jonathan goes to th store and purchases 3 pencils for 0 .28 each, and x number of erasers for 0.38each write an expression that shows how much jonathan spent

Answer:

5%

Step-by-step explanation:

to work out what percent 17 is out of 340 we can formulate an equation

so 340(x%)=17

when we solve for x we get 5

To find tan x/2, given that tan x=3 and x terminates in π < x < (3π/2), we can use the half-angle formula for tangent. The value of tan (x/2) is ±1/√2.

To find tan x/2, given that tan x=3 and x terminates in π < x < (3π/2), we can use the half-angle formula for tangent. The half-angle formula for tangent is tan(x/2) = ±√((1-cosx) / (1+cosx)). Since tan x=3, we need to find the value of cos x first.

Given that tan x = 3, we can use the fact that tan x = sin x / cos x to find the value of cos x. Rearranging the equation, we have cos x = sin x / tan x = 1 / 3. Now, we can substitute this value of cos x into the half-angle formula to find tan (x/2).

tan (x/2) = ±√((1-cos x) / (1+cos x))
tan (x/2) = ±√((1-1/3) / (1+1/3))
tan (x/2) = ±√((2/3) / (4/3))
tan (x/2) = ±√(2/4)
tan (x/2) = ±√(1/2)
tan (x/2) = ±1/√2

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Using the concept of similar triangles, we found that Dixon's height is 6 feet, assuming that the light source causing the shadows is consistent.

This question is about the concept of similar triangles in Mathematics. If Ariadne's shadow is 15 feet long and she is 5 feet tall, it means the ratio of her height to her shadow length is 5:15 or 1:3. If Dixon's shadow is 18 feet long, and we assume the light source creating the shadows is the same, then the same ratio can apply to him, since their shadows will be proportional to their heights. Therefore, if the ratio of Ariadne's height to her shadow length is equal to the ratio of Dixon's height to his shadow length, we can form the following equation and solve for Dixon's height: 5/15 = x/18 where 'x' is Dixon's height. Solving this equation, we find that Dixon's height is 6 feet.

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Barbara Mack owes approximately $2543.78 at the end of 4 years with 6% interest compounded continuously.

To find the total amount Barbara Mack owes after 4 years with a 6% continuously compounded interest rate, we use the formula:

A = P[tex]e^{rt}[/tex]

with P = $2000,

r = 0.06, and

t = 4

A = 2000 x [tex]e^{0.06 * 4}[/tex].

When we calculate e(0.06*4), we'll get a certain number that you then multiply by 2000 to find the total amount owed.

A= 2000 x [tex]2.71828 ^{0.24}[/tex]

A= 2543.78 ( approx)

So, Barbara Mack owes approximately $2543.78 at the end of 4 years with 6% interest compounded continuously.

The calories in a 21-oz iced tea that is originally 78 calories in a 13-oz serving, multiply the calories per ounce by the new serving size for a total of 126 calories.

The 13-oz iced tea contains 78 calories. To find the calories in a 21-oz iced tea:

Calculate the calories per ounce: 78 calories ÷ 13 oz = 6 calories/oz

Multiply the calories per ounce by the 21-oz serving size: 6 calories/oz × 21 oz = 126 calories in a 21-oz iced tea

There are 1001 different choices of 10 questions.

d. Since the student can choose any 10 questions out of the 14, the number of different choices of 10 questions is given by the combination formula, which is C(14,10). Using the formula for combinations, we have:

C(14,10) = 14! / (10!(14-10)!)

= 14! / (10!4!)

= (14*13*12*11) / (4*3*2*1) = 1001

Therefore, there are 1001 different choices of 10 questions.

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Answer: Amount she earn on the sale is $42.9.

Step-by-step explanation:

Since we have given that

A furniture salesperson sells a couch for $1560.

Percentage of commission she receive on the sale of the couch = 2.75%

So, Amount she earn on the sale is given by

[tex]2.75\%\ of\ 1560\\\\=\frac{2.75}{100}\times 1560\\\\=0.0275\times 1560\\\\=\$42.9[/tex]

Hence, amount she earn on the sale is $42.9.

To write an equation relating the total cost to the number of tickets purchased with a fixed fee, set up a system of equations using the given information and solve for the variables.

To write an equation relating the total cost to the number of tickets purchased, we need to determine the cost of one ticket and the fixed fee added by the ticket agency. Let's assign the ticket price as x and the fixed fee as y. Based on the given information, we can set up two equations:

5x + y = 93

3x + y = 57

Now, we can solve this system of equations to find the values of x and y and write the final equation relating the total cost to the number of tickets purchased.

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Given a Poisson distribution with 0.05 flaws/sq ft and 10 sq ft panels, each car has a 60.65% chance of no flaws.

The probability of at least 1 car with flaws is 99.35%.

Considering only 1 car with flaws, the final probability of at most 1 car with flaws is 90.2%.

Probability of at most 1 car with flaws: 90.2%

Here's how to calculate the probability that at most 1 car out of 10 has any surface flaws, given the Poisson distribution parameters:

1. Define parameters:

Mean flaws per square foot (λ) = 0.05

Area of plastic panel per car (A) = 10 square feet

Number of cars (N) = 10

2. Calculate probability of no flaws:

Probability of no flaws in one car (P(X=0)) = e^(-λA) = e^(-0.0510) ≈ 0.6065

3. Calculate probability of 1 car with flaws (complementary probability):

Probability of at least 1 car with flaws (1 - P(no flaws in all cars))

P(X ≥ 1) = 1 - (P(X=0))^N = 1 - (0.6065)^10 ≈ 0.9935

Probability of exactly 1 car with flaws (P(X=1)) = N * P(X=0) * (1-P(X=0))^N-1

≈ 10 * 0.6065 * (1 - 0.6065)^9 ≈ 0.3869

4. Final probability:

Probability of at most 1 car with flaws (P(X ≤ 1)) = P(X=0) + P(X=1) ≈ 0.6065 + 0.3869 ≈ 0.9934

The probability that at most 1 car out of 10 has any surface flaws is approximately 90.2%.

Therefore, Given a Poisson distribution with 0.05 flaws/sq ft and 10 sq ft panels, each car has a 60.65% chance of no flaws.

The probability of at least 1 car with flaws is 99.35%.

Considering only 1 car with flaws, the final probability of at most 1 car with flaws is 90.2%.

The probable question may be: The number of surface flaws in plastic panels used in the interior of automobile has a Poisson distribution with a man of 0.05 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel. If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws?

a. The probability of no surface flaws in an auto's interior is approximately 0.7408.

b. The probability of none of the 10 cars having any surface flaws is approximately 0.0498.

c. The probability of at most 1 car having any surface flaws is approximately 0.9631.

a. Probability of no surface flaws:

Calculate the lambda parameter: The lambda parameter for the Poisson distribution represents the expected number of flaws, which is calculated as the mean flaws per square foot multiplied by the total area.

In this case, [tex]\lambda[/tex] = 0.03 flaws/sq ft * 10 sq ft = 0.3 flaws.

Use the Poisson probability formula: The probability of no flaws (x = 0) in a Poisson distribution is given by [tex]e^{(-\lambda)[/tex].

Plugging in lambda = 0.3, we get

P(x = 0) = [tex]e^{(-0.3)[/tex] ≈ 0.7408.

b. Probability of none of the 10 cars having flaws:

Treat each car as an independent event: Since the flaws are random and independent for each car, we can treat each car as a separate event with the same probability of no flaws (0.7408) calculated in part (a).

Calculate the combined probability: To get the probability of none of the 10 cars having flaws, we simply multiply the individual probabilities.

P(no flaws in all 10 cars) = [tex](0.7408)^{10[/tex] ≈ 0.0498.

c. Probability of at most 1 car having flaws:

Calculate probabilities for 0 and 1 flaws: We need the probabilities of 0 flaws (already calculated in part (a)) and 1 flaw (x = 1) to determine the probability of at most 1 flaw.

Probability of 1 flaw: Using the Poisson formula again,

P(x = 1) = [tex]\lambda[/tex] * [tex]e^{(-\lambda)[/tex] = 0.3 * [tex]e^{(-0.3)[/tex] ≈ 0.2222.

Probability of at most 1 flaw: This includes both scenarios with 0 and 1 flaws. P(at most 1 flaw) = P(0 flaws) + P(1 flaw) = 0.7408 + 0.2222 ≈ 0.9631.

Question:-

The number of surface flaws in plastic panels used in the interior of automobiles has a Poisson distribution with a mean of 0.03 flaws per square foot of plastic panel. Assume an automobile interior contains 10 square feet of plastic panel.

a. What is the probability that there are no surface flaws in an auto's interior?

b. If 10 cars are sold to a rental company, what is the probability that none of the 10 cars has any surface flaws?

c. If 10 cars are sold to a rental company, what is the probability that at most 1 car has any surface flaws? Round your answers to four decimal places (e.g. 98.7654).

Final answer:

By applying the given linear equation, we can calculate the average cinema admission price for specific years, find out in which year the price was approximately $7.88, and predict when it might reach $10.04.

Explanation:

The question involves solving a linear equation to complete a table, find a specific year based on the ticket price, and predict when the ticket price will reach a certain amount. To complete these steps, we apply the equation y=0.28x+5.92, where x represents the number of years after 2003, and y gives the price in dollars.

For a, plug in the values of x (2, 5, 8) into the equation to find y.

For b, set y=7.88 and solve for x (years after 2003) by rearranging the equation.

For c, with a target price of $10.04, use the equation again to solve for x.

When x=2, y=6.48.

When x=5, y=7.32.

When x=8, y=8.16.

For a ticket price of $7.88, solve for x: x =  (7.88 - 5.92) / 0.28 = 7 years after 2003, which is 2010.

To predict when the ticket price reaches $10.04, solve for x: x =  (10.04 - 5.92) / 0.28 = 14.71, rounding to 15 years after 2003, which is 2018.

It will take her 13 weeks to save enough money for a trip to the Six Flags amusement park

Comparison is an effort to compare two or more objects in terms of shape or size, or number  

Proportional Comparisons / Directly proportional are comparisons of two or more numbers where one number increases, the other numbers also increase at the same rate  

 Can be formulated  

[tex]\displaystyle \frac {x1} {y1} = \frac {x2} {y2}[/tex]

 so that if:  

 x = 2  

 then  

[tex]\displaystyle y ={ \frac {y} {x} \times \: 2}[/tex]

 While the reversal value comparison / inversely proportional is the comparison of two or more numbers where one number increases, the other number decreases in value  

or when one value decreases at the same rate that the other increases  

Can be formulated  

[tex]\displaystyle \frac {x1} {y2} = \frac {x2} {y1}[/tex]

so that if:  

 x = 2  

 then  

[tex]\displaystyle y = \frac {x} {y} \times \: 2[/tex]

Michelle wants to save $150

she saves $12 each week

the number of weeks needed to save money

every weeks , she save $12 or we can make equation 1:

1 weeks = $12

the amount of money needed to travel to the six flags amusement park

= $150

we can make equation 2

? weeks = $150

Because this includes Proportional Comparisons / Directly proportional,

from two equation above , we can make comparison :

[tex]\displaystyle \frac{1\:weeks}{\$12} =\frac{x\:weeks}{\$150}[/tex]

[tex]\displaystyle x\:weeks=\frac{\$150\times1\:weeks}{\$12}[/tex]

[tex]\large{\boxed{x\:weeks= 12.5}}[/tex]

or we round up to :

[tex]\large{\boxed{\bold{13\:weeks}}}[/tex]

1,092 flowers are arranged into 26 vases  

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dividing 878 by 31  

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round trips  

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Keywords: save money,a trip to park, Proportional Comparisons / Directly proportional

Final answer:

Ava can capture the chip on square 72 by using the +30 change card once to reach 66, and then the +1 change card six times to reach the final value of 72.

Explanation:

Ava's game piece is on square number 36, and she wants to capture a chip on square number 72. By using the change cards, Ava needs to adjust her position from 36 to 72 with the change cards provided. The change cards are: -10, +30, -1, +1, and -2. To determine if Ava can capture the chip, we need to see if we can use the cards to add up to a net change of +36 (since 72 - 36 = 36).

By analyzing the cards, we can use the +30 card once, which would take Ava's position from 36 to 66. Next, she can use the +1 card six times to go from 66 to 72. Ava does not need to utilize the -10, -1, or -2 cards as they would move her backwards. Therefore, Ava can indeed capture the chip using the change cards provided.

The steps Ava should follow are:

Use the +1 card six times to move from 66 to 72.

To complete the partial worksheet for Bill's Company, you need to record the appropriate adjusting entries using the given data. Once the adjustments are recorded, you can transfer the balances to the adjusted trial balance column.

To complete the partial worksheet for Bill's Company, we need to record the appropriate adjusting entries using the given data. Let's go step by step:

Once you complete these steps, you will have the adjusted trial balance with the appropriate balances extended from the adjustments.

The equivalent value of the expression k = ( 2F/p )

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

F = ( 1/2 ) kp

On simplifying , we get

Multiply by 2 on both sides , we get

2F = kp

Divide by p on both sides , we get

k = 2F/p

Hence , the expression is k = 2F/p

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