Which is the correct classification of startroot 18 endroot? irrational number, non-repeating decimalirrational number, terminating decimalrational number, terminating decimalrational number, non-repeating decimal.

The answers are:

a) The z-score for a light bulb that lasts 500 hours is -10.

b) For a sample of 20 light bulbs, the probability that the average lifespan will be less than 980 hours is approximately 0.0367, or 3.67%.

c) The z-score for a light bulb that lasts 400 hours is -12. This is even more unusual than a lifespan of 500 hours.

d) Given the lifespan follows a normal distribution with a mean of 1000 hours, 50% of the light bulbs will have a lifespan less than 1000 hours.

a) The z-score is calculated as:

z = (X - μ) / σ

Where X is the data point, μ is the mean, and σ is the standard deviation. Here, X = 500 hours, μ = 1000 hours, and σ = 50 hours. So,

z = (500 - 1000) / 50 = -10.

The z-score for a bulb that lasts 500 hours is -10. This is far from the mean, indicating that a bulb lasting only 500 hours is very unusual for this brand of bulbs.

b) If a customer buys 20 of these light bulbs, we're now interested in the average lifespan of these bulbs. . In this case, n = 20, so the standard error is

50/√20

≈ 11.18 hours.

z = (980 - 1000) / 11.18 ≈ -1.79.

The probability that z is less than -1.79 is approximately 0.0367, or 3.67%.

c) The z-score for a bulb with a lifespan of 400 hours can be calculated as:

z = (400 - 1000) / 50 = -12.

The probability associated with z = -12 is virtually zero. So the probability of getting a bulb with a mean lifespan of 400 hours is virtually zero.

d) The mean lifespan is 1000 hours, so half of the light bulbs will have a lifespan less than 1000 hours. Since the lifespan follows a normal distribution, the mean, median, and mode are the same. So, 50% of light bulbs will have a lifespan less than 1000 hours.

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Answer:

59

Step-by-step explanation:

Answer:

The mean of this data set is 10.6

Step-by-step explanation:

To find the Mean of a data set, you add up all the values and then divide by the number of values.

3 + 4 + 6 + 7 + 10 + 15 + 19 + 21 = 85

This data set has 8 values.

85 ÷ 8 = 10.6

Answer:

3 / 4r

Step-by-step explanation:

Simplify : 7r/ 2 ÷ 14r²/3

7r/ 2 ÷ 14r²/3

Changing the ÷ sign to multiplication :

Multiply 7r/2 by the reciprocal of the denominator :

7r/ 2 * 3/14r²

((7 * r) / 2) * (3) / 14 * r * r

= 3 / 4r

For clarity, kindly check attached picture for detailed simplification.

Step-by-step explanation:

5304637_2951874

=2352763

2352763÷2

=1176381.5

Answer: $105

Step-by-step explanation:

On the first day he earned 5; second day he earns square of 5 ie. 25; third day is 3 times of the second day, so it's 25x3 = 75. Add these 3 days together to get the answer, which is 105 dollars.

Answer:

$3.70

Step-by-step explanation:

4 quaters= 1$

4=1

8=2

12=3

7 dimes =70

so there for

$3.70

Answer:

$3. 70

Step-by-step explanation:

Each dime equals 10 cents. There are 7 dimes. 10+10+10+10=10+10+10= 70

Each quarter equals 25 cents. add 25, 12 times, 25,25,25,25,25,25,25,25,25,25,25,25=300. Just add a decimal.

Answer:

\( \sqrt{ {1}^{2} + {2}^{2} + {( - 2)}^{2} } = \sqrt{1 + 4 + 4} = \sqrt{9} = 3\)

(1, 2, -2) is 3 units away from the origin.

(0, 0, 5) is 5 units away from the origin.

So (0, 0, 5) is farther away from the origin.

Answer:

$6.60

Step-by-step explanation:

If it is a 10% increase, you change the 10% to 0.1.

Then multiply the 0.1 and the $6 together which you will then get 0.6.

Then add the original amount ($6)

$6 + $0.6 = $6.60

Answer: 450

Step-by-step explanation:

The impact propensity can be interpreted as the slope coefficient for the tax personal exemption (pe) or its first lag in

the regression equation.

To determine the impact propensity in the regression of the general fertility rate (GFR) on the tax personal exemption

(PE) and its first lag, you should follow these steps:

Estimate the regression model using the available data. The model should look like this:

GFR = β0 + β1 × PE + β2 × PE_lag + ε

Where GFR is the general fertility rate, PE is the tax personal exemption, PE_lag is the tax personal exemption's first

lag, and ε is the error term.

Obtain the estimated coefficients (β0, β1, and β2) from the fitted regression model.

These coefficients will help you determine the impact propensity.

Calculate the impact propensity. The impact propensity in this context refers to the change in the general fertility rate

resulting from a one-unit increase in the tax personal exemption, taking into account both its current and lagged

effects.

To find the impact propensity, sum the coefficients for the tax personal exemption and its first lag:

Impact propensity = β1 + β2

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The number of servings of the stew the club can make is 24

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

The dot plot

From the dot plot, we have

Total = 4/8 * 2 + 6/8 + 1 * 3 + 1 2/8 * 1

Evaluate

Total = 6

Each serving can take 1/4 pounds

So, we have

Total = 6/(1/4)

Evaluate

Total = 24

Hence, the servings of the stew the club can make is 24

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Answer:

3.87 ounces

Step-by-step explanation:

12.9×.3= 3.87

( when you multiply percentages, 30% turns into

.3)

Step-by-step explanation:

x^2 -2kx +7k -12 = 0

two equal roots -->Δ = b^2 -4ac = 4k^2 - 4(7k-12)=0 = 4(k^2 - 7k +12)=4(k-4)(k-3)=0

so k =3 and k =4

Answer:

4/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that a student selected at random takes math or science = probability a student takes maths + probability a student takes science

probability a student takes maths = number of maths students / total number of students

probability a student takes science = number of science students / total number of students

(500 / 2000) + (1100 / 2000) = 1600/2000 = 4/5

Using the simplex method, the optimal solution for the given linear programming problem is x = 2, y = 2, z = 0, with the maximum objective value of P = 10.



a. To rewrite the formulation in standard form, we need to replace the inequalities with equality constraints and introduce non-negative variables. Let's assume x, y, and z as the non-negative variables:

Maximize P = 3x + 2y + 4z

Subject to:2x + y + z + s1 = 8

x + 2y + 3z + s2 = 10

x, y, z ≥ 0

b. Utilizing the linear programming simplex method, we can solve the above formulation. After setting up the initial tableau, we perform iterations by selecting a pivot element and applying the simplex algorithm until an optimal solution is reached. The algorithm involves row operations to pivot the tableau until all coefficients in the objective row are non-negative. This ensures the optimality condition is satisfied, and the maximum value of P is obtained.

To provide a brief solution within 120 words, we determine the optimal solution by applying the simplex method to the above formulation. After performing the necessary iterations, we find that the maximum value of P occurs when x = 2, y = 2, z = 0, with P = 10. Therefore, the maximum value of P is 10, and the solution for the given problem is x = 2, y = 2, and z = 0.

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Answer:

Gross Income = $ 43400

Adjusted Gross Income=$40500

Taxable Income = $33840

Step-by-step explanation:

given that-

Income paid to man

Wages = $41,500

Savings Interest = $1900

Tax Def Contribution=$2900

Deductions= $6660

personal exemption =$4050

Gross Income = Income paid to man = 41500 + 1900 = $ 43400

Adjusted Gross Income = Income - Tax Def Contribution =  $43400-$2900=$40500

Taxable Income = AGI - Deductions  = 40500 - 6660 = $33840

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The -value of the test is 1.90. This indicates that the mean processing time is significantly greater than 5.5 hours, supporting the manufacturer's desire to set a standard time required by employees to complete a certain process

The t-value will be equal to 1.39 for the given statistics.

To test if the mean processing time exceeds 5.5 hours, we can use a one-sample t-test.

The null hypothesis is that the mean processing time is less than or equal to 5.5 hours:

H0: µ ≤ 5.5

The alternative hypothesis is that the mean processing time is greater than 5.5 hours:

Ha: µ > 5.5

We will use a significance level of 0.05.

The formula for the t-test statistic is:

t = (X - µ) / (s / √n)

Where:

X = sample mean

µ = hypothesized population mean

s = sample standard deviation

n = sample size

Substituting the given values, we get:

t = (6 - 5.5) / (2 / √21) = 1.386

The degree of freedom for the t-test is n-1 = 20.

Using a t-table or calculator, the p-value associated with a t-value of 1.386 and 20 degrees of freedom is 0.093.

Since the p-value (0.093) is greater than the significance level (0.05), we fail to reject the null hypothesis. Therefore, there is not enough evidence to suggest that the mean processing time exceeds 5.5 hours.

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Answer:

It is not factorable

Step-by-step explanation:

The expression is not factorable with rational numbers.

Answer:

This is not factorable.

Step-by-step explanation:

This is not factorable.

The problem situation that can be represented by this inequality is A. Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $22.50 each. How many comic books, c, would each boy purchase if Charles’ total amount due is greater than or equal to Victor’s total?

It should be noted that an inequality is used to illustrate the expressions that are not equal.

In this case, it should be noted that the inequality given is illustrated as 25 + 12.50c ≥ 22.50c − 95.

Therefore, the information that illustrates this is that Charles and Victor went to a comic store and purchased some comic books. Charles purchased c comic books for $12.50 each and then spent $25.00 on a comic book portfolio. Victor sold a vintage comic book to the store for $95.00 and then purchased c more comic books for $22.50 each.

In conclusion, the correct option is A.

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Answer:

The answer is 9.45

Step-by-step explanation:

2.7*3.5=9.45

Answer:

265

Step-by-step explanation:

because she had 500 and now she has 765 so he gave her 265

Answer:

265

Step-by-step explanation:

Because before her Uncle visited she had 500 cents and he gave her a total of ? cents she now has 765.

Meaning what = 765 when you add it to 500.

500 + ?=765. we know 500 + 200=700 but she has 65 more than 700 so s you add that to our answer we get 765.

 5 0 0

 2 6 5

+______

   7    6  5=765

Hope it helps have a great day:)

Answer:

5x + 1 + (5x^2-1)/5x^2-1)

Step-by-step explanation:

Answer:

d. 6

Step-by-step explanation:

Given, a-5> -1

Both sides add 5, and we get

a > 4

So a is 6.

The expression can be simplified by combining any like terms, which in this case are 5g and 5g. When added together, they become 10g.

The expression 5g5g–10g can be simplified by performing the following steps:

1. Multiply 5g and 5g, to get 25g2.

Subtract 10g from 25g, to get 15g.

3. Simplify to 10g.

Simplifying the expression 5g5g–10g involves combining like terms. Like terms are terms that have the same variable, in this case the letter g. To simplify, first we need to multiply the two 5g terms together, giving us 25g. Then, we subtract 10g from 25g, to get 15g. Finally, we can simplify further by combining any remaining like terms, which in this case there are none. Therefore, when all is said and done, the expression can be simplified to 10g. This is because 10g is the only like term in the expression.

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The number of hamburgers sold on Friday was 442.

Let us form the linear equation to find the number of burgers;

Let the cheeseburger be represented by x.

Since there were 67 more cheeseburgers sold than hamburgers. This means that hamburgers will be:

The number of hamburgers = x + 67.

Since the local hamburger shop sold a combined total of 817 hamburgers and cheeseburgers. This will be:

x + x + 67 = 817

2x + 67= 817

2x = 817 - 67

2x = 750

x = 750 / 2

x = 375

So, 375 cheeseburgers were sold on Friday.

Therefore, the number of hamburgers sold will be:

= 817 - 375

= 442

Thus, the number of hamburgers sold on Friday was 442.

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Answer:

10 cm³

Step-by-step explanation:

The total surface area of a cube = 6 cm²

The formula for the surface area of the cube is :

A = 6a², a is the side of the cube

6 = 6a²

a = 1 cm

Now, the length of the formed cuboid = 2 cm

Breadth = 1 cm

Height = 1 cm

Required volume of the formed cubiod is :

V = 2(lb+bh+hl)

Put all the values,

V = 2(2(1)+1(1)+2(1))

V = 10 cm³

So, the required volume of the formed cuboid is equal to 10 cm³

If the yearly cost for the dental claims are normally distributed , then the yearly cost at which 35% of the employee fall at or below is $91.35  .

In the question ,

it is given that ,

the yearly cost for the dental claims are normally distributed ;

and the mean (μ) is 105 , standard deviation(σ) is 35 .

we know that the z value that corresponds to 35th percentile from standard normal table is : z = -0.385  ;

let the yearly cost be "x" ;

the yearly cost can be calculated using the formula ;

x = z×(σ) + μ

x = (-0.385)×35 + 105

Simplifying further ,

we get ;

x = 91.525

x ≈ 91.53

Therefore , the correct option is (d) 91.53  .

The given question is incomplete , the complete question is

The yearly cost of dental claims for the employees of the local shoe manufacturing company is normally distributed with a mean of $105 and a standard deviation of $35. what is the yearly cost at which 35% of the employees fall at or below is ?

(a) $118.48

(b) $127.29

(c) $82.71

(d) $91.53

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Jonathan will need five hours to complete as many puzzles (p) as Allison.

Any value associated with a variable that results in equal outcomes, i.e., tends to equalize the Left Hand Side (LHS) and Dominant Hand Side (RHS) of the formula equal, is a solution to an equation. To solve an equation, you must find the formula's workable answer.

Let p be the total number of math issues and h be the duration in hours. The equation is then presented as,

p = 9h + 10           ...1

p = 5h + 30          ...2

From equations 1 and 2, then we have

9h + 10 = 5h + 30

4h = 20

h = 5

Jonathan will need five hours to complete as many puzzles (p) as Allison.

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Step 1

The slope(m) is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line. Sometimes the ratio is expressed as a quotient ("rise over run"), giving the same number for every two distinct points on the same line.

From the question we will have;