I half dozen cupcakes cost $15. What constant of proportionality relates to the numbers of cupcakes and the total cost? Write an equation that represents its relationship

Final answer:

To find the remaining area after cutting a 3-inch square from a 6x8 rectangle, subtract the area of the square (9 square inches) from the area of the rectangle (48 square inches), resulting in 39 square inches left.

Explanation:

Calculating the Remaining Area of a Rectangle

To determine the area of the remaining paper after a square is cut off, we must first know the area of the initial rectangle and the area of the square that was removed. The area of the rectangle is found by multiplying its length by its width. Rectangle area = length × width, so it is 6 inches × 8 inches = 48 square inches. The cut-off square has a side length of 3 inches, so its area is 3 inches × 3 inches = 9 square inches.

Subtract the area of the square from the area of the rectangle to get the remaining paper area. Remaining area = rectangle area - square area, which equals 48 square inches - 9 square inches = 39 square inches.

Answer:

0.5 seconds

Step-by-step explanation:

Two rockets are launched at the same time, but from different heights.

[tex]y = -16t^2+ 150t + 5[/tex]

[tex]y = -16t^2 + 160t[/tex]

when the heights are same then y are equal. So equation both equations and solve for t

[tex]-16t^2+ 150t + 5= -16t^2+ 160t[/tex]

Add -16t^2 on both sides

[tex]+ 150t + 5=160t[/tex]

Subtract 150 t from both sides

[tex]5=10t[/tex]

Divide 10 on both sides

t=0.5 seconds

Sandy would have $67.04 more euros if she traded on the day with the most favorable exchange rate compared to the least favorable one.

To find the difference in euros between the most favorable and least favorable exchange rates, we first need to know the exchange rates for both scenarios.

Let's denote the exchange rate for the most favorable day as [tex]\( R_{\text{max}} \)[/tex] euros per dollar, and the exchange rate for the least favorable day as [tex]\( R_{\text{min}} \)[/tex] euros per dollar.

If Sandy has $829.04 to convert, then the number of euros she would get on the most favorable day is[tex]\( 829.04 \times R_{\text{max}} \)[/tex], and the number of euros she would get on the least favorable day is [tex]\( 829.04 \times R_{\text{min}} \).[/tex]

The difference in euros between the two scenarios is:

[tex]\[ \text{Difference} = 829.04 \times R_{\text{max}} - 829.04 \times R_{\text{min}} \][/tex]

To find the options:

[tex]a. \( \text{Difference} = 33.49 \)[/tex]

[tex]b. \( \text{Difference} = 55.96 \)[/tex]

[tex]c. \( \text{Difference} = 67.04 \)[/tex]

[tex]d. \( \text{Difference} = 107.99 \)[/tex]

We calculate the difference using each option for the exchange rate difference, then choose the one closest to the result.

After calculating, the closest option to the result is [tex]\( \textbf{c. 67.04} \).[/tex]

Answer:

Step-by-step explanation:

The Chef bought he had 8 cartons with 36 eggs in each carton. This means that the total number of eggs that the Chef bought is

36 × 8 = 288 eggs

He uses 2/5 for Fridays breakfast. This means that the number of eggs that he used on Friday is

2/5 × 8= 16/5 cartons

The remaining number of cartons would be

8 - 16/5 = 24/5 cartons

He used 3/8 of the remaining for Saturdays breakfast. This means that the number of eggs that he used on Saturday is

3/8 × 24/5 = 9/5 cartons

Total number of cartons that he used is

16/5 + 9/5 = 25/5 = 5 cartons

Since one carton contains 36 eggs, then the total number of eggs that the Chef used is

5 × 36 = 180 eggs

Answer: the speed of the river is 9km/h

Step-by-step explanation:

Let x represent the speed of the river current.

He rides 140 km downstream in a river in the same time it takes to ride 35km upstream. This means that his speed was higher when riding downstream and it was lower when riding upstream.

Assuming he rode in the direction of the river current when coming downstream and rode against the current when going upstream.

time = distance/speed

Manuel has a boat that can move at a speed of 15 km/h

His downstream speed would be

15 + x

time spent coming downstream would be

140/(15 + x)

His downstream speed would be

15 - x

time spent going downstream would be

35/(15 - x)

Since the time is the same, then

140/(15 + x) = 35/(15 - x)

Crossmultiplying

140(15 - x) = 35(15 + x)

2100 - 140x = 525 + 35x

140x + 35x = 2100 - 525

175x = 1575

x = 1575/175

x = 9

Answer:

5. No, the distribution is skewed to the left with a mean age greater than 36.

Step-by-step explanation:

The problem is presented in the photo below.  It says the following:

Let random variable S represent the age of the attendees at a local concert. The following histogram shows the probability distribution of the random variable S. Alfonso claims that the distribution of S is symmetric with a mean age of 36. Does the histogram supports Alfonso's claim.

Consider the given histogram at the photo below. it is an left-skew histogram , since it has a long tail to the left side.

We need to estimate the mean of the given data. To do so, we need to multiply each class midpoint with its probability, and sum them.

For example, for the first one, the midpoint is 32 and the probability is 0.03 (read the value on the y-axis). For, the second one, the midpoint is 33 and the probability is 0.04, for the third the midpoint is 34 and the probability is 0.05, and so on. All needed values are presented below.

Therefore, we obtain

[tex]\mu = 0.03 \cdot 32 + 0.04 \cdot 33 + 0.05\cdot 34 + 0.10 \cdot 35 + 0.11 \cdot 36 + 0.13 \cdot 37 + 0.25 \cdot 38 + 0.20 \cdot 39 + 0.09 \cdot 40[/tex]

which yields

                                       [tex]\mu = 37.15[/tex]

Therefore, this histogram is left-skewed with mean greater than 36.

Answer:Luke needs to deposit money into his savings account for 10 weeks before he can pay back his sister and buy the iPad.

Step-by-step explanation:

The cost of the iPad that Luke wants to buy is $575

before Luke can buy the iPad, he must give his sister $55 that he owes her. This means that the total amount of money that he must save would be 575 + 55 = $630

He will be able to deposit $65 into a savings account when he receives his paycheck each Friday.

Let x represent the number weeks it takes him to save enough money in his account. Therefore, the total amount that he saves for x weeks would be 65 × x = 65x

Therefore,

65x = 630

x = 630/65

x = 9.69

Answer:

heterozygous (Aa) are 0.085 = or 8.54%

Step-by-step explanation:

The heterozygous individuals are carriers of the sickle cell trait. They have a genotype of Aa and are represented by the 2pq term

in the H-W equilibrium equations.

According to the question 0.2% of the population is affected with sickle cell anemia, thus q^2

= 0.2% = 0.002 in decimal. So, q =

sqr(q^2)

or sqr(0.002) =

0.04472

and p + q = 1, thus p = 1 – q = 1 – 0.04472 = 0.96

Thus, A allele has a frequency of 0.96 and the a allele has a frequency of 0.04472. Therefore, the

percentage of the population that is heterozygous (Aa) and are carriers is = 2pq = 2× 0.04472× 0.96 =0.085 = or 8.54%

The graph of y=|x| would look like graph A

The reflected graph (mirrored image) would be graph D

Answer:

Arianna multiplied the dividend by the divisor instead of finding the reciprocal.

Step-by-step explanation:

The fraction division problem Arianna solved is [tex]\frac{2}{3}\div \frac{4}{5}[/tex]

Adrianna's next step is  [tex]\frac{2}{3}\times \frac{4}{5}[/tex]

We are supposed to choose from the options the most accurate description of Arianna's work.

The mistake Arianna committed is that, she did not reciprocate the [tex]\frac{4}{5}[/tex] before multiplying.

Therefore the correct answer is:

Arianna multiplied the dividend by the divisor instead of finding the reciprocal.

Answer:

the probability that the average loss from fire in the sample is no greater than $275 is 0.9938

Step-by-step explanation:

given information:

mean, μ = $250

std deviation, σ = $1000

random sample, n = 10000

x = $275

P([tex]x[/tex] ∠_ 275) = P(z < (z ∠ (x - μ)/(σ/√n))

                    = P (z ∠ (275 - 250)/(1000/√10000)

                    = P(z ∠ 2.5)

                     =  0.9938

The probability that the average loss from fire in the sample is no greater than $275 is 99.38%.

the probability that the average loss from fire in the sample is no greater than $275,

[tex]P(z\leq x)=P[z< \dfrac{(x-\mu )}{(\dfrac{\sigma}{\sqrt n})}][/tex]

[tex]P(z\leq 275)=P[z< \dfrac{(275-250 )}{(\dfrac{1000}{ \sqrt {10000}})}][/tex]

[tex]P(z\leq 275)=P[z< \dfrac{(25 )}{(10)}][/tex]

[tex]P(z\leq 275)=P[z< {(2.5)}][/tex]

[tex]P(z\leq 275)=0.9938[/tex]

P(x ≤ $275) = 99.38%

Hence, the probability that the average loss from fire in the sample is not greater than $275 is 99.38%.

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Answer:

Step-by-step explanation:

We would apply the formula for determining simple interest which is expressed as

I = PRT/100

Where

P represents the principal

R represents interest rate

T represents time in years

I = interest after t years

From the information given

T =172 days = 172/365 = 0.47 years

P = $4400

R = 6%

Therefore

I = (4400 × 6 × 0.47)/100

I = 12408/100

I = $124.08

The maturity of the loan would be

4400 + 124.08 = $4524.08

Answer:

After simplifying we get (x,y) as (1,3).

Step-by-step explanation:

Given:

[tex]x+7y=22[/tex],

[tex]x-7y=-17[/tex]

We need to use elimination method to solve the and simplify the equations.

Solution;

Let [tex]x+7y=22[/tex] ⇒ equation 1

Also Let [tex]4x-7y=-17[/tex]⇒ equation 2

Now by solving the equation we get;

first we will Add equation 2 from equation 1 we get;

[tex](x+7y)+(4x-7y)=22+(-17)\\\\x+7y+4x-7y=22-17\\\\5x=5[/tex]

Now Dividing  both side by 5 using division property of equality we get;

[tex]\frac{5x}{5}=\frac{5}{5}\\\\x=1[/tex]

Now Substituting the vale of x in equation 1 we get;

[tex]x+7y=22\\\\1+7y=22[/tex]

subtracting both side by 1 using subtraction property of equality we get;

[tex]1+7y-1=22-1\\\\7y=21[/tex]

Now Dividing  both side by 7 using division property of equality we get;

[tex]\frac{7y}{7}=\frac{21}{7}\\\\y=3[/tex]

Hence we can say that, After simplifying we get (x,y) as (1,3).

Answer: Random sampling

Step-by-step explanation:

In the given situation , the population of interest is "all adults"

Since the man got selected randomly from entire population of adults by the marketing company, it means the type of sampling method was used is random sampling technique.

Hence, the correct answer is "random"

Hi, your question was incomplete hence I have attached the complete version of the question below.

Answer:

5x^3 y^2

Step-by-step explanation:

Using the property of the product of the exponents on the base and removing the parentheses,

(125x^9y^6)^(1/3) = (125)^(1/3) * (x^9)^(1/3) * (y^6)^(1/3)

= (125)^(1/3) * (x)^9*(1/3) * (y)^6*(1/3)

= 5 * (x)^3 * (y)^2                                                    

= 5 x^3 y^2

hence the required result is 5 x^3 y^2

Question is not proper, Proper question is given below;

36% of the beans in Pythagoras's soup are lentils, and 33 1/3% of those lentils are green.

If Pythagoras removes all green lentils from his soup, then x% of the original beans remain. What is x?

Answer:

88% of the original beans remains [tex](x)[/tex] after removing green lentils.

Step-by-step explanation:

Given:

Let the Original beans be 'n'.

Now given:

36% of the beans in Pythagoras's soup are lentils.

So we can say that;

Amount of lentils = [tex]\frac{36}{100}n=0.36n[/tex]

Also Given:

33 1/3% of those lentils are green

Amount of green lentils = [tex]33\frac{1}{3}\%\ \ Or \ \ \frac{100}{3}\%[/tex]

Amount of green lentils = [tex]\frac{100}{3}\times 0.36n\times\frac{1}{100}= 0.12n[/tex]

Now we need find the percentage of original beans remain after removing green lentils.

Solution:

percentage of original beans remain  ⇒ [tex]x\%[/tex]

To percentage of original beans remain after removing green lentils we will subtract Amount of green lentils from Original beans  and then multiplied by 100.

framing in equation form we get;

[tex]x\%[/tex] = [tex](n-0.12n)\times 100=88n \ \ \ Or \ \ \ 88\%[/tex]

Hence 88% of the original beans remains [tex](x)[/tex] after removing green lentils.

Answer:

x = 88

Step-by-step explanation:

We know that 36% of the letters are vowels. Of these, one-third are Os

(Since 33 1/3% = 33 1/3 divided by 100 = 1/3.) One-third of 36% is 12%, so 12% of the total letters in Pythagoras' soup are Os. When these are removed from the soup, 100 - 12=88% of the original letters remain.

So, x = 88

Hope this helps!

Final answer:

The magnitude of vector B is 1. There is no valid direction angle theta for vector B.

Explanation:

Part A:

The magnitude of vector B can be found using the formula for the magnitude of the vector product:

|A x B| = |A||B|sin(theta)

Given |A x B| = 12, |A| = 8, and |B| = ?

Using the formula above, we can solve for |B|:

12 = 8 * |B| * sin(theta)

sin(theta) = 12 / (8 * |B|) = 1.5 / |B|

Sine of any angle lies between -1 and 1, therefore 1.5 / |B| should lie in this range

|-1| <= 1.5 / |B| <= |1|

1 <= 1.5 / |B| <= 1

1.5 <= |B| <= 1

The magnitude of vector B is 1.

Part B:

The direction angle theta can be found using the formula:

cos(theta) = Bz / |B|

Given Bz = |B| and sin(theta) = 1.5 / |B|

1.5 / |B| = sqrt(1 - sin^2(theta)) = sqrt(1 - 1) = sqrt(0) = 0

This implies that sin(theta) = 1.5 / |B| = 0, which is not possible

Hence, there is no valid direction angle theta for vector B.

Final answer:

The magnitude of vector B is 1.5 m. The direction angle θ of vector B measured from the +y-direction to the +z-direction is 90°.

Explanation:

Part A: To find the magnitude of vector B, we need to use the relationship between the magnitude of the vector product A x B and the magnitudes of vectors A and B. According to the given information, the magnitude of the vector product A x B is 12.0 m². Since the vector product is in the +z-direction, we can conclude that the magnitudes of vectors A and B multiplied by the sine of the angle between them equals 12.0 m².

Let's use this information to find the magnitude of vector B:

|A x B| = |A||B|sin(θ)

12.0 m² = 8.0 m * |B| * sin(90°)

|B| = 12.0 m² / (8.0 m * sin(90°))

|B| = 12.0 m² / 8.0 m = 1.5 m

Therefore, the magnitude of vector B is 1.5 m.

Part B: To find the direction angle θ of vector B measured from the +y-direction to the +z-direction, we can use the relationship between the components of vectors A and B and the direction angle θ:

tan(θ) = By / Bz

Substituting the given information into the equation:

tan(θ) = 0 / Bz

Since vector B has no x-component, we know that Bx = 0. Therefore, we only need to find the value of Bz to determine the direction angle θ.

Recall that |B| = 1.5 m. Using the Pythagorean theorem, we can find the value of Bz:

|B|² = Bx² + By² + Bz²

(1.5 m)² = (0)² + (0)² + Bz²

Bz² = (1.5 m)²

Bz = 1.5 m

Since Bz > 0, we know that the direction angle θ is in the positive range. In this case, the direction angle θ is 90° measured from the +y-direction to the +z-direction.

The required function is: [tex]f(t) = -0.05t+12[/tex]

Step-by-step explanation:

We have to write a function for the remaining figurines Colin has to paint.

Here

f is the function that represents number of figurines remaining

t represents time in minutes as the unit of measurement is minutes

f will be a function of t

It is mentioned in the problem that after working for 60 minutes, he has 9 figurines left to paint.

This means that

f(60) = 9

It is also given that he takes 20 minutes to paint one figurine which means in 60 minutes he will have painted 3 figurines

So at start total figurines that needed to be painted will be:

9+3 = 12

Which means that

f(0) = 12

By using these two points we can find the slope of the function

[tex]m = \frac{Change\ in\ figurines}{Change\ in\ time}\\m = \frac{9-12}{60-0}\\m = \frac{-3}{60}\\m = -0.05[/tex]

The function will be:

[tex]f(t) = mt+b[/tex]

Putting the value of slope

[tex]f(t) = -0.05t+b[/tex]

b is the initial value of figurines so

[tex]f(t) = -0.05t+12[/tex]

Keywords: Functions, slope

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Answer:

product of the constants P will be

P = 12

Step-by-step explanation:

the quadratic equation

F= x² + t*x - 9

has as solution

a and b= [-t  ± √( t² - 4*1*(-9)) ] /2]

then

a - b = -t/2

a= b - t/2

since b is an integer , then t/2 should be an integer , then t=2*n , where n is any integer

also

a and b= [-t  ± √( t² - 4*1*(-9)) ] /2] = [-2*n  ± √(4*n²+36 )] /2  = -n  ± n √ (1+9/ n²]

since n are integers , then √ (1+9/ n²]  should be and integer and therefore

9/ n² should be an integer. Then the possible values of n are

n=1 and n=3

therefore the possible values of t are

t₁=2*1 = 2

t₂=2*3 = 6

the product of the constants P will be

P=t₁*t₂ = 12

Answer:

729

Step-by-step explanation:

Answer:

The three consecutive natural numbers are 9,10,11

Step-by-step explanation:

Step 1 : -

Let x be the number

Given three consecutive natural numbers are x, x+1,x+2

Given data are three consecutive natural numbers are such that the square of the middle number exceeds the difference of the squares of the other two numbers by 60

that is [tex](x+1)^2 = (x+2)^2 - x^2 +60{\tex]

step 2:-

on simplification on both sides are , we get

by using [tex](a+b)^2 = a^2+2 a b+b^2[\tex]

[tex]x^2+2 x+1 = x^2+4 x+4-x^2+60[\tex]

cancelling x^2 terms and simplify

[tex] x^2 -2 x-63=0[\tex]

now finding factors of [tex] 63 = 9 X 7[\tex]

[tex] x^2 - 9 x+7 x -63=0 [\tex]

[tex] x(x-9)+7(x-90 =0 [\tex]

[tex]( x+7)(x-9) =0 [\tex]

here x= -7 is not an natural number

so we have to take x=9

therefore the three consecutive natural numbers are

x,x+1,x+2

The three consecutive natural numbers are  9 , 10, 11

Answer:

three consecutive  natural numbers are

5,6,7

Step-by-step explanation:

Let x, x+1  and x+2 are the three consecutive natural numbers

middle number is x+1

square of middle number is [tex](x+1)^2=x^2+2x+1[/tex]

difference of square of other two numbers is

[tex]x^2-(x+2)^2= x^2-x^2-4x-4=-4x-4[/tex]

the square of the middle number exceeds the difference of the squares of the other two numbers by 60

So [tex]x^2+2x+1=-4x-4+60[/tex]

[tex]x^2+2x+1+4x+4-60=0[/tex]

[tex]x^2+6x-55=0[/tex]

[tex](x+11)(x-5)=0[/tex]

[tex]x+11=0, x=-11[/tex]

[tex]x-5=0, x=5[/tex]

we take only natural number so x=5

three consecutive  natural numbers are

5,6,7

Answer:

In terms of negative correlation, I would say it's the longer you exercise, the more you sweat.

Answer:

Its D. The younger the child, the more sleep they need.

Step-by-step explanation:

Answer:

$6.83

Step-by-step explanation:

To start off, we would want to graph the points.

Once we have our graph, we see our correlation is positive, meaning that every year past 1950, the price of 1 movie ticket increases.

Our next step would to figure out the linear regression, or to guess a best line of fit. Once we do so, we should see where the movie tickets should approxametly rise to.

We then use the best line of fit to estimate the price in 2015, or when x = 65 (65 years after 1950).

The answer closest to the estimate would be 6.83. Attached image is the graph on Desmos.

Answer: 1) Percentage, Probability, Proportion

Step-by-step explanation:

In statistics,

▪Proportion means a fraction of the total.

▪Percentage means a number or a ratio, expressed as a fraction of 100. Here, the total is 100.

▪Probability which may look slightly different from the other two means a number between 0 and 1, showing the exact likelihood of an event happening. Which in context can mean, a number showing a fraction of an event happening out of the whole (0 to 1).

▪Critical value means a point in hypothesis testing on the test distribution that is compared to the test statistic to determine whether to reject the null hypothesis.

In the four definitions, the odd one out is Critical Value.

So the option without critical value in it is option 1) Percentage, Probability, Proportion since we can use the three interchangeable.

Answer:

1. Percentage, Probability, and Proportion

Step-by-step explanation:

Proportion means a portion of a whole e.g. 2/5

Percentage means a ratio of a number expressed as a fraction of 100 e.g 20/100

Probability- This means the likelihood of an event to occur e.g 1/2

All these three terms are usually expressed as a Fraction of a Number which makes them similar.

Answer:              [tex]f(x)=2(\dfrac{2}{3})^x[/tex]

Step-by-step explanation:

We know that the exponential decay equation is given by :-

[tex]y=Ab^x[/tex]

, where A = initial value.

b = Multiplicative growth rate  ( b <1 for decay)

x= time period.

Note : b ≠1 and b>0.

Let's check all the functions:

, here b =2 >1 , so this function does not represent exponential decay.

here b = [tex]-\dfrac{1}{5}[/tex]  but b should be greater than 0 for exponential function, so this function does not represent exponential decay.

Here , [tex]b=\frac{7}{2}>1[/tex] , so this function does not represent exponential decay.

Here , [tex]b=\dfrac{2}{3}<1[/tex]  , so this function represents exponential decay.

Hence, the correct answer is [tex]f(x)=2(\dfrac{2}{3})^x[/tex] .

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

We will see that the correct option is:

----------------------------------------

The form of the general exponential decay is:

f(x) = A*(r)^x

Where A is the initial value, x is the variable, and r is the rate at which it decreases, where r must be a number between 0 and 1.

The given options are:

Because r must be between zero and one, the only option that meets that requirement is the last one, where r = 2/3.

Then the function that represents an exponential decay is the last one:

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Answer:

1.21%

Step-by-step explanation:

We have been given that a savings and loan pays a nominal rate of 1.2​% on savings deposits. We are asked to find the effective annual yield, when interest is compounded 10 comma 00010,000 times per year.

We will use Annual Percentage Yield formula to solve our given problem.

[tex]APY=(1+\frac{r}{n})^n-1[/tex], where,

r = Annual interest rate in decimal form,

n = Number of times interest is compounded per year.    

[tex]1.2\%=\frac{.2}{100}=0.012[/tex]

[tex]APY=(1+\frac{0.012}{10,000})^{10,000}-1[/tex]

[tex]APY=(1+0.0000012)^{10,000}-1[/tex]

[tex]APY=(1.0000012)^{10,000}-1[/tex]

[tex]APY=1.0120722815791632-1[/tex]

[tex]APY=0.0120722815791632[/tex]

[tex]0.0120722815791632\times 100\%=1.20722815791632\%\approx 1.21\%[/tex]

Therefore, the effective annual yield would be 1.21%.

–21 + x

Explanation:

Step 1: Given expression: –4 + (–17) + x

Step 2: In the algebraic property, positive × negative = negative

So, –4 + (–17) + x = –4 – 17 + x

Step 3: Add two negative numbers, the result will be sum with minus sign

–4 – 17 + x = –21 + x

Hence,  –21 + x is the required equation.

Question:

Ana participated in a charity walk. She raised $0.25 for each 1/2 mile that she walked.The first day Ana walked 11 miles.The second day, she walked 14 miles.How much money did Ana raised?

Answer:

Ana raised $ 12.5

Solution:

From given question,

First day walk = 11 miles

Second day walk = 14 miles

Let us first calculate the total distance she walked

Total distance = first day walk + second day walk

Total distance = 11 + 14 = 25 miles

Thus she walked for 25 miles

Given that,

She raised $0.25 for each 1/2 mile that she walked

[tex]\frac{1}{2} \text{ mile} = 0.25 \text{ dollars }[/tex]

Therefore, for 1 mile we get,

[tex]\frac{1}{2} \times 2 \text{ mile} = 0.25 \times 2 \text{ dollars }\\\\1 \text{ mile } = 0.5 \text{ dollars }[/tex]

Now calculate for 25 miles

[tex]25 \text{ mile } = 25 \times 0.5 = 12.5 \text{ dollars }[/tex]

Thus she raised $ 12.5

Answer:

[tex]a=100 +2.97*15=144.55[/tex]

So the value of height that separates the bottom 99.85% of data from the top 0.5% is 144.55.  

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the IQ of a population, and for this case we know the distribution for X is given by:

[tex]X \sim N(100,15)[/tex]  

Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]

For this part we want to find a value a, such that we satisfy this condition:

[tex]P(X>a)=0.0015[/tex]   (a)

[tex]P(X<a)=0.9985[/tex]   (b)

Since we want the 0.15% of the people in the right tail since says above.

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.9985 of the area on the left and 0.0015 of the area on the right it's z=2.97. On this case P(Z<2.97)=0.9985 and P(z>2.97)=0.0015

If we use condition (b) from previous we have this:

[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.99985[/tex]  

[tex]P(z<\frac{a-\mu}{\sigma})=0.9985[/tex]

But we know which value of z satisfy the previous equation so then we can do this:

[tex]z=2.97=\frac{a-100}{15}[/tex]

And if we solve for a we got

[tex]a=100 +2.97*15=144.55[/tex]

So the value of height that separates the bottom 99.85% of data from the top 0.5% is 144.55.  

The IQ score that only approximately 0.15% of people surpass, under the given conditions, is 145. A score over 145 is achieved by applying the formula for standard deviation and z-score in a normal distribution.

The distribution of IQ scores is approximately normal with a mean of 100 and a standard deviation of 15. When we say 0.15% of people have an IQ over a certain score, we're referring to the tail end of the distribution. This is a z-score question where we need to find the z-score corresponding to a percentile. With 0.15% in the tail, we have 99.85% below this value.

Using a z-score table or a calculator, the z-score for 99.85% is approximately 3. Below to calculate the IQ score, we use the formula:

IQ = mean + z*(standard deviation)

Substituting the values:

IQ = 100 + 3*15 = 145

Therefore, only about 0.15% of people have an IQ over 145.

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Answer:

Nt=10 (m=4,n=6)

Step-by-step explanation:

we have that m = amount of time used by the large washing machine to wash a load of clothes and n = amount of time used by the small washing machine to wash a load of clothes, so

[tex]m=\frac{Tt}{Tpm}=\frac{2h}{\frac{1h}{2}}=4\\n=\frac{Tt}{Tpn}=\frac{2h}{\frac{1h}{3}}=6[/tex]

Nt=m+n=10

where Tt = time frame, Tpm= m' time frame, Tpn = n' time frame and Nt = total number of charges

Answer: Total laundry done in 2hours=110

Step-by-step explanation:

Let m be large washing machines

Let n be small washing machines

Load of laundry for large machine=30mins

Load of laundry in small machine=20 mins

2 hours laundry =2×60=120mins

For m in 2hrs=120/30=4

For n in 2hrs=120/20=6

m loads in 2hrs=4m

n loads in 2hrs=6n

1st statement:n=3m

Substituting

4m+6(3)=x

4m+18m=x

X=22m

Value of m cannot be determined because statement 1 is insufficient

From the 2nd statement: 2m+3n=55

Multiply both sides by2

4m+6n=110

Answer: Population parameter.

Step-by-step explanation:

Population parameter : It is a number that summarize a term for the whole population . For example :population proportion , population mean , etc.

Sample statistics: It is a number that summarize a term for the sample . For example : sample proportion , sample mean, etc.

By considering the given statement :

Population of interest : " all instructors at school "

Since 75% of all instructors at your school teach 2 or more classes.

It means , 75% is describing population proportion of all instructors at your school teach 2 or more classes..

i.e. The numerical value describes a population parameter.