The claim that the mean amount of sleep for adults is less than 7 hours. Choose the correct statement about null and alternative hypothesis.
a) H0: µ > 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
b) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
H2: µ > 7 hours (second alternative hypothesis and original claim)
c) H0: µ = 7 hours (null hypothesis)
H1: µ < 7 hours (alternative hypothesis and original claim)
d) H0: µ < 7 hours (null hypothesis)
H1: µ ≥≥ 7 hours (alternative hypothesis and original claim)

Answer:

  D.  65°

Step-by-step explanation:

The measure of the angle at crossed chords is the average of the measures of the intercepted arcs:

  m∠XYZ = (1/2)(arc XZ +arc WV)

  m∠XYZ = (1/2)(86° +44°) = 130°/2

  m∠XYZ = 65°

Answer:

Step-by-step explanation:

This is a combination question. Combination has to do with selection. For example if r objects are to be selected from n pool of oblects, this can be done in nCr number of ways.

nCr = n!/(n-r)r!

According to the question, if a radio show can only play 10 records out of 12 records available, this can be done in 12C10 number of ways.

12C10 = 12!/(12-10)!10!

= 12!/2!10!

= 12*11*10!/2*10!

= 12*11/2

= 6*11

= 66 different ways

Answer: 72 arrangements

Step-by-step explanation:

The books are:

Statistics,  calculus, geometry, algebra, and trigonometry.

So we have 5 books.

We want that algebra and trigonometry are not together.

Suppose that we have 5 positions:

Now, we can start with algebra in the first position.

Now, we have 3 positions for trigonometry (3rd, 4th and 5th).

Now, once those two books are in position, we have 3 other positions and 3 other books, so for the first selection we have 3 options, for the second position we have 2 options, and for the last option we have 1 option.

The number of combinations is equal to the number of options in each selection:

3*(3*2*1) = 18

Now, if Algebra is in the second place, then for trigonometry we have only 2 possible options (4th and 5th)

and for the other 3 books again we have 3*2*1 combinations:

the total number of combinations is:

2*(3*2*1) = 12

If algebra is in the 3rd position, trigonometry has 2 options (1st and 5th)

For the other 3 books, we have 3*2*1 combinations.

The total number of combinations is:

(3*2*1)*2 = 12

in the fourth position is the same as the second position, so here we have again 12 combinations.

For the fifth position is the same as for the first position, so we have 18 combinations.

The total number of combinations is:

C = 18 + 12 +12 +12 +18 = 72

Answer:

  (2/5)√5 ≈ 0.894427

Step-by-step explanation:

You require the y-coordinate of the point that satisfies two equations:

  x^2 +y^2 = 1

  y = 2x

Substituting for x, we have ...

  (y/2)^2 +y^2 = 1

  y^2(5/4) = 1

  y^2 = 4/5

  y = (2/5)√5 ≈ 0.894427

The sine of the angle is (2/5)√5 ≈ 0.894427.

Answer:

The answer would be C.

Step-by-step explanation:

Answer:

a) P(1) = 0.1637

b) [tex]P(x\geq 2) = 0.0176[/tex]

c) E(x) = 0.2

Step-by-step explanation:

If X follows a poisson distribution, the probability that a disk has exactly x missing pulses is:

[tex]P(x)=\frac{e^{-m}*m^x}{x!}[/tex]

Where m is the mean and it is equal to the value of lambda. So, replacing the value of m by 0.2, we get that the probability that a disk has exactly one missing pulse is equal to:

[tex]P(1)=\frac{e^{-0.2}*0.2^1}{1!}=0.1637[/tex]

Additionally, the probability that a disk has at least two missing pulses can be calculated as:

[tex]P(x\geq 2)=1-P(x<2)[/tex]

Where [tex]P(x<2)=P(0)+P(1)[/tex].

Then, [tex]P(0)[/tex] and [tex]P(x\geq 2)[/tex] are calculated as:

[tex]P(0)=\frac{e^{-0.2}*0.2^0}{0!}=0.8187\\P(x\geq 2) = 1 - (0.8187 + 0.1637)\\P(x\geq 2) = 0.0176[/tex]

Finally, In the poisson distribution, E(x) is equal to lambda. So E(x) = 0.2

Answer:

first term = -2

fourth term = -16

eighth term = -256

Step-by-step explanation:

Given;

A sequence with function;

A(n) = -2x2^(n-1)

The first, fourth, and eighth terms of the sequence can be calculated by substituting their corresponding values of n;

First term A(1); n = 1

A(1) = -2x2^(1-1) = -2×1 = -2

Fourth term A(4); n = 4

A(4) = -2x2^(4-1) = -2×8 = -16

Eighth term A(8); n = 8

A(8) = -2x2^(8-1) = -2×128 = -256

Therefore,

first term = -2

fourth term = -16

eighth term = -256

Answer:

1050 in total, 52.50 for each athlete

Step-by-step explanation:

We can start by writing an equation with x as the number of athletes

250+40x= Total cost

Now we can substitute 20 for x

250+40(20)

250+800

1050

The total cost is 1050

If you need the amount that each athlete is paying individually, just divide it by 20

1050/20=52.50

52.50 for each athlete

Answer:

Step-by-step explanation:

1). [tex](\frac{-4}{9})\times (\frac{7}{4})=(-1)(\frac{4}{9})(\frac{7}{4} )[/tex]

                [tex]=-\frac{7}{9}[/tex] [Negative]

2). [tex](-2\frac{3}{4})(-1\frac{1}{5})=(-1)(2\frac{3}{4})(-1)(1\frac{1}{5})[/tex]

                        [tex]=(-1)^2(2\frac{3}{4})(1\frac{1}{5})[/tex]

                        [tex]=(2\frac{3}{4})(1\frac{1}{5})[/tex] [Positive]

3). (3)(-3)(-3)(-3)(-3) = 3.(-1).3.(-1).3.(-1).3(-1).(3)

                              = (-1)⁴(3)⁵

                              = (3)⁵ [Positive]

4). [tex](-\frac{1}{6})(-2)(-\frac{3}{5})(-9)[/tex] = [tex](-1)(\frac{1}{6})(-1)(2)(-1)(\frac{3}{5})(-1)(9)[/tex]

                                   = [tex](-1)^4(\frac{1}{6})(2)(\frac{3}{5})(9)[/tex]

                                   = [tex](\frac{1}{6})(2)(\frac{3}{5})(9)[/tex] [Positive]

5). [tex](-\frac{4}{7})(-\frac{3}{5})(-9)=(-1)(\frac{4}{7})(-1)(\frac{3}{5})(-1)(9)[/tex]

                            [tex]=(-1)^3(\frac{4}{7})(\frac{3}{5})(9)[/tex]

                            [tex]=-(\frac{4}{7})(\frac{3}{5})(9)[/tex] [Negative]

6). [tex](-\frac{10}{7})(\frac{8}{3})=(-1)(\frac{10}{7})(\frac{8}{3})[/tex]

                    [tex]=-(\frac{10}{7})(\frac{8}{3})[/tex] [Negative]

Answer:

$36

Step-by-step explanation:

30 is 5/6 of the game, so we can think that 1/6 is equal to 6, since 5(6) is 30.

If we add another sixth, we get 36, which will be the total cost of the game.

Answer:

The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

Step-by-step explanation:

The general form of a regression equation is:

[tex]y=\alpha +\beta_{1}x_{1}+\beta_{2}x_{2}+...+\beta_{n}x_{n}[/tex]

Here,

α = y-intercept

βi = regression coefficients, (i = 1, 2, ..., n)

A regression analysis is performed to determine whether the predictor variables are statistically significant or not.

The output of the regression analysis consists of two tables.

One is the regression output and the other is the ANOVA table.

The regression output table is used to display which predictor variables are statistically significant and which are not.

The test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

And the ANOVA table displays overall regression analysis.

The F-test statistic is used to for the overall regression analysis.

Thus, the test statistic used to determine whether a particular predictor in a regression analysis is statistically significant is:

[tex]t=\frac{\beta_{i}}{S.E._{\beta_{i}}}[/tex]

Answer:

C

Step-by-step explanation:

(3,15) and (4,12)

Answer:

C or (3, 15) and (4, 12)

Step-by-step explanation:

I just took the test on Edge 2020

Answer:

C

Step-by-step explanation:

The equation must be equal to c since that is the total cost.

c = 1.18v

Plug in 98 for v to find the answer.

c = 1.18(98)

c = $115.64

Answer:

20

Step-by-step explanation:

224÷4 = 56+40 = 96÷2 = 48+12 = 60÷3 = 20

If Ronnie goes to the racetrack with his buddies on a weekly basis. How much did he start with the first week is $20.

Hence:

4 [2 (3x - 12) -40] = 224

4 [6x - 24 - 40] = 224

Collect like term

24x - 256= 224

24x/24 = 480/24

Divide both side by 24

x=480/24

x=$20

Therefore How much did he start with the first week is $20.

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Answer:

Step-by-step explanation:

y-|x|+3

y=|x|+3

vertex=(0,3)

y=|x-4|-7

vertex(4,-7)

Answer:

20 Lizard lollies.

Step-by-step explanation:

There are 10 lizard lollis.  This is out of 10+4+6 = 20 total treats.  This makes the probability of drawing a lizard lollis 10/20 = 1/2.

This means out of 40 treats handed out, we can expect him to give out 1/2(40) = 20 lizard lollis.

Answer:

[tex]\frac{dy}{dx}[/tex] = - 21[tex]x^{6}[/tex] + 6x² + 1

Step-by-step explanation:

Differentiate each term using the power rule

[tex]\frac{d}{dx}[/tex] (a[tex]x^{n}[/tex] ) = na[tex]x^{n-1}[/tex]

Given

y = - 3[tex]x^{7}[/tex] + 2x³ + x , then

[tex]\frac{dy}{dx}[/tex] = (7 × - 3 )[tex]x^{6}[/tex] + (3 × 2)x² + (1 × 1 )[tex]x^{0}[/tex]

    = - 21[tex]x^{6}[/tex] + 6x² + 1

Answer:

Yes, it's also true about the confidence interval method.

Step-by-step explanation:

The confidence interval includes all the null hypothesis values for the population mean that would be accepted by the hypothesis test at the significance level of 5%. Now, it means this assumes a two-sided alternative.

Now, when testing claims about

population​ proportions, the critical method and the​ P-value method are equivalent due to the fact that they always produce the same result. Similarly, a conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

So, Yes the confidence interval method and the​ P-value or critical methods will always lead to the same conclusion when the tested parameter is the standard deviation.

Answer:

A.

Step-by-step explanation:

B is wrong because irrational numbers can include pie.

C and D are wrong because irrational numbers don't get a whole number, and instead gives a decimal numbers.

Answer:

  3 square units

Step-by-step explanation:

Put the numbers in the formula and do the arithmetic.

  A = 12(1/2)² = 12(1/4) = 3 . . . square units

__

Comment on the working

It might be helpful to you to see how this works when the units of the number are attached to the number.

  A = 12(1/2 unit)² = 12(1/2 unit)(1/2 unit) = 12(1/2)(1/2)(unit)(unit) = 3 unit²

I often choose to keep the units with the numbers, just to make sure that the numbers and units are correct. For example, you can multiply inches by feet, but you get in·ft, which is not square inches and not square feet. You have to do a conversion to get the result in square units.

The inverse of the given permutation matrix A is

                          [tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

To find the inverse of the given permutation matrix A:

[tex]\[ A = \begin{bmatrix}0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\0 & 1 & 0 & 0 \\1 & 0 & 0 & 0 \\\end{bmatrix} \][/tex]

Utilize the concept that the inverse of a permutation matrix is its transpose.

Therefore, the inverse of matrix A is:

[tex]\[ A^{-1} = A^T \][/tex]

Taking the transpose of matrix A, gives

[tex]\[ A^{-1} = \begin{bmatrix}0 & 0 & 0 & 1 \\0 & 0 & 1 & 0 \\1 & 0 & 0 & 0 \\0 & 1 & 0 & 0 \\\end{bmatrix} \][/tex]

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Answer:

  4 blue fish for every 5 orange fish

Step-by-step explanation:

(orange fish) = (1 1/4)·(blue fish) . . . . . the given relation

(orange fish) = (5/4)·(blue fish) . . . . . write as improper fraction

(orange fish)/(blue fish) = 5/4  . . . . .  divide by "blue fish"

There are 4 blue fish for every 5 orange fish.

Answer: B. f is always negative on the interval

========================================================

Explanation:

-1/5 = -0.2

Pick any number for x that will make the interval -0.2 < x < 2 to be true. I find x = 0 to be easiest.

Plug it into f(x)

f(x) = (5x+1)(4x-8)(x+6)

f(0) = (5(0)+1)(4(0)-8)(0+6)

f(0) = (1)(-8)(6)

f(0) = -48

We get a negative result.

So we can rule out choice A which says that f is always positive. Either f is always negative on this interval, or it's a mix of being positive and negative.

-------------

Note that the roots of f(x) are -1/5, 2 and -6. This is from solving f(x) = 0

Use the zero product property to solve (5x+1)(4x-8)(x+6) to find the three roots mentioned.

The roots of -1/5 and 2 form the boundary of the interval mentioned at the top of the problem. There are no roots in between -1/5 and 2, so this means that f(x) stays entirely negative on this interval. There is no way f(x) becomes positive on this interval because it would have to cross over the x axis, thus forming another root. But again there are no roots between -1/5 and 2.

A graph confirms we have the correct answer. Check out the image attached below. Note the portion from x = -0.2 to x = 2 is entirely below the x axis.

Answer:

200√3

Step-by-step explanation:

The triangle given here is a special right triangle, one with angles measuring 30-60-90 degrees. The rule for triangles like these are that the side opposite the 30° angle can be considered x, and the side opposite the 60° angle is x√3, while the hypotenuse, or side opposite the right angle, is 2x. All we need to know here are the two legs to find the area.

Since b is opposite the 30° angle, it is x, while side RS is opposite the 60° angle, meaning it is equal to x√3, meaning that the area of the triangle is 1/2*x*x√3. We can substitute in 20 for x, making our area 1/2*20*20√3. Multiplying we get 10*20√3, or 200√3.

Answer:

His final velocity is 48.03 m/s

Step-by-step explanation:

Using SI units  (m, kg, s)

a = 3.7

x0 = 25

x1 = 300

v0 = 16.5

Apply kinematics formula

v1^2 - v0^2 = 2a(x1-x0)

solve for v1

Final velocity

v1 = sqrt(2a(x1-x0)+v0^2)

= sqrt( 2(3.7)(300-25)+16.5^2) )

= 48.03 m/s

Answer:

1:3

Step-by-step explanation:

10 red cards, 10 black cards, and 20 blue cards

We want the ratio of red to other cards

red : blue and black

10 : 10+20

10 : 30

Divide each side by 10

10/10 : 30/10

1:3

Hey there! :)

Answer:

D: [8, 12].

R: [-10, -6].

Step-by-step explanation:

Notice that the endpoints of the graph are closed circles. This means that square brackets will be used:

The graphed equation is from x = 8 to x = 12. Therefore, the domain of the function is:

D: [8, 12].

The range goes from y = -10 to -6. Therefore:

R: [-10, -6].

Answer:

D: [8 , 12]

R: [-10 , -6]

Step-by-step explanation:

Well for this parabola domain and rage are acttually limited because of the solid dots you see on the graph.

So first things first, what is range? Well range is the amount of y values on a line or anything in a graph.

And what’s domain? Domain is the amount of x values on a line or whatnot.

So let’s do domain first.

On the parabola the first x value is 8 and the last is 12 so we have to write this in interval notation which is  [8 , 12].

Now for range the lowest y value is -10 and the highest is -6 so in interval notation it is [-10 , -6].

Answer:

y = (x - 4)² + 2 , x ≥ 4.

Step-by-step explanation:

Finding the inverse of

f(x) = 4 + √(x - 2)

Begin by swapping the x and y variables in the equation:

x = 4 + √(y - 2)

Subtract 4 from both sides:

x - 4 = √(y - 2)

Square both sides:

(x - 4)² = y - 2

Add 2 to both sides to get your equation:

y = (x - 4)² + 2

However, the domain restriction also needs to be included since the question involves finding the inverse of a square root function. In this case, the domain restriction would be x ≥ 4.

Answer:

58.1 and 17

Step-by-step explanation:

For the first triangles the similarity ratio is 1:7 so x is 8.3 × 7 = 58.1

For the second triangles the similarity ratio is 1:5 so x is 3.4 × 5 = 17

Answer:

Step-by-step explanation:

Let d represent the number of dimes. Then d-9 is the number of nickels. The total value (in cents) is ...

  10d +5(d-9) = 180

  15d -45 = 180 . . . . . simplify

  d -3 = 12 . . . . . . . . . .divide by 15

  d = 15

  15 -9 = 6 = number of nickels

Sue has 15 dimes and 6 nickels.

Answer:

15 dimes, 6 nickels

Step-by-step explanation:

D = # of dimes, and N = # of nickels

10D + 5N = 180

D = N + 9

Substitute:

10 (N + 9) + 5N = 180

10N + 90 + 5N = 180

15N = 90

N = 6

D = 15

Answer:

Step-by-step explanation:

[tex] - \frac{4}{9} + \frac{7}{12} + ( - \frac{ 3}{8} )[/tex]

When there is a (+) in front of an expression in parentheses, the expression remains the same:

[tex] - \frac{4}{9} + \frac{7}{12} - \frac{3}{8} [/tex]

[tex] \frac{ - 4 \times 8 + 7 \times 6 - 3 \times 9}{72} [/tex]

Calculate the sum of difference

[tex] \frac{ - 32 + 42 - 27}{72} [/tex]

[tex] \frac{10 - 27}{72} [/tex]

[tex] - \frac{17}{72} [/tex]

Hope this helps..

Good luck on your assignment...