if the odds on a particular football team winning a bowl game are 2:3 that means the percent chance that the team will win is:

The derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

a) To find f'(x) for f(x) = x*sin(x), we can use the product rule and the derivative of the sine function.

Using the product rule, we have:

f'(x) = (xsin(x))' = xsin'(x) + sin(x)*x'

The derivative of sin(x) is cos(x), and the derivative of x with respect to x is 1. Therefore:

f'(x) = x*cos(x) + sin(x)

So, the derivative of f(x) = xsin(x) is f'(x) = xcos(x) + sin(x).

(b) To find f'(x) for f(x) = sech^(-1)(x^2), we can use the chain rule and the derivative of the inverse hyperbolic secant function.

Let u = x^2. Then, f(x) can be rewritten as f(u) = sech^(-1)(u).

Using the chain rule, we have:

f'(x) = f'(u) * u'

The derivative of sech^(-1)(u) can be found using the derivative of the inverse hyperbolic secant function:

(sech^(-1)(u))' = 1/sqrt(1 - u^2)

Since u = x^2, we have:

f'(x) = 1/sqrt(1 - (x^2)^2) * (x^2)'

Simplifying:

f'(x) = 1/sqrt(1 - x^4) * 2x

So, the derivative of f(x) = sech^(-1)(x^2) is f'(x) = 2x/sqrt(1 - x^4).

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The exponential function that determines the value of the car after x years is y = 18000(0.65)ˣ. Here the rate of decrease is the same each year.

The exponential function is the function that gives the relationship between the input and the output with a rate of increase or decreases exponentially. It is given by the formula,

y = abˣ

Where 'a' is the initial value, 't' is the time, and 'b' is the rate. If b > 1, then the function is said to be the exponential growth function, and if b < 1, the function is said to be the exponential decay function.

Given that, a car is sold for $18,000.

So, the initial value a = 18000.

After one year (x = 1), the value of the car is $11,700 i.e., y = 11700. So we can write the exponential function as

11700 = 18000(b)¹

⇒ b = 11700/18000 = 0.65

Since b < 1, the function is exponentially decaying.

Then, the value of the car after 'x' years is given by the exponential decay function as

y = 18000(0.65)ˣ

(It is given that, the rate of decrease is the same each year).

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The area of the shaded sector is 4π square units.

To find the area of the shaded sector, we need to calculate the central angle formed by the sector. In this case, we are given that the angle JIK is 90 degrees, which means it forms a quarter of a full circle.

Since a full circle has 360 degrees, the central angle of the shaded sector is 90 degrees.

Next, we need to determine the radius of the circle. The line segment IJ represents the radius of the circle, and it is given as 4 units.

The formula to calculate the area of a sector is A = (θ/360) * π * r², where θ is the central angle and r is the radius of the circle.

Plugging in the values, we have A = (90/360) * π * 4².

Simplifying, A = (1/4) * π * 16.

Further simplifying, A = (1/4) * π * 16.

Canceling out the common factors, A = π * 4.

Hence, the area of the shaded sector is 4π square units.

Therefore, the area of the shaded sector, expressed as a fraction times π, is 4π/1.

In summary, the area of the shaded sector is 4π square units, or 4π/1 when expressed as a fraction times π.

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Answer:

50

Step-by-step explanation:

The sum of angles in a triangle is 180 so the answer is 180 - 90 - 40 = 50.

Also, for your first question, 2 corresponding angles of the triangles must be congruent.

Answer:

B. 50°

Step-by-step explanation:

40°+90°+y = 180°

130°+y°=180°

y° =180°-130°

y = 50° (sum of the interior angles in a triangle=180°)

\((\stackrel{x_1}{1}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{k}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{k}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{5}-\underset{x_1}{1}}}~~ = ~~\stackrel{\stackrel{m}{\downarrow }}{2} \\\\\\ \cfrac{k-3}{4}=2\implies k-3=8\implies k=11\)

ANSWER and EXPLANATION

B. We are to describe the relationship between bridge length and breaking weight.

To do this, we need to check the graph.

In doing that, we will see that the breaking weight appears to decrease as the Bridge length increases.

We can conclude then that the breaking weight and bridge length have an inverse relationship.

That is shown in the graph.

The highest value of the breaking weight is 14 and that is when the value of bridge length is at its lowest (4).

The lowest value of the breaking weight is 3 and that is when the value of the bridge length is at its highest (11)

Hence, there is an inverse relationship between them.4)

Answer:

510.1

Step-by-step explanation:

convert m to km by dividing by 1000 and add all of the numbers together

Using PEDMAS to simplify the expression, the result is -830t² + 164t + 5798.4

To solve this problem, we have to simplify the expression. This is a process of breaking it down from a complex form to the least possible form. In doing this, we often apply mathematical operations such as multiplication, addition, subtraction etc.

In the expression 362.4 * 16 - 2t + 83t * (2 - 10t)

Let's apply PEDMAS here

362.4 * 16 = 5798.4

83t (2 - 10t) = 166t - 830t²

We can bring them together now;

5798.4 - 2t + 166t - 830t²

Collecting like terms

-830t² + 164t + 5798.4

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Answer: ( . = multiplication sign)

1. 24

2.  4 questions

3.  3 questions

Step-by-step explanation:

1. You first need to find how many points each part was worth. To do this, you need to find the lowest common multiple for 6 and 8. The lowest common multiple is 24.

2.  Part A has questions that were each worth 6 points so, you need to find the value of  X in this equation: X . 6 = 24 .

The value of X is 4.

3. Part B had questions that were 8 points each so you need to find the value of X in this equation: X . 8 = 24  .

X = 3

Answer: Z = 65

Step-by-step explanation:

An inscribed angle is equal to 1/2 the circumference of the part of the circle across from it. Since we are given angle 50, we know the part of the circle’s circumference across from it equals 100. We also know a whole circle’s circumference is equal to 360. Let’s take 360-100 and see the remaining parts of the circumference is equal to 260. Since the two parts left of the circumference are labeled as x, we know they are equal. So, 260/2 = 130.

X=130. Notice that X is directly across from inscribed angle Z. This means Z = 1/2 X.

Z= 130/2

Z= 65

After six years, the population will grow to 586,455 if compounded annually at a rate of 7.5%.

This is exactly like a compound interest problem where the interest rate is 7.5% compounded annually for 6 years.

If we use the compound interest formula A = P(1+r/n)nt where A is the end amount to be found, p = initial amount (p= 380,000), n = number of times the interest is compounded annually (n= 1) and t is the time in years (t=6)

A = 380,000(1 + .075/1)1(6)

A = 380,000(1.075)6

A = 586,454.58 people

Rounded to the nearest whole number

the population after 6 years should be

586,455 people

Hence we get the required answer.

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Your question is incomplete. Please find the missing content below.

A city has a population of 380,000 people. suppost that each year the population grows by 7.5%. what will be the population after 6 years.

Step-by-step explanation:

The standard deviation of the sampling distribution of the sample mean length for a sample of 4 songs is 0.2 minutes.

It is known that the lengths of songs played on a radio station follow a normal distribution with mean 3.6 minutes and standard deviation 0.4 minutes. To find the standard deviation of the sampling distribution of the sample mean length for a sample of 4 songs, you can use the formula:

Standard deviation of sampling distribution = (population standard deviation) / √(sample size)

In this case, the population standard deviation is 0.4 minutes, and the sample size is 4. Plug these values into the formula:

Standard deviation of sampling distribution = 0.4 / √4 = 0.4 / 2 = 0.2 minutes

So, the standard deviation of the sampling distribution of the sample mean length for a sample of 4 songs is 0.2 minutes.

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Answer: an acute angle so it bout 55

Step-by-step explanation:

Answer:

V  =  339 in³

Step-by-step explanation:

The formula for the volume of a sphere of radius r is V = (4/3)πr³

Here the diameter is 18 m, so the radius must be 9 m, and the volume of the sphere is

V = (4/3)(3.14)(9 m)², or

V  =  339 in³

Answer:

$942.60

Step-by-step explanation:

Future Value (FV)= $1,000

Number of periods (n)= 2

Interest rate (i)= 3% = 0.03

To calculate the present value (PV), we need to use the following formula:  

FV= PV*(1í)^n  

Isolating PV:  

PV= FV/(1+i)^n

Pv=1,000/(1.03^2)

$942.60

Hope this helps, have a great day :)

Option A is correct answer; i.e. 102 homes were sold in 2017.

A pie chart is a type of graph that records data in a circular manner that is further divided into sectors for representing the data of that particular part out of the whole part.

Here,

Total Homes sold in 2017 = 850 homes.

Homes sold in Southwest region = 12 % of the total.

                                                      = 0.12 X 850

                                                      = 102.

Thus, option A is correct answer; i.e. 102 homes were sold in 2017.

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The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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Answer:

x=8

y=10

z=9

Step-by-step explanation:

Answer: the answer should be D 13 m

Step-by-step explanation: hope this helps :)

Answer:

\(13\)m is the hypotenuse of the right triangle

Step-by-step explanation:

Using the Pythagorean Theorem,

\(a^{2} + b^{2} = c^{2} \\7^{2}+11^{2} = c^{2} \\49 + 121 = c^{2} \\170 = c^{2} \\\sqrt{170 } = 13.04\)

When we round to the nearest tenth,

\(13.04 = 13\)

Hence , the hypotenuse of a right triangle is 13m

Based on the cost of the copy paper and the discount on ink cartridges, the cost of the ink cartridge is $15 each.

First find the amount paid for the ink cartridges:

= Total spent - cost of copy paper

= 175 - 45

= $130

He got a discount of $2 per cartridge. For 10 cartridges he got a discount of:

= 2 x 10

= $20

The cost of each ink cartridge is:

= (Amount spent on ink cartridges + Discount) / Number of cartridges

= (130 + 20) / 10

= $15 each

In conclusion, each cartridge cost $15.

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The error Justin made in his calculation is "He should have added the values in the numerator before dividing by 2".

The correct answer choice is option B

(x + y + 5) / 2

Where,

x and y are his parents’ current heights in inches,

Mom’s height = 54 inches

Dad’s height = 71 inches

Substitute into the expression

(71 + 54 + 5) / 2

= 130/2

= 65 inches

Justin's work:

( 71 + 54 + 5 ) / 2

= 71 + 27 + 5

= 103 inches

Therefore, Justin should have added the numerators before dividing by 2.

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A test of nonverbal intelligence is a type of cognitive assessment that measures an individual's ability to solve problems and think abstractly without the use of language.

Unlike traditional intelligence tests that rely heavily on verbal abilities such as vocabulary, reading, and verbal reasoning, nonverbal intelligence tests use visual-spatial and abstract reasoning tasks that do not require the use of language.

Nonverbal intelligence tests can be particularly useful for individuals who have language or communication difficulties, such as those with speech and language disorders, or those who are non-native speakers of the language in which the test is administered. They can also be used to assess individuals who have difficulty with traditional tests due to visual or hearing impairments.

Examples of nonverbal intelligence tests include Raven's Progressive Matrices, the Naglieri Nonverbal Ability Test (NNAT), and the Universal Nonverbal Intelligence Test (UNIT). These tests typically involve completing visual pattern recognition and completion tasks, spatial reasoning tasks, and other nonverbal problem-solving tasks.

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It takes the second marathoner 4 hours and 40 minutes to complete the marathon.

Let's assume the distance of the marathon is "d" miles.

The first marathoner runs at a constant speed for 4 hours, so we can find their speed as:

speed = distance / time = d / 4

The second marathoner starts by running at 4 times the speed of the first marathoner, so their speed is:

speed = 4(d / 4) = d

For the second half of the race, the second marathoner's speed drops to 3/4 of the first marathoner's speed. Let's assume it takes "t" hours for the second marathoner to complete the second half of the race. Then, we can write:

d / 2 = (3/4)(d / 4)(t)

Simplifying this equation, we get:

t = (2/3) hours

So the total time it takes the second marathoner to finish the race is:

4 + (2/3) = 4 2/3 hours = 4 hours and 40 minutes.

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The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

√81 = 9

-√144  = -44

√4/25 = 2/25

√0.36 = 0

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