High Fructose Corn Syrup (HFCS) is a sweetener in food products that is linked to obesity and type II diabetes. The mean annual consumption in the United States in 2008 of HFCS was 60 lbs with a standard deviation of 20 lbs. Assume the population follows a Normal Distribution.
a. Find the probability a randomly selected American consumes more than 50 lbs of HFCS per year.
b. Find the probability a randomly selected American consumes between 30 and 90 lbs of HFCS per year.
c. Find the 80th percentile of annual consumption of HFCS.
d. In a sample of 40 Americans how many would you expect to consume more than 50 pounds of HFCS per year.
e. Between what two numbers would you expect to contain 95% of Americans HFCS annual consumption?
f. Find the quartile and Interquartile range for this population.
g. A teenager who loves soda consumes 105 lbs of HFCS per year. Is this result unusual?

Answer:

[tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]

Step-by-step explanation:

[tex]x^{-\frac{5}{3} }[/tex] = [tex](\sqrt[3]{x} )^{-5}[/tex] = [tex]\frac{1}{(\sqrt[3]{x} )^5}[/tex]

Answer:  D.) The second difference is constant.

Step-by-step explanation:

The rate of change of a quadratic function is a linear function. The rate of change of that is constant, so second differences of a quadratic number pattern are constant.

Answer:

D.

Step-by-step explanation:

Answer:

(3) x ≥ -3

(4) 2.5 gallons

(4) -12x + 36

Step-by-step explanation:

Hey there!

1)

Well its a solid dot meaning it will be equal to.

So we can cross out 1 and 2.

And it's going to the right meaning x is greater than or equal to -3.

(3) x ≥ -3

2)

Well if each milk container has 1 quart then there is 10 quarts.

And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.

(4) 2.5 gallons

4)

16 - 4(3x - 5)

16 - 12x + 20

-12x + 36

(4) -12x + 36

Hope this helps :)

Answer:

Variance=134.8943 kg

Step-by-step explanation:

The relationship between standard deviation and variance is that standard deviation is the square root of the variance.

So given the value of standard deviation to be 11.6144kg, the variance will be the square of the number.

Standard deviation= √variance

Standard deviation ²=√variance²

Standard deviation ² = variance

11.6144²= variance

134.8943

Variance=134.8943 kg

Answer:

122.4409 kg

Step-by-step explanation:

Answer: vector equation r = (7+3t)i + (4+2t)j + (5 - 5t)k

parametric equations: x = 7 + 3t; y = 4 + 2t; z = 5 - 5t

Step-by-step explanation: The vector equation is a line of the form:

r = [tex]r_{0}[/tex] + t.v

where

[tex]r_{0}[/tex] is the position vector;

v is the vector;

For point (7,4,5):

[tex]r_{0}[/tex] = 7i + 4j + 5k

Then, the equation is:

r = 7i + 4j + 5k + t(3i + 2j - k)

r = (7 + 3t)i + (4 + 2t)j + (5 - 5t)k

The parametric equations of the line are of the form:

x = [tex]x_{0}[/tex] + at

y = [tex]y_{0}[/tex] + bt

z = [tex]z_{0}[/tex] + ct

So, the parametric equations are:

x = 7 + 3t

y = 4 + 2t

z = 5 - 5t

Answer:

.154

Step-by-step explanation:

There are 52 cards

There are 4 aces and 4  9's for a total of 8 cars

P (ace or 9) = number of aces or 9's / total

                   = 8/52 = 2 /13 =.153846154

To the nearest thousandth

                      = .154

Answer:

0.154

Step-by-step explanation:

We want to find the probability of drawing an ace or a 9.

P(ace or 9)= aces and 9s / total cards

There are 4 aces and 4 9s in a standard deck of cards. This means there is a total of 8 aces and 9s.

In a standard deck of cards, there is a total of 52 cards.

P(ace or 9)= aces and 9s / total

aces and 9s= 8

total= 52

P(ace or 9)= 8/52

This fraction can be simplified. Both the numerator and denominator can be evenly divided by 4.

P(ace or 9)= (8/4) / (52/4)

P(ace or 9)= 2/13

P(ace or 9)= 0.153846153846154

Round to the nearest thousandth. The 8 in the ten thousandth place tell sus to round the 3 up to a 4.

P(ace or 9) = 0.154

The probability of drawing an ace or 9 is 0.154

Answer:

7.81

Step-by-step explanation:

its a triangular shape

let x = 4 + 2 = 6

let y = 5

length between two points = h

h² = x² + y²

h² = 6² + 5²

h = sqrt of 61

h = 7.81

Answer:

The size square removed from each corner = 32.15 cm²

Step-by-step explanation:

The volume of the box = Length * Breadth * Height

Let r be the size  removed from each corner

Note that at maximum volume, [tex]\frac{dV}{dr} = 0[/tex]

The original length of the cardboard is 119 cm, if you remove a  size of r (This typically will be the height of the box)  from the corner, since there are two corners corresponding to the length of the box, the length of the box will be:

Length, L = 119 - 2r

Similarly for the breadth, B = 24 - 2r

And the height as stated earlier, H = r

Volume, V = L*B*H

V = (119-2r)(24-2r)r

V = r(2856 - 238r - 48r + 4r²)

V = 4r³ - 286r² + 2856r

At maximum volume dV/dr = 0

dV/dr = 12r² - 572r + 2856

12r² - 572r + 2856 = 0

By solving the quadratic equation above for the value of r:

r = 5.67 or 42

r cannot be 42 because the  size removed from the corner of the cardboard cannot be more than the width of the cardboard.

Note that the area of a square is r²

Therefore, the size square removed from each corner = 5.67² = 32.15 cm²

Answer:

0

Step-by-step explanation:

x ^2/2 + y^2/2 = 0

Then x and y can be 0

0^2/2 + 0^2/2

0/2 +0/2 = 0

0 + 0 = 0

0 = 0

Answer:

you would change it 4 times a year

Step-by-step explanation:

if there is 12 months in a year and 3 mounths equal 6000 then divide 12/3=4

Answer:

44

Step-by-step explanation:

The integers 2,8,9 and 25 fit to the terms of the problem.

So the smallest two are 2 and 8 =>2*8=16

and 9*25=225

Note that another pair of integers which product is 16 can be 1 and 16.

However it means that both numbers which product is 225 are bigger  than 16 - this is not possible so 16*16=256>225

So only numbers 2,8,9 and 25 fit to the terms of the problem.

Note that there is no any integer number between 8 and 9 . So there are four integers in total and these integers are 2,8,9 and 25.

The sum of these integers is 2+8+9+25=44

Answer:

A)Option D

B)P(X = 15) = 0.1325

Step-by-step explanation:

A) From the question, the information given follows binomial distribution because there are two mutually exclusive outcomes for each​ trial, there is a fixed number of trials. The outcome of one trial does not affect the outcome of ​another, and the probability of success is the same for each trial.

So option D is correct.

B) From the question, we are told that the poll reported that 66 percent of adults were satisfied with the job. Thus, probability is; p = 0.66

Let X be the number of adults satisfied with the job. Since 25 are selected,

Thus;

P(X = 15) = C(25, 15) * (0.66)^(15) * (1 - 0.66)^(25 - 15)

P(X = 15) = 3268760 × 0.00196407937 × 0.00002064378

P(X = 15) = 0.1325

Answer:

This question is incomplete, i will answer it as:

"The initial population of a town is ​A, and it grows with a doubling time of 10 years. What will the population be in X ​years?"

Ok, the growth of a population usually is an exponential growth, so we can write this as:

P(t) = A*exp(r*t)

Where A is the initial population.

r is the rate of growth, and t is our variable, in this case, number of years.

Now we know that when t = 10y, the population doubles, so we should have:

P(10y) = 2*A = A*exp(r*10y)

2 = exp(r*10)

ln(2) = r*10

ln(2)/10 = r = 0.069.

Then our equation is:

P(t) = A*exp(0.069*t)

Now, if we want to know the population in X years, we need to replace the variable t by X

P(t = X) = A*exp(0.069*X)

Answer:

C. Box plot B

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]p(x \leqslant 0) = p( - 5) + p( - 3) + p( - 2) + p(0)[/tex]

[tex] = 0.17 + 0.13 + 0.33 + 0.16 [/tex]

[tex] = 0.79[/tex]

Hope this helps...

Best regards!!

Answer:

y=3/2x+1   0,1  2,4  4,7

Step-by-step explanation:

-3x+2y=2

+3x

2y=3x+2

/2    /2    /2

y=3/2x+1

Answer:

3/8

Step-by-step explanation:

The bag contains 4 green marbles, 8 yellow marbles and 20 red marbles.

The total number of marbles is 32.

She chooses one from the bag.

The probability of the marble not being red is:

P(not red) = 1 - P(red)

P(not red) = 1 - (20 / 32) = 1 - 5/8

P(not red) = 3/8

The probability of it not being red is 3/8.

The probability that the shirt that is chosen at random from the drawer is not a white shirt, can be found to be  47 %

The probability that the shirt picked is not a white shirt can be found by first finding the number of shirts that are not white shorts in the drawer. This number is :

= Number of black shirts + Gray shirts

= 3 + 4

= 7 shirts

Then, find the total number of shirts in the drawer, including the white shirts :
=  Number of black shirts + Gray shirts  + White shirts

= 3 + 8 + 4

= 15 shirts

The probability that when a shirt is chosen at random, that it is not a white shirt is :

= Number of shirts that are not white / Total number of shirts

= 7 / 15

= 47 %

Find out more on probability at https://brainly.com/question/27831410

#SPJ1

Answer:

[tex]\large \boxed{\sf \ \ v_0=32 \ \ }[/tex]

Step-by-step explanation:

Hello,

The equation is

[tex]y=f(x)=-16x^2+v_0 \cdot x[/tex]

The ball hits the ground 2 seconds after the player kicks it, it means that f(2)=0.

We need to find [tex]v_0[/tex]  such that f(2)=0.

[tex]f(2)=-16\cdot 2^2+v_0 \cdot 2=-64+2v_0=0\\\\\text{*** add 64 to both sides ***}\\\\2v_0=64\\\\\text{*** divide by 2 both sides ***} \\\\v_0=\dfrac{64}{2}=32[/tex]

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

v0 = 32 ft/s

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given f(x, y, z) = x sin(yz), the formula for calculating the gradient of the function is expressed as ∇f(x, y, z) = fx(x, y, z)i+ fy(x, y, z)j+fz(x, y, z)k where;

fx, fy and fz are the differential of the functions with respect to x, y and z respectively.

a) ∇f(x, y, z) = sin(yz)i + xzcos(yz)j + xycos(yz)k

The gradient of f =  sin(yz)i + xzcos(yz)j + xycos(yz)k

b) Directional derivative of f at (1,2,0) in the direction of v = i + 4j − k is expressed as ∇f(1, 2, 0)*v

∇f(1, 2, 0) = sin(2(0))i +1*0cos(2*0)j + 1*2cos(2*0)k

∇f(1, 2, 0) = sin0i +0cos(0)j + 2cos(0)k

∇f(1, 2, 0) = 0i +0j + 2k

Given v = i + 4j − k

∇f(1, 2, 0)*v (note that this is the dot product of the two vectors)

∇f(1, 2, 0)*v =  (0i +0j + 2k)*(i + 4j − k )

Given i.i = j.j = k.k =1 and i.j=j.i=j.k=k.j=i.k = 0

∇f(1, 2, 0)*v = 0(i.i)+4*0(j.j)+2(-1)k.k

∇f(1, 2, 0)*v = 0(1)+0(1)-2(1)

∇f(1, 2, 0)*v =0+0-2

∇f(1, 2, 0)*v= -2

Hence, the directional derivative of f at (1, 2, 0) in the direction of v = i + 4j − k is -2

Answer:

$20.84

Step-by-step explanation:

To solve the above question, we would be using the z score formula

The formula for calculating a z-score :

z = (x - μ)/σ,

where x is the raw score

μ is the population mean

σ is the population standard deviation

x = unknown

μ = $17.90

σ = $1.50

We were not given z score in the above question but this can be determined.

We are told in the question to find the amount that the highest 2.5% of the employees hourly wages is greater than.

Hence, our confidence interval = 100 - 2.5 = 97.5%

The z score for 97.5% = 1.96

Below are inequalities equations with more explanation.

P(X ≥ x) = 2.5% = 0.025

P(X ≤ x) = 1 - 0.025 = 0.975

P (X - μ)/σ ≤ (x - μ)/σ) = 0.975

z ≤ (x - μ)/σ = 0.975

z ≤ 1.96 = 0.975

z = (x - μ)/σ,

1.96 = x - 17.90/1.5

Cross Multiply

1.96 × 1.5 = x - 17.90

x = (1.96 × 1.5) + 17.90

x = 2.94 + 17.90

x = 20.84

Therefore, the amount that the highest 2.5% of the employees hourly wages is greater than is $20.84

Answer:

The p-value is 0.809.

Step-by-step explanation:

In this case we need to perform a significance test for the standard deviation.

The hypothesis is defined as follows:

H₀: σ₀ = 4 vs. Hₐ: σ₀ ≤ 4

The information provided is:

n = 9

s = 3

Compute the Chi-square test statistic as follows:

[tex]\chi^{2}=\frac{(n-1)s^{2}}{\sigma_{0}^{2}}[/tex]

     [tex]=\frac{(9-1)\cdot (3)^{2}}{(4)^{2}}\\\\=\frac{8\times 9}{16}\\\\=4.5[/tex]

The test statistic value is 4.5.

The degrees of freedom is:

df = n - 1

   = 9 - 1

   = 8

Compute the p-value as follows:

[tex]p-value=P(\chi^{2}_{9}>4.5)=0.809[/tex]

*Use a Chi-square table.

Thus, the p-value is 0.809.

Answer:

she has covered 6 miles in 1 ½ hours

Step-by-step explanation:

you need to learn how to read a graph.

it quite easy actually.

just look where the line on the graph is on 1.5 hours ( you can count the boxes if you don't know where 1.5 or 1 ½ is)

Answer:

It does not have an answer as 3x != 3x + 13 or not equalivalent

Step-by-step explanation:

Answer:

no solution

Step-by-step explanation:

3x+8=9+3x-14

Combine like terms

3x+8 = 3x -5

Subtract 3x from each side

8 = -5

This is never true so there is no solution

Answer:

The plus 5 is a vertical translation. It would move g(x) up 5 units at all points. So just take g(x) and move the curve up 5 units.

Answer: 59.342

Step-by-step explanation:

The chi-square critical values are used to find the confidence interval for σ.

Left critical value = [tex]\chi^2_{\alpha/2, n-1}[/tex] [i.e. chi-square value from chi-square table corresponding to degree of freedom n-1 and significance level of [tex]\alpha/2[/tex]]

To find : left critical value for 95% confidence interval for σ with n = 41.

Significance level : [tex]\alpha=1-0.95=0.05[/tex]

degree of freedom = 41-1=40

Now, the  left critical value for 95% confidence interval for σ with n = 41 is the chi-square value corresponding  to degree of freedom n-1 and [tex]\alpha/2=0.025[/tex]

=59.342  [from chi-square table ]

Answer:

Step-by-step explanation:

y = -5x² - 4x + 1 is a quadratic and thus is defined on the domain "all real numbers."  Because of the negative sign in front of the x^2 term, we know that this parabolic curve opens downward.  The x-coordinate of the vertex is x = -b/[2a], which in this case is x = 4/[2*-5], or -4/10, or -2/5.  Using synthetic division to determine the y-coordinate of the vertex, we get vertex (-2/5, 9/5).  9/5 is the maximum y value.  The range is (-infinity, 9/5].

Answer:

The daily rate is $33 and the per mile rate is $0.35

Step-by-step explanation:

4x + 440y = 286

3x + 190y = 165.5

We can solve this systems of equations by multiplying the second statement by [tex]-\frac{4}{3}[/tex] to try and eliminate the x variable.

4x + 440y = 286

-4x - [tex]\frac{760}{3}[/tex]y = -220[tex]\frac{2}{3}[/tex]

[tex]\frac{560}{3}[/tex] y= [tex]\frac{196}{3}[/tex]

560y = 196

y = 0.35

So, the rate per mile is 0.35. Now, with this info, let's find the daily rate by plugging it into the equation.

[tex]4x + 440\cdot0.35 = 286\\4x + 154 = 286\\4x = 132\\x = 33[/tex]

So, the daily rate is $33 and the mile rate is $0.35.

Hope this helped!

Answer:

the daily fee =33 dollars

and the mileage charge.=0.35

let d: be daily fee and m for mileage

cost of rental =(d*number of days)+ (m*number of mileage)

her first trip: 4d+440m=286

her second trip: 3d+190m=165.5

solve by addition and elimination

4d+440m=286 ⇒ multiply by 3 ⇒12d +1320m=(3)286

3d+190m=165.5⇒ multiply by 4⇒12d+190(4)m=4(165.5)

12d+1320m=858

12d+760m=662

subtract two equation to eliminate d

12d+1320m-12d-760m=858-662

560m=196

m=7/20=0.35 for on mileage

d: 4d+440m=286

4d=286-440(0.35)

d=(286-154)/4 33 dollars