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Bob Nale is the owner of Nale's Quick Fill. Bob would like to
estimate the mean number of gallons of gasoline sold to his

The formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).

Given n balls, m of which are red and n - m are blue, if a collection of n < min{m, n - m} balls is taken out at random without replacement, the probability that exactly k balls are red can be calculated using the Hypergeometric Distribution. The formula for the probability that exactly k balls are red is given by: P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n)

where C(n, k) denotes the number of combinations of n things taken k at a time, and is given by: C(n, k) = n! / (k! * (n - k)!).

Therefore, the formula for the probability that exactly k balls are red when a collection of n < min{m, n - m} balls is taken out at random without replacement is given by:

P(k red balls) = (C(m, k) * C(n - m, n - k)) / C(n, n) = (m! / (k! * (m - k)!) * (n - m)! / ((n - k)! * (n - m - n + k)!)) / (n! / (n! * 0!)) = (m! * (n - m)!) / (k! * (m - k)! * (n - k)! * n!).

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Step-by-step explanation:

initial value is when t = 0 = 19900

growth (since it does not depreciate)

percentage: (1.21 x 19900 / 19900) - 100 = 21%

Topic: Logarithms, Percentage

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

The standard form of a quadratic equation is:

in this equation the vertex is (h,k). Moreover, if a>0 the parabola opens upward and vertex is a reletive minimum; if a<0 the parabola opens downward and the vertex is a maximum.

In this case the vertex is (-2,-1) and since a=1/3 then this is a minimum of the parabola.

The feature NOT associated with the function h(x) is that the domain of h(x) is [0.).

The function h(x) is defined as (x - 5)² - log₁ x + 6.

Let's analyze each given option to determine which one is NOT a key feature of h(x).

Option 1 states that the domain of h(x) is [0, ∞).

However, the function h(x) contains a logarithm term, which is only defined for positive values of x.

Therefore, the domain of h(x) is actually (0, ∞).

This option is not a key feature of h(x).

Option 2 states that the x-intercept of h(x) is (5, 0).

To find the x-intercept, we set h(x) = 0 and solve for x. In this case, we have (x - 5)² - log₁ x + 6 = 0.

However, since the logarithm term is always positive, it can never equal zero.

Therefore, the function h(x) does not have an x-intercept at (5, 0).

This option is a key feature of h(x).

Option 3 states that the y-intercept of h(x) is (0, 25).

To find the y-intercept, we set x = 0 and evaluate h(x). Plugging in x = 0, we get (0 - 5)² - log₁ 0 + 6.

However, the logarithm of 0 is undefined, so the y-intercept of h(x) is not (0, 25).

This option is not a key feature of h(x).

Option 4 states that the end behavior of h(x) is as x approaches infinity, h(x) approaches infinity.

This is true because as x becomes larger, the square term (x - 5)² dominates, causing h(x) to approach positive infinity.

This option is a key feature of h(x).

In conclusion, the key feature of h(x) that is NOT mentioned in the given options is that the domain of h(x) is (0, ∞).

Therefore, the correct answer is:

O The domain of h(x) is (0, ∞).

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Answer: ≈40.2

Step-by-step explanation:

(2x-1)*(x+1)=90

Distribute

2x^2-1=90

Add 1 to both sides.

2x^2=91

Divide both sides by 2

x^2=45.5

Square both sides.

x≈6.7

Check work by plugging x into both original sides and multiplying them.

(2(6.7)-1)*((6.7)+1)=90

12.4*7.7=95.48

Side lengths are approximately 12.4 and 7.7.

12.4*2=24.8

7.7*2=15.4

24.8+15.4=40.2

Answer:

sorry for being late but it was hard, x=6.5

then perimeter is 39

Step-by-step explanation:

12+12+7.5+7.5=39

(a) To determine how fast the population is growing when it reaches 5 million people, we can substitute P(t) = 5 into the differential equation P'(t) = 0.06P(t). This gives us P'(t) = 0.06(5) = 0.3 million people per year. Therefore, the population is growing at a rate of 0.3 million people per year when it reaches 5 million people.

(b) To determine the population size when it is growing at a rate of 700,000 people per year, we can set P'(t) = 700,000 and solve for P(t). From the given differential equation, we have 0.06P(t) = 700,000, which implies P(t) = 700,000/0.06 = 11,666,666.67 million people. Therefore, the population size is approximately 11.67 million people when it is growing at a rate of 700,000 people per year.

(c) To find a formula for P(t), we can solve the differential equation P'(t) = 0.06P(t). This is a separable differential equation, and integrating both sides gives us ln(P(t)) = 0.06t + C, where C is the constant of integration. By exponentiating both sides, we get P(t) = e^(0.06t+C). Using the initial condition P(0) = 3, we can find the value of C. Substituting t = 0 and P(0) = 3 into the equation, we have 3 = e^C. Therefore, the formula for P(t) is P(t) = 3e^(0.06t).

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Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

The amount Janelle will earn with the compound interest option can be calculated using the formula for compound interest:

\(A = P(1 + r/n)^{(nt)}\)

Where:
A is the total amount after interest has been compounded
P is the principal amount (the initial deposit)
r is the annual interest rate (expressed as a decimal)
n is the number of times interest is compounded per year
t is the number of years

In this case, Janelle deposits 3,000 at an interest rate of 3% for 7 years. We'll compare the simple interest and compound interest options.

For the simple interest option, the interest is calculated using the formula:

I = P * r * t

Where:

I is the total interest earned

Using the given values, we can calculate the interest earned with simple interest:

I = 3000 * 0.03 * 7
I = 630

Now, let's calculate the total amount earned with the compound interest option.

Since the interest is compounded monthly, the interest rate needs to be divided by 12 and the number of years needs to be multiplied by 12:

r = 0.03/12

t = 7 * 12

Using these values, we can calculate the total amount with compound interest:

\(A = 3000 * (1 + 0.03/12)^{(7*12)}\)

A ≈ 3,729.19

To find out how much more Janelle will earn with the compound interest option, we subtract the initial deposit from the total amount with compound interest:

Difference = A - P
Difference = 3,729.19 - 3,000
Difference ≈ 729.19

Therefore, Janelle will earn approximately 729.19 more with the compound interest option compared to the simple interest option over a period of 7 years.

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The volume of the Cylinder is 24.11 cubic feet.

Volume refers to the amount of space occupied by a three-dimensional object, measured in cubic units.

The radius of the cylinder is half the diameter of the circular base, so:

r = 2.6/2 = 1.3 feet

The volume of the cylinder is given by:

V = πr²h

Substituting the values given:

V = 3.14 × 1.3² × 4.4 ≈ 24.11 cubic feet

Rounding to the nearest hundredth:

V ≈ 24.11 cubic feet

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Answer:B

Step-by-step explanation:The negative sign represents fraction that is (one over)

Answer:

28.3

Step-by-step explanation:

formula for area of of a circle is

A = πr²

3² = 9

3.14 * 9 = 28.26

rounded to tenth power = 28.3

Hope this helps dude

If your target number of calories to lose weight is 1,703 per day, but you are consuming 2,399 calories per day, then your target is to consume approximately 70% of the calories you are currently consuming.

To find the percentage of the target calories in relation to the current calories, we can divide the target calories by the current calories and multiply by 100. So, the calculation would be:

Percentage = (Target Calories / Current Calories) * 100

Substituting the values, we get:

Percentage = (1,703 / 2,399) * 100 ≈ 70%

Therefore, your target is to consume approximately 70% of the calories you are currently consuming in order to meet your weight loss goal.

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Answer:

p=28.2

Step-by-step explanation:

l=9.8

w=4.3

it was close tho

Answer :    28.4 cm

                                                   Lower     Upper

Length is given as 9.8    -->         9.75 ≤ L < 9.85

width is given as 4.3      -->           4.25 ≤ w < 4.35

Perimeter = 2L + 2w     (Upper bound)

               = 2(9.85) + 2(4.35)

               =   19.7      +   8.7

               =   28.4

The solution of the given equation is: \(y(t) = $\frac{7}{200}(sin(2t)-6cos(2t)+3te^{-21t})$\)

Given equation is: y'' - 18y' + 60y' + 200

y = 0, y(0) = 0, y'(0) = 0, y''(0) = 7

The solution of the equation can be found using the characteristic equation:

\(V\) is given as \($m^2 + 42m + 100 = 0$\)

Using the quadratic formula: \($m=\frac{-42\pm \sqrt{(-42)^2-4(1)(100)}}{2(1)}$\)

Solving, \($m=-21\pm 2i$\)

So the general solution is \($y = c_1e^{(-21+i2)t}+c_2e^{(-21-i2)t}$\)

Substituting y(0) = 0 we get:

\($y(0) = c_1 + c_2 = 0$\)

Thus, \($c_2 = -c_1$\)

Substituting y'(0) = 0:

\($y'(t) = (-21 + i2)c_1e^{(-21+i2)t}+(-21-i2)c_2e^{(-21-i2)t}$\)

When \($t = 0$\), $y'(0) = (-21 + i2)c_1 + (-21-i2)c_2 = 0$

Thus, \($c_2 = -c_1$\)

Substituting y''(0) = 7:\($y''(t) = (-21 + i2)^2c_1e^{(-21+i2)t}+(-21-i2)^2c_2e^{(-21-i2)t}$\)

When \($t = 0$\), \($y''(0) = (-21 + i2)^2c_1 + (-21-i2)^2c_2 = 7$\)

Thus, \($c_1 = \frac{7}{2i^2(21-i2)}$\) and \($c_2 = \frac{7}{2i^2(21+i2)}$\)

Now we have the values of $c_1$ and $c_2$, substitute in the above equation.

So, the solution of the given equation is: \(y(t) = $\frac{7}{200}(sin(2t)-6cos(2t)+3te^{-21t})$\)

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Answer:

11\(\pi\)

Step-by-step explanation:

To find the circumference of a circle, the formula is:

d * \(\pi\) = c

We already know the diameter, so we just plug that in:

11 * \(\pi\) = c

11\(\pi\) = c

Let me know if you have any questions.

Answer:

First time sending a shipment to Amazon Warehouse here.

I have a question in regards to filling information for my inventory.

I have a total of 20 BOXES ready to be sent. Each individual -BOX- contains 8 smaLL boxes inside. Each smaLL box contains 6 units.

Also, I should specify I’m sending 4 colors, same item. 4 -BOX- red, 4 -BOX- blue, 6 -BOX- steel, 6 -BOX- black. ( 20 BOXES total)

Would you fill it this way:

Review Shipment Contents:

Units Per Case — Number of Cases — Shipped

RED 48 — 4 — 192

BLUE 48 — 4 — 192

STEEL 48 — 6 — 288

BLACK 48 — 6 — 288

                                               ---TOTAL UNITS = 960  

Shipping Service

SHIPMENT PACKING

ONE SKU PER BOX

SELECT PACK LIST FORMAT

File format Total # of boxes

20 ???

I’m counting Units Per Case as the total number of units in a BOX. And Number of Cases as the number of BOXES. Is this Right?

My confusion is differentiating BOXES and CASES.

I was also thinking about counting Each smaLL box as a Case (Units per Case =6 units) and Number of Cases would be “32”; 4 BOXES of one color , 32 CASES total.

I might be over complicating myself but really need your help on this one so I send the right information to Amazon.

The formula to find the tangent line to a curve at a given point is y = f'(x) (x - x₀) + f(x₀).

The derivative of the function, f'(x) is calculated at the given point, x₀. Then, the equation of the tangent line is found by substituting the x₀ and f'(x) values into the formula.

To find the tangent line to a curve at a given point, the formula for the slope of the tangent line must be used. The slope of a tangent line is equal to the derivative of the function at that point. The resulting equation is a line with a slope equal to the derivative of the function at the given point, and a y-intercept equal to the value of the function at the given point. For example, if you want to find the tangent line to the function f(x) = 4x² + 3 at the point (2, 19), the derivative of the function at that point is f'(x) = 8x = 8(2) = 16. Then, the equation of the tangent line is y = 16(x - 2) + 19.

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The distribution does not represent a probability distribution. The correct option is b.

A probability distribution should satisfy two main conditions: (1) the sum of the probabilities for all possible outcomes should be equal to 1, and (2) the probabilities for each outcome should be between 0 and 1 (inclusive).

In this distribution, the probabilities for the outcomes are 0.3, 0.4, 0.3, and 0.1 for the values of X as 3, 6, 9, and 0, respectively. However, the sum of these probabilities is 1.1, which violates the first condition of a probability distribution.

Therefore, this distribution does not meet the requirements of a probability distribution and is not a valid probability distribution. The correct answer is option b.

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a) On plotting we get a bell-shaped curve with its maximum at x = 2.5.

b) c is equal to 2.641(approximately). The probability that the actual tracking weight is greater than the prescribed weight is  approximately 0.1

c) The probability that the actual tracking weight is within 0.1 grams of the prescribed weight is approx. 0.063.

d) The probability that the actual weight differs from the prescribed weight by more than 0.2 grams is approx.  0.019.

a) On closely obsorving the possible graph, the graph of f(x) is a bell-shaped curve with its maximum at x = 2.5 and symmetric about this point.

b) To find the value of c, we need to integrate f(x) from 2.5 to infinity and set it equal to 1, since the area under the curve represents the total probability.

∫[2.5, ∞] 0.1(1 - (x - 2.5)^2) dx = 1

After integrating, we get:

0.1[x - (x - 2.5)^3/3] [2.5, ∞] = 1

Simplifying and solving for c, we get:

c = 2.5 + [(3/2) - (10/3π)] ≈ 2.641

Therefore, the probability that the actual tracking weight is greater than 2.5 grams is:

P(x > 2.5) = ∫[2.5, ∞] 0.1(1 - (x - 2.5)^2) dx

= 0.1[2.5 - (2.5 - 2.5)^3/3] = 0.1

c) The probability that the actual tracking weight is within 0.1 grams of the prescribed weight is:

P(2.4 ≤ x ≤ 2.6) = ∫[2.4, 2.6] 0.1(1 - (x - 2.5)^2) dx

= 0.1[2(0.1) + (2/3)π(0.1)^3] ≈ 0.063

d) The probability that the actual weight differs from the prescribed weight by more than 0.2 grams is:

P(|x - 2.5| > 0.2) = P(x < 2.3 or x > 2.7)

= ∫[0, 2.3] 0.1(1 - (x - 2.5)^2) dx + ∫[2.7, ∞] 0.1(1 - (x - 2.5)^2) dx

= 0.1[(2.3 - 2.5) + (3/2 - (5/3)π - (2.7 - 2.5))] ≈ 0.019

Therefore, the probability that the actual weight differs from the prescribed weight by more than 0.2 grams is approximately 0.019.

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The complete and correct question is :

Suppose the tracking weight of a stereo cartridge set to track at 2.5 grams on a particular turntable can be modeled by the continuous function f(x) = 0.1(1 - (x - 2.5)^2), where x represents the actual tracking weight in grams.

a) Sketch the graph of f(x).

b) Find the value of c. What is the probability that the actual tracking weight is greater than 2.5 grams?

c) What is the probability that the actual tracking weight is within 0.1 grams of the prescribed weight?

d) What is the probability that the actual weight differs from the prescribed weight by more than 0.2 grams?

Answer:

x < 4

Step-by-step explanation:

The dotted line  is x = 4

The shaded area is below x = 4.

So, x <4

Answer:

Step-by-step explanation:

Hello. i would love to help but do you have a graph so i can see

Answer:

yessir $22.10 for 2.6 pounds. Come by the market sometime eh?

The Values of (a+b)ab are undefined.

Given that, a = 3an and db = -2We need to find the values of (a+b)

Now, we have a = 3an... equation (1)Also, we have db = -2... equation (2)From equation (1), we get: n = 1/3... equation (3)Putting equation (3) in equation (1), we get: a = a/3a = 3... equation (4)Now, putting equation (4) in equation (1), we get: a = 3an... 3 = 3(1/3)n = 1

From equation (2), we have: db = -2=> d = -2/b... equation (5)Multiplying equation (1) and equation (2), we get: a*db = 3an * -2=> ab = -6n... equation (6)Putting values of n and a in equation (6), we get: ab = -6*1=> ab = -6... equation (7)Now, we need to find the value of (a+b).For this, we add equations (1) and (5),

we get a + d = 3an - 2/b=> a + (-2/b) = 3a(1) - 2/b=> a - 3a + 2/b = -2/b=> -2a + 2/b = -2/b=> -2a = 0=> a = 0From equation (1), we have a = 3an=> 0 = 3(1/3)n=> n = 0

Therefore, from equation (5), we have:d = -2/b=> 0 = -2/b=> b = ∞Now, we know that (a+b)ab = (0+∞)(0*∞) = undefined

Therefore, the values of (a+b)ab are undefined.

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Answer:

\(Area= 8\)

Step-by-step explanation:

Given

\(I = (-9,-8)\)

\(J = (-5,-6)\)

\(K = (-7,-3)\)

The complete part of the question is to calculate the area of IJK

The area is calculated using:

\(Area = \frac{1}{2}|x_1y_2 - x_2y_1 + x_2y_3 - x_3y_2 + x_3y_1 - x_1y_3 |\)

Where:

\(I = (-9,-8)\) --- \((x_1,y_1)\)

\(J = (-5,-6)\) --- \((x_2,y_2)\)

\(K = (-7,-3)\) --- \((x_3,y_3)\)

So, we have:

\(Area = \frac{1}{2}|(-9*-6) - (-5*-8) + (-5*-3) - (-7*-6) + (-7*-8) - (-9*-3) |\)

Solve the brackets

\(Area = \frac{1}{2}|54 - 40 + 15- 42 + 56 - 27 |\)

\(Area = \frac{1}{2}|16|\)

The absolute value of 16 is 16

So:

\(Area = \frac{1}{2} * 16\)

\(Area= 8\)

Answer:

1. A

2. C

3. A

4. B

Step-by-step explanation:

To solve 1-3 you just take the percent and divide it by 100. Ex: 57%/100 = 0.57. Then you take that number and multiply it by the cost of it. Ex: 0.57 * 899 = 512.43. 512.43 is 57% of 899. I hope this helps :)

Answer: x>55/9

Step-by-step explanation: Divide both sides by  9  

     x-(55/9)  > 0

Add  55/9  to both sides

            x > 55/9

Inequality plot for

        9.000 x  - 55.000  >  0

Answer: x=\(p^{9}\)

nah nah nvm give charpriv brainliest

Answer:

answer is D

The difference of the two means is not significant, so the null hypothesis must be accepted.

A) The annual growth rate between 1993 and 2004, is approximately 5.68%.  B) Converting the growth rate from part A to percentage form, is approximately 5.68%.  C) Assuming the house value continues to grow at the same annual growth rate, the estimated value in the year 2009 would be approximately $215,000

A) The annual growth rate between 1993 and 2004, assuming exponential growth, can be calculated using the formula: growth rate = (final value / initial value) ^ (1 / number of years) - 1. In this case, the initial value is $95,000, and the final value is $165,000. The number of years is 2004 - 1993 = 11. Plugging these values into the formula, we get: growth rate = (165,000 / 95,000) ^ (1 / 11) - 1 ≈ 0.0568.

B) Converting the growth rate from part A to percentage form, we multiply it by 100. Therefore, the correct answer in percentage form is approximately 5.68%.

Now let's move on to part C. Assuming the house value continues to grow at the same percentage, we can calculate the value in the year 2009. We know that the value in 2004 was $165,000. To find the value in 2009, we need to calculate the growth over a period of 5 years. Using the growth rate of 5.68% (or 0.0568 as a decimal), we can calculate the value in 2009 as follows: value in 2009 = value in 2004 (1 + growth rate) ^ number of years = 165,000 (1 + 0.0568) ^ 5 ≈ $215,291.

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