1. Helen took four tests, for which her mean score was 26. Later on, it was found that her score in the English test was wrongly recorded as 51 instead of 15. What was the corrected mean score?

The payoff matrix that Gabriel and Nia use demonstrates the zero-sum between two players by showing each person's earnings as a function of both of their choices.

The reward matrix or payoff matrix is a double-entry table, similar to another Table, that holds all of the payments made by one player to the other for each selected strategy. Since one player's payment equals the other player's gain, the game is referred to as zero-sum.

The example case scenario can be used to demonstrate the calculation in the payout matrix above;

If the row player has n strategies and the column player has m strategies, the matrix must have n & m cells and contain a total of 2 n m reward values. The row player's name appears in a payment matrix to the left of the matrix, while the column player's name appears above the matrix. Since one player's payment equals the other player's gain, the game of payout matrix is referred to as zero-sum.

To learn more about function here:

https://brainly.com/question/29633660

#SPJ4

A rectangle's greatest area is 32 square units.

Given:

A parabola's equation is y = 12 - x2, which is an even function

As a result, its rectangular shape is also even at the origin.

We are aware that the area of a rectangle is equal to its length times its width.

Here,

width = y, length = 2x

A = 2x, where (12 -  [tex]x^{2}[/tex])

⇒ A = 24x - 2[tex]x^{3}[/tex]

Consider the A derivative with regard to x.

⇒ A' = 24 - 6 [tex]x^{2}[/tex]

When A' = 0, the area is the largest.

⇒ 24 - 6x2 = 0

⇒ [tex]x^{2}[/tex] = 4

⇒ x = 2

Replace x with its value in y = 12 -  [tex]x^{2}[/tex].

⇒ y = 12 - 4

⇒ y = 8

Area = 2(2)(8) = 32

Hence, a rectangle's greatest area is 32 square units.

To learn more about function:

https://brainly.com/question/21145944

#SPJ4

The equation of the line is y+1/2=3(x-2) when a line with a slope of 3 and passes through the points (2, -1/2).

Given that,

We have to find what is the equation describes a line with a slope of 3 and passes through the points (2, -1/2).

We know that,

The equation of the line is represented by (y-y₁)=m(x-x₁)

Here,

Point (2,-1/2)

Slope is 3.

Substitute in the equation,

(y-(-1/2)=3(x-2)

(y+1/2)=3(x-2)

Therefore, The equation of the line is y+1/2=3(x-2) when a line with a slope of 3 and passes through the points (2, -1/2).

To learn more about equation visit: https://brainly.com/question/29657983

#SPJ4

Answer:

[tex]a_{n}[/tex] = 8n + 17

Step-by-step explanation:

there is a common difference between consecutive terms in the sequence

33 - 25 = 41 - 33 = 8

this indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = 25 and d = 8 , then explicit formula is

[tex]a_{n}[/tex] = 25 + 8(n - 1) = 25 + 8n - 8 = 8n + 17

9 x (46+70) 5 - 32 (40 - 219) = 11428

Using the BODMAS rule, we solve the brackets first,

9 x (46+70) 5 - 32 (40 - 219)

= 9 x 116 x 5 - 32 x -179

Next, we solve the multiplication signs

9 x 116 x 5 - 32 x -179

= 5520 - ( -5728)

Solving the subtraction sign, we get

5520 - ( -5728)

= 11428

Hence, the answer is 11428

To learn more about BODMAS :

https://brainly.com/question/723406

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

What is Average?

The middle number, which is obtained by dividing the sum of all the numbers by the variety of numbers, is the average value in a set of numbers. To calculate the average of a set of data, add up all the values and divide the result by the total number of values.

(a) f(x) = x2 – 8x + 10

f = 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/5-2 [tex]\int\limits^5_2 {x^{2} -8x+10} \, dx[/tex]

Here, a=2

b=5

f(x) =x2 – 8x + 10

f = 1/3 (x³/3 - 8x²/2+10x)5/2

f = -25/9 -20/9

f = -45/9

= -5

Mean Value Theorem

If f(x) = continous on (a, b)

If f(x) = differentiable on (a, b)

Then f(c) = f(b) -f(a)/b-a

were c∈ (a,b)

Here, f(c) = f(-5)-f(2)/5-2

f(c) = -5+2/3

f(c) = -1 ......................(1)

Here, f(x) = x²-8x+10

f(c) = c²-8c+10

f(x) = 2c-8...................(2)

equating 1&2

2c -8 = -1

2c = -1 +8

c = 7/2

c∈ (2,5)

(b) f(x) = Vx on [1, 16]

f = [tex]\sqrt{x}[/tex] on (1 ,16)

f= 1/b-a [tex]\int\limits^b_a {f(n)} \, dx[/tex]

f = 1/16-1 [tex]\int\limits^6_1 {\sqrt{x} } \, dx[/tex]

f = ( 2x (3/2)/45)₁¹⁶

f = 128/45-2/45

f = 126/45

= 14/5

Mean Value Theorem

f(x) = [tex]\sqrt{x}[/tex]

f(c) =[tex]\sqrt{c}[/tex]

f(c) = 1/2[tex]\sqrt{c}[/tex]....................(1)

we know that

f(c) = f(b)-f(a)/b-a

f(c) = f(16)-f(1)/16-1

f(c) = [tex]\sqrt{16}[/tex] -[tex]\sqrt{1}[/tex]/15

f(c) = 4-1/15

= 3/15.....................(2)

Equating (1) and (2)

1/2[tex]\sqrt{c}[/tex] = 3/15

2[tex]\sqrt{c}[/tex] = 15/3

2[tex]\sqrt{c}[/tex] = 5

[tex]\sqrt{c}[/tex] = 5/2

c = (5/2)²

=25/4

c≅ 6.25

6.25 = (1 ,16)

The average value of the given function on the given interval is = 7/2 and 6.25 respectively

To learn more about Average visit

brainly.com/question/27193544

#SPJ4

The following pricing strategies could be ethical in many situations is price discrimination.

Predatory pricing is a strategy in which a company establishes a price that is too low to get new customers.

Price baiting is a strategy in which businesses make customers believe that they will have to pay less than the actual price of the product.

Price gouging is when a company puts a price that is too high for a product in a level that is not reasonable and this is considered to be unethical.

Price discrimination is a strategy in which businesses charge different prices to different customers based on what they believe that a group of customers would be willing to pay.

For example, when an airline sees that a specific route has a high demand, it increases the price of the ticket.

learn more about the price here:

https://brainly.com/question/19091385

#SPJ4

Answer:

D. Price discrimination

Answer:

  y = 9x² +9x +2

Step-by-step explanation:

You want a quadratic equation with roots -1/3 and -2/3.

When p is a root of a polynomial, x-p is a factor. That means your quadratic will have factors (x -(-1/3)) and (x -(-2/3)). If we want integer coefficients, we can multiply each of these by 3:

  y = (3x+1)(3x+2)

  y = 9x² +9x +2 . . . . . . the result of multiplying it out

The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.

Given that,

There is a line of unassembled furniture produced by The Mean Corporation. The customer care manager is aware that 0.63 of customers have had no issues putting together their furniture at home based on past data.

The null and alternative hypotheses are:

H₀: π = 0.63

H₁: π > 0.63

We have to find

(a) Calculate the test statistic (z).

(b) Calculate the P-value.

We know that,

a) z = p - π / √(π(1-π)/n)

      = 0.67 - 0.63 / √(0.63×0.37/102)

      = 0.04 / 0.0478

      = 0.84

b) p value(one tailed) is 0.2005.

Therefore, The test statistic z = 0.84 and P-value is 0.2005 when there is a line of unassembled furniture produced by The Mean Corporation.

To learn more about statistic visit: https://brainly.com/question/11969248

#SPJ4

Answer:

0

Step-by-step explanation:

For given expressions:

1. 3x+2 ≥ {}

This is not a sentence.

2. x-y=1

This is an open sentence.

3. 2x+y > 0

This is an open sentence.

4. x4y+=

This is not a sentence.

In this question, we have been given some expressions.

We need to check which expression is a sentence.

We know that a mathematical sentence makes a statement about two expressions. The two expressions wither use variables, numbers or combination of both.

1.  3x+2 ≥ {}

this is not a sentence. Because when we use comparision than we must have two value to compare.

2. x-y=1

We know that an open sentence containing the sign ‘=‘

So, above expression is a sentence.

For x = 3 and y = 2,

x - y = 3 - 2

       = 1

For x = 9 and y = 8,

x - y = 9 - 8

       = 1

3. 2x+y > 0

This is an open sentence, as it is not known whether or not the sentence is true or false

4. x4y+=

This is not a sentence.

Therefore, for given expressions:

1. 3x+2 ≥ {}

This is not a sentence.

2. x-y=1

This is a sentence.

3. 2x+y > 0

This is a sentence.

4. x4y+=

This is not a sentence.

Learn more about an expression here:

https://brainly.com/question/1859113

#SPJ4

Layla should by not more than 4 outfits in order not to exceed her budget

The inequality expression is n  ≤ 4

price of a new bicycles = $418.55

2 bicycle reflectors = $19.39

a pair of bike gloves = $27.23

new biking outfits = $38.86 each

Nora's total money to spend at a bicycle store = $38.86

Layla's spending will never exceed the total spending at the bike shop, so it will be less than or equal to the total of other items

We write the expression as;

$640 ≤ $418.55 + 2 * $19.39 + $27.23 + n * $38.86

where n represents the number of the new biking outfits

$640 - ( $418.55+ 2 * $19.39 + $27.23 ) ≤. + n * $38.86

( $640 - ( $418.55 + 2 * $19.39 + $27.23 ) ) /  $38.86≥ n

( $640 - $484.56 ) /  $38.86 ≥ n

( $155.44) /  $38.86  ≥ n

4  ≥ n

Layla should by not more than 4 outfits in order not to exceed her budget

Read more on inequalities here: brainly.com/question/11613554

#SPJ4

C. The Roth IRA reduces the tax burden because its taxes are calculated in a lower bracket.

In a traditional IRA, contributions may be tax-deductible in the year they are made, but withdrawals in retirement are taxed as ordinary income. This means that the $1000.00 investment in a traditional IRA would be taxed at the investor's ordinary income tax rate when it is withdrawn in retirement. If the investor's ordinary income tax rate is 12%, then the tax burden on the $1000.00 investment in a traditional IRA would be $120.00.

In a Roth IRA, contributions are not tax-deductible, but withdrawals in retirement are tax-free. This means that the $1000.00 investment in a Roth IRA would be taxed at the investor's ordinary income tax rate when it is made, but it would not be taxed when it is withdrawn in retirement. If the investor's ordinary income tax rate is 10%, then the tax burden on the $1000.00 investment in a Roth IRA would be $100.00.

Overall, the tax burden on the $1000.00 investment in a Roth IRA is lower than the tax burden on the same investment in a traditional IRA because the taxes on the Roth IRA are calculated in a lower bracket (10% vs 12%).

Division C’s highest acceptable transfer price if it were to buy 4,000 units from Division B should be $58.

The transfer price is the price that Division B should charge Division C for the internal supply of goods or services.

Ordinarily, the transfer price equals the outlay cost (production cost) plus the opportunity cost (profit from selling outside).

The highest acceptable transfer price that Division C should reflect the market price at which Division C could acquire the parts from outside.

Division B:

Outside market selling price per unit = $60

Variable cost per unit = $44

Fixed cost per unit = $8

Capacity in units = 20,000 units

Units sold outside by Division B = 15,000 units

Excess units = 5,000 units (20,000 - 15,000)

Units required by Division C = 4,000 units

Outside supplier's price per unit = $58

Thus, the highest acceptable transfer price should be $58 and not $60.

Learn more about transfer pricing at https://brainly.com/question/15698480

#SPJ1

For this sample, a confidence interval based on the t distribution with 95% degrees of freedom would be appropriate.

In most research, the 95% confidence interval (95 CI) is reported. If the confidence interval (e.g., 95%CI 0.9-1.1) crosses 1, it is assumed that there is no difference between the research arms.

In the two-tailed t table, determine the critical value of t. Add s/n to the crucial value of t. Calculate the top limit of the confidence interval by adding this value to the mean, and the lower limit by deducting this value from the mean.

With a significance level of 0.05 (i.e., a confidence level of 95%), the confidence interval is calculated using the T function.

The critical value for a 99% confidence interval for this sample, according to Table 1, is 2.576.

The t distribution is a symmetric distribution with a peak in the middle that gets closer to the horizontal axis as it moves away from the centre.

To learn more about The t Distribution refer to:

https://brainly.com/question/29734811

#SPJ4

5/4 cannot be the probability of an event as its value is greater than 1 and probability always lies between 0 and 1. Yes, 3 by 5 can be the probability of an event.

We know that the probability of an event is the chance of occurring of an event. The ways of showing probability could be in ratio or it could be in percentage and the percent may be between 0%-100%

The value of 5/4 = 1.25 which is greater than 1, so it cannot be the probaility of any event.

The value of 3/4 = 0.75, its value is less than 1, so it can be the probability of an event.

The probability of an event always lie between 0 and 1. It is equal to zero if the event will never occur and is equal to 1 if the event is certain to occur.

Therefore,  the probability of an event  cannot be 5/4 but 3 by 5 can be the probability of an event. as its value of 5/4 is greater than 1 whereas the value of 3/5 is less than 1 and probalilty always lies between 0 and 1.

To learn more about probability refer here

https://brainly.com/question/25870256

#SPJ4

So option b. x² -1 is the correct option of the given statement Because option b satisfy the requirement of not a polynomial.

An expression for a polynomial can be generated using only the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables (also known as indeterminates) and coefficients make up a polynomial.

It is possible to identify the polynomials by seeing which formulae only include the operations addition, subtraction, multiplication, and non-negative integer exponents. Expressions that include extra operations are regarded as non-polynomial expressions. Specify the grounds for the expressions' non-polynomial status.

Any function in an equation that uses only positive integer exponents or non-negative integer powers of a variable is known as a polynomial function. These equations include, for instance, the cubic equation, the quadratic equation, and others. A polynomial with an exponent of 1 is, for instance, 2x+5.

To know more about polynomials visit:

https://brainly.com/question/29182596

#SPJ4

Answer:

The difference is multiplied by 4 can be represented as 4 (x - 1/2) According to the question, 4 (x - 1/2) = 5 x - 1/2 = 5/4 x = 5/4 + 1/2 x = (5 + 2)/4 x = 7/4 Therefore, the number is 7/4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Im assuming the question is to write this into actual numbers,

answer: 4(5-x)

Answer:

isnt it 72

Step-by-step explanation:

since it is that kind of triangle

Any n-dimensional vector should be able to be represented in space.

The highest degree of terms is written first when writing a polynomial in its standard form, then the next highest degree, and so on.

If there are multiple variables in a single term, add the exponents of each term together and choose the largest sum or highest power of the variable to determine the polynomial's degree.

It should be possible to represent any n-dimensional vector in space. It can only express polynomials of degree n if it only has terms of degree n.

To learn more about the standard form of a polynomial, visit the link below:

brainly.com/question/26552651

#SPJ4

The absolute value of |-32| is 32; absolute value of |27| is 27; absolute value of |-12| is 12; absolute value of -|14| is -14.

The Absolute value |x| of a real number x is the non-negative value of x without regard to its sign.

|x| = x ; |-x| = x

Therefore absolute value of

|-32| = 32

|27| = 27

|-12| = 12

- |14| = - 14

Absolute value describes the distance from zero that a number is on the number line , without considering direction. The absolute value of a number is never negative. Sometimes a sign is attributed to a numeric value to signify the direction, in addition to the value.

The absolute value of a number is defined as its magnitude irrespective of the sign of the number.

To know more about absolute value here

https://brainly.com/question/24534147

#SPJ4

From two populations, independent random samples were drawn, each having 80 observations. The test statistic should be z = 2.18 because samples from populations 1 and 2 yielded 33 and 28 successes, respectively.

P-value is set at 0.030.

State the null and alternate hypotheses in step one.

H0: (p1-p2) = 0

Ha: (p1-p2) ≠ 0

Step 2: Calculate the test statistic

We can calculate the test statistic using the formula:

z = (p1-p2)/√(p(1−p)(1/n1+1/n2))

where,

p = (successes in sample 1 + successes in sample 2)/(n1+n2)

= (33 + 28)/(80 + 80)

= 61/160

= 0.30

n1 = sample size of population 1

= 80

n2 = sample size of population 2

= 80

Therefore,

z = (p1-p2)/√(p(1−p)(1/n1+1/n2))

= (33/80 - 28/80)/√(0.38125(1−0.38125)(1/80+1/80))

=2.18

Learn more about test statistic here

https://brainly.com/question/14128303

#SPJ4

Answer:

I think its (-4,2)

Step-by-step explanation:

The equation of the line perpendicular to the line y = 3x+7 is 3y = -x-17

The slope or gradient of a line is a number that describes both the direction and the steepness of the line.

Given that, a line is perpendicular to line y = 3x+7 and passing through points (-2,-5)

The slope of perpendicular lines is negative reciprocal of each other.

Therefore, the slope of the asked line is -1/3

Finding c,

-5 = -1/3x(-2)+c

c = -17/3

Therefore, the equation of the line is y = -1/3x-17/3 or 3y = -x-17

Hence, The equation of the line perpendicular to the line y = 3x+7 is

3y = -x-17

For more references on slope, click;

https://brainly.com/question/3605446

#SPJ1

1. Completing the percentage table about the payment for a pair of jeans bought by Terese at a clothing store is as follows:

Dollar Amount      Percentage

                              % off the

                         original amount

$75                         25%

2. The coupon gives Terese 25% off the original amount.

3. The amount Terese paid for the jeans (before tax) was $56.25.

4. The number of yellow candies in the bag is 15.

5. In the Math test, Blair, who answered 27 questions correctly out of 35, scored 77 percent.

6. The true statement about the amount of money Jeffrey has concerning Louis is A. Jeffry has $66.

Cost of a pair of jeans = $75

Coupon value = $18.75

Amount paid = $56.25

The coupon percentage = 25% ($18.75/$75 x 100)

Yellow candy = 25%

The total number of candies in the bag = 60

The number of yellow candy = 15 (60 x 25%)

The total number of questions = 35

The number of questions answered correctly = 27

Percent scored by Blair = 77% (27/35 x 100)

The amount of money Louis has = $110

The percentage of Louis' money that Jeffry has = 60%

The amount Jeffry has = $66 ($110 x 60%)

Learn more about percentages at https://brainly.com/question/24877689

#SPJ1

Answer:

y=1/3x+2

Step-by-step explanation:

................

Answer:

y=1/3x+2

Step-by-step explanation:

slope intercept form: y=xm+b

6y=2x+12

/6       /6

y=2/6x+2

y=1/3x+2

have a great day!

To conduct a hypothesis test for the difference between two population proportions under independent sampling is,

n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5.

What is population proportion?

In statistics, a population proportion is a parameter that describes a percentage value connected to a population. It is typically denoted by P or the Greek letter π.

As per central limit theorem sample size needs to be greater than 30.

So required conditions are Only if n1 ≥ 30 and n2 ≥ 30.

Also for normal approximation we need the condition

[tex]np \geq 5 and[/tex]  n(1 - p) ≥ 5

So one more condition is Only if

n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5

Hence,  to conduct a hypothesis test for the difference between two population proportions under independent sampling is

n1p1 ≥ 5, n1(1−p1) ≥ 5, and n2p2 ≥ 5,n2(1−p2) ≥ 5

To know more about population proportion, click on the link

https://brainly.com/question/18514274

#SPJ4

The probability of choosing a red or a blue marble is 0.475.

What is probability?

Probability is that the branch of arithmetic regarding numerical descriptions of however probably an incident is to occur, or however probably it's that a proposition is true. The likelihood of an incident could be a range between 0 and 1.

Main body:

number of red marbles =19

number of blue marbles = 19

number of yellow marbles = 42

total number of balls = 19+19+42

                                   =80

probability of choosing a red or a blue marble = 19+19

P(red or blue ) = 38/80

                        = 0.475

hence the probability of choosing a red or a blue marble is 0.475.

To know more about probability , visit:

https://brainly.com/question/13604758

#SPJ1

Answer: the answer is your mom

Step-by-step explanation:

Answer:

Step-by-step explanation: 720 ways overall , First and Last set = 24 ways, Probability of First and Last happening =130