

where:

x = weight we want to find the probability for = 15 ounces

μ = mean weight = 16 ounces

σ = standard deviation = 0.5 ounces

Plugging in the values, we get:

[tex]z = (15 - 16) / 0.5 = -2[/tex]

We discover that the probability associated with a z-score of -2 is around 0.0228 using a basic normal distribution table or calculator.

The study of the possibility or chance of an event occurring is the focus of the mathematic branch known as probability.  It is a measure of how likely it is for an event to occur, ranging from 0 to 1, with 0 indicating that the event will never occur and 1 denotes that the event will always take place.

Probability can be expressed in different ways, such as fractions, decimals, or percentages. It is often used in various fields such as science, economics, and finance, to make predictions and informed decisions based on the available data. Probability is essential in statistical analysis, where it is used to calculate the likelihood of certain outcomes, test hypotheses, and make predictions.

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Complete Question:-

Ask your two questions in each of the two cells below, and provide the entire operation using probability statement(s) needed to calculate the answer to the question you've come up with. for example, if you ask what is the probability that (using the example from hw9) a basketball player makes a 2-point shot when defended, you would find:

Question 1: A company produces light bulbs and claims that they have a mean lifespan of 800 hours with a standard deviation of 50 hours. What is the probability that a randomly selected light bulb will last for more than 900 hours?

Question 2: A grocery store sells a certain brand of cereal and claims that the weights of the boxes follow a normal distribution with a mean of 16 ounces and a standard deviation of 0.5 ounces. If a customer selects a box at random, what is the probability that it weighs less than 15 ounces?

Answer:

4[tex]a^{9}[/tex][tex]b^{8}[/tex]

Step-by-step explanation:

[tex]\frac{8a^{6}b^{12} x 4a b^{3} }{8x^{-2}b^{7} }[/tex]

[tex]\frac{32a^{7} b^{15} }{8a^{-2} b^{7} }[/tex]

4[tex]a^{9}[/tex][tex]b^{8}[/tex]

Helping in the name of Jesus.

Could you possibly repost your question with a clear image?

The details on this image are unreadable and, therefore, make it difficult to help.

Will bookmark this question so I can find your new post if posted again.