A population numbers 12,000 organisms initially and grows by 17.5% each year.
Suppose P represents population, and t the number of years of growth. An exponential model for the population can be written in the form P = a â‹… b t where
P =

Answer:

A and D

Step-by-step explanation:

Total ice cream bars sold = sum of chocolate sold , vanilla and strawberry ice-creams sold.

=(1/2)x2 + (6/11)x + 8 + (5/9)x2 + (2/3) +(1/3)x2 + 4x +(4/3) (Given in the question)

=(25/18)x2 + (50/11)x + 10 (Adding terms corresponding to x2,x ,constant respectively)

Difference in chocolate and strawberry bars =[ (1/2)x2 + (6/11)x + 8] - [(1/3)x2 + 4x +(4/3)]

= (1/6)x2 - (38/11)x +(20/3)

So, the correct options are A and D

Answer:

298/99

Step-by-step explanation:

hope that helped!

Answer:

z = 3

Step-by-step explanation:

\(14 - z = 11\)

\( - 11 = 11 - 14\)

\( - z = - 3\)

\(\boxed{\green{z = 3}}\)

\(14 - z = 11 \\ \\ z = 11 + 15 \\ \\ z = 26\)

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer:

1244 DCD

Step-by-step explanation:

Answer: bro i would help but for some reason it wont lemme view the pic.

Step-by-step explanation: Sorry man/girl! Have A Great Day!!!

Answer:

d and its only 10 so there ya go

Answer:x=-3 y=26

Step-by-step explanation:

3x+y=17.............(1)

x+2y=49..............(11)

From (11) x=49-2y

Substitute x=49-2y in 3x+y=17

3(49-2y) + y=17

Open bracket

147-6y+y=17

147-5y=17

Collect like terms

5y=147-17

5y=130

Divide both sides by 5

5y/5=130/5

y=26

Substitute y=26 in x+2y=49

x+2(26)=49

x+52=49

Collect like terms

x=49-52

x=-3

Answer:

It has a single solution: x = -3, y = 26.

Step-by-step explanation:

Answer: 149,150,151

Step-by-step explanation:

1.st solution

Let the smallest number is x.

So next consecutive number is x+1

So the third consecutive number is x+2

So the sum of these three numbers is:

x+x+1+x+2=450

3x+3=450

3x=447

x=149  - first number

Second number is 149+1=150

Third number is 150+1=151

2-nd solution

The sum of 3 numbers in row is 450. It means that average  number is 450:3=150 - is the number which is in the middle

So the first one number is 150-1=149 and the third number is 150+1=151

Answer:

C

Step-by-step explanation:

20+22+24=66

22+24+26=72

24+26+28=78

26+28+30=84

\(\rightarrow\)Square root of 9 is a whole number that is multiplied by itself to get the original number. The actual value of square root of 9 is 3.

√9 = ±3

\(\rightarrow\)If we square +3 or -3, the resulting value will be equal to 9.

\(\sf{(+3)^2 = 9}\)

\(\sf{(-3)^2 = 9}\)

\(\rightarrow\)Number 9 is an odd number and not a prime number. Prime numbers have only two factors, 1 and the number itself. But as we know, 9 have three multiple factors, 1, 3 and 9 itself. Thus, we can write the number 9 in the form of multiple as;

\(\rightarrow\)You know that number 9 is a multiple of 3 or when 3 is multiplied by itself, we get the number 9. Therefore, we can write the square root of 9 as;

➾\(\sf{\sqrt{9}}\)

➾\(\sf{\sqrt{3×3}}\)

➾\(\sf{\sqrt{3^2}}\)

\(\rightarrow\)The square cancels the square root of a number. Therefore, if we cancel the square root with a square in the above expression, we get,

➾\(\sf{\sqrt{9}}\) = ±3

__________________________________

Hope it helps you:)

Answer:

4 units right, 2 units up

Step-by-step explanation:

For \(g(x)=(x-4)^2+2\), the graph of \(f(x)=x^2\) would need to move 4 units to the right and 2 units up. Hence, the vertex would be \((4,2)\) if we compare the function g(x) with the form \(y=a(x-h)^2+k\).

The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

Answer:

D

Step-by-step explanDation:

If the data were transformed and points with the coordinates

(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.

To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.

Let's calculate the logarithms for the given data:

x     y            log(y)

1     12          log(12) = 1.079

2     83        log(83) = 1.919

3     580      log(580) = 2.763

Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)

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Answer:

proportional/equal

Step-by-step explanation:

doesnt need

Answer:

The nature of the image formed by a concave mirror depends on the magnification produced by the mirror.

(a) If the magnification produced by the mirror is +3, it indicates that the image formed is magnified and upright. The positive sign of the magnification indicates that the image is virtual. The size of the image will be larger than the size of the object.

(b) If the magnification produced by the mirror is -1, it indicates that the image formed is of the same size as the object but inverted. The negative sign of the magnification indicates that the image is real and formed on the opposite side of the object. The size of the image will be the same as the size of the object, but it will be inverted.

In both cases, the concave mirror is acting as a converging mirror, meaning it brings light rays together to form an image. The specific size of the image cannot be determined without additional information, such as the distance of the object from the mirror and the focal length of the mirror.

Answer: The nature of the image formed by a concave mirror can be determined based on the sign of the magnification produced.

(a) If the magnification is positive (+3), it indicates that the image is magnified and upright. In this case, the image is virtual and located on the same side as the object. The size of the image will be three times larger than the size of the object.

(b) If the magnification is negative (-1), it indicates that the image is diminished and inverted. In this case, the image is real and located on the opposite side of the object. The size of the image will be the same as the size of the object, but it will be inverted.

It's important to note that the actual size of the image cannot be determined solely based on the magnification. The magnification only gives information about the relative size of the image compared to the object. To determine the actual size, additional information, such as the size and distance of the object, is required.

If the screen's diagonal measurement is 13 inches, the height is equal to 12 inches.

Pythagorean theorem can be defined as a mathematical expression in Euclidean geometry that is typically used for calculating any of the three (3) side lengths of a right-angled triangle.

Mathematically, Pythagorean's theorem is modeled by this mathematical expression:

x² + y² = z²

Since this new TV screen has a width that is 7 inches longer than its height, we have;

x = y + 7

y = x - 7

Substituting the given parameters into Pythagorean's theorem, we have;

x² + y² = z²

x² + (x - 7)² = 13²

x² + x² - 14x + 49 = 169

2x² - 14x - 120 = 0

Dividing all through by 2, we have:

x² - 7x - 60 = 0

Next, we would solve this quadratic equation by using the factorization method:

x² - 12x + 5x - 60 = 0

x(x - 12) + 5(x - 12) = 0

(x + 5)(x - 12) = 0

x = -5 or 12

Note: We would ignore -5 since height cannot be a negative value.

Therefore, height, x is equal to 12 inches.

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We can start solving this problem by using the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let x be the height of the screen and x+7 be the width.

the diagonal of the screen is the hypotenuse of the triangle,

Therefore we can write the equation as:

(x+7)^2 + x^2 = (13)^2

By solving this equation we can find the height of the screen:

x^2 + 14x + 49 = 169

x^2 + 14x - 120 = 0

(x-12)(x+10) = 0

x = 12

So the height of the screen is 12 inches.

Answer:

Step-by-step explanation:

We will apply the definition of the derivative. Then we use algebra to expand and simplify the numerator. Next, we can cancel a factor of

h

in the numerator and denominator since

h

is approaching zero but not actually equal to zero. Finally, we can simply substitute zero for

h

to evaluate the limit.

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I believe the expression you provided is:

(log(x) + 4x^3) / x

To find the discontinuities of this expression, we need to identify any values of x that would cause the expression to be undefined. These values are called the discontinuities.

There are two types of discontinuities to look for:

Removable discontinuities: These occur when a function is undefined at a certain point but can be made continuous by redefining the function at that point.

Non-removable discontinuities: These occur when a function is undefined at a certain point and cannot be made continuous by redefining the function at that point.

To find the discontinuities of the given expression, we need to look for values of x that would make the denominator equal to zero, as this would result in a non-removable discontinuity.

So we solve the equation:

x = 0

This means that x cannot be equal to zero, as it would make the denominator zero and the expression undefined.

Therefore, the only discontinuity of the expression is at x = 0.

Note that there are no removable discontinuities in this expression, as the expression is continuous everywhere except at x = 0.

If there are 7 red balls and 10 black balls in a bag, then we can say that  red and black balls are present in the bag in ratio 7: 10

Ratio is a relationship between two or more values. a  units per b units.

a/b or a:b .

A part to part ratio of 7:10 can be written in the form of example given below:

If there are 7 red balls  and 10 black balls in a bag, then we can say that red and black balls are present in the bag in ratio 7:10

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Answer:

184

Step-by-step explanation:

2*(6*5+6*14+5*14)=184

Answer:

Decimal

Step-by-step explanation:

its a Decimal because 0.5 is an fact a decimal and its is equal to half and you can put 2 and 2 together and say it is a decimal just by how it looks

:) i hope you get the question righttt trust me its right i got it right on flocabulary.

The missing word into place is Decimal. Hence option 3 is true.

Used the concept of decimal number that states,

In Algebra, decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Given that the number is,

0.5

Now the number is written as,

0.5

5/10

1/2

And, the number 0.5 is in the form of a Decimal.

Hence, The missing word place is Decimal.

Therefore, option 3 is true.

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Answer:

Inferential study

Step-by-step explanation:

From the question, we understand that the professor concluded that majority of the class (of 198 students) preferred in class assessment based on the response from 67% of the sample size (i.e 30 students)

When decisions or conclusions are made about an overall population based on a survey carried out on a smaller sample, such study is referred to as an inferential study or inferential research.

Descriptive study on the other hand focuses on the features rather than the result of the experiment of the dataset.

Answer:

7⅓ servings of popcorn.

Explanation:

Each person receives 3/4 cup of popcorn.

To determine how many servings of popcorn are in 5½ cups, we divide:

We solve the expression above:

There are 7⅓ servings of popcorn.

The median of the distances is M = 6.5 kilometers

Given data ,

To find the median of a set of numbers, we arrange the numbers in ascending order and then locate the middle value. If there is an odd number of values, the median is the middle number. If there is an even number of values, the median is the average of the two middle numbers.

Arranging the given set of numbers in ascending order: {4, 5, 8, 11}

Since the set has an even number of values, the median is the average of the two middle numbers. In this case, the two middle numbers are 5 and 8. To find the average, we add these two numbers and divide by 2:

(5 + 8) / 2 = 13 / 2 = 6.5

Hence , the median of the given set {4, 5, 8, 11} is 6.5

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The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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Answer:

30 cubic inch

Step-by-step explanation: