Powers of 10 make it very easy to write large and small numbers, but as a result it can also be easy to forget the large differences between different powers. We can compare any two numbers by dividing them. For example, we say that 12 is four times as large as 3 because 12÷3=4. Complete the sentences below comparing pairs of powers of 10.

Step-by-step explanation:

θ is in quadrant IV, so:

sin θ < 0

cos θ > 0

tan θ = sin θ / cos θ < 0

csc θ = 1 / sin θ < 0

sec θ = 1 / cos θ > 0

Without doing any calculations, we can see only the third option fits (in the second option, sin θ / cos θ = -9/18, not -18/9.  In the fourth option, csc θ and sec θ are switched).

Let's go ahead and calculate the values.  There are several ways to solve this.  One way is to use Pythagorean identities (ex., 1 + cot²θ = csc²θ).  Another way is to simply draw a triangle in the fourth quadrant.

cot θ = 1 / tan θ, and tan θ = opposite / adjacent.  So cot θ = adjacent / opposite.  If we draw a triangle with angle θ, where the adjacent side is 9 and the opposite side is -18, then we can use Pythagorean theorem to find the hypotenuse:

c² = a² + b²

c² = (9)² + (-18)²

c = √405

Therefore:

sin θ = -18 / √405

cos θ = 9 / √405

csc θ = √405 / 18

sec θ = √405 / 9

tan θ = -18/9

Answer:

8. A

9. C

10. A

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:

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:

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

Answer:

3x + 4y = -24.

Step-by-step explanation:

y= -3/4 x-6

Multiply through by 4:

4y = -3x - 24

3x + 4y = -24.

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°

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:

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:

  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:  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:

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:

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

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:     [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%).

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:

The amount of work completed by Jing in 1 hour is 0.075 which is option A

Step-by-step explanation:

Melissa & Jing can complete the work in 5 hours

This means that the amount of work completed by Melissa & Jing working together in 1 hour is (1÷5) = 0.2

Melissa will do the job in 8 hours, which means that the amount of job completed by Melissa working alone in 1 hour is (1÷8) = 0.125

The amount of work completed by Jing when he works alone in 1 hour will be the difference of amount of work completed by both of them in 1 hour with the amount completed by only Melissa in 1 hour.

There Amount of work completed by Jing in an hour = 0.2 - 0.125 = 0.075

Answer: option A

Step-by-step explanation:

Answer:

C

Step-by-step explaination:

A statistic is a data obtained by sampling a population

A sample is a part of a population studied for the purpose of testing of an hypothesis

6076 is a statistical value because it represents a part (sample) of the whole population

The value of 23% is a statistic calculated from a sample of 6076 adults in public restrooms.

In this question, the value of 23% represents the proportion of adults in public restrooms who did not wash their hands before exiting. Since this value is calculated from a sample of 6076 adults, it is considered a statistic. A statistic is a number that represents a property of a sample. On the other hand, a parameter is a numerical characteristic of the entire population. In this case, if we had data for all adults in public restrooms, the proportion would be a parameter.

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:

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:

Step-by-step explanation:

The x-intercepts are where y = 0.

  (x +1)^2/9 +(0 -2)^2/8 = 1

  (x +1)^2/9 +1/2 = 1 . . . . . simplify a bit

  (x +1)^2 = 9/2 . . . . . . . . .subtract 1/2, multiply by 9; next: square root, add -1

  x = -1 ±√4.5 . . . . . x-intercepts

__

The y-intercepts are where x=0.

  (0+1)^2/9 +(y-2)^2/8 = 1

  1/9 + (y -2)^2/8 = 1 . . . . . simplify a bit

  (y -2)^2 = 64/9 . . . . . . . . subtract 1/9, multiply by 8,

  y = 2 ±8/3 . . . . . . take the square root, add 2 . . . . y-intercepts

Answer: Yes.

The remaining 2/3 elephants left could be a mix of blue and green shared equally.

Step-by-step explanation:

Total number of elephants= 1200

Number of possible colours=3 (blue,green and pink)

Number of pink elephants =1/3 of 1200

Number of pink elephants =1/3×1200

Pink elephants are 400

The remaining fraction will b 1-1/3=2/3

Total number of elephants - number of pink elephants = remaining number of elephants => 1200-400=800

It is true that 400 elephants are definitely blue because the number of elephants remaining is twice 400

Given:

Total number of elephants = 1200

Colours available:

Blue

Pink

Pink & green

Pure Pink = 1/3 of 1200

= 1/3 × 1200

= 1200/3

Pure Pink = 400

Elephants remaining = Total number of elephants - Pure Pink

= 1200 - 400

= 800

Therefore, it is true that 400 elephants are definitely blue because the number of elephants remaining is twice 400

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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:

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.

Answer:

Step-by-step explanation:

VA= -2

HA= -5

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

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: 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:

  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:

(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