the batteries from a certain manufacturer have a mean lifetime of 850 hours, with a standard deviation of 70 hours. assuming that the lifetimes are normally distributed, complete the following statements.
a) Approximately 68%, 75%, 95% or 99.7% of the batteries have lifetimes between 640 hours and 1060 hours.
(b) Approximately 95% of the batteries have lifetimes between___ hours and ___hours.

\( - 9x + 3y - 27 = 0 \\ a = - 9 \\ b = 3 \\ c = 0 \\ {b}^{2} - 4ac = 9 - 4( - 9)( - 27) = 0 \\ x = \frac{ - b}{2a} = \frac{ - 3}{ - 18} = \frac{1}{6} \\ x = \frac{1}{6} \\ y = ( - 9 \times \frac{1}{6} ) + 3y = 27 \\ \frac{ - 3}{2} + 3y = 27 \\ 3y = 27 + \frac{3}{2 } \\ 3y = \frac{57}{2} \\ y = \frac{57}{6} = \frac{19}{2} \\ \)

i hope it helps u.....

The value of x for f(x)=g(x) is f(-3/4) = g(-3/4).

To find the values of x for which f(x) equals g(x), we need to set the two functions equal to each other.

So, we have: x² - 2x - 8 = 1/4x - 1 We can simplify this equation by multiplying both sides by 4 to get rid of the fraction: 4x² - 8x - 32 = x - 4

Now, we can rearrange this equation into standard quadratic form: 4x² - 9x - 28 = 0

We can solve for x using the quadratic formula:

x = [9 ± √(9² - 4(4)(-28))] / 8 x = [9 ± √(529)] / 8 x = [9 ± 23] / 8

So, the values of x for which f(x) = g(x) are:

x = -3/4 or x = 7/4

Therefore, f(-3/4) = g(-3/4) and f(7/4) = g(7/4).

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Answer:

tm-tj is just the expansion of t(m-j)

Step-by-step explanation:

To show how they are equivalent it would be best to substitute values for t, m and j.

Let t = 5

Let m = 2

Let j = 1

tm-tj = t(m-j)

5x2 - 5x1 = 5(2-1)

10 - 5 = 5(1)

5 = 5

Therefore tm-tj = t(m-j)

The Delhi metro track increased by 20% in the last two years.

The Delhi metro track increased from 200 km to 240 km in the last two years. To calculate the percentage increase, we need to find the difference between the new and old lengths, divide it by the old length, and then multiply by 100.
The difference in length is 240 km - 200 km = 40 km.
The percentage increase, we divide the difference by the old length: 40 km ÷ 200 km = 0.2.
Finally, we multiply by 100 to get the percentage: 0.2 × 100 = 20%.
Therefore, the Delhi metro track increased by 20% in the last two years.
Another way to calculate the percentage increase is by using the formula:
Percentage increase = (new value - old value) ÷ old value × 100.
In this case, the new value is 240 km and the old value is 200 km.
So, the percentage increase = (240 km - 200 km) ÷ 200 km × 100 = 40 km ÷ 200 km × 100 = 0.2 × 100 = 20%.
Therefore, the Delhi metro track increased by 20% in the last two years.

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To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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The estimation of 0.000007328 is \(7\times10^{-6\).

Estimation is he ability to guess the amount of anything without actual measurement.

The number (n) is given as:

\(\text{n}=0.000007328\)

Multiply by 1

\(\text{n}=0.000007328\times1\)

The number is to be rounded to the nearest millionth.

So, we substitute \(\frac{1000000}{1000000}\) for 1

\(\text{n}=0.000007328\times1\)

\(\text{n}=0.000007328\times\dfrac{1000000}{1000000}\)

This becomes

\(\text{n}=7.328\times\dfrac{1}{1000000}\)

Express the fraction as a power of 10

\(\text{n}=7.328\times10^{-6\)

Approximate to a single digit

\(\rightarrow\bold{n=7\times10^{-6}}\)

Therefore, the estimation of 0.000007328 is \(7\times10^{-6}\).

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The slope of the line in the diagram shon is

B. 1/3

In mathematics, slope refers to the measure of how steep a line is. It quantifies the rate at which a line rises or falls as it moves horizontally.

Slope is typically denoted by the letter "m" and is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line.

To calculate slope we use the formula

= vertical distance / horizontal distance

= 1 / 3

hence the  slope of the line is 1/3

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Answer:

1,750 km

Step-by-step explanation:

According to the scenario, computation of the given data are as follows,

Train speed = 350 km per hour

So, we can calculate the total distance covered by train in 5 hours by using following formula,

Distance covered in 5 hours = 5 × 350 km

= 1,750 km

Hence, the train will travel 1,750 km to reach its destination.

Answer: 59

Step-by-step explanation:

Answer:

x = 33

Step-by-step explanation:

b^2 = c^2− a^2 = 652 − 562 = 4225 − 3136 = 1089 =33^2

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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Where 12 samples of 100 printed circuit boards were tested and the number of defective boards in each sample is provided, a control chart that should be constructed to monitor the process is the p-chart.

The p-chart, also known as the proportion chart, is used to monitor the proportion of nonconforming items in a sample. In this case, the number of defective printed circuit boards in each sample can be used to calculate the proportion of defective boards.

To construct the p-chart, you would calculate the proportion of defective boards for each sample by dividing the number of defective boards by the total number of boards in that sample. Then, you can plot these proportions on the control chart to monitor the process over time.

The p-chart helps to identify any shifts or trends in the proportion of defective boards, allowing the quality assurance department to take appropriate actions to maintain or improve the process quality.

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The equation of a line that is parallel to 4x+3y=12 and passes through the point (3, 4) is 4x+3y = 24

The standard form of equation of line is y=m x+ b

where m is slope of line and b is y-intercept.

According to the question,

The required line is parallel to line whose equation is 4x + 3y = 12

Slope of given line =

3y = 12 - 4x

dividing by 3 both sides,

y = 12/3 - 4/3x

=> y = 4 - 4/3x

Slope of given line = -4/3

If two lines are parallel their slopes are equal to each other

Hence , Slope of required line : m = -4/3

Equation of line : y = -4/3x + b ------------(1)

It is given that required line also passes through the point = (3,4)

substituting the values of x = 3 and y=4 in equation (1)

=> (4) = (-4/3)(3) + b

=> 4 = -4 +b

=> b = 8

Substituting the value of b,

The equation of required line is y = -4/3x + 8

multiplying by 3 both sides,

3y = -4x + 24

=> 4x+3y = 24

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The system of equations has one solution. The two equations are intersecting lines.

The substitution method is one of the algebraic methods to solve simultaneous linear equations. It involves substituting the value of any one of the variables from one equation into the other equation.

We have the equations are:

y = 12 x + 2 ___eq.(1)

2y = x + 4 ____eq.(2)

You have to plug in y for 12x+2 in the second equation.

2(12x+2)=x+4

Simplify the equation:

24x + 4 = x + 4

Subtract 24x from each side

4 = -23x+4

Subtract 4 from each side

0 = 23x

Divide each side by 23

x=0

Now, plug in 0 to one equation.

y=12(0)+2

y=2

The lines intersect at one point, (0,2)

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Answer:

the cost is now $5.40

Step-by-step explanation:

if 18.00 is 100%, and we need to find the new price we need to make 30% into a decimal. which is 0.3. then we multiply 0.3 times 18.00, and that equals 5.4, but since we are dealing with money the answer would be $5.40.

we multiply if we are trying to find the new amount and we divide to find the old amount.

The surface area of the larger prism is 3 times larger than the surface area of the smaller prism.

A prism is a three-dimensional geometric shape that has two identical polygonal bases connected by rectangular faces. The surface area of a prism refers to the total area of all its faces.

The surface area of a prism is usually expressed in square units, such as square centimeters (cm²) or square meters (m²).

It represents the total amount of space that would need to be covered if all the faces of the prism were completely filled in.

Calculating the surface area of a prism is important in various real-world applications, such as architecture, engineering, and manufacturing, where understanding the amount of material needed or the amount of surface that will be exposed is necessary.

To determine how many times larger the surface area of the larger prism is compared to the smaller prism, we need to divide the surface area of the larger prism by the surface area of the smaller prism.

Let's denote the surface area of the larger prism as \(A_{large\) and the surface area of the smaller prism as \(A_{small\).

If we divide \(A_{large}\) by \(A_{smal\), we get:

\(A_{large} / A_{small} = 6 / 2\)

= 3.

Therefore, the surface area of the larger prism is 3 times larger than the surface area of the smaller prism.

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Answer: Equation 3

Step-by-step explanation:

It does not have any exponents, meaning it's linear

Answer:

equation 3

Step-by-step explanation:

no exponents

Answer:

1 slice will be left because there are 16 slices and 15 guests

Step-by-step explanation:

There are approximately 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

Anna has 2 dozen Rollo bars, which is equivalent to 2 x 12 = 24 Rollo bars.

She also has 1 dozen apples, which is equivalent to 1 x 12 = 12 apples.

So, Anna has a total of 24 + 12 = 36 treats to hand out.

Now, she needs to hand out 1 treat to each of the 36 children who come to her door.

This can be thought of as selecting 1 treat from the total of 36 treats for each child, without replacement, as each child can only receive 1 treat.

The number of ways to do this is given by the concept of permutations, denoted by "nPr", which is calculated as;

nPr = n! / (n - r)!

where n is the total number of items (treats) to choose from, and r is the number of items (treats) to choose.

In this case, n = 36 (total number of treats) and r = 36 (number of children).

Plugging in the values, we get;

36P36 = 36! / (36 - 36)! = 36! / 0! = 36!

Since 0! (0 factorial) is equal to 1, we can simplify further:

36! / 1 = 36!

36! ≈ 3.72 x 10⁴¹

So, there are 3.72 x 10⁴¹ ways that Anna can hand out 1 treat to each of the 36 children who come to her door.

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The required sample size is 99 salespeople.

To estimate the population mean of travel days per year for salespeople with 98% confidence and a margin of error of 6 days, we need to determine the appropriate sample size. We can use the formula n = (z^2 * σ^2) / E^2, where n is the sample size, z is the z-score corresponding to the desired confidence level, σ is the standard deviation of the population (or sample, if known), and E is the desired margin of error. In this case, z = 2.33 (from the z distribution table for a 98% confidence level), σ = 32 (from the pilot study), and E = 6. Plugging these values into the formula gives us n = (2.33^2 * 32^2) / 6^2, which is approximately 98.68. We need to round this up to the next whole number, which is 99. Therefore, we should sample 99 salespeople to estimate the mean number of travel days per year for salespeople with 98% confidence and a margin of error of 6 days.

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Answer:

-14°C

Step-by-step explanation:

6 + 8 = 14

So in 24 hour time that would be 2pm

From 6am to 2pm is 8 hours

If the degrees is going down by 2 you would times the 8 by 2 because it is doubled

That = 16

Then you'll minus 16°C from the 2°C

2°C - 16°C

= -14°C

Answer:

the answer is c ASA

Step-by-step explanation:

i think I. not sure

The value of y in the given figure is 108°.

The angles formed by a transversal line on the same side and position of the line, if lines are parallel then the corresponding angle are congruent.

Given is a figure, where two line AB and CD are being intersected by a transversal FE,

Let FE intersects AB and CD at P and O, respectively, (refer to the figure attached)

Since, AB ║ CD

Therefore, ∠ FPB  ≅ ∠ POD by the definition of corresponding angles,

2x+16 = 3x-12

x = 28

∠ POD = 28×3-12 = 72°

∠ POD and ∠ EOD are forming linear pair and therefore are supplementary,

∠ POD + y = 180°

72° + y =180°

y = 180°-72°

y = 108°

Hence, y = 108°

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The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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Answer:

The answer is option D, 50. :)

Answer:c)38 units

Step-by-step explanation:

edge

The expression that represents the correct factorization of the polynomial 8x³  +  125 exists (2x + 5) (4x²  -  10x  +  25)

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an equation made up of variables, constants, and exponents (No division operation by a variable).

A polynomial is not an expression that contains a variable with exponents that are negative or fractional, divides by a variable, or has a variable inside a radical.

Let the given polynomial expression be 8x³  +  125

The expression 8x³  +  125 can be rewritten as (2x)³ + 5³

By using the sum of cubes formula, we get

(2x)³ + 5³  =  (2x  + 5)( ((2x)² - 2x(5) + 5²)

8x³  +  125 = (2x + 5) (4x²  -  10x  +  25)

Therefore, the expression that represents the correct factorization of the polynomial 8x³  +  125 is (2x + 5) (4x²  -  10x  +  25)

The complete question is:

A polynomial expression of degree three is shown below. 8x^3 + 125 Which expression represents the correct factorization of the polynomial?

A (2x + 5)(4x + 10x + 25)

B (2x + 5)(4x + 10x-25)

C (2x + 5)(4x - 10x +25)

D (4x + 25)(2x - 10x+5)

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Answer:

Your answer would be 198.

Step-by-step explanation:

Brainliest please! I am so close to getting my next ranking! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!

The a = 0.01 critical value for the chi - square statistic with 13 degrees of freedom is given by 27.688.

Hence the correct option is (A).

Here given distribution is Chi - squared distribution.

two parameters of chi - squared distribution are given by ' a ' and ' d ' where d is degree of freedom.

The critical value against chi squared distribution changes according to the change of the values of a and d.

The table chi squared distribution is given by,

Here we have to find the critical value for the chi - squared statistic with 13 degrees of freedom when a = 0.01.

Therefore, a = 0.01 and d = 13

From the given table we can see that when a = 0.01 and d = 13 the critical value is given by 27.688.

Hence the correct option is (A).

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The value of Kearney's retirement savings when he retired at age 68 is approximately $351,115.71

To calculate the value of Kearney's retirement savings when he retired, we can use the formula for the future value of an ordinary annuity with monthly compounding of interest:

FV = P * [(1 + r)^n - 1] / r

Where:
FV is the future value of the annuity (retirement savings)
P is the monthly payment or investment amount ($200)
r is the monthly interest rate (5.5% / 12)
n is the number of compounding periods (number of months from age 30 to age 68, which is 68 - 30 = 38 years * 12 months/year = 456 months)

Let's calculate the value of Kearney's retirement savings:

r = 5.5% / 12 = 0.0045833 (monthly interest rate)
n = 456 (number of months)

FV = 200 * [(1 + 0.0045833)^456 - 1] / 0.0045833

Calculating the value:

FV ≈ $351,115.71

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