Write an exponential function to model the following situation: A population starting at 740 animals
decreases at an annual rate of 12%. Use your function to determine about how many animals there will
be after 5 years.
A. 390
B. 150
CC. 680
D. 340

Answer:

r=

\(r = \frac{d}{2} \\ r = \frac{5}{2} \\ r = 2.5cm\)

Answer: I think 134.4

Step-by-step explanation:

Answer:

160

Step-by-step explanation:

The paint in the pot is an illustration of a linear equation and the weight of the full pot is 11.2 kg

The given parameters can be represented using the following ordered pairs:

(x,y) = {(0.5, 5.8) and (0.25, 3.1)}

The slope of the equation is calculated using:

m = (y2 - y1)/(x2 - x1)

This gives

m = (3.1 - 5.8)/(0.25 - 0.5)

Evaluate

m = 10.8

The equation is then calculated using:

y = m(x - x1) + y1

This gives

y =  10.8(x - 0.5) + 5.8

Expand

y =  10.8x + 0.4

When the pot is full, we have x = 1

So, the equation becomes:

y =  10.8 * 1 + 0.4

Evaluate

y =  11.2

Hence, the weight of the full pot is 11.2 kg

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Solving a system of equations we can see that the washer costs $750, and the dryer costs $250.

Let's define the variables:

x = cost of the washer.

y = cost of the dryer.

We know that the cost combined is $1000, then:

x  + y = 1000

And the washer cost 3 times the cost of the dryer, then we will get:

x = 3y

So we have a system of equations, we can replace the second equation into the first one, so we will get:

3y + y = 1000

4y = 1000

y = 1000/4

y = 250

The cost of the washer is:

x = 3*250 = 750

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Answer:

B

Step-by-step explanation:

BBBB

The solution to the system of equations is x = 4 and y = 0. In summary, the correct substitution step for the system is: -4x - 6(x - 4) = -16 .C answer is correct

To solve the given system of equations:

1) y = x - 4

2) -4x - 6y = -16

We can use the substitution method to eliminate one variable and solve for the other.

Step 1: Solve the first equation (1) for y in terms of x.

  y = x - 4

Step 2: Substitute the expression for y from equation (1) into equation (2).

  -4x - 6(x - 4) = -16

Step 3: Simplify and solve for x.

  -4x - 6x + 24 = -16

  -10x + 24 = -16

  -10x = -16 - 24

  -10x = -40

  x = -40 / -10

  x = 4

Step 4: Substitute the value of x back into equation (1) to solve for y.

  y = 4 - 4

  y = 0

Therefore, the solution to the system of equations is x = 4 and y = 0.

In summary, the correct substitution step for the system is:

-4x - 6(x - 4) = -16

By substituting the expression for y from equation (1) into equation (2) and simplifying, we obtain the equation -4x - 6y = -16, which can be further solved to find the values of x and y. C answer is correct

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There is a unique solution (x = 0, y = 5) that satisfies both equations, the system of equations has one solution. There is a unique solution (x = 0, y = 5) that satisfies both equations, the system of equations has one solution.

To determine the number of solutions for the given system of equations:

y = -2x + 5

4y + x - 20 = 0

We can solve the system of equations using various methods such as substitution, elimination, or graphing. Let's solve it using the elimination method:

First, we'll multiply the first equation by 4 to make the coefficients of x in both equations equal:

4y = -8x + 20

4y + x - 20 = 0

Next, we'll subtract equation 1 from equation 2 to eliminate the y term:

(4y + x - 20) - (4y = -8x + 20)

This simplifies to:

x = 0

Now, we substitute this value of x back into the first equation to find the value of y:

y = -2(0) + 5

y = 5

we have found the values x = 0 and y = 5, which satisfy both equations simultaneously.

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Mrs. Wu initially had $1062.40.

Let's break down the given information step by step:

1. Mrs. Wu spent 1/6 of her money on a dress and 2 blouses.

  Let's assume Mrs. Wu's total money is represented by the variable M. She spent 1/6 of M on the dress, which means she spent (1/6)M on the dress and the same amount on two blouses.

2. The dress cost 3 times as much as each blouse.

  Let's assume the cost of each blouse is represented by the variable B. Therefore, the cost of the dress would be 3B.

3. Mrs. Wu spent 3/4 of her remaining money on a watch.

  After spending on the dress and blouses, Mrs. Wu has (M - (1/6)M) = (5/6)M remaining. She spent 3/4 of this remaining money on a watch, which is (3/4) * (5/6)M = (15/24)M.

4. She spent $220.50 more on the watch than on the dress.

  The amount spent on the watch is (15/24)M, and the amount spent on the dress is (1/6)M. The difference between these amounts is $220.50.

To find the value of M, we can set up an equation:

(15/24)M - (1/6)M = $220.50

Simplifying the equation:

(15/24 - 1/6)M = $220.50

(5/24)M = $220.50

Multiplying both sides by (24/5):

M = $220.50 * (24/5)

M = $1062.40

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Here is the attached image for the answer. If you write it in in slope-intercept form, y=mx+b. You will get the answer below in the attached image.

Answer:

P = \(\frac{91}{703}\) ≅ 12.95%.

Step-by-step explanation:

The total amount of chocolates in the box is 8 + 16 + 14 = 38, 14 of which are solid.

Let's calculate the probability of getting a solid chocolate in the first selection:

\(P(1S) = \frac{14}{38} = \frac{7}{19}.\)

Given that the first piece was solid, there are now 37 pieces of chocolate in the box, 13 of which are solid. Let's now calculate the probability of selecting another solid chocolate:

\(P(2S\,|\,1S) = \frac{13}{37}.\)

Thus, the probability of selecting two solid chocolates in a row is the product of the two probabilities calculated above:

\(P = \frac{7}{19}\,.\,\frac{13}{37} = \frac{91}{703}.\)

Answer:

0.9 = 90% probability that the suspect actually committed the crime.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

\(P(B|A) = \frac{P(A \cap B)}{P(A)}\)

In which

P(B|A) is the probability of event B happening, given that A happened.

\(P(A \cap B)\) is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Charged

Event B: Committed the crime.

16% of crimes of this type end up in a criminal charge.

This means that \(P(A) = 0.16\)

Probability of being charged and committing the crime:

90% of 16%, so:

\(P(A \cap B) = 0.9*0.16\)

What is the chance that the suspect actually committed the crime?

\(P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.9*0.16}{0.16} = 0.9\)

0.9 = 90% probability that the suspect actually committed the crime.

Answer:

7  4/5

Step-by-step explanation:

= 13/5  x  3

= 39/5

= 7  4/5

Here we have a combination without repetition (the order doesn't matter but you can repeat an athlete). The formula is:

Where n is the total number of athletes, and r is the number of athletes you have to select, then n=7 and r=4, then:

Thus, 35 four-person relay teams can be selected among the seven athletes.

The expected value ( mean) of the sample proportion is 50 that is shown in a step-by-step manner.

Step: 1

21- It is claimed that 25 % of students who take Algebra get

an A in the course. i.e.,  = 0.25

If a random sample of =200 students is selected.

The expected value ( mean) of the sample proportion

= n x p

= 0.25*200

= 50

An average of n numbers computed by adding some function of the numbers and dividing by some function of n. Expected value (also known as EV, expectation, average, or mean value) is a long-run average value of random variables. It also indicates the probability-weighted average of all possible values. Expected value is a commonly used financial concept

The expected value ( mean) of the sample proportion is 50.

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As a result, the point on the number line that represents 10 miles would be much more to the right and outside the bounds of the image.

The line number 10.12, for instance, refers to page 10, line 12. The part of the line number to the left of the period is referred to as the "page" or "part," and the part to the right is referred to as the "line."

A number line is a representation of numbers along a straight line. It acts as a template for grouping and contrasting numbers. Any real number, including all whole numbers and natural numbers, can be represented by it.

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Question:

The distance from Cory's home to the library is mile. Which point is at on the number line?

A. Point A

B. Point B

C. Point C

D. Point D

Answer: 43% (rounded)

:

The percentile of 6.2 in the given data set is 40%.

To determine the percentile of 6.2 in the given data set, we can use the following steps:

Arrange the data set in ascending order:

4.2, 4.6, 5.1, 6.2, 6.3, 6.6, 6.7, 6.8, 7.1, 7.2

Count the number of data points that are less than or equal to 6.2. In this case, there are 4 data points that satisfy this condition: 4.2, 4.6, 5.1, and 6.2.

Calculate the percentile using the formula:

Percentile = (Number of data points less than or equal to the given value / Total number of data points) × 100

In this case, the percentile of 6.2 can be calculated as:

Percentile = (4 / 10) × 100 = 40%

The percentile of 6.2 in the sample data set is therefore 40%.

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The required value of y for the given segment AB is given as y = 16, -8.

A line is a straight curve connecting two points or more showing the shortest distance between the initial and final points.

here,
A(0, 4), B(5, y), and AB = 13.

Applying the distance formula,
D = √[[x₂ - x₁]² + [y₂- y₁]²]

Substitue the value in the above expression,
13 = √[[5 - 0]² + [y - 4]²]
169 = 25 + [y - 4]²
[y - 4]² = 144
y - 4 = ± 12

y = 16, -8

Thus, the required value of y for the given segment AB is given as y = 16, -8.

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The growth rate of the population, given the initial population and the population after 10 years is 12. 5 % every 10 years.

To find the percent change or growth rate of a quantity between two different values, you can use the formula:

Percent change = ( new value - old value ) / old value x 100%

The new value would be the population of the village after 10 years which is 450 people.

The old value is the initial population of the village which is 400

The growth rate of the population is:
= ( 450 - 400 ) / 400 x 100 %

= 12. 5 %

The growth rate for the village is therefore 12. 5 % every ten years.

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Answer:

\(y=-4x+5\)

Step-by-step explanation:

The equation of a line with slope \(m\) and \(y\)-intercept \((0,b)\) is \(y=mx+b\).

The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

2.06

Step-by-step explanation:

The formula for critical value = Margin of Error / Standard Error

Margin of Error = z × Standard deviation/√n

Mean for the month of March = $305.30

Standard deviation = $46.50

n = number of samples = 26 homes

z score for 95% confidence interval = 1.96

= 1.96 × $46.50/√26

= 17.874024556

Standard error = standard deviation/√n

= $46.50/√26

= 9.1194002839

Critical value = Margin of Error/Standard Error

= 17.874024556/9.1194002839

= 2.06

Answer:

x= y+2/3+4

Step-by-step explanation:

Answer:

S = {(3,p), (3,0), (4,q), (1,4)} is a set of ordered pairs, where the first element of each ordered pair is an integer and the second element is a variable. The set consists of four ordered pairs:

(3,p): The first element is 3 and the second element is p.

(3,0): The first element is 3 and the second element is 0.

(4,q): The first element is 4 and the second element is q.

(1,4): The first element is 1 and the second element is 4.

Answer:

No graph was put in, but heres a helpful answer.

Step-by-step explanation:

There is no graph, but

Y=-1(2x-2)+1

y=-2x+2+1

y=-2x+3

The required graph has been attached below that represents the equation of the parabola y = – (x – 1)² + 1.

A parabola is a U-shaped curve this is drawn for a quadratic function,

f(x) = ax² + b x + c.

The graph of the parabola is downward (or opens down), when the price of a is much less than 0, a < 0. The graph of the parabola is upward (or opens up) when the value of a is more than 0, a > 0.

The equation of the parabola is given in the question, as follows:

y = – (x – 1)² + 1

As we know that parabola is, an open curve is a conic segment produced via the intersection of a proper circular cone and a plane parallel to an element of the cone.

Here, (1,1) is most likely to be the relative maximum for this graph.

The required graph has been attached below that represents the equation y = – (x – 1)² + 1.

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Answer:

x>9

Interval!

(9,infinty)

Step-by-step explanation:

2x>18

divide by 2

x>9

This means that the interval is

(9,infinty) because after 9 x exists, whereas from (-infinity, 9) x does not exist

The function g(x) in the form a(x-h)^2 + k is: \(g(x) = (x + 2)^2 - 4\)

Starting with\(f(x) = x^2\), the translation 2 units left and 4 units down would result in the following transformation:

g(x) = f(x + 2) - 4

Substituting\(f(x) = x^2:\)

\(g(x) = (x + 2)^2 - 4\)

Expanding the square:

\(g(x) = x^2 + 4x + 4 - 4\)

Simplifying:

\(g(x) = x^2 + 4x\)

Now we need to rewrite this expression in the form \(a(x-h)^2 + k.\) To do this, we will complete the square:

\(g(x) = x^2 + 4x\\g(x) = (x^2 + 4x + 4) - 4\\g(x) = (x + 2)^2 - 4\)

Therefore, the function g(x) in the form a(x-h)^2 + k is:

\(g(x) = (x + 2)^2 - 4\)

Where a = 1, h = -2, and k = -4.

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The equation to model the given work is 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.

The teams will share 5.4 liters of olive oil. To find out how much each team will receive, we can divide the total amount of olive oil by the number of teams:

5.4 liters ÷ 10 teams = 0.54 liters per team

However, it's usually more convenient to express this in grams for equation, so we need to convert liters to grams.

The conversion factor for olive oil is approximately 0.92 grams per milliliter (or 920 grams per liter). So, we can multiply 0.54 liters per team by 920 grams per liter to get:

0.54 liters per team × 920 grams per liter = 497.28 grams per team

Therefore, each team will receive 497.28 grams of olive oil as per the work.

Equation: 5.4 liters / 10 teams = 0.54 liters per team, and 0.54 liters per team × 920 grams per liter = 497.28 grams per team.

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