1 When an aero plane took off, it was noted that for every 100 m rise in altitude, the temperature dropped by 1 1/2 C. The plane reached an altitude 25 times the distance of 100 m, by how much the temperature would have dropped if the Ground temperature was 27 1/2 C

Answer:

The answer is below

Step-by-step explanation:

1. y = 3x                is a linear function because it doesn't have any power

2. y =- 2+5x          is a linear function because it doesn't have any power

3. 2x + y= 10          is a linear function because it doesn't have any power

4. f(x) = 4x^2         it isn't a linear function because x is elevated to a power

5. -3/x + y = 15      is a linear function because it doesn't have any power

6. x + y + 8            is a linear function because it doesn't have any power

The first, second, third and sixth functions are linear functions, as they comply with the standard linear function format, y = mx + c. The fourth and fifth functions are not linear because they do not follow this standard format.

A linear function is a function whose graph is a straight line. The general form of a linear function is y = mx + c, where m is the slope of the line, and c is the y-intercept.

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Answer:

  A. (1, -1)

  B. (1, -1), (2, 0)

  C. x = 0

Step-by-step explanation:

A graph is a plot of all the points that are solutions to an equation.

Part A:

A point will be a solution to two equations if it is a point of intersection of their graphs. The one point that is a solution to both p(x) and g(x) is the one point where their graphs intersect: the red and blue lines cross at (1, -1).

__

Part B:

Any other point on the graph p(x) will be another solution of it. One that is near to the point of intersection with g(x) is the point where p(x) crosses the x-axis: (2, 0). Of course, the solution listed in Part A is also a solution to p(x).

__

Part C:

The point where the graph of g(x) crosses the graph of f(x) is (0, 3). The x-value that makes g(x) = f(x) is x=0. That is the solution to this equation. (We don't really care what the values of f(0) and g(0) are--just that they are equal.)

Answer:

The answer to your question is: 3) between 12 and 13

Step-by-step explanation:

Just get the square root of 151, and compare your result with the options.

√ 151 = 12.28

Then, the only possibility is (3) 12 and 13.

Answer:

The answer is 9.10, ($9.10).

Step-by-step explanation:

Oh just to let you know that other answer (joke) was such a loser joke.

Answer:

At most 5 -->  x ≤ 5

Larger than 5 -->  x > 5

Below 5 -->  x < 5

Not less than 5 -->  x ≥ 5

Step-by-step explanation:

I learned how to figure this out like this: "The smaller number eats the bigger one", since the symbols "<" and ">" looks like an open mouth.

The symbols "≥" and "≤" mean that it is larger or equal to the number shown.

In the first case, it means that the number that represents "x" could be any up to the number 5 (including it). And in the last case, it means that the number that represents "x", could be any starting from 5(including it).

Answer:

The first customer that will get four free tickets is 50th customer

Step-by-step explanation:

Find the least common multiple of numbers 10 and 25. First, factorize these numbers:

[tex]10=2\cdot \underline{5}\\ \\25=\underline{5}\cdot 5\\ \\LCM(10,25)=\underline{5}\cdot 2\cdot 5=50[/tex]

When finding LCM, first write the all common multiples (underlined 5) and then multiply them by remaining multiples (2 and 5). You get 50 as LCM(10,25). This means that each 50th customer will get four free tickets.

Final answer:

The first customer who will receive four free tickets is the 100th customer.

Explanation:

To determine the first customer who will receive four free tickets, we need to find the smallest positive integer that is divisible by both 10 and 25. This is called the least common multiple (LCM). To find the LCM of 10 and 25, we can list the multiples of each number until we find a common multiple:

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100

Multiples of 25: 25, 50, 75, 100

The LCM of 10 and 25 is 100. Therefore, the first customer who will receive four free tickets is the 100th customer.

Answer:

75%

Step-by-step explanation:

100%-25%= 75%

He would have paid 75% of the original price..

Answer:

C. [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

Let x be the original price of laptop computer.

We have been given that Luis purchased a laptop computer that was marked down by 2/5 of the original price.

The price of laptop computer after mark-down would be x minus 2/5 of x.

[tex]\text{The price of laptop computer after mark-down}=x-\frac{2}{5}x[/tex]

[tex]\text{The price of laptop computer after mark-down}=\frac{5}{5}x-\frac{2}{5}x[/tex]

[tex]\text{The price of laptop computer after mark-down}=\frac{5-2}{5}x[/tex]

[tex]\text{The price of laptop computer after mark-down}=\frac{3}{5}x[/tex]

Therefore, Luis paid [tex]\frac{3}{5}[/tex] of the original price.

The percentage of men who gave an excellent rating is 70%. The percentage of women who gave an excellent rating is 64%. The total percentage of customers giving an excellent rating is 67%.

To find the percentage of men who gave an excellent rating, we divide the number of men who gave an excellent rating (175) by the total number of men surveyed (250) and multiply by 100.

So the percentage of men who gave an excellent rating is 70%.

To find the percentage of women who gave an excellent rating, we divide the number of women who gave an excellent rating (160) by the total number of women surveyed (250) and multiply by 100.

So the percentage of women who gave an excellent rating is 64%.

To find the total percentage of customers who gave an excellent rating, we divide the total number of customers who gave an excellent rating (175 + 160 = 335) by the total number of customers surveyed (500) and multiply by 100. So the total percentage of customers who gave an excellent rating is 67%.

The percentage of men who gave an excellent rating is 70%, the percentage of women who gave an excellent rating is 80%, and the total percentage of customers giving an excellent rating is 67%.

First, let's calculate the percentage of men who gave an excellent rating:

- There are 250 men surveyed.

- Out of these, 175 men rated the customer service as excellent.

- To find the percentage, we use the formula: (Number of men who rated excellent / Total number of men) × 100.

- Plugging in the numbers, we get: (175 / 250) × 100.

- Simplifying this, we divide both the numerator and the denominator by 25 to get: (7 / 10) × 100.

- This simplifies to 70%.

Next, we calculate the percentage of women who gave an excellent rating:

- There are 250 women surveyed.

- Out of these, 160 women rated the customer service as excellent.

- Using the same formula as before: (Number of women who rated excellent / Total number of women) × 100.

- Plugging in the numbers, we get: (160 / 250) × 100.

- Simplifying this, we divide both the numerator and the denominator by 40 to get: (4 / 5) × 100.

- This simplifies to 80%.

Finally, we calculate the total percentage of customers who gave an excellent rating:

- The total number of customers surveyed is 500 (250 men + 250 women).

- The total number of excellent ratings is 175 from men and 160 from women, which sums up to 335.

- Using the formula: (Total number of excellent ratings / Total number of customers) × 100.

- Plugging in the numbers, we get: (335 / 500) × 100.

- Simplifying this, we divide both the numerator and the denominator by 5 to get: (67 / 100) × 100.

- This simplifies to 67%.

- Percentage of men giving an excellent rating: 70%

- Percentage of women giving an excellent rating: 80%

- Total percentage of customers giving an excellent rating: 67%

Answer:

The answer to your question is: d = 12

Step-by-step explanation:

                                             6(d+1)−2d=54

     Expand                          6d + 6 -2d = 54

                                            6d - 2d = 54 - 6

     Simplify                          4d = 48

                                             d = 48 / 4

        Result                           d = 12

Answer:

Option c: all real numbers greater than 0

Step-by-step explanation:

we have

[tex]f(x)=\frac{1}{7}(9^{x})[/tex]

This is a exponential function of the form

[tex]f(x)=a(b^{x})[/tex]

where

a is the initial value (y-intercept)

b is the base

r is the rate

b=(1+r)

In this problem we have

a=1/7

b=9

r=b-1 ----> r=9-1=8 -----> r=800%

using a graphing tool

see the attached figure

The domain is the interval ------> (-∞,∞)

The domain is all real numbers

The range is the interval ---------> (0,∞)

The range is all real numbers greater than zero

Answer: all real numbers greater than 0

Step-by-step explanation:

Range is the set of y values for which the function is defined                    using a graphing tool

The domain is the interval ----> (-∞,∞) All real numbers

For all positive and negative values for x the value of y is always positive

The range is the interval ---->(0,∞)

All real numbers greater than 0

Let [tex]\mu[/tex] be the population mean.

Null hypothesis : [tex]\mu=12[/tex]

Alternative hypothesis : [tex]\mu<12[/tex]

Since Alternative hypothesis is left tailed so , the test is a left tailed test.

Given : n=33 > 30 , so we use z-test.

Test statistic : [tex]z=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

i.e. [tex]z=\dfrac{11.2-12}{\dfrac{1.6}{\sqrt{33}}}\approx-2.87[/tex]

Using z-value table,

P-value for left tailed test =[tex]P(z<-2.87)=0.0020524[/tex]

Since , the p-value (0.0020524) is less than the 0.05 level of significance, it means we reject the null hypothesis.

Therefore, we have enough evidence to support the claim that the mean completion time has decreased under new management.

Answer:

a) 4.9 % of all parts is defective or 0.049 of the total parts.

b)  0.5102 is the probability that the defective part was supplied by S1

Step-by-step explanation:

N is the total number of parts from supplier S1, S2 and S3.

N1 = 0.5*N is the total number of part supplied by S1

N2 = 0.2*N is the total number of part supplied by S2  

N3 = 0.3*N is the total number of part supplied by S3

a) if Nd1 is the number of defective parts from supplier S1, Nd2 is the number of defective parts from supplier S2 and Nd3 is the number of defective parts from supplier S3, the the total defective parts Nd is:

Nd = Nd1 + Nd2 + Nd3, where

Nd1 = 0.05*N1 = 0.05*0.5*N = 0.025*N,

Nd2 = 0.03*N2 = 0.03*0.2*N = 0.006*N,

Nd3 = 0.06*N3 = 0.06*0.3*N = 0.018*N,

Then Nd = Nd1 + Nd2 + Nd3 =  0.049*N, so Nd/N = 0.049

b) [tex]P(S1 \vert d) = \frac{P(S1,d)}{P(d)} = \frac{P(d \vert S1)}{P(d)} = \frac{0.05*0.5}{0.049} \approx 0.5102[/tex]

for the last expression I used the Bayes tehorem.

[tex]P(S1 \vert d)[/tex] is the probability that occur S1 given that d (defective) is true. This a conditional probability.

see at https://en.wikipedia.org/wiki/Bayes%27_theorem

The overall defect portion from all suppliers is 4.9%. If a part is defective, the probability that it was supplied by S1 is approximately 51.02%.

To determine what portion of all the parts is defective, we calculate a weighted average of the defect rates based on the supplier portion contributions. The calculation is as follows:

The overall defect rate is the sum of these contributions, which is [tex]2.5 + 0.6 + 1.8 = 4.9%.[/tex]

For part (b), the probability that the defective part was supplied by S1 can be found using Bayes' theorem:

If a part is defective, the probability of it being from S1 is the probability that S1 provided a defective part over the probability that any part is defective. This probability is ([tex]0.50 * 0.05) / 0.049 = 0.025 / 0.049 \approx 0.5102 or 51.02%.[/tex]

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Answer:

  y = x + 4

Step-by-step explanation:

The line of reflection is the perpendicular bisector of segment AA', so passes through point (A+A')/2 = (-2, 2) and is perpendicular to the line through A and A'. That line is y = -x, so the point-slope equation of the line of reflection is ...

  y = 1(x -(-2)) +2

  y = x +4

The line of reflection between triangle ABC and its image A'B'C' is y = -x. The point-slope equation of the line of reflection is y = x+4.

To find the line of reflection between triangle ABC and its image A'B'C', we can observe that the corresponding points have the same x-coordinates and their y-coordinates are negatives of each other. Since the line of reflection is the perpendicular bisector of the segment joining each original point and its image, we can use the coordinates of two corresponding points to find the equation of the line. In this case, we can use points A and A', and points B and B' to determine the line of reflection.

Using the coordinates A(-4, 4) and A'(0, 0), we can calculate the slope of the line as (0 - 4) / (0 - (-4)) = -1. The midpoint between A and A' is (-2, 2), which lies on the line. So, the equation of the line is y = -x.

Similarly, using the coordinates B(-4, 1) and B'(-3, 0), we can calculate the slope as (0 - 1) / (-3 - (-4)) = 1. The midpoint between B and B' is (-3.5, 0.5), which also lies on the line y = x. Therefore, the line of reflection is y = -x.

So, the point-slope equation of the line of reflection is:

 y = 1(x -(-2)) +2

 y = x +4

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The graph for reflection is given below:

Answer:

The answer to your question is:

a) C = 2g + 155c

b) g = 25 grapes

c) c = 3

Step-by-step explanation:

Data

grapes = g = 2 calories

cheese = c = 155 calories

a) Equation, we consider the amount of grapes and the calores given.

Total calories = C = 2g + 155c

b) We consider that the slices of cheese stays the same

                       2g + 155 = 205

                       2g = 205 -155

                        2g = 50

                        g = 50/2 = 25 grapes

c) Then the number of grapes stays the same

                       2(25) + 155c = 515

                       50 + 155c = 515

                       155c = 515 - 50

                        155c = 465

                        c = 465/155

                        c = 3 slices of cheese

Answer: Jill got the larger smoothie and its volume is 1609.14 cubic cm.

Step-by-step explanation:

Since we have given that

Jill purchased the cylindrical container.

Height of container = 8 cm

Radius = 8 cm

So, volume of cylindrical container would be

[tex]\pi r^2h\\\\=\dfrac{22}{7}\times 8\times 8\times 8\\\\=1609.14\ cm^3[/tex]

Marcy purchased the rectangular container.

Height of container = 8 cm

Width = 8 cm

Length = 8 cm

so, volume of rectangular container would be

[tex]l\times b\times h\\\\=8\times 8\times 8\\\\=512\ cm^3[/tex]

Hence, Jill got the larger smoothie and its volume is 1609.14 cubic cm.

Answer:

x = 10

Step-by-step explanation:

-36 = -6(2x-14)

6 = 2x-14

20 =2x

10 = x

Answer:

-x = -10

Step-by-step explanation:

-36 = -12x + 84

-120 = -12x

-10 = -x

Answer:

the total charge is

[tex]Q=24(1-\exp(-1))nC\approx15.171nC[/tex]

Step-by-step explanation:

Since x is measured from the center, that means that x=0 is the center so the edges of the rod correspond to x=-6 and x=6. that meas that the total charge can be calculated as

[tex]Q=\int^{6}_{-6}2\exp\left(\frac{-|x|}{6}\right)dx[/tex]

separating the integral from -6 to 0 and from 0 to 6, taking into account that |x|=-x for x<0 and |x|=x for x >=0, we get[tex]Q=\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx+\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx[/tex]

using the substitution x=-u in the first integral we get[tex]\int^{0}_{-6}2\exp\left(\frac{x}{6}\right)dx=-\int^{0}_{6}2\exp\left(\frac{-u}{6}\right)du=\int^{6}_{0}2\exp\left(\frac{-u}{6}\right)du[/tex]

which is the same as the first integral. Thus, the total charge is given by

[tex]Q=2\int^{6}_{0}2\exp\left(\frac{-x}{6}\right)dx[/tex]

integrating we get

[tex]Q=4(-6\exp\left(\frac{-x}{6}\right))\big|^{6}_{0}=-24(\exp(-6/6)-\exp(0))=24(1-\exp(-1))[/tex]

The total charge is Q= 15.171nC.

Since x is measured from the center, that means that x=0 is the center.

So, the edges of the rod correspond to

x=-6 and x=6.

That means that the total charge can be calculated as

[tex]Q= \int\limits^6_ 6 2 exp(-|x|/6)dx[/tex]

separating the integral from -6 to 0 and from 0 to 6,

Taking into account that

|x|=-x for x<0

and |x|=x for x >=0

Thus, the total charge is given by:

[tex]Q= 2\int\limits^6_0 2exp (-x/6), dx[/tex]

When we integrate, we get:

Q= 24(1- exp(-1))nC ≈

15.171nC

Read more about integration here:
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Answer: 180

Step-by-step explanation:

divide 45 by 7.5 to get the amount of dollars earned per hour

45/7.5 = 6

6(x)= 30hours, = 6(30) = $180

Answer:

$180

Step-by-step explanation:

let pay be p and hours worked be h

Given p varies directly as h then the equation relating them is

p = kh ← k is the constant of variation

To find k use the condition p = 45 when h = 7.5, then

k = [tex]\frac{p}{h}[/tex] = [tex]\frac{45}{7.5}[/tex] = 6, thus

p = 6h ← equation of variation

When h = 30, then

p = 6 × 30 = $180

Answer:

The answer to your question is:

length = 12

width = 6

Step-by-step explanation:

Perimeter of a parallelogram = 2 length + 2 width

We know that width = length - 6

So

          60 = 2 length + 2(length -6)

          60 = 2 length + 2 length - 12

           60 - 12 = 4 length

           48 = 4 length

         length = 48/4 = 12 meters

         width = length - 12

                    = 12 - 6

                     = 6

Answer:

12

6

Step-by-step explanation:

Answer:

The answer to your question is: 99 m²

Step-by-step explanation:

Data

height = 11 m

area of the square base = 9 m²

Formula

Volume of a right rectangular prism = area of the base x height

                                                           = 11 x 9     substitution

                                                           = 99 m²

Answer: Simple random sampling.

Step-by-step explanation:

A simple random sample is basically a subset (with size n) from the entire population, where the chance of getting selected for each element is equal.

Given :A research company believes teens today are getting less than the recommended hours of sleep. The company takes a list of 2000 teen volunteers and assigns each volunteer a number. A

A random number generator is used to select 350 individuals to take part in a sleep survey.

It is a simple random sampling because the researcher selected participants randomly such that the chance to get selected for each of them remains same.

Answer:

Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.

Step-by-step explanation:

We are given the following information:

n = 16

[tex]t_{statistic} = 1.94[/tex]

[tex]\alpha = 0.05[/tex]

Now,

Right One-tail Test

[tex]t_{critical} \text{ at 0.05 level of significance, 15 degree of freedom } = 1.753[/tex]

[tex]t_{stat} > t_{critical}[/tex]

We reject the null hypothesis in this case.

Two-tail Test

Now, [tex]t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = \pm 2.131[/tex]

[tex]-2.131 < t_{stat} < 2.131[/tex]

We accept the null hypothesis in this case.

Option 3) We reject the null hypothesis with one tail test and accept the null hypothesis with two tail test.

The correct decision for this hypothesis test is to reject the null hypothesis with a one-tailed test but fail to reject with two tails.

To make a decision in a hypothesis test, we compare the t statistic to the critical value. In this case, the t statistic is 1.94. Since the treatment is expected to increase scores and the sample mean shows an increase, we are conducting a one-tailed test. Looking at the critical value for a = 0.05 for a one-tailed test using the t15 distribution, we find that it is 1.753. Since the t statistic (1.94) is greater than the critical value (1.753), we reject the null hypothesis. Therefore, the correct decision for this hypothesis test is to reject the null hypothesis with a one-tailed test but fail to reject with two tails.

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60 ≥ 35 + 5t

-35 -35

25 ≥ 5t

5 5

t≤5

his mistake was that he used ≤ for at least instead of using ≥. so at end, when I solved, I saw that Sven should spend 5 minutes or less on each scale.

Answer:

24/18=1.333

20/16=1.25

6/4=1.5 (the ratio to achieve9

1.333 is more close to 1.5 than 1.25 (11% difference compared to 17%)

Step-by-step explanation:

Answer:

16 in. X 20 in will keep more.

Step-by-step explanation:

Length of picture = 4 inches

Breadth of picture = 6 inches

Area of picture=[tex]length  \times breadth[/tex]

                        =[tex]4 \times 6[/tex]

                        =[tex]24 inches^2[/tex]

Length of frame 1 = 16 inches

Breadth of frame 1 = 20 inches

Area of frame 1 = [tex]16 \times 20 = 320 inches^2[/tex]

So, % of picture can fit in frame 1= [tex]\frac{\text{original picture area }}{\text{Frame 1 area }} \times 100[/tex]

                                                   = [tex]\frac{24}{320} \times 100[/tex]

                                                   = [tex]7.5 %[/tex]

Length of frame 2 = 18 inches

Breadth of frame 2 = 24 inches

Area of frame 2 = [tex]18 \times 24 = 432 inches^2[/tex]

So, % of picture can fit in frame 2 = [tex]\frac{\text{original picture area }}{\text{Frame 1 area }} \times 100[/tex]

                                                   = [tex]\frac{24}{432} \times 100[/tex]

                                                   = [tex]5.56 %[/tex]

Since % of picture can fit in frame 1 is more than frame 2 .

So, 16 in. X 20 in will keep more.

Answer:

Step-by-step explanation:

From the problem statement, each box of candles has the following range of candles:

[tex]78 \leq x \leq 82[/tex]

We also know that we have 50 boxes of candles, so we multiply the above range by 50 to get the range of candles:

[tex]3900 \leq x \leq 4100[/tex]

Finally, each candle costs $2, so we have the final range of cost:

[tex]7800 \leq x \leq 8200[/tex]

By calculating the cost of producing the minimum and maximum number of candles that can be packaged in 50 boxes, we determine the range of possible production costs, x, is $7,800 to $8,200.

The student needs to calculate the range of possible production costs for 50 boxes of candles, given that each box contains an average of 80 candles and the number of candles can vary by at most two from this average. Since each candle costs two dollars to produce, we can find the minimum and maximum number of candles in one box by subtracting and adding two to the average, respectively (78 and 82 candles). Multiplying these numbers by the cost per candle gives us the cost per box, and then multiplying by the number of boxes (50) gives us the total production cost range for all boxes.

To calculate the minimum cost, we use the minimum number of candles per box: 78 candles per box × $2 per candle × 50 boxes = $7,800. To calculate the maximum cost, we use the maximum number of candles per box: 82 candles per box × $2 per candle × 50 boxes = $8,200. Therefore, the range for the possible production costs, x, for 50 boxes of candles is $7,800 ≤ x ≤ $8,200, which corresponds to answer choice D.

Answer:

Using backward reasoning we want to show that "We can never get nine 0's".

Step-by-step explanation:

Basically in order to create nine 0's, the previous step had to have all 0's or all 1's. There is no other way possible, because between any two equal bits you insert a 0.

If we consider two cases for the second-to-last step:

There were 9 0's:

We obtain nine 0's if all bits in the previous step were the same, thus all bit were 0's or all bits were 1's. If the previous step contained all 0's, then we have the same case as the current iteration step. Since initially the circle did not contain only 0's, the circle had to contain something else than only 0's at some point and thus there exists a point where the circle contained only 1's.

There were 9 1's:

A circle contains only 1's, if every pair of the consecutive nine digits is different. However this is impossible, because there are five 1's and four 0's (we have an odd number of bits!), thus if the 1's and 0's alternate, then we obtain that 1's that will be next to each other (which would result in a 1 in the next step). Thus, we obtained a contradiction and thus assumption that the circle contains nine 0's after iteratins the procedure is false. This then means that you can never get nine 0's.

To summarize, in order to create nine 0's, the previous step had to have all 0's or al 1's. As we didn't start the arrange with all 0's, the only way is having all 1's, but having all 1's will not be possible in our case since we have an odd number of bits.

999 is 3 times 333, so the ratio will have to be multiplied by three.

No of cherries needed = 240240240 * 3 = 720720720 cherries

Answer:

width of a singles court = 27 feet

Step-by-step explanation:

Width of a doubles tennis court = 36 feet

Width of a singles tennis court = 75% of 36

[tex]width = 75\% \times 36 \\ width = \frac{75}{100} \times 36 \\ width = \frac{3} {4} \times 36 \\ width = \frac{108}{4} = 27[/tex]