The larger bag of ferret food is on sale at the SuperPetMart
for $89. Ferroza made the following table. Explain to
Ferroza why the cost of food at SuperPetMart is not a
proportional relationship.
Ferret Food
Weight
(pounds)
0
5
30
Cost
($)
$0
17.50
89

Answer:

q + q + 4

Step-by-step explanation:

q + q +4

Step-by-step explanation:

Sn= a+[n-1]d

S2= a+[2-1]d

8.5 = a+d _______Equation 1

S5 = a+[5-1]d

13=a+4d ________Equation 2

Subtract Equation 1 from Equation 2

13=a+4d

-

8.5= a+d

________

4.5= 3d

d=1.5

Substituting d=1.5 in equation 1

8.5=a+1.5

a=8.5-1.5

a=7

Sum of terms of an A.P =

Sn= n/2[2a+(n-1)d]

292= n/2[2×7+(n-1)d]

292=n/2[14+(n-1)1.5

292×2=n[14+(n-1)1.5]

584=n[14+1.5n-1.5]

584= 14n+1.5n²-1.5n

584= 1.5n²+12.5n

1.5n²+12.5n-584

1.5n²-24n+36.5n-584

1.5n(n-16)+36.5(n-16)

(1.5n+36.5)(n-16)

**n-16=0

n=16

Answer:

x=65

y=20

Step-by-step explanation:

The equation of line d is perpendicular to line c is y=-4/3 x+5.

The equation of line is y=3/4 x-2.

The increase divided by the run, or the ratio of the rise to the run, is known as the line's slope. In the coordinate plane, it describes the slope of the line.

In the equation of line is y=3/4 x-2, slope=m=3/4

The slope of a line perpendicular to given line is m1=-1/m2

So, the slope of a perpendicular line is -4/3

Substitute m=-4/3 and (x, y)=(6, -3) in y=mx+c, we get

-3=-4/3 (6)+c

⇒ -3=-8+c

⇒ c=5

Now, substitute m=-4/3 and c=5 in y=mx+c, we get

y=-4/3 x+5

Therefore, the equation of line d is perpendicular to line c is y=-4/3 x+5.

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The coordinates of point A(12, -4) after a dilation with a scale factor of 1/4 are A'(3, -1).

To find the coordinates of point A(12, -4) after a dilation with a scale factor of 1/4, we need to multiply the x-coordinate and the y-coordinate of point A by the scale factor.

The formula for dilation is:

(x', y') = (k * x, k * y)

Using the given scale factor, we have:

k = 1/4

Calculating the coordinates after dilation:

x' = (1/4) * 12 = 3

y' = (1/4) * (-4) = -1

Therefore, after a dilation with a scale factor of 1/4, the coordinates of point A(12, -4) become A'(3, -1).

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It will take 1.5 minutes to boil half liter of water .

Given,

Electric kettle take 3 minutes to boil a liter of water.

Now,

1 liter of water boils in 3 minutes .

so,

1 liter ⇒ boils in 3 minutes

1/2 liter ⇒ boils in 3/2 minutes

Thus,

1/2 liter boils in 1.5 minutes in an electric kettle .

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Examining the figure properly shows that chord AB in the circle has its length to be equal to 16

Information given from the question is interpreted as

let the center of the circle be O

BE = opposite = ?

OE = adjacent = 6

OB = OA = hypotenuse = radius = 10

Using Pythagoras theorem given by the  the formula

hypotenuse² = opposite² + adjacent²

plugging the values as in the problem

10² = BE² + 6²

100 = BE² + 36

BE² =  100 - 36

BE = √64

BE = 8

Since line OE is the perpendicular bisector, BE = AE

and from the figure AB = BE + AE

= 8 + 8

= 16

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The summation notation for the series 500+490+480+ . . . . . . . +20+10 is

\(25500-10\sum\limits^{50}_{n=1} {n}\)

A summation notation is used to express a long summation into a single notation.

The given series is:

    500+490+480+ . . . . . . . +20+10

This is an arithmetic series with:

a(1) = 500, and

d = 490 - 500 = -10

The last term is a(n) = 10. Find n first by using the nth term formula of an arithmetic sequence:

a(n) = a(1) + (n-1) . d

10 = 500 + (n-1) . (-10)

10 = 500 -10n + 10

10 n = 500

n = 50

Write the explicit formula for the nth term:

a(n) = a(1) + (n-1) . d

a(n) = 500 + (n-1) . (-10)

a(n) = 500 -10n + 10

a(n) = 510 - 10n

The series is the summation notation from n=1 to n = 50

\(=\sum\limits^{50}_{n=1} {a(n)}\)

\(=\sum\limits^{50}_{n=1} {(510-10n)}\)

\(=\sum\limits^{50}_{n=1} {510} -\sum\limits^{50}_{n=1} {10n}\)

\(=510\times50-10\sum\limits^{50}_{n=1} {n}\)

\(=25500-10\sum\limits^{50}_{n=1} {n}\)

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a. The probability that exactly ten arrive during the hour and all ten have no violations is given by the Poisson distribution, P(X=10) = (e-α*(α10)/(10!) = 0.024

b. The probability that y arrive during the hour, of which ten have no violations is given by the Binomial distribution, P(Y=y) = (y!/(10!*(y-10)!))*(0.510)*(0.5y-10)

c. The probability that ten "no-violation" cars arrive during the next hour is given by summing the probabilities in part (b) from y=10 to [infinity]. This is given by P(Y≥10) = Σy=10 to ∞P(Y=y) = 1 - Σy=0 to 9P(Y=y).

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Brad's logic is flawed and does not hold any scientific basis. The gender of a child is determined by the combination of genetic factors from both parents

. Each pregnancy is an independent event, and the probability of having a boy or a girl is not influenced by the gender of the previous children. The belief that having a certain number of children of one gender increases the likelihood of having a child of the opposite gender is known as the "gamblers fallacy" or "Monte Carlo fallacy." In reality, the probability of having a boy or a girl remains approximately 50% for each pregnancy, regardless of the gender composition of the existing children.

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Answer:

see below

Step-by-step explanation:

4.2 x 10^6 − 1.2 x 10^5 − 2.5 x 10^5

All exponent have to have the same number

42 x 10^5 − 1.2 x 10^5 − 2.5 x 10^5

Subtract the number

42 - 1.2 - 2.5 = 38.3

Add back the exponent

38.3 * 10 ^5

This is not in scientific notation

Move the decimal one place to the left and add one to the exponent

3.83 * 10^6

3.3 x 10^9 + 2.6 x 10^9 + 7.7 x 10^8

All exponent have to have the same number

3.3 x 10^9 + 2.6 x 10^9 + .77 x 10^9

Add the numbers

3.3+2.6+.77 =6.67

Add back the exponent

6.67*10^9

This is in scientific notation

8.0 x 10^4 − 3.4 x 10^4 − 1.2 x 10^3

All exponent have to have the same number

8.0 x 10^4 − 3.4 x 10^4 − .12 x 10^4

Subtract

8.0 - 3.4 - .12 = 4.48

Add back the exponent

4.48* 10^4

This is in scientific notation

Given the expression: 40 + 20/4

So to solve this expression, we will first divide because of PEMDAS. 20/4 equals 5. So that leaves us with 40 + 5, which is 45.

Hope this helped!

The jewelry store sells a total of 50 different ring options.

To determine the total number of ring options, we need to multiply the number of options for each category together.

First, we have two categories: metal (gold and platinum) and gemstone (five options).

For the metal category, we have two choices: gold or platinum.

For the gemstone category, we have five choices: let's say they are diamond, ruby, emerald, sapphire, and amethyst.

To calculate the total number of ring options, we multiply the number of choices in each category:

Number of metal choices = 2 (gold or platinum)

Number of gemstone choices = 5 (diamond, ruby, emerald, sapphire, amethyst)

Total number of ring options = Number of metal choices × Number of gemstone choices

= 2 × 5

= 10

Therefore, the jewelry store sells a total of 10 different ring options.

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The number of student tickets sold is 310, and the number of adult tickets sold is 202.

To find the number of student and adult tickets sold, we can set up a system of equations based on the given information.

Let's assume that the number of student tickets sold is 'c.' Since each student ticket costs $5, the total amount collected from the student tickets is 5c dollars.

The number of adult tickets sold can be represented as (512 - c) because the total number of tickets sold is 512, and c represents the number of student tickets sold. Each adult ticket costs $10, so the total amount collected from adult tickets is 10(512 - c) dollars.

According to the given information, the total amount collected from both types of tickets is $3,570. Therefore, we can set up the following equation:

5c + 10(512 - c) = 3,570

Simplifying the equation:

5c + 5120 - 10c = 3,570

-5c = 3,570 - 5120

-5c = -1,550

Dividing both sides of the equation by -5:

c = 310

Hence, the number of student tickets sold is 310, and the number of adult tickets sold is (512 - 310) = 202.

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Complete question:

For a school drama performance, student tickets cost $5 each and adult tickets cost $10 each. The sellers collected $3,570 from 512 tickets sold. If c is the number of student tickets sold, which equation can be used to find the number of tickets sold of each type?

Answer:

She is incorrect

Step-by-step explanation:

If you square 4 you get 16 and divide 16 and 2 you get 8 so shes wrong.

Answer: Clara is incorrect

Step-by-step explanation:

The square root of 4 is 2

2 ÷ 2 = 1

You end up with 1 not 4, therefore, Clara is wrong.

Edit: Look at the other answer, I sadly made a mistake thinking the question said square root but it said square I apologize .

In this equation, it will require 175 + 7x - 550 - 8x water to fill both tanks to the same level.

A formula that describes how two expressions on each side of a sign are connected. It typically has an equal sign and one variable. akin to this 2. 2x - 4 = 2. The variable x is present in the preceding example.

Algebraically speaking, an equation is a statement that shows the equality of two mathematical expressions. For instance, the expressions 3x + 5 and 14 make up the equation 3x + 5 = 14, with the word "equal" separating them.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

You start first  by the number of minutes that have passed.

Regardless of how many minutes have passed, the second had loses.

=175 + 7 liters

=550 liters loses 8 times

= 175 + 7x - 550 - 8x

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Answer:

Option B is your answer

Step-by-step explanation:

..

Answer:

y = - 27/5

Step-by-step explanation:

4(3) - 5y = 39

12 - 5y = 39

-5y = 39 - 12 = 27

y = - 27/5

Using the central limit theorem, for different sample sizes, we find the probabilities Pr(Y < 68) ≈ 0.9439, Pr(68 < Y < 69) ≈ 0.0590, and Pr(Y > 66) ≈ 0.0228.

a) In a random sample of size n = 69, we can approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 69 ≈ 0.7101. To find Pr(Y < 68), we calculate the z-score using the formula z = (x - μ) / σ, where x is the value we want to find the probability for.

z = (68 - 65) / √(0.7101) ≈ 1.5953

Using a standard normal distribution table or a calculator, we find the probability associated with z = 1.5953 to be approximately 0.9439. Therefore, Pr(Y < 68) ≈ 0.9439.

b) In a random sample of size n = 124, we can again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 124 ≈ 0.3952. To find Pr(68 < Y < 69), we calculate the z-scores for the lower and upper limits.

Lower z-score: z1 = (68 - 65) / √(0.3952) ≈ 1.5225

Upper z-score: z2 = (69 - 65) / √(0.3952) ≈ 2.5346

Using the standard normal distribution table or a calculator, we find the probability associated with z1 = 1.5225 to be approximately 0.9357 and the probability associated with z2 = 2.5346 to be approximately 0.9947. Therefore, Pr(68 < Y < 69) ≈ 0.9947 - 0.9357 ≈ 0.0590.

c) In a random sample of size n = 196, we can once again approximate the distribution of the sample mean using a normal distribution. The mean of the sample mean will still be equal to the population mean μY = 65, and the variance of the sample mean will be σY^2 / n = 49 / 196 ≈ 0.2500. To find Pr(Y > 66), we calculate the z-score.

z = (66 - 65) / √(0.2500) = 2

Using the standard normal distribution table or a calculator, we find the probability associated with z = 2 to be approximately 0.9772. Therefore, Pr(Y > 66) ≈ 1 - 0.9772 ≈ 0.0228.

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28 would be your answer

hope it helped you

Answer:

28

Step-by-step explanation:

+10

3r=84

/////////

3     3

r = 28

By using the concept of confidence interval, it is obtained that

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

What is Confidence interval?

Let the quantity which is to be estimated is \(\theta\).  A confidence interval for the parameter θ, with confidence level \(\alpha\) is the interval (a, b), where

P(a < \(\theta\) < b) = \(\alpha\), P is the probability

Here the  average commute time in minutes (\(\mu\)) is to be calculated

95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25)

This means that it is 95% confident that the interval (15.75, 28.25) contains the population mean commute time in minutes using public transit

So the correct interpretation is

We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

Second option is correct

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Complete Question

A researcher finds a 95% confidence interval for the average commute time in minutes using public transit is (15.75, 28.25). What is the correct interpretation of this interval?

A) There is a 95% chance commute time in minutes using public transit is between 15.75 and 28.25 minutes.

B) We are 95% confident that the interval 15.75 < μ < 28.25 contains the population mean commute time in minutes using public transportation.

C) We are 95% confident that all commute time in minutes for the population using public transit is between 15.75 and 28.25 minutes.

D) We are 95% confident that the interval 15.75 < μ < 28.25 contains the sample mean commute time in minutes using public transportation.

Answer:

To find the probability of a randomly selected point falling into the red-shaded triangle within the circle, compare the area of the triangle to the total area of the circle.

Step-by-step explanation:

Answer:

-4, 2

Step-by-step explanation:

x² + 2x - 8 = 0

[(x + 1)² - 1] - 8 = 0

(x + 1)² - 9 = 0

(x + 1)² = 9

x + 1 = ±√9 = ±3

x = -3 - 1, +3 - 1

= -4, 2.

Answer:

c

Step-by-step explanation:

Answer:

According to the question

52 + 48 < 60

8 x <2

80 can be use within 2 gigabytes

Step-by-step explanation

♣ Question:

Under his cell phone plan, Santiago pays a flat cost of $52 per month and $4 per gigabyte. He wants to keep his bill under $60 per month

To Find: An inequality which can be used to determine a, the number of gigabytes Santiago can use while staying within his budget.

Based on the given conditions,

formulate:

52 + 4 x (x = 60)

52 + 4x = 60

4x = 60 - 52

4x = 8

x = 8/4

x = 2

•♣••♠••♣••♠••♣••♠••♣••♠••♣•

The probability of 2 customers in the system is 0.1418.

In order to find the probability of 2 customers in the system, the M/M/1 queuing model is to be applied.

M/M/1 model is a single-server queue model that assumes a Poisson arrival pattern and an exponential service pattern.

The service time is exponential and has a mean of 5 minutes.

Let's start calculating the values for the M/M/1 model:

For arrival rate, λ = 7 customers per hour

For service rate, μ = 12 customers per hour

The utilization factor can be determined using the following formula:ρ = λ/μ = 7/12

                                                                                                                               = 0.5833

The probability of 2 customers in the system can be found using the following formula:

P2 = (1 - ρ)(ρ)2= (1 - 0.5833)(0.5833)2

     = 0.1418

Therefore, the probability of 2 customers in the system is option B, i.e., 0.1418.

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The statement is not always true.

The statement is only sometimes true.

We have,

Part A:

The statement "the product of two negative rational numbers is greater than either factor" is never true.

Let a = -1/2 and b = -1/3.

Then ab = (-1/2)(-1/3) = 1/6, which is less than both a and b.

Let c = -1/4 and d = -2/3.

Then cd = (-1/4)(-2/3) = 1/6, which is also less than both c and d.

Both of these examples demonstrate that the product of two negative rational numbers can be less than either factor and therefore the statement is not always true.

Part B:

The statement "the product of two positive rational numbers is greater than either factor" is sometimes true, but not always. To see why, consider the following examples:

Let e = 1/2 and f = 1/3.

Then ef = (1/2)(1/3) = 1/6, which is less than both e and f.

Let g = 2/3 and h = 3/4.

Then gh = (2/3)(3/4) = 1/2, which is greater than both g and h.

These examples demonstrate that the product of two positive rational numbers can be less than either factor (in the first example) or greater than both factors (in the second example).

Therefore, the statement is only sometimes true.

Thus,

The statement is not always true.

The statement is only sometimes true.

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Answer:

v=20π ft/s

Step-by-step explanation:

Given:

Distance from the security car to the movie theater, D=25 ft

Distance of the reflection from the car, d=30 ft

Speed of rotation of the strobe lights, 2 rev/s

To find the speed at which the reflection of the security strobe lights is moving along the wall of the movie theater, we need to calculate the linear velocity of the reflection when it is 30 ft from the car.

We can start by finding the angular velocity in radians per second. Since the strobe lights rotate at 2 revolutions per second, we can convert this to radians per second.

ω=2πf

=> ω=2π(2)

=> ω=4π rad/s

The distance between the security car and the reflection on the wall of the theater is...

r=30-25= 5 ft

The speed of reflection is given as (this is the linear velocity)...

v=ωr

Plug our know values into the equation.

v=ωr

=> v=(4π)(5)

∴ v=20π ft/s

Thus, the problem is solved.

The speed of the reflection of the security strobe lights along the wall of the movie theater is 2π ft/s.

To solve this problem, we can use the concept of related rates. Let's consider the following variables:

x: Distance between the security car and the movie theater wall

y: Distance between the reflection of the security strobe lights and the security car

θ: Angle between the line connecting the security car and the movie theater wall and the line connecting the security car and the reflection of the strobe lights

We are given:

x = 25 ft (constant)

y = 30 ft (changing)

θ = 2 revolutions per second (constant)

We need to find the speed at which the reflection of the security strobe lights is moving along the wall (dy/dt) when the reflection is 30 ft from the car.

Since we have a right triangle formed by the security car, the movie theater wall, and the reflection of the strobe lights, we can use the Pythagorean theorem:

x^2 + y^2 = z^2

Differentiating both sides of the equation with respect to time (t), we get:

2x(dx/dt) + 2y(dy/dt) = 2z(dz/dt)

Since x is constant, dx/dt = 0. Also, dz/dt is the rate at which the angle θ is changing, which is given as 2 revolutions per second.

Plugging in the known values, we have:

2(25)(0) + 2(30)(dy/dt) = 2(30)(2π)

Simplifying the equation, we find:

60(dy/dt) = 120π

Dividing both sides by 60, we get:

dy/dt = 2π ft/s

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Answer:

Rational. 7.9 can be written as a fraction