1 point
The value of an automobile decreases each year and is described by the equation (t)- 24 000(0.95)',
where t is the number of years after the car is purchased. Estimate the rate at which the value of the auto
is changing 5 years after it is purchased.
a. -$1250/year
b. -$950/year
C. -$150/year
d. $150/year

As per the population function, the population of mosquitoes in the area at any time is 400000 = 200000e⁷ˣ

Population function:

Population function means  the effective population served over the course of a time

Given,

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of other factors, the population doubles each week. There are 200000 mosquitoes in the area initially , and predators (birds, bats, and so forth) eat 20000 mosquitoes/day.

Here we need to determine the population of mosquitoes in the area at any time.

Here we have to note that we have two time frames in the information given; weeks and days.

Now, we want the population after predation lets choose time in days.

We know that the population doubles every seven days (ignoring predation) so if P(t) is the population function we have IVP

So, for one week, the population function of the given situation is,

=> dP/dt = rP

=> P(0) = 200000

And we know that,

=> P(7) = 2P(0)

While we solving the IVP for P then we get

[tex]P=Ce^{rt}[/tex]

While we apply,  P(0) = 200,000 then we get the value of C = 200,000

So, the given function is rewritten as

[tex]P=200000e^{rt}[/tex]

Now we have to use P(7) = 2P(0), then we get,

400000 = 200000e⁷ˣ

Therefore, we have to use this function to find the population of mosquitoes in the area anytime.

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Answer:

64

Step-by-step explanation:

Double the miles because you doubles the time.

Answer:

Kathryn and her mom will drive 64 miles in 1 hour.

Step-by-step explanation:

Since they can drive 32 miles in 30 minutes, 30 minutes is half of one hour. So, since it is half, we can double 32 miles as well to get 64 miles in 1 hour.

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The mistake that Raquel made in simplifying the expression is given as follows:

The square is applied only to the number 3, not to the sum of 5 and 3.

Hence the correct simplified version is:

(5 + 3²) + 18 = (5 + 9) + 18 = 32.

The expression for this problem is given as follows:

(5 + 3²) + 18.

The parenthesis takes precedence, hence the first operation to be solved is of:

5 + 3².

Then the square is the operation that takes precedence, hence the expression is given as follows:

5 + 3² = 5 + 9.

Here is where Raquel's mistake lays, as only the number 3 is squared, the number 5 is not, hence 3 is squared and then added to 5.

Then the correct result of the expression is obtained as follows:

5 + 9 + 18 = 32.

The problem is given by the image shown at the end of the answer.

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The graph of a relation that is a function is the last option that is in the attachment below.

A graph that represents a relation that is a function is a graph whose x-values each have exactly one corresponding y-value. That is to say, no two y-values correspond to one x-value in the graph of a relation that represents a function.

All of the graphs represents relations that have different y-values that correspond to an x-value except the graph at the bottom far right, whose diagram is attached below.

The graph attached below has exactly one y-value that corresponds to each x-value on the graph. Therefore, the relation is a function.

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The probabilities are given as follows:

a) Tails and odd number: 1/4.

b) Tails or odd number: 3/4.

c) Tails or odd number, but not simultaneously: 1/2.

The probability of an event in an experiment is calculated as the number of desired outcomes of the experiment divided by the number of total outcomes of the experiment.

For each event, the probabilities are given as follows:

Hence the probability of both events is of:

p = 1/2 x 1/2 = 1/4.

The or probability is composed as follows:

Hence the ´probability is of:

3 x 1/4 = 3/4.

Removing the simultaneous event, the probability is of:

3/4 - 1/4 = 2/4 = 1/2.

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40 is a common multiple of 6 and 10

False:

Multiples of 6: 6, 12, 18, 24, 30, 36, 42...

Multiples of 10: 10, 20, 30, 40...

(2) The fraction 5/6 is greater than 7/10

True:

Find common denominators. Note that what you multiply to the denominator, you multiply to the numerator.

(5/6) x (5/5) = 25/30

(7/10) x (3/3) = 21/30

25/30 > 21/30 ∴ 5/6 is greater than 7/10

(3) The fraction 42/60 is an equivalent form of 7/10

True:

Find a common denominator. Note that what you multiply to the denominator, you multiply to the numerator.

(7/10) x (6/6) = 42/10

42/10 = 42/10 ∴ 7/10 = 42/10

(4) The only value that can be used as a common denominator is 60.

False:

While 60 is a plausible denominator, there are other denominators that can be used. Remember that what you do to the denominator, you do to the numerator.

(5) Ten is a multiple of 6.

False:

Multiples of 6: 6, 12, 18, 24, 30...

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In the given number, the digit that has the greatest value is 1.

We are given a number. The number is a natural number. Natural numbers are the numbers used in mathematics for counting and ordering. Cardinal numbers are those used for counting, and ordinal numbers are those used for ordering. The number contains five digits. We need to find the digit that has the greatest value. We know that as we go left, the place value of the digit increases by a factor of 10. So, the place value of the number is maximum for the digit that is present at the leftmost position in a number.

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Answer:

First term: 3

Common difference: -1

Step-by-step explanation:

3rd term: 1

6th term: x

10th term: 3x

Formula for the nth term using the common difference d and the first term a1:

an = a1 + (n - 1)d

Third term: a3 = a1 + (3 - 1)d = a1 + 2d = 1

6th term: a6 = a1 + (6 - 1)d = a1 + 5d = x

10th term: a10 = a1 + (10 - 1)d = a1 + 9d = 3x

a1 + 2d = 1       Eq. 1

a1 + 5d = x      Eq. 2

a1 + 9d = 3x    Eq. 3

Eq. 2 - Eq. 1

3d = x - 1

Eq. 3 - Eq. 2

4d = 2x

x = 2d

3d = x - 1

Substitute 2d for x.

3d = 2d - 1

d = -1

a1 + 2d = 1

a1 + 2(-1) = 1

a1 = 3

Check:

Here are the first 10 terms:

3, 2, 1, 0, -1, -2, -3, -4, -5, -6

The third term is 1. Correct

The tenth term (-6) is 3 times the 6th term (-2). Correct

Answer:

First term: 3

Common difference: -1

The left-hand side of the equation becomes (x - 4)² while the right side of the equation is 25

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

The standard form of a quadratic equation is given by:

0 = Ax² + Bx + C

Where A, B and C are constants.

Given the quadratic equation:

x² - 8x = 9

To solve the quadratic equation using the completing square method, add to both sides the square of half the coefficient of x, hence:

x² - 8x + (-4)² = 9 + (-4)²

(x - 4)² = 9 + 16

(x - 4)² = 25

The solution to the equation is (x - 4)² = 25

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The exponential function of the given graph is y = 4ˣ

Exponential function:

the general form of the exponential function is written as,

y = aˣ

Where

a > 0 and a ≠ 1.

Here a is called the base and x is called the exponent.

Given,

Here we have the graph and the point (2,16)

Now, we have to find the exponential function form this graph and point.

We already know that the general form of the exponential function is

y = aˣ

Here we have point (2,16), now we have to apply this point value on the general form in order to find the value of a,

So, when we apply the point values, then we get,

16 = a²

Now, move the power value to the other side, then we get,

a = √16

a = 4

Therefore, the exponential function of the given graph is,

y = 4ˣ

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Answer:

(3x-4y) (2x+1)

Answer:

These are consecutive interior angles.

Consecutive interior angles always add up to 180 degrees.

If they add up to 180 degrees, then we can use this equation:

(x + 5) + (9x - 55) = 180

And then solve for it:

10 x - 50 = 180

10x = 130

x = 13

Ta - da! works like magic

Answer:

Shipping is the conveyance of goods to a desired destination, usually through the help of transportation means

Answer:

Step-by-step explanation:

1. the act or business of sending or transporting goods. 

Example:-

To cause to go or be taken from one place to another we shipped those books out yesterday.

a - 2b + c = -6 (1)

a = -5c - 12 (2)

-a + 6b + 4c = 3 (3)

Putting (2) into (1) & (3) gives

(-5c -12) - 2b + c = -6 (5)

-(-5c - 12) + 6b +4c =3 (6)

Neatening it up gives

-2b - 4c = 6 (7)

6b + 9c = -9 (8)

Using simulataenous equations, we want to cancel out either b or c. b in this case is easier. Multiplying (7) makes that possible

(7) * 3

gives

-6b - 12c = 18 (9)

Adding (8) & (9) gives

-3c = 9

c = -3

Now we know c we can use that to calculate b in one of the previous equations.

Using (7)

-2b -4(-3) = 6

-2b = -6

b = 3

Now, b & c are known, we can use these in any equation with a to get the final unknown.

Using (1)

a - 2(3) + (-3) = -6

a = 3

Plugging a,b&c back into each (1) (2) & (3) to check you get the right answer is also a good sanity check that you've not made any mistakes in your previous working!

Answer:2

Step-by-step explanation:

Answer:

5.4

(use the pythagorean theorem, you get 5.39, round that to the nearest 10, you get 5.4.)

3)

x= 16

4)

x= 51

please ask any questions in the comments below if needed

Answer: 3. 16=X  4. X=51

Step-by-step explanation:

Okay so for number 3, both angles are the same because of the parallel lines, so you can have the angles be equal to each other. Then just do the math. Giving you 16 as the answer

For 4 the angles added up together equal 180 because of the parallel lines. So you have to make them add up and then equal to 180, at the ending the answer is 51.

The temperature of the patient will be 99.7°F.

Temperature simply means the degree of hotness and coldness that can be found in a body.

In this case, the patient's temperature is 1.1 above normal and 98.6 Fahrenheit is considered normal.

Therefore, the temperature of the patient will be the addition of the temperature given. This will be:

= 98.6 + 1.1

= 99.7°F

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Answer: I think its the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

2.5 x 7 = 17.5

10^-10 x 10^-6 = 10^(-10-6) = 10^-16

17.5 x 10^-16

1.75 x 10^-16 x 10

1.75 x 10^(-16+1)

1.75 x 10^-15

The solution of the system is, x = 9/2, y = 9/2.

System of equations?

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Consider, the given system of equations,

3x - y = 9              ..(1)

x + 3y = 18            ..(2)

From equation (1),

3x = y + 9

x = (y + 9)/3

x = y/3 + 3

Plug x = y/3 + 3 in equation (2),

y/3 + 3 + 3y = 18

10y/3 = 15

10y = 45

y = 9/2

Plug y = 9/2 in equation (1).

3x - 9/2 = 9

3x = 9 + 9/2

3x = 27/2

x = 27/6

x = 9/2

Hence, the solution of the system is, x = 9/2, y = 9/2.

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There are several methods to formulate a mathematical equation. A model, in its simplest basic form, is a quantitative declaration that two major theoretical findings are comparable.

A mathematical equation can be defined in a variety of ways. In its most basic form, a model is a mathematical assertion that indicates that two theoretical results are equal. 3x + 5 = 14, for example, is an equation inside which 3x + 5 and 14 are two formulas separated by an 'equal' sign. In mathematics, the most fundamental and elementary algebraic equations are comprised of one or more parameters.

Type of the mathematical equations are as follows:

A math statement is not the same as a maths problem. Between two arithmetic statements, a solution will always employ the equivalent (=) symbol.

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Answer: Equations can vary!

Step-by-step explanation: 1. Equations can be as simple as a math sentence with always an equal sign, make sure it balances, for example, 1+1=2

2. Equations can be complicated sometimes, with variables, but still you have to BALANCE both sides EQUALLY. One question is: 1+x=3

It seems simple and it is, and yeah you've actually done lots of equations throughout your life. Ever heard of algebra, it consists of equations, have you ever seen this 1+?=3? That's an equation with a variable that is represented as, or sometimes a box. You might take a look and say easy. I know, but the traditional steps are to take one on both sides first, but never forget what you do on one side you ALWAYS have to do to the other side. This is an easy equation question, there are going to be much more complex ones in the future.  

Answer:

Step-by-step explanation:

Effective annual interest rate is an investment’s annual rate

of interest when compounding occurs more than a year.

The effective interest rate is calculated as if compounded

annually. The effective rate is calculated in following way…..

r = effective annual rate

i = nominal rate

n = number of periods

= (1+i/n)^n -1

For example, a nominal interest rate 6% compounded

monthly is equivalent to an effective interest rate of 6.17%

So, option A is the correct answer.

Answer:

∴ He can travel 660 miles in 12 hours on the next day.

Step-by-step explanation:

Since the rate of travelling is equal on both days,

    8 hours = 440 miles travelled

    2 hours = 110 miles travelled

∴ 12 hours = 660 miles travelled

a. distribution of X is  (257,45)

b. Probability that a randomly hit fly ball travels less than 284 feet is 0.2257

c. The 70th percentile for the distribution of distance of fly balls is 290 feet.

What do you mean by normal distribution?

In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable.

It is given that we have a normal distribution with mean of 257 feet and standard deviation of 45 feet.

X be the distance in feet for a fly ball.

a. As mean of the normal distribution is 257 and standard deviation is 45 feet

Therefore, distribution of X is (257,45)

b. Probability that a randomly hit fly ball travels less than 284 feet,

P(X < 284) =

The z-score can be calculated as

z = (x - μ)/σ = (284-257)/45 = 27/45 = 0.6

So, the equivalent z-score form can be given as:

P(X < 284) = P(Z < 0.6) = 0.2257

c. The 70th percentile of the distribution of fly balls is given by a raw score such that:

P(X < x)=70%⇒ x = ?

Using formula , z = (x - μ)/σ  ⇒ x = zσ + μ

P(Z < z) = 0.7000

Now, we can use the cumulative standard normal distribution table:

z = 0.7000 + 0.04  = 0.74

Finally, the required random variable can be computed as:

x = zσ + μ  = 0.74 × 45 + 257 = 33.3 + 257 = 290.3

That means P(X < 290.3) feet =70%

Therefore, the 70th percentile of the distribution of fly balls is approximately 290 feet

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.

The lowest possible number of voters for the democratic candidate are,

3120 to 4080.

What is election?

A populace selects a person or people to hold public office through a formal group decision-making process called an election. Since the 17th century, elections have been the primary means by which modern representative democracies have been governed.

Given: A voter polling research group determined that 30% of the voters in a county would vote for the democratic candidate with a +4% margin of error.

They anticipate only 12,000 people will turn out to vote in this election.

If 12000 voters participate in the election, then 30% of them are, 3600.

Now we must add and subtract 4% of the total voters to 3600 people.

4% of the total voters = 480.

So,

3600 + 480 = 4080

3600 - 480 = 3120

Therefore, 3120 to 4080 voters represent the lowest possible number of voters for the democratic candidate.

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The cost of bag of popcorn is $7.5 and that of one drink is $5.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have Xochitl who went into a movie theatre and bought 6 bags of popcorn and 4 drinks, costing a total of $65, Alonso went into the same movie theatre and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50.

Assume that the cost of one popcorn bag is $[x] and one drink is $[y]. Then we can write -

6x + 4y = 65

9x + 8y = 107.5

Plot the graph of both equations and the points of intersection would be the solution set. Refer to the graph below. We get x = $7.5 and y = $5.

Therefore, the cost of bag of popcorn is $7.5 and that of one drink is $5.

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5)

1= 102

2= 102

3= 78

ask any questions in the comments below if needed:)

Answer:

The slope of the line is 1/2.