A car depreciates in value at a rate of 14% of its value annually. Julie purchased the new car
for $42,000. If Julie has owned the car for 4 years, how much would the car's value be?

To find the probability of saving a total of $20, we need to calculate the probability of both scenarios happening and add them together.

Scenario 1: Camera gets a 10% discount and game gets no discount.
The probability of the camera getting a 10% discount is 0.2 (or 20%) since there is a 20% chance of getting a discount on any item.
The probability of the game getting no discount is 0.8 (or 80%) since there is an 80% chance of not getting a discount on any item.
So, the probability of this scenario happening is 0.2 * 0.8 = 0.16 (or 16%).

Scenario 2: Game gets a 25% discount and camera gets no discount.
The probability of the game getting a 25% discount is 0.25 (or 25%) since there is a 25% chance of getting a discount on any item.
The probability of the camera getting no discount is 0.8 (or 80%) since there is an 80% chance of not getting a discount on any item.
So, the probability of this scenario happening is 0.25 * 0.8 = 0.2 (or 20%).

Therefore, the probability of saving a total of $20 is the sum of the probabilities of both scenarios: 0.16 + 0.2 = 0.36 (or 36%).

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The given rational expression is 4y + 16 y + 4. To find the restricted values of y, we need to identify any values of y that would make the expression undefined.

In this case, the expression is in the form of a sum, so we don't have any denominators that could lead to division by zero. Therefore, there are no restricted values of y for this rational expression.

The expression 4y + 16 y + 4 is defined for all real numbers. We can evaluate it for any value of y without encountering any restrictions.

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The linear optimization technique for allocating constrained resources among different products is linear programming. (option d).

In the context of allocating constrained resources, linear optimization aims to maximize the output of a system while minimizing the input required to produce that output. This is achieved by formulating the problem as a set of linear equations or inequalities, which represent the constraints on the resources.

The linear equations or inequalities define the relationship between the input and output variables, which are typically expressed as linear functions. These functions represent the production possibilities of each product or activity and the available resources, such as labor, materials, and equipment.

The goal of linear optimization is to find the optimal values of the input and output variables that satisfy the constraints and maximize the objective function. The objective function is a linear function that represents the measure of performance or profitability of the system.

Hence the correct option is (d).

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Step-by-step explanation:

2x + 4y = 36

2 × 4 + 4y = 36

8 + 4y = 36

4y = 36 - 8

4y = 28

y = 28 ÷ 4

y = 7

Answer:

Your new account balance is -$5.35

Step-by-step explanation:

-20.85 + 15.50 = -5.35

Step-by-step explanation:

if you need to know the formula yourself, then this is actually physics and not just mathematics.

anyway, we assume this happens on the surface of Earth.

so, with Earth's gravity and such the formula for the height of the bullet at a certain time is

h(t) = -16t² + v0×t + staying height =

= -16t² + 1200t + 5

the x-intercept is the time, when the bullet falls back down and hits the ground. in other words. when it's height = 0.

0 = -16t² + 1200t + 5

a quadratic equation

ax² + bx + c = 0

has the genetic solution

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = t

a = -16

b = 1200

c = 5

t = (-1200 ± sqrt(1200² - 4×-16×5))/(2×-16) =

= (-1200 ± sqrt(1,440,000 + 320))/-32 =

= (-1200 ± sqrt(1,440,320))/-32 =

= (-1200 ± sqrt(64×22505))/-32 =

= (-16×75 ± 8×sqrt(22505))/-32 =

= (75/2 ± 1/4 × sqrt(22505))

t1 = 75/2 + 1/4 × 150.0166657... = 75.00416644... seconds

t2 = 75/2 - 1/4 × 150.0166657... = -0.004166435... seconds

after about 75 seconds the bullet will hit the ground (x-intercept).

the t2 solution is the theoretical extension of the flight curve backwards in time (remember, the staying height is 5 ft, but using the shot graph and the corresponding accelerations the bullet would have started 0.004166435... seconds before the shot on the ground, and this is therefore also an x-intercept.

for the vertex (the max. height of the bullet) we need the zero of the first derivation (the extreme point of the function).

h'(t) = -32t + 1200 = 0

32t = 1200

t = 1200/32 = 37.5 seconds

so, after 37.5 seconds the bullet reaches is maximum height, which is

-16×37.5² + 1200×37.5 + 5 = 22,505 ft

so, the vertex is (37.5, 22505).

Out of a whole population, a sample is a small part which is considered for any survey.  

The population in this case would be all the one-bedroom apartments available for rent near the college.

The sample would be the listings that Greg is looking at in the local newspaper and on the internet site.

Sample: listings in a local newspaper and on an Internet site              

Population: all available apartments near the college          

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if P(a) equals to 0.5, then, what we can say about P(a | b) is that It is equal to 0.5.

This refers to those events that occur independently without getting affected by the occurrence of another event.

Given that:P(A) =0.5

A and B are two independent events. When two events are independent then, the first event that occurred does not affect the probability that the other event will occur.

Therefore, what we can say about P(a | b) is that It is equal to 0.5.

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The value of c is 98 and the expected value of X is 0.

To find the value of c, we integrate the joint probability density function over the entire range of x and y, and set the result equal to 1 (since the total probability over the entire range must equal 1):

Integrating f(x,y) over the range -y/14 ≤ x ≤ y/14 and 0 < y < ∞:

∫∫ f(x,y) dx dy = c ∫0^∞ ∫-y/14^y/14 (y^2 - 196x^2) e^(-y) dx dy

Using integration by parts with u = y^2 - 196x^2 and dv = e^(-y) dx, we get:

∫-y/14^y/14 (y^2 - 196x^2) e^(-y) dx = (-1/196) e^(-y) [(y^2 + 196y/14 + 98) - (y^2 - 196y/14 + 98)]

= (-1/98) e^(-y) y

Integrating over the range 0 < y < ∞:

c ∫0^∞ (-1/98) e^(-y) y dy = c/98

Setting this equal to 1:

c/98 = 1

c = 98

Therefore, the joint probability density function is:

f(x,y) = 98(y^2 - 196x^2) e^(-y), -y/14 ≤ x ≤ y/14, 0 < y < ∞

To find the expected value of X, we integrate X times the marginal probability density function over the range of X:

f_X(x) = ∫f(x,y) dy from 0 to ∞:

= 98 ∫0^∞ (y^2 - 196x^2) e^(-y) dy

= 98 [(2/7) - 28x^2]

So the expected value of X is:

E(X) = ∫x f_X(x) dx from -∞ to ∞:

= ∫-∞^∞ x f_X(x) dx

= 98 ∫-∞^∞ x [(2/7) - 28x^2] dx

= 0

Therefore, the expected value of X is 0.

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Answer:

Hypotenuse

Step-by-step explanation:

We have the Pythagorean Theorem.

In simple terms, the Pythagorean Theorem can be explained by one equation.

\(a^{2} + b^{2} + c^{2}\)

a and b being the legs while c being the hypotenuse.

Looking at the sentence, we can see that hypotenuse is our answer.

An inequality for this situation "A cruise ship can carry at most 3500 passengers." is x ≤ 3,500.

A graph of the inequality x ≤ 3,500 is shown in the image attached below.

What is an inequality?

In Mathematics and Geometry, an inequality simply refers to a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the inequality symbols;

Note: At most simply refers to less than or equal to (≤) in Mathematics.

Since the cruise ship can only carry at most 3500 passengers, an inequality that models this situation is given by;

x ≤ 3,500

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The length of the hall is 21 meters which dimensions in the ratio 7 : 5 : 3.

Let's assume that the internal dimensions of the hall are 7x, 5x, and 3x.

The volume of the rectangular hall is given by:

Volume = Length × Width × Height

Substituting the internal dimensions in terms of x, we get:

Volume = (7x) × (5x) × (3x)

Simplifying the expression, we get:

Volume = 105x³

Given that the volume of the hall is 2835 m², we can set up an equation:

105x³ = 2835

Dividing both sides by 105, we get:

x³ = 27

Taking the cube root on both sides, we get:

x = 3

Therefore, the internal dimensions of the hall are:

Length = 7x = 7(3) = 21 m

Width = 5x = 5(3) = 15 m

Height = 3x = 3(3) = 9 m

Hence, the length of the hall is 21 meters.

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Answer:

I think it's 70%.

Answer:

B. 34.4

General Formulas and Concepts:

Pre-Algebra

Trigonometry

Step-by-step explanation:

Step 1: Define

∠ = 24°

opposite = 14

hypotenuse = x

Step 2: Find x

And we have our final answer!

Common resources are those that are available to everyone and not owned by any individual or group. Examples include air, water, fish in the ocean, and even public parks. Since no one owns them, there is no direct incentive for any individual to conserve or protect these resources.

In fact, the opposite is often true - individuals may feel that they have a right to use these resources as much as they want, leading to overuse and overconsumption. This is known as the tragedy of the commons, where individuals act in their own self-interest, leading to the depletion of a shared resource. To avoid this, it is important to have regulations and policies in place to encourage responsible use of common resources and prevent overuse and overconsumption.

The answer is A) True
Common resources refer to natural or man-made resources that are not individually owned but are available to everyone in a community. Since these resources are not owned by any specific person or organization, there is a lack of control and regulation over their use. This lack of ownership creates an incentive for people to overuse and overconsume these resources, as individuals may want to take advantage of the resources before others do.

This overuse and overconsumption can lead to depletion or degradation of the common resources, making them less available or useful for future generations. In order to prevent this outcome, it is essential to implement proper management and conservation strategies that help maintain the sustainability and accessibility of these shared resources for all users.

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The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.

To find out how long each sprinkler was used, we can set up a system of equations. Let's say the Alexander family used their sprinkler for x hours, and the Chen family used their sprinkler for y hours.

From the given information, we know that the water output rate for the Alexander family's sprinkler is 30 liters per hour. Therefore, the total water output from their sprinkler is 30x liters.

Similarly, the water output rate for the Chen family's sprinkler is 40 liters per hour, resulting in a total water output of 40y liters.

Since the combined total water output from both sprinklers is 2250 liters, we can set up the equation 30x + 40y = 2250.

We also know that the families used their sprinklers for a combined total of 65 hours, so we can set up the equation x + y = 65.

Now we can solve this system of equations to find the values of x and y, which represent the number of hours each sprinkler was used.

By solving the equation we get,

The Alexander family used their sprinkler for 35 hours, and the Chen family used their sprinkler for 30 hours.

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Answer:

14

Step-by-step explanation:

x=4 y=1

Substitute them into the equation 3x-4yy+6

3(4)-4(1)+6

12-4+6

the average rate of change of the function over the interval 1 ≤ x ≤ 9​ is 3.75.

It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.

Given the function g(x)=-x²+5x+14, within the interval 1 ≤ x ≤ 9

At the lower interval x = 1

g(x) = -1 +5 + 14

g(x) = 18

At the lower interval x = 9

g(x) = -9²+5*9+14

g(x) = -22

The average change of the function will be expressed as:

Δy/Δx = (-22 - 8)/ (9-1)

Δy/Δx = -30/8

Δy/Δx = 3.75

therefore, the average rate of change of the function over the interval 1 ≤ x ≤ 9​ is 3.75.

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Answer: 12 and sqaure root of 194

Step-by-step explanation:

solution 1: 12 because if 13 is the missing side length of the hypotenuse then you would do 5^2 - 13^2 which is 169-25 = 144. the square root of 144 is 12

solution 2: the other solution is trying to get the hypotenuse. you would do 5^2 + 13^2 which is 25 + 169.. therefore the sum is 194. the answer would be the square root of 194

Answer:

7/8-1x2/4x2

7/8-2/8=5/8

5/8

An argumentative essay is a genre of writing the requires the student explore a topic; collect, generate and evaluate evidence; and establish a position on the topic in a concise manner.

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Answer:

sin = 12/13 and tan = 12/5

The value of sin α will be 12/13 and tan α  will be 12/5 for the given triangle such that cosα= 5/13.

Trigonometric functions are functions for right angle triangle which gives the relation between the angle and sides of the triangle.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

The trigonometric functions are found in the four quadrants, as well as their graphs, domains, and differentiation and integration.

We know that

sin²α  + cos²α  =1  ⇒ sin²α  = 1 - cos²α

Given that cosα = 5/13 so by putting it

sin²α  = 1 - (5/13)²

sin²α  = 144/169  ⇒ sinα = 12/13.

Now since tanα = sinα /cosα  

tanα  = (12/13) ÷ ( 5/13)

tanα = 12/5.

Hence the value of sinα will be 12/13 and tanα will be 12/5.

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A) The required population sets are

Population set 1 : Women whose mothers took the drug DES during pregnancy.

Population set 2 : Women whose mothers did not take the drug DES during pregnancy.

B) It is a survay not experiment.

C) The estimate of the number of women out of 1,000 who would be expected to have tissue abnormalities is 16 per 1000 people.

D) The estimate of the number of women out of 1,000 who would be expected to have not tissue abnormalities is 8 per 1000 people.

E) Yes, medical studies often use a relatively large sample to represent the population in the best possible way so that results can be more reliable and can be generalized.

The purpose of a research study is that to uncover something hidden or unknown. Because the study does not use the entire set of data, but it consider sample in an appropriate manner to represent the population as accurately as possible. We have a seven-year medical research study : Women whose mothers took the drug DES during pregnancy were twice as likely to develop tissue abnormalities that might lead to cancer as were women whose mothers did not take the drug.

A) Population is defined as the entire group that we want to draw conclusions. In this case, population seta are :

Population set 1 : Women whose mothers took the drug DES during pregnancy.

Population set 2 : Women whose mothers did not take the drug DES during pregnancy.

B) Since, there is no manipulation in the variables has been done, it is not an experiment but a survey.

C.)Consider a sample from population of women whose mothers took the drug DES during pregnancy. Sample size, n = 3980

The number of women who developed tissue abnormalities that might lead to cancer, x = 63

The sample proportion, p = x/n = 63/3980

≈0.0158

A descriptive statistic that used to estimate the number of women out of 1000. So, population who have tissue abnormalities out of 1000,

Required number = 0.0158 ×1000 ≈15.8 ≈ 16

i.e., 16 per 1000 people

D) Now, for the population of women whose mothers did not take the drug DES during pregnancy, the estimate of the number of women out of 1000

1000 who would be expected to have tissue abnormalities can be given as:

Required number ≈ 8 per 1000 people ( because those who took drug have twice the risk).

E) Yes, medical studies often use a relatively large sample to represent the population in the best possible way so that results can be more reliable and can be generalized, which is the main purpose of the medical study.

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First, write the numbers using a vertical array with the

Transitional forms in the fossil record, including Archaeopteryx, provide evidence for the pattern of evolution known as "gradualism."

This pattern suggests that species change over time through a slow and continuous process of accumulation of small, incremental changes. Transitional fossils like Archaeopteryx exhibit characteristics that are intermediate between two different groups of organisms, indicating a gradual transition from one form to another.

The presence of transitional fossils supports the idea that species do not undergo abrupt transformations but instead evolve gradually over long periods of time.

These fossils provide a tangible link between different groups of organisms, such as dinosaurs and birds in the case of Archaeopteryx, and offer evidence for the gradual transformation of one group into another. This supports the broader concept of evolution as a slow and continuous process of change in populations over generations.

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Answer:

13 9/14

Step-by-step explanation:

Add the blue + red fabric

1. Make the denominator the same

6 7/14 + 7 2/14

2. Add

6 7/14 + 7 2/14 = 13 9/14

Answer:

13 9/14

Step-by-step explanation: You would change 1/7 into 2/14 for a common denominator then add 2/14 and 7/14 and get 9/14 and 6+7=13 so it would be 13 9/14. Plzzzz give me brainliest

The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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Answer:

ano po grade ninyo. ano po

Answer:M(-0,5;0)

Step-by-step explanation: