Instructions: Using triangle ABC, and the information given, evaluate the trigonometric function. cos(A)=(24)/(25) and a=14. Find b,c,sin(A),tan(A),cos(B), and cot(B)

Answer:

$318

Step-by-step explanation:

First, we want to set up an equation to solve this problem by using the information given to us. We're asked for the total cost, so we want one side of the equation to be \(R(x)=\). Then, we know that the initial cost is $150, no matter how many miles we drive. We are also told that each mile is $1.75.

\(R(x)=150+1.75x\)

The problem tells us that we are driving 96 miles, so we can plug in 96 for \(x\) and solve.

\(R(x)=150+1.75(96)\\R(x)=150+168\\R(x)=318\)

The total cost of the rental is going to $318.

Hope this helps!

(a) The number of solutions is 455

(b) The number of solutions if each variable xi is an integer greater than or equal to one is 165

(a) This problem can be solved using the stars and bars technique. We need to distribute 12 identical objects (stars) among 4 distinct boxes (corresponding to the variables) such that each box can have zero or more stars. The number of solutions is therefore (12+4-1) choose (4-1) = 455.

(b) We can convert this problem into the previous one by subtracting 1 from each xi, so that we are now looking for non-negative integers. We need to distribute 8 identical objects (12-4) among 4 distinct boxes (corresponding to the variables) such that each box can have zero or more objects. The number of solutions is therefore (8+4-1) choose (4-1) = 165.

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Your question is incomplete but probably the full question is:

How many solutions are there to the equation x1+x2+x3+x4=12 if:

(a) Each variable xi is an integer greater than or equal to zero?

(b) Each variable xi is an integer greater than or equal to one?

By the incenter property, this angle is half of the measure of ∠AEC Hence, the measure of ∠DEP is half of the measure of ∠AEC.

Since ΔDEP is congruent to ΔDCP by the SAS (Side-Angle-Side) postulate, the corresponding angles of these triangles are equal.

Therefore, the measure of ∠DEP is equal to the measure of ∠DCP.

Since P is the incenter of ΔAEC, ∠DCP is the angle formed by the bisector of ∠AEC.

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The information is not enough to prove that triangles DEF and OPQ are congruent through SAS, as we need two equal side lengths and one angle measure.

The Side-Angle-Side (SAS) congruence theorem states that if two sides of two similar triangles form a proportional relationship, and the angle measure between these two triangles is the same, then the two triangles are congruent.

The parameters given for this problem are given as follows:

As we are given only one side, instead of the two sides needed, we have that the information given is not enough to prove that the two triangles are congruent by the SAS congruence theorem.

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The revenue generated by the drama club play on the first night is given as:

The production teams projects the revenue earned each successive day to be 70% of the previous day. Therefore, we expect a 30% cut in revenue generated in each successive day for next five days.

Using the above information we can forecast the revenue to be generated in next 5 days as follows:

We can write the revenue for 6 days in a sequential form as follows:

We see that the above sequence follows a geometric progression. Where the parameters of geometric progression are as such:

Where for this sequence the constant parameters are:

The revenue earned ( Rn ) at the nth day till 5 days can be modeled by using geomtric progression nth terms formula as such:

By plugging in the respective constants ( a and r ) we can get the function rule that models the given situation as such:

Where, n = The nth consecutive day of the working week!

Answer:

1 : 400

Step-by-step explanation:

\(\frac{3.5 x 10^{3} }{3.5 x 10^{3} } : \frac{1.4 x 10^{6 } }{3.5 x 10^{3} }\)

1 : .4 x \(10^{3}\)

1 : 4 x \(10^{2}\)

1 : 400

Answer:

$25

Step-by-step explanation:

.05x500=25

hope this helps

Answer:

He will pay $25 worth of tax

Step-by-step explanation:

percent/100=is/of

5/100=x/500

solve the proportion

5×500/100

2,500/100

25

Lin collected 1.4 times that of Diego's recycling collection.

Let x be the amount Diego collected in kg of recycling.

Then, Lin collected 2/5 more than that is

x + 2/5x = 7/5x kg of recycling

.Let x be the amount of recycling Diego collected in kg.

Then, Lin collected 2/5 more than that, so Lin's collection is

x + 2/5x,

which is equivalent to 7/5x kg of recycling.

This means that Lin's recycling collection is 1.4 times that of Diego's.'

For example, if Diego collected 10 kg of recycling, then Lin collected

2/5 * 10 = 4 kg

more than that, which is a total of 14 kg.

Therefore, Lin collected 1.4 times that of Diego's recycling collection.
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Answer: 36.95

Step-by-step explanation:

Because its an equilateral triangle, each side is equal. We can split the equilateral into a 30-60-90 triangle. The base is x, the height is x\(\sqrt{3}\) and the hypotenuse is 2x.

32/\(\sqrt{3}\) = 18.4752086

So the height is equal to:

x = 18.4752086

18.4752086\(\sqrt{3}\)

Since the hypotenuse is 2x, we can calculate that with:

2x

= 2(18.4752086)

= 36.9504172

The length of each side is 36.95

Step-by-step explanation:

10 % of 2700 = 270

so he had 2970 rupee

20% of 2970 = 594

so customer have to pay 2970 + 594 = 3564

Answer:

an apple would remain

Step-by-step explanation:

In this problem, we are dealing with a random variable related to people's opinions on a new building project. We are given four options for the correct wording of the random variable and need to determine the correct one. Additionally, we are asked to calculate probabilities associated with the number of people who favor the new building project, ranging from exactly 4 to at most 6.

a) The correct wording for the random variable is "rv = the number of people who are in favor of a new building project." This wording accurately represents the random variable as the count of individuals who support the project.

b) To calculate the probability that exactly 4 people favor the new building project, we need to use the binomial probability formula. Assuming the probability of a person favoring the project is p, we can calculate P(X = 4) = (number of ways to choose 4 out of 10) * (p^4) * ((1-p)^(10-4)). The value of p is not given in the problem, so this calculation requires additional information.

c) To find the probability that less than 4 people favor the new building project, we can calculate P(X < 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3). Again, the value of p is needed to perform the calculations.

d) The probability that more than 4 people favor the new building project can be calculated as P(X > 4) = 1 - P(X ≤ 4) = 1 - (P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)).

e) The probability that exactly 6 people favor the new building project can be calculated as P(X = 6) using the binomial probability formula.

f) To find the probability that at least 6 people favor the new building project, we can calculate P(X ≥ 6) = P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10).

g) Finally, to determine the probability that at most 6 people favor the new building project, we can calculate P(X ≤ 6) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6).

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Answer:

2 divided by 5

Step-by-step explanation:

Hope this helped!! Give brainliest

The division 2÷5 describe the two rectangular strips in a row, the top of each strip is labeled 1. Each strip is divided into 5 equal parts.

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 two rectangular strips in a row, the top of each strip is labeled 1. Each strip is divided into 5 equal parts.

So the one strip represents one whole and two represents 2

So each strip represent 2÷5

Thus, the division 2÷5 describe the two rectangular strips in a row, the top of each strip is labeled 1. Each strip is divided into 5 equal parts.

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Answer:

.8Km

Step-by-step explanation:

There is exactly 100,000 CM in every KM, if someone such as Ben was to measure out 80,000, to convert to KM you'd take the given value and divide by the appropriate values.

80,000cm / 100,000cm = .8 KM

The probability of guessing the correct answer for each question is 1/4, while the probability of guessing incorrectly is 3/4.

To calculate the probability of answering at most one correct answer, we need to consider two cases: answering zero correct answers and answering one correct answer.

For the case of answering zero correct answers, the probability can be calculated as (3/4)^5, as there are five independent attempts to answer incorrectly.

For the case of answering one correct answer, we have to consider the probability of guessing the correct answer on one question and incorrectly guessing the rest. Since there are five questions, the probability for this case is 5 * (1/4) * (3/4)^4.

To obtain the probability of answering at most one correct answer, we sum up the probabilities of the two cases:

Probability = (3/4)^5 + 5 * (1/4) * (3/4)^4.

Therefore, by calculating this expression, you can determine the probability of answering at most one correct answer among five questions when guessing randomly.

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Given an AR(1) process with drift X = α + βX_{t-1} + ε_t, where α = 2, β = 0.7, and ε_t ~ N(0, 1).To find the mean of the process, we note that the AR(1) process has a mean of μ = α / (1 - β).

So, the mean is 6.67, the variance is 5.41, the first three ACF are 0.68, 0.326, and 0.161, and the first three PACF are 0.7, -0.131, and 0.003.

So, substituting α = 2 and β = 0.7,

we have:μ = α / (1 - β)

= 2 / (1 - 0.7)

= 6.67

To find the variance, we note that the AR(1) process has a variance of σ^2 = (1 / (1 - β^2)).

So, substituting β = 0.7,

we have:σ^2 = (1 / (1 - β^2))

= (1 / (1 - 0.7^2))

= 5.41

To find the first three autocorrelation functions (ACF) and the first 3 partial autocorrelation functions (PACF), we can use the formulas:ρ(k) = β^kρ(1)and

ϕ(k) = β^k for k ≥ 1 and

ρ(0) = 1andϕ(0) = 1

To find the first three ACF, we can substitute k = 1, k = 2, and k = 3 into the formula:

ρ(k) = β^kρ(1) and use the fact that

ρ(1) = β / (1 - β^2).

So, we have:ρ(1) = β / (1 - β^2)

= 0.68ρ(2) = β^2ρ(1)

= (0.7)^2(0.68) = 0.326ρ(3)

= β^3ρ(1) = (0.7)^3(0.68)

= 0.161

To find the first three PACF, we can use the Durbin-Levinson algorithm: ϕ(1) = β = 0.7

ϕ(2) = (ρ(2) - ϕ(1)ρ(1)) / (1 - ϕ(1)^2)

= (0.326 - 0.7(0.68)) / (1 - 0.7^2) = -0.131

ϕ(3) = (ρ(3) - ϕ(1)ρ(2) - ϕ(2)ρ(1)) / (1 - ϕ(1)^2 - ϕ(2)^2)

= (0.161 - 0.7(0.326) - (-0.131)(0.68)) / (1 - 0.7^2 - (-0.131)^2) = 0.003

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Step functions are functions that have different values for different intervals of the input variable. They are often used to model situations where a quantity changes abruptly at certain points in time.

In this case, the function g(t) is defined using three different step functions: u1(t), u3(t), and u4(t). Let's start by looking at each of these step functions in turn: u1(t) is the unit step function, which is defined as:

\(u1(t) = { 0 if t < 0\)

\({ 1 if t > = 0\)

In other words, u1(t) is equal to 0 for negative values of t, and 1 for non-negative values of t. This means that the graph of u1(t) is a horizontal line at y=0 for t < 0, and a horizontal line at y=1 for t >= 0. Here's what the graph looks like:

u3(t) is another unit step function, but with a shift of 3 units to the right:

\(u3(t) = { 0 if t < 3\)

\({ 1 if t > = 3\)

This means that the graph of u3(t) is a horizontal line at y=0 for t < 3, and a horizontal line at y=1 for \(t > = 3\). Here's what the graph looks like:

u4(t) is another unit step function, but with a shift of 4 units to the right:

\(u4(t) = { 0 if t < 4\)

\({ 1 if t > = 4\). This means that the graph of u4(t) is a horizontal line at y=0 for t < 4, and a horizontal line at y=1 for \(t > = 4.\) Here's what the graph looks like:

Now let's look at the function g(t) \(= u1(t) + 2u3(t) - 6u4(t)\). This function is a linear combination of the three-step functions we just examined, with different coefficients for each one.

For t < 0, all three step functions are equal to 0, so g(t) is also equal to 0. For \(t > = 0\), the values of the three-step functions depend on the value of t relative to the shifts in u3(t) and u4(t).

If t < 3, then \(u3(t) = 0\) and \(u4(t) = 0,\) so \(g(t) = u1(t)\)= \(1.\)

If 3 <= t < 4, then \(u3(t) = 1\) and \(u4(t) = 0\), so \(g(t) = u1(t) + 2u3(t) = 1 + 2 = 3.\)

If t >= 4, then \(u3(t) = 1\) and \(u4(t) = 1\), so \(g(t) = u1(t) + 2u3(t) - 6\)

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Answer:

total commission= $2,600

Step-by-step explanation:

Giving the following information:

He earns a 10 percent commission on the first $5,000 and 15 percent on all sales over $5,000.

First, we need to structure the total commission formula:

total commission= 0.10*x + 0.15*y

X= sales up to $5,000

Y= sales from $5,001 to infinity

Now, sales for $19,000 sales:

total commission= 0.1*5,000 + 0.15*14,000

total commission= $2,600

Answer:

326.5

Step-by-step explanation:

Answer:

y=8x-4

Step-by-step explanation:

slope intercept form: y=mx+b

y= 8x-4

8x because slope is 8 and m=slope

-4 because y intercept is -4. if at x=1, y=4 you go back one x making you go down 8 y values and 4-8= -4

Answer:

y=8x + -4

Step-by-step explanation:

you have to find your y-intercept

if (1,4) is the point your working with you subtract 1,8

1-1=0

4-8=-4

your new plot point would be (0,-4)

making that your y-intercept because x=0

making your equation y=8x+ -4

Answer:

2)a. A = π(5²) = 25π cm²

b. h = 17 cm

c. V = 25π(17) = 425π cm³

d. V = about 1,335.2 cm³

Answer:

Let's solve for x.

3x+y=−6

Step 1: Add -y to both sides.

3x + y + −y = −6 + −y

3x = − y − 6

Step 2: Divide both sides by 3.

3x  / 3  =  − y −6 /  3

x =  − 1  / 3 y −2

Answer:

x = − 1  / 3 y −2

Hope it helps

Please mark me as the brainliest

Thank you

Answer:

x = 2 + y/3

Step-by-step explanation:

Add

y

to both sides of the equation.

3 x = 6 + y

Divide each term by

3

and simplify.

The equation of hyperboloid of one sheet: \(\frac{x^{2} }{A^{2} } +\frac{y^{2} }{B^{2} } -\frac{z^{2} }{C^{2} } =1\) which is used to calculate hyperboloid.

The most challenging quadric surface is probably the hyperboloid of a single sheet. For starters, it is puzzling since its equation is quite similar to that of a hyperboloid with two sheets. For information on how to tell them apart, see to the section on the two-sheeted hyperboloid. Its cross portions are also highly intricate equation.

Having said all of that, everyone who has watched The Simpsons, even for the first time, will recognize this form. One-sheet hyperboloids have a striking resemblance to Springfield Nuclear Power Plant cooling towers.

The cross sections of a straightforward one-sheeted hyperboloid with A = B = C = 1.

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Step-by-step explanation:

Given:

The speed of the water flowing through the pipe into the tank = 1.2 m/s

The area of cross-section of the pipe = 6 cm? = 0.0006 m?

To find:

The no. of litres of water flowing into the tank in 1 hour

Solution:

According to the given values in the question, we will first find the volume of water flowing into the tank through the pipe in 1 second

so,the volume of water flowing into the tank in 1 second is given by,

=[Area of the cross-section of pipe ] x [ The speed of the water flowing into the tank ] =

[0.0006 m²] × [ 1.2 m/s ]

\( = 7.2 \times {10}^{ - 4} {m}^{3} \)

Now,

The volume of water flowing into the tank in 1 hour is given by,

=[ The volume of water flowing in 1 second ] x 3600

where,( 1 hour = 3600 seconds)

=[7.2×10-4 m³] × [3600 seconds ]

= 2.592 m³

We have 1 m³= 1000 litres

so,

2.592 m³ = 2.592 x 10³ = 2592 litres

Thus, the number of litres of water flowing into the tank in 1 hour is 2592 litres.

The number of litres of water flowing into the tank in 1 hour is 2592 litres.

Speed can be calculated as the ratio of distance traveled to the time taken

Given:

The speed of the water flowing through the pipe into the tank id 1.2 m/s

The area of cross-section of the pipe is 6 cm? = 0.0006 m?

We have To find The no. of litres of water flowing into the tank in 1 hour

According to the given values, we will first find the volume of water flowing into the tank through the pipe in 1 second.

thus ,the volume of water flowing into the tank in 1 second is given by,

= [Area of the cross-section of pipe ] x [ The speed of the water flowing into the tank ] =

[0.0006 m²] × [ 1.2 m/s ] = 7.2×10-4 m³

Now,

The volume of water flowing into the tank in 1 hour is given by;

=[ The volume of water flowing in 1 second ] x 3600

where,( 1 hour = 3600 seconds)

= [7.2×10-4 m³] × [3600 seconds ]

= 2.592 m³

We have 1 m³= 1000 litres

so, 2.592 m³ = 2.592 x 10³ = 2592 litres

Therefore, the number of litres of water flowing into the tank in 1 hour is 2592 litres.

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Answer:

c. 35 shrubs

Step-by-step explanation:

\( \frac{37.1 \times 15}{15.9} = 35 \)

Answer:

do you think you can write them in chat or copy n paste?? please because i can solve these but i need a beet look

Step-by-step explanation:

Linear equations involve equalities (i.e., "=") and are used to represent lines in a coordinate plane. Linear inequalities, on the other hand, involve inequalities (i.e., "<", ">", "<=", ">=") and are used to represent regions or areas of a coordinate plane that satisfy certain conditions.

A linear equation can be expressed in the form "y = mx + b," where "m" represents the slope of the line and "b" represents the y-intercept. Given the values of "m" and "b," you can calculate the y-coordinate for any given x-coordinate, and vice versa. The graph of a linear equation is a straight line.

A linear inequality is expressed in the form "y < mx + b," "y > mx + b," "y <= mx + b," or "y >= mx + b." Instead of representing a single line, a linear inequality represents a shaded region on the coordinate plane that satisfies the given condition. To graph a linear inequality, you can choose a test point not on the line and check whether it satisfies the inequality. If it does, shade the region containing the test point; otherwise, shade the other region.

In summary, the main difference between linear equations and linear inequalities is the use of equalities versus inequalities. Linear equations represent lines, while linear inequalities represent shaded regions on the coordinate plane. Equations deal with exact solutions, whereas inequalities deal with a range of possible solutions. Understanding the distinctions between these concepts is important in various areas of mathematics, such as algebra and geometry.

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