The graph shows g(x), which is a translation of
f(x) = = x². Write the function rule for g(x).
-10 -8 -6 -4
-2
104
-8-
-6-
-4-
2-
0
-2-
-4-
-6
-8-
-10₂
2
4
6
8
Write your answer in the form a(x − h)² + k,
where a, h, and k are integers or simplified
fractions.
g(x) =?

In a population of rabbits that has reached carrying capacity, the growth curve would exhibit logistic growth.

Logistic growth is characterized by an S-shaped curve, which represents a rapid initial growth followed by a slowed growth rate as the population approaches its carrying capacity.

The carrying capacity is the maximum number of individuals that an environment can support, taking into account factors such as food availability and habitat space.

In this situation, the rabbit population would experience density-dependent factors, such as competition for resources, which would limit their growth and maintain the population around the carrying capacity.

Eventually, the growth curve would stabilize, with the population size fluctuating slightly around the carrying capacity due to environmental factors or other influences.

Learn more about logistic growth at

https://brainly.com/question/29765933

#SPJ11

The solution is : Mrs Davis earns 3,150 on her investment.

We have,

The amount of interest earned by the account is found using the interest formula:

 I = Prt . . . .

where,

P is the principal invested at rate r for t years

we get,

Using the given values, we find the interest to be ...

 I = 15,000×0.07×3

  = 3,150

Mrs Davis earns 3,150 on her investment.

Learn more about interest here:

brainly.com/question/13324776

#SPJ1

complete question:

Mrs Davis invests 15,000 into a savings account that pays 7%interest for 3 years how much interest does mrs Davis earn

if you assume 2 person in the centre

there are 4! possibilities that other people can ve sorted.

but the 2 person can sit in 2 ways.

so the answer is 4!.4

= 96

Answer: 45.580

Explanation: x=2279/50=45.580

The answer to the subtraction of the numbers 698000003120006200130 and 299900503811873452 is 39809949918812678.

Subtraction is an arithmetic operation that involves finding the difference between two numbers. It is the process of taking away a quantity from another quantity, or finding the result when one quantity is subtracted from another.

According to the given information:

Let's subtract the numbers step by step.

First, let's align the numbers vertically, lining up the digits by place value:

698000003120006200130

     - 299900503811873452

Now, let's start subtracting from the rightmost digit (the ones place) to the leftmost digit (the highest place value).

Step 1: Subtract the ones place:

0 - 2 = -2. Write -2 in the ones place and borrow 1 from the tens place of the first number.

Step 2: Subtract the tens place:

1 (after borrowing) - 5 = -4. Write -4 in the tens place and borrow 1 from the hundreds place of the first number.

Step 3: Subtract the hundreds place:

2 (after borrowing) - 4 = -2. Write -2 in the hundreds place and borrow 1 from the thousands place of the first number.

Step 4: Continue this process for each place value, borrowing as necessary:

(No borrowing needed for the next few steps)

Step 5: Finally, subtract the numbers in the highest place value:

6 - 2 = 4. Write 4 in the highest place value.

So, the result of the subtraction is 39809949918812678.

To know more about subtraction visit: https://brainly.com/question/2346316

#SPJ1

The rewritten function after completing the square is h(x) = 4(x - 4.5)² - 81

To complete the square and rewrite the function in the desired form, we can follow these steps, Factor out the leading coefficient of the quadratic term (in this case, 4) from the first two terms:

h(x) = 4(x² - 9x) + 81

To complete the square, we need to add and subtract a constant term inside the parentheses that will make the expression a perfect square trinomial. To determine this constant term, we can take half of the coefficient of the x-term, square it, and add it to the expression. Half of -9 is -4.5, so we have,

h(x) = 4(x² - 9x + (-4.5)² - (-4.5)²) + 81

Simplify the expression inside the parentheses by combining like terms and factoring the perfect square trinomial,

h(x) = 4((x - 4.5)² - 20.25) + 81

Distribute the 4 and simplify,

h(x) = 4(x - 4.5)² - 81

Therefore, the function h(x) can be rewritten in the desired form as:

h(x) = 4(x - 4.5)² - 81

To know more about completing the square, visit,

https://brainly.com/question/13981588

#SPJ1

Answer:

s^45/t^81

Step-by-step explanation:

Answer:

a. x²-1

b. x²+x-6

c. x²-4x+4

Step-by-step explanation:

a. (x+1)(x-1)

   x²-x+x-1

   x²-1

b. (x-2)(x+3)

   x²+3x-2x-6

   x²+x-6

c. (x-2)²

   (x-2)(x-2)

   x²-2x-2x+4

   x²-4x+4

Answer: B

Step-by-step explanation: As slope is "rise over run", and only B has a decreasing rise (y-value), it must be the only one with a negative slope.

The probability that the age of that student will be 15 years is 0.18.

The probability that the age of that student will be 16 years or older is 0.62.

We know that if frequency of a certain value is f and total number of bservations is n, then relative frequency is f/n. It can be treated as probability of the occurence of that value.

(a) Let X denotes the age of selected student.

(i) P( age of that student will be 15 years)= P(X=15)= 0.18

(ii) P( student is 16 years of age or older)= P(X=16)+P(X=17)+P(X=18)= 0.22+0.27+0.13= 0.62

(b) If 1200 students are selected, then number of students with age 15 years= 1200× 0.18 = 216

Learn more about probability on

https://brainly.com/question/24756209

#SPJ1

The mathematical term used to designate a trapezoid (or trapezium in the UK) having its two non-parallel sides of equal length is an isosceles trapezoid.

The mathematical term used to designate a trapezoid having its two non-parallel sides of equal length is called an isosceles trapezoid or isosceles trapezium in the UK.

This shape is also sometimes referred to as a regular trapezoid, but the term "isosceles trapezoid" is more commonly used.

A trapezoid is a four-sided polygon that has two parallel sides and two non-parallel sides. The parallel sides of a trapezoid are called the bases, and the non-parallel sides are called the legs. The distance between the bases is called the height of the trapezoid.

The area of a trapezoid is given by:

Area = ((base1 + base2) x height) / 2

where base1 and base2 are the lengths of the two parallel sides, and height is the distance between the parallel sides.

Know more about trapezoid here:

https://brainly.com/question/1410008

#SPJ11

Answer:

x divided by 2 times 2 simplifies to x.

Step-by-step explanation:

Answer:

The expression "x divided by 2 times 2" can be simplified as follows: x / 2 * 2 = x * (2 / 2) = x * 1 = x

Therefore, the answer is x.

Step-by-step explanation:

The drawing of the front elevation of the figure is added as an attachment, as required

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

The figure

The side elevation has been drawn

This means that we need to draw the front elevation

From the figure, we can see that

The front elevation is a rectangle with the dimension of 2m by 0.5m

This implies that we draw a rectangle with the dimension of 2m by 0.5m

See attachment for the required figure of the front elevation of the figure

Read more about dimensions at

https://brainly.com/question/27404871

#SPJ1

The lateral surface area and volume of the shape will be 2405.4 square feet and 10,324.6 cubic feet, respectively.

Given information:

Base length, a = 34 ft and b = 10 ft

Height, h = 24.7 ft

Slant height, l = 27 ft

Width, w = 19 ft

The volume of the shape is calculated as,

V = 1/2 x (34 + 10) x 24.7 x 19

V = 10,324.6 cubic feet

The surface area is calculated as,

SA = 2(19 x 27) + 1/2 x (34 + 10) x 24.7 + 10 x 19 + 34 x 19

SA = 1026 + 543.4 + 190 + 646

SA = 2405.4 square feet

More about the volume and surface area link is given below.

https://brainly.com/question/15585435

#SPJ1

Riley has collected approximately 22.7 grams of the trace element in his sample.

To calculate the amount of trace element collected by Riley, we first need to find the volume of the cylinder-shaped container that he used. The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

Plugging in the values given in the problem, we get:

V = π(5.7 cm)²(13.6 cm)

V ≈ 1338.6 cubic centimeters

Since the sample contains 0.017 grams of the trace element per cubic centimeter of water, we can find the total amount of trace element collected by multiplying the volume of the sample by the concentration of the trace element:

0.017 grams/cubic centimeter × 1338.6 cubic centimeters ≈ 22.7 grams

To learn more about sample click on,

https://brainly.com/question/30370657

#SPJ4

Answer:

The half-life formula is given as:

t(1/2) = (ln 2) / k

where k is the decay constant.

Given:

mass of substance = 22 g

k = 0.138

We need to find t(1/2) in days.

First, we need to find the decay rate, λ, which is related to k as follows:

λ = k / ln 2

λ = 0.138 / ln 2

λ ≈ 0.199

Now we can substitute λ into the half-life formula to get:

t(1/2) = (ln 2) / λ

t(1/2) = (ln 2) / 0.199

t(1/2) ≈ 3.5 days (rounded to the nearest tenth)

Therefore, the substance's half-life is approximately 3.5 days.

The total length of the three rods is 125cm

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

This statements are interpreted into mathematical equation or expression.

representing length of rod A,B,C by x,y,z respectively

x: y = 3:2

therefore x/y = 3/2

x:z = 2:5= x/z = 2/5

The smallest length will be y and longest will be z

z-y = 55

x/y = 3/2

3y = 2x

y = 2/3( x)

x/z = 2/5

2z = 5x

z = 5/2(x)

we can say;

5/2(x) -2/3(x) = 55

(15x - 4x)/6 = 55

11x = 55×6

x = 5 × 6 = 30 cm

y = 2/3 × 30 = 20cm

z = 5/2 × 30 = 75 cm

Therefore the total length = 30+20+75 = 125cm

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

Answer:

a)7

b)3

Step-by-step explanation:

a)8x7=56

b)80-56=24

24/8=3

Answer:

Step-by-step explanation:

The average rate of change of a function over an interval is given by the formula:

average rate of change = (f(b) - f(a)) / (b - a)

where a and b are the endpoints of the interval.

For the function f(x) = -0.5x^2, we have:

f(-3) = -0.5(-3)^2 = -4.5

f(3) = -0.5(3)^2 = -4.5

So the average rate of change of f(x) over the interval -3 < x < 3 is:

average rate of change = (f(3) - f(-3)) / (3 - (-3))

average rate of change = (-4.5 - (-4.5)) / 6

average rate of change = 0

For the function g(x) = -1.5x^2, we have:

g(-3) = -1.5(-3)^2 = -13.5

g(3) = -1.5(3)^2 = -13.5

So the average rate of change of g(x) over the interval -3 < x < 3 is:

average rate of change = (g(3) - g(-3)) / (3 - (-3))

average rate of change = (-13.5 - (-13.5)) / 6

average rate of change = 0

Therefore, the average rates of change for both f(x) = -0.5x^2 and g(x) = -1.5x^2 over the interval -3 < x < 3 are 0. This means that the functions are constant over this interval, and their slopes are not changing.

The number of line segments that will be needed to create step 4 of the sequence is 30.

A line segment is a given straight line which has two terminating points, each at its two ends.

In the given sequence, it can be observed that each end point of the line segment requires two other line segment for extension in the next step.

step 1 = 2

step 2 = 2 + 4

           = 6

step 3 = 6 + 8

          = 14

step 4 = 14 + 16

          = 30

So that comparing the line segments in the steps given, the number of line segments that will be needed to create step 4 of the sequence is 30.

Learn more about line segment at https://brainly.com/question/17374569

#SPJ1

Answer:

Second option:

y = - 3x - 1

Step-by-step explanation:

The line cuts the y-axis at y = -1; this is the y-intercept of the slope-line equation and corresponds to the constant term in the equation

The equation of the line will be of the form
y = mx - 1

where m is the slope

To find slope, find two points on the line(x1, y1) and (x2, y2)  which can be easily distinguished

The difference between their y values is called the rise: y2 - y1

The difference between the corresponding x values is called the run: x2 - x1

Slope m = rise/run

In the graph, two easily distinguishable points are (0, -1) and (1, -4)

Therefore rise = y2 - y1 = -4 - (- 1) = -4 + 1 = -3

run = x2 - x1 = 1 - 0 = 1

Slope = -3/1 = -3

Therefore the equation of the line is
y = - 3x - 1

This is the second option

Answer:

The Correct answer is 381

Step-by-step explanation:

5334÷14

=381

Answer:

B

Step-by-step explanation:

Adjacent angles sum to 180 degrees  <====supplementary

Answer:

7:8

Step-by-step explanation:

El número de hombres en la encuesta es:

150 - 80 = 70

Por lo tanto, la razón de hombres a mujeres es:

hombres / mujeres = 70 / 80

Para simplificar esta razón, podemos dividir ambos términos por 10, ya que 10 es un factor común:

hombres / mujeres = (70/10) / (80/10) = 7/8

Por lo tanto, la razón hombres:mujeres en su forma más simple es 7:8

Answer: 7:8

Step-by-step explanation:

80 = women

70 = men

150 = Total

Ratio of Men: Women

= 70:80

= 7:8

The number of possible outcomes is option (c) 16 when Camila flips a fair coin two times and then spins a four-section spinner.

There are two independent events: flipping a coin twice and spinning a spinner with 4 equal sections.

The number of possible outcomes for flipping a coin twice is 2 x 2 = 4 (HH, HT, TH, TT).

The number of possible outcomes for spinning a 4-section spinner is 4.

To find the total number of possible outcomes, we need to multiply the number of possible outcomes for each event

Total number of possible outcomes = 4 x 4 = 16

Therefore, the correct option is (c) 16

Learn more about independent events here

brainly.com/question/30905572

#SPJ4

A moderately negative correlation between both of them variables is shown by the resultant correlation coefficient of -0.55.

We can construct a correlation matrix to determine the relationship between the number the group visits received and the fructosamine level. This indicates that the fructosamine level typically decreases as the amount of group visits increases.

This could imply that patients can keep better control of glucose, as seen by lower fructosamine levels, by participating in group visits and getting support or education about managing diabetes.

It's crucial to remember that a connection does not necessarily indicate a cause.

Further study is required to show a causal link between the fructosamine level and the number the group visits that participants attended. Overall, the moderately negative correlation points to some potential benefits of group visits for treating diabetes.

Learn more about correlation here:

https://brainly.com/question/18498382

#SPJ4

We can be 90% confident that the true proportion of newborns born at a healthy weight lies between 0.653 and 0.747.

The maximal margin of error (e) at 90% confidence is 0.055. To construct a 90% confidence interval for the true proportion of interest, we can use the formula:

where the z-score for a 90% confidence level is 1.645.

The standard error can be calculated using the formula:

where n is the sample size.

Substituting the values, we get:

Therefore, we can be 90% confident that the true proportion of newborns born at a healthy weight lies between 0.653 and 0.747.

Learn More about confidence interval

https://brainly.com/question/20309162

#SPJ4

The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16.


To find the point estimate of the difference in the population mean exercised between underclassmen and upperclassmen, you need to subtract the sample mean of underclassmen from the sample mean of upperclassmen.

Sample mean of upperclassmen = 0.76
Sample mean of underclassmen = 0.60

Point estimate = Sample mean of upperclassmen - Sample mean of underclassmen
Point estimate = 0.76 - 0.60
Point estimate = 0.16


The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16, which indicates that on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours.

To know more about Point estimate, visit

https://brainly.com/question/30734674

#SPJ11

2) 'Two things can be qualitatively identical without being numerically identical ' is true.

The true statement is, 2 ) 'Two things can be qualitatively identical without being numerically identical'.

This is known as the problem of universals in philosophy, which deals with the question of whether qualities or properties (such as redness or roundness) exist independently of the objects that possess them. Two objects can share the same qualities or properties, but still be distinct entities. For example, two apples can be qualitatively identical in terms of their color, size, and shape, but they are still two separate objects.

To learn more about qualitatively here:

https://brainly.com/question/5949851

#SPJ4