Express the height of the tree in terms of
trigonometric ratios. (MGSE9-12.G.SRT.6, MGSE9-
12.G.SRT.7)
A. 90 cos 50°
B. 90 sin 50⁰
C. 90 cot 50°
D. 90 tan 50⁰

a=180-79=101

c=180-83=97

a+c+d+b=360

101+97+2x=360

198+2x=360

2x=360-198=162

X=162/2=81

a=101

b=97

b and d=81

After evaluating integral ∫(30 / (4 + x²)) dx using a trigonometric identity, we got 15 arctan(x/2) + C as answer

To create the substitution triangle, we consider the right triangle formed by the substitution. Let's label the sides of the triangle as follows:

Opposite side: x Adjacent side: 2 Hypotenuse: Using the Pythagorean theorem, we can find the length of the hypotenuse:

Hypotenuse² = Opposite side² + Adjacent side² Hypotenuse² = x² + 2² Hypotenuse = √(x² + 4)

Now, we define the substitution variables: x = 2tanθ dx = 2sec²θ dθ (differentiate both sides with respect to θ) Substituting these variables into the integral, we have:

∫(30 / (4 + x²)) dx = ∫(30 / (4 + (2tanθ)²)) (2sec²θ) dθ = 60 ∫(sec²θ / (4 + 4tan²θ)) dθ = 60 ∫(sec²θ / 4(1 + tan²θ)) dθ Using the identity tan²θ + 1 = sec²θ, we can simplify the integrand: ∫(30 / (4 + x²)) dx = 60 ∫(sec²θ / 4sec²θ) dθ = 60/4 ∫dθ = 15θ + C

Finally, we substitute back the value of θ in terms of x:

15θ + C = 15arctan(x/2) + C Therefore, the evaluated integral is 15arctan(x/2) + C.

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The 12 months past and the fruit turned into sonic the hedge hog #PERIODAHHPERIODUHH

The given expression is

First, we solve the powers and the root

We solve the products on each side of the fraction

Now, we divide whole numbers each other and powers each other

The probability that x is less than 6 is 5/8.

If x is a discrete uniform random variable ranging from one to eight, then each value from one to eight is equally likely to occur, and the probability of any particular value is 1/8.

To find p(x < 6), we need to add up the probabilities of all the values of x that are less than 6:

p(x < 6) = p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)

Since x is a discrete uniform random variable, the probability of each of these values is 1/8, so we can substitute that into the equation:

p(x < 6) = (1/8) + (1/8) + (1/8) + (1/8) + (1/8)

Simplifying, we get:

p(x < 6) = 5/8

Therefore, the probability that x is less than 6 is 5/8.

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Hey there!

1/5 + 3/10
= 2/10 + 3/10

= 2 + 3/10 - 0

= 5/10

= 5 ÷ 5 / 10 ÷ 5

= 1 / 2

Therefore, your answer is: 1/2

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

I'm pretty postive its B because the table starts with 10 But I also thiks it A

Step-by-step explanation:

Hi

3*5000 +X*2500 = 25 000

15 000 + 2 500X = 25 000

                2 500X = 25 000 - 15 000

                       2 500 X = 10 000

                               x = 10 000 / 2 500

                                 X = 100/25

                                   X = 4

You need 4 post for  B

3*5000 + 4* 2 500 =  15 000 + 10 000 = 25 000

Answer:

its the first one

Step-by-step explanation:

Answer:

4/3 as an improper fraction or 1 1/3 as a mixed number

Step-by-step explanation:

4 divided by 3= 4/3 =1 1/3

The 4 divided by 3 answers as a fraction is 4/3 and 4 is in the numerator and 3 is in the denominator.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

We have:

The expression in words is  4 divided by 3 answers as a fraction.

As we know, the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

Here we have to division:

= 4 ÷ 3

or

= 4/3

4 is in the numerator and 3 is in the denominator.

Thus, the 4 divided by 3 answers as a fraction is 4/3 and 4 is in the numerator and 3 is in the denominator.

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To calculate the duration of the shift, you need to subtract the clock-in time from the clock-out time.

In this case, the shift worker clocked in at 1730 hours (5:30 PM) and clocked out at 0330 hours (3:30 AM). However, since the clock is based on a 24-hour format, it's necessary to consider that the clock-out time of 0330 hours actually refers to the next day.

To calculate the duration of the shift, you can perform the following steps:

1. Calculate the duration until midnight (0000 hours) on the same day:

  - The time between 1730 hours and 0000 hours is 6 hours and 30 minutes (1730 - 0000 = 6:30 PM to 12:00 AM).

2. Calculate the duration from midnight (0000 hours) to the clock-out time:

  - The time between 0000 hours and 0330 hours is 3 hours and 30 minutes (12:00 AM to 3:30 AM).

3. Add the durations from step 1 and step 2 to find the total duration of the shift:

  - 6 hours and 30 minutes + 3 hours and 30 minutes = 10 hours.

Therefore, the duration of the shift was 10 hours.

Answer: a+b=32

4a+7b=200

a = 15

b = 20

There are 15 four pointers and 20 seven pointers. You can plug in the numbers to check.

it only 5 points but it’s okay.

Step-by-step explanation:

Answer:i think it is 7/3

Step-by-step explanation:

Answer:

well 12 x 10 = 120 so 120 x 10 = 1200 and 5 x 5 = 25 so 25 x 10 = 250 and 1200 + 250 would be 1450

The values of a, b, c are 152°, 28°, 152° respectively.

Angles around a point describes the sum of angles that can be arranged together so that they form a full turn.

The sum of angles at a point will give 360°.

This means that a + b + c + 28 = 360

c +28 = 180° ( angle on a straight line)

c = 180 -28

c = 152°

c = a( alternate angles are equal)

therefore the value of a = 152°

b = 28( alternate angles are equal)

therefore the value of b is 28

therefore the values of a, b, c are 152°, 28°, 152° respectively

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The mandible is moving and the cusp "moving" with the arrow is in the either the working or rotating side, while the other side is referred to as either the balancing or orbiting side.

Given that;

The mandible is moving and the cusp "moving" with the arrow is in the ?

Now, We know that;

The side of the mandible that moves sideways is referred to as either the working or rotating side, while the other side is referred to as either the balancing or orbiting side.

Thus, The mandible is moving and the cusp "moving" with the arrow is in the either the working or rotating side, while the other side is referred to as either the balancing or orbiting side.

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Answer:

(6,1)

Step-by-step explanation:

Step-by-step explanation:

Given that,

The area of a blackboard is \(1\dfrac{1}{3}=\dfrac{4}{3}\ \text{yards}^2\)

The area of poster is \(\dfrac{8}{9}\ \text{yards}^2\)

We need to find the unit rate of the blackboard's area to the poster's area. So, it can be calcualted by dividing blackboard's area to the poster's area.

So,

\(\dfrac{\dfrac{4}{3}}{\dfrac{8}{9}}=\dfrac{4}{3}\times \dfrac{9}{8}\\\\=1.5\)

So, the rate of \(1.5\ \text{yard}^2\).

The probability that a white ball was selected from the box with initially a white balls given that a white ball was selected from the box with a new ball is (a+1)/(a+b+3).

Let's define the events:

- Event A: the white ball was selected from the box with initially a white balls

- Event B: a white ball was selected from the box with a new ball

We want to find the probability of Event A given that Event B has occurred, which can be denoted as P(A|B).

We can use Bayes' theorem to calculate this probability:

P(A|B) = P(B|A) * P(A) / P(B)

where P(B|A) is the probability of selecting a white ball from the box with a new ball given that the ball added to the box was white, P(A) is the prior probability of selecting a ball from the box with initially a white balls, and P(B) is the probability of selecting a white ball from either box.

Since a ball was added to the box with initially a white balls, there are now a+1 white balls and b black balls in that box, and there are b+1 white balls and a black balls in the other box. Therefore, the probability of selecting a white ball from the box with a new ball given that the ball added to the box was white is (a+1)/(2a+2+b+1) = (a+1)/(a+b+2).

The prior probability of selecting a ball from the box with initially a white balls is 1/2, since we are equally likely to select from either box.

The probability of selecting a white ball from either box can be calculated using the law of total probability:

P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)

where P(not A) = 1 - P(A) is the probability of selecting from the box with initially a black balls.

P(B|not A) is the probability of selecting a white ball from the box with a new ball given that the ball added to the box was black, which is (b+1)/(2a+2+b+1) = (b+1)/(a+b+2).

Therefore,

P(B) = (a+1)/(2a+2+b+2) * 1/2 + (b+1)/(2a+2+b+2) * 1/2 = (a+b+2)/(2a+2+b+2) = (a+b+2)/(2(a+b)+4)

Now we can substitute these values into Bayes' theorem:

P(A|B) = (a+1)/(a+b+2) * 1/2 / ((a+1)/(a+b+2) * 1/2 + (b+1)/(a+b+2) * 1/2)

Simplifying this expression gives:

P(A|B) = (a+1)/(a+b+3)

Therefore, the probability that the white ball was selected from the box with initially a white balls given that a white ball was selected from the box with a new ball is (a+1)/(a+b+3).

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Answer:

Step-by-step explanation: add 4 to cancel out, dive both sides by 3, y=1.3 repeating

Answer:

a) \(C(t)=245,000\cdot(1.035)^t\)

b) Nicki's house is worth $281,143 in 4 years

Step-by-step explanation:

Exponential Growth Function

The exponential function is commonly used to model natural growing or decaying processes where the change is proportional to the actual quantity.

An exponential growth function is expressed as:

\(C(t)=C_o\cdot(1+r)^t\)

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the growth positive rate, expressed in decimal

Nicki paid Co=$245,000 for a house and it's known that home prices increase by r=3.5%=0.035 each year.

a)

Substituting the given values, the equation is:

\(C(t)=245,000\cdot(1+0.035)^t\)

\(\mathbf{C(t)=245,000\cdot(1.035)^t}\)

b) The value of Nicki's house in t=4 years is:

\(C(4)=245,000\cdot(1.035)^4\)

\(C(4)=245,000\cdot 1.148=281,143\)

Nicki's house is worth $281,143 in 4 years

Answer:

¾

Step-by-step explanation:

\(\boxed{slope = \frac{y1 - y2}{x1 - x2} }\)

☆ (x₁, y₁) is the first coordinate and (x₂, y₂) is the second coordinate

Slope of line

\( = \frac{6 - 3}{0 - ( - 4)} \)

\( =\frac{3}{4} \)

Answer:

6. 12cm

7. 11.2 cm

8. 92 degrees

9. 53 degrees

10. 37.5 cm

11. $ 693.12

Step-by-step explanation:

For questions 6-9 the triangle is congurent which means both their angles will be equal.

For the sides you can see that the second triangle is 1.5 times smaller than the first one as taking one of the sides 21/14= 1.5

So for Q. 6 we can multiply side PQ by 1.5.

For Q.7 divide CA by 1.5.

For Q. 10 we can do cross multiplication:

5/4 = x/30

= 150= 4x

= 37.5=x

For Q 11 we can see the size of the paper is 1.9 times bigger than the original one (38/20)

So the shorter side is 30.4 cm.

Then we have to find the area of the paper to multiply the two dimensions and we get 1155.2 square inches.

Then to figure out the money we multiply again and we get $693.12.

Answer:

86.6% ; 93.4%

Step-by-step explanation:

To obtain the population proportion from the sample, we calculate the confidence interval ;

Confidence interval = phat ± margin of error

Phat = 90% ; margin of error = +3.4%

Hence,

90% ± 3.4%

(90 - 3.4)% ; (90 + 3.4)%

86.6% ; 93.4%

Answer:

The convergent series are;

\(\sum \limits _{n = 1}^\infty \left( \dfrac{1}{5} \right) ^n\)

(And)

\(\sum \limits _{n = 1}^\infty \left( \dfrac{1}{10} \right) ^n\)

Step-by-step explanation:

A series in mathematics is the sum of a sequence of numbers to infinity

A convergent series is a series that sums to a limit

From the given options, we have;

First option

\(\sum \limits _{n = 1}^\infty \dfrac{2\cdot n}{n + 1}\)

As 'n' increases, 2·n becomes more larger than n + 1, and the series diverges

Second option

\(\sum \limits _{n = 1}^\infty \dfrac{n^2 - 1}{n - 2}\)

As 'n' increases, n² - 1, becomes more larger than n - 2, and the series diverges

Third option

\(\sum \limits _{n = 1}^\infty \left( \dfrac{1}{5} \right) ^n\)

As 'n' increases, \(\left( \dfrac{1}{5} \right) ^n\), becomes more smaller and tend to '0', therefore, the series converges

Fourth option

\(\sum \limits _{n = 1}^\infty \left( \dfrac{1}{10} \right) ^n\)

As 'n' increases, \(3 \times\left( \dfrac{1}{10} \right) ^n\), becomes more smaller and tend to '0', therefore, the series converges

Fifth option

\(\sum \limits _{n = 1}^\infty \dfrac{1}{10} \cdot (3) ^n\)

As 'n' increases, \(\dfrac{1}{10} \cdot (3) ^n\), becomes more larger and tend to infinity, therefore, the series diverges.

Answer:

C and D

Step-by-step explanation:

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