lucy is standing in a stadium and has the option of running up a staircase 0r down a staircase for exercise.The function f(x)=1/25...

The average rate of change for the function given in the table, over the interval 2 ≤ x ≤ 6 is: C) 15.

The average rate of a function over an interval can be calculated using the formula:

Average rate of change = change in y / change in x

When x = 2, y = 7

When x = 6, y = 67

Thus,

Average rate of change = 67 - 7 / 6 - 2

Average rate of change = 60 / 4

= 15

Option C is correct.

Answer:

x ≥ 1

Step-by-step explanation:

8 + 4x ≥ 12

Subtract 8 from each side

8-8 + 4x ≥ 12-8

4x ≥ 4

Divide by 4

4x/4 ≥ 4/4

x ≥ 1

The solution to the inequality 8 + 4x ≥ 12 is x ≥ 1. Therefore, the correct answer is A. x ≥ 1.

Correct option is A.

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Answer:

Step-by-step explanation:

The picture helps a lot in understanding what the problem is.  I could not understand what you typed.

OK, I can evaluate these log expressions.

A.  log  3  (base 27)  =  (1/3)   because   27^(1/3) = 3

B. log 27  (base 81) =  (3/4)   because  81^ (3/4) = 3^3 = 27

C. log 27  (base 9) = (3/2)   because   9^(3/2) = 27

D. log 27 ( base 1/3) =  -3    because  (1/3)^-3 = 27

Answer:

D,C,B,A

Step-by-step explanation:

Answer: 0.2 times

Step-by-step explanation:

Answer:

times it

Step-by-step explanation:

Answer:

It is a negative correlation there is one outlier, it is going from the top left to the bottom right. a line could be drawn through it. it could be linear but i would  say non linear.

Step-by-step explanation:

Answer:

Negative correlation

Step-by-step explanation:

The trend shown by the data points appear to be downward sloping, indicating negative correlation between the variables

Answer:

there is no y intercept. if there was it would be at the end of -3x

Final answer:

To find (f - g)(x), subtract g(x) from f(x) which gives (f - g)(x) = (3x - 1) - (x + 2), resulting in 2x - 3 as the correct answer.

Explanation:

To find (f - g)(x), you need to subtract the function g(x) from the function f(x). The given functions are f(x) = 3x - 1 and g(x) = x + 2.

Subtraction of the functions is performed as follows:

(f - g)(x) = f(x) - g(x)

(f - g)(x) = (3x - 1) - (x + 2)

(f - g)(x) = 3x - 1 - x - 2

(f - g)(x) = 2x - 3

The correct answer for (f - g)(x) is 2x - 3, which corresponds to option B.

Answer:

Yes!

Step-by-step explanation:

0.5 is half, and 1.00 is whole so 3/4 would be correct because it is in between 0.5 and 1.00

Yes, Chris says that 3/4 is halfway between 0.5 and 100%.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

Chris says that 3/4 is halfway between 0.5 and 100%.

Midway of 0.5 and 1 is,

(1 + 0.5)/2 = 0.75

100% as a decimal is 1.0.

That means,

3/4 = 0.75.

0.5 < 0.75 < 1

Therefore, Chris is correct.

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Answer:

Probability that exactly one of the eggs is cracked is 0.0198.

Step-by-step explanation:

We are given that the probability that an egg on a production line is cracked is 0.01.

Two eggs are selected at random from the production line.

The above situation can be represented through binomial distribution;

[tex]P(X = r) = \binom{n}{r} \times p^{r} \times (1-p)^{n-r};x=0,1,2,3,.......[/tex]

where, n = number trials (samples) taken = 2 eggs

           r = number of success = exactly one

           p = probability of success which in our question is probability that

                 an egg on a production line is cracked i.e; p = 0.01

Let X = Number of eggs on a production line that is cracked

So, X ~ Binom(n = 2, p = 0.01)

Now, probability that exactly one of the eggs is cracked is given by = P(X = 1)

                P(X = 1)  =  [tex]\binom{2}{1} \times 0.01^{1} \times (1-0.01)^{2-1}[/tex]

                               =  [tex]2 \times 0.01 \times (0.99)^{1}[/tex]

                               =  0.0198

Therefore, the probability that exactly one of the eggs is cracked is 0.0198.

Answer:

3/21, 14.29%, or 14.29

Step-by-step explanation:

John has 21 total marbles, which includes 3 blue ones.

(That's 3 over 21)

Hope this helps!

The required probability of getting blue marble would be 1/7.

Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Given that bag contains 6 red marbles, 3 blue marbles, 7 yellow marbles, and 5 green marbles.

The total number of outcomes = 6 + 3 + 7 + 5 = 21

So n(S) = 21

Number of blue marbles = 3

Number of favorable outcomes, n(E) = 3

If John reaches into the bag and randomly pulls out a marble

So the probability of getting blue marble would be as:

⇒ P(E) = n(E)/n(S)

⇒ P(E) = 3/21

⇒ P(E) = 1/7

Therefore, the required probability of getting blue marble would be 1/7.

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Answer:

m= 3, -3

Step-by-step explanation:

Hope this helps!

To compare the rates of temperature increase for the two engines, you can look at the slopes of their temperature vs. rotation speed graphs. To determine which engine was hotter at a rotation speed of 20 cycles per second, you can compare the corresponding temperature values on the graphs.

The question asks which engine's temperature increases more for each increase of 1 cycle per second. To determine this, we need to compare the rates of change of temperature for both engines. The rate of change of temperature for the first engine can be determined by finding the slope of the temperature vs. rotation speed graph. From the graph, it can be seen that the slope of the line connecting two points on the graph represents the rate of change of temperature per unit increase in rotation speed. By comparing the slopes of the two graphs, we can determine which engine's temperature increases more for each increase of 1 cycle per second.

To determine which engine was hotter when it rotated at 20 cycles per second, we can look at the corresponding temperature values on the graph. By finding the temperature value for each engine when the rotation speed is 20 cycles per second, we can compare the two temperatures to determine which engine was hotter.

To uniquely construct an isosceles triangle, you would either need the lengths of two sides and the angle between them, two sides and the angle opposite to one of them, or two angles and any side.

Julius is examining the principles of constructions in geometry. To construct a unique isosceles triangle, certain specific information is needed. An isosceles triangle is a triangle with two sides of equal length, and the angles opposite these sides are of equal measure too.

In general, there are three common cases in which the information given would be enough to construct only one unique isosceles triangle:

If other information is given, it may or may not be possible to construct a unique isosceles triangle. For example, given only the lengths of two sides, multiple different isosceles triangles can be made, depending on the size of the included angle.

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Answer:

[tex](x + 11)2 + (y + 6)2 = 184[/tex]

Answer: The answer would be (x+11)2+(y+6)2=324

Step-by-step explanation: I just got it right on my test :)

Answer:

44 %

Step-by-step explanation:

22 divided by 50 is 0.44 which is 44 percent

Answer:

40%

Step-by-step explanation:

Answer:

The length of side F'G' is 17.5 units

Step-by-step explanation:

Given

Quadrilateral, EFGH.

EF = 2 units

EH = 6 units

GH = 5.5 units

FG = 7 units

Scale Factor = 2.5

Required

Length of F'G'

To dilate a shape means to increase or reduce the size of that shape using a given scale factor.

The length of the new shape is calculated by multiplying the scale factor by the length of the old shape.

The question requires that we calculate F'G'.

Here, F'G' is formed as a result of the dilation of side FG.

From the formula stated above.

F'G' = Scale Factor * FG

From the given diagram, FG = 7 units

And scale factor = 2.5

So, F'G' = 2.5 * 7 units

F'G' = 17.5 units

Hence, the length of side F'G' is 17.5 units

Answer:

the screen it very tight( squished together)

Step-by-step explanation:

Answer:

Step-by-step explanation:

y=2x²-12x-32

=2(x²-6x+9-9)-32

=2(x-3)²-18-32

=2(x-3)²-50

so vertex is (3,-50)

again 2x²-12x-32=0

or  x²-6x-16=0

or x²-8x+2x-16=0

or x(x-8)+2(x-8)=0

(x-8)(x+2)=0

x=8,-2

8>-2

d=8

e=-2

f=3

Final answer:

The total cost of the watch will be $0.67 less if purchased from Tick Tock.

Explanation:

To find out how much less the total cost of the watch will be if purchased from Tick Tock, we need to calculate the shipping fee for both websites and subtract that amount from the total cost.

For Watches for Less, the shipping fee is 4% of $45, which is $1.80.

For Tick Tock, the shipping fee is 2.5% of $45, which is $1.13.

Therefore, the total cost of the watch from Tick Tock will be $45 - $1.13 = $43.87. The total cost from Watches for Less will be $45 - $1.80 = $43.20.

The difference in the total cost is $43.87 - $43.20 = $0.67.

Therefore, the total cost of the watch will be $0.67 less if purchased from Tick Tock.

Hey!!

They are adjacent angles.

Both angles have common side and vertex.

Hope it will help u...

x + y = 64

x = y + 6

y + 6 + y = 64

2y + 6 = 64

2y = 58

x = y + 6

x = 28 + 6

34 + 28 = 64

34 - 28 = 6

Final answer:

The two numbers are 35 and 29, with the larger number being 35 and the smaller number being 29, which is 6 less than 35.

Explanation:

To find the two numbers whose sum is 64, with the smaller number being 6 less than the larger number, we can use a system of equations. Let the larger number be represented by x and the smaller number by y.

From the problem statement, we have two equations:

Substituting the second equation into the first gives us:

x + (x - 6) = 64

This simplifies to:

2x - 6 = 64

Adding 6 to both sides gives us:

2x = 70

Dividing both sides by 2 gives us:

x = 35

Since y = x - 6, we find that:

y = 35 - 6 = 29

Therefore, the larger number is 35 and the smaller number is 29.

Answer:

The 64 ounce jug of milk costs $0.010 more per ounce than the 128 ounce jug of milk/

Step-by-step explanation:

3.20/128=$0.025 per ounce jug of milk

2.24/64=$0.035 per ounce jug of milk

0.035 - 0.025 = .010

Answer:

2/3

Step-by-step explanation:

Answer:

ABC ≅ DCB by SAS

Step-by-step explanation:

1. Segment DB ≅ segment AC because it was given

2. Angle C ≅ angle B because it was given

3. Segment CB ≅ segment CB because of Reflexive Property

4. Triangle ABC ≅ DCB because of SAS (side-angle-side postulate)

Hope I helped and please give me brainliest!

Answer:

7.5%

Step-by-step explanation:

75 is 7.5% of 1000

Hope this helps!

Answer:

[tex]m\angle 1 =60.75^\circ \\m\angle 2 =119.25^\circ[/tex]

Step-by-step explanation:

From the diagram:

[tex]m\angle 1 =60.75^\circ $(Corresponding Angles)\\[/tex]

Now Angle 1 and Angle 2 are on a straight line, therefore:

[tex]m\angle 1 +m\angle 2 =180^\circ $(Linear Postulate)\\Since m\angle 1=60.75^\circ\\60.75^\circ +m\angle 2 =180^\circ\\m\angle 2=180^\circ-60.75^\circ\\m\angle 2 =119.25^\circ[/tex]

Answer:   60.75    

               119.25

Step-by-step explanation:

Answer:

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

Answer:

Probability that the student scored between 455 and 573 on the exam is 0.38292.

Step-by-step explanation:

We are given that Math scores on the SAT exam are normally distributed with a mean of 514 and a standard deviation of 118.

Let X = Math scores on the SAT exam

So, X ~ Normal([tex]\mu=514,\sigma^{2} =118^{2}[/tex])

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

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

where, [tex]\mu[/tex] = population mean score = 514

           [tex]\sigma[/tex] = standard deviation = 118

Now, the probability that the student scored between 455 and 573 on the exam is given by = P(455 < X < 573)

       P(455 < X < 573) = P(X < 573) - P(X [tex]\leq[/tex] 455)

       P(X < 573) = P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{573-514}{118}[/tex] ) = P(Z < 0.50) = 0.69146

       P(X [tex]\leq[/tex] 2.9) = P( [tex]\frac{X-\mu}{\sigma}[/tex] [tex]\leq[/tex] [tex]\frac{455-514}{118}[/tex] ) = P(Z [tex]\leq[/tex] -0.50) = 1 - P(Z < 0.50)

                                                         = 1 - 0.69146 = 0.30854

The above probability is calculated by looking at the value of x = 0.50 in the z table which has an area of 0.69146.

Therefore, P(455 < X < 573) = 0.69146 - 0.30854 = 0.38292

Hence, probability that the student scored between 455 and 573 on the exam is 0.38292.

Answer: 4,838.40

Step-by-step explanation: 12,600* 3.2%*12