i will mark brainliest determine the value of y for the inequality 4 times the quantity y plus one fifth end quantity is less than or equal to four fifths. y ≥ 0 y ≤ 0 y is greater than or equal to negative 1 over 40 y is less than or equal to negative 1 over 40

The required by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

Mathematical induction is a method of proof commonly used in mathematics to prove that a statement is true for all positive integers.

The process involves two steps:

Here,
First, we need to prove the statement is true for the base case n=0,

When n=0, we have,

\(\sum_{i=1}^{1} i * 2^i = 1*2^1 = 2\)

and

\(n * 2^{n+2} + 2 = 0*2^{0+2} + 2 = 2\)

Therefore, the statement is true for n=0.

Next, we assume the statement is true for some arbitrary integer k, meaning:

\(\sum_{i=1}^{k+1} i * 2^i = k * 2^{k+2} + 2\)

We want to show that the statement is also true for n=k+1,

\(\sum_{i=1}^{k+2} i * 2^i = (k+1) * 2^{k+3} + 2\)

We can rewrite the left-hand side of the equation as,

\(=\sum_{i=1}^{k+2} i * 2^i \\= \sum_{i=1}^{k+1} i * 2^i + (k+2) * 2^{k+2} \\= k * 2^{k+2} + 2 + (k+2) * 2^{k+2} \\= (k+1) * 2^{k+3} + 2\)

This last step used the assumption that the statement is true for n=k.

Therefore, by the principle of mathematical induction, the statement is true for all integers n ≥ 0.

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Answer:

15 19/20

Step-by-step explanation:

95 cents means 95/100 then reduce that and you get 19/20 and then on the end you still have the $15

The equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

Let position vector of point P be:

p = 3 i + j + 2 k

Let position vector of point Q be:

q = i - 2 j - 4 k

So, PQ = Q - P

PQ = n = i - 2 j - 4 k - (3 i + j + 2 k)

n = i - 2 j - 4 k - 3 i - j - 2 k

n = - 2 i - 3 j - 6 k

The Equation of plane passing through point Q and perpendicular to PQ will be:

(r - q).n = 0

r n = q n

q n = (i - 2 j - 4 k) . (- 2 i - 3 j - 6 k)

q n = - 2 + 6 + 24

q n = 28

r n = 28

r (- 2 i - 3 j - 6 k) = 28

r (2 i + 3 j + 6 k) + 28 = 0

Therefore the equation for the plane passing through Q and perpendicular to line PQ is r (2 i + 3 j + 6 k) + 28 = 0.

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Answer:

1. True.

3. True

4. True

Step-by-step explanation:

1. The absolute/ modulus of each number is always positive therefore true

2. Take for instance -2, it's opposite will be +2. thus the statement is false

3. True. zero takes no sign hence it's the only number whose opposite is itself.

4. Yes. absolute means it is positive and opposite of negative is positive too

5. absolute value of opposite of 2 is +2, the opposite of absolute value of 2 is -2. thus the statement is false

6. False. zero is neither positive nor negative

a. P(A'UB) is 0.885106

b. The probability that an order requests an optional high speed processor, given that the order requests extra memory is 0.776397.

c. The probability that an order requests extra memory, given that the order DOES NOT requests an optional high speed processor is 0.123711

The probability of an occurrence is a number used in science to describe how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place.

To find the probabilities:

a. A"UB = 510 + 72 + 250 = 832

Total outcomes = 940

The required probability is 832/940 = 0.885106

b. The required probability is 250/250 + 72 = 0.776397

c. The required probability is 72/510 + 72 = 72/582 = 0.123711

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Work Shown:

LCM = (product of two numbers)/(HCF of the two numbers)

LCM = 1536/16

LCM = 96

The interval for horizontal distance is

(59.9 ,74.2)  ( ranging from 59.9 feet to 74.2 feet)

As per given in the question,

The length of the ladder (l) is 40feet

The angle of elevation in the triangle is \(60^0\)

a) In a Δ ABC

One angle is given as 60 and the one side length (length of ladder) is given as 40 feet

The height of the slide is

\(sin\theta=\frac{opposite}{hypotenuse}\)

\(sin60^0\) = \(\frac{h}{40}\)                                 where the value of   ( \(sin60^0={\frac{\sqrt{3} }{2} }\))

=> \(\frac{\sqrt{3} }{2}\) = \(\frac{h}{40}\)

=> h = 20\(\sqrt{3}\)

Approximately the height of the slide is 34.64 feet

b)    In Δ DEF,

        \(\theta = tan^{-1} \frac{h}{d}\)                                                           ----( 1)

=>  \(Tan^{-1} (\frac{34.6}{d} )\)

c)  the angle of depression is \(\theta=25^0\) and \(\theta=30^0\)

first for the value \(\theta=30^0\)

substitute the value of \(\theta\) in equation (1)

\(tan30^0=(\frac{34.63)}{d})\)            where the value of ( \(Tan 30^0=\frac{1}{\sqrt{3} }\))

=> \(\frac{1}{\sqrt{3} } =\frac{34.63}{d}\)

=> d = 59.99

now

substitute the value \(\theta=25^0\) in equation (1)

\(tan25^0=(\frac{34.6}{d} )\)

=> d = 74.28

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Answer:

(Opt.D) x = 14

Step-by-step explanation:

<A + <B = 180 (Adjacent angles of a parallelogram are supplementary)

∴36 + 11x - 10 = 180

26 + 11x = 180

11x = 180 - 26

11x = 154

x = 154/11

x = 14

Hope this helps u

Please mark as brainliest

Thank You

At least 3 decimal places, the probability that a person who tests positive actually has the disease is approximately 0.002482.

Bayes' relates the conditional probabilities of two events A and B as follows:

P(A | B) = P(B | A) × P(A) / P(B)

P(A) is the prior probability of A, P(B | A) is the conditional probability of B given A, P(B) is the marginal probability of B and P(A | B) is the conditional probability of A given B.

Let's define the following events:

D: the person has the disease

T: the person tests positive

We are interested in finding P(D | T) the probability that a person who tests positive actually has the disease.

We are given that:

P(D) = 0.009 (the incidence rate of the disease)

P(T | D') = 0.03 (the false positive rate, i.e., the probability of testing positive given that the person does not have the disease)

P(T' | D) = 0.06 (the false negative rate, i.e., the probability of testing negative given that the person has the disease)

We can compute the marginal probability of testing positive as follows:

P(T) = P(T | D) × P(D) + P(T | D') × P(D')

= (1 - P(T' | D)) × P(D) + P(T | D') × (1 - P(D))

Plugging in the given values, we get:

P(T) = (1 - 0.06) × 0.009 + 0.03 × (1 - 0.009)

≈ 0.0325

Now we can use Bayes' to compute P(D | T):

P(D | T) = P(T | D) × P(D) / P(T)

Plugging in the given values and the computed value of P(T), we get:

P(D | T) = (1 - P(T' | D)) × P(D) / P(T)

≈ (1 - 0.06) × 0.009 / 0.0325

≈ 0.002482

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Answer:

The answer is b.

Step-by-step explanation:

Answer:

a) 1:48000 b)1.6128km

Step-by-step explanation:

Answer:

1, 2, 3, 6 are all factors of 42

Answer:

  y = x³ -2x² -13x -10

Step-by-step explanation:

You want a polynomial with x-intercepts -2, -1, and 5, and a y-intercept of -10.

A polynomial with zero x = p will have a factor of (x -p). The three given zeros mean factors of the desired polynomial will be ...

  p(x) = (x -(-2))(x -(-1))(x -5) = (x +2)(x +1)(x -5)

Expanding this gives ...

  p(x) = (x +2)(x² -4x -5) = x³ -2x² -13x -10

This polynomial has a constant of -10, which will be its y-intercept. No additional scaling is needed.

The polynomial function is ...

  y = x³ -2x² -13x -10

Answer:

give brainliest if correct

Step-by-step explanation:

Let's call the distance from the ball to the base of the goal "x". We can use the tangent function to set up an equation:

tan(27°) = opposite/adjacent

In this case, the opposite side is the height of the goal (9 feet) and the adjacent side is the distance we want to find (x). So we can rewrite the equation as:

tan(27°) = 9/x

To solve for x, we can cross-multiply and then divide by tan(27°):

tan(27°) * x = 9

x = 9 / tan(27°)

Using a calculator, we get:

x ≈ 17.20 feet

So the distance from the ball to the base of the goal is approximately 17.20 feet.

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Answer:

Step-by-step explanation:

h(-9) = (-9)^2 - 2(-9) = 81  + 18 - 99

g(99) = 99 + 4 = 103

answer is C

Answer: 36

Step-by-step explanation:

Answer:

The area of the dilated figure is the area of the original figure multiplied by the square of the scale factor.

Step-by-step explanation:

The third side of the triangle 12.5

A triangle is a polygon with three edges and three vertices. The important property of a triangle is that the sum of the internal angles of a triangle is equal to 180 degrees. This property is called angle sum property of triangle.

we the measurements of given two sides of the triangle 16.5 and 29

In a triangle, the sum of any two sides should be greater than the third side and the difference between any two sides should be lesser than that of the third side.

The sum of two sides rule

\(x + 16.5 > 29\\ x > 29 - 16.5\\ x > 12.5\\\)

The difference between the two sides rule

\(29 - 16.5 < x \\ 12.5 < x\)

Therefore, the value of x is 12.5

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Answer:

1+1 is cannot be

Step-by-step explanation:

jajauajhwhahwwhhahwhauwu

Answer:

-10 :)

Hey champ! Here's the 'splination!

equation: 50-5x=100

50=-5x. (subtract 50 from both sides)

-10=x (divide both sides by -5)

Answer:

J (-3,3), G (0,3), H (4,9), I (3,3)

Step-by-step explanation:

When your dilating a figuring it either gets larger or smaller. Since this is a positive number, and it is not a fraction then the figure is getting larger. Now you multiply each of the original coordinates by 3 to get the dilated coordinates.

(For learning purposes only)

a)  If I randomly catch any one fish from this tank, the probability of catching a medium-sized fish from the tank is 0.3182.
b) the probability of catching a medium-sized guppy from the tank is 0.1391.

c) the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.

d) the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.

e)  the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.
f) 0.1384 is not equal to 0.1391, which indicates that the two events are not independent

Probability is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, with 0 indicating impossibility and 1 indicating certainty.

The explanation to the above probability answer are given below:

a)

From the contingency table, we can see that the total number of medium-sized fish is 96. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized fish is:

Probability of catching a medium-sized fish = Total number of medium-sized fish / Total number of fish

Probability of catching a medium-sized fish = 96 / 302

Probability of catching a medium-sized fish = 0.3182

Therefore, the probability of catching a medium-sized fish from the tank is 0.3182

b)
From the contingency table, we can see that the total number of medium-sized guppies is 42. The total number of fish in the tank is 302. Therefore, the probability of catching a medium-sized guppy is:

Probability of catching a medium-sized guppy = Total number of medium-sized guppies / Total number of fish

Probability of catching a medium-sized guppy = 42 / 302

Probability of catching a medium-sized guppy = 0.1391

Therefore, the probability of catching a medium-sized guppy from the tank is 0.1391.

c)

From the contingency table, we can see that the number of medium-sized guppies is 42, and the number of medium-sized fish is 96. Therefore, the probability of catching a guppy if we randomly select a medium-sized fish is:

Probability of catching a guppy given a medium-sized fish = Number of medium-sized guppies / Total number of medium-sized fish

Probability of catching a guppy given a medium-sized fish = 42 / 96

Probability of catching a guppy given a medium-sized fish = 0.4375

Therefore, the probability of catching a guppy if we randomly select a medium-sized fish from the tank is 0.4375.

d)
To calculate the probability of catching a medium-sized guppy if we randomly select a guppy from the tank, we need to find the number of medium-sized guppies in the tank and divide it by the total number of guppies in the tank.

From the contingency table, we can see that the number of medium-sized guppies is 42, and the total number of guppies is 131. Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is:

Probability of catching a medium-sized guppy given a guppy = Number of medium-sized guppies / Total number of guppies

Probability of catching a medium-sized guppy given a guppy = 42 / 131

Probability of catching a medium-sized guppy given a guppy = 0.3206

Therefore, the probability of catching a medium-sized guppy if we randomly select a guppy from the tank is 0.3206.


e)

From the contingency table, we can see that the total number of non-goldfish is 190 (45 medium goldfish + 70 small guppy + 42 medium guppy + 9 medium gourami + 10 large gourami + 14 small gourami). The total number of fish in the tank is 302. Therefore, the probability of catching a fish that is not a goldfish is:

Probability of catching a fish that is not a goldfish = Total number of non-goldfish / Total number of fish

Probability of catching a fish that is not a goldfish = 190 / 302

Probability of catching a fish that is not a goldfish = 0.6291

Therefore, the probability of catching a fish that is not a goldfish if we randomly select a fish from the tank is 0.6291.

f)

From the contingency table, we can see that the probability of randomly catching a guppy is 131/302, which is approximately 0.4344. Similarly, the probability of randomly catching a medium-sized fish is 96/302, which is approximately 0.3182.

Now, let's consider the joint probability of randomly catching a medium-sized guppy, which we calculated earlier to be 42/302, or approximately 0.1391. To determine if the events are independent, we need to compare the product of the probabilities of the individual events (catching a guppy and catching a medium-sized fish) to the joint probability of the events occurring together.

If the events are independent, then the product of their individual probabilities should be equal to the joint probability:

P(catching a guppy) x P(catching a medium-sized fish)
= P(catching a medium-sized guppy)

0.4344 x 0.3182 = 0.1391

0.1384 is not equal to 0.1391, which indicates that the two events are not independent.

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Answer:

yes

Step-by-step explanation:

3.68-3=0.68 (SHE HAS ENOUGH!!!)

Answer:

1,187.5

Step-by-step explanation:

Convert inch to feet or convert feet to inch. Convert inch to feet by:

Calculate the inch by subtracting it from the same amount of length(12) and multiplying it by 100

Answer:

32

Step-by-step explanation:

8 ÷ \(\frac{1}{4}\) = 8 x 4 = 32

If the Federal Reserve sells $60,000 in Treasury bonds to a bank at 8% interest, the immediate effect on the money supply is B. It is decreased by $60,000.

One of the monetary factors that decreases the money supply in the economic is when the Federal Reserve raises the banks' reserve requirements.

Another factor that can decrease the money supply is the sale of treasury bonds to banks.

Raising the interest rates also decreases the money supply.

Thus, by selling $60,000 in Treasury bonds to a bank at 8% interest, it decreases the money supply.

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There are three area options for the number of bricks:

The number of bricks that can be painted out is equal to the paint area (A), in square centimeters, divided to the area of a brick (A'), in square centimeters. That is:

n = A / A'

A' = w · h

Where:

There are three possible answers:

Case 1: A = 93750 cm², w = 22.5 cm, h = 10 cm

A' = 22.5 · 10

A' = 225

n = 93750 / 225

n = 416.667

n = 416

Case 2: A = 93750 cm², w = 22.5 cm, h = 7.5 cm

A' = 22.5 · 7.5

A' = 168.75

n = 93750 / 168.75

n = 555.556

n = 555

Case 3: A = 93750 cm², w = 10 cm, h = 7.5 cm

A' = 10 · 7.5

A = 75

n = 93750 / 75

n = 1250

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Answer:

............... .......

Answer:

Step-by-step explanation:

None of these answers is correct.  The graph does not represent a proportional relationship because it does not go through (0, 0).

Answer:

D. The graph does not show a proportional relationship because a line that increases by 1 in the y-value cannot have a constant of proportionality.

Step-by-step explanation:

All proportional relationships can be written as \(y=kx\), where \(k\) is some constant of proportionality. Therefore, all proportional relationships must pass through the origin (0, 0). Since the line shown does not pass through the origin, it cannot be a proportional relationship and we eliminate the first two answer choices.

The graph shows a straight line which represents a linear function, a prerequisite to being a proportional relationship. However, the function for the line is \(y=x+1\), which is does not follow the format \(y=kx\) and therefore does not pass through the origin. Because of this, the line does not have a constant of proportionality and therefore the answer is D. The graph does not show a proportional relationship because a line that increases by 1 in the y-value cannot have a constant of proportionality.