Regina made 1,240 pot holders. She wants to sell them in packages of 10. How many
packages will she have? Explain your thinking.

a)[tex]$z=\frac{40.5-40}{\frac{1.25}{\sqrt{10}}}=1.265$[/tex]

Now we can calculate the p value since we have a right tailed test the p values is given by:

[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]

And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .

b) [tex]$p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029$[/tex]

c) [tex]$\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$[/tex]

d) We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:

[tex]n=\frac{\left(z_\alpha+z_s\right)^2 \sigma^2}{(x-\mu)^2}[/tex]

The true mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:

[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]

e) For this case we can calculate a one sided confidence interval given by:

[tex]$\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)$[/tex]

And if we replace we got:

[tex]$40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152$[/tex]

And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]

And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.

What is null hypothesis?

In a scientific setting, a hypothesis (plural: hypotheses) is a testable claim about the relationship between two or more variables or a suggested explanation for a phenomenon that has been observed.

Part a

We have the following data given:

n=10 represent the sample size

[tex]$\bar{x}=40.5$[/tex] represent the sample mean

[tex]$\sigma=1.25$[/tex]represent the population deviation.

We want to test the following hypothesis:

Null: [tex]$\mu \leq 40$[/tex]

Alternative: [tex]$\mu > 40$[/tex]

The significance level provided was [tex]$\alpha=0.05$[/tex]

The statistic for this case since we have the population deviation is given by:[tex]z=\frac{\bar{x}-\mu}{\frac{-\mu}{\sqrt{n}}}$[/tex]

If we replace the values given we got:

[tex]$z=\frac{40.5-40}{\frac{1.24}{\sqrt{10}}}=1.265$[/tex]

Now we can calculate the p value since we have a right tailed test the p values is given by:

[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]

And since the [tex]$p_v > \alpha$[/tex] we have enough evidence to FAIL to reject the null hypothesis. So then there is not evidence to support the claim that the mean is greater than 40 .

Part b

The p value on this case is given by:

[tex]p_v=P(Z > 1.265)=1-P(Z < 1.265)=1-0.897=0.1029[/tex]

Part c

For this case the probability of type II error is defined as the probability of incorrectly retaining the null hypothesis and is defined like this:

[tex]\beta=P\left(Z < z_\alpha-\frac{(x-\mu) \sqrt{n}}{\sigma}\right)[/tex]

Where [tex]$z_\alpha=1.645$[/tex]represent the critical value for the test that accumulates 0.05 of the area on the right tail of the normal standard distribution.

The true mean on this case is assumed [tex]$\mu=42$[/tex], so then we can replace like this:

[tex]\beta=P\left(Z < 1.645-\frac{2 \sqrt{10}}{1.25}\right)=P(Z < -3.409)=0.000326$$[/tex]

Part d

We want to ensure that the probability of error type II not exceeds 0.1, and for this case we can use the following formula:

[tex]n=\frac{\left(z_\alpha+z_\beta\right)^2 \sigma^2}{(x-\mu)^2}[/tex]

The ture mean for this case is [tex]$\mu=44$[/tex] and we want [tex]$\beta < 0.1$[/tex] so then [tex]$z_{1-0.1}=z_{0.9}=1.29$[/tex] represent the value on the normal standard distribution that accumulates 0.1 of the area on the right tail. And we can replace like this:

[tex]n=\frac{(1.65+1.29)^2 1.25^2}{(44-40)^2}=0.844 \approx 1[/tex]

Part e

For this case we can calculate a one sided confidence interval given by:

[tex]\left(-\infty, \bar{x}+z_\alpha \frac{\sigma}{\sqrt{n}}\right)[/tex]

And if we replace we got:

[tex]40.5+1.65 \frac{1.25}{\sqrt{10}}=41.152[/tex]

And the confidence interval would be [tex]$(-\infty, 41.152)$[/tex]

And since 40 is on the confidence interval we don't have enough evidence to reject the null hypothesis on this case.

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The height the anchor begins to drop is 17.5 m

Since a Naval Carrier dropped anchor off the coast. The massive anchor drops at 3.5 m/s and will be 52.5 meters under the surface of the water after 20 seconds.

Let

The total height the anchor drops is thus H = h + h'

Now, the total height the anchor drops H = vt where

So, equating both equations, we have

vt = h + h'

Making h subject of the formula, we have that

h = vt - h'

Given that

Substituting the values of the variables into the equation, we have that

h = vt - h'

h = 3.5 m/s × 20 s - 52.5 m

h = 70 m - 52.5 m

h = 17.5 m

So, the anchor drops 17.5 m

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Answer:

To solve a system of equations without graphing, you can use one of several methods, such as substitution or elimination. Here's how you can solve this system using substitution:

First, solve one of the equations for one of the variables in terms of the other variable. For example, you can solve the first equation for y:

5x + 14y = -5

y = (-5 - 5x) / 14

Substitute this expression for y into the second equation, to get an equation in terms of x:

-3x + 10((-5 - 5x) / 14) = 72

Simplify this equation to get an equation in terms of x:

-3x - 50 - 35x = 72

-38x - 50 = 72

-38x = 122

x = -3.316

Substitute this value for x back into one of the original equations to solve for y:

y = (-5 - 5(-3.316)) / 14

y = (5 + 16.58) / 14

y = 21.58 / 14

y = 1.546

So the solution to the system of equations is (x, y) = (-3.316, 1.546).

Alternatively, you could solve the system using elimination. To do this, you would add the two equations to eliminate one of the variables, and then solve the resulting equation for the remaining variable.

Answer:

its 14

Step-by-step explanation:

50 didvdied by 20 is 18 so here u go

Answer:

Step-by-step explanation:

the product between the mixed numbers is equal to 12 and 1 over 60, which is the first option.

How to find the product between two mixed numbers?

A mixed number is a number that is written as the addition of a whole number and an improper fraction.

Remember that the mixed number "negative two and one third" is written as:

-2 ¹/₃ = (-2 - 1/3)

Here we want to solve the product:

(-2 - 1/3)*(-5 - 15/100)

Notice that all the signs are negative, so the outcome will be positive:

(-2 - 1/3)*(-5 - 15/100) = 2*5 + (1/3)*5 + 2*(15/100) + (1/3)*(15/100)

                                 = 10 + 5/3 + 30/100 + 5/100

                                 = 10 + 5/3 + 3/10 + 1/20

                                  = 10 + 3/3 + 2/3 + 6/20 + 1/20

                                  = 11 + 2/3 + 7/20 = 11 + 40/60 + 21/60

                                  = 11 + 61/60 = 11 + 60/60 + 1/60 = 12 + 1/60

Then the product between the mixed numbers is equal to 12 and 1 over 60, which is the first option.

Answer:

12 1/60

Step-by-step explanation:

-2 1/3 × (-5 15/100) =

= -7/3 × (-5 3/20)

= 7/3 × 103/20

= 721/60

= 12 1/60

Using Pythagoras theorem, 11.31 is  the length of one leg of a right triangle .

What is the Pythagorean theorem in plain English?

The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.

                           This is written as a2 + b2 = c2 in the familiar algebraic notation.

Theorem: a^2 + b^2 = c^2. a and b are the legs, and c is the hypotenuse.                  

                       14^2 + b^2 = 18^2

                        196 + b² = 324

                            b² = 324 - 196

                              b = √128

                             b = 11.31

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We have to set ∠AMN equal to ∠D.

What are angles?

In Euclidean geometry, an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.

Label the rows (A nearest the screen, through G at back) and the seat numbers (starting with 1 on the far left of the diagram) and count towards the right.

The seat is not equal to 1 and will align to point D.

Viewing angle is in terms of another angle

Set ∠AMN equal to ∠D.

Hence, we have to set ∠AMN equal to ∠D.

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The measure of ∠JKM is 145°.

The measure of an exterior angle of a triangle is bigger than either of the measures of the distant interior angles, according to the external angle theorem, Proposition 1.16 in Euclid's Elements.

Because the parallel postulate is not required for its proof, this is a fundamental conclusion in absolute geometry. Three of a triangle's corners are its vertices.

Two angles are produced by a triangle's sides (line segments) meeting at its apex (four angles if you consider the sides of the triangle to be lines instead of line segments). An interior angle of the triangle is the only one of these angles that has the third side of the triangle inside of it.

Here it is given that, ∠JLK= 70°

                                 ∠LJK = x°

(2x-5)°= 70°+x°

now applying exterior angle theorem,

x=75°

substitute 75 for x in 2x-5 to find m∠JKM.

=2x-5

=2×75-5

=145°

Hence, The measure of ∠JKM is 145°

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Answer:

y=3x+10

Step-by-step explanation:

The formula for an equation in slope-intercept is y=mx+b. m is the slope and b is the y-intercept

The 3 is the slope because it says that you have to pay that amount per game so that is the rate. 10 is the y-int because it says that you have to pay a one-time fee and a y-intercept is just once and isn't a rate.

The percentage of oxygen in the water is 0.0002%.

A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.

To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.

Given that a 2000 ml sample of water was collected and found to have 0.004 mL of oxygen. Therefore, the percentage oxygen in water is equal to,

Percentage = Volume of oxygen in the water / Volume of water

                   = 0.004 mL / 2000 mL

                   = 0.004 mL / 2 mL

                   = 0.0002% of water

Therefore, the percentage of oxygen in the water is 0.0002%.

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False, an industry standard is to randomly select 10% of the completed surveys for purposes of making a call-back to validate that the interview was conducted.

What are industries standards?

A collection of standards within an industry referring to how activities are typically carried out in their respective domains of production.

                  In other words, it refers to the standards that are commonly accepted by an industry's participants.

Why is this industry norm?

Industry standards are primarily intended to make products compatible with one another and to ensure that consumers can mix and match products from various brands without risk.

                             Best Industry Standards refers to benchmarks that, taking into account elements like the nature and size of the parties, are in the upper quartile in the relevant industry for the delivery of comparable services that are essentially similar to the Services or the relevant part of them.

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30 red playing chip were given to him.

Let m be the number of red playing chips and n be the number of blue playing chips.

since Jack purchased 50 playing chips, we get an equation.

m + n = 50              .............(1)

He pais $400 for these 50 chips, so we get an equation,

10m + 5n = 400         ........(2)

From equation (1) we get,

m = 50 - n               ...............(3)

Substitute above value of m in equation (2),

10(50 - n) + 5n = 400        

500 - 10n + 5n = 400

-5n = -100

n = 20

Substitute above value of n in equation (3),

m = 50 - 20

m = 30

Therefore, the number of red playing chips = 30

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The rectangle's area is increasing at a pace of 128 in2 /s.

What in math is a rate?

A rate is a unique ratio where the two words are expressed in several units. For instance, the price is 69 for 12 ounces if a 12-ounce can of maize costs 69. This is not a proportion of two comparable units, like shirts. This ratio compares two dissimilar units: ounces and cents

Give L and W the length and breadth, respectively. The rectangle's surface area is

A = L ⋅ W.

To obtain, differentiate both sides of the aforementioned equation with regard to time t.

dA ⁄ dt = dL ⁄ dt ⋅ W + L ⋅ dW ⁄ dt

Given the circumstances,

dL ⁄ dt = 10 and dW ⁄ dt = 4

So at the moment when L = 12 and W = 2,

dA ⁄ dt = (10)(12) + 4(2 )

          = 128

The rectangle's area is increasing at a pace of 128 in2 /s.

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Step-by-step explanation:

sign of truelove or truefriendship is the probability of both draw a heart

Answer: 5.6 kg of Mac n cheese per dollar.

Step-by-step explanation:

1 pound = 0.45 kg

So take 2.50 divided by 0.45 = 5.6 kg of Mac n cheese per dollar.

Answer: 14/16 & 28/32

Step-by-step explanation: For 14/16, is simply multiplied 7/8 by 2 for the numerator and denominator, so 7 x 2 = 14, and 8 x 2=16. And, I did the same thing for 28/32. Just multiply both sides by 4. I hope this helped!

Step-by-step explanation:

8x + 3y = 7 --------(1)

2x + y = 2 ----------(2)

y = 2 – 2x ---------(3)

just substitute for y in equation (1)

8x + 3(2–2x) = 7

8x + 6 – 6x = 7

8x – 6x + 6 = 7

2x = 7 – 6

2x = 1

x = ½

since x = ½ just substitute for x in equation(3)

y = 2 – 2x

y = 2 – 2(½)

y = 2 – 1

y = 1

so x = ½,y = 1

i hope this helped

Answer:  [tex]h = \frac{J-2b}{2r}[/tex]

Work Shown:

[tex]J = 2hr + 2b\\\\J - 2b= 2hr\\\\h = \frac{J-2b}{2r}[/tex]

Explanation:

In the 2nd step, we isolate the "2hr" by subtracting both sides by 2b. This is do unto the +2b done to the right side initially. We want 2hr all by itself since it contains h.

Then to fully isolate h, we divide both sides by 2r. It might help to think of 2hr as 2r*h so you can pull out the terms easier. The division is done to undo the multiplication.

If writing out the final step using a keyboard, then you would say (J-2b)/(2r). Use parenthesis to indicate which terms are being divided.

The rationale that supports this statement is:

​Situational experiences are interpreted differently.

Now, According to the question:

Let's Know:

What is the Rationale of the Study?

The rationale of the study explains the reason why the study was conducted (in an article or thesis) or why the study should be conducted (in a proposal). This means the study rationale should explain to the reader or examiner why the study is/was necessary.

We know that :

There are different levels and combinations of concerns among individual students.

Hence, The rationale that supports this statement is:

​Situational experiences are interpreted differently.

In the question;

There are different levels and combinations of concerns among individual students.

what is the rationale that supports this statement?

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The probability that among those selected the second smallest in 2020 is 1/3

In this question, we have been given six distinct integers are selected at random from 2018, 2019, 2020, . . . , 2027

We need to find the probability that among those selected the second smallest in 2020.

Here, total integers are: 10

The total number of ways to choose six distinct integers :

10C6

= 10!/6!(10 - 6)!

= 210

Assume 2020 is the second-lowest number.

There are 5 numbers left to choose, 4 of which must be greater than 2020.

This is equivalent to choosing 4 numbers from the seven numbers larger than 2020, and 1 number from the two numbers less than 2020

using combination formula,

7C4 * 2C1

= 35 * 2

= 70

So, the probability would be,

P = 70/210

P = 1/3

Therefore, the required probability is 1/3  

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Answer:

[tex]2\frac{6}{7}[/tex]

Step-by-step explanation:

-5(-4/7)

First:

A negative multiplied by a negative is positive, so we can remove the negative symbols.

5(4/7)

Multiply:

[tex]\frac{5(4)}{7}[/tex]

20/7

Convert into a mixed number:

2 6/7

The Wonderful Wizard of Oz, according to American historian Henry Littlefield, was a metaphor for the 1890s Populist movement, which was an uprising by disaffected manufacturing and agricultural workers to gain control from the financial elite. Littlefield made this claim in 1964.

Judy Garland's character Dorothy and her dog Toto are carried away in their home to the fantastical country of Oz as a cyclone tear across Kansas.

As they travel along the Yellow Brick Road to the Emerald City to visit the Wizard, they encounter characters like the brainless Scarecrow (Ray Bolger), the heartless Tin Man (Jack Haley), and the Cowardly Lion (Bert Lahr).

The Wizard of Oz set and filming process was toxic, from bosses demanding their injured and sickly players return to set despite still needing to heal to the director smacking a 16-year-old and forcing her to take drugs to control her hunger and keep thin.

Therefore, the Wonderful Wizard of Oz, according to American historian Henry Littlefield, was a metaphor for the 1890s Populist movement, which was an uprising by disaffected manufacturing and agricultural workers to gain control from the financial elite. Littlefield made this claim in 1964.

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The function is an exponential growth function growth decay percent rate of change of the function is 110 %.

Given :

What type of exponential function is f(x)=0. 75(2. 1)^x what is the function's percent rate of change.

we know that,

exponential growth function in the form of y = a ( 1 + r )^x

on comparing both functions we get ,

1 + r = 2.1

r = 2.1 - 1

r = 21 / 10 - 1

= 21 - 10 / 10

= 11 / 10

= 1.1

converting into percentage:

= 1.1 * 100 %

= 110 %

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The true equation would be = DE/DF = AB/AC

What does an equivalent ratio look like?

When we compare two ratios, they are said to be equivalent. To determine whether two or more ratios are equivalent, they can be compared to one another. For instance, the ratios 1:2 and 2:4 are equivalent.

Are all proportions an equivalent ratio?

Proportional quantities are represented by a collection of corresponding ratios. We can claim, for instance, that 2:3 and 4:6 are proportionate.

Is proportion a constant?

"X is to Y as A Is to B" is how a proportion is expressed. Cross products are the xb and ay products. A proportion's cross products are consistently equal.

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Answer:

y= 0.25x

Step-by-step explanation:

First, use the slope formula to calculate the slope.

Second, solve for the y-intercept using the slope and one of the points.

Finally, once you've determined m and b, you can enter them into the slope-intercept form of a line (y = mx + b) to obtain the equation for the line.

The likelihood of winning after one roll in a game is 1/6. This is because there are only two ways to win on the first roll: by rolling a 7 or an 11.

The possibility that an event will occur is gauged by probability. It is a mathematical idea that measures the probability or possibility that a specific event will occur. Probability is expressed as a number between 0 and 1, where 0 denotes that the event is highly unlikely to occur and 1 denotes that it will definitely happen. Making predictions and judgments based on the likelihood of an event occurring is a common use of probability in many disciplines, including statistics, economics, and gambling. The number of successful outcomes is divided by the total number of possible outcomes to determine probability. For example, if a coin is flipped and has a 50% chance of landing on heads, the probability of the coin falling on chiefs is 0.5.

How to solve?

Since there are 6 possible outcomes on a single roll of a pair of dice (1, 2, 3, 4, 5, 6), the likelihood of winning on the first roll is 1/6.

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Answer:

The answer is 246

Step-by-step explanation:

So,

S₁₂ = 12/2 [2(4) + (12 - 1)3]

S₁₂ = 6 [8 + (11)3]

S₁₂ = 6 × (8 + 33)

S₁₂ = 6 × 41

S₁₂ = 246

Thus, The S₁₂ of given A.P is 246

Blossoms age now will be 5 years.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Let Blossom age be x

The information will be illustrated as:

3x + 5 = 2(x + 5)

3x + 5 = 2x + 10

3x - 2x = 10 - 5

x = 5.

Therefore, Blossoms age now will be 5 years.

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The total distance Desiree travelled was 14km.

Always remember,

Average speed= Total distance travelled/ Total time taken

So, in this case, we have to find the distance,

Distance= Speed × Time

When she  ran 16km per hour for 30 minutes,

⇒ Distance= 16×30/60

⇒ Distance= 8km --------------------(1)

When she ran 8km per hour for 45 minutes,

⇒ Distance= 8×45/60

⇒ Distance= 6km --------------------(2)

Adding equations (1) and (2) we get,

⇒ Distance = 8+6=14km

Hence, the Total Distance travelled was 14km.

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