A class of 32 students earned
grades of A, B, C, or Don a test.
One-fourth of the students earned
an A Half of the remaining students
earned a B. Two students earned a
D. What fraction of the students
earned a C?

Answer:

Step-by-step explanation:

STEP

1

:

           10

Simplify   ——

           x

Equation at the end of step

1

:

                       10

 ((((x4)-(5•(x2)))-6x)-——)-3

                       x

STEP

2

:

Equation at the end of step

2

:

                           10    

 ((((x4) -  5x2) -  6x) -  ——) -  3

                           x      

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  x  as the denominator :

                     x4 - 5x2 - 6x     (x4 - 5x2 - 6x) • x

    x4 - 5x2 - 6x =  —————————————  =  ———————————————————

                           1                    x        

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  x4 - 5x2 - 6x  =   x • (x3 - 5x - 6)

Polynomial Roots Calculator :

4.2    Find roots (zeroes) of :       F(x) = x3 - 5x - 6

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -6.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,3 ,6

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -2.00    

     -2       1        -2.00        -4.00    

     -3       1        -3.00        -18.00    

     -6       1        -6.00        -192.00    

     1       1        1.00        -10.00    

     2       1        2.00        -8.00    

     3       1        3.00        6.00    

     6       1        6.00        180.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

x • (x3-5x-6) • x - (10)     x5 - 5x3 - 6x2 - 10

————————————————————————  =  ———————————————————

           x                          x        

Equation at the end of step

4

:

 (x5 - 5x3 - 6x2 - 10)    

 ————————————————————— -  3

           x              

STEP

5

:

Rewriting the whole as an Equivalent Fraction

5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  x  as the denominator :

        3     3 • x

   3 =  —  =  —————

        1       x  

Checking for a perfect cube :

5.2    x5 - 5x3 - 6x2 - 10  is not a perfect cube

Trying to factor by pulling out :

5.3      Factoring:  x5 - 5x3 - 6x2 - 10

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -6x2 - 10

Group 2:  x5 - 5x3

Pull out from each group separately :

Group 1:   (3x2 + 5) • (-2)

Group 2:   (x2 - 5) • (x3)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

5.4    Find roots (zeroes) of :       F(x) = x5 - 5x3 - 6x2 - 10

    See theory in step 4.2

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -10.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,5 ,10

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -12.00    

     -2       1        -2.00        -26.00    

     -5       1        -5.00       -2660.00    

     -10       1       -10.00       -95610.00    

     1       1        1.00        -20.00    

     2       1        2.00        -42.00    

     5       1        5.00        2340.00    

     10       1        10.00       94390.00    

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

5.5       Adding up the two equivalent fractions

(x5-5x3-6x2-10) - (3 • x)      x5 - 5x3 - 6x2 - 3x - 10

—————————————————————————  =  ————————————————————————

            x                            x            

Polynomial Roots Calculator :

5.6    Find roots (zeroes) of :       F(x) = x5 - 5x3 - 6x2 - 3x - 10

    See theory in step 4.2

In this case, the Leading Coefficient is  1  and the Trailing Constant is  -10.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,2 ,5 ,10

Let us test ....

  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -9.00    

     -2       1        -2.00        -20.00    

     -5       1        -5.00       -2645.00    

     -10       1       -10.00       -95580.00    

     1       1        1.00        -23.00    

     2       1        2.00        -48.00    

     5       1        5.00        2325.00    

     10       1        10.00       94360.00    

Polynomial Roots Calculator found no rational roots

Final result :

 x5 - 5x3 - 6x2 - 3x - 10

 ————————————————————————

            x            

====================================================

Explanation:

The variable n is a placeholder for a number. Specifically some positive number. Let's say that n = 50. This means Eric biked 50 miles last year.

That would mean in total he biked 50+457 = 507 miles overall over the two years.

Since we don't know what n is, we don't replace it with 50. So we just keep n as it is. We would keep it as n+457

Once, or if, we find out the value of n, then we can replace that letter with that number.

Answer:

all i think

Step-by-step explanation:

because you just do the math 3 times 3 five times and do the same with the next

Answer: 14.

Step-by-step explanation:

Answer:

$280 in 40 hours!

(Just multiply)

Answer:

This is correct

Step-by-step explanation:

7.00 multiplied by 2 on both sides will give you an equivalent answer which is 140 and 40 hours. good job!

Answer:

There will be 11 graduation programs in partially filled box.

Step-by-step explanation:

It is given that:

Number of graduation programs need to be shipped = 419

Number of programs in each box = 24

Number of boxes = [tex]\frac{419}{24}[/tex]

Number of boxes = [tex]17\frac{11}{24}[/tex]

Here,

17 is the number of full boxes and 11 is the remainder.

Therefore,

There will be 11 graduation programs in partially filled box.

Answer:

11

Step-by-step explanation:

hope this helps plz mark brainliest

The function of the graph of a translation of the graph of f(x) = x shifted 5 units to the right is g(x) = x - 5, so option B is correct, the graph is also attached below.

When a function from one set to the other is utilized, every element of X receives precisely one element of Y. The function's domain and co-domain are collective terms used to refer to the sets X and Y, respectively.

Given:

f(x) = x, shifted 5 units to the right

A translation is a change in the graph's direction, either horizontally or vertically, parallel to the -axis.

Here, the translation is of 5 units,

Thus, the new function will be,

g(x) = x - 5

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Answer:

17.) D

18.) C

19.) B

Step-by-step explanation:

Answer: 45

Step-by-step explanation: 160-115= 45 you do this because the angles are across the vertex from each other.

Answer:

X=45

Step-by-step explanation:

Method 1 ( the long one)

So AED and CEB are vertical angles, that means that the are the same and have the same value.

So 115 plus x equal 160.

                            115 + x = 160

from there we just have to subtract 115 from both sides to get x by itself.

                            115 + x = 160

                           -115         -115

                       _________________

                                   x=45

Method 2 (short one

If you know that those are vertical angles, then just subtract 115 from 160 and there you go. You get 45.

Answer:

The jacket increase by 25% in price.

Step-by-step explanation:

Given that:

Sale price of jacket = $210

New cost of jacket = $262.50

Change = New cost - Sale price

Change = 262.50 - 210 = $52.50

Percent increase = [tex]\frac{Change}{Sale\ price}*100[/tex]

Percent increase = [tex]\frac{52.50}{210}*100[/tex]

Percent increase = 0.25 * 100

Percent increase = 25%

Hence,

The jacket increase by 25% in price.

Answer:

Step-by-step explanation:

Answer:

5 (3x + 6y - 2)

Step-by-step explanation:

GCF is 5. Sorry late response

Answer:

Step-by-step explanation:

You have  to do total ratio

that will give you 20/15

Answer:

m

Step-by-step explanation:

The ratio 5 : 13 in this situation represents number of Lilies to the number of tulips and zinnias in Myra's flower bed.

A ratio shows us the number of times a number contains another number.

Given that Myra’s flower bed has three types of flowers. There are 7 lilies, 5 tulips, and 6 zinnias. Therefore, the ratio of number of Lilies to the number of tulips and zinnias are,
Ratio = Number of Lilies : Number of tulips and zinnias
Ratio = 5 : (7+6)

Ratio = 5 : 13

Hence, the ratio 5 : 13 in this situation represents number of Lilies to the number of tulips and zinnias.

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Answer:

it would be C

Step-by-step explanation:

because she had a 50/100 percent chance to get potato chips rather than pretzels.

Answer:

d is 6,6 and 4,is -94 and plus 8

Step-by-step explanation:

(-2, -4.5)

Second answer down

The price of the movie itself is $19.99.

19.99 x 6% = 1.1994

19.99 + 1.1994 = 21.1894

Answer: $21.19

The equivalent of the expression, 35 (8 – 3)  is (35 × 8 ) - (35 × 3). The answer is C.(35 × 8) – (35 × 3)

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation.

Therefore, let's simplify the expression to the its' equivalent as follows:

Hence,

35 (8 – 3) = 35(5) = 175

Therefore,  the equivalent is as follows:

35 (8 – 3)

Open the bracket by multiplying as follows;

35 (8 – 3)  = (35 × 8 ) - (35 × 3)

The correct option is C. (35 × 8) – (35 × 3)

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Answer:

$6.16

Step-by-step explanation:

Answer:

Caramels=$16.24

Milk chocolate=$22.40

All together= $29.04

Step-by-step explanation:

Answer:

Step-by-step explanation:

The equation of a circle with center at  [tex]C(-2, 7)[/tex]  and Point [tex]P(1, 11)[/tex] will be   [tex](x+2)^2+(y-7)^2=25[/tex] .

What is equation of a circle ?

Equation of a circle is written in the form [tex](x-h)^2+(y-k)^2=r^2[/tex] where [tex](h,k)[/tex]   is the center and  [tex]r[/tex]  is the radius.

We have,

Center at  [tex]C(-2, 7)[/tex]

i.e. [tex]h=-2[/tex], [tex]k=7[/tex],

And

Point [tex]P(1, 11)[/tex]

i.e. [tex]x=1[/tex], [tex]y=11[/tex]

Now,

To determine Radius of the circle;

[tex]r^2=(x-h)^2+(y-k)^2[/tex]

[tex]r^2=(1-(-2))^2+(11-7)^2[/tex]

[tex]r=\sqrt{3^2+4^2} =\sqrt{25}[/tex]

[tex]r=5[/tex]

So, radius of the circle is [tex]5[/tex] .

Now,

Equation of a circle ;

[tex](x-h)^2+(y-k)^2=r^2[/tex]

[tex](x-(-2))^2+(y-7)^2=5^2[/tex]

[tex](x+2)^2+(y-7)^2=25[/tex]

So, the Equation of a circle is  [tex](x+2)^2+(y-7)^2=25[/tex] .

Hence, we can say that the equation of a circle with center at  [tex]C(-2, 7)[/tex]  and Point [tex]P(1, 11)[/tex]  is   [tex](x+2)^2+(y-7)^2=25[/tex] .

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The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . i think the answer is this

Answer:

8/25

Step-by-step explanation:

To change 32% to a fraction:

Divide 32% by 100%, obtaining 0.32

This 0.32 is equivalent to 32/100, which in turn is equivalent to 8/25.

Answer:

2

Step-by-step explanation:

[tex]x^{3} =8\\x=\sqrt[3]{8} \\x=2[/tex]

use your calculator

Answer:

Step-by-step explanation:

HAHAHAHAHA! NOT IN THE MOOD!

Answer:

You have $360.

Step-by-step explanation:

Answer:

$13 + $10 +$30 +($100 x 3) + $7 = $360

Step-by-step explanation:

i hope this helps! Have a nice day!