6. Use the data below to make a scatter plot in Desmos and find the
exponential regression equation. Round to the nearest hundredth if
necessary. Do not type spaces.
Time (years)

7. Using your equation from #6, find out how much the Fire Dragons
comic book would be worth in 55 years.
Your answer

The graph of the given ordered pair is plotted and attached below.

Ordered pair:

Ordered pair refers the composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses.

Given,

Here we have the following ordered pair.

(0, 0) (10, 125) (20, 250) (30, 375) (40, 500)

Now, we have to plot the graph for this ordered pair.

In the given question, we have to perform the following steps.

After all these steps we get the graph like the following.

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The answer is, 1/6th cup of chocolate will she needs in order to make her cookies using fraction.

What is a fraction?

If the numerator is bigger, it is referred to as an improper fraction and can also be expressed as a mixed number, which is a whole-number quotient with a proper-fraction remainder.

Any fraction can be expressed in decimal form by dividing it by its denominator. One or more digits may continue to repeat indefinitely or the result may come to a stop at some point.

The amount of chocolate required for this recipe is 2/3rd of a cup for a batch.

She has to make for a 1/4th of that batch.

So the amount of chocolate needed is also 1/4 for the batch which will be = 1/4*2/3 of cup.

= 1/6th of the cup.

Hence, 1/6th cup of chocolate will she need in order to make her cookies.

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x = - 8 is not a root of √(x + 12) - 6 = x, since it is an extraneous solution.

In this question we have a radical equation that offer two possible roots. A root is an extraneous solutions when it brings out an absurd (i.e. 1 = 4) when the expression is evaluated. First, write the radical equation:

√(x + 12) - 6 = x

Second, use algebra properties to find the possible roots of the radical equation:

√(x + 12) - 6 = x

√(x + 12) = x + 6

x + 12 = x² + 12 · x + 36

x² + 11 · x + 24 = 0

(x + 3) · (x + 8) = 0

x = - 3 or x = - 8

Third, evaluate the radical equation at each root:

√(- 3 + 12) - 6 = - 3

√9 - 6 = - 3

3 - 6 = - 3

- 3 = - 3 (TRUE)

√(- 8 + 12) - 6 = - 8

√4 - 6 = - 8

2 - 6 = - 8

- 4 = - 8 (FALSE)

x = - 8 is an extraneous solution.

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The prediction of the wind chill for the wind speed 4 mi/h is 14 degrees

Here, we have the following parameters:

Equation of the trend line: y = 0.36x + 12.6

Where

x = Wind speed

y = Wind chill

Also, we have

x = 4 mi/h i.e. the wind speed

Substitute x = 4  in the equation y = 0.36x + 12.6

So, we have

y = 0.36 x 4 + 12.6

Evaluate the equation

y = 14.04

Approximate

y = 14

Hence, the wind chill  is 14 degrees

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The probability of getting both these numbers correctly is of:

0.028%.

The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.

In this problem, the probabilities are presented as follows:

The probability of getting both these numbers correctly is given by the multiplication of the probabilities of getting the correct number on each trial, hence:

p = 1/60 x 1/59 = 0.00028 = 0.028%.

The problem states that two numbers are selected from a set of 60, and it asks for the probability that both are guessed correctly.

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Answer:

225

Step-by-step explanation:

a1 = 1

a15 = 29

sum = n/2 ( a1 + a15) =  (15/2) ( 1 + 29) = 225

The probability that the animal patient is NOT a bird as a simplified fraction is 11/13.

What is probability?

The study of probabilities, which are determined by the ratio of favorable occurrences to probable cases, is known as probability.

As given in the question,

Number of dog patients is 5,

Number of cat patients is 6, and

Number of bird patients is 2.

So,

Total number of animal patients = 5 + 6 +2 = 13

Total number of ways of picking 1 animal patient = 13C1 = 13

Number of patients that are NOT birds = 11

So,

probability that the animal patient picked is not a BIRD = 11C1 / 13C1 = 11/13

Therefore, the probability that the animal patient is NOT a bird is 11/13.

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Step-by-step explanation:

To find the next term or number, we'll need to keep subtracting 5. So the formula is: n-5

Answer:

Slope = -5/2

Y-intercept = -9

Step-by-step explanation:

Hello!

The equation is given in Slope-Intercept Form: y= mx + b

Since the slope is the coefficient of the x-term, the slope of this equation is -5/2, or -2.5

The y-intercept is the numerical constant, which is given the by the integer -9.

The percentage increase for the money the class has raised is 10% and they will need $ 2115 to make the percentage increase to 99%.

According to the question,

We have the following information:

Initial price in the year = $1500

Final price they have = $1650

a) Now, we know that following formula is used to find the percentage increase in the price:

Percentage increase = 100*(final price-initial price)/initial price

Percentage increase = 100*(1650-1500)/1500

Percentage increase = 100*(150)/1500

Percentage increase = 10%

b) Now, we will find the final price when the percentage increase is 99%.

Let's take the final price to be $x.

99 = 100*(x-1500)/1500

99 = (x-1500)/15

Using the cross multiplication method:

x-1500 = 15*99

x-1500 = 615

x = 615+1500

x = 2115

Hence, the percentage increase for the money the class has raised is 10% and they will need $ 2115 to make the percentage increase to 99%.

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The number of ways to select the banners is given as follows:

a. Matching with the country: 362,880, using the arrangements formula.

b. Not matching with the country: 60,949,324,800, using the permutation formula.

The number of possible arrangements of n elements is obtained by the factorial of n, that is:

[tex]A_n = n![/tex]

For item a, the arrangements formula is used, as the banner has to match the country, hence only the countries are arranged and then the specific banner is matched with this country.

Considering that there are nine countries, the number of ways of selecting and matching nine banners with a country is calculated as follows:

Total = 9! = 362,880.

The number of possible permutations of x elements from a set of n elements is obtained by the equation as follows:

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

For item b, 9 banners are taken from a set of 20, and the permutation formula is used as the order in which the banners are chosen is important, hence the number of ways of selecting nine banners without having to match them with a country is obtained as follows:

N = 20!/(20 - 9)! = 20!/11! = 60,949,324,800.

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The probability that both male and female are non-smokers is 0.56.

Given that, at a local college, 198 of the male students are smokers and 792 are non-smokers.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favorable outcomes/Total number of outcomes

Number of male smokers=198

Number of male non-smokers=792

Total number of male smokers=198+792

= 990

Number of female smokers=330

Number of female non-smokers=770

Total number of female smokers=330+770

= 1100

Probability that both are non-smokers is given by

P(both are non-smokers ) = P(Male non-smoker) × P(female non-smoker)

= 792/990 × 770/1100

= 0.8 × 0.7

= 0.56

Therefore, the probability that both male and female are non-smokers is 0.56.

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Answer:30

Step-by-step explanation:

Peanut brittle costs $0.33 more per ounce than the almond bark option (C) is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

A candy company sells peanut brittle and almond bark.

Almond: $6/(10 oz) = $0.60/oz

Bark: $9/(10 oz) = $0.90/oz

0.90 - 0.60 = $0.90

Peanut brittle costs $0.33 more per ounce than almond bark.

Thus, peanut brittle costs $0.33 more per ounce than the almond bark option (C) is correct.

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Answer:

Almond bark costs $0.50 more per ounce than peanut brittle.

Step-by-step explanation:

Answer: Freddy

Step-by-step explanation:

Choose a common denominator for all the fractions.  Let's use 140.  

Christian:  3/7 = 60/140

Freddy:  3/10 = 42/140

Skyler:  3/4 = 105/140

The least value is 42/140

Answer:

2⁵ that is my answer for the question

Answer: 2^5

Step-by-step explanation:

3^3 = 27

1^10 = 1

2^5 = 32

5^2 = 25

Answer:

Step-by-step explanation:

so they are just asking for some numbers multiplied together to get 0.24

any two , as long as one is great than 1  soo  , try 2

2 * ? = 0.24

I suspect you can see the answer now?

The greatest number of identical goodie bags Carlos can make is 24.

Therefore will be 3 granola bars and 2 popcorn balls in each bag.

From the information, Carlos is making goodie bags for a party and every goodie bag has exactly the same treats in it.

Carlos has 72 granola bars and 48 small popcorn balls. It should be noted that the greatest common factor between 72 and 48 is 24.

Therefore, granola bars will be:

= 72/24

= 3 in each bag

Popcorn will be:

= 48/24

= 2 in each bag.

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Answer:

96% rounded to the nearest percent.

Step-by-step explanation:

Divide 100 by 23 which is approximately 4.35

Multiply 4.35 by 22 which is 95.7%.

If you round 95.7 to the nearest percent, it would be 96%.

Answer:

95.6521739%

explanation:

22 is 95.6522% of 23

Answer:

A

Step-by-step explanation:

Right triangle hypotenuse can be calculated using

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

Answer:

slope is 3/2

Step-by-step explanation:

m = y2 - y1 / x2 - x1

m = -1 - 2 / 2 - 4

m = -3/-2 ( can be simplified )

simplified ver. = 3/2

Answer:

Slope is 3/2

Step-by-step explanation:

To find slope, subtract the y's, put that on top of a fraction. Then subtract the x's and put that on the bottom of the fraction.

(4,2) and (2,-1)

Subtract y's:

2 - -1

=3

Put it on top of a fraction:

3/something

Subtract the x's:

4 - 2

= 2, put that on the bottom of the fraction.

3/2

Slope is 3/2.

Answer:

the answer is 135

Step-by-step explanation:

The expression that can used to determine the total number of credit cards opened at the two locations can be written as Option A.

( A + B ) ( t ) = 35 + t

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

The equation of function for number of credit cards at location A at t months is given by A( t ) = 10 + 2t

The equation of function for number of credit cards at location B at t months is given by B( t ) = 25 - t

Now , A function assigns the value of each element of one set to the other specific element of another set.

So ,

The total number of credit cards that are opened at both the location A and B is given by the equation =
Number of credit cards at location A at t months + Number of credit cards at location B at t months

The total number of credit cards that are opened at both the location A and B is given by the equation = A( t ) + B( t )

                                                   = ( A + B ) ( t )

                                                   = 10 + 2t + 25 - t

                                                   = 35 + t

Hence , the equation for the function of total number of credit cards opened at the two locations is given as ( A + B ) ( t ) = 35 + t

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The 95% confidence interval for the population mean adjusted distribution volume, using the t-distribution, is given as follows:

(43.479, 61.281).

The t-distribution is used when the standard deviation for the population is not known, and the bounds of the confidence interval are given according to the rule presented as follows:

[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]

In which the variables of the equation are listed as follows:

The sample is given as follows:

22, 40, 41, 42, 43, 48, 51, 58, 62, 66, 67, 70, 71.

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 13 - 1 = 12 df, is t = 2.1788.

Using a calculator with the sample, the parameters for the interval are:

[tex]\overline{x} = 52.38, s = 14.73, n = 13[/tex]

Hence the lower bound of the interval is calculated as follows:

52.38 - 2.1788 x 14.73/sqrt(13) = 43.479.

The upper bound of the interval is calculated as follows:

52.38 + 2.1788 x 14.73/sqrt(13) = 61.281.

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Using the trigonometry relation, the value of sin2x=4√2/9, cos2x=7/9 and tan2x=4√2/7.

In the given question, we have to find the value of sin(2x), cos(2x) and tan(2x).

The given value of six=1/3, x in quadrant first.

We firstly finding the value of cosx.

cosx = √1-(sinx)^2

Now putting the value of sinx

cosx = √1-(1/3)^2

cosx = √1 -1/9

cosx = √(9-1)/9

cosx = √8/9

cosx = 2√2/3

We know that;

sin2x=2sinxcosx

sin2x=2* 1/3 * 2√2/3

sin2x=4√2/9

Now finding the value of cos2x

We know that;

cos2x=1-2(sinx)^2

cos2x=1-2(1/3)^2

cos2x=1 -2/9

cos2x=(9-2)/9

cos2x=7/9

Now finding the value of tan2x

As we know that

tan2x=sin2x/cos2x

tan2x=(4√2/9)/(7/9)

tan2x=4√2/7

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Answer:

Step-by-step explanation:

You want Elga's age, given that Alvin is 15 years younger and the sum of their ages is 43.

Let e represent Elga's age. Then (e-15) is Alvin's age, and the sum of their ages is ...

  e +(e -15) = 43

  2e = 58 . . . . . . . add 15

  e = 29 . . . . . . . divide by 2

Elga's age is 29.

  e -15 = 29 -15 = 14 . . . . Alvin's age

The explorer stood 2.63m away from the flag pole.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight. If the line of sight is upward from the horizontal line, then the angle formed is an angle of elevation.

If the pole is 3m high, and his eye is 1.6 meters from the ground.

Then distance from the top of the pole and his eyes  would be 3 - 1.6 = 1.4m

The angle of elevation between the line of sight and the horizontal = 28°

so the horizontal, angle of elevation and the distance between sight and top of pole form a right angle triangle.

Let the distance of the explorer from foot of pole be x,

so that,

tan 28 = 1.4/x

by cross multiplying,

x tan28 = 1.4

x = 1.4/tan28

x = 1.4/0.5317

x = 2.63m

In conclusion, the distance of the explorer to the base of the flagpole is 2.63m

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Using theoretical probability, the probability of selecting green ball is 3/11, not selecting green ball is 8/11, selecting orange ball is 6/11 and not selecting orange ball is 5/11.

In the given question,

A bag has 2 red, 3 green, and 6 orange balls.

So total number of balls = 2+3+6 = 11

We have to find the theoretical probability.

(a) We have to find the theoretical probability of selecting green ball.

P(G) = Total number of green balls/Total number of balls

P(G) = 3/11

Hence, the probability of selecting green ball is 3/11.

(b) Now we have to find the theoretical probability of not selecting green ball.

Except green ball there is having red and orange i.e.

Total remaining balls except green = 2+6 = 8

P(G) = Total number of balls except green balls/Total number of balls

P(G) = 8/11

Hence, the probability of not selecting green ball is 8/11.

(c) Now we have to find the theoretical probability of selecting orange ball.

P(G) = Total number of orange balls/Total number of balls

P(G) = 6/11

Hence, the probability of selecting green ball is 6/11.

(d) Now we have to find the theoretical probability of not selecting orange ball.

Except orange ball there is having red and green balls i.e.

Total remaining balls except orange = 2+3 = 5

P(G) = Total number of balls except orange balls/Total number of balls

P(G) = 5/11

Hence, the probability of not selecting orange ball is 5/11.

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