find the radius of convergence of the power series. (if you need to use or –, enter infinity or –infinity, respectively.) [infinity] x5n (5n)! n = 0

Based on the temperature at 6:00 am and the temperature at 6:00pm, the change in temperature can be shown by the formula D. |–5 – 7| = |–12| = 12°F.

To find the change in temperature, you need to subtract the temperature at 6: 00 pm from the temperature at 6: 00 am.

The change in temperature is therefore:

= | temperature at 6 am - temperature at 6pm |

= | -5 - 7 |

= | - 12 °F|

The absolute value of - 12 °F is 12 °F which was therefore the change in temperature.

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Answer:

85%(estimated)

Step-by-step explanation:

150-22=128

changed ÷ original x 100%

128 ÷ 150 x 100%

≈ 85%

Answer:

BC= 1.7101

Step-by-step explanation:

The following is one way to perform the calculation. It may not be the best way.

Let a represent line BC, and b represent line CA, and c represent line AB.

b = c × sin(β)

= 4.69846

\(a = \sqrt{c^{2} -b^{2} } = \sqrt{52 - 4.69846310392952}= \sqrt{ 2.9244444610128} = 1.7101\)

Answer:

< HZG = 142 degrees

Step-by-step explanation:

180-38 = 142

<HZJ + <HZG = 180 degrees degrees (linear pair angles)

The average number of road accidents per year in a specific town is 325. We will assume that the distribution of the number of accidents per week follows a Poisson distribution with a rate of 325/52 = 6.25 accidents per week.

To find the mean and standard deviation of the number of accidents per week: Mean = rate = 6.25 accidents per week Standard deviation = sqrt(rate) = sqrt(6.25) = 2.5 accidents per week.

Therefore, the mean and standard deviation of the number of accidents per week are 6.25 and 2.5, respectively)To find the probability of there being less than 5 accidents in a given week:

P(X < 5) = P(X ≤ 4)

(since the number of accidents is a discrete random variable)Using the Poisson distribution with a rate of 6.25 accidents per week, we getups(X ≤ 4) = 0.2656 (to 4 decimal places)

Taking the natural logarithm of both Sides\('ll(0.82)X ≥ ln(0.95)X ≥ ln(0.95)/ln(0.82)X ≥ 8.47\) (rounded up)

Therefore, the factory should purchase at least 9 generators to achieve at least a 95% probability of successfully powering the machines during a power outage.

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a)

Values of the given angles  ∠A = 123°  , ∠B = 123° ,∠C = 57.

Given ,

One angle of the figure as 123°.

Now,

∠C and 123° form linear pair.

So,

∠C + 123° = 180°

∠C = 57°

Now,

∠C and ∠B are pairs of interior angles on same side of transversal, thus they are supplementary.

∠C + ∠B = 180°

Substitute the value of ∠C

53° + ∠B = 180°

∠B = 127°

Now,

∠B and ∠A are vertically opposite angles.

Thus,

∠B = ∠A

So,

∠A = 127° .

Hence,

∠A= 127°

∠B = 127°

∠C = 57°

b)

Values of ∠D = 98°, ∠E = 98°, ∠F = 98° .

Given one angle as 82°

Now,

∠F and 82° form linear pair.

So,

∠F + 82° = 180°

∠F = 98°

Now,

∠D and ∠F are corresponding angles. Thus,

∠D = ∠F

∠D = 98° .

Now,

∠D and ∠E are vertically opposite angles.

Thus,

∠D = ∠E

∠E = 98°.

Hence,

∠D = 98°

∠E = 98°

∠F = 98°

c)

Values of ∠G = 75° and ∠H = 75°

Given one angle as 75° .

∠H and 75° are corresponding angles. Thus,

∠H = 75°

Now,

∠H and ∠G are vertically opposite angles.

So,

∠G = 75° .

Hence,

∠G = 75°

∠H = 75°

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To convert steps to miles, use the average stride length to calculate the distance covered by the steps.The average stride length for a person is approximately 2.5 feet, and there are approximately 5,280 feet in a mile.

Unit conversion is the process of changing a quantity from one unit of measurement to another, while maintaining its value. This is often done to compare measurements in different systems of units or to express a measurement in a unit that is more appropriate for a particular situation.

For example, converting between metric units (such as grams or meters) and imperial units (such as ounces or feet) is a common type of unit conversion. The process of unit conversion involves using a conversion factor, which is a ratio that relates the units being converted.  

To convert steps to miles, simply multiply the number of steps taken by the average stride length, and then divide the result by 5,280.

For example, if you take 10,000 steps, the distance covered would be approximately 4.47 miles (10,000 x 2.5 / 5,280).

Keep in mind that the average stride length can vary based on factors such as height, age, and fitness level, so it is important to measure your own stride length for the most accurate results.

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Answer:

the first person gets €80, the second person gets €40, the third person gets €20 and the fourth person gets €10.

Step-by-step explanation:

Let’s call the amount of money that the first person gets “x”. Then, the second person gets half of x, which is x/2. The third person gets half of x/2, which is x/4. The fourth person gets half of x/4, which is x/8.

The sum of these amounts should be equal to 150€.

x + x/2 + x/4 + x/8 = 150

Multiplying both sides by 8 gives:

8x + 4x + 2x + x = 1200

15x = 1200

x = 80

Therefore, the first person gets €80, the second person gets €40, the third person gets €20 and the fourth person gets €10.

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the radius, in centimeters, of this circle is 3 centimenters.

The area of ​​the circle is calculated through the product between the constant π and the measurement of the radius squared (r²). Thus, we have the following formula: A = π .

The formula for the area of a circle is given by:

A = πr^2

Knowing that the area is 9π.

Putting the values in the formula:

\(9 \pi = \pi r^2\\9=r^2\\r=3\)

Therefore, the radius of the circle is 3 centimeters.

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Answer:

D. 40 cups

Step-by-step explanation:

10÷2=5

5×8=40

She will use 40 cups of trail mix

Answer:

\(m= -2\frac{1}{13}\)

Step-by-step explanation:

2m-27/3=5m

x3.             x3

2m-27=15m

-2m.     -2m

-27=13m

/13.   /13

-27/13=m

-2 1/13=m

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The probability that the first person who subscribes to the five-second rule is the 5th person you talk to is q⁴ * p.

To calculate the probability that the first person who subscribes to the five-second rule is the 5th person you talk to, we need to consider the following terms: probability, independent events, and complementary events.

Step 1: Determine the probability of a single event.
Let's assume the probability of a person subscribing to the five-second rule is p, and the probability of a person not subscribing to the five-second rule is q. Since these are complementary events, p + q = 1.

Step 2: Consider the first four people not subscribing to the rule.
Since we want the 5th person to be the first one subscribing to the rule, the first four people must not subscribe to it. The probability of this happening is q * q * q * q, or q⁴.

Step 3: Calculate the probability of the 5th person subscribing to the rule.
Now, we need to multiply the probability of the first four people not subscribing (q^4) by the probability of the 5th person subscribing (p).

The probability that the first person who subscribes to the five-second rule is the 5th person you talk to is q⁴ * p.

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Answer:

k is the smallest number such that 2(to the k)>n

Step-by-step explanation:

Frequency distribution is defined as the number of times the value occurs. It contains the class interval as well as the corresponding frequencies. A pivot table is used to represent the frequency distribution.

The "2 to the k" rule states that 2 to the power k should be less than equal n, where n is the number of the given data points. It should be the smallest number.

Thus the answer is : k is the smallest number such that 2(to the k)>n.

Answer:

the other factor is (x+7)

Step-by-step explanation:

Given x^2+11x+28

factor into

x^2+7x + 4x + 28

=x(x+7) + 4(x+7)

= (x+4)(x+7)

Answer: the other factor is (x+7)

Answer:

3

Step-by-step explanation:

2*2=4

10/2=5

+-6

4-6=-2+5=3

Answer:

I think it's 4

Step-by-step explanation:

if x+y is 7 and x-y is 3 then the answer is 4

Answer:

X=2, y=5

Step-by-step explanation:

X+y=7

x-Y=-3

————-

2x+ 0 =4

2x=4

x=2

solve for y using either equation

x+y=7

2+y=7

y=5

check answers by substituting x and y value in either equation:

x+y=7

2+5=7

7=7

or

x-y=-3

2-5=-3

-3=-3

Answer:

C   19.2

Step-by-step explanation:

Corresponding parts have the same proportion

x/24 = 20.8/26

multiply both sides by 24

x = 20.8/26 * 24

x = 19.2

Answer:

C

Step-by-step explanation:

Since the triangles are similar then the ratios of corresponding sides are equal, that is

\(\frac{AC}{DF}\) = \(\frac{AB}{DE}\) , substitute values

\(\frac{x}{24}\) = \(\frac{20.8}{26}\) ( cross- multiply )

26x = 499.2 ( divide both sides by 26 )

x = 19.2 → C

Given equation g = x-1/k in terms of x would be x = 1 + gk

for given question,

we have been given an equation g = x-1/k

Dyani began solving the equation g = x-1/k for x by using the addition property of equality.

We solve given equation for x.

⇒ g = x-1/k                      ..........(Given)

⇒ gk = (x - 1/k)k               .........(Multiply both the sides by k)

⇒ gk = x - 1

⇒ gk + 1 = x - 1 + 1           .........(Add 1 to each side)

⇒ gk + 1 = x

⇒ x = 1 + gk

Therefore, given equation g = x-1/k in terms of x would be x = 1 + gk

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Answer:

A straight line.

Step-by-step explanation:

\(3y = -2x + 12\) on a coordinate plane is a line having slope \(\frac{-2}{3}\) and y-intercept  \((0,4)\) .

Firstly we try to find the slope-intercept form: \(y = mx+c\)

m = slope

c = y-intercept

We have,   \(3y = -2x + 12\)

=> \(y = \frac{-2x+12}{3}\)

=> \(y = \frac{-2}{3} x +\frac{12}{3}\)

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

Hence, by the slope-intercept form, we have

m = slope = \(\frac{-2}{3}\)

c = y-intercept = \(4\)

Now we pick two points to define a line: say \(x = 0\) and \(x=3\)

When  \(x = 0\) we have \(y=4\)

When  \(x = 3\) we have \(y=2\)

Hence,  \(3y = -2x + 12\) on a coordinate plane is a line having slope \(\frac{-2}{3}\) and y-intercept  \((0,4)\) .

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Answer:

£4.38

Step-by-step explanation:

You need to find 1/4 and then add it on

The sum of the inside angles of a 6 sides figure is 720

Add the known angles together:

90 + 112 + 131 + 154 + 118 = 605

Subtract the sum of the known angles from 720 for x:

x = 720 - 605 = 115

x = 115 degrees.

Answer:

The sum of the interior angles of the hexagon is 720°

\(x + 154 + 131 + 112 + 90 + 118 = 720 \\ x + 605 = 720 \\ x = 720 - 605 \\ \boxed{x = 115}\)

For houses with the same square footage, number of bedrooms, number of bathrooms, and number of garages, a 1-year increase in the age of the house can result in various effects on average. Some potential effects may include:

1. Decrease in market value: As houses age, their market value may decline due to wear and tear, outdated features, or the perception of lower quality compared to newer homes.

2. Increase in maintenance costs: Older houses may require more frequent repairs and maintenance, leading to higher ongoing expenses for homeowners.

3. Potential decrease in energy efficiency: Older houses might have outdated insulation, windows, or appliances, resulting in higher energy consumption and costs.

4. Changes in neighborhood dynamics: As houses age, the neighborhood may undergo demographic shifts or changes in property values, which can impact the overall desirability and perception of the area.

It's important to note that these effects can vary depending on various factors such as location, housing market conditions, and overall maintenance and renovations of the property.

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(a) The expected profit of this policy to the insurance company is $520.10.

(b) The interpretation value of expected profit in (a) in the context of the problem is small probability of the policyholder's death.

(a) The expected profit to the insurance company can be calculated as follows:

Expected Profit = (Probability of Survival * Premium) - (Probability of Death * Death Benefit)

Probability of Survival = 0.997

Probability of Death = 1 - Probability of Survival = 1 - 0.997 = 0.003

Premium = $780

Death Benefit = $250,000

Expected Profit = (0.997 * $780) - (0.003 * $250,000) = $520.10

Therefore, the expected profit to the insurance company from selling this policy is $520.10.

(b) The expected profit of $520.10 represents the average profit that the insurance company can expect to earn from selling this type of policy to similar customers over time.

In the context of this problem, it means that if the insurance company sells many policies like this one, they can expect to make a profit of about $520.10 per policy, on average, after accounting for the small probability of the policyholder's death.

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The solution of the expression are as follows;

y = -2

x = 1

2x + 3y = -4

-3x + 5y = -13

Using substitution method

2x = -4 - 3y

x = - 2 - 3 / 2 y

Hence,

-3(- 2 - 3 / 2 y) + 5y = -13

6 + 9 / 2 y + 5y = -13

9 / 2 y + 5y = -13  - 6

9 / 2 y + 5y = - 19

9y + 10y / 2 = -19

19y / 2 = -19

cross multiply

19y = -38

y = -38 / 19

y = -2

Hence,

2x + 3(-2) = -4

2x = -4 + 6

2x = 2

x = 2 / 2

x = 1

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Answer:

So, the prime factorization of 828 can be written as 2^2 × 3^2 × 23 where 2, 3, and 23 are prime.

Step-by-step explanation:

828 / 2 = 414

414 / 3 = 138

138 / 2 = 69

69 / 23 = 3

3 / 3 = 1

Mean= 0, as the expected value of white noise is 0.Auto covariance function= E(W t W t−2) − E(W t ) E(W t−2) = 0 − 0 = 0Since mean is constant and autocovariance is not dependent on t, the process is a stationary process.

Mean = 0 as expected value of white noise is 0.Auto covariance function = E(W t (W t +3t)) − E(W t ) E(W t +3t)= 0 − 0 = 0Since mean is constant and autocovariance is not dependent on t, the process is a stationary process.

Mean = E(W t 2)=1, as the expected value of squared white noise is .

Auto covariance function= E(W t 2W t−2 2) − E(W t 2) E(W t−2 2) = 1 − 1 = 0.

Since mean is constant and autocovariance is not dependent on t, the process is a stationary process.

Mean = 0 as expected value of white noise is 0.

Auto covariance function = E(W t W t−1) − E(W t ) E(W t−1) = 0 − 0 = 0Since mean is constant and autocovariance is not dependent on t, the process is a stationary process.

For all the given cases, we have a stationary process. The reason is that the mean is constant and autocovariance is not dependent on t. Mean and autocovariance of each case is given:

Z t = W t − W t−2,Mean= 0,Autocovariance= 0, Z t = W t + 3tMean= 0Autocovariance= 0

Z t = W t2.

Mean= 1.

Autocovariance= 0

Z t = W t W t−1,Mean= 0,

Autocovariance= 0.Therefore, all the given cases follow the property of a stationary process

For each of the given cases, the mean and autocovariance have been found and it has been concluded that all the given cases are stationary processes.

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Answer:

Step-by-step explanation:

x + x-7=31

2x=38

x=19

The solution of the equation 3z minus 2 is equal to 46 is 16.

The given equation '3z minus 2 is equal to 46' can be written as

    3z - 2  =   46

Now solving for z because the value of z will give the required solution of the given equation. So now finding the z from the equation:

   3z = 46  + 2

   3z =  48

   z = 48/3

   z = 16

The value of the z is 16 which represents the solution of the given equation i.e 3z minus 2 is equal to 46.

Therefore it is concluded that the solution of the equation 3z minus 2 is equal to 46 is 16.

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The researcher can conclude that after 8 weeks of excessive calorie intake, there is a statistically significant increase in weight gain among the participants (p < .001).

The JASP output indicates that a non-parametric Wilcoxon signed-rank test was conducted to compare the weight before and after the 8-week period of excessive caloric intake. The p-value obtained from the analysis is less than .001, indicating that the difference in weight before and after the intervention is highly significant. This means that the excessive calorie intake led to a substantial increase in weight among the participants.

The use of a non-parametric test suggests that the assumption of normality was violated, which could be due to the small sample size or the nature of the data distribution. Nevertheless, the violation of normality does not invalidate the findings. The low p-value suggests strong evidence against the null hypothesis, supporting the conclusion that the 8-week period of excessive calorie intake resulted in a statistically significant weight gain.

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