Simplify
(y + 1)
(y + 1)?

Answer:

Step-by-step explanation:

This is an exponential function of the form:

\(y=a(1-r)^x\) where a is the initial value and (1 - r) is the growth rate (which in our case is a decay, actually!). Our initial value is 75000 and our rate of change in the population is 15% or .15. Filling in our model:

\(y=75000(1-.15)^x\) and simplifying:

\(y=75000(.85)^x\) This turns out to be a decay problem because the value inside the parenthesis is less than 100%.

x is our time, so the model is as stated above.

Answer:

Look below

Step-by-step explanation:

The answer would be (0,2) or (2,2)

Please mark me as brainliest

Answer:

1,3

Step-by-step explanation:

first off let's take a looksie at the picture above, hmmm the vertex is at (-1 , 0) and it has another point at (0 , 1) ok hmmm

\(~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{a~is~negative}{op ens~\cap}\qquad \stackrel{a~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=0\\ \end{cases}\implies y=a(~~x-(-1)~~)^2 + 0\hspace{4em}\textit{we also know that} \begin{cases} x=0\\ y=1 \end{cases}\)

\(1=a(~~0-(-1)~~)^2 + 0\implies 1=a(1)^2\implies 1=a \\\\\\ y=1(~~x-(-1)~~)^2 + 0\implies {\Large \begin{array}{llll} y=(x+1)^2 \end{array}}\)

Answer:

96sq ft. u just multiple the length by the height then square it

Answer: 200 cats in total

Step-by-step explanation:

60 calico cats represents 30% of the total cat population in the shelter.

That means that if we find 30% of the total number of cats, the number we will get is 60.

Assuming the total is x, representing this in equation form makes it:

x * 30% = 60

x = 60 / 30%

x = 200 cats in total

Answer:

Step-by-step explanation:

\(\frac{g}{f} (x)=\frac{g(x)}{f(x)} \\=\frac{3x^2+x}{4x} \\=\frac{x(3x+1)}{4x} \\=\frac{3x+1}{4}\)

The correct answer could be either a) 3π/2 or b) 7π/6

To find the value of x, we need to use the inverse of the secant function, which is the cosine function.

Given that sec(32π + x) = 2, we can rewrite it as:

1/cos(32π + x) = 2

Now, we can take the reciprocal of both sides to obtain:

cos(32π + x) = 1/2

To find the value of x, we need to determine the angle whose cosine is 1/2. This corresponds to an angle of π/3 or 2π/3.

Therefore, x can be equal to either:

a) 3π/2 + π/3 = 5π/6

or

b) 3π/2 + 2π/3 = 7π/6

So, the correct answer could be either a) 3π/2 or b) 7π/6, depending on the specific range or interval you are considering for the value of x.

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The Probability of red light is 0.3

P(red) = 0.3

The probability that out of the next eight eastbound cars that arrive randomly at the light, exactly three will be stopped by a red light be 0.25.

P(exactly three get stopped by red light)=0.25

The correct option is (d) P(red)=.3,P(exactly 3 get stopped)=.25

A binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.

The occurrence,

p= probability of a red light

 =\(\frac{15}{15+5+30}\)

 = \(\frac{15}{50}\)

 = 0.3

Hence, Probability of getting red light be,

P (red)= 0.3

Now, the Binomial distribution formula,

Probability=( \(_r^nC\))\(\;p^{r} \;q^{n-r}\)

where, r = number of times for a specific outcome within n trials

\(_r^nC\)   = number of combinations

p = probability of success on a single trial

q = probability of failure on a single trial

n = number of trial

According to question,

          = 1- 0.3

          = 0.7

Now using the formula, ( \(_r^nC\))\(\;p^{r} \;q^{n-r}\)

P( exactly 3  get stopped) = ( \(_3^8C\))\(\;(0.3)^{3} \;(0.7)^{8-3}\)

                                            = \(\frac{8!}{3!(8-3)!}\) \((0.027) \; (0.7)^{5}\)

                                           =  \(\frac{8!}{3!(5)!}\)\((0.027) \; (0.16807)\)

                                           = \(\frac{8 * 7 * 6 }{3 * 2}\) x 0.027 x 0.16807

                                           = 56 x 0.00453789

                                           = 0.25412184

                                          ≈ 0.25

Hence, Probability of next eight eastbound so that exactly three will stopped by a red light be 0.25.

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Answer:

its 12cm

Step-by-step explanation:

Answer:

P' = (2, -6)

Step-by-step explanation:

In this translation, you just need to substitute x and y into the given translation to find what P' is. (x is -6 since it's the x-value of P, and y is -2 since it's the y-value of P):

where T(x, y) = (x + 8, y - 4) and x = -6 and y = -2,

T(-6, -2) = ((-6) + 8), (-2) - 4) (substitute x and y into the translation)

T(-6, -2) = (2, -6) (add and subtract)

So, P' = (2, -6)

The relative frequency of students that are of the 1 to 5 class and are left-handed is 40%.

Relative frequency is the ratio of the number of times an event occurs to the number of trials. This can be expressed as a fraction, a percentage, or a proportion.

This can be calculated using the following equation:

Relative Frequency = (Number of Left-Handed Students in 1 to 5 Class / Total Number of Students in 1 to 5 Class) x 100

Relative Frequency = (17 / (17 + 25)) x 100

Relative Frequency = 40%

This calculation shows that 40% of students in the 1 to 5 class are left-handed. This percentage can be rounded to the nearest whole percentage, giving the answer of 40%.

By comparing the relative frequency of left-handed students in the 1 to 5 class to the relative frequency in the other classes, it can be seen that the 1 to 5 class has the highest relative frequency of left-handed students.

This could be due to the developmental stage of students in this age group, as studies have shown that being left-handed is more common in children aged 5 to 10 than in adults.

Alternatively, it could be due to cultural factors, such as left-handed students feeling more comfortable in the 1 to 5 class due to the younger age group.

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The bird settles on the branch at the rate of 2.33 meters per second.

The rate of change refers to the traveling speed of the bird when perching on the branch.

The rate of change (which is speed) is the distance (altitude) divided by time.

The bird's flying altitude above ground = 10 meters

Time in seconds to settle on a branch = 3 seconds

The altitude above ground after settling on the branch = 3 meters

The change in altitude = 7 meters (10 - 3)

Rate of change = 2.33 meters per second (7/3)

Thus, the rate of change that the bird used to settle on the branch is 2.33 meters per second.

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Answer:

-2.33

Step-by-step explanation:

Answer:

B. y = 4x + 3

Step-by-step explanation:

Slope - intercept form is y = mx + b

m is the slope and b is the y - intercept

The slope is 4, so y = 4x + b

The y - intercept is 3, so y = 4x + 3

I hope this helps :)

The probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

The given probability distribution table shows the probabilities of having 1, 2, or 3 computers in a randomly selected home in Queens. However, the probability of having 4 or more computers is not given in the table.

To find the probability of having 4 or more computers in a randomly selected home, we can use the complement rule. The complement rule states that the probability of an event happening is equal to 1 minus the probability of the event not happening. In this case, the event we are interested in is having 4 or more computers in a home, and the complement of this event is having 1, 2, or 3 computers in a home.

So, the probability of having 4 or more computers in a randomly selected home in Queens can be calculated as:

P(4 or more) = 1 - P(1 or 2 or 3)

P(1 or 2 or 3) = P(1) + P(2) + P(3) = 0.4 + 0.3 + 0.2 = 0.9

P(4 or more) = 1 - 0.9 = 0.1

Therefore, the probability that a randomly selected home in Queens has 4 or more computers is 0.1 or 10%. The correct answer is (b) 0.10.

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Answer:

about $0.13

Step-by-step explanation:

Answer:

13 cents

Step-by-step explanation:

1.59 divided by 12

X, y, z denote children's movies, western movies, and horror movies, respectively. The related system of equations is formed and solved.

\(\left\{\begin{matrix} \qquad\qquad\ \dfrac{60}{100}x + \dfrac{50}{100}y =\dfrac{30}{100}(x+y+z)\\ \dfrac{20}{100}x+ \dfrac{60}{100}y+ \dfrac{60}{100}z= \dfrac{1}{2}(x+y+z) \\ \ \ \ x+100=y \end{matrix} \right.\\)

Simplifying the system of equations, we have

\(\left\{\begin{matrix} 3x + 2y -3z=0\\ -3x+ y+ z= 0 \\ \ \ \ x+100=y \end{matrix} \right.\ \ \Longrightarrow \ \left\{\begin{matrix} 5x-3z=-200\\ -2x+ z= -100 \end{matrix} \right.\\)

\(\ \ \ 5x-3z=-200\\\underline{-6x+3z=-300} \ \Rightarrow \ x=500\\\ \ -x+0= \ 500\)

                                       \(y&=500+100=600\\ z&=3(500)-600=900\)

The video store has 500 children's movies, 600 westerns and 900 horror movies.

The area between two negative scores can be found by taking the absolute difference between the two scores.

The area between two negative scores can be found by taking the absolute difference between the two scores. This is because the absolute difference gives us the distance between the two scores without considering their signs.

To calculate the area between two negative scores, follow these steps:

1. Identify the two negative scores.
2. Subtract the smaller negative score from the larger negative score.
3. Take the absolute value of the result to remove the negative sign.
4. The absolute difference between the two negative scores represents the area between them.

For example, let's say we have two negative scores, -5 and -10. To find the area between them, we subtract -5 from -10, resulting in -10 - (-5) = -10 + 5 = -15. Since we are interested in the distance, we take the absolute value of -15, which gives us 15. Therefore, the area between -5 and -10 is 15.

The absolute difference between two negative scores gives us the area between them. This approach is applicable whenever we want to find the distance or area between any two numbers, not just negative scores.

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Answer:

Step-by-step explanation:

a) $3.30/6kg = 0.55 dollars per kilogram

b) 448km/7h = 64 kiliometres per hour

For each unit rate, divide the units in where usually the biggest one is on top

Have a good one

Answer:

Vertically opposite angles are equal

So

x = 75°

Vertically opposite angles are equal

So

5y = 135°

Divide both sides by 5

y = 27

Hope this helps you

Answer:

Step-by-step explanation:

Simplify: (x + 3)*(+ 2)

(x + 3)*(+ 2) =

2x + 6

Inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process.

Inverse distance weighting is a method used in geostatistics to estimate values at unsampled locations based on values at surrounding sample locations. It works by assigning weights to the sample points based on their proximity to the unsampled point. The closer a sample point is to the unsampled point, the higher its weight. The weights are then used to calculate a weighted average of the sample values, which is used as the estimate for the unsampled location.
The benefit of inverse distance weighting over a simple average is that it takes into account the spatial variability of the data. A simple average treats all sample points equally, regardless of their distance from the unsampled point. This can lead to inaccurate estimates if there is a high degree of spatial variability in the data. In contrast, inverse distance weighting gives more weight to sample points that are closer to the unsampled point, which is likely to provide a more accurate estimate.
Another advantage of inverse distance weighting is that it allows for the incorporation of multiple variables into the estimation process. For example, if there are two variables of interest (e.g., temperature and precipitation), inverse distance weighting can be used to estimate values for both variables simultaneously. This is not possible with a simple average.
Overall, inverse distance weighting is a useful tool for estimating values at unsampled locations in geostatistics. Its ability to account for spatial variability and incorporate multiple variables makes it a powerful technique for analyzing spatial data.

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Answer:

y=14-2x; 6x+3y=42

2x+y=17; -6x=3y-51

Step-by-step explanation:

Dependent equations will have infinite solutions. One way to tell if a system of equations is dependent is to put all of the equations into standard form. Here, we can use the form ...

 ax + by = c

where a, b, c are mutually prime integers and "a" is positive. When dependent equations are put in this form, they resolve to the same equation.

Here, the rearrangement is accomplished by putting the x- and y-terms on the same side of the equal sign, with the x-term having a positive coefficient. If necessary, the constant is put on the other side, and any common factors removed from all of them.

Then the sets of equations are ...

2x +5y = 31

6x -y = 13 . . . . not dependent

__

2x +y = 10

6x +3y = -7 . . . . not dependent

__

2x +y = 14

2x +y = 14 . . . . dependent

__

2x +y = 13

4x -3y = -19 . . . . not dependent

__

2x +y = 14

x +2y = 13 . . . . not dependent

__

2x +y = 17

2x +y = 17 . . . . dependent

__

The 3rd and 5th sets of equations are dependent, so have infinite solutions.

_____

The second set of equations is inconsistent, so has no solutions.

The function that is likely the best fit is given as follows:

Logarithmic regression.

The function of a best fit is a logarithmic regression, as the function starts with a fast increasing rate until it approaches the vertical asymptote.

As for the other options, we have that:

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The Fundamental Rule can be used over a set of categories when one or more out of several choices in each of the categories is to have opted.

The fundamental counting principle is a rule used to count the total number of possible outcomes in a situation. It states that if there are n ways of doing something, and m ways of doing another thing after that, then there are n × m ways to perform both of these actions.

For example : consider an example of a person who runs a business of sewing neckties. he can make ties to be unique based on the following factors: color, shape and design. suppose he has a choice of 5 colors, 3 shapes and 4 different design patterns. To find the number of unique ties he can make, it becomes a complex calculation if we are counting by the traditional method. So , in this case, the number of ties the person can stick with the available combination is calculated using the Fundamental Principle of counting definition as:

total number of unique ties = 5× 3× 4

                                              = 60
We assume that we are using the English alphabet with 26 distinct letters.

we consider our question to be a 4 steps process. We can accomplish the first step in 02 ways( since it must be can S or T). The second step can also be accomplished in 02 ways ( since it must also be on s or T). The third step can be accomplished in 10 ways ( since there are no restrictions on choice of letter for this step) and the last step can also be accomplished in 10 ways ( since there are no restrictions on choice of letter for this step).

Hence, the total number of ways to accomplish the entire process is 2.2.10.10 = 400 ways. That is, there are 400 different four letter secret codes that can be formed if the first letter must be an S or T.

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Answer:

let number be x

30=5% of X

3000=5x

X=600

so,5% of 600 is 30

Answer:

Step-by-step explanation:

1. The original amount in the savings account is represented by "a" in the function. Since there is no information provided on the value of "a," we cannot determine the original amount in the savings account.

2. The function shows that the savings account grows by a factor of 1.013 for each day that passes. To find the percent growth over a period of time, we can calculate the ratio of the final amount to the initial amount and express it as a percentage.

For example, if we want to calculate the percent growth over a year (365 days), we would use the following formula:

percent growth = (f(365) / f(0) - 1) x 100%

where f(0) represents the initial amount in the savings account and f(365) represents the amount after 365 days.

Using the function f(x) = 2000(1.013), we can calculate:

f(365) = 2000(1.013)^365 ≈ 2559.16

f(0) = 2000

percent growth = (2559.16 / 2000 - 1) x 100% ≈ 28%

Therefore, the savings account grows by approximately 28% per year.

3. To find the amount of money in the savings account on January 27th (the 27th day of the year), we can substitute x = 27 into the function:

f(27) = 2000(1.013)^27 ≈ 2043.54

Therefore, on January 27th, you would have approximately $2043.54 in your savings account.

a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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\(5 + n = 12 \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \)

If a triangle has a perimeter of 48 kilometers. Two of the sides measure 12 kilometers and 20 kilometers. The length of the third side is 16.

Let x km represent  the length of the third side

Let Length of other two sides is  12 km  and  20 km.

Hence,

Perimeter of triangle = Sum of all sides =  48 km

12 + 20 + x = 48

32 +x = 48

x = 48 - 32

x = 16

Therefore we can conclude that the length of the third side is 16.

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