Parallel lines: Solve for Y

Answer:

The function to determine the value of your car (in dollars) in terms of the number of years t since 2012 is:

[tex]f(t) = 10000(0.9407)^t[/tex]

Step-by-step explanation:

Value of the car:

Constant rate of change, so the value of the car in t years after 2012 is given by:

[tex]f(t) = f(0)(1-r)^t[/tex]

In which f(0) is the initial value and r is the decay rate, as a decimal.

In 2012 your car was worth $10,000.

This means that [tex]f(0) = 10000[/tex], thus:

[tex]f(t) = 10000(1-r)^t[/tex]

2014 your car was worth $8,850.

2014 - 2012 = 2, so:

[tex]f(2) = 8850[/tex]

We use this to find 1 - r.

[tex]f(t) = 10000(1-r)^t[/tex]

[tex]8850 = 10000(1-r)^2[/tex]

[tex](1-r)^2 = \frac{8850}{10000}[/tex]

[tex](1-r)^2 = 0.885[/tex]

[tex]\sqrt{(1-r)^2} = \sqrt{0.885}[/tex]

[tex]1 - r = 0.9407[/tex]

Thus

[tex]f(t) = 10000(1-r)^t[/tex]

[tex]f(t) = 10000(0.9407)^t[/tex]

9514 1404 393

Answer:

  (e) f′(x)=2xg(x)+x²g′(x)

Step-by-step explanation:

The product rule applies.

  (uv)' = u'v +uv'

__

Here, we have u=x² and v=g(x). Then u'=2x and v'=g'(x).

  f(x) = x²·g(x)

  f'(x) = 2x·g(x) +x²·g'(x)

here's the answer to your question

solve for x

3x-7y=-27

5x+9y=17

multiply 9, 7

27x -63y =-243

35x +63y = 119

add and cancel y out

62x = -124

x = -2

plug in x

-6-7y=-27

-7y=-21

y = 3

answer:

y = 3

x = -2

Answer:

20% of students prefer to go to the aquarium

50% of teachers prefer to go to the aquarium

Step-by-step explanation:

1.

8 students prefer the aquarium out of 40 students.

Set up an equation:

Variable x = percentage of students

8/40 = x/100

Cross multiply:

8 × 100 = 40 × x

800 = 40x

20 = x

Divide:

20%

Check your work:

40 students × 20%

Convert percentage into decimal:

40 × 0.20

8

8 students prefered the aquarium so this is correct!

2.

5 teachers prefer the aquarium out of 10 teachers.

Set up an equation:

Variable x = percentage of teachers

5/10 = x/100

5 × 100 = 10 × x

500 = 10x

50 = x

50%

Check your work:

10 × 0.50

5

Correct!

Answer:

2, 8

Step-by-step explanation:

-1/2x^2 + 5x = 8

-x^2 + 10x = 16 (Multiplying both sides of the equation by 2)

-x^2 + 10x  - 16 = 0

x^2 - 10x + 16 = 0 (changing the signs)

x^2 -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

x-2 = 0

x = 2

or

x -8 = 0

x = 8

Answer from Gauthmath

The values of x are solutions to this equation that is 2, 8

An equation is an expression that shows the relationship between two or more numbers and variables.

We are given that the equation as;

-1/2x² + 5x = 8

-x² + 10x = 16

Now Multiplying both sides of the equation by 2;

-x² + 10x  - 16 = 0

Or

x² - 10x + 16 = 0

x² -2x -8x +16 = 0

x (x-2) -8 (x-2) = 0

(x-2) (x-8)

The solution are;

x-2 = 0

x = 2

or

x -8 = 0

x = 8

Learn more about equations here;

https://brainly.com/question/25180086

#SPJ2

Answer:

YWX = DFE

Step-by-step explanation:

AAS means angle angle side. so, we need 2 angles and 1 side.

we have 1 side and one angle confirmed.

so, we need one of the other two angles (W or Y vs. F or D) confirmed.

they probably want W and F as answer, as Y and D would make it a special case of AAS : ASA.

Answer:

y=-\frac{2}{3}\approx -0.666666667

Answer:

C)

Step-by-step explanation:

Just see the length of the R line, A and B are almost the same large when you add them.

Answer: Yes you are correct. The answer is choice A

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

Explanation:

If you used the z-table, you should find that P(Z < 1) = 0.84 approximately.

So by symmetry, P(Z > -1) = 0.84 approximately as well.

We'll convert the z score z = -1 into its corresponding x score

z = (x-mu)/sigma

-1 = (x-180)/15

-15 = x-180

x-180 = -15

x = -15+180

x = 165

We don't land on any of the answer choices listed, but we get fairly close to 165.2, which is choice A. So you are correct.

I have a feeling that the table you have is probably more accurate than the one I'm using, so it's possible that you'd land exactly on 165.2 when following the steps above.

Answer:

194.9

Step-by-step explanation:

ON EDG

Answer:

(6,-6)

Step-by-step explanation:

First let's identify the current coordinates of D

It appears that D is located at (2 , -2)

Now let's find the coordinate of D if it were dilated by a scale factor of 3.

To find the coordinates of a point after a dilation you simply multiply the x and y values of the pre image coordinates by the scale factor

In this case the scale factor is 3 and the coordinates are (2,-2)

That being said let's apply the dilation rule

Current coordinates: (2,-2)

Scale factor:3

Multiply x and y values by scale factor

(2 * 3 , -2 * 3) --------> (6 , -6)

The coordinates of D' would be (6,-6)

9514 1404 393

Answer:

  C. More than 1 solution

Step-by-step explanation:

Divide the second equation by 3.

  y -x = -3

Add x.

  y = x -3

This matches the first equation exactly, meaning that any solution to the first equation is also a solution to the second equation. There are an infinite number of possibilities. There is "More than 1 solution."

Answer:

40$+60$=100$ spent

120$sold

90$ payed

70$ refund

120 (sold) -90 (payed) =30+70 (refund) =100$ (profit)

Step-by-step explanation:

You spent 100$

And you sold and got 120 but you payed 90$ from 120$ money left is 30$

Then they refunded you (pay back the money (give you the money ))

So the money that your left with is 30$ and the refund money is 70$

So add the money that your left with is gives you 100$

Answer:

Rs. 80

Step-by-step explanation:

Given that :

Purchase price = 70

Profit = 6

Discount = 5%

Let selling price = x

Selling price * (1 - discount) = (purchase price + profit)

x * (1 - 5%) = (70 + 6)

x * (1 - 0.05) = 76

x * 0.95 = 76

0.95x = 76

x = 76 / 0.95

x = 80

Hence, selling price = Rs. 80

Answer:

Step-by-step explanation:

Answer:

5180.56 Dollars...........

Answer:

We need to assume that the relationship is linear.

a) Remember that a linear relation is written as:

y = a*x + b

then we will have:

p(x) = a*x + b

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

If we know that the line passes through the points (a, b) and (c, d), then the slope can be written as:

y = (d - b)/(c - a)

In this case, we know that:

if the ticket has a price of $12, the average attendance is 25,000

Then we can define this with the point:

(25,000 , $12)

We also know that when the price is $9, the attendance is 29,000

This can be represented with the point:

(29,000, $9)

Then we can find the slope as:

a = ($9 - $12)/(29,000 - 25,000) = -$3/4,000 = -$0.00075

Then the equation is something like:

y = (-$0.00075)*x + b

to find the value of b we can use one of the known points.

For example, the point (25,000 , $12) means that when x = 25,000, the price is $12

then:

$12 = (-$0.00075)*25,000 + b

$12 = -$18.75 + b

$12 + $18.75 = b

$30.75 = b

Then the equation is:

p(x) = (-$0.00075)*x + $30.75

b) We want to find the ticket price such that it maximizes the revenue.

The revenue will be equal to the price per ticket, p(x) times the total attendance, x.

Then the revenue can be written as:

r(x) = x*p(x) = x*( (-$0.00075)*x + $30.75 )

r(x) =  (-$0.00075)*x^2 + $30.75*x

So we want to find the maximum revenue.

Notice that this is a quadratic equation with a negative leading coefficient, thus the maximum will be at the vertex.

Remember that for an equation like:

y = a*x^2 + bx + c

the x-value of the vertex is:

x = -b/2a

Then in our case, the x-value will be:

x = -$30.75/(2*(-$0.00075)) = 20,500

Then the revenue is maximized for x = 20,500

And the price for this x-vale is given by:

p( 20,500) =  (-$0.00075)*20,500 + $30.75 = $15.375

which should be rounded to $15.38

Answer:

200

Step-by-step explanation:

Break down 25 = 5*5

Break down 8 = 2*2*2

They have no common factors

The least common multiple is

5*5*2*2*2 = 25*8 = 200

Answer:

200

Step-by-step explanation:

list the factors of 25: 5,5

factors of 8:2,2,2,

Answer:

255,024

Step-by-step explanation:

24 x 23 x 22 x 21

24 options for the first member

23 options for the second member

22 options for the third member

21 options for the last member

Answer:

19

Step-by-step explanation:

3a -2^3 ÷b

Let a = 7 and b = 4

3*7 -2^3 ÷4

PEMDAS says exponents first

3*7 -8 ÷4

Multiply and divide from left to right

21 - 2

Subtract

19

Answer:

5%

Step-by-step explanation:

Bank amount=PA*(1+r/100)^t

4410=4000*(1+x/100)^2

1.05=(1+x/100), x=5%

Answer:

18

Step-by-step explanation:

x squared -6 +13

5 squared-6×3+2+13

25-20+13

5+13

=18

Answer:

b) two-sample z-test for proportions

Step-by-step explanation:

The most appropriate test to use for the research hypothesis stated above is the two sample z-test for proportions, this is because, the experiment has two independent groups (male and female) with the result of each group not affecting the result of the other. The experiment clearly stses that, it is to estimate the difference in proportion, hence, it is a test of proportions rather than mean. Also when performing, a two sample tests of proportion, the Z distribution is used.

Answer:

− 8 a ^7

Step-by-step explanation:

See picture for steps :)

Answer:

[tex]\displaystyle y' = \frac{\sqrt{y} + y}{4\sqrt{x}y \Big( y^\Big{\frac{3}{2}} + \sqrt{y} + 2y \Big) + \sqrt{x} + x}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:                                                           [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]

Derivative Property [Addition/Subtraction]:                                                         [tex]\displaystyle \frac{d}{dx}[f(x) + g(x)] = \frac{d}{dx}[f(x)] + \frac{d}{dx}[g(x)][/tex]

Basic Power Rule:

Derivative Rule [Quotient Rule]:                                                                           [tex]\displaystyle \frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}[/tex]

Derivative Rule [Chain Rule]:                                                                                 [tex]\displaystyle \frac{d}{dx}[f(g(x))] =f'(g(x)) \cdot g'(x)[/tex]

Implicit Differentiation

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{\sqrt{x} + 1}{\sqrt{y} + 1} = y^2[/tex]

Step 2: Differentiate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

Book: College Calculus 10e

Answer:

a) 0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.

b) Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.

Step-by-step explanation:

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

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

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 p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

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

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

Mean of 6.05 ounces and a standard deviation of .18 ounces.

This means that [tex]\mu = 6.05, \sigma = 0.18[/tex]

Sample of 36:

This means that [tex]n = 36, s = \frac{0.18}{\sqrt{36}} = 0.03[/tex]

a. Find the probability that the mean weight of the sample is less than 5.97 ounces.

This is the p-value of z when X = 5.97. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{5.97 - 6.05}{0.03}[/tex]

[tex]Z = -2.67[/tex]

[tex]Z = -2.67[/tex] has a p-value of 0.0038.

0.0038 = 0.38% probability that the mean weight of the sample is less than 5.97 ounces.

b. Suppose your random sample of 36 cans of salmon produced a mean weight that is less than 5.97 ounces. Comment on the statement made by the manufacturer.

Given a mean of 6.05 ounces, it is very unlikely that a sample mean of less than 5.97 ounces, which means that the true mean must be recalculated.

Answer:

Step-by-step explanation:

Given,

[tex] {25x}^{2} - \frac{1}{49} [/tex]

[tex] = {(5x)}^{2} - {( \frac{1}{7}) }^{2} [/tex]

Since,

[tex] {x}^{2} - {y}^{2} = (x + y)(x - y)[/tex]

Then,

[tex] = (5x + \frac{1}{7} )(5x - \frac{1}{7} )(ans)[/tex]