15,000 blue trout were released into the Meherrin River for a scientific study. The function, f(x) = 15,000( _ 9 8 ) x , represents the number of blue trout after x years. In 5 years, what happens to the population?

The question involves calculating the volume of a right rectangular prism and dividing it by the volume of a unit cube to find out how many such cubes can fit inside the prism.

The question is about finding how many unit cubes, each with edge lengths of 1/2 meter, can fit inside a right rectangular prism whose edge lengths are 4/5 meter, 3/4 meter, and 5/8 meter. To solve this, we first calculate the volume of the prism and then divide it by the volume of a unit cube to determine how many such cubes can fit inside the prism.

Step-by-step Solution:

By applying the above steps, we'll know the exact number of unit cubes that can fit inside the given right rectangular prism.

The transformed equation results in [tex]f(x) = 3(x - 2)^2 - 3 = 3x^2-12x+9[/tex].

Let's start with the function[tex]f(x) = x^2[/tex]. We need to apply the following transformations:

Let's break down each transformation step-by-step.

Therefore, the equation of the transformed function is [tex]f(x) = 3(x - 2)^2 - 3[/tex].

Answer: Multiplying and Dividing are inverse operations

Multiplying by a number is the same as dividing by its reciprocal

Step-by-step explanation:

Answer:

Multiply and divide are inverse operations.

Multiply by a number is the same as divide by its reciprocal.

Step-by-step explanation:

To divide by a fraction, you can multiply by its inverse.

If a number is defined as a/b, then the reciprocal of the number is b/a.

The given equation is

[tex]\frac{5}{8}\div \frac{2}{3}=\frac{5}{8}\times \frac{3}{2}[/tex]

Here, [tex]\frac{3}{2}[/tex] and [tex]\frac{2}{3}[/tex] are inverse of each other.

Reason 1:

Multiply and divide are inverse operations.

Reason 2:

Multiply by a number is the same as divide by its reciprocal.

Answer:

y=3.15

Step-by-step explanation:

I am assuming you meant 2.8y in your equation.

Plug in for x

6.4(3)+2.8y=44.4

6.4*3=19.2

So now 19.2 + 2.8y = 44.4

44.4-19.2=25.2

25.2/2.8=3.15

Meaning Y=3.15

Answer:

log3 81 = 4

Step-by-step explanation:

Convert the exponential equation to a logarithmic equation using the logarithm base (3)(3) of the right side (81)(81) equals the exponent (4)(4).

log3(81)=4

or

you can remember this

loga Y= X

so, a^x =y

The logarithmic form of the equation 81=3^4 is log3 81 = 4. It uses the base number 3 (which is being raised to a power), the result of the multiplication (81), and the number of times 3 is multiplied by itself (4).

The logarithmic form of the equation 81=3^4 can be found by applying the basic principles of logarithms. Remember, a logarithm is another way to express exponentiation, in a format that involves the base number, the exponent, and the result. Therefore, the logarithmic form of 81=3^4 is written as log3 81 = 4.

To understand this, consider the logarithmic expression log3 81 = 4. The base number (3 in this case) is the number being multiplied repeatedly (the number being raised to a power). The number 81 is the result of this multiplication, and 4 is the number of times base number, 3, is multiplied by itself to get 81. So, in this case, 3 to the power of 4 (3*3*3*3) equals 81.

So, in short, for the equation 81=3^4, the logarithmic form will be log3 81 = 4. This equation reads as "log base 3 of 81 equals 4".

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Answer:

144ft^2

Step-by-step explanation:

since it's a kite, there are two pairs of congruent (exactly the same shape) triangles

bc of this you can find one triangle from each pair and double it

e.g.

[tex] \frac{6 \times 8}{2}=24[/tex]

[tex] \frac{12 \times 8}{2}= 48[/tex]

so you would do 2(24+48)=144

Answer:

Step-by-step explanation:

-7/3, -2 5/8, -2.9

-2 1/3, -2 5/8, -2 9/10

-2 9/10, -2 5/8, -2 1/3

this is the order from least to greatest

-2.9, -2 5/8, -7/3

Answer:

The answer is -2.9, -2[tex]\frac{5}{8}[/tex], -[tex]\frac{7}{3}[/tex]

Step-by-step explanation:

Since the numbers get higher, the negative numbers that are like -2.9 and -2.3 are considered to be less than -1.9 because they are on the left side further from -1.9 and since -1.9 is closer to 0, it is greater than -2.9 and -2.3. The way I explained is just an example.

Answer:

It only counts as a zero when the y-intercept is (0,0).

Step-by-step explanation:

The zeros of a quadratic function are always written as (x,0), while the y-intercept is always written as (0,y). Therefore, in order for a y-intercept to be a zero, it must be (0,0), because the y-coordinate in any zero is 0. At any other time, the y-intercept is not a zero.

Final answer:

The y-intercept represents the starting value of the relationship when x is zero, but it is not considered a zero itself.

Explanation:

The y-intercept, also represented as 'b' in the equation y = mx + b, is the point where the line intersects the y-axis. It indicates the starting value of the relationship when x is zero. However, the y-intercept does not count as a zero because it represents a specific value on the y-axis, rather than being a zero value on the x-axis. For example, if the y-intercept is 5, it means that the line starts at the point (0, 5) on the coordinate plane.

Answer:

[tex]f^{-1} (x)=\frac{x+6}{7}[/tex]

Step-by-step explanation:

To find the inverse of a function, we must substitute in y for f(x), swap the locations of y and x, and then solve for y

[tex]y=7x-6\\\\x=7y-6\\\\x+6=7y\\\\y=\frac{x+6}{7} \\\\f^{-1} (x)=\frac{x+6}{7}[/tex]

The inverse of the given function [tex]f^{-1}(x)=\frac{x+6}{7}[/tex].

We have given that,F(x) = 7x - 6

We have to determine the value of the inverse function.

An inverse is a function that serves to undo another function.

That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

To find the inverse of a function,

we must substitute in y for f(x), swap the locations of y and x, and then solve for y,

[tex]y=7x-6\\x=7y-6\\x+6=7y\\y=\frac{x+6}{7}[/tex]

We get the value of [tex]y=(x+6)/7.[/tex]

Taking inverse on both sides so we get,[tex]f^{-1}(x)=\frac{x+6}{7}[/tex]

Therefore the inverse of the given function [tex]f^{-1}(x)=\frac{x+6}{7}[/tex].

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Answer:

Step-by-step explanation:

First, you can reduce it

4(n^2-11n+30)

This should make it easier to work with. But remember, keep the 4 there. You cannot just get rid of it because it would change the value of the equation

Now find factors of 30 that have a difference or ad up to 11.

Factors of 30:

1, 30

2, 15

3, 10

5, 6

Ahh  yes, 5 and 6 add to 11

4(n-5)(n-6)

40square +30square

which is2500

2500 square root is 50

so answer is 50

Answer:

About 23 in

Step-by-step explanation:

2908.33/7=415.475

415.475/[tex]\pi[/tex]=132.31

132.31 sqr rt = r = 11.5

2r=d

d=23 aprox

The diameter of the cylinder is approximately 22.94 inches.

To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:

Volume [tex]= \pi \times r^2 \times h,[/tex]

where π is a mathematical constant (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.

Given that the height of the cylinder is 7 inches and the volume is 2,908.33 cubic inches, we can rearrange the formula to solve for the radius:

Volume [tex]= \pi \times r^2 \times h[/tex]

[tex]2,908.33 = \pi \times r^2 \times 7[/tex]

Dividing both sides of the equation by 7π, we have:

[tex]r^2[/tex] = 2,908.33 / (7π)

[tex]r^2[/tex] ≈ 131.50

Taking the square root of both sides, we get:

r ≈ √131.50

r ≈ 11.47.

The radius of the cylinder is approximately 11.47 inches.

To find the diameter, we multiply the radius by 2:

d = 2 [tex]\times[/tex] r

d ≈ 2 [tex]\times[/tex] 11.47

d ≈ 22.94

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Answer: 25 heads 25 tails

Step-by-step explanation: you would have a 50/50 chance to get heads or tails so sence there are 2 sides you would get 25 heads and 25 tails

Answer: 25 Times Head And 25 Time Tails

Step-by-step explanation: If you flip a dime in the air and if you flip it 50 times, there is an equally likely chance of flipping heads or tails. Equally likely chance means 50%. Ofcourse, it's not very likely that it would be exactly 25 times for heads and tails. Therefore, if I flipped a dime 50 times I would expect it to land  near 25 times on heads and 25 times around tails.

Have A Great Day!

Answer:

1. 5/6 cakes  2.3/10 pizzas  3.  4/8=1/2 bars  4. 12/20= 3/5 chips 5. 10/17 carrots

Step-by-step explanation:

ANSWER

12 ft

EXPLANATION

The volume of a cylinder is calculated using the formula

[tex]V=\pi {r}^{2} h[/tex]

From the question, the volume was given as 540π ft³ .

The height is given as 15 ft.

We substitute the values to obtain:

[tex]540\pi=\pi {r}^{2} \times 15[/tex]

This implies that;

[tex] {r}^{2} = \frac{540\pi}{15\pi} [/tex]

We simplify to get;

[tex] {r}^{2}=36[/tex]

Take positive square root to obtain:

[tex]r = \sqrt{36} [/tex]

[tex]r = 6ft[/tex]

The diameter is twice the radius.

Hence the diameter is 12ft

The answer is:

The diameter of the cylinder is equal to 12 feet.

Why?

To find the diameter of the cylinder we need to use the formula to calculate its volume.

So,  we have:

[tex]Volume=\pi *r^{2}*h[/tex]

We are given the following dimensions of the cylinder:

[tex]Volume=540\pift^{3}\\\\Height=15ft^{3}[/tex]

Now, using substituting and isolating the radius in order to find the diameter, we have:

[tex]Volume=\pi *r^{2}*h\\\\r^{2}=\frac{Volume}{\pi *h} \\\\r=\sqrt{\frac{Volume}{\pi *h} }[/tex]

Therefore, we have:

[tex]r=\sqrt{\frac{Volume}{\pi *h}}\\\\r=\sqrt{\frac{540\pi ft^{3}}{\pi *15ft}}\\\\r=\sqrt{36ft^{2} }=6ft[/tex]

We know the radius, then, calculating the diameter we have:

[tex]diameter=2*radius=2*6ft=12ft[/tex]

Hence, we have that the diameter of the cylinder is equal to 12 feet.

Have a nice day!

Answer:

I think A i think

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

Look at x = -2 on the graph (on the x-axis).  Draw a vertical line through x = -2.  If this line passes through a dark dot (which indicates that a y-value is associated with that x-value), we have evaluated the function.  The dot in question is (-2, 0) (dark dot).  The same vertical line passes through (-2, -2), but this is not the correct y value for x = -2 (it's an open circle).

The value of [tex]f(-2)[/tex] is [tex]0[/tex].

Given:

The graph of the function [tex]f(x)[/tex].

To find:

The value of [tex]f(-2)[/tex].

Explanation:

In the given graph there is an open circle at [tex](-2,-2)[/tex] and a closed circle at [tex](-2,0)[/tex]. It means the point [tex](-2,0)[/tex] is included in the function but the points [tex](-2,-2)[/tex] does not included in the function.

[tex]f(-2)=0[/tex]

Therefore, the value of [tex]f(-2)[/tex] is [tex]0[/tex].

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Answer:

x = 7

Step-by-step explanation:

Subtract 7.2 from both sides of 11.3x + 7.2 = 86.3, obtaining:

11.3x = 79.1

Then x = 79.1 / 11.3 = 7

The answer is x = 7.

Please, when you list possible answers, separate them from one another using commas, semicolons or new entry lines.  Thank you.

6x^2 - 37x + 22

Use the FOIL method to multiply the binomials.

First monomial in each binomial: 3x * 2x = 6x^2

Outside monomials: 3x * -11 = -33x

Inside monomials: -2 * 2x = -4x

Last monomial in each binomial: -2 * -11 = 22

Now, just add: 6x^2 - 33x - 4x + 22 = 6x^2 - 37x + 22

Answer:

6x^2 - 37x + 22

Step-by-step explanation:

Answer:

4.1 =y

Step-by-step explanation:

This is a problem involving trig.

sin of a angle is equal to opposite side divided by hypotenuse

sin 36 = y / 7

Multiply each side by 7

7 sin 36 = y/7 * 7

7 sin 36 = y

4.1144 = y

To 1 decimal place

4.1 =y

Answer:

You're correct

The slope is -2/5; and the y-intercept is  -1/3

Step-by-step explanation:

Slope = (-13/30 + 1/30) / (1/4 + 3/4)

= (-12/30) / ( 4/4)

= - 2/5

Slope intercept form: y = mx + b, where b = y-intercept

b = y - mx

b = (-3/5) - (-2/5)(2/3)

b = -3/5 + 4/15

b = -9/15 + 4/15

b = -5/15

b = -1/3

Answer

Slope = -2/5; y-intercept = -1/3

The slope and the y-intercept of the linear function is;

Option A; slope is -2/5 and y-intercept is -1/3

      m = (y2 - y1)/(x2 - x1)

Let's make use of the first 2 coordinates to get the slope;

x1 = -3/4

x2 = -1/2

y1 = -1/30

y2 = -2/15

m = (-2/15 + 1/30)/(-1/2 + 3/4)

m = (-1/10)/(1/4)

m = -2/5

We know equation of a line in slope intercept form is;

y = mx + c

where m is slope and c is y-intercept

-1/30 = (-2/5)(-3/4) + c

-1/30 - 3/10 = c

c = -1/3

Thus, y-intercept is -1/3 and slope is -2/5

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the answer is Chelsea spent more than $12.75

Option 4, 'Chelsea spent more than $12.75,' matches the given inequality d > 12.75, as it directly corresponds with the 'greater than' symbol in the inequality. So, option 4 is correct.

The inequality d > 12.75 translates to "d is greater than 12.75." Looking at the options provided, we can find a situation that matches the inequality by understanding the meaning of the inequality symbol. Option 4, which says "Chelsea spent more than $12.75," directly corresponds to the inequality given. In this scenario, the amount Chelsea spent (d) is greater than $12.75, which is exactly what the inequality d > 12.75 signifies.

Since it’s a square all sides are even. Meaning you multiply 7/12 by 4. Giving you 7/3 or 2 ⅓. Hope this helps!

The perimeter of a square piece of cardboard with each side measuring 7/12 meter is found by using the formula P = 4a. After calculation, the perimeter is 2 1/3 meters.

The question asks us to calculate the perimeter of a square piece of cardboard with each side measuring 7/12 meter. To find the perimeter of a square, we use the formula P = 4a, where 'P' is the perimeter and 'a' is the length of one side. Since all sides of a square are equal, we simply multiply the length of one side by 4.

In this case, the length of one side (a) is 7/12 meter, so the perimeter (P) would be:

P = 4 × (7/12 meter)
P = (4 × 7/12) meter
P = 28/12 meter
P = 7/3 meter (after simplifying)
P = 2 1/3 meters (in mixed numbers)

Therefore, the perimeter of the square piece of cardboard is 2 1/3 meters.

Answer:

25x^2-40x+16

Step-by-step explanation:

(5x-4)(5x-4)

= 25x^2-20x-20x+16

=25x^2-40x+16

Answer:

[tex]Area=176cm^2[/tex]

Step-by-step explanation:

The area of a trapezoid is calculated using the formula:

[tex]Area=\frac{1}{2}(Sum\:of\:bases)\times height[/tex]

We substitute the values into the formula to obtain:

[tex]Area=\frac{1}{2}(12+10)\times16[/tex]

We simplify the parenthesis to get:

[tex]Area=\frac{1}{2}(22)\times16[/tex]

We simplify further to obtain;

[tex]Area=176cm^2[/tex]

Answer:

Option 1: 176 cm^2

Step-by-step explanation:

In order to find the area of trapezoid, we need to know the length of two sides(bases) and the vertical height to trapezoid

Here in the given trapezoid

base1 = a = 10cm

base2 = b= 12cm

and

h = 16 cm

The formula for area of trapezoid is:

[tex]Area = \frac{1}{2} (a+b)*h[/tex]

Putting the values

[tex]= \frac{1}{2} (10+12) * 16[/tex]

[tex]= \frac{1}{2} (22)(16)[/tex]

[tex]= \frac{1}{2} * 352[/tex]

[tex]Area = 176 cm^{2}[/tex]

Option 1 is the correct answer..

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{2}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{2}{3}}\qquad \stackrel{negative~reciprocal}{+\cfrac{2}{3}\implies \cfrac{2}{3}}}[/tex]

Answer:

-5, -3, -2

Step-by-step explanation:

This is correct because you are adding each by -2. The inputs are -3, -2,-1, 0,-1

the outputs become -5,-4,-3,-2,-1

Hopefully I helped

For this case we must propose a function of the form[tex]y = f (x)[/tex]that complies with the given relation:

We have the values of "x", that is, the entry is given by:

-3, -2, -1,0,1

If we propose:

[tex]f (x) = x-2[/tex]

We have the values of "and", that is, the output will be given by:

[tex]f (-3) = - 3-2 = -5\\f (-2) = - 2-2 = -4\\f (-1) = - 1-2 = -3\\f (0) = 0-2 = -2\\f (1) = 1-2 = -1[/tex]

The relationship is fulfilled.

Then, the function is f (x) = x-2

Answer:

[tex]-5, -4, -3, -2, -1\\f (x) = x-2[/tex]

Answer:

1050 ft²

Step-by-step explanation:

Enlarging the polygon by a factor of 5 has the effect of increasing the area by a factor of 5², that is 25

new area = 25 × 42 = 1050 ft²

Answer:

Answer:

{x ∈ R ∣ x ≠ 4/5}

Step-by-step explanation:

Answer:

domain is set of all real number except 4/5

Step-by-step explanation:

[tex]f(x)= \frac{x-3}{x}[/tex]

[tex]g(x)=5x-4[/tex]

Now we find (fºg)(x)

(fºg)(x)=f(g(x))

We plug in g(x) inside in f(x)

[tex]f(g(x))=f(5x-4)= \frac{(5x-4)-3}{5x-4}[/tex]

Now simplify the numerator

[tex]f(g(x))=\frac{(5x-4)-3}{5x-4}=\frac{5x-7}{5x-4}[/tex]

To find out domain we set the denominator =0 and solve for x

[tex]5x-4=0[/tex]

Add 4 on both sides

[tex]5x=4[/tex]

Divide both sides by 5

[tex]x=\frac{4}{5}[/tex]

So domain is set of all real number except 4/5

Answer:

The mean will stay the same.

The standard deviation will decrease.

Step-by-step explanation:

For the 5 cards, she has received, the mean will be:

μ=(∑x)/n

=125/5

=25

The mean is 25 and the standard deviation is 10.  

σ=10

If a new card is received with $25, then the sum will be $150  

So the new mean will be:

μ'=(∑x)/n

=150/6

=25

And the new standard deviation will be:  

σ'= 9.12

We can clearly see that  

μ= μ'

and

σ> σ'

So the mean will remain the same and standard deviation will decrease. .