The graph below shows the ages of the top five male finishers in the Mt. Washington Auto Road Bicycle Hillclimb each year from 2017 through 2021.

1. Write the relation of this situation as a set of ordered pairs in terms of (age, finishing place).
2. Identify the domain and range of the relation.

3. Do the ordered pairs represent a function? Explain.

The piecewise function for the monthly charge W(x) for a customer who uses x hours of electricity is given by:

The graph of the function is given at the end of the answer.

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, we have that:

The monthly charge is calculated differently according to the number of kWh of electricity used, divided into two cases as follows:

For up to 300 hours, the base charge of $50 plus the hourly fee of $0.0650 is charged, hence:

W(x) = 50 + 0.0650x, 0 ≤ x ≤ 300.

For more than 300 hours, the customer is charge 50 + 300 x 0.0650 = $69.5, plus the hourly fee of $0.0850, hence:

W(x) = 69.5 + 0.0850x, x > 300.

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The expressions that are equal to 7⁸ x 7 are:

B. For (7¹⁸)/7⁹

C. For (7³)³

E. For 7⁴ x 7⁵

Exponential functions now have formula f(x) = bx, where b > 0 and b 1. As in any exponential expression, b serves termed the base and x is called its exponent. The proliferation of bacteria is an example of such an exponential function.

A. For 7³ x 7³

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7³ ⁺ ³

Calculate the sum or difference: 7⁶

Calculate power : 117649

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: False

Solution: False

B. For (7¹⁸)/7⁹

Reduce the fraction: 7⁹

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

C. For (7³)³

simplify using exponent power rule : 7⁹

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

D. For 7⁴ + 7⁵:

Calculate the power: 2401 + 16807

Calculate the sum or difference: 19208

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: False

Solution: False

E. For 7⁴ x 7⁵:

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁴ ⁺ ⁵

Calculate the sum or difference: 7⁶

Calculate power : 40353607

simplify using exponent rule with the same base: aⁿ x aˣ

= aⁿ ⁺ ˣ

= 7⁸ ⁺ ¹

Calculate the sum or difference: 7⁹

Calculate power : 40353607

Check equivalency: True

Solution: True

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I understand that the question you are looking for is:

Select all the expressions that are equivalent to 7⁸ x 7.

A. For 7³ x 7³

B. For (7¹⁸)/7⁹

C. For (7³)³

D. For 7⁴ + 7⁵:

E. For 7⁴ x 7⁵

Answer:

none

Step-by-step explanation:

point steeler

3 houseplants will weigh 15 kg (Refer to the tape diagram below).

The weight of 3 household plants will be about 15 kg.

Therefore, the weight of 3 household plants will be about 15 kg (Refer to the tape diagram below).

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The set of months having 31 days will be S = { January, March, May, July, August, October, December }.

A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets.

We know that there are 12 months in a year.

From these months, we get that the months that have 31 days are:

January

March

May

July

August

October

December

The set of months having 31 days will be:

S = { January, March, May, July, August, October, December }

Therefore, we get that, the set of months having 31 days will be S = { January, March, May, July, August, October, December }.

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Rory can make 43 metaballs from the remaining beef.

Rory has 6 pounds of ground beef on hand for making meatballs.

He makes 9 meatballs with 5/8 pounds of meat per meatball.

We must subtract 5/8 from 6.

There are 43/8 pounds of ground beef remaining.

As a result, the number of 1/8 pound meatballs produced from 21/8 pound ground beef can be calculated as follows:

Therefore, Rory can make 43 metaballs from the remaining beef.

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AAnswer:

Las Letras A B C , en matematicas el valor puede variar ; ya que ya depende del valor que se le otorge o ya si es una operacion , pues el valor que se obtiene , es decir las letras en matematicas no tiene o poseen un valor fijo

Step-by-step explanation:

Answer:

39 is the sum of their ages

Step-by-step explanation:

Hope this helps :)

Answer: f(x^2) = x^2 - 5

Horse runs at the faster rate i.e. at the rate of 58 feet per seconds.

According to the given question.

A bear can run 400 feet in 8 seconds.

A horse can run 290 feet in 5 seconds.

As we know that, the measurement of the speed at which something happens is called rate.

Therefore, form distance rate formula (rate = distance/time)

The rate of the bear =  400/8 = 50 feet/sec

And the rate of the horse = 290/5 = 58 feet/sec

Therefore, horse can run faster than bear.

Hence, horse runs at the faster rate i.e. at the rate of 58 feet per seconds.

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Answer:

Step-by-step explanation:

Point G has coordinates (4, -2).

After reflection across the x-axis it s coordinates will change as per rule:

Applied to point G:

After dilation by a scale factor of 2 the coordinates will change as per rule:

Applied to point G:

Yes; The construction demonstrates how to bisect an angle correctly using technology because Circles D & E have the same radius

How to properly bisect an angle?

In construction of angles and lines, bisection means dividing either a given angle or line segment into two equal parts. This means after the construction, the two parts must have equal measure.

The steps to bisect a line segment are as follows;

1. Draw the required length of the line segment AB.

2. With point A and radius of the compass greater than half of AB, describe arcs above and below the segment.

3. With the same radius as in step 2 and point B, describe two arcs above and below the segment. These would intersect that of step 2 at C and D.

4. Join the points of intersection of the arcs with a straight line CD.

Now, in this given question with the circle, we can see that line AG is the line that bisects the angle EAD.

Now, we see that circles C and D have the same radius and as such the construction demonstrated is correct for that very reason.

Answer: yes

Step-by-step explanation: the construction correctly shows how to bisect an angle using technology because circles D and E have the same radius. 

The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].

The Domain of a function f(x) is the set of all values for which the function is defined.

The Range of a function is the set of all values that f takes.

As, [tex]sec x=\frac{1}{cos x}[/tex] , so sec x is defined where [tex]cos x \neq 0[/tex].

It implies, sec(3.14t/4) is defined where [tex]cos(3.14t/4)\neq 0[/tex].

The cosine is 0 at [tex](2n+1)\frac{\pi }{2}[/tex] , where n is any integer.

Now, [tex]\frac{3.14t}{4} =\frac{(2n+1)\pi }{2}[/tex]

         [tex]\frac{\pi t}{4} =\frac{(2n+1)\pi }{2}[/tex]

       [tex]t=2(2n+1)\\t=2+4n[/tex]

Since, the range of cos x is [-1,1], so sec x will never be less than 1, but can grow infinitely large as cos x approaches 0.

Thus, The domain of sec(3.14t/4) is all real numbers except 2+4n, where n is any integer and range of sec(3.14t/4) is [tex](\infty,-1] \cup [1,\infty)[/tex].

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Answer:

c) 1

Step-by-step explanation:

Solving for the value of s,

→ 3s - 12 = -9

→ 3s = -9 + 12

→ s = 3/3

→ [ s = 1 ]

Thus, option (c) is correct.

coordinates of the new station= (5,98/4)

When two lines intersect at a point then the angle between them can be expressed in terms of their slopes and is given by the following formula:

tan θ = |

|where

are the slopes of the line AB and CD respectively.

If

is positive then the angle between the lines is acute. If

is negative then the angle between the lines is obtuse.

Slope of Vertical Lines

Vertical lines have no slope, as they do not have any steepness. Or it can be said, we cannot define the steepness of vertical lines.

A vertical line will have no values for x-coordinates. So, as per the formula of slope of the line,

Slope, m = (y2 – y1)/(x2 – x1)

But for vertical lines, x2 = x1 = 0

Therefore,

m = (y2 – y1)/0 = undefined

In the same way, the slope of horizontal line is equal to 0, since the y-coordinates are zero.

m = 0/(x2 – x1) = 0 [for horizontal line]

Positive and Negative Slope

If the value of slope of a line is positive, it shows that line goes up as we move along or the rise over run is positive.

If the value of slope is negative, then the line goes done in the graph as we move along the x-axis.

Let R,Q,T be the points that divide the line into 3:4 equal parts

Let the Q = (x,y)

R(1, 2) and T(8, 23) ,

x = m1x1+m2x2/m1+m2

y = m1y1+m2y2/m1+m2

X= 3.1+4.8/7

x= 3+32/7

x=35/7

x=5

y=2.3+23.4/3+4

y= 6+92/4

y=98/4

y= 24.5

(x,y) = (5,98/4)

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Answer:

44

Step-by-step explanation:

20 ÷ 5 = 4 minutes per page

4 x 11 pages = 44

Answer:

A

Step-by-step explanation:

The domain of g(x) is the set of all real numbers. Meaning that all the numbers between the min and max of g would be -7 ≤ x ≤ 7.

Using integrals, the desired probabilities and measures are given as follows:

a) P(X < 6) = 0.84375 = 84.375%.

b) P(X < 13) = 1 = 100%.

c) P(6 < X < 8) = 0.15625 = 15.625%.

d) P(X > 5) = 0.31641 = 31.641%.

e) x = 6.434.

The distribution is given as follows, simplifying the operations:

f(x) = 0.09375x - 0.01171875x², 0 ≤ x ≤ 8.

Hence the density function is:

[tex]\int_{a}^{b} f(x) dx[/tex]

[tex]\int_{a}^{b} (0.09375x - 0.01171875x^2) dx[/tex]

[tex]0.046875x^2 - 0.00390625x^3|_{x=a}^{x = b}[/tex]

Applying the Fundamental Theorem of Calculus:

P(a < X < b) = 0.046875b² - 0.00390625b³ - 0.046875a² + 0.00390625a³

Hence, for item a:

P(X < 6) = 0.046875(6)² - 0.00390625(6)³.

P(X < 6) = 0.84375 = 84.375%.

For item b, the entire distribution is below 13, hence:

P(X < 13) = 1 = 100%.

For item c:

P(6 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(6)² + 0.00390625(6)³.

P(6 < X < 8) = 0.15625 = 15.625%.

For item d:

P(5 < X < 8) = 0.046875(8)² - 0.00390625(8)³ - 0.046875(5)² + 0.00390625(5)³.

P(X > 5) = 0.31641 = 31.641%.

For item e:

We have to find b when a = 0 and P(X < b) = 0.9, hence:

0.046875b² - 0.00390625b³ = 0.9.

Using a calculator, the solution in the range of the distribution is given by:

b = x = 6.434.

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Answer:

Option 2

Step-by-step explanation:

The temperature changes for each day are 32.12 °C (Day 1) and 33.02 °C (Day 2), respectively. The day 2 registered the highest temperature change.

Herein we find a table with the temperatures at sunrise and sunset in two days and we need to determine the temperature change for each period and conclude in what day the change was the highest. The temperature change can be found by using the following formula:

ΔT = T' - T

Where:

The temperature changes for each day are 32.12 °C (Day 1) and 33.02 °C (Day 2), respectively. The day 2 registered the highest temperature change.

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We the Probability of pulling either fork or spoon as 1.

We are given that:

We have a fork and a spoon in a bag.

Total number of items in a bag = 1 + 1 = 2

Now, we need to tell the probability of either pulling a fork or a spoon.

Now,

Probability of pulling a fork = 1 / 2 = 0.5

Probability of pulling a spoon = 1 / 2 = 0.5

So, the Probability of pulling either of them will be = 1 / 2 + 1 / 2 = 1

Therefore, we the Probability of pulling either fork or spoon as 1.

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Answer:

16

Step-by-step explanation:

[tex]-7+3^2\\3^2\\=9\\=-7+9\\=-7+9 = 2\\=2\times \:8\\2\times \:8=16\\\boxed{16}[/tex]

Answer:

7/10

Step-by-step explanation:

Rewriting 0.7 as a fraction would be 7/10. 0.7 can also be 0.70, and 70/100

Answer:

D. F

Step-by-step explanation:

Both F and G are not on plane P

The value of the integer number is -1

The statement is given as:

The sum of an integer and 7 times the next consecutive odd integer is 6

Let the integer value be x

So, the next consecutive odd integer is x + 2

When represented as an equation, we have

x + 7(x + 2) = 6

Open the bracket

x + 7x + 14 = 6

Evaluate the like terms

8x = -8

Divide both sides by 8

x = -1

Hence, the value of the integer number is -1

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Answer:

14 in

Step-by-step explanation:

the formula for the circumference of a circle is

2×pi×r

or (because the diameter is 2×r)

pi×d

with r being the radius and d being the diameter.

44 = pi×d

d = 44/pi = 14.00563499... in ≈ 14 in

Answer: ann is 69 and beth is 138

Step-by-step explanation:

The least value is 11.

[tex]$$\begin{aligned}&\mathrm{S}=\frac{1}{1-(1 / 2)}=2 \\&\mathrm{~S}_{\mathrm{n}}=\frac{1-(1 / 2)^{\mathrm{n}}}{1-(1 / 2)}=2-\frac{1}{2^{\mathrm{n}-1}}\end{aligned}$$[/tex]

[tex]$$\mathrm{S}-\mathrm{S}_{\mathrm{n}}=\frac{1}{2^{\mathrm{n}-1}} < \frac{1}{1000} \text { or } 2^{\mathrm{n}-1} \geq 1000$$[/tex]

Now [tex]$2^{10}=32 \times 32=1024$[/tex]

[tex]$$\therefore n-1 \geq 10 \text { or } n \geq 11$$[/tex]

Hence the least value is 11.

If you have a positive term in your quadratic equation, it will also have a minimum value. This minimum value can be found by graphing the function or solving one of the two equations. If you have the equation y = a[tex]x^2[/tex] + bx + c, you may use the equation min = c - [tex]b^2[/tex]/4a to determine the minimum value.

A quadratic equation is a second-order polynomial equation in a single variable x a[tex]x^2[/tex]+bx+c=0. with a ≠ 0 . The fundamental theorem of algebra assures that it has at least one solution because it is a second-order polynomial equation.

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