Gary has a brother and a sister in college. He traveled 2 x 10^3 miles to visit his sister. He traveled 4. 2 x 10^5 miles to visit his brother. The distance Gary traveled to visit his brother is how many times as much as the distance Gary traveled to visit his sister?

Answer:

123

Step-by-step explanation:

We can square and cube the equation, then multiply the results together.

(a + \(\frac{1}{a}\)) = 3 ← square both sides

a² + 2 + \(\frac{1}{a^2}\) = 9 ( subtract 2 from both sides )

a² + \(\frac{1}{a^2}\) = 7 → (1)

-----------------------

Now cube both sides

a³ + \(\frac{1}{a^3}\) + 3(a + \(\frac{1}{a}\)) = 27

a³ + \(\frac{1}{a^3}\) + 3(3) = 27

a³ + \(\frac{1}{a^3}\) + 9 = 27 ( subtract 9 from both sides )

a³ + \(\frac{1}{a^3}\) = 18 → (2)

------------------------------

Multiply (1) and (2)

(a² + \(\frac{1}{a^2}\) )(a³ + \(\frac{1}{a^3}\) ) = 7(18)

\(a^{5}\)  + ( \(\frac{1}{a}\) + a) + \(\frac{1}{a^5}\) = 126

\(a^{5}\) + 3 + \(\frac{1}{a^5}\) = 126 ( subtract 3 from both sides )

\(a^{5}\) + \(\frac{1}{a^5}\) = 123

The perimeter of Rebekah's new mural is 9 meters.

The whole distance that a rectangle's borders, or its sides, cover is known as its perimeter. Given that a rectangle has four sides, the perimeter of the rectangle will be equal to the total of its four sides.

Given:

A rectangular mural measures 1 meter by 3 meters.

Rebekah creates a new mural that is 0.5 meters longer.

The perimeter of Rebekah's new mural,

= 2 (1.5 + 3)

= 9 meters.

Therefore, the perimeter is 9 meters.

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Answer:

9

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Given

f(x) = \(\frac{1}{x+2}\)

The denominator cannot be zero as this would make f(x) undefined.

Equating the denominator to zero and solving gives the value that x cannot be and if the numerator is non zero for this value then it is a vertical asymptote.

x + 2 = 0 ⇒ x = - 2

The equation of the vertical asymptote is x = - 2

Answer:

The diameter of the circle would be: 6.4 cm. rounded or 6.36619772 cm.

The radius of the circle would be: 3.2 cm. rounded or 3.18309886 cm.

Step-by-step explanation:

So, the first step would be : D = \(\frac{20}{\pi }\)

Then : D = 20 ÷ \(\pi\)

Finally, the answer will be : 6.36619772 cm. or 6.4 cm.

The first step would be : r = \(\frac{20}{2\pi }\)

Then : 20 ÷ 6.2831853071796 (2\(\pi\))

Finally, the answer will be : 3.18309886 cm. or 3.2 cm.

Answer:

To expand (x + 4)², we can use the formula for squaring a binomial: (a + b)² = a² + 2ab + b². In this case, a = x and b = 4.

So,

(x + 4)² = x² + 2(x)(4) + 4²

= x² + 8x + 16

Thus, (x+4)² when expanded and simplified gives x² + 8x + 16.

Step-by-step explanation:

Answer:

x²n+ 8x + 16

Step-by-step explanation:

(x + 4)²

= (x + 4)(x + 4)

each term in the second factor is multiplied by each term in the first factor, that is

x(x + 4) + 4(x + 4) ← distribute parenthesis

= x² + 4x + 4x + 16 ← collect like terms

= x² + 8x + 16

Answer:

Step-by-step explanation:

\(\sf \left(2x+\cfrac{1}{2}\right)+\left(8x-2\cfrac{1}{2}\right)\)

We'll need to convert the mixed number 2 1/2 to improper fraction.

\(\sf \left(2x+\cfrac{1}{2}\right)+\left(8x-\cfrac{5}{2}\right)\)

Simplify...

\(\sf 2x+\cfrac{1}{2}+8x-\cfrac{5}{2}\)

Add similar elements.

\(\sf 10x+\cfrac{1}{2}-\cfrac{5}{2}\)

\(\sf 10x+\cfrac{-4}{2}\)

Divide numbers..

\(\sf 10x-2\)

_______________________

a) Probability of drawing a Blue, then a Red:

There are a total of 11 marbles in the bag. The probability of drawing a Blue on the first draw is 3/11. After drawing a Blue, there are 10 marbles left in the bag, including 5 Red marbles. The probability of drawing a Red on the second draw is 5/10. Therefore, the probability of drawing a Blue, then a Red is (3/11) * (5/10) = 15/110 = 3/22.

b) Probability of drawing a Red, then a White:

The probability of drawing a Red on the first draw is 5/11. After drawing a Red, there are 10 marbles left in the bag, including 3 White marbles. The probability of drawing a White on the second draw is 3/10. Therefore, the probability of drawing a Red, then a White is (5/11) * (3/10) = 15/110 = 3/22.

c) Probability of drawing three Blues in a row:

The probability of drawing a Blue on the first draw is 3/11. After drawing a Blue, there are 10 marbles left in the bag, including 2 Blue marbles. The probability of drawing a Blue on the second draw is 2/10. After drawing two Blues, there are 9 marbles left in the bag, including 1 Blue marble. The probability of drawing a Blue on the third draw is 1/9. Therefore, the probability of drawing a Blue, then a Blue, then a Blue is (3/11) * (2/10) * (1/9) = 6/990 = 1/165.

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Answer:

3.14 in²

Step-by-step explanation:

π= pi = 3.14

r = 2/2 = 1 inch

the diameter is the straight line that passes through the centre of a circle and touches the two edges of the circle.

A radius is half of the diameter

3.14 x 1² = 3.14 in²

Answer: 12.56

Step-by-step explanation: Find area with Pie:

A= Pie x radius squared so 2 x 2 = 4 with what then we multiply

3.14 x 4 = 12.56

OR

Unless the radius is not 2 and 2 is diameter than we just divided 2 by 2 and get 1 the whole then 1 squared is 1 and 3.14 x 1 = 3.14

The monthly payment for the loan is $328.05. So we can determine that the family can afford the monthly payment.

Money spend =  $400

Time = 120 months

Loan amount = $30,000

Interest rate = 6.5%.

The formula is given P = \(PV*(i / (1 - (1+i)^{-n}))\)

The interest should be calculated at the monthly rate. So, we can divide the interest rate by 12.

i = 0.065/12 = 0.00541667  

Substituting the values into the formula,

P = \(30000 * 0.00541667 / (1 - (1+0.00541667)^{-120})\)

P = $328.05

Therefore, we can conclude that the monthly payment for the loan is $328.05.

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The students who read newspapers is 30, and the read story books is 90.

Let number of students read newspapers as N and story books as S.

We have

Out of 110 students, 10 read neither newspaper nor story book.

This means that these 10 students are not included in either N or S.

As, students who read story books is three times read newspapers. then, S = 3N.

So, the total number of students who either read newspapers or story books is given by:

= 110 - 10

= 100

and, the total number of students who either read newspapers or story books is given by:

N + S - 20 = 100

Substituting S = 3N, we have:

N + 3N - 20 = 100

4N - 20 = 100

4N = 120

N = 30

Now, we can calculate the number of students who read story books:

S = 3N = 3 c 30 = 90

Therefore, the students who read newspapers is 30, and the read story books is 90.

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Answer:

1) 12 units^2

2) 4 units^2

3) 2units^2

Step-by-step explanation:

count the squares

An equation is formed of two equal expressions. The missing pieces of the solution of the quadratic equation are 50, 3, and -8.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

To fill the missing piece of the solution of the quadratic equation, you need to balance each of the equations. Therefore, the solution to the problem can be written as,

\(-32 = 2(x^2 + 10x)\\\\-32 + 50 = 2(x^2 + 10x + 25)\\\\18 = 2(x + 5)^2\\\\9 = (x + 5)2\\\\\pm 3= x + 5\\\\x = -2\ \ {\rm or}\ \ x = -8\)

Thus, the solution of the quadratic equation is -2 or -8.

Hence, the missing pieces of the solution of the quadratic equation are 50, 3, and -8.

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A student's probability of having a sister are 1/2 or 0.5 if they do not have a brother.

Using the above data table, we must determine the likelihood that a student without a brother also has a sister. Analysing the table now

has a sibling: 5

possesses no sisters: 2

has an 18-year-old brother

possesses no brothers: 4

We are looking for the likelihood that a student has a sister and neither a brother (as indicated by the statement "Does not have a brother"). In this instance, there are two children who do not have a brother but do have a sister, making that number the number of positive outcomes.

No matter whether a student has a sister or not, the total number of outcomes is equal to the number of students who do not have a brother. According to the table, there are 4 students without brothers.

As a result, the likelihood that a student who doesn't have a brother will have a sister can be determined as follows:

Probability is calculated as the ratio of the number of favourable outcomes to all possible outcomes.

Probability equals 2/4

Probability equals 0.5 or half.

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Answer:

B. 970,000

Step-by-step explanation:

Move the decimal 5 places to the right, since the exponent is a positive 5.

9.7 x 10⁵ = 970,000.

If it is a negative exponent, you would have to move the decimal to the left.

Answer:

x= 1/2

Step-by-step explanation:

Let's solve your equation step-by-step.

−2x+3−5x−4=−3x−8+10x

Step 1: Simplify both sides of the equation.

−2x+3−5x−4=−3x−8+10x

−2x+3+−5x+−4=−3x+−8+10x

(−2x+−5x)+(3+−4)=(−3x+10x)+(−8)(Combine Like Terms)

−7x+−1=7x+−8

−7x−1=7x−8

Step 2: Subtract 7x from both sides.

−7x−1−7x=7x−8−7x

−14x−1=−8

Step 3: Add 1 to both sides.

−14x−1+1=−8+1

−14x=−7

Step 4: Divide both sides by -14.

Answer:

6 or 60. 45 is in it. Best I can explain

Answer:

162

Step-by-step explanation:

step 1. our output value is 360

step 2. we represent the unknown value with x

step3. from step 1 above, 360= 100%

step 4. similarity, x=45%

step 5. this result in a pair of simple equations

360=100%(1)

x=45%(2)

step 6. by dividing equation 1 and 2 and noting that both the RHS (right hand side) of both equations have the same unit (%); we have

360/x = 45/100

x=162

therefore, 45% of 360 is 162

hope this helps!!!

Answer:

15.5^2 + 14.0^ = 20.8^2

436.25 = 432.64

it is not a triangle because a+b is not = c

Answer: These given lengths do not make up a right triangle.

Step-by-step explanation:

In order to figure out if this is a right triangle or not, we would need to use the Pythagorean Theorem in order to verify if these lengths satisfy the properties of a right triangle. We would need to use the formula a^2 + b^2 = c^2.

14^2 + 15.5^2 = 20.8^2

196 + 240.25 = 432.64

436.25 ≠ 432.64

Therefore, this is not a right triangle.

If only two out of the five people show up for the meeting, it is possible in 10 different ways.

If five people plan to meet after school and there will be one group of five people if they all show up, but only two people show up, we need to determine the number of ways this can happen.

To find the number of ways two people can show up out of the five, we can use combinations. In a combination, the order of selection does not matter.

The number of ways to choose two people out of five can be calculated using the formula for combinations, denoted as "nCr", where n is the total number of people and r is the number of people we want to choose.

In this case, we want to choose 2 people out of 5, so the calculation would be:

5C2 = (5!)/(2!(5-2)!) = (5!)/(2!3!) = (5 \(\times\) 4)/(2 \(\times\) 1) = 10

Therefore, there are 10 possible ways for two people to show up out of the five if all of them plan to meet after school.

These 10 possibilities could be different combinations of any two individuals out of the five.

To determine the specific combinations, you can list all the pairs or use a combination formula calculator.

It's important to note that the order in which the two people show up does not matter, as long as they are two out of the five originally planning to meet.

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120

Step-by-step explanation:

turning $54 to cents

$1= 100c

$54=54×100= 5400

calling the number of 20c coins a and 50c coins b

20a + 50b= 5400 ...equ(1)

since there are twice as many 20c coins as 50c coins

a=2b ...equ(2)

substituting a=2b in equ(1)

20(2b) + 50b = 5400

40b + 50b = 5400

90b = 5400

dividing both sides by 90

b= 60

to get the number of 20c coins I'm substituting b=60 in equ(2)

a= 2×60

a=120

therefore the number of 20c coins is 120

Answers:

5.8x10-7= 51

5.15x10^6= 5150000

6.37x10-^2= 637

5.545x10-7= 55450000

Answer: c

Step-by-step explanation:

Answer:

what are the options...

Step-by-step explanation:

The width of a confidence interval will be option (A)  narrower for 99% confidence than 95% confidence.

A confidence interval is a range of values within which we believe a population parameter, such as the mean or proportion, is likely to fall. It is calculated based on a sample of data and a chosen level of confidence, typically expressed as a percentage.

The width of a confidence interval depends on three factors: the level of confidence, the sample size, and the standard deviation

The width of a confidence interval depends on the level of confidence, sample size, and standard deviation. A higher level of confidence results in a wider interval, while a larger sample size and a smaller standard deviation result in a narrower interval.

Therefore, A 99% confidence interval will be wider than a 95% confidence interval, as it needs to include a larger range of possible values to provide a higher level of confidence.

Therefore, the correct option is (A) narrower for 99% confidence than 95% confidence.

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The given question is incomplete, the complete question is:

The width of a confidence interval will be:

A. narrower for 99% confidence than 95% confidence.

B. narrower for a sample size of 100 than for a sample size of 50.

C. wider for 90% confidence than 95% confidence.

D. wider when the sample standard deviation (s) is small than when s is large

95% of the students have study hours between 10.75 and 13.25 hours and the percentage of the students have study hours that are above 12 is 92%.

Given average of 12 % studying required, population mean of 15 hours, standard deviation of 3 hours.

We have to find the confidence interval for 95% students and the percentage of the students that have studied above 12 hours.

Margin of error=z*σ\(\sqrt{n}\)

z value for the p value 0.95 is 1.96.

Margin of error=1.96*3/\(\sqrt{22}\)

=5.88/4.69

=1.25

Upper interval=Mean +margin of error

=12+1.25

=13.25

Lower interval=Mean- margin of error

=12-1.25

=10.75

The confidence interval (10.75,13.25).

Now we will calculate the percentage of the students that are above 12.

z value when X=12, z=12-15/15

=-3/15

=-0.2

p value of -0.2 will be =0.5+0.4207=0.9207

=0.9207*100

Percentage=92.07%

Approx=92%.

Hence the confidence interval is (10.75 , 13.25) and 92% students have studied above 12.

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Question is incomplete as it should include  sample size of 22.

Answer:

v=5

Step-by-step explanation:

you are trying to make 4v into v right ?

so simply divide it by 4 - the same if it was 4a or 7a or 9k, always start by dividing by the number

then you need to balance the two sides - so whatever number you divide the letter by (which is the 4 in this case) , you do the same with the other side , so whatever number is after the equal sign , divide it by 4

PART ONE                                      ↓ 4v  =   20  

           DIVIDE BY 4                       →  v   =    20

PART TWO                                          v   =   20 ↓

                                                            v   =     5 ←           DIVIDE BY 4

Answer:

wut

Step-by-step explanation:

The first 3 consecutive odd numbers are 1,3,5. x and x + 2 are consecutive odd numbers if x is an odd number.

Consecutive numbers are those that always appear in the same order, from smallest to largest.

For instance:

The numbers 1, 2, 3, 4, 5, 6, and so on are consecutive.

consecutive odd numbers:

Let's call the odd number "x." The subsequent term becomes "x + 4" and the next consecutive odd number becomes "x + 2."

Numbers that begin with 1, 3, 5, 7, or 9 are considered odd. 1, 3, 5, 7, 9, 11, 13, 15, and so on are examples of consecutive odd numbers.

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For the given function ƒ(x, y) = 3x² − 5x³y³ + 7y²x²: a. The directional derivative of ƒ at the point P(1, 1) in the direction of a given vector needs to be found. b. The direction of maximum rate of change of ƒ at the point P(1, 1) should be determined. c. The maximum rate of change of ƒ needs to be calculated.

To find the directional derivative at point P(1, 1) in the direction of a given vector, we can use the formula:

Dƒ(P) = ∇ƒ(P) · v,

where ∇ƒ(P) represents the gradient of ƒ at point P and v is the given vector.

To find the direction of maximum rate of change at point P(1, 1), we need to find the direction in which the gradient ∇ƒ(P) is a maximum.

Lastly, to calculate the maximum rate of change, we need to find the magnitude of the gradient vector ∇ƒ(P), which represents the rate of change of ƒ in the direction of maximum increase.

By solving these calculations, we can determine the directional derivative, the direction of maximum rate of change, and the maximum rate of change for the given function.

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