68. REAL-WORLD APPLICATIONS
At noon, a barista notices that she has $20 in her tip jar. If she makes an average of $0.50 from each customer, how much will she have in her tip jar if she serves n more customers during her shift?

The percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.

The percentage is similar to the fractional representation of quantities, where the quantity is shown as a part of the whole, but here the whole is fixed to be 100.

To derive a percentage in fractional form, we divide it by 100.

To derive a fractional form in percentage, we multiply it by 100.

In the question, we are given that 80 cars of 300 cars are black.

We are asked the percentage of cars that are black.

The fraction representing black cars of whole cars can be shown as 80/300 = 4/15.

To convert this into a percentage, we multiply it by 100.

Thus, the percentage of cars that are black = 4/15 * 100% = 80/3% = 26 2/3% = 26.67%.

Thus, the percentage of cars that are black when 80 cars of 300 cars are black is 26.67 or 26 2/3 %.

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Answer: y=40

Step-by-step explanation:

because a triangle adds up to 180 degrees, and you subtract 180-15-26.5-90[the right angle]=40

Answer:

Option D

Step-by-step explanation:

Looking at the graph each jump is 2 units on the x-axis and y-axis :

We are looking for a quadratic with x values of 3 and 6 when y=0  

Solving the last quadratic gives us :

(x-3)(x-6)=0

x = 3 , x = 6

Our answer will be Option D

Hope this helped and have a good day  

Answer:

D: [tex]y=x^{2} -9x+18\\[/tex]

Step-by-step explanation:

x intercept of the curve is 3 and 6

meaning that when y=0, x is either 3 or 6

mathematically stated:

0 = (x - 3)  (x - 6)

0=x(x-6)-3(x-6)

[tex]0=x^{2} -6x-3x+18\\therefore \ y=x^{2} -9x+18\\[/tex]

Answer:

10 . 44 ft

Step-by-step explanation:

sin 50 = opposite leg / hypotenuse = 8 / x

8 / sin 50 = x    = 10 .44  ft

Answer:

10.433cm

Step-by-step explanation:

Using SOH from TOACAHSOH,

[tex]sin50deg = \frac{opposite}{hypotenuse} [/tex]

From here we know there the opposite is 8ft (height of the ring) and hypotenuse is what we want to find, distance between you and the ring.

[tex]sin(50) = \frac{8}{x} \\ x \sin(50) = 8 \\ x = \frac{8}{ \sin(50) } \\ x = 10.443cm(rounded \: to \: 5sf)[/tex]

The graph of the linear equation can be seen in the image below.

Here we have the linear equation:

y = (2/5)*x - 6

To graph it, we just need to find two points on the line, and then connect them with a line.

To find the points we just evaluate in two values of x.

if x = 0.

y = (2/5)*0 - 6 = -6

Then we have the point (0, -6)

If x = 5.

y = (2/5)*5 - 6 = 2 - 6 = -4

Then we have the point (5, - 4)

Now we can graph these two points and connect them with a line. The graph of the line can be seen below.

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The correct expression for the inverse proportion is k/7 = 3/1

Given the inequality xy = k

If y is inversely proportional to x, then;

y = k/x

Given that y = 3, and  x = 7, then;

3 = k/7

Swap

k/7 = 3

k/7 = 3/1

Hence the correct expression for the inverse proportion is k/7 = 3/1

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Hello and Good Morning/Afternoon

Let's take this problem step-by-step

The Line DF is '5x + 7' cm long

The Line DF is made up of two lines DE and EF

    ⇒ therefore

          [tex]DE + EF = \\ 7 + 4x + 3 = 5x + 7\\10+4x=5x+7\\5x-4x=10-7\\x=3[/tex]

Let's plug x's value into '5x + 7'

    [tex]\hookrightarrow DF = 5(3) +7=22[/tex]

Answer: 22cm

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Answer: 20

Step-by-step explanation:

By CPCTC,

[tex]3x-10=2x+10\\\\x=20[/tex]

Answer:

Option no. B is a unit tile in that tesselation

i.e rectangular shape

Step-by-step explanation:

Well, it's because we all know that tesselation

only use one shape and it's sum is always 360°

meanwhile sum of rectangle=360°

as each side of rectangle are 90°

90°*4=360°##

I hope it helped you to understand more clearly...

The angle pairs that we can observe from the figure are

Straight angle pairs, often referred to as linear pairs, are formed when two lines cross, creating two side-by-side angles that sum to 180 degrees. The requirement that the two angles in a straight angle or linear pair be adjacent is crucial. The two angles cannot form a linear pair if they are not side-by-side (share the same side) (even if they add to 180 degrees). Check out the depiction of straight angle/linear pairings in the picture below.

The angle pairs that we can observe from the figure are

As we can see in the following figure that supplementary angles are called angle pairs.

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Using linear function concepts, a system of equations with no solutions is created when:

[tex]m = -2, b \neq \frac{3}{2}[/tex]

A linear function is modeled by:

y = mx + b

In which:

The intersection of two lines is the solution of a system of equations. If two lines have the same slope and different intercepts, they will never intercept, that is, the system will not have a solution.

The lines are given as follows:

Hence, for a system with no solution, we need that:

[tex]m = -2, b \neq \frac{3}{2}[/tex]

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If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

1. If the order does not matter, combination is used

[tex]\left ({n} \atop {r}} \right.)=\frac{n!}{r!(n-r)!}[/tex]

Here, n=6 r=3

using formula,we get

[tex]\left ( {{6} \atop {3}} \right)=\frac{6!}{3!3!} =5*4=20[/tex]

2. If an order is important, Permutation will be applicable

[tex]^{n}P_{r} = \frac{n!}{(n-r)!} \\[/tex]

∴[tex]^{6} P_{3} =\frac{6!}{3!(6-3)!}=\frac{6!}{3!} =120[/tex]

3. the probability that the three newest cars end up parked in the driveway

P=[tex]\frac{No. of possible outcomes for 3 cars}{total possibilities}[/tex]

=[tex]\frac{6*4*5}{6!}[/tex]

=[tex]\frac{120}{720}[/tex]

=[tex]\frac{1}{6}[/tex] ≈ 0.167

Hence, If the order does not matter, cars can be arranged in 20 ways

If an order is important, cars can be arranged in 120 ways

The probability that the three newest cars end up parked in the driveway is 0.167

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Answer:

To show that 2 triangles are congruent, both triangles must have the same the same size and shape. Basically both triangles must have the same 3 angles and 3 sides.

Step-by-step explanation:

This means that the corresponding sides are equal and the corresponding angles are equal. We can tell whether two triangles are congruent without testing all the sides and all the angles of the two triangles.

Hope this helped! :D

Answer:

Step-by-step explanation:

Follow this rules

-0.22 as  a repeating fraction is -22/99

The decimal is given as:

-0.22

Express as fraction

-22/100

Subtract 1 from the denominator to rewrite it as a repeating number

-22/99

Hence, -0.22 as  a repeating fraction is -22/99

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The statement that are true about the dilation are:

A. M'N' is 18 units.

D. The dilation is an enlargement.

F. Scale factor is 3.

Given that rectangle LMNP is dilated using the rule Dp.3, it means that rectangle LMNN is enlarged times 3 to get rectangle L'M'N'P'.

This means that the scale factor is 3.

We would have the following:

M'N' = 6 × 3 = 18 units.

Therefore, the statements that are true are:

A. M'N' is 18 units.

D. The dilation is an enlargement.

F. Scale factor is 3.

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Answer:  A. The length of line segment M'N' is 18 units,  D. The dilation is an enlargement, & F. The scale factor is 3.

Step-by-step explanation:  TRUST ME!!! Answer is correct in Edge.  :)

Answers: A, D & F.  

Answer:

50

Step-by-step explanation:

→ Evaluate n as 1, 2, 3 and 4 in 5n

5, 10, 15 and 20

→ Find the sum of these numbers

5 + 10 + 15 + 20 = 50

Answer:

25.40134119

Step-by-step explanation:

1000/39.368

Answer:

Step-by-step explanation:

So in this case you need to use the Pythagorean Theorem which states that: [tex]a^2+b^2=c^2[/tex] where c is the value of the hypotenuse, and a and b are the other two sides (the order in which you put them doesn't matter). So in this case I'll say a=8.4 (I could've also input it as b, doesn't matter) and c=10.5 (here it does matter, c is hypotenuse, it's not the other sides...)

So given this information we have the equation:

[tex](8.4 cm)^2 + b^2 = (10.5 cm)^2\\[/tex]

Square known values:

[tex]70.56 cm^2 + b^2 = 110.25 cm^2[/tex]

subtract 70.56 cm^2 from both sides

[tex]b^2 =39.69 cm^2[/tex]

Take the square root of both sides

[tex]b=6.3 cm[/tex]

x=6.3 cm

Problem 3: a = 9 cm, c=20 cm

Input known values

[tex](9 cm)^2 + b^2 = (20 cm)^2[/tex]

Square known values

[tex]81 cm^2 + b^2 = 400 cm^2[/tex]

Subtract 81 cm^2 from both sides

[tex]b^2 = 319cm^2[/tex]

take the square root of both sides

[tex]b\approx 17.86 cm[/tex]

so the side x is approximately 17.86 cm

Answer:

no matter what he has to pay $52

Step-by-step explanation:

because it is annually.

Answer:

[tex](x+8)^2=y;\ x\ge -8[/tex]

Step-by-step explanation:

So the inverse is when the x and y are swapped

Original equation:

[tex]y=\sqrt{x}-8[/tex]

Swap x and y:

[tex]x=\sqrt{y}-8[/tex]

add 8 to both equations:

[tex]x+8=\sqrt{y}[/tex]

Square both sides

[tex](x+8)^2=y[/tex]

Now while this looks like a normal quadratic, it has to have the range restriction the original function had, but as it's domain restriction. So the range of the original function was y >= -8, because the smallest value you could input is 0, and the square root of that is 0, then subtract 8 and you get -8. So the domain is x >= -8

Using it's concept, the desired probability is given as follows:

P(decaf or sugar) = 0.41.

A probability is given by the number of desired outcomes divided by the number of total outcomes. A probability can also be represented as a proportion.

From the table, we have that:

Hence:

P(decaf or sugar) = 0.22 + 0.19 = 0.41.

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(a) The lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

(b) The lateral surface area of the cone is 136π sq units and the total surface area is 200π sq units.

(c) The lateral surface area of the cylinder is 242π sq units and the total surface area is 484π sq units.

L.S.A = Ph

where;

h² = 17² - 8²

h² = 225

h = 15

L.S.A = (3 x 16) x 15 = 720 sq units

T.S.A = PH + 2B

T.S.A = 720 + 2(16) = 752 sq units

L.S.A = πrt

where;

r² = 17² - 15²

r² = 64

r = 8

L.S.A = π(8)(17) = 136π sq units

T.S.A = πrt + πr²

T.S.A = 136π sq units + π(8)²

T.S.A = 200π sq units

L.S.A = 2πrh

where;

L.S.A = 2π(11 x 11) = 242π sq units

T.S.A = 2πrh + 2πr² = 2πr(r + h)

T.S.A = 2π(11)(11 + 11)

T.S.A = 484π sq units.

Thus, the lateral surface area of the prism is 720 sq units and the total surface area is 752 sq units.

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Answer: Option 4

Step-by-step explanation:

Each value of x maps onto only one value of y.

Answer:

distributive property

Step-by-step explanation:

(3x + 7) + (2x + 8)

each of the parenthesis has a multiplier of 1 , placed outside the parenthesis.

then multiplying the terms inside the parenthesis by 1 gives

3x + 7 + 2x + 8

If the fraction of times an event happened in the past is used as the basis for assigning a probability to the event, this is Empirical probability.

If the events are mutually exclusive, special additional rules can be applied. -Additional general rules can be used if the events are not mutually exclusive. Events A and B must be mutually exclusive.

If the occurrence of one event is not completely affected by the occurrence of another event, such an event is probabilistically called an independent event, and the event affected by another event is a dependent event. Is called dependent events.

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The utilization rate is 83.33

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

An average of 10 cars per hour are expected to arrive according to a Poisson distribution. They will be served at an average rate of 12 cars per hour, with exponential service times,

Then, the utilization rate is 83.33.

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Hence, the required algebraic expression is 8([tex]x^2[/tex]+4x+4) + 17 -32

expression is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.). This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/Variable, Math Operator, Number/Variable)

We were given y = 8[tex]x^2[/tex]+32x+17

To convert to vertex form, We factor out the leading coefficient which is 8.

Next, we form a perfect square by adding and subtracting 32 to get,

[tex]y=8(x^2+4x)+8(4)+17-8(4)[/tex]

We factor and combine the first two terms with a common factor of 8

This simplifies to,

              8([tex]x^2[/tex]+4x+4) + 17 -32

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Answer:

Answer is y = 8(x2 + 4x +

4

) + 17 +

-32

Step-by-step explanation:

Work Shown:

[tex]b^2 = a^2 + c^2 - 2*a*c*\cos(B)\\\\b^2 = 150^2 + 30^2 - 2*150*30*\cos(150)\\\\b^2 \approx 31194.22863406\\\\b \approx \sqrt{31194.22863406}\\\\b \approx 176.618879608211\\\\b \approx 176.6\\\\[/tex]