The Hall family and the Nguyen family each used their sprinklers last summer. The water output rate for the Hall family's sprinkler was 35L per hour. The water output rate for the Nguyen family's sprinkler was 15L per hour. The families used their sprinklers for a combined total of 50 hours, resulting in a total water output of 1050L. How long was each sprinkler used?

Answer:64mi/hour

Step-by-step explanation:

V=speed × time

V=s×t .....equation (1)

v=576

for taking one hour: t-1

speed is: s+8

From equation(1)

V=(s+8)(t-1)

(s+8)(t-1)=576

Expand the bracket

st-s+8t-8=576

Substitute the value of st which is 576

576-s+8t-8=576

Collect the like terms

-s+8t-8=0

s=8t-8

Subtitude into the value of s

576= (8t-8)×t

576=8t^2-8t

8t^2-8t=576

8t^2-8t-576=0 (divide both by 8)

t^2-t-72=0

By factorization method

Product is (-9 and 8)

(t-9)(t+8)=0

t=9 or t=-8

V=s×t

576=s×9

9s=576

s=576/9

s=64mi/hour

Answer:

The park is 31 inches wide in the drawing.

Step-by-step explanation:

Given:

Vicky drew a scale drawing of a city. She used the scale 1 inch : 2 yards.

The actual width of a neighborhood park is 62 yards.

Now, to find the width of park in drawing.

Let the width of park in drawing be [tex]x.[/tex]

The scale drawing of the city is 1 inch : 2 yards.

So, 1 inch is equivalent to 2 yards.

Thus, [tex]x[/tex] is equivalent to 62 yards.

Now, to get the width of park in drawing by using cross multiplication method:

[tex]\frac{1}{2} =\frac{x}{62}[/tex]

By cross multiplying we get:

[tex]62=2x[/tex]

Dividing both sides by 2 we get:

[tex]31=x[/tex]

[tex]x=31\ inches.[/tex]

Therefore, the park is 31 inches wide in the drawing.

Answer:

Answer:

31 inches

Step-by-step explanation:

62 yds divided by 2 equals 31 in

Step-by-step explanation:

Step-by-step explanation:

Let l be the length of track.

Running speed = 4 m/s

Jogging speed = 2 m/s

Total time taken = 2 minutes 6 seconds. = 126 seconds

That is

            [tex]\frac{l}{4}+\frac{l}{2}=126\\\\0.75l=126\\\\l=168m[/tex]

Length of track is 168 meter

To find the length of the track, we need to calculate the time it took for the sprint and the jog back, and set up an equation using the formula for distance. Simplifying the equation will give us the length of the track. The length of the track is 168 meters.

To find the length of the track, we need to use the formula for distance: distance = rate × time. Let's call the length of the track 'd' meters. The sprinter ran to the end of the track at 4 meters per second, so the time it took for the sprint is d/4 seconds. The jog back to the starting point at 2 meters per second takes a time of d/2 seconds. And the total time given is 2 minutes 6 seconds, which can be converted to seconds as 126 seconds. So we can set up the equation: d/4 + d/2 = 126.

Simplifying the equation, we can multiply each term by 4 to get d + 2d = 504. Combining like terms gives us 3d = 504. Dividing both sides by 3, we find that the length of the track is d = 168 meters.

Therefore, the length of the track is 168 meters.

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Answer:

V≈950.3

Step-by-step explanation:

d = 12.2mm

r = 1/2 d = 6.1

V = 4/3 Pi r^3

V = 1.33 (3.14) (6.1)^3

V = 950.3

Answer:

8. A

9. C

10. A

Answer:

plane speed = 520 mph

wind speed = 20 mph

Step-by-step explanation:

let the speed of the wind be w mph and the speed of the plane be p mph

flying from NY to NM,

time taken = 3 hr 36 min = 3.6 hr

average ground speed = total distance / time taken

= 1800 / 3.6 = 500 mph

since it is a headwind, the plane speed will be slowed down by the head wind, resulting in a lower ground speed.

we can write the following equation:

ground speed = plane speed - wind speed

500 = p - w ------(eq1)

flying from NY to NM (return flight),

time taken = 3 hr 20 min = 3.333 hr

average ground speed = total distance / time taken

= 1800 / 3.333 = 540 mph

on the return trip, the headwind becomes a tailwind, hence the total ground speed would be faster than the plane's air speed , we can write the following equation:

ground speed = plane speed + wind speed

540 = p +  w ------(eq2)

with these 2 systems of equations, we can solve for p & w using either substitution of elimination method.

eventually you will end up with

plane speed = 520 mph

wind speed = 20 mph

   Speed of airplane is 520 miles per hour and speed of the wind is 20 miles per hour.

    Let the speed of an airplane = x miles per minute

And the speed of the wind = y miles per minute

Distance between New York City and Albuquerque = 1800 miles

Airplane covers the distance between New York City and Albuquerque in 3 hours 36 minutes Or 3.6 hours.

In return journey, airplane covers this journey in 3 hours 20 minutes Or 3.33 hours.

Since, airplane takes more time from New York City to Albuquerque,

Therefore, airplane covered this distance against the wind,

And the speed of the airplane against the wind = (x - y) miles per hour

Expression for the speed,

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

(x - y) = [tex]\frac{1800}{3.6}[/tex]

x - y = 500 ------- (1)

Speed of airplane in return journey = (x + y) miles per hour

And the equation will be,

x + y = [tex]\frac{1800}{3.33}[/tex]

x + y = 540 ------- (2)

By adding equation (1) and (2),

(x - y) + (x + y) = 500 + 540

2x = 1040

x = 520 miles per hour

From equation (1),

520 - y = 500

y = 20 miles per hour

       Therefore, speed of airplane is 520 miles per hour and the speed of wind is 20 miles per hour.

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Answer:

∠2 and ∠3

Step-by-step explanation:

Given:

lines a and line b are parallel and cut by transversal.

We need to find the which angles from line a are congruent to ∠7

Solution:

Now we know that;

line a║line b , So by corresponding angle postulate which states that;

"When two parallel lines are cut by a transversal , the resulting corresponding angles are congruent."

so  we can say that;

∠2 ≅ ∠6

Also by Vertical angle theorem which states that;

"If two angles are  vertical angles, then they are congruent ."

so  we can say that;

∠2 ≅ ∠3    and  ∠6 ≅ ∠7

So by Transitive Property of Congruence which states that;

When [tex]a \cong b\ \ \ and \ \ \ b\cong c \ \ \ so \ \ \ a\cong c[/tex]

so  we can say that;

∠2 ≅ ∠3 ≅ ∠6 ≅ ∠7

Hence measure ∠2 and ∠3 are congruent to measure ∠7.

Answer: it’s C

Step-by-step explanation:

Answer:

Yes ,it represents a binomial experiment.

Step-by-step explanation:

In order for a probability experiment to represent a binomial experiment ,there are three conditions.

1) There should be a fixed number of trials.

2) Trials should be independent.

3)Each trial can result in two outcomes.

In this experiment ,there is a fixed number of trial ,since it is administered to 180180 individuals.

Outcome on an individual does not affect the outcome of others.

Individuals respond as favorably or not ,so it can be reduced to two outcomes.

All conditions are met, so it can be considered as binomial experiment.

Answer:

the answer is 2x=9-0

Step-by-step explanation:

put it in the cAC  PAPER

Answer:

Its C

Step-by-step explanation:

Correct on ed genuity

g(x) + 3 x+4; x  greater or equal to -4

Answer:     [tex]\dfrac{1}{2}[/tex]

Step-by-step explanation:

We know that probability for any event = [tex]\dfrac{\text{Number of favorable outcomes}}{\text{Total outcomes}}[/tex]

Given : Charlotte has 6 cherry candies, 3 grape candies, and 3 lime candies.

I..e Total pieces of candies she has = 6+3+3=  12

Now , If Charlotte randomly pulls one piece of candy out of the bag, what is the probability that it will be cherry is given by :-

[tex]\text{P(cherry)}=\dfrac{\text{Number of cherries}}{\text{Total candies}}\\\\=\dfrac{6}{12}\\\\=\dfrac{1}{2}[/tex]

Hence, the  probability that it will be cherry is [tex]\dfrac{1}{2}[/tex] .

The probability that Charlotte will pull a cherry candy out of the bag is 0.50 or 50%.

To determine the probability that Charlotte will randomly pull a cherry candy from the bag, we need to use the basic probability formula:

Probability = (Number of favourable outcomes) / (Total number of possible outcomes)

Step-by-Step Solution

Therefore, the probability that Charlotte will pull a cherry candy out of the bag is 0.50 (or 50%).

It will take 4 seconds for the rock to hit the water.

To find out when the rock hits the water, we need to determine the time at which the height h becomes 0, because hitting the water means the height is 0.

Given the equation for the height h of the rock as a function of time t:

[tex]\[ h = -16t^2 + 52t + 48 \][/tex]

We set h to 0 and solve for t:

[tex]\[ 0 = -16t^2 + 52t + 48 \][/tex]

This is a quadratic equation. We can solve it using the quadratic formula:

[tex]\[ t = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where a = -16, b = 52, and c = 48 .

Plugging in these values:

[tex]\[ t = \frac{{-52 \pm \sqrt{{52^2 - 4(-16)(48)}}}}{{2(-16)}} \][/tex]

[tex]\[ t = \frac{{-52 \pm \sqrt{{2704 + 3072}}}}{{-32}} \][/tex]

[tex]\[ t = \frac{{-52 \pm \sqrt{{5776}}}}{{-32}} \][/tex]

[tex]\[ t = \frac{{-52 \pm 76}}{{-32}} \][/tex]

Now we have two possible values for t:

[tex]\[ t_1 = \frac{{-52 + 76}}{{-32}} \][/tex]

[tex]\[ t_2 = \frac{{-52 - 76}}{{-32}} \][/tex]

[tex]\[ t_1 = \frac{{24}}{{-32}} = -\frac{3}{4} \][/tex]

[tex]\[ t_2 = \frac{{-128}}{{-32}} = 4 \][/tex]

Since time cannot be negative, we discuss, and the only valid solution is t = 4.

Therefore, it will take 4 seconds for the rock to hit the water.

Answer:

30

Step-by-step explanation:

we multiply each number. There are 3 pairs of pants 5 shirts and 2 pairs of shoes, so we multiply 3x5x2 to get 30

The number of different outfits that Jane has to choose from is 30

If a work A can be done in p ways, and another work B can be done in q ways, then both A and B can be done in p×q ways.

Remember that this count doesn't differentiate between order of doing A first or B first then doing other work after the first work.

Thus, doing A then B is considered same as doing B then A

It is given that:

There are 3 pairs of pants,  5 shirts to choose from and 2 pairs of shoes to choose from.

One outfit would include one-one of these 3 things.

Thus, they all together can be chosen in 3 × 5 × 2 = 30 ways.

So there are 30 different outfit that Jane has to choose from.

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Answer:

3x + 4y = -24.

Step-by-step explanation:

y= -3/4 x-6

Multiply through by 4:

4y = -3x - 24

3x + 4y = -24.

Answer:

Step-by-step explanation:

VA= -2

HA= -5

F(x)= 2(x+5)/-(x+2)

Answer:  15 hours

Step-by-step explanation:

Given : Patrick, by himself, can paint four rooms in 10 hours.

i..e Time taken by Patrick to paint the 4 walls =  10 hours.

Since rate of work = [tex]\dfrac{Work}{Time}[/tex]

We consider the entire job as 1.

Then, the rate of work done by Patrick = [tex]\dfrac{1}{10}[/tex]

If he hires April to help, they can do the same hob together in 6 hours.

i.e.  the rate of work done by Patrick and April together = [tex]\dfrac{1}{6}[/tex]

Then, the rate of work done by April = rate of work done by Patrick and April together - rate of work done by Patrick

[tex]\dfrac{1}{t}=\dfrac{1}{6}-\dfrac{1}{10}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{10-6}{60}=\dfrac{4}{60}\\\\\Rightarrow\ \dfrac{1}{t}=\dfrac{1}{15}\\\\\Rightarrow\ t=15[/tex]

Hence,it will take 15 hours April to paint four rooms .

Answer:

C

Step-by-step explanation:

Final answer:

Traveling by car would cost a total of $356, while traveling by plane would total $535. These costs include expenses for gas, food, and lodging when traveling by car, and the airfare and cab fare when traveling by plane. Therefore, Option c is the correct answer.

Explanation:

To find the total cost for each mode of transportation for Daniel and Elizabeth, one must calculate the expenses for both the car trip and the plane trip.

Cost by Car:

Gas: $60

Food: $25 per day for 4 days for 2 people = $200 ($25 x 4 days x 2 people)

Lodging: $48 per night for 2 nights = $96 ($48 x 2 nights)

Total Car Cost: $60 (gas) + $200 (food) + $96 (lodging) = $356

Cost by Plane:

Round-trip airfare for two: $260 per person x 2 = $520

Round-trip cab fare: $15

Total Plane Cost: $520 (airfare) + $15 (cab) = $535

Comparing both options, traveling by car would cost $356, and by plane, it would cost $535. Therefore, Option C is the correct answer.

Question is Incomplete; Complete question is given below;

The amount of pay Rachel will earn in an 8 hour shift if Rachel earns $3 more per hour than Leah's pay, [tex]p.[/tex] Using the given variables, write an expression for given situation.

Answer:

The expression for the amount Rachel will earn in 8 hrs shift is [tex]24+8p.[/tex]

Step-by-step explanation:

Given:

Leah's pay per hour is [tex]'p '.[/tex]

Now given:

Rachel earns $3 more per hour than Leah's pay.

So we can say that;

Rachel's pay per hour = [tex]3+p[/tex]

Now Number of hours Rachel work = 8 hrs

We need to write an expression for the amount Rachel will earn in 8 hrs shift.

Solution:

Now we know that;

the amount Rachel will earn is equal to Number of hours Rachel work multiplied by Rachel's pay per hour.

framing in expression form we get;

the amount Rachel will earn = [tex]8(3+p) =24+8p[/tex]

Hence The expression for the amount Rachel will earn in 8 hrs shift is [tex]24+8p.[/tex]

Answer:

The answer to your question is    the second option     [tex]\frac{1}{x^{48}y^{36}z^{6}}[/tex]

Step-by-step explanation:

Expression

                       [tex][\frac{(x^{2}y^{3})^{-2}}{(x^{6}y^{3}z)^{2}}]^{3}[/tex]

Process

1.- Divide the fraction in numerator and denominator

a) Numerator  

 [(x²y³)⁻²]³ = (x⁻⁴y⁻⁶)³ = x⁻¹²y⁻¹⁸

b) Denominator

 [(x⁶y³z)²]²= (x¹²y⁶z²)³ = x³⁶y¹⁸z⁶

2.- Simplify like terms

a) x⁻¹²x⁻³⁶ = x⁻⁴⁸

b) y⁻¹⁸y⁻¹⁸= y⁻³⁶

c) z⁻⁶

3.- Write the fraction

        [tex]\frac{1}{x^{48}y^{36}z^{6}}[/tex]

Answer:

First, Second, and fourth answers :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The lunch bill for marty and breanna at a dinner totaled $18.37. Tax on the meal was 6%. The amount of tax on the meal would be

6/100 × 18.37 = 0.06 × 18.37 = $1.1022

Cost of the meal including the tax would be

18.37 + 1.1022 = $19.4722

They wanted to leave a 15% tip. The amount of the tip would be

15/100 × 18.37 = 0.15 × 18.37 = $2.7555

Therefore, the total cost of the meal, including tax and tip would be

19.4722 + 2.7555 = $22.23

Final answer:

In the sales comparison approach, using comparables of different ages requires adjustments for age or vintage to estimate the accurate value of the subject property considering physical and economic differences.

Explanation:

In the sales comparison approach, the use of comparables that vary significantly in age compared to the subject property is an example of adjusting for age or vintage. When appraising a subject property that is 10 years old, by using comparables that are five and 15 years old, an appraiser is attempting to account for differences in physical deterioration, functional obsolescence, and external obsolescence that may exist. A key part of this approach is applying adjustments to the comparables to reflect these differences, thereby arriving at a more accurate value for the subject property.

It is important to ensure that the base year used for comparison is consistent, and adjustments are made for any significant differences in market conditions or property features. The age adjustment is just one of many adjustments that might be made, including location, size, and condition. This process requires careful consideration and professional judgment to ensure that the end value is reflective of the current market.

Answer:

  8 groups

Step-by-step explanation:

The number of possible groups can be found from ...

  (10.5 cups)/(1.2 cups/group) = 8.75 groups

Ms. Paulino has enough candy to give the exact amount required to 8 groups.

_____

She will have (3/4)×(1 1/5) = 9/10 of a cup of candy left over.

Answer:

The answer to your question is a ) 127°    b) 80°

Step-by-step explanation:

a) We have to consider that the sum of the interior angles in a triangle equals 180°.

Then,

          89 + (5x - 7) + [180 - (14x + 1)] = 180

Simplification

          89 + 5x - 7 + 180 - 14x - 1 = 180

          5x - 14x = 180 - 89 + 7 - 180 + 1

                 - 9x = -81

                     x = -81 / -9

                     x = 9

Exterior angle = 14(9) + 1

                       = 127°  

b) The process is the same that the previous problem

          30 + (4x + 2) + [180 - (8 + 6x)] = 180

Simplification

          30 + 4x + 2 + 180 - 8 - 6x = 180

          4x - 6x = 180' - 30 - 2 + 8 - 180

               -2x = -24

                  x = -24/-2

                  x = 12

The measure of the external angle is = 8 + 6(12)

                                                              = 8 + 72

                                                              = 80°

Answer: the cost of one Soda was $1.75

Step-by-step explanation:

Let x represent the cost of one hot dog.

Let y represent the cost of one Soda.

At the baseball game, Adam bought 3 hot dogs and 2 sodas for $11. It means that

3x + 2y = 11 - - - - - - - - - - 1

In a later time, he purchased 2 hot dogs and 3 sodas for $10.25. It means that

2x + 3y = 10.25 - - - - - - - - -2

Multiplying equation 1 by 2 and equation 2 by 3, it becomes

6x + 4y = 22

6x + 9y = 30.75

Subtracting, it becomes

- 5y = - 8.75

y = - 8.75/- 5

y = 1.75

Substituting y = 1.75 into equation 1, it becomes

3x + 2 × 1.75 = 11

3x + 3.5 = 11

3x = 11 - 3.5 = 7.5

x = 7.5/3 = 2.5

Answer:

Step-by-step explanation:

Let m represent the number of miles that she drives per day.

She works 5 days per week. This means that the total number of miles that she drives in a week would be

5 × m = 5m

Ms.Franks drives a maximum of 150 miles per week to and from work. Therefore, the inequality that shows m the number of miles she drives per day would be

5m ≤ 150

m ≤ 150/5

m ≤ 30

The amount he can spend for everything else is less than or equal to 1363

The inequality is : [tex]s\leq 1363[/tex]

Solution:

Let "s" represent the brother's money to spend

Your brother has $2000 saved for a vacation

His airplane ticket is $637

Write an expression for the total money spent by adding "s" and the price of plane ticket $ 637

We can frame a inequality as:

[tex]s+637\leq 2000[/tex]

Here we have used "less than or equal to" symbol, because he can spent only up to 2000

Solve the inequality for "s"

[tex]s+637\leq 2000\\\\\text{Add -637 on both sides of inequality }\\\\s+637-637\leq 2000-637\\\\s\leq 1363[/tex]

Thus the amount he can spend for everything else is less than or equal to 1363

Answer:

(a) Number of inches that have burned from the candle since it was lit is (1.1t) inches

(b) The remaining length of the candle is (16 - 1.1t) inches

Step-by-step explanation:

(a). Length of candle before it was lit = 16 inches

Constant rate at which at which candle burns = 1.1 inches per hour

Let t represent the number of hours that have elapsed since the candle was lit

In 1 hour, 1.1 inches of the candle burned

Therefore, in t hours, (1.1t) inches of the candle would have burned since the candle was lit

(b) Remaining length of candle = length of candle before it was lit - length of candle that have burned = 16 inches - 1.1t inches = (16 - 1.1t) inches

Answer:

Step-by-step explanation:

Heres the complete question:

A uranium mining town reported population declines of 3.2%, 5.2%, and 4.7% for the three successive five-year periods 1985–89, 1990–94, and 1995–99. If the population at the end of 1999 was 9,320:

How many people lived in the town at the beginning of 1985? (Round your answer to the nearest whole number.)

solution:

Let the population of the town at the beginning of 1985 be P. Then, given that in the first five-year period the population declined by 3.2%, i.e., 0.032, the population of the town at the end of 1989 would be

(1 – 0.032)P = 0.968P.

Again, given that in the second five-year period the population declined by 5.2%, i.e., 0.052, the population of the town at the end of 1994 would be

(1 – 0.052)(0.968P) = 0.948 x 0.968P = 0.917664P.

Finally, given that in the third five-year period the population declined by 4.7%, i.e., 0.047, the population of the town at the end of 1999 would be

(1 – 0.047)(0.917664P) = 0.874533792P.

We are given, 0.874533792P = 9320 or

P = 9320/0.874533792 = 10657.11.

Thus, 10657 people lived in the town at the beginning of 1985

Final answer:

This is a mathematics question requiring the computation of past populations based on given percentage declines and the population at the end of 1999.

Explanation:

The question involves calculating the population of a uranium mining town at a prior date based on given percentage declines over successive five-year periods and the known population at the end of 1999. Since the population at the end of 1999 was 9,320, we work backward using the given percentage declines for each five-year period to estimate the population at the beginning of 1985. The calculation takes into account a 3.2% decline for 1985-89, a 5.2% decline for 1990-94, and a 4.7% decline for 1995-99. By applying these percentage changes in reverse, we can determine the population at the start of 1985.

Answer:

  x = 4

Step-by-step explanation:

We assume your equation is intended to be ...

  2^(2x+7) = 2^15

Equating exponents gives ...

  2x +7 = 15

  2x = 8 . . . . . . subtract 7

  x = 4 . . . . . . . divide by 2

The value of x is 4.

The equation 2^2x+7 = 2^15 is solved by equating the exponents, simplifying the equation to find x, resulting in x = 4.

In the given question, you're dealing with an equation in the form of 22x+7 = 215. We can solve such problems by applying the rule that if ax = ay, then x = y.

Here the base for both the sides of equation is 2, thus 2z where x can be equated on both sides.

Comparing both sides of the equation, we get: 2x + 7 = 15.

To isolate x, we subtract 7 from both sides, therefore, x = (15 – 7) / 2 => x = 4.

So the solution to the equation 22x+7 = 215 is x = 4.

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Answer:

  2/5 g/cm

Step-by-step explanation:

When you want to know "A per B", divide the given quantity of A by the corresponding quantity of B. ("Per" essentially means "divided by".)

It can be convenient to choose table values that make the division easy:

  12 g/(30 cm) = 4/10 g/cm = 0.4 g/cm

  20 g/(50 cm) = 2/5 g/cm . . . . . . . . . . . . . same as 0.4 g/cm

Answer:

The solution for the expression is:

[tex]x=-\frac{11}{2}[/tex]

Step-by-step explanation:

Given expression:

[tex]3(x-2)=5(x+1)[/tex]

To graph the solution set.

Solution:

We will first solve for [tex]x[/tex] to find the solution for the expression.

We have:

[tex]3(x-2)=5(x+1)[/tex]

Using distribution:

[tex]3x-6=5x+5[/tex]

Adding 6 both sides.

[tex]3x-6+6=5x+5+6[/tex]

[tex]3x=5x+11[/tex]

Subtracting both sides by [tex]5x[/tex].

[tex]3x-5x=5x-5x+11[/tex]

[tex]-2x=11[/tex]

Dividing both sides by 2.

[tex]\frac{-2x}{-2}=\frac{11}{-2}[/tex]

∴ [tex]x=-\frac{11}{2}[/tex]

The correct graph that represents the solution is given below.