There were three ant hills in Mrs. Brown's yard. The first ant hill had 4,867,190 ants. The second ant hill had 6,256,304 ants, and the third ant hill had 3,993,102 ants. Choose the best estimate of the number of ants in Mrs. Brown's yard

Answer:

Step-by-step explanation:

Rules:

Take out the GCF (greatest common factor)

a)  [tex]9m^{4} -9m^{3}[/tex]             >take out GCF, what both terms can be divided by

  =9m³(m-1)                >when taking out GCF, divide both terms by GCF

b)  [tex]25x^{9}y^{10}-35x^{7}y^{5}[/tex]    >GCF is [tex]=5x^{7}y^{5}[/tex]

[tex]=5x^{7}y^{5}(5x^{2} y^{5}-7)[/tex]

c)   (x-1)(x-1)-3(x-1)​        >GCF is (x-1)

  =(x-1) [(x-1) - 3]          >within the bracket you can combine like terms

  =(x-1) (x-4)

Step-by-step explanation:

A) 9m^4 - 9m^3 = 9m^3 (m - 1)

As for the number, you already took 9 out because it's common for both. As for the m, m^4 is the same as m×m×m×m. So the common between both is m×m×m = m^3.

B) 25x^9y^10 - 35x^7y^5 umm are you sure it's well written? How do you have a power in a power?

C) (x-1)(x-1)-3(x-1) = (x²-1x-1x+1) - (3x-3)

= x² - 2x + 1 - 3x + 3

= x² - 5x + 4

The volume of the sphere is 4 π × 3 × h. Option C

To determine the expression, we need to know the formula for volume of a sphere.

The formula that is used for calculating the volume of a sphere is expressed as;

V = 1/3 πr²h

Given that the parameters of the formula are;

Now, substitute the values, we have;

Volume, V= 4/3 × π × 3² × h

Multiply the values, we get;

Volume =4 π × 3² × h/3

Divide the values

Volume =4 π × 3 × h

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Answer: 3

Step-by-step explanation:

Answer:

2hrs 24 mins

Step-by-step explanation:

Ok so let's make this problem a bit simpler by splitting it up.

Tim paints a room in 6 hours.

So, we can also say that she paints 1/6 of that room in 1 hour

Bella paints it in 4 hours

So, we can also say that she paints 1/4 of that room in 1 hour

Now, lets see what we have:

Bella: 1/4 every hour

Tim: 1/6 every hour

The problem states that they are working together, so we need to add the values we have:

1/4 + 1/6

We cannot just add them, we must make them have the same common denominator.

LCD is 12, you can find that by just doing the times tables for 4 and 6 and seeing what number they match on first.

3/12 + 2/12 = 5/12

So, tim and bella working together paint 5/12 of a room in 1 hour.

They paint 5/12 of a room in 60 minutes

They paint 1/12 of the room in 12 minutes(divide both values by 5)

So if they paint 1/12 of the room in 12 minutes, we can multiply both values by 12 to get our answer.

They paint the full room in 144 minutes(12*12).

144 minutes is 2 hours and 24 minutes

Answer:

Answer:17

Explanation: 5-0.75=4.25 4.25÷0.25=17

Hope this helps

To find the rate of change of the volume of the cone, we need to use the formula for the volume of a cone:

V = (1/3)πr^2h

Taking the derivative of both sides with respect to time, we get:

dV/dt = (1/3)π[2rh(dr/dt) + r^2(dh/dt)]

Substituting the given values:

r = 40 in (radius is increasing at a rate of 4 in/s)
h = 20 in (height is decreasing at a rate of 3 in/s)
dr/dt = 4 in/s
dh/dt = -3 in/s

Plugging these into the formula:

dV/dt = (1/3)π[2(40)(20)(4) + (40)^2(-3)]

dV/dt = (1/3)π[3200 - 4800]

dV/dt = (1/3)π(-1600)

dV/dt = -1681.99 in^3/s

Therefore, the volume of the cone is decreasing at a rate of approximately 1681.99 cubic inches per second when the radius is 40 inches and the height is 20 inches.
To find the rate at which the volume of the cone is changing, we can use the formula for the volume of a cone (V = (1/3)πr^2h) and differentiate it with respect to time (t).

Given:
dr/dt = 4 inches per second (increasing radius)
dh/dt = -3 inches per second (decreasing height)
r = 40 inches
h = 20 inches

First, let's differentiate the volume formula with respect to time:
dV/dt = d/dt[(1/3)πr^2h]

Using the product and chain rules, we get:
dV/dt = (1/3)π(2r(dr/dt)h + r^2(dh/dt))

Now, plug in the given values:
dV/dt = (1/3)π(2(40)(4)(20) + (40)^2(-3))

Simplify:
dV/dt = (1/3)π(6400 - 4800)

dV/dt = (1/3)π(1600)

Finally, calculate the rate:
dV/dt ≈ 1675.52 cubic inches per second

So, the volume of the cone is changing at a rate of approximately 1675.52 cubic inches per second.

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The ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).

What is function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

Here the given function is y=-4x+20.

Now put x=6 and y=4 then,

=> 4=-4(6)+20

=> 4 = -24+20

=> 4 ≠ -4.

Then the coordinate (6,4) dost not satisfy the function.

Put x=0 and y=20 then,

=> 20 = -4(0)+20

=> 20= 0+20

=> 20=20

Hence the coordinate (0,20) satisfy the function.

Now put x=-4 and y=20 then,

=> 20 = -4(-4)+20

=> 20 = 16+20

=> 20 ≠ 36

Hence the coordinate (-4,20) does not satisfy the function.

Now put x=10 and y=-20 then,

=> -20 = -4(10)+20

=> -20 = -40+20

=> -20=-20

Then the coordinate (10,-20) satisfy the function.

Hence the ordered pairs that satisfy the function is B)(0,20) and D)(10,-20).

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The Gross Profit Margin Ratio for Frontier Art Gallery is 69.38%, calculated by dividing the Gross Profit by Net Sales and multiplying the result by 100 to get the percentage.

Gross Profit Margin Ratio is calculated by dividing the Gross Profit by Net Sales and multiplying the result by 100 to get the percentage

Gross Profit = Net Sales - Cost of Merchandise Sold

Gross Profit = $62,481.45 - $19,123.49

Gross Profit = $43,357.96

Gross Profit Margin Ratio = (Gross Profit / Net Sales) x 100

Gross Profit Margin Ratio = ($43,357.96 / $62,481.45) x 100

Gross Profit Margin Ratio = 69.38%

Therefore, the Gross Profit Margin Ratio for Frontier Art Gallery is 69.38%.

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The length of the straight line between the school and the fire station is 4.6 miles.

We can form a right-angled triangle with the school at the right-angle.

The distance between the school and the fire station is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can calculate the length of the hypotenuse:

h^2 = 4.3^2 + 1.7^2

h^2 = 21.38

h ≈ 4.62

Rounding to the nearest tenth, the length of the straight line between the school and the fire station is approximately 4.6 miles.

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Answer:

A BOB, C TOT

Step-by-step explanation:

If we draw a vertical line throgh the word the left side is the mirror image of the right.

The length of the other side of the quadrilateral is 10.67 inches.

The other side of the quadrilateral measures 10.67 inches. This can be found by using the formula for the area of a quadrilateral, which is (1/2) x diagonal x height. We know the total area and one side length, so we can solve for the height. The height is 10.67 inches, which is the length of the other side.

To find the length of the other side of the quadrilateral, we need to use the formula for the area of a quadrilateral, which is (1/2) x diagonal x height.

We know the total area of the quadrilateral is 36.18 square inches, and we can assume that the side given (6.7 inches) is one of the diagonals. We can solve for the height, which represents the length of the other side.

Using algebra, we can rearrange the formula to solve for the height:

Area = (1/2) x diagonal x height

36.18 = (1/2) x 6.7 x height

Multiplying both sides by 2:

72.36 = 6.7 x height

Dividing both sides by 6.7:

height = 10.67 inches

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In ΔMNO, possible values of ∠N are 64.6° and 115.4°.

To find the possible values of ∠N, follow these steps:

1. Since the sum of angles in a triangle is 180°, we first find ∠O by subtracting ∠M from 180°: 180° - 38° = 142°.

2. Next, we use the Law of Sines to find the sine of ∠N: sin(∠N) = (n * sin(∠O)) / m = (88 * sin(142°)) / 60.

3. Solve for sin(∠N), which gives us two possible values: sin(∠N) ≈ 0.8988 and sin(∠N) ≈ -0.8988.

4. Find the inverse sine (arcsin) of both values to get the possible angles for ∠N: arcsin(0.8988) ≈ 64.6° and arcsin(-0.8988) ≈ 115.4° (adding 180° to the negative result).

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The figure that we have is an equilateral triangle. AD is the height of the triangle while BC represents the length of one of the sides. To get the length of one of the sides, we can use the expression;

S= 2/sqrt3 * h

To get the relationship between AD and BC, we need to first note that the shape is an equilateral triangle. Next, we identify AD as the height of the triangle and BC as the length of one of the three equal sides.

So, the relationship between the height and sides is obtained with the formula: S= 2/sqrt3 * h or S = 1.1547 * h.

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The estimate is 7/15.

The given expression is

4/5-1/3

We see that the denominators of both functions are different

So, the numerators can't be added/subtracted directly.

For this, we need to find the equivalent fraction of the given fractions, and the equivalent fractions should have the same denominator.

Now, the denominators are 5 and 3.

To have a common denominator in both fractions, we find the LCM of the denominators.

∴ The LCM of 5 and 3 = 15

Converting the fraction 4/5 into a fraction with 15 as the denominator,

4/5=4×3/5×3=12/15.

The same for 1/3

1/3= 1×5/3×5=5/15

Replacing 4/5 and 1/3 with the equivalent fractions in the given expression, we get,

12/15-5/15=(12-5)/15=7/15

Hence, the estimate is 7/15.

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Answer:

Step-by-step explanation:

The value of 2s in 43,290 is 2,000, while the value of 2s in 32,865 is 20.

B. 200 is 1/20 the value of 2,000.

This statement is correct, as 200 is 1/10 of 2,000, and there are two 0s in the value of 2s in 43,290 compared to one 0 in the value of 2s in 32,865.

The equations that are TRUE based on the exponential function 2x = 8, are I, III and V.

To convert this equation into log equation, we will apply the general rule of logarithm equation as follows;

2x = 8

log2(2x) = log2(8)

Using the logarithmic rule that;

logb(xy) = ylogb(x),

We can simplify the left side of the equation to;

xlog2(2) = log2(8)

Since log2(2) = 1, we can simplify the equation further to;

x = log2(8)

Also in linear equation, we have

2x = 8

x = 8/2

x = 4

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Answer:

Combining like terms,

(4x - 6) + (5x + 1) = 9x - 5

The area of the sign can be calculated by finding the area of the trapezoid shape. The formula for the area of a trapezoid is A = (1/2) * (base1 + base2) * height. In this case, the bases are 5.5 feet (half of 11 feet, which is the flat top of the five-sided figure) and 9 feet (the entire length of the image), and the height is 4 feet. Plugging these values into the formula, we get:

A = (1/2) * (5.5 + 9) * 4

A = (1/2) * 14.5 * 4

A = 7.25 * 4

A = 29

So, the area of the sign is 29 square feet.

The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 71.5 inches, the width is given as 60 inches, and the volume is given as 43,972.5 in^3. We can solve for the height by dividing the volume by the product of the length and width:

Height = Volume / (Length * Width)

Height = 43,972.5 / (71.5 * 60)

Height ≈ 10.25 inches

So, the height needed to reach the desired volume is approximately 10.25 inches.

The area of the rectangular box face can be calculated by finding the length of the sides of the rectangle using the given coordinates, and then using the formula for the area of a rectangle, which is A = length * width. In this case, the length is the difference between the x-coordinates of the two points on the x-axis (4 - (-8) = 12) and the width is the difference between the y-coordinates of the two points on the y-axis (4 - (-2) = 6). Plugging these values into the formula, we get:

A = 12 * 6

A = 72

So, the area of the label needed to cover the face of the box is 72 square inches.

The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, we can use the given coordinates of the four points to find the lengths of the sides. The length is the difference between the x-coordinates of the two points on the x-axis (3 - (-2) = 5) and the width is the difference between the y-coordinates of the two points on the y-axis (6 - (-3) = 9). Since the opposite sides of a rectangle have equal lengths, the perimeter is twice the sum of the length and width:

Perimeter = 2 * (Length + Width)

Perimeter = 2 * (5 + 9)

Perimeter = 2 * 14

Perimeter = 28

So, the perimeter of the rectangle created by the points is 28 units.

The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the length is given as 14.2 yards (14 and one-fifth yards), the width is given as 7 yards, and the height is given as 8 yards. Plugging these values into the formula, we get:

Volume = Length * Width * Height

Volume = 14.2 * 7 * 8

Volume ≈ 795.2

So, the volume of the rectangular prism is approximately 795.2 cubic yards. Answer: seven hundred ninety-five and one-fifth yd3

Answer:

The largest volume that such a box can have is (3/4)²(3/2)²/4 = 1.6875 m³

Step-by-step explanation:

4. Let the sides of the rectangle be 'l' and 'w', where lw = A, the fixed area. The perimeter P is given by P = 2l + 2w. To minimize P, we need to find the values of 'l' and 'w' that make P as small as possible. Solving the equation for 'w' in terms of 'l' from lw = A, we get w = A/l. Substituting this into the equation for P, we get P = 2l + 2(A/l). Taking the derivative of P with respect to 'l' and setting it to zero, we get 2 - 2A/l² = 0, which implies l = √A. Substituting this value into lw = A, we get w = √A. Therefore, a square with sides of length √A has the minimum perimeter among all rectangles with a fixed area of A.

Let the side length of the square base be 'x' and the height of the box be 'h'. Then the volume of the box is V = x²h = 400. We need to minimize the surface area S of the box, which is given by S = x² + 4xh. Solving the equation for 'h' in terms of 'x' from V = x²h, we get h = 400/x². Substituting this into the equation for S, we get S = x²+ 4x(400/x²) = x² + 1600/x. Taking the derivative of S with respect to 'x' and setting it to zero, we get 2x - 1600/x² = 0, which implies x = 10 cm. Therefore, the dimensions of the box that minimizes the amount of material used are 10 cm x 10 cm x 4 cm.

Let the side length of the square cut out from each corner be 'x', and the height of the box be 'h'. Then the volume of the box is V = x²h. The length and width of the base of the box are (3-2x) and (3-2x) respectively. We need to maximize the volume V of the box subject to the constraint that the length and width of the base are positive. Taking the derivative of V with respect to 'x' and setting it to zero, we get h = (3-2x)²/4. Substituting this into the equation for V, we get V = x²(3-2x)²/4. Taking the derivative of V with respect to 'x' and setting it to zero, we get x = 3/4 m. Therefore, the largest volume that such a box can have is (3/4)²(3/2)²/4 = 1.6875 m³

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The absolute potential (V) at a point due to a point charge (Q) is given by the formula: V = kQ / r

where k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2), Q is the charge in Coulombs, and r is the distance between the point and the charge.

First, we'll find the absolute potential at point A (3, 2, 3) m due to the charge Q = 0.4 nC at the origin.

1. Convert Q to Coulombs: Q = 0.4 nC = 0.4 x 10^(-9) C
2. Find the distance r between the origin and point A using the Pythagorean theorem: r = √(3^2 + 2^2 + 3^2) = √(9 + 4 + 9) = √22
3. Calculate V at point A: V_A = (8.99 x 10^9)(0.4 x 10^(-9)) / √22 ≈ 25.67 V

Now, we'll calculate the absolute potential at the new position (5, 3, 3) m due to the charge Q relocated to point B (5, 3, 3) m.

1. Find the distance r between point B and the new position: r = √((5-5)^2 + (3-3)^2 + (3-3)^2) = 0 (same point)
2. Since r = 0, the absolute potential at the new position is undefined (potential would go to infinity if r approaches 0).

So, the absolute potential at point A is approximately 25.67 V, and the absolute potential at the new position is undefined.

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Using the exponential function to estimate the average price of a gallon of orange juice in 2020, the average price in 2020 is $6.39

To estimate the average price of a gallon of orange juice in 2020 using the given exponential function f(x) = 1.07(1.03^x) + 3.79, first, determine the number of years after 1990, which is r:

r = 2020 - 1990 = 30

Next, substitute r with 30 into the function:

f(30) = 1.07(1.03^30) + 3.79

Calculate the value of f(30):

f(30) ≈ 1.07(2.427) + 3.79 ≈ 2.599 + 3.79 ≈ 6.389

Round your answer to the nearest cent:

Average price in 2020 ≈ $6.39

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The population in this study is the jars of marinara sauce produced at the Barilla plant in Ames, IA.

The population in this study refers to all jars of marinara sauce produced at the Barilla plant in Ames, IA in the last week. It represents the entire set of jars that the quality assurance engineer could potentially sample from.

The population mean is stated as 26.2 ounces, indicating the average amount of sauce per jar for the entire population. The population standard deviation is given as 0.04 ounces, representing the variability in the amount of sauce across all jars produced.

The quality assurance engineer randomly selected a sample of 34 jars from this population and found the mean amount of sauce per jar to be 26.197 ounces.

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The critical point(s) of the function f(x) = x^3 + x - 3 + 2 are determined to find the x-coordinate(s) of the local minimum or local maximum.

To find the critical point(s) of the given function, we need to first find the derivative of the function and then solve for the value(s) of x that make the derivative equal to zero.

Given function: f(x) = x^3 + x - 3 + 2

Find the derivative of the function f(x) with respect to x.

f'(x) = 3x^2 + 1

Set the derivative f'(x) equal to zero and solve for x.

3x^2 + 1 = 0

Subtract 1 from both sides of the equation.

3x^2 = -1

Divide both sides of the equation by 3.

x^2 = -1/3

Take the square root of both sides of the equation.

x = ±√(-1/3)

Since the square root of a negative number is not a real number, the function f(x) does not have any real critical points. Therefore, the critical point(s) for the function f(x) = x^3 + x - 3 + 2 is DNE (Does Not Exist) in terms of real numbers.

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The length of the diagonal of Stacy's ceiling using the Pythagorean Theorem and trigonometry is 35.36 ft.

(a) Using the Pythagorean Theorem:

Since the ceiling is a square, we can treat it as two right triangles. Let's call the length of the diagonal 'd'. Now, we can apply the Pythagorean Theorem (a² + b² = c²) to one of the right triangles:

a² + b² = d²
25² + 25² = d²
625 + 625 = d²
1250 = d²

Now, take the square root of both sides:

√1250 = d
d ≈ 35.36 ft

(b) Using trigonometry:

In one of the right triangles, the angle between the two sides of the square (25 ft each) is 45 degrees. We can use the tangent function (tan) to relate the angle to the side lengths:

tan(45) = opposite side / adjacent side
tan(45) = 25 / 25

Since tan(45) = 1, we have 1 = 1, which confirms the angle is 45 degrees. Now, we can use the sine or cosine function to find the diagonal:

sin(45) = opposite side / hypotenuse
sin(45) = 25 / d

OR

cos(45) = adjacent side / hypotenuse
cos(45) = 25 / d

Both functions give us the same result since the angles are 45 degrees. Solving for 'd':

d = 25 / sin(45)
d ≈ 35.36 ft

So, the length of the diagonal of Stacy's ceiling is approximately 35.36 ft using both methods.

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The null hypothesis (H0) is that there is no significant difference in mean weight loss between men and women, or μm - μw = 0. The alternative hypothesis (Ha) is that there is a significant difference in mean weight loss between men and women, or μm - μw ≠ 0.

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This procedure is not appropriate because (A) the two sample proportions were not computed from independent samples.

Independent samples are those chosen at random such that their observations do not depend on the values of other observations. Many statistical analyses are predicated on the assumption of independent samples. Others are intended to evaluate non-independent samples.

Assume that quality inspectors want to compare two laboratories to see if their blood tests produce identical results. Both labs receive blood samples drawn from the same ten children for analysis.

The test results are not independent because both labs analyzed blood samples from the same ten youngsters. The inspectors would need to perform a paired t-test, which is based on the assumption that samples are dependent, to compare the average blood test results from the two labs.

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Correct question:

A polling organization asks a random sample of 1,000 registered voters which of two candidates they plan to vote for in an upcoming election. Candidate A is preferred by 400 respondents, Candidate B is preferred by 500 respondents, and 100 respondents are undecided. George uses a large sample confidence interval for two proportions to estimate the difference in the population proportions favoring the two candidates. This procedure is not appropriate because

(A) the two sample proportions were not computed from independent samples

(B) the sample size was too small

(C) the third category, undecided, makes the procedure invalid

(D) the sample proportions are different: therefore the variances are probably different as well

(E) George should have taken the difference interval for a single proportion instead 500-400 1,000 and then used a large sample confidence

The typical population of a New Jersey county can be described as being around 445,349 people which is also the median population of a New Jersey country.

Based on the given information, the median population of a New Jersey county is 445,349 people. This means that half of the counties in the state have a population above this number, while the other half have a population below it.

However, it is important to note that the range of county populations in New Jersey is quite large, with some counties having as little as 60,000 people and others having almost 1,000,000 people. This indicates that there is significant variability in the population size of counties across the state.

The interquartile range (IQR) of county populations is also provided, which tells us that the middle 50% of county populations fall within a range of 467,983 people. This suggests that while there is variability in county populations, there is also some level of consistency in the distribution of populations across the state.

Overall, the typical population of a New Jersey county can be described as being around 445,349 people, with some counties having significantly larger or smaller populations.

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Where the above graph and conditions are given,  the value of k that satisfies g(x) = f(x+k) is k = -2.

We can determine the value of k by using the given relationship between g(x) and f(x+k).

If g(x) = f(x + k), then we can substitute the given values of x in g(x) to get:

g(-1) = f(-1 + k) --> 5 = f(-1 + k)

g(0) = f(0 + k) --> 4 = f(k)

g(1) = f(1 + k) --> 3 = f(1 + k)

g(2) = f(2 + k) --> 2 = f(2 + k)

g(3) = f(3 + k) --> 3 = f(3 + k)

We know that f(x) is a v-shaped graph with a vertex at (0,2) and points at (-1,3) and (1,3). Therefore, we can conclude that f(k) = 4, which means that k is the x-coordinate of the vertex of f(x) shifted to the left or right.

Since the vertex of f(x) is at (0,2), and the x-coordinate of the vertex of f(x+k) is at k, we have:

k = 0 --> vertex of f(x+k) is at (0,2)

k = -1 --> vertex of f(x+k) is at (-1,2)

k = 1 --> vertex of f(x+k) is at (1,2)

k = 2 --> vertex of f(x+k) is at (2,2)

Therefore, the value of k that satisfies g(x) = f(x+k) is k = -2.

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The probability of not rolling a multiple of 4 with the 6 sided dice is P =0.5

A 6D dice has the 6 outcomes {1, 2, 3, 4, 5, 6}, The ones that are a factor of 4 are:

{1, 2, 4}

Then 3 out of 6 outcomes are a factor of 4, thus, the other 3 aren't factors of 4.

Then the probability of not rolling a multiple of 4 is given by the quotient between the number of outcomes that arent multiples of 4 and the total number of outcomes.

P = 3/6 = 0.5

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The inverse function of f(x) = ∛(8x) + 4 is f^-1(x) = 1/8(y - 4)^3

To find the inverse function of f(x), we need to solve for x in terms of f(x).

To find the inverse function of f(x) = ∛(8x) + 4, we can follow these steps:

Step 1: Replace f(x) with y:

y = ∛(8x) + 4

Step 2: Solve for x in terms of y:

y - 4 = ∛(8x)

Cube both sides:

(y - 4)^3 = 8x

x = 1/8(y - 4)^3

Step 3: Replace x with f^-1(x):

f^-1(x) = 1/8(y - 4)^3

Therefore, the inverse function of f(x) is f^-1(x) = 1/8(y - 4)^3

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