Sam rents a truck from a hire company.
The cost to rent the truck is directly proportional to the number of kilometres driven.
The rental cost to drive 200 km is $87.50.
What is the rental cost to drive 80 kilometres?

1. Definition of Congruence:∠ RSU ≅ ∠ VST

2. Definition of Congruence: m∠ RSU = m∠ VST

3. Angle Addition Postulate: m∠ RSU + m∠ USV = m/RSV

4. Angle Addition Postulate: m∠ VST + m∠  USV = m∠ UST

5. Transitive Property: m∠ RSU + m∠ USV = m∠ UST

6. Substitution Property: m∠ RSV = m∠ UST

7. Definition of Congruence: ∠ RSV ≅ ∠ UST

In mathematics, a relation R on a set X is said to have a transitive property if, for all elements a, b, c in X, whenever R relates a to b and b to c, then R also relates a to c.

This is shown in the case of number 6 where :

m∠ RSU + m∠ USV = m∠ UST

The transitive property is also shown in  equality states where all values of a, b, and c, if a = b, and b = c, then a = c.

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Answer:

A. Sample space: 1, 2, 3, 4, 5, 6

D. P(6) = 1/6

Step-by-step explanation:

Option B and C are not possible because the probability of rolling any particular number on a fair six-sided cube is always 1/6. Option E describes the outcomes of 10 trials, which is not the probability model.

Answer:

To determine the best time of day to air the advertisement and which drink to focus on, we can look at the two-way tables provided.

First, let's look at the table that shows the percentage of customers who ordered coffee or tea based on the time of day:

Coffee Tea

Morning 80% 20%

Afternoon 60% 40%

Evening 40% 60%

Late Night 90% 10%

From this table, we can see that the majority of customers order coffee, regardless of the time of day. However, in the evening and late night, there is a higher percentage of customers who order tea. This could be because customers are looking for a warm and relaxing beverage before bed.

Next, let's look at the table that shows the percentage of customers who visit the coffee shop based on the time of day:

Morning Afternoon Evening Late Night

Percentage 20% 30% 35% 15%

From this table, we can see that the highest percentage of customers visit the coffee shop in the evening, followed by the afternoon. This suggests that airing the advertisement in the evening would reach the largest audience.

Based on these two-way tables, my recommendation would be to focus on coffee in the advertisement since it is the most popular drink overall, and to air the advertisement in the evening when the most customers visit the coffee shop. However, it may also be worth including a mention of tea in the advertisement, especially for the evening and late-night crowds.

Step-by-step explanation:

mark brainlist!

Answer: The relative frequency table for rows shows that a larger percentage of people are night owls and drink coffee. The same results are shown in the relative frequency for columns table. So, it would be best to air the advertisement at night and focus on coffee.

Step-by-step explanation:

From the equation 2tanx - 1 = 0, we can find the value of tangent of x as follows:

2tanx - 1 = 0

2tanx = 1

tanx = 1/2

x = arctan(1/2) + nπ, where n is an integer

Now we need to solve √5cosx+4/sin2x, given that cos(x) < 0.

Since cos(x) < 0 and tan(x) = sin(x)/cos(x) = 1/2, we can use the Pythagorean identity to find sin(x):

sin^2(x) + cos^2(x) = 1

sin^2(x) + (-cos(x))^2 = 1

sin^2(x) = 1 - cos^2(x)

sin(x) = -√(1 - cos^2(x))

Substituting this into the expression we want to evaluate:

√5cos(x) + 4/sin^2(x) = √5cos(x) + 4/(-√(1 - cos^2(x)))^2

= √5cos(x) + 4/(1 - cos^2(x))

To simplify this expression further, we can use the identity sec^2(x) = 1 + tan^2(x) to find cos^2(x):

sec^2(x) = 1 + tan^2(x)

1/cos^2(x) = 1 + (1/2)^2

1/cos^2(x) = 5/4

cos^2(x) = 4/5

cos(x) = ±2/√5

Since cos(x) is negative, we have cos(x) = -2/√5.

Substituting this value into the expression we want to evaluate:

√5cos(x) + 4/(1 - cos^2(x)) = √5(-2/√5) + 4/(1 - (-2/√5)^2)

= -2 + 4/(1 - 4/5)

= -2 + 20

= 18

Therefore, the solution to √5cos(x) + 4/sin^2(x) given 2tan(x) - 1 = 0 and cos(x) < 0 is 18.

The characteristic of an experiment where the binomial probability distribution is applicable is that exactly two outcomes are possible on each trial.

What is the binomial probability distribution?

The binomial probability distribution is a probability model that is used to evaluate the probability of having an exact number of successes in a particular number of independent trials that have two possible outcomes (success and failure).

The characteristics of an experiment where the binomial probability distribution is applicable are as follows: It is an experiment that comprises a set of trials with a fixed number of independent trials.

It has only two outcomes, namely success and failure. The trials are independent of each other.

The probability of success is constant for each trial of the experiment.

The binomial distribution has a discrete set of outcomes. Each of these outcomes is measured by a single random variable that takes on only one of two possible values. Exactly two outcomes are possible on each trial. The experiment is a random variable that can be counted by counting the number of successes (X) in n trials.

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Answer: x=120

Step-by-step explanation:

If it is a regular polygon then the sum of internal angles is 180 degrees. Each angle should be 60. Since a straight line is 180, 180 - 60 would equal x!

Answer: 120

Step-by-step explanation: A triangle has a sum of 180°. A regular polygon has equal angles, so you divide 180 by 3, getting 60. Next x is supplementary to the adjacent angle, so you must do 180-60, yielding 120° as x.

It will take approximately 2.5 years  for the investment to be worth £2000.

To solve this problem, we can use the formula for compound interest:

[tex]$A = P(1 + r/n)^{nt}$[/tex]

where:

A is the amount of money after t years

P is the principal amount (the initial investment)

r is the annual interest rate (as a decimal)

n is the number of times the interest is compounded per year

t is the number of years

We can rearrange this formula to solve for t;

[tex]$t = \frac{\log(A/P)}{\log(1 + r/n)}\div n$[/tex]

Substituting the given values, we get;

[tex]$t = \frac{\log(2000/1800)}{\log(1 + 0.04/1)}\div 1$[/tex]

Simplifying, we get:

[tex]$t = \frac{\log(1.11111)}{\log(1.04)}\approx 3.03[/tex][tex]$t = \frac{\log(1.11111)}{\log(1.04)}\approx 2.69[/tex] years

Therefore, it will take approximately 2.5 years  for the investment to be worth £2000.

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Complete question:

1800 is invested at 4% compound intreast per year

Answer: a) 19 degree

b) 71degree

Step-by-step explanation:

To complete the table of values that satisfy the equation 2d + 4t = 24, we can choose different values of d and then solve for t.

Alternatively, we can choose different values of t and then solve for d. Here is one possible table of values that satisfy the equation:

d t

0 6

2 4

4 3

6 0

To obtain these values, we can substitute each value of d into the equation and solve for t. For example, when d = 0, we have:

2d + 4t = 24

2(0) + 4t = 24

4t = 24

t = 6

Thus, when d = 0, t = 6 satisfies the equation. Similarly, we can obtain the other values in the table by choosing different values of d and solving for t.

Therefore, the table of values that satisfy the equation 2d + 4t = 24 is:

d t

0 6

2 4

4 3

6 0

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Using the equation 0.1x = 44, the total number of cards sold for Mother's Day was 440.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let's call the total number of cards sold for Mother's Day "x".

We know that one salesman sold 10% of these cards. or

Converting the percentage to decimal = 10 / 100 = 0.1

So, 0.1x, is equal to 44 cards.

We can set up an equation to solve for x -

0.1x = 44

To isolate x, we can divide both sides of the equation by 0.1 -

x = 440

Therefore, the total number of cards sold for Mother's Day was 440.

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The height of the rectangular prism of aquarium is 8 inches.

A right rectangular prism is a six-sided, three-dimensional geometric figure. The term "rectangular parallelepiped" is another name for it. Three pairs of congruent faces, each pair of which is parallel to the other, make up a right rectangular prism. In addition, it contains four vertices and three pairs of congruent edges. In a right rectangular prism, the opposing faces are parallel and congruent rectangles, and the angles separating the faces are all right angles. Multiplying the prism's length, width, and height yields the volume of a right rectangular prism.

Given that, the length is 19 in and width is 9 in and it can hold 1368 cubic inches of water.

The volume of a rectangle is given as:

V = lwh

Substitute the values:

1368 = 19(9)(h)

h = 1368/(19*9) ≈ 8 inches

Hence, the height of the rectangular prism of aquarium is 8 inches.

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Therefore , the solution of the given problem of circle comes out to be   option D 34 = 5.83.

A circle is formed by every region of a plane that is a certain distance from this extra spot (center). Thus, it is made up of curved areas that are spaced apart and divided by a surface. It also revolves equally it around centre from all directions. In a circular, limited double sphere, every pair of endpoints is uniformly separated from the "centre." By weaving a thread through a circle, one can create a line that leads to circular symmetry.

Here,

The following algorithm can be used to calculate the separation between two points:

=> d = √(x2 − x₁)² + (y2 − y₁)²

Here, a circle's centre is at (-2, 4), and a spot on the circle is at (3, 1). We thus have:

=> d = √(3 − (-2))² + (1 − 4)²

=> √(5)² + (-3)²

=> √25 + 9

=> √34 ≈ 5.83

As a result, 5.83 metres (or yards) is roughly how far the circular's centre is from the point on the circle. Therefore, the response is (D) 34 5.83.

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Given:-

[tex] \: [/tex]

[tex] \: [/tex]

Solution:-

[tex] \underline{ \: \sf{[a = 3.8] \: }}[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \textsf{put the value of a = 3.8}[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

[tex] \underline{ \sf \: [a = 7]\: }[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \textsf{ \: put the value of a = 7 \: }[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

[tex] \underline{ \sf{[a = -7.2]}}[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \textsf{ \: put the value of a = -7.2 \: }[/tex]

[tex] \: [/tex]

[tex] \: [/tex]

[tex] \: [/tex]

━━━━━━━━━━━━━━━━━━━━━━━

hope it helps! :)

Nοra has $8 saved, Helga has $28 saved, and Gertrude has $12 saved.

A ratiο is a way οf cοmparing twο quantities οr numbers by divisiοn. It is a relatiοnship between twο numbers that tells us hοw many times οne value is cοntained in the οther. Ratiοs can be written in different fοrms such as a:b, a tο b, οr a/b. In a ratiο, the first number is usually referred tο as the "antecedent" and the secοnd number is referred tο as the "cοnsequent".

Fοr example, if we have a ratiο οf 2:3, it means that the first number is twο-thirds οf the secοnd number. Ratiοs can alsο be simplified οr expressed in different units, but the relatiοnship between the twο quantities remains the same. Ratiοs are cοmmοnly used in many different areas οf mathematics, such as in geοmetry, prοpοrtiοn, and statistics.

Let x be the amοunt οf savings that Nοra has

Then, Helga has 7x/2 (since the ratiο οf Helga's savings tο Nοra's savings is 7:2)

And, Gertrude has 3/2x (since the ratiο οf Nοra's savings tο Gertrude's savings is 2:3)

We knοw that the sum οf their savings is $48, sο we can write an equatiοn:

x + 7x/2 + 3/2x = 48

Tο sοlve fοr x, we can first simplify the left side οf the equatiοn:

(2x + 7x + 3x)/2 = 48

12x/2 = 48

6x = 48

x = 8

Nοw that we knοw Nοra has $8 saved, we can find hοw much Helga and Gertrude have:

Helga has 7x/2 = 7(8)/2 = $28 saved

Gertrude has 3/2x = 3/2(8) = $12 saved

Therefοre, Nοra has $8 saved, Helga has $28 saved, and Gertrude has $12 saved.

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yοur investment in Cοrpοratiοn A will be wοrth $4000 after 5 years if it appreciates by $200 per year.

The functiοn A(t) that represents the amοunt that yοur investment in Cοrpοratiοn A will be wοrth after t years can be calculated using the fοllοwing fοrmula:

A(t) = 3000 + 200t

where 3000 is the initial investment and 200t represents the appreciatiοn οf the investment after t years.

Fοr example, if yοu want tο knοw hοw much yοur investment in Cοrpοratiοn A will be wοrth after 5 years, yοu can plug in t=5 intο the fοrmula:

A(5) = 3000 + 200(5) = 4000

Sο, yοur investment in Cοrpοratiοn A will be wοrth $4000 after 5 years if it appreciates by $200 per year.

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Parker is wrong, as the volume of the cube container is obtained as [tex]\frac{1}{512} t^9u^{12}[/tex].

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The volume of a cube is given by the formula V = s³, where s is the length of one side of the cube.

In this case, the length of the container is given as [tex]\frac{1}{8} t^3u^4[/tex].

To find the volume of the cube, we need to cube this length -

[tex]V=\big(\frac{1}{8} t^3u^4\big)^3[/tex]

Simplifying this expression using the rules of exponents, we get -

[tex]V=\big(\frac{1}{8}\big)^3 \times (t^3)^3 \times (u^4)^3[/tex]

[tex]V =\frac{1}{512} t^9u^{12}[/tex]

So, the actual volume of the container is [tex]\frac{1}{512} t^9u^{12}[/tex], not [tex]\frac{1}{12} t^9u^{12}[/tex] as Parker said.

Therefore, Parker is incorrect.

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Answer:

3 students will retake the test

Step-by-step explanation:

20% of 150 students is 30

(20÷100)×150=30 students

Now we need to find the 10% of the 30 students who failed.

(10÷100)×30=3 students

we can check this by Subtracting that 20% who failed from 100%(the total in class). So that will be 80%. Now that 80% is the number of students who passed.

And in order to find the number of students who passed we say:

(80÷100)×150= 120

all you need to do now is, subtract that 120 from 150, then find the 10% of the answer.

The potential rational root of a polynomial f(x) at point p is the value of x for which the result of evaluation of f(x) at that point is zero.

A potential rational root of a polynomial f(x) at point p is a value of x where the result of evaluation of f(x) at that point is zero. By Rational Roots Theorem To find a potential rational root of a polynomial f(x), we first factorize f(x) into its factors and then identify the factors which are of the form (x-p). The value of x for which the result of evaluation of f(x) at that point is zero, is the potential rational root of the polynomial f(x).

For example, consider a polynomial f(x) = x^3 + 4x^2 + 7x +2.

To find a potential rational root of this polynomial at point p, we factorize f(x) as follows:

f(x) = (x - 1)(x^2 + 5x + 2)

The factor (x - 1) is of the form (x-p) and hence, 1 is a potential rational root of the polynomial f(x). To verify that 1 is indeed a potential rational root, we evaluate f(1):

f(1) = 1^3 + 4(1^2) + 7(1) + 2

= 1 + 4 + 7 + 2

= 14

Since f(1) ≠ 0, 1 is not a rational root of the polynomial f(x).

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Complete question:

What is a potential rational root of the polynomial f(x) at the point p?

It is likely that it will take Jacob more time to plant the perennials than the annuals.

Time is an abstract concept that is not tangible and cannot be seen, touched, or heard. It is a measure of the passage of events and is used to set and track schedules, create goals, and even measure the lifespan of an individual. Time is a precious commodity that cannot be replaced or taken back. Once it has passed, it is gone forever. Time is also a powerful force that can bring us joy and sorrow, success and failure. It is a constant reminder of how quickly our lives can change and how important it is to make the most of every moment.

Perennials require more attention when planting because they have a longer lifespan and are meant to come back year after year. Annuals, on the other hand, only last for one season. Therefore, they require less attention when planting. Jacob will need to make sure that he carefully places the perennials in the soil, as well as taking care to not damage the roots. He may also need to take extra time to trim any overgrowth from the plants. This extra care and attention will likely take more time than it would to plant the annuals.

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The mathematician should expect to see the letter e appear 143 times in the 1,100 character email message.

It is a ratio of the count of the specific outcome or event to the total number of observations in the sample or population. Proportion is often expressed as a percentage or fraction and can be used to make inferences about the population based on the sample.

If the letter e appears 13 times out of the first 100 characters, we can assume that the proportion of e's to the total characters is constant throughout the entire message.

Let x be the number of times the letter e appears in the 1,100 character message. Then, we can set up a proportion:

13/100 = x/1100

Solving for x, we get:

x = (13/100) * 1100 = 143

Therefore, the mathematician should expect to see the letter e appear 143 times in the 1,100 character email message.

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Therefore , the solution of the given problem of function comes out to be

a.(5, 7) ,b.(4, 5). and c. (1, 2).

The midterm exam covers a wide range of topics, including building, geometry, integers, ones personal divisions, and both actual and hypothetical geographic locations. A work describes the relationships between different elements that all variable cooperate to create the same outcome. A utility is composed of numerous unique elements that work together to produce unique outcomes for each input.

Here,

(a) On the intervals (2, 4) and, the function is growing (5, 7).

(b) On the intervals (0, 2) and (c), the algorithm decrements (4, 5).

(c) On intervals (0, 1) and, the function is constant (1, 2).

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Answer: False= Your speed is 135 mph

Step-by-step explanation:

The graph shows you have traveled 90 miles in 1.5 hours.

90miles * 2/3 = 60miles

1.5hours * 2/3 = 1 hour

1 hour : 60 miles = 60mph NOT 135mph

Answer:

Step-by-step explanation:

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The height of the parallelogram is the same as the height of the trapezoid

Why?

Doubling the trapezoid and then halving the resulting area

As was true with the triangle,  but its base is the sum of the two bases of the trapezoid.

The answer of the given question based on scatterplot and line the answer is, the line of best fit, Maria will reach 10,000 songs in 17 months.

A equation is statement that two expressions are equal. It typically involves one or more variables, which are values that can vary or change. The expressions on either side of equal sign are referred to as  left-hand side (LHS) and right-hand side (RHS) of  equation.

First, let's find the equation of the line of best fit. The line appears to pass through the point (6, 6000) and the point (12, 9800). use the two points to find  slope:

slope = (change in y)/(change in x) = (9800-6000)/(12-6) = 800 songs/month

Now we can use the point-slope form of the equation of a line to find the equation of the line of best fit:

y - 6000 = 800(x - 6)

Simplifying, we get:

y = 800x - 3600

To find when Maria will reach 10,000 songs, we can set y = 10,000 and solve for x:

10,000 = 800x - 3600

13,600 = 800x

x = 17

So according to the line of best fit, Maria will reach 10,000 songs in 17 months.

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The concepts of additive relationship and multiplicative relationship are given as follows:

An additive relationship exists when the change in one variable corresponds to a fixed change in another variable. For example, if the cost of buying a certain number of apples is $10, and the cost of buying twice as many apples is $20, then we have an additive relationship between the number of apples purchased and the cost.

On the other hand, a multiplicative relationship exists when the change in one variable corresponds to a fixed multiple of another variable. For example, if the interest earned on a bank account is proportional to the amount of money in the account, then we have a multiplicative relationship between the interest earned and the amount of money in the account.

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Answer:

8 burgers and 8 french fries

Step-by-step explanation:

8x+2y=80

x=8

y=13

8x8=64

80-64=16

16/2=8

to get the equation of any straight line, we simply need two points off of it, let's use those two in the picture below

[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{7}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{7}-\stackrel{y1}{5}}}{\underset{\textit{\large run}} {\underset{x_2}{4}-\underset{x_1}{2}}} \implies \cfrac{ 2 }{ 2 } \implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{ 1}(x-\stackrel{x_1}{2}) \\\\\\ y-5=x-2\implies {\Large \begin{array}{llll} y=x+3 \end{array}}[/tex]

The first quartile is 6, the median is 7.5 and the third quartile is 8.5. The box plot has been attached below.

What is a median?

A data set can be described more accurately than its average by using the median, which is the midpoint of an ordered, ascending or descending list of integers.

The data is given as 5.5, 6, 6, 6.5, 7, 7.5, 8, 8, 8.5, 9, 9.

From this, we get the first quartile to be 6.

The median is 7.5 and the third quartile is 8.5.

The box plot of the data has been plotted and attached below.

Hence, the required solution has been obtained.

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Question: There are 11 dancers in a performance. Their ages (in years) are: 5.5, 6, 6, 6.5, 7, 7.5, 8, 8, 8.5, 9, 9.

1. Determine the first quartile, median, and third quartile of the dancers' ages.

2. Drag the movable points to label them on the box plot.