A line has a slope of -2 / 3 and passes through the point (-3, 8). What is the equation of the line?
O y=3x+6
O y=x+8
O y=6x-2/3
O y=8x-2/3

Answer:

6

Step-by-step explanation:

First, simplify the exponents:

2*(3^6*3*-5)

2*((3*3*3*3*3*3)*(1/3*3*3*3*3))

2*(729*0.00411522633)

Then solve from there:

2*2.99999999457

5.99999998914

Since there is only whole numbers and a fraction present, im assuming you have to round:

5.99999998914

6

6 is your answer

Hope this helps!

Answer:$20

Step-by-step explanation:

16 divided by 10 = 1.6 (10%)

1.6 times 2 = 3.2 (20%)

16 + 3.2 = 19.2

1.6 divided by 2 = 0.8 (5%)

19.2 + 0.8 = 20$

Let me know if I helped! :D

Answer:

Answer:

63

Step-by-step explanation:

John's percentage:

36 and 48 have a common factor of 12 so divide both of them by 12.

36/12= 3 and 48/12=4 therefore

so 36/48= 3/4 which is 75% but we don't need to focus on the percent.

Don's no. of shirts:

we know Don has 84 shirts so we say

3/4 of 84= no. of shirts that Don put in his closet

84/4=21 21x3=63

Don put 63 shirts in his closet.

Hope that helped! Anymore questions just ask! :)

The formulas for cos(6θ) and sin(6θ) using de Moivre's theorem are:

cos(6θ) = Re[(cosθ + isinθ)^6]

sin(6θ) = Im[(cosθ + isinθ)^6]

To find the formulas for cos(6θ) and sin(6θ) using de Moivre's theorem, we can start by expressing (cosθ + isinθ) raised to the power of 6. According to de Moivre's theorem, this can be written as (cos(6θ) + isin(6θ)).

Expanding (cosθ + isinθ)^6 using the binomial theorem, we get:

(cosθ + isinθ)^6 = C(6, 0)(cosθ)^6(isinθ)^0 + C(6, 1)(cosθ)^5(isinθ)^1 + C(6, 2)(cosθ)^4(isinθ)^2 + C(6, 3)(cosθ)^3(isinθ)^3 + C(6, 4)(cosθ)^2(isinθ)^4 + C(6, 5)(cosθ)^1(isinθ)^5 + C(6, 6)(cosθ)^0(isinθ)^6

Simplifying this expression, we can calculate each term separately. The terms with odd powers of isinθ will be imaginary and will contribute to sin(6θ), while the terms with even powers of isinθ will be real and will contribute to cos(6θ). After evaluating the terms and combining like terms, we obtain the formulas for cos(6θ) and sin(6θ).

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The quotient and remainder are x³ -5x² + 10x - 17 and 55.

What is Synthetic division?

When the divisor is a linear factor, synthetic division is a technique used to carry out the division operation on polynomials.

Here, (x+2) is a linear factor which indicates that synthetic division can be applied.

So, we will divide the x^4 - 3x^3 - 7x + 1 by x+2.

(refer the attached solution)

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The dimensions of the box can be represented as (6-2x) inches by (24-2x) inches by "x" inches.

From a 24-inch by 6-inch piece of cardboard, square corners are cut so the sides can fold up to form a box without a top. To determine the dimensions and construct the box, we need to consider the shape of the cardboard and the requirements for folding and creating the box.

The initial piece of cardboard is a rectangle measuring 24 inches by 6 inches. To form the box without a top, we need to remove squares from each corner.

Let's assume the side length of the square cutouts is "x" inches. After cutting out squares from each corner, the remaining cardboard will have dimensions (24-2x) inches by (6-2x) inches.

To create a box, the remaining cardboard should fold up along the edges. The length of the box will be the width of the remaining cardboard, which is (6-2x) inches.

The width of the box will be the length of the remaining cardboard, which is (24-2x) inches. The height of the box will be the size of the square cutouts, which is "x" inches.

Therefore, the dimensions of the box can be represented as (6-2x) inches by (24-2x) inches by "x" inches. To construct the box, the remaining cardboard should be folded along the edges, and the sides should be secured together.

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Answer:

11.6

Size = 5

Mean = 47

The manufacturers need to test at least 725 light bulbs to estimate the percentage of defective light bulbs with a 97% confidence interval and a margin of error of 3.6%.

To determine the sample size needed to estimate the percentage of defective light bulbs with a 97% confidence interval and a margin of error of 3.6%, we can use the formula:

n = (z^2 * p * q) /\(E^2\)

where:

n = sample size

z = z-score for the desired confidence level (97% confidence level corresponds to a z-score of 1.8808)

p = estimated proportion of defective light bulbs (unknown)

q = 1 - p

E = margin of error as a proportion (0.036)

Since the proportion of defective light bulbs is unknown, we can assume a conservative estimate of 0.5, which gives the maximum possible sample size. Thus, we have:

n = (\(1.8808^2\) * 0.5 * 0.5) / \(0.036^2\) = 724.75

Rounding up to the nearest whole number, we get:

n = 725

Therefore, the manufacturers need to test at least 725 light bulbs to estimate the percentage of defective light bulbs with a 97% confidence interval and a margin of error of 3.6%.

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Answer:

65

Step-by-step explanation:

The inside of a triangle is 180 degrees and the other two angles are the same so 50+65+65 =180. The answer is 65

Answer:

96

Step-by-step explanation:

first off you know that it is a square pyramid, so you can assume that all base lengths are 6.

i am going to find the base first. it is 36 because 6*6-36 save this in your mental memory

next, we have to find the 4 triangles

we know that they are 5 by 6 but you have to divide them by 2

so 30/2=15 and there are 4 of them

15*4=60

now add together 60 and 36 and you get 96

hope this helps!

Answer:

y = -2x - 3

Step-by-step explanation:

Answer:

y=(10×10)÷(1-2) =N

Step-by-step explanation:

y -is the numerical angle of triangle

10×10because the triangle have a ten angle

1-2 cause the line of triangle

The derivate of a function f(x) is determinated as:

For the function

First we have to determine de f ( x + h ) as follow:

Then we calculate and simplify the coeficient in the first formula

------------------------------------------------------------------------------------The equation of the tangent:

First you need to know that the derivate of a function is equal to the slope (m) of the tangent of this function

And the equation to thist tangent in a specific point will be find using the next formula:

We have to calculate the slope in the point x =4 using the derivate:

In the point x=4

Calculate the value of f(x0) substituting in the function the given point x:

Knowing that we put the value of m and f(x0) in the equation of the tangent:

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

The normal line

The slope of the normal line is the opposite of the slope of theu tangent in an espesific point:

So in this situation is:

The equation of the normal line is given by the next formula:

Replacing the data we obtain:

While language and cultural differences may exist, mathematical ideas and concepts can be communicated and understood by people from all over the world

What is Maths ?

Mathematics, commonly referred to as "math," is a branch of knowledge concerned with the study of numbers, quantities, shapes, and patterns.

Mathematics is often considered a universal language because it is based on fundamental principles and concepts that can be expressed and understood in a consistent and objective manner across different cultures, languages, and backgrounds. Mathematical symbols and formulas have the same meaning and application regardless of the language or culture of the person using them.

Moreover, mathematics is used in many fields and industries, including science, engineering, finance, and technology, and it provides a common framework for communication and problem-solving in these areas. Mathematical concepts and principles can be used to describe and model phenomena and relationships in the physical world, and to develop solutions and technologies that have global applications.

Therefore, while language and cultural differences may exist, mathematical ideas and concepts can be communicated and understood by people from all over the world, making mathematics a language that transcends national and cultural boundaries.

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Answer:

1 ) 597

2 ) 346

Step-by-step explanation:

1 )

A.P : - 15, - 7, 1, ...

Here,

a = - 15

d = - 7 - ( - 15 )

= - 7 + 15

d = 8

65th term is t65.

t65 = a + ( 65 - 1 )d

= a + 64 d

= - 15 + 64 ( 8 )

= - 15 + 512

t65 = 597

Therefore,

65th term = 597

2 )

A.P = 3, 10, 17, 24, ...

Here,

a = 3

d = 10 - 3 = 7

50th term is t50.

t50 = a + ( 50 - 1 )d

= a + 49d

= 3 + 49 ( 7 )

= 3 + 343

t50 = 346

Therefore,

50th term = 346

Answer:

65ᵗʰ Term of the sequence is 479

50ᵗʰ Term of the sequence is 346

Step-by-step explanation:

Here,

First Term = a₁ = 3

Second Term = a₂ = 10

Third Term = a₃ = 17

Now,

Common Difference (d)

d = a₂ - a₁ = (-7) - (-15) = -7 + 15 = 8

d = a₃ - a₂ = 1 - (-7) = 1 + 7 = 8

Here, Common Difference is same everywhere

Now, For 65ᵗʰ term, n = 65

aₙ = a + (n - 1)d

a₆₅ = (-15) + (65 - 1) × 8

a₆₅ = (-15) + 64 × 8

a₆₅ = (-15) + 512

a₆₅ = 479

Thus, 65ᵗʰ Term of the sequence is 479

Here,

First Term = a₁ = -15

Second Term = a₂ = -7

Third Term = a₃ = 1

Now,

Common Difference (d)

d = a₂ - a₁ = 10 - 3 = 7

d = a₃ - a₂ = 17 - 10 = 7

Here, Common Difference is same everywhere

Now, For 50ᵗʰ term, n = 50

aₙ = a + (n - 1)d

a₅₀ = 3 + (50 - 1) × 7

a₅₀ = 3 + 49 × 7

a₅₀ = 3 + 343

a₅₀ = 346

Thus, 50ᵗʰ Term of the sequence is 346

-TheUnknownScientist

Answer:

8.8 Minutes or 528 Second.

Step-by-step explanation:

↓[ Read Below ]↓

Important Info:

Leslie Ran 3 Mile Race.

2nd Mile = 10% longer than 1st and 3rd Miles took her 24s longer than 2nd Mile

Question to Answer:

Leslie’s total time for the race was 26 minutes how long did the second mile take her?

Explanation/Solution:

Let for first mile, she took x minutes . And second mile took her 10 percent longer, so second mile took

x+ 10/100x = 110/100x=1.1x

And the third mile took 24 seconds longer as compared to second mile .

So third mile took

1.1x+24/60 = (1.1x+0.4) Minutes

And the total time for the race was 26 minutes, that is

x+1.1x+1.1x+0.4=26

3.2x=26-0.4

3.2x=25.6

x= 25.6/3.2 = 8 Minutes

So the first mile took 8 minutes. And therefore second mile took

= 1.1 (8) = 8.8 Minutes

Also Equal to 528 Second.

[RevyBreeze]

Given that y be a binomial random variable with parameters n = 30 and pi.

Assume a beta (1,2) distribution as the prior for pi and suppose the observed number of successes is y = 18. We need to find the 99% credible interval for pi, rounded to three decimal places.

Step 1: Let the prior distribution of pi be Beta (a, b), where a = 1, b = 2, as given.

Step 2: Given y = 18, the likelihood function for the Binomial distribution is given by: P(Y = 18|pi)

= 30C18 * pi¹⁸ * (1- pi)¹²

Step 3: Posterior Distribution of pi. The posterior distribution of pi will be: P(pi| Y = y) ∝ P(Y = y| pi) * P(pi)P(pi| Y = y)

= P(Y = y| pi) * P(pi) / P(Y = y)

Here, P(Y = y) is the normalizing constant and it can be found by integrating the numerator with respect to pi over the range (0, 1).

P(Y = y) = ∫P(Y = y| pi) * P(pi) d(pi)

= ∫30C18 * pi¹⁸ * (1- pi)¹² * pi0.2-1 * (1- pi)²⁻¹

d(pi) = ∫30C18 * pi18.2 * (1- pi)¹³ * d(pi) = 0.0270 (approx)

P(pi| Y = y) = P(Y = y| pi) * P(pi) / P(Y = y) ∝ pi18.2-1 * (1- pi)¹³⁻¹ * pi0.2-1 * (1- pi)²⁻¹

P(pi| Y = y) = pi18.2 * (1- pi)¹³ / 0.0270

Hence, P(pi| Y = y) = 0.0232 pi18.2 * (1- pi)¹³

Step 4: Credible Interval A credible interval is the range of values of a parameter, in this case, pi, for which the posterior probability (degree of belief) is specified. A 99% credible interval for pi is defined such that the probability of pi being inside that interval is 0.99.

P(pi| Y = y) = pi18.2 * (1- pi)¹³ / 0.0232

Since, pi has a Beta distribution with parameters a = 19.2 and b = 15, we can obtain the 99% credible interval using the following quantiles:0.005th quantile:

P(pi < pi1) = 0.005 =>

pi1 = 0.219990.99

5th quantile: P(pi < pi2) = 0.995

=> pi2 = 0.63031

Thus, the 99% credible interval for pi, rounded to three decimal places is (0.220, 0.630).Hence, the required answer is (0.220, 0.630).

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Answer:

Step-by-step explanation:

34

Answer:

(+8×5) + (-6)

(+40) + (-6)

(+40-6)

(+34)

Answer:

168

Step-by-step explanation:

LxWxH

L=6

W=4

H=7

6x4=24

24x7=168

Answer:

63,168 square inches

Step-by-step explanation:

A=2(wl+hl+hw)

A= 2{(4*6)+(7*6)+(7*4)}

A= 188

188 square inches for each candle

188 square inches times 336 candles= 63,168 square inches in total.

Hope this helped <3 Brainliest? :)

(a) The probability of a typist's net rate being at most 58 wpm is 0.5000.

(b) The probability of a typist's net rate being between 8 and 108 wpm is 0.9544.

(c) The probability that both typists' rates exceed 108 wpm is approximately 0.0005202.

(d) Typists with typing speeds of 36.96 wpm or less would qualify for special training available to the slowest 20% of typists.

(a) To find the probability that a randomly selected typist's net rate is at most 58 wpm, we need to calculate the area under the normal curve up to 58 wpm.

Using the Z-score formula: Z = (X - μ) / σ

where X is the value we want to find the probability for, μ is the mean, and σ is the standard deviation.

In this case, X = 58 wpm, μ = 58 wpm, and σ = 25 wpm.

Z = (58 - 58) / 25 = 0

We can then use a Z-table or a statistical calculator to find the corresponding cumulative probability for Z = 0. The cumulative probability for Z = 0 is 0.5000.

Therefore, the probability that a randomly selected typist's net rate is at most 58 wpm is 0.5000.

To find the probability that a randomly selected typist's net rate is less than 58 wpm, we need to subtract the probability from 58 wpm to the left tail of the distribution.

P(X < 58) = P(X ≤ 58) - P(X = 58)

          = 0.5000 - 0 (since the probability of a specific value is negligible in a continuous distribution)

          = 0.5000

Therefore, the probability that a randomly selected typist's net rate is less than 58 wpm is 0.5000.

(b) To find the probability that a randomly selected typist's net rate is between 8 and 108 wpm, we need to calculate the area under the normal curve between these two values.

First, we calculate the Z-scores for the two boundaries:

Z1 = (8 - 58) / 25 = -2

Z2 = (108 - 58) / 25 = 2

Using the Z-table or a statistical calculator, we find the cumulative probabilities for Z = -2 and Z = 2.

P(-2 < Z < 2) = P(Z < 2) - P(Z < -2)

             = 0.9772 - 0.0228

             = 0.9544

Therefore, the probability that a randomly selected typist's net rate is between 8 and 108 wpm is 0.9544.

(c) To find the probability that both typists' typing rates exceed 108 wpm, we need to find the probability that a typist's rate is greater than 108 wpm and multiply it by itself since the typists are selected independently.

The probability that a typist's rate is greater than 108 wpm can be calculated using the Z-score formula:

Z = (X - μ) / σ

where X = 108 wpm, μ = 58 wpm, and σ = 25 wpm.

Z = (108 - 58) / 25 = 2

Using the Z-table or a statistical calculator, we find the cumulative probability for Z = 2.

P(Z > 2) = 1 - P(Z < 2)

         = 1 - 0.9772

         = 0.0228

Since the typists are selected independently, we multiply this probability by itself:

P(both typists' rates exceed 108 wpm) = 0.0228 * 0.0228

                                     = 0.000520224

Therefore, the probability that both typists' typing rates exceed 108 wpm is approximately 0.0005202.

(d) To find the typing speeds that qualify individuals for the special training available to the slowest 20% of

typists, we need to find the threshold value of the net typing rate below which only 20% of typists fall.

Using the Z-score formula:

Z = (X - μ) / σ

where Z is the Z-score corresponding to the 20th percentile, X is the typing speed we want to find, μ = 58 wpm, and σ = 25 wpm.

From the Z-table or a statistical calculator, we find the Z-score corresponding to the 20th percentile is approximately -0.8416.

Solving the equation for Z, we get:

-0.8416 = (X - 58) / 25

Simplifying:

-0.8416 * 25 = X - 58

-21.04 = X - 58

X = -21.04 + 58

X = 36.96

Therefore, typing speeds of 36.96 wpm or less would qualify individuals for this training.

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16.32 X 8.1 = 132.192

The variable "area of the circle" would likely be classified as a continuous variable, as it can take on any value within a certain range (e.g. 0 to infinity), and the difference between any two values within that range can be any positive value.

The variable "number of equal slices in a pizza" would likely be classified as a discrete variable, as it can only take on certain integer values (e.g. 1, 2, 3, etc.). Similarly, the variable "portion of the pizza in one slice" would also be classified as a discrete variable, as it can only take on certain values (e.g. 1/2, 1/3, 1/4, etc.).

The variable "air temperature in Saint Paul, MN" would likely be classified as a continuous variable, as it can take on any value within a certain range (e.g. -40 to 120 degrees Fahrenheit), and the difference between any two values within that range can be any positive value.

The variable "last four digits of a Social Security number" would likely be classified as a discrete variable, as it can only take on certain integer values (e.g. 0001 to 9999).

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Answer:

11/32

Step-by-step explanation:

Given that:

Red section (R) = 3 ; white section (W) = 3 ; green section (G) = 2

Total Number of sections = 8

Probability of getting the same color on two spins :

Probability = (required outcome / Total possible outcomes)

Either P(RR) or P(WW) or P(GG)

(3/8 * 3/8) + (3/8 * 3/8) + (2/8 * 2/8)

9/64 + 9/64 + 4/64

(9 + 9 + 4) / 64

22 / 64

= 11/32

the probability of getting the same color twice is

\(\frac{11}{32}\)

Given :

A spinner is evenly divided into eight sections: three are red, three are white and two are green.

Total of 8 sections.

red=3

white =3

green =2

Probability of getting two red color =\(\frac{3}{8} \cdot \frac{3}{8}= \frac{9}{64}\)

Probability of getting two white colors =\(\frac{3}{8} \cdot \frac{3}{8}= \frac{9}{64}\)

Probability of getting two green colors=\(\frac{2}{8} \cdot \frac{2}{8}= \frac{4}{64}\)

Probability (getting same color twice)=\(\frac{9}{64} + \frac{9}{64}+ \frac{4}{64}=\frac{22}{64} =\frac{11}{32}\)

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According to the solving Mrs. Weatherford spends 15 percent of each weekday  25 hours and 20 minutes in her car.

A % is a relative figure that represents the hundredth part of any amount. One percent (symbolized 1%) is one hundredth part; consequently, 100 percent denotes the complete amount and 200 percent defines twice the supplied amount.

The most fundamental use of percentages is really to compare one number to another, with the second number rebased to 100. Assume we want to know the number among employed females as both a percentage of all employees.

Mrs. Weatherford drives 15% of the time during the week.

We know that:

1 week  = 7days

1day  = 24 hours

So 7 days  = 7 x 24

                  = 168 hours

Mrs. Weatherford drives 15% of the time during the week.

So,

(168/100) * 15

1.68 * 15

25.2 hours

According to the solving Mrs. Weatherford spends 25 hours and 20 minutes in her car.

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Answer:

imma say 10/4

Step-by-step explanation:sorry if wrong

Answer: 5 feet 2 yards

Step-by-step explanation: Just divide both of the numbers by a number that both of them can go through

Answer:

(8x - 9y)2

Step-by-step explanation:

64x2−144xy+81y2

Equation at the end of step 1:  

((64 • (x2)) -  144xy) +  34y2

The Equation at the end of step 2:

(26x2 -  144xy) +  34y2

Step 3:

(8x - 9y)2

Answer:

(8x - 9y)2

Using the normal distribution we can calculate that the clothing store should store 35 t-shirts such that the probability is 16% .

We must first identify the z-score for this percentile. How do we accomplish this? We must determine the precise value of z that resolves the equation shown below.

Pr(Z<z) = 0.84

The value of z that solves the equation above cannot be made directly, it is solved either by looking at a standard normal distribution table or by approximation .

Based on this, we find that that the solution is z = 0.995, because from the normal table we see that

Pr(Z 0.995) = 0.84

Therefore, the percentile we are looking for is computed using the following formula:

P84 = μ + 2 Χ σ

= 30+ 0.995 x 5

= 34.972

≈ 35

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(5−2i)−(2−i)+(−6+i)

=5-2i-2+i-6+i

=5-6-2-2i+i+i

=-3-2i+2i

=-3