What are the intervals of increase and decrease for the absolute value function below?

1. Increase: x > 0, decrease: x < 0
2. Increase: x < 0, decrease: x > 0
3. Increase: y < 0, decrease: y > 0
4. Increase: y > 0, decrease: y > 0

Answer:

9.25x

Step-by-step explanation:

Answer:

angle 2 is 104

angle 9 is 66

angle 10 is 114

angle 7 is 76

Step-by-step explanation:

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct. The correct option is A.

To compare the volumes of the rectangular pyramid and the rectangular prism, we need to find the base area (BA) of the pyramid. The volume (V) of a pyramid is given by the formula:

\(V = \dfrac{1}{3} \times BA \times h\)

where BA is the base area and h is the height.

Given that the volume of the pyramid is 40 units³ and the height is 6 units, we can find the base area:

40 = (1/3) x BA x 6

Now, solve for BA:

\(BA = \dfrac{(40 \times 3)} { 6}\\BA = 20\ units^2\)

Now, let's check the options:

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.

The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, not 40 units³. So, this statement is incorrect.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.

We have already determined that the base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

This statement matches our calculations. The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, which is three times the volume of the pyramid. So, this statement is correct.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

The base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.

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The complete question is attached below:

A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?

A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.

A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.

A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.

You have d dollars to buy fence to enclose a rectangular plot of land. the fence for the top and bottom costs $a per foot and for the sides it costs $b per foot.

To find the dimensions of the plot with the largest area.

Total Money = D dollars

Total cost for top and bottom fence = $4(2x)

Total cost for sides fence = $8(2y)

Hence total cost of fencing = 4(2x)+8(2y) = 8x+16y

C = 8x+16y

Given cost (c) = D dollars

D = 8x+16y

Now Area of the plot A = xy

A = xy is optimizing function and D = 8x+16y

= \((\frac{D-16y}{8})=x\)

A = \(\frac{D-16y}{8}y\)

For A to be maximum \(\frac{dA}{dy}=0\)

A = \(\frac{D}{8}y-\frac{16}{8}y^{2}\)

\(\frac{dA}{dy} = \frac{D}{8}-\frac{16}{8}(2y)\)

\(\frac{dA}{dy} = \frac{D}{8}-4y\)

\(\frac{dA}{dy} = 0 = \frac{D}{8}-4y=0\)

\(\frac{D}{8} = 4y = y = \frac{D}{32}\)

Now \(\frac{d^{2}A }{dy^{2}} = -4 = -ve number\)

for y = \(\frac{D}{32}\) area is maximum

\(x = \frac{D-16y}{8} = \frac{D-16 (\frac{D}{32} )}{8} = \frac{D}{16}\)

Say the top and bottom dimensions are = \(\frac{D}{16}\)

Sides dimensions are = \(\frac{D}{32}\)

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The age of a meteor with a 238U / 206Pb ratio of 1/3 can be determined using the half-life of 238U (4.5 billion years), giving an age of 4.5 billion years. Non-radiogenic 206Pb in the sample would affect the age estimate.

The decay of 238U to 206Pb is an example of radioactive decay, where the parent isotope (238U) decays into a daughter isotope (206Pb) over time. The half-life of 238U is 4.5 billion years, which means that half of the original amount of 238U will decay into 206Pb after 4.5 billion years.

Suppose we start with a sample of meteor that has a 238U / 206Pb ratio of 1/3. This means that for every 1 atom of 238U, there are 3 atoms of 206Pb in the sample. Let's assume that all of the 206Pb in the sample is due to the decay of 238U.

After one half-life of 238U, half of the 238U in the sample will have decayed into 206Pb, and the ratio of 238U / 206Pb will be 1/6 (since we started with 1/3 and one half-life has passed). After two half-lives, three-quarters of the 238U will have decayed into 206Pb, and the ratio of 238U / 206Pb will be 1/11 (since there are now 1 atom of 238U for every 11 atoms of 206Pb).

To determine the age of the sample, we can use the formula for radioactive decay:

N(t) = N0 * (1/2)^(t/T)

where N(t) is the number of radioactive atoms remaining at time t, N0 is the initial number of radioactive atoms, T is the half-life, and t is the time that has elapsed.

In this case, we can use the ratio of 238U / 206Pb to calculate the initial number of 238U atoms, since we know that there are 3 atoms of 206Pb for every 1 atom of 238U in the sample. Let N0 be the initial number of 238U atoms, then we have:

N0 / (3N0) = 1 / 3

Solving for N0, we get:

N0 = 3

Using the formula for radioactive decay, we can solve for the age of the sample:

N(t) / N0 = (1/2)^(t/T)

Substituting the given values, we have:

1/2 = (1/2)^(t/4.5x10^9)

Solving for t, we get:

t = 4.5 billion years

Therefore, the age of the sample is 4.5 billion years.

If the meteor originally contained some 206Pb from a source other than radioactive decay, this would affect our age estimate because we assumed that all of the 206Pb in the sample was due to the decay of 238U. If there was some non-radiogenic 206Pb in the sample, then the amount of 238U that had decayed would be overestimated, leading to an age estimate that is too old. To account for this, we would need to measure the amount of non-radiogenic 206Pb in the sample and subtract it from the total amount of 206Pb to get the radiogenic component due to the decay of 238U.

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y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

Given,

y-intercept 4 and slope -1/5

Now y=-1/5x+4

Hence y=-1/5x+4 is the equation in slope-intercept form for the line with y-intercept 4 and slope -1/5

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We have a 1/6 chance of rolling doubles on the first roll. The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.

So we have a total of 36 outcomes over here. So we have 36 possibilities, and if we simplify this, 6/36 is 1/6. So the chance of rolling doubles on two six-sided dice numbered 1 to 6 is 1/6.

The odds of rolling a double on the second turn but not the first are (5/6) x (1/6) = 5/36.

We'll now look at the chances of getting out of jail by rolling doubles. Because there are more possibilities to examine, this probability is significantly more complex to compute.

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-0.05 is the average rate of change in median age per year from 1930 to 1960.

The ratio can be defined as the number that can be used to represent one quantity as a percentage of another. Only when the two numbers in a ratio have the same unit can they be compared. Ratios are used to compare two objects.

Given,  a data set that gives the median age of an American man at the time of his first marriage.

Year                             Median age

1910                              25.1

1920                             24.6

1930                             24.3

1940                             24.3

1950                             22.8

1960                             22.8

1970                             23.2

1980                             24.7

1990                             26.1

2000                             26.8

The average rate of change from 1930 to 1960 = (-24.3 + 22.8) / (1960-1930)

The average rate of change from 1930 to 1960 = -0.05

Therefore, the average rate of change in median age per year from 1930 to 1960 is -0.05.

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Answer: To determine the break-even quantity, we need to find the point where the revenue equals the cost. In other words, we need to solve the equation R(x) = C(x).

Given:

Setting R(x) = C(x), we have:

Subtracting 135x from both sides of the equation:

Simplifying the left side:

Dividing both sides by 45:

The break-even quantity is 1,236 units.

Since the break-even quantity (1,236 units) is less than the maximum number of units that can be sold (2,097 units), the firm can produce the product because it would make money.

To determine the break-even quantity and decide whether to proceed with the production of the new product, we need to analyze the cost and revenue data provided.

The cost function is given as C(x) = 135x + 55,620, where x represents the quantity of units produced. The revenue function is given as R(x) = 180x. To break even, the total cost and total revenue should be equal. We can set up an equation based on this condition: C(x) = R(x). Substituting the given cost and revenue functions: 135x + 55,620 = 180x

To solve for x, we can subtract 135x from both sides: 55,620 = 45x. Now, divide both sides by 45: x = 1,236. The break-even quantity is 1,236 units.

Since the number of units that can be sold is no more than 2,097 units, which is greater than the break-even quantity of 1,236 units, the firm can produce the product. The break-even point indicates the minimum number of units that need to be sold to cover the costs, and since the firm can sell more than the break-even quantity, it has the potential to make a profit. However, further analysis of other factors such as market demand, competition, and potential profitability should also be considered before making a final decision.

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Answer:

slope- 1

y-int- y=2x+-2

Step-by-step explanation:

In the equation of a straight line (when the equation is written as "y = mx + b"), the slope is the number "m" that is multiplied on the x, and "b" is the y-intercept (that is, the point where the line crosses the vertical y-axis). This useful form of the line equation is sensibly named the "slope-intercept form".

Answer:

Yes they are.

Answer:

oop sorry it is YES (auto correct sorry)

Step-by-step explanation:

7

10

=  

7 × 2

10 × 2

=  

14

20

Answer:

541

Step-by-step explanation:

Divide 6492 by 12

6492/12=541

Answer:

541

Step-by-step explanation:

6492/12

The equation for the ellipse is: \($\frac{x^2}{37}\) + \($\frac{y^2}{25}\) \(= 1$$\)

The standard equation for an ellipse centered at the origin is:

\($\frac{x^2}{a^2}\) + \($\frac{y^2}{b^2}\) \(= 1$$\)

where a is the distance from the center to a vertex, and b is the distance from the center to a co-vertex.

In this case, the vertices are located at \($(\pm\sqrt{37}, 0)$\), which means \($a=\sqrt{37}$\). The distance between the foci is \($2c=2\sqrt{12}=2\sqrt{3\times 4}=2\sqrt{3}\times 2=4\sqrt{3}$\), which means \($c=2\sqrt{3}$\).

The value of b can be found using the relationship between a, b, and c in an ellipse:

\($$a^2 = b^2 + c^2$$\)

Substituting the values we know, we get:

\($$37 = b^2 + (2\sqrt{3})^2$$\)

Simplifying:

\($$37 = b^2 + 12$$\)

\($$b^2 = 37 - 12 = 25$$\)

Taking the square root of both sides, we get:

\($$b = \pm 5$$\)

Since the co-vertices are located at \($(0,\pm b)$\), we can see that \($b=5$\) (and not -5, since the ellipse is centered at the origin).

Therefore, the equation for the ellipse is:

\($\frac{x^2}{37}\) + \($\frac{y^2}{25}\) \($ = 1$$\)

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Answer:

No, it is not proportional.

Step-by-step explanation:

This can be determined by looking at the first two items in the chart. I have looked at them all to find a certain pattern, but there wasn't any. The salesman earns $250 for one car sale, and he also earns $600 for two car sales, while this seems like it's just adding a $100 bonus, if you look at the third item on the chart adds a $200 bonus. You could be thinking that this is just adding a $100 bonus for how many cars were sold before, but then you move onto the fourth item on the chart. Which would give you $1,300 if the pattern was continued, yet instead the amount listed is $1,076.

Approximately normal with mean is $206,274 and standard deviation is $3,788 and this can be determined by applying the central limit theorem, option A.

There were 5,317 previously owned homes sold in a western city in the year 2000.

The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881.

Simple random samples of size 100.

According to the central limit theorem the approximately normal mean is $206274.

Now, to determine the approximately normal standard deviation, use the below formula:

\(s=\frac{\sigma}{\sqrt{n} }\)

where 's' is the approximately normal standard deviation, 'n' is the sample size, and  is the standard deviation.

Now, put the known values in the equation (1).

s = 37881 / √100

= 3788.1

s ≈ 3788

Therefore, option A is correct that Approximately normal with mean $206,274 and standard deviation $3,788.

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Complete question:

There were 5,317 previously owned homes sold in a western city in the year 2000. The distribution of the sales prices of these homes was strongly right-skewed, with a mean of $206,274 and a standard deviation of $37,881. If all possible simple random samples of size 100 are drawn from this population and the mean is computed for each of these samples, which of the following describes the sampling distribution of the sample mean?

(A) Approximately normal with mean $206,274 and standard deviation $3,788

(B) Approximately normal with mean $206,274 and standard deviation $37,881

(C) Approximately normal with mean $206,274 and standard deviation $520

(D) Strongly right-skewed with mean $206,274 and standard deviation $3,788

(E) Strongly right-skewed with mean $206,274 and standard deviation $37,881

Answer: The length of the radius is 13/2 m.

Step-by-step explanation:

The circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle and π is pi (approximately 3.14159).

Given that C = 13πm. To find the length of the radius, we can divide both sides of the equation by 2π:

C = 2πr

13πm = 2πr

r = 13πm/2π

r=13/2 m.

The length of the radius of the circle is 6.5 m

If the circumference of the circle is C and the radius is r

Therefore, C= 2πr

According to the sum, the circumference of the circle is 13π m

Substituting that value in the equation,

13π= 2πr

=> r= 13π/ 2π

=> r= 6.5 m

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Yes, the relationship holds true for all rectangles, regardless of the dimensions of the rectangle.

The opposite sides of a rectangle are equal in length and parallel to each other. Therefore, if we let the length of the rectangle be l and the width be w, then the opposite sides of the rectangle will have lengths of l and w, respectively. This can be written as the rule:

l = opposite side of the rectangle

w = adjacent side of the rectangle

Therefore, the opposite sides of a rectangle can be expressed as l = 2w, or w = 0.5l. This relationship holds true for all rectangles because by definition, a rectangle has four right angles and opposite sides that are equal in length. As a result, manipulating the sides of the rectangle will not change this relationship.

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Correct option is A,  f(x) -2 has changed the parent function f(x) = (0.5)x to its new appearance.

The parent function f(x) = log5x has been modified by reflecting it over the x-axis, extending it vertically by a factor of three, and moving it down by three units.

In the picture below you can see the blue line is the graph of the function

f(x) = log(5x) and the green line is the graph of the function

g(x) = log[5(x + 4)] - 2

Since the function f passes at point (2, 1), we must reduce it by 2 units to ensure that it also passes at position (-2, -1). To do this, we add 2 to the function f.

We only need to add 4 to the variable x to have the function go left when we obtain log(5x) - 2.

The function shifts to the left when you add a number to x;

The function moves to the right when you remove a number from x;

The function increases when you add a number to it;

The function decreases when you take a number away from it.

Then we get a function g(x) = log[5 (x + 4)] - 2.

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The calculated measure of angle y is 60 degrees

from the question, we have the following parameters that can be used in our computation:

The figure

From the figure, we can see that

The shape can be divided into two triangles such that

Each triangle is an equilateral triangle

The measure of an angle in an equilateral triangle is 60 degrees

using the above as a guide, we have the following:

y = 60

Hence, the value of y is 60 degrees

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According to the midsegment theorem, the midsegments are parallel to

and half the length of the opposite side.

The completed statement are as follows;

Reasons:

From the given graph of ΔABC, we have;

Coordinates of the points A, B, and C are; A(-5, 2), B(1, -2), and C(-3, -6)

The coordinates of the point D and E on \(\mathbf{\overline{DE}}\) are; D(-4, -2), and E(-2, 0)

The coordinates of the point F is; F(-1, -4)

\(\displaystyle Slope \ of \ line \ \overline{AC} = \mathbf{\frac{(-6) - 2}{-3 - (-5)} = \frac{-8}{2}} = -4\)

\(\displaystyle Slope \ of \ line \ \overline{EF} = \frac{0 - (-4)}{-2 - (-1)} = \frac{4}{-1} = -4\)

Length of EF  = √((-1 - (-2))² + (-4 - 0)²) = √(17)

Length of AC = √((-3 - (-5))² + (-6 - 2)²) = √(4 × 17) = 2·√(17)

Therefore, we have;

Because the slope of \(\mathbf{\overline {EF}}\) and \(\mathbf{\overline {AC}}\) are both , -4, \(\overline {EF}\) ║ \(\overline {AC}\). EF = \(\underline{\sqrt{17}}\), and AC

= \(\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}\),. Because \(\underline{\sqrt{17}}\) = \(\underline{\frac{1}{2} \cdot 2 \cdot \sqrt{17}}\), \(EF =\mathbf{ \frac{1}{2} AC}\)

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Answer:

a=5/9r

Step-by-step explanation:

if the proportion of body height and arm height is 5 to 9, that would be the proportion of the

Answer:

17.3

Step-by-step explanation:

square root of 300 is 17.32050808

17.32050808 rounded is 17.3

∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements from the given information

Two angles are given.

∠g = (2x-90)°

∠h = (180-2x)°

We have to find the statement which is true about the angles g and h.

If both angles are greater than zero.

Complementary angles add up to 90 degrees

i.e., ∠g and ∠h are complementary if ∠g + ∠h = 90°.

Substituting the given values:

∠g + ∠h

= (2x-90)° + (180-2x)° = 90°

Thus, ∠g and ∠h are complementary angles.

and both the angles are less than 90 degrees so we can tell that angles ∠g and ∠h  are acute.

So the statement ∠g and ∠h are acute angles is also true

Hence, ∠g and ∠h are complementary angles and ∠g and ∠h are acute angles are true statements

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The area of the triangle is 31.54 square units

From the question, we have the following parameters that can be used in our computation:

We have the following values

a = 7 units

c = 11 units

B = 55 degrees

The area of the triangle is calculated using the following area formula

Area = 1/2absin(C)

Substitute the known values in the above equation, so, we have the following representation

Area = 1/2 * 7 * 11 * sin(55 degrees)

Evaluate

Area = 31.54

Hence, the area is 31.54 square units

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Answer:

8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent.

Step-by-step explanation:

Solve addition and subtraction word problems, and add and subtract within 10.

Simplifying, we get:

w = (2, -1, 5)

To write the vector w = (2, -1, 5) as the sum of a vector parallel to u = (1, 4, -2) and a vector orthogonal to u, we need to find the projection of w onto u and then subtract it from w to obtain the orthogonal component.

The parallel component of w with respect to u is given by the scalar projection of w onto u, which is calculated as:

\(proj_{u}\)(w) = (w · u) / \(||u||^2\) * u

where · represents the dot product and\(||u||^2\) is the squared magnitude of u.

Let's calculate the parallel component first:

\(proj_{u}\)(w) = ((2, -1, 5) · (1, 4, -2)) / \(||(1, 4, -2)||^2\) * (1, 4, -2)

= (2 + (-4) + (-10)) / (\(1^2 + 4^2\)+\((-2)^2\)) * (1, 4, -2)

= (-12) / (1 + 16 + 4) * (1, 4, -2)

= (-12) / 21 * (1, 4, -2)

= (-12/21, -48/21, 24/21)

Simplifying, we have:

parallel component = (-4/7, -16/7, 8/7)

Now, to find the orthogonal component, we can subtract the parallel component from w:

orthogonal component = w - parallel component

= (2, -1, 5) - (-4/7, -16/7, 8/7)

= (2 + 4/7, -1 + 16/7, 5 - 8/7)

= (14/7 + 4/7, -7/7 + 16/7, 35/7 - 8/7)

= (18/7, 9/7, 27/7)

Therefore, we can write the vector w = (2, -1, 5) as the sum of a vector parallel to u = (1, 4, -2) and a vector orthogonal to u as:

w = parallel component + orthogonal component

w = (-4/7, -16/7, 8/7) + (18/7, 9/7, 27/7)

w = (14/7, -7/7, 35/7)

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The values of x are x = 0 and x = 2.The solution to the system of equations is (x, y) = (0, 5) and (2, 1).

To find the solution of the system of equations:

y = x² - 4x + 5

y = -x² + 5

We can set the two equations equal to each other:

x² - 4x + 5 = -x² + 5

Bringing all terms to one side:

x² + x² - 4x + 5 - 5 = 0

Combining like terms:

2x² - 4x = 0

Factoring out 2x:

2x(x - 2) = 0

Setting each factor equal to zero:

2x = 0    or   x - 2 = 0

Solving for x:

For 2x = 0:

x = 0

For x - 2 = 0:

x = 2

So, the values of x are x = 0 and x = 2.

To find the corresponding values of y, we substitute these x-values back into either of the original equations. Let's use the first equation:

For x = 0:

y = (0)² - 4(0) + 5

y = 5

So, when x = 0, y = 5.

For x = 2:

y = (2)² - 4(2) + 5

y = 4 - 8 + 5

y = 1

So, when x = 2, y = 1.

Therefore, the solution to the system of equations is (x, y) = (0, 5) and (2, 1).

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Answer:

28 cm area

Step-by-step explanation: