Assume the TV warranty or replacement times for TV sets are normally distributed with a mean of 9.2 years and a standard deviation of 1.1 years. Find the probability that a randomly selected TV will have a replacement time of less than 6 years.

The Mean distance is 4,145,760,000  miles

The correct option is (a)

Given,

The mean distance from Venus to the sun is 67,240,000 miles.

The mean distance from Mars to the sun is 4,213,000,000 miles.

Now, According to the question

Subtract the distance of Mars to the sun from Venus to the sun :

Let's Calculate the mean distance:

= 4,213,000,000 - 67,240,000

= 4,145,760,000 miles

Hence, The Mean distance is 4,145,760,000 miles.

The correct option is (a)

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Given:

Required:

To find the domain of the given function.

Explanation:

Now consider

David takes a car to get to the airport in time for his trip. 210 miles distance is the airport from his house in miles.

Given that,

David takes a car to get to the airport in time for his trip. He travels 35 miles in the first hour but understands that if he keeps going at this rate, he will be one hour late. For the final 15 miles to the airport, he speeds up by 15 mph and gets there 30 minutes early.

We have to find how far is the airport from his house in miles.

Distance traveled after 1 hour

Let us take the distance traveled after first 1 hour as y

Distance/speed = time

After 1 hour his speed = (35 + 15) = 50 mph

Total time count of 1 hour and 30 mins is 1.5 hr

y/50 + 1.5 = y/35

Multiply through by350

7y + 525 = 10y

3y = 525

y = 525/3

y = 175 miles

In the first 1 hour, at 35 mph, distance covered = 35 miles

Distance from his home to airport = 175 miles + 35 miles = 210 miles

Therefore, the distance between David's home and the airport is 210 miles.

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The probability of getting a green marble first and a red marble second exists 5/26.

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

Given: Red marbles = 3

Green marbles = 10

So, the total marbles = 3 + 10 = 13

Probability = Favorable outcomes  / Total outcomes

Since, here replacement is not allowed,

Therefore, the probability of getting a green marble and a red marble

= first red and second green + first green second red

= 3/13 × 10/12+ 10/13 × 3/12

= 2 × 3/13 × 10/12

= 30/78

= 5/13

The probability of getting a green marble first and a red marble second

= 10/13 × 3/12

= 30/156

= 5/26

Therefore, the probability of getting a green marble first and a red marble second exists 5/26.

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Step-by-step explanation:

You can add the two fractions by turning 1/2 and 5/6 to have the same denominator. Turn 1/2 into a fraction with a denominator of 6. That simplifies to 1 1/3. Hope this helps yo

The value of the function c(75) for  c(p) = 0.15p is c(75) = $11.25

From the question, the function definition is given as

c(p) = 0.15p

The above function is a linear function

This is so because it is represented as  y = mx where m is the slope

The function value to calculate is given as

c(75)

This means that we calculate c(p) when p = 75

So, we have

c(75) = 0.15(75)

This gives

c(75) = 0.15 x (75)

Evaluate the product

c(75) = 11.25

Hence, the function value is c(75) = 11.25

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Answer:

2a

Step-by-step explanation:

8a² / 4a

8/4 a²-¹

2a

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Answer:

2a

Step-by-step explanation:

8a^2 = 4a x 2a

8a^2 ➗ 4a

= ( 4a x 2a )/4a

= 2a

Applying the distributive property and precedence of operations, the results to each side of the expression is of 2/5, hence they property holds.

The left-hand side of the expression is defined as follows:

2/5(4/3-1/3)

Applying the distributive property, 2/5 multiplies each term as follows:

2/5(4/3-1/3) = 8/15 - 2/15

(multiplication of fractions -> multiply numerators and denominators with themselves).

They have common denominator, then the subtraction of the fractions is calculated as follows:

2/5(4/3-1/3) = 8/15 - 2/15 = 6/15

6 and 15 are divisible by 3, hence the fraction is simplified as follows:

6/15 = 2/5.

The right-hand side of the expression is given as follows:

2/5 x 4/3 - 2/5 x 1/3

We have two operations, subtraction and multiplication. The multiplication has higher precedence, hence:

2/5 x 4/3 - 2/5 x 1/3 = 8/15 - 2/15

Then the procedure is the same as the left-hand side, obtaining an equal result, and so the distributive property holds.

2/5(4/3-1/3)=2/5*4/3-2/5*1/3

We need to solve:

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The polynomial for the given graph is P(x) = (x+2)(x+8)(x-1)(x-4)

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x. In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.

Given,

The polynomial for the given graph is:

P(x) = (x+2)(x+8)(x-1)(x-4)

Each non-zero term in a polynomial function is made up of a number, known as the term's coefficient, and a variable raised to a non-negative integer power. A polynomial function can be either zero or the sum of a finite number of non-zero terms.

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Answer:

A)  8/15

Step-by-step explanation:

3 / 5 x 8/9

(3/5)(8/9)

(3*8)/(5*9)

(24/45)

8/15

Answer:

8/15

Step-by-step explanation:

3 / 5 x 8/9

Multiplying fractions

Rewriting

3/9 * 8/5

Simplify

1/3 * 8/5

Multiply the numerators

1*8 =8

Multiply the denominators

3*5 = 15

8/15

[tex]0.744\div6[/tex]

Simplify:

[tex]\frac{0.744}{6}[/tex]

[tex]=0.124[/tex]

Answer:

No, it is not.

Step-by-step explanation:

A function only has exactly one output for each input. In other words, for each X input, there is only one Y output. In the given set of coordinates, 3 is repeated as an input, which makes this set of coordinates not a function.

Answer:

u = 24

Step-by-step explanation:

-7/8u = -21

Solve for u

Multiply each side by -8/7

-8/7 *-7/8u = -21 *-8/7

u =3*8

u = 24

Answer:

u = 1/24

Write the equation:

–7/8u = –21

Get rid of fraction:

–7/2^3 • u = –21

–7 = ( – (8u) ) 21

Solve:

–7 = –8u + 21

–7 + 8u = –8u + 8u + 21

–7 + 8u = 21

–7 + 7 + 8u = 21 + 7

8u = 21 + 7

8u = 28

u = 1/24

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Answer:

AD

Step-by-step explanation:

Answer:

Step-by-step explanation:

1.34(b + 2) = 9.38
=> (b+2) = [tex]\frac{9.38}{1.34}[/tex]
=> (b+2) = [tex]\frac{9.38}{1.34}[/tex] x [tex]\frac{100}{100}[/tex]
=>  b+2  = 7
=> b = 7-2
=> b = 5

To solve the equation, we must subject b
so as 1.34 is in multiplication form with (b+2), if we take it to the other side of equals sign, it will be inverse which means it will be dividing 9.38

by multiplying 100/100 with the fraction, the  decimals can be removed (100 because the dot of decimal is considered one and there are two digits after dot, so two zeroes)
then by simple division we can find 7
then as 2 is added with be if it goes to other side it will be inverted and be subtracted from 7
so we get 5

The distance between C and D is 17.26 units

What is meant by distance?

Distance is a numerical or qualitative measurement of the distance between two objects or places. Distance can refer to a physical length or an estimate based on other factors in physics or common use (e.g. "two counties over"). Because spatial cognition is a rich source of conceptual metaphors in human thought, the term is frequently used metaphorically to mean a measurement of the amount of difference between two similar objects (such as statistical distance between probability distributions or edit distance between text strings) or a degree of separation (as exemplified by distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such conceptions of measurement, both real and metaphorical.

Distance CD = √{(-9-8)² + (-6+3)²}

                      = √{(-17)² + (-3)²}

                      = √{289 + 9}

                      = √298

                      = 17.26 units

Hence, the distance between C and D is 17.26 units

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Answer: 17.3

Step-by-step explanation:

The percentage of students that like rap that are also in grades 9–10 = 32%.

A frequency table is the type of table that shows the number of occurrence of different types of variables of an experiment.

From the frequency table given;

In grade 9 - 10;

Rap students = 40 students

Rock students = 30 students

Country students = 55 students

The total students in grade 9 - 10 = 125

Therefore, the percentage of rap students in grade 9 - 10;

= 40/125×100/1

= 4000/125

= 32%

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First of all, let's draw the net:

In which l= 3 units, h=2 units and w= 4 units.

The surface area will be:

SA= 2*h*w +2*l*w + 2*h*l

SA = 2*2*4 + 2*3*4 + 2*2*3

SA =16+24+12

SA= 52units²

The volume will be:

V=L*h*w

V= 3*2*4

V= 24 units³

To begin with

we have the inequality

To solve

Step 1: we will collect like terms

simplify the inequality above

Hence, the answer is

To draw the shape

Part B is correct

Length =9 , second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem.

x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.

L= 4 + W

Area is 45, so

L times W = 45

substituting the value of L, we get (4+W)*W=45, after simplifying this we get

4W+W2=45

W2+4W-45=0, this is a quadratic equation and after solving this we get the factors 9 and -5

( W+9) and (W-5) = 0

we get W=-9 or W=5, since width cannot be negative, so width = 5

substituting the value of W=5 in L = 4 +5, we get length = 9

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Second-order polynomial equation in one variable, length = 9. a 0. Since it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution.

A quadratic equation, or second-order polynomial equation with a single variable, is x ax2 + bx + c = 0. a 0. Since it is a second-order polynomial equation, which is ensured by the algebraic fundamental theorem, it must have at least one solution. The solution might be straightforward or difficult.

L= 4 + W

Since the area is 45, L times W = 45. Substituting the value of L, we get (4+W)*W=45. Simplifying this, we get 4W+W2=45. W2+4W-45. = 0. This is a quadratic equation, and after solving it, we get the factors 9 and -5. Since width cannot be negative, we get W=-9 or W=5. Substituting the value of W=5 in L = 4 + 5,

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The required area of triangle Δ STU would be 4 square units.

Triangle is defined as a basic polygonal shape of a triangle that has three sides and three interior angles. It is one of the fundamental shapes in geometry and is represented by the symbol Δ.

The given triangle Δ STU, with vertices S(2,2), T(7,3), and U(5,6), is drawn inside a rectangle.

The area of triangle Δ STU =  rectangle ABCS - Δ ABS - Δ BTU - Δ STC

The area of triangle Δ STU = 4 × 5 - 1/2 × 3 × 4 - 1/2 × 5 × 1 - 1/2 × 3 × 2

The area of triangle Δ STU = 8/2

The area of triangle Δ STU = 4 square units

Hence, the required area of triangle Δ STU would be 4 square units.

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The volume of the cone is:

The volume of a cone is given by the formula:

Given radius, r = 8, and height, h = 4, we have:

Deterministic.

The relationship between the variables is deterministic. A deterministic relationship refers to a relationship in which the dependent variable does not depend on other elements (variables) other than the independent element classified in the relationship. The independent variable (element) in the relationship possesses an exact value. Hence deterministic relationship is also named as the exact relationship between variables.

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First, rewrite the equation in its slope intercept form:

(slope intercept form: y = mx + b where m = slope ; b = y-axis intercept)

15x + 12y = -108​

Subtract 15x from both sides:

15x + 12y - 15x = -108​ - 15x

12y = -108 - 15x

Divide both sides by 12:

12y/12 = (-108 - 15x)/12

y = -5x/4 - 9

As you can see the slope of this line is -5/4

Now, two lines are perpendicular if:

m1*m2 = -1

Where:

m1 = Slope of the line 1

m2 = Slope of the line 2

m1 in this case would be -5/4

so:

-5/4* m2 = -1

Solving for m2:

m2 = -1/(-5/4) = 4/5 = 0.8

The materials and cost of Kara's project obtained using Pythagorean theorem, are;

(a) Distance between fence posts is 2•√(14) feet

(b) Kara needs about 12 fence posts

(c) Kara will need 22 diagonal pieces

(d) Kara's total cost is $281

Pythagoras theorem can be stated as, the square of the length of the hypotenuse side of a right triangle is equal to the sum of the squares of the other two sides.

The drawing obtained from a similar question consists of two diagonals between consecutive posts.

(a) The given parameters are;

Height of the fence post = 5 feet

Length of the diagonal pieces = 9 feet

The distance, d, between the fence posts using Pythagorean theorem gives;

d² = 9² - 5² = 56

d = 2•√(14)

The distances between the fence posts should therefore be 2•√(14) feet

(b) The number of fence posts, n, is given by the equation;

2•√(14) × n = 93

Which gives;

[tex] \displaystyle {n = \frac{93 }{2 \cdot \sqrt{14}} \approx 12.43}[/tex]

Given that after the 12th post, the 1st post comes next and the distance remaining is less than d, the number of posts, n is 12

(c) The number of diagonal pieces, m, needed, given that there are two diagonal pieces between two posts and there is only 11 in between spaces, gives;

m = 2 × 11 = 22

There are 22 diagonal pieces

(d) Cost of a fence post = $17

Cost of a diagonal piece = $3.5

Total cost, C, is therefore;

C = 12 × 17 + 22 × 3.5 = 281

Kara's total cost is $281

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Step-by-step explanation:

Deshaun is going to rent a truck for one day. There are two companies he can choose from, and they have the following prices. Company A charges $84 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.60 for every mile driven. For what mileages will Company A charge less than Company B? (Use m for the number of miles driven, and solve your inequality for m.)

inequality: 0.6m + 75 < 84

subtract 75 from both sides:

0.6m + 75 - 75 < 84 - 75

0.6m  < 9

divide both sides by 0.6:

0.6m/0.6 < 9/0.6

m < 15

SO:

For anything less than 15 miles, Company A charges less than Company B.

Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy are 16.

Sample timings as observed are 3.5, 3.1, 4.0, 3.5, and 3.9.

Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5

The average sample time (X) is 3.6.

Observed time (T) Mean (X) (X - T) (X - T)^2

3.5 3.6 0.1 0.01

3.1 3.6 0.5 0.25

4.0 3.6 -0.4 0.16

3.5 3.6 0.1 0.01

3.9 3.6 -0.3 0.09

Allow Standard deviation to be S.

2 in (X-T) - 1 n

[tex]S=\sqrt{\frac{0.52}{4}}[/tex]

S = 0.3605

Considering that (h) = 0.05,

Given that 95% of the time,

Z value at 95% confidence interval = 1.96

Let N be the number of observations.

2 N= Z.S hX

[tex]N=(\frac{1.96X0.3605}{0.05X3.6})[/tex]

N = 15.4

N = 16 (rounded off to next whole number) (rounded off to next whole number)

Consequently, 16 observations are required.

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Answer:

Step-by-step explanation:

Number of observations would be necessary to determine the true cycle time with a 95% confidence level and an accuracy of 16.

Sample-time average (X) = (3.5+3.1+4+3.5+3.9)/5

The average sample time (X) is 3.6. Observed time (T) Mean (X) (XT) (X-T)^2

3.5 3.6 0.1 0.01

3.1 3.6 0.5 0.25

4.0 3.6 -0.4 0.16

3.5 3.6 0.1 0.01

3.9 3.6-0.3 0.09

Allow Standard deviation to be S.

2 in (X-T) - 1n

S=√0.52/4

S=0.3605

Considering that (h) = 0.05,

Given that 95% of the time,

Z value at 95% confidence interval = 1.96 Let N be the number of observations.

2 N=Z.S hx

N=(1.96X0.3605)÷(0.05×3.6)

N = 15.4

N = 16 (rounded off to next whole number) (rounded off to next whole number) Consequently, 16 observations are required.

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Answer:

D. $870; $31,320 from deposits and $3,680 from interest

Explanation:

In order to calculate the monthly payment, we use the formula below:

Given:

• The Financial Goal, A= $35,000

• Rate = 7.5% = 0.075

• Number of compounding period = 12 (Monthly)

• Time, t = 3 years

Substitute into the given formula:

The monthly payment is $870.

Option D is correct.

The value of 6 divided by 396 is 0.1515.

Multiplication is the inverse of division. If 3 groups of 4 add up to 12, 12 split into 3 equal groups adds up to 4 in each group in division. The primary purpose of division is to determine how many equal groups are formed or how many people are in each group when equitably sharing.

The steps include:

Step 1: Take the first digit of the dividend from the left.

Step 2: Divide it by the divisor and write the answer on top as the quotient.

Step 3: Subtract the result from the digit and then write the difference below.

Step 4: Bring down the next digit of the dividend.

In this case, 6/396 will give the value illustrated above.

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The initial amount that was deposited by Clare is $725.

The equation for the amount of money in Clare's bank account after x months will be 725 + 175x

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.

Let the amount deposited initially be x.

Based on the information, this will be illustrated as:

x + 175(10) = 2475

x + 1750 = 2475

Collect like terms

x = 2475 - 1750

x = 725

The initial amount is $725.

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