Trigonometry need help on this one

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\(\bullet\large\text{ Negatives are below 0 \& is on the left side of the number line.}\\\bullet\large\text{ Positives are above 0 \& is on the right side of the number line.}\\\\\star\large\textsf{ Negative \& negative equals positive}\\\star\large\textsf{ Positive \& positive equals positive}\\\star\large\textsf{ Negative \& positive equals negative}\\\star\large\textsf{ Positive \& negative equals negative}\)

\(\large\text{5 + (-3)}\\\large\textsf{= 5 - 3}}\\\large\textsf{= 2}\\\\\huge\boxed{\textsf{Therefore, your answer is: 2}}\huge\checkmark\)

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Answer:

1.

Step-by-step explanation:

distance = √(X2 - X1)^2 + (Y2 - Y1)^2

= √(-1 - 2)^2 + (9 - 8)^2

= √(-3)^2 + (1)^2

= √ 9 + 1

= √10

Answer:The distance is √10

Step-by-step explanation:

Answer:

it should be this

Step-by-step explanation:

y= 1/3 and then -4

The value of P'(5) = 65 and  P'(6) = 65.

Mr. Wutz owns a hot dog business called 'Wutz upDogs.' The daily profit function is given by P(x) = 65x + 7, where x is the number of hot dogs sold.

To evaluate P'(6), the derivative of P(x) at x = 6, we need to use the power rule for derivatives. The power rule states that d/dx(xn) = nxn-1. Therefore, P'(6) = 65(6)1 = 65 dollars per hot dog.

To evaluate P'(5), the derivative of P(x) at x = 5, we use the same power rule. Therefore, P'(5) = 65(5)1 = 65 dollars per hot dog.

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In a linear equation, 9.14 does he save by paying off the loan when the next payment is due .

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                               Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Jan  293  18  311  1,507 16.25%

Feb  296  15  311  1,212 32.67%

Mar 298           12  311   913 49.25%

Apr  301            9  311   612 66.00%

May  304    6  311  308 82.92%

Jun  308    3  311    0        100.00%

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The statement that correctly describes how to show the relationship between the exterior angle and the interior angles using tracing paper is A. Trace ∠2. Move the paper so that ∠2 and ∠3 are adjacent angles. Then trace ∠3. Place the paper on top of ∠1 to show that ∠2 and ∠3 together are the same size as ∠1.

Instructing to trace ∠2 first, move the paper so that ∠2 and ∠3 are placed alongside one another. Then, succeeding the action taken beforehand, trace ∠3. Subsequently, rest the paper atop ∠1 in order to signify that, when combined, ∠2 and ∠3 possess an equivalent measure in comparison with ∠1.

Reason for this is based on the exterior angle adjacent to angle 2 being labeled inclusively as 1. As stated within the Exterior Angle Theorem, the magnitude of an exterior angle of a triangle shares equal dimensions to the aggregate measurement of its remote interior angles.

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Answer:

0+10i

Step-by-step explanation:

First, the square root of 100 is 10 because 10*10 is 100.

i=-1

Therefore, to get rid of the minus, it would be 10i

Since there is nothing else to solve,

the answer is 0+10i

Answer:100

IQ scores have a bell-shaped distribution with a mean of 100.

Answer:

Amy has 12 5¢ coins

Step-by-step explanation:

Let x represent 20¢ coins and y represent 5¢ coins.

Amy has four more 20¢ coins than 5¢ coins. Hence:

\(x=y+4\)

And the total value of all her coins is $3.80. Thus:

\(0.2x+0.05y=3.8\)

This yields a system of equations:

\(\displaystyle \begin{cases} x=y+4 \\ 0.2x+0.05y=3.8\end{cases}\)

We can solve by substitution. Substitute the first equation into the first:

\(\displaystyle 0.2(y+4)+0.05y=3.8\)

Distribute:

\(\displaystyle 0.2y+0.8+0.05y=3.8\)

Combine like terms:

\(\displaystyle 0.25y = 3\)

And divide both sides by 0.25. Hence:

\(y=12\)

Thus, Amy has 12 5¢ coins.

Using the first equation:

\(x=y+4\)

Substitute:

\(x=(12)+4=16\)

Thus, Amy has 16 20¢ coins.

In conclusion, Amy has 12 5¢ coins and 16 20¢ coins.

The Cobb-Douglas utility function satisfies the properties of local non-satiation, decreasing marginal utility for both goods, quasi-concavity, and homotheticity.

The Cobb-Douglas utility function u(x1, x2) = xi^(α) * x2^(β), where α and β are both greater than zero, satisfies the following properties:

(a) Local non-satiation:

This property states that at each point of the consumption set, there is always another bundle that is arbitrarily close and strictly preferred. Thus, the function has local non-satiation.

(b) Decreasing marginal utility for both goods 1 and 2: The marginal utility of a good measures the utility obtained by consuming one more unit of it. The marginal utility of x1 can be obtained as:

MU1 = α * xi^(α−1) * x2^(β)

The marginal utility of x2 can be obtained as:

MU2 = β * xi^(α) * x2^(β−1)

Therefore, both marginal utilities are decreasing in x1 and x2, satisfying this property.

(c) Quasi-concavity:

The Cobb-Douglas function is quasi-concave. This means that the upper contour set of any level set of the function is convex. This can be proved by taking the second partial derivative of the function and checking whether it is negative or not.

(d) Homotheticity:

The Cobb-Douglas function is homothetic. This means that its shape is independent of the total level of utility. The proof can be achieved by checking whether the function is homogeneous of degree one or not. This is true, since multiplying the inputs by any positive scalar λ leads to a proportional increase in the output.

In conclusion, the Cobb-Douglas utility function satisfies all four properties - local non-satiation, decreasing marginal utility for both goods 1 and 2, quasi-concavity, and homotheticity.

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To create the requested graph, we'll follow these steps:

1. Take the first and second derivative of the total cost function.

2. Check for concavity and inflection points using the second derivative.

3. Find the average cost function and its relative extrema.

4. Find the marginal cost function and its relative extrema.

5. Verify the point of intersection between the average and marginal cost functions.

6. Graph the total cost curve, the marginal cost curve, and the average cost curve.

Let's go through these steps:

1. Taking the first and second derivatives of the total cost function:

TC = 2Q^3 - 12Q^2 + 225Q

Taking the first derivative:

TC' = 6Q^2 - 24Q + 225

Taking the second derivative:

TC'' = 12Q - 24

2. Checking for concavity and inflection points using the second derivative:

Since TC'' is a linear function, it does not change sign. Therefore, there are no inflection points. The concavity of the total cost curve remains the same.

3. Finding the average cost function and its relative extrema:

The average cost (AC) is calculated by dividing the total cost (TC) by the quantity (Q):

AC = TC / Q

Substituting the total cost function:

AC = (2Q^3 - 12Q^2 + 225Q) / Q

Simplifying:

AC = 2Q^2 - 12Q + 225

To find the relative extrema, we take the derivative of the average cost function:

AC' = 4Q - 12

Setting AC' = 0 to find critical points:

4Q - 12 = 0

4Q = 12

Q = 3

Therefore, the relative minimum point of the average cost function occurs at Q = 3.

4. Finding the marginal cost function and its relative extrema:

The marginal cost (MC) is calculated by taking the derivative of the total cost function:

MC = TC'

Substituting the first derivative of the total cost function:

MC = 6Q^2 - 24Q + 225

To find the relative extrema, we take the derivative of the marginal cost function:

MC' = 12Q - 24

Setting MC' = 0 to find critical points:

12Q - 24 = 0

12Q = 24

Q = 2

Therefore, the relative minimum point of the marginal cost function occurs at Q = 2.

5. Verifying the point of intersection between the average and marginal cost functions:

To find the point of intersection, we set the average cost function equal to the marginal cost function:

2Q^2 - 12Q + 225 = 6Q^2 - 24Q + 225

Simplifying and rearranging:

4Q^2 - 12Q = 0

4Q(Q - 3) = 0

The solutions are Q = 0 and Q = 3. However, since Q > 0 (as noted in the instructions), the point of intersection occurs at Q = 3.

6. Graphing the total cost curve, marginal cost curve, and average cost curve:

Please refer to the attached graph with two panels. The first panel depicts the total cost curve, indicating the inflection point (none in this case). The second panel depicts the marginal cost curve, average cost curve, and their points of intersection and relative extrema.

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Answer:

no solution

Step-by-step explanation:

h - 4h + 10 = - 3h , that is

- 3h + 10 = - 3h ( subtract 10 from both sides )

- 3h = - 3h - 10 ( add 3h to both sides )

0 = - 10 ← false statement

this false statement indicates the equation has no solution

The p-value for the test is 0.044, which is less than the significance level of 0.10. Therefore, we can reject the null hypothesis and conclude that there is a significant difference between the two population means.

The t-statistic for the test is -2.31. The critical value for the test at a significance level of 0.10 is 1.645. Since the t-statistic is less than the critical value, we can reject the null hypothesis.

The p-value is the probability of obtaining a t-statistic at least as extreme as the one we observed, assuming that the null hypothesis is true. In this case, the p-value is 0.044. This means that there is a 4.4% chance of obtaining a t-statistic at least as extreme as -2.31 if the population means are actually equal.

Since the p-value is less than the significance level, we can conclude that the results of the test are statistically significant. This means that we can reject the null hypothesis and conclude that there is a significant difference between the two population means.\

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P(Picking a striped shirt and a pink tie)

= 2/(4 + 3 + 2) * 3/(2 + 3 + 3)

= 2/9 * 3/8

= 1/12

1/12  is the probability that on the first day of school he picks a red tie OR a blue tie.

Probability = number of paths to success. A total number of possible outcomes. For example, the probability of flipping a coin and getting heads is ½. This is because there is one way to get heads and the total number of possible outcomes is 2 (heads or tails). We write P(heads) = ½.

Probability provides information about the probability that something will happen. For example, meteorologists use weather patterns to predict the likelihood of rain. Epidemiology uses probability theory to understand the relationship between exposure and risk of health effects.

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Answer:

It will take 3 weeks for both of us to have collected  the same amount. Each of us will have collected 23 items at that  time.

Step-by-step explanation:

Let x=weeks

Me: y=14+3x

Friend: y=8+5x

14+3x=8+5x

14=8+2x

6=2x

3=x

y=14+3(3)=23

Answer:

The equation of the line is;

3y = 2x-8

Step-by-step explanation:

Firstly, we need the to get the slope of the given line

To do this, we will write the equation of the line in the standard form

the standard form

is;

y = mx + b

where m is the slope and b is the y-intercept

y -4 = 2/3(x-3)

y -4 = 2x/3 - 2

y = 2x/3 -2 + 4

y = 2x/3 + 2

with respect to the given equation, the slope of the line is 2/3

Mathematically, when two lines are parallel, the slopes of the line are equal

So now, we want to find the equation of the line that has a slope of 2/3 and passes through the point (1,-2)

so;

y = 2x/3 + b

So substitute the values of (1,-2)

1 for x and -2 for y

-2 = 2/3(1) + b

-2 = 2/3 + b

b = -2 - 2/3

b = (-6-2)/3 = -8/3

So the equation of that line is;

y = 2/3x - 8/3

Multiply through by 3

3y = 2x - 8

Answer:32/5

Step-by-step explanation:

32/5

Answer:

Solution: 6.4% as a fraction is 32/5.

Step-by-step explanation:

The events are mutually exclusive events, so P(A|B) is 0.

In this question,

If two events are mutually exclusive, there is no chance that both events will occur. Being the intersection an operation whose result is made up of the non-repeated and common events of two or more sets, that is, given two events A and B, their intersection is made up of the elementary events that they have in common, then

⇒ A ∩ B = 0

Now the conditional probability, P(A|B) = \(\frac{P(A \cap B )}{P(B)}\)

⇒ \(\frac{0}{0.10}\)

⇒ 0.

Hence we can conclude that the events are mutually exclusive events, so P(A|B) is 0.

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The value of the given and completed expression in this problem is

-1

Combined operations are defined as a set of operations applied to the same problem, for example addition, subtraction, multiplication, are frequently used in arithmetic polynomials.

In this case we have an arithmetic polynomial.

We complete the expression as follows:

1 + 2 - 3 + 4 - 5

We group the positive terms on one side and negative terms on the other:

The value of the expression (1 + 2 - 3 + 4 - 5) is -1

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Answer:

From the diagram you can see that we have constructed a right triangle, with height A and base 15.Length of shadow = 15 feet.Height of flagpole = A.We know the angle of elevation is 40∘. Using this angle and the tangent ratio, we can find A.tan(40∘)=oppositeadjacent=A15∴tan(40∘)=A15Rearranging:A=15tan(40∘)By calculator:A=12.59 feet.  ( 2 d.p.)

The absolute value equation has no solutions.

Here we have an absolute value equation:

-12 = |j - 1| + 2

Now, remember that an absolute value is always positive, then the two terms in the right side are positives, while the one in the left side is negative.

Then the equation can't be true, because |j - 1| + 2 can't be negative, so the correct option is the first one, there is no solution.

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The best option is letter C. t = 2h + 32

Step-by-step explanation:

a.pi×30^2

b.pi×30^2×80

hope i helped

plss mark brainliest

Step-by-step explanation:

Given, r = 30cm

h= 80cm

a)

\(2\pi \times r {}^{2} \)

=5654.867 cm²

b) volume of cylindrical tank

\(\pi {r}^{2} h\)

=226194.671 cm2

\(1cm {}^{2} = 1ml\)

=226194.671ml

=226.195litres

Given :

After 4 days, a plant is measured to be 10 inches tall.

Later, after a total of 20 days, then height is measured to be 18 inches.

To Find :

The rate of growth for the plant.

Solution :

We know, rate is given by :

\(Rat e=\dfrac{\text{Change in height}}{\text{Time taken}}\\\\Rate = \dfrac{18-10}{20-4}\\\\Rate = 0.5 \ inch/day\)

Therefore, rate of increase of height is 0.5 inch/day .

Hence, this is the required solution.

Given :

Gary made a scale drawing of his game room.

The scale drawing has a length of 3 inches and a width of 5 inches.

To Find :

If the game room has an actual length of 12 feet, which equation could be used to determine w, the width of the game room.

Solution :

We know, during making scale drawing of any thing the shape of the object is same as the real one i.e. the ratio of each dimension remains constant.

Let, width of the gaming room is w.

\(\dfrac{w}{5}=\dfrac{12}{3}\\\\w = 20\ inches\)

Therefore, the width of the game room is 20 inches.

The inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is: w ≥ 10

To find the inequality that can be used to determine the number of weeks it can take for the animal shelter to meet its fundraising goal, we need to consider the total expenses and donations.

Let's break down the expenses and donations:

Expenses:

Annual rental = $2,500

Weekly expenses = $450

Donations:

One-time donation = $125

Pledged donations per week = $680

Let w represent the number of weeks it takes for the shelter to meet its goal.

Total expenses for w weeks = Annual rental + Weekly expenses * w

Total expenses = $2,500 + $450w

Total donations for w weeks = One-time donation + Pledged donations per week * w

Total donations = $125 + $680w

To meet the goal, the total donations must be greater than or equal to the total expenses. Therefore, the inequality is:

Total donations ≥ Total expenses

$125 + $680w ≥ $2,500 + $450w

Simplifying the inequality, we have:

$230w ≥ $2,375

Dividing both sides of the inequality by 230, we get:

w ≥ $2,375 / $230

Rounding the result to the nearest whole number, we have:

w ≥ 10

Therefore, the inequality that can be used to find w, the number of weeks it can take for the shelter to meet its goal, is:

w ≥ 10

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Answer:

Ans: n−√5

Step-by-step explanation:

the value of F(9) is approximately 23.308.

To find the value of F(9) given that F(x) is an antiderivative of (ln x)^3/x and F(1) = 0, we can use the fundamental theorem of calculus.

According to the fundamental theorem of calculus, if F(x) is an antiderivative of a function f(x), then:

∫[a,b] f(x) dx = F(b) - F(a)

Since F(1) = 0, we can write:

∫[1,9] (ln x)^3/x dx = F(9) - F(1)

To evaluate the integral, we can make a substitution:

Let u = ln x, then du = (1/x) dx

The integral becomes:

∫[ln 1, ln 9] u^3 du

Integrating u^3 with respect to u:

[(1/4)u^4] | [ln 1, ln 9] = (1/4)(ln 9)^4 - (1/4)(ln 1)^4

Since ln 1 = 0, we have:

(1/4)(ln 9)^4 - (1/4)(ln 1)^4 = (1/4)(ln 9)^4

Therefore, F(9) - F(1) = (1/4)(ln 9)^4

Since F(1) = 0, we can conclude that F(9) = (1/4)(ln 9)^4.

Calculating this value:

F(9) = (1/4)(ln 9)^4 ≈ 23.308

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