Use triangle ABC to write the value of sin B as a ratio. Use triangle ABC to write the value of sin B as a ratio.

Answer:

  8.5 years

Step-by-step explanation:

You want to know the number of years until 18500 depreciates to 9100 at the rate of 8% per year.

The depreciation rate given as a percentage of current value tells you the depreciation is exponential. The formula will be ...

  value = (initial value) × (1 - (depreciation rate))^t

where the rate is "per year" and t is in years.

  value = 18500·(1 -0.08)^t

  9100 = 18500·0.92^t . . . . fill in the value of interest

  9100/18500 = 0.92^t . . . . divide by 18500

  log(91/185) = t·log(0.92) . . . . take logarithms

  t = log(91/185)/log(0.92) ≈ -0.3081/-0.03621 ≈ 8.509

It will be about 8.5 years until the value is $9100.

__

Additional comment

The graph shows the solution to ...

  18500·0.92^t -9100 = 0

We find it fairly easy to locate an x-intercept, so we wrote the equation in the forms that makes the x-intercept the solution.

The speed of the current when it takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream is 25mph.

Given to us

Speed of the boat = 5 mph

It takes the boat 3 hours to travel upstream

2 hours to travel the same distance downstream

Let the distance traveled by boat be L.

We know that when the boat is going upstream the water current will provide resistance to the boat, therefore,

\(L = (S_c-S_b)\times T_u\)

where L is the distance traveled by boat, \(\rm S_c\ and\ S_b\) are the speed of current and boat respectively, And \(T_u\) is the time of the boat during the downstream journey.

\(L = (S_c-5)\times 3\)

We know that when the boat is going downstream the water current will provide help to the boat, therefore,

\(L = (S_c+S_b)\times T_d\)

\(L = (S_c+5)\times 2\)

We already have two-equation for the distance traveled by boat therefore, we will equate both the equations,

\((S_c-5)\times 3 = (S_c+5)\times 2\)

\(3S_c-15= 2S_c+10\\\\3S_c-2S_c = 10+15\\\\S_c = 25\rm\ mph\)

Hence, the speed of the current when it takes the boat 3 hours to travel upstream but only 2 hours to travel the same distance downstream is 25mph.

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Answer:

5mph

Step-by-step explanation:

edge2022

Answer:

Step-by-step explanation:

You want to know how to determine the y-intercepts of a rational function, and their possible number.

A rational function f(x) is the ratio of two polynomial functions p(x) and q(x):

  f(x) = p(x)/q(x)

As such, both numerator and denominator have single function values for any value of the independent variable. The y-intercept of f(x) is ...

  f(0) = p(0)/q(0)

The values of p(0) and q(0) are simply the constant terms in those respective functions.

The simple way to find the y-intercept is to look at the ratio of the constant terms in the polynomial functions making up the rational function. If that is defined, there is one y-intercept. If it is undefined (q(0)=0), then there are no y-intercepts.

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The product of the two given fractions is 1/12.

Given that, 1/4 of 1/3.

The product of two fractions is the product of the numerators and the product of the denominators.

Product of two fractions = Product of their numerators / Product of their denominators

1/4 × 1/3

= (1×1)/(4×3)

= 1/12

Therefore, the product of the two given fractions is 1/12.

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(7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)

a complex number is an element of a number system that extends the real numbers with a specific element denoted i, called the imaginary unit

The given expression is

(4-i√2)/(4+i√2)

Now we have to rationalize the above expression

((4-i√2)/(4+i√2))×((4-i√2)/(4-i√2))

(4-i√2)(4-i√2)/(4+i√2)(4-i√2)

16-4i√2-4i√2-2/16-2

16-8i√2-2/14

14-8i√2/14

2(7-4i√2)/2(7)

(7-4i)√2/7

Hence (7-4i)√2/7 is the simplified form of (4-i√2)/(4+i√2)

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Answer:

94

Step-by-step explanation:

all angles add up to 180

56+30 = 86

180-86=94

Answer: 90,000

To find the LCM (Least Common Multiple) of a number, list the multiples of each number.

Multiples of 900

Since they're a lot, we will extend it to the short version.

900, 2700, 9900, 37800, 85500, 90000

Multiples of 30000

30000, 60000, 90000, 120000, 150000

Looking at both multiples, the least common multiple is 90000, as it is listed in both 900 and 30000.

Hence, 90,000 is the answer.

Answer:

5040

Step-by-step explanation:

an illustration of permutations

The given parameter is:

number of days

dinners for 7 days

Substitute known values

Answer:

T= 4(2M-3N) ÷ 3

T = 4(2(6)-3(-3)) ÷ 3

T = 4(12+9)÷3

T= 4(21) ÷ 3

T = 84 ÷ 3

T = 28

I hope I helped you^_^

Answer:

the first answer choice

Step-by-step explanation:

have a great day :D

The mass of the vehicle accelerating at a rate of 1.8 m/s2 is 2100 N

is 3600 kg.

In physics, mass is a quantitative measurement of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the application of a force. The change caused by an applied force is smaller the more mass a body has.

We know mass = force×accelaration.

Given, The net force on a vehicle that is accelerating at a rate of 1.8 m/s² is 2100 N.

Therefore, By putting the values in the formula mass = force×accelaration

we get,

mass = 1.8×2100 kg.

mass = 3600 kg.

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The table below is a quadratic function.

A quadratic function is an Algebraic function with the power of its variable as 2.

This function normally has three algebraic terms, the x-square term, the x-term and the constant term.

Analysis:

The X-column values increases from -2 to 1, while the f(x) column which is the y-column increase from -9, until it gets to 1, where the value falls to -5.

A typical behavior of an inverted-v curve which is a quadratic curve.

If it were a linear function, as x values increase, y value would either keep increasing or decreasing, it does not change its orientation.

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Answer:

\(9x^{2} +81\)

Step-by-step explanation:

I Guess.

Answer:

3(x^2 + 27)

My answer was totally off! I just re evaluated the equation and I got this:

LMK if it's wrong :)

Answer:

a) -2.5x+3.9+1.7x

circle: 2.5x and 1.7x

variables: x

b) 1 1/2+t+2/3s

no like terms

variables: s and t

c) 15k+2/3k+3m

circle: 15k and 2/3k

variables: k and m

Answer:

-4.5

Step-by-step explanation:

\(6x+5.5=3x-8\\\)

\(6x-3x=-8-5.5\)

\(3x=-13.5\)

\(x=\frac{-13.5}{3}\)

\(x=-4.5\)

Answer:

As, this question is incomplete and without data we can not answer this question. But we can make it complete by adding our own values. Let's do it and calculate.

Average Time = 23.4 minutes is the time that Mrs Brim wanted to see.

Step-by-step explanation:

As, this question is incomplete and without data we can not answer this question. But we can make it complete by adding our own values. Let's do it and calculate.

Let's suppose, there are 10 students in the class of Mrs. Brim and she took 5 tests on subsequent days and made chart to know the average time her students took to solve the test.

Total time of test = 30 minutes

Average time taken by the students to solve the test on Day 1 = 25 minutes.

Average time taken by the students to solve the test on Day 2 = 27 minutes.

Average time taken by the students to solve the test on Day 3 = 22 minutes.

Average time taken by the students to solve the test on Day 4  = 23 minutes.

Average time taken by the students to solve the test on Day 5 = 20 minutes.

Average Time in all Tests = Sum of all times / total number of days

Average Time = (25 + 27 + 22 + 23 + 20) / 5 days

Average Time = 117/5

Average Time = 23.4 minutes is the time that Mrs Brim wanted to see.

Answer:

-6+-10=-16

Step-by-step explanation:

+ - = -

........

Answer:

You did not post an image.

Step-by-step explanation:

Answer:

Step-by-step explanation:

A. The data appears to be reported. The heights occur with roughly the same frequency.

A histogram is a graphical representation of a frequency distribution, where the x-axis represents the values of the data, and the y-axis represents the frequency of those values. If the heights are reported, the last digit of the heights should be randomly distributed and the frequency of each digit should be roughly the same, which is the case in a histogram with uniform distribution. This is in contrast to a histogram with non-uniform distribution, where certain heights occur a disproportionate number of times, which is more likely to happen when the heights are measured. Therefore, based on the information provided, it can be concluded that the data appears to be reported.

Answer: 50%

Step-by-step explanation:

For an even # to result, the fraction would be 3/6 or 1/2 which would become 0.5 or 50%.

(a) The probability of rolling a 3 is 1/6.

(b) The probability of rolling a 10 is 0 since a standard six-sided die only has numbers from 1 to 6.

(c) The probability of rolling an even number is 3/6 or 1/2. This is because there are three even numbers (2, 4, and 6) out of the six possible outcomes.

(a) The probability of rolling a 3 on a six-sided die is 1/6. There are 6 possible outcomes when rolling a die, and only 1 of those outcomes is a 3.

(b) The probability of rolling a 10 on a six-sided die is 0. There are no possible outcomes when rolling a die that will result in a 10.

(c) The probability of rolling an even number on a six-sided die is 1/2. There are 3 possible outcomes when rolling a die that will result in an even number: 2, 4, and 6.

Here are the answers in mathematical notation:

(a) P(3) = 1/6

(b) P(10) = 0

(c) P(even) = 1/2

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The percent change in the price of the lawnmower over the 2 years is -8.1%.

To find the percent change in the price of the lawnmower over the 2 years, we can use the formula:

percent change = (new value - old value) / old value * 100%

Plugging in the values given in the problem, we get:

percent change = (329.99 - 358.99) / 358.99 * 100%

percent change = -8.1%

Therefore, the percent change in the price of the lawnmower over the 2 years is -8.1%. Note that the negative sign indicates a decrease in price.

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Answer:

rain gauges

Step-by-step explanation:

hello

the equation given is

the slope of the equation is equal to 2

the points are (-5 ,1)

t

Answer:

100 lol

Step-by-step explanation:

ty for the points! <3

Answer:

100

Step-by-step explanation:

Answer:

$0.59

Step-by-step explanation:

Craig worked at a grocery store. He decided to find the average price of canned green beans.

Average = sum of data/no of data

There are 4 price of green beans.

So,

\(A=\dfrac{0.45+0.56+0.63+0.72}{4}\\\\=\$0.59\)

So, the average price is $0.59.

Answer:

-3 and -5m =-3 over -5

Step-by-step explanation:

Answer:

m = -1/3

Step-by-step explanation:

m = -1 - (-2) / -4 - (-1)

m = -1 + 2 / -4 + 1

m = 1/-3

m = -1/3

The addition equation to represent Jackson's net change in money is x + (-y) = 4.63

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

Jackson receives 4.63 as his change at the grocery store. He places it into a charity donation jar at the register.

WE need to Write an addition equation to represent Jackson's net change in money.

Given that :

The change received = 4.63

The Net change in money :

Let initial amount before purchase is represented by  x

The Cost of item purchased = y (negative as it is incurred)

The Net change in money:

Initial amount + cost of item purchased = change received

x + (-y) = 4.63

Therefore, an addition equation to represent Jackson's net change in money is x + (-y) = 4.63

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