i think it is e but I am not sure. If someone knows the answer, please reply

The measure of the exterior angle in this case is 60+60 = 120 degrees.

What is exterior angle ?

An exterior angle of a polygon is an angle formed between one side of the polygon and a line extended from the endpoint of the opposite side. An exterior angle can be formed by standing outside of the polygon and looking at it.

In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it. In any convex polygon, the sum of the measures of the exterior angles is always 360 degrees.

The support for a window air-conditioning unit forms a triangle. A triangle is a three-sided polygon, and all the interior angles in a triangle add up to 180 degrees. Therefore, the measure of each interior angle of a triangle is (180/3) = 60 degrees.

An exterior angle of a triangle is the angle formed between one side of the triangle and a line extended from the endpoint of the opposite side. In a triangle, the measure of an exterior angle is equal to the sum of the measures of the two interior angles opposite to it.

Therefore, the measure of the exterior angle in this case is 60+60 = 120 degrees.

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The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

There are a total of 15 people in the group. A committee of size 5 is to be chosen from a group of 7 men and 8 women randomly. Therefore, the sample space for this situation is 15C5 ways to choose 5 people from a total of 15 people. 15C5 = 3003 ways. That means there are 3003 ways to select 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003. That means the probability of selecting any one committee out of 3003 committees is 1/3003.To compute the probability of selecting any given committee, we first need to determine how many possible committees can be formed from the group of 15 people. The number of ways to choose 5 people from a total of 15 people is given by 15C5. This can be calculated as follows:15C5 = (15!)/((15-5)! * 5!) = (15 * 14 * 13 * 12 * 11)/(5 * 4 * 3 * 2 * 1) = 3003Therefore, there are 3003 ways to select a committee of 5 people from the group of 15 people. The probability of selecting any given committee is 1/3003.

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Answer:

Correct option is

B

0

D

−1

sinx+sin2x+sin3x

=sin(2x−x)+sin2x+sin(2x+x)

=2sin2xcosx+sin2x [ by using sin(A+B)=sinAcosB+sinBcosA and sin(A−B)=sinAcosB−sinBcosA ]

=sin2x(2cosx+1)........(i)

cosx+cos2x+cos3x

=cos(2x−x)+cos2x+cos(2x+x)

=2cos2xcosx+cos2x [By using cos(a−b)=cosa⋅cosb+sina⋅sinb and cos(a+b)=cosa⋅cosb−sina⋅sinb]

=cos2x(2cosx+1).....(ii)

∴(sinx+sin2x+sin3x)

2

+(cosx+cos2x+cos3x)

2

=1

sin

2

2x(2cosx+1)

2

+cos

2

2x(2cosx+1)

2

=1.......[From(i)(ii)]

⇒(2cosx+1)

2

=1

⇒2cosx+1=±1

∴cosx=0or−1

The answer is C.) The model is not a good fit.

Dirk plants 8 diff herbs and keep the small pot in his kitchen he starts with a 4 lb. bag of soil and puts the same amount in each pot. if he uses all the soil how many oz does he add to each pot​

step 1

Divide 4 lb by 8

so

4/8=1/2 lb in each pot

Remember that

1 lb=16 oz

1/2 lb=8 oz

therefore

Answer:

The answer is A

Negative 21 divided by negative 1.4

Step-by-step explanation:

Answer:

A its probably wrong but tell me if is

Step-by-step explanation:

=========================================================

Explanation:

Find the prime factorization of 72 and 162

Here's a simplified version of each

We have these unique primes: 2, 3

Circle the terms that have the largest exponents for each of those unique primes. So you'll circle 2^3 and 3^4. Those items circled will multiply together to get the LCM.

This means 2^3*3^4 is the LCM (lowest common multiple).

2^3*3^4 turns into 648, but your teacher wants you to keep the LCM in prime factor form.

------------------------------

Now onto the HCF (highest common factor; aka GCF).

Looking at

We again see '2's and '3's as the unique primes. Both have at 1 copy of '2' between them. They also both have 3^2 between them. It might help to think of 3^4 as 3^2*3^2.

Those common factors you circled are then multiplied.

Overall, the HCF is 2*3^2 = 2*9 = 18

-----------------------------

Side note: The HCF is useful to help reduce fractions, while the LCM is useful to help find the LCD (lowest common denominator) when adding or subtracting fractions of different denominators. There are other applications of each of these.

Answer:

LCM= 648

HCF= 18

Step-by-step explanation:

a. U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d.  U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct). This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income.

a. The optimization problem of the representative agent involves maximizing the present discounted value of utility subject to the period-by-period budget constraint. The Euler equation is derived as follows:

At each period t, the agent maximizes the utility function U(ct) = ln(ct) subject to the budget constraint ct = (1 + r)wt + yt, where wt is the agent's wealth at time t. Taking the derivative of U(ct) with respect to ct and applying the chain rule, we obtain: U'(ct) = β(1 + r)U'(ct+1). This equation is known as the Euler equation, which represents the intertemporal marginal rate of substitution between consumption at time t and consumption at time t+1.

b. The Euler equation between time 1 and time 3 can be written as U'(c1) = β(1 + r)U'(c2), where c1 and c2 represent consumption at time 1 and time 2, respectively.

Similarly, we can write the Euler equation between time 2 and time 3 as U'(c2) = β(1 + r)U'(c3). Combining these two equations, we fin

d U'(c1) = β(1 + r)^2U'(c3). This relationship shows that the marginal utility of consumption at time 1 is equal to the discounted marginal utility of consumption at time 3.

c. The present discounted value of optimal lifetime consumption can be written as C0 = ∑t=0[infinity]​(β(1 + r))^tct. This equation represents the sum of the discounted values of consumption at each period, where the discount factor β(1 + r) accounts for the diminishing value of future consumption.

d. The present discounted value of optimal lifetime utility can be written as U0 = ∑t=0[infinity]​(β(1 + r))^tln(ct).

This equation represents the sum of the discounted values of utility at each period, where the discount factor β(1 + r) reflects the time preference and the logarithmic utility function captures the agent's preference for consumption.

e. The present discounted value of lifetime income, denoted as Y0, can be expressed as Y0 = y0 + (1 + γ)y1 + (1 + γ)^2y2 + ..., where γ represents the growth rate of income. The income in each period is multiplied by (1 + γ) to account for the increasing income over time.

This assumption of income growth allows for a more realistic representation of the agent's economic environment, where income tends to increase over time due to factors such as productivity growth or wage increases.

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Answer:

Yes.

Step-by-step explanation: 8/3 is equal to 32/12, but simplified. Hope this helps!

Answer:

-5.17 , 5 , 6 , 26 , 33 , 37

Step-by-step explanation:

the negative numbers are usually the least . All u had to do was put the other numbers from least to greatest <3

- Mark me brainliest !

Answer:

- 5.17

5

6

26

33

37

hope this helps :)

The area of the triangle is mathematically given as

A=20.8cm

This is further explained below.

The region that is surrounded by the perimeter of the triangle, also known as the three sides of the triangle, is referred to as the area of the triangle.

The space that is encompassed by all three of a triangle's sides is referred to as the triangle's area.

It is computed with the assistance of a variety of formulae that differ according to the kind of triangle, and the results are represented in square units such as centimeters squared, inches squared, and so on.

Generally, the equation for Area the is mathematically given as

A = 1/2 * base * height

Therefore

A= 1/2 * 8 * 5.2

A=20.8cm

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The radius of convergence is 1, and the interval of convergence for the given power series Σ (x-5)^n is (4, 6).

To find the radius of convergence and the interval of convergence for the given power series\(Σ (x-5)^n,\) we can use the Ratio Test.

Step 1: Apply the Ratio Test
The Ratio Test states that if the limit as n approaches infinity of the absolute value of the ratio of consecutive terms is L, then:
- If L < 1, the series converges.
- If L > 1, the series diverges.
- If L = 1, the test is inconclusive.

Step 2: Set up the Ratio Test for our power series
We have the series Σ (x-5)^n. Calculate the ratio of consecutive terms as follows:
\(|((x-5)^(n+1))/(x-5)^n| = |(x-5)|\)

Step 3: Find the limit as n approaches infinity
Since our ratio does not depend on n, the limit as n approaches infinity is simply:
L = |(x-5)|

Step 4: Determine the radius of convergence
For convergence, we need L < 1, which translates to:
|(x-5)| < 1

Step 5: Find the interval of convergence
Now, solve the inequality for x:
-1 < (x-5) < 1
4 < x < 6

So, the interval of convergence is (4, 6).

In conclusion, The radius of convergence is 1, and the interval of convergence for the given power series\(Σ (x-5)^n is (4, 6).\)

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Answer: y = -1*x^2 - 4

Step-by-step explanation:

A generic quadratic equation is written as:

y = a*x^2 + b*x + c

we need to find the values of a, b, and c

We have the table:

x     y = f(x)

-4     -20

-3       -13

-2        -8

-1         -5

0         -4

1          -5

In the table we can see two things:

y(0) = a*0^2 + b*0 + c = c = -4

Then we know that:

y(x) = a*x^2 + b*x - 4

Now we only need to find a and b.

We also can see that we have symmetry around the point x = 0, this means that x = 0 is the vertex of the quadratic equation, and for a general case the vertex is at:

x = -b/2a

and this is equal to zero:

-b/2a = 0

then we must have b = 0.

So for now, the equation is:

y = a*x^2 -4

Now we can just replace the values of any of the points to find the value of a, for example we can use the point (1, -5)

this means that:

y = -5 = a*1^2 - 4

    -5 = a - 4

    -5 + 4 = a

        -1 = a

Then the quadratic equation is:

y = -1*x^2 - 4

A financial investment broker earns 4% on each customer dollar invested. If the broker invests $50,000, the commission on the investment is $2,000.

The commission earned by the broker on the investment will be equal to 4% of the total investment amount.

So, the commission earned by the broker on investing $50,000 will be:

Commission = 4% of $50,000

Commission = (4/100) x $50,000

Commission = 4 x  $500

Commission = $2,000

Therefore, the commission earned by the broker on investing $50,000 will be $2,000.

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Answer:

Emily have 33 cookies.

Step-by-step explanation:

Given that:

Batches of cookies baked = 3

Number of cookies in each batch = 13

Total number of cookies = 3 * 13 = 39 cookies

She ate 2 cookies.

Remaining = 39 - 2 = 37 cookies

She gave 10 to her neighbor

Remaining = 37 - 10 = 27 cookies

1 batch = dozen cookies

half batch = 6 cookies

Total cookies = 27 + 6 = 33 cookies

Hence,

Emily have 33 cookies.

Answer:

62.17 days

Step-by-step explanation:

The computation of the number of days  is shown below:

Given that

A(t)=10 × 0.5^(t ÷ 18.72)

1 = 10 × 0.5 ^ (t ÷ 18.72)

0.1 = 0.5 ^ (t ÷ 18.72)

Now consider the log in both sides

ln(0.1) = ln(0.5)^ (t ÷ 18.72)

ln(0.1)  ÷  ln(0.5) = (t ÷ 18.72)

3.321928095  = (t ÷ 18.72)

So, t = 62.17 days

With the help of log, we can easily compute it

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Explanation: To solve this question first we need to know that the terminal point pair (little red point in the image) represented by the coordinates represent the (cosine, sine) as shown bellow

We also need to understand that the "tan" formula can be expressed as follows

So all we need to do is to substitute and calculate.

Step 1: Let's substitute the values and calculate as follows

Step 2: Now let's rationalize the result as follows

Final answer: So the final answer is

.

This real-world problem has the limitations 75< x <110 and 0< y\(\leq\) 50, hence:

option (C) is the best choice.

The term "inequality" refers to a mathematical expression in which both sides have mathematical signs that are either less than or greater than one another, and the expression is one where the two sides are not on equal footing.

We have:

Your senior vacation is scheduled to include a class trip to a beach. Only when it's between 75 and 110 degrees do guests at the resort get access to the pool. 50 passengers can go with you.

Let y be the number of passengers and x be the temperature

75 to 110 degrees are the range of the temperature.

75 < x < 110

50 passengers can go with you.

0 < y ≤ 50

In order to illustrate this real-world issue, the limitations are 75 <x <110 and 0< y \(\leq\)50.

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Answer:

\(\frac{9}{20}\)

Step-by-step explanation:

See picture below :)

Answer:

x = 5

Step-by-step explanation:

have a nice day

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Answer:

∠ C = 100°

Step-by-step explanation:

since 2 sides of the triangle are congruent then the triangle is isosceles with base angles congruent.

consider the angle inside the triangle to the left of 140°

this angle and 140° are a linear pair and sum to 180°

angle + 140° = 180° ( subtract 140° from both sides )

angle = 40°

then the angle on the left of the triangle = 40° ( base angles congruent )

the sum of the angles in a triangle = 180° , so

∠ C + 40° + 40° = 180°

∠ C + 80° = 180° ( subtract 80° from both sides )

∠ C = 100°

Answer:

68 degrees fahrenheit.

Step-by-step explanation:

Formula:

(20°C × 9/5) + 32 = 68°F

Answer:

Its around 68F

Step-by-step explanation:

Hope this helped

Answer:

$7.5

Step-by-step explanation:

Answer:

jvjjvscsjcsjsvjscjsvhchhcuhcjwcwh ejcisvsufjdtsydghcwhcjwvhsvjscekfdjsvjsfjsvkdvs

Step-by-step explanation:

30y

Answer:

Rule of thumb is;

Your cumulative total student loans taken as at the time you are graduating should be less than your proposed annual starting salary.

Step-by-step explanation:

When calculating the loan a college student can afford, a rule of thumb comes in very handy which is that:

Your cumulative total student loans taken as at the time you are graduating should be less than your proposed annual starting salary.

This is because If your total student loan debt is less than your proposed annual income, it means all things being equal, you would be able to pay back the loan in about 10 years or less. However, if the loan debt exceeds your proposed income, it means you are likely to going to struggle and find it very difficult to repay your loan.

Answer:

The 3rd option

Step-by-step explanation: