need some help with this functions homework question

After answering the presented question, we can conclude that As a equation result, the empty weight of the fish tank is 69 pounds.

A mathematical equation is a formula that connects two statements and denotes equivalence with the equals symbol (=). An equation is a mathematical statement that shows the equality of two mathematical expressions in algebra. In the equation 3x + 5 = 14, for example, the equal sign separates the variables 3x + 5 and 14. A mathematical formula describes the connection between the two sentences that occur on opposite sides of a letter. The symbol and the single variable are frequently the same. As in 2x - 4 Equals 2, for instance.

30 inches equals 30/12 feet equals 2.5 feet

12 inches equals 12/12 feet equals 1 foot

As a result, the tank's water capacity is:

V = 2.5 ft x 1 ft x 1 foot = 2.5 cubic feet

The weight of the water in the tank may then be calculated by multiplying the volume by the weight per cubic foot:

water weight = V x weight per cubic foot = 2.5 ft3 x 62.4 lb/ft3 = 156 lbs

Because the loaded tank weighs 225 pounds, the empty tank weighs:

empty tank weight Equals full tank weight - water weight = 225 lb - 156 lb = 69 lb

As a result, the empty weight of the fish tank is 69 pounds.

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The length of one of the sides of the square base is 6 inches.

Let's denote the length of one of the sides of the square base by "s" and the height of the pyramid by "h". Then, the surface area of the pyramid can be expressed as:

Surface area = area of square base + sum of areas of four triangular faces

Surface area = s^2 + 4(1/2)(s)(h)

We know that the surface area is 116 in^2 and the sum of the areas of the four triangular faces is 80 in^2. So we can substitute these values into the equation:

116 = s^2 + 4(1/2)(s)(h)

80 = 4(1/2)(s)(h)

We can simplify the second equation to get:

20 = (1/2)(s)(h)

We can solve for h by substituting the value of (1/2)(s)(h) from the second equation into the first equation:

116 = s^2 + 4(20)

116 = s^2 + 80

s^2 = 36

s = 6

Therefore, the length of one of the sides of the square base is 6 inches.

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By using the substitution method, we will see that the value of y is 23.

Here we have a system of linear equations, the system is:

y - x = 11

x = 12

The second equation is trivial, it just gives the value of x. Then we can use the substitution method and replace it in the first equation, then we will get:

y - 12 = 11

Now we can solve this for y, we will get:

y = 11 + 12

y = 23

That is the value of y.

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Answer:

Min: 1

Q1: 2
Median: 7
Q3: 9
Max: 11.5

Step-by-step explanation:

The five bars of the box plot correspond (from left-to-right) to the numbers in the five-number summary.

The first bar represents the minimum, which in this case is 1.

The second bar represents the first quartile (Q1), which in this case is 2.

The third bar represents the median, which in this case is 7.

The fourth bar represents the third quartile (Q3), which in this case is 9.

And the fifth bar represents the maximum, which in this case is 11.5.

Answer:

Min: 1

Q1: 2

Median: 7

Q3: 9

Max: 11.5

Step-by-step explanation:

I hope it helps:)

It is a better deal for Ella to use the loyalty card, since that way she will end up saving $0.29 for she would not have to pay for the sixth soda.

Using the loyalty card at the local store, Ella would get one soda for free after buying 5 sodas at the regular price of $0.89 each, which means she would pay for 5 sodas and get one free. So the total cost would be:

5 x $0.89 = $4.45

At the local fast food restaurant, the cost of each soda is $0.79, so for 6 sodas, the cost would be:

6 x $0.79 = $4.74.

Therefore, using the loyalty card at the local store is the better deal as Ella would save $0.29 compared to buying the sodas at the local fast food restaurant.

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Answer: 0.41

Step-by-step explanation:
To find the decimal point of a fraction, divide the numerator (the top half of the fraction) by the denominator (the bottom half of the fraction).

41 over 100 as a decimal point would be 41 divided by 100

Which produces the equivalent decimal, 0.41

P.S this is also how you find the percent of a number. To get the percent, move the decimal point 2 digits over (0.41 to 41.) and then add the percentage sign to the end of the number (41%)

0.41 = 41%

so 41 over 100 is 0.41, and 41 is also 41% of 100 (per cent means per 100)

Best of luck in 5th grade :)

If g(x) is the graph of f(x) where f(x) and g)(x) both are functions and f(x) is  shifted up 2 units, then the  formula for g(x) is g(x)= f(x) + 2

A function from one set X to another allocates exactly one element of the other set Y to each element of X. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

Here, we have

Given: If g(x) is the graph of f(x) shifted up 2 units. Here f(x) and g(x) are functions.

We have to write the formula for g(x).

Shifting up 2 units means you add 2 to f(x).

Shifted right 0 unit means you subtract 0 from the argument of the function f(x) (i.e. from x).

g(x) = f(x - 0) + 2

g(x) = f(x) + 2

Hence, the formula is g(x) = f(x) + 2

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well, is simply $400 plus 5% of $5000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of 5000}}{\left( \cfrac{5}{100} \right)5000}\implies 250\hspace{5em}\underset{ \textit{total earnings} }{\stackrel{400~~ + ~~250 }{\text{\LARGE 650}}}[/tex]

Answer:

$650

Step-by-step explanation:

5% of 5000 is 250. 250 + 400 = 650.

You would have earned $650 last week.

Note that when rewritten, the sum using sigma notation becomes Option B.

The rewritten sum using sigma notation with k as the index variable:

∑[k/(k+2)(k+1)], from k=1 to infinity

where ∑ denotes the sum from k=1 to infinity, and k represents the index of the summation.

In other words, the kth term of the series is k/(k+2)(k+1), and we are adding up all the terms of the series starting with k=1 and going to infinity.

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The acres of land that will be pollinated by 18 beehives is 48 acres of land.

The table shows the ratio of the number of beehives to the number of acres of the orchard.

The bees pollinate the plant at a constant rate. Let's find the acres of land that will be pollinated by 18 beehives.

Therefore, using the constant rate,

y = kx

where

Therefore,

8 = 3k

k = 8 / 3

Therefore, let's find the acres of land for 18 beehives

y = 8 / 3 × 18

y = 144 / 3

y  = 48 acres.

Therefore,

number of acres pollinated by 18 beehives = 48 acres

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One additional point on the coordinate plane so that the graph continues to represent y as a function of x is (5.-5).

In graphing, there are two main types of coordinates that are commonly used to locate and plot points:

1. Cartesian coordinates and polar coordinates. Cartesian coordinates, also referred to as rectangular coordinates, are located on a two-dimensional plane and use two perpendicular axes (x and y) to determine the position of a point. The horizontal axis (x) represents movement along the x-axis, and the vertical axis (y) represents movement along the y-axis. The origin is the point where the two axes meet and is assigned the coordinates (0, 0). The coordinates of any point are represented in the form (x, y).

2. Polar coordinates, on the other hand, use a central point (pole) and an angle and radial distance to locate a point. Polar coordinates are used to describe more complex functions and are often used in engineering and physics. The radial distance (r) is the distance from the pole to the point, and the angle (θ) represents the orientation or direction of the point. The coordinates of a point in polar form are represented in the form (r, θ).

To represent y as a function of x, there can be only one y-value for each x-value. Looking at the given points, it appears that there are no repeated x-values. So, to continue the graph, we just need to find the y-value for any new x-value that we choose.

One approach is to look for a pattern or trend in the given points. From the given points, we can see that as x increases, y first decreases, then increases, and then decreases again. So, we might choose a new x-value that is outside the given range, such as x = 5, and try to estimate the corresponding y-value based on the pattern we observed.

Using this approach, we can see that as x increases beyond 4, the corresponding y-values should continue to decrease. So, we might estimate that the point (5,-5) would be a reasonable choice to continue the graph. However, it's important to note that this is just one possible choice, and there may be other valid points that could be used to extend the graph.

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17.  The geometric mean of 14 and 32 is approximately 21.166.

18. The geometric mean of 6 and 40.5 is approximately 15.588.

19. The geometric mean of 15 and 24 is approximately 18.330.

What is mean?

In statistics, the mean (also known as the arithmetic mean or average) is a measure of central tendency that represents the sum of a set of numbers divided by the total number of numbers in the set.

To find the geometric mean of two numbers a and b, we use the formula:

x = √a.b

Using this formula, we can find the geometric mean of each pair of numbers:

To find the geometric mean of 14 and 32, we use the formula:

x = √14.32

x = √448

x ≈ 21.166

Therefore, the geometric mean of 14 and 32 is approximately 21.166.

To find the geometric mean of 6 and 40.5, we use the formula:

x = √6.40.5

x = √243

x ≈ 15.588

Therefore, the geometric mean of 6 and 40.5 is approximately 15.588.

To find the geometric mean of 15 and 24, we use the formula:

x = √15.24

x ≈ 18.330

Therefore, the geometric mean of 15 and 24 is approximately 18.330.

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Answer: 512/27 cubic yards.

Step-by-step explanation:

To find the volume of a cube, we need to cube the length of one of its edges.

The edge length of the cube is 2 2/3 yards or 8/3 yards.

Volume of the cube = (edge length)^3 = (8/3)^3 = 512/27 cubic yards.

Therefore, the volume of the cube with an edge length of 2 2/3 yards is 512/27 cubic yards.

Answer: C:10 Hope it helped! Bye bye :>

Step-by-step explanation:

.

Answer: Harry got 16 questions right  

Step-by-step explanation: 20% of 80 is 16 hope it helps

Answer:

(b) 11/15

Step-by-step explanation:

We can use the formula:

P(A U B) = P(A) + P(B) - P(A n B)

where P(A n B) is the probability of the intersection of events A and B.

We are given:

P(A) = 2/3

P(B) = 4/5

P(A U B) = 11/15

Substituting these values into the formula, we get:

11/15 = 2/3 + 4/5 - P(A n B)

To solve for P(A n B), we can simplify the right-hand side:

11/15 = 10/15 + 12/15 - P(A n B)

11/15 = 22/15 - P(A n B)

P(A n B) = 22/15 - 11/15

P(A n B) = 11/15

Therefore, the answer is (b) 11/15.

Answer:

x = -8 and y = 3

Step-by-step explanation:

Solve the system of equations by substitution:

x + y = 6

y = 5x

Substitute the value of y from the second equation into the first equation:

x + (5x) = 6

6x = 6

x = 1

Now, substitute the value of x into the second equation to find y:

y = 5(1)

y = 5

So, the solution to the system of equations is x = 1 and y = 5.

Solve the system using substitution:

y = -6x + 36

6y - x + 6 = 0

Substitute the value of y from the first equation into the second equation:

6(-6x + 36) - x + 6 = 0

-36x + 216 - x + 6 = 0

-37x + 222 = 0

-37x = -222

x = 6

Now, substitute the value of x into the first equation to find y:

y = -6(6) + 36

y = -36 + 36

y = 0

So, the solution to the system of equations is x = 6 and y = 0.

Solve by the substitution method:

5x + 9y = -13

-6x + y = 51

Rearrange the second equation to isolate y:

y = 6x + 51

Substitute the value of y from the second equation into the first equation:

5x + 9(6x + 51) = -13

5x + 54x + 459 = -13

59x + 459 = -13

59x = -472

x = -8

Now, substitute the value of x into the second equation to find y:

y = 6(-8) + 51

y = -48 + 51

y = 3

So, the solution to the system of equations is x = -8 and y = 3.

Answer:

1) x=1, y=5
2) x=6, y=0

3) x = -8, y = 99

Step-by-step explanation:

1)
x + 5x = 6

6x = 6

x = 1

y = 5

2)

y = -6x + 36

6y - x + 6 = 0

6(-6x + 36) - x + 6 = 0

-37x + 222 = 0

x = 6

y = 0

3)

5x + 9y = -13

-6x + y = 51

y = 6x + 51

5x + 9(6x + 51) = -13

59x + 459 = -13

x = -8

y = 99

9x-2+52=180

That's the answer

Answer:

14.44444444444444444444444444444444444

Step-by-step explanation:

9x - 2 + 52 = 180

simplify

9x +50 = 180

9x = 130

14.4444444444

Answer:

Step-by-step explanation:

Let's begin by assigning variables to represent the amounts invested in each vehicle.

Let x be the amount invested in CDs,

y be the amount invested in bonds, and

z be the amount invested in stocks.

From the problem statement, we know that:

x + y + z = 125000 (the total amount invested)

y = x + 60000 (the amount invested in bonds is $60000 more than in CDs)

0.0475x + 0.037y + 0.109z = 7970 (the total annual income from the investments)

We can use the second equation to substitute for y in the other two equations, giving us a system of two equations in two variables:

x + (x + 60000) + z = 125000

0.0475x + 0.037(x + 60000) + 0.109z = 7970

Simplifying the first equation, we get:

2x + 60000 + z = 125000

2x + z = 65000

Substituting z = 65000 - 2x into the second equation, we get:

0.0475x + 0.037(x + 60000) + 0.109(65000 - 2x) = 7970

Simplifying and solving for x, we get:

0.0475x + 0.037x + 0.109(65000) - 0.218x + 0.109(2x) = 7970 - 0.109(60000)

0.026x = 1730

x = 66538.46

So, $66538.46 was invested in CDs. Using the equations y = x + 60000 and z = 65000 - 2x, we can calculate that $126,538.46 was invested in bonds and $45,923.08 was invested in stocks.

Therefore, $66538.46 was invested in CDs, $126,538.46 was invested in bonds, and $45,923.08 was invested in stocks.

Answer: To three decimal places, k ≈ 0.052.

Step-by-step explanation: We are given the exponential growth function A = 29e^kt, where A is the population in millions t years after 1980.

In 1980, the population was 29 million, so A = 29 when t = 0. Substituting these values into the equation, we get:

29 = 29e^k(0)

29 = 29e^0

29 = 29

This confirms that the equation is true for t = 0.

In 1985, the population was 38 million, so A = 38 when t = 5. Substituting these values into the equation, we get:

38 = 29e^k(5)

Dividing both sides by 29, we get:

38/29 = e^5k

Taking the natural logarithm of both sides, we get:

ln(38/29) = 5k

Solving for k, we get:

k = ln(38/29) / 5 ≈ 0.052

Therefore, to three decimal places, k ≈ 0.052.

The value of the vehicle 13 years after purchase is $13,695.24.

What is exponential decay?

Exponential decay is a mathematical process in which a quantity decreases over time in a manner proportional to its current value. This means that the rate of decay is proportional to the amount of the substance remaining, and as the amount of the substance decreases, the rate of decay also decreases.

We can use the formula for exponential decay to find the approximate value of the vehicle 13 years after the purchase:

[tex]$V = V_0 e^{-rt}$[/tex]

where V0 is the initial value of the vehicle, r is the annual depreciation rate (as a decimal), t is the number of years since purchase, and e is the mathematical constant approximately equal to 2.71828.

Substituting the given values, we get:

[tex]$V \approx 29800 e^{-0.06*13}$[/tex]

[tex]$V \approx 29800 e^{-0.78}$[/tex]

V ≈ 29800 x 0.4593

V ≈ 13695.24

Therefore, the approximate value of the vehicle 13 years after purchase is $13,695.24.

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By solving the equation 2x² + 5x + xy = 2  , we found y'(2) = 1 by differentiation.

A technique for determining a function's derivative is differentiation. Mathematicians use a procedure called differentiation to determine a function's instantaneous rate of change based on one of its variables.

The most typical illustration is velocity, which is the rate at which a distance changes in relation to time.

To find y'(2) by implicit differentiation, we will need to take the derivative of both sides of the equation with respect to x, using the product rule for the term xy:

[tex]2x^2 + 5x + xy = 2[/tex]

Differentiating both sides with respect to x, we get:

4x + 5 + x(dy/dx) + y = 0

Now we can solve for dy/dx:

x(dy/dx) + y = -4x - 5

dy/dx = (-4x - 5 - y)/x

To find y'(2), we need to substitute x=2 and y=-8 into the equation we just derived:

y'(2) = (-4(2) - 5 - (-8))/2

y'(2) = (-8 + 5 + 4)

y'(2) = 1

Therefore, y'(2) = 1.

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Answer:

30[tex]units^{2}[/tex]

Step-by-step explanation:

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]12^{2}[/tex] + [tex]b^{2}[/tex] = [tex]13^{2}[/tex]  The hypotenuse needs to be c

144 + [tex]b^{2}[/tex] = 169  Subtract 144 from both sides

[tex]b^{2}[/tex] = 25

[tex]\sqrt{b^{2} }[/tex] = [tex]\sqrt{25}[/tex]

b = 5

Area of a triangle"

a = [tex]\frac{lw}{2}[/tex]

a = [tex]\frac{12x5}{2}[/tex]a = 30[tex]units^{2}[/tex]

Helping in the name of Jesus.

A sample size of at least 275 mice must be weighed in order to estimate the mean weight with a 95% confidence interval with a margin of error of 0.4 grams is used.

We may use the formula to determine the minimal sample size n required to estimate the mean weight of mice with a 95% confidence interval and a margin of error of 0.4 grams:

[tex]n = (\frac{ z * 6}{E} )^{2}[/tex]

where z is the required degree of confidence (in this case, 95% equates to a z-score of 1.96), б is the standard deviation (3 grams), and E is the maximum permissible error (0.4 grams).

When we enter the given values into the formula, we get:

[tex]n = [(1.96*3)/0.4]^2\\n = 274.576...[/tex]

We round up to the nearest integer because we can't have a fraction of a mouse and get:

n = 275 (rounded near to 100th)

As a result, a sample size of at least 275 mice must be weighed in order to estimate the mean weight with a 95% confidence interval with a margin of error of 0.4 grams is used.

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Value of variable x in the equation is 2.

In mathematics, an equation is a statement that two expressions are equivalent. It comprises of two sides with a phrase on each, usually divided by an equal symbol (=). An equation declares that for some or all of the values of the variables in the equation, the two expressions have the same value. Equations can include one or more variables and can be either linear or nonlinear. Finding the values of the variables that make the equation true is the first step in solving an equation.

Given equation

3(x+6)=24

Dividing the terms by 3, we get

x+6=8

x=8-6

x=2

Hence, value of variable x in the equation is 2.

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Step-by-step explanation:

Loretta's error is that she only took the square root of the coefficient 16, but forgot to take the square root of the variables m and n.

The correct solution is:

The square root of 16 is 4.

The square root of m^2 is m.

The square root of n^20 is n^10.

Putting it all together, we get:

√(16m^2n^20) = √16 * √(m^2) * √(n^20) = 4mn^10

Therefore, the correct answer is 4mn^10, not 8mn^10.

Answer:

92.74%.

Step-by-step explanation:

This is a binomial probability problem where the probability of rolling a six on a single roll of a fair die is p = 1/6, and the number of trials is n = 12.

Let X be the number of sixes rolled in 12 rolls. We want to find the probability of X ≤ 4.

Using the binomial probability formula, we have:

P(X ≤ 4) = Σ P(X = k) for k = 0 to 4where P(X = k) = (n choose k) p^k (1-p)^(n-k)

Thus, the probability of rolling no more than 4 sixes is:

P(X ≤ 4) = Σ P(X = k) for k = 0 to 4

= P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= (12 choose 0) (1/6)^0 (5/6)^12 + (12 choose 1) (1/6)^1 (5/6)^11 + (12 choose 2) (1/6)^2 (5/6)^10 + (12 choose 3) (1/6)^3 (5/6)^9 + (12 choose 4) (1/6)^4 (5/6)^8

= 0.9274 (rounded to four decimal places)

Therefore, the probability of rolling no more than 4 sixes in 12 rolls of a die is approximately 0.9274 or 92.74%.

The value of y which will make the lines j, k and l parallel as required to be determined in the given task content is; y = 8.

It follows from the given task content that the value of y which holds true for the given condition be determined.

By observation, the ratio which must hold is;

(2y - 10) / 9 = 4 / (10 - 4).

6 (2y - 10) = 9 × 4

12y - 60 = 36

12y = 96

y = 8.

Ultimately, the required value of x in the task content is; y = 8.

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Answer:

approximately 0.5774

Step-by-step explanation:

The cotangent (cot) of an angle is the reciprocal of the tangent (tan) of that angle. Mathematically, it can be expressed as:

cot(θ) = 1 / tan(θ)

Given that cot(θ) = 1.7321, we can use this value to find the tangent of angle θ.

cot(θ) = 1 / tan(θ)

1.7321 = 1 / tan(θ)

To solve for tan(θ), we can take the reciprocal of both sides of the equation:

1 / 1.7321 = tan(θ)

0.5774 ≈ tan(θ)

So, the tangent of angle θ is approximately 0.5774.