Rachel scored 670 on the analytic portion of the GRE (Graduate Record Exam). GRE scores are normally distributed with a mean of 600 and a standard deviation of 30. How many standard deviations is Rachel's score above the mean?

[tex]\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ T(\stackrel{x_1}{6}~,~\stackrel{y_1}{3})\qquad U(\stackrel{x_2}{6}~,~\stackrel{y_2}{9}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{6+6}{2}~~,~~\cfrac{9+3}{2} \right)\implies \left( \cfrac{12}{2}~~,~~\cfrac{12}{2} \right)\implies \stackrel{M}{(6,6)}[/tex]

Answer:

Step-by-step explanation:

Let x represent the amount invested at 9%. Then Roberto's interest was ...

  x(9%) +(10000-x)(6%) = 810

  0.03x + 600 = 810 . . . . . . . . . simplify

  0.03x = 210 . . . . . . . . . . . . . . . subtract 600

  x = 210/0.03 = 7000 . . . . . . . divide by the coefficient of x

Roberto invested $7000 at the higher interest rate.

To solve the problem, set up a system of equations using x and y for the amount invested at 6% and 9% respectively. Solve the system of equations to find the values of x and y, which represent the amounts invested at each interest rate. Roberto invested $3000 at 6% and $7000 at 9%

To solve this problem, we can set up a system of equations. Let x represent the amount invested at 6% and y represent the amount invested at 9%. The equation for the total amount invested is x + y = $10000. The equation for the total interest earned is 0.06x + 0.09y = $810. We can solve this system of equations to find the values of x and y.

Therefore, Roberto invested $3000 at 6% and $7000 at 9%.

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Answer:

A number line from 0 to 60 in increments of 6. A point is at 36 and a bold line starts at 36 and is pointing to the left. ⇒ last answer

Step-by-step explanation:

* Lets explain how to solve the problem

- When solving an inequality, there are some important points:

# If the inequality is x > a, then it represented on the number line by

  a ray with empty small circle as end starts at a and pointed to

  the right (⇒ ∞)

# If the inequality is x ≥ a, then it represented on the number line by

  a ray with bold small circle as end starts at a and pointed to the

  right (⇒ ∞)

# If the inequality is x < a, then it represented on the number line

  by a ray with empty small circle as end starts at a and pointed to

  the left (⇒ -∞)

# If the inequality is x ≤ a, then it represented on the number line by

  a ray with bold small circle as end starts at a and pointed to the

  left (⇒ -∞)

* Lets solve the problem

∵ 1/2 x ≤ 18

- Multiply both sides by 2

∴ x ≤ 36

- To represent it draw a number line from 0 to 60 and the counted

 by 6 as 0, 6, 12, 18, 24, 30, 36, 42, 48, 54, 60

- Draw a ray with bold end starts at 36 and pointed to the left

∴ A number line from 0 to 60 in increments of 6. A point is at 36 and

  a bold line starts at 36 and is pointing to the left.

Answer:

Option: D

Step-by-step explanation:) hope this helps have a great day ! :)

brainliest would be very appreciated

Answer:

Part A) In the scale drawing the length of the swimming pool is 10 cm and the width is 5 cm

Part B) The actual length of the bus is 45 ft

Step-by-step explanation:

Part A) Make a scale drawing of the swimming pool where 1 centimeter represents 5 meters

we know that

The scale is [tex]\frac{1}{5} \frac{cm}{m}[/tex]

To find out the dimensions of the pool in the scale drawing, multiply the actual dimensions by the scale factor

Find the length in the scale drawing

[tex]\frac{1}{5} \frac{cm}{m}(50\ m)=10\ cm[/tex]

Find the width in the scale drawing

[tex]\frac{1}{5} \frac{cm}{m}(25\ m)=5\ cm[/tex]

Part B) What is the actual length of the bus?

we know that

The scale is [tex]\frac{0.5}{5} \frac{in}{ft}=0.1\frac{in}{ft}[/tex]

The length of the school bus is 4 1/2 inches on the scale drawing

To find out the actual length of the bus, divide the length in the scale drawing by the scale

Convert mixed number to an improper fraction

[tex]4\frac{1}{2}\ in=\frac{4*2+1}{2}=\frac{9}{2}\ in[/tex]

Find the actual length of the bus

[tex]\frac{\frac{9}{2}\ in}{0.1\frac{in}{ft}}=45\ ft[/tex]

Answer:

a.0011100000

b.1010010001

c.0111001110

Step-by-step explanation:

We are given that a universal set

U={1,2,3,4,5,...10}

We  have to express each given set with bit strings , where the ith bit in the string is 1 if i is in the set and 0 otherwise

a.{3,4,5}

For 1=0  because 1 is not in the given set

For 3=1, For 4=2 , For 5=1 because 3,4 and 5 are in the set

For 2=0

For 6=0

For 7=0

For 8=0

For 9=0

For 10=0

Therefore, bit string=0011100000

b.{1,3,6,10}

For 1,3,6 and 10 write 1 because these elements are present in the set and for 2,4,5,7,8,9 write 0 because these elements are not present in the set

Bit string =1010010001

c.{2,3,4,7,8,9}

Similarly

Those elements which are present in the set then for those elements write 1 otherwise 0.

Bit string =0111001110

Answer:

The answer to your question is: length = 14 ft; width = 3 ft

Step-by-step explanation:

Data

Area = 42 ft²

length = 8 + 2w

w = width = ?

length = ?

Formula

Area = length x width = l x w

Substitution

                     42 = (2w + 8)w

                     42 = 2w² + 8w

                     2w² + 8w - 42 = 0

                                                                  Dividing by 2

                      w² + 4w - 21 = 0                 Factorize

                     (w + 7) (w - 3) = 0

                     w1 = -7                      w2 = 3

     It's not possible to have negative widths

So the answer is w = 3 ft

      length = 2(3) + 8

      length = 6 + 8

      length = 14 ft

The length and width of the rectangle barn are 14 feet and 3 feet, respectively.

The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.

Let the width of the rectangle be represented by x. Therefore, the dimension of the barn is,

Width = x

Length = 2x + 8

The area of a rectangular wall of a barn is 42 square feet.

Area = Width × Length

Area = x × (2x+8)

42 square feet = x(2x + 8)

42 = 2x² + 8x

2x² + 8x - 42 = 0

x² + 4x - 21 = 0

x² + 7x - 3x - 21 = 0

x(x + 7) - 3(x + 7) = 0

(x + 7)(x - 3) = 0

x = -7, 3

Since width can not be negative, therefore, the length and the width of the wall of the barn are,

Width = x = 3

Length = 2x+8 = 2(3)+8 = 14

Hence, the length and width of the rectangle barn are 14 feet and 3 feet, respectively.

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Answer:

time period is 260.57 years

Step-by-step explanation:

given data

growth rate = 3.4 % = 0.034

population = 4118000

area  P = 29000000000 square yard

to find out

time period that one person for every square yard of​ land need

solution

we will apply here population growth formula that is

total population P  = initial population × [tex]e^{rt}[/tex]    ..............1

here r is rate of growth and t is time period and

we consider here initial population is current population

so put value in equation 1 to get t

29000000000 = 4118000 × [tex]e^{0.034t}[/tex]

take ln both side

ln 7042.25 = ln [tex]e^{0.034t}[/tex]

8.8596 = 0.034 t

t = 260.57

so time period is 260.57 years

Answer:

A. 160 balls

Step-by-step explanation:

First we find the volume of each sphere.

diameter = d = 0.75 in.

radius = r = d/2 = 0.75/2 in. = 0.375 in.

V = (4/3)π(r^3) = (4/3)(3.14159)(0.375 in.)^3 = 0.221 in.^3

Because of the assumption about the space occupied by a sphere in random packing, we now calculate 190% of the volume of the sphere.

190%V = 1.9 * 0.221 in.^3 = 0.420 in.^3

Now we calculate the volume of the box.

V = LWH = 3 in. * 3 in. * 7.5 in. = 67.5 in.^3

To find out the number of balls that fit in the box, we divide the volume of the box by the randomly packed ball volume.

number of balls = (67.5 in.^3)/(0.420 in.^3) = 160.8

Answer: 160 balls

Explanation:

The cost for retaining the services when no time is spent is $18. That $18 is the minimum cost of the service call.

The added cost each hour is $48, so the per-hour charge is $48.

Answer:

24 minutes.

Step-by-step explanation:

Let D represent the distance from school to home and T represent time.

We have been given that your brother takes 40 minutes to get to school.

[tex]\text{Speed}=\frac{\text{Distance}}{\text{Time}}[/tex]

[tex]\text{Your brother's speed}=\frac{D}{40}[/tex]

You take 30 minutes to get to school.

[tex]\text{Your speed}=\frac{D}{30}[/tex]

Your brother left 4 minutes before you did, so distance traveled by him would be:

[tex]\frac{D}{40}\times (T+8)[/tex]

You speed: [tex]\frac{D}{30}\times T[/tex]

You will catch your brother, when both distances would be same:

[tex]\frac{D}{40}\times (T+8)=\frac{D}{30}\times T[/tex]

Cross multiply:

[tex]30D(T+8)=40DT[/tex]

Use distributive property:

[tex]30DT+240D=40DT[/tex]

[tex]30DT-30DT+240D=40DT-30DT[/tex]

[tex]240D=10DT[/tex]

Switch sides:

[tex]10DT=240D[/tex]

[tex]\frac{10DT}{10D}=\frac{240D}{10D}[/tex]

[tex]T=24[/tex]

Therefore, it will take you 24 minutes to catch up your brother.

To catch up to your brother who has a 4-minute head start, it will take you 12 minutes.

To determine how long it will take for you to catch up with your brother on the way to school, we need to consider the different walking speeds and the time advantage your brother has.

First, let's determine your walking speeds. If your brother takes 40 minutes to reach school and you take 30 minutes for the same route, then assuming you both walk at a constant speed, we can say that your walking speed is 4/3 times faster than your brother's speed because 40 minutes divided by 30 minutes equals 4/3.

Now, given that your brother has a 4-minute head start, let's calculate the time it takes for you to catch up to him:

Therefore, it will take you 12 minutes to catch up with your brother.

Answer: Hi!

Let's start, you have 3 boxes and 3 types off eggs inside of each. The fact that they each box is labelled incorrectly means that inside the box labelled Large, only can be the set of small or mixed eggs.

So, let's suppose we open this Box labelled LARGE and inside of it we find the small eggs.

now we have two remaining boxes, the labeled SMALL and the labelled MIXED.

the MIXED can only contain the set of large eggs or the set of small, because you know that is wrong labelled, and also you know that the small eggs are in the first box that you oppened, so here are the large eggs, and now in the last box is the last set of eggs, the mixed one.

So you only will need to open one box to know which eggs are in what box.

Answer:In 20 weeks they will have the same amount of money.

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

We are given that

Jim has currently balance=$1250

Sally has currently balance=$1400

Jim deposits money per week=$27.50

Sally deposits per week=$20

We have to find how many weeks  they will have the same amount of money.

Let w be the week .After w week they have same amount

According to question

[tex]1250+27.50 w=1400+20w[/tex]

[tex]27.50 w-20 w=1400-1250[/tex]

[tex]7.5 w=150[/tex]

[tex]w=\frac{150}{7.5}=20[/tex]

After 20 weeks , they will have the same amount of money.

Answer: so in the first 7 games, eh scored between 3 and 18 touchdowns.

if you assume there is a even distribution, you will get a media of (18 -3) /2 + 3 = 10.5

so yes, in theory he will score 10.5 more or less.

the first error is assuming that he will score at least 10.5 on watching this result, 10.5 is the most probable number, not the minimum.

the second problem here, is that you are doing statistics with just 7 samples, that is not enough samples to do proper statistics.

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 7^{-\frac{5}{6}}\cdot 7^{-\frac{7}{6}}\implies 7^{-\frac{5}{6}-\frac{7}{6}}\implies 7^{\frac{-5-7}{6}}\implies 7^{\frac{-12}{6}}\implies 7^{-2}\implies \cfrac{1}{7^2}\implies \cfrac{1}{49}[/tex]

Answer:

Sarah must has to ride with average speed 10 miles per hour.

Step-by-step explanation:

Average Speed tells the rate at which object is travelling his whole journey.

[tex]Average\ Speed\=\ \frac{Total\ distance\ traveled}{Total\ time\ taken}[/tex]

∴  [tex]Average\ Speed=\dfrac{2.5}{\frac{15}{60}}[/tex]

⇒  [tex]Average\ Speed=\dfrac{2.5}{15}\times 60[/tex]

⇒ Average Speed = 10 miles per hour

Hence, Sarah has to travel with average speed more than 10 miles per hour.

Answer:8,400. I think that is the answer. Hope you get it right.

Answer:

-1/32

Step-by-step explanation:

we have

[tex](-\frac{1}{2})^{3} )(-\frac{1}{2})^{2})[/tex]

Remember that

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents

so

[tex](-\frac{1}{2})^{3} )(-\frac{1}{2})^{2})=(-\frac{1}{2})^{3+2})=(-\frac{1}{2})^{5})=-\frac{1}{32}[/tex]

Answer:

This is actually an interview question for IT jobs!

The game strategy changes if there can be communication or not.

If there is no communication then I would pick the expected value of the game, meaning the sum of each value times the probability of it showing up on the die (1/21) or:

[tex]E(x) = 1*\frac{1}{21} +2*\frac{1}{21}+3*\frac{1}{21}+...+21*\frac{1}{21}[/tex]=[tex]\frac{231}{21} =11[/tex]

This mathematically minimizes the difference between my pick and the one that comes from the roll.

If there is communication, and a consensus can be reached, then the most reasonable answer would be the one that gives all of us the same possibility to win: 4, 11, 18, so each of us covers 7 numbers, and each of us would have 1/3 chances to win.

If there is communication, and a consensus cannot be reached, then I would have to calculate the difference between both their pics, if it is smaller than the expected value, and it inclines towards high numbers, for example: 10, 18, then i would pick one less than the smallest, meaning 9, because i would cover 1-9, the one picking 10 would cover 10-14 and 18 would cover 15-21. My range would be bigger. If it is smaller than the expected value, and it inclines towards low numbers, i would pick one over the highest, for example 4, 9. I would pick 10. If the difference is bigger than  the expected value then i would calculate whether i would cover more picking a number in the middle of their range or to the side, depending on their pick. For example, if they pick 9, 21, I would cover more range picking 8 than 15.

To maximize odds of winning in a game with a 21-faced die, choose a number in the middle range, such as 11, or strategically select a number that evenly splits the range of possible outcomes, taking into account the numbers chosen by other players.

The best strategy for choosing a number in a game with a 21-faced die is to select a number that lies in the middle range, as this increases the probability that your number will be closest to the outcome of the roll. With a 21-faced die, the middle number is 11. Assuming other players may not choose the same number, if you pick first, go for 11. If other players have already picked numbers, choose a number that splits the remaining range of outcomes as evenly as possible. This method leverages the concept of probability which, unlike games of pure luck like roulette, gives you some control as you can make educated guesses based on the remaining numbers, just as skill is involved in games like blackjack where decisions are critical to the outcome.

In gambling games like blackjack, skillful play can reduce the house edge whereas in roulette, every spin is independent of the last. The outcomes of particular numbers being rolled in a dice game can inform your strategy to some extent - for example, knowing that seven is the most common result when rolling two six-sided dice because there are more combinations that produce this sum. However, with a single die, as in the scenario with the 21-sided die, each face has an equal probability of landing face up, so strategic choice becomes more about distancing your choice from others to maximize your chances of being closest to the roll's outcome.

Answer:

  [146.25, 153.75] yards

Step-by-step explanation:

2.5% of 150 yards is ...

  0.025 × 150 yd = 3.75 yd

This amount can be added or subtracted from the nominal length, so the range of lengths is ...

  from 150 yd -3.75 yd = 146.25 yd

  to 150 yd +3.75 yd = 153.75 yd

Answer:

[tex]y = 8x + 3[/tex]

Step-by-step explanation:

All you have to do is take the given information and put it into the Slope-Intercept Formula.

I am joyous to assist you anytime.

When trying to find a root of a number ( the little number included with the square root symbol) this is the same as raising the number to that fraction.

Example : ∛5 would be the same as 5^1/3

So in the given problem the 5th root can be written as x^1/5

Now the number is 13^3, so to simplify the 5th root, the value could be written as 13^3/5

Answer:

When trying to find a root of a number ( the little number included with the square root symbol) this is the same as raising the number to that fraction.

Example : ∛5 would be the same as 5^1/3

So in the given problem the 5th root can be written as x^1/5

Now the number is 13^3, so to simplify the 5th root, the value could be written as 13^3/5

Step-by-step explanation:

Answer:

[tex] -4 = m[/tex]

Step-by-step explanation:

According to the Point-Slope Formula, y - y₁ = m(x - x₁), m represents the rate of change [slope], so in this case, -4 is our slope.

I am joyous to assist you anytime.

Answer:

a) 1/3 of a clean room

Step-by-step explanation:

First at all, we need to calculate how much takes Jacob cleaning a room.

So we divide 1 hour by 2 rooms

1 hour = 60 min

and [tex]\frac{60min}{2 rooms}  =  30 min/room[/tex]

Now, we must to know how much takes William to cook a meal:

In 60 minutes William cooks 9 meals

so we have:

[tex]\frac{60min}(9 meals} = 6 \frac{2}{3} minutes/meal \\[/tex]

that means William spends 6 minutes and 40 sec cooking a meal.\

Now we can solve:

In 6 minutes and 40 sec, how many rooms can Jacob clean?

We know Jacob spend 30 minutes cleaning a room so in 10 minutes or 1/3 of a clean room Williams had already cooked another meal. Thus, the closest answer is a)1/3 of a clean room.

Answer:

Step-by-step explanation:

Use the Compound Amount equation:  A = P(1+r/n)^(nt), where P is the original amount (principal), r is the interest rate as a decimal fraction, n is the number of compounding periods per year, and t is the number of years.  Here we have:

A = ($2665.79)(1 + 0.048/4)^(4*11), or:

A = ($2665.79)(1.012)^44 = $4505.76.

Subtracting the principal amount from this result, we get:

$4505.76 - $2665.79 = $1839.97

This matches the third of the four given possible answers.

Final answer:

To calculate the interest earned, use the formula for compound interest: CI = P(1 + r/n)^(nt) - P. Plugging in the given values, the interest earned by Nelson is $1,839.97.

Explanation:

To calculate the interest earned, we can use the formula for compound interest:

CI = P(1 + r/n)^(nt) - P

Where CI is the compound interest, P is the principal amount, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years.

Plugging in the given values, we have:

CI = 2665.79(1 + 0.048/4)^(4*11) - 2665.79

Calculating this, we find that the interest earned is $1,839.97.

Answer:

You need the total of square feet of the mural before you can divide 50 square feet to it and get your answer of how many pints of paint you will need.

For example.

Mural size is 2800 square feet

1 pint per 50 square feet

Work out problem.

2800 square feet ÷ 50 square feet= ?

 = 56 pints of paint

Answer:

15 seconds

Step-by-step explanation:

Because the split id 25% and 75%, we could create another average pretending that there are four kids, one who ran in 12 seconds, and three who ran in 16.

Equation for averages: (a₁ + a₂ + a₃ + ... [tex]a_{n}[/tex])/ n

Plug in: (12 + 16 + 16 + 16)/4

Add: 60/4

Divide: 15 seconds

Answer:

  0.0001

Step-by-step explanation:

The value of the number is 0.0001. That presentation meets the format requirements for your literal.

To express 1.0e-4 as a floating-point literal in long form without scientific notation, write it as 0.0001, which means moving the decimal four places to the left.

To type 1.0e-4 as a floating-point literal with a single digit before and four digits after the decimal point without using scientific notation, we need to convert the exponent to its decimal representation. The exponent “e-4” indicates that the decimal point is to be moved 4 places to the left.

The number 1.0e-4 in long form is 0.0001. This is because the exponent part “e-4” of the scientific notation corresponds to dividing the number by 10,000 (which is 10⁴), turning 1 into 0.0001. To express this number with one digit before the decimal point and four digits after, we write it as 0.0001.

When converting from scientific notation or using significant figures, remember that all digits reported in front of the multiplication sign are significant, zero functions as a placeholder for the decimal point, and negative exponents indicate division by powers of ten.

Answer:

b) x ≥ 3000 gallons

Step-by-step explanation:

Part a)

Production of Year 1 = x gallons

By each year the producer will increase the production by 500 gallons. So,

Production in Year 2 = x + 500 gallons

Similarly,

Production in Year 3 = x + 500 + 500 = x + 1000 gallons

Production in Year 4 = x + 1000 + 500 = x + 1500 gallons

Production in Year 5 = x + 1500 + 500 = x + 2000 gallons

Part b)

The maple syrup producer wants to produced atleast 20,000 gallons in 5 years.

Total amount produced in 5 years = x + x + 500 + x + 1000 + x + 1500 + x + 2000

Total amount produced in 5 years = 5x + 5000

Since, producer wants total production to be atleast 20,000, we can set up the inequality as:

5x + 5000 ≥ 20000

Subtracting 5000 from both sides, we get:

5x ≥ 15000

Dividing both sides by 5, we get:

x ≥ 3000

This means, in the first year the production of maple syrup must be atleast 3,000 gallons i.e 3000 gallons or more to have a total of atleast 20,000 gallons in 5 years.

Answer:222

Step-by-step explanation:

add it

The pipes need to be moved 2.25 feet.

To determine how many feet the pipes need to be moved:

Therefore, the pipes need to be moved 2.25 feet away from the wall to achieve the required clearance.