1. WX=_________ units.

Answer:

[tex]\textsf{1.} \quad y=a \cdot 2^5\;\;\textsf{(where $a$ is the initial population)}[/tex]

[tex]\textsf{2.} \quad 2^{-3}[/tex]

[tex]\textsf{3.} \quad y=a \cdot 2^{2}\;\;\textsf{(where $a$ is the initial population)}[/tex]

[tex]\textsf{4.} \quad y=a \cdot 2^{8}\;\;\textsf{(where $a$ is the initial population)}[/tex]

[tex]\textsf{5.} \quad 64[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function}\\\\$y=ab^x$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $b$ is the base (growth/decay factor) in decimal form.\\\end{minipage}}[/tex]

Given that organism A's population doubles every day for the first 5 days:

Therefore, an exponential expression to express organism A's population growth in the first 5 days is:

[tex]\boxed{y=a \cdot 2^5}[/tex]

(where a is the initial population).

Given expression showing organism A's decrease in population over the next 3 days:

To rewrite the expression with the same base but one exponent,

[tex]\textsf{apply the exponent rule} \quad (a^b)^c=a^{bc}:[/tex]

[tex]\implies 2^{-3}[/tex]

Combine the increase and decrease in organism A's population after 8 days by multiplying the rates.  So the exponential expression for the total change in organism A's population after 8 days is:

[tex]\implies y=a \cdot 2^5 \cdot 2^{-3}[/tex]

[tex]\textsf{Apply the exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]

[tex]\implies y=a \cdot 2^{5-3}[/tex]

[tex]\implies y=a \cdot 2^{2}[/tex]

As organism B's population grows at the same rate as organism A, but is not infected with the virus, its population doubles each day.  Therefore, an exponential expression showing its increase in population over the same 8 days is:

[tex]\boxed{y=a \cdot 2^8}[/tex]

where a is the initial population.

To calculate how many times greater organism B's population is than organism A's population after 8 days, divide the expression for organism B by the expression for organism A:

[tex]\implies \dfrac{a \cdot 2^8}{a \cdot 2^2}[/tex]

[tex]\implies \dfrac{2^8}{2^2}[/tex]

[tex]\textsf{Apply the exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 2^{8-2}[/tex]

[tex]\implies 2^6=64[/tex]

The mean, median, and mode 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7 are 6.2, 7, and 9.

A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.

From the data set:

0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7

Mean = ( 0+ 4+ 6+11+ 9+ 8+ 9+ 1+ 5+ 9+7)/11 = 6.2

The mean is the middle number(s) in a data set. Hence

Median = 7

The mode is the most occurring number in a data set

Hence,

Mode = 9

Thus, the mean, median, and mode 0, 4, 6, 11, 9, 8, 9, 1, 5, 9, 7 are 6.2, 7, and 9.

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The solution is x > 3. The values of x are greater than 3.

It is a mathematical symbol that represent the non-equal comparison between different terms as well as other mathematical expressions. Inequality is various types such as greater than >, less than <, greater than or equal ≥ and less than or equal ≤.

Given, 0.3 (x -4) > -0.3

at first, we will remove the parenthesis and multiply by the given factor

0.3 × x - 0.3× 4 > -0.3

0.3x - 1.2 > - 0.3

now we add 1.2 to both side in order to isolate the variable terms

0.3x - 1.2+1.2 > - 0.3 + 1.2

0.3x > 0.9

in the next both side is divided by 0.3

0.3x/ 0.3 > 0.9/ 0.3

x > 3

the above is the result

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The following series can be classified as

1 + 2 + 4 + 8 ... +..  is divergent series.

200 + 100 + 50 + 25 ... is convergent series

1/2 + 2/3 + 8/9 + 32/27 ... is divergent series.

10 + 5 + 0 - 5 + .... is convergent series

4 - 2 + 1 - 1/2 + .... is convergent series

4 - 8 + 16 - 32 ..... is  convergent series  

If a series converges to a value as its terms approach infinity, it is said to be convergent. Example:

Series of terms which are squares of natural numbers

=> 1, 4, 9, 16, 25.... which goes upto infinity

Hence given series is the Convergent series

If a series does not converge to a value but instead keeps on increasing or dropping as the terms of the series tend to infinitely, it is said to be divergent. Example: 1, 1/2, 1/3, 1/4 ... etc

Where it tends to 0 as the term goes to infinity.  

Note:

If the common ratio lies between (-1, +1), then the series is convergent if it does not lie between (-1, +1) then the series is divergent.

Here given series are

1 + 2 + 4 + 8 ... +

Here common ratio = 2/1 = 2  

Common ratio, 2 > 1

1 + 2 + 4 + 8 ... +..  is divergent series.

200 + 100 + 50 + 25 ...

Common ratio = 100/200 = 1/2

Common ratio, 1/2 < 1

200 + 100 + 50 + 25 ... is convergent series

1/2 + 2/3 + 8/9 + 32/27 ...

Common ratio = 2/3 / 1/2 = 4/3

Common ratio, 4/3 > 1

1/2 + 2/3 + 8/9 + 32/27 ... is divergent series.

10 + 5 + 0 - 5 + ....

Common ratio = 5/10 = 1/2

Common ratio, 1/2 < 1

10 + 5 + 0 - 5 + .... is convergent series

4 - 2 + 1 - 1/2 + ....

Common ratio = -2/4 = -1/2

Common ratio, -1/2 < 1

4 - 2 + 1 - 1/2 + .... is convergent series

4 - 8 + 16 - 32 .....

Common ratio = - 8/4 = -2

Common ratio, -2 < 1

4 - 8 + 16 - 32 ..... is  convergent series  

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The solution is (-1,2.5) .

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.

Here given that,

y=3+1/2x

⇒2y-x=6 ...........(1)

3x+2y=2...........(2)

Now, subtracting (1) & (2) we get,

-4x=4

⇒x= -1

And, y=2.5

Hence. required solution is x= -1 & y=2.5

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Answer:

-7 is the further number from 0

Step-by-step explanation:

So lets say you start at 0

count 4 spaces to the right because it is a positive 4

and count 7 spaces to the left because it is a negative 7

7 is greater than 4 which means -7 is farther from 0 than 4 on a number line

Answer:

x=1

Step-by-step explanation:

.................................

Answer: (2n + 2 + n) x 2 and (2n + 2) x 2 + n x 2

Step-by-step explanation:

width = n

length = 2n + 2

perimeter = (2n + 2 + n) x 2

perimeter = (2n + 2) x 2 + n x 2

The lines are perpendicular because the product of their slopes is -1

The slope-intercept form of the equation of a straight line is:

y = mx + c,

where m is the slope and c is the y-intercept

When two lines are perpendicular, the product of their slope is -1 i.e.

m₁ × m₂ = -1

where m₁ and m₂ represent the slope of the lines

But when two lines are parallel, they have the same slope i.e.

m₁ = m₂

Let's examine the equations:

y-3=4(x+4) and x+4y=16

First write the equations in slope-intercept form. That is:

y-3 = 4(x+4)

y-3 = 4x+16

y = 4x+16+3

y = 4x+19   (slope, m = 4 )

x+4y = 16

4y = -x + 16

y = (-1/4)x + 4   (slope, m = -1/4 )

Since the slopes of the lines are not the equal, they are not parallel.

Since the product of the slopes of the line is -1 (i.e. 4 × -1/4 = -1), they are perpendicular.

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Laila should create a "box plot" to display the data would display the median, minimum, and maximum clearly.

A box and whisker plot (also known as a box plot) depicts a five-number summary of a set of data: lowest, lower quartile, median, upper quartile, and maximum.

To present the data, Laila should make a box plot.

This is because a box plot would clearly display the median, minimum, and maximum salary, which is what Laila wants to show.

A histogram cannot be used to determine the median, and a dot plot would not work well because there are too many different values in the data set.

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The addition of 2/3 with the addition of 4/9 and 7/9 is 1 8/9

The addition of fractions teaches us to add two or more fractions with the same or different denominators. The addition of fraction depends on two major conditions: Same denominators. Different denominators.

When adding fractions of same denominator, it easier, for example 2/5+1/5 =( 2+1)/5 = 3/5

But, the addition of fractions with different denominators, we have to find the LCM of the two denominator. for example 1/2+1/3, the LCM of 2 and 3 is 6, Therefore; = (3+2)/6 = 5/6

Similarly, 2/3+( 4/9+7/9)

2/3 + 11/9 =( 6+11)/9

= 17/9 = 1 8/9

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Answer: 0

Step-by-step explanation:

To find the y-coordinate of point Q, we first need to find the coordinates of point Q. Since points P, Q, and R are collinear and the ratio of PQ to PR is 3/4, we know that the ratio of their x-coordinates and y-coordinates must also be 3/4.

Let's call the coordinates of point Q (x, y). We know that the x-coordinate of point Q is 3/4 of the way between the x-coordinates of points P and R. This means that the x-coordinate of point Q is (3/4) * (-4 - 3) + 3 = -1.

Similarly, the y-coordinate of point Q is (3/4) of the way between the y-coordinates of points P and R. This means that the y-coordinate of point Q is (3/4) * (5 - (-5)) - 5 = 0.

Therefore, the coordinates of point Q are (-1, 0). The y-coordinate of point Q is 0.

The coordinates of point Q are (3, -5), and the y-coordinate of point Q is -5.

Collinear points are points that lie on the same straight line. In other words, if you can draw a straight line through two or more points, then those points are said to be collinear.

Given that the ratio of PQ to PR is 3/4.

Let's assume the coordinates of point Q are (x, y).

Using the midpoint formula, we can find the coordinates of the midpoint M of line segment PR:

M = ((x1 + x2)/2, (y1 + y2)/2)

Substituting the coordinates of points P (3, -5) and R (-4, 5), we have:

M = ((3 - 4)/2, (-5 + 5)/2) = (-1/2, 0)

and, M = ((x + (-4))/2, (y + 5)/2)

Equating the x-coordinates and y-coordinates, we get:

-1/2 = (x - 4)/2 => x - 4 = -1 => x = 3

0 = (y + 5)/2 => y + 5 = 0 => y = -5

Therefore, the coordinates of point Q are (3, -5), and the y-coordinate of point Q is -5.

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Answer:

a + B = [tex]\frac{1}{3}[/tex]

Step-by-step explanation:

the sum of the roots a + B = - [tex]\frac{b}{a}[/tex]

where a and b are the coefficients in the standard quadratic equation

ax² + bx + c = 0 ( a ≠ 0 )

3x² - x - 5 = 0 ← is in standard form

with a = 3 and b = - 1 , then

a + B = - [tex]\frac{-1}{3}[/tex] = [tex]\frac{1}{3}[/tex]

Using the common factors of 266, the set of possible dimensions of the field are:

The dimensions of a rectangle include four sides, two lengths, and two widths.

The fencing is three-sided with a total width of 14 m (7 x 2) and a length of 38 m.  The total length of the fencing will be 52 m (14 + 38) while the area of the land is 266 m (38 x 7).

Thus, the dimensions that meet the criteria for the area and the length of fencing that Josiah has to do are based on the common factors of 266, which are 38 m in length and 7 m in width.

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On solving the provided question, we can say that - here in inequality equation  value of p for the inequality [tex]4p - 5 \leq 25[/tex] is [tex]7.5[/tex]

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Inequality results from an imbalance, thus. In mathematics, an inequality establishes the relationship between two values that are not equal. Egality is not the same as inequality. Use the not equal symbol () in most cases when two values are not equal. To contrast values, whether they are tiny or huge, different inequalities are employed. By adjusting both sides until just the variables are left, you may eliminate many straightforward inequalities. However, several factors cause inequality: Divide or add negative values on both sides. Switch the left and right.

here,

4p - 5 ≤ 25

[tex]4p - 5 \leq 25\\4p \leq 25 + 5\\4p \leq 30\\p \leq 30/4\\p \leq 7.5[/tex]

value of p for the inequality [tex]4p - 5 \leq 25[/tex] is [tex]7.5[/tex]

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If choice which is equivalent to the product √2√5 √8 exists 4√5.

In order to write numbers, bases and powers are used in the exponential form. It informs us of the amount of times we must actually multiply a number in order to obtain the answer.

We must ascertain the terms' prime factorization in order to formulate an expression in exponential form.

Factor and rewrite the radicand in exponential form:

√2 × √((2²) × 2) × √5

Rewrite the expression using √n/ab = √n/a × √n/b

Substitute the values in the above equation, we get

√2 × √((2²) × 2 × √5

Simplify the radical expression: √2 × 2 × √2 × 2

Rewrite the expression: (2 × 2) × (√2 × √2)

Simplify the radical expression:

= 4√5

Therefore, the correct answer is option B. 8/10

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If choice which is equivalent to the product √2√5 √8 exists 4√5.

In order to write numbers, bases and powers are used in the exponential form. It informs us of the amount of times we must actually multiply a number in order to obtain the answer.

We must ascertain the terms' prime factorization in order to formulate an expression in exponential form.

Factor and rewrite the radicand in exponential form:

√2 × √((2²) × 2) × √5

Rewrite the expression using √n/ab = √n/a × √n/b

Substitute the values in the above equation, we get

√2 × √((2²) × 2 × √5

Simplify the radical expression: √2 × 2 × √2 × 2

Rewrite the expression: (2 × 2) × (√2 × √2)

Simplify the radical expression:

= 4√5

Therefore, the correct answer is option B. 8/10

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Answer:

|BC| = 24.5

Step-by-step explanation:

It is stared that the triangles are similar triangles.

Since they are similar triangles, we can find the length of the missing side using the ratio of similar sides.

DE/AB = EC/BC

[tex] \frac{6}{21} = \frac{2x + 3}{13x - 1.5} [/tex]

78x - 9 = 42x + 63

78x - 42x = 63 + 9

37x = 72

x = 2

now, replace x with 2 in the given expression for the length of BC:

13x - 1.5 = 13×2 - 1.5

|BC| = 24.5

Answer:

To solve this problem, you can set up an equation using the given information. Let "x" be the number in question.

We are told that 10 more than 32% of x is equal to 26. This can be written as:

10 + 0.32x = 26

To solve for x, you can start by subtracting 10 from both sides of the equation:

10 + 0.32x - 10 = 26 - 10

This simplifies to:

0.32x = 16

To isolate the x term, you can divide both sides of the equation by 0.32:

(0.32x)/0.32 = 16/0.32

This simplifies to:

x = 50

Therefore, the number we are trying to find is 50.

By using the vertical line test, the relation graphed above is a function. Therefore, the correct answer choice is: A. yes.

In Mathematics, a vertical line test can be defined as a technique which is typically used to determine whether or not a given relation is a function.

According to the vertical line test, a vertical line must cut through the x-coordinate (x-axis) on the graph of a function at only one (1) point, in order for it to represent a function. Else, the relation does not represent a function because it can only have one output value (y) for a unique input value (x).

In conclusion, we can reasonably infer and logically deduce that relation graphed above represents a function because it passed the vertical line test as shown in the graph attached below.

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Answer: function

Step-by-step explanation:

Answer:

251.2

Step-by-step explanation:

The formula for the volume of a cylinder is [tex]\pi r^2h[/tex]. Plugging in your measurements...

Height = 20 inches.

Radius = 2 inches.

The volume is [tex]\pi2^2h[/tex].

Simplification...

[tex]\pi2^220 = \pi4(20)= 4\pi 20[/tex].

[tex]\pi[/tex] ≈ [tex]3.14[/tex]

3.14 * 4 = 12.56

12.56*20 = 251.2

f(x)=|x+4|-1 with a vertical stretch by a factor of 5, so the translation function becomes: 5|x + 4| - 5.

According to operations like multiplication or sum/subtraction either in its definition or in its domain, a translation is represented by a change in the function graph. Examples include shifting to the left or right or up or down, compressing or extending vertically or horizontally, and reflecting across the x- or y-axis.

For this problem, the function is given by:

f(x) = |x + 4| - 1.

For a vertical stretch by a factor of 5, the function is multiplied by 5, hence the translated function is given by:

g(x) = 5f(x) = 5(|x + 4| - 1) = 5|x + 4| - 5.

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The function to represent the given scenario is y=25+0.15x and the number of miles travelled is 240 miles.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Given that, Bang-up Motors will rent-a-car for $25 plus $0.15 per mile traveled.

a) Let the number of hours be x and the total number of hours be y.

Now, y=25+0.15x

b) If your bill was $61, then the number of miles are

61=25+0.15x

0.15x=36

x=36/0.15

x= 240 miles

Therefore, the number of miles travelled is 240 miles.

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Using mathematical operations, the recipe that consumes more sugar is the one for 3¹/₂ dozen cookies, which uses 3 cups.

The basic mathematical operations include addition, subtraction, division, and multiplication.

In this situation, we apply the division and multiplication operations to determine the number of cups of sugar required by the dozen cookies' recipe.

Rita's recipe for 3¹/₂ dozen cookies:

1 dozen = 12 units

The number of cookies = 42 (3¹/₂ x 12)

The number of cups of sugar = 3

Recipe for a dozen cookies:

The number of cookies = 12

The cups of sugar required = 0.86 cups (3/42 x 12)

Thus, the recipe for a dozen cookies will require less sugar than the recipe for 3¹/₂ dozen cookies.

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[tex]f^-1(x) = (5x-15)/2[/tex]

To find the inverse of a function, you need to switch the roles of the input and output.

So, if we let y = f(x), then the inverse function, denoted as f^(-1)(x), would be x = [tex]f^-1(y)[/tex].

In this case, we can start by setting y = (2x+15)/5.

Then, we can solve for x to find the inverse function:

y = (2x+15)/5

5y = 2x + 15

2x = 5y - 15

x = (5y-15)/2

Therefore, the inverse of f(x) = (2x+15)/5 is [tex]f^-1(x) = (5x-15)/2[/tex].

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The value of the function f(g(1)) = 1

A function is a mathematical expression that shows the relationship between two variables.

Consider functions f and g.

f(x) = 3 √x + 1, to determine the value of f(g(1)), we substitute g(x) into the equation for f(x).

So, f(x) = 3 √x + 1

f(g(x)) = 3√x + 1

f(g(x)) = 3√g(x) + 1

So, substititng x = 1, we have that

f(g(1)) = 3√g(1) + 1

We see that from the table g(1) = 0.

So, susbtituting the values of the variables into the equation, we have that

f(g(1)) = 3√g(1) + 1

f(g(1)) = 3√0 + 1

= 3(0) + 1

= 0 + 1

= 1

So, f(g(1)) = 1

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Answer:

the answer is 27/10j + 1/8