A vintage guitar is being auctioned. The graph below traces the prices quoted by bidders at different time intervals, measured in minutes, since the auction began.

Which statement is true about the graph?

A. The average rate of change is greater for interval D than for interval E because the line is increasing more quickly at interval D than at interval E.

B. The average rate of change is greater for interval C than for interval B because the line is increasing more slowly at interval C than at interval B.

C. The average rate of change is greater for interval A than for interval B because the line is increasing more slowly at interval A than at interval B.

D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.

The mathematical expectation is a weighted sum:

[tex]E(X) = \displaystyle \sum_{i=1}^n x_ip(x_i)[/tex]

i.e. we multiply each outcome with its probability, and sum all these terms.

There are 16 possible outcomes for the spin, and here's table with wins/losses:

[tex]\begin{array}{c|cccc}&1&4&4&5\\1&L&L&L&L\\4&L&W&W&W\\4&L&W&W&W\\5&L&W&W&W\end{array}[/tex]

So, there are 9 winning spins and 7 losing spins. Since all the spins have the same probability, the probablity of winning $8 is 9/16, and the probability of losing $2 is 7/16. This leads to a mathematical expectation of

[tex]E(A) = 8\cdot \dfrac{9}{16}-2\dfrac{7}{16} = \dfrac{29}{8}[/tex]

In the case of the three coin flips, all triplets have the same probability of 1/8, and the eight triplets are

TTT, TTH, THT, HTT, THH, HTH, HHT, TTT

So, Danielle wins with 3 triplets, and loses with 5 triplets. The mathematical expectation is

[tex]E(B) = 6\cdot \dfrac{3}{8}-1\dfrac{5}{8} = \dfrac{13}{8}[/tex]

So, the first method is better, and the difference is 29/8-13/8 = 2.

After calculating the expected values, Danielle expects to make $0.875 more by choosing Option B over Option A, as it has a higher mathematical expectation.

To calculate which option has a greater mathematical expectation (expected value), we must consider the possible outcomes of each option and their probabilities. We then multiply each outcome by its probability and sum the results.

We have 3 possible sums that would result in Danielle winning $8: 5+4, 4+5, and 4+4. Any other sum results in losing $2. The probability of spinning a 5 on the first spin is 1/4, and so is the probability of spinning a 4. Therefore, the probability of getting a sum greater than 6 is:

P(sum > 6) = P(5+4) + P(4+5) + P(4+4) = (1/4)*(1/4) + (1/4)*(1/4) + (1/4)*(1/4) = 3/16.

The probability of getting a sum of 6 or less is 1 - 3/16 = 13/16. The expected value for Option A is:

E(A) = (3/16)*$8 + (13/16)*(-$2) = $0.25.

Danielle wins $6 if she gets exactly one head. The probability of getting exactly one head in three flips (HHT, HTH, THH) is:

P(exactly one head) = [tex](1/2)^3 + (1/2)^3 + (1/2)^3 = 3/8[/tex].

The probability of not getting exactly one head is 1 - 3/8 = 5/8. The expected value for Option B is:

E(B) = (3/8)*$6 + (5/8)*(-$1) = $1.125.

Comparing the expected values, Option B has a higher expected value than Option A. Therefore, the amount Danielle expects to make by choosing Option B over Option A is:

E(B) - E(A) = $1.125 - $0.25 = $0.875.

Danielle expects to make $0.875 more by choosing Option B.

Answer:

(13.8,1.42) (18,3.7)(16.7,3.21) and so on REMEMBER ITS (X,Y)

Step-by-step explanation:

well, let's say we know "r" and also "y", can we get the angle and the rectangular "x"?

[tex]\bf \begin{cases} y=rsin(\theta )\\ x=rcos(\theta ) \end{cases} \\\\[-0.35em] ~\dotfill\\\\ y=rsin(\theta )\implies \cfrac{y}{r}=sin(\theta )\implies sin^{-1}\left( \cfrac{y}{r} \right)=\theta[/tex]

and once we know what angle θ is, since x = rcos(θ), we know "r" already, and we know θ as well, so we know "x" as well.

Knowing the radius 'r' and the y-coordinate 'y', we can calculate both, Cartesian and polar coordinates. We calculate 'x' using the Pythagorean Theorem. The angle in polar coordinates is then obtained using this 'x' and 'r' through the arccos function.

In the context of polar coordinates and rectangular coordinates, if we know the radius 'r' and the y-coordinate 'y', we can potentially locate the specific point in the Cartesian plane. However, it's important to note that the conversion between polar and rectangular coordinates typically relies on both r and the angle Ф in polar coordinates and x, y in rectangular coordinates.

The answer to the posed question would be (d), it is possible to get Cartesian coordinates and polar coordinates.

We can get 'x' by using Pythagorean Theorem as x = sqrt(r^2 - y^2).

Similarly, the angle Ф in polar coordinates can be obtained if we know 'r' and 'x' (which we've now calculated) using the formula Ф = arccos(x / r)

Therefore, we can indeed calculate both, Cartesian and polar coordinates using the only 'r' and 'y'.

https://brainly.com/question/34631229

#SPJ12

You can use the Pythagorean theorem to solve.

Distance = √(650^2 + 150^2)

Distance = √(422500 + 22500)

Distance = √(445000)

Distance = 667.08 miles

Rounded to the nearest whole mile = 667 miles.

The calculated distance is approximately 667.08 miles.

Calculating the Distance of the Eagle from Its Nest

To determine the distance of the eagle from its nest after flying 650 miles east and 150 miles south, we can use the Pythagorean theorem, which is applicable for right-angled triangles.

The eagle's eastward flight of 650 miles and southward flight of 150 miles form the two perpendicular sides of a right triangle, while the hypotenuse represents the straight-line distance from the nest.

The formula for the Pythagorean theorem is:

a² + b² = c²

Where:
a = 650 miles
b = 150 miles
c = the distance from the nest

Therefore, the distance of the eagle from his nest is approximately 667.08 miles.

Answer:

the mode

the mean

Step-by-step explanation:

Measures of central tendency are measures of center or location of a distribution or a data set. The most commonly used measures of center of a distribution are the;

mean

median

mode.

Answer:

-18

Step-by-step explanation:

A geometric sequence has a common ratio.  So the second term divided by the first term is the same as the third term divided by the second.

6 / -2 = -3

x / 6 = -3

x = -18

Answer:

The conic section that represents the equation 3x + 4y = 12 is a line.

3x + 4y = 12 represents the equation of the line from the given options of the conic section  circle ,ellipse,  parabola,  hyperbola,  line.

" Conic section defined as the curve which is obtained when the plane is cut out from the cone."

According to the question,

Circle : Equation of the circle given by [tex](x-h)^{2} + (y-k)^{2} =r^{2}[/tex]

Conic section circle is not the correct answer.

Ellipse :  Equation of the ellipse given by [tex]\frac{x^{2} }{a^{2}} + \frac{y^{2} }{b^{2}}=1[/tex]

Conic section ellipse is not the correct answer.

Parabola : Equation of the Parabola given by [tex]y^{2} = 4ax[/tex]

Conic section parabola is not the correct answer.

Hyperbola: Equation of the Hyperbola given by [tex]\frac{x^{2} }{a^{2}} - \frac{y^{2} }{b^{2}}=1[/tex]

Conic section hyperbola is not the correct answer.

Line : Equation of the line given by [tex]Ax + By + C =0[/tex]

3x + 4y = 12 represents [tex]Ax + By + C =0[/tex] .

Hence, 3x + 4y = 12 represents the equation of the line.

Learn more about conic section here

https://brainly.com/question/22105866

#SPJ3

Answer:

f(t) = 5(4)^t

f(3) = 5(4^3) = 5 * 64 = 320

There are [tex]2^{10}[/tex] possible outcomes when flipping 10 coins.  Of those  [tex] {10 \choose 8} [/tex]  have exactly 8 heads.   So the probability is

[tex]p = \dfrac{ {10 \choose 8} }{ 2^{10} } = \dfrac{10(9)/2}{2^{10}}=\dfrac{45}{1024}[/tex]

Answer: 45/1024

Answer: OPTION C

Step-by-step explanation:

Remember that:

[tex]\sqrt[n]{a^n}=a[/tex]

And the Product of powers property establishes that:

[tex]a^m*a^n=a^{(mn)}[/tex]

Rewrite the expression:

[tex]\frac{\sqrt{18x} }{\sqrt{32} }[/tex]

Descompose 18 and 32 into their prime factors:

[tex]18=2*3*3=2*3^2\\32=2*2*2*2*2=2^5=2^4*2[/tex]

Substitute into the expression, then:

[tex]\frac{\sqrt{(2*3^2)x} }{\sqrt{2^4*2} }[/tex]

Finally,simplifying, you get:

[tex]\frac{3\sqrt{(2)x} }{2^2\sqrt{2} }=\frac{3\sqrt{2x}}{4\sqrt{2}}=\frac{(3)(\sqrt{x})(\sqrt{2})}{(4)(\sqrt{2})}= \frac{3\sqrt{x}}{4}[/tex]

Answer:

r = 1/2

Step-by-step explanation:

Each entry is diminished by a factor of 1/2 times the previous entry.

so r = 1/2

The next number in the series is 1 and then the one after that is 1/2 and then 1/4 ...

Answer: $3.20

Step-by-step explanation:

$3.50 reduced by 20%= $3.30

$3.30-10%= $3.20.

If Willie ends up with only 20CDs that would be half of what he had at first and 20 plus 20 which would be the other half would be 40. 6 minus 40 would be 34 which he started with.

Answer:34

Step-by-step explanation:

Answer:  C) (x + 5i)(x - 5i)

Step-by-step explanation:

x² + 25 can be rewritten as x² - (-25)

Now use the difference of squares to factor: a² - b² = (a + b)(a - b)

√x² = x      √-25 = 5i

--> x² + 25 = (x + 5i)(x - 5i)

Answer:d

Step-by-step explanation:

d

Follow below steps:

The student asked which statement is true about the value of the expression (6^-n)(6^n). To find the value of this expression, we can use the laws of exponents. These laws state that when we multiply powers with the same base, we add the exponents. Since one exponent is negative and the other is positive but both absolute values of the exponents are equal, their sum will be zero. So, (6^-n)(6^n) simplifies to 6^(n-n), which simplifies further to 6^0. According to the rules of exponents, any number raised to the power of zero is equal to 1. Therefore, the value of the expression is 1 for all values of n.

[tex]\textbf{Answer}[/tex]

65 degrees

[tex]\textbf{Explanation}[/tex]

Determine which trigonomic function is required

The opposite leg is 13 and the adjacent leg is 6

We will be using tangent function

tan^-1 (13/6)

tan^-1 (13/6) = 65

for this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle. Then, according to the figure we have:

[tex]tg (x) = \frac {13} {6}\\x = arctg (\frac {13} {6})\\x = 65.22485943[/tex]

Round,

[tex]x = 65[/tex] degrees

Answer:

65

Answer:

c

Step-by-step explanation:

Answer:

16 x 32

Step-by-step explanation:

If you enlarge by 8 times, you are multiplying each dimension by 8.  2*8=16 and 4*8=32

By multiplying each dimension of the original photograph (2" x 4") by the scale factor (8), we get the dimensions of the enlarged photograph as 16" (length) and 32" (width)

The problem you presented is a simple application of scale factors in math. You need to determine the new dimensions of the enlarged photograph. For a rectangular photograph with original dimensions of 2" x 4", if the photograph is enlarged by a scale factor of eight, we multiply each dimension by the factor 8.

So, for the length: 2" x 8 = 16"

And, for the width: 4" x 8 = 32"

Therefore, the dimensions of the new photograph after enlargement would be 16" by 32".

https://brainly.com/question/30215044

#SPJ3

Answer:

First option: True.

Step-by-step explanation:

To know if the volume of this cylinder is 496.21 ft³, you need to use the formula for calculate the volume of a cylinder:

[tex]V=\pi r^2h[/tex]

Where "r" is the radius and "h" is the height.

You can observe in the figure that the radius of the cylinder is 4.5 feet and the height is 7.8 feet.

Then, knowing this, you can substitute these values into the formula.

Therefore, the volume of this cylinder is:

[tex]V=\pi (4.5ft)^2(7.8ft)\\V=496.21ft^3[/tex]

Then the answer is: True.

The remainder is non-zero, so [tex]x-3[/tex] is not a factor of [tex]2x^3-4x^2-8[/tex] (or whatever the given polynomial is supposed to be)

The Remainder Theorem suggests that if you substitute '3' into the polynomial equation [tex]2x^3 - 4x^2 - 8x + 1[/tex], the result is -5, which is the same as the remainder of that polynomial equation divided by x - 3.

Eric used the Remainder Theorem in his calculation, which is a mathematical principle in algebra. It states that the remainder of a polynomial f(x), when divided by a linear divisor x - a, is equal to f(a). In this scenario, when he plugged '3' (the value of 'a') into the equation [tex]2x^3 - 4x^2 - 8x + 1[/tex], he obtained a resultant value of -5.

This indicates that when the polynomial [tex]2x^3 - 4x^2 - 8x + 1[/tex] is divided by x - 3, the remainder is -5. This remainder would also be the result if 3 substituted for x in the original polynomial equation, as per the Remainder Theorem.

https://brainly.com/question/35460223

#SPJ3

Answer:

B. √{x} + √{x - 1}

Step-by-step explanation:

As hinted in the question, we have to simplify the denominator.

To understand it easier, let's imagine we have x - y in the denominator.  If we multiply it with x + y we'll get x² - y², right?  Check the next line:

(x - y) (x + y) = x² + xy -xy - y² = x² - y²

If we have the square of those nasty square roots, it will be much simpler to deal with.  So, let's multiply the initial fraction using x+y, but with the real values:

[tex]\frac{1}{\sqrt{x} - \sqrt{x - 1} } * \frac{\sqrt{x} + \sqrt{x - 1}}{\sqrt{x} - \sqrt{x - 1}} = \frac{\sqrt{x} + \sqrt{x - 1}}{(\sqrt{x} )^{2} - (\sqrt{x - 1} )^{2} }[/tex]

Then we simplify:

[tex]\frac{\sqrt{x} + \sqrt{x - 1}}{(\sqrt{x} )^{2} - (\sqrt{x - 1} )^{2} } = \frac{\sqrt{x} + \sqrt{x - 1}}{(x) - (x - 1) } = \frac{\sqrt{x} + \sqrt{x - 1}}{ 1 }[/tex]

So, the answer is B. √{x} + √{x - 1}

Answer: B

Step-by-step explanation:

Answer:

  √33 cm ≈ 5.745 cm

Step-by-step explanation:

Let b represent the third side. If the third side is not the hypotenuse, then the longest of the given sides must be the hypotenuse. The Pythagorean theorem tells us ...

  4^2 + b^2 = 7^2

  b^2 = 49 -16 = 33 . . . . . . . . subtract 16

  b = √33 ≈ 5.745 . . . . . . . . . take the square root

The third side is √33 cm long, about 5.745 cm.

To find the length of the third side of a right triangle, apply the Pythagorean theorem by squaring the given sides and calculating the square root of their sum. In this case, the third side would be approximately 5.74 cm.

To find the length of the third side of a right triangle when the other two sides are 4 cm and 7 cm, you can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

Given sides are 4 cm and 7 cm

Let's assume the third side is x

Applying the Pythagorean theorem: 4² + x² = 7²

Solving for x: 16 + x² = 49 => x² = 33 => x = √33 cm

Therefore, the length of the third side is approximately 5.74 cm

Answer:

The rule for finding a reflection of a point across the y-axis is that the y-coordinate will stay the same but the x-coordinate will become its opposite. Thus, in the context of the problem, point (3,6) would become (-3,6) if reflected across the y-axis.

Step-by-step explanation: If you were going to reflect a point across the x-axis, the x-coordinate would stay the same. You're not moving it and it shouldn't change signs. The y-coordinate, however, would become its opposite because it'd be joining a new quadrant. Think of it like this:

Y-AXIS = Y remains the same and gains a neighbor; X changes because it isn't the center of attention.

X-AXIS = X remains the same and gains a neighbor; Y changes because it isn't the center of attention.

Basically, the letter of the axis is the number that doesn't change.

I hope I helped!

Answer:

4.782608696  x  10^10

Step-by-step explanation:

47.83.

To find the result of 330 billion divided by 6.9 billion, we can simplify the question by dividing both numbers by a billion, which gives us 330 divided by 6.9. Now, we perform the division: 330 \/ 6.9 = 47.8260869565. However, since we're dealing with significant figures usually present in population data, we might want to round the answer to a reasonable number of significant digits. So the result would be approximately 47.83.

Answer:

f-1(x)=x-7/3

Step-by-step explanation:

The inverse of f(x) is, [tex]f^{-1}(x)=\frac{x-7}{3}[/tex]

Given function is, [tex]y=f(x)=3x+7[/tex]

Solve for x.

                 [tex]y=3x+7\\\\3x=y-7\\\\x=\frac{y-7}{3}[/tex]

Therefore, inverse function of f(x) is,

                     [tex]f^{-1}(x)=\frac{x-7}{3}[/tex]

Learn more about the Inverse function here:

https://brainly.com/question/11821506

Answer:

1/4 ft vertically per 1 ft horizontally, or 3inches per foot

Step-by-step explanation:

Translate these words into symbols:  One point is at (4 ft, 12 in) and the other is at (6 ft, 18 in).  Now find the slope of the line connecting these two points:

As we move from (4 ft, 12 in) to (6 ft, 18 in), x increases by 2 ft and y increases by (1/2) ft.

Thus, the slope of this line is m = rise / run = (1/2 ft) / (2 ft) = (1/4) ft per ft

Answer:

D) 3 inches up per foot across

Step-by-step explanation:

Pretty sure its right

Answer:

36 dream catcherss

Step-by-step explanation:

Jane's production rate:  

1 dream catcher

6 days

Zena's production rate:  

1 dream catcher

4 days

Production rate when working together:  

1

6

+  

1

4

=  

5

12

. This ratio means it will take 12 days to make 5 dream catchers.

Set up a ratio for 15 dream catchers.  

dream catcher

days

=  

5

12

=  

15

d

→ 5d = (12)(15) → 5d = 180 → d = 36

Answer: 36 days

Step-by-step explanation:

Hi, to answer this we have to calculate the production rate of each one, by dividing the number of catchers by the time spent.

Jane: 1/6 dream catcher per day

Zena: 1/4 dream Catcher per day

Adding both results:

1/6 +1/4 =5/12 dream catcher per day (both)

Finally we have to divide the 15 dream catchers needed by the rate (5/12 per day) to obtain the number of days that will take to make 15 dream catchers

x = 15 / (5/12) =36 days.

Feel free to ask for more if needed or if you did not understand something.

Answer:

slope= 2  y-intercept= -3

Step-by-step explanation:

the equation y=2x-3 is in slope-intercept form (y=mx+b), and m is the slope and b is the y-int. m=2 and b=-3

Answer:

  A

Step-by-step explanation:

Repeated values in the domain of a function are not allowed.

B: -6 is repeated in the domain

C: a list of numbers, not a relation

D; 7 is repeated in the domain

__

A is a relation with no repeated domain values. It matches the requirement.

Rectangle RECT has a twice larger area than Triangle TRI. The area of Triangle TRI is mn/2 square centimeters, while the area of Rectangle RECT is mn square centimeters.

Comparing the Areas of Triangle TRI and Rectangle RECT:

Step 1: Calculate the Area of Triangle TRI:

The formula for the area of a triangle is (1/2) * base * height.

In this case, the base is m centimeters and the height is n centimeters.

Therefore, the area of Triangle TRI = (1/2) * m * n = mn/2 square centimeters.

Step 2: Calculate the Area of Rectangle RECT:

The formula for the area of a rectangle is length * width.

In this case, the length is n centimeters and the width is m centimeters.

Therefore, the area of Rectangle RECT = n * m square centimeters.

Step 3: Compare the Areas:

Now we have the areas of both shapes:

Triangle TRI: mn/2 square centimeters

Rectangle RECT: mn square centimeters

Observe that the area of Rectangle RECT is exactly twice the area of Triangle TRI.