what is larger multiple of 6

Answer:

x = 30.

Step-by-step explanation:

8x - 3(2x - 4) = 3(x - 6)

8x - 3*2x + - 3*-4 = 3*x + 3 * -6

8x - 6x + 12 = 3x - 18

2x + 12 = 3x - 18

2x - 3x  + 12 = 3x - 3x - 18

-x + 12 = -18

-x + 12 - 12 = -18 - 12

-x = -33

-x/-1 = -30/-1

x = 30.

Answer:

\(x=30\)

Step-by-step explanation:

\(8x-3\left(2x-4\right)=3\left(x-6\right)\)

First, we will expand \(-3\left(2x-4\right)\) by applying the distributive property:

\(-3\times \:2x-\left(-3\right)\times \:4\)

** \(-\left(-a\right)=a\)

\(-6x+12\)

\(8x-6x+12=3\left(x-6\right)\)

Expand, \(3\left(x-6\right):\)

\(3x-3\times \:6\)

\(3x-18\)

\(2x+12=3x-18\)

Subtract 12 from both sides:

\(2x+12-12=3x-18-12\)

\(2x=3x-30\)

Subtract 3x from both sides:

\(2x-3x=3x-30-3x\)

\(-x=-30\)

Divide both sides by -1:

\(\frac{-x}{-1}=\frac{-30}{-1}\)

\(x=30\)

________________________

Answer:

Since the student is equally likely to select pizza, nachos, or chicken for lunch, the probability of selecting each of these options is 1/3.

The probability that the student does not select chicken is the probability of selecting pizza or nachos, which are the two options other than chicken. Since these two options are equally likely, the probability of selecting pizza or nachos is 1/2.

Therefore, the probability that the student does not select chicken is 1/2.

The cross sectional area of the cargo trailer floor, which is a composite figure consisting of a square and an isosceles triangle, indicates that the volume of the inside of the trailer is about 3,952 ft³.

A composite figure is a figure comprising of two or more regular figures.

The possible cross section of the trailer, obtained from a similar question on the internet, includes a composite figure, which includes a rectangle and an isosceles triangle.

Please find attached the cross section of the Cargo Trailer Floor created with MS Word.

The dimensions of the rectangle are; Width = 6 ft, length = 10 ft

The dimensions of the triangle are; Base length 6 ft, leg length = 4 ft

Height of the triangular cross section = √(4² - (6/2)²) = √(7)

The cross sectional area of the trailer, A = 6 × 10 + (1/2) × 6 × √(7)

A = 60 + 3·√7

Volume of the trailer, V = Cross sectional area × Height

V = (60 + 3·√7) × 6.5 = 3900 + 19.5·√7

Volume of the trailer = (3,900 + 19.5·√(7)) ft³ ≈ 3952 ft³

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Answer: -17

Explanation: If g(x) = 4x - 5, then g(-3) = 4(-3) - 5 which simplifies to -17.

Answer:

-5

Step-by-step explanation:

Answer:

1st and 6th option, 35 adult tickets

Step-by-step explanation:

So we know adult tickets are x and children tickets are y.

The total number of tickets is 57, so

x + y = 57

The adult tickets are worth 6 and the children's tickets are worth 2.50.

The total cost is 265.

6x + 2.5y = 265

Now, the system of equations.

6x + 2.5y = 265

-6x - 6y = -342

-3.5y = -77

y = -77/-3.5

y = 22

Plugging y back in

x + 22 = 57

x = 35 adult tickets sold

* $265 worth of tickets were sold

* Adult tickets cost $6

* Child tickets cost $2.50

* 57 tickets were sold

Let x represents the number of adult tickets sold and y as the number of child ticket sold

Which squations equation represents the scenerio? select 2 options

so ,the equations would be

⤿ x + y = 57 ✓

⤿ 6x + 2.5y = 265 ✓

x + y = 57.....(1)

6x + 2.5y = 265.....(2)

Multiplying equation 1st by 6

we get,

6x + 6y = 342 ...(3)

subtracting equation (3) by equation (2)

we get,

6x + 6y = 342

-6x + 2.5y= 265

_____________

ㅤㅤ 3.5y =

ㅤㅤ y = 77/3.5

ㅤㅤ y = 22

_______________

______________________________

_______________________________

_______________________________

Answer:

Inequality Form: x > −8

Interval Notation: (−8, ∞)

Step-by-step explanation:

−2 < x/4

Rewrite so x is on the left side of the i nequality.

x/4 > −2

Multiply both sides of the equation by 4.

x > −2 ⋅ 4

Multiply −2 by 4.

x > −8

The result can be shown in multiple forms.

Inequality Form:

x > −8

Interval Notation:

(−8, ∞)

Answer:

3.5

Step-by-step explanation:

28 days = 4 weeks

28 divided by 4 = 1 week

14 gallons divided by 4 = 3.5

Step-by-step explanation:

the volume of a cylinder is as for any other regular 3D object :

ground area ×height

the ground area of a cylinder is a circle, so it is

pi×radius² × height

the radius is always half of the diameter (of the diameter is airways twice the radius).

radius = 6/2 = 3 ft.

the volume is then

pi × 3² × 9 = pi × 9 × 9 = pi × 81 ft³

so, the answer is 81pi ft³.

Step 1

Draw the unit circle required

Step 2

Find the value sec(7π/6) in cosine

Step 3

Find cos(7π/6)

The trigonometric unit circle and a trigonometric table gives;

Step 4

Find sec(7π/6)

Step 5

Rationalize the denominator

Hence,

a) Diminishing returns start at x = 1,  where the marginal revenue will be less than the marginal cost

b)At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

a) At what level of advertising spending does diminishing returns start?

Diminishing returns refers to a situation when the marginal return on investment decreases as more resources are devoted to it. For instance, in case of Coffee Junction, increasing the advertising expenditure may lead to higher revenue, but the marginal revenue (revenue generated by each additional dollar spent) will gradually decrease.

b) How much revenue will the company earn at that level of advertising spending?

At x = 1, the company will earn R(1) = -32 + 6 + 18 + 4 = -4,000 dollars.

c) What does 0≤x≤25 tell us with respect to this problem?

In this problem, 0 ≤ x ≤ 25 implies that the Coffee Junction company has the capacity to spend a maximum of 25,000 dollars per month on advertisements.

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Answer:

120 is 60% of 200

Step-by-step explanation:

Step 1 = 120 = 60% × Y

Step 2 = 120 = 60/100 × Y

Step 3 = Y = 120 × 100/60

Step 4 = Y = 120 × 100 ÷ 60

Step 5 = Y = 200

Answer: D) Hypotenuse = 17 m, Adjacent = 15 m, Opposite = 8 m

The sale price of the green beans represents a decrease of 16.67% compared to the original price of the beans.

To find the percent increase or decrease in the price of a can of green beans during the sale, we need to compare the sale price with the original price.

During the sale, the green beans were sold at a rate of 3 cans for $1.25, or approximately 41.67 cents per can:

Sale price per can = $1.25 / 3 = $0.4167 ≈ 41.67 cents

The original price of a can of green beans was 50 cents.

To find the percent increase or decrease in the price, we can use the following formula:

Percent increase or decrease = ((New value - Old value) / Old value) x 100%

Substituting the values, we get:

Percent increase or decrease = ((0.4167 - 0.5) / 0.5) x 100%

Percent increase or decrease = (-0.0833 / 0.5) x 100%

Percent increase or decrease = -16.67%

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The exact area of the region described is 771/50 square units.

To find the area of the region described, we need to determine the points of intersection of the given curves and then calculate the area enclosed by those curves.

First, let's find the points of intersection by setting the equations equal to each other:

y - 2(x + 1) = y - 3(x + 1)

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

Simplifying these equations, we get:

-2x - y + 1 = 0 ----(1)

3x - y - 7 = 0 ----(2)

To find the points of intersection, we can solve this system of equations.

Subtracting equation (2) from equation (1), we get:

-5x + 8 = 0

x = 8/5

Plugging this value of x into equation (1), we get:

-2(8/5) - y + 1 = 0

-16/5 - y + 1 = 0

y = 16/5 - 1

y = 11/5

So the points of intersection are (8/5, 11/5).

Now, let's determine the region bounded by these curves.

The curves y - 2(x + 1) and y - 3(x + 1) intersect at (8/5, 11/5), and the curve x - 5 intersects the x-axis at x = 5.

To find the area, we integrate the upper curve and subtract the lower curve with respect to x, over the interval [5, 8/5]:

Area = ∫[5, 8/5] [y - 2(x + 1)] - [y - 3(x + 1)] dx

Simplifying, we get:

Area = ∫[5, 8/5] -x - 1 dx

Integrating, we have:

Area = [-x^2/2 - x] evaluated from 5 to 8/5

Substituting the limits of integration, we get:

Area = [-(8/5)^2/2 - 8/5] - [-(5)^2/2 - 5]

Simplifying, we get:

Area = [-64/50 - 8/5] - [-25/2 - 5]

Area = [-64/50 - 40/50] - [-25/2 - 10/2]

Area = [-104/50] - [-35/2]

Area = -104/50 + 35/2

Area = (-104 + 875) / 50

Area = 771/50

Therefore, the exact area of the region described is 771/50 square units.

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The sum of all possible x-coordinates that satisfy the given conditions is 666.

Let's consider two triangles, Triangle A and Triangle B, with areas A and B, respectively. The base of Triangle A is x units long, and its height is y units. Triangle B has a base of y units and a height of x units.

The area of a triangle is given by the formula A = (1/2) * base * height. Therefore, the area of Triangle A is A = (1/2) * x * y, and the area of Triangle B is B = (1/2) * y * x. Since multiplication is commutative, we can simplify the expressions as A = B = (1/2) * x * y.

We are given that A + B = 108. Substituting the values of A and B, we get (1/2) * x * y + (1/2) * x * y = 108. Simplifying the equation, we have x * y + x * y = 216, which further simplifies to 2 * x * y = 216.

To find the sum of all possible x-coordinates, we need to consider the factors of 216. The factors of 216 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 27, 36, 54, 72, 108, and 216. Since x * y = 216/2 = 108, we can deduce that for each factor of 216, there is a corresponding value of y that satisfies the equation.

The sum of all possible x-coordinates would be the sum of all the factors of 216, which is 1 + 2 + 3 + 4 + 6 + 8 + 9 + 12 + 18 + 24 + 27 + 36 + 54 + 72 + 108 + 216 = 666.

In summary, the sum of all possible x-coordinates that satisfy the given conditions is 666.

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The probability that exactly 2 out of 20 registered voters voted in a local election is 0.382, or about 38.2%.

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

This is a binomial probability problem, where we have a fixed number of trials (n=20) and each trial is either a success (voted in a local election) or a failure (did not vote in a local election).

The probability of success for each trial is p=0.18 (since the typical voter turnout is 18%). We want to find the probability of exactly 2 successes in 20 trials.

We can use the binomial probability formula to solve this problem:

\(P(X = k) = (n choose k) * p^k * (1-p)^{n-k}\)

where X is the random variable representing the number of successes (voters who voted in a local election), k is the number of successes we're interested in (k=2), n is the total number of trials (n=20), p is the probability of success (p=0.18), and (n choose k) is the binomial coefficient, which represents the number of ways to choose k successes from n trials and is calculated as:

(n choose k) = n! / (k! * (n-k)!)

Plugging in the values, we get:

\(P(X = 2) = (20 choose 2) * 0.18^{2} * (1-0.18)^{20-2}\)

= (190) * 0.0324 * 0.8222

= 0.382

Therefore, the probability that exactly 2 out of 20 registered voters voted in a local election is 0.382, or about 38.2%.

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1 newton-meter = 0.73756 pound-feet

To convert a value in newton-meters to pound-feet, you simply need to multiply the value in newton-meters by the conversion factor.

For example, let's say we have a torque of 100 newton-meters, and we want to convert this to pound-feet. Using the conversion factor above, we have:

100 newton-meters * 0.73756 pound-feet/newton-meter = 73.756 pound-feet

Answer:

Jacob is \(16\) years old.

Step-by-step explanation:

Let the age of Jacob be \(x\) years.

Jacob’s sister is \(5\) years younger than he is.

So, the age of Jacob's sister be \(x-5\) years.

Jacob's twin brothers are \(3\) years older than he is.

So, the age of each of the twin brother be \(x+3\) years.

Jacob's mom is \(3\) times his age.

So, the age of Jacob's mom be \(3x\) years.

Jacob's dad is \(4\) years older than his mom.

So, the age of Jacob's dad be \(3x+4\) years.

Now, the total of all the ages of all his family members is \(165\) years.

So, \(x+x-5+x+3+x+3+3x+3x+4=165\)

\(\Rightarrow 10x+5=165\)

\(\Rightarrow 10x=165-5\)

\(\Rightarrow 10x=160\)

\(\Rightarrow x=\frac{160}{10}\)

\(\Rightarrow x=16\)

Hence, Jacob is \(16\) years old.

The expressions represent the service fee charge on her account balance is 4x+3.

Given that,

Every time money is withdrawn from an ATM run by a different bank, Marley's Bank levies a $3 service fee. Marley needs to make four ATM withdrawals from a different bank while she is abroad.

We have to find which expressions represent the service fee charge on her account balance.

The expression we can write as,

4x+3

Because 4 times he has taken from ATM money and adding the service fee $3.

Therefore, The expressions represent the service fee charge on her account balance is 4x+3.

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Answer:

8 47 7445

Step-by-step explanation:

gur hre hrdifngg

Answer: a = 7, b = 14, c = 7, d = 7√3

Step-by-step explanation:

Using SOHCAHTOA, we can find a:

sin(45) = a / (7√2)

We can use either SOHCAHTOA or Phthagoras' Theorem to find c. I will use SOHCAHTOA as I prefer this:

cos(45) = c / (7√2)

SOHCAHTOA for b:

sin(30) = a / b = 7 / b

SOHCAHTOA for d:

cos(30) = d / b = d / 14

To estimate the probability that a randomly selected person would pass the driving test on the first attempt, we can divide the number of people who passed on the first attempt (6500) by the total number of people who took the test (10,000).

Probability = Number of favorable outcomes / Total number of possible outcomes.In this case, the favorable outcome is passing the test on the first attempt, and the possible outcomes are all the people who took the test.

Probability = 6500 / 10000= 0.65

Therefore, the estimated probability that a randomly selected person would pass the driving test on the first attempt is 0.65 or 65%. This means that there is a 65% chance that a randomly selected person from the group of 10,000 would pass the driving test on their first try.

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Answer:

64 units sqr.

Step-by-step explanation:

If the frame is 2 units wide, there is 4 units total on the top and bottom, extra. So, adding that to our units, it is 7+4 = 11 by 5+4 = 9  NINE BY 11. 9*11 = 99, and 99-35 = 64. So it is 64

Answer: B: triangle ABC and triangle MNO

the second one is C: triangle JLK and triangle PQR

Step-by-step explanation: Plato

AABC and AMNO can be shown to be congruent by a sequence of reflections and translations.

A vertex (plural: vertices) is a point in geometry where two or more straight lines intersect.

Vertices are typically the corners or points where the curve changes direction in two-dimensional shapes such as triangles, rectangles, and circles.

Vertices are the points where the edges of three-dimensional shapes such as cubes, pyramids, and spheres meet. Vertices is the plural of vertex.

AABC and AMNO can be shown to be congruent by a sequence of reflections and translations.

AXYZ can be shown to be congruent by a single rotation.

KL and APQR cannot be shown to be congruent by either a sequence of reflections and translations or a single rotation.

Thus, this can be the answer for the given scenario.

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The number of choice out of 7 that consumer have are 42.

The term permutation alludes to a numerical computation of the quantity of ways a specific set can be sorted out. Set forth plainly, a change is a word that depicts the quantity of ways things can be requested or organized. With stages, the request for the course of action matters.

Number of choices of side dishes does a customer have,

total dishes(n)=7 , r = 2

ⁿP₂

⁷P₂

7×6 = 42

Thus required number of ways are 42.

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Answer:

D

Step-by-step explanation:

8% in decimal form is written out as 0.08, so right away the answer is either C or D.

Then if you have "s" = 1875, you would get:

350 + (0.08 × 1875) = 500

That would mean any number greater than 1875 will give you a total more than 500.

Therefore the answer is D.

Fix(2.5) is equal to 1. The expected value of X (E(X)) is equal to 13/36. P(X > 0.3 and X < 0.6) is equal to 0.432.

A continuous random variable X has a probability density function (pdf) given by:

fix (x) = {x² + 4/3 x if 0 < x < 1

0 otherwise. Let's solve the questions step-by-step: To find the cumulative distribution function (CDF) Fix(t) of X, we integrate the pdf from 0 to t. To find Fix(-3), we integrate the pdf from 0 to -3, which is not possible since -3 is outside the valid range of x (0 < x < 1). Therefore, Fix(-3) does not exist. To find Fix(0.6), we integrate the pdf from 0 to 0.6:

∫(0 to 0.6) (x² + 4/3 x) dx = [1/3 x³ + 2/3 x²] (0 to 0.6)

= (1/3 × 0.6³ + 2/3 × 0.6²)

= 0.432.

Therefore, Fix(0.6) is equal to 0.432. To find Fix(2.5), we integrate the pdf from 0 to 1 (since the valid range of x is 0 < x < 1):

∫(0 to 1) (x² + 4/3 x) dx = [1/3 x³ + 2/3 x²] (0 to 1)

(1/3 × 1³ + 2/3 × 1²) = 1.

Therefore, Fix(2.5) is equal to 1. To find the expected value of X (E(X)), we need to integrate x times the pdf from 0 to 1:

E(X) = ∫(0 to 1) x × (x² + 4/3 x) dx.

Simplifying the integral:

E(X) = ∫(0 to 1) (x³ + 4/3 xv) dx

= [1/4 x⁴ + 4/9 x³] (0 to 1)

= (1/4 × 1³ + 4/9 × 1³)

= 13/36.

Therefore, the expected value of X (E(X)) is equal to 13/36. To find P(X > 0.3 and X < 0.6), we need to use the definition of conditional probability:

P(X > 0.3 and X < 0.6) = P(X < 0.6) - P(X < 0.3).

Using the CDF we obtained earlier, we have:

P(X > 0.3 and X < 0.6) = Fix(0.6) - Fix(0.3)

= 0.432 - 0

= 0.432.

Therefore, P(X > 0.3 and X < 0.6) is equal to 0.432.

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Answer:

15 hours

Step-by-step explanation: