In ΔIJK, k = 590 inches, ∠I=86° and ∠J=29°. Find the length of j, to the nearest 10th of an inch

Answer:

Radius: 5.75

circumference:36.13

area:103.87

There you go!!

Answer:

radius : 5.75

circumference: 36.14

area: 103.91

'One inch represents 2,000 feet' is a verbal type scale.

The link between a length unit on a map and its corresponding length on the ground is known as the map scale. It will be beneficial for you to carefully study this section because we will use map scale principles throughout the course.

We can use three distinct scales to relate a map to the ground:

'One inch represents 2,000 feet' is an example of a Verbal scale. The relationship between a map distance and a ground distance is expressed verbally using a verbal scale.

Here, it is inferred that one inch on the map corresponds to 2000 feet on the ground. Popular atlases and maps frequently use verbal scales.

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Answer:

0.33333333333e3

Step-by-step explanation:

e = infinity

9514 1404 393

Answer:

  143.1 ft

Step-by-step explanation:

Assuming the rope is tied to the boat, and that the geometry can be modeled by a right triangle, the Pythagorean theorem is helpful.

  150² = 45² + d²

  d = √(150² -45²) = √20475 ≈ 143.1 . . . . feet

The horizontal distance between the man and the boat is about 143.1 feet.

The correct equation for comparing the alternatives with a salvage value of $7,000 after 4 years and a MARR of 12% per year is b. PWX = -20,000 - 9000(P/A,12%,4) + 5000(P/F,12%,2) - 15000(P/F,12%,2).

The correct equation for the present worth (PW) when comparing the alternatives with a salvage value of $7,000 after 4 years and a MARR of 12% per year is:

b. PWX = -20,000 - 9000(P/A,12%,4) + 5000(P/F,12%,2) - 15000(P/F,12%,2)

This equation takes into account the initial cost of -$20,000, the cash inflow of $9,000 per year for 4 years (P/A,12%,4), the salvage value of $5,000 at the end of year 2 (P/F,12%,2), and the salvage value of $15,000 at the end of year 4 (P/F,12%,4).

Therefore, the correct option is b. PWX = -20,000 - 9000(P/A,12%,4) + 5000(P/F,12%,2) - 15000(P/F,12%,2).

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The equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x

The expression is given as:

3/2(6x^2 - 2/3x)

Open the bracket

3/2*6x^2 - 3/2*2/3x

Evaluate the product

9x^2 - x

Hence, the equivalent expression of 3/2(6x^2 - 2/3x) is 9x^2 - x

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Answer:

\(f^{-1}(x)=\sqrt{x+1}-3\)

Step-by-step explanation:

We have the function:

\(f(x)=y=x^2+6x+8\) with the domain restriction \(\{x\geq -3\}\).

And we want to find the inverse of our function.

To find the inverse of our function, we take the following steps:

Therefore, our inverse will be:

\(x=y^2+6y+8\)

First, let's subtract 8 from both sides. So:

\(x-8=y^2+6y\)

To solve for y, we can complete the square. To complete the square, we:

Our b term is 6. \(6/2=3\), and \(3^2=9\). So, we will add 9 to both sides. This yields:

\((x-8)+9=(y^2+6y+9)\)

Simplify the left. Complete the square on the right. So:

\(x+1=(y+3)^2\)

Take the square root of both sides and solve for y:

\(y+3=\sqrt{x+1}\Rightarrow y=\sqrt{x+1}-3\)

Subtract 3 from both sides. So, our inverse is:

\(f^{-1}(x)=\sqrt{x+1}-3\)

Part 2)

See below for graph.

Here is also a good time to reinforce the idea of inverses. Notice that the domain of our original function f(x) is \(x\geq-3\). So, this means that the range of f(x) is (looking at the graph) is \(y\geq-1\).

When we find the inverse, we will flip the domain and range. Therefore, the domain of our inverse function will be the range of our original function, and the range of our inverse function will be the domain of our original function.

From the graph, we can see that f⁻¹(x) has a domain of \(x\geq-1\) and a range of \(y\geq -3\). Therefore, their domain and range are indeed opposites.

And we're done!

Answer:

5x​(5x+1)^2

= 5x(25x^2+10x+1)

= 125x^3+50x^2+5x

Answer:

In this case, 9,  x⁶  and y⁸ are all perfect squares, so we can take that out, saying:

9x⁶y⁸ = (3x³y⁴)²

Answer:

Hi there,

Make Nick's age = x

Caroline's age = x + 12

Mark's age = x - 4

x + (x + 12) + (x - 4)

Remove brackets

x + x + 12 + x - 4 = 44

Collect like terms

3x = 44 - 12 + 4

3x = 36

x = 12

Mark is 8 yrs old

Nick is 12 yrs old

Caroline is 24 yrs old

Youngest is Mark = 8 years old.

Hope this helps :-)

Answer:

Hi there, Youngest is Mark = 8 years old.

Step-by-step explanation:

Make Nick's age = x

Caroline's age = x + 12

Mark's age = x - 4

x + (x + 12) + (x - 4)

Remove brackets

x + x + 12 + x - 4 = 44

Collect like terms

3x = 44 - 12 + 4

3x = 36

x = 12

Mark is 8 yrs old

Nick is 12 yrs old

Caroline is 24 yrs old

Youngest is Mark = 8 years old.

Hope this helps :-

Answer:

38

Step-by-step explanation:

v=u+at

v=16+11(2) Do multiplication first

v=16+22

v=38

Answer:

38

Step-by-step explanation:

1. Plug in the each number for its variable to get v = 16 + 11 x 2

2. Multiply 11 and 2 to get 22

3. add 16 to 22 to get 38

we need to use the Pythagoras theorem

we have the next information

b=200

c=400

rounded to the nearest whole number a=346

the answer is 346

x − 3 = 6 − 2 x = − 8 √ x = 3

Answer:

85361.1415927

Step-by-step explanation:

Answer:

85361.141

Step-by-step explanation:

did it on a calculator

Using p-hat formula and probability,

we get

a) Sampling distribution of p-hat = 0.02029286

b)The probability that in a random sample of 500 adults more than 30% do not own a credit card is

=0.3121

c) The probability that in a random sample of 500 adults between 25% and 30% do not own a credit card is 0.6635

We have given that

29% of adults do not own a credit card according to creditcard.com.

a) Sample size (n) = 500 of adults have own credit card

sample proportion, for the adults do not own a credit= 29% = 0.29

Normal distribution exits here with p

= 1-0.29=0.71 and

Standard error (p-hat) =sqrt(p(1-p)/n)

=sqrt(0.71× 0.29/500)

p-hat = 0.02029286

b) Now, more than 30% do not have own credit card.

P(p-hat>0.3) = P((phat- p)/sqrt(p×(1-p)/n) >(0.3-0.29)/sqrt(0.29× (1-0.29)/500))

=P(Z>0.49) =0.3121 (from standard normal table)

c) Sample size (n) = 500 and p-hat lies between 25% to 30% .

P(0.25<phat<0.3)

= P((0.25-0.29)/sqrt(0.29*(1-0.29)/500) <Z< (0.3-0.29)/sqrt(0.29*(1-0.29)/500))

=P(-1.97<Z<0.49)

=0.6635 (from standard normal table)

Hence, we calculated all the required probabilities.

a) p-hat = 0.02029286

b) P(p-hat>0.3) =0.3121

c) P(0.25<phat<0.3) =0.6635

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Complete question:

According to creditcard.com, 29% of adults do not own a credit card.

a. Suppose a random sample of 500 adults is asked, "Do you own a credit card?" Describe the sampling distribution of p-hat, the proportion of adults who own a credit card.

b. What is the probability that in a random sample of 500 adults more than 30% do not own a credit card?

c. What is the probability that in a random sample of 500 adults between 25% and 30% do not own a credit card?

Answer:

x^2 - 14x + 49

Step-by-step explanation:

(x - 7)^2 is equivalent to (x - 7)(x - 7), which in turn is x^2 - 14x + 49

the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.

Pastels weekly salary includes base pay plus commission of his sales.

the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars.

find pastels salary in dollars for a week when his sales were 0$

the model is given as

s=700+0.07c

let us solve for c, the sales made

s =700 +0.07c given sales is 0$

then s=700

Hence , the equation s=700+0.07c models between his weekly sales in dollars and the amount of his sales in dollars. pastels salary in dollars for a week when his sales were 0$ is $700.

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Convert it to a decimal and multiply is the best way to describe rate in simple interest formula.

The real yearly cost of funds over the course of a loan is the annual rate that is charged for borrowing (or made by investing), expressed as a single percentage number. An interest rate indicates how expensive borrowing is or how lucrative saving is. Therefore, if you are a borrower, the interest rate is the sum you pay for borrowing money and is expressed as a percentage of the overall loan amount.

Given

The r in the simple interest formula stands for rate.

Convert it to a decimal and multiply is the best way to describe rate in formula.

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Opportunity cost is the price of giving up an option. An opportunity cost is the price you pay for selecting a particular option over another. Opportunity cost is the benefits you lose by choosing one alternative over another one.”

The value of the next-highest-valued alternative use of a resource is what economists mean when they talk about its "opportunity cost." You cannot, for instance, read a book at home during the time you would have spent seeing a movie and spend the money you would have spent on something else.

Opportunity cost is frequently referred to as the second-best option. The loss of benefit that would have been realized if a different option had been taken is sometimes referred to as the alternative cost. The loss of advantage as a result of a change in decision is another way to explain it.

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Answer:

-12/3

Step-by-step explanation:

The formula to get slope is m=y1-y2 and x1-x2

REMEMBER SLOPE IS Y/X NOT X/Y

It is a 180 because you but those numbers together

The length of the hypotenuse of the triangle is 6 inches, which is option D.

In order to find the hypotenuse of a right triangle, we use the Pythagorean theorem which is `a²+b²=c²`where `a` and `b` are the legs of the triangle and `c` is the hypotenuse. Here, the question mentions that the shortest side of the right triangle measures 3 inches and one angle of the triangle measures 60 degrees. Therefore, we need to find the length of the other leg and hypotenuse.The trigonometric ratios of a 60 degree angle are:

`sin 60 = √3/2`, `cos 60 = 1/2`, `tan 60 = √3`.

Now, we have the value of sin 60 which is `√3/2`. We can use it to find the other leg of the right triangle as follows:

Let `x` be the other leg.So, `sin 60° = opposite / hypotenuse => √3/2 = x / c`

Multiplying both sides by `c`, we get: `x = c(√3/2)`

Now, using the Pythagorean theorem, we can write:

`3² + (c(√3/2))² = c²`9 + 3/4 c² = c²

Multiplying both sides by 4 gives:

36 + 3c² = 4c²Simplifying: c² = 36 ⇒ c = 6

Thus, the length of the hypotenuse of the triangle is 6 inches, which is option D.

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The student made the following mistake: The use of operator "+" in binomial (x - 4) instead of "-" when factoring the quadratic equation x² - 3 · x - 4.

In this problem we find the case of a quadratic equation that must factorized by algebra properties. We present the complete procedure to show what mistake the student did. First, write the original expression:

x² - 3 · x - 4

Second, use definition of addition, associative and distributive properties:

x² - 4 · x + x - 4

Third, use conmutative property:

x² + x - 4 · x - 4

Fourth, use distribute property:

x · (x + 1) - 4 · (x + 1)

Fifth, apply commutative and distributive properties:

(x - 4) · (x + 1)

Sixth, use commutative property:

(x + 1) · (x - 4)

The student wrote the operator "+" instead of "-" in binomial (x - 4) of the quadratic equation x² - 3 · x - 4.

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When the function has a horizontal tangent line or a vertical asymptote at the point where the switch would occur.

A curve may not switch from increasing to decreasing or vice versa from one interval to an adjacent interval when the function has a horizontal tangent line or a vertical asymptote at the point where the switch would occur.

In other words, if the derivative of the function is zero or undefined at the point where the switch would occur, then the curve will not switch from increasing to decreasing or vice versa at that point.

For example, consider the function f(x) = 1/x. This function is decreasing for x > 0 and increasing for x < 0. However, the function has a vertical asymptote at x = 0, so the curve does not switch from decreasing to increasing or vice versa at x = 0.

Similarly, consider the function g(x) = x^3. This function is increasing for all values of x, but it has a horizontal tangent line at x = 0, so the curve does not switch from increasing to decreasing at x = 0

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Answer:

proofs attached to answer

Step-by-step explanation:

proofs attached to answer

Answer:

1. 8x+10

2. 25x-7

Step-by-step explanation:

Answer:

1) 8x + 10

2) 25x - 7

The population of the colony of rabbits can be modeled by the following equation:

P(t) = 15 * b^t

where P(t) is the population of the colony at time t, and b is the growth factor.

We know that after 5 years, the population is 360 rabbits. Solving for b, we get:

360 = 15 * b^5

b^5 = 24

b = 2

Therefore, the growth factor is 2. This means that the population of the colony doubles every 5 years.

To find the population of the colony after t years, we can plug in t into the equation:

P(t) = 15 * 2^t

For example, after 10 years, the population of the colony will be:

P(10) = 15 * 2^10 = 1024

So, the population of the colony of rabbits will reach 1024 rabbits after 10 years.

The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

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The percentage of the students who wore a silly hat is 64 %.

The percentage is defined as a ratio expressed as a fraction of 100.

We have been given that Last Tuesday was a silly hat day at Aaron's school. 64 students wore a silly hats and 36 students did not.

We have to determine the percentage of the students who wore a silly hat

The total number of students = 64 students wore silly hats and 36 students did not.

The total number of students = 64 + 36 = 100

We have to determine the percentage of the students who wore a silly hat

The percentage of the students wore a silly hat = (64/ 100) × 100

The percentage of the students wore a silly hat = 0.64 × 100

The percentage of the students wore a silly hat = 64 %

Thus, the percentage of students who wore silly hats is 64 %.

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