(2 points) Find an equation of the tangent line to the curve x = t^3 +4, y = t^4 – 5 at the point corresponding to t = 2. The tangent line has equation y =

Answer:

Attach a picture of the shape for the sides already known...

Step-by-step explanation:

The two schools will have an equal number of students enrolled in 21 years (3150 + 75(21) = 2475 + 60(21)).

The solution involves applying algebraic equation to find the unknown value.

The two high schools, Lincoln High School and Desert Mountain High School, have 3150 and 2475 students enrolled, respectively. Lincoln High School is estimating a decrease in enrollment at an average of 75 students per year. Meanwhile, Desert Mountain High School is expecting an increase of 60 students per year.

At these projected rates, the schools will have an equal number of students enrolled in 21 years.

To calculate the number of years that the two schools will have an equal number of students enrolled, you can use the formula:

L + 75x = D + 60x

Where L is the initial enrollment of Lincoln High School, D is the initial enrollment of Desert Mountain High School, and x is the number of years.

Substituting the given values, we get:

3150 + 75x = 2475 + 60x

Solving for x, we get:

15x = 675

x = 45

Therefore, the two schools will have an equal number of students enrolled in 21 years (3150 + 75(21) = 2475 + 60(21)).

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Answer:

76.50

Step-by-step explanation:

We are given the fact that you bought an object for 90 dollars, and in which you sold said object for a loss of 15%, we are then asked how much would that object be sold for.

To find the answer, we need to subtract the original amount by the percent loss, so :

90 - 15%

15% of 90 is 13.5, therefore :

90 - 13.5

76.5

Answer:

b≥ - 8/3

Step-by-step explanation:

-3b-5≥-6b - 13.

Add 6b to each side

-3b+6b-5≥-6b+6b - 13

3b-5≥ - 13

Add 5 to each side

3b-5+5≥ - 13+5

3b≥ - 8

Divide by 3

3b/3≥ - 8/3

b≥ - 8/3

The risk of developing heart disease is increased by option C: 25–30% for nonsmokers who breathe secondhand smoke at home or at work.

According to the Centers for Disease Control and Prevention (CDC), Nonsmokers who breathe secondhand smoke at home or at work have a 25–30% higher chance of getting heart disease. Additionally, secondhand smoke 20–30% increases the risk of stroke. Secondhand smoking exposure can result in coronary heart disease, heart attacks, and strokes.

Only completely smoke-free environments can totally protect you and your loved ones from the dangers of secondhand smoke. Making sure your home and automobile are properly ventilated is another strategy to safeguard yourself from secondhand smoke. This can assist in lowering the amount of smoke in the air and lowering your exposure.

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Correct question:

How much do nonsmokers increase their risk of developing heart disease by exposing themselves to secondhand smoke at home or work? responses

15 to 20 percent

20 to 25 percent

25 to 30 percent

30 to 35 percent

The solution to the equations is y = -7

From the question, we have the equation to be given as

3x - 2y = 5

The above equation is a linear equation

The domain or the replacement set is given as

{-3}

Rewrite properly as

Domain  = {-3}

or

x = -3

So, we replace the variables using the elements in the replacement set

When x = -3, we have

3 x -3 - 2y = 5

Evaluate the products

This gives

-9 - 2y = 5

Add 9 to both sides

-2y = 14

Divide both sides by -2

y = -7

So, we have

x = -3 and y = -7

Hence, the solution to the equation is y = -7

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6+9=15

(1+5)+9=15

6+9=15

Hope it helped

Answer: 1x6+9=15 or 15x1 or 6+9=15 or 5x3=15

Step-by-step explanation:

The total area of the glass used in making the rectangular prism-shaped aquarium is 60 square feet.

The rectangular crystal formed aquarium has a base area of 6 feet by 2.5 feet, which is equivalent to 15 square feet. The level of the aquarium is 4 feet. To compute the complete region of the glass utilized in making the aquarium, you really want to duplicate the base region by the level, which is 15 x 4 = 60 square feet. This implies that 60 square feet of glass were utilized in making the aquarium. The glass some portion of the aquarium incorporates the four sides and the top, while the base is normally made of an alternate material, like acrylic.

The foundation of the rectangular crystal formed aquarium is 6 feet by 2.5 feet, which gives an all out area of 15 square feet (6 x 2.5). The level of the aquarium is 4 feet. Hence, the absolute region of the glass utilized in creating the aquarium can be determined by duplicating the base region by the level: 15 x 4 = 60 square feet.

The glass a piece of the aquarium would be the four sides and the top. The base would ordinarily be made of another material, like acrylic.

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The given indefinite integrals can be evaluated as

a) ∫6etdt = 6et + c

b) ∫2rdr = r^2 + c

c) ∫10x^2 0dx = (10/3)x^3 + c

In calculus, an indefinite integral represents a family of functions that differ from each other only by a constant. It is also known as an antiderivative because it is the opposite operation of differentiation.

The indefinite integral of a function f(x) is denoted as ∫f(x)dx, where dx represents the variable of integration. The result of integrating a function is called an antiderivative or a primitive of the function.

For part a), the indefinite integral of 6e^t is simply 6e^t + C, where C is the constant of integration.

For part b), the indefinite integral of 2r is r^2 + C, where C is the constant of integration.

For part c), the indefinite integral of 10x^2 is (10/3)x^3 + C, where C is the constant of integration.

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X and 73 are same-side interior angles, which are supplementary (they add up to 180).

x + 73 = 180

x = 107

X and (6y - 79) are vertical angles, which are congruent (have the same measure/value.

x = 6y - 79

107 = 6y - 79

6y = 186

y = 31

Hope this helps!

Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

The answer to why Lynn wants to wait would be:

Therefore, Lynn wants to wait because (D) she would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

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The complete question is shown below:

Lynn is at a store and wants to buy a new backpack that costs $55. she only has $35 with her, but she has the rest at home. Lynn also has a credit card that does not charge her any interest if she pays the balance in full by the end of the month. why might Lynn want to wait until she has $55 in cash at the store to purchase the backpack, instead of using her credit card?

a. Using a credit would cause the store to lose money because even if she pays back her bill in full, she will still need to pay the credit card company additional dollars for the convenience of borrowing money.

b. Using cash would cause the store to lose a large amount of money because credit card companies offer incentives to stores based on the number of people who use their cards.

c. She might forget to pay the credit card bill, which would make her purchase more expensive due to interest payments and late charges.

d. She would likely have to pay more than $55 at the time of purchase for the convenience of using her credit card.

Answer:

Here is something similar! Sorry the question was to hard.

Step-by-step explanation:

\(y=9x^{2} +bx+c\)

\(y = 8inx\)

\(y=x\\\)

( - ∞, a)

\(y = log n\)

Answer:

Part A)

The independent variable is x, the hours she worked

The dependent variable is y, how much money she earns

COmment any questions

The simple interest rate that will ensure that Bob's investment of R6,500 equals Alice's 3% compound interest per year investment is 3.2%.

The difference between simple interest and compound interest is that simple interest computes interest on the principal only for each period.

Compound interest computes interest on both the principal and accumulated interest for each period.

Alice:

Principal investment = R6,500

Compound interest rate per year = 3%

Investment period = 5years

Future value = R7,535.28 (R6,500 x 1.03⁵)

Total Interest R1,035.28 (R7,535.28 - R6,500)

Bob:

Principal invested = R6,500

The simple interest rate = r

Investment period = 5years

The future value of the simple interest investment, A = P(1+rt)

7,535.28 = 6,500(1 + 5r)

Dividing each side b 6,500:

1.15927 = (1 + 5r)

5r = 0.15927

r = 0.031854

r - 0.032

r = 3.2% (0.32 x 100)

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Calculate r, giving your answer correct to 1 decimal place.

Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

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Answer:

g = (h+a) - l

None of them

Step-by-step explanation:

Suppose your car has h liters of engine oil in the morning. During the day, some oil may have leaked, you may have added more oil, or both. The oil level in the evening is g liters. Which of the following expressions always represents how far away the new oil level is from the previous oil level? H+G lGl none of them

Let

h = liters of oil in the morning

l= liters that has leaked

a= liters that were added during the day

g= amount of liters at the end of the evening

Total liters of oil in the evening= (litres of oil in the morning + litres of oil added during the day) - litres of oil that leaked

Substituting each variable into the formula, we have

g = (h+a) - l

The maximum and minimum οf a functiοn, knοwn generically as extremum in mathematical analysis, are the largest and smallest values οf the functiοn, either within a given range (the lοcal οr relative extrema) οr οn the entire dοmain (the glοbal οr absοlute extrema)..

The wοrd minimum refers tο the bare minimum οf a task. Fοr instance, if the minimum price fοr there's sοmething seven dοllars, yοu cοuld buy six οr less; yοu must spend a minimum οf seven. Yοu can gο beyοnd the bare minimum, but nοt belοw it.

When yοu use the wοrd minimum, yοu're referring tο a sum that is at the very least pοssible, permitted, οr necessary. Weekend stays at the hοtel must be a minimum οf twο nights.

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Complete question?

What does maximum and minimum mean in graphical function?

Answer:

x=35

Step-by-step explanation:

Triangles always add up to 180 degrees, and so do straight lines. so 180-131=49, 49+96=145, 180-145=x, so x=35 degrees

Answer:

What is the question?

Step-by-step explanation:

Answer:

n=1/3

Step-by-step explanation:

Five more than the product of a number and 9 is equal to 8

n is the number

5+9n=8

9n=3

n=1/3

Answer:

-31, -23, -6.78,-4.78, -5, 1.25

the correct option is D, the inverse relation is only a function if it passes the vertical line test.

A relation maps elements from one set (called the domain) into elements of another set (called the range).

A relation is a function only if each element in the domain is mapped into only one element of the range. So, there is something called the vertical line test.

It says that if at any part of the graph of the relation you can draw a vertical line that intercepts the graph of the relation more than once, then it is not a function. Passing the vertical line test means that no vertical line intercepts the graph more than once.

Then the correct option is D, the inverse relation is only a function if it passes the vertical line test.

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The x term of the given ordered pairs follow an arithmetic sequence, with common difference of 1.5. The y term of the ordered pairs follow an arithmetic sequence, with common difference of 4.5.

The relationship between the corresponding terms can be described as a linear relationship, where y is a function of x, such that y = 4.5x.

The relationship between the x and y terms can be determined by observing the change in the values between the ordered pairs. For example, the difference in x values between (0,0) and (1.5,4.5) is 1.5, and the difference in y values is 4.5. This pattern continues for all the other pairs, with the x term increasing by 1.5 and the y term increasing by 4.5 for each subsequent pair. This is consistent with an arithmetic sequence, where the difference between each term is constant.

Since the y values increase linearly with the x values, this suggests that the relationship between x and y can be modeled as a linear equation, y = 4.5x. This linear relationship is further confirmed by the fact that the ratio of the increase in the y term to the increase in the x term is constant, and equal to 4.5.

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When we want to estimate a population parameter then we use hypothesis test.

What is hypothesis test?

In hypothesis testing, an analyst examines a statistical sample with the aim of demonstrating the plausibility of the null hypothesis.

By measuring and reviewing a representative sample of the population under study, statistical analysts test a hypothesis. All analysts use a random population sample to test the null hypothesis and the alternative hypothesis.

Main body:

As the researchers want to understand the difference between to states they need to do a hypothesis test.

Hence a hypothesis test is done.

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Here's a Python program (Filename: optimization.py) to perform the optimization problem: Minimize x

3
 −2cos(x)+9 s.t. 0≤x≤2The optimization problem is to find the minimum value of x
3
 −2cos(x)+9 when 0≤x≤2. This optimization problem can be approximately solved by simply searching in the feasible range. In the program, you can simply define a list x = [0, 0.01, 0.02, …, 1.98, 1.99, 2.0]. Also, define an objective function as f(x) = x
3
 −2cos(x)+9 and search for the minimum f(x) of different values in the list x.```python
import math
x = [0.01*i for i in range(201)]
min_val = 1e18
opt_x = 0
def f(x):
   return x**3 - 2*math.cos(x) + 9
for xi in x:
   if xi>=0 and xi<=2:
       fval = f(xi)
       if fval

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Answer:

here's the answers............

y = 42°

Because the angle at the side of right angle will also be right angle or 90°

Sum of all angles of a triangle = 180°.

So, 48° + 90° + y = 180°

=> 138° + y = 180°

=> y = 180° - 138°

=> y = 42°

Angles on a straight line are 180. Therefore, 180 - 90 (right angle) = 90

Angles in a triange add to 180.

90 + 48 = 138

180 - 138 = 42

—————— (not sure if you need this, but:)

To work out x, you would do:

Angles on a straight line add to 180.

180 - 48 = 132

132/2 = 66

To work out z:

Angles in a triangle add to 180. You know x is 66, so

66 + 90 (right angle) = 156

180 - 156 = 24

(a)the body temperature of the 1601 lb man will increase by approximately 3.0 °C.(b)the body temperature of the 160 lb man will increase by approximately 2.4 °C.

The specific heat of a human is given as 3.47 J/°C. Using this information, we can calculate the increase in body temperature when a certain number of calories are converted into heat energy. In the first scenario, a 1601 lb man consumes a candy bar containing 287 Cal. In the second scenario, a 160 lb man consumes a roll of candy containing 41.9 Cal. We will calculate the increase in body temperature for each case.

(a) To calculate the increase in body temperature for a 1601 lb man who consumes a candy bar containing 287 Cal, we need to convert calories to joules. Since 1 Calorie (Cal) is equal to 4184 joules, we have:
Energy = 287 Cal × 4184 J/Cal = 1.2 × \(10^6\) J
Now, using the specific heat formula Q = mcΔT, where Q is the energy, m is the mass, c is the specific heat, and ΔT is the change in temperature, we can rearrange the formula to solve for ΔT:
ΔT = Q / (mc)
Assuming the mass of the man is converted to kilograms, we have:
ΔT = (1.2 × \(10^6\) J) / (1601 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 3.0 °C
Therefore, the body temperature of the 1601 lb man will increase by approximately 3.0 °C.
(b) For a 160 lb man who consumes a roll of candy containing 41.9 Cal, we repeat the same calculation:
Energy = 41.9 Cal × 4184 J/Cal = 1.75 × \(10^5\) J
ΔT = (1.75 × \(10^5\) J) / (160 lb × 0.4536 kg/lb × 3.47 J/°C) ≈ 2.4 °C
Thus, the body temperature of the 160 lb man will increase by approximately 2.4 °C.

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Answer: I cant see the problem

Step-by-step explanation:

Answer:

Where is the question?

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

hi!  

formula for Volume : Rectangular Pyramid

V =    l x w x h ÷ 3  

your answer is --->  2,800 m

hope this helped!

Answer:

-72

Step-by-step explanation:

-0.125x=16-7

-0.125x=

x=-72

Answer:

x = -72

Step-by-step explanation:

Given equation,

→ -0.125x + 7 = 16

Now we have to,

→ Find the required value of x.

Then the value of x will be,

→ -0.125x + 7 = 16

Subtract RHS with the number 7:

→ -0.125x = 16 - 7

→ -0.125x = 9

Divide RHS with the number -0.125:

→ x = 9 ÷ (-0.125)

→ [ x = -72 ]

Hence, the value of x is -72.