What’s the area of the figure?

Answer:

Step-by-step explanation:

Suppose you drive a car 392 miles on one tank of gas. The tank holds 14 gallons of gas. This means that

1 gallon of gas would be used to drive 392/14 = 28 miles

a) The number of miles traveled varies directly with the number of gallons of gas used.

Let x =number of gallons of gas you use.

Let y = the number of miles travelled.

Since y varies directly with x, we will introduce a constant of proportionality, k. Therefore,

y = kx

If 28 miles will require 1 gallon of gas, it means

28 = 1×k

k = 28

So y = 28x

b) we want to determine how far you can drive with 3.7 gallons of gas.

x = 3.7

y = 28x = 28×3.7

y = 103.6 miles

Answer:

a) 80 ibs

b) 40 ibs

Step-by-step explanation:

Let X be the pound of the high quality bean at $6.50

(120-x) will be the pound of the cheaper bean at $2.50

6.5x + 2.5(120 - x) = 5.17(120)

6.5x + 300 - 2.5x = 620.4

Collect like terms

6.5x - 2.5x = 620.4 - 300

4x = 320.4

x = 320.4/4

x= 80.1

x = 80 ibs(to the nearest pounds)

For the cheaper bean we have 120 -x

= 120 - 80

= 40 ibs

Sarah would blend 80 ibs of quality bean and 40 ibs of cheaper bean

Sarah should blend 80 pounds of high quality beans and 40 pounds of cheaper beans to achieve her target blend of 120 pounds at $5.17 per pound.

Sarah Meeham needs to blend high quality and cheaper coffee beans to create a blend selling for $5.17 per pound, using a total of 120 pounds. Let x be the pounds of high-quality beans and 120 - x be the pounds of cheaper beans. Setting up the equation for the total cost of the blend, we have:

6.50x + 2.50(120 - x) = 5.17 \\times 120

Solving for x, we get:

6.50x + 300 - 2.50x = 620.4

4x = 320.4

x = 80.1

To the nearest pound, Sarah should blend 80 pounds of high quality beans and 120 - 80 = 40 pounds of cheaper beans.

Answer:

Step-by-step explanation:

g(-2)=2(-2)^3+3(-2)^2-3(-2)+4=-16+12+6+4=6

g(-1)=2(-1)^3+3(-1)^2-3(-1)+4=-2+3+3+4=8

it does  not change sign ,so there is no real zero between -2 and -1.

Answer:

  431,646

Step-by-step explanation:

The problem statement tells us ...

  34,100 = 0.079 × (sold to date)

Dividing by 0.079, we get ...

  34,100/0.079 = (sold to date) ≈ 431,646

About 431,646 copies have been sold to date.

The total number of books sold to date is approximately 431,646. This was determined by using the percentage of the total sales represented by the first month's sales (7.9%) and the number of books sold in the first month (34,100 copies).

To solve this problem, we need to understand that the 34,100 books sold in the first month represent 7.9% of the total number of copies sold to date. In mathematics, percentage is a way of expressing a number as a fraction of 100. Here, we need to find the whole, where 7.9% is equivalent to 34,100 copies.

To do this, we use this formula:

So, the calculation would be:

The result we get from the calculator is approximately 431,646 copies. This means, approximately 431,646 copies were sold to date.

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Answer:

test statistic (Z) is 2.5767 and p-value of the test is .009975

Step-by-step explanation:

[tex]H_{0}[/tex]: percentage of students who smoke did not change

[tex]H_{a}[/tex]: percentage of students who smoke has changed

z-statistic for the sample proportion can be calculated as follows:

z=[tex]\frac{p(s)-p}{\sqrt{\frac{p*(1-p)}{N} } }[/tex] where

Then, z=[tex]\frac{0.25-0.18}{\sqrt{\frac{0.18*0.82}{200} } }[/tex] ≈ 2.5767

What is being surveyed is if the percentage of students who smoke has changed over the last five years, therefore we need to seek two tailed p-value, which is .009975.

This p value is significant at 99% confidence level. Since .009975 <α/2=0.005, there is significant evidence that the percentage of students who smoke has changed over the last five years

Answer:

0.0421

Step-by-step explanation:

Mean(μ) = 12.00 oz

Standard deviation (σ) = 0.11 oz

Z = (x - μ)/σ

Z = (12.19 - 12.00) / 0.11

Z= 0.19/0.11

Z = 1.727

From the normal distribution table, Z = 1.727 = 0.4579

Φ(Z) = 0.4579

Recall that if Z is positive

Pr(x>a) = 0.5 - Φ(Z)

Pr(x > 12.19) = 0.5 - 0.4579

= 0.0421

Answer:

B) The sample size was 100

Step-by-step explanation:

Number of sample size in January = 100

Number of sample size in March   = 100

Number of sample size in June     = 100

Number of sample size in  September = 100

The average sample size for the study = (100 +100+100+100)/4  

                                                                =  400/4

                                                                = 100

So the average sample size for the study is 100 women between 18 to 21 years.

Answer:

(d) a matched pairs experiment.

Step-by-step explanation:

The correct answer is option D that is d) a matched pairs experiment.

A matched pair experiment is special case of randomize block design. This experiment can be used when the statement has two treatment conditions and subjects are grouped into pair based on some treatment. For each pair, random treatments are assigned to the subjects. It is an improvement over complete randomized design.

This is an experiment because a treatment (the MP3 players) was assigned to different members of the sample(the assembly line workers) randomly.

This study is a d) matched pairs experiment where assembly line workers are given portable mp3 players to play their chosen music while working for one month and then work without music for another month, with the order determined randomly.

This study is a matched pairs experiment because each worker serves as their own control by experiencing both treatments, with the order of treatments determined randomly. In a matched pairs experiment, participants are paired up based on similar characteristics, and each pair is randomly assigned to different treatments. Here, the workers are matched based on their own preferences for the music they choose.

The workers are given portable mp3 players and can choose their own music, which serves as the treatment variable. The productivity of the workers is measured in two different months, one with music and one without music. By comparing the workers' productivity in the two months, the study aims to determine the effect of music on productivity.

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Answer:

  96 m²

Step-by-step explanation:

The figure is a trapezoid with bases of length 10 m and 22 m, and height 6 m. Putting these numbers into the formula for area of a trapezoid gives ...

  A = (1/2)(b1 +b2)h

  = (1/2)(10 m +22 m)(6 m) = 96 m²

The area of the figure is 96 m².

Answer:

(a) The ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7  \times (-1)^{n-1}\\[/tex].

Step-by-step explanation:

Here, the given sequence is 7, -7, 7, -7, ...

The first term = 7, Second term = -7, Third term =-7 and so on..

Now check the given sequence for each given formula, we get:

(1)  [tex]a_n = 7  \times (-1)^{n-1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (-1)^{1-1}\\[/tex]

                                       [tex]= 7 \times (-1)^0 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (-1)^{2-1}\\[/tex]

                                       [tex]= 7 \times (-1)^1 =  7 \times (-1) = -7 \implies a_2 = -7[/tex]

Hence, the given formula satisfies the given sequence.

(2)  [tex]a_n = 7  \times (-1)^{n}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (-1)^{1}\\[/tex]

                                       [tex]= 7 \times (-1)^1 =  7 \times (-1) = -7 \implies a_1 = -7[/tex]

But, First term = 7

Hence, the given formula DO NOT satisfy the given sequence.

(3)  [tex]a_n = 7  \times (1)^{n-1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (1)^{1-1}\\[/tex]

                                       [tex]= 7 \times (1)^0 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (1)^{2-1}\\[/tex]

                                       [tex]= 7 \times (1)^1 =  7 \times (1) = 7 \implies a_2 = 7[/tex]

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

(4) [tex]a_n = 7  \times (1)^{n+1}\\[/tex]

Now, for n = 1 : [tex]a_1 = 7  \times (1)^{1+1}\\[/tex]

                                       [tex]= 7 \times (1)^2 =  7 \times 1 = 7 \implies a_1 = 7[/tex]

Similarly, for, n = 2:  [tex]a_2 = 7  \times (1)^{2+1}\\[/tex]

                                       [tex]= 7 \times (1)^3 =  7 \times (1) = 7 \implies a_2 = 7[/tex]

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

So, the ONLY explicit rule for the nth term of the sequence is [tex]a_n = 7  \times (-1)^{n-1}\\[/tex].

Answer:

an=7•(-1)^n-1

Step-by-step explanation:

For this case we have the following arithmetic sequence:

[tex]a_ {n} = 15 + 5 (n-1)[/tex]

To write in function form, we apply distributive property to the terms within parentheses:

[tex]f (n) = 15 + 5n-5[/tex]

Different signs are subtracted and the major sign is placed.

We simplify:

[tex]f (n) = 5n + 10[/tex]

Answer:

[tex]f (n) = 5n + 10[/tex]

Option C

The explicit formula for the arithmetic sequence an=15+5(n−1) in function form is f(n)=5n+10.

The explicit formula for the arithmetic sequence an=15+5(n−1) in function form is f(n)=5n+10 (Option C).

The arithmetic sequence is represented as an=15+5(n−1). This equation can be further simplified to an=15+5n-5, which eventually gives us an=5n+10. So the explicit formula for this arithmetic sequence in function form is option C, which is f(n)=5n+10. This function f(n), directly gives us the nth term of the arithmetic sequence.

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To find the probability of both Alex and Bob winning at least 2 games during their 5 games chess play, principles of geometric probability and the Multiplication rule are used. The equation _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))] is formed considering Alex is 3 times more likely to win than Bob.

Calculating Probability of Games

In this scenario, Alex and Bob are playing 5 games with Alex being 3 times more likely to win than Bob. The primary question is to find the probability for both of them winning at least 2 games.

We would utilize the principles of geometric probability to solve this. Geometric probability treats each game as a Bernoulli trial, a game of win or lose. Moreover, we operate with the Multiplication rule in finding the probability of both events, Alex and Bob winning 2 games, happening.

Firstly, we define the probability of Alex winning as p, therefore, the probability of Bob winning is p/3. Bob and Alex must win 2 games each, leaving one game open to any outcome. Since the games are independent, the Multiplication rule applies. Therefore, the probability is calculated by multiplying probabilities for each win and possible combinations of five games taken two at a time. In other words, the equation will look like  _(p^2)*(5 choose 2)*((p/3)^2)*(5 choose 2)*[(p+(p/3))].

The resulting value will be the probability for both of them winning at least 2 games.

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Answer:

Yes this makes sense

Step-by-step explanation:

When their is one outlier it makes the average spike which can present misleading data while with median the outlier is left relatively unaffected.

Answer:

Yes this makes sense.

Step-by-step explanation:

The given dataset consists of 15 apartment rents. A data value which is an outlier (much larger than the rest) will increase the overall mean value of the population but it may not affect the median. Let us take an example of 15 sample rent value in ascending order,

100,120,130,140,150,170,175,185,190,200,220,250,280,290,1000

Here , mean rent will become high due to the single high rent datapoint(1000) but the median won't be impacted.

Answer:

The answer to your question is Stacy multiplies the second equation by 4.

Step-by-step explanation:

                                             24x - 39y = 165    (I)

                                             - 6x + 13y = -51     (II)

Multiply the second equation by 4

                                             24x -    39 y = 165

                                           -24x  +   52y  = -204  

Simplify

                                              0    +  13y = 39

                                                           y = 39/ 13

                                                           y = 3

Find "x" value                       24x - 39(3) = 165

                                             24x - 117 = 165

                                             24x = 165 + 117

                                             24x = 282

                                                 x = 282 / 24

                                                 x = 47/4

The quadratic function is [tex]y=1x^{2} + (-8)x + 4[/tex]

Step-by-step explanation:

The quadratic function given is [tex]ax^{2} + bx + c=y[/tex]

and same quadratic function is passes through (-3​,37​), ​(2​,-8​), ​(-1​,13)

Replacing points one by one

we get,

For (-3​,37​) :

[tex]a(-3)^{2} + b(-3) + c=37[/tex]

[tex]9a + -3b + c=37[/tex] = equation 1

For (2​,-8​) :

[tex]a(2)^{2} + b(2) + c=(-8)[/tex]

[tex]4a + 2b + c=(-8)[/tex] =  equation 2

For ​(-1​,13)

[tex]a(-1)^{2} + b(-1) + c=(13)[/tex]

[tex]a + -1b + c=13[/tex] = equation 3

Solving the linear equation to get values of a,b,c

Subtract equation 2 with equation 3

we get,[tex](4a + 2b + c)-(a + -1b + c)=(-8)-13[/tex]

[tex](3a + 3b )=(-21)[/tex]

[tex](a + b )=(-7)[/tex]  = equation 4

Now, Subtract equation 1 with equation 2

we get,[tex](9a + -3b + c)-(4a + 2b + c)=(37)-(-8)[/tex]

[tex](5a - 5b )=(45)[/tex]

[tex](a - b )=(9)[/tex]  = equation 5

Now, Add equation 4 with equation 5

we get,[tex](a + b)+(a - b)=(-7)+(9)[/tex]

[tex](2a - 0b )=(2)[/tex]

[tex](a)=1[/tex]  

Replacing value of a in equation 5

[tex](a - b )=(9)[/tex]

[tex](1 - b )=(9)[/tex]

[tex](b)=(-8)[/tex]

Replacing value of a and b in equation 1

[tex]9a + -3b + c=37[/tex]

[tex]9(1) + -3(-8) + c=37[/tex]

[tex]9 + 24 + c=37[/tex]

[tex] c=4[/tex]

Thus,

The quadratic function [tex]y=1x^{2} + (-8)x + 4[/tex]

Answer:

The person will pay $ 510 more as income tax per month .

Step-by-step explanation:

Given as :

The monthly income of person = $ 25000

The amount paid as income tax per year =$ 9000

So,The amount paid as income tax per month =$ [tex]\frac{9000}{12}[/tex] = $750

Or, x% is the income tax of the monthly income

I.e x % of 25000 = 750

∴ x % = [tex]\frac{750}{25000}[/tex]

Or, x =  [tex]\frac{750}{25000}[/tex] × 100

I.e x = 3 %

Now, since the income tax is increase by 0.5 % per month

So, x' = 3 % + 0.5 % = 3.5 %

And The monthly income increase by $ 11000

I.e New monthly income = $ 25000 + $ 11000 = $ 36000

Now, The income tax which the person pay now is 3.5 % of $ 36000

i.e The income tax which the person pay now = 0.035×36000 = 1260 per month

so, The income tax which the person pay now as per year = 1260 × 12 =        $ 15,120

∴ The increase income tax per month = $ 1260 - $ 750 = $ 510

Hence The person will pay $ 510 more as income tax per month . Answer

Final answer:

To calculate the additional income tax the person will pay per month, we add the tax increase due to the salary increase to the original increased tax after the 0.5% hike. The total increased monthly tax payment amounts to $930.

Explanation:

The question is asking how much more income tax a person will pay per month after their salary is increased and the government increased income tax by 0.5%. To find the additional income tax that a person will pay, we need to consider the initial monthly income, the new monthly income, the old annual tax amount, and the increased tax rate.

Originally, the person earned $25,000 per month and paid $9,000 in income tax yearly. With the 0.5% monthly increase in tax, we first need to calculate the monthly increase based on the initial salary. The monthly increase is 0.5% of $25,000, which is $125. Therefore, the new monthly tax without accounting for the salary increase is the old monthly tax plus the $125 increase.

The monthly tax paid before the income increase was $9,000 / 12 months = $750 per month. After the 0.5% monthly increase, the tax becomes $750 + $125 = $875 per month. But the person's monthly earnings were increased by $11,000, resulting in a new monthly income of $25,000 + $11,000 = $36,000.

To calculate how much more in income tax the person will pay on the additional $11,000 monthly earnings at the increased rate: 0.5% of $11,000 is $55. So the additional tax per month is $55. Therefore, the total increased monthly tax is $875 + $55 = $930.

The slope of a line perpendicular to the line with equation y=4x+1 is -1/4. This is found by taking the negative reciprocal of the original line's slope, which is 4.

The slope of a line that is perpendicular to a given line can be determined by taking the negative reciprocal of the slope of the given line.

Given the equation y=4x+1, we can see that the slope (m) is 4.

Therefore, a line that is perpendicular to this line would have a slope that is the negative reciprocal of 4, which is -1/4.

The concept of perpendicular lines in coordinate geometry implies that two lines are perpendicular if the product of their slopes is -1.

Our given line has a positive slope, hence the slope of its perpendicular counterpart must be negative. A positive slope indicates that the line moves up as we move from left to right, whereas a negative slope indicates that the line moves down.

Answer:

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

Step-by-step explanation:

Given lines,

y = 2x - 5,

y = -x + 1

Subtracting these two equations,

0 = 3x - 6

[tex]\implies 3x = 6[/tex]

[tex]\implies x = \frac{6}{3}=2[/tex]

By first equation,

[tex]y=2(2) -5=4-5 = -1[/tex]

Thus, point of intersecting would be (2, -1).

Now, the equation of a line is y = mx + c,

Where,

m = slope of the line,

So, the slope of the line [tex]y=\frac{1}{2}x+4[/tex] is 1/2.

∵ two parallel lines have same slope.

Hence,

Equation of the parallel line passes through (2, -1),

[tex]y+1=\frac{1}{2}(x-2)[/tex]

[tex]y+1=\frac{1}{2}x - 1[/tex]

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

Answer:

x = 7.8

Step-by-step explanation:

If AE is parallel to BD, then you can use the theorem called ratio of sides of parallel line.

AC/AB = EC/ED

x+11/x = 12/5

x=7.8

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. The length of the unknown sides will be equal to 7.857 units.

Two figures are known as similar figures if there the corresponding angles are equal and the corresponding sider is in ratio. It is denoted by the symbol "~".

For the two similar triangles, ΔAEC and ΔBDC, the ratio of the sides will be,

11/7 = (11+x)/(5+7)

11/7 = (11+x)/12

(11×12)/7 = 11+x

18.857 - 11 = x

x = 7.857

Hence, the length of the unknown sides will be equal to 7.857 units.

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Answer:

Step-by-step explanation:

Total number of students: 33 +47 +37 = 117 students

Students in 9th class = 37

So probabilty of selecting a 9th class student from a class of 117 students is:

=>(Total student in 9th class)/(Total student in the sample)

=>37/117 =>Ans

To find the probability of selecting a ninth-grade student from a school population, divide the number of ninth-grade students by the total population.

To find the probability that a randomly selected student is in the ninth-grade, we need to calculate the fraction of ninth-grade students out of the total population of students. Here's how:

The probability that the randomly selected student is in the ninth-grade is approximately 0.316, or 31.6%.

Answer:

a) C

b) A

Step-by-step explanation:

The wingspan is the dependent variable while the bird height is the independent variable.

a) Since R2 is the dependent variable, it can be expressed by the independent variable. An R2 of 93% represents 93% of the variation in the wingspan which can be explained by using the birds height. This means that the appropriateness of the model should not be determined by R2 but by using a scatter plot.

b) The model predicts the value of wingspan using the value of bird height. We cannot say that the bird 10 inches tall has a wingspan if 17 inches instead, we say that the wingspan of the bird which is 10 inches tall is 17 inches.

It is therefore possible that the wing span is not exactly 17 inches

Final answer:

The R2 value does not indicate the appropriateness of the model, and regression models provide predictions, not actual values.

Explanation:

A. R2 is an indication of the nonlinearity of the model, not the appropriateness of the model. A regression line is the indicator of an appropriate model.

A bird 10 inches tall will have a wingspan of 17 inches.

A. Regression models give predictions, not actual values. The student should have said, "The model predicts that a bird 10 inches tall is expected to have a wingspan of 17 inches."

Final answer:

To determine the length of a Bengal tiger's tail, which is 30% of its total length of 96 cm, we calculate 30% of 96 to get a tail length of approximately 28.8 cm.

Explanation:

The question asks us to calculate the length of a Bengal tiger's tail given that it is 30% of its total length. If the total length of the tiger is 96 cm, we can find the length of the tail by calculating 30% of 96 cm.

To find 30% of 96, we convert the percentage into a decimal by dividing by 100 and then multiply by the total length:

30% = 30/100 = 0.3

0.3 x 96 cm = 28.8 cm

Therefore, the length of the Bengal tiger's tail is approximately 28.8 cm.

Answer:

4.45

Step-by-step explanation:

cos(70)= BC/13

BC=13*cos(70)

BC= 4.45 cm

The maximum possible width of the fence is 7.5 feet.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

Let's start by assigning variables to the length and width of the fence.

Let x be the width of the fence in feet, then the length of the fence is x + 10 feet

(since the length is at least 10 feet longer than the width).

Now,

The perimeter of the fence is the sum of the lengths of all its sides.

Since the fence has four sides of equal length,

The perimeter is 4 times the length of one side.

So,

The equation for the perimeter, P, in terms of x.

P = 4(x + x + 10)

  = 8x + 40

Now,

We know that Jake wants the perimeter to be no more than 100 feet,

So we can write an inequality:

8x + 40 ≤ 100

Solving for x:

8x ≤ 60

x ≤ 7.5

Therefore,

The maximum possible width of the fence is 7.5 feet.

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Final answer:

To find the maximum width for Jake's fence with the given constraints, set up inequalities with the perimeter and length requirements. Solving for the width, we find that the maximum possible width Jake can use is 20 feet.

Explanation:

Jake is constructing a fence around his property and wishes for the perimeter to not exceed 100 feet, while the length must be at least 10 feet longer than the width. Let's denote the width of the property as w and the length as l. According to the constraints:

The perimeter (2w + 2l) ≤ 100 feet

The length (l) ≥ w + 10 feet

Using these inequalities, we have:

2w + 2(w + 10) ≤ 100

2w + 2w + 20 ≤ 100

4w ≤ 80

w ≤ 20

The maximum possible width is therefore 20 feet.

Answer:

Step-by-step explanation:

The relation between speed, time, and distance is ...

  speed = distance/time

Against the wind, the speed is ...

  (3310 mi)/(5 h) = 662 mi/h

With the wind, the speed is ...

  (3810 mi)/(5 h) = 762 mi/h

The jet stream adds to the speed in one direction, and subtracts in the other direction, so the difference in travel speeds is twice the speed of the jet stream:

  (762 mi/h -662 mi/h)/2 = jet stream speed = 50 mi/h

__

The speed of the plane is the average of the two speeds, or the sum of jet stream speed and the lower speed, or the difference of the higher speed and the jet stream speed. Any of these calculations will give the plane's speed in still air:

  (762+662)/2 = 662 +50 = 762 -50 = 712 . . . mi/h

Answer:

Option C.

Step-by-step explanation:

Let x represent the number of loaves of pumpkin bread and y represent the number of loaves of zucchini bread Susan bakes.

              Pumpkin bread           zucchini bread                Total

Eggs               2                                     3                           15        

Flour(cups)     3                                     4                           16

Selling price    $5                                  $4

Susan wants to maximize the money raised at the bake sale.

Objective function :

[tex]P=5x+4y[/tex]

Subject to constraints:

[tex]2x+3y\leq 15[/tex]

[tex]3x+4y\leq 16[/tex]

[tex]x,y \geq 0[/tex]

Since the objective function is P = 5x + 4y, therefore the correct option is C.

Answer:

c

Step-by-step explanation:

i got it correct on edgenunity

Answer: (D) 3.21

Step-by-step explanation:

Let [tex]t_A=[/tex] Time taken by one outlet to fill the pool.

[tex]t_B=[/tex]Time taken by second outlet to fill the pool.

Given : The time taken by one outlet to fill the entire pool : [tex]t_A=[/tex] 9 hours

The time taken by second outlet to fill the entire pool : [tex]t_B=[/tex] 5 hours

Now , if both outlets are used at the same time, approximately what is the number of hours required to fill the pool (T) , then the time required to fill the pool will be :_

[tex]\dfrac{1}{T}=\dfrac{1}{t_A}+\dfrac{1}{t_B}\\\\\Rightarrow =\dfrac{1}{T}=\dfrac{1}{9}+\dfrac{1}{5}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{9+5}{(9)(5)}=\dfrac{14}{45}\\\\\Rightarrow\ T=\dfrac{45}{14}=3.21428571429\approx3.21[/tex]

Hence, the approximate time taken by both outlets to fill the pool together = 3.21 hours.

Thus , the correct option is  (D) 3.21

The question is about rate, time and work. Using the given rates of the outlets, we determine the combined rate. We then use the time = work/rate formula to calculate the time it would take for both outlets to fill the pool, which comes out to approximately 3.21 hours.

This question is a typical problem in rate time and work, which is a common topic in mathematics especially algebra. The problem talks about two outlets with different rates filling a pool.

Let's consider the rate of the first outlet as 1/9 pool/hour and the second outlet as 1/5 pool/hour. If both outlets are working at the same time, their rates would add up. Hence, the combined rate would be 1/9 + 1/5 = 14/45 pool/hour.

To find how long it would take for both outlets to fill the pool, we use the equation time = work/rate. Plugging in our values, we get time = 1 pool / 14/45 pool/hour. Therefore, the time is amounts to approximately 3.21 hours.

Therefore, "the correct answer is (D) 3.21".

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Answer:

15.5 yards

They will be picked up at an elevation of 15.5 yards

Step-by-step explanation:

Here we are going to make the ski slope of the mountain as the hypotenuse of a right-angled triangle where the top of the slope and bottom of the slope are two ends of the hypotenuse.

We first have to find the height of the top of the mountain with respect to the bottom.

Here we have been given heights with respect to sea level above and below.

Clearly, sum of the distances above and below sea level will be total elevation with respect to the bottom.

h1 - Height of summit above sea level

h2 - Height of bottom below sea level

Hb - Elevation of top w.r.t bottom

Hb = h1 + h2

Hb = [tex]17\frac{3}{4}+13\frac{1}{4}[/tex]

Hb = 31 yards

Now, the ski lift is picking them up in the middle of the slope (hypotenuse of the triangle).

By midpoint theorem line segment parallel to base joins the midpoints of the other 2 sides.

Thus the elevation will clearly be half of total elevation.

Height at which they are picked up is Hb/2

Therefore,

They will be picked up at an elevation of 15.5 yards

Answer:

No real roots

Step-by-step explanation:

The given quadratic equation is

[tex] {x}^{2} + 5x + 7 = 0[/tex]

Comparing this to the general quadratic equation:

[tex]a {x}^{2} + bx + c = 0[/tex]

We have a=1, b=5 and c=7

Recall that the discriminant is

[tex]D = {b}^{2} - 4ac[/tex]

We plug in the values to get:

[tex]D = {5}^{2} - 4(1)(7)[/tex]

[tex]D =25- 28 = - 3[/tex]

Since the discriminant is less than zero, the given equation has no real roots

Answer:

2l + 2w = 96 ..... eqn1

lw = 504 ...... eqn2

Step-by-step explanation:

To model this case where we have two unknowns l and w, we need two equations.

Firstly, the perimeter of a rectangle is given by

2l + 2w = p

Where l,w and p are length, width and perimeter of the rectangle respectively.

Hence,

2l + 2w = 96 ... eqn1

Secondly, the area of a rectangle is given by

Length × width = Area

Hence,

l × w = 504

lw = 504 ... eqn2

With these two equations the solutions to the length and width of the rectangular pool can be derived.

Answer:

D. 2l+2w=96

    lw=504

Step-by-step explanation:

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