Solve. Assume the exercise describes a linear relationship. When writing a linear equation, write the equation in slope-intercept form.The average value of a certain type of automobile was $13,980 in 1995 and depreciated to $7860 in 1999. Let y be the average value of the automobile in the year x, where x = 0 represents 1995. Write a linear equation that models the value of the automobile in terms of the year x.

Answer:

\(58 + \frac{ {15x}^{3} }{y} - {3x}^{2} \)

Step-by-step explanation:

1) Use this rule: a/b × c/d = ac/bd.

\(4 + 54 + \frac{5x \times {3x}^{2} }{y} - {3x}^{2} \)

2) Take out the constants.

\(4+54 + \frac{(5 \times 3) {xx}^{2} }{y} - {3x}^{2} \)

3) Simplify 5 × 3 to 15.

\(4 + 54 + \frac{ {15xx}^{2} }{y} - {3x}^{2} \)

4) Use the product rule: x^a x^b = x^a + b.

\(4 + 54 + \frac{15xx^{2} }{y} - 3x^{2} \)

5) Simplify 1 + 2 to 3.

\(4 + 54 + \frac{15 {x}^{3} }{y} - {3x}^{2} \)

6) Collect like terms.

\((4 + 54) + \frac{15 {x}^{3} }{y} - {3x}^{2} \)

7) Simplify.

\(58 + \frac{ {15x}^{3} }{y} - {3x}^{2} \)

Therefor, the answer is 58 + 15x³ / y - 3x².

Answer:

25.12 cm³

Step-by-step explanation:

Formula = πr² * h/3

= 3.14 * 4 * 6/3

= 3.14 * 8

= 25.12

Units = cm³

25.12 cm³

If my answer is incorrect, pls correct me!

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-Chetan K

Step-by-step explanation:

The height of the water in the can is a function of time, because it depends on the time the water flows out each minute.

The height h in cm is a function f of time t in minutes since poking the hole, h= f(t)h=f(t). The expression for f(t) = 20. \frac{2}{3}^{t}f(t)=20.

3

2

t

The values of f -> f(0) = 20f(0)=20; f(1) = \frac{40}{3}f(1)=

3

40

; f(2) = \frac{80}{9}f(2)=

9

80

; f(3) = \frac{160}{27}f(3)=

27

160

The value of f(5) = \frac{640}{243}f(5)=

243

640

The level of water approaches close to the x-axis as time moves on. It does not completely approach zero.

Sorry if wrong answer

a. The height of the water in the can is a function of time because it changes as time progresses.

b. The exponential function for f(t) is  \(f(t) = 20(1/3)^t\).

c. f(0) = 20, f(1) = 6.67, f(2) = 2.22, and f(3) = 0.74.

d.  f(4) represents the height of the water in the can 4 minutes after the beginning of the experiment.

An exponential function is defined as a function whose value is a constant raised to the power of an argument is called an exponential function.

a. The height of the water in the can is a function of time because it changes as time progresses.

As water drains out of the can through the tube, the height of the water in the can decreases over time.

b. Using the formula for exponential functions, \(f(t) = ab^t\), where a is the initial height of the water, b is the factor by which the height decreases each minute, and t is the time in minutes since the beginning of the experiment.

Here, the initial height of the water in the can is 20 cm, and it decreases by a factor of 1/3 each minute.

This means that b is 1/3, and a is 20.

Therefore, the expression for f(t) is:

\(f(t) = 20(1/3)^t\)

c. To find the values of f(t) when t is 0, 1, 2, and 3, we substitute these values into the expression for f(t):

f(0) = 20 (1/3)⁰ = 20

f(1) = 20(1/3)¹ = 6.67

f(2) = 20(1/3)² = 2.22

f(3) = 20(1/3)³ = 0.74

So, when t is 0, the height of the water in the can is 20 cm, and it decreases exponentially by a factor of 1/3 each minute.

d. To find f(4), we substitute 4 into the expression for f(t):

f(4) = 20(1/3)⁴ = 0.25

Here, f(4) represents the height of the water in the can 4 minutes after the beginning of the experiment.

At this time, the height of the water in the can have decreased to 0.25 cm, which is almost completely drained.

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Answer: 4/13

Step-by-step explanation:

Number of cards in a deck = 52

Number of spades = 13

Number of aces = 4

Number of ace of spade = 1

Probability of either a spade or an ace :

P(spade or ace) = P(spade U ace)

P(spade U ace) = p(spade) + p(ace) - p(spade n ace)

Probability = required outcome / Total possible outcomes

P(spade) = 13 / 52

P(ace) = 4 / 52

P(spade n ace) = 1 / 52

P(spade U ace) = p(spade) + p(ace) - p(spade n ace)

= 13/52 + 4/52 - 1/52

= 16 / 52 = 4 /13

Answer:

5/2 or 2.5

Step-by-step explanation:

Divide both sides by 2.

The nearest kilometers to 999.09344471 km is 1000 km.

Given value is 999.09344471 Km.

We have to calculate the round off value to the nearest kilometers. we know that after the decimal if the value of tenth place is 5 or bigger than 5 then we add 1 to the tens place digit, this is the fundamental rule of rounding off.

Now on following this rule from the very right hand side up to the tenth place digit we come to the conclusion that only  the value after the decimal (934) is to be rounded off which is (900).

So 999.09344471 km is finally becomes 999.900 km after rounding of to nearest hundredth value.

Again rounding off 999.900 km to nearest km so it becomes 1000 km.

The nearest kilometers to 999.09344471 km is 1000 km.

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An addition equation that could be used to find the length of the other piece of material is,

38 = 19 + x.

Combining objects and counting them as one big group is done through addition. In arithmetic, addition is the process of adding two or more integers together. Addends are the numbers that are added, and the sum refers to the outcome of the operation.

Given:

A piece of material measures 38 inches.

Courtney cuts the piece of material into two pieces.

One piece measures 19 inches.

Let x be the length of other pieces.

An addition equation that could be used to find the length of the other piece of material is,

38 = 19 + x

Therefore, 19 + x = 38 is an addition equation.

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The distance from the midpoint of the hypotenuse of any vertex is:

\(\sqrt{(0-a)^2 +(2b - b)^2} \\\)   = \(\sqrt{(2a - a)^2 +(0 -b)^2}\)

= \(\sqrt{a-0)^2 + (b -0)^2}\)

Right Angle Triangle:

A right triangle is a triangle with one of its angles 90 degrees. An angle of 90 degrees is called a right angle, so a triangle with a right angle is called a right triangle. In this triangle, we can use the Pythagorean law to easily understand the relationship of the various sides. The side opposite the right angle is the largest side and is called the hypotenuse.

In a right triangle we have:

                  (Hypotenuse)2 = (Base)2 + (Altitude)2

Mid point Theorem:

The midpoint theorem states that the line segment joining the midpoints of any two sides of a triangle is parallel to the third side and equal to half the length of the third side. This theorem is used in many places in real life. For example, if we don't have a measuring tool, you can use the midpoint theorem to cut a bar in half.

If we have a line segment whose endpoint coordinates are given by

(x₁, y₁) and (x₂, y₂), we can find the coordinates of the midpoint of the line segment using the following formula:

Let (xₙ , yₙ ) Coordinates of the midpoint of the segment. Then

(xₙ, yₙ) = ( (x₁+ x₂/2 , (y₁ + y₂)/2 )

This is known as the midpoint theorem.

According to the Question:

Suppose that we have two points (x₁ ,y₁)  and (x₂, y₂). The distance between them is given by:

D = \(\sqrt{(x_2-x_1)^2 + (y_2- y_1)^2 }\)

Hence the distance from the midpoint of the hypotenuse to any vertex is given by:

    \(\sqrt{(0-a)^2 +(2b - b)^2} \\\)

= \(\sqrt{(2a - a)^2 +(0 -b)^2}\)

= \(\sqrt{a-0)^2 + (b -0)^2}\)

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Answer: The last option. X is greater than or equal to -3

Step-by-step explanation:

If you are searching for all of the values highlighted in red, then it must be every single value greater than x=-3 including the value itself (the dot located on the value is shaded, therefore you must include it within the domain).

Answer:

y≥1/2x is the answer for this problem

Step-by-step explanation:

Multiply (4/10) by 10 to find the sum using common denominators:

\( \frac{4 \times 10}{10 \times 10} = \frac{40}{100} \)

Add:

\( \frac{40}{100} + \frac{20}{100} = \frac{60}{100} \)

60/100 is your unsimplified answer.

Divide (60/100) by 20:

\( \frac{60 \div 20}{100 \div 20} = \frac{3}{5} \)

3/5 is your simplified answer.

A) The algebraic expression will be 12d + 7 = 91

B) He drives 7 miles per day to work.

For 11 days straight, Ms. Chung drove the same distance every day going to and coming from work.

The distance she drove on Saturday was; 0.9 miles.

The number of miles she drives per day:

84 miles/12

= 7 miles per day

Let the number of miles she travels be day = d

12d + 7 = 91 miles

12d + 7 = 91

12d = 91 - 7

12d = 84

d = 84/12

d = 7 miles per day

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Using the radius of the Ferris wheel and the angle between the two positions, the time spent on the ride when they're 28 meters above the ground is 12 minutes

The radius of the Ferris wheel is 30 / 2 = 15 meters.

The highest point on the Ferris wheel is 15 + 4 = 19 meters above the ground.

The time spent higher than 28 meters is the time spent between the 12 o'clock and 8 o'clock positions.

The angle between these two positions is 180 degrees.

The time spent at each position is 10 minutes / 360 degrees * 180 degrees = 6 minutes.

Therefore, the total time spent higher than 28 meters is 6 minutes * 2 = 12 minutes.

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Answer: No

Step-by-step explanation:

to be proportional, both numbers have to increase by the same number

because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in

Answer:

22 passengers

Step-by-step explanation:

the full answer is 21.02702702702703

Hope this helps!

Brainliest pls

Have a great day!

Answer:

778/37

Step-by-step explanation:

778 divided by 37

21.027027...

or 778/37

The parameter p is the population proportion, that is the proportion of the population that thinks the tuition is too high.  POPULATION=Students at Glenn's school. (b). The numerical value of that estimates p is \(\hat{p}\)\(=\frac{38}{50} =0.76\).  (c). Yes, the population is more than 10 times as large as the sample size.

(a). He conducts SRS interviews with 50 of his college's 2400 pupils. Of those surveyed, 38 believe that tuition is too costly.

The people under study make up the population.

POPULATION=Students at Glenn's school

The parameter p is the population proportion, that is the proportion of the population that thinks the tuition is too high.

This sample proportion can be used to estimate the true proportion of students in the entire population who think tuition is too high. However, it's important to note that the sample proportion is only an estimate and may not be exactly equal to the true population proportion. The level of precision of this estimate can be quantified using a confidence interval.

(b) The sample proportions is the number of people who think the dorm food is good divided by the sample size:

⇒\(\hat{p}=\frac{38}{50} =0.76\)

(c). Yes, the population is larger than the sample size by more than 10 times.

⇒n\(\hat{p}\)=38>10

⇒n(1-\(\hat{p}\))=12>10 and the sample is a simple random sample.

Therefore, the POPULATION=Students at Glenn's school. The numerical value of that estimates p is \(\hat{p}=\frac{38}{50} =0.76\).  Yes, the population is more than 10 times as large as the sample size.

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Based on the information, we can infer that the tables are completed as follows: 5, 10, 15, 4, 8.

To complete the table of the ratios we must take into account the information provided in the fragment. According to the above, in box A for every two markers there are 5 pencils and in box B for every three markers there are 4 pencils. Then the ratios would be the following:

Box A

box B

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the second equation is correct

Step-by-step explanation:

I got it right on the test

The result is that x = 8 is the smallest positive number such that f(x) surpasses g(x).

An integer is a whole number that may be positive, minus, or zero and is not a percentage. Integer examples include: -5, 1, 5, 8, 97, as well as 3,043. The following figures are examples of non-integer numbers: -1.43, 1 3/4, 3.14,.09, and 5,643.1.

To find the smallest positive integer x for which f(x) exceeds g(x)

we need to set the two functions equal to each other and solve for x:

f(x) = g(x)

-x² + 5x = -10x + 10

Simplifying the equation, we get:

x² + 15x - 10 = 0

Using the quadratic formula, we can solve for x:

x = (-15 ± sqrt(15² - 4(1)(-10))) / (2(1))

x = (-15 ± sqrt(265)) / 2

The two possible solutions are approximately -0.372 and -14.628. Since we are looking for the smallest positive integer solution, we take the ceiling of the positive solution to get x = 8.

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Answer: \(m\angle BAM=30^{\circ}\)

Step-by-step explanation:

\(AD=x\sqrt{3}\) (Pythagorean theorem)

\(m\angle ACD=60^{\circ}\) (30-60-90 triangle)

\(m\angle MCA=30^{\circ}\) (angle subtraction)

\(m\angle MAC=30^{\circ}\) (base angles theorem)

\(m\angle CAD=30^{\circ}\) (30-60-90 triangle)

\(m\angle BAM=30^{\circ}\) (angle subtraction)

The HCF of the two numbers is 1.

Let the two numbers be a and b. From the problem statement, we have:

HCF(a, b) = LCM(a, b) / 5

And we know that:

a * b = 720

We can use the prime factorization of 720 to find the values of a and b. The prime factorization of 720 is:

720 = \(2^{4}\) * \(3^{2}\) * 5

Since a * b = 720, we know that a and b must have the same prime factors as 720, just in different combinations. We can try different combinations of prime factors until we find two numbers whose product is 720.

One such pair of numbers is a = 45 and b = 16. These numbers have a greatest common factor of 1, and their least common multiple is:

LCM(45, 16) = 720

So we can check that:

HCF(45, 16) = LCM(45, 16) / 5

1 = 144 / 5

Thus, the HCF of the two numbers is 1.

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The answer should be 5 3/4. :)

Answer:

[-3,5]

Step-by-step explanation:

Interval notation is a shorthand way of writing and interval of values.  To describe an interval, imagine the two endpoints on the number-line.  Then, list the two endpoint values, leftmost point from the number-line first, separated by a comma.  Lastly, include the appropriate brackets for each endpoint:

For our situation, the two endpoints are -3 and 5.  -3 is to the left of 5 on the number-line, so -3 should be listed first

\(-3,5\)

Lastly, the directions say "including -3 and 5", so both endpoints should be included.

The final result for the interval is \([-3,5]\)

Answer:

The answer would be A.

Step-by-step explanation: In order to find the answer you would need A

I actually have no idea, I'm guessing- ;-;

Answer:

1. work is the time it takes to move an object once acted upon by a force

Step-by-step explanation:

given

23÷3(45+4)

23÷3(49)

23/147

Answer:

41.4 I believe

Step-by-step explanation:

First we start in the () so we do 45+4= 49.

Next we divide 23 by 3 and we get 7.66666667, but we reduce that to 7.6.

Then we have 7.6 I don't know the sign we have to use, I used subtraction, so we do 7.6 - 49, which actually gives us -41.4,

Let me know if you have any questions. I couldn't do this 100% because I didn't know the choices but try this and if not, I apologize.

If the two angles are complementary, then their sum is 90 degrees.

The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.

Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.

If the two angles are complementary, then their sum is 90 degrees.

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The maximum area of the tile to contain both grounds is 12x²y²

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

Area of ground A = 12x^2y sq. units

Area of ground B = 6xy^2sq units

Rewrite these areas properly

So, we have the following representation

Area of ground A = 12x²y sq. units

Area of ground B = 6xy² sq units

Express the areas as the products of their prime factors

This gives

Area of ground A = 2 * 2 * 3 * x * x * y

Area of ground B = 2 * 3 * x * y * y

From the above products, we have

Least common multiple = 2 * 2 * 3 * x * x *y * y

Evaluate the products

Least common multiple = 12x²y²

This represents the greatest area

Hence, the greatest area is 12x²y²

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Answer: 19.2 miles is 30.72 km

Step-by-step explanation:

Since 5 miles is 8 km, divide 8/5 to find out how many miles is one kilometer.

8/5 = 1.6

Multiply 19.2*1.6 to find out how many kilometers 19.2 miles is.

19.2*1.6 = 30.72

(Note that when you search it up online, 19.2 miles is actually 30.9 km, because 5 miles isn't exactly 8km!)

Answer:

\(k\ge \:-3\)

Step-by-step explanation:

\(12\ge \:-4k\)

\(-4k\le \:12\)

\(\left(-4k\right)\left(-1\right)\ge \:12\left(-1\right)\)

\(4k\ge \:-12\)

\(\frac{4k}{4}\ge \frac{-12}{4}\)

\(k\ge \:-3\)