The royal fruit company produces two types of fruit drinks. the first type is 20% pure fruit juice, and the second is 70% pure fruit juice. The company is attempting to produce a fruit drink that contains 35% pure fruit juice. How many pints of each of the two existing types of drinks must be used to make 60 pints of a mixture that is 35% pure fruit juice?

Answer:

yque   ha haceqr ailluey

Step-by-step explanation:

Answer:

The common difference is 6

Step-by-step explanation:

To find the common difference take the second term and subtract the first term

8 -2 = 6

Check by taking the third term and subtracting the second term

14-8 =6

And so forth

Answer:

6n - 4

Step-by-step explanation:

1. Find the numbers between the 2 terms.

2. Times by n.

3. We now must minus the first number in thee sequence from whatever you 6n equals. (6-2, 12-6 ETC)

Answer:

75.76% probability that there will be 10 or more customers at this bank in one hour.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

In which

x is the number of sucesses

e = 2.71828 is the Euler number

[tex]\mu[/tex] is the mean in the given interval.

A bank gets an average of 12 customers per hour.

This means that [tex]\mu = 12[/tex]

Find the probability that there will be 10 or more customers at this bank in one hour.

Either there are less than 10 customers, or there are 10 or more. The sum of the probabilities of these events is 1. Then

[tex]P(X < 10) + P(X \geq 10) = 1[/tex]

We want [tex]P(X \geq 10)[/tex]

Then

[tex]P(X \geq 10) = 1 - P(X < 10)[/tex]

In which

[tex]P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)[/tex]

So

[tex]P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}[/tex]

[tex]P(X = 0) = \frac{e^{-12}*12^{0}}{(0)!} \approx 0[/tex]

[tex]P(X = 1) = \frac{e^{-12}*12^{1}}{(1)!} = 0.0001[/tex]

[tex]P(X = 2) = \frac{e^{-12}*12^{2}}{(2)!} = 0.0004[/tex]

[tex]P(X = 3) = \frac{e^{-12}*12^{3}}{(3)!} = 0.0018[/tex]

[tex]P(X = 4) = \frac{e^{-12}*12^{4}}{(4)!} = 0.0053[/tex]

[tex]P(X = 5) = \frac{e^{-12}*12^{5}}{(5)!} = 0.0127[/tex]

[tex]P(X = 6) = \frac{e^{-12}*12^{6}}{(6)!} = 0.0255[/tex]

[tex]P(X = 7) = \frac{e^{-12}*12^{7}}{(7)!} = 0.0437[/tex]

[tex]P(X = 8) = \frac{e^{-12}*12^{8}}{(8)!} = 0.0655[/tex]

[tex]P(X = 9) = \frac{e^{-12}*12^{9}}{(9)!} = 0.0874[/tex]

[tex]P(X < 10) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) = 0 + 0.0001 + 0.0004 + 0.0018 + 0.0053 + 0.0127 + 0.0255 + 0.0437 + 0.0655 + 0.0874 = 0.2424[/tex]

Then

[tex]P(X \geq 10) = 1 - P(X < 10) = 1 - 0.2424 = 0.7576[/tex]

75.76% probability that there will be 10 or more customers at this bank in one hour.

Answer:

Simplify by using addition property of equality.

Step-by-step explanation:

She added the 1 to 1/2, therefore it's addition.

Since this is the equivalent expression in step 2, hence the corresponding statement is simplify by combining like terms.

Given the equation given in the table as;

1/2 - 2x + 1 = -13/2

Simplify by combining like terms.

1/2 + 1 - 2x = -13/2

3/2 - 2x = -13/2

Since this is the equivalent expression in step 2, hence the corresponding statement is simplify by combining like terms.

Learn more on factoring here; https://brainly.com/question/24673551

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Answer:

it’s C

Step-by-step explanation:

No, the vertices of the image and pre-image do not correspond

No, the vertices of the image and pre-image do not correspond, Micaela tried to rotate the square 180° about the origin. Hence, option C is correct.

A figure can be rotated by 90 degrees clockwise by rotating each vertex of the figure 90 degrees clockwise about the origin.

Let's take the vertices of a square with points at (+1,+1), (-1,+1), (-1,-1), and (+1,-1), centered at the origin, can be found in the following positions after rotation:

Micaela's rotation must be accurate if it led to the same points. Her rotation is incorrect if the points are different, though.

It is impossible to tell if Micaela's rotation is accurate without more details or a diagram.

Thus, option C is correct.

For more information about rotation about the origin, click here:

https://brainly.com/question/30198965

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Answer: k = 5

Step-by-step explanation:

Box A has more counters than box B

3 * 4 = 12

4 + 8 = 12

So if k was equal to 4, then both boxes would have the same amount.

3 * 5 = 15

5 + 8 = 13

15 > 13

If k was equal to 5, then Box A would contain more counters than Box B.

Answer:

  -5 < x-1 < 5

Step-by-step explanation:

Consider |a|. This has the value -a when a < 0. So, if we write the inequality ...

  |a| < b

it is equivalent to two inequalities:

  a < b . . . . for a ≥ 0

  -a < b . . . for a < 0

Multiplying by -1. the latter inequality is ...

  a > -b . . . for a < 0

Written using the < symbol, this is ...

  -b < a

So, the original inequality can be written as the two inequalities ...

  -b < a (for a < 0)   or   a < b (for a ≥ 0)

Since these are disjoint, we can form their union as ...

  -b < a < b

__

Above, we have a = x-1, b = 5, so the inequality |x-1| < 5 can be written ...

  -5 < x -1 < 5

Answer:

C)  –5 < x – 1 < 5  on edge.

Step-by-step explanation: Edge 2021. I got it correct.

Answer:

Step-by-step explanation:

The tangent lines meet the radii at 90 degrees.

The way the diagram is drawn, the following formula will work

<AOB + <OAC + OBC + 10 = 360

<OAC = 90

<OBC = 90

<AOB + 90 + 90 + 10 = 360

<AOB + 190 = 360

<AOB = 360 - 190

<AOB = 170

Answer:

The expected value of this game is -$0.26.

Step-by-step explanation:

Expected value:

Each possible earning/loss multiplied by it's probability.

Probability:

Number of desired outcomes divided by the number of total outcomes.

In this question, the order in which the numbers are chosen is not important. So we use the combinations formula to solve.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Probability of winning:

Desired outcomes:

The 6 correct numbers, so [tex]D = 6[/tex]

Total outcomes:

6 numbers from a set of 21. So

[tex]T = C_{21,6} = \frac{21!}{6!15!} = 54264[/tex]

Probability:

[tex]p = \frac{1}{54265}[/tex]

Expected value

[tex]\frac{1}{54265}[/tex] probability of earning 40,000.

[tex]\frac{54264}{54265}[/tex] probability of losing 1. So

[tex]E = \frac{40,000}{54265} - \frac{54264}{54265} = -0.26[/tex]

The expected value of this game is -$0.26.

Answer:

D. e - 35

Step-by-step explanation:

We have that:

George earned e extra points.

Kate earned k extra points.

Kate earned 35 fewer extra credit points than George.

This means that k is e subtracted by 35, that is:

k = e - 35

So the correct answer is:

D. e - 35

Answer:

25%

Step-by-step explanation:

She watched in total 60 movies. Out of that total, she rated 15 of them as very good. Thus, she rated 15/60 or 1/4 or a quarter of them as very good.

To convert 1/4 into a percentage, simply divide them and you get 0.25. The percentage is the first two digits after the decimal, which is 25%.

Answer:

4 over 28 = 1 over 7

Step-by-step explanation:

28 divided by 4 = 7

4 divided by 4 = 1

so 1 over 7

Answer:

There are 36 education paths available to Carlos based on the schools around where he lives.

Step-by-step explanation:

Complete Question

Carlos is almost old enough to go to school. Based on where he lives, there are 6 elementary schools, 3 middle schools, and 2 high schools that he has the option of attending. How many different education paths are available to Carlos? Assume he will attend only one of each type of school.

Solution

We can use mathematics or manually writing out the possible combinations of elementary, middle and high school that Carlos can attend.

Using Mathematics

There are 6 elementary schools, meaning Carlos can make his choice in 6 ways.

There are 3 middle schools, meaning Carlos can make his choice in 3 ways.

Together with the elementary school choice, Carlos can make these two choices in 6 × 3 ways.

There are 2 high schools, Carlos can make his choice in 2 ways.

Combined with the elementary and middle school choices, Carlos can make his choices in 6×3×2 ways = 36 ways.

Manually

If we name the 6 elementary schools letters A, B, C, D, E and F.

Name the 3 middle schools letters a, b and c.

Name the 2 high schools numbers 1 and 2.

The different combinations of the 3 choices include

Aa1, Aa2, Ab1, Ab2, Ac1, Ac2

Ba1, Ba2, Bb1, Bb2, Bc1, Bc2

Ca1, Ca2, Cb1, Cb2, Cc1, Cc2

Da1, Da2, Db1, Db2, Dc1, Dc2

Ea1, Ea2, Eb1, Eb2, Ec1, Ec2

Fa1, Fa2, Fb1, Fb2, Fc1, Fc2

Evident now that there are 36 ways in which the 3 stages of schools can be combined. There are 36 education paths available to Carlos based on the schools around where he lives assuming that he will attend only one of each type of school.

Hope this Helps!!!

Answer:

36 education paths

Step-by-step explanation:

Hope this helps!

Answer:

Step-by-step explanation:

The 50 people might be random, depending on when the question was done.  

The 50 people might be random if there's roughly the same number of men as women, but to accomplish this, Isabella would have to pick a time when men would be out shopping.

The 16 are certainly not random, and the question itself is kind of biased.  I would say the answer should be no.

Answer:

ggg

Step-by-step explanation:

gg

Answer:

-30000/100

300 0/1

Step-by-step explanation:

We have the following numbers -18 and 16 2/3, the first is an integer and the second is a mixed number, the first thing is to pass the mixed number to a decimal number.

16 2/3 = 16.67

We do the multiplication:

−18⋅16 2/3 = -300

We have an improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number), therefore it would be:

-30000/100

How mixed number would it be:

300 0/1

Answer:

Check below, please

Step-by-step explanation:

Step-by-step explanation:

1.For which values of x is f '(x) zero? (Enter your answers as a comma-separated list.)

When the derivative of a function is equal to zero, then it occurs when we have either a local minimum or a local maximum point. So for our x-coordinates we can say

 [tex]f'(x)=0\: at \:x=2, and\: x=-2[/tex]

2. For which values of x is f '(x) positive?

Whenever we have  

 [tex]f'(x)>0[/tex]

then function is increasing. Since if we could start tracing tangent lines over that graph, those tangent lines would point up.

 [tex]f'(x)>0 \:at [-4,-2) \:and\:(2, \infty)[/tex]

3. For which values of x is f '(x) negative?  

On the other hand, every time the function is decreasing its derivative would be negative. The opposite case of the previous explanation. So

 [tex]f'(x) <0 \: at\: [-2,2][/tex]

4.What do these values mean?

 [tex]f(x) \:is \:increasing\:when\:f'(x) >0\\\\f(x)\:is\:decreasing\:when f'(x)<0[/tex]

5.(b) For which values of x is f ''(x) zero?

In its inflection points, i.e. when the concavity of the curve changes. Since the function was not provided. There's no way to be precise, but roughly

at x=-4 and x=4

Answer:

a) 7.14% probability that Benny was learning to ride a bike using the training wheels

b) 28% probability that Benny was learning to ride a bike using the training wheels

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

[tex]P(B|A) = \frac{P(B)*P(A|B)}{P(A)}[/tex]

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

Benny came home crying with a bruise on his knee, after falling. His mom is trying to guess how Benny was trying to learn to ride a bike.

a) Assuming that the probability that Benny was using each of these 3 methods is equal, what is the probability that Benny was learning to ride a bike using the training wheels?

So

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that Benny was using each of these 3 methods is equal

This means that [tex]P(B) = \frac{1}{3}[/tex]

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that [tex]P(A|B) = 0.1[/tex]

Probability of falling:

1/3 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

1/3 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

1/3 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

[tex]P(A) = \frac{0.1 + 0.5 + 0.8}{3} = 0.4667[/tex]

So

[tex]P(B|A) = \frac{\frac{1}{3}*0.1}{0.4667} = 0.0714[/tex]

7.14% probability that Benny was learning to ride a bike using the training wheels

b) Since Benny's mom knows Benny so well, she knows that the probability that he was using training wheels is 0.7, regular bike is 0.2, and unicycle is 0.1. What is the probability now that Benny fell while using the training wheels?

Similar as above, just some probabilities change.

Event A: Benny fell

Event B: Benny was using training wheels.

The probability that he was using training wheels is 0.7

This means that [tex]P(B) = 0.7[/tex]

He did some research, and discovered that if he rides a bike with training wheels, the probability of falling is 0.1;

This means that [tex]P(A|B) = 0.1[/tex]

Probability of falling:

0.7 of the time, he uses training wheels. With training wheels, the probability of falling is 0.1.

0.2 of the time, he uses the bike without training wheels. Without training wheels, the probability of falling is 0.5

0.1 of the time, he uses the unicycle, for which he has an 0.8 probability of falling. Then

[tex]P(A) = 0.7*0.1 + 0.2*0.5 + 0.1*0.8 = 0.25[/tex]

So

[tex]P(B|A) = \frac{0.7*0.1}{0.25} = 0.28[/tex]

28% probability that Benny was learning to ride a bike using the training wheels

you divide 40 by 70. then get 1.75 then times 1.75 by A and B which would be 60 * 1.75 = 105 so that means she has 105 ounces for A and for B do the same thing, 85 * 1.75 = 148.75 for B.  :D i would like brainliest plz this took a lot of my time (also stay safe!!!)

Answer:

Given the values: 67,72,86,75,89,89,87 ,90 ,99 and 100.

To create a stem and leaf plot

We place the first digit in the Stem Column and the Second digit in the plot column.

Stem-and-leaf plot of the test scores

[tex]\left|\begin{array}{c|ccccccc}Stem&Leaf\\---&--&--&--&--\\6&7&\\7&2&5\\8&6&7&9&9\\9&0&9\\10&0\end{array}\right|[/tex]

The stem and leaf plot enables us at a glance to see the values or range of the values that are most prevalent.

From the above stem and leaf plot, we can see that values in the range of 80-89 are most prevalent.

Answer:

[tex]40c^{-11}d^4[/tex]

Step-by-step explanation:

[tex](-5c^{-7}d^3)(8c^{-4}d^1)= \\\\(5\cdot 8)(c^{-7}\cdot c^{-4})(d^3 \cdot d^1)= \\\\(40c^{-11}d^4)[/tex]

Hope this helps!

Answer:

The E. Coli will grow at a rate of approximately 800% an hour.

Answer:

Step-by-step explanation:

Let x represent the numerator and y represent the denominator.

The numerator of a rational number is greater than its denominator by 3. It means that

x = y + 3

If the new number becomes 13/4 when the numerator is tripled and the denominator is decreased by 23, it means that

3x/(y - 23) = 13/4

Cross multiplying, it becomes

3x × 4 = 13(y - 23)

12x = 13y - 299- - - - - - - - - - -1

Substituting x = y + 3 into equation 1, it becomes

12(y + 3) = 13y - 299

12y + 36 = 13y - 299

13y - 12y = 36 + 299

y = 335

x = y + 3 = 335 + 3

x = 338

The original number is 338/335

Answer:

There are 12 choices for the first person, 11 for the second and 10 for the third so the answer is 12 * 11 * 10 = 1320.

Answer:

1320 sorry if I’m wrong and btw I’m not positive if the answer is right or wrong but I think it’s that.

Step-by-step explanation:

Answer:

The mean and standard deviation changed to 23.5 and 14.62 respectively, based on all 12 samples.

Step-by-step explanation:

We are given that the Six samples are collected of the number of scanning errors: 36, 14, 21, 39, 11, and 2 errors, per 1,000 scans each.

Representing the data in tabular form;

           X                            [tex]X - \bar X[/tex]                            [tex](X - \bar X)^{2}[/tex]

          36                     36 - 20.5 = 15.5                   240.25

          14                      14 - 20.5 = -6.5                     42.25  

          21                       21 - 20.5 = 0.5                      0.25

          39                      39 - 20.5 = 18.5                   342.25

           11                        11 - 20.5 = -9.5                     90.25

           2                         2 - 20.5 = -18.5                  342.25    

        Total                                                                 1057.5      

Now, the mean of these value is given by;

        Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                         =  [tex]\frac{36+14+21+39+11+2}{6}[/tex]

                         =  [tex]\frac{123}{6}[/tex]  =  20.5

Standard deviation formula for discrete distribution is given by;

           Standard deviation, [tex]\sigma[/tex]  =  [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]

                                                 =  [tex]\sqrt{\frac{1057.5 }{6-1} }[/tex] = 14.54

Now, the manager has six more samples taken:

33, 45, 34, 17, 1, and 29 errors, per 1,000 scans each

So, the modified table would be;

           X                            [tex]X - \bar X[/tex]                            [tex](X - \bar X)^{2}[/tex]

          36                     36 - 23.5 = 12.5                   156.25

          14                      14 - 23.5 = -9.5                     90.25  

          21                       21 - 23.5 = -2.5                     6.25

          39                      39 - 23.5 = 15.5                   240.25

           11                        11 - 23.5 = -12.5                   156.25

           2                         2 - 23.5 = -21.5                   462.25    

          33                       33 - 23.5 = 9.5                     90.25

         45                        45 - 23.5 = 21.5                   462.25

         34                        34 - 23.5 = 10.5                   110.25

          17                         17 - 23.5 = -6.5                    42.25

           1                           1 - 23.5 = -22.5                   506.25

          29                        29 - 23.5 = 5.5                   30.25      

        Total                                                                    2353      

Now, the mean of these value is given by;

        Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                         =  [tex]\frac{36+14+21+39+11+2+33+45+34+17+1+29}{12}[/tex]

                         =  [tex]\frac{282}{12}[/tex]  =  23.5

Standard deviation formula for discrete distribution is given by;

           Standard deviation, [tex]\sigma[/tex]  =  [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]

                                                 =  [tex]\sqrt{\frac{2353 }{12-1} }[/tex] = 14.62

Answer:

Vertical parabolas give an important piece of information: When the parabola opens up, the vertex is the lowest point on the graph — called the minimum, or min. When the parabola opens down, the vertex is the highest point on the graph — called the maximum, or max.

Step-by-step explanation:

The y coordinate of the vertex tells you the highest or lowest point, depending on whether the parabola opens downward or upward.

For something like y = -2(x-5)^2 + 10, it opens downward and has the vertex at (5,10). The highest point is (5,10) so the largest y value or output is y = 10. This is the maximum of the function. Note the value of 'a' is a = -2 which is negative. Also note the vertex form y = a(x-h)^2 + k with vertex (h,k).

For an example like y = 7(x+2)^2 - 8 we have a = 7 so the parabola opens upward meaning we'll have a minimum this time. The lowest point is the vertex (h,k) = (-2,-8). The minimum of the function is y = -8.

Answer:

All rhombi are parallelograms.

All squares are rhombi.

No trapezoid is a rectangle.

Answer:

(1) 4.09% of the New York City commutes are for less than 26 minutes.

(2) 14.32% are between 26 and 32 minutes.

(3) 54.23% are between 26 and 40 minutes.

Step-by-step explanation:

We are given that the longest one-way travel time is in New York City, where the mean time is 38.5 minutes.

Assume the distribution of travel times in New York City follows the normal probability distribution and the standard deviation is 7.2 minutes.

Let X = travel times in New York City.

So, X ~ Normal([tex]\mu=38.5,\sigma^{2} =7.2^{2}[/tex])

The z-score probability distribution for the normal distribution is given by;

                           Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean travel time = 38.5 minutes

           [tex]\sigma[/tex] = standard deviation = 7.2 minutes

(1) The percent of the New York City commutes that are less than 26 minutes is given by = P(X < 26 minutes)

    P(X < 26 minutes) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{26-38.5}{7.2}[/tex] ) = P(Z < -1.74) = 1 - P(Z [tex]\leq[/tex] 1.74)

                                                                 = 1 - 0.9591 = 0.0409 = 4.09%

The above probability is calculated by looking at the value of x = 1.74 in the z table which has an area of 0.9591.

(2) The percent of the New York City commutes that are between 26 and 32 minutes is given by = P(26 min < X < 32 min) = P(X < 32 min) - P(X [tex]\leq[/tex] 26 min)

    P(X < 32 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{32-38.5}{7.2}[/tex] ) = P(Z < -0.90) = 1 - P(Z [tex]\leq[/tex] 0.90)

                                                          = 1 - 0.8159 = 0.1841

    P(X [tex]\leq[/tex] 26 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{26-38.5}{7.2}[/tex] ) = P(Z [tex]\leq[/tex] -1.74) = 1 - P(Z < 1.74)

                                                           = 1 - 0.9591 = 0.0409

The above probability is calculated by looking at the value of x = 0.90 and x = 1.74 in the z table which has an area of 0.8159 and 0.881 respectively.

Therefore, P(26 min < X < 32 min) = 0.1841 - 0.0409 = 0.1432 or 14.32%.

(3) The percent of the New York City commutes that are between 26 and 40 minutes is given by = P(26 min < X < 40 min) = P(X < 40 min) - P(X [tex]\leq[/tex] 26 min)

    P(X < 40 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{40-38.5}{7.2}[/tex] ) = P(Z < 0.21) = 0.5832

    P(X [tex]\leq[/tex] 26 min) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{26-38.5}{7.2}[/tex] ) = P(Z [tex]\leq[/tex] -1.74) = 1 - P(Z < 1.74)

                                                           = 1 - 0.9591 = 0.0409

The above probability is calculated by looking at the value of x = 0.21 and x = 1.74 in the z table which has an area of 0.5832 and 0.881 respectively.

Therefore, P(26 min < X < 40 min) = 0.5832 - 0.0409 = 0.5423 or 54.23%

Answer : The correct statements are,

AC = 5 cm

BA = 4 cm

The perimeter of triangle ABC is 12 cm.

Step-by-step explanation :

As we know that a, b, and c are midpoints of the sides of right triangle that means midpoint divide the side in equal parts.

Now we have to calculate the sides of triangle ABC by using Pythagoras theorem.

Using Pythagoras theorem in ΔACF :

[tex](AC)^2=(FA)^2+(CF)^2[/tex]

Now put all the values in the above expression, we get the value of side AC.

[tex](AC)^2=(3)^2+(4)^2[/tex]

[tex]AC=\sqrt{(9)^2+(16)^2}[/tex]

[tex]AC=5cm[/tex]

Using Pythagoras theorem in ΔDAB :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BD)^2=(AD)^2+(BA)^2[/tex]

Now put all the values in the above expression, we get the value of side BA.

[tex](5)^2=(3)^2+(BA)^2[/tex]

[tex]BA=\sqrt{(5)^2-(3)^2}[/tex]

[tex]BA=4cm[/tex]

Using Pythagoras theorem in ΔBEC :

[tex](Hypotenuse)^2=(Perpendicular)^2+(Base)^2[/tex]

[tex](BE)^2=(CE)^2+(CB)^2[/tex]

Now put all the values in the above expression, we get the value of side CB.

[tex](5)^2=(4)^2+(CB)^2[/tex]

[tex]CB=\sqrt{(5)^2-(4)^2}[/tex]

[tex]CB=3cm[/tex]

Now we have to calculate the perimeter of ΔABC.

Perimeter of ΔABC = Side AB + Side CB+ Side AC

Perimeter of ΔABC = 4 + 3 + 5

Perimeter of ΔABC = 12 cm

Now we have to calculate the area of ΔABC.

Area of ΔABC = [tex]\frac{1}{2}\times 4\times 3=6cm^2[/tex]

Now we have to calculate the area of ΔDEF.

Area of ΔDEF = [tex]\frac{1}{2}\times 8\times 6=24cm^2[/tex]

Area of ΔABC = [tex]\frac{6}{24}\times[/tex] Area of ΔDEF

Area of ΔABC = [tex]\frac{1}{4}[/tex] Area of ΔDEF

Answer:

I would say the second one

Step-by-step explanation:

f(x) has a range of y<0, because it is reflected over the x axis

g(x) = -5/7(3/5)^-x is also reflected over the x axis, except also in the y axis. Regardless of the reflection in the y-axis, y still cannot be equal to or greater than 0. Therefore, I believe it is the second choice.

(The third and forth choice are the same, which rules them both out. The first on reflects it over the y-axis, meaning that x can be greater than 0.)