Find the slope of the line that passes through (1, 11) and (3, 10),
Simplify your answer and write it as a proper fraction, improper fraction, or integer,

\(\log_b\left( \dfrac 1{10} \right)\\\\=\log_b 1 - \log_b 10\\\\=0-2.303\\\\=-2.303\)

The p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis. There is insufficient evidence to support the claim p-value greater than the significance level 0.05.

Consider the above given that

⇒\(& \alpha=0.05 \quad \mathrm{n}=34 \mathrm{~s}^2=0.0005 \\\)

⇒\(H_{0} : \sigma^2 \leq 0.0004 \\\)

⇒\(H_{a} : \sigma^2 > 0.0004\)

The null and alternative hypothesis test statistic:

⇒\(& \mathrm{x}^2=\left(\frac{\mathrm{n}-1}{\sigma^2}\right) \mathrm{s}^2 \\\)

\(& =\left(\frac{34-1}{0.0004}\right) 0.0005 \\\)

⇒\(& \mathrm{x}^2=\left(\frac{33}{0.004}\right) \times 0.0005 \\\)

\(& =82,500 \times 0.0005 \\\)

⇒\(& \mathrm{x}^2=41.25\)

⇒\(h_{0} : $\sigma^2$ is that or equal to $0.0004$\)

⇒\(h_{a} : $\sigma^2$ is greater that $0.0004$\)

⇒p value=p(z>41.25)

⇒p value=0.1533

By using P Value from Chi-Square Calculator

⇒p value=0.1533

⇒P value >0.05

Fail to reject the null hypothesis.

Therefore, the p-value is 0.1533, so p-value>0.05 fail to reject the null hypothesis.

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The competitive advantage of some small Americans factories such as in tolerance contract manufacturing lies in their ability to produce parts with very narrow requirements, or tolerances, that are typical in the aerospace industry. consider a product with specifications that call for a maximum variance in the lengths of the parts of 0.0004. suppose the sample variance for 34 parts turns out to be \(s^{2}=0.0005\) . use \(\alpha=0.05\) , to test whether population variance specification is violated.

\(H_{0} \\H_{a}\)

Test statistic:

The p-value is-------.

Answer:

y=25000(0.84)^ty=25000(0.84)^3y=$14817.6

Step-by-step explanation:

Answer:

$10,546.88

Step-by-step explanation:

25,000(0.75)^3 is the formula/function you would use, which gives you 10,546.875, and then you'd round to the nearest hundredth.

Also took the exam

There are 70 grandparents, 140 parents, and 190 children in attendance at the family reunion

Given data ,

Let's denote the number of grandparents as "g", the number of parents as "p", and the number of children as "c".

Given that there were 400 people total at the family reunion, we can write the equation:

g + p + c = 400

Now , there were twice as many parents as grandparents, so we can write:

p = 2g

And we are given that there were 50 more children than parents, so we can write:

c = p + 50

Now we can use the equations (1), (2), and (3) to solve for the values of g, p, and c.

On simplifying the equation , we get

g + 2g + (2g + 50) = 400

5g + 50 = 400

5g = 400 - 50

5g = 350

g = 350 / 5

g = 70

Now we can substitute the value of g into (2) to find the value of p:

p = 2g = 2 x 70 = 140

And we can substitute the value of p into (3) to find the value of c:

c = p + 50 = 140 + 50 = 190

Hence , there were 70 grandparents, 140 parents, and 190 children in attendance at the family reunion

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The measure of the angle B of the triangle is 78.15 degrees

From the question, we have the following parameters that can be used in our computation:

A = 25 degrees

a = 9.5 units

b = 22 units

Using the law of sines, the angle B is calculated as

sin(A)/a = sin(B)/b

So, we have

sin(25)/9.5= sin(b)/22

This gives

sin(b) = 22 * sin(25)/9.5

Evaluate

sin(b) = 0.9787

Take the arc sin of both sides

b = 78.15

Hence, the measure of the angle is 78.15 degrees

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Answer:

\(x=\frac{3}{2}\\ y=\frac{1}{2}\)

Step-by-step explanation:

\(y=-x+2\\y=3x-4\)

Let's solve one of them for x.

\(y=3x-4\)

Add 4

\(y+4=3x\)

Divide by 3.

\(x=\frac{y+4}{3}\)

Now, plug the value of y in the formula, or you can plug the value of x in the other equation. I'll take this one.

\(x=\frac{y+4}{3}\)

\(x=\frac{(-x+2)+4}{3}\)

\(x=\frac{-x+2+4}{3}\)

\(x=\frac{-x+6}{3}\)

Multiply by 3 to get rid of the denominator.

\(3x=-x+6\)

add x

\(3x+x=6\)

Combine like terms;

\(4x=6\)

Divide by 4.

\(x=\frac{6}{4}\)

Simplify.

\(x=\frac{3}{2}\)

Now that you found the value of x, replace it in any of the equations to find y.

\(y=-x+2\\y=-(\frac{3}{2})+2\\ y=-\frac{3}{2}+2\)

\(y=\frac{-3+2*2}{2} \\y=\frac{-3+4}{2} \\y=\frac{1}{2}\)

Proof:

\(y=3x-4\\\frac{1}{2}=3(\frac{3}{2})-4\\\frac{1}{2}=(\frac{9}{2})-4\)

\(\frac{1}{2}=\frac{9-4*2}{2}\)

\(\frac{1}{2}=\frac{9-8}{2}\)

\(\frac{1}{2}=\frac{1}{2}\)

Answer:

13 and a half

Step-by-step explanation:

54 / 4 simple math honey, let me know if you need more help my door is always open!

An expression to represent the situation is 54/4.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Given that, a package of cookies includes 54 chocolate chip cookies.

Peter is going to split these cookies with 4 of his friends.

So, the expression is Total number of cookies/Number of friends

= 54/4

= 13.5

Therefore, an expression to represent the situation is 54/4.

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Answer: $7.40

Step-by-step explanation:

You can use $177.60 divide by 24 boxed lunches equals $7.40
Since you have to distribute 177.60 in 24 boxes.

Answer:

Step-by-step explanation:

According to the question, the equation is:

Let's see

The interest for Part 1 is approximately $385.10.

The interest for Part 2 is approximately $709.31.

The formula is as follows:

Interest is calculated as follows: Principal * Rate * Time

Where

Part 1:

$132,000 is the principal.

(Decimal) Rate = 12% = 0.12

Time = 8 days/365 days.

How much interest is there in Part 1?

Interest is calculated as follows : $132,000 * 0.12 * (8/365) = $385.10

Therefore, the interest for Part 1 is approximately $385.10.

Part 2:

$106,750 as the principal

(Decimal) Rate = 12% = 0.12

Time = 20 days / 365 days.

How much interest will there be in Part 2

Interest is calculated as follows : $106,750 * 0.12 * (20/365) = $709.31

Therefore, the interest for Part 2 is approximately $709.31.

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Solution

The formula for the z-score is given as:

- Thus, we can find the z-score as follows:

Answer:

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

Step-by-step explanation:

Given - A lab animal may eat any one of three foods each day. Laboratory records show that if the animal chooses one food on one trial, it will choose the same food on the next trial with a probability of 50%, and it will choose the other foods on the next trial with equal probabilities of 25%.

To find - If the animal chooses food #1 on an initial trial, what is the probability that it will choose food #2 on the second trial after the initial trial?

Proof -

By the given information, we get the stohastic matrix

\(H = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\)

As we know that,

The matrix is a Markov chain \(x_{k+1} = Hx_{k}\)

Let

The initial state vector be

\(x_{0} = \left[\begin{array}{ccc}1\\0\\0\end{array}\right]\)

we choose this initial vector because given that If the animal chooses food #1 on an initial trial.

Now,

\(x_{1} = Hx_{0} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}1\\0\\0\end{array}\right] \\= \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]\)

∴ we get

\(x_{1} = \left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right]\)

Now,

\(x_{2} = Hx_{1} \\ = \left[\begin{array}{ccc}0.5&0.25&0.25\\0.25&0.5&0.25\\0.25&0.25&0.5\end{array}\right]\left[\begin{array}{ccc}0.5\\0.25\\0.25\end{array}\right] \\= \left[\begin{array}{ccc}0.25+0.0625+0.0625\\0.125+0.125+0.0625\\0.125+0.0625+0.125\end{array}\right]\\= \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]\)

∴ we get

\(x_{2} = \left[\begin{array}{ccc}0.375\\0.3125\\0.3125\end{array}\right]\)

∴ we get

The probability that it will choose food #2 on the second trial after the initial trial = 0.3125

Answer:

Find the volume of the cone, the answer i got was 37.68 but it asked to round so it should be 37.7

Hope this helps :)

Answer:

If we want to find volume of cone we must use this formule: πr²*high/3.

Step-by-step explanation:

let's solve step by step

firstly you know the radius is 3 and high is 4

if we accept π to 3. the answer is must be (3*3*4)/3 and finally the answer is 12 units³

The graph of the feasible region is attached

From the question, we have the following parameters that can be used in our computation:

\(\left\{ \begin{array}{lr} y + 7x \ge 10 \\ 8y + 2x \ge 20 \\ y + x \ge 4 \\ y + x\le 10 \\ x \ge 0 \\ y \ge 0\end{array}\)

To plot the graph of the feasible region, we plot each inequality in the domain x ≥ 0 and y ≥ 0

Using the above as a guide, the graph is attached

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Answer:

145

Step-by-step explanation:

360-180-35=145

\(x = 145\)

.........

The person is approximately 8.43 miles from home, and they need to walk in the direction of approximately 26.6 degrees east of north to head directly home.

To determine the distance from home, we can use the concept of vector addition. The person walks 4 miles west, which can be represented as a vector (-4, 0) in a coordinate plane. Then, they walk 5 miles southwest, which can be represented as a vector (-3.54, -3.54) since southwest is a combination of west and south. Adding these two vectors together gives us (-7.54, -3.54).

To find the magnitude or distance from home, we use the Pythagorean theorem. The distance is given by sqrt((-7.54)^2 + (-3.54)^2) = 8.43 miles (approximately).

To determine the direction to head directly home, we need to find the angle between the vector (-7.54, -3.54) and the positive x-axis. We can use trigonometry to find this angle. The tangent of the angle is given by the ratio of the y-coordinate to the x-coordinate, which is -3.54 / -7.54. Taking the inverse tangent of this value gives us approximately 26.6 degrees.

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Answer: it will take Anthony 8 nights to finish the book.

Step-by-step explanation:

To find how many nights it will take Anthony to finish the book, we can use the following steps:

Determine how much of the book Anthony has left to read:

Total chapters in the book = 2 1/3 + 1/3 = 2 2/3 chapters

Amount of book left to read = 2 2/3 - 0 = 2 2/3 chapters

Determine how much of the book Anthony reads each night:

Amount of book read each night = 1/3 chapter

Divide the number of books left to read by the number of books read each night to find the number of nights it will take to finish the book:

Number of nights = (2 2/3) ÷ (1/3) = (8/3) ÷ (1/3) = 8

Therefore, it will take Anthony 8 nights to finish the book.

Answer:

B.

Step-by-step explanation:

No matter what a square is a regular polygon

Rollaway Skates is cheaper when the number of people is less than or equal to 4. For example, the cost for 2 people at Rollaway Skates is $10, while the cost for 2 people at Wheelie's Skates and Stuff is $106.

Wheelie's Skates and Stuff is cheaper when the number of people is greater than or equal to 5. For example, the cost for 6 people at Rollaway Skates is $30, while the cost for 6 people at Wheelie's Skates and Stuff is $118.

I hope this helps! Do you have any other questions?

Answer:

16xthe equal parts squares

Step-by-step explanation:

if that is correct let me know of the ewuation

The length of EB is approximately 14.6 units when rounded to the nearest tenth.

To find the length of EB, we can use the property of similar triangles in this diagram. By looking at triangle DFE and triangle CFB, we can see that they are similar triangles.

Using the similarity ratio, we can set up the proportion:

DF / CF = DE / EB

Plugging in the given values, we have:

13.1 / 10.9 = 17.5 / EB

To find EB, we can cross-multiply and solve for EB:

13.1 * EB = 10.9 * 17.5

EB = (10.9 * 17.5) / 13.1

EB ≈ 14.6

Therefore, the length of EB is approximately 14.6 units when rounded to the nearest tenth.

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Using the basic rational function, f(x) = 1/x, a rational inverse function with the given transformations is:

h(x) = g(x) + k = (1/2) / (x - h) + k

From the question, we are to create a rational inverse function that the given transformations

Let's start with a basic rational function:

f(x) = 1/x

To obtain a vertical compression of factor a, we need to multiply the function by a constant less than 1. Let's choose a = 1/2:

g(x) = (1/2) f(x) = (1/2) / x

To shift the function horizontally to the right by h units, we need to replace x with x - h:

g(x) = (1/2) / (x - h)

Finally, to shift the function vertically up by k units, we need to add k to the whole function:

h(x) = g(x) + k = (1/2) / (x - h) + k

Hence, a rational inverse function with the given transformations is:

h(x) = g(x) + k = (1/2) / (x - h) + k

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A sample of matter experiences a decrease in average kinetic energy as it continues to cool. One would anticipate that the particles will eventually come to a complete stop. The temperature at which particles should theoretically stop moving is absolute zero. Thus, option B is correct.

What theory directly contradicts concept of absolute zero?

All molecules are predicted to have zero kinetic energy and, as a result, no molecular motion at absolute zero (273.15°C). Zero is a hypothetical value (it has never been reached).

Absolute zero signifies that there is no kinetic energy involved in random motion. A substance's atoms don't move relative to one another.

Therefore, Kinetic energy because it can create heat which goes against the absolute zero. A gas molecule's kinetic energy tends to zero when the temperature reaches absolute zero.

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The area of the square with a side length of 3.1 meters is 9.61 square meters.

To find the area of a square, we need to multiply the length of one side by itself. In this case, the square has a side length of 3.1 m.

Area of a square = side length × side length

Substituting the given side length into the formula:

Area = 3.1 m × 3.1 m

To perform the calculation:

Area = 9.61 m²

It's worth noting that when calculating the area, we are working with squared units. In this case, the side length is in meters, so the area is expressed in square meters (m²). The area represents the amount of space enclosed within the square.

Remember, to find the area of any square, you simply need to multiply the length of one side by itself.

The area of the square with a side length of 3.1 meters is 9.61 square meters.

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Keisha pay $0.5 for per pound of flour.

If b is not equal to 0, an ordered pair of integers a and b, represented as a / b, is a ratio. A proportion is an equation that equalizes two ratios.. A fraction is of the form a/b. The total amount for per pound of weight is given by dividing the total cost by total weight.

Keisha bought 6 pounds of flour for $3. To find the amount for per pound flour, we have to divide the total amount by total pound of weight.

So, dividing $3 by 6 pound, we get

\(\frac{3}{6}=\frac{1}{2} \\=0.5\)

So, 0.5$ needs to be paid for per pound of flour.

Therefore, Keisha pay $0.5 for per pound of flour.

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Answer:

x = 2

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × breadth

given the rectangles have equal areas then equating the two areas gives

4x × 9 = 4(6x + 6) , that is

36x = 24x + 24 ( subtract 24x from both sides )

12x = 24 ( divide both sides by 12 )

x = 2

9514 1404 393

Answer:

  7.4

Step-by-step explanation:

Put the given value into the formula and do the arithmetic.

  R = log(2.4×10^7)

  R ≈ 7.3802 ≈ 7.4

The earthquake is about 7.4 on the Richter scale.

Answer:

Step-by-step explanation:

Add all sides together and set equal to 360

x+1 + x+2 + x+3 + x+4 =360

Combine Like Terms

4x + 10 = 360

get rid of the ten on both sides

4x = 350

Divide both sides by 4

x = 87.5

The perimeter and area of the figure are 10+6√5 and 20

The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter. The sum of the lengths of all the sides in a rectangle is its perimeter, or P. A rectangle's opposite sides are equal, hence it has two equal lengths and two equal widths. The following formula is used to determine a rectangle's perimeter: Diameter is equal to the sum of the following dimensions: length, width, height, and width.

There are numerous practical uses for calculating the perimeter. The size of the fence needed to enclose a yard or garden is known as the calculated perimeter. The circumference of a wheel or circle, which measures its perimeter, indicates how far it may travel in a single rotation.

AC=√4²+2²=√20=2√5

AB=√8²+4²=4√5

BC=√8²+6²=√100=10

Perimeter=a+b+c

=AC+AB+BC

=2√5+4√5+10

=10+6√5

Area=20

The perimeter and area of the figure are 10+6√5 and 20

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