Student work
TRY IT #1
Write each of the following as a rational number.
b. 3
c-4

Answer:

$7.80

Step-by-step explanation:

Find the cost to download 1 song. Divide 6 from 4.68

4.68/6 = 0.78

Each song costs $0.78.

Find the amount 10 songs cost. Multiply 0.78 with 10:

10 x 0.78 = 7.80

$7.80 is your answer.

~

Hi

6 = 4.68

10 = X

X = 10*4.68 /6

X = 46.8/6

X = 7.8

Step-by-step explanation:

Hey, there!!

I hope you mean to subtract (-137) +(-43) from sum of -103 and 27.

First, add -103 + 27

[tex] = - 103 + 27[/tex]

[tex] = - 76[/tex]

{As ( minus + plus )= subtracts with sign which has greator value. }

now,

[tex]( - 137) + ( - 43) = - 180[/tex]

{ minus + minus = add with minus sign}.

Now, subtracting -180 from -76.

=(-76) - (-180 )

Now, multiply the sign (- × -)= +

so, -180 becomes +180

= -76+180

= 104..... is answer.

Hope it helps...

Answer:

104

Step-by-step explanation:

With what you provide, the expression would be:

[tex](-103+27)-(-137+-43)[/tex], which equals to:

[tex](-76)-(-180)= (-76)+(180)=104[/tex].      [negative minus a negative equals positive]

So, the answer would be 104.

Answer:

Hey there!

The coordinates of the point Q are (0, 2)

Let me know if this helps :)

Answer:

8.25

Step-by-step explanation:

[tex]\frac{8r^2 - 14 r + 3}{r+5} = 4r -1[/tex]

[tex]8r^2 - 14r + 3= (4r -1)(r + 5)[/tex]

[tex]8r^2 - 14r + 3= 4 {r}^{2} + 19r - 5[/tex]

[tex]4 {r}^{2} - 33r + 8=0[/tex]

[tex]4 {r}^{2} - 32r - r + 8 = 0[/tex]

[tex]4r(r - 8) - 1(r - 8) = 0[/tex]

[tex](4r - 1)(r - 8)[/tex]

[tex]r = 8 \: or \: \frac{1}{4} [/tex]

Therefore the sum of all values of r

[tex]8 + \frac{1}{4} = 8 \frac{1}{4} [/tex]

Answer:

10

Step-by-step explanation:

The most number of questions answered correctly are 10 and 11.

The typical number of questions a student answered correctly can be represented by the middle most value that is common to the data set.

If the data set is distributed evenly, the median, or the middle most value will fall on the 15th and 16th dots, which represents 10 correct correct challenge questions answered.

The typical number is 10.

Answer:

[tex]10[/tex]

Answer:

C

Step-by-step explanation:

The definition of a limit is the value a function it is approaching as the limit approaches a certain point.

We have the limit:

[tex]\lim_{x\to3} f(x)=5[/tex]

In other words, the value of f(x) as x approaches 3 approaches 5.

We do not care what happens at x=3. Rather, the limit tells us that as x approaches or gets closer to x=3, the function f(x) gets closer to 5.

Thus, the correct answer is C.

Hello, please consider the following.

We will multiply the numerator and denominator by

[tex]4+\sqrt{6x}[/tex]

to get rid of the root in the denominator.

First of all, we cannot divide by 0, right? So, we need to make sure that the denominator is different from 0.

[tex]4-\sqrt{6x} =0<=>\sqrt{6x}=4\\\\\text{Take the square}\\\\6x=4^2=16\\\\x=\dfrac{16}{6}=\dfrac{8}{3}[/tex]

We need to take any x real number different from 8/3 then and simplify the expression.

Let's do it!

[tex]\begin{aligned}\dfrac{4}{4-\sqrt{6x}}&=\dfrac{4(4+\sqrt{6x})}{(4+\sqrt{6x})(4-\sqrt{6x})}\\\\&=\dfrac{4(4+\sqrt{6x})}{(4^2-\sqrt{6x}^2)}\\\\&=\dfrac{4(4+\sqrt{6x})}{(16-6x)}\\\\&=\dfrac{2(4+\sqrt{6x})}{(8-3x)}\\\\&\large \boxed{=\dfrac{8+2\sqrt{6x}}{8-3x}}\end{aligned}[/tex]

Thank you

Answer:

D) 89.6 %

Average  or mean of the given data = 89.6 %

Step-by-step explanation:

Step(i):-

Given data

        X      :     82        100        84

P(X=x)       :    0.40      0.40     0.20

Step(ii)

Let 'X' be the discrete distribution

Mean of the discrete distribution = ∑ x P( x=x)

                                                       = 82 ×0.40 +100 ×0.40 +84 ×0.20

                                                       = 89.6

Final answer:-

Average of the given data = 89.6 %

Answer:

V = 150π units^3

Step-by-step explanation:

The volume of this cylinder is V = πr²h = π(5 units)^2·(6 units), or

V = 150π units^3

The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.

The volume of a solid is the total space it contains in the three-dimensional space.

The volume of a cylinder can be given by the formula,

V = πr²h cube units,

where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

In the question, we are asked to find the volume of the cylinder shown in the figure.

The cylinder has a base radius (r) of 5 units, and height (h) of 6 units.

So, we can find its volume using the formula,

V = πr²h cube units,

where V is the volume, r is the radius of the base of the cylinder, and h is the height of the cylinder.

∴ The volume of the cylinder = π(5²)6 cube units

or, the volume of the cylinder = π*25*6 cube units

or, the volume of the cylinder = 150π cube units

or, the volume of the cylinder = 150*3.14 cube units = 471 cube units.

∴ The volume of the given cylinder as shown in the diagram is 150π cube units or 471 cube units.

Learn more about the volume of the cylinder at

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Answer: B

Step-by-step explanation:

a is negtive  bcs grph opens down. h value is -1 and k is +2

Answer:

1. 40 % is 40 / 100

by cancelling it the output is 2 /5

2. 35% is 35 / 100

7 / 20 is your answer

plz brainlist me and follow me

The translation of the given graph has done in two steps.

1. Horizontal shift of 5 units to the left

2. Vertical shift of 4 units in the downwards direction.

"The translation of a graph is its rigid movement, vertically or horizontally."

The given translation of graph is:

[tex]y = (x - 6)^{2} + 7[/tex] to [tex]y = (x - 1)^{2} + 3[/tex]

Here, two types of translation has done to the first graph.

1. First of all, there is a horizontal shift of 5 units to the left has done.

[tex]y = (x - 6)^{2}[/tex] ⇒ [tex]y = [(x - 1) - 5)]^{2}[/tex]

2.After that, there is a vertical shift of 4 units in the downwards direction.

[tex]y = (x - 6)^{2} + 7[/tex]  ⇒ [tex]y = (x - 1)^{2} + 3[/tex]

Learn more about the translation of a graph here: https://brainly.com/question/12982455

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Answer:

50

Step-by-step explanation:

Ratio is

Total number is

Since F type pencils number is known:

Then total number is:

Answer:

0

Step-by-step explanation:

Hello!

To solve this we put in the values given to us for x and go till we get one this is true.

The values given for x are -0.5, 0, and 1

                 1                  

5 + 1 - 12 = 2(1) - 7

Combine like terms

-6 = -5

Since -6 does equal -5 the answer is not 1

                 0                  

5 + 0 - 12 = 2(0) - 7

Combine like terms

-7 = -7

Since -7 equals -7 the answer is 0

Hope this Helps!

Answer:

[tex]\huge \boxed{\mathrm{12}}[/tex]

Step-by-step explanation:

R is a point on the line segment QS.

QR = 2

RS = 10

QS = 2 + 10

QS = 12

The length of the line segment QS is 12 units.

Given that, point R is on the line segment QS. Given QR =2 and RS = 10.

We need to determine the length of QS.

A line segment is a part of a line that has two endpoints and a fixed length. It is different from a line that does not have a beginning or an end and which can be extended in both directions.

Here, since R is in between QS, QS=QR+RS

=2+10=12 units

Therefore, the length of the line segment QS is 12 units.

To learn more about the line segment visit:

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Answer:

the 2 is in the hundreds and hundredths place

Answer:

ŷ = 6.69X - 706.18 ; ŷ = 270.56 ; B. The predicted value is not close to the actual diastolic reading.

Step-by-step explanation:

Systolic reading(x) :

117

134

150

113

138

113

144

145

Diastolic (y) :

85

74

86

55

75

80

106

841

Using the online regression calculator, the regression equation obtained using the data values provided above is:

ŷ = 6.69X - 706.18

Comparing with the regression equation formula: ŷ = mX + c

Where :

ŷ = predicted variable (Diastolic)

m = 6.69 = gradient or slope of the regression line

c = - 706.18 = intercept ( where the regression line intersects the y-axis).

2.) What is the best predicted diastolic pressure for a person with a systolic reading of 146

X = 146

ŷ = 6.69(146) - 706.18

ŷ = 976.74 - 706.18

ŷ = 270.56

The predicted value, 270.56 is not close to the actual Diastolic reading of 91.0

Answer: There is no x-intercept for this quadratic equation.

Step-by-step explanation:

An x-intercept is when the y-value of the point if equal to zero. There is no x-intercept for this quadratic equation. This can be supported by the fact that this equation cannot be factored.

Answer:

4

Step-by-step explanation:

y = 4x + 12

In y = mx+b

The coefficient of x (m) is the slope.

So the slope is 4

Answer:

The slope is 4

Step-by-step explanation:

y = 4x +12

This is in slope intercept form

y = mx+b where m is the slope and b is the y intercept

The slope is 4 and the y intercept is 12

Step-by-step explanation:

first you group like terms.

-3s-s+8+1-2

-4s+7

Answer:

-4s + 7

Step-by-step explanation:

We need to combine like terms. Like terms are terms whose variables (and exponents) are the same (note that they could be constants as well). Basically, they are "like" each other. In this case, the like terms are -3s and - s and also 1, 8, and -2. -3s - s = -4s and 1 + 8 - 2 = 7 so the answer is -4s + 7.

Answer:

So Jeff is faster with 7 km per hour

Step-by-step explanation:

Jeff says I can run 7 kilometers per hour!

Cameron says "I can run 100 meters per minute!!

To actually know which one of them is the fastest we will convert their speed to be in the same unit

Let's convert meters per minute to kilometers per hour

100 meters per minute= 100 M/m

100 meters per minute= 100 *60/1000

100 meters per minute= 6000/1000

100 meters per minute= 6 km /h

100 meters per minute= 6 kilometers per hour

So Jeff is faster with 7 km per hour

Answer:

Jeff is faster than Cameron. Khan Academy

Step-by-step explanation:

Answer:

87 women

Step-by-step explanation:

4x+3x=203

7x=203

x=29

29*3=87 :D

Answer:

y= -5/3x + 8

Step-by-step explanation:

parallel lines have the same slope

5x + 3y = 6

3y = -5x + 6

y = -5/3x + 2

the new line will have the slope (-5/3x)

y = (-5/3x) + b

plug in the (x, y) value to find b

-2 = -5/3(6) + b

-2 = -10 + b

b = 8

your equation is: y= -5/3x + 8

Answer:

7p + 4

Step-by-step explanation:

7p - (-5) + (-1)

7p + 5 -1

7p + 4

Answer:

Step-by-step explanation:

For

The number 30 / 15 belongs to the whole, integer, and rational numbers. the correct option is C.

A numeral system is a way of writing numbers; it's a way of mathematically notating a collection of numbers by utilizing a consistent set of digits or other symbols.

The number set from 0 to infinity are called whole numbers. The number set from negative infinity to positive infinity are called integers.

A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively.

The given number 30 / 15 is in the form of a rational number that can also be written as 2. Then the number 30 / 15 can be the whole, integer, and rational number.

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Answer: B.) 1 and 111 only.

Step-by-step explanation:

75% = 75/100 = 0.75

0.75 falls into the category of rational numbers. Rational numbers comprises of numbers which can be expressed in the form a/b where a and b are integers and B is not 0. Here, both 75 and 100 are integers, thus 75% is a rational number.

Irrational numbers are the opposite of rational numbers thus, 75% is not irrational.

All rational numbers and irrational numbers are REAL numbers, hence, 75% is a real number.

Natural numbers are whole digits starting from 1 e.g ( 1, 2, 3,......). Hence 75% is not a natural number

Whole numbers are natural numbers including 0. (0, 1, 2,.....). Hence, 75% is not a whole number

Integer numbers are comprises of both positive and negative whole numbers. (..., - 1, - 2, 0, 1, 2,...). Hence, 75% is not an integer.

Hey There!!

STEP 1:

1

Simplify ——————————

(4x + 3y)2

Equation at the end of step

(4x-3y) 1

——————————————————————————— ÷ ————————

(((16•(x2))+24xy)+(9•(y2))) (4x+3y)2

STEP 2:

Equation at the end of step

2

:

(4x-3y) 1

——————————————————————— ÷ ————————

(((16•(x2))+24xy)+32y2) (4x+3y)2

STEP 3:

Equation at the end of step

(4x - 3y) 1

—————————————————————— ÷ ——————————

((24x2 + 24xy) + 32y2) (4x + 3y)2

STEP 4:

4x - 3y

Simplify —————————————————

16x2 + 24xy + 9y2

Trying to factor a multi variable polynomial :

4.1 Factoring 16x2 + 24xy + 9y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (4x + 3y)•(4x + 3y)

Detecting a perfect square :

4.2 16x2 +24xy +9y2 is a perfect square

It factors into (4x+3y)•(4x+3y)

which is another way of writing (4x+3y)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Equation at the end of step

4:

(4x - 3y) 1

—————————— ÷ ——————————

(4x + 3y)2 (4x + 3y)2

STEP 5:

4x-3y 1

Divide ———————— by ————————

(4x+3y)2 (4x+3y)2

5.1 Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

4x - 3y 1 4x - 3y (4x + 3y)2

—————————— ÷ —————————— = —————————— • ——————————

(4x + 3y)2 (4x + 3y)2 (4x + 3y)2 1

Canceling Out :

5.2 Cancel out (4x + 3y)2 which appears on both sides of the fraction line.

Final result :

4x - 3y

Hope It Helped!~ ♡

ItsNobody~ ☆

Answer:

The  probability is  [tex]P(14 < X < 20 ) = 0.5354[/tex]  

Step-by-step explanation:

From the question we are told that

   The  proportion that live with their parents is  [tex]\r p = 0.142[/tex]

   The  sample  size is n =  125

Given that there are two possible outcomes and that this outcomes are independent of each other then we can say the Recent census data follows a Binomial distribution

  i.e  

       [tex]X \ \~ \ B( \mu , \sigma )[/tex]

Now the mean is evaluated as

      [tex]\mu = n * \r p[/tex]

      [tex]\mu = 125 * 0.142[/tex]

      [tex]\mu = 17.75[/tex]

Generally the proportion that are not staying with parents is  

      [tex]\r q = 1 - \r p[/tex]

= >    [tex]\r q = 0.858[/tex]

The standard deviation is mathematically evaluated as

     [tex]\sigma = \sqrt{n * \r p * \r q }[/tex]

     [tex]\sigma = \sqrt{ 125 * 0.142 * 0.858 }[/tex]

    [tex]\sigma = 3.90[/tex]

Given the n is large  then we can use normal approximation to evaluate the probability as follows  

     [tex]P(14 < X < 20 ) = P( \frac{ 14 - 17.75}{3.90} <\frac{ X - \mu }{\sigma } < \frac{ 20 - 17.75}{3.90} )[/tex]

Now applying continuity correction

      [tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < \frac{ X - \mu }{\sigma } < \frac{ 19.5 - 17.75}{3.90} )[/tex]

Generally  

    [tex]\frac{ X - \mu }{\sigma } = Z ( The \ standardized \ value \ of X )[/tex]

    [tex]P(14 < X < 20 ) = P( \frac{ 13.5 - 17.75}{3.90} < Z< \frac{ 19.5 - 17.75}{3.90} )[/tex]

     [tex]P(14 < X < 20 ) = P( -1.0897 < Z< 0.449 } )[/tex]

    [tex]P(14 < X < 20 ) = P( Z< 0.449 ) - P(Z < -1.0897)[/tex]

So  for the z -  table  

         [tex]P( Z< 0.449 ) = 0.67328[/tex]

         [tex]P(Z < -1.0897) = 0.13792[/tex]

 [tex]P(14 < X < 20 ) = 0.67328 - 0.13792[/tex]    

  [tex]P(14 < X < 20 ) = 0.5354[/tex]  

Answer:

a). converges

b). diverges

c). converges

Step-by-step explanation:

{ [tex]$ a_n $[/tex] } = { [tex]$ nr^n $[/tex] }

Using radio test,

L = [tex]$ \lim_{n \rightarrow \infty} |\frac{a_n + 1}{a_n}| $[/tex]

   = [tex]$ \lim_{n \rightarrow \infty} |\frac{(n+1)r^{n+1}}{nr^n}| $[/tex]

   = [tex]$ \lim_{n \rightarrow \infty} |(1+\frac{1}{n})^r| $[/tex]

   = [tex]$ \lim_{n \rightarrow \infty} |r| $[/tex]

   = |r|

Therefore, [tex]$a_n$[/tex] converges in |r| < 1

a). r = 1/5

    [tex]$\{ a_n \}= \{\frac{1}{5}, n \}$[/tex]

This sequence is monotonically decreasing and bounded.

0 < [tex]$ a_n $[/tex] < 1

Hence, { [tex]$ a_n $[/tex] } converges.

b). r = 1

    { [tex]$ a_n $[/tex] } = { n }

This sequence is monotonically increasing sequence which is not bounded.

Hence, { [tex]$ a_n $[/tex] } diverges.

c). r = 1/6

[tex]$\{ a_n \}= \{\frac{1}{6}, n \}$[/tex]

This sequence is monotonically decreasing and bounded.

0 < [tex]$ a_n $[/tex] < 1

Hence, { [tex]$ a_n $[/tex] } converges.

For  |r| < 1, the [tex]$a_n$[/tex] converges.