Use the frequency distribution shown below to construct and expand frequency distributions

Answer:

The square root of 36 is 6 8 cube root is 2 125 cube root is 5 The rationalisation of 12 is 2×2×3

The solutions to the given quadratic equation 4x² - 4x - 1 = 0 are x = ( 1 - √2 )/2,  ( 1 +√2 )/2.

A quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

To solve for x, we use the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given the equation in the question;

4x² - 4x - 1 = 0

Compared to the standard form ax² + bx + c = 0

Plug these values into the quadratic formula above.

x = (-b±√(b² - 4ac)) / (2a)

x = (-(-4) ± √((-4)² - ( 4 × 4 × -1 ))) / (2 × 8)

x = ( 4 ± √( 16 - ( -16) ) / (8)

x = ( 4 ± √( 16 + 16) ) / (8)

x = ( 4 ± √( 32) ) / (8)

32 can be written as 4²×2

x = ( 4 ± √( 4²×2 ) ) / (8)

x = ( 4 ± 4√2 ) / (8)

x = ( 1 ± √2 ) / 2

x = ( 1 - √2 )/2,  ( 1 +√2 )/2

Therefore, the solutions to the given quadratic equation 4x² - 4x - 1 = 0 are x = ( 1 - √2 )/2,  ( 1 +√2 )/2.

Learn more about quadratic equations here: brainly.com/question/1863222

#SPJ1

A) In one hour  Graham drove 33 3/4 miles

B) To drive one mile Grahman will take 4/127 hours

a) change into improper fractions

42 1/3 = 127/3

1 1/3 = 4/3

he takes 4/3 hours to drive 127/3 miles

in one hour he will drive 127/3 × 3/4 = 127/4 = 33 3/4 miles

So in 1 hour he will drive 33 3/4 miles

b) he covers 127/3 miles in 4/3 hours

to cover 1 mile he will take = 4/3 × 3/127 = 4/127 hours

Graham will take 4/127 hours to cover 1 mile.

Learn more about time and distance here :

https://brainly.com/question/11465962

#SPJ9

Answer: The value of RIG is 59 degrees and the value of ZIM is 31    degrees.

Given: Lines AM,ZG, RI are parallel

angle RIM = 90 degree and lines AM,ZG and RI intersect at point I.

Concept: All angles on the same line make an angle of 180 degree.

Since all angles on a line make an angle sum of 180 degree

So using the above property of straight lines,

Angle RIA + angle RIG + angle GIM = 180 degree

90 + 4z+7 +x+2 = 180

4z+x = 81  ----- (1)

Angle AIZ + angle AIR + angle RIG = 180 degree

3x-56 + 90 + 4z+7=180

3x +4z =139 ----- (2)

3(81-4z) +4z =139

243 -8z =139

z=13

x= 81- 52 = 29

For more information about angles, visit https://brainly.com/question/25716982

#SPJ9

Answer:

timmy neorons, descaration

Step-by-step explanation:

New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand New Zealand

The decimal form of the fraction 10 / 66 is 0.15.

Fractions represent the parts of a whole or collection of objects.  

In other words fractions are represented as a numerical value, which defines a part of a whole.

Fractions has a numerator and a denominator.

The numerator is at the top while the denominator is below.

A decimal is a number that consists of a whole and a fractional part.

Therefore, let's convert the fractions 10 / 66 to decimal.

Hence,

10 / 66 ÷ 2 / 2 = 5 / 33

Therefore,

5 / 33 = 0.15151515151 = 0.15

learn more on fractions and decimal here: https://brainly.com/question/16370839

#SPJ1

To make a profit Kelsey must make and sell more than 49  additional pendants

in this given sum we need to find how many additional pendents kelsey need to make and sell to make profit .  The information that are give in the sum

she has to pay $200 for the rent

materials for each pendant is $ 7.8 .

for 10 pendants  the total will be 10*7.8 = $78

Therefore she will spend a total of $(78 +200) = $278

So to make a profit the amount of pendants kelsey make multiply it by 13.50 should be greater than the totall amount she spend in making 10 pendants $278 added to the number  of pendants she makes multiply by 7.8 that is the total cost

let the no. of pendants she need to make be x

we can write then above explanation as

13.50x >278 + 7.8x

=> 13.5x - 7.8x > 278 +7.8x - 7.8x      [subtracting 7.8x on both side]

=> 5.7x > 278

=> x > 278/5.7 = 48.77 = 49 (approx.)

Kelsey needs to make more than 49 pendants rto make a profit.

Learn more about linear inequation here

https://brainly.com/question/11173049

#SPJ9

Answer:

83

Step-by-step explanation:

[tex] \frac{ - 332}{ - 4} = 83[/tex]

Answer:

17.04 x 6.2= 105.648

Hope this helps :)

Answer:

Median

Step-by-step explanation:

i think median would be better than mean. This is because with mean, your adding it together then dividing it(by 3 in this case), making the end number higher. tou dont want a higher number in this case.

ex: your numbers are 50, 55,and 90

median = 55 (as it's the middle number)

mean = 65 ( 90+ 55+ 50 / 3)

so median is the lower number, meaning it would be better in this** case.

Answer: The amount less will be with held weekly for federal income tax is $40.65.

Step-by-step explanation:

Given data,

Nico Joven presently earns $348.40 per week.

The amount of money deducted from federal income tax is:

                          = $348.40/2

                          = $174.20

He claims himself and his mother as allowances.

He is single. He is to get a new job classification, which will result in a 15% increase in pay.

The increase in pay will be:

                           = 15% × $348.40

                           = $52.26

After his marriage, he will claim his wife, himself, and his mother as allowances.

The new salary will be the addition which is $400.66.

The new money with held will be:

                            = $400.66/3

                            = $133.55

The amount less withheld will be:

                      = $174.20 - $133.55

                      = $40.65

Therefore,

The amount  less will be with held weekly for federal income tax is $40.65.

Learn more about event correlation here: brainly.com/question/19908153

#SPJ9

Answer:

36.6

Step-by-step explanation:

Answer:

X = 36.5

Z = 19

Angle RIG is 69

angle ZIM is 126.5

Step-by-step explanation:

angle AIZ and ZIP

x + 3x - 56 = 90

    4x - 56 = 90

            4x = 90 + 56

            4x/4 = 146/4

                x  = 36.5

Plugin the value of x in (3x -56)

      3x - 56

     (3(36.5) - 56)

     (109.5 - 56) =  53.5

       Angle AIZ = 53.5

Angle RIG is 4z + 7. Convert the letter x in (x + 2)  to Z and solve for z

4z + 7 + z + 2 = 90

         5z + 9 = 90

                5z = 90 - 9

                5z/5 = 81/5

                   z = 16.2

                        Z + 2

                      16.2 + 2 = 18.2

           Angle GIM is 18.2 degrees

  Plugin the the value of z into 4z + 7 for angle RIG

   4z + 7

   (4(16.2) + 7) = 71.8

 Angle RIG = 71.8 degrees

Using the Empirical Rule, it is found that:

a) 68% of the people have an IQ score between 81 and 119.

b) 0.3% of people has an IQ score less than 43 or greater than 157.

c) 16% of people has an IQ score greater than 119.

It states that, for a normally distributed random variable:

In item a, 81 and 119 are the bounds within 1 standard deviation of the mean, hence 68% of the people have an IQ score between 81 and 119.

In item b, 43 and 157 are the bounds within 3 standard deviations of the mean, hence 0.3% of the distribution is outside this range, that is, 0.3% of people has an IQ score less than 43 or greater than 157.

In item c, considering the symmetry of the normal distribution, the upper 16% has IQ score greater than 119, hence 16% of people has an IQ score greater than 119.

More can be learned about the Empirical Rule at https://brainly.com/question/24537145

#SPJ1

Answer:

Fractional distillation

Step-by-step explanation:

Fractional distillation is the process by which oil refineries separate crude oil into different, more useful hydrocarbon products based on their relative molecular weights in a distillation tower.

By solving a system of equations we conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.

First, let's define the variables we will use to solve this problem:

We know that they want to get 55 ounces, then:

x + y = 55

And the concentration of these 55 ounces must be 16%, then we can write other equation:

0.1*x + 0.2*y = 0.16*55

Then we have a system of equations:

x + y = 55

0.1*x + 0.2*y = 0.16*55

Isolating x on the first equation we get:

x = 55 - y

Now we can replace that in the other equation so we get:

0.1*(55 - y) + 0.2*y = 0.16*55 = 8.8

Now we can solve this for y.

5.5 - 0.1*y + 0.2*y = 8.8

5.5 + 0.1*y = 8.8

y = (8.8 - 5.5)/0.1 = 33

Then the value of x is:

x = 55 - y = 55 - 33 = 22

We conclude that they need to use 22 ounces of the 10% alloy and 33 ounces of the 20% alloy.

If you want to learn more about systems of equations:

https://brainly.com/question/13729904

#SPJ1

The will have to work for 3 weeks in order to save money for down payment of car.

Unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given in the question is a story of john works at the mall, 20 hours a week and makes $8.50 an hour. He is saving for a car and needs a down payment of $500.

Assume that he has to work 'x' number of weeks for down payment.

For 1 hour, John earns → $8.50

Number of hours he work in the mall per week → 20 hours

Amount of money collected in one week → $8.50 x 20 = $170

Money needed for down payment → $500

In 1 week, John earns → $170

So, he earns $1 in → 1 / 170 weeks

Therefore, he will earn $500 in →

(1 / 170) x 500 = 2.94 = 3 weeks (approx.)

Therefore, he will have to work for 3 weeks in order to save money for down payment of car.

To solve more questions on Unitary method, visit the link below-

https://brainly.com/question/14215658

#SPJ1

The expression using factoring is 4 * (33 + 57)

The expression is given as

(132 + 228)

Factor out 2 from the expression

So, we have

(132 + 228) = 2 * (66 + !14)

Factor out 2 from the expression

So, we have

(132 + 228) = 2 * 2 * (33 + 57)

This gives

(132 + 228) = 4 * (33 + 57)

Hence, the expression using factoring is 4 * (33 + 57)

Read more about expressions at:

brainly.com/question/723406

#SPJ1

Answer: 12

Step-by-step explanation: f(-4)= 2-3(-4) which =2+12=14

The side of one side of the square is determined as: 8.5 meters.

A square is a quadrilateral shape that has four sides that have the same length and four interior angles that are right angles (90 degrees).

The perimeter of a square is the sum of all the sides of a square which can be calculated using the following formula given as,:

Perimeter = 4(s), where s represents the length of one side of the square.

We are given that:

Perimeter of the square = 34 meters

Therefore:

34 = 4(s)

Divide both sides by 4

34/4 = 4(s)/4

8.5 = s

s = 8.5 m

Thus, the side of one side of the square is determined as: 8.5 meters.

Learn more about the perimeter of a square on:

https://brainly.com/question/25092270

#SPJ1

The percent of total inventory is Apple, rounded to the nearest tenth of a percent is 15.0%

How do we determine the percentage of claims in Apple?

Out of the total claims of 4,280 items in inventory, the number of claims in Apple is determined as the total claims minus the number of claims attributable to IBM, such that the percentage of total inventory in Apple is computed as the number Apple's claims divided by total claims

number of claims in Apple=total claims-number of claims in IBM

total claims=4,280

number of claims in IBM=3636

number of claims in Apple=4280-3636

number of claims in Apple=644

% of claims in Apple=number of claims in Apple/total claims

% of claims in Apple=644/4280

% of claims in Apple=15.0%(rounded to 1 decimal place as shown in the options provided)

Find out  more about percentages on:brainly.com/question/15069465

#SPJ1

Answer:

1,314,000 minutes is equal to 2.5 years.

Brainliest, please :)

The military drone must ascend 12250 from its position of 3500ft above sea level feet so that it is vertically in the middle of the plane and the submarine.

To solve this problem we need to understand the concept of sea-level. The sea-level is defined as the average height of all water bodies of the earth. Below sea level is effectively taken as negative length and above sea -level is taken as positive length.

Let us consider the drone will have to ascend x feet to be vertically in between the plane and the submarine.

The submarine is 3500 feet below the sea level.

The plane is 35000 feet above the sea level.

Now we know that the drone is at a height of 3500 feet above the sea level.

Total distance between the drone and the ship=35000-(-3500)=38500ft

Middle point of the two=38500/2 = 19250 feet from the plane

Height above sea level for the drone should be=35000-19250=15750 ft

height of the drone=3500ft

The drone should ascend=15750-3500=12250 feet

To learn more about problems relating to sea - level visit:

https://brainly.com/question/28229060

#SPJ9

70%

Given: 50 total, 20 red, 15 blue

20 + 15 = 35

35 ÷ 50 = .7

.7 • 100 = 70

70% are blue or red.

Answer:

No solutions

Step-by-step explanation:

To solve systems of inequations with absolute values you need to isolate the items inside of the absolute value brackets then solve for x.

[tex]|\frac{x}{4}+5|=-7\\\frac{x}{4}+5=-7\\\frac{x}{4}=-12 \\x=-48[/tex]

Therefore our answers would be -48 and 48, however there are no answers to this solution as if you try either it does not equal -7. Furthermore graphing both sides of the equations shows there is no intersection.

Answer:

  (i)  (x√x)/3 -(√x)/2

  (ii)  f(x) = x³/27 +3x -5

Step-by-step explanation:

You want the value of the integral in each case. One integral is indefinite, the other has conditions specified.

In each case, the power rule applies:

  [tex]\displaystyle \int{x^n}\,dx=\dfrac{x^{n+1}}{n+1}[/tex]

The integral can be rewritten as the sum of two integrals involving half powers.

  [tex]\displaystyle \int{\dfrac{2x-1}{4\sqrt{x}}}\,dx=\dfrac{1}{2}\int{x^{\frac{1}{2}}}\,dx-\dfrac{1}{4}\int{x^{-\frac{1}{2}}}\,dx=\dfrac{x^{\frac{3}{2}}}{2\left(\dfrac{3}{2}\right)}-\dfrac{x^{\frac{1}{2}}}{4\left(\dfrac{1}{2}\right)}\\\\=\boxed{\dfrac{1}{3}x\sqrt{x}-\dfrac{1}{2}\sqrt{x}}[/tex]

You are given the derivative and three conditions:

Together with the integral, the conditions give rise to three equations in the three unknown coefficients.

  [tex]\displaystyle f(x) = \int{ax^2+b}\,dx=\dfrac{a}{3}x^3+bx+c[/tex]

Then the equations we can write for a, b, c are ...

  f'(3) = 4   ⇒   a(3²) +b = 4

  f(3) = 5   ⇒   (a/3)(3³) +b(3) +c = 5

  f(0) = -5   ⇒   a(0³) +b(0) +c = -5

The last equation gives the value of c = -5, so the remaining equations become ...

  9a +b = 4

  9a +3b = 10

Subtracting the first from the second, we have ...

  (9a +3b) -(9a +b) = (10) -(4)

  2b = 6

  b = 3

Using this in the first equation, we find 'a' to be ...

  9a +3 = 4

  a = 1/9

Then f(x) is ...

  [tex]\boxed{f(x)=\dfrac{1}{27}x^3+3x-5}[/tex]

Answer:

I tried to solve I got the value of a drink but a popcorn's value comes in negative... Can you recheck it please.......

[tex] \eta \times \eta \times \eta = 60 \\ \eta {}^{3} = 60 \\ \eta = \sqrt[3]{60} \approx3.91487[/tex]

See below for the explanation on how discriminant be used to determine the number of solutions

Let a trinomial in standard form be represented as

y = ax^2 + bx + c

The discriminant (d) is calculated as

d = b^2 - 4ac

The solutions are dependent on the following conditions

Read more about discriminant at

https://brainly.com/question/64103

#SPJ1