If f(x) is the total cost, in dollars, of x candles, which of the following statements best describes the meaning of f(2)=6

Hey there! I'm happy to help!

If the triangles are similar, the ratio between all of the sides is the same.

We see that to get the 4.2 in the big triangle to the 2.4 in the smaller triangle, we must divide by 1.75 (we get this from 4.2/2.4=1.75). So, if the ratio between all the sides is the same in both triangles, we can divide 6.3 by 1.75 to get y.

6.3/1.75=3.6

Therefore, the length of y is B. 3.6.

Have a wonderful day! :D

Answer:

3.6 = y

Step-by-step explanation:

We can use ratios to solve

2.4             y

----------- = ------------

4.2              6.3

Using cross products

2.4 * 6.3 = 4.2 y

15.12=4.2y

Divide by 4.2

15.12/4.2 = 4.2y/4.2

3.6 = y

Answer:

See Below.

Step-by-step explanation:

We have the expression:

[tex]3pf^2-21p^2f+6pf-42p^2[/tex]

Part A:

Find the GCF. Notice that we have a three in every term and a p in every term. Thus, the GCF will be 3p. Factor:

[tex]3p(f^2-7pf+2f-14p)[/tex]

This is the most we can do.

Part B:

Continuing from where we left off, we can factor the entire expression by grouping:

[tex]\displaystyle \begin{aligned} &= 3p(f^2-7pf+2f-14p) \\ \\ &= 3p(f(f-7p)+2(f-7p)) \\ \\ &=3p((f+2)(f-7p))\end{aligned}[/tex]

Answer: 26 games in total.

Step-by-step explanation:

If in each game we have one winner and one loser, then after each game we have one less player.

first, out of 37 players, we can write it as 36 players  + 1 player that does not play in the first round

the 36 players play games. Because in each game we need 2 players, we have a total of 36/2 = 18 games

in those 18 games, we eliminate 18 players, so now we have 37 - 18 = 19 players.

Now, we can write 19 = 18 players + 1 player that does not play this round.

From the 18 players, we have 18/2 = 9 games.

And from those 9 games, we lose 9 players, so now we have:

19 - 9 = 10 players.

Now from those 10 players, we have 10/2 = 5 games, so after those 5 games we have 10 - 5 = 5 players.

Now we can write 5 = 4 players + 1 player that does not play this round.

from the 4 players we have 4/2 = 2 games, after those 2 games we end with 5 - 2 = 3 players.

And from those last 3 players, we have two games, where in each game one player is eliminated until we have only one winner.

Then the total number of games is:

18 + 9 + 5 + 2 + 2 = 26 games

Answer:

53.076923

Step-by-step explanation:

130% as a decimal is 1.3

Divide 69 by 1.3:

69 /1.3 = 53.076923

Answer:

30

Step-by-step explanation:

The unknown number is x.

Start with x.

To increase x by 130%, you need to add 130%of x to x.

x + 130% of x

The sum equals 69.

x + 130% of x = 69

x + 130% * x = 69

1x + 1.3x = 69

2.3x = 69

x = 30

Answer: The number is 30.

Answer:

no

Step-by-step explanation:

its not divisible by 10

you can also see that it ends with a 6

sorry if thats wrong

Answer:

no b/c the last digit does not end with a ten

Answer:

Sacramento

Step-by-step explanation:

S 11+9+14+12+8=54

SF 11+8+8+9+12=48

The statement that is true about the information in the table is that the data is non-linear.

The easier way to study the table is by graphing it. Here we have the points:

(11, 11), (12, 9), (9, 8), (8, 8), and (14, 12).

The graph of these points can be seen below, there you can see that the data in the table is clearly non-linear, as we can't draw a line that contains the points on the table.

So the correct option is non-linear.

If you want to learn more about tables, you can read:

https://brainly.com/question/7301139

Answer:

We can group x³ and 2x², their GCF is x² so it becomes x²(x + 2). 12x + 24 has a GCF of 12 so it becomes 12(x + 2). Since both terms have the (x + 2) factor, the answer is (x + 2)(x² + 12).

Answer: y = 2/5 --> y = 0.4

Step-by-step explanation:

5y = 2 is a horizontal line at y = 2/5

so the y-value is 2/5 = 0.4 at EVERY x-value.

Answer:

74°.

Step-by-step explanation:

From the question given above,

Cos A = 0.2785

To get the value of angle A, we simply find the inverse of Cos as shown below:

Cos A = 0.2785

Take the inverse of Cos.

A = Cos¯¹ 0.2785

A = 73.8° ≈ 74°

Therefore, the value of angle A is approximately 74°

Answer:

Domain > 0,  Range C(x) > 2

Step-by-step explanation:

x is the distance, distance is always large than 0 => x > 0

=> Domain x > 0

Multiply both sides by 0.75

=> 0.75x > 0

Add both sides by 2

=> 0.75x + 2 > 0 + 2

=> 0.75x + 2 > 2

=> Range C(x) = 0.75x + 2 > 2

Answer:

13/90

Step-by-step explanation:

The decimal that you wrote is mixed non terminal decimal. Which means all the number don't repeat themselves.

The denominator of a non terminating decimal is always 9 even though it depends on the type of the decimal, whether it is simple or mixed

The denominator of the given decimal is 90. The denominator is 2 digit number since the given decimal is also 2 digit decimal even though it is under repeating bars.

And the numerator is 10, 13-3.

We subtract 3 since it is the one repeating itself.

Hope it helps ;) ❤❤❤

Answer:

0.9168

Step-by-step explanation:

From the data given:

Mean = 110

standard deviation = 5

Let consider a random sample n =49 which have a mean between 109 and 112.

The test statistics can be computed as:

[tex]Z_1 = \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z_1 = \dfrac{109- 110}{\dfrac{5}{\sqrt{49}}}[/tex]

[tex]Z_1= \dfrac{-1}{\dfrac{5}{7}}[/tex]

[tex]Z_1[/tex]  = -1.4

[tex]Z_2= \dfrac{x- \bar x}{\dfrac{\sigma}{\sqrt{n}}}[/tex]

[tex]Z_2 = \dfrac{112- 110}{\dfrac{5}{\sqrt{49}}}[/tex]

[tex]Z_2 = \dfrac{2}{\dfrac{5}{7}}[/tex]

[tex]Z_2 =2.8[/tex]

Thus; P(109  <  [tex]\overline x[/tex]  <  112) = P( - 1.4 < Z < 2.8)

= P(Z < 2.8) - P( Z < -1.4)

= 0.9974 - 0.0806

= 0.9168

Answer:

Total consumer spending is 160

Step-by-step explanation:

Here , we are interested in calculating the total consumer spending.

In a long run perfect competition market, price interest with MC and minimum point of AC

Hence , P = AC

this means that Q = 40,000/P = 40,000/150 = 266.67 which is approximately 267 potatoes will be consumed

The total consumer spending is thus 267 * 0.6 = 160

Answer: C. [tex]\sqrt{9} * \sqrt{4}[/tex]

Step-by-step explanation:

There is a square root rule that states [tex]\sqrt{x*y} = \sqrt{x} * \sqrt{y} \\[/tex]

We can apply this rule to this problem.

Given [tex]\sqrt{9*4}[/tex]

We can use the rule to make it equal to [tex]\sqrt{9} * \sqrt{4}[/tex]

This is answer choice C.

Answer: c

Step-by-step explanation: 9*4=36          36* 36 = 1296

9 * 9 = 81      4 * 4 = 16       81 * 16 =  1296    hope this helps

Answer:

The inclination of the through the points (5, 14) and (9, 18) is 45°

Step-by-step explanation:

The given point has coordinates (5, 14) and (9, 18)

To find the inclination, θ, of the line passing the two points, with point 1 having coordinates (x₁, y₁) and point 2,  having coordinates (x₂, y₂), we have to look for the slope as follows;

The slope, m = Change in the y-coordinate ÷ Change in the x-coordinate

[tex]m = \dfrac{y_2 - y_1}{x_2-x_1}[/tex]

Where:

y₁ = The y-coordinate of point 1 = 14

x₁ = The x-coordinate of point 1 = 5

y₂ = The y-coordinate of point 2 = 18

x₂ = The x-coordinate of point 2 = 9

Substituting, we have;

[tex]m = \dfrac{18 - 14}{9-5} = \dfrac{4}{4} = 1[/tex]

The inclination of the line is the angle the line makes with x-axis

Since the slope gives the ratio of the opposite and adjacent segment to the angle of inclination, the arc-tangent of the slope will give the angle in degrees as follows;

[tex]tan^{-1}m = tan^{-1} \left (\dfrac{y_2 - y_1}{x_2-x_1} \right) = \theta[/tex]

given that m = 1, we have;

tan⁻¹(m) = θ = tan⁻¹(1) =  45°.

Answer:

8

Step-by-step explanation:

Assuming, the canvas has the shape of a square. By the square area formula we can derive its side:

[tex]S=l^{2}\\64=l^{2}\\l=\sqrt{64}\\ l=8\: ft[/tex]

Then Each side of the painting measures 8 feet, the length of frame must have 8 feet long, and the width is decided by the framer.

Answer:

The answer is C: 32 ft

Step-by-step explanation:

If you take the square root of the area of 64 ft ^2, you get 8. then it asks what is the length needed for the frame as in the entire frame. So you just have to multiply 8 by 4 which is the number of sides. Also, I got this right on the edg quiz.

Answer: 1 and 3/4 hours were spent rehearsing act 2.

Step-by-step explanation:

5 1/2 total hours spent rehearsing.

take the 3 3/4 hours from act 1.

Subtract 3 3/4 from 5 1/2 to get time spent for act 2.

5 1/2 - 3 3/4 = 7/4

7/4 = 1 3/4

Hope this helps

Answer:

1 3/4 hours

Step-by-step explanation:

Given the time taken to rehearse for act 1 and 2 of a school play to be 5 1/2 hours, if 3 3/4 were spent rehearsing act 1, the amount of time that will be spent in rehearsing act 2 can simply be gotten by taken the difference between the total time taken for both and time spent on act 1.

Mathematically, act1 + act 2 = 5 1/2 hours

If act 1 = 3 3/4 hours

act 2 =  5 1/2 hours - act 1

act 2 =  5 1/2 hours - 3 3/4 hours

Taking the difference between the two values;

= 5 1/2 - 3 3/4

= 11/2 - 15/4

= (22-15)/4

= 7/4 hours

The time taken for practising act 2 will be 1 3/4 hours

Answer:

x = [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

Given function;

y = 5 + x - x²

To find the maximum value, follow these steps

(i) Find the first derivative (which is the slope) of the given function with respect to x. i.e;

[tex]y^{'}[/tex] = [tex]\frac{dy}{dx}[/tex] = [tex]\frac{d(5 + x - x^2)}{dx}[/tex]

[tex]y^{'}[/tex] = [tex]1 - 2x[/tex]

(ii) From the result in (i) determine the value of x for which the slope is zero. i.e.

x for which

1 - 2x = 0

=> 1 = 2x

=> x = [tex]\frac{1}{2}[/tex]

Therefore, the value of x for which the function is maximum is [tex]\frac{1}{2}[/tex]

Answer:

x = 1/2

Step-by-step explanation:

The standard equation of a quadratic function is given by:

y = ax² + bx + c, If a > 0 then the graph has a minimum but if a < 0, then the graph has a maximum. To find the maximum or minimum, we differentiate the function with respect to x and equate to zero that is y'(x) = 0.

For the function y = 5 + x - x², a = -1 < 0, therefore it has a maximum.

Differentiating with respect to x:

y'(x) = 1 - 2x

Equating to zero

-2x + 1 = 0

-2x = -1

x = -1/ -2

x = 1/2

The function has a maximum at x = 1/2

Answer:

0.578

Step-by-step explanation:

If you pick three burritos at random, find the probability of the given event. (Round your answer to three decimal places.)

Given that there are 14 orders at the ratio by of:

6 with hot peppers

8 without hot peppers

At most two have hot peppers.

Binomial Problem with n = 3 ; p(hot) = 6/8

P(0<= x <=2) = 1 - P(x = 3)

= 1 - (6/8)^3

= 1 - ( 3/4 )^3

= 1 - ( 27/64 )^3

= 1- (37/64)

= 1 - 0.421875

= 0.578125

= 0.578

Answer:

0.72 is it rounded to the nearest hundredth. I think there was a typo. if you actually mean hundred like 100 then 0 is the answer.

0.72

Answer:

.720

Step-by-step explanation:

9 rounds up

Answer:

(C) x² - 5x - 14

Step-by-step explanation:

The roots of any quadratic equation will always make the equation equal to 0. So, we can test each equation with the values -2 and 7 to test if both values make the equation 0.

Let's start with A. x² + 5x - 14.

(-2²) + (5 × -2) - 14

4 - 10 - 14 = -20, so we already know that A doesn't work as it doesn't equal 0.

Let's try B. (x+2)² + 7.

(-2+2)² + 7

0² + 7

0+7 = 7, so B doesn't work either.

Let's try C. x² - 5x - 14.

(-2²) - (5×-2) -14

4 + 10 - 14 = 0, ooh we're on to something here! However, for this equation to work, both -2 AND 7 have to work with it. Let's try 7.

(7²) - (5×7) - 14

49 - 35 - 14 = 0, so yes! Both -2 and 7 work for this equation.  Therefore, the roots -2 and 7 work for the quadratic function of x² - 5x - 14, C.

Hope this helped!

Answer:

The mean pressure applied to the driver’s head during a crash test is not significantly different for each type of car.

Step-by-step explanation:

A one-way ANOVA is used to test whether there is significant difference between the means for more than two groups.

In this case we need to test whether the mean pressure applied to the driver’s head during a crash test is significantly different for each type of car.

So, a one-way ANOVA would be used.

The hypothesis can be defined as follows:

H₀: There is no difference between the means, i.e. [tex]\mu_{1}=\mu_{2}=\mu_{3}[/tex]

Hₐ: There is a significant difference between the means, i.e. at least one of the mean is different.

Use MS-Excel to perform the ANOVA test.

Go to Data – Data Analysis – Anova: Single Factor

Enter the data and enter Alpha as 0.05.

Press OK.

The output is attached below.

The F-test statistic value is, F = 5.143.

The p-value of the test is, p-value = 0.072.

Decision Rule:

If the p-value of the test is less than the significance level then the null hypothesis will be rejected.

p-value = 0.072 > α = 0.05

The null hypothesis will not be rejected.

Conclusion:

The mean pressure applied to the driver’s head during a crash test is not significantly different for each type of car.

Answer:

C= 3g

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex]Opposite = r\\Hypotenuse = 13\\\alpha = 34\\Using SOHCAHTOA\\Sin \alpha = \frac{opp}{hyp} \\Sin 34 = \frac{r}{13} \\0.559 = \frac{r}{13} \\Cross \: Multiply\\r = 0.559\times 13\\r = 7.267\\r = 7.27[/tex]

Answer:

2x - 2

Step-by-step explanation:

Here is the completer question

lim as Δx → 0 [(x + Δx)²- 2(x + Δx) + 3 - (x² - 2x + 3)]/Δx

Solution

lim as Δx → 0 [(x + Δx)²- 2(x + Δx) + 3 - (x² - 2x + 3)]/Δx

Expanding the brackets, we have

lim as Δx → 0 [(x² + 2xΔx + (Δx)²- 2x - 2Δx + 3 - x² + 2x - 3)]/Δx

Collecting like terms. we have

lim as Δx → 0 [(x² - x² + 2xΔx - 2Δx + (Δx)²- 2x  + 2x + 3 - 3)]/Δx

Simplifying, we have

lim as Δx → 0 [(0 + 2xΔx - 2Δx + (Δx)² + 0 + 0)]/Δx

lim as Δx → 0 [2xΔx - 2Δx + (Δx)²]/Δx

Dividing through by Δx, we have

lim as Δx → 0 [2x - 2 + (Δx)]

Inserting Δx = 0, we have

= lim as Δx → 0 (2x -2 + 0)

= 2x -2

So lim as Δx → 0 [(x + Δx)²- 2(x + Δx) + 3 - (x² - 2x + 3)]/Δx = 2x -2

Answer:

0.09

Step-by-step explanation:

11.52 / 128

First, divide both numerator and denominator by 2:

2.88 / 32

Divide both numerator and denominator by 4:

0.72 / 8

Divide 0.72 by 8, you get 0.09.

Answer:

  0.92

Step-by-step explanation:

Each year, the value declines. This eliminates choices A and D.

The decline from 33000 to 30360 is slightly less than 10%, so the multiplier from one year to the next is slightly more than 1 -10% = 90%. The only choice in range is ...

  0.92 . . . . the third listed choice

Answer:

Step-by-step explanation:

first term = a = 3

common ratio = 2nd term ÷ first term

                       = 12 ÷ 3

                      r = 4

[tex]a_{n} = ar^{n-1}\\\\a_{10}=3*4^{9}\\\\\\ = 3 * 262144\\\\= 786432[/tex]

Answer:

[tex]\frac{4}{3}[/tex]

Step-by-step explanation:

The area of a regular octahedron is given by:

area = [tex]2\sqrt{3}\ *edge^2[/tex]. Let a is the length of the edge (diagonal).

area = [tex]2\sqrt{3}\ *a^2[/tex]

Given that the diagonal of the octahedron is equal to height (h) of the tetrahedron i.e.

a = h, where h is the height of the tetrahedron and a is the diagonal of the octahedron. Let the edge of the tetrrahedron be e. To find the edge of the tetrahedron, we use:

[tex]h=\sqrt{\frac{2}{3} } e\\but\ h=a\\a=\sqrt{\frac{2}{3} } e\\e=\sqrt{\frac{3}{2} }a[/tex]

The area of a tetrahedron is given by:

area = [tex]\sqrt{3}\ *edge^2[/tex] = [tex]\sqrt{3} *(\sqrt{\frac{3}{2} }a)^2=\frac{3}{2}\sqrt{3} *a^2[/tex]

The ratio of area of regular octahedron to area tetrahedron regular is given as:

Ratio = [tex]\frac{2\sqrt{3}\ *a^2}{\frac{3}{2} \sqrt{3}*a^2} =\frac{4}{3}[/tex]

Answer:

(-13)^35

Step-by-step explanation:

As instructed,

(-13) * (-13) ...(-13) 35 times is represnted as

(-13)^35

( = -972786042517719014174576083150881262357   .... by the way)