HELP

At a Junk Yard a study was conducted using 48 cars and found that the average mileage on a car before it was junked was 164,000 and the population standard deviation is known to be approximately 28,000. Construct a 99% confidence interval of what the actual average mileage is for a car before it is junked.

ANSWER :

[tex] \rm{1.)16a {}^{3}b {}^{17} }[/tex]

= (2ab^5)^4

= 2ab^5×2ab^5×2ab^5×2ab^5

= 16a^4b^9

= 16a^4b^9/ab^3

= 16a^3b^17

[tex] \rm2.) \frac{x {}^{6} y {}^{10} }{a {}^{2}b {}^{14} } [/tex]

= (x^3y^5)^2

= (x^6y^10)

= (ab^7)^2

= (ab^14)

= (x^6y^10)/ab^14

[tex] \rm3.)4mn {}^{7} [/tex]

= 5mn^7 - 1

= 4mn^7

Answer:
y = -1/3x + 1

Step-by-step explanation:

1) For a perpendicular line, the slope is the opposite reciprocal. What this means is that, the slope will be the opposite sign and flipped.

~-1/3 will be the new slope

2) Then you have to rewrite the problem using the point slope form which is y - y1 = m(x-x1). The values that we will be plugging in for x1 and y1 will be from the coordinate that you provided.

~ y - (-2) = -1/3(x-9)

3) Now simplify everything you can
~y+2 = -1/3(x-9)

4) Now distribute the -1/3
~y+2 = -1/3x + (9)(1/3)
~y+2 = -1/3x + 3

5) Now we need to subtract 2 from both sides to get y by itself.

~y = -1/3x + 1

The postulate that can be used to prove the two triangles are congruent is the HL this is the last option

HL is an acronym that means Hypotenuse Leg. The Hypotenuse leg theorem is used in proving angle congruency in right angle triangle.

The theorem says that, two angles of a right angle triangle that have equal

then two triangles are congruent

The figure in the problem is a right angle triangle that is sharing same hypotenuse hence the hypotenuse is equal. and one other leg is marked to be equal

Therefore, this theorem says that the two triangle are congruent

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The greatest number of bags Caesar can make is 16 bags. Each of these bags will have 5 boxes of pasta and 8 jars of sauce.

Find the greatest common factor of 32 and 48

The greatest common factor of 32 and 48 is 16

So, the greatest number of bags Caesar can make is 16 bags

Number of pasta in each bag = 32/16

= 5 boxes of pasta per bag

Number of sauce in each bag = 48/16

= 8 jars of sauce per bag

If Caesar made fewer bags, he would have boxes of pasta and jars of sauce remaining.

He could use 8 bags but this is not the greatest number he could use.

Therefore, Caesar can use the greatest common factor to determine the highest number of bags he could use.

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Answer:

16

Step-by-step explanation:

40/5 then x the answer by 2 and you get 16 with now deposits or withdraws

The probability that no one enters between 12:00 and 12:05 is 0.082.

The probability that at least 4 people enter the casino during that time is 0.242

Given that people enter the casino at the rate of 1 every 2 minutes. A random variable X is defined as the number of people entering the casino between the time period of 12:00 and 12:05. Since we are given in the question that people enter the casino at the rate of 1 every minute, hence in the given time period they enter at the rate of 2.5.

P(X=0) = [tex]e^{-2.5}[/tex] = 0.082

Hence the probability that no one enters between 12:00 and 12:05 is 0.082.

The required probability is simply

P(X≥4) = 1 - P(X=0) - P(X=1) - P(X=2) - P(X=3)

= 1 - [tex]e^{-2.5}[/tex] - 2.5[tex]e^{-2.5}[/tex] - (((2.5)² / 2)[tex]e^{-2.5}[/tex] ) - (((2.5³)/3!)[tex]e^{-2.5}[/tex])

= 0.242

Hence, the probability that at least 4 people enter the casino during that time is 0.242

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With the help of permutanions and combinations we can conclude the answer.

acc to our question-

Hence ,permutanions and combinations concept helped us to reach our solution.

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Answer:

Step-by-step explanation:

a=apples

a/7

The dimension of pen that maximize the area is 150 ft by 150 ft.

What is the dimension of a area?

In mathematics, a dimension is the length or width of an area, region, or space in one direction. It is just the measurement of an object's length, width, and height.

Given the perimeter of the rectangular is 600 ft.

Assume that the length of the rectangular be l and the breadth be b.

The perimeter of the rectangular is 2(l+b).

According the question:

2(l+b) = 600

Divide both sides by 2:

(l+b) = 300

l = 300 - b

The area of rectangular is A = lb

Substitute the value of l in the above equation:

A = (300 - b) b

A = 300b - b^2

The maximum value of a quadratic polynomial Ax^2+BX+C is at x = - B/(2A).

Compare Ax^2+BX+C  with 300b - b^2:

A = -1 and B = 300.

Putting A = -1 and B = 300 in b= - B/(2A).

b= - 300/(2×(-1))

b = 150.

Putting b =150 in l = 300 - b

l = 300 - 150

l = 150

The dimension is 150 ft × 150 ft.

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The number of green marbles removed from the bag is 3.

We will use the Formula of Probability:

In mathematics, the probability is defined as the ratio between the number of favorable outcomes and the total number of outcomes.

p(A) = n(A) / n(S)

p(A) is the probability of event A.

n(A) is the number of outcomes with respect to A.

n(S) is the total number of possible outcomes.

Given in the Question:

A bag contains 14 blue, 6 red, 12 green, and 8 purple marbles.

So the total number of marbles in the bag = 40

It is given that 25 marble are removed from the bag randomly

thus, the remaining marbles in the bag = 40 - 25 = 15

It is given that the probability of drawing a green marble from the bag after removing 25 marbles is 3/5.

So, for finding the number of green marbles in the bag after removing we can write,

n(A) = p(A) × n(S)

here, A is the event of drawing the number of green marbles and p(A) = 3/5 and  n(s) = 15 (after removing)

Thus, the number of green marbles in the bag after removing = 3/5 × 15

So, the number of green marbles left in the bag = 9

then, the green marbles removed from the bag = 12 - 9 = 3.

Therefore, only 3 green marbles are removed from the bag.

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Con base en el uso de simbología para el acertijo, la edad del conductor es 27 años.

Los acertijos no deben ser entendidos literalmente, sino simbólicamente. Cada elemento representa algo figurativo.

Este acertijo parece incoherente debido a estar incompleto y es preciso añadir un criterio adicional que permita brindar sentido al contenido, este criterio es asumir que un pasajero simboliza un año, que el autobús simboliza al conductor, que el ingreso de un pasajero implica sumar un año a la edad del conductor, que el egreso de un pasajero implica restar un año a la edad del conductor y que la población resultante dentro del autobús es la edad del conductor.

En consecuencia, efectuamos la siguiente operación para determinar la edad del conductor:

x = 56 - 31 + 18 - 16

x = 27

El conductor tiene una edad de 27 años.

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Answer:

I believe the answer is Yes because there is a constant arithmetic sequence and I believe the common difference is 4.

Answer:

1. 5x +2

2. 6x/5

Step-by-step explanation:

Answer:

Step-by-step explanation:

And here is how to use it:

Example: simplify √12

12 is 4 times 3:

√12 = √(4 × 3)

Use the rule:

√(4 × 3) = √4 × √3

And the square root of 4 is 2:

√4 × √3 = 2√3

So √12 is simpler as 2√3

Another example:

Example: simplify √8

√8 = √(4×2) = √4 × √2 = 2√2

(Because the square root of 4 is 2)

And another:

Example: simplify √18

√18 = √(9 × 2) = √9 × √2 = 3√2

It often helps to factor the numbers (into prime numbers is best):

Example: simplify √6 × √15

First we can combine the two numbers:

√6 × √15 = √(6 × 15)

Then we factor them:

√(6 × 15) = √(2 × 3 × 3 × 5)

Then we see two 3s, and decide to "pull them out":

√(2 × 3 × 3 × 5) = √(3 × 3) × √(2 × 5) = 3√10

Fractions

There is a similar rule for fractions:

root a / root b  = root (a / b)

Example: simplify √30 / √10

First we can combine the two numbers:

√30 / √10 = √(30 / 10)

Then simplify:

√(30 / 10) = √3

Some Harder Examples

Example: simplify  

√20 × √5

√2

See if you can follow the steps:

√20 × √5

√2

√(2 × 2 × 5) × √5

√2

√2 × √2 × √5 × √5

√2

√2 × √5 × √5

√2 × 5

5√2

Example: simplify 2√12 + 9√3

First simplify 2√12:

2√12 = 2 × 2√3 = 4√3

Now both terms have √3, we can add them:

4√3 + 9√3 = (4+9)√3 = 13√3

B) The missing angle at the intersection point of both triangles is; x = 15°

C) The missing angle is gotten as; x = 61°

B) In the second image given, we can see two angles;

Now, we know that sum of angles in a triangle is 180 degrees. Thus, for the interior angles, we have;

90 + 5x - 14 + y = 180

where y is the third interior angle

Now, we know that sum of angles on a straight line is equal to 180 degrees. Thus;

y = 180 - (9x + 16)

Put 180 - (9x + 16) for y into the first equation to get;

90 + 5x - 14 + 180 - (9x + 16) = 180

180 will cancel out to get;

90 + 5x - 14 - (9x + 16) = 0

4x = 90 - 14 - 16

4x = 60

x = 60/4

x = 15°

C) The missing angle of the triangle with side of 12y + 3 is an alternate angle to get;

Missing angle = 63°

Sum of angles in a triangle is 180 degrees. Thus;

56 + 63 + 3rd angle = 180

3rd angle = 180 - (56 + 63)

3rd angle = 61°

Thus, x = 61° because they are opposite angles

Also, the two given sides are equal to each other as shown. Thus;

51 = 12y + 3

12y = 51 - 3

12y = 48

y = 48/12

y = 4

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The probability that the average completion time for a sample of 28 students will be more than 24 minutes is 0.46

The mean of freshman mason basic completion time  is 24.6 minutes

The standard deviation is 5.8 minutes

The probability of completion for a sample of 28 students will be more than 24 minutes and can be found using the normal distribution,

                      P(x > 24)

We need to find the standard form of this random sample using the formula,

              Z = X - μ / σ

where Z is the standard form

           X is the random sample

          μ is the mean

          σ is the standard deviation

Let us substitute the known values in the above equation, we get

                  Z = 24 - 24.6/5.8

                     = -0.6 / 5.8

                     = -0.103

So the standard form is

         P(x > 24) = P(z > -0.103)

By using the z-table, we could find the value of z,

        P(z > -0.103) = 0.46

Therefore, the probability is 0.46

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The perimeter of the floor in the scale drawing is 32 inches.

Using ratio and proportion, determine the width of the scale drawing of the floor.

actual length / scale length = actual width / scale width

36 feet / 9 inches = 28 feet / scale width

scale width = 28 feet (9 inches / 36 feet)

scale width = 7 inches

Perimeter is defined as distance around a two-dimensional shape.

The perimeter of a rectangle can be calculated using the formula below.

P = 2(l + w)

where P = perimeter

l = length

w =width

Plug in the values of the dimension of the scale drawing and determine its perimeter.

P = 2(l + w)

P = 2(9 inches + 7 inches)

P = 32 inches

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The 20 and 21 unit leg lengths of the right triangles ΔACD and ΔBCD formed by the altitude CD indicates, by using Pythagorean theorem that the length of BC is 29 units

A right triangle is a triangle that has two perpendicular sides. The altitude of a triangle is perpendicular to the base of the triangle, forming two right triangles in acute triangle.

Angle ∠A = 45°

The length of the segment the altitude CD divides AB into = 20 and 21 units

Please find attached a drawing created using MS Word based on the question parameters.

[tex]tan(\angle A) = \dfrac{CD}{AD}[/tex]

AD = 20

Therefore;

[tex]tan(45^{\circ}) = \dfrac{CD}{20}[/tex]

CD = 20 × tan(45) = 20

Pythagorean theorem applied to right triangle ΔCBD, indicates that;

[tex]\overline{BC}^2[/tex] = [tex]\overline{CD}^2[/tex] + [tex]\overline{DB}^2[/tex]

DB = 21 units, which gives;

[tex]\overline{BC}^2[/tex] = 20² + 21² = 841

BC = √(841) = 29

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x = -1 and y = -13, (-1,-13) is the solution to the system of equation y = 3x - 10 and y = -2x - 15.

Given the system of equation in the question;

To find the solution to the system of equation, replace the occurrence of y in the second equation with y = 3x - 10  and solve for x.

y = -2x - 15

3x - 10 = -2x - 15

Add 10 to both sides

3x - 10 + 10 = -2x - 15 + 10

3x = -2x - 15 + 10

Add 2x to both sides

3x + 2x = -2x + 2x - 15 + 10

3x + 2x = - 15 + 10

Add like terms

5x = -5

x = -5/5

x = -1

Now, to solve for y, replace all occurrence of x with -1 in the first equation and solve for y.

y = 3x - 10

y = 3( -1 ) - 10

y = -3 - 10

y = -13

Therefore, the solution to the system of equation is (-1,-13).

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Answer:

Step-by-step explanation:

(2 1/2) : (1/4) = 10/1 =10

Answer:

4√3

Step-by-step explanation:

This is a special right triangle with angle measures 30°-60°-90° and side lengths represented with a-a√3-2a respectively to angle measures.

Here, hypotenuse is given as 8 which is represented with 2a, so a = 4

Then x will be 4√3 as it's represented with a√3.

The value of x is [tex]4\sqrt{3}[/tex] .

What is a trignometric function?

The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Mention all trignometric function ?

sinФ ,cosФ ,tanФ ,cosecФ ,secФ ,cotФ

What is the trick to remember trignometric formulas ?

Some People Have Curly Brown Hair Turned Permanently Brown

sinФ=[tex]\frac{p}{h}[/tex]

cosФ=[tex]\frac{b}{h}[/tex]

tanФ=[tex]\frac{p}{b}[/tex]

cosecФ=[tex]\frac{h}{p}[/tex]

secФ=[tex]\frac{h}{b}[/tex]

tanФ=[tex]\frac{b}{p}[/tex]

Given:

A right angled triangle with

base, b

perpendicular, p

hypotenuse, h=8

angle ,Ф = 60°

So by trignometric formulas ,we get

sinФ = sin60° =[tex]\frac{p}{h}[/tex]

⇒[tex]\frac{\sqrt{3} }{2} = \frac{x}{8}[/tex]

⇒[tex]x = 4\sqrt{3}[/tex]

Hence ,the value of x is obtained .

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Answer:

24.4 km

Step-by-step explanation:

The Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse of the triangle, and a and b are the legs. Plugging in your values, we get:

20^2 + 14^2 = c^2

Simplify: 400 + 196 = c^2

Simplify again: 596 = c^2

Square root both sides to cancel out the exponent on the right: 24.4131=c

Round: 24.4

The length of the line segment BD is 3 centimeters.

Herein we find two triangles proportional to each other. According to Thales's theorem, two triangles are proportional when both have congruent angles. The geometric system is represented by the following expression:

AB / AD = BC / DE = AC / AE

By direct inspection we notice that the two triangles are proportional as they have congruent angles. If we know that DE = 10 cm, BC = 8 cm and AB = 12 cm, then the side AD has the following measure:

12 cm / AD = 8 cm / 10 cm

AD = (10 cm / 8 cm) × 12 cm

AD = 15 cm

And the length of the line segment BD is:

BD = AD - AB

BD = 15 cm - 12 cm

BD = 3 cm

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The AGI and taxable income is $23,670 and $11,270

How to calculate AGI(Adjusted gross income) ?

The AGI calculation can be done as,

We have given that,

Gross income = $23670

1 Exemption = $12400

Adjustment = 0

Deduction = 0

Find AGI and Taxable income

AGI = Adjusted gross income

we know,

AGI = Total income - Any deduction or any adjustment  

AGI = ($23,670 + $12400)  - (0 + 0)

AGI = $36070

Now, Calculate taxable income

Taxable income = Gross income - 1 Exemption

                           = $23670 - $12400

                           = $11,270

Hence, the AGI and taxable income is $36,070 and $11,270

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Answer: D is the answer

Step-by-step explanation:

$23,670 and $11,270

Answer: D.

Step-by-step explanation:

In  linear equation ,Shirley takes 1.66 hours to paint the deck alone.

What in mathematics is a linear equation?

Let Shirley's time = x

Let Craig's time  = 5x

(5x + x)/2 = 5

We split up the hours by 2 because we want to find out how much time individually.

6x/2 = 5

6x = 10

 x = 1.66

Shirley takes 1.66 hours to paint the deck alone.

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The proportion of the 30 sampled bottles are more than 12 ounces is 0.30. The value is most affected by the error will be mean.

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency. A data set's mean (average) is calculated by adding all of the numbers in the set, then dividing by the total number of values in the set. When a data set is ranked from least to greatest, the median is the midpoint.

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