The scores on a statistics test had a mean of 81 and a standard deviation of 9. One student was absent on the test day, and his score wasn’t included in the calculation. If his score of 84 was added to the distribution of scores, what would happen to the mean and standard deviation?.

The area of the triangle is  5√11 cm²

The area of a triangle can be found as follows:

area of a triangle = 1 / 2 bh

where

Therefore,

b = base of the triangle = 2(√6² - 5²) = 2(√36 - 25) = 2√11 cm

h = height of the triangle = 5 cm

area of the triangle = 1 / 2 × 2√11 × 5

area of the triangle = 5√11

area of the triangle =  5√11 cm²

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Answer:

Step-by-step explanation:

Here's why:

64 and 32 are both divisible by 8. 64 / 8 = 8 and 32 / 8 is 4.

So then, we make the denominator 8 and numerator 1.

Answer:a

Step-by-step explanation:a is easy

The amount of butter that Tony needs to put in each cake will be 2.25 cups.

From the information, Tony is making a tiered cake for a party and he use 9 cups of butter from the refrigerator to make 4 cakes.

The amount of butter that he needs to put in each cake will be:.

= Number if cups / Number of cakes

= 9 / 4.

= 2.25 cups

Therefore, the amount of butter that Tony needs to put in each cake will be 2.25 cups.

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Answer:

(2(y-2)+3) (2(y-2)-3)

Step-by-step explanation:

In mathematics, the difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2 = in elementary algebra.

Answer:The answer would be the third one $0.07 per minute

it is given in question that Tanners parent give him x dollars per month plus 20% extra in February therefore the amount become 0.2x

What do you mean percentage?

percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity.

Tanner's parents give him x dollars per month  for his allowance.

however, since his birthday is in february

he gets an extra 20% bonus that month.

pick all the expressions that represent how much tanner's allowance is in february month

20% = 20/100

       = 2/10

        =1/5

         = 0.2

since it is given in question that Tanners parent give him x dollars per month plus 20% extra in February

therefore the amount become 0.2x

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The sequence of transformations that maps triangle DEF into triangle ABC is:

A 90º rotation about point F, then a translation along the directed line segment FC.

Transformations in the graph of a function are classified as follows:

For this problem, we have that:

Thus the correct sequence is given by Sequence B.

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The equation of the line is y=2x+15.

Given point (1,17) and the slope m=2

The universal equation for any straight line is y=mx+c. m is the line's slope, and c is the y-intercept.

To find the equation of the line formulae is [tex](y-y_{1})=m(x-x_{1})\\[/tex]

Here, m=2 , [tex]x_{1}=1 \\[/tex] and [tex]y_{1}=17[/tex]

substituting the values we get

y-17=2(x-1)

y-17=2x-2

y=2x+15

Therefore, The equation of the line is y=2x+15.

The equation of line is an algebraic representation of a set of points in a coordinate system that form a line. The several points in the coordinate axis that form a line are represented as a set of variables x, y to build an algebraic equation known as an equation of a line. We can use the equation of any line to determine if a given point is on the line or not.

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For Maritza to keep her average of 12 points, she needs 14 points in her subsequent game.

An individual data set's mean is its average. The concept of mean informs us of the quantity of data in its entirety.

In other words, this same deviation of data from across all data sets is built on the mean.

Mean = sum of data / Number of data

points given for the 6 games:

11,12,10,8,14 and 15

Let's say this same point in the seventh game is x, keeping the average at 12.

The average for the 7th game is.

(11 + 12 + 10 + 8 + 14 + 15 + x )/7 = 12

(70 + x )/7 = 12

70 + x = 84

x = 24

For Maritza to keep her average of 12 points, she needs 14 points in her subsequent game.

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The quotient of the expression is 4x+1.

An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined

Given:

The expression is

[tex](4x^{2} - 7x - 2) / (x-2)[/tex]

By long division method the following steps are :

Divide the tens column dividend by the divisor. Then Multiply the divisor by the quotient in the tens place column ,Subtract the product from the divisor then at last Bring down the dividend in the ones column and repeat.

We have to find the quotient of the expression.

According to given question we have

[tex](4x^{2} - 7x - 2) / (x-2)\\\\=(x-2)(4x+1)/(x-2)\\\\=4x+1[/tex]

Therefore, the quotient of the expression is 4x+1.

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Answer:

Step-by-step explanation:

Es de dividir 8/5 entre los 4 niños, tipo:

8/5 ÷ 1/4 =8/20 esto sale de multiplicar 8x1 y 4x5 debido a que cuando divides fracciones, se multiplican los factores.

Luego 8/20 se simplifica dividiendo todo por 4 y queda 2/5 que es el resultado.

Respuesta: Cada niño comió 2/5

Espero te sirva!

The price that would yield maximum revenue is $260  and maximum revenue is $1,690,000

What is the revenue function?

The fact that total revenue of  the company is the price per purse multiplied by the number of purses sold, means that the revenue modelled function is simply price multiplied by the quantity sold as shown below:

R(x)=P*x

R(x)=Px

R(3000)=$400*3,000

R(3000)=$1200,000

Note for every 500 more purses, the price reduces by $20

R(3500)=$380*3,500

R(3500)=$1,330,000

R(4000)=$360*4000

R(4000)=$1,440,000

R(4500)=$340*4500

R(4500)=$1,530,000

R(5000)=$320*5000

R(5000)=$1,600,000

R(5500)=$300*5500

R(5500)=$1,650,000

R(6000)=$280*6000

R(6000)=$1680,000

R(6500)=$260*6500

R(6500)=$1,690,000

R(7000)=$240*7000

R(7000)=$1,680,000

The total revenue fell at 7,000 purses, which means that the maximum revenue is $1,690,000 at 6500 purses

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The solution to the absolute value inequality is 5.6 ≤ x ≤ 6.4.

Let's represent the weight of the bag of chips as "x" (in ounces). The bag is allowed to go on the market if its weight is within 0.4 oz of 6 oz.

An absolute value inequality that models this situation is:

| x - 6 | ≤ 0.4

Now, let's solve the inequality:

1. x - 6 ≤ 0.4

  Add 6 to both sides:

  x ≤ 6.4

2. x - 6 ≥ -0.4

  Add 6 to both sides:

  x ≥ 5.6

The solution to the absolute value inequality is 5.6 ≤ x ≤ 6.4. This means the weight of the bag of chips must be between 5.6 ounces and 6.4 ounces (inclusive) to be allowed on the market.

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[tex]a_n = 4+ (n-1)(-7)[/tex]  is the explicit formula for the sequence | a₁ = 4

| an = an-1 - 7

We have given [tex]a_1 = 4[/tex]

If [tex]a_n = a_{n-1} - 7[/tex]

Then, [tex]a_2 = a_{(2-1)} - 7[/tex]

⇒ [tex]a_2 = a_1 - 7[/tex]

⇒ [tex]a_2 = 4 - 7[/tex]

⇒ [tex]a_2 = -3[/tex]

Now, common difference (d) = [tex]a_2 - a_1[/tex] = -3 - 4 = -7

The explicit formula for arithmetic sequence is expressed as

[tex]a_n = a+ (n-1)d[/tex]   Where a is the 1st term, [tex]a_n[/tex] is the nth term and d is the common difference.

With given information explicit formula:

[tex]a_n = 4+ (n-1)(-7)[/tex]

Without expressing the other terms of the sequence, explicit formulas are always utilized to represent any term of the sequence. The word "explicit" means something that may be found directly without having to know the other phrases in the sequence.

A single formula, known as the explicit formula, can be used to describe each term in a series in an individual way. Without knowing the prior term in the series, the explicit formula makes it simple to locate any term. The explicit formulas for various sequences are provided here:

An = a + (n - 1) d, where a is the first term and d is the common difference, an is the arithmetic sequence.

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Answer:

17/35, 18/35

Step-by-step explanation:

Find the common denominator to add those fractions together.

5 x 7 = 35 so the common denominator is 35. 1 x 7 is 7 so 1/5 is 7/35. 2 x 5 is 10 so 2/7 is 10/35.

10/35 + 7/35 = 17/35

They ate 17/35.

35/35 - 17/35 = 18/35

18/35 remains.

To solve this problem, simply add the fractions!

To add fractions, you must follow a rule called the Common Denominator Rule. Unlike multiplication and division of fractions, wehre the denominator can be a different number, you must convert your denominators to the same number in order to subtract or add fractions.

A common factor of [tex]\frac{1}{5}[/tex] and  [tex]\frac{2}{7}[/tex] is 35 as 5 ×7 = 35

Multiply the numerator and denominator of 1/5 by 7: [tex]\frac{(1)(7)}{(5)(7)}= \frac{7}{35}[/tex]

Multiply the numerator and denominator of 2/7 by 5: [tex]\frac{(2)(5)}{(7)(5)} =\frac{10}{35}[/tex]

Now add [tex]\frac{7}{35} + \frac{10}{35}[/tex] = [tex]\frac{17}{35}[/tex] : They ate [tex]\frac{17}{35}[/tex] of the bag

To find what fraction of the bag remains, subtract what they ate from 1.

*1 can also be written as [tex]\frac{35}{35}[/tex]*

[tex]\frac{35}{35} -\frac{17}{35} = \frac{18}{35}[/tex]

18/35 of the bag remains

Answer: The total cost of the fences=$165.6

Step-by-step explanation:

Let a = the length of the side if the square.

The perimeter of the square is 60 ft

                                   4a = 60ft

divide both sides by

                                  4a = 60/4

                                    a = 15 ft

The garden is surrounded by two fences, one fence is around the perimeter of the garden, whereas the second fence is 3 feet from the first fence on the outside

Expand to get:

                               4*a + 4(a + 2*3)

Replace a with 15 to get:

                         =  4*15 + 4(15 + 6) 60 + 4(21) 60+84

                         = 144ft

The cost of the fence is $1.15 per foot

The cost of 144 ft fence will be:

                       = 144*1.15

                       = $165.6

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The value of x and y can be written as x=y=3. Therefore, the value of both x and y is equal to 3.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given the two the system of equations as follows,

y = x

2x + 3y = 15

Now, if we substitute the value of y from the first equation in the second, then we can write,

2x + 3y = 15

2x + 3x = 15

5x = 15

x = 15/5

x = 3

Therefore, the value of x and y can be written as x=y=3.

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The solution of the expression (d-6)(2e-3)+(d-6)(e+1) is 3de -18e -2d + 12 .

According to the given question.

We have an expression (d-6)(2e-3)+(d-6)(e+1).

Here, we have to find the solution of the given expression.

As we know that, an action or process of solving a problem.

Therefore, the solution of the expression (d-6)(2e-3)+(d-6)(e+1) is given by

(d-6)(2e-3)+(d-6)(e+1)

= 2de -12e -3d + 18 + de -6e + d - 6            (by distributive rule)

= 3de -18e -2d + 12

Hence, the solution of the expression (d-6)(2e-3)+(d-6)(e+1) is 3de -18e -2d + 12 .

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Answer:

i hope this is the answer

Step-by-step explanation:

Answer:

3.75 miles per hour

Step-by-step explanation:

Diane is walking 2.5 miles in 40 minutes.

2.5/40 = 0.0625 miles per minute

There are 60 minutes in an hour.

0.0625 * 60 = 3.75

Diane is walking at a speed of 3.75 miles per hour.

Here, we have to calculate the walking speed of Diane in miles per hour, we need to convert the time from minutes to hours since the walking distance is given in miles.

Diane walks 2.5 miles in 40 minutes.

To convert 40 minutes to hours, we divide by 60 (since there are 60 minutes in an hour):

40 minutes ÷ 60 = 2/3 hours

Now, we can calculate Diane's walking speed (or rate) in miles per hour:

Diane's walking speed = Distance / Time

Diane's walking speed = 2.5 miles / (2/3) hours

To divide by a fraction, we can multiply by its reciprocal:

Diane's walking speed = 2.5 miles * (3/2) hours

Now, simplify:

Diane's walking speed = 7.5 miles / 2 hours

Finally, divide:

Diane's walking speed = 3.75 miles per hour

So, Diane is walking at a speed of 3.75 miles per hour.

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The value of input are {1, 2, 3, 4, 5}.

The value of output are {4, 5}.

What is Coordinates?

A pair of numbers which describe the exact position of a point on a cartesian plane by using the horizontal and vertical lines is called the coordinates.

The points are given as;

{(1, 5) , (2, 4) , (3, 5) , (3, 4) , (4, 4) , (5, 5)}

Now, All points are shown in graph.

Clearly, The input of points are,

x = {1, 2, 3, 4, 5}.

And, The output of points are,

y = {4, 5}

So, The value of input are {1, 2, 3, 4, 5}.

The value of output are {4, 5}.

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The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

Let the actual width of the picnic area be x yards.

According to the given question.

Laura measured a picnic area near the river and made a scale drawing.

The scale she used was 3 inches : 2 yards.

⇒ The scale is 3 inches : 2 yards

The width of the picnic area in the drawing is 90 inches.

As we know that, a proportion is a fraction of a total amount, and the measures are related using a rule of three.

Thereofore, the acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards is given by

3inches : 2 yards = 90inches : x

⇒ 3x = 180

⇒ x = 60yards

The acutal width of the picnic area by using proportion if the scale used is 3 inches : 2 yards will be 60 yards.

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The computation is that the width is 21.5 feet and the height is 12.5.

Let the height = h

Let the width = (3 × h) - 16 = 3h - 16

Therefore, the dimensions will be:

h + 3h - 16 = 34

4h = 34 + 16

4h = 50

Divide

h = 50/4

h = 12.5

Therefore width = 3h - 16 = 3(12.5) - 16

= 37.5 - 16

= 21.5

The width is 21.5 feet and the height is 12.5.

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The given function is not the odd function.

According to the statement

We have to find about the odd function.

So, For this purpose, we know that the

The odd function is that the function f is odd if the subsequent equation holds for all x and −x within the domain of f : −f(x)=f(−x) − f ( x ) = f ( − x ) Geometrically, the graph of an odd function has rotational symmetry with relevance the origin, meaning that its graph remains unchanged after a rotation of 180∘ about the origin.

From the given information:

dimetri says that a function that's fabricated from terms where the variable is raised only to an odd power are going to be an odd function

Then

Algebraically, an odd function is one where f(-x) = -f(x). this suggests that if we substitute -x for each x within the function, it should be the identical as switching every sign up the function. This doesn't always work.

For example, if f(x)=x³+7:

f(-x)=(-x)³+7=-x³+7.

However, since the 7 did not become -7, it is not the same as -f(x), so it is not an odd function.

So, The given function is not the odd function.

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The number of distinct values that we can draw(with replacement) is;

=  [tex]\frac{ ((2n-1)!)}{ n!(n -1)! }[/tex]

Here,

The given set is = {1, 2, 3, ……, n}

n number of drawn from this set with replacement.

Then we have to find number of distinct values that we can draw.

What is combination?

The field of mathematics concerned with problems of selection, arrangement, and operation within a finite or discrete system.

Now,

The given set is = {1, 2, 3, ……, n}

n number of drawn from this set with replacement.

Since, we know we draw p things from q with replacement then

Number of ways =  [tex]^{p+q-1} C_q[/tex]

Here number of element in the set = n

And number of element we have to draw with replacement = n

Therefore, number of distinct values that we can draw

= [tex]^{n+n-1} C_n[/tex]

= [tex]^{2n-1} C_n[/tex]

= [tex]\frac{(2n-1)!}{n!(2n -1 - n)!}[/tex]

=   [tex]\frac{((2n-1)!)}{n!(n -1)!}[/tex]

Hence, The number of distinct values that we can draw(with replacement) is;

=  [tex]\frac{ ((2n-1)!)}{ n!(n -1)! }[/tex]

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54.5 % students got failed

• Percentage in mathematics is defined as the number or ratio which can be expresses as a fraction of 100. If we want to calculate the percent of the number, we need to divide the number by the whole and multiply by 100.

• Percentage are dimensionless quantity. Percentage means pert per hundred. Percentage can also be represented in fraction form such as 0.5% or 0.25%.

• For example Prince got 98% marks in Maths which means that he has scored 98 marks out of 100.

According to the Question

Number of boys = 1100

Number of girls = 900

%age of boys passed = 50%

%age of girls passed = 40%

No of boys failed = ((100-50)*1100)/100

= 550

No of girl failed = ((100-40)*900)/100

= 540

Total number of students =1100+900 = 2000

Total number of students failed = 1090

Percentage  of students failed = 1090/2000 *100 = 54.5

54.5 % students got failed

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Answer: (-4.5,-3)

Step-by-step explanation:

                  (-9,-2)    (9,-6)    1:3

      [tex]\displaystyle\\\boxed {x=\frac{x_1+\lambda x_2}{1+ \lambda} \ \ \ \ \ \ y=\frac{y_1+\lambda y_2}{1+\lambda} }[/tex]  

[tex]\displaystyle\\x_1=-9\ \ \ \ x_2=9\ \ \ \ \ y_1=-2\ \ \ \ \ \ y_2=-6\ \ \ \ \ \lambda=1:3=\frac{1}{3} \\\\x=\frac{-9+(\frac{1}{3})(9) }{1+\frac{1}{3} } \\\\x=\frac{-9+3}{\frac{(1)(3)+1}{3} } \\\\x=\frac{-6}{\frac{3+1}{3} } \\\\x=\frac{(-6)(3)}{4} \\\\x=\frac{-18}{4}\\\\x=-4.5 \\\\y=\frac{-2+(\frac{1}{3} )(-6)}{1+\frac{1}{3} } \\\\y=\frac{-2+(-2)}{\frac{4}{3} } \\\\y=\frac{(-4)(3)}{4} \\\\y=-3\\Thus,(-4.5,-3)[/tex]

The answer of the given inequality is 5/2<x<5

To solve this given inequality we need to 1st understand what is inequality then we will be easily able to solve this sum.

It is a relationship between inequal values. the word inequality means not equal. to compare the values whether it is less or greater than then different inequalities are used. We can easily identify when an equation is called an inequality equation when we will see the sign ≤ , ≥ ,< ,>. This sign means that the expression is an inequality.

Here in the sum we will be solving the equation in two parts in the 1st part we will be taking the  part 2x<4x-5 and in the 2nd part we wil take the equation 4x-5<15

On solving the 1st part :

∴ 2x<4x-5

=> 2x-4x<-5

=> -2x<-5

=> 2x>5     [Multiplying boyh sides by minus sign]

=> x>5/2

On solving the 2nd part :

∴ 4x-5<15

=> 4x<15+5

=> 4x<20

=> x<5

So on solving the inequality we got that  5/2<x<5

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