What is the equation of a line that passes through the points (3, 6) and (8, 4)?

Answer:

2eXz2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

3(x+4) = 18

distribute 3 into parenthesis

3x +12 = 18

subtract 12

3x = 6

divide by 3 to get x by itself

x = 2

Rewrite all the numbers as decimals:

14/5 = 2.8

2.6 is already a decimal

2 1/8 = 2.125

2.8 is the largest number so rob is closest to being finished.

2.8 is the largest number then rob is closest to being finished.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the holes need to be at least 3 feet deep. So far robs hole is 14/5, sams are 2.6 feet and toms is 2 1/8 feet.

Rewrite all the numbers as decimals:-

14/5 = 2.8

2.6 is already a decimal:-

2 1/8 = 2.125

Therefore, 2.8 is the largest number then rob is closest to being finished.

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Answer: 5

Step-by-step explanation:

If the length is equal to x, the width is 3(x+2). To make it easier, we simplify 3(x+2) to 3x+6.

Perimeter is 2(l+w).

Substitute 2(l+w) with our values of length and width. You get:

2(x+(3x+6))=52

Then you solve the equation:

2(x+(3x+6))=52

2(4x+6)=52

8x+12=52

8x=40

x=5

The length is 5.

The researcher will need 25 participants to obtain 20 measurements within each of the 25 conditions in this within-subject design.

To determine the number of participants needed for a within-subject design with 25 conditions and 20 measurements within each condition, we need to consider the concept of counterbalancing. Counterbalancing involves systematically varying the order of conditions across participants to account for potential order effects.

In this case, each participant will need to complete all 25 conditions, with 20 measurements within each condition. Therefore, we can calculate the total number of measurements per participant:

Total measurements per participant = Number of conditions × Number of measurements per condition

Total measurements per participant = 25 × 20

Total measurements per participant = 500

To determine the number of participants needed, we divide the total number of measurements by the number of measurements per participant:

Number of participants = Total measurements / Measurements per participant

Number of participants = 500 / 20

Number of participants = 25

Therefore, the researcher will need 25 participants to obtain 20 measurements within each of the 25 conditions in this within-subject design.

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Answer:

i. $26

ii. $(8 + 3t)

Step-by-step explanation:

Given that: automatic fee is $8, and fee per hour is $3. Then;

i. If he left his car in the lot for 6 hours, amount to be paid can be calculated as thus;

since fee per hour is $3, then for 6 hours; the fee = 6 x $3

                                                                                   = $18

Total amount to be paid after 6 hours = automatic fee + $18

                                                               = $8 + $18

                                                               = $26

For parking his car for 6 hours, he would pay $26

ii. Amount paid for t hours = automatic fee + $ 3 x t

                                                          = $(8 + 3t)

Answer:

19 books were checked out.

Step-by-step explanation:

284 + 28 = 312

312 - 293 =  19

the value of the expression is 12.

To solve the following using BEDMAS 5X4 - (3 + 1)2 ÷ 2:BEDMAS is an acronym that represents the order of operations for arithmetic operations in the correct order, that is, "Brackets", "Exponents", "Division and Multiplication", and "Addition and Subtraction."The full form of BEDMAS is- B stands for Brackets.E stands for Exponents.D stands for Division.M stands for Multiplication.A stands for Addition.S stands for Subtraction.

The given expression is;5X4 - (3 + 1)2 ÷ 2When we solve this expression using the BEDMAS rule of the order of operations, we get;= 5 x 4 - (3 + 1) x 2 ÷ 2[Since brackets comes first, then multiplication and division, followed by addition and subtraction.]= 20 - 4 x 2 ÷ 2[Perform multiplication: 3 + 1 = 4 and 4 x 2 = 8]= 20 - 8[Perform Division: 8 ÷ 2 = 4]= 12Therefore, the value of the expression is 12.The solution of the given expression using the BEDMAS rule of the order of operations is explained. The BEDMAS rule defines the correct order in which arithmetic operations should be performed.

It consists of four fundamental operations. They are brackets, exponents, multiplication and division, and addition and subtraction. The expression, 5X4 - (3 + 1)2 ÷ 2, can be solved using the BEDMAS rule of operations. First, we will simplify the brackets, followed by division and multiplication, then addition and subtraction. We will get the following expression 5 x 4 - (3 + 1) x 2 ÷ 2. We will then perform multiplication by finding the product of (3 + 1) and 2, which equals 8. Finally, we will perform division by dividing 8 by 2, which equals 4. After we have completed these steps, we will subtract 8 from 20 to get the final answer of 12.

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Answer:

x = 2

Step-by-step explanation:

a. Yes, the distribution of the number of cases of type II diabetes in the United States can be approximated by a Poisson distribution since it is a rare event and the number of cases is independent of each other.
b. The probability is calculated as P(X ≤ 10) = e^(-12) * 12^10 / 10!, which is approximately 0.112.
c. we can subtract the probability of X ≤ 10 from the probability of X ≤ 15. The probability is calculated as P(10 < X < 15) = P(X ≤ 15) - P(X ≤ 10) = e^(-12) * (12^11 / 11! + 12^12 / 12! + 12^13 / 13! + 12^14 / 14!) ≈ 0.215.
d. The probability of observing 19 or more cases can be calculated using the Poisson distribution formula, P(X ≥ 19) = 1 - P(X ≤ 18) = 1 - e^(-12) * (12^0 / 0! + 12^1 / 1! + ... + 12^18 / 18!) ≈ 0.0002, which is a very small probability.

a. The distribution of the number of cases of type II diabetes in the United States can be approximated by a Poisson distribution if the cases are rare, random, and independent events. Given the incidence rate of 12 per 100,000, it can be considered a rare event, and if we assume the cases are independent and random, we can approximate the distribution using a Poisson distribution. The mean (λ) is equal to the incidence rate, which is 12 cases per 100,000.

b. To find the probability that the number of cases of type II diabetes is less than or equal to 10 per 100,000, we need to calculate the cumulative probability for the Poisson distribution with λ = 12 and k = 10. This can be found using the formula:

P(X ≤ 10) = Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 10

c. To find the probability that the number of cases of type II diabetes is greater than 10 but less than 15 per 100,000, we need to calculate the probability for the Poisson distribution with λ = 12 and k = 11, 12, 13, and 14. This can be found using the formula:

P(10 < X < 15) = Σ [e^(-λ) * (λ^k) / k!] for k = 11 to 14

d. To determine if we would expect to observe 19 or more cases of type II diabetes per 100,000 in the United States, we can find the probability of observing 19 or more cases using the Poisson distribution with λ = 12. This can be found using the formula:

P(X ≥ 19) = 1 - P(X ≤ 18) = 1 - Σ [e^(-λ) * (λ^k) / k!] for k = 0 to 18

If the probability is low (typically less than 0.05), then it would be unlikely to observe 19 or more cases of type II diabetes per 100,000 in the United States.

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The length of the fold is 10 inches. the square of the hypotenuse (the length of the fold) is equal to the sum of the squares of the other two sides.

To find the length of the fold, we can use the Pythagorean Theorem. Let's assume that the length of the fold is x inches. Since the corner of the paper is folded over, it creates a right triangle with the width of the paper (8 inches) as one side and the length of the fold (x inches) as another side.

According to the Pythagorean Theorem, the square of the hypotenuse (the length of the fold) is equal to the sum of the squares of the other two sides. In this case, we have:

x^2 = 8^2 + 6^2

Simplifying the equation:

x^2 = 64 + 36

x^2 = 100

Taking the square root of both sides:

x = √100

x = 10

Therefore, the length of the fold is 10 inches.

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The length of the fold of the rectangular paper, determined using the Pythagorean theorem, is approximately 11.31 inches.

The question requires us to find the length of the fold when a corner of a rectangular piece of paper of width 8 inches is folded over to coincide with a point on the opposite side. From the given information, we know the width of the paper is 8 inches. The paper is folded such that a corner touches the mid-point of the opposite side, forming a right-angled triangle. In this triangle, one side is half the width of the paper i.e., 4 inches, and the hypotenuse is the fold we need to find. By using the Pythagorean theorem (which states that in a right-angled triangle, the square of the hypotenuse, c, is equal to the sum of squares of the other two sides, a and b; c² = a² + b²), we get the fold as square root of (8^2 + 8^2) = 11.31 inches. Therefore, the length of the fold is approximately 11.31 inches.

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The equation of the parabola is y = 2(x - 1)² + 3

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

Vertex = (1. 3)

Point = (2, 5)

These parameters can be expressed as

(h, k) = (1, 3)

(x, y) = (2. 5)

A parabola can be represented as

y = a(x - h)² + k

Substitute the known values in the above equation, so, we have the following representation

y = a(x - 1)² + 3

Next, we have

5 = a(2 - 1)² + 3

Evaluate the difference and the exponent

5 = a + 3

So, we have

a = 2

Substitute a = 2 in y = a(x - 1)² + 3

y = 2(x - 1)² + 3

Hence, the equation is y = 2(x - 1)² + 3

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Answer:

B, C, E

Step-by-step explanation:

Exponent Rules

\(a^b \cdot a^c=a^{b+c}\)

\(\dfrac{a^b}{a^c}=a^{b-c}\)

\(a^n \cdot b^n=(ab)^n\)

\(a^0=1\)

\(\dfrac{1}{a^b}=a^{-b}\)

\((a^b)^c=a^{bc}\)

\(\textsf{A}\quad42^{-3} \cdot 42^8=42^{-3+8}=42^5\)

\(\textsf{B}\quad \dfrac{42^{-7}}{42^{-2}}=42^{-7-(-2)}=42^{-5}\)

\(\textsf{C}\quad \dfrac{6^{-5}}{7^5}=6^{-5} \cdot 7^{-5}=(6 \cdot 7)^{-5}=42^{-5}\)

\(\textsf{D}\quad 42^0 \cdot 42^5=1 \cdot 42^5=42^5\)

\(\textsf{E}\quad \left(\dfrac{1}{42^{-5}}\right)^{-1}=(42^5)^{-1}=42^{-5}\)

\(\textsf{F}\quad \left(\dfrac{6^{-5}}{7^5}\right)^{-1}=\left(6^{-5} \cdot 7^{-5}\right)^{-1}=\left(\left(6 \cdot 7\right)^{-5}\right)^{-1}=42^{-5(-1)}=42^5\)

Check one by one

#A

\(\\ \rm\Rrightarrow 42^{-3}42^8=42^{-3+8}=42^5\)

#B

\(\\ \rm\Rrightarrow \dfrac{42^{-7}}{42^{-2}}=42^{-7+2}=42^{-5}\checkmark\)

#C

\(\\ \rm\Rrightarrow \dfrac{6^{-5}}{7^5}=6^{-5}7^{-5}=42^{-5}\checkmark\)

#d

\(\\ \rm\Rrightarrow 42^0.42^5=42^{0+5}=42^5\)

#e

\(\\ \rm\Rrightarrow \left(\dfrac{1}{42^{-5}}\right)^{-1}=42^{-5}\checkmark\)

#f

\(\\ \rm\Rrightarrow \left(\dfrac{6^{-5}}{7^5}\right)^{-1}\)

\(\\ \rm\Rrightarrow (42^{-5})^{-1}\)

\(\\ \rm\Rrightarrow 42^5\)

Given an angle that is positive, less than 360°, and coterminal with 395° is 35°.

Subtract 360° from 395°.

We know that 1 revolution is equal to 360°.

Therefore, a positive angle that is less than 360° and coterminal with 395° is 35°.

When an angle is less than 360° and shares the same terminal side with another angle that is less than 360°, then the angle is referred to as a coterminal angle.

In other words, the two angles have the same initial side and terminal side but can be either positive or negative.

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Answer:

Dang, too difficult. Anyways,

In a right triangle, if one angle is 45 degrees, it means that the other two angles must be 45 degrees as well, making it an isosceles right triangle. Given that the length of one leg is 4√2 m, we can determine the lengths of the missing sides using the properties of an isosceles right triangle.

Since an isosceles right triangle has two equal legs, the lengths of the vertical leg and horizontal leg will be the same. Let's denote the length of each leg as "m."

Using the Pythagorean theorem, we can find the length of the hypotenuse (the side opposite the right angle) in terms of "m":

hypotenuse^2 = leg^2 + leg^2

hypotenuse^2 = m^2 + m^2

hypotenuse^2 = 2m^2

To find the length of the hypotenuse, we take the square root of both sides:

hypotenuse = √(2m^2) = √2 * m

In summary, for the given isosceles right triangle with one leg measuring 4√2 m, both the vertical leg and horizontal leg will have a length of "m," while the length of the hypotenuse will be √2 * m.

The values of the angles and sides of the given right angle triangle are:

1) sin Q = 9/13

2) AB = 10

The common three trigonometric ratios in a right angle triangle are:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

1) To find sin Q from the triangle, we have:

sin Q = pPR/PQ

sin Q = 9/15

2) Using Pythagoras theorem, we can find side AB as:

AB = √(6² + 8²)

AB = √100

AB = 10

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Answer:

1 1/2

Step-by-step explanation:

3/2= 1 1/2

Answer:

Step-by-step explanation:

The spending is the cost plus expenses:

Net income is the difference of money made and spent:

It is all the numbers multiplied together. 135

Answer:

\(\Huge\boxed{D.135 cm^3}\)

Step-by-step explanation:

Hello There!

We can find the volume of the figure by using the formula for volume of a rectangular prism

\(V=lwh\)

where l = length, w = width and h = height

we are given all of the dimensions so all we have to do is plug in the values

so

V = 3 x 9 x 5

3x9=27

27x5=135

so the volume of the rectangular prism is 135 cm³

Answer:

y=24/5x+24

Step-by-step explanation:

You must find your slope first. (72-48=24)(10-5=5). (24/5 does not simplify so your slope is just 24/5). Then you can use either y=mx+b or y-y1=m(x-x1) to find your b. I will use y=mx+b. So you would plug in you first coordinate (5,48) and your slop (24/5). You put 48 as your y and 24/5 as your m and 5 as your x but you keep b as itself because you don´t know it yet. So it would look like this (48=24/5(5)+b). Now you have to distribute. (48=24+b). Now since 24 is positive you must subtract it to get b by itself  so (48-24=24) So your b=24. Your equation is y=24/5x+24.

Hope this helped!

The relationship between two variables in which one variable doubles when the other variable doubles is called a direct proportion or direct relationship.

This means that the two variables are directly related, and their values increase or decrease in the same proportion.

In mathematical terms, this is represented by a linear equation in the form of y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of proportionality.

Therefore, when x doubles, y doubles as well, and when x triples, y triples as well.

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Answer:

length of each section is 15/6 = 2 1/2

Step-by-step explanation:

Answer:

2.5 feet

Step-by-step explanation:

All you have to do is take 15 and divide it by 6 and you will get 2.5

hope that helps.

Answer:

\((x-5)^2+(y+2)^2=16\)

Step-by-step explanation:

lol brainlessly...

General Circle function: \((x-h)^2+(y-k)^2=r^2\), where h is the x-coordinate of the center, k is the y-coordinate of the center, and r is the radius.

The radius of the circle is half the diameter so: 8 / 2 = 4

The x-coordinate of the circle is 5

The y-coordinate of the circle is -2

Plug in.

\((x-5)^2+(y-(-2))^2=4^2\)

\((x-5)^2+(y+2)^2=16\)

Georgia  takes 24 minutes to clean the espresso machine by herself.

The correct answer is an option D.

The equation for the situation is:

\(\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8}\)

here, x is the number of minutes it takes Georgia to clean the machine by herself.

We need to find the value of x.

Consider the equation,

\(\frac{1}{x} +\frac{1}{x-12} =\frac{1}{8} \\\\\frac{(x -12)+x}{x(x-12)}=\frac{1}{8}\\\\\frac{x -12+x}{x^2-12x}=\frac{1}{8}\)

(2x - 12) × 8 = x² - 12x

16x - 96 =  x² - 12x

x² - 12x -16x + 96 = 0

x² - 28x + 96 = 0

x²-24x-4x+96 = 0

(x - 24)(x - 4) = 0

x = 24 or x = 4

If x = 4, then x - 12 would be negative which is not possible.

Thus, it takes 24 minutes for Georgia.

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Find the complete question below.

Answer:

The factors of 15 are as follows - 1, 3, 5 and 15

Step-by-step explanation:

Factors are numbers that divides another number, leaving no remainder

Answer:

180

Step-by-step explanation:

60 * 4 = 240

240 / 20 = 12 groups of 20

12*15 = 180

180 cookies

By definition. a Translation is a transformation in which a figure is moved a fixed distance in a fixed direction.

The Image is the figure obtained after the transformation and the Pre-Image is the original figure.

In this case, you know that the figure shown in the picture must be translated 5 units up. Therefore, the rule for this transformation is:

You can identify that the marked point on the Pre-Image has the following coordinates:

Therefore, applying the rule for this transformation, you get that the coordinates of the marked point in the final figure, are:

The answer is:

Coordinates of the marked point in the original figure:

Coordinates of the marked point in the final figure:

this is 90 60 30 formula for example

90 meet 2x

30 meet x

and

60 meet x√3

so 90 meet 5

30 meet 5/2=2.5

and 60 meet 2.5√3

so the answer is 2.5

Answer:

2.5

Step-by-step explanation:

\(\sin 30\degree = \frac{x}{5}\\\therefore x = 5\sin 30\degree\\\therefore x = 5 \times \frac{1}{2}\\\therefore x = 2.5\)

The measure of the central angle m ∠JIK is 160°.

Given that the circle I, in which IJ is the radius of 9 units, the area of shaded sector = 36π, we need to find the m ∠JIK, the central angle.

Area of the sector = central angle / 360° × π × radius²

∴ 36π = m ∠JIK / 360° × π × 9²

m ∠JIK = 360° × 4 / 9

m ∠JIK = 160°

Hence, the measure of the central angle m ∠JIK is 160°.

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