2. The service life of a battery used in a cardiac pacemaker is assumed to be normally distributed. A random sample of ten batteries is subjected to an accelerated life test by running them continuously at an elevated temperature until failure, and the follow­ ing lifetimes (in hours) are obtained: 25.5, 26.1, 26.8, 23.2, 24.2, 28.4, 25.0, 27.8, 27.3, and 25.7. a. The manufacturer wants to be certain that the mean battery life exceeds 25 h. What conclusions can be drawn from these data (use a= 0.05)? b. Construct a 90% two-sided confidence interval on mean life in the accelerated test.

The slope-intercept form of a line is:

y = mx + b

Where m is the slope and b is the y-intercept.

Two lines having slopes m1 and m2 are perpendicular if

m1 * m2 = -1

We are given the equation of one line:

It's required to find the equation of another line that is perpendicular to it. We have m1 = 1/3, let's find the other slope:

The slope of the required line is -3. Now we use the point through which the line passes (-2, 2).

We use the point-slope form of the line:

y - k = m( x - h)

Where (h,k) = (-2, 2) is the point. Substituting:

Operating:

Answer:

25

Step-by-step explanation:

Number of rows: x

Number of trees per row: y

So x rows multiplied by y trees per row = 700

x × y = 700

xy = 700

This is our first equation

x rows = y trees per row plus three (or x rows minus three = y trees)

x = y + 3

So if x = y + 3,

In xy = 700, we can substitute the x because we have it's value

(y + 3)y = 700

y² + 3y = 700

Divide 3 by 2 then square the answer = 2.25

y² + 3y + 2.25 = 700 + 2.25

Simplify

(y + 1.5)² = 702.25

Get the square root of both sides

(y + 1.5) = ±26.5

y = 26.5 - 1.5 or -26.5 - 1.5

So y is either 25 or -28 (A negative number of trees doesn't make sense so we'll stick with 25

Answer:

simple interest=$97.50.

compound interest= $100.668

Step-by-step explanation:

Given:

Principal (P) = $750

Rate (R) = 6.5% (in decimal form, 0.065)

Time (T) = 2 years

Simple Interest = Principal*Rate*Time

Using the formula, the simple interest is calculated as follows:

Simple Interest = $750*0.065*2 = $97.50

Therefore, the simple interest for $750 with a 6.5% interest rate over 2 years is $97.50.

Again:

Compound Interest = Principal*(1 + Rate)^(Time)-Principal

Using the same values as above, the compound interest can be calculated as follows:

Compound Interest = $750*(1+0.065)^(2)-$750

= $750*1.065^2 -$750

= $750 × 1.134225 - $750

= $850.66875-$750

= $100.668

Therefore, the compound interest for $750 with a 6.5% interest rate over 2 years is $100.668

Answer:

Step-by-step explanation:

x+y-22=-16

But x =-7

then

-7+y-22=-16

y-29=-16

y=-16+29

y=13

The smallest number of edges that would need be duplicated to eulerize the graph is 10.

Given that a graph has 20 vertices.

In order for a graph to be eulerized, it has to added an edge to each vertex having odd valence.

Here total number of vertices = 20

So, the smallest number of edges that would need be duplicated to eulerize the graph is half of the total number of vertices.

Number of edges = 20/2 = 10

Hence it is needed 10 edges to eulerize the graph.

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Answer:

  54

Step-by-step explanation:

  \((\sqrt{6} + \sqrt{24})^2=(\sqrt{6}+2\sqrt{6})^2\\\\=(3\sqrt{6})^2=(3^2)(6)=\boxed{54}\)

Answer:

15 mph

Step-by-step explanation

i used a calculator but correct me if im wrong pls

From the solution above, the missing exponent is 6

Answer:

10:30 On the Next day

Step-by-step explanation:

This Is a Answer

Answer:

the first one.

The associations that best describe the scatter plot is Option A and C

When below-average values also tend to occur together and above-average values of one variable tend to be accompanied by below-average values of the other, there is a positive association between the two variables. When the average values of two variables tend to be below average, two variables have a negative connection.

Note that a statistical term used to describe a straight-line relationship between two variables is a linear relationship (or linear association).

Additionally, a straight line connecting the spots indicates a linear association. As a result, the scatter plot indicates that as practice time increases,  giving off also rise.

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The association that describe the scatter plot is

A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events (called variables).

The connection is positive if the variables tend to rise and fall together. When one variable tends to rise while the other falls, there is a negative connection.

The connection between the variables demonstrates a straight line in the positive direction. hence the option having linear and positive association is the correct choice

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The needed number of days at 10 degrees is given as follows:

11 days.

The slope-intercept equation for a linear function is presented as follows:

y = mx + b

In which:

For this problem, we have that when x decreases by 5, y increases by 2, hence the slope m is given as follows:

m = -2/5

m = -0.4.

Hence the time needed for a temperature of 10 degrees is given as follows:

9 + 2 = 11 days.

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The total height of the three jumps is A = 20.744 feet

Given data ,

1st high jump score: 7.016 feet

2nd high jump score: 5.42 feet

3rd high jump score: 8.308 feet

On adding the scores , we get

7.016 + 5.42 + 8.308 = 20.744 feet

On simplifying the equation , we get

A = 20.744 feet

Hence , Oliver jumped a total of 20.744 feet in the three high jumps

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Answer:

Well, the smallest successive composites with gap 17, 73, 2, and 19 would have to be:

1. $341 = 11 \times 31$

2. $458 = 2 \times 299$

3. $460 = 2^2 \times 5 \times 23$

4. $479 = 13 \times 37$

Answer:   the top of the ladder is at 24 feet from the ground

Step-by-step explanation:

Use the Pythagorean theorem to solve for the unknown, since we notice that the ladder is the hypotenuse of a right angle triangle formed by the horizontal distance from the wall to the base of the ladder, and the height of the top of the ladder against the wall. We need to find one of the triangle's sides given its hypotenuse and the other side, so we use the formula:

answer: the range is 41.

to find the range of this data set, we first need to find the minimum and maximum values - which are 59 and 100.

then we subtract the minimum from the maximum.

59 - 100 = 41.

So, the spread of the numbers 4, 6, 7, 9, 9 is 5.

Spread can refer to different things depending on the context. Here are a few examples:

In finance, spread refers to the difference between the bid price and the ask price of a security or asset. The bid price is the highest price a buyer is willing to pay for a security, while the ask price is the lowest price a seller is willing to accept. The spread represents the cost of trading that security or asset and is typically measured in basis points (hundredths of a percentage point).

In sports betting, spread refers to the point spread or handicap that is assigned to a team in order to make the betting odds more even. For example, if a football team is favored to win by 7 points, they may be assigned a -7-point spread, meaning they would have to win by more than 7 points for a bet on them to be successful.

In epidemiology, spread refers to the transmission of a disease from one person to another. The spread of a disease can be influenced by a variety of factors, including the infectiousness of the disease, the proximity and frequency of contact between people, and the effectiveness of measures to prevent transmission (such as vaccines or masks).

In cooking, spread can refer to a variety of ingredients that are used to spread on bread or crackers, such as butter, jam, or peanut butter.

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Answer:

1.75

Step-by-step explanation

Perhaps, 1 7/8 is a bit of an Improper fraction, therefore Multiply the side number of this Improper fraction (1x7) Witch will give you 7/8 times that against 2 and you will get 1.75. (Forget the last period by the number.)

Answer:

25.6

Step-by-step explanation:

Add 6.4 to all the sides and add them all together-

6.4+6.4+6.4+6.4 = 25.6

The transformations for each function are given as follows:

1) Vertical compression by a factor of 5.

2) Vertical compression by a factor of 5 and a reflection over the x-axis.

The parent function for this problem is given as follows:

f(x) = 1/x.

For item 1, we have that x was multiplied by five, as the multiplication was in the domain, the transformation was a vertical compression by a factor of 5.

For item 1, along with the multiplication of x by 5, the function was also multiplied by -1, meaning that the function was reflected over the x-axis.

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The required amount to be paid into the fund each period is $1535.21. which the correct answer would be option (B).

Lee Associates borrowed $60,000 in total. The corporation intends to establish a sinking fund to repay the debt after 12 years.

Assuming a semiannual compounding rate of 8%,

As per the given information, the required solution would be as:

Amount to be paid into the fund each semi-annual period will be

= Loan Amount/((1+r/2)²ⁿ⁻¹)/(r/2))

= 60000/(((1+8%/2)²ˣ¹²⁻¹)/(8%/2))

= $1535.21

Thus, the required amount to be paid into the fund each period is $1535.21.

Hence, the correct answer would be an option (B).

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Answer:

El precio de lista es \(pv=42000 $\).

Step-by-step explanation:

Se puede usar la siguinete ecuacion

\(pv=pc+g\)

pv es el rpecio de venta

pc es el precio de compra $28000

g la ganancia 20%pc+20%pv

Entonces tenemos:

\(pv=28000+0.2pc+0.2pv\)

\(pv-0.2pv=28000+(0.2*28000)\)

\(0.8pv=28000+(0.2*28000)\)

Por lo tanto, el precio de lista es \(pv=42000 $\).

Espero te haya sido de mucha ayuda!

You would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

To find the range in which you would expect to find the middle 98% of most pregnancies, you can use the concept of z-scores and the standard normal distribution.

For the given data:

Mean (μ) = 269 days

Standard deviation (σ) = 17 days

To find the range, we need to find the z-scores corresponding to the 1% and 99% percentiles. Since the normal distribution is symmetric, we can find the z-scores by subtracting and adding the respective values from the mean.

To find the z-score for the 1% percentile (lower bound):

z1 = Φ^(-1)(0.01)

Similarly, to find the z-score for the 99% percentile (upper bound):

z2 = Φ^(-1)(0.99)

Now, we can calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

To find the corresponding values in terms of days, we multiply the z-scores by the standard deviation and add/subtract them from the mean:

lower bound = μ + (z1 * σ) = 269 + (-2.33 * 17) ≈ 229.4 days

upper bound = μ + (z2 * σ) = 269 + (2.33 * 17) ≈ 308.6 days

Therefore, you would expect to find the middle 98% of most pregnancies between approximately 229.4 days and 308.6 days.

Now, let's consider drawing samples of size 58 from this population. The mean and standard deviation of the sample means can be calculated as follows:

Mean of sample means (μ') = μ = 269 days

Standard deviation of sample means (σ') = σ / sqrt(n) = 17 / sqrt(58) ≈ 2.229

To find the range in which you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample, we repeat the previous steps using the mean of the sample means (μ') and the standard deviation of the sample means (σ').

Now, calculate the z-scores:

z1 = Φ^(-1)(0.01) ≈ -2.33

z2 = Φ^(-1)(0.99) ≈ 2.33

Multiply the z-scores by the standard deviation of the sample means and add/subtract them from the mean of the sample means:

lower bound = μ' + (z1 * σ') = 269 + (-2.33 * 2.229) ≈ 264.0 days

upper bound = μ' + (z2 * σ') = 269 + (2.33 * 2.229) ≈ 274.1 days

Therefore, you would expect to find the middle 98% of most averages for the lengths of pregnancies in the sample between approximately 264.0 days and 274.1 days.

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Answer:

No, right answer is = 1017.36

Answer:

1017.36

Step-by-step explanation:

All your work is correct, but the final answer is not. In the problem it says to use 3.14 as pi, but when you multiplied you did:

\(\pi * 6^{2}*9 = 1017.88\)

instead of

\(3.14*6^{2}*9 = 1017.36\)

like you had written above. So the final is actually supposed to be 1017.36

Answer:

10

I hope this helps!

The sum of the measures of the interior angles of a nonagon is 1260 degrees

The measure of each interior angle of a regular octagon is 135 degrees

A nonagon is a polygon with nine sides, and the formula to calculate the sum of the measures of the interior angles of a polygon with n sides is:

Sum of interior angles = (n-2) x 180 degrees

Therefore, the sum of the measures of the interior angles of a nonagon is:

Sum of interior angles = (9-2) x 180 degrees = 1260 degrees

An octagon is a polygon with eight sides, and the formula to calculate the measure of each interior angle of a regular polygon with n sides is:

Measure of each interior angle = (n-2) x 180 degrees / n

Therefore, the measure of each interior angle of a regular octagon is:

Measure of each interior angle = (8-2) x 180 degrees / 8 = 135 degrees

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Answer:

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Step-by-step explanation:

Suppose that, in the past, 40% of all adults favored capital punishment. Test if the proportion has increased:

At the null hypothesis, we test if the proportion is still of 40%, that is:

\(H_0: p = 0.4\)

At the alternative hypothesis, we test if the proportion has increased, that is, is greater than 40%, so:

\(H_1: p > 0.4\)

The test statistic is:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

In which X is the sample mean, \(\mu\) is the value tested at the null hypothesis, \(\sigma\) is the standard deviation and n is the size of the sample.

0.4 is tested at the null hypothesis:

This means that \(\mu = 0.4, \sigma = \sqrt{0.4*0.6}\)

Random sample of 15 adults, 8 favor capital punishment.

This means that \(n = 15, X = \frac{8}{15} = 0.5333\)

Value of the test statistic:

\(z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}\)

\(z = \frac{0.5333 - 0.4}{\frac{\sqrt{0.4*0.6}}{\sqrt{15}}}\)

\(z = 1.05\)

P-value of the test and decision:

The p-value of the test is the probability of finding a sample proportion of 0.5333 or more, which is 1 subtracted by the p-value of z = 1.05.

Looking at the z-table, z = 1.05 has a p-value of 0.8531.

1 - 0.8531 = 0.1469.

The p-value of the test is 0.1469 > 0.05, which means that there is no reason to believe that the proportion of adults favoring capital punishment today has increased, using a 0.05 level of significance.

Answer:

G(-3, 0)

H(-2, 4)

Step-by-step explanation:

Rule for the rotation of a point by 90 degrees about counterclockwise about the origin is,

(x, y) → (-y, x)

Coordinates of the extreme ends of segment A and B are,

A(0, 3) and B(4, 2)

Rotation by the given rule to find the image points,

A(0, 3) → G(-3, 0)

And B(4, 2) → H(-2, 4)

Therefore, new segments will have the extreme ends at G(-3, 0) and H(-2, 4)