the average life of a certain type of small motor is 10 years with a standard deviation of 2 years. the manufacturer replaces free of charge any motor that fails during a warranty period. if she is willing to replace only 3% of the motors that fail, how long should should the warranty period last? assume that the lifetime of a motor follows a normal distribution.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 5y - 6x = 5[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 5y = 6x + 5[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + \frac{5}{5} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{6}{5} x + 1[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

The two whole numbers  between which is √12 are 3 and 4.

What is an example of a whole number?

Any positive number that does not contain a fractional or decimal component is referred to as a whole number. The numbers 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers, for instance, as a result. -3, 2.7, or 3 12 are examples of non-whole numbers.

The closest perfect squares near 12 are 16 and 9 which are the perfect squares of 4 and 3 respectively Therefore the root of 12 lies between 3 and 4.

i.e  3 < √12 < 4

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Step-by-step explanation:

The length of the band is the number of units it covers

The actual length of the band is: \mathbf{40 + 10\pi}40+10π

The diameter of 1 pencil is given as:

\mathbf{d = 10}d=10

The circumference of 1 pencil is:

\mathbf{C = \pi d}C=πd

So, we have:

\mathbf{C = 10\pi }C=10π

Multiply by 4, to calculate the circumference of all pencils

\mathbf{4C =4 \times 10\pi }4C=4×10π

\mathbf{4C =40\pi }4C=40π

The rubber band covers a quarter of the 4 pencils.

So, we divide by 4

\mathbf{C = 10\pi }C=10π

The length of the band on one pencil is:

\mathbf{L = 10}L=10

Multiply by 4, for the 4 pencils

\mathbf{L = 40}L=40

So, the actual length of the band is:

\mathbf{Length = 40 + 10\pi}Length=40+10π

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The coordinates of the other endpoint of the Line segment is (-2,-5).

If M(x.y) divides the line formed by two points A(a,b) and B(c,d) into a ratio m:n. Then the coordinates of the point M can be found out by using the formula,

x = (mc + na)/(m+n)

y = (md + nb)/(m+n)

This above mentioned formula is known as The section Formula.

The one of the End point of the line is (10,-1) and the point (7,-2) is dividing the line in the ratio of 1:3.

Let us assume the other end point to be (a,b).

Now, applying Section Formula,

7 = [(1)(a)+(3)(10)]/4 and

-2 = [(1)(b)+(3)(-1)]/4

Further solving,

a = -2 and

b = -5

So, the coordinates of the endpoint is (-2,-5).

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Considering that the pumpkin is on the ground at x = 0 and x = 50, it is found that:

5. The roots of the quadratic function are: r1 = 0, r2 = 50.

6. The function is written as follows: y = a(x - 0)(x - 50).

7. The leading coefficient is a = -0.0992.

8. The function is: y = -0.0992(x - 0)(x - 50).

9. Applying the distributive property, the function is: y = -0.0992(x² - 50x).

10. The graph is given at the end of the answer.

A quadratic function of roots x' and x'' is defined as follows:

y = a(x - x')(x - x'').

In the context of this problem, the roots are the values of x when the pumpkin is on the ground, hence:

x' = 0, x'' = 50.

Hence, considering the roots, the function is written as:

y = a(x - 0)(x - 50).

The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet(mean of the roots), hence the vertex is given by these following coordinates:

(25, 62)

The coordinates are used to find the value of a, which is the leading coefficient of the function, as follows:

62 = a(25² - 50 x 25)

62 = -625a

a = -62/625

a = -0.0992.

Then the equation is written as:

y = -0.0992(x - 0)(x - 50).

The distributive property means that the outer term multiplies each the inside terms, and then the common terms are added, hence the function is:

y = -0.0992(x² - 50x).

Which is sketched at the end of the answer.

The pumpkin is on the ground when x = 0 and x = 50.

The maximum height obtained by the pumpkin is of 62 feet, after a horizontal distance of 25 feet.

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Answer: the answer to that problem is

X=2

Answer: Similar by SAS

Step-by-step explanation:

Note that [tex]\frac{AC}{AB}=\frac{JG}{HG}=\frac{1}{4}[/tex].

So, the triangles are similar by SAS (since the congruent angle is included between the proportional sides).

The decimal notation of 4.93 x 10³ will be 4930.00.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

The expression is;

4.93 x 10³

Now, Solve for decimal notation as;

4.93 x 10³ = 4.93 x 10 x 10 x 10

               = 49.3 x 10 x 10

               = 493 x 10

              = 4930.00

Thus, The decimal notation of 4.93 x 10³ will be 4930.00.

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Answer: 2/15  in/hour

Step-by-step explanation:

[tex]\displaystyle\\1)\ 6:36=\\\\6\frac{36}{60}=\\\\6\frac{3(12)}{5(12)}=\\\\6\frac{3}{5}=\\\\\frac{6*5+3}{5}=\\\\\frac{30+3}{5}=\\\\\frac{33}{5} \ hours[/tex]

[tex]\displaystyle\\2)\ 9-\frac{33}{5} =\\\\\frac{9(5)-33}{5}=\\\\\frac{45-33}{5} =\\\\\frac{12}{5}\ hours[/tex]

[tex]\displaystyle\\3)\ \frac{8}{25}:\frac{12}{5} =\\\\\frac{8}{25}*\frac{5}{12} =\\\\\frac{8(5)}{25(12)} =\\\\\frac{2*4*5}{5*5*4*3} =\\\\\frac{2}{5*3} =\\\\\frac{2}{15}\ in/hour[/tex]

Answer:

php 40,000

Step-by-step explanation:

In the ratio, Marvin corresponds to 12 and Victor to 2.

Marvin invested php 240,000.

His part of the ratio is 12.

240,000/12 = 20,000

Victor's part in the ratio is 2.

Victor's investment amount is 2 × php 20,000 = php 40,000

Percent of the games do not cost $1 or $2 is 35%.

A fraction of a number out of 100% is referred to as a percentage, sometimes known as a percent. Percentage refers to a portion of a total amount and signifies "per 100." For instance, 45% signifies 45% of the total or 45 out of 100.

By dividing the value by the entire value and multiplying the result by 100, one may determine the percentage. The percentage calculation formula is (value/total value)100%.

Given,

games = 58

5/8 is 62.5%

2.5% + 62.5% = 65%

100%-65% = 35%

A third of the games (35%) are free.

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Complete question -

At a carnival, 58 of the games cost $1. Another 2.5% of the games cost $2. What percent of the games do not cost $1 or $2?

Step-by-step explanation:

-1 × -3/10

=> 3/10

Multiplicative Inverse/Reciprocal of 3/10 = 10/3

A triangle is translated 6 units left and then dilated by a factor of 0.5. the statement about the triangle's image and pre-image that is correct is: The image and pre-image are not congruent figures because one of the  transformations is a rigid transformation, and the other is not.

Transformation is a term that refers to movement of an image from one position to the other.

When the intervals or distances between the points of the image being moved is not altered then the transformation is rigid transformation. However when the interval is altered it is a rigid transformation.

Translation is a rigid transformation while dilation is a non rigid transformation.

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Justin has sold 5 popsicles so from the original 9 if we take away 5, he has 4 popsicles left to eat.

Hey there!

[tex]3-3k+7k=5b[/tex]

Assuming you're trying to solve for b or k, I'll solve both.

Solve for b:

[tex]3-3k+7k=5b[/tex]

We will need to flip the equation:

[tex]5b=4k+3[/tex]

Now, let's divide both sides by 5:

[tex]\frac{5b}{5} =\frac{4k+3}{5}[/tex]

[tex]b=\frac{4}{5} k+\frac{3}{5}[/tex]

Solve for k:

[tex]3-3k+7k=5b[/tex]

Let's add -3 to both sides:

[tex]4k+3+-3=5b+-3\\4k=5b-3[/tex]

Now, let's divide both sides by 4:

[tex]\frac{4k}{4} =\frac{5b-3}{4}[/tex]

[tex]k=\frac{5}{4} b+\frac{-3}{4}[/tex]

Now, we've solved for b and k.

Hope this helps!

Answer:

860 degrees

Step-by-step explanation:

-210+210=0

0+650=650

650+210=860

The nth term for the given series is given by 4n-3.

What is meant by series?

The number series is 1, 5, 9, 13, 17,...

Common deviation (d)=5-1=4

A=1 is the first phrase.

A+(n1)d=1+(n1) is the formula for the nth term.

4=4n−3

∴tn =4n−3

The nth term for the given series is given by 4n-3.

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We identify the proportional relationship because it does not have a constant term, the correct option is:

y = (1/4)x

A proportional relationship between two variables x and y is written as:

y = k*x

Where k is called the constant of proportionality.

Here the options are:

The only option that has not a constant term is the second one:

y = (1/4)*x

And that is the proportional relationship.

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Answer:

y=(1/4)x

Step-by-step explanation:

I took the test :)

If you have saved some money to purchase five different songs to download to your portable music device. The inequality that represents the prices you can pay for each song if you have saved no more than 20 dollars is : 5 x ≤ 20.

Given:

Numbers of different songs to download = 5

Cost = $20

Hence,

The inequality  is ; 5 x ≤ 20

Now let solve the inequality

5 x ≤ 20

x = 20 /5

x = 4

So,

=  x ≤ 4

Therefore the inequality is  5 x ≤ 20.

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If we reflect a triangle in a line, translate a triangle, rotate a triangle, and reflect it in a point result in an image that will be congruent to the original( pre-image) triangle.

This is a problem from triangular geometry. We can solve this problem by following a few steps.

Here a triangle ABC is given and the triangle is at first reflected and then translated, thereafter it rotates and is later reflected.

After all, these processes the value of ∠A, ∠B, and ∠ C remains the same as usual concerning ∠A''', ∠B''', ∠ and C'', as they just changes coordinates not geometric structures.

After all these processes the length of the triangle AB, AC, BD, and A'''B''', B'''C''', C'''A''' remains the same as usual.

∵ We can conclude that ΔABC ≅ ΔA'''B'''C'''

( As AB = A'''B''', BC = B'''C''', ∠ABC = ∠ A'''B'''C''' )

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The point which describe the rate of change for the line modeled by y = 4/3x+2 would be; C. Vertical change of 4 units for each horizontal change of 3 units

Suppose that the considered linear equation is of the form y=mx+c

Then, when we change x by 1 unit, then:

[tex]y + \delta y = m(x + 1) + c\\mx + c + \delta y = mx + c + m\\\delta y = m[/tex]

where  [tex]\delta y[/tex]  shows the change in y as x changes by 1 unit.

It is found that this change is the value of 'm' called slope of the line this equation represents (each linear equation represents a line).

We have been given that the line modeled by y = 4/3x+2

The slope is given as m = 4/3

The point which describe the rate of change for the line modeled by y = 4/3x+2 would be;

C. Vertical change of 4 units for each horizontal change of 3 units

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Simply put, probability is the likelihood that something will occur.When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.Statistics is the study of events that follow a probability distribution.

Calculate probability ?

Therefore,

p = 0.43

if, in fact, 43% of shoppers make a purchase before leaving a store;

p = 78/200

=  0.39

if, in a sample of 200 shoppers, 78 make a purchase.

The sample proportion is a random variable that can't be predicted with certainty because it fluctuates from sample to sample.

It will be represented as a random variable by the letter P.

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The equivalent expression is 54 divided by 18, and the quotient is 3.

Answer:

-32

Step-by-step explanation:

m=3 , n=-1 ( given )

then, -4(m-n)2 = -4(3-(-1))2 = -32

It will take 30 weeks to have to have the same amount of money as my sister if I have $60 and my sister has $120. I am saving $7 per week and my sister is saving $5 per week.

A mathematical sentence that uses the equal sign, =, to show that two expressions are equal is known as an equation. Look for key words or phrases such as "is," "the same as," or "equals" to determine where to place the equal sign when writing a word sentence as an equation. Make an equation out of the word sentence.

A mathematical statement made up of two expressions joined by an equal sign is known as an equation. 3x - 5 = 16 is an example of an equation. We get the value of the variable x as x = 7 after solving this equation. Linear equations are classified into three types: point-slope, standard, and slope-intercept.

The given condition,

You have $60 and your sister has $120. You are saving $7 per week and your sister is saving $5 per week.

Let x be the time period in weeks. So we need same amount of money.

60+7x=120+5x

This is the equation needed.

2x=60

x=30 weeks

If I have $60 and my sister has $120, it will take 30 weeks for me to have the same amount of money as my sister. I save $7 per week, and my sister saves $5 per week.

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80 : 22 :: x : 11

x = (11 x 80) / 22

x = 880/22

x = 40

The missing number is 40

Rose walks 3.2 miles every day. How many miles will she have walked in 5 days?

3.2*5 = 16 miles

Christie was on a road trip. She travelled 320.95 miles on day one, 231.45 miles on day two, and 120.32 miles on day three. How many miles did she travel during her three-day trip?

320.95 + 231.45 + 120.32 = 672.72 miles

Hugh drove 774.4 miles. His car averaged 24.2 miles per gallon of gas. How many gallons of gas did the car use?

774.4/24.2 = 32 gallons

Answer:

Step-by-step explanation:

Question a: Solve for c

0.9c = 17.01 - 18.9r

c = 17.01-18.9r/0.9

c = 18.9 - 2.1r

Question b: Solve for r

18.9r = 17.01-0.9c

r =  9 - [tex]\frac{0.9}{18.9}[/tex]c

r = -10/21c + 9

(0.9/18.9 = 10/21)

Question c:

It will be best to use the equation that solves for c because this helps us determine how much chicken is bought.

c = 18.9 - 2.1r

Substitute r with 3.25

c = 18.9 - 2.1(3.25)

c= 18.9 - 6.825

c = 12.075

Answer:

yes

Step-by-step explanation:

ac goes straight forever and df does straight forever and they are parallel

This is an instance of conditional probability and the formula to use is;

Where:

P(A|B) = the probability of event A occurring given that event B occurred

P(A ∩ B) = the probability that both events A and B occur

P(B) = the probability of event B

Therefore, the probability that A occurs given that B occurs is 5/6