In 2010, the population of a city was 87,000. From 2010 to 2015, the population grew by 7.7%. From 2015 to 2020, it fell by 4.5%. To the nearest 100 people, what was the population in 2020?

Answer: C,A,D

Step-by-step explanation:

The standard form of the quadratic function that has the indicated vertex and whose graph passes through the given point is 1/36(x +4)² - 1.

Equation of a quadratic function in the vertex form is given by;

f(x) = a(x - h)² + k

Here, (h, k) is the vertex of the parabola representing the quadratic function;

Given;

Vertex of the quadratic function (−4, −1);

Parabola passes through a point  (−2, 4);

Substitute the vertex in the quadratic function;

f(x) = a(x +4)² - 1

Because, this parabola passes through a point (7, 0),

0 = a(-2- 4)² - 1

0 = 36a - 1

a = 1/36

Equation of the quadratic function will be;

f(x) = 1/36(x +4)² - 1

Therefore, equation of the quadratic function will be f(x) = 1/36(x +4)² - 1;

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Answer:

where's the figure??

Step-by-step explanation:

i think this question is incomplete

We subtract 8 from the x-coordinate and add 20 to the y-coordinate of the original point.

In mathematics, translation refers to the process of moving an object from one location to another, without rotating or scaling it. The movement is described by a vector, which is a directed line segment that specifies the direction and distance of the movement.

In two-dimensional geometry, a translation can be represented by a shift of an object along the x- and y-axes. For example, if a point is translated by a vector (a, b), its new position will be (x + a, y + b), where (x, y) is the original position of the point.

Translations can also be performed on shapes, such as lines, polygons, or curves. The effect of a translation on a shape is to create a new shape that is identical to the original shape, but located in a different position.

A translation is a transformation that moves a figure in a certain direction and by a certain distance without rotating or reflecting it. To find the rule for a translation, we need to find the vector that represents the displacement between the original point and the translated point.

Given two points A (2, -5) and A' (-6, 15), the translation vector is given by:

Translation vector = A' - A = (-6, 15) - (2, -5) = (-6 - 2, 15 - (-5)) = (-8, 20)

So, the rule for the translation is:

(x, y) -> (x - 8, y + 20)

This means that to apply the translation, we subtract 8 from the x-coordinate and add 20 to the y-coordinate of the original point.

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The first term is 2, the common difference is 2 and the sum of the first ten terms is 110

An equation is an expression that contains numbers and variables linked together by mathematical operations of addition, subtraction, multiplication, division and exponents. An equation can either  be linear, quadratic, cubic, depending of the degree of the variable.

An arithmetic term is given as:

[tex]a_n=a+(n-1)d[/tex]

where a is the first term and d is the common difference.

The 5th term and 8th term of an AP are 10 and 16. Hence:

a + 4d = 10    (1)

and:

a + 7d = 16     (2)

subtract equation 1 from 2 to get d:

3d = 6

d = 2

Common difference is 2

a + 4d = 10

a + 4(2) = 10

a = 2

First term is 2

The sum of first ten terms is:

[tex]S_{10}=\frac{n}{2} (2a+(n-1)d)=\frac{10}{2}(2(2)+(10-1)2) = 110[/tex]

The sum is 110

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Answer:

y-intercept: 5

slope: -1

equation: y = -x + 5

Step-by-step explanation:

The y-intercept is when x is 0, and it is shown on the table as 5.

The slope can be found by doing [tex]y_1-y_2/x_1-x_2[/tex], which is 6-5/-1-0 = 1/-1 = -1.

The equation is y = mx + b, so we can write it as y = -x + 5

The equation represents a direct proportion

The proportionality constant is 1.2

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

a=1.2b

The above equation is a proportional linear equation

A proportional linear equation is represented as

y = kx

Where

The constant of proportionality is k

Using the above as a guide, we have the following:

The equation a=1.2b is a direct proportion and the proportionality constant is 1.2

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Answer:

53 and 3/5's of a percent

Step-by-step explanation:

Answer:

7a - 4ab + 3b

Step-by-step explanation:

5a - 3ab + 6b - (ab - 2a + 3b)

=5a - 3ab + 6b - ab + 2a - 3b

=7a - 4ab + 3b

The expression to represent the phrase "6 times a number plus 3" is:

"6n + 3".

"n" represents an unknown number, and "6" and "3" are constants. The expression means that 6 is being multiplied by "n" to get an intermediate result, and then 3 is being added to that result to get the final answer.

For example, if n = 2, then the expression would evaluate to 6 * 2 + 3 = 12 + 3 = 15. So, the expression "6n + 3" represents the mathematical relationship between the unknown number "n" and the final result.

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Step-by-step explanation:

Step One→ Solve one equation for either x or y.

Step Two→ Substitute the expression from step one into the 2nd equation.

Step Three→ Solve the second equation for the given variable.

Step Four→ Plug you solution back into the first equation.

Step Five→ Write your solution as a point.

The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

Melissa bought some books. She spent a total of $58 after a discount of $8 off of her total purchase. Each book cost $6.

Let 'x' be the number of books. Then the equation is given as,

6x - 8 = 58

Simplify the equation, then we have

6x - 8 = 58

6x = 66

x = 11

The equation that represents the number of books will be 6x - 8 = 58. And the number of books will be 11.

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Answer/Solution:

15a^5b^15

Explanation:

First, multiply the numbers, then combine the exponents until you get the answer.

The population of bacteria after h hours is 0.075.

Bacterial growth is proliferation of bacterium into two daughter cells, in a process called binary fission. Providing no event occurs, the resulting daughter cells are genetically identical to the original cell. Hence, bacterial growth occurs. Both daughter cells from the division do not necessarily survive. However, if the surviving number exceeds unity on average, the bacterial population undergoes exponential growth.

The equation that models the population of bacteria h-hours after the original 275 bacteria were measured is given by:

P(h) = 275 × [tex](1 + 0.075)^h[/tex]

p(h)=0.075

where P(h) is the population of bacteria after h hours and 0.075 is the growth rate of 7.5% per hour.

Therefore, the population of bacteria after h hours is 0.075.

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The graph represents this inequality which has been attached below. The number line with a closed circle on the number 56 and a line shaded to the left.

In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.

The water slide is 56 feet in height. A closed and shaded circle to the left of the graph indicates the inequality x 56.

The graph showing the inequality x 56 on the number line starting at 56 is represented as a closed and shaded circle.

Thus, the required graph has been attached below.

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The probability you expect the spinner to not land on B is 0.4.

Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes

Given that, a spinner is divided into three equal parts A, B, and C.

The repeated experiment of spinning the spinner twice is simulated 125 times.

The total number of outcomes = 125

The number of favorable outcomes = 12+18+15+17+13= 75

Probability of landing on B = 75/125

= 0.6

Probability of not landing on B

= 1-0.6

= 0.4

Therefore, the probability you expect the spinner to not land on B is 0.4.

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"Your question is incomplete, probably the complete question/missing part is:"

A spinner is divided into three equal parts A, B, and C. The repeated experiment of spinning the spinner twice is simulated 125 times. A table of outcomes is shown.

Based on the table, for what probability can you expect the spinner to not land on B?

(A) 0.10

(B) 0.33

(C) 0.40

(D 0.66

Answer:

Step-by-step explanation:

I gotchu.

sinP = 5/14

       = 0.36

P = sin^-1(5/14)

P = 20.92

The quadratic equation that we need to solve is:

96 = 208 - 16t^2

And the solution is t = √7

We know that the height equation is the quadratic equation below:

h = h0 - 16t^2

If the initial height is 208, then we can write:

h = 208 - 16t^2

Now we can find how long takes to reach a height of 96 feet, then we can write:

96 = 208 - 16t^2

That is the equation we need to solve.

Solving that for t we will get:

96= 208 - 16t^2

16t^2 = 208 - 96

16t^2 = 112

t^2 =112/167

t = √7

The correct option is the last one.

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Answer: The savings per movie with the pass is $3.50 - $1.00 = $2.50. For the pass to benefit Seth's father, Seth must attend enough movies such that the total savings is equal to or greater than $40.

Let's call x the number of times Seth must attend for the pass to benefit his father. Then:

$2.50x >= $40

Solving for x:

$2.50x/$2.50 >= $40/$2.50

x >= 16

So Seth must attend at least 16 movies in order for the pass to benefit his father.

In a coin flip experiment, you would see a pattern of 50/50 heads and tails if every student in the class skewed their findings to show 5 heads and 5 tails.

This is due to the fact that each participant purposefully altered their results to display an equal number of heads and tails.

It is crucial to remember that this pattern does not accurately reflect the chances of either getting heads or tails in a fair coin flip. The results cannot be taken as a representative sample of a fair coin flip because everyone purposefully slanted their findings. It is crucial to conduct experiments with appropriate controls and prevent results bias in order to acquire reliable findings.

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The cumulative frequency and relative cumulative frequency for students who earned a score of 20 or lower on the quiz is 29; 58%. (option d)

Cumulative frequency refers to the running total of frequencies, or the sum of frequencies up to a certain point. In this case, the cumulative frequency is the number of students who scored 20 or lower on the quiz.

Relative cumulative frequency, on the other hand, expresses the cumulative frequency as a percentage of the total number of students in the sample. To find the relative cumulative frequency, we divide the cumulative frequency by the total number of students and multiply by 100.

Therefore, for students who scored 20 or lower on the quiz, the cumulative frequency is 29 and the relative cumulative frequency is 58% (29/50 * 100).

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Answer: 38, 76%

Step-by-step explanation:

Recall that for cumulative frequency we add up all the values that fall above or below a given bin of data. So, if we want all scores less than 20 it should be the first four bins with a total of:

8 plus 8 plus 13 plus 9 equals 38

To get the relative frequency we take the total in the bins for scores of 20 and lower divided by the total of all bins:

38 over 50 equals 0.76 equals 76 percent sign

This means that Tyler can type 6 words in the same amount of time it takes Kyla to type 3 words. This means that Tyler is able to type twice as many words as Kyla per minute.

1. Define a variable

We define a variable called "Tyler" to represent how many words per minute Tyler can type.

2. Write the expression to represent the problem

The expression to represent the problem is "Tyler = 3 * 2", which means that Tyler can type twice as many words per minute as Kyla, who can type 3 words per minute.

The answer is that Tyler can type 6 words per minute, which is twice as many as Kyla can type.

This means that Tyler can type 6 words in the same amount of time it takes Kyla to type 3 words. This means that Tyler is able to type twice as many words as Kyla per minute.

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Answer:

Step-by-step explanation:

The mean and standard deviation of two surveys do not give enough information to determine which statement is true. To compare the two surveys and determine which is true, you would need additional information such as the sample sizes, the confidence intervals for the means, and/or a hypothesis test comparing the means of the two surveys.

The discount amount based on 35% discount offered on $89.95 is $31.5.

The discount amount can be calculated by the formula -

Final amount = original price - discount percentage × original price

The method of solving this formula will be to first multiply followed by subtraction according to PEMDAS rule.

Now, keep the values in formula

Final amount = 89.95 - 35/100 × 89.95

Performing multiplication and division on Right Hand Side of the equation

Final amount = 89.95 - 31.48

Now performing subtraction on Right Hand Side of the equation

Final amount = $58.47

Here we see that that the discount amount is $31.48

Round to nearest penny = $31.5

Thus, the discount amount is $31.5.

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The table should be completed as follows;

Coordinate   Key feature    Does the coordinate        Justification

                                                  make sense  ___________________

(-7.565, 0)   it is a key feature          yes                     it is a zero (root).

(0, 37)          it is a key feature          yes                     it is the y-intercept.

(6, 46)          it is a key feature          yes                     it is the vertex.

A reasonable constraint for the context in set builder notation is {y|y ∈ R ≤ 46}.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two or more variable on a graph, with a maximum exponent of two (2).

In Mathematics, the y-intercept of any graph such as a quadratic function, generally occur at the point where the value of "x" is equal to zero (x = 0).

In this scenario, the y-intercept of this quadratic function can be calculated as follows;

G(x) = -1/4(x²) + 3x + 37

G(0) = -1/4(0²) + 3(0) + 37

G(0) = 37.

In conclusion, the vertex (maximum point) of this quadratic function is given by the ordered pair (6, 46).

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option B is correct, the equation or function of the graph is y≥3/4x-3.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The line passing through points (4,0) and (0,3)

Slope=3/-4=-3/4

Now let us find y intercept

0=-3/4(4)+b

0=-3+b

b=3

Hence, option B is correct, the equation or function of the graph is y≥3/4x-3.

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In a right triangle, the Pythagorean theorem states that the sum of the legs squared is equal to the hypotenuse squared.

Or that a² + b² = c²

Where and and b are the legs and c is the hypotenuse

(Note that the hypotenuse is the longest side and the legs are the two shorter sides)

Here, we are given the length of the hypotenuse as well as the length of one of the legs. Given this we are asked to find the other leg UT.

We can find the length of UT by plugging in the given values into the Pythagorean Theorem and then solving for the missing variable.

Because the given hypotenuse is 17 we can say that c = 17 and since a leg is given we can say that a = 8

Plugging this into the formula we acquire (b is UT or the other leg)

8² + b² = 17²

==> evaluate the exponents

64 + b² = 289

==> subtract 65 from both sides

b² = 225

==> take the square root of both sides

b = 15

The length of UT is 15

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The value of z is found by dividing y by x, which results in  z =[tex]-\frac{16}{63}$[/tex]

To solve for z, we can use the equation [tex]$x\cdot z = y$[/tex]. We know that [tex]$x = \frac{7}{8}$[/tex] and [tex]$y = -\frac{2}{9}$[/tex],

Therefore, we can enter these values into the equation as substitutes:

[tex]$\frac{7}{8} \cdot z = -\frac{2}{9}$[/tex]

Next, In order to separate z, we must divide both sides of the equation by [tex]$\frac{7}{8}$[/tex]:

[tex]$z = \frac{-\frac{2}{9}}{\frac{7}{8}}$[/tex]

To divide by[tex]$\frac{7}{8}$[/tex], The fraction can be rotated, then multiplied by its reciprocal, which is [tex]$\frac{8}{7}$[/tex]

[tex]$z = \frac{-\frac{2}{9}}{\frac{7}{8}} \cdot \frac{8}{7}$[/tex]

The fraction on the right can be made simpler as follows:

[tex]$z = -\frac{2}{9} \cdot \frac{8}{7} = -\frac{16}{63}$[/tex]

So, The value of z is found by dividing y by x, which results in  z =[tex]-\frac{16}{63}$[/tex]

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