Please, someone, help me?

Please, Someone, Help Me?

Answers

Answer 1

The equation that represents the total amount is y = 50(4+x).

What is Equation:

The mathematical statement that shows two mathematical terms have equal values is known as an equation. An equation simply states that two things are equal.

Equations contain both constant terms and algebraic terms which are combined by operations like Adding and subtraction etc.

Here we have

An electrician charges a callout fee of $ 200 and $ 50 per hour

Given that the total amount charged is y for x hours

As we know the electrician charges $ 50 per hour

=> The charge per x hours = 50x

And callout fee = $ 200

The equation that represents the above situation is

=> y = 200 + 50x

=> y = 50(4+x)

Therefore,

The equation that represents the total amount is y = 50(4+x)

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Related Questions

Can someone help me with this?

Answers

omgggg thats what she said

Can you help me with this

2. Natalie is selling candles to raise money for her softball team. The team has two different options for selling the candles. The first option is to sell a package of 5 candles for $18. The second option is to sell individual candles for $4 each.
(a) The team wants to earn $1404. How many candles do the members need to sell if they sell candles only in packages? How many candles do they need to sell if they sell only single candles? Explain your answer using an equation for each situation.
(b) Describe at least one advantage of selling the candles in packages. Describe at least one disadvantage of selling the candles in packages

Answers

a) The amounts that the team needs to sell is given as follows:

Packages: 390 candles.Single candles: 351 candles.

b) The advantage and disadvantage is given as follows:

Advantage: Better opportunity cost when a person needs one candle, the person will have to purchase the entire package.Disadvantage: Lower revenue per candle.

How to obtain the amounts?

The amounts needed are found applying the proportion, considering the costs and the number of candles.

A package of 5 candles for $18, hence the number of candles needed to earn $1404, in packages, is given as follows:

5 candles - $18

n candles - $1404

Applying cross multiplication, we have that:

18n = 5 x 1404

n = 5 x 1404/18

n = 390 candles.

With a single candle, the number of candles is calculated as follows:

1404/4 = 351 candles.

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Two sides of a triangle are 17 and 53. The third side is?

Answers

Answer:

the answer would be e because you can't determine the side length

Answer: (B)

Step-by-step explanation:

Step 1: Find minimum values of the third side.

53-17 = 36

Step 2: Find maximum values of the third side.

17+53 = 70

Step 3: Find equation

36 < x < 70

[(6x2.99)-1] ÷2

Please help me

Answers

Answer: Answer is 8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2

16.94 / 2

8.47

Answer:

8.47

Step-by-step explanation:

[(6x2.99)-1] ÷2  16.94 /2 =8.47

Cathy was not watching her dog's eating habits and his weight went from 40 pounds to 48
pounds. By what percentage did the dog's weight increase?

Answers

Answer:

Step-by-step explanation:

To find the percentage increase in the dog's weight, you can use the following formula:

percentage increase = (final value - initial value) / initial value x 100%

In this case, the initial value is 40 pounds and the final value is 48 pounds, so the percentage increase is:

percentage increase = (48 - 40) / 40 x 100% = 8 / 40 x 100% = 20%

Therefore, the dog's weight increased by 20%.

A vector field F is shown. Use the interpretation of divergence derived in this section to determine whether div F is positive or negative at P_1 and at P_2.a. div F is negative at both P_1 and P_2. b. div F is positive at P_1 and negative at P_2. c. div F is positive at both P_1 and P_2. d. div F is negative at P_1 and positive at P_2.

Answers

As pre the concept of vector, div F is negative at P1 and divF is positive at P2.

In math the term vector refers the quantity that has both magnitude and direction but not position

Here we have to determine whether div F is positive or negative at P1 and at P2.

Let us consider if  div F(P)>0, the net flow is outward near P and P is called a source and if  div F(P)<0, the net flow is inward near P and P is called a sink.

Here by observing the graph of F, we have identified that the vectors end near the P1 are the larger than the vectors starts near the point P1,

So, the net flow is inward near P1 and div F is negative at P1

Where P1 is called a sink

Whereas, by observing the graph of F we have identified that the vectors end near P2 are shorter than the vectors starts near the point P2,

So, the net flow is outward and div F   is positive at P2 and the P2 is called a source

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help help help help plsssss

Answers

Answer:true, false, false, true

Step-by-step explanation:

A local entrepreneur would like to know if those who live in an urban or rural community are more likely to buy a real Christmas tree. He takes a random sample of 100 people who reside in the city and a separate random sample of 100 people who live in the village and asks them if they buy a real tree at Christmas time. Of the urban participants, 22 buy a real tree. Of the rural participants, 28 buy a real tree. Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree, and let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree. What is the p-value?
.32
.16
.07
.18

Answers

The value of p is 0.16. So the option b is correct.

A local entrepreneur takes a random sample of 100 people.

Of the urban participants, 22 buy a real tree.

Of the rural participants, 28 buy a real tree.

Let p1 = the proportion of all people who live in rural communities and buy a real Christmas tree.

Let p2 = the proportion of all people who live in urban communities and buy a real Christmas tree.

We have to find the p-value

p1 = X1/N1

p1 = 28/100

p1 = 0.28

p2 = X2/N2

p2 = 22/100

p2 = 0.22

p = (X1 + X2)/(N1 + N2)

p = (28+22)/(100+100)

p = 0.25

Below are the null and alternative Hypothesis,

Null Hypothesis, H0: p1 = p2

Alternate Hypothesis, Ha: p1 > p2

Test statistic

z = (p1 - p2)/√(p*(1-p)*(1/N1 + 1/N2))

z = (0.28-0.22)/√(0.25*(1-0.25)*(1/100 + 1/100))

z = 0.9798

P-value Approach

P-value = 0.16

Hence, the option A is correct. 0.16 is the p-value.

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19
Select the correct answer.
What is the solution to this equation?
log₃(4 x)-2log₃ x=2
A. 1/36
B. 9/4
C. 4/9
D. 36

Answers

The answer is C. 4/9

Does the histogram appear to depict data that have a normal distribution? O A. The histogram appears to depict a normal distribution. The frequencies generally decrease to a minimum and then increase. O B. The histogram does not appear to depict a normal distribution. The frequencies generally increase and the histogram is roughly symmetric. O C. The hidtogram does not appear to depict a normal distribution. The frequencies generally decrease to a minimum and then increase, and the histogram is roughly symmetric. OD. The histogram appears to depict a normal distribution. The frequencies generally increase to a maximum and then decrease, and the histogram is roughly symmetric The table below shows the frequency distribution of the weights (in grams) of pre-1964 quarters. Frequency Weight (g) 6.000-6.049 6.050-6.099 6.100-6.149 6.150-6.199 6.200-6.249 6.250 6.299 6.300-6.349 6.350-6.399 Use the frequency distribution to construct a histogram. Does the histogram appear to depict data that have a normal distribution? Why or why not?

Answers

The histogram appears to roughly estimate a normal distribution. The frequencies normally increase to a maximum and then​ decrease, and the histogram is symmetric.

The Graph of Normal Distribution is bell-shaped. Here the value of y is less for the lower value of x and then the value of y is increased for a larger value of x, but after some time value of y again getting decreases as the value of x increases.

For the Histogram to appear to be a normal distribution, the graph of the histogram must have the same nature. Thus, option B is only the correct option.

The histogram is made up of many columns and bars that are vertical with no gaps between bars with different labels of numeric data of different heights showing the size of the group of different labels.

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Find the midpoint of the line segment with the given endpoints.

Answers

Answer

2x73

Step-by-step explanation:

Answer:

(11.5, 7.5)

Step-by-step explanation:

17 + 6 / 2 = 11.5

2 + 13 / 2 = 7.5

A train travels at 80 miles per hour. An equation can be written that compares the time (t) with the distance (d). What is the domain and range?

1. The domain is distance (d) and the range is time (t).

2. The domain is time (t) and the range is distance (d).

3. The domain is time (t) and the range is 80.

4. The domain is 80 and the range is time (t).

Answers

The required answer is the domain is time (t) and the range is a distance (d) i.e. Option 2.

What are domain and range?

The value range that can be plugged into a function is known as its domain. In a function like f, this set represents the x values f(x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

From the given question, and the above definition of domain and range,

the time (t) acts as an x-values or input value and the distance (d) acts as a y-value or output value

Hence, the domain is time (t) and the range is a distance (d) i.e. Option 2.

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Eli and Amy brought in 3 packs of stickers to give out to their two classes. They had enough for Mrs. O’s 21 students, Mrs. L's 24 students and even had 15 stickers left over! How many stickers were in each pack?

ill give brainliest semester ends tommorow

Answers

Answer: We can set up the equation 21 stickers/pack + 24 stickers/pack + x stickers/pack = 15 stickers.

We can solve this equation to find that x, the number of stickers in each pack, is equal to 6 stickers/pack. Answer: 6

Answer: 20

Step-by-step explanation:

24 + 21 = 45

45 + 15 = 60

60 / 3 = 20

If sin =−0.093 and 00 ≤ <3600, then what is to the nearest tenth of a degree?
A. 5.3⁰ or 174.7⁰
B. 185.3⁰ or 354.7⁰
C. 174.7⁰ or 185.3⁰
D. 2.2⁰ or 0.9⁰

Answers

There are two angles for the sine function such that sin θ = - 0.093: (i) 185.3°, (ii) 354.7°.

What are the approximate values of a trigonometric function?

In this problem we must determine two values of the angle of the sine function such that its result is - 0.093. According to the features of the trigonometric function, sine is negative for angles between 180° and 360°.

Since trigonometric functions are trascendent functions, we can only obtain approximate values of the angle by means of inverse trigonometric functions and numerical methods. There are two possible solutions:

sin⁻¹ - 0.093

θ₁ ≈ 185.336° or θ₂ ≈ 354.664°

θ₁ ≈ 185.3° or θ₂ ≈ 354.7°

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Refer to the above diagram. Economies of scale: A) are evident over the entire range of output. B) occur over the OQ range of output. C) begin at output 03. D) occur only over the

Answers

Economies of scale occur when average cost declines with an increase in output. This occurs up to output level Q1.

Diseconomies of scale occur when average cost increases with an increase in output. This begins at output level Q3.

The phenomenon known as economies of scale occurs when the size or magnitude of the production generated by a business increases while the average cost per unit of output decreases.

The Long Run Average Cost Curve demonstrates how a firm's average expenses change over time. The shift from point A to point B illustrates how the cost per unit decreases as the curve slopes down. Because of economies of scale, the average cost grows less proportionally to output over the downward sloping region of the curve.

Minimum efficient scale is the level of output where economies of scale have been fully exploited.

A competitive firm produces at the minimum point of ATC in the long run and thus achieves productive efficiency.

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The list shows the number of books read by the students in Ms. Alonzo’s class each week for two months.

25, 7, 13, 8, 22, 7, 13, 8

Which stem and leaf plot represents the same data?

Answers

stem                            leaf

0                               7, 7, 8, 8

1                                   3 , 3

2                                   5, 2

What is stem and leaf plot ?

A stem and leaf plot, also known as a stem and leaf diagram, arranges data in a way that makes it simple to see how often certain sorts of values occur. It is a graph that displays ordered numerical data. A stem and a leaf are divided into each piece of data.

A stem and leaf plot is shown as a customized table with the first or final digit of each data value divided into a stem and the remaining digit in a leaf. The stem and leaf plot key is the symbol " | " that is used to display stem and leaf values.

For instance, the stem and leaf plot key is used to represent 46 as 4 on the stem and 6 on the leaf.

in 2|5 , 2 is the stem side and 5 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

in 2|2 , 2 is the stem side and 2 is the leaf side

in 0|7 , 0 is the stem side and 7 is the leaf side

in 1|3 , 1 is the stem side and 3 is the leaf side

in 0|8 , 0 is the stem side and 8 is the leaf side

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let w represent the number of attempted experiments to get one experiment that is not successful. the random variable w has a geometric distribution with mean 4 and standard deviation 3.5. which of the following is the best interpretation of the standard deviation? responses a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments. a single value randomly selecte

Answers

The best interpretation of the standard deviation on this problem is given as follows:

A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.

How to interpret the standard deviation?

The standard deviation of a data-set is calculated as the square root of the sum of the differences squared between each observation of the data-set and the mean, divided by the number of observations in the data-set.

The interpretation of this calculation is that the standard deviation represents by how much each value of the distribution is expected to vary from the mean, on average.

This means that the correct statement is given as follows:

A single value randomly selected from the distribution of w will vary from 4 by 3.5 attempted experiments.

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use the intermediate value theorem to show that there is a root of the given equation in the specified interval.

Answers

To use the intermediate value theorem to show that there is a root of the given equation in the specified interval, we first need to find the values of the function at the two endpoints of the interval. Let's say the function is denoted by f(x) and the interval is [a, b].

If f(a) and f(b) have opposite signs (one is positive and the other is negative), then by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [a, b]. This is because the intermediate value theorem states that if a function is continuous on a closed interval and the function takes on different values at the endpoints of the interval, then there must be at least one point in the interval where the function takes on the value of the intermediate value between the two endpoints.

For example, suppose we have the equation f(x) = x^2 - 3 and we want to show that there is a root of the equation in the interval [1, 2]. We can evaluate the function at the two endpoints of the interval:

f(1) = 1^2 - 3 = -2

f(2) = 2^2 - 3 = 1

Since f(1) and f(2) have opposite signs, by the intermediate value theorem, there must be at least one root of the equation f(x) = 0 in the interval [1, 2]. To find the root, we can use a root-finding algorithm such as bisection or Newton's method.

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a service center receives an average of 0.7 customer complaints per hour. management's goal is to receive fewer than three complaints each hour. assume the number of complaints follows the poisson distribution. determine the probability that exactly four complaints will be received during the next eight hours.

Answers

The probability that exactly four complaints will be received during the next eight hours is 15.41%.

A discrete probability distribution called the Poisson distribution provides the likelihood that an event will occur a specific number of times over the course of a given period of time or location. The formula for this distribution is given by [tex]P(X=x)=\frac{e^{-\mu}\times \mu ^x}{x!}[/tex] where x is the number of successes, μ is the mean, and e is Euler's number.

Given n = 8 hours then, μ = 0.7n = 0.7×8 = 5.6.

Then, the probability that exactly four complaints are received is,

[tex]\begin{aligned}P(X=4)&=\frac{e^{-5.6}\times5.6^4}{4!}\\&=0.1541\end{aligned}[/tex]

The required answer is 15.41%.

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Please help me with this!

1) express the original claim in symbolic form

2) identify the null and the alternative hypotheses

Answers

The alternative hypothesis is often abbreviated as Ha or H1. When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < o

What is hypothesis?

A hypothesis is a theory put up to explain a phenomenon. A hypothesis must be testable according to the scientific method for it to be considered a scientific hypothesis. Scientists typically build their scientific ideas on prior observations that cannot be adequately explained by the current body of knowledge.

In statistics, the null hypothesis is usually denoted by letter H with subscript '0' (zero), such that H0. It is pronounced as H-null or H-zero or H-nought

At the same time, the alternative hypothesis expresses the observations determined by the non-random cause.It is represented by H1 or Ha.

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Reshawn read 25 pages of his book each day until he finished the book. His book was 400 pages long. Which sketch represents this solution

Answers

Graph (C) which has points (0, 400) and (16, 0) represent the solution to the given situation of Rashawn.

What is a graph?

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.

Graphs and charts are useful visual aids because they make information accessible and quick to understand.

Therefore, it is not unexpected that print and electronic media frequently use graphs.

When data is displayed as a graph rather than a table, it can often be easier to understand because the graph might show a pattern or comparison.

So, Rashawn consumed 25 pages of his book daily till it was finished. There were 400 pages in his book.

400 / 25 = 16 days is the estimated number of days he needs to finish the book.

He will have 400 pages finished in 0 days and 0 pages in 16 days.

As a result, the situation is represented by a graph with a line segment in the first quadrant.

Days are shown on the x-axis, and Pages left are listed on the y-axis.

The line segment's ends are (0, 400) and (16, 0).

Therefore, graph (C) which has points (0, 400) and (16, 0) represent the solution of the given situation of Rashawn.

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Complete question:
Rashawn read 25 pages of his book each day until he finished the book. His book was 400 pages long.

Which sketch represents this situation?

a) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 400 end ordered pair and begin ordered pair 25 comma 0 end ordered pair.

b) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 comma 16 end ordered pair and begin ordered pair 400 comma 0 end ordered pair.

c) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 400 end ordered pair and begin ordered pair 16 commas 0 ends ordered pair.

d) A graph in the first quadrant containing a line segment. The x axis is labeled Days and the y-axis is labeled Pages remaining. The endpoints of the line segment are begin ordered pair 0 commas 25 ends ordered pair and begin ordered pair 400 commas 0 ends ordered pair.

A fair coin is tossed 10 times. Find the probability of satisfying the condition that that the coin does not land on tails twice in a row

Answers

The probability of tossing 10 tails in a row is  [tex]\frac{1}{1024}[/tex]

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

Given that,

When a fair coin is tossed 10 times, the sample size (n) is:

n = [tex]2^{10}[/tex]

This is so because a fair coin has 2 sides.

So, we have:

n = 1024

There is only one occurrence of having 10 tails in a row in the 1024 possible outcomes.

So, the probability is:

P = [tex]\frac{1}{1024}[/tex]

Therefore,

The probability of tossing 10 tails in a row is  [tex]\frac{1}{1024}[/tex]

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silicone implant augmentation rhinoplasty is used to correct congenital nose deformities. the success of the procedure depends on various biomechanical properties of the human nasal periosteum and fascia. an article reported that for a sample of 20 (newly deceased) adults, the mean failure strain (%) was 26.0, and the standard deviation was 3.4.a. Assuming a normal distribution for failure strain, estimate true average strain in
a way that converys information about precision and reliability.
b. Predict the strain for a single adult in a way that conveys information about
precision and reliability. How does the prediction compare to the estimate
calculated in part (a)?

Answers

A true average strain in a way that converys information about precision and reliability (24.33, 27.67)

From given information we have:

the sample size n = 20

the mean failure strain x(bar) = 26.0

the standard deviation s = 3.4

Assuming a normal distribution for failure strain, we need to estimate true average strain in a way that converys information about precision and reliability.

A 95% confidence interval is necessary; other confidence intervals can be calculated in a similar way.

c = 0.95 or 95%

In the table with the critical values for t distributions in the appendix, locate the row beginning with degrees of freedom.

Here, the degree of freedom :

df = 20 - 1

df = 19

and  α = (1-c)/2

          = 0.025

To find the t-value:

t_(α/2) = 2.145

Therefore, the error margin is:

E = t_(α/2) × s/√n​

E = 2.145× 3.4/√19

E ≈ 1.67

And the confidence interval would be,

(x{bar} - E, x{bar} + E) = (24.33, 27.67)

Therefore, the confidence interval is: (24.33, 27.67)

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Jeremy has 3/4 pound of fish food if fish food is used to feed 24 fish how much food is there for each fish

Answers

Answer:

There is 1/32 pound food for each fish

Step-by-step explanation:

24 fish = 3/4 pound food

1 fish = (3/4)/24 pound food = 1/32 pound food

(Problem solved by using unitary method)

What is the slope-intercept equation for this line?

Answers

Answer:

y = -1/2x - 2

Step-by-step explanation:

y = mx+b, m = -1/2, and b (the y-intercept) is -2.

3. "Seventeen less than twice a number is -49."

Answers

Answer: the number is -16

Step-by-step explanation: if you add 17 to -49, you will get -32. you do this because it is 17 less than NOT more than. that would be called inverse operations. then, you divide that number by 2 to get -16. again, you use inverse operations because you are going backwards to try and find the number.

Answer: -16

Step-by-step explanation: So, to solve, we should write an equation. It should look like this:

2x - 17 = -49

So, using inverse operations, we would add 17 to - 49, which is -32, then divide that by 2, which would be -16. I hope this helped!

P.S. our new equation would look like 2(16) - 17 = -49

32-17 = 49

32 + -17 = 49

49 = 49

It checks out.

(a) Find a vector function, r(t), that represents the curve of intersection of the two surfaces.
The cylinder
x2 + y2 = 25
and the surface
z = xy
r(t)=??
(b)Find a vector function, r(t), that represents the curve of intersection of the two surfaces.
The paraboloid
z = 7x2 + y2
and the parabolic cylinder
y = 2x2
r(t)=???

Answers

(a) A vector function, r(t), that represents the cylinder x^2+y^2 = 25 and the surface z = xy.

(b) A vector function, r(t), that represents the paraboloid z = 7x^2 + y^2 and the parabolic cylinder y = 2x^2 is r(t) = <t, 2t^2, 7t^2+4t^4.

(a) We have to find a vector function, r(t), that represents the curve of intersection of the two surfaces.

The cylinder x^2+y^2 = 25 and the surface z = xy.

The given cylinder is x^2+y^2 = 25

We can write it as

x^2+y^2 = 5^2………………(1)

The given surface is z = xy………………..(2)

Let x = 5cost and y = 5sint, then x and y satisfy the equation 1

Now putting x=5cost and y=5sint in equation (2), we get

z = (5cost)(5sint)

z = 25sintcost

Now x=5cost, y=5sint and z=25sintcost

Hence, r(t) = <x(t),y(t),z(t)>

r(t) = <5cost, 5sint, 25sintcost>

(b) We have to find a vector function, r(t), that represents the curve of intersection of the two surfaces.

The paraboloid z = 7x^2 + y^2 and the parabolic cylinder y = 2x^2.

The given paraboloid z = 7x^2+y^2………………………(1)

The parabolic cylinder y = 2x^2……………………….(2)

Let x = t, then from equation 2

y = 2t^2

Now putting the value of x and y in equation (1)

z = 7t^2+(2t^2)^2

z = 7t^2+4t^4

Now x=t, y=2t^2 and z=7t^2+4t^4

Hence, r(t) = <x(t),y(t),z(t)>

r(t) = <t, 2t^2, 7t^2+4t^4>

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i need the answers please

Answers

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

What is the property of slopes of parallel lines and perpendicular lines?

If two lines are given and they are parallel to each other then the slopes are equal and for perpendicular lines, the product of their slopes is equal to -1.

(7) The line AB is passing through the points (-1, 5/2) and (3/2, -1/2).

   Slope = y2 - y2/x2 - x1

              = (-1/2 - 5/2)/(3/2-(-1))

              = -6/5

   As line AB and line CD are parallel in nature so the slope of line CD is also -6/5.

(8) The line AB is passing through the points (1/2, 1) and (5/2, 5/2).

    Slope = y2 - y2/x2 - x1

              = (5/2 - 1)/(5/2-1/2)

              =3/2/2

             = 3/4

    Line CD is passing through points (1, 1) and (2, 3).

    Slope = y2 - y2/x2 - x1

              = (3 - 1)/(2-1)

              =2/2

             = 1

  As the product of their slopes is not equal to -1.

  So lines are neither parallel nor perpendicular.

(9) Slope of AB can be computed as (-2, 1) and (-5, 5)

     Slope = 5 - 1/-5 + 2

                = 4/-3.

  The slope of line passing through the point P = -4/3 as we have to draw the parallel line.

 Point P = (-1, 3)

Equation of the line :

      y - 3 = -4/3(x + 1)

    3y +9 = -4x - 4

   3y = -4x - 13

Now we can draw the line

(10) Slope of line AB = -4/3

    So the slope of the line passing through point P should be 3/4 in order to be perpendicular to line AB.

     Equation of the line passing through point P:

       y - 3 = 3/4(x - (-1))

       y - 3 = 3/4(x+1)

Hence,

(7) Slope of line AB = -6/5 and Slope of the line CD = -6/5 and line AB and line CD are parallel in nature.

(8)Slope of line AB = 3/4 and the Slope of line CD = 1 and line AB and line CD is neither parallel nor perpendicular.

(9) We have drawn the graph passing through the point P and parallel to line AB.

(10)We have drawn the graph passing through the point P and perpendicular to line AB.

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Question
1/3 Marks
The prism shown has a volume of 35 cm³.
Work out h, the height of the triangular cross section.
h = Answ cm
13/27 Marks
+
hi
4 cm
7 cm

Answers

The height of the triangular cross section is equal to 2.5 cm.

How to calculate the volume of a rectangular prism?

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H or Volume = base area × length

Where:

L represents the length of a rectangular prism.W represents the width of a rectangular prism.H represents the height of a rectangular prism.

Next, we would determine the base area of this rectangular prism by using the formula for the area of a triangle:

Area of triangle = 1/2 × base area × height

Area of triangle = 1/2 × 4 × h

Area of triangle = 2h

Now, we can determine the height of this rectangular prism as follows;

Volume = base area × length

35 = 2h × 7

Height, h = 35/14

Height, h = 2.5 cm.

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Each of the 9 reindeer have 8 jingle bells on their collar. There are 12 more bells on the reins. How many bells in all?

Answers

Answer: 84 bells

Step-by-step explanation:

12 + 9x8

84

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