Teri and Lee are playing a game that consists of consists of spinning a spinner with eight equal spaces numbered 1 through 8, and then flipping two coins at the same time.
Terri wins 10 points if the spin is greater than 5 and the coins are different (one head and one tail).
Lee wins 15 points if the spin is an even number and the coins are both tails.
Is the game is fair or unfair? Why?

A.The game is not fair, because Terri’s expected value is 10(4/8)(2/4)=2.5 and Lee’s expected value is 15(4/8)(1/4)=1.875.
B.The game is fair, because Terri’s expected value is 10(3/8)(2/4)=1.875 and Lee’s expected value is 15(4/8)(1/4)=1.875.
C.The game is not fair, because Terri’s expected value is 10(38)(13)=1.25 and Lee’s expected value is 15(4/8)(1/3)=2.5.

The soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day for the soft drink vendor, we need to use the formula P(x) = 0.001x^2 + 3x + 1800, where x is the number of cans of soda pop sold in one day.

To find the maximum profit, we need to find the vertex of the parabola represented by the profit function. The x-coordinate of the vertex is given by -b/2a, where a = 0.001 and b = 3. Plugging in these values, we get x = -3/(2*0.001) = -1500.

Since the soft drink vendor cannot sell a negative number of cans, we know that the maximum profit occurs at the closest whole number to x = -1500, which is x = 1500.

To find the maximum profit per day, we can plug in x = 1500 into the profit function:

P(1500) = 0.001(1500)^2 + 3(1500) + 1800 = $5250

Therefore, the soft drink vendor's maximum profit per day is $5250, and he must sell 1500 cans of soda pop to reach the maximum profit.

To find the maximum profit per day and the number of cans needed to reach that profit, we'll first need to find the critical point of the given quadratic profit function, P(x) = -0.001x^2 + 3x - 1800.

Step 1: Find the derivative of P(x) with respect to x. This will give us the rate of change of profit as the number of cans sold changes.

P'(x) = -0.002x + 3

Step 2: Set the derivative equal to zero and solve for x. This will give us the critical point where the maximum profit occurs.

-0.002x + 3 = 0

x = 1500 cans

Step 3: Substitute the critical point (x = 1500) back into the profit function P(x) to find the maximum profit.

P(1500) = -0.001(1500)^2 + 3(1500) - 1800

P(1500) = $600

So, the maximum profit per day is $600, and the soft drink vendor must sell 1500 cans to reach the maximum profit.

Learn more about profit at: brainly.com/question/15699405

#SPJ11

The maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

The profit function for the soft drink vendor is given by:

P(x) = \(0.001x^2 + 3x + 1800\)

To find the maximum profit, we need to find the vertex of the parabola represented by this function. The x-coordinate of the vertex can be found using the formula:

x = -b / (2a)

where a = 0.001 and b = 3. Substituting these values, we get:

x = -3 / (2 * 0.001) = -1500

Since the value of x cannot be negative in this context, we know that the maximum profit occurs at x = 1500. To find the maximum profit, we substitute this value of x into the profit function:

P(1500) =\(0.001(1500)^2 + 3(1500) + 1800 = $4800\)

Therefore, the maximum profit per day is $4800, and the vendor must sell 1500 cans of soda pop to reach this maximum profit.

Learn more about maximum profit

https://brainly.com/question/29248429

#SPJ4

Answer:

20 to 70 songs as a percent increase is 250%

Step-by-step explanation:

The old number (x, and in this case, 20) is subtracted by the new number (y, 70). The difference of x-y is divided by x (20). The quadrant is multiplied by 100, giving you the answer (250%).

The monthly payments for the same loan would be approximately $694.12.

To calculate the annual payment required to pay off a four-year, $27,000 loan at an interest rate of 9 percent EAR, we can use the formula for the present value of an ordinary annuity:

PV = PMT * (1 - (1 + r)^(-n)) / r

Where:

PV = Loan amount = $27,000

PMT = Annual payment

r = Interest rate per period = 9% = 0.09

n = Number of periods = 4

Plugging in these values into the formula, we can solve for PMT:

$27,000 = PMT * (1 - (1 + 0.09)^(-4)) / 0.09

Simplifying the equation, we have:

$27,000 = PMT * (1 - 0.708222) / 0.09

$27,000 = PMT * 0.291778 / 0.09

PMT = $27,000 * 0.09 / 0.291778

PMT ≈ $8,329.40 (annual payment)

To calculate the monthly payments for the same loan, we can divide the annual payment by 12:

Monthly payment = $8,329.40 / 12

Monthly payment ≈ $694.12

Therefore, the monthly payments for the same loan would be approximately $694.12.

learn more about payments on

https://brainly.com/question/15136793

#SPJ11

The questions for grade 7 math worksheets are typically prepared by math teachers, curriculum specialists, and educational publishers.

These professionals use their knowledge of math concepts and pedagogy to create questions that are appropriate for the grade level and aligned with educational standards.

Additionally, they may use feedback from students and other teachers to refine the questions and ensure they are effective for teaching and learning. It is important for the questions to be clear, accurate, and challenging in order to help students develop their math skills and prepare for more advanced concepts.

To know more about pedagogy click on below link:

https://brainly.com/question/30400049#

#SPJ11

Answer:

Step-by-step explanation:

Given

As we see on the graph the function g(x) is the stretched form of f(x) and there is no horizontal or vertical shift

So It is achieved as:

Correct answer choice is

Answer:

$ 4500

Step-by-step explanation:

Dejar;

Principal sea P

El tiempo sea T

Tasa sea R

Interés sea yo

De la pregunta;

R = 8%, T = 1 año, I = $ 360, P =?

De;

I = PRT / 100

100I = PRT

P = 100 I / RT

P = 100 * 360/8 * 1

P = $ 4500

Answer:

rise over run and if it is (1,2) and (2,3) you would do y2 or 3- y1 or 2 so that is 1.

x2-x1 or 2-1 also 1 and that is 1/1 also 1

Answer:

y = 10

Step-by-step explanation:

The second equation is already solved for x:

x = y - 3

Substitute x in the first equation with y - 3 and solve for y.

4y - 9x = -23

4y - 9(y - 3) = -23

4y - 9y + 27 = -23

-5y = -50

y = 10

Answer:

480

Step-by-step explanation:

4% of 12,000=480

The probability that a randomly chosen plant is detected incorrectly is 0.02965 = 2.965%.

From the question, we have the following parameters that can be used in our computation:

Using the above as a guide, we have the following:

Probability = 2% * 3.5% + 3% * 96.5%

Evaluate

Probability = 0.02965

Rewrite as

Probability = 2.965%

Hence, the probability is 2.965%.

Read more about probabilities at

https://brainly.com/question/31649379

#SPJ4

Question

The test to detect the presence of a certain protein is 98% accurate for corn plants that have the protein and 97% accurate for corn plants that do not have the protein.

If 3.5% of the corn plants in a given population actually have the protein, the probability that a randomly chosen plant is detected incorrectly is

Answer:

46.67$

Step-by-step explanation:

using the is/of method and %/100

60/100 x 28/x  cross mult

2800/60x = 46.666

round to nearest hundreth

Answer:

\( \boxed{ \bold{ \huge{ \boxed{ \sf{ \: 14.25 \: \% \: }}}}}\)

Step-by-step explanation:

Given,

Principal ( P ) = $ 6000

Amount ( A ) = $ 14550

Time ( T ) = 10 years

Rate ( R ) = ?

Finding the Interest

The sum of principal and interest is called an amount.

From the definition,

\( \boxed{ \sf{Amount = \: Principal + Interest}}\)

plug the values

⇒\( \sf{14550 = 6000 + Interest}\)

Swap the sides of the equation

⇒\( \sf{6000 + Interest = 14550}\)

Move 6000 to right hand side and change its sign

⇒\( \sf{Interest = 14550 - 6000}\)

Subtract 6000 from 14550

⇒\( \sf{Interest = \: 8550 \: }\)

Interest = $ 8550

Finding the rate

\( { \boxed{ \sf{Rate = \frac{Interest \times 100}{Principal \times Time}}}} \)

plug the values

⇒\( \sf{ Rate = \frac{8550 \times 100}{6000 \times 10} }\)

Calculate

⇒\( \sf{Rate = \frac{855000}{60000} }\)

⇒\( \sf{Rate = 14.25 \: \% \: }\)

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

Answer:

14 votes

Step-by-step explanation:

To find 70% of 20, first convert the percentage into a decimal. Move the decimal place two places to the left.

Now take the 20 and multiply it by 0.70.

You will end up with 14 as your answer.

Answer:

There were 118 monthly members before the incentive

Step-by-step explanation:

Let the total number of incentive

Monthly membership after incentive = a

Yearly membership after incentive = b

a/b = 5/8

We are told in the question that: 59 monthly members after the incentive,

5/8 = 59/b

Cross Multiply

5b = 59 × 8

b = 59 × 8/5

b = 472/5

b = 94.4

Therefore, number of yearly members = 94.4

Total number of Membership after incentive

= 94.4 + 59

= 153.4

Note that total number of members before incentive = total number of members after incentive

From the question, At the beginning of the year the ratio of monthly to yearly was 10:3.

Monthly membership after incentive = a

Yearly membership after incentive = b

a/b = 10/3

10b = 3a

b = 3a/10

a + b = 153.4

a + 3a/10 = 153.4

10 × a + 3a × 1/ 10 = 153.4

10a + 3a = 10 × 153.4

13a = 1534

Divide both sides by 13

a = 1534/13

a = 118

Therefore, the number of members before monthly incentive = 118

The correct option is C which is (2x+1)(x+5).

Answer:

1749.6

Step-by-step explanation:

Answer:

jbvfksbvfkfjbfbk

Step-by-step explanation:

ghjkeflj

Answer:

353.25 miles.

Step-by-step explanation:
multiply 78.5 mph by 4.5 hours

The total amount earned when he waits 18 tables is $143

The total amount earned when he waits t tables is $35 + $6t

The equation that can be used to determine the total amount Carson earns is a linear equation. A linear equation is an equation that when drawn on a graph yields a straight line.

A linear equation increases by a constant amount. The highest power of a variable in a linear equation is 1.

The form of a linear equation is y = a + bx

Where:

Total amount earned = guaranteed wage + (tip per table x total number of tables he waits)

Total amount earned when he waits 18 tables: $35 + ($6 x 18)

$35 + $108 = $143

Total amount earned when he waits t tables: $35 + ($6 x t)

$35 + $6t

To learn more about linear functions, please check: https://brainly.com/question/26434260

#SPJ1

Answer:

3 because I just answered in the thing

The number of fourths in fraction 3/4 is 3.

The correct option is 3.

To determine how many fourths are in 3/4, we can divide 3/4 by 1/4, as dividing by a fraction is equivalent to multiplying by its reciprocal.

So, 3/4 divided by 1/4 can be written as (3/4) x (4/1):

(3/4) x (4/1)

= (3 x 4) / (4 x 1)

= 12/4

Simplifying the fraction, we divide both the numerator and denominator by their greatest common divisor, which is 4:

12/4

= (12/4) / (4/4)

= 3/1

Therefore, there are 3-fourths (3/4) in 3/4. This means that 3/4 is equivalent to 3 times 1/4.

Out of the provided options, the correct answer is 3.

Hence, the number of fourths in 3/4 is 3.

To learn more about the fractions;

https://brainly.com/question/10354322

#SPJ6

The length of segment BD on the triangle is given as follows:

BD = 12.5 units.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

The parallel lines in this problem are given as follows:

BC and DE.

Then the proportional segments are given as follows:

AB and AC.

Thus the proportional relationship that relates these side lengths is given as follows:

(x - 2)/3 = (x + 3)/5.

Applying cross multiplication, the value of x is obtained as follows:

3x + 9 = 5x - 10

2x = 19

x = 19/2

x = 9.5.

Then the length of BD is obtained as follows:

BD = x + 3 = 9.5 + 3 = 12.5.

More can be learned about proportional relationships at brainly.com/question/10424180

#SPJ1

Answer:

8

Step-by-step explanation:

357÷17=21

168÷21=8

so $357 divided by the 17 hours is 21

then you do the $21 per hour multiplied by the money is what he makes then divide 21 and 168

The logarithmic form is written as logₐ(X)=b. It is a rearrangement of the exponential form, aᵇ=X.

What is Logarithmic Form?

The logarithmic form is written as logₐ(X)=b. It is generally the rearrangement of the exponential form, aᵇ=X. Any exponential equation can be written as a logarithm. The logarithmic form is mostly used to calculate an exponent of an equation. The logₐ(X)=b. is read as “log base a of X equals b“.

The logarithmic form is simply a rearrangement of an equation written in exponential form. The same numbers are used but they are written in a different order. The word log is written which implies that the logarithm function is being used.

Therefore, If the logarithmic form is logₐ(X)=b. then it is a rearranged as the exponential form as aᵇ=X.

To learn more about logarithm refer here

brainly.com/question/237323

#SPJ4

Answer:

Rs 400

Step-by-step explanation:

MP: market price

CP: cost price

MP = 1.4CP

(MP - 0.15MP) - CP = 76

0.85MP - CP = 76

0.85(1.4CP) - CP = 76

1.19MP - MP = 76

0.19MP = 76

MP = 400

the completed multiplication table is:  40  45  50  ,72  54  60 and 56  90  70 .by using common factor  logic we can solve this question.

what is  common factor ?

A common factor is a number that divides evenly into two or more other numbers. For example, the common factors of 12 and 18 are 1, 2, 3, and 6, because all of these numbers divide evenly into both 12 and 18.

In the given question,

From the given table, we can see that:

The first row reads 40, 45, 50 (which are multiples of 5).

The second row has an unknown number (let's call it x), 54, and 60.

The third row reads 56, an unknown number (let's call it y), 70 (which are also multiples of 7).

To find the missing numbers, we can use the fact that multiplication is commutative, meaning that the order of the factors does not matter. Therefore, we can fill in the missing numbers by looking for factors that are common to both the row and column headers.

Starting with the second row, we can see that the common factor between x and 54 is 9, since 9 x 6 = 54 and 9 x x = ?. So, the missing number in the second row is 9 x 10 = 90.

Moving on to the first column, we can see that the common factor between 40 and 56 is 8, since 8 x 5 = 40 and 8 x 7 = 56. So, the missing number in the second row, first column is 8 x 9 = 72.

Finally, we can find the missing number in the first row, second column by finding the common factor between 45 and 60, which is 15, since 15 x 3 = 45 and 15 x 4 = 60. So, the missing number in the first row, second column is 15 x 5 = 75.

Therefore, the completed multiplication table is:

40  45  50

72  54  60

56  90  70

To know more about  common factor , visit:

https://brainly.com/question/11221202

#SPJ1

The given statement is sometimes true.

Given that we need to determine if for all real numbers a and b, a ≠ 0, the equation ∣ax+b∣ = 0 will have one solution.

Let's analyze the equation ∣ax + b∣ = 0. The absolute value function ∣x∣ is defined as follows:

∣x∣ =

x, if x ≥ 0

-x, if x < 0

In our equation, we have ∣ax + b∣ = 0. According to the definition of the absolute value function, the expression ax + b must be equal to 0, as the absolute value of any real number can only be 0 if the number itself is 0.

Therefore, we can write the equation as follows:

ax + b = 0

Now, let's consider different cases for a and b:

Case: a ≠ 0 and b ≠ 0

In this case, the equation ax + b = 0 represents a linear equation with a non-zero slope (since a ≠ 0). A linear equation with a non-zero slope will intersect the x-axis at a single point.

Hence, the equation ∣ax + b∣ = 0 will have one solution.

Case: a = 0 and b ≠ 0

If a = 0, the equation becomes 0x + b = 0, which simplifies to b = 0. In this case, the equation has no solution since b ≠ 0.

Case: a ≠ 0 and b = 0

If b = 0, the equation becomes ax + 0 = 0, which simplifies to ax = 0. For any non-zero value of a, the equation will have one solution, x = 0.

In conclusion, the equation ∣ax + b∣ = 0 will have one solution for all real numbers a and b if a ≠ 0 and b = 0. Otherwise, it will have one solution only when both a and b are non-zero.

Therefore, the statement is sometimes true.

Learn more about absolute value function click;

https://brainly.com/question/29004017

#SPJ4

(a) The hypothesis test aims to determine if the population mean speed of all cars is less than 65 mi/h. The null hypothesis (H₀) states that the population mean speed is 65 mi/h or greater, while the alternative hypothesis (H₁) states that the population mean speed is less than 65 mi/h. In this case, the claim corresponds to the alternative hypothesis. The significance level, denoted by α, is given as 0.05.

(b) To find the p-value using a calculator, we need to perform a one-sample t-test. Using the provided data, we can calculate the test statistic and determine the p-value associated with it. The test statistic is calculated as t = (sample mean - hypothesized mean) / (sample standard deviation / √n), where n is the sample size. In this case, the hypothesized mean is 65 mi/h.

Using a calculator, the sample mean is calculated as 65.0833 mi/h, the sample standard deviation is 4.7977 mi/h, and the sample size is 12. Entering these values into the calculator's t-test function with the appropriate options, we can obtain the p-value.

(c) The decision whether to reject or fail to reject the null hypothesis is based on comparing the p-value to the significance level. If the p-value is less than or equal to the significance level (α), we reject the null hypothesis. Otherwise, if the p-value is greater than the significance level, we fail to reject the null hypothesis.

(d) Based on the calculated p-value and the significance level of 0.05, we compare the p-value to α. If the p-value is less than or equal to 0.05, we reject the null hypothesis. On the other hand, if the p-value is greater than 0.05, we fail to reject the null hypothesis.

In summary, we set up the null hypothesis and the alternative hypothesis to test the claim that the population mean speed of all cars is less than 65 mi/h. By calculating the p-value using a calculator and comparing it to the significance level, we make a decision to either reject or fail to reject the null hypothesis. Finally, we state our conclusion based on the decision made in the hypothesis test.

To learn more about hypothesis test click here : brainly.com/question/17099835

#SPJ11

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

For similar question on population proportion.

https://brainly.com/question/29516589  

#SPJ8

The person needs to have more than 64,900 postage stamps to break the record.

It is given in the question that:-

Current postage stamp collection record = 150,000

Postage stamps with the three friends are 10000, 75000 and 100.

We have to find the number of postage stamps required by him to break the record.

Let the postage stamps with him be x.

Total postage stamps with the three friends = 10000+75000+100 = 85,100

Hence, we can write the inequality,

150000 < 85100 + x

x > 150,000-85,100

x > 64,900

Hence, he needs to have more than 64,900 postage stamps with him to break the record.

To learn more about inequality, here:-

https://brainly.com/question/28823603

#SPJ1