Let f(x) = 2√3x and g(x) = -4√3x. Find (f-g)(x), then evaluate when x = 12.

Let's first assign variables to the numbers given.

We're given:

Plug the second equation into the first one and solve for y:

[tex]x+y=367\\(y+95)+y=367\\2y+95=367\\2y=272\\y=136[/tex]

Therefore, they sold 136 chocolate cones.

They sold 136 chocolate ice cream cones.

The product of 2√3 and 3√12 in simplified form is 6√36. To simplify this expression, we can first multiply 2 and 3 to get 6. Then, we can simplify the square root of 3 and the square root of 12 by finding their prime factorizations:

√3 = √(3 * 1) = √3

√12 = √(12 * 1) = √(2^2 * 3) = 2√3

So, 2√3 = 2 * √3 = 2 * √3

And, 3√12 = 3 * 2√3 = 6√3

Finally, the product of 2√3 and 3√12 is 6 * 6√3 = 6√36.

The volume of the rectangular prism will be 1008 cubic inches and the volume of the pyramid is 504 cubic inches.

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

The volume of the rectangular prism will be the multiplication of the three parameters which are Length, Width, and Height of the prism.

The volume of the pyramid is the product of half of the area of the base and the height of the pyramid,

The volume of prism = 14 x 12 x 6

The volume of the prism = 1008 cubic inches

The volume of the pyramid,

Volume = 1/2 x Base area x H

Volume = 1/2 x 72 x 14

Volume = 504 cubic inches.

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Amount of square feet of outdoor carpet needed for the hole is 6 feet².

Area of a two dimensional shape is the total region which is bounded by the object's shape.

Given is a triangular region with a hole in the shape of a rectangle.

We need to find the area of the hole in order to find the amount of square feet of outdoor carpet needed for the hole.

Area of a rectangle = Length × Width

From the figure,

Length = 3 feet and Width = 2 feet

Area = 3 × 2 = 6 feet²

Hence 6 feet² of outdoor carpet is needed for the hole.

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Note that the function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.

Recall that the function for the trapezoid area is:

A(x)=(B+b)*h/2

where

B and b are the bases and

h is the height.

Thus, given a height of 14 and one base length of 5 with the length of its other base

With the given data: h=14 B and b =5 and x (it may vary which one is bigger)

So that function becomes:

A(x)=(5+x) * 14/2

A(x)=(5+x)*7

So if you want the inverse function, you have to operate to find x:

A(x)/7=5+x

A(x)/7-5=x

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Answer:

32x95%?

Step-by-step explanation:

Im so confused with this question statement.

Answer:

Each one-inch binder costs $2.67 and each two-inch binder costs $6.

Step-by-step explanation:

Let's call the cost of a one-inch binder "x" and the cost of a two-inch binder "y".

From Hansen's purchase, we know that 3x + 2y = $20.

From Pam's purchase, we know that 3x + 5y = $32.

We can use these two equations to solve for the cost of each size of binder. If we subtract the first equation from the second, we get:

2y = $32 - $20 = $12

So, y = $6, which is the cost of a two-inch binder.

Next, we can plug this value back into either of the original equations to find the cost of a one-inch binder:

3x + 2($6) = $20

Expanding the right side, we get:

3x + $12 = $20

Subtracting $12 from both sides, we get:

3x = $8

Finally, dividing both sides by 3, we find that:

x = $2.67

So, each one-inch binder costs $2.67 and each two-inch binder costs $6.

Answer:

C. m4/n2    :))))

answer is

5(-1) = -5 +23 = 18

Natural numbers are sometimes known as counting numbers. Numbers that can be counted but not zero. Whole numbers are a modest extension of natural numbers and include Zero.

A subset of the natural numbers are the positive integers, often known as non-negative integers. Here are a few instances: 1, 2, 3, 4, 5, 6,... In other words, the "natural numbers" are the collection of all whole numbers that do not include 0.

There are just a limited amount of parts to it. Example: A = 1, 2, 3, and 4. An infinite set has unlimited items. All entire numbers are in a set called  whole numbers.

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Answer:

Step-by-step explanation:

You want to know the number of points and the number of turns when Tony and his cousin will have the same score. Tony has 12 points and earns 10 points per turn; his cousin has 0 points and earns 14 points per turn.

The attachment shows a table of points and turns. It shows the score will be tied at 42 points after 3 turns.

Tony's points can be described by ...

  p = 12 +10t . . . . . . . . 12 points in addition to 10 per turn

Cousin's points can be described by ...

  p = 0 + 14t . . . . . . . . . 14 points per turn added to the current score of 0

These will be equal when ...

  p = p

  12 +10t = 0 +14t . . . . substitute for p in both cases

  12 = 4t . . . . . . . . . . subtract 10t

  3 = t . . . . . . . . . . divide by 4

  p = 14·3 = 42 . . . . the scores after 3 turns

If random sample yielded these observed scores: 6 12 5 10 6 9 12 20 5 23 10 20 11 28 13 18. The 99% confidence interval for the mean height of both groups combined is approximately (3.92, 20.58) cm.

To calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution, since the sample size is relatively small (less than 30) and the population standard deviation is unknown.

First, we need to calculate the sample mean and sample standard deviation. The sample mean can be calculated by adding up all the observed scores and dividing by the total number of scores. In this case, the sample mean is (6+12+5+10+6+9+12+20+5+23+10+20+11+28+13+18) / 16 = 12.25 cm.

The sample standard deviation can be calculated using the formula:

s = √((∑(x - x')^2) / (n - 1))

where x is each observed score, x' is the sample mean, and n is the sample size. In this case, the sample standard deviation is approximately 7.05 cm.

Next, we need to calculate the t-value for a 99% confidence level, with 15 degrees of freedom (16 - 1). Using a t-table or a statistical software, we can find that the t-value is approximately 2.947.

Finally, we can calculate the confidence interval using the formula:

Confidence interval = sample mean ± (t-value * (sample standard deviation / √(sample size)))

Plugging in the values, we get:

Confidence interval = 12.25 ± (2.947 * (7.05 / √(16))) = 12.25 ± 8.33

In summary, to calculate the 99% confidence interval for the mean height of both groups combined, we can use the t-distribution and the formula for confidence intervals. We need to calculate the sample mean, sample standard deviation, t-value for the desired confidence level, and then plug these values into the formula to get the confidence interval.

This interval represents the range of values within which we can be 99% confident that the true mean height of both groups combined falls.

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[tex]\begin{array}{llll} f(x)~from\\\\ x_1 ~~ to ~~ x_2 \end{array}~\hfill slope = m \implies \cfrac{ \stackrel{rise}{f(x_2) - f(x_1)}}{ \underset{run}{x_2 - x_1}}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array} \\\\[-0.35em] ~\dotfill\\\\ m(t)=800(1.08)^t \qquad \begin{cases} t_1=2\\ t_2=4 \end{cases}\implies \cfrac{m(4)-m(2)}{4 - 2} \\\\\\ \cfrac{800(1.08)^4~~ - ~~800(1.08)^2}{2} ~~ \approx ~~ \cfrac{1088.39-933.12}{2}~~ \approx ~~\text{\LARGE 78} ~~ \frac{\$}{year}[/tex]

Answer: 8.8 moles

Step-by-step explanation:

Fun Fun! Chemistry :)

So, 5.3 x [tex]10^{24}[/tex] atoms can be converted to moles by dividing by Avogadros number, (6.02 x 10^23). This is because Avogadros number of atoms form one mole.

So the answer is about 8.8 moles of Kr

The population of rabbits in the year 2013 is 1186.

To predict the population of rabbits in the year 2013, we can use exponential growth. The formula for exponential growth is:

P = P₀ * e^(rt)

where:

P = final population

P₀ = initial population (950)

r = the growth rate (we need to find this)

t = time elapsed (13 years)

We can use the data from 2003 to find the growth rate:

1000 = 950 * e^(r * 3)

1000 = 950 * e^(3r)

1000/950 = e^(3r)

ln (1000/950) = 3r

r = (ln(1000 / 950)) / 3

r = 0.0171

Now that we have the growth rate, we can use it to find the population in 2013:

P = 950 * e^(0.0171 * 13)

P = 1186

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Approximately one full tablespoon of coffee powder is required for each 200 ml cup of coffee. We advise using seven teaspoons of ground coffee to produce a full litre of filter coffee at once.

To create coffee, coffee beans must first be roasted. Coffee is a dark-colored, bitter, and slightly acidic beverage that stimulates individuals due to its high caffeine content. In terms of sales, hot beverages have the largest market worldwide. The roasted beans are ground into tiny particles, frequently steeped in hot water, and then filtered to create a cup of coffee. Despite the fact that coffee is typically served hot, it is frequently served cold or iced. Unroasted green coffee beans are made by separating the seeds from the fruits of the Coffea plant. To produce a cup of coffee, the roasted beans are ground into tiny particles, regularly soaked in hot water, and then filtered. Coffee is commonly served cold or iced even though it is traditionally served hot.

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The Durbin-Watson test is used to determine if a regression has autocorrelation and can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model, as represented by the formula AR(t) = ρ * AR(t-1).

a. Both cross-section and time-series multiple regressions should be checked for autocorrelation.

b. Autocorrelation is the correlation of a variable with itself over successive time periods. In the context of a regression, it is the correlation between the residuals or errors of a regression model over successive time periods.

c. The Durbin-Watson test is used to determine if a regression has autocorrelation.

d. Autocorrelation can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model. This is known as the autoregressive model. The formula for calculating the autoregressive coefficient is: AR(t) = ρ * AR(t-1), where ρ is the correlation coefficient.

The Durbin-Watson test is used to determine if a regression has autocorrelation and can be corrected by adding lagged values of the independent and dependent variables as additional predictors in the regression model, as represented by the formula AR(t) = ρ * AR(t-1).

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The height of the triangle is the distance that is found between the tip of the triangle at the top to the base of the triangle.

A triangle's height is determined by drawing a perpendicular line from its vertex to its opposite side. The altitude, sometimes referred to as the triangle's height, forms a right-angle triangle with the base.

The length of a perpendicular segment from the base to the vertex directly across from it determines the height that corresponds to it. The vertex that is not an endpoint of the base is the one on the opposite side.

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A system of equations that could be used to find the length (in hours) of each type of workout

7a + 9b = 12

5a + 3b = 6

Solve this system of equations by multiplying both sides of one of the equation so that when the equations are added or subtracted there will only be one variable.

-I will multiply both sides of the 2nd equation by -3

-3*(5a + 3b) = 6*-3

-15a - 9b = -18

-Now I will get rid of the variable b by adding the two equations together.

      7a + 9b = 12

+   -15a - 9b = -18

     -8a = -6

a = -6/-8

a= 3/4 (45 minutes)

-Now plug 3/4 into one of the original equations as a to solve for b.

-I will use the 2nd original equation.

5a + 3b = 6

5(3/4) + 3b = 6

15/4 + 3b = 6

3b = 9/4

b = 9/12 = 3/4 (45 minutes)

Both workout plans last the same amount of time.

Plan A lasts 45 minutes.

Plan B lasts 45 minutes.

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Answer:

Shrub $7

Rose Bush $8

Step-by-step explanation:

First, write them as equations

10r + 4s = $108

5r + s = $47

Next, multiply

10r + 2s = $94

10r + 4s = $108

Then, Subtract

2s = $14

After, Divide

s = $7

Then, plug in and solve

5s + $7 = $47

$40/5s = 8$

$8 = r

$7 = s

Answer: The bushes cost $8 and the shrubs cost 7$

Step-by-step explanation:

For this question you must use system of equations, trial and error will take a very long time.

So yeah, here is how you solve it-

First set up equations (b represents the amount of bushes and s represents the amount of shrubs):

5b + 1s = 47

10b+4s=108

Next you can either solve via elimination or the substitution method. I will show elimination here. Elimination works by slightly modifying one of the equations so that it cancels when it is added to the other equation:

(I modified the first equation)

-4(5b+1s = 47) = -20b-4s=-188

(Then add)

     -20b-4s=-188

  +    10b+4s=108

This equals: -10b=-80

Next you just solve for b:

b=-80/-10

b=8

To then find s, plug b into one of the original equations and solve for s:

(I plugged it into the first equation)

5(8)+1s=47

40+s=47

s=7

So the bushes cost $8 and the shrubs cost 7$

Hope this helps :)

Answer:

$96

Step-by-step explanation:

We know

$22 if it has 11 attendees.

$22 divided 11 = $2 per attendee

So, we know per attendee costs $2

If there are 48 attendees, how much will the picnic cost?

2 x 48 = $96

So, the picnic cost $96.

If Zach moved the existing sand from the old terrarium into the new terrarium , then the sand in the new terrarium will be  5cm deep .

The dimensions of the old terrarium is = 20 by 50   cm  ;

The dimensions of the new terrarium is = 25 by 64 cm ;

So , amount of sand that Zach has is =  Volume of sand in the old terrarium, that is ( Area of base of the old terrarium) × (height of sand) ;

Volume of Sand = 20 × 50 × 8 = 8000 cm³  ;

When Zach moves the sand to the new terrarium, volume of sand will be same, so we can write the equation ;

⇒ 20 × 50 × 8 = 25 × 64 × h  ;

where h is = height of sand in new terrarium.

Now solving for h, we get ;

⇒ h = (20 × 50 × 8 cm)/(25 × 64 )

⇒h = 8000/1600  ;

⇒ h = 5 cm  ;

Therefore, the sand will be 5 centimeters deep in the new terrarium.

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The given question is incomplete , the complete question is

Zach keeps his pet chameleon pinky in a terrarium with the dimensions 20 by 50 cm . there's sand in the bottom of the terrarium that reaches a height of 8 88 centimeters.

Zach gets a new terrarium for pinky that is larger. the base of the new terrarium is 25 by 64 centimeters. Zach moved the existing sand to the new terrarium. how deep will the sand be in the new terrarium ?

Answer:

12 minutes

Step-by-step explanation:

To estimate the time for a trip that is 6 miles long, we need to solve for x in the equation y = 0.467x + 0.417, where y represents the distance in miles.

First, we substitute the value of y, which is 6:

6 = 0.467x + 0.417

Next, we subtract 0.417 from both sides:

5.583 = 0.467x

Finally, we divide both sides by 0.467:

x = 12

So, the estimated time for a trip that is 6 miles long is 12 minutes.

A 1/2

its just like you have 1 cookie and 2 apples whats the ratio to cookies from apples

We need  9 sophomore girls to make sex and class independent when a student is selected at random.

No. of freshman boys     (fb) = 4

No. of freshman girls      (fg) = 6

No. of sophomore boys (sb) = 6

Let, the no. of sophomore girls = sg

The total number of students in the class T = fb + fg + sb +sg

                                                                     T = 4+6+6+sg

                                                                     T = 16 + sg

The probability of selecting a girl is  P(G) = (fg + sg) / T

                                                                    = (6+sg)/(16+sg)

The probability of selecting a sophomore is  P(S) = (sb + sg)/T

                                                                                  = (6+sg)/(16+sg)

As the events are independent, the probability of selecting a sophomore girl is                       P(sg) = P(G)*P(S)

                       sg/(16+sg) = (6+sg)*(6+sg)/(16+sg)(16+sg)

                       sg(16+sg)  = (6+sg)(6+sg)

                       16sg + [tex]sg^{2}[/tex] = 36 + 6sg + 6sg + [tex]sg^{2}[/tex]

                                 4sg = 36

                                   sg = 9

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In given lines, y = -1/4 x + 7 represents a transversal line.

A transversal is a line that, at two different locations, cuts through two lines in the same plane. Various types of angles in pairs, including successive internal angles, corresponding angles, and alternate angles, are produced by a transversal intersection with two lines.      

Here we have

y = 1/6x - 3  ---- (1)    

y = -1/4 x + 7 ---- (2)  

y = 1/6x - 9 ---- (3)        

Here given lines are in y = mx + c form

The slope of the line (1) is 1/6

The slope of the line (2) is -1/4

The slope of the line (3) is 1/6

As we can see that line (1) and line (3) have the same slope,

Hence, Lines (1) and (3) are two parallel lines

where Line (2) is transversal which cuts the given two parallel lines  

Therefore,

In given lines, y = -1/4 x + 7 represents a transversal line.

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Answer: 1/6 of an hour

Step-by-step explanation: multiply the numerator and denominator by 3 of 1/2 and 1/3 to get 3/6 and 2/6. There is 1/6 more

After 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

Let's start by defining some variables:

We can then use this information to set up two equations that represent how much money each person has saved:

J = 20j + 8

M = 18m + 26

We want to know when J and M are equal, so we can set these equations equal to each other:

20j + 8 = 18m + 26

We can simplify this equation by subtracting 8 from both sides:

20j = 18m + 18

Then, we can divide both sides by 2 to simplify the equation further:

10j = 9m + 9

We want to find the smallest values of j and m that make this equation true. We can start by trying j = 1 and then incrementing j until we find a value that makes the right-hand side of the equation (9m + 9) divisible by 10. We can then solve for m and check that the left-hand side of the equation (10j) is equal to the same value.

If we try j = 1, we get:

10(1) = 9m + 9

Simplifying this equation gives us:

m = 1

So, if Jeremy tutors his cousin for 1 week and Mary babysits her sister for 1 week, they will both have the same amount of money saved. We can check this by plugging j = 1 and m = 1 into the original equations for J and M:

J = 20j + 8 = 20(1) + 8 = 28

M = 18m + 26 = 18(1) + 26 = 44

So, after 1 week of tutoring and babysitting, Jeremy and Mary will have saved the same amount of money ($28).

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