Prove the following identity. Make sure to include all steps taken. [tex]\frac{1+cos\theta }{sin\theta}+\frac{sin\theta}{1+cos\theta}=2csc\theta[/tex]

Hey there! :)

Answer:

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]

Step-by-step explanation:

Given:

f(x) = 5x² + 2

Switch the x and y variables in the equation:

x = 5y² + 2

Subtract 2 from both sides:

x - 2 = 5y²

Divide 5 from both sides:

[tex]\frac{1}{5}(x-2) = y^{2}[/tex]

Square root both sides:

y = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]

**Make sure to add a ±  sign when finding the inverse of a parabolic function.

Therefore, the inverse of this function is:

[tex]f^{-1}(x)[/tex] = ± [tex]\sqrt{\frac{1}{5}(x-2) }[/tex]

Answer:

T < -25

Step-by-step explanation:

Was correct on TTM

Answer:

The dollar amount 8 years from now of $500 invested at 7% annual interest is $859.09

Step-by-step explanation:

In order to calculate the dollar amount 8 years from now of $500 invested at 7% annual interest we would have to calculate the following formula:

dollar amount=PV*(1+r)∧n

According to the given data we have the following:

PV=$500

r=7%

n=8

Therefore, dollar amount=$500*(1+0.07)∧8

dollar amount=$859.09

The dollar amount 8 years from now of $500 invested at 7% annual interest is $859.09

Answer:

SSA the only other right one missing is ASA

Answer:

A. 7√3 in

Step-by-step explanation:

We first have to draw out the altitude on the triangle. When we do so, we should see that we will get 2 congruent 30-60-90 triangles. From there, our h height is x and we use tan∅ to solve:

tan60° = x/7

x = 7tan60°

x = 7√3

Answer:

It's A

Step-by-step explanation:

Answer:

63.00

Step-by-step explanation:

25.1 × 2.51

Multiply.

= 63.001

Round to two decimal places.

63.00

Answer:

63.00

Step-by-step explanation:

when u multiply 25.1 by 25.1 you get 630.01. Then u have to move the decimal over to the left once and then u get 63.00

Answer:  243/5 = 48.6

Step-by-step explanation:

  a₁,  375,  a₃,   a₄,  81 , a₆

First, let's find the ratio (r). There are three multiple from 375 to 81.

[tex]375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}[/tex]

Next, let's find a₆ which is one multiple from 81.

[tex]a_6=81\bigg(\dfrac{3}{5}\bigg)^1\\\\\\.\quad =\large\boxed{\dfrac{243}{5}}[/tex]

Answer:

Step-by-step explanation:

H0: mu is equal to $108.50

Ha: mu is not equal to $108.50

This test is a two tailed test and using the z tat formula, we can ascertain if there is a difference.

z = x-u / sd/√n

Where x is $112, u is $108.50 sd is $16 and n is 64

z = 112-108.50 / 16/√64

z = 3.5/(16/8)

z = 3.5/2

z = 1.75

To help us arrive at a conclusion, we need to find the p value using alpha id = 0.05. The p value is 0.08. Since the p value is great than 0.05, we fail to reject the null and conclude that there is not enough statistical evidence to prove that the average room price is significantly different from $108.50

Answer:

50%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

Heads coming up at most 600 times when a fair coin is flipped 1000 times.

600/1000

= 0.6

0.6 × 100

= 60

Answer:

A

Step-by-step explanation:

For lines to be parallel, their slopes need to be the same.

For lines to be perpendicular, the product of their slopes needs to be -1.

None of these conditions are met since the slopes are 2 and 4 respectively.

Sooo.... The answer must be A! :)

Answer:

The lines given are neither perpendicular nor are they parallel.

Step-by-step explanation:

In order for two lines to be be parallel, they must have the same slope but different y-intercepts. In order for two lines to be perpendicular, one line has to have a slope that is the negative reciprocal of the other line.

We are given two line equations.

y = 2x

y = 4x + 1

These lines do not represent a perpendicular situation nor do they represent a parallel situation.

Answer:

[tex]\frac{12}{x^2 +7x}[/tex]

Step-by-step explanation:

Simply multiply straight across which you get

12/X X × ( X +7 )

Then just multiply X into the parenthesis

Hope this helps :)

Answer:

  1.23

Step-by-step explanation:

"Appropriate technology" makes short work of this.

Answer:

upper sum= 0.859

lower sum = 0.659

Step-by-step explanation:

y = √(1 − x²)

if n= 5

Answer:

d = 3 in

Step-by-step explanation:

Since we are trying to find the diameter, and the diameter is given to us as 3 in, our diameter is 3 in.

Answer:

Yes

Since the time taken t= 7.58 hours required to complete both buildings is less than the 8-hours shift then she can finish the two buildings.

Step-by-step explanation:

Given;

Building A = 3,000 square feet

Building B = 2,460 square feet

Total area of building A and B = 3,000+2460

= 5460 square feet

Rate = 5 seconds per square foot

Time taken to complete both buildings is;

Time t = Total area × rate per area.

t = 5460 × 5 seconds

t = 27300 seconds

t = 27300/60 minutes = 455 minutes

t = 455/60 hours

t = 7.583333333333 hours

t = 7.58 hours

Since the time taken t required to complete both buildings is less than the 8-hours shift then she can finish the two buildings.

Answer:

The correct answer is the last option (-2, 8)

Step-by-step explanation:

You can see that the lines intersect at the point -2, 8.

Hope this helped! :)

Answer:

D.

Step-by-step explanation:

The point (-2,8) is the only given point that is on the two lines in this graph.

If you want to make sure, you can just use a graphing calculator on your laptop/ computer & zoom in on it. Hopefully this helps & gets a brainliest. Thx for giving me time.

Answer: a. 12.4 years

Step-by-step explanation:

Function to represent exponential growth continuously:

[tex]A=A_0e^{rt}[/tex]  ...(i)

, where [tex]A_0[/tex] = initial amount, r= rate of interest ( in decimal) , A = Amount after t years.

As per given , we have

[tex]A_0=\$1300\\\\r=8\%=0.08\\\\ A=\$3500[/tex]

To find : t

Put all values in (i) ,

[tex]3500=(1300)e^{0.08t}\\\\\Rightarrow\ 2.6923077=e^{0.08t}[/tex]

Taking natural log on both sides

[tex]\ln(2.6923076)= 0.08t\\\\\Rightarrow\ 0.99039867=0.08t\\\\\Rightarrow\ t=\dfrac{0.99039866}{0.08}=12.37998325\approx12.4[/tex]

Hence, it would take 12.4 years.

so, the correct option is a. 12.4 years .

Answer:

2800

Step-by-step explanation:

2826 to the nearest hundred is 2800

Answer:

-17x + y = 128

Step-by-step explanation:

First, find the slope.

[tex]m=\frac{y_{2}-y_{1} }{x_{2}- x_{1} }\\m=\frac{9-(-8) }{-7-(-8)}\\m=\frac{9+8 }{-7+8}\\m=\frac{17}{1} \\m=17[/tex]

Now, use point-slope form to find the equation.

y - y = m(x - x)

y - 9 = 17(x - (-7))

y - 9 = 17(x + 7)

y - 9 = 17x + 119

y = 17x + 128

Since your equation needs to be in Ax + By = C form, rearrange the equation so that the x and y values are on the left side of the equation.

y = 17x + 128

-17x + y = 128

Here the l'Hospital's Rule is appropriate, as the limit is in the form [tex]\infty / \infty[/tex]. Take a look at the procedure below -

[tex]\lim_{x \to \infty} x^4e^{-x^3} = \lim_{x \to \infty} \frac{x^4}{e^{x^3}}[/tex],

At this point, one can conclude that the solution should " boil down " to the expression [tex]4 / \infty[/tex], and thus the solution is 0.

Hope that helps!

Answer:

tan∅ = 3√29/10

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

cos∅ = adjacent/hypotenuse

Since we are given cos∅ = 10/19, we know that one leg is 10 and the hypotenuse is 19. We need to find the missing leg length:

10² + b² = 19²

b² = 19² - 10²

b = √261

b = 3√29

We know that tan∅ equals opposite over adjacent. Our adjacent is given to us by cos∅, so we simply plug in our values:

tan∅ = opposite/adjacent

tan∅ = 3√29/10

Answer:

tan theta = 2 sqrt(5) /15

Step-by-step explanation:

sin theta = opp / hypotenuse

sin theta = 2/7

We can use the Pythagorean theorem to find the length of the adjacent side

a^2 + b^2 = c^2

2^2 +adj^2 = 7^2

4 + adj^2 = 49

adj ^2 = 49-4

adj^2 = 45

Taking the square root of each side

adj = sqrt(45) = sqrt(9*5) =sqrt(9) sqrt(5) = 3 sqrt(5)

The tan theta = opp/ adj

tan theta = 2 / 3 sqrt(5)

Multiply by sqrt(5) / sqrt(5)

                = 2 sqrt(5) / 3 *5

                 = 2 sqrt(5) /15

Answer:

13

Step-by-step explanation:

We can find the missing side length by using the pythagorean theorem

a² + b² = c²

5² + 12² = c²

25 + 144 = c²

169 = c²

13 = c

So, 13 is the missing side length.

Answer:

Nikki grows 20 tomato plants and she measures their heights.

We want to complete the frequency table.

All we have to do is count the number of values that fall between each range.

The values are:

5  10  12  16  14

17  20  15  10  7

13  11  6  18  15

6  12  17  8  12

  Height              Frequency

-> 5 ≤ h < 10             5

10 ≤ h < 15                8

15 ≤ h < 20               6

20 ≤ h < 25               1

Answer:

x=-52

Step-by-step explanation:

1/3x=-17 1/3

x=-52

Answer:

C.

Step-by-step explanation:

Area of a Sector Formula: A = x/360πr²

Since we are given x and r, simply plug it in:

A = 40/360π(4)²

A = 1/9π(16)

A = 16π/9

Answer:

Step-by-step explanation:

[tex]angle \: theta = 40 \: degree \\ theta = 40 \times \frac{\pi}{180 } \\ theta = \frac{2\pi}{9} [/tex]

Radius= 4 cm

[tex]area = \frac{1}{2} \times theta \: \times {r}^{2} \\ \: \: \: \: \: \: \: \: \: = \frac{1}{2} \times \frac{2\pi}{9} \times {4}^{2} \\ \: \: \: \: \: \: \: \: = \frac{1}{2} \times \frac{2\pi}{9} \times 16 \\ \: \: \: \: \: \: \: = \frac{16\pi}{9 \: {cm}^{2} } [/tex]

Hope this helps....

Good luck on your assignment...

Answer:

220 grams.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question:

[tex]\mu = 212, \sigma = 20, n = 22, s = \frac{20}{\sqrt{22}} = 4.264[/tex]

If you pick 22 fruits at random, then 3% of the time, their mean weight will be greater than how many grams?

We have to find the 100 - 3 = 97th percentile, which is X when Z has a pvalue of 0.97. So X when Z = 1.88.

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]1.88 = \frac{X - 212}{4.264}[/tex]

[tex]X - 212 = 1.88*4.264[/tex]

[tex]X = 220[/tex]

The answer is 220 grams.

Answer:

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

Step-by-step explanation:

Average cost is the cost per unit of production. It is expressed mathematically as the total cost divided by the total number of units produced.

If total cost = C(x, y)

Average cost = C(x, y) ÷ (x+y)

For this question, total cost function is

C(x, y) = 200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾

The average cost is simply this total cost function divided by the total number of units produced.

Average cost

= [200,000 + 5,700x + 4,200y − 100,000e−⁰•⁰¹⁽ˣ ⁺ ʸ⁾] ÷ (x + y)

If numerical values are then provided, this can then be worked around. But as the numerical values are absent, the average cost function just remains in this its raw form.

Hope this Helps!!!

Answer:

B. y=-4x+2

Step-by-step explanation:

y-6=-4x-4

y=-4x-4+6

y=-4x+2