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Answer:

The average rate of change of the given function over the interval [2, 4] is -4.

Step-by-step explanation:

To find the average rate of change of a function f(x) over the interval [a, b], we should use the formula:

[tex]\boxed{\textsf{Average rate of change}=\dfrac{f(b)-f(a)}{b-a}}[/tex]

Given function:

[tex]f(x) = x^3 - 7x^2 + 10x[/tex]

To find the average rate of change of the given function over the interval [2, 4], we need to first find the values of f(2) and f(4).

[tex]\begin{aligned}f(2) &= (2)^3 - 7(2)^2 + 10(2)\\&= 8 - 7(4) + 10(2)\\&= 8 - 28 + 20\\&= -20 + 20\\&= 0\end{aligned}[/tex]

[tex]\begin{aligned}f(4) &= (4)^3 - 7(4)^2 + 10(4)\\&= 64 - 7(16) + 10(4)\\&= 64 - 112 + 40\\&= -48+ 40\\&= -8\end{aligned}[/tex]

Substitute the values into the formula for the average rate of change over the interval [2, 4]:

[tex]\textsf{Average rate of change} = \dfrac{f(4) - f(2)}{4 - 2} = \dfrac{-8-0}{4-2}=\dfrac{-8}{2}=-4[/tex]

Therefore, the average rate of change of the given function over the interval [2, 4] is -4.

After answering the presented question, we can conclude that probability Therefore, the probability of not selecting a white shirt is 16/24 = 2/3. So, the answer is (B) 2/3.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many fields, including statistics, economics, science, and engineering.

There are 24 t-shirts in the basket, and 4 are navy, 12 are red, so the remaining (24 - 4 - 12) = 8 t-shirts must be white.

The probability of not selecting a white shirt can be found by dividing the number of non-white shirts by the total number of shirts in the basket.

The number of non-white shirts is 4 (navy) + 12 (red) = 16.

Therefore, the probability of not selecting a white shirt is 16/24 = 2/3.

So, the answer is (B) 2/3.

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No, it is not sufficient for the environmentalist to use a simple random sample of 101 cars. The reason is that the sample size should be determined based on the required level of precision and the desired level of confidence in the hypothesis test.

In this case, since the environmentalist is claiming that the percentage of hybrids in the city is higher than the national percentage of 3%, it would be appropriate to use a one-tailed hypothesis test. The null hypothesis would be that the percentage of hybrids in the city is equal to 3%, and the alternative hypothesis would be that the percentage of hybrids in the city is greater than 3%.

To determine the sample size needed for this hypothesis test, the environmentalist would need to specify the desired level of significance (e.g., 0.05) and the desired level of power (e.g., 0.80). Based on these parameters, the environmentalist could use a statistical power calculator to determine the required sample size.

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Answer:

the height of the water in Container B is 22.48 feet.

Step-by-step explanation:

Answer:

C. cos A = 1 and sin B = 1.

Step-by-step explanation:

The angles in a triangle must add up to 180°. Since angle C is 90°, angles A and B must add up to 90°. Therefore, the sine of angle A and the sine of angle B must both equal 1. Since the sine of an angle is equal to the cosine of its complement, cos A = 1 and sin B = 1.

2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.

A circle is a two-dimensional object in geometry made up of all points in a plane that seem to be equidistant from a certain point known as the centre. The radius of a circle is the distance from the centre to any point on the circle. The diameter is the length of a line joining two points on a circle and running through its centre. The area of a circle is the space inside of it, and the circumference is the distances around the edge. Tangent lines perpendicular to radii, inscribed and encircled angles in relation to the diameter, and a constant diameter to diameter ratio (pi) are only a few of the crucial characteristics of circles.

given

The circle has a radius of 7 feet, and its area is:

A=r2 = (22/7)x7/2 = 154 square feet

The circle is divided into six equal sections, each of which will have the following area:

6 / 154 = 25.67 square feet (rounded to two decimal places)

An region of two of the pieces will include:

2 x 25.67 square feet equals 51.34 square feet. Hence, option 3—51 1/3 square feet—is the correct response.

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The first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.

A mathematical entity with both magnitude (size) and direction is called a vector. It can be depicted graphically as an arrow, with the direction and length of the arrow representing the magnitude and direction, respectively.

To describe the location of the ship at 2:30 pm, we need to find its position vector relative to the port. Since the ship travels at a bearing of 214°, we can represent its motion by a vector with magnitude 15 (the average speed in miles per hour) and direction 214° (measured counterclockwise from due south).

First, let's convert the direction to radians:

214° = (214/180)π = 1.1868π

Then, we can write the vector in component form as follows:

v = (15 cos(1.1868π), 15 sin(1.1868π)) ≈ (-6.20, -13.56)

So the ship's position at 2:30 pm can be represented by the vector v ≈ (-6.20, -13.56), which means that it is approximately 6.20 miles west and 13.56 miles south of the port.

In the scenario, the ship's average speed of 15 miles per hour means that it travels 15 miles in one hour. Therefore, in two and a half hours (from noon to 2:30 pm), the ship travels 37.5 miles in the direction of 214°. The components of the position vector indicate the distance the ship has traveled in the westward and southward directions, respectively, relative to the port. Therefore, the first component (-6.20) means that the ship has traveled 6.20 miles westward of the port, and the second component (-13.56) means that it has traveled 13.56 miles southward of the port.

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Answer:

Mary is 36 years old

Her son is 12 years old

Step-by-step explanation:

Let's assume, that Mary's son is x years old and Mary is 3x years old

Let's write 2 equations according to the given information:

x = 3x (Mary is 3 times older than her son)

3x + 12 = 2(x + 12) (after 12 years, she will be 2 times older than her son)

3x + 12 = 2x + 24

3x - 2x = 24 - 12

x = 12

That means, Mary's son is 12 years old

Mary is 3 × 12 = 36 years old

This is used to calculate the height of the object at any time t during its flight.

The equation you provided represents the height of an object (in meters) at time t (in seconds) when it is thrown or projected upward with an initial velocity of v (in meters per second) from an initial height of hi (in meters) above the ground.

The acceleration due to gravity is taken to be -9.8 m/[tex]s^2[/tex] (negative since it acts downward), and the formula for the height is derived from the equation of motion:

h(t) = -1/2 [tex]gt^2[/tex] + vt + hi

Where:

g = 9.8 m/[tex]s^2[/tex] (acceleration due to gravity)

t = time (in seconds)

v = initial velocity (in meters per second)

hi = initial height (in meters)

The coefficient -4.9 in the equation you provided is simply half of the acceleration due to gravity (-9.8/2 = -4.9).

This is because the object is thrown upward and experiences a deceleration due to gravity that decreases its upward velocity by 9.8 m/[tex]s^2[/tex] until it reaches the maximum height and then starts to fall back down.

So, for any given initial velocity and height, this equation can be used to calculate the height of the object at any time t during its flight.

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Answer:

- Y-intercept: (0, 2) or just 2

- Slope: -1

- Line: y + x = 2 or y = -x + 2

Step-by-step explanation:

Answer: divide 1/5 by the price of the CD

Formula: A = P(1+r/n)(nt)

Step-by-step explanation: , if you have a $1,000 CD with a term of three years and an APY of 5%, you can multiply $1,000 by 5% to find the interest

Answer:

20% of his money

Step-by-step explanation:

it's 1/5 of 100% of his money

Answer:

I have graphed it in the explanation part.

Step-by-step explanation:

First, we have to rewrite the two equations in the form y = mx + b.

2x - y = 4

-y = -2x + 4

y = 2x - 4

x - y = -2

-y = -x - 2

y = x + 2

As we see from the graph, the intersect point is at (6, 8)

The point with the y-coordinate of 0 splits the directed line segment from J to K into a 5:1 ratio.

An X coordinate value denotes a location that is relative to a point of reference to the east or west. A Y coordinate value denotes a location that is relative to a point of reference to the north or south.

Considering J (1, -10) and K (7, 2)

In this case, let's suppose that point L divides the directed line segment from J to K into a 5:1 ratio.

We know that from coordinate geometry's inherent characteristics.

The point's coordinates are (x1, y1), (x2, y2) where they meet in the ratio of m:n.

[tex](\frac{mx_{2}+nx_{1} }{m+n}, \frac{my_{2}+ny_{1} }{m+n} )[/tex]

Now putting the respective values,

= ([tex](\frac{(5 .1)(1 .1) }{5 +1} , \frac{(5 . 2)(1 . (-10))}{5+1}[/tex]

= (6, 0)

Therefore, the y-coordinate of the point that divides the directed line segment from J to K into a ratio of 5:1 is 0.

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The area of the bases of the second triangular pyramid will be 3 times the first one.

What is a triangular pyramid?

A tetrahedron is a four-sided, three-dimensional object that is also known as a triangular pyramid. Its triangular base is formed by three triangles, the sides of which meet at the apex above the base.

We are given that a triangular pyramid with a volume of 90 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H

⇒ 90 = [tex]\frac{1}{3}[/tex] * A * 15

⇒ 90 = A * 5

⇒ A = 18 square inches.

Similarly, another pyramid with a volume of 270 cubic inches has a height of 15 inches.

So, area of the bases is

⇒ Volume = [tex]\frac{1}{3}[/tex] * A * H

⇒ 270 = [tex]\frac{1}{3}[/tex] * A * 15

⇒ 270 = A * 5

⇒ A = 54 square inches.

Hence, the area of the bases of the second triangular pyramid will be 3 times the first one.

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Since we know that the equation has the solutions  [tex]x = 4[/tex] and [tex]x = -4[/tex] the value of a could be either  [tex]8[/tex] or  [tex]-8[/tex] .

We know that the product of two factors is equal to zero only when at least one of the factors is zero.

[tex](x + 4) \ (2x - a) = 0[/tex]

This equation has two factors:  [tex](x + 4)[/tex] and [tex](2x - a)[/tex] . We can set each of these factors equal to zero and solve for x to find the values that make the equation true.

Setting  [tex](x + 4)[/tex] equal to zero, we get:

[tex]x + 4 = 0[/tex]

[tex]x = -4[/tex]

This means that  [tex]-4[/tex] is one of the solutions of the equation.

Setting  [tex](2x - a)[/tex] equal to zero, we get:

[tex]2x - a = 0[/tex]

[tex]2x = a[/tex]

[tex]x = a/2[/tex]

This means that [tex]a/2[/tex] is another solution of the equation.

Since we know that the equation has the solutions  [tex]x = 4[/tex] and [tex]x = -4[/tex]  , we can substitute these values into the expression we found for x in terms of a to get:

[tex]a/2 = 4[/tex] or  [tex]a/2 = -4[/tex]

Solving for a in each case, we get:

[tex]a = 8[/tex] or [tex]a = -8[/tex]

Therefore, the value of a could be either  [tex]8[/tex] or  [tex]-8[/tex] .

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Answer:

The answer to your problem is:

AB= 30cm

BD= 16cm

Step-by-step explanation:

Since the one shown is to be dilated by a factor of 2, our new dimensions are 2x / 2y. We multiply each side length by two to get our new dilated image.

Which the side lengths being:

AB= 30cm

BD= 16cm

Thus the answer to the problem is:

AB= 30cm

BD= 16cm

The calculated length of AC from the right triangles is 320 units

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

The right triangle

The length of the segment AC is calculated as

sin(30) = 160/AC

Make AC the subject

So, we have

AC = 160/sin(30)

When evaluated, we get

AC = 320

Hence the length of AC is 320 units

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Answer:

140.

Step-by-step explanation:

Answer:140

Step-by-step explanation:

A stratified random sample is preferred when the population is heterogeneous, ensuring a proportional representation of each subgroup, and allowing for more accurate comparisons and reliable inferences about the population.

When the community under study is heterogeneous, which means it can be broken down into different divisions or sectors, a stratified random sample is usually favored over a basic random sample.

In this situation, a stratified random sample makes it possible for each stratum to be proportionally reflected in the sample, guaranteeing that each subset is properly represented. When analyzing the differences or parallels between various subgroups, this method can be especially helpful.

For instance, a business might want to poll to find out how satisfied customers are with its offerings. They might choose to select a stratified random sample based on customer demographic categories or regions as opposed to a straightforward random sample.

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The question is -

Provide an example of when you might want to take a stratified random sample instead of a simple random sample and explain what the advantages of a stratified random sample might be.

Answer:

1/6

Step-by-step explanation:

There is a 1/3 chance that you will get either a blue, red or green.
It is also a 1/2 chance that you will get an even number on a die.
1/3x1/2=1/6.

Therefore our answer is 1/6

Answer:

Let the no. of adults be x and no. of children be y

Cost of ticket if there are x adults = 6x

Cost of ticket if there are y children=3y

Step-by-step explanation:

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Answer:

6 children and 4 adults

Step-by-step explanation:

The distance on Ralph's map is 1.89 inches.

To find the number of inches needed to represent 13.2 miles on Ralph's map of Virginia Beach using a scale of 1 inch for every 7 miles, follow these steps
1. Divide the actual distance (13.2 miles) by the scale ratio (7 miles per inch): 13.2 miles ÷ 7 miles/inch = 1.8857 inches
2. Round the result to the nearest inch: 1.8857 inches ≈ 2 inches
So, the closest number of inches needed to represent the 13.2-mile distance on Ralph's map is 2 inches.
Ralph's map of Virginia Beach uses a scale of 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
The closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
The scale of Ralph's map of Virginia Beach is 1 inch for every 7 miles.
Ralph runs a distance of 13.2 miles from his house in Virginia Beach every weekend.
To determine the number of inches needed to represent this distance on Ralph's map, we can use a proportion as follows:
1 inch / 7 miles = x inches / 13.2 miles
Cross-multiplying gives:
7x = 13.2x = 13.2 / 7x ≈ 1.89
So, the closest number of inches needed to represent this distance on Ralph's map is 1.89 inches.
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Answer:

≈ 0,9

Step-by-step explanation:

To the nearest tenth:

[tex] \frac{20}{23} ≈0.9[/tex]

The lengths of the missing sides are:

x = 6

y = 3√2

Here we can see a right triangle, we want to find the two missing lengths in it.

We know the measure of one angle, and the length of the adjacent cathetus of it, then we can use trigonometric relations:

cos(a) = (adjacent cathetus)/hypotenuse

tan(a) = (opposite cathetus)/(adjacent cathetus)

Replacing the values that we know, we will get:

cos(45°) = 3√2/x

Solving for x:

x = ( 3√2)/cos(45°) = 3√2*(2/√2) = 6

And to get the value of y we use the other:

tan(45°) = y/ ( 3√2)

1 = y/ ( 3√2)

( 3√2) = y

These are the lengths.

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Determine the proper prism's base. The base takes the form of the prism's base. Calculate the base's area. The appropriate prism's height should be measured. Multiply the base's area by the prism's height.

A prism is a three-dimensional geometric object with two parallel, congruent bases and rectangular sides connecting the bases. The prism's name is derived from the design of its base. For instance, the bases of a triangular prism, rectangular prism, and so on, are all triangular. The distance between the two parallel bases of a prism determines its height. The formula V = Bh, where B is the area of the base and h is the height of the prism, can be used to determine the volume of a prism.

The formula V = Bh can be explained as follows:

Determine the proper prism's base. The base takes the form of the prism's base. The base, for instance, might be a triangle, square, rectangle, or any other polygon.

Calculate the base's area. The formula's B stands in for this.

The appropriate prism's height should be measured.

To get the volume, multiply the base's area by the prism's height.

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Answer:

96

Step-by-step explanation:

Because it is

The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.

In mathematics, the unitary approach is a way for handling proportional problems. The unitary technique involves determining the value of one unit and using that value to estimate the worth of other units or the total. It is frequently applied in scenarios found in daily life, such as figuring out the cost of a single item when the cost of several are known, or figuring out how long it will take to finish a task when only a portion of the time is known. The unitary approach is a quick and effective method for resolving a variety of mathematical issues.

given

We must divide the overall number of health clubs by the entire population in order to calculate the number of health clubs per capita:

Health club density is calculated as the sum of all clubs divided by the total population.

Per-person health club availability is 81 out of 581,000.

Per-person health club density = 0.000139

The state of Wyoming has 0.000139 health clubs per population, rounded to six decimal places.

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Putting the negative sign to the numerator, we have the value of x = -6/7.

An algebraic expression is a mathematical phrase that can include numbers, variables, and operators (such as addition, subtraction, multiplication, and division), as well as grouping symbols like parentheses.

The given equation is:

x³ = -216/343

To solve for x, we can take the cube root of both sides of the equation:

∛(x³) = -∛(216/343)

x = -∛(216/343)

Solving for numerator:

216 =  6 × 6 × 6

∛216 = 6

Solving for denominator:

343 = 7 × 7 × 7

∛343  = 7

Therefore,

x = -∛(216/343)

x = -(6/7)

x = -6/7

Putting the negative sign to the numerator, we have the value of x = -6/7.

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