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8th grade Pre-algebra

The intensity at a distance of 14 feet is 18.29 ft

The intensity (I) of a light source is inversely proportional to the square of the distance (d) from the source.

Light intensity refers to the strength or amount of light produced by a specific lamp source

The light intensity is measured in terms of lumens per square foot or lumens per square meter.

Therefore,

I ∝ 1 / d²

Hence,

I = k / d²

where

Therefore,

k = Id²

k = 16 × 16

k = 256

Hence,

I = 256 / 14

I = 18.2857142857

I = 18.29 ft

Therefore, the intensity at a distance of 14 feet is 18.29 ft

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Answer:

2 : 12

Step-by-step explanation:

There are 2 blue triangles, so 2 will come first. It's then followed by the sum of blue and yellow, which is 2 + 10, which is 12. So, the ratio is 2 : 12.

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The solution of x is x = 0, x =2 and x = -5

The equation is given as:

2x^3+6x^2-20x=0​

Factor out x

x(2x^2+6x-20)=0​

Split the equation

x = 0 or 2x^2+6x - 20=0​

Solve for x in 2x^2+6x - 20=0​

Expand the equation

2x^2 + 10x - 4x - 20 = 0

Factorize the equation

(2x - 4)(x +5) = 0

Split the equation

2x - 4 = 0 and x + 5 = 0

Solve for x

x =2 and x = -5

Hence, the solution of x is x = 0, x =2 and x = -5

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Using the z-distribution, a sample of 609 nickels has to be weighed.

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

The margin of error is:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

For this problem, the parameters are:

[tex]M = 20, \sigma = 300, z = 1.645[/tex]

We solve for n to find the sample size, then:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]20 = 1.645\frac{300}{\sqrt{n}}[/tex]

[tex]20\sqrt{n} = 1.645 \times 300[/tex]

[tex]\sqrt{n} = 1.645 \times 15[/tex]

[tex](\sqrt{n})^2 = (1.645 \times 15)^2[/tex]

n = 608.9

Rounding up, a sample of 609 nickels has to be weighed.

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he instructions to find the LCM of 20, 35 and 40 are the next:

1. Decompose all numbers into prime factors

20 2 10 2 5 5 1

35 5 7 7 1  

40 2 20 2 10 2 5 5 1  

2. Write all numbers as the product of its prime factors

Prime factors of 20 = 22 . 5

Prime factors of 35 = 5 . 7

Prime factors of 40 = 23 . 5

3. Choose the common and uncommon prime factors with the greatest exponent

Common prime factors: 5

Common prime factors with the greatest exponent: 51

Uncommon prime factors: 2 , 7

Uncommon prime factors with the greatest exponent: 23, 71

4. Calculate the Least Common Multiple or LCM

Remember, to find the LCM of several numbers you must multiply the common and uncommon prime factors with the greatest exponent of those numbers.

LCM = 51. 23. 71 = 280

Answer:

undefined

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2  x_1)

slope = (-3 - 4)/(6 - 6)

slope = -7/0

Since division by zero is undefined, this line has undefined slope.

Answer:

CIRCLE

Step-by-step explanation:

The fat percentage in the second type(40 liters) of milk is 1%

Fats in 40 liters of milk = Total fat - fats in 80 litrrs milk

= 3% - 2%

= 1%

Therefore, the fat percentage in the second type of milk is 1%

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The missing Statement and reason for the transverse line angles is; m∠YXD = 60° and  Supplementary angles sum up to 180°.

Statement 1; AB ║ CD

Reason 1; Given

Statement 2; m∠ZYB = 60°

Reason 2; Given

Statement 3; ∠YXD and ∠DXW form a linear pair

Reason 3; Definition of Linear Pair

Statement 4; m∠YXD = 60°

Reason 4; Corresponding angles have equal measure.

Statement 5; m∠DXW = 120°

Linear pairs usually sum up to 180° because they are supplementary angles. Thus;

m∠YXD = 180° - 60° = 120°

Reason 5; Supplementary angles sum up to 180°.

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The value of m∠7, given the data from the question is 80°

Alternate angle theorem states as follow:

When two parallel lines are cut by a line (i.e transversal), then the alternate interior angles or alternate exterior angles are aqual.

From the diagram,

From the above, we can see that m∠3 and m∠7 are alternate angles.

Therefore,

m∠7 = m∠3

m∠7 = 80°

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Complete question

please see attached photo

the equation of the new function is:

[tex]g(x) = 2^{x - 5} - 7[/tex]

We have a function:

[tex]f(x) = 2^x[/tex]

And we want to shift it five units to the right, and seven units down, then the new function will be:

[tex]g(x) = f(x - 5) - 7[/tex]

If we now replace f(x), we get:

[tex]g(x) = 2^{x - 5} - 7[/tex]

That is the equation of the new function.

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Answer:

The equation is 5x - 9 = 2x + 23.

The answer is option A.

Step-by-step explanation:

Answer:

t=20

Step-by-step explanation:

t-19=1

t-19(+19)=1+19

t=20

Answer: -7

Step-by-step explanation:

First, lets use the functions to find the answer to f(-8) and g(4)

f(-8) is the same as asking for the value of y when x is -8

Therefore, f(-8) = -5 (according to the graph)

Using the same rule, g(4) would be the value of y when x = 4 which,

according to the graph, g(4) = 3

Plug these values back into the original equation to get:

[tex]-1*f(-8)-4*g(4)=?\\=-1*-5-4*3\\[/tex]

using the order of operations, we will multiply the values first

[tex](-1*-5)+(-4*3)\\=5+(-12)\\=5-12\\=-7[/tex]

Answer:

-7

Step-by-step explanation:

Answer:

x = 34

Step-by-step explanation:

complementary angle sum to 90°

sum the 2 angles and equate to 90

x + x + 22 = 90

2x + 22 = 90 ( subtract 22 from both sides )

2x = 68 ( divide both sides by 2 )

x = 34

The probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

Probabilities are used to determine the chances, likelihood, possibilities of an event or collection of events

The given parameters are:

Mean = 0.8

Variance = 0.0004

Calculate Standard deviation using

σ = √σ²

This gives

σ = √0.0004

Evaluate

σ = 0.2

Calculate the z-score at x = 0.84 using

z = (x - [tex]\bar x[/tex])/σ = √σ²

This gives

z = (0.84 - 0.8)/0.02

Evaluate

z = 2

The probability is then represented as:

P(x > 0.84) = P(z > 2)

Next, we look up the value of the z table of probabilities

From the z table of probabilities, we have:

P(x > 0.84) = 0.977

Hence, the probability that the diameter of a randomly selected pipe will exceed 0.84 inch is 0.977

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The volume of the composite figure is 655.44 unit³.

The information is incomplete. An overview will be given. Let's assume that the shape is a cylinder.

The volume of a cylinder is πr²h

Assumed radius = 7

Assumed height = 4

The volume will be:

= πr²h

= 3.14 × 7² × 4

= 615.44 unit³

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Answer:

(-4,3）

Step-by-step explanation:

The intervals are denoted as:

Closed intervals = [a, b]

This interval includes a and b.

Open intervals = (a, b)

This interval does not include a and b.

The interval that denotes the values between -4 and 3 on the given number line is [-4, 3].

The intervals are numbers or values between two given point

The intervals are denoted as:

Closed intervals = [a, b]

This interval includes a and b.

Open intervals = (a, b)

This interval does not include a and b.

We have,

A number line.

The set of values that is in the blue line is from -4 to 3.

This means that the blue line includes values from -4 to 3.

There are infinite numbers between -4 to 3.

The blue line denoted that the values -4 and 3 are also included.

The interval that denotes the values between -4 and 3 is:

= [-4, 3]

Thus,

The interval that denotes the values between -4 and 3 on the given number line is [-4, 3].

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The preparation of the Cash Flow Statement for Nikea Inc. for the year ended December 31, 2013, is as follows:

Direct Method:

Nikea Inc.

Cash received from customers  $600,000

Cash paid to suppliers of goods (400,000)

Cash paid to vendors of servides (30,000)

Cash from operating activities    $170,000

Indirect Method:

Nikea Inc.

For the year ended December 31, 2013

Net income                                $150,000

Add non-cash expenses:

Depreciation                                 20,000

Cash from operating activities $170,000

The direct method of preparing the Cash Flow Statement starts with the operating income and adds the non-cash expenses to obtain the cash flow from operating activities.

On the other hand, the indirect method reconciles the accounts receivable and payable to extract the exact cash flows received from customers or paid to suppliers of goods and services.

Both methods of determining the cash flow from operating activities yield the same result.

Nikea’s income statement for the year 2013

Sales                          $600,000

Cost of Goods Sold   (400,000)

Gross Profit                 200,000

Operating Expenses   (30,000)

Deprecation                (20,000)

Net Income                 150,000

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Answer:

the number 27 is a composite

Step-by-step explanation:

Yes, since 27 has more than two factors . 1, 3, 9, 27. In other words, 27 is a composite number because 27 has more than 2 factors

Answer:

The number 27 is composite.

Answer:

80

Step-by-step explanation:

1) if the number of hamburgers is 'h', number of cheesburgers is 'c', then

2) the condition 'The number of cheeseburgers sold was three times the number of hamburgers' can be written as c=3h. Also

3) the condition 'combined total of 320' can be written as h+c=320, then

4) it is possible to make up the system of equations:

[tex]\left \{ {{c=3h} \atop {c+h=320}} \right. \ = > \ \left \{ {{c=240} \atop {h=80}} \right.[/tex]

5) finally, number of hamburgers is 80.

Answer:

hold shift then press the lil right  arrow next to the question mark

Step-by-step explanation:

Answer:

shift  +  >

Step-by-step explanation:

Hope this helps

$13,000 was invested at 6% whereas $7,000 was invested at 10% using simple interest approach

What is simple interest?

Simple interest is determined as the amount invested multiplied by the interest rate and the number of years that investment lasts.

I=PRT

I=interest

P=principal

R=rate of return

T=time

Let X be the amount invested at 6%

I at 6%=6%*X*1

I=0.06X

The amount invested at 10% is 20,000-X

total interest=0.06X+0.10*(20000-X)

total interest=1,480

1480=0.06X+0.10*(20000-X)

1480=0.06X+2000-0.10X

1480-2000=0.06X-0.10X

-520=-0.04X

X=-520/-0.04

X=13,000

13,000 was invested at 6%

amount invested at 10%=20,000-X

amount invested at 10%=20,000-13,000

amount invested at 10%=7,000

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Answer:

Step-by-step explanation:

Given

Leg =  10

Leg = 6

hypotenuse = ?

equation

c^2 = a^2 + b^2

a = 10

b = 6

Solution

c^2 = 10^2 + 6^2                  Expand

c^2 = 100 + 36                     Combine

c^2 = 136                              Take the square root of both sides

√c^2 = √136

c = 11.66

answer

hypotenuse = 11.66

Answer:

484

Step-by-step explanation:

because a=22² , which is equal to 484

because a=22² , which is equal to 484, but a=c hence C is equal to 484

[tex]|\Omega|=15\\|A|=7+4=11\\\\P(A)=\dfrac{11}{15}\approx73.3\%[/tex]

Answer:

RED COUNTER: 7/15

BLUE COUNTER: 4/15

Hope it helps,

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The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

From the question, we are to write the list of data points used to generate the given histogram

The list of data points used to generate the histogram is

   x            Frequency

15-20              0

20-25             4

25-30              6

30-35              3

35-40              4

40-45              0

45-50              3

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hi,

a point is given  ( x; y)

standar line equation is  :  y = ax+b

So  with  (3;5)  and  (8;15)  we have  :  

   3a+b = 5

   8a+b = 15

so :  

8a+b - ( 3a +b) =  15 -5

8a +b -3a -b = 10

8a-3a = 10

5a = 10

   a = 10/5

    a = 2

if a = 2  so  3*2 +b = 5

                     6+b = 5

                       b = 5-6

                       b = -1

so let check :  

8*2 + (-1) = 16 -1 = 15

and  3*2 -1 = 6-1 = 5

coordonnate works for both point, so line  is   y = 2x -1

Answer: 4.08x2

Step-by-step explanation:

Answer:

4.08x2

Step-by-step explanation: