How could you represent the division as a fraction if 5 peopld shared 2 blocks if 6 people shared 5 blocks

9 inches

The volume of a cylinder is given by ...

... V = πr²h

The least height will be the height that makes the volume exactly that which is necessary.

... 324π in³ = π·(6 in)²·h . . . . . . fill in the given information

... (324π in³)/(36π in²) = h = 9 in . . . . . divide by the coefficient of h

The least possible container height is 9 inches.

Answer:

Option A. [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex]

Step-by-step explanation:

Recursive formula of the geometric sequence is given as [tex]a_{1}=(-7)[/tex]

and [tex]a_{n}=\frac{1}{3}(a_{n-1})[/tex]

From these formulas it is clear that first term of the sequence a1 = -7

and common ratio of the sequence = [tex]\frac{1}{3}[/tex]

Since explicit formula of any geometric sequence is represented by

[tex]a_{n}=a_{1}(r)^{n-1}[/tex]

Therefore, [tex]a_{n}=(-7)(\frac{1}{3} )^{n-1}[/tex] will be the explicit formula of the given geometric sequence.

Final answer:

To calculate the arc length of a circle with a radius of 5 feet and a central angle of 42 degrees, convert the angle to radians and multiply by the radius to get the arc length, which is 7π/6 feet or approximately 3.665 feet.

Explanation:

To find the arc length s subtended by a central angle of 42 degrees in a circle with a radius of 5 feet, first convert the angle from degrees to radians. Since there are 2π radians in 360 degrees, you multiply the angle in degrees by π/180 to get radians. Therefore, the central angle in radians is 42 * (π/180) = 7π/30 radians. The arc length s is then found by multiplying the central angle in radians by the radius of the circle (s = rθ).
Using the formula s = rθ, you have:
s = 5 * (7π/30) = 35π/30 = 7π/6 feet.
Therefore, the arc length s is 7π/6 feet, or approximately 3.665 feet.

In the context of measurements, 3 inches is equivalent to 1/4 or 0.25 of a foot because 1 foot is composed of 12 inches.

The student is asking about the fraction that represents 3 inches in relation to a foot. In order to answer this, we need to know that 1 foot equals 12 inches. Therefore, we can represent 3 inches as a fraction of a foot by dividing 3 (the number of inches) by 12 (the number of inches in a foot). So, 3 inches is 1/4 or 0.25 of a foot.

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The point of intersection between the given line and plane is (1/6, -5/3, 5/2). This is determined by substituting the parametric line equations into the plane equation, simplifying to find the value of the parameter t, and substituting that value back into the line equations.

The given line and plane equations are, x = 1 + t, y = 2t, z = -3t and x + y - z = -4 respectively. To find where the line intersects the plane, we need to substitute the parametric line equations into the plane equation.

Step by Step Solution

Step 1: Substitute x, y, and z from the line equation into the plane equation, giving you (1+t) + 2t - (-3t) = -4.
Step 2: Simplify the equation to find the value of t. You get 6t + 1 = -4, so t = -5/6.
Step 3: Substitute t = -5/6 into the line equations to find x = 1/6, y = -5/3, and z = 5/2.

So, the point P where the line intersects the plane is (1/6, -5/3, 5/2).

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The length of the shorter leg of the right triangle is 14 feet.

Let's denote the length of the shorter leg as x. According to the given information, the longer leg is 7 feet more than the shorter leg, so the length of the longer leg is x + 7. The hypotenuse is 7 feet less than twice the shorter leg, making the hypotenuse 2x - 7.

By applying the Pythagorean Theorem, which states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a) and b in a right triangle ([tex]\(c^2 = a^2 + b^2\)[/tex]), we can set up the equation:

[tex]\[(2x - 7)^2 = x^2 + (x + 7)^2\][/tex]

Solving this quadratic equation provides the value of x, representing the length of the shorter leg. After solving, we find x = 14, so the length of the shorter leg is 14 feet.

Understanding and applying the Pythagorean Theorem is crucial in solving problems related to right triangles. In this scenario, the theorem helps establish a relationship between the lengths of the sides, allowing us to find the length of the shorter leg based on the given conditions.

Answer:

Refer the attached graph.

Step-by-step explanation:

Given : Equation [tex]2x-y=2[/tex]

To find : What is the graph of the equation ?

Solution :

To plot the graph of the equation we have to determine the x and y-intercept of the equation as  [tex]2x-y=2[/tex] is a linear equation.

For x-intercept, put y=0

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

[tex]x=\frac{2}{2}[/tex]

[tex]x=1[/tex]

Point is (1,0).

For y-intercept, put x=0

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

[tex]-y=2[/tex]

[tex]y=-2[/tex]

Point is (0,-2).

So, The graph passing through (1,0) and (0,-2) with linear line.

Refer the attached figure below.

The graph of the equation 2x - y = 2 will be a straight line passing through the points (0, -2), (1, 0), and (-1, -4).

We have,

To graph the equation 2x - y = 2, we can start by rearranging it in the slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

Rearranging the equation:

2x - y = 2

y = -2x + 2

y = 2x - 2

Now we have the equation in slope-intercept form, where the slope (m) is 2 and the y-intercept (b) is -2.

To graph this equation, you can plot the y-intercept at (0, -2), and then use the slope to find additional points.

The slope of 2 means that for every 1 unit increase in x, y will increase by 2.

So, from the y-intercept (0, -2), you can move 1 unit to the right and 2 units up to get another point (1, 0).

Similarly, you can move 1 unit to the left and 2 units down to get another point (-1, -4).

Now you can plot these points and draw a straight line through them to represent the graph of the equation.

Thus,

The graph of the equation 2x - y = 2 will be a straight line passing through the points (0, -2), (1, 0), and (-1, -4).

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Answer:

B. [tex]2x^2+\frac{3x}{2}-5[/tex]

Step-by-step explanation:

Given functions,

[tex]f(x)=\frac{x}{2}-2[/tex]

[tex]g(x)=2x^2+x-3[/tex]

Since, (f+g)(x) = f(x) + g(x)

[tex]=\frac{x}{2}-2+2x^2+x-3[/tex]

[tex]=2x^2+\frac{x+2x}{2}-5[/tex]    ( combine like terms )

[tex]=2x^2+\frac{3x}{2}-5[/tex]

Option 'B' is correct.

0.2x+4-3>-7-6.2x

0.2x+1>-7-6.2x

0.2x+0.6x>-8

0.8x>-8

the correct answer is: x>-1.25

0.30 as a fraction is 30/100 = 3/10

0.30 as a percent = 0.30 * 100 = 30%

 answer is D. 3/10 and 30%

.30 is .3

do .30 divided by 1 and you get 3/10

Percentage= move the decimal 2 places to the right and you get 30%

So your answer is D.

total cards = 30 + 25 + 45 = 100

25 are basket ball

25/100 = 0.25

0.25 = 25%

 25% are basketball

Answer:

25%

Step-by-step explanation:

By dividing the total number of bows (110) by the number of bows that fit in one bag (10), we find that Kate can fill 11 bags with her bows.

To find out how many bags Kate can fill with her bows, we need to divide the total number of bows by the number of bows that fit in one bag. In this case, Kate has 110 bows and 10 bows fit in one bag.

So, we divide 110 by 10: 110 / 10 = 11

Therefore, Kate can fill 11 bags with her 110 bows.

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Kate can fill 11 bags with her 110 bows.

Given:

Kate has 110 bows

No. of bows fit in the bag = 10

No. of bags she can fill:

110 bows ÷ 10 bows per bag

= [tex]\frac{110}{10}[/tex]

= 11 bags.

So, Kate can fill 11 bags with her 110 bows.

The interquartile range (IQR) is 5 minutes. Any values below 19.5 minutes or above 39.5 minutes would be considered outliers. In this data set, both the minimum time of 15 minutes and the maximum time of 50 minutes are outliers.

The question is whether there are any outliers in the finish times of a group of runners based on the IQR definition. To determine this, we first calculate the interquartile range (IQR), which is the range of the middle 50 percent of the data. Q1 = 32 min - 2 For this data set, we calculate the IQR by subtracting the first quartile (Q1) from the third quartile (Q3). Here, IQR = Q3 - 7 min = 5 min.

Next, we multiply the IQR by 1.5, which is our test for outliers. This gives 1.5 * IQR = 1.5 * 5 min = 7.5 min.

An outlier is defined as a data point that is below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR. So, any time less than 27 min - 7.5 min = 19.5 min or greater than 32 min + 7.5 min = 39.5 min would be considered an outlier.

Given the five-number summary: min=15 min, Q1=27 min, median=31 min, Q3=32 min, max=50 min, we can clearly see that the minimum time of 15 min is an outlier because it's less than 19.5 min. Also, the maximum time of 50 min is an outlier because it's greater than 39.5 min.

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The minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the given data set.

To determine if there are any outliers using the 1.5 * IQR (interquartile range) definition, we need to calculate the IQR first. The IQR is the difference between the third quartile (Q3) and the first quartile (Q1).

Given:

- Q1 = 27 minutes

- Q3 = 32 minutes

We can calculate the IQR as follows:

[tex]\[ IQR = Q3 - Q1 = 32 - 27 = 5 \text{ minutes} \][/tex]

Now, we can use the 1.5 * IQR rule to find the lower and upper bounds for potential outliers:

Lower Bound: Q1 - 1.5 * IQR

Upper Bound: Q3 + 1.5 * IQR

[tex]\[ \text{Lower Bound} = 27 - 1.5 \times 5 = 27 - 7.5 = 19.5 \text{ minutes} \]\[ \text{Upper Bound} = 32 + 1.5 \times 5 = 32 + 7.5 = 39.5 \text{ minutes} \][/tex]

Any finish times below 19.5 minutes or above 39.5 minutes would be considered potential outliers according to the 1.5 * IQR rule.

Since the minimum time is 15 minutes and below the lower bound of 19.5 minutes, there is at least one outlier in the data set.

Final answer:

Compound probability problems use 'and' or 'or', applying multiplication or addition rules respectively, and can be visualized with Venn or tree diagrams.

Explanation:

Probability problems containing the words and or or are considered compound probability problems. The word and typically indicates the use of the multiplication rule, implying that you need to find the likelihood of both events occurring together, which is the product of their individual probabilities. Conversely, when you encounter the word or, it suggests the need for the addition rule, implying that you should add the probabilities of each event and subtract the probability of both events occurring together to find the total probability of either event happening. This can be visualized through Venn diagrams, which are useful in representing the different events and their intersections, as well as tree diagrams which provide a visual way of breaking down compound probabilities.

Answer:

Option D.

Step-by-step explanation:

We have to find the equation of the parabola which has vertex at ( 0,3 )

If we write the equation of a parabola in the vertex from then we will write

y = ( x - h )² + (k)²

In this equation ( h, k) will be the vertex.

(a) y = (x-3)² + 0

    so ( 3,0) will be the vertex

(b) y = ( x+3)² + 0

   or y = [x - (-3)]² + 0

   then ( -3,0) will be the vertex

(c) y = (x² - 3)

   y = ( x-0 )² + (-3)

  then ( 0, -3) is the vertex.

(d) y = x² + 3

    y = ( x-0 )² + 3

Then ( 0, 3 ) will be the vertex of this parabola.

Option D. is the answer.

The height of the frame is 1.5 meters.

The Width of the frame is 1 meter.

The perimeter of a rectangle is defined as the addition of the lengths of the rectangle's four sides.

The perimeter of a rectangle = 2(L+W)

Where W is the width of the rectangle  and L is the length of the rectangle

Given that,

P = 5 meters

w = 2/3h = 0.67h

We have to determine the height of the frame.

The perimeter of the frame = 2h + 2W

We know all the other values So we can plug in values to solve for h:

5 = 2h + 2(.67h)

5 = 2h+ 1.33h

5 = 3.33h

5/3.33 = h

h = 1.5

So the height of the frame is 1.5 meters

We need to find the width and we know that W = 0.67h

W = 0.67(1.5)

W = 1

So the Width of the frame is 1 meter.

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