Express 4 as a fraction. A) 1 1 B) 1 4 C) 4 1 D) 4 4

50 people

Let x represent the number of people on the cruise. The amount they each must pay is ...

... ($58 -(x -42)) = $100 -x

The revenue from the group is the product of the number of people and the amount each pays:

... r(x) = x·(100 -x)

This describes a downward-opeing parabola with zeros at x=0 and x=100. The vertex (maximum) will be found halfway between those zeros, at x=50.

A group size of 50 maximizes revenue from the cruise.

The numerator can be found by multiplying each of these fractions by 100. It can be helpful to reduce these fractions first.

Here, we calculate those numerators.

a) 15/60 · 100 = 1/4 · 100 = 100/4 = 25

b) 30/60 · 100 = 1/2 · 100 = 100/2 = 50

c) 25/75 · 100 = 1/3 · 100 = 100/3 = 33 1/3

Of course, the denominator is 100, so the fractions are ...

... 15/60 = 25/100

... 30/60 = 50/100

... 25/75 = (33 1/3)/100

_____

Comment on this solution

Effectively, we have multiplied each fraction by 1 = 100/100. That is ...

... fraction × (100/100) = (fraction × 100)/100

This changes the form, but not the value.

Answer:

$9800

Step-by-step explanation:

commission = 5% × car price

20 × commission = 100% × car price . . . . . . multiply by 20

20 × $490 = car price = $9800 . . . . . . . . . . fill in given value of commission

The price of a car on which a salesperson earns a 5% commission of $490 is calculated by dividing the commission amount by the commission rate as a decimal (0.05), resulting in a car price of $9,800.

The question is asking to calculate the price of a car based on the commission earned by the salesperson. The salesperson receives a 5% commission on each sale and has earned $490 from the sale of one car.

To find the price of the car, we need to set up a simple equation. If 5% of the price results in a $490 commission, we need to divide the commission by the percentage rate expressed as a decimal.

The calculation will look as follows:

Convert the commission percentage to a decimal: 5% = 0.05.

Divide the commission earned by the decimal rate: $490 ÷ 0.05.

The result is the price of the car.

So, $490 ÷ 0.05 = $9,800.

Therefore, the price of the car is $9,800.

Answer:

D. $5.37

Step-by-step explanation:

We need to figure out how much grapes cost per pound

Change the mixed number to an improper fraction

7 1/5 = (5*7+1) /5 = 36/5

$12.89 / 36/5

Copy dot flip

12.89 * 5/36 = 1.79 per lb

If we are purchasing 3 pounds, we will multiply by 3

3 lbs * $1.79 / lb = $5.37

Answer:

17.9

Step-by-step explanation:

Here we are given a right angled triangle with a known angle of 72°, length of the perpendicular to be 17 feet and we are to find the length of the hypotenuse x.

For that, we can use the formula for sin for which we need an angle and the lengths of base and hypotenuse.

[tex]sin \alpha =\frac{perpendicular}{x}[/tex]

So putting in the given values to get:

[tex]sin 72=\frac{17}{x} [/tex]

[tex]x=\frac{17}{sin 72}[/tex]

[tex]x=17.8[/tex]

Therefore, the length of six cars is the closest to 17.9.

b(3) = -16

b(2) = b(1) -7 = -2 -7 = -9

b(3) = b(2) -7 = -9 -7 = -16

Answer: b(3)= -16

Step-by-step explanation:

Answer:

Yes

Step-by-step explanation:

3+5 is 8 and 6+2 is also 8. You can draw 3 apples with 5 other apples, and count that there are 8 of them and draw 6 apples with 2 other apples that make up 8 apples. Or you can rearrange the apples to be 5 and 3 and 6 and 2.

Answer:

4

Step-by-step explanation:

8 2/9 is close to 8

3 6/7 is close to 4

8 2/9 - 3 6/7  is close to 8-4 = 4

My estimate is 4

Answer:

65550 is the population at the end of 2017

Step-by-step explanation:

Population at the beginning of 2106:  60000

Increased 15% in 2016

Increase = 60000*.15 = 9000

New population = 60000+9000 = 69000

The population at the beginning of 2017: 69000

Decrease by 5% in 2017

Decrease 69000*.05 = 69000*.05 = 3450

New population = 69000-3450=65550

The population at the end of 2017 is 65550

Answer:

y = 3x +8

Step-by-step explanation:

The slope of the given line is -1/3. The slope of a perpendicular line is the opposite of the reciprocal of that: -1/(-1/3) = 3.

Then, in point-slope form, the equation of the line is ...

... y - k = m(x - h) . . . . . for slope m through point (h, k)

... y - 5 = 3(x -(-1)) . . . . . for line of slope 3 through (-1, 5)

... y = 3x +8 . . . . . . . . . simplify

Answer:

27 ^6

Step-by-step explanation:

The first step is to split the expression into 2 parts  (ab)^x = a^x b^x

(3a^2)^3

3^3  a^2 ^3

27 a^2^3

We can then us the power of power rule to simplify the exponents x^a^b = x^(ab)

27 a^(2*3)

27 ^6

In 4 months, the total cost of Yoga Studio A would equal that of Yoga Studio B

The cost of Yoga Studio A at any given month can be represented as:

= Membership fee + (Monthly fee x Number of months)

Assuming number of months is x, the formula would be:

= 24 + (21.50 × x)

= 24 + 21.50x

Yoga Studio B would be:

= 41 + (17.25 × x)

= 41 + 17.25x

In order to find the month that these costs would be equal, equate both formulas:

24 + 21.50x = 41 + 17.25x

21.50x - 17.25x = 41 - 24

4.25x = 17

x = 17 / 4.25

x = 4 months

In conclusion, their costs would be the same in the 4th month.

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Answer:

D. differences

Step-by-step explanation:

One way to identify a linear function is by checking the differences over equal intervals. If they are the same, then the function is linear.

Answer:

D. Differences

Step-by-step explanation:

Linear function grow by equal differences over equal intervals as, on a graph, it is shown by a steady increasing line. Exponential functions, on the other hand, do not.

Answer:

x = 3

Step-by-step explanation:

f'(x) = 0 for x = 3 and x = 4 . . . . by the zero product rule.

The coefficient of x² in f'(x) is negative, so the parabola opens downward.

f''(x) is positive for x < 3.5, so the coordinate x = 3 represents a relative minimum.

Answer:

False

Step-by-step explanation:

It is the exponent of a base.

The variable in an exponential function is always the exponent of the power is false.

When the expression of function is such that it involves the input to be present as an exponent (power) of some constant, then such function is called exponential function.

Their usual form is specified below. They are written in several such equivalent forms.

The variable in an exponential function is always the exponent of the power is false. It is the exponent of a base.

Learn more about exponential  here:

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Answer:

XY = 150

Step-by-step explanation:

AB = 8

W Z = 80

SF = 10

8 x 10 = 80

So if BC = 15

XY = 15 x 10 = 150

Answer:

Step-by-step explanation:

you can solve with a proportion

8 : 15 = 80 : x

x = 15 * 80 : 8

x = 150

or you find the rate from AD and WZ

8 : 80

simplify

1 : 10

15 * 10 = 150

45° and 135°

If the smaller is represented by x, then the larger is 3x. The two angles are supplementary, so ...

... x + 3x = 180°

... 4x = 180°

... 180°/4 = x = 45°

... 3x = 135°

The two angles are 45° and 135°.

Answer:

45° and 135°

Step-by-step explanation:

If the smaller is represented by x, then the larger is 3x. The two angles are supplementary, so ...

... x + 3x = 180°

... 4x = 180°

... 180°/4 = x = 45°

... 3x = 135°

The two angles are 45° and 135°.

Step-by-step explanation:

The polynomial function f(x) having roots [tex]-2 + \sqrt(8)[/tex] and 9 would have factors  [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9). These roots can be determined by setting the known values equal to x and subtracting from x.

In mathematics, specifically in polynomial functions, the roots of a function are values that make the function equal to zero. These roots correspond to the factors of the polynomial function. If a function f(x) has roots -2 + square root 8 and 9, then the factors of f(x) will be those values set equal to x and then subtracted from x.

Therefore, the corresponding factors would be  [tex]x - (-2 + \sqrt{8})[/tex] and (x - 9). When you simplify these, they become [tex](x + 2 - \sqrt(8))[/tex] and (x - 9). To further simplify, we know that  [tex]\sqrt(8) = 2\times \sqrt(2),[/tex] therefore we get  [tex](x + 2 - 2\times \sqrt(2))[/tex] and (x - 9).

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If a polynomial function has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of the polynomial.

Polynomial functions are mathematical expressions comprising variables, coefficients, and non-negative integer exponents. They are used in various fields, including mathematics, physics, engineering, and computer science. They model relationships between variables, aiding in solving equations, analyzing data, and predicting outcomes in diverse applications.

If the polynomial function f(x) has roots -2 + Square root 8 and 9, then x - (-2 + Square root 8) and x - 9 must be factors of f(x). This is because if a number is a root of a polynomial, then the polynomial can be divided evenly by the corresponding linear factor.

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Answer:

68

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

... Tan = Opposite/Adjacent

For this geometry, this means ...

... tan(x°) = 5/2

Taking the inverse tangent, we can find x.

... x° = arctan(5/2) ≈ 68.199°

... x ≈ 68

Answer:

the first selection (see below)

Step-by-step explanation:

The average rate of change (m) on the interval [x1, x2] is given by ...

... m = (g(x2) -g(x1))/(x2 -x1)

For g(x) = -x²-4x and (x1, x2) = (6, 8), the expression is the one attached.

Answer:

[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]

Step-by-step explanation:

average rate of change of the function g(x) = -x^2 - 4x on the interval 6 ≤ x ≤ 8

To find average rate of change we use formula

Average =[tex]\frac{g(x_2)-g(x_1)}{x^2-x_1}[/tex]

use the given interval 6<=-x<=8

x2=8  and x1= 6

we replace the value in the given formula

g(x) = -x^2 - 4x

[tex]g(8) = -8^2 - 4(8)[/tex]

[tex]g(6) = -6^2 - 4(6)[/tex]

x2-x1 is 8-6

So equation becomes

[tex]\frac{[-8^2 - 4(8)]- [-6^2 - 4(6)]}{8-6}[/tex]

Answer:

64

Step-by-step explanation:

Since 64 is a multiple of itself and of all the other numbers, the answer is 64.

Answer:

Step-by-step explanation:

A graphing calculator can show you the intercepts.

___

Or you can figure them out.

The y-intercept is where x=0, so is ...

  y = log(12·0 +7) -3 = log(7) -3 ≈ -2.1549 ≈ -2.15

___

The x-intercept is where y = 0, so is ...

  0 = log(12x +7) -3

  3 = log(12x +7) . . . . . . add 3

  10^3 = 12x +7 . . . . . . . take the antilog

  993 = 12x . . . . . . . . . . subtract 7

  993/12 = x = 82.75 . . . divide by the coefficient of x

3x = -4y

To solve for X, divide both sides by 3:

x = -4y / 3

The answer is D.

f(x) = 3·2^x

When x=0, any exponential term will have a value of 1, so the y-intercept is the multiplier of the exponential function. Here, it is 3.

When x=1, the exponential term will have a value equal to its base, so the multiplier just found will be multiplied by the base value. Here, f(1) = 3·2, so the base of the exponential term is 2.

Given these considerations, the function is ...

... f(x) = 3·2^x

_____

Comment on notation

The caret (^) is used to signify an exponent. When the exponent consists of anything other than a single number or variable, it must be put in parentheses: 2^(1/2), for example.

The expressions you have written all look like linear functions.

Answer:

C. The length of one lap.

Step-by-step explanation:

In the first four words, the problem statement tells you that L is the number of laps run. It is not the length of one lap.

_____

Comment on the problem presentation

Appropriate punctuation would be very helpful. Apparently, it is a 1/4-mile track, not a 14-mile track. Apparently, the distance is 1 1/2 miles, not 112 miles. Copying and pasting problem text often leaves out the special symbols used on some web sites. Some editing is usually needed.

Answer:

P

Step-by-step explanation:

The distance doesn't change during segment Q, so that is when the cyclist is stopped. The segment before that is labeled P.

The question asks the label of the segment before the one where the cyclist was stopped, so the appropriate choice is P.

Answer:

it is Q

Step-by-step explanation:

Because it is stopped and its a strait line making it look like it is taking a brake.

Answer:

The probability is about 7.7%

Step-by-step explanation:

A probability is the ratio of the number of relevant outcomes and the number of all possible outcomes. To answer this question we do some counting first:

Consider two draws. We are interested in the second draw being an Ace, the first draw can either be an Ace or not, so, there are two cases of a relevant outcomes (all without replacement):

(number of relevant oucomes n ) = (number of cases of Ace-Ace draws) + (number of cases of NonAce-Ace draws):

[tex]n=4\cdot 3+{48\cdot4}= 204[/tex]

(number of possible outcomes) = (number of choices at first draw) * (number of choices at second draw) = 52 * 51 = 2652

The probability is then

P = 204/2652 = 0.0769, or about 7.7%

Answer:

Table B shows a proportional relationship.

Step-by-step explanation:

In a proportional relationship two quantities vary directly with each other. It means

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

Where, k is the constant of variation.

The ordered pairs of table A are (-2,2), (-1,3), (0,0) and (1,5).

From these ordered pairs we can conclude that the value of y-coordinate is not changing according to the x-coordinate because the values of x increased by 1 for each ordered pair but the value of y is not increasing in the same proportion..

The ordered pairs of table B are (-1,-3), (0,0), (1,3) and (2,6). The value of y increasing at a constant rate 3 and the value of y-coordinate is 3 times of x-coordinate.

Choose any two ordered pairs of table B. Let the two points are (0,0) and (1,3), then the constant of variation is

[tex]k=\frac{y_2-y_1}{x_2-x_1}=\frac{3-0}{1-0}=3[/tex]

The proportional relationship is defined as

[tex]y=3x[/tex]

Therefore, 3 is the constant of variation and rate of change.

So, Table B shows a proportional relationship.

Answer:

Table B Shows proportional relationship.

Step-by-step explanation:

Correct answers are the green and yellow dots. Hope this helps. The red dot I got wrong.

Multiplying it out using the distributive property, you have ...

... x^4 -(x^4 -7x^2 +7x^2 -49)

... = x^4 -x^4 +7x^2 -7x^2 +49 . . . . distribute the minus sign

... = x^4(1 -1) +x^2(7 -7) +49 . . . . . . collect like terms

... = 0 +0 + 49 . . . . . . . . . . . . . . . . . .simplify

... = 49

Step-by-step explanation:

1. See the attachment for the filled-in diagram. Adding the contents of the figure gives the sum at the bottom, matching selection C.

2. If we let "d" represent the length of the second volyage, then the total length of the two voyages is ...

... (d+43) + d = 1003

... 2d = 960 . . . . . . . subtract 43

... d = 480 . . . . . . . . divide by 2

The second voyage lasted 480 days.

3. 1.9% - 1.9/100 = 0.019. Adding this fraction to the original means the original is multiplied by 1 +0.019 = 1.019. Doing this multiplication each year for t years means the multiplier is (1.019)^t.

Since the starting value (in 1975) is 4 (billion), the population t years after that is ...

... P(t) = 4(1.019)^t