In ΔIJK, the measure of ∠K=90°, IK = 9, JI = 41, and KJ = 40. What ratio represents the sine of ∠I?

The equation of the perpendicular line is y = 3x + 9

From the question, we have the following parameters that can be used in our computation:

Line; y = -x/3 + 3/5

The slope of the above line is

m = -1/3

The slopes of perpendicular lines are opposite reciporcals

So, the new slope is -1/(-1/3)

New = 3

The line passes through (-2, 3)

So, we have

y = mx + c

Where

m = 3

This gives

3 * -2 + c = 3

Evaluate

c = 9

So, we have

y = 3x + 9

Hence, the equation of the perpendicular line is y = 3x + 9

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To determine the total grade we mutiply each one by the percentage it represents of the overall grade in decimal form and add them, that is:

Therefore, the overall grade is 69

use this formula and solve the question

AREA OF BASE = 1 by 2 ×base × Height

Answer:

no hablo espanol Lo siento

The signed number representation for David losing 15 dollars is -15, indicating a decrease of 15 units in his pocket.

We can use a negative value since he lost money to represent the change of David losing 15 dollars from his pocket using signed numbers. Using a signed number system, we represent positive values as regular numbers and negative values with a minus sign (-) in front of the number. So, in this case, the change can be represented as: -15

The negative sign (-) indicates that David lost 15 dollars. In signed number notation, the minus sign represents a decrease or a loss, while a positive sign (+) represents an increase or a gain.

In summary, the signed number representation for David losing 15 dollars is -15, indicating a decrease of 15 units in his pocket.

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Answer:

3,240°

Step-by-step explanation:

Sum of interior angles of n-sided polygon is given as (n - 2)180. Where n = number of sides of the polygon.

Sum of angles of a convex 20-gon = (20 - 2)180

= (18)180 = 3,240°

Sum of interior angles of a convex 20-gon = 3,240°

Answer:

3,240

Step-by-step explanation:

(n-2)180 n is the number of sides

Substitute 20 for n, then simplify

(20 - 2)180 = (18)180 = 3,240

If a series an is defined by the equations a1 = 2 an+1 = 3 + cos(n) / √n · an, then  Σan is absolutely convergent. Therefore, the answer is: a) absolutely convergent.

To determine whether Σan is absolutely convergent, conditionally convergent, or divergent, we need to analyze the behavior of the series as n approaches infinity.

First, let's look at the absolute value of the terms in the series:

|an| = |2 × (3 + cos(n) / √n · an-1)|
    = |6 + 2cos(n) / √n · an-1|

Next, we can use the Comparison Test by comparing the series to a known convergent or divergent series. Let's compare the series to the p-series:

∑1/n^p

where p = 3/2. This series is known to converge by the p-test.

Now, we can rewrite the absolute value of an in terms of the p-series:

|an| = |6 + 2cos(n) / √n · an-1|
     ≤ |6 + 2 / √n · an-1|          (since cos(n) ≤ 1)
     ≤ 6 + 2 / √n · |an-1|           (using the triangle inequality)

Therefore, we have:

|an| ≤ 6 + 2 / √n · |an-1|

If we take the limit of both sides as n approaches infinity, we get:

lim n→∞ (6 + 2 / √n · |an-1|) / |an-1|
= lim n→∞ (6 / |an-1|) + (2 / (√n · |an-1|))
= 6 / lim n→∞ |an-1| + 0

Since lim n→∞ |an-1| exists (as an is a well-defined series), we can conclude that the limit is a finite number. Therefore, by the Comparison Test, Σ|an| converges.

Finally, we can use the Ratio Test to determine whether Σan converges absolutely or conditionally:

lim n→∞ |an+1 / an|
= lim n→∞ |(3 + cos(n+1) / √(n+1) · an) / an|
= lim n→∞ |(3 + cos(n+1)) / (√(n+1) · an)|

Using L'Hopital's Rule, we can show that the limit of the cosine term is 0, and the limit of the denominator is infinity. Therefore, the limit of the ratio is 0.

Since the limit of the ratio is less than 1, we can conclude that Σan converges absolutely.

Therefore, the answer is: a) absolutely convergent.

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Answer:c

Step-by-step explanation:

Answer:

hello, sorry i'm late, your answer would be: option b, y/x = 2/3

Step-by-step explanation:

proof:

a. The probability of selecting a red ball from Urn A and then the probability of selecting a red ball from Urn B after one red ball has been transferred. b. The probability of selecting a red ball from Urn B, taking into account the transfer of one ball from Urn A. c. The probability that the first ball was red can be calculated using conditional probability.

a. To calculate the probability that both balls chosen are red, we multiply the probability of selecting a red ball from Urn A (2 out of 5) by the probability of selecting a red ball from Urn B (6 out of 7, since one red ball was added). So the probability is (2/5) * (6/7) = 12/35.

b. To calculate the probability that the second ball chosen is red, we consider that there are now a total of 6 red balls and 7 balls in Urn B. Therefore, the probability is 6/7.

c. To find the probability that the first ball was red given that the second ball is red, we use conditional probability. The probability that both balls are red (12/35) divided by the probability that the second ball is red (6/7) gives us (12/35) / (6/7) = 4/5. Therefore, the probability that the first ball was red given that the second ball is red is 4/5.

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In the given study comparing the effects of regular-fat cheese to reduced-fat cheese on LDL cholesterol levels, the dependent variable(s) refers to the outcome(s) that are being measured or observed. In this case, the dependent variable in this study is: b. LDL levels

The dependent variable is the variable that is measured or observed to assess the effect of the independent variable(s). In this case, the study is comparing the effects of regular-fat cheese and reduced-fat cheese on LDL cholesterol levels.

LDL cholesterol levels are the outcome being measured to determine the impact of the different types of cheese on cholesterol. Therefore, option b, LDL levels, is the dependent variable in this study. Options a (regular fat cheese) and c (reduced fat cheese) are not the dependent variables but rather the independent variables, as they are the different conditions being compared to assess their effect on LDL levels.

Option d (both a and b) and option e (both b and c) are incorrect because regular-fat cheese (option a) is an independent variable, not a dependent variable.

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The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Answer:

F. y = 9.5x + 22.5

Step-by-step explanation:

let the number of shirts be x

For every shirt he pays $9.50 and $22.5 is the additional price

The Mean-Value-Theorem is being used to explain why the driver received a speeding ticket even though they were traveling at exactly 60 mph at both radar-detectors. It suggests that there must have been a moment during the trip where the driver's speed was above the speed limit.

The Mean-Value Theorem is a theorem from calculus that states that for a continuous function on a closed interval, there exists at least one point in the interval where the instantaneous rate of change (the derivative) of the function is equal to the average rate of change of the function over the interval.

In this case, the police unit used the two radar detectors to determine the average-speed of the driver between the two points. The distance between the two detectors is 159 miles, and the time it took for the driver to travel that distance was 2 hours (from 2pm to 4pm), so the average speed of the driver was 159/2 = 79.5 mph.

However, the speed-limit on the highway is 65 mph, so the driver was exceeding the speed limit and received a speeding-ticket.

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Answer:

\(y = \frac{2}{3} x - 8\)

f(0)=-8

Step-by-step explanation:

Slope=rise/run=(-4-(-10))/(6-(-3))=6/9=2/3=m

y=m*x+q

-4=(2/3)*(6)+q

q=-8

f(0)=(2/3)*(0)-8=-8

Answer:

1000 pennies 100 is 1 10th 400 makes 500 which is half of 1000

The value of the given expression 6/(y-z) - 2/(y-z) is 4/(y-z). Option 3 is the correct answer.

In algebra, like terms are those in which the same variable(s) are raised to the same power (s). Because they both have the same variable (y) raised to the same power, the expressions 2xy and -5y are similar (1). When combining terms that have similar coefficients, it's important to preserve the exponent and variable constants.

The given expression is 6/(y-z) - 2/(y-z).

Simplifying the expression by combining the like terms we have:

(6 - 2)/(y-z) = 4/(y-z)

Hence, the value of the given expression is option 3 4/(y-z).

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The value of PV based on the question requirements is given as R27 281,09.

There is a consistent increase in the withdrawals, with a growth rate of 6% per annum. The interest accrues at a yearly rate of 8%, and is compounded twice a year.

Having an interest rate that is calculated and added every three months. The accelerated growth of withdrawals surpasses the pace at which interest is accumulating, causing the eventual depletion of the savings account's value.

To calculate the value of the savings account, we need to use the future value of an annuity formula. The formula is:

\(FV = PV * [((1 + r)^n - (1 + g)^n) / (r - g)]\)

where:

FV is the future value of the annuity

PV is the present value of the annuity

r is the interest rate

n is the number of payments

g is the growth rate

In this case, the present value is the amount that needs to be deposited into the savings account, the interest rate is 8% p.a. compounded quarterly, the number of payments is 6 (24 / 4), and the growth rate is 6% p.a. compounded semi-annually.

Plugging these values into the formula, we get:

\(FV = PV * [((1 + r)^n - (1 + g)^n) / (r - g)]\\FV = PV * [((1 + 0.02)^6 - (1 + 0.03)^6) / (0.02 - 0.03)]\\FV = PV * 10.766\)

Solving for PV, we get:

PV = FV / 10.766

PV = 27 281,09

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Answer:

I would recommend that if it is re-testable, keep that slide open and open another so you can copy from the other slide

Answer: y=-4x-13

Step-by-step explanation:

To find the parallel line, we know that the slope must stay the same. Parallel lines NEVER touch or cross. Therefore, the slope MUST be the same. All we have to do is to find the y-intercept by plugging in the given point.

-5=-4(-2)+b           [multiply]

-5=8+b                  [subtract both sides by 8]

b=-13

Now, we know that the equation is y=-4x-13.

Answer:

5(2.2y+3.4)=5(y-2)+6y has no solution

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The third one down.

32.1y+3.1+2.4y-8.2=34.5y-5.1

Combine like terms

34.5y + 3.1 - 8.2 = 34.5y - 5.1

34.5y - 5.1 = 34.5y - 5.1              y can be anything

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

Remove the brackets from D

11y + 17 = 5y - 10 + 6y

11y + 17 = 11y - 10

This gives 17 = - 10 which of course is nonsense.

D has no solution.

Answer:

500 + (100 x 5) = 1000

Step-by-step explanation:

Answer:

False. Selection bias cannot be avoided by making sure the sample size is large enough.

Selection bias refers to the systematic differences between the sample and the population from which it is drawn, which can lead to inaccurate conclusions. A large sample size does not guarantee that the sample is representative of the population, and a sample can still be biased even if it is large.

There are various types of selection bias, such as self-selection bias, which occurs when participants choose whether or not to participate in a study, and availability bias, which occurs when participants are only selected from a specific subgroup of the population. These types of bias cannot be avoided by increasing the sample size.

To avoid selection bias, researchers must make sure the sample is representative of the population by using appropriate sampling methods such as random sampling and stratified sampling. Additionally, the design of the study, the way the data is collected, and the way the data is analyzed must be done with great care to minimize bias.

Step-by-step explanation:

The General Multiplication Rule in probability states that the probability of the intersection (occurrence) of two events, A and B, is equal to the product of their individual probabilities. The formula can be written as follows:

p(A and B) = p(A) * p(B | A)

where p(A) represents the probability of event A occurring, and p(B | A) represents the probability of event B occurring given that event A has already occurred.

The formula reflects the idea that the probability of both events occurring is equal to the probability of one event occurring, multiplied by the probability of the other event occurring given that the first event has already happened.

For example, let's say we have two events: "rolling a 6 on a dice" (A) and "choosing a spade from a deck of cards" (B). The probability of rolling a 6 on a dice is 1/6, and the probability of choosing a spade given that a 6 was rolled is 13/52. Using the general multiplication rule, the probability of both events occurring would be (1/6) * (13/52) = 13/312.

In summary, the general multiplication rule is a fundamental concept in probability that helps us calculate the probability of the intersection of two events.

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The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

In the question ,

it is given that ,

the initial point of the vector = (1 , -1)

the terminal point of the vector = (4,2)

we know that the vector with initial point (x₁ , y₁) and (x₂ , y₂) is calculated using the formula

V = (x₂ - x₁)i + (y₂ - y₁)j

Substituting the values from the point ,

we get the vector as

V = (4 - 1)i + (2 -(-1))j

V = 3i + (2 + 1)j

V = 3i + 3j

Therefore , The vector as a linear combination of the standard unit vectors is written as 3i+3j , the correct option is (a) .

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Answer:

Time to sleep bro

Step-by-step explanation:

have sweet dreams

Answer:

The answer simplified would be:

-4y^2+3y+5

If you combine the like terms, you will get this answer.

You have to add 8y^2 to -12y^2 and you get -4y^2.

Hope this helps you! :)

Answer:

the window would be 72ft²

Step-by-step explanation:

A window is rectangular in shape.

the area of a rectangle is give as length * breadth

but this question say that the manufacturer wants to enlarge the window by 1.5

therefore we are going to multiply the length by 1.5 and the breadth also by 1.5 to get the new area of the bigger window.

length = 8 * 1.5

= 12

width = 4 * 1.5

= 6

The new area would be = l * b

= 12 * 6

= 72ft²

Answer:

If its a true or false question its false

Step-by-step explanation:

Answer:

6 ft

Step-by-step explanation:

18 * 5 = 90

90 / 15 = 6

Answer:

6 ft

Step-by-step explanation:

First, find the ratio of the tree and its shadow.

18:15

Simply it:

6:5

Therefore, for every six feet an object is, 5 feet its shadow is.

So since the ornament has a 5ft shadow, the lawn ornament must be six feet tall.

Answer:

D) 33

Step-by-step explanation:

(x+4)²-3, so when x=2

(2+4)²-3

6²-3

36-3

33