The coordinates of the endpoints of GH are G(2,7) and H(11,16). Point I is on GH and divides it such that GI:HI is 4:5. What are the coordinates of I?

Answer:

−  2x^ 3  +  8 x ^2

Step-by-step explanation:

Hope this helps:)

Answer:

p = 0.259264214

Step-by-step explanation:

26 - 7 = 19 with good brakes

Probability of picking 4 with good brakes

p = 19/26 * 18/25 * 17/24 * 16/23

p = 0.259264214

The probability that all the randomly chosen cars have good brakes is approximately 0.169 or 16.9%.

To calculate the probability that all the randomly chosen cars have good brakes, we need to consider the number of cars with good brakes and the total number of cars.

Total number of cars assembled: 26

Number of cars with bad brakes: 7

To calculate the probability, we can use the concept of combinations.

The number of ways to select 4 cars out of the remaining 26-7 = 19 cars with good brakes is given by the combination formula:

C(n, r) = n! / (r! * (n-r)!)

where n is the total number of cars with good brakes and r is the number of cars to be randomly selected.

In this case, n = 19 and r = 4.

The total number of ways to select 4 cars from the total pool of 26 cars is given by the combination formula:

C(26, 4) = 26! / (4! * (26-4)!)

Now, we calculate the probability that all the randomly chosen cars have good brakes:

Probability = (Number of favorable outcomes) / (Number of total outcomes)

Number of favorable outcomes = C(19, 4)

Number of total outcomes = C(26, 4)

Probability = C(19, 4) / C(26, 4)

Using a calculator, we can compute these combinations and evaluate the probability:

Probability ≈ 0.169

Therefore, the probability that all the randomly chosen cars have good brakes is approximately 0.169 or 16.9%.

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Answer:

The equation that relates b to a is;

Explanation:

We want to write an equation that represent the data on the table;

The data can be represented with a linear relationship with origin (0,0), since they both start from (0,0). It can be represented by a proportional relation of the form;

The constant of proportionality is the ratio of b/a;

Using the data on the table we can get k;

Therefore, the equation that relates b to a is;

To find all points on the x-axis that are 16 units away from the point (5, -8), we can use the distance formula. The distance between two points (x₁, y₁) and (x₂, y₂) is given by the formula:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, the y-coordinate of the point (5, -8) is -8, which lies on the x-axis. So, any point on the x-axis will have a y-coordinate of 0. Let's substitute the given values and solve for the x-coordinate.

d = √((x - 5)² + (0 - (-8))²)

Simplifying:

d = √((x - 5)² + 64)

Now, we want the distance d to be equal to 16 units. So, we set up the equation:

16 = √((x - 5)² + 64)

Squaring both sides of the equation to eliminate the square root:

16² = (x - 5)² + 64

256 = (x - 5)² + 64

Subtracting 64 from both sides:

192 = (x - 5)²

Taking the square root of both sides

√192 = x - 5

±√192 = x - 5

x = 5 ± √192

Therefore, the two points on the x-axis that are 16 units away from the point (5, -8) are:

Point 1: (5 + √192, 0)

Point 2: (5 - √192, 0)

In summary, the points on the x-axis that are 16 units away from the point (5, -8) are (5 + √192, 0) and (5 - √192, 0).

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Answer:

  5√5 ≈ 11.18 units

Step-by-step explanation:

The Pythagorean theorem can be used to find the unknown leg of a triangle with hypotenuse 15 and one leg 10:

  d = √(15^2 -10^2) = 5√(3^2 -2^2) = 5√5

The plane is 5√5 units from the center of the sphere.

Answer:

Derek would have to buy 3 packs of 8 hotdogs and 2  packs of 12 hotdog buns.

Step-by-step explanation:

This is because 8 times 3 is 24 and 12 times 2 is 24.

8 and 12 both have a common multiple, which is 24.

So if he buys 3 packs of hotdogs, which come in packs of 8, he'll get 24.

And if he buys 2 packs of buns, which come in packs of 12, he'll get 24.

#teamtrees #WAP (Water And Plant)

Answer:

3 packs of hotdogs and 2 packs of buns

Step-by-step explanation:

Let \(h =\) number of hotdogs, and \(b =\) number of buns

8\(h\) = 12\(b\)

LCM of 8 and 12 is 24

8\(h\) = 24

\(h\) = 3

12\(b\) = 24

\(b\) = 2

\(\therefore\) Derek needs to buy 3 packs of hotdogs and 2 packs of buns to have the same number of each.

Hope this helps :)

The swimming pool can hold a volume of 3.456 cubic meters of water.

The volume of water that the swimming pool can hold can be calculated by multiplying the base area of the pool by its depth. In this case, the base area is given as 192 m² and the depth is 1.8 cm.

However, it is important to note that the depth should be converted to meters before performing the calculation.

To convert 1.8 cm to meters, we divide it by 100 (since there are 100 centimeters in a meter):

Depth = 1.8 cm ÷ 100 = 0.018 m

Now we can calculate the volume of water using the formula:

Volume = Base Area × Depth

Substituting the given values, we get:

Volume = 192 m² × 0.018 m = 3.456 m³

Therefore, the swimming pool can hold a volume of 3.456 cubic meters of water.

In the explanation, we use the formula for calculating the volume of a rectangular prism, which is given by multiplying the base area by the depth. We convert the depth from centimeters to meters and then substitute the given values into the formula to find the volume of water that the swimming pool can hold, which is 3.456 cubic meters.

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The angle measures for this problem are given as follows:

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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Answer:

120 balls

Step-by-step explanation:

Ten dozen is 120.

Answer:

3

Step-by-step explanation:

Answer:

Add -62 and 4

Step-by-step explanation:

Step-by-step explanation:

-62+4=-20

-58=-20

58=20

Step-by-step explanation:

756 = 2² * 3³ * 7.

For 756n to be a perfect cube, all of its prime factors must have a power that is a multiple of 3.

How to get from 2² to 2³: Multiply by 2.

3³ has already a power that is a multiple of 3.

How to get from 7 to 7³: Multiply by 7².

Hence n = 2 * 7² = 98.

Answer:

To calculate how much you would have to deposit today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn, we can use the formula for the present value of an annuity due:

PV = PMT × ((1 - (1 + r/n)^(-n×t)) / (r/n)) × (1 + r/n)

where:

- PV is the present value of the annuity due (the amount you would have to deposit today)

- PMT is the monthly payment ($75)

- r is the annual interest rate (3.5%)

- n is the number of times interest is compounded per year (12 for monthly compounding)

- t is the number of years (10)

PV = 75 × ((1 - (1 + 0.035/12)^(-12×10)) / (0.035/12)) × (1 + 0.035/12) = **$7,360.47**

Therefore, you would have to deposit **$7,360.47** today to accumulate the same amount of money that $75 monthly payments at a rate of 3.5% compounding monthly for 10 years in an annuity would earn.

Answer:

No. It is an inverse variation.

Step-by-step explanation:

6= xy

Making y the subject of formula:

\(y = \frac{6}{x} \)

For a direct variation, the equation would be in the form of y=kx, where k is a constant.

However, the equation above is in the form of \(y = \frac{k}{x} \).

Thus, 6=xy does not show direct variation.

Answer:

30

Step-by-step explanation:

7 1/2 is 15/2 as an improper fraction

15/2 ÷ 1/4 = 15/2 · 4 which is 30

Answer:

30 doses

Step-by-step explanation:

convert 7 1/2 into an improper fraction: 15/2

multiply it by 2/2 to have a common denominator: 30/4

Answer:

50.41 minus 1.71 is 48.70 divided by 5 is 9.74

Answer:

$319.60

Step-by-step explanation:

Normal Game console cost : $399.50

Discount: %20 (0.20)

$399.50×0.20= $79.90

Total cost of discount $79.90

$399.50-$79.90= $319.60

New cost after Discount= $319.60

9514 1404 393

Answer:

  1/2 + 1/6

Step-by-step explanation:

  2/3 = 1/2 + 1/6

__

The sum of unit fractions is called an Egyptian Fraction. There are several different algorithms for finding such a sum. Here, we are starting with the form ...

  2/p

where p is a small prime. Then the sum can be written as ...

  1/((p+1)/2) +1/(p(p+1)/2) = 1/(4/2) +1/(3(4/2)) = 1/2 + 1/6

A different algorithm is used when p is a composite number.

__

Using the "greedy" algorithm, we can find the largest unit fraction less than 2/3 to be ...

  1/ceil(3/2) = 1/2

Then the largest unit fraction in the remainder is similarly found. The remainder is ...

  2/3 -1/2 = 1/6 . . . . already a unit fraction

So, the sum is ...

  2/3 = 1/2 + 1/6

The quadratic function for the value of David's investment indicates;

(i) $45,000

(ii) 9.375 months

A quadratic function is a function that can be expressed in the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, and c are numbers.

The model of the value of the investment in the bank obtained from the amount of his retirement funds David invested in the bank can be presented as follows;

a = 45 + 75·t - 4·t²

Where;

a = The value of the investment in thousand of dollars after t months

t = The number of months of the investment

(i) The initial amount David invested can be found by plugging in t = 0, in the function for the amount David invested in the bank, as follows;

a = 45 + 75 × 0 - 4 × 0² = 45

The initial amount David invested is; a = $45,000

(ii) The number of months it takes for David investment to reach a maximum value can be found from the quadratic function as follows;

The number of months t(max) at the maximum amount is; t(max) = -75/(2 × (-4)) = 9.375

Therefore, it will take 9.375 months for David's investment to reach a maximum value

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(a) The mean of the relevant distribution is 2.4 defective pistons.

(b) The standard deviation of the distribution is 1.539.

The mean of the relevant distribution is the expected number of defective pistons that we would expect to get from a sample of 80 pistons produced by this machine. The mean is calculated by multiplying the probability of a defective piston (3%) with the number of pistons in the sample (80). In this case, the mean is 2.4 defective pistons. The standard deviation of the distribution quantifies the uncertainty of our estimate. It is calculated by taking the square root of the variance, which is the expected value of the squared differences between the number of defective pistons in the sample and the mean. In this case, the standard deviation is 1.539. This means that, in theory, we would expect 68% of the samples to contain between 0.861 and 4.139 defective pistons.

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Answer:

20 %

Step-by-step explanation:

Percentage = \(\frac{2}{10}*100\)

                   = 2 * 10

                   = 20%

Based on equations, Angus worked 6 hours on Saturday and 10 hours at his after-school job last week earning a total of $127.80.

The hourly rate at Angus' Saturday job = $8.80

The hourly rate at Angus' after-school job = $7.50

The total earnings last week = $127.80

Let the hours Angus worked at Saturday job = x

Let the hours Angus worked after-school = 4 + x

The total hours worked = x + x + 4

2x + 4

The total earnings last week 127.80 = 8.8x + 7.5x + 4 (7.5)

127.80 = 8.8x + 7.5x + 30

127.8 - 30 = 16.3x

x = 6 hours

x + 4 = 10 hours

2x + 4 = 16 (12 + 4)

Check:

Earnings at Saturday job = $52.80 ($8.80 x 6)

Earnings at after-school job = $75.00 ($7.50 x 10)

Total earnings = $127.80

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\(\bold{\huge{\green{\underline{ Solution}}}}\)

\(\bold{\underline{ Given :- }}\)

\(\bold{\underline{ To \: Find :- }}\)

\(\bold{\underline{ Let's \: Begin :- }}\)

In the given right angled triangle, we have

Now, By using trigonometric ratios

\(\bold{\pink{ Sin Φ = }}{\bold{\pink{\frac{Perpendicular }{Hypotenuse}}}}\)

\(\bold{\red{ Cos Φ = }}{\bold{\red{\frac{Base}{Hypotenuse }}}}\)

\(\bold{\blue { tan Φ = }}{\bold{\blue{\frac{Perpendicular }{Base }}}}\)

According to the question :-

\(\bold{ Cos \: 45° = }{\bold{\frac{2}{m}}}\)

\(\bold{ 1/√2= }{\bold{\frac{2}{m}}}\)

\(\bold{\red{ m = 2√2 \: units }}\)

Therefore,

Let the unknown angle be x

\(\sf{ 45° + x + 90° = 180° }\)

\(\sf{ x = 180° - 135 ° }\)

\(\sf{ x = 45° }\)

Now,

\(\bold{ Cos \: x° = }{\bold{\frac{n}{2√2}}}\)

\(\bold{ Cos \: 45° = }{\bold{\frac{n}{2√2}}}\)

\(\bold{ 1/√2= }{\bold{\frac{n}{2√2}}}\)

\(\bold { n = 2√2/√2 }\)

\(\bold{\red{ n = 2\: units }}\)

Thus, The value of m = 2√2 and n = 2

\(\sf{\blue{ Hence, \: option \: D \: is \: Correct }}\)

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

We have,

To find the probability that an antigen test comes back positive, we need to consider both the true positive rate (probability of a positive test given that the person is infected) and the false positive rate.

Now,

Prevalence of coronavirus in California: 3 out of 1000

False positive rate of the antigen test: 0.05 (5 out of 100)

Let's calculate the probability of a positive test result.

The true positive rate can be calculated as 1 minus the false negative rate (probability of a negative test given that the person is infected):

True positive rate = 1 - 0.2 = 0.8 (or 80 out of 100)

The probability of a positive test result can be calculated using Bayes' theorem:

P(Positive test) = P(Positive test | Infected) x P(Infected) + P(Positive test | Not Infected) x P(Not Infected)

P(Positive test) = (0.8 x 3/1000) + (0.05 x 997/1000)

P(Positive test) = 0.0024 + 0.04985

P(Positive test) = 0.05225

Therefore,

The probability that an antigen test comes back positive is approximately 0.05225, or about 5.225%.

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Answer:

Step-by-step explanation: