Solve the inequality.
[tex]12( \frac{1}{2} \times - \frac{1}{3} ) > 8 - 2 \times [/tex]
A.
[tex] \times > - \frac{1}{2} [/tex]
B.
[tex] \times > \frac{3}{2} [/tex]
C.
[tex] \times > \frac{1}{2} [/tex]
D.
[tex] \times > 3[/tex]
​

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

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: 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:

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:

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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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: 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 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:

  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:

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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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]

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:

a. When two variables change in the same direction, one remaining larger than the other by the same factor - direct relationship

b. To insert between neighboring points or estimate by taking an average of known values - interpolate

c. A relationship between two variables in which the product remains constant. When one variable increases the other decreases in proportion so that the product is unchanged - inverse relationship

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

No of cherries needed = 240240240 * 3 = 720720720 cherries

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:

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:

16.197 seconds

Step-by-step explanation:

the time and the final place fot both cars is the same.

for the Boxster we have

X = Vboxster . T

being

X the distancance from the initial place of the Boxter to the meeting point

Vboxster the speed of the Boxster (26m/s)

T the time

and for the Scion

X = Xo + Vscion . T

Being

Xo the initial point of the Scion (115m)

X the distancance from the initial place of the Boxster to the meeting point

Vscion the speed of the Scion (18.9 m/s)

T the time

                 Xo + Vscion . T  = Vboxster . T

                                    Xo   = Vboxster . T - Vscion . T

                                   Xo   = (Vboxster  - Vscion) . T

Xo/(Vboxster  - Vscion)   =  T

    115m/ (26-18.9) m.s-1 = T

                          16.197 s = T

Answer:

a)t = 16.2s  : time it takes for the Boxster to catch the Scion

b)The displacement of the Boxster (db) is 115 m more than the displacement of the Scion(ds)

db =ds+115

Step-by-step explanation:

Conceptual analysis

We apply the formula for constant speed movement:

v= d/t Formula (1)

v = speed in m/s

d: distance in m

t: time in s

Problem development

The time of Scion (ts) is equal time of Boxster (tb)

t (s) =tb=t

The displacement of the Boxster is 115 m more than the displacement of the Scion

db =ds+115

we apply formula (1 )car kinematics  :

Scion kinematics

18.9=ds/t

t =ds /18.9 Equation (1)

Boxster kinematics

26=db/t

26=(ds+115)/t

t=(ds+115)/26 Equation (2)

Equation (1) = Equation (2)

ds /18.9 =(ds+115)/26

18.9(ds+115)= 26 ds

18.9ds+18.9*115=26 ds

2173.5= 26 ds-18.9ds

2173.5=7.1ds

ds =2173.5÷7.1

ds=306.12m

We replace ds=306.12m in the equation (1)

t =306.12÷18.9

t = 16.2s

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:

  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:

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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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:

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: 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:

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:

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.

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:

A

Step-by-step explanation:

A: The possibility of promoting child labor is a concern about globalization