What type of number is 90.65i?
Real, Imaginary, or Complex?

Answer:

0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this problem, we have that:

[tex]\mu = 606, \sigma = 62, n = 99, s = \frac{62}{\sqrt{99}} = 6.23[/tex]

What is the probability that the mean battery life would be greater than 619 minutes?

This is 1 subtracted by the pvalue of Z when X = 619. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{619 - 606}{6.23}[/tex]

[tex]Z = 2.09[/tex]

[tex]Z = 2.09[/tex] has a pvalue of 0.9817

1 - 0.9817 = 0.0183

0.0183 = 1.83% probability that the mean battery life would be greater than 619 minutes

Answer:

The expression isTotal number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)

Step-by-step explanation:

A box= 12 cupcakes

Sean's order

Sister's graduation=5 boxes

Variety show party=3.5 boxes

Total number of cupcakes Sean orders=5 boxes (12 cupcakes)+ 3.5 boxes (12 cupcakes)

Total number of cupcakes Sean orders=5(12)+3.5(12)

=60+42

=102 cupcakes

Answer:

Max revenue: R = $679.73

Step-by-step explanation:

total people = 100

each person orders 1 of 2 dishes

salad price = $10 - 0.04x

turkey price = $12 - 0.02*y^2

so  x + y = 100

s = 10 - 0.04x

t = 12 - 0.02*y^2

Revenue =  s*x  + t*y  

Revenue = (10 - 0.04x)*x  + (12 - 0.02y^2)*y

y = 100 - x

so

Revenue = (10 - 0.04x)*x  +  (12 - 0.02*(100 - x)^2 )*(100 - x)

R =

R = (10 - 0.04x)*x  +  (12 - 0.02*(100 - x)^2 )*(100 - x)

R = 10x - 0.04x*x  +  (12 - 0.02*(10000 - 200x + xx)  )*(100 - x)

R = 10x - 0.04x*x  +  (12 -  200 + 4x -0.02 xx  )*(100 - x)

R = 10x - 0.04x*x  +  (-188 + 4x -0.02 xx  )*(100 - x)

R = 10x - 0.04x*x  +  (-188 + 4x -0.02 xx  )*100  -x (-188 + 4x -0.02 xx  )

R = 10x - 0.04x*x  +  -18800 + 400x -2 xx   -x (-188 + 4x -0.02 xx  )

R = 10x - 0.04x*x  +  -18800 + 400x -2 xx   +  188x - 4xx +0.02 xxx  

R = 10x - 0.04x*x  +  -18800     +  588x     -6 xx  +   0.02 xxx  

R =   -18800     +  598x     -6.04 xx  +   0.02 xxx  

dR/dx = 598 - 12.08x  + 0.06 x^2

set = 0

598 - 12.08x + 0.06xx = 0

299 - 6.04x + 0.03xx = 0

x = -(-6.04)/(2*0.03)  +  root((-6.04)^2  - 4*0.03*299) / 2*0.03

x = 100.6667  - root(36.4816 - 35.88) / 0.06

x  = 100.6667 - 12.927

x = 87.739

so that is where you get the maximum revenue, when you sell 87.7 salad plates and 12.2605 turkey dishes

Revenue = (10 - 0.04*87.739)*87.739  + (12 - 0.02(12.2605)^2)*12.2605

Revenue = 569.464715  + 110.266

R = $679.7307

R = $679.73

To find the maximum revenue, differentiate the revenue functions of salads and turkey plates with respect to the number of salads sold, considering a total of 100 guests, find critical points, and use the second derivative test or sign changes to identify the maximum revenue. Ensure that the number of meals are integers.

To determine the maximum revenue for the food truck, we need to derive the revenue functions for salad and turkey plates and then find the total revenue function. Assuming s salads and t turkey plates are sold, the price functions are Ps(s) = 10 - 0.04s for salads and Pt(t) = 12 - 0.02t2 for turkey plates. The revenue functions would be Rs(s) = s × Ps(s) and Rt(t) = t × Pt(t). Because there are 100 guests, s + t = 100, hence t = 100 - s. We substitute t in Rt and add Rs and Rt for the total revenue R(s). To find the maximum revenue, we differentiate R(s) with respect to s, find critical points, and check these for the maximum value using the second derivative test or analyzing the sign changes of R'(s). Remember to check if the critical points result in s and t being positive integers, as per the conditions given.

Answer:

124.4

Step-by-step explanation:

12 x 9.95 = 119.4 dollars

119.4+5.00=124.4

The total cost is $124.40.

Answer:

Step-by-step explanation:

Answer:

124.4

Step-by-step explanation:

12 x 9.95 = 119.4 dollars

119.4+5.00=124.4

The total cost is $124.40.

Answer:

The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.

Step-by-step explanation:

We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:

[tex]\alpha = \frac{1-0.85}{2} = 0.075[/tex]

Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].

So it is z with a pvalue of [tex]1-0.075 = 0.925[/tex], so [tex]z = 1.44[/tex]

Now, find the margin of error M as such

[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]

In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.

[tex]M = 1.44\frac{12.6}{\sqrt{717}} = 0.7[/tex]

The lower end of the interval is the sample mean subtracted by M. So it is 21.1 - 0.7 = $20.4.

The upper end of the interval is the sample mean added to M. So it is 21.1 + 0.7 = $21.8.

The 85% confidence interval for the mean per capita income in thousands of dollars is between $20.4 and $21.8.

We have been given that the length of an edge of a square pyramid is 7 and altitude of the pyramid is 12. We are asked to find the volume of the pyramid.

We will use volume of pyramid formula to solve our given problem.

[tex]V=\frac{1}{3}\cdot b\cdot h[/tex], where,

b = Area of base of pyramid,

h = Height of pyramid.

We know that area of a square is square of its side length, so area of the base of pyramid would be [tex]7^2=49[/tex].

The height of the pyramid will be equal to altitude.

[tex]V=\frac{1}{3}\cdot 49\cdot 12[/tex]

[tex]V=49\cdot 4[/tex]

[tex]V=196[/tex]

Therefore, the volume of the given pyramid would be 196 cubic units and 3rd option is the correct choice.

Answer: The length of pencil is 16 centimetres and length of crayons is 8 centimetres

Step-by-step explanation:

Let the length of crayon =[tex]x[/tex]

Length of a pencil =[tex]2x[/tex]

As according to question that the sum of their length is 24 centimetres

So we have

[tex]x+2x=24\\\\\Rightarrow 3x= 24 \\\\\Rightarrow x= \dfrac{24}{3} =8[/tex]

Therefore the length of crayon = 8 centimetres

Length of pencil= [tex]2x= 2\times x = 2\times 8 =16[/tex] centimetres

Hence, the length of pencil is 16 centimetres and length of crayons is 8 centimetres

Given Information:

Unit labor cost = 0.9

Hourly output per worker = $32.50

Required Information:

Hourly compensation per worker = ?

Answer:

Hourly compensation per worker = $36

Step-by-step explanation:

The unit labor cost is given by

[tex]U = \frac{O}{W}[/tex]

Where W is the hourly compensation per worker, O is the hourly output per worker and U is the unit labor cost.

Re-arranging for the hourly compensation yields,

[tex]U = \frac{O}{W}\\\\W =\frac{O}{U}\\ \\[/tex]

Now substitute the given values

[tex]W =\frac{32.50}{0.9}\\\\W = 36.11\\\\W = \$ 36[/tex]

Therefore, the hourly compensation per worker is $36.

Bonus:

Unit labor cost is the amount incurred with regard to labor expenses to produce one unit of a product. Calculating the unit labor cost helps in analyzing other aspects of the business such as product pricing, profit margin, sales etc.

Answer:

Wideness ≈ 40 m

He will be able to do it .

Step-by-step explanation:

He wants to estimate the width of a river so he can get to the other side to save the world . The width of the river is the side  AB. From the scale above 2 right angle triangle are formed . The smaller triangle is CDE and the larger triangle is  CAB.

The angle ECD can be gotten below

tan C = opposite/adjacent

tan C = 8/6

tan C = 1.3333

C = tan⁻¹ 1.333

C = 53.1301022854

C = 53. 13°

∠ACB = ∠ECD (vertically opposite angles)

Using the angle to find the wideness of the river AB in triangle CAB.

tan C = opposite/adjacent

tan 53.13° = AB/30

AB = 30 tan 53.13

AB = 30 × 1.33332837108

AB = 39.9998511323

AB ≈ 40 m

He will be able to do it.

Answer:

(C)

Step-by-step explanation:

To find 70 percent of 82

Write 70 percent as 7*10 percent.

Write 10 percent as [tex]\frac{10}{100}= \frac{1}{10}[/tex].

Then, find [tex]\frac{1}{10}$ of 82[/tex]

[tex]82 X\frac{1}{10}=8.2[/tex]

Multiply 8.2 by 7: 8.2 X 7 =57.4

Therefore, 70 percent of 82 is 57.4.

The steps in Option C are the correct steps.

Answer:

The answer to ur question is C

Step-by-step explanation:

Answer:

okay my daughter is in 6th grade so the answer is c 45 dollars per 3 hours

Step-by-step explanation:

Answer:

The formula to find the volume of a hemisphere is 2TTr3 / 3, where pi is 3.14, and the radius is half of the diameter.

Step-by-step explanation:

Answer:

hiii, the answer would be

b. 2/3 pi 3

hope this helps :)

Step-by-step explanation:

i just did the assignment

Answer:

Step-by-step explanation:

hello : here is an solution

Answer:

(-3,9)

Step-by-step explanation:

Use any of the method for solving systems of equations (substitution,elimination,equal to each other)

The solution to the system of equations y = 4x + 3 and 2x - 3y = 21 is x = -3 and y = -9, found by substitution.

The solution to the system of equations y = 4x + 3 and 2x - 3y = 21 is found by using the substitution or elimination methods.

To use substitution, we can first express y from the first equation and substitute it into the second equation. As an example, substituting y from y = 4x + 3 into the second equation yields:

2x - 3(4x + 3) = 21

2x - 12x - 9 = 21

-10x = 30

x = -3

Then, we substitute x back into the first equation to find y:

y = 4(-3) + 3

y = -12 + 3

y = -9

The solution to the system of equations is x = -3 and y = -9.

Answer: The equation you could use is 4x = 3x + 3

Step-by-step explanation:

THE SQUARE

A square has sides with 4 equal sides. If one side is equal to x, then every other side is also x.

Add x + x + x + x to get the square’s perimeter.

The sqaure’s perimeter is 4x.

THE TRIANGLE

An equilateral triangle has equal sides too. If one side is x + 1, every other side is x + 1 too.

Add, (x + 1) + (x + 1) + (x + 1)

the triangles perimeter is 3x + 1

BOTH

The triangle and the square have the same perimeter. Therefore,

4x = 3x + 3. That is the equation.

( The solution would be x = 3, by the way)

Answer:

Step 1 : 1000 * 2 * 9

Step 2 : 1000 * 18

Step 3 : 18000

Step-by-step explanation:

Step 3

2000 * 9 = y ⇒ 18000

y = 18000

Step 1

Solving for this, we have:

Let a be the unknown variable

a * 2 * 9 = 18000

18a = 18000

a = 1000

Therefore, when we multiply 1000 by 2 & 9, we have 18000

Step 2

Solving for this, we have:

Let a be the unknown variable

a * 18 = 18000

18a = 18000

a = 1000

Therefore, when we multiply 1000 by 18, we have 18000

We therefore see that the value of the unknown variables (a, y) is shown above & the product of all the steps (step 1 - 3) is 18000

Answer:

12 cm³

Step-by-step explanation:

Let's say the radius of the sphere and cylinder is r and the height is h. However, notice that the "height" of the sphere is the same thing as the diameter, which is 2r, so h = 2r.

The volume of a sphere is denoted by: [tex]V=\frac{4}{3} \pi r^3[/tex] , where r is the radius.

The volume of a cylinder is denoted by: [tex]V=\pi r^2h[/tex], where r is the radius and h is the height. Plug in 2r for h and 18 for V:

[tex]V=\pi r^2h[/tex]

[tex]18=\pi r^2*2r=2\pi r^3[/tex]

[tex]\pi r^3=18/2=9[/tex]

Now plug in 9 for πr³ in the volume formula for the sphere:

[tex]V=\frac{4}{3} \pi r^3[/tex]

[tex]V=\frac{4}{3} *9=12[/tex]

The volume of the sphere is 12 cm³.

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 17

For the alternative hypothesis,

µ < 17

This is a left tailed test.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 80,

Degrees of freedom, df = n - 1 = 80 - 1 = 79

t = (x - µ)/(s/√n)

Where

x = sample mean = 15.6

µ = population mean = 17

s = samples standard deviation = 4.5

t = (15.6 - 17)/(4.5/√80) = - 2.78

We would determine the p value using the t test calculator. It becomes

p = 0.0034

Since alpha, 0.05 > than the p value, 0.0043, then we would reject the null hypothesis.

The data supports the professor’s claim. The average number of hours per week spent studying for students at her college is less than 17 hours per week.

Answer:

a.)Easy to produce, d.)affordable, and e.)abundant

Step-by-step explanation:

i got it correct on the instructions

The correct options are easy to produce, affordable, and abundant​.

A nonrenewable resource is a natural substance that is not replenished with the speed at which it is consumed.

A non-renewable resource is defined as the natural resources which are not readily replaced through natural means and it takes thousands of years for their renewal.

Examples of non-renewable resources include Fossil fuels such as natural gas, oil, and coal.

There are many advantages of non-renewable resources such as:

Hence, the correct options are easy to produce, affordable, and abundant​.

Learn more about the nonrenewable resource here;

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Answer:

r + 6 = 90

Step-by-step explanation:

Answer:

90 = r6

Step-by-step explanation:

90 is the answer or product (multiplication) of Rita's age (r) and 6.

Meaning r times 6 = 90

Answer:

1.5267% probability that he loses AT MOST 3 times

Step-by-step explanation:

For each game that Andy plays, there are only two possible outcomes. Either he wins, or he loses. The probability of winning a game is independent of other games. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

The chance of winning a certain game at a carnival is 2 in 5.

So the chance of losing is (5-2) in 5, that is 3 in 5.

So [tex]p = \frac{3}{5} = 0.6[/tex]

12 games:

This means that [tex]n = 12[/tex].

What is the probability that he loses AT MOST 3 times?

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex].

In which:

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{12,0}.(0.6)^{0}.(0.4)^{12} = 0.000017[/tex]

[tex]P(X = 1) = C_{12,1}.(0.6)^{1}.(0.4)^{11} = 0.000302[/tex]

[tex]P(X = 2) = C_{12,2}.(0.6)^{2}.(0.4)^{10} = 0.002491[/tex]

[tex]P(X = 3) = C_{12,3}.(0.6)^{3}.(0.4)^{9} = 0.012457[/tex]

[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.000017 + 0.000302 + 0.002491 + 0.012457 = 0.015267[/tex]

1.5267% probability that he loses AT MOST 3 times

Answer:

8

Step-by-step explanation:

Answer:

Check the explanation

Step-by-step explanation:

Kindly check the attached images for the step by step explanation to the question

Answer:

The tip is $3.06

Step-by-step explanation:

To find the tip, take the amount of the bill and multiply by 18%

17 * 18%

17 * .18

3.06

The tip is $3.06

Answer:

There is a multiplication error. The payment should be $48 per month.

Step-by-step explanation:

i took the assignment hopes this help can i get brainliest plzzzzz

The pet store owner made an error in his calculation. When you multiply the amount of each payment ($49) by the number of payments (6), the result is $294, not $288.

The information provided in the question implies a situation that involves simple mathematics; specifically, multiplication and addition. To determine the total cost of the snake, it would be necessary to multiply the number of payments (6) by the individual amount of each payment ($49).

Here's how:

This means that

the pet store owner is asking for $294 in total

, not $288. Thus, the error that the pet store owner made was in the calculation of the total amount due for the snake.

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Answer:

5,95,9005,11,9010

Step-by-step explanation:

Answer:

Step-by-step explanation:

2x - 5

2(3) - 5

2 times 3 = 6

6-5=1

B) is the answer

I think the answer is B because you have to plug in 1 for the expression.

-Dhruva;)