what is the value of cotθ if the terminal side of angle θ intersects the unit circle in the first quadrant at x=415?

Answer:

Hypotenuse = 29

Step-by-step explanation:

SOLVING A RIGHT TRIANGLE:

You have been given two legs, 20 and 21.

USE PYTHAGOREAN THEROM:

\(A^2+B^2=C^2\\20^2+21^2=C^2\\400+441=C^2\\\sqrt{841} =\sqrt{C^2}\\29=C\)

SIDE DE = 29

Your hypotenuse is c2, which is  29.

Let's find ANGLE D & E using trig,

D = 46

E = 43

Answer:

9/4

Step-by-step explanation:

for the line y = 9/4x + 2, its slope is 9/4

The slopes of parallel lines are equal so the slope of the parallel line is also 9/4

Answer:

Length is greater than width, So your question is wrong I think.

The required annual premium rate for the given term life policy is $50,850.

Term life insurance  covers you for a particular measure of time - basically, the strategy's term. The length of the term can change to suit your specific conditions. You can likewise look over two changed sorts of term disaster protection: diminishing term protection and level term protection.

Annual Premium Rate implies, if pertinent, the exceptional rate so determined on the Statements Page of this Strategy to be utilized in processing a premium to be transmitted yearly.

Jacob needs to purchase a $500,000 15-year term life strategy, and the yearly superior rate (per $1000 of presumptive worth) for his age bunch is $6. 78.

Number of 1000 of every 500000 will be 500000/1000 = 500

the yearly superior rate (per $1000 of assumed worth) for his age bunch is $6. 78.

Absolute premium is 500 x 6.78 = 3390

The premium each year is 3390

For quite some time, the all out premium is

15 x 3390 = 50850

Thus, over all premium jacob have paid $50850.

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Answer:

4:24

Step-by-step explanation:

12 + 4 + 8 = 24 and there are only 4 bananas. So, the answer is 4:24

hope that helps!!

Answer: 1 : 6

Step-by-step explanation: 4 over 24 equals 1/6th or 1:6 .

For figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

What is the Basic Proportionality Theorem?

The Basic Proportionality Theorem (can be abbreviated as BPT) states that, if a line is parallel to a side of a triangle that intersects the other sides into two distinct points, then the line divides those sides in proportion.

Figure 2)

By using the Basic Proportionality Theorem, we can write

                        \(\frac{11}{22}=\frac{x}{42-x}\\\\\frac{1}{2}=\frac{x}{42-x}\\\\42-x=2x\\\\3x=42\\\\x=14\)

Now for figure 3)

            By using Pythagoras' theorem, we can write

                        \(24^2+(x+7)^2=(2x-10)^2\\\\576+x^2+14x+49=4x^2-40x+100\\\\3x^2-54x+51=0\\\\x^2-18x+17=0\\\\x^2-17x-x+17=0\\\\(x-17)(x-1)=0\\\\x=17 $ or $ x=1\)

Hence, for figure 2) the value of the 'x' would be x = 14.

and for figure 3) the value of the 'x' would be x = 17 or x = 1 .

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Answer:

Graph A

Step-by-step explanation:

The value of the house, V after x years is modeled by the exponential equation

V = 200000(1.06)ˣ

We can eliminate graphs B and C since the rise is too extreme for a 6% increase in base price

We can eliminate graph D since the graph starts at 100,000 and not 200,000. Even after 5 years, the graph shows the price to be less than 200,000 which is not possible for a rate increase.

That leaves us with Graph A

We can double-check:

After 5 years the value would be 200, 000 x 1.06⁵  ≈ $267,645

After 10 years the value would be 200, 000 x 1.06¹⁰ = $358,170

Graph A models these values.

Hence Graph A models the situation

Answer:

the answer is letter A.

Step-by-step explanation:

m=y²-y¹/x²-x¹

m=(-6)-16/(-19)-15

m=-22/-34

m=11/17

Answer:

Slope is -.25 =

Minus 25%

Step-by-step explanation:

x1 y1  x2 y2

6 3.5  8 3

(Y2-Y1) (3)-(3.5)=   -0.5  ΔY -0.5

(X2-X1) (8)-(6)=    2  ΔX 2

slope= -  1/4    

B= 5          

Y =-0.25X +5    

The percentage change is -25% the price of fuel is decreased by 25%.

The equation of line is given as,

y = mx + c

Where m is the slope and c is the y-intercept.

Let the data is

x₁= 6 ,   y₁ = 3.5  

x₂ = 8 , y₂ =  3

Calculate the change,

(Y₂ -Y₁ ) = (3)-(3.5)

ΔY = -0.5

(X₂-X₁) = (8)-(6)

ΔX = 2

Calculate the slope,

Slope = ΔY/ ΔX

Slope = -0.5 / 2

Slope = - 1/4 = -0.25

The equation formed by using the above data is,

Y =-0.25X +5    

Therefore, the percentage change is -25% the price of fuel is decreased by 25%.

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Attached is a plot that compares the two variables, income and revenue using the test statistic.

(A) A statistic (a quantity obtained from the sample) used in statistical hypothesis testing is known as a test statistic.

A test statistic, which can be thought of as a numerical summary of a data set that condenses the data into a single value that can be used to conduct the hypothesis test, is how a hypothesis test is commonly expressed.

In general, a test statistic is chosen or defined in a way that quantifies, within observed data, behaviors that would separate the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there isn't an explicitly stated alternative hypothesis.

(B) Weakly positive association, r = 0.423.

(C) df = n-2 = 25-2 = 23 One-tailed Critical Value: = 0.05 T = 1.319

T, the test statistic, is defined as r*Sqrt[(n-2)/(1-r2)] = 0.423*Sqrt[(25-2)/(1-0.4232)]. = 2.24

We can infer that there is a positive link between the variables because 2.24 > 1.319.

(D) The variation in the number of rooms occupied accounts for around 18% of the variation in revenue, according to the formula r2 = 0.4232 = 0.179.

Therefore, attached is a plot that compares the two variables, income and revenue using the test statistic.

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Answer:

\(x\) would be \((1/3)\) when \(y = 3\).

Step-by-step explanation:

The question states that \(x\) varies "inversely" as \(y^2\). In other words, there is a non-zero number \(a\) (a constant) such that:

\(\displaystyle x = \frac{a}{y^2}\).

The challenging part is to find the value of \(a\) in this equation.

Given that \(x = 3\) when \(y = -1\), replace the \(x\) in this equation with \(3\) and \(y\) with \((-1)\). This equation should still be valid:

\(\displaystyle 3 = \frac{a}{(-1)^{2}}\).

Solve for \(a\):

\(a = 3 \times (-1)^2 = 3\).

Hence, the relation between \(x\) and \(y\) becomes:

\(\displaystyle x = \frac{3}{y^2}\).

Find the value of \(x\) when \(y = 3\) by replacing the \(y\) in this equation with \(3\).

\(\displaystyle x = \frac{3}{3^2} = \frac{1}{3}\).

In other words, the value of \(x\) would be \(\displaystyle \frac{1}{3}\) when \(y = 3\).

The correct answer is 0.00544 m^3.

To calculate the volume of a cylindrical steel bar, we need to use the formula:

Volume = π * (radius^2) * height

Given that the diameter of the round steel bar is 76 mm, we can calculate the radius by dividing the diameter by 2:

Radius = diameter / 2 = 76 mm / 2 = 38 mm = 0.038 m

The length of the steel bar is given as 1.2 m.

Now we can substitute these values into the formula:

Volume = π * (0.038^2) * 1.2

Volume = 3.14159 * (0.038^2) * 1.2

Volume ≈ 0.005439632 m^3

Rounded to four decimal places, the volume of the 1.2 m long steel bar is approximately 0.0054 m^3.

Therefore, the correct answer is 0.00544 m^3.

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Answer:

Step-by-step explanation:

Commutative property

It will be nice if you give me brainliest.Good luck!

Answer:

4500 feat

Step-by-step explanation:

6m=3000f

9m=x

we cross multiply and get

x= 9m × 3000f ÷ 6m

x= 4500 feat

The value of the equation x² - x + 3 is 37/9.

We have,

We can start by multiplying both sides of the equation by x:

2x - 3/x = x + 1

2x - 3 = x^2 + x

Rearranging and simplifying, we get:

x^2 - x + 3 = (2x - 3) + x^2

x^2 - x + 3 = x^2 + 2x - 3

-x + 3 = 2x - 3

5 = 3x

x = 5/3

Now we can substitute x into the equation x^2 - x + 3:

x^2 - x + 3 = (5/3)^2 - 5/3 + 3

x^2 - x + 3 = 25/9 - 15/9 + 27/9

x^2 - x + 3 = 37/9

Therefore,

The value of x² - x + 3 is 37/9.

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Answer:

7.8

0.2

Step-by-step explanation:

2 is in the ones place, to get to six you need the value of 2 in the tenths place (0.2)

2+5.8 is 7.8 (add the ones places together to get 7)

0.2+5.8=6 (add in the tenths place)

Answer:

Explanation: Notice that if x is Real then x2≥0 , so x2+25 has no linear factors with Real coefficients

Answer:

48 plants

Step-by-step explanation:

Answer:

-12

hope this helps!

add me as a friend if u can<3

We have two fractions being divided. When we divide two fractions, we flip the second fraction and multiply

1/12 divided by 1/6 = 1/12 * 6/1

-------

From here we multiply straight across.

The numerators multiply to get 1*6 = 6

The denominators multiply to 12*1 = 12

We end up with 6/12 which reduces to 1/2 when you divide both parts by the GCF 6

Answer:

Step-by-step explanation:

-2(x-5)=-14

-2x+10=-14

-2x=-14-10

-2x=-24

-x=12

x=-12

The given table represents the counts from three independent random samples taken from three major cities regarding whether teenagers consumed a soft drink in the past week.

By summing up the counts of teenagers who consumed a soft drink from all three cities and dividing it by the total number of teenagers surveyed, we can calculate the overall proportion. Dividing this proportion by the total number of teenagers and multiplying by 100 will give us the percentage of teenagers who consumed a soft drink.

For example, if the first city had a count of 150 teenagers who consumed a soft drink out of a total of 300 surveyed, the second city had 200 out of 400, and the third city had 180 out of 350, the overall proportion would be (150 + 200 + 180) / (300 + 400 + 350) = 530 / 1050. Multiplying this by 100, we find that approximately 50.48% of teenagers consumed a soft drink in the past week based on the combined sample.

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A research center conducted a national survey about teenage behavior. Teens were asked whether they had consumed a soft drink in the past week. The following table shows the counts for three independent random samples from major cities. Baltimore Yes 727 Detroit 1,232 431 1,663 San Diego 1,482 798 2,280 Total 3,441 1,406 4,847 No 177 904 Total (a) Suppose one teen is randomly selected from each city's sample. A researcher claims that the likelihood of selecting a teen from Baltimore who consumed a soft drink in the past week is less than the likelihood of selecting a teen from either one of the other cities who consumed a soft drink in the past week because Baltimore has the least number of teens who consumed a soft drink. Is the researcher's claim correct? Explain your answer. (b) Consider the values in the table. (i) Baltimore Detroit San Diego 0 0.1 0.9 1.0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Relative Frequency of Response (ii) Which city had the smallest proportion of teens who consumed a soft drink in the previous week? Determine the value of the proportion. (c) Consider the inference procedure that is appropriate for investigating whether there is a difference among the three cities in the proportion of all teens who consumed a soft drink in the past week. (i) Identify the appropriate inference procedure. (ii) Identify the hypotheses of the test.

In an experiment, the variable being measured or tested is known as the dependent variable.

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The equation that shows the relation ship between t and p is 0 ≤ t < 270.

A linear equation is an algebraic equation where the highest power of the variable is 1, and the equation represents a straight line when graphed.

Break down the information given in the problem to form an equation that relates the time t and the number of yards of painted fence p:

Tom painted 8 yards before running away, so Sid had to paint the remaining length of the fence, which is L - 8 yards, where L is the total length of the fence.

From noon to 12:30 p.m., Sid painted 14 - 8 = 6 yards.

From 12:30 p.m. to 2:00 p.m., Sid painted 32 - 14 = 18 yards.

From 2:00 p.m. to 2:30 p.m., Sid painted 38 - 32 = 6 yards.

We want to find an equation that relates the time t (in minutes) to the number of yards of painted fence p.

Based on the information above, we can create a piecewise equation that relates t and p:

p = { 8 + 0.2t, 0 ≤ t < 30

14 + 0.6(t - 30), 30 ≤ t < 90

32 + 0.4(t - 90), 90 ≤ t < 150

38 + 0.2(t - 150), 150 ≤ t < 210 }

Explanation of the equation:

The first segment of the piecewise equation, 8 + 0.2t, represents the yards of fence painted by Tom (8) plus the yards painted by Sid in the first 30 minutes (0.2t), where 0 ≤ t < 30.

The second segment, 14 + 0.6 (t - 30), represents the additional yards painted by Sid between 12:30 p.m. and 2:00 p.m., where 30 ≤ t < 90. The expression (t - 30) represents the time elapsed since 12:30 p.m., and the coefficient 0.6 represents the rate at which Sid is painting the fence in yards per minute during this period.

The third segment, 32 + 0.4 (t - 90), represents the additional yards painted by Sid between 2:00 p.m. and 2:30 p.m., where 90 ≤ t < 150. The expression (t - 90) represents the time elapsed since 2:00 p.m., and the coefficient 0.4 represents the rate at which Sid is painting the fence in yards per minute during this period.

The fourth segment, 38 + 0.2 (t - 150), represents the additional yards painted by Sid between 2:30 p.m. and 4:30 p.m., where 150 ≤ t < 210. The expression (t - 150) represents the time elapsed since 2:30 p.m., and the coefficient 0.2 represents the rate at which Sid is painting the fence in yards per minute during this period.

Note that we have limited the time t to be between noon and 4:30 p.m., which corresponds to 0 ≤ t < 270.

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Given data: Current population of a small town = 2681 people.

The town's population is tripling every 12 years.

We need to approximate the population of the town 6 years from now.

Solution: Let P be the population of the town after 6 years.

The population of the town triples every 12 years, which means that for every 12 years, the population is multiplied by 3.

Therefore, the population P after 6 years from now will be:\(P = (2681 people) x 3^{(6 years / 12 years)}P = (2681 people) x 3^{0.5}P = 2681 people x 1.732P = 4642 people.\)

Therefore, the approximate population of the town 6 years from now is 4642 people.

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Step-by-step explanation:

I don't have that much time to wait for all the clarifications, so I will make some assumptions based on what I saw in your comments so far.

please change the numbers in the calculation (and the recalculate) as necessary :

we are dealing with a triangular prism that acts as a ramp.

triangular means that the sides are in the shape of triangles.

but the front, the back and also the bottom areas are rectangles.

the area of a rectangle is length×width.

the area of a triangle is baseline×height/2

since it is supposed to be a ramp, I assume the triangle shape of the sides is right-angled. that means the back side of the ramp is standing straight up (90° angle with the bottom).

the height of the ramp is the height of the triangle side areas, and is simply the left leg of the triangle (again, going straight up with a 90° angle to the baseline).

I understand the height is 14 in.

I assume the front length is 50 in. and the depth of the ramp (the length of the baseline of the triangular sides) is 48 in.

now we get the length of the inclined "front" leg of the side triangles via Pythagoras

c² = a² + b²

with c being the side opposite of the 90° angle (exactly the inclined leg we are looking for) :

c² = 14² + 48² = 196 + 2304 = 2500

c = 50 in

that means our front rectangle of the ramp is actually a square of 50in × 50in.

the entire ramp is to be painted. that means really every side, including the bottom.

so, the whole surface area is the sum of the individual areas.

we have

1 (inclined) front area 50in × 50in

1 back side (straight up) 50in × 14in

1 bottom area 50in × 48in

2 side triangles 48in × 14in / 2 = 48in × 14in

so, we get as total area

50×50 = 2500 in²

50×14 = 700 in²

50×48 = 2400 in²

48×14 = 672 in²

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

6272 in²

now, one can of spray paint can cover 2000 in².

that means we need

6272 / 2000 = 3.136 cans.

and since we cannot buy fractions of cans, we need to round up.

we need 4 cans to do the painting job.

Answer:8.4

Step-by-step explanation:

Ten percent of 14 is 1.4 so add 1.4 4 times or multiple 1.4 by 4 and you get 5.6, then subtract 14 by 5.6 and you get 8.4

The possible coordinates of the point G on the number line as described in the task content are; 5 or -3.

It follows from the task content that the distance between points E and G as given by EG = 4.

Since, the point E has a coordinate of 1, it follows the point G is 4 units less or greater than 1 on the number line.

Ultimately, the possible coordinates of point G are; 1 - 4 = -3 and 1+4 = 5.

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