what are the number of possible outcomes on a 5 question test with each question having 4 possible answers

The shortest total length of fence this can be done with will be 440 m as the total area is 2000 m².

The length of a shape's outline is its perimeter. You must add the lengths of all four sides of a rectangle or square to determine its perimeter. In this instance, x represents the rectangle's length and y its width. The distance around an object is called the perimeter. For instance, the yard of your home is fenced in. The fence's length serves as the perimeter. Your fence is 200 feet long if the yard is 50 feet by 50 feet.

Here,

The area=2000 m²

xy=2000

x=2000/y

p=4x+2y

p=4*(2000/y)+2y

=8000/y+2y

p'=-8000/y²+2

-8000/y²+2=0

2y²-8000=0

y²-4000=

y²=4000

y= 20 m

p=8000/20+2*20

p=400+40=440 m

Given that the total area is 2000 m², the shortest total length of fence that can be used is 440 m.

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The required value of ∠ABC in the given triangle is 50°

The relation between interior and exterior angles of the triangle are related as, the sum two interior angles of triangle is equal to the opposite exterior angle of that triangle.

As we see in the given question, the sum of angle ∠A and ∠B is equal to the exterior angle which is 145°

⇒ 2x° + 95° = 145°

⇒ 2x° = 145° - 95°

⇒ 2x = 50°

Thus, required answer of angle ∠ABC is 50°

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The total spots moved, after the 3 plays is 15 spots to the left.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

Given that the football team lost 5 yards on each 3 plays.

Assume that a number line to be able to see how far in the field did they lost in 3 games.

Therefore,

1 : 5  (1 game is to 5 yards)

3 : 15 (3 games is to 15 yards )

After the first play, we would move to the left on the line 5 spots (to simulate 5 yards lost) and then make a dot to show your new position.

The total spots moved, after the 3 plays is 15 spots to the left.

Hence, All they lost 15 yards in 3 games.

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The dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

Let length be l and width be b of garden .

According to question ,

l + 2b = 1040

Area of garden = l * b

Substituting value of l in formula for area ,

Area = ( 1040 - 2b ) * b = 1040b - 2[tex]b^{2}[/tex]

Taking derivative of Area wrt. b and putting it equal to 0 ,

1040 - 4b = 0

b = 1040 / 4

b = 260 feet

Therefore , l = 1040 - 520 = 520 feet .

Maximum Area = 260 * 520 = 135200 [tex]feet^{2}[/tex] .

Hence , the dimensions 520 by 360 feet would guarantee that the garden has the greatest possible area .

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Step-by-step explanation:

4(2x-17) = 4x+(-5)

Open the bracket

8x - 68 = 4x - 5

Collect like terms

8x - 4x = -5 + 68

2x = 63

x = 63/2

x = 31.5

Answer:

x=17/14 y=5/21

The value of angle A and B are 60° and 120° respectively.

It is important to note that in isosceles trapezoid, the angles adjacent to the bases are congruent.

Therefore A = D

B = C

When in the right angle, the hypothenuse is twice the leg, the angle opposite it will be:

ABK = 30°

Also, KBC = 90°

Therefore, B = 30° + 90° = 120°

A = D = 180° - 120° = 60°

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Complete question:

Given: ABCD trapeziod, AB=DC, BK - altitude, AB=8, AK=4

Find: mA and mB.

The estimate of the population proportion of defectives is 0.05.

Given that,

There are 10 different samples of 50 observations, that is, total of 500 observations.

To find : The estimate of the population proportion of defectives

And total number of defectives from 500 observations is (5+1+1+2+3+3+1+4+2+3) = 25

Thus, the point estimate for the population proportion defectives will be,

=25/500=0.05

or just obtain the individual proportion of each sample and then take their average to obtain the same result.

Thus, the point estimate for the population proportion defectives will be 0.05

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The corresponding estimate for numbers in 1,2,3 and 4 are 10, 24, 21 and 153

Estimation and approximation is the process of using rounded values when presenting numerical data and making rough calculations.

The digits 1,2,3 and are rounded down and digits 5,6,7,8 and 9 are rounded up

1.  2.1 x 5.12 =  2 x 5 = 10

Explanation: The number after the digit 2 in 2.1 is 1, we will round down 2.1 to 2. Also, the number after the digit 5 in 5.12 is 1, we will round down 5.12 to 5

2. 12.3 x 1.6 = 12 x 2 = 24

Explanation: The number after the digit 12 in 12.3 is 3, we will round down 12.3 to 12. Also, the number after the digit 1 in 1.6 is 6, we will round up 1.6 to 2

3. 6.5 x 3.1 = 7 x 3 = 21

Explanation: The number after the digit 6 in 6.5 is 5, we will round up 6.5 to 7. Also, the number after the digit 3 in 3.1 is 1, we will round down 3.1 to 3

4. 51.3 x 2.7 = 51 x 3 = 153

Explanation: The number after the digit 51 in 51.3 is 3, we will round down 51.3 to 51. Also, the number after the digit 2 in 2.7 is 7, we will round up 2.7 to 3

Therefore, the estimate for 1,2,3 and 4 are 10, 24, 21 and 153 respectively

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Answer:

-2.6 x 10-3

Step-by-step explanation:

if you enter the equation into a calculator it will do it for you. If you want to do it with a calculator heres how to. You would move the decimal to the first whole number for example in this case 2. How many places is that? 3. Whenever a decimal point moves to the right the spot is negative. You would then write it 2.6 with 10 (exponent -3)

Answer:

Step-by-step explanation:

To rewrite in scientific notation means to add an exponent such as e-3 in this case or [tex]10^{x}[/tex] where x is the exponent.

you would convert -0.0026 to -2.6e-3 or [tex]-2.6*10^{-3}[/tex]

The basic way of converting to scientific notation is to move your number a certain amount of decimal places until there is one number left before the decimal mark. Then the amount of values moved turns into you're exponent. A negative exponent means your are going towards a smaller number. Make sure to keep the current sign of the number

Step-by-step explanation:

the angles between 2 intersecting lines must be the same on both sides of either line, they are just left-right mirrored.

so,

123 = 2v + 1

2v = 122

v = 61

The solutions of the quadratic equation using the quadratic formula is x = 3 + 2√2 and x = 3 - 2√2

From the question, we are to solve the given quadratic equation using the quadratic formula

The given quadratic equation is

x² - 6x + 1 = 0

Using the quadratic formula,

x = [-b±√(b² - 4ac)] / 2a

a = 1, b = -6, and c = 1

Thus,

x = [-(-6) ±√((-6)² - 4(1)(1))] / 2(1)

x = [6 ±√(36 - 4)] / 2

x = [6 ±√(32)] / 2

x = [6 ± 4√2] / 2

x = [2(3 ± 2√2)] / 2

x = 2(3 ± 2√2) / 2

x = (3 ± 2√2)

x = 3 + 2√2 and 3 - 2√2

Hence, the roots are 3 + 2√2 and 3 - 2√2

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Darryl receive $579.44  in dividends every year .

In the question ,
it is given that

Darryl's portfolio

number of shares of Essentia Inc. = 66

dividend received from each share in a year = $1.79 per share

So , amount of dividend received from Essentia Inc. = 66 × 1.79

= $118.14

number of shares of SFT Legal = 95

dividend received from each share in a year = $2.62 per share

So , amount of dividend received from SFT Legal = 95 × 2.62

= $248.9

number of shares of Grath Oil = 180

dividend received from each share in a year = $1.18 per share

So , amount of dividend received from Essentia Inc. = 180 × 1.18

= $212.4

So , total dividend Darryl receives = $118.14 + $248.9 + $212.4

= $579.44

Therefore , amount of dividend received by Darryl each year is $579.44  .

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Answer:

its A.

Step-by-step explanation:

For the given equation, the slope is 3 and the y-intercept is -5. From the graph, it is possible to see that the point (0,0) does not satisfy the equation.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=x+19. A line equation also can be represented by the point-slope form: [tex](y-y_1)=m(x-x_1)[/tex].

m= the slope.

[tex](x_1,y_1)[/tex]= the coordinate of a point.

For the given example: m=1 and b=19.

The question gives: y + 2 = 3(x - 1). Therefore,

y + 2 = 3(x - 1)

y=3x-3-2

y=3x-5

If y=3x-5 . Here, you have a standard form of a linear equation y=mx+b. Where:

m= the slope. It can be calculated for Δy/Δx.

b= the constant term that represents the y-intercept

Thus, the slope is 3 and the y-intercept is -5.

For this, you should do a table with points

x     y= 3x-5

-2   y=3*(-2)-5=-6-5= -11

-1    y=3*(-1)-5=-3-5= -8

0   y=3*(0)-5=0-5= -5

1    y=3*(1)-5=3-5= -2

2    y=3*(2)-5=6-5= 1

Draw a graph from these points, see the attached image.

The point (0,0) does not satisfy the equation because when x=0 because y is different than zero (0). See below.

y= 3x-5, for x=0

y=3*0-5

y=0-5

y=-5

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The current price of the clarinet and the various discounts and markups illustrate that the amount the store paid was $90.

First find out the selling price of the clarinet:

= Discounted price / ( 1 - discount rate)

= 93.60 / ( 1 - 20%)

= $117

This selling price is 30% more than what the store paid so the price the store paid was:

= Selling price / ( 1 + rate of increase)

= 117 / ( 1 + 30%)

= $90

In conclusion, the amount the store paid was $90.

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Complete question

A music store buys instruments and then sells them for 30% more than they paid. During a 20% off sale, the store offers a clarinet for $93.60.

How much did the store pay for the clarinet?

The price of gasoline when Ryan's mother started driving is $0. 45

A fraction can be defined as the part of a whole set, data or element.

The different types of fractions include;

Example of mixed fractions; 2 1/ 3

Example of simple fractions; 1/ 2

Example of proper fractions; 2/5

From the information given, we have;

Price of a gallon of gasoline is $2. 25

1/ 5 of $2.25

This is represented as;

1/ 5 × $2.25

Multiply the values

$0. 45

Hence, the value is $0. 45

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it's a easy question I think you can solve it

Answer:

Your first option is correct but your second is wrong

Step-by-step explanation:

In option b-

when an employee receives 10% additional for each of the following weeks:

10% of 200=  10/100 x200= 20

it means he will get $20 in extra in every week

so it will be- 220,240,260

Answer:

Step-by-step explanation:

There are 15 circles and 6 squares.

Total shapes:

Ratio of squares to total shapes:

Answer:

the answer is 2:7

Step-by-step explanation:

6÷3 : 21÷3

=2:7

The strategy which would eliminate a variable in the system of equations is to multiply the top equation by 6 ,multiply the bottom equation by -5 then add the equation and is denoted as option B.

This is a mathematical term which is made up of two expressions and is connected by an equal sign.

In the example given below:

8x + 5y = -7

-7x + 6y = -4

We can multiply the top by 6 and the bottom by -5 which will result in:

48x + 30y = -42

35x - 30y = 20

They are then added to each other to give:

48x + 35x + 30y - 30y = -42 + 20

83x = - 22

x = -22/83

From this we can notice that the variable y was eliminated which is why option B is the correct choice.

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The number of full turns per minute is 235.

Given that, a cycle Wheel does 1645 full turns in 7 minutes.

The 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.

Here,

The number of full turns per minute = Number of full turns/Number of minutes

= 1645/7

= 235 full turns per minute

Therefore, the number of full turns per minute is 235.

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Answer:

x=0.75

Step-by-step explanation:

5x=3.75

/5.  /5

x=0.75

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There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

Information about the possibility that something will happen is provided by probability. For instance, meteorologists use weather patterns to forecast the likelihood of rain. Probability theory is utilized in epidemiology to comprehend the connection between exposures and the risk of health outcomes. Probability is the likelihood that something will occur or the probability that something will happen. Probability is the measure of how likely it is that a coin will land heads up after being tossed into the air.

Given,

On a particular busy section of the garden state parkway in new jersey, police use radar guns to detect speeding drivers. assume the time that elapses between successive speeders is exponentially distributed with the mean of 15 minutes.

Either the wait is over 25 minutes or it is less than 25 minutes. Decimal 1 represents the total of these events' probabilities. So,

P( X ≤ 25) + P(X > 25) = 1

For P(X > 25):

1 -P(X ≤ 25)

1 - e ⁻⁰⁶⁶⁶⁽²⁵⁾

0.1892

There is an 18.92% chance that there will be a wait of more than 25 minutes between speeders.

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Answer:

x = -1

Step-by-step explanation:

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Answer:

-1

Step-by-step explanation:

Replace the variable x with 1 in the expression .

f(1)= 2(1) - 3

Remove the parenthasis

2(1) - 3

Multiply 2 by 1

2 - 3

subtract 2 from 3

-1

The hawk is closer to the ground after 8 minutes

It is 130 feet closer

We have the equation as;

Also, x represents the descending time in minutes

Now, let's substitute the value of x as 8 minutes in the equations

If x = 8

For equation (1)

y = - 20(8) + 350

expand the bracket

y = - 160 + 350

y = 190 feet

For equation (2)

y = -10(8) + 400

expand the bracket

y = -80 + 400

y = 320 feet

The hawk is closer after 8 minutes

The distance from the ground(eagle) - The distance from the ground(hawk)

320 - 190

130 feet

Hence, the hawk is closer to the ground

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By applying the lowest common multiple approach, Kyra may have acquired up to 12 rocks.

What does common factor mean?

A common factor is a whole number that is a factor of at least two other numbers. The highest common factor is the largest factor that will divide into two or more numbers (HCF). The phrase "lowest common multiple" refers to the smallest multiple that two or more numbers have in common (LCM).

The least common multiple of 2, 3, and 4 can be used to determine how much rock Kyra has.

Several of:

2 = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20

3 = 3, 6, 9, 12, 15, 18, 21

4 = 4, 8, 12, 16, 20

The smallest number that 2, 3, and 4 have in common is 12. There are therefore 12 rock piles in Kyra's possession.

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