Arc length calculations Find the arc length of the following curves on the given interval.y=1/3 x^(3/2) on [0,60]

Here, given the equation in the question, we want to make y the subject of the formula;

Answer:

Step-by-step explanation:

The expression f - 5(2f – 3) is equivalent to two other expressions, option (a) -11f-3 and option (b) -11f + 15.

In mathematics, an expression is a combination of symbols, operated on by certain mathematical operations to create a numerical value or a function.

To understand why this is the case, let's break down the expression.

The first part of the expression is just the variable f, so that is unchanged. The second part involves the multiplication of -5 and (2f – 3).

To evaluate this part, we need to use the order of operations. First, we multiply -5 and 2f and get -10f.

Then, we subtract 3 from this result and get -11f.

Therefore, the expression f - 5(2f – 3) is equivalent to -11f-3 and -11f + 15.

Therefore, the correct options are both (a) and (b).

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Complete Question:

Which expressions are equivalent to - f - 5(2f – 3)?

Choose all answers that apply:

a) -11f-3

b)-11f + 15

c) None of the above​

Answer:

x=7

Step-by-step explanation:

11+3=14, x+x=2x, divided by two, x=7

Answer:

y = 1/2x - 2.5

Step-by-step explanation:

(15, 5) and (42, 18.5)

Slope:

m=(y2-y1)/(x2-x1)

m=(18.5 - 5)/(42 - 15)

m = (13.5)/27

m = 1/2

y - y1 = m(x - x1)

y - 5 = 1/2(x - 15)

y - 5 = 1/2x - 7.5

y = 1/2x - 2.5

Answer:

2   or    1/2

Step-by-step explanation:

change in y over change in x

you didnt define what what x and what was y so ill provide both answers and you can figure which is correct

42-15/18.50-5   =27/13.5   =2

18.50-5/42-15    =13.5/27  =1/2

S(-5;3) Q(-2;2) R(-3;-2) T(-6;-1)

When reflected over the y-axis, their x values will change sign

S(5;3) Q(2;2) R(3;-2) T(6;-1)

Translate 3 units to the right, their x values will increase by 3

S(8;3) Q(5;2) R(6;-2) T(9;-1)

A 3unit shifted graph shifted is shown in the figure

Suppose the graph is drawn on the coordinate plane.

Let the shifting be (x,y) → (x+a, y+b)

Then, add 'a' to all x coordinates of the graph's points. Add 'b' to all y coordinates of the graph's points.

The resultant set of new points will be plotted.

Given;

Coordinates to be shifted 3 units (-5,3) , (-2,2) (-3,-2)and (-6,-1)

shifting formula;

    (x,y)= (x+a, y+b)

here we have to shift only to the right side so only x coordinates will be affected

(-5+3,3) = (-2,3)

(-2+3,2) = (1,2)    

(-3+3,-2) = (0,-2)

(-6+3,-1) = (-3,-1)

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The probability the subscriber has cable service is : 0.1163

We have a information from the question:

There is a 0.24 probability the subscriber has a DVR player.

and, If the subscriber does not have cable service (e.g., has satellite service)

There is a 0.7 probability the subscriber has a DVR player.

Assume 75% of subscribers have cable service.

Now, According to the question:

Let A1 be the event subscriber has cable service and A2  subscriber does not have cable service

A1 and A2 are mutually exclusive and exhaustive

P(A1) = 0.75, P(A2) = 0.25

B = Subscriber has a DVD player

P(B/A1) =0.24 and P(B/A2) = 0.7

Probability for the subscriber does not have a DVR player

=> 0.75 × (1 - 0.24) + 0.25(1 - 0.7)

=> P(B') = P(A1B')+P(A2B') = 0.57 + 0.075 = 0.645

Hence, Required probability = P(A2/B') = P(A2B')/P(B)

=> 0.075/ 0.645

=> 0.1163.

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The given question is incomplete, complete question is:

If a television service subscriber has cable service, there is a 0.24 probability the subscriber has a DVR player. If the subscriber does not have cable service (e.g., has satellite service), there is a 0.7 probability the subscriber has a DVR player. Assume 75% of subscribers have cable service and answer the following for a randomly selected television service subscriber: If the subscriber does not have a DVR player, what is the probability the subscriber has cable service

Answer:

8.2857142857143

Step-by-step explanation:

Convert the mixed number to an improper fraction

134=1×4+34=74

Convert the fraction to a decimal through long division

We know that

74

is the same as

7÷4

Then using

Long Division for 7 divided by 4

gives us

=1.75

Our input equation has now become

14.50÷1.75=

14.50÷1.75=8.2857142857143

a) No, a single spray of 10 grams of butter would not be enough to entirely cover the area of 4 slices of toast at 2 meters. The area of 4 slices of toast is larger than the area of 1 slice of toast, meaning that it would require more butter than 10 grams to cover the entire area.

b) A single spray of 10 grams of butter would be enough to cover the area of 8 slices of toast at 3 meters.

c) These changes would affect the amount of butter on each piece of toast in that there would be more butter on each piece with a larger rack and further distance from the "butter gun".

d) At 5 meters from the gun, our up-and-coming chef would be able to spray 16 slices of toast with a single burst of 10 grams of butter. Each piece of toast would also have more butter than it would if it was sprayed at a closer distance.

e) To duplicate the original single-slice toast at 5 meters from the gun, the chef would need to reduce the amount of butter being sprayed. He could do this by simply reducing the distance between the gun and the toast rack.

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Complete question :

A harried chef can't keep up with his breakfast orders and decides to automate the process with a "butter gun." The gun provides a 10 gram burst of butter spray with each hit of the trigger. He starts with a rack that holds one piece of toast 1 meter away. The demand again exceeds supply and he realizes he can use the same gun to produce more toast by placing a larger rack at a greater distance. He finds that a four-slice rack works at a distance of 2 meters. Pleased with profits he carries the idea a step further and puts a holder 3 meters away, maintaining a 10 gram spray. See figure below.a) If 1 spray entirely covers the area of a single slice at 1 meter, can it entirely cover the area of 4 slices at 2 meters? Why or why not?b) How many slices can one spray cover with a 3 meter arragnement?c) How do these changes affect the amount of butter on each piece of toastd) Our up-and-coming chef moves the fun back to 5 meters. Predict how much toast he can spray and how much better each piece gets.e) Explain how he could duplicate the original single-slice toast at 5 meters from the gun.

Using the binomial probability function formula, the probability that the sample contains exactly 2 graduate students is 0.215.

The probability that the sample of 5 students contains exactly 2 graduate students using the binomial probability function can be determined by using the formula below:

P(X = k) = (n choose k) * p^k * (1 - p)^(n - k)

where n is the sample size, k is the number of successes, p is the probability of success, and (n choose k) = n! / (k! * (n - k)!) denotes the number of ways to choose k items from a set of n items.

Using the formula above and the information given, the probability of the sample containing exactly 2 graduate students can be calculated as follows:

P(X = 2) = (5 choose 2) * (0.32)² * (1 - 0.32)^(5 - 2) = 0.215

Where (5 choose 2) = 5! / (2! * (5 - 2)!) = 10 is the number of ways to choose 2 graduate students from a sample of 5 students.

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Answer:

undefined

Step-by-step explanation:

line is straight up and down

Answer:

Undefined. It ends up being 3/0 which can't happen so it remains undefined.

Step-by-step explanation:

Answer:

The bus travels at 48 miles per hour.

Step-by-step explanation:

It is given that:

Distance between school and house = 8 miles

Time taken by bus = 10 minutes = \(\frac{10}{60}=\frac{1}{6}\ hour\)

Speed of bus = \(\frac{distance}{time}\)

Speed of bus = \(\frac{8}{\frac{1}{6}}\)

Speed of bus = 8*6 miles per hour

Speed of bus = 48 miles per hour

Therefore,

The bus travels at 48 miles per hour.

Answer:

f(-4)=7

Step-by-step explanation:

If you input the x as -4, you just add - to -3, which equals -7. The equation wants the absolute value of it, so the answer would be 7.

Explanation:

Two lines are parallel if they have the same slope. The given line y = -3x - 2 is in slope-intercept form (y = mx + b) where the slope is -3. Therefore, any line with a slope of -3 will be parallel to this line.

Examples

\(y =-3x+2\)

\(y=-3x-4\)

Answer:

.71

Step-by-step explanation:

We only need to look at the brown eyes row

2+2+10 =14

Brown hair is 10

P(brown hair) = brown hair / total

                        =10/14 =5/7 = .714285714

Answer:

Step-by-step explanation:

12/100 × 20000

= 2400

Price customer must pay = 20,000+ 2400 = 22400.

If price of a machine is given as GHC 20,000 plus VAT. If the VAT rate is 12%. Then 22400 is the price that a customer must pay for the machine.

Percentage, a relative value indicating hundredth parts of any quantity.

Given,

The price of a machine is given as GHC 20,000 plus VAT

The VAT rate is 12%,

We need to find how much a customer has to pay for the machine..

12% is changed to decimal number by dividing with 100.

12/100=0.12

Now multiply 20000 with 0.12 to find 12% of 20000

0.12×20000=2400

Now we have to add 2400 with 20000 to get the cost of machine after adding VTA

20000+2400=22400

Hence 22400 is the price that a customer must pay for the machine.

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To find the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7, let's analyze the given information.

The sum of the second term (s2), fifth term (s5), and seventh term (s7) themselves form an arithmetic sequence.

Let's denote the second term as a + 2d, the fifth term as a + 5d, and the seventh term as a + 7d, where 'a' is the first term and 'd' is the common difference.

Using the arithmetic sequence formula for the sum of terms, we have:

s2 = (2/2) * (2a + (2-1)d) = 2a + d

s5 = (5/2) * (2a + (5-1)d) = 5a + 6d

s7 = (7/2) * (2a + (7-1)d) = 7a + 12d

Since the sums s2, s5, and s7 themselves form an arithmetic sequence, we can express their differences:

s5 - s2 = (5a + 6d) - (2a + d) = 3a + 5d

s7 - s5 = (7a + 12d) - (5a + 6d) = 2a + 6d

Now, equating the differences, we have:

3a + 5d = 2a + 6d

Simplifying the equation, we find:

a = d

Therefore, the common difference for the arithmetic sequence formed by the series sums s2, s5, and s7 is 'd'.

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Answer:

The estimated answer would be 9

Step-by-step explanation:

The answer I received in the calculator was 8.94422. Since the tenths, place value(9) is closer to 9.0 than 8.0, we round up. I hope this helps you.

This is an example of a hypothesis. A hypothesis is an educated guess or prediction about the relationship between variables based on prior knowledge or experience.

In this case, the marketing researcher has formed a hypothesis that increasing the advertising budget by $100,000 will result in a 5% increase in local profits in St. Louis over the next three months. This hypothesis can be tested through further research and data analysis to determine if it is supported by the evidence.

A hypothesis is a statement that proposes a potential relationship between two or more variables. It is often used in scientific research to provide a starting point for further investigation and to guide the development of experiments or studies. In the example you provided, the marketing researcher has formed a hypothesis that increasing the advertising budget by $100,000 in St. Louis will result in a 5% increase in local profits over the next three months.

The purpose of forming a hypothesis is to make predictions about what might happen in a certain situation based on prior knowledge or experience. In this case, the marketing researcher may have observed similar trends in the past or may have data to support their belief that increasing the advertising budget will lead to increased profits. The hypothesis provides a clear direction for the research, as the researcher can now design and conduct studies to test the hypothesis and see if it is supported by the evidence.

If the results of the studies support the hypothesis, it provides evidence that there is a relationship between advertising budget and local profits, and the researcher can make recommendations to the company to increase advertising budget in order to increase profits. On the other hand, if the results do not support the hypothesis, the researcher may need to revise the hypothesis or come up with a new one to explain the results.

In conclusion, a hypothesis is a critical component of the scientific research process, as it provides a starting point for further investigation and helps guide the development of studies

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we can conclude that ∠1 ≅ ∠3 and ∠2 ≅ ∠4, which is the desired conclusion.

What is a triangle ?

Triangle can be defined in which it consists of three sides, three angles and sum of three angles is always 180 degrees.

In the given image, we can see that two lines intersect at point P. Let's call them line l and line m.

Statement: Vertical angles are congruent

∠1 ≅ ∠3 and ∠2 ≅ ∠4

Definition of vertical angles: Vertical angles are formed by two intersecting lines and are opposite to each other. In the given diagram, ∠1 and ∠3 are vertical angles, and ∠2 and ∠4 are vertical angles.

When two lines intersect, they form two pairs of vertical angles.

By the Vertical Angles Theorem, vertical angles are congruent. This means that ∠1 is congruent to ∠3, and ∠2 is congruent to ∠4.

Therefore, we can conclude that ∠1 ≅ ∠3 and ∠2 ≅ ∠4, which is the desired conclusion.

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The grapefruit juice contains 0.001 times (or 0.1%) the hydrogen ion concentration of the tomato juice. In other words, the grapefruit juice is 10 times more acidic than the tomato juice.

The pH scale is a logarithmic scale that measures the acidity or alkalinity of a solution. Each unit on the pH scale represents a tenfold difference in acidity or alkalinity. A lower pH value indicates a higher acidity, while a higher pH value indicates a higher alkalinity.

Given:

pH of grapefruit juice = 3

pH of tomato juice = 4

The pH of grapefruit juice is lower than the pH of tomato juice, which means grapefruit juice is more acidic than tomato juice. To determine the difference in acidity between the two juices, we can compare the hydrogen ion concentration (H+) in each solution.

The formula to calculate the hydrogen ion concentration from the pH value is:

\([H+] = 10^{-pH}\)

For grapefruit juice:

[H+] = 10⁻³

For tomato juice:

[H+] = 10⁻⁴

Now, let's calculate the hydrogen ion concentration for each juice:

[H+] in grapefruit juice = 10⁻³ = 0.001

[H+] in tomato juice = 10⁻⁴ = 0.0001

Therefore, the grapefruit juice contains 0.001 times (or 0.1%) the hydrogen ion concentration of the tomato juice. In other words, the grapefruit juice is 10 times more acidic than the tomato juice.

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Your total vacation budget would be $280, considering the $160 spent on groceries and the estimated cost of eating out 3 times at $40 per meal from linear equation concept.

For your vacation at the beach, you have already spent $160 on groceries for the week. In addition, you anticipate spending $40 each time you eat out.

To determine your overall budget for the vacation, you need to consider how many times you plan to eat out during the week. Let's say you plan to eat out 'x' number of times.

Since each time you eat out costs $40, the total amount spent on eating out can be represented by the equation:

Total spent on eating out = $40 * x

Adding this to the amount spent on groceries, the total vacation budget can be calculated as:

Total budget = Amount spent on groceries + Total spent on eating out

Total budget = $160 + ($40 * x)

For example, if you plan to eat out 3 times during the week, the calculation would be:

Total budget = $160 + ($40 * 3)

Total budget = $160 + $120

Total budget = $280

In this case, your total vacation budget would be $280, considering the $160 spent on groceries and the estimated cost of eating out 3 times at $40 per meal.

The total budget will vary depending on the number of times you plan to eat out. By adjusting the value of 'x', you can calculate the specific total budget for your vacation.

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Answer:

Below.

Step-by-step explanation:

(1/3)X = 849

x = 849*3 = 2547

The total pay per month of an operator is equal to $2547.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that an operator in the plant receives a monthly salary. His rent, which is $849, takes up exactly 1/3.

The total monthly salary will be calculated as,

(1/3)X = 849

X = 849 x 3

X= 2547

Therefore, the total pay per month of an operator is equal to $2547.

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Answer:

5.507605086

5.50

Step-by-step explanation:

Answer:

none of those answers are correct unless u mean 5 and 3/4

Step-by-step explanation:

Answer:

C

Step-by-step explanation: