Solve using the square root method

Answer:

6%

Step-by-step explanation:

3/20=4/x

It is a indirect proportion so we reciprocal,

Then,

3/20=x/40

3×40=20×x

120=20x

x=120/20

x=6

The required probability for the given case is 0.4779.

The binomial distribution is based on the binomial theorem which can be written as (a + b)ⁿ = ⁿC₀aⁿb⁰ +  ⁿC₁aⁿ⁻¹b¹ + ⁿC₂aⁿ⁻²b²+ ....+  ⁿCₙa₀bⁿ.

In order to use in the probability, there should be events independent of each other and the sum of there probabilities is 1.

Given that,

The total number of students are 20.

And, the probability that a student cheats is 3/20 = 0.15.

The number of students chosen by the teacher is 4.

Thus, the probability that at least one student cheats can be found by binomial distribution as,

P(at least one student cheats) = ⁴C₁(0.15)¹(0.85)³ + ⁴C₂(0.15)²(0.85)² +  ⁴C₃(0.15)³(0.85)¹ + ⁴C₄(0.15)⁴(0.85)⁰

= 4 × 0.15 × 0.6141 + 6 × 0.0225 × 0.7225 + 4 × 0.003375 × 0.85 + 1 × 0.00050625

= 0.4779

Hence, the probability that at least one student selected by the teacher does cheating is 0.4779.

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Answer:

A and C

Step-by-step explanation:

1) -5(4x-6)-14=-4x+16

-20x+30-14+4x-16=0

-16x=0

x=16

3)4x-8(x-2)=-4x+16

-4x+16=-4x+16

Answer:

A

Step-by-step explanation:

8% = .08 in decimal form

10 000 ( 1 + .08)^10 =

Answer:

it's a that's the answer

The number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

Fraction number is the number which is a part of a whole number. It is written with a numerator and denominator. Fraction number are written as,

[tex]\dfrac{a}{b}[/tex]

Here (a) is the numerator and (b) is the denominator.

Last week, Ken ran 10 laps around the lake. Heather ran 2/3 as many laps around the lake as Ken did. Thus, the number of laps heather ran is,

[tex]x=\dfrac{2}{3}\times10\\x=\dfrac{20}{3}[/tex]

Hence, the number of laps around the lake did Heather run last week when the Ken ran 10 laps around the lake is 20/3.

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Answer: a= -18

              b= -28 inches      c=30 pounds

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

OPTION D

Step-by-step explanation:

[tex]3x + \frac{1}{2} y = - 4[/tex]

[tex]6x + y = - 8[/tex]

[tex]y = - 6x - 8[/tex]

I hope it helped you

A) no property

B) distributive property of multiplication

C) no property

D) no property

E) no property

     [tex]\downarrow[/tex]

     [tex]no\ property[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]distributive\ property\ of\ multiplication[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]no\ property[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]no\ property[/tex]

____________________________________

    [tex]\downarrow[/tex]

    [tex]no\ property[/tex]

I hope this helps you

:)

Answer:

D and E

Step-by-step explanation:

i took the quiz on usa test prep

Answer:

Pink is the least likely to be chosen because it has the lowest frequency.

Step-by-step explanation:

Answer:

the value of k is 27.

Step-by-step explanation:

find by using formula y2-y1/x2-x1

The proportionality shows the relation between two values.  The value of the constant of variation is 5.

The proportionality shows the relation between two values.

As given in the question the quantity q varies inversely with the square of m and directly with the product of r and x. Therefore, the proportionality can be written as,

[tex]q \propto \dfrac{rx}{m^2}[/tex]

Now to remove the proportionality add a constant to the equation which is the constant of variation.

[tex]q =k\dfrac{rx}{m^2}[/tex]

When m is 4 and the product of r and x is 8 then the value of q is 2.5. Therefore, the value of k can be written as,

[tex]q =k\dfrac{rx}{m^2}\\\\2.5 = k\dfrac{8}{4^2}\\\\\dfrac{2.5 \times 16}{8}=k\\\\k=5[/tex]

Thus, the value of the constant of variation is 5.

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Answer:

See below

Step-by-step explanation:

Square objects have four sides of equal length

so the perimeter of the drawing will be   4 * 2.5 = 10 inches

  area of drawing = 2.5 x 2.5 = 6.25 in^2

the actual object will have side lengths

       2.5 in  / 1 inch/ 5mm = 12.5 mm

   four sides each 12. 5 mm = 50 mm

      area of object = 12.5 x 12.5 = 156.25 mm^2

Answer:

range: 70

Step-by-step explanation:

range is the difference between the highest and lowest values.

[tex]Answer ☘️[/tex]

★ Important points to know

[tex] {\boxed{ \bold{Exterior \: Angle \: Theorem : - }}}[/tex]

★ Let's solve :-

[tex] \sf ↪\angle \: 65 \degree + \angle \: 30 \degree =\angle \:B\\ \\ \sf ↪\angle \: 95 \degree = \angle \:B[/tex]

Hence option A 95⁰ is the right ans ✓

[tex]\sf{\:мѕнαcкεя\: ♪...}[/tex]

[tex]\sf\large \green{\underbrace{\red{Answer⋆}}}:[/tex]

To find :-

The angle ∠ABC = ?

Given :-

∠BCD = 65°

∠BDC = 30°

Solution :-

Firstly we have to find ∠CBD, with the help of ∠CBD, we will able to find ∠ABC.

To find ∠CBD, we will use angle sum formula

(=> The sum of angles of all 3 sides of triangle is equal to 180°).

∠CBD + ∠BCD + ∠BDC = 180° (angle sum property)

∠CBD + 65° + 30° = 180°

∠CBD + 95° = 180°

∠CBD = 180° - 95°

∠CBD = 85°

Now we have ∠CBD, and in the diagram ∠CBD and ∠ABD lies on the same line but it is seperated by line BC, it means they are linear pair and the sum of both angles (∠CBD and ∠ABC) is equal to 180°.

∠ABC + ∠CBD = 180° (linear pair)

∠ABC + 85° = 180°

∠ABC = 180° - 85°

∠ABC = 95°

Result :-

The ∠ABC is 95° by using the above method.

Choose the first option

(A) 95°

The term used to describe the process of assigning values to responses in a research instrument and grouping them is called: coding.

In data analysis, before raw data can be processed, the researcher groups and assigns values to each response in the research instrument for easy collation and analysis.

This is referred to as coding, in research analysis.

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Answer: 14.5

Step-by-step explanation: (1½ ×3 ) + (2½ ×4)² = 4.5 + 10

Answer:

step 1

Find the average growth per year of the populations of rabbits farm A

Over the first 2 years

for t=0

numbers of rabbits=5 (is not exact)

for t=2

numbers of rabbits=40

average=[40-5]/2---------> 17.5

step 2

Find the average growth per year of the populations of rabbits farm B

Over the first 2 years

for t=0

numbers of rabbits=5 (is not exact)

for t=2

numbers of rabbits=30

average=[30-5]/2---------> 12.5

step 3

Compare the average growth per year of the populations of rabbits on both farms

farm A=17.5

farm B=12.5

the average rate of population growth of rabbits in farm A is greater than average rate of population growth of rabbits in farm B by about 5 rabbits per year.

therefore

the answer is the option C)

the average rate of population growth of rabbits in farm A is greater than average rate of population growth of rabbits in farm B by about 6 rabbits per year.

Step-by-step explanation:

Answer:

A. The amount of money you have at the end of the statement period

Step-by-step explanation:

A "closing balance" is the The amount of money you have at the end of the statement period

Answer:

$30

Step-by-step explanation:

if something is 50% off that is the same as saying half off.

so you simply do 60 divided by 2 and you get 30

Answer:

$30

Step-by-step explanation:

You get this anaswer by multiplying 60 (the cost of the suitcase) by 0.50 (50 percent as a decimal) and get 30 then subtract 30 by 30 to get the total cost.

Answer:

x + 5y = 30

x + 5(0) = 30

x1 = 30    y1 = 0

x + 5y = 30

1(0) + 5y = 30

y2 = 6    x2 = 0

(x1,y1) and (x2,y2)

(30,0) and (0,6)

Step-by-step explanation:

Answer:

3.14     (or pi )  feet  

Step-by-step explanation:

Entire circle circumference  = pi *d  = 8 pi    feet

45 degrees is a fraction of the entire 360 degrees of the circle

   45 / 360  *  8 pi = pi =  3.14 ft

Answer:

v=3,m=2

Step-by-step explanation:

You can find the complete solution in given attachment

I hope it helped you

Answer:

80 degrees

Step-by-step explanation:

The three angles of the triangle must sum to 180 degrees

70 + 30 + x = 180

x = 180 -70-30 = 80

Answer:

x=11.1

Step-by-step explanation:

we can use the sine function: (opposite/hypotenuse)

sin(46)=8/x

x=8/(sin46)

11.1

Answer:

The value of x is equal to 30.

Step-by-step explanation:

Let's define what are 2 equations are:

Since we are dealing with a straight line, the line's angle will always equal 180°.

Since the 2 angles must add up to 180°, then they must be supplementary angles.

We can set up our equation to solve for x:

This equation states that the 2 angles, given in formulas, must be equal to the angle of the line.

We can now solve this equation and get a value of x:

∴ we have found the value of x to be equal to 30.

Hope this helps!

Answer:

D. 11/9

Step-by-step explanation:

Which of the following fractions is the largest?

A. 5/81

B. 75/81

C. 10/9

D. 11/9

To make things easier, convert the fractions to decimals:

A. 5/81 = 0.062

B. 75/81 = 0.93

C. 10/9 = 1.11

D. 11/9 = 1.22

As we can see, 11/9 or 1.22, is the largest of all the values.

Hope this helps!

To make the denominators of the given fractions equivalent, we need to determine the LCM of the denominators. Clearly, the denominators of the set of fractions are 81, 81, 9, and 9 respectively.

LCM = 81 (81 × 1 = 81 and 9 × 9 = 81)

Multiply the denominators such that the denominator is equivalent to 81. Keep in mind that if we are multiplying a number (x), the numerator must be multiplied by the same number (x) .

   ⇒ 5/81, 75/81, 10/9, 11/9

   ⇒ (5 × 1)/(81 × 1), (75 × 1)/(81 × 1), (10 × 9)/(9 × 9), (11 × 9)/(9 × 9)

   ⇒ (5)/(81), (75)/(81), (90)/(81), (99)/(81)

   ⇒ 5/81, 75/81, 90/81, 99/81

Since 99 > 90 > 75 > 5, we can tell that 99/81 is the largest as:

Therefore, 11/9 is the largest fraction in the set.

Answer:

Heavenly,  we need the forumula for the area of a triangle, do you know it?

Step-by-step explanation:

Area of a triangle is (1/2 ) * B*H

where B = base

H = height

then

A = 1/2* B * H

A is given to be 20

B = b

H = b+4

plug all those into the formula,

20 = (1/2)*b*(b+4)

use your algebra skillz  :P

20 = 1/2 *( [tex]b^{2}[/tex] + 4b)

20*2 = [tex]b^{2}[/tex] + 4b

40 = [tex]b^{2}[/tex] + 4b

0 = [tex]b^{2}[/tex] + 4b-40

rewrite the above so it's in x format

[tex]x^{2}[/tex] + 4x -40 = 0

use the quadratic formula to find  x  , and for our problem, remember that x represents the base,  or b,  but don't mix it up with the b in the quadatic fomula,  with the b of the triangle, which is the base,  they are differnt "b"s   :P

X = (b±[tex]\sqrt{b^{2}-4*a*c }[/tex] ) / 2*a

a = 1

b = 4

c = -40

x = (4±[tex]\sqrt{4^{2}-4*1*(-40) }[/tex]  ) /2*1

x = ( 4±[tex]\sqrt{16+160}[/tex] ) / 2

x = (4±[tex]\sqrt{176}[/tex] ) / 2

x = (4±13.266499)/2

x= 2±6.633249

x = 2 + 6.633249 = 8.633

b= 8.633 cm

The annual premium result in an annual out-of-pocket expense that is about the same as her current plan is $0.28 per $100 of value.

Insurance premiums are paid for policies that cover all the basic needs such as healthcare, home, and life insurance.

We are given Amount of insurance policy for Stephanie = $ 355,000

Annual premium = $ 0.42 per $100

Deductible amount = $ 500

Total Annual out of pocket expense

= [($355,000/100) x $0.42] + $500

= $1,991  

Now, the New Deductible amount that Stephanie wants is $ 1000

So, Let the annual premium be x

To find the annual premium in an annual out-of-pocket expense that is about the same as her current plan when the deductible amount increases to $1000

355,000x / 100 + 1000 = 1991

3550x + 1000 = 1991

3550x = 1991 - 1000

3550x = 991

x = 991/3550

x = 0.279≈0.28

Hence the annual premium result in an annual out-of-pocket expense that is about the same as her current plan is $0.28 per $100 of value.

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