16 - 2t = t + 9 + 4t

Answer:

2520

Step-by-step explanation:

There are 7 letters in MCHNLRN and they can be arranged into 7 ways:

7! = 5040 ways in total

However, the letter 'N' is repeated so we have to divide it by 2.

5040 ÷ 2 = 2520 ways

Answer:

2,520 ways

Step-by-step explanation:

MCHNLRN has 7 letters with one repetition.

therefore, =7!/2!

=2,520 ways

The value of the car 4 years after it was purchased is  $16,270.86.

Depreciation is when the value of an asset declines with the passage of time as a result of wear and tear.

The equation that would be used to determine the value of car with the passage of time would be an exponential equation.

Value of the car after t years = \(p(1 -r)^{\frac{t}{3}\)

Where:

Value of the car after 4 years  = \(41,000(1 -0.5)^{\frac{4}{3}\) = $16,270.86

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Answer:

C

Step-by-step explanation:

0 is base like for example negatives are below and positives are above and zero is the thing right in between so sea level would be 0!

Correct answer is 0.

Sea level si always the parameter to use when indicating the elevation of any place on earth. If you happen to be located at the same altitude than the sea, then you are at level 0 altitude in any unit of measure.

Answer:

The similar one are 1 and 5

A. Triangle DEF where ∠D is 35° and ∠E is 20°.

C. Triangle JKL where ∠J is 35° and ∠L is 125°.

D. Triangle MNO where ∠N is 20° and ∠O is 125°.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the sum of all the interior angles of a triangle is equal to 180°.

Given, A triangle ABC has ∠A = 35° and ∠B = 20°.

∴ ∠C = 180° - 35° - 20°.

∠C = 125°.

Triangle will be similar if every corresponding angle of different triangles has the same measure.

So, Triangles that are similar to triangle ABC is triangle DEF where ∠D is 35° and ∠E is 20°.

Triangle JKL where ∠J is 35° and ∠L is 125°.

Triangle MNO where ∠N is 20° and ∠O is 125°.

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Answer: actual answer is y=3/2x+4

Step-by-step explanation: plug b in the original formula

The equation of the line as of the condition given is y = 3x/2 + 3/2.

Given that,
The equation of the line that passes through the point (-6,-5) and has a slope of 3/2 is to be determined.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
The point-slope form of the line is given as,
y - y₁ = m (x - x₁)
From the given substitute the point and slope in the above equation,
y + 6 = 3/2 [x + 5]
y = 3x/2 + 15/2 - 6

y = 3x/2 + 3/2

Thus, the equation of the line as of the condition given is y = 3x/2 + 3/2.

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Answer:

y \(\geq\) 3x + 3

y < -x - 2

Step-by-step explanation:

For the first one, you can see that the slope is 3 and the y-intercept is 3, so the equation of the line would be y = 3x + 3. Then, since the shaded area is above the line it would be greater than and since the line isn't dashed it is greater than or equal to.

The completed equation is y \(\geq\) 3x + 3

For the second one, you can see that the slope is -1 and the y intercept is -2, so the equation of the line would be y = -x - 2. Then, since the shaded area is below the line and the line is dashed, the completed equation is y < -x -2

Answer: 0

Step-by-step explanation:

Let's solve your equation step-by-step.

5+2(n+1)=2n

Step 1: Simplify both sides of the equation.

5+2(n+1)=2n

5+(2)(n)+(2)(1)=2n(Distribute)

5+2n+2=2n

(2n)+(5+2)=2n(Combine Like Terms)

2n+7=2n

2n+7=2n

Step 2: Subtract 2n from both sides.

2n+7−2n=2n−2n

7=0

Step 3: Subtract 7 from both sides.

7−7=0−7

0=−7

The cost of gas is proportional to the volume of gas because a constant rate of $3.15 to 1 gallon of gas.

From the given table;

The volume of the first gas Layla bought = 3 gallons.

The cost of the 3 gallons = 9.45

Therefore the cost of 1 gallon = ?

That is:

3 gallons = $9.45

1 gallon = X

Make X the subject of formula:

X = 9.45/3 = $3.15

Therefore, the cost of 11 gallons of gas would be = 11×3.15 = $34.65. This is because the cost of 1 gallon would be = $3.15.

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Answer:

Step-by-step explanation:

On this page, an interesting example is presented that allows the student to obtain expressions for a general case after examining the first two or three situations. It is an exercise in geometric progressions, a common topic in elementary-level Mathematics courses.

Bounces in the horizontal plane

Balon7.gif (2174 bytes)  

When a ball bounces off a rigid board, the component of the velocity perpendicular to the board decreases in value, leaving the parallel component unchanged

v x = u x

v y = -e u y

Heights of successive bounces

Suppose a ball is dropped from an initial height h . We are going to calculate the heights of the successive bounces.

1.-First bounce

The velocity of the ball before it hits the ground is calculated by applying the principle of conservation of energy

The velocity of the ball after the collision is (in modulus) v 1 = e u 1

The ball ascends with an initial velocity v 1 , and reaches a maximum height h 1 which is calculated by applying the principle of conservation of energy

2.-Second bounce

The velocity of the ball before it hits the ground is calculated by applying the principle of conservation of energy

The velocity of the ball after the collision is v 2 = e u 2

The ball ascends with an initial velocity v 2 , and reaches a maximum height h 2 which is calculated by applying the principle of conservation of energy

3.-Bounce n

After collision n , the maximum height the ball reaches is

h n = e 2n h

Loss of energy experienced by the ball

In the first collision, the ball loses an energy

In the second collision, the ball loses an energy

In the collision n the ball loses an energy

The sum of Δ E 1 + Δ E 2 + Δ E 3 +…. Δ E n is the energy lost by the ball after n collisions. After infinite collisions the ball will have lost all its initial energy mgh . We are going to check it by adding the infinite terms of a geometric progression of ratio e 2 and whose first term is Δ E 1

Time it takes for the ball to stop.

The time it takes for the ball to reach the ground when dropped from a height h from rest is

The ball bounces and rises to a height h 1 , then falls back to the ground. The time it takes to go up and down is

The ball bounces and rises to a height h 2 , and then falls back to the ground. The time it takes to go up and down is

The total time after infinite bounces is the sum of t 0 and the terms of a geometric progression whose first term is 2 t 0 e and whose ratio is e.

If the ball is given a horizontal initial velocity v x . After infinite bounces, it moves a horiz

Answer:

here ya go :)

the black line is y=-2x-3

the lavender line is y=-x+6

Answer: 13

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

There are 12 1/4s in 3

Add the extra 1/4 + 13 1/4s

Answer:

Step-by-step explanation:

Its 4.51

Answer:

The 3.907 is approximate.

====================================

Explanation:

x = number of hours that elapse

y = f(x) = number of tokens

If we use a graphing tool like a TI84 or GeoGebra, then the approximate solution to -3(2)^(x+1) + 90 = 0 is roughly x = 3.907

At around 3.907 hours is when the number of tokens is y = 0. Therefore, this is the approximate upper limit for the domain. The lower limit is x = 0.

The domain spans from x = 0 to roughly x = 3.907, and we shorten that down to 0 ≤ x ≤ 3.907

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

Plug in x = 0 to find y = 84. This is the largest value in the range.

The smallest value is y = 0.

The range spans from y = 0 to y = 84, so we get 0 ≤ y ≤ 84

Keep in mind y is the number of tokens. A fractional amount of tokens does not make sense, so we must have y be a whole number 1,2,3,...,83,84.

The x value can be fractional because 3.907 hours for instance is valid.

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

Extra info:

Answer: 932,400

Step-by-step explanation:777 x 1200

Answer: 30%

Step-by-step explanation: 21/70 = 21 divide 70 = 0.3 = 30%

Answer:

f¹(x) = x - 3

To find the inverse of a function, just "trade" and y and solve for the "new" y. The graph of the inverse is the reflection of the original function over the line y = x.

Rewrite the function f(x) = x + 3

as the equation y = x + 3

Trade x and y.

x = y + 3

Solve for the "new" y.

= y + 3

3 - 3

Subtract 3 from both sides

y = x= 3

The symbol for the inverse is f-¹(x)

f¹(x) = x - 3

Step-by-step explanation:

brainlies me plss

\(f(x) = x -3 \\\\\text{Write f(x) as}~ y = x -3}\\\\\text{Now replace x and y,}\\\\x = y-3\\\\\text{Solve for y:}\\\\y = x+3 \\\\\implies f^{-1}(x) = x +3 ,~ \text{This is the inverse of given function.}\)

The required value of x for a given isosceles triangle is 16.

What is an isosceles triangle?

A triangle with two sides that have the same length is said to be an isosceles. When two sides of an isosceles triangle are equal, the angles across from those two sides likewise match up and are always equal.

Given that, the isosceles triangle then

two angles are equal

So, (5x-7)° = (8x-55)°

or, 8x - 5x = 55-7

or, 3x = 48

or, x = 48/3 = 16

Hence, the required value of x is 16.

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Given:

Cost of current model = $51, 000

Cost of the next model is 3.3% less than the cost of the current model.

Mathematical interpretation of the second statement:

Substituting, we have:

Hence, the price of the next model in dollars is $49317

The price decrease in dollars is the difference between the cost of the next model and the cost of the current model.

Hence, the price decrease in dollars is $1683

Answer:

(i) price decrease = $ 1683

(ii) price of the next model = $49317

The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

Any equation using the formula ax² + bx + c = 0 is a quadratic equation.

where a, b and c are constants, and x is an unknown variable.

It is called "quadratic" because the variable is squared (in other words, raised to the power of 2).

The most common way to solve a quadratic equation is to factor it into two linear equations, which can then be solved using the methods of linear algebra.

Another way is to use the quadratic formula, which expresses the roots of the equation in terms of the coefficients a, b and c.

It is called a quadratic equation because it can be written in the form

ax² + bx + c = 0

which is the standard form for a quadratic equation.

Examples:

1) x² + 4x – 5 = 0

2) 4x² – 7x + 3 = 0

3) 2x² + 3x – 4 = 0

Therefore , The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

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The ratio means that for every 2 motor boats, there are 3 sail boats. 6 sail boats must also enter so that the ratio remains the same. A possible missing information will be the total number of ships in the armada.

A ratio is a mathematical expression that represents the relationship between two quantities or numbers. It is a comparison of two numbers, often written in the form of a fraction or with a colon. Ratios are used to express how much of one thing there is in relation to another.

1. a. The ratio of motor boats to sail boats can be written in three ways:

As a fraction: 2/3

With a colon: 2:3

With the word "to": 2 to 3

This ratio means that for every 2 motor boats, there are 3 sail boats. Alternatively, it can be interpreted as for every 3 sail boats, there are 2 motor boats. The ratio does not specify the total number of boats, only the relative proportion of motor boats to sail boats.

b. To keep the ratio between motor boats and sail boats the same, we need to maintain the same ratio of motor boats to sail boats.

Currently, the ratio of motor boats to sail boats is 2:3.

Let x be the number of sail boats needed to maintain the ratio.

After x sail boats enter, the total number of boats will be 2 + x motor boats and 3 + x sail boats.

The ratio of motor boats to sail boats will still be 2:3, so we can write,

\(\frac{(2 + x)}{(3 + x)}\) = \(\frac{2}{3}\)

Cross-multiplying, we get,

2(3 + x) = 3(2 + x)

6 + 2x = 6 + 3x

x = 6

Therefore, 6 sail boats must also enter so that the ratio remains the same.

2. To find the total number of galleons and galleys in the Spanish armada, we need at least one additional piece of information. The ratio of 5:1 tells us that for every 5 galleons, there is 1 galley. However, we don't know the total number of galleons and galleys in the armada.

One possible missing information that could help us find the total number of galleons and galleys is the total number of ships in the armada. If we knew the total number of ships, we could find the number of galleons and galleys in the armada.

For example, let's say the total number of ships in the armada is 100. And let number of galleons = a and number of galleys = b. Then,

a + b = 100

\(\frac{a}{b}\) = 5/1

b = a/5

Substituting this expression into the first equation, we get:

a+ (a/5) = 100

(6a/5) = 100

a = 500/6 ≈ 83.33

Then b = (1/5)(83.33) = 16.67

However, since we cannot have a fractional part of a ship, we can round up or down to get whole numbers. Therefore, we can conclude that the Spanish armada had approximately 83 galleons and 17 galleys, based on the given ratio of 5:1.

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The scaled triangle will be larger than the initial size by a factor 2.

The scaled square will be smaller than the initial side by a factor 4.

Dilation refers to a transformation that changes the size of a geometric figure without altering its shape.

Dilation involves scaling an object by a certain factor, that might result in  enlarging or reducing its dimensions uniformly in all directions.

Based on the given diagram, the new length and size of the object is calculated as follows;

For the triangle, (measure the length with ruler)

For the square; (measure the length with ruler)

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Answer:

y=5x-37

Step-by-step explanation:

y-y1=m(x-x1)

y-3=5(x-8)

y=5x-40+3

y=5x-37

Given, Option A: Hourly wage is $19 and the salesperson works 40 hours per week. So, he will earn in a week \(\sf = 19 \times 40 = \$760\)

Now, according to option b, he will get 8% commission on weekly sales.

Let. x = the amount of weekly sales.

To earn the same amount of option A, he will have to equal the 8% of x to $760

So, \(\sf \dfrac{8x}{100}=760\)

Or, \(\sf 8x= 76000\)

Or, \(\sf x= \dfrac{76000}{8}=9500\)

the salesman needs to make a weekly sales of $9,500 to earn the same amount with two options.

Answer:

the 2nd one

Step-by-step explanation:

Answer:

no solution, 1/3x - 2 ≠ 1/3x + 3

where is the 'y'?

Step-by-step explanation:

Answer:

The value of x is 5

The length of YZ is 5 units

Step-by-step explanation:

If a point lies on a line segment, then it divides it into 2 parts, the sum of their length equals the length of the line segment

Let us use this fact to solve the question

∵ Point Y is between points X and Z

→ By using the fact above

∴ XY + YZ = XZ

∵ XY = 4x and XZ = x

∵ XZ = 25

→ Substitute then in the equation above

∴ 4x + x = 25

→ Add the like terms in the left side

∴ 5x = 25

→ Divide both sides by 5 to find x

∵ \(\frac{5x}{5}\) = \(\frac{25}{5}\)

∴ x = 5

∴ The value of x is 5

∵ YZ = x

∵ x = 5

∴ YZ = 5

∴ The length of YZ is 5 units

Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \(\mu\) and standard deviation \(\sigma\), the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(s = \frac{\sigma}{\sqrt{n}}\).

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \(\mu = p\) and standard deviation \(s = \sqrt{\frac{p(1-p)}{n}}\)

In this question, we have that:

\(\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2\)

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when \(X = 260\). So

\(Z = \frac{X - \mu}{\sigma}\)

By the Central Limit Theorem

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{260 - 270}{21.2}\)

\(Z = -0.47\)

\(Z = -0.47\) has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

The linear equation is.

y = -0.4*x + 28

Using that, we can see that a person that spends 10 hours in social media is about 45 years old.

Remember that the general linear equation is:

y = a*x + b

Where a is the slope and b is the y-intercept.

If we know that a line passes through two points (x₁, y₁) and (x₂, y₂), then the slope is given by:

\(a = (y_1 - y_2)/(x_1 - x_2)\)

In this case we have the two points:

(50, 8) and (20, 20)

Where the first value is the age and the second is the time they spend on social media.

Using these values, we can get the slope:

\(a = (20 - 8)/(20 - 50) = 12/-30 = -0.4\)

Then the line is something like:

y = -0.4*x + b

To find the value of b we can evaluate the point (20, 20), this gives:

20 = -0.4*20 + b

20 + 0.4*20  = b

28 = b

Then the linear equation that models this situation is:

y = -0.4*x + 28

Using this, the age of a person who spends 10 hours per week in social media is given by solving:

10 = -0.4*x + 28

(10 - 28)/-0.4 = x

45 = x

So a person that spends 10 hours in social media is about 45 years old.

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