Students on the school track team may compete in up to 3 events. The probability distribution for the number of events in which a student competes is provided. Let X = the number of events a student competes in. Calculate the median of the distribution.


0.5
1
1.5
2

You have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.

What is the division?

A division is a process of splitting a specific amount into equal parts. For example, we can divide a group of 20 members into 4 groups of 5 members each or 5 groups of 4 members each, and so on.

To find out how many lemons you have, you need to take into consideration that you have 21 cuts available to divide the lemons.

With each cut, you can divide one whole lemon into two pieces or divide one section of lemon into two smaller pieces.

So, with 21 cuts, you can have a maximum of 2²¹ (2097152) pieces of lemon.

Since you have 30 jugs and each jug needs to have a piece of lemon, you would need at least 30 pieces of lemon.

To get 30 pieces of lemon with the minimum number of whole lemons, you would need 7 whole lemons (7 * 2 = 14 pieces, 14 * 2 = 28 pieces, 28 * 2 = 56 pieces, 56 - 30 = 26 pieces left over).

Therefore, you have 7 lemons, by the consideration that you have 21 cuts available to divide the lemons.

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Answer: The regular price is $9

Step-by-step explanation: We do 35/5 to find the cost of each book. You get 7,then add 2 to get 9

(35/5)+2

Step-by-step explanation:

The indefinite integral of the polynomial function (x^4 + 2x^3 + 3x^2 + 4x + 5) is:

∫(x^4 + 2x^3 + 3x^2 + 4x + 5)dx = (x^5)/5 + x^4 + (3/2)x^2 + (2/3)x^3 + 5x + C

where C is an arbitrary constant of integration.

Answer:

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Question 3:

4/5 ×10.

To do fraction multiplication all you need to do is put the number that's not in a fraction and put 1 as the denominator:

For example Q3:

Put 10 over 1 so its 10/1.

now just multiply fractions as normal .

4/5 ×10/1= 40/5.

As this is an improper fraction you will have to see how many times 5 fits into 40 which is 8.

So for Q3 your answer is 8.

You can carry out these step for each question but only do the last step if the fraction is improper(top heavy).

To convert 1.05 x 10^-8 to standard form, we simply need to move the decimal point 8 places to the left, since the exponent is negative.

1.05 x 10^-8 = 0.0000000105

Therefore, 1.05 x 10^-8 in standard form is 0.0000000105.

Answer:

0.0000000105.

Step-by-step explanation:

Answer:

32 cubic [tex]cm^{3}[/tex]

Step-by-step explanation:

Since each cube is 1 by 1 we can just count blocks to get its width length and height.

Width = 2

Length = 4

Height = 4

Volume= LxWxH

Volume= 4x2x4

Volume = 32 cubic [tex]cm^{3}[/tex]

Answer:

158.29 m²

Step-by-step explanation:

A = πr²

A = 3.14 × 7.1 m × 7.1 m

A = 158.29 m²

If the length of of a square increases from 3 inches to 7inches,the perimeter will increase from 12 inches to 28 inches. The perimeter will increase by 16inches

Square is a regular quadrilateral, which has all the four sides of equal length and all four angles are also equal. The angles of the square are at right-angle or equal to 90-degrees. Also, the diagonals of the square are equal and bisect each other at 90 degrees.

The perimeter of a square is determined by adding all the sides together.

Therefore the perimeter of square = 4l

when the length is 3 inches, the perimeter = 4×3 = 12inches

when the length is 7inches , the = 4× 7 = 28inches

Therefore the perimeter increased from 12inches to 28inches. It increases by 16 inches

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When the side length of a square increased from 3 inches to 7 inches, the perimeter increased from 12 inches to 28 inches

The perimeter of a square can be represented as follows:

The perimeter of a square is the sum of the whole sides of the square.

perimeter of a square  = 4l

where

l  = side length

Recall the whole sides of a square is equal.

Therefore,

The side of the square is formally 3 inches.

Hence,

perimeter of a square = 4 × 3

perimeter of a square = 12 inches.

When the side length is increased to 7 inches.

Hence,

perimeter of a square = 4 × 7

perimeter of a square = 28 inches

Therefore, when the side length of a square increased from 3 inches to 7 inches, the perimeter increased from 12 inches to 28 inches

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Answer:

She has 27 quarters

Step-by-step explanation:

Let:

x = Number of nickels

y = Number of quarters

US$0.05 = 5 cents = monetary value of a nickel

US$0.25 = 25 cents = monetary value of a quarter

                      x + y = 68

                     x = 68 - y  ---- --------  (equation i)

                0.05x + 0.25y = 8.80----- (equation ii)

These two are linear simultaneous equations, which can be solved either by substitution, elimination or graphical method.

Substitution method:

Substitute (equation i) into (equation ii) to solve for y:

0.05(68 - y) + 0.25y = 8.80

Expand the brackets by applying the Distributive Law and then bring all the like terms together. y needs to be isolated and made the subject of the equation:

= 3.4 - 0.05y + 0.25y = 8.80

= 0.25y - 0.05y = 8.80 - 3.40

= 0.20y = 5.40

= y = [tex]\frac{5.40}{0.20}[/tex]

∴ y = number of quarters = 27

Answer:

Both Jill and John are correct.

Step-by-step explanation:

Triangle A and B are both similar to the triangle in question. They all have angles of 30, 60, and 90 degrees. We can infer this because all triangles have 180 degrees and the square in the corner means that it is a right angle (90 degrees).

Answer:

4+0.80x

Step-by-step explanation:

The equation of slope-intercept form for the line is,

⇒ y = 1/2x - 8

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Slope = 1/2

y - intercept = - 8

We know that;

The equation of slope-intercept form for the line is,

y = mx + b

Where, m is slope and y - intercept of the line.

Substitute all the values we get;

y = mx + b

y = 1/2x - 8

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What will the dimensions of some cross-sections of a cuboid be when cutting depends on the viewpoint.

We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.

Suppose we have a cuboid shape of a wooden block.

The height of the wooden block is h, the width of the wooden block is w and the length of the wooden block is l.

Now if we cut the wooden block along the red line a look at it from the top it will look like a rectangle width width 'w' and length 'l'.

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Answer: A. A rectangle 4 inches by 2 inches

Step-by-step explanation:

The vertex of the function is (x, y) = (-4, -14), so the vertex is at (x = -4, y = -14).

The equation can be written in vertex form by completing the square:

M(x) = x^2 + 8x - 10 = (x^2 + 8x) - 10 + (8/2)^2

= (x + 4)^2 - 14

The vertex of the function is (x, y) = (-4, -14), so the vertex is at (x = -4, y = -14).

To find the vertex of a quadratic function, you can use the formula:

Vertex = (x, y) = ( -b / 2a, f( -b / 2a) )

Where "a", "b", and "c" are the coefficients of the quadratic function in the standard form:

f(x) = ax^2 + bx + c

Note that the vertex of a quadratic function is either a minimum or maximum point, depending on the sign of the coefficient "a". If "a" is positive, the vertex represents the minimum point of the parabola. If "a" is negative, the vertex represents the maximum point of the parabola.

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The angle measures for this problem are given as follows:

Angle 3 has the same measure as angle 1, thus:

m < 3 = m < 1 = 68º.

Angles 1, 2 and 3 form a ray, adding to 180º, meaning that the measure of angle 2 is obtained as follows:

m < 2 + 2 x 68 = 180

m < 2 = 44º.

The sum of the internal angles of a triangle is of 180º, hence the measure of angle 5 is given as follows:

44 + m < 5  + 35 = 180

m < 5 = 180 - 79

m < 5 = 101º.

Each exterior angle is supplementary with it's interior angle, having their measures adding to 180º, hence the measures of angles 4 and 7 are obtained as follows:

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Answer:

  x ≈ -2.803

Step-by-step explanation:

You want to use the iterative formula x = ∛(5x -8) to find a solution to x³ -5x +8 = 0, starting with x₁ = -3.

Your iterator appears to be found by solving for x:

  x³ -5x +8 = 0

  x³ = 5x -8 . . . . . . add 5x-8

  x = ∛(5x -8) . . . . take the cube root

The attached table shows some iterations using this formula. To 3 dp, the solution is x ≈ -2.803.

__

Additional comment

Using a faster-converging iteration technique, we find the solution to be about ...

  x ≈ -2.8025​887521

The solution above is accurate to 3 dp.

The value of the equation is f ( x ) = x³ + 3x² - 25x - 75 and ( x + 5 ) is a factor of the equation

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

f ( x ) = x³ + 3x² - 25x - 75   be equation (1)

Now , ( x + 5 ) is a factor of the equation ,

So , x + 5 = 0

Subtracting 5 on both sides of the equation , we get

x = -5

Substitute the value of x in equation (1) , we get

f ( -5 ) = ( -5 )³ + 3 ( -5 )² - ( 25 ) ( -5 ) - 75 = 0

-125 + 3 ( 25 ) + 125 - 75 = 0

-125 + 75 + 125 - 75 = 0

0 = 0

Hence , ( x + 5 ) is a factor of the equation

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Answer:  a) 0.00000047 = 4.7*10 7square. b) 0.0000000738 = 73.8 * 10 9 square .

Step-by-step explanation:

Answer: [tex]4.7 x 10^{-7}[/tex]

Answer: 3 jackets and 5 sweaters

Step-by-step explanation:

j = jeans      s = sweaters

175 = 25j + 20s  ---- this will calculate the cost

8 = j + s ----- how much she bought

j = 8 - s; plug this into the cost

175 = 25(8-s) + 20s

175 = 200 - 25 + 20s; subtract 200 on both sides

-25 = -5s divide -5 to isolate the s

s = 5 Shelly bought 5 sweaters

now plug s = 5 in how much she bought

8 = j + 5

j = 3 Shelly bought 3 jackets

Both teams can complete the search in a time period of 4 hours.

Distance is a measurement of how far apart two points or objects are from one another. Time is a unit used to describe how long it takes for an object to travel between two points. Speed is a unit used to describe how quickly or slowly an item or a point moves.  

Here we have

Two search-and-rescue teams leave base camp at the same time,
looking for a lost child.

The first team, on horseback, heads north at 3 mph,  

The second team, on foot, heads south at 2.5 mph.

Let both teams complete searching in 'x' mins

The distance traveled by 1st team in 'x' mins = 3 × x  

= 3x  m

The distance traveled by 2nd team in 'x' mins = 2.5 × x  

= 2.5x m    

As we know total distance = 22 miles

=> 3x + 2.5x = 22 miles

=> 5.5x = 22 miles

=> x = 4 hrs  

Therefore,

Both teams can complete the search in a time period of 4 hours.

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A straight line that continuously approaches a certain curve without ever meeting it is an asymptote. In other words, an asymptote is a line that a curve travels towards as it approaches infinity.

Set the denominator to zero and solve for x to discover the vertical asymptotes. Set each factor to zero and solve as this has already been factored. The asymptotes are expressed as equations of lines since they are lines. Asymptotes for the vertical line are x = 3 and x = 1.

An asymptote of a curve in analytic geometry is a line where the distance between the curve and the line gets closer to zero as one or both of the x or y coordinates tends to infinity.

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9.) The transformation performed in the function[tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function [tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

What is the transformation of the function?

The term "transformation of a function" refers to the process of altering the appearance of a function, either by shifting, stretching, or reflecting it along the coordinate axes.

9.) The transformation performed in the function [tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function[tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞. As x approaches positive infinity, the value of 4^x approaches positive infinity, making the value of the function approach positive infinity.

Hence,

9.) The transformation performed in the function[tex]f(x) = \frac{1}{2}^{-x}[/tex] is a reflection across the x-axis.

10.) The transformations performed in the function [tex]f(x) = -log_5(x-2)+17[/tex]are a reflection across the x-axis, a vertical shift upward by 17 units, and a horizontal shift to the right by 2 units.

12.) The horizontal asymptote of f(x) = 4^x + 6 is y = +∞.

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Chen here tried to classify shapes from least specific to most specific. But the order is incorrect. The correct order is Quadrilateral, parallelogram, rhombus, square.

A quadrilateral is a shape having four sides. Any shapes with a four side is a quadrilateral. It can be an undetermined shape or a parallelogram, rectangle, rhombus or square. Parallelogram have four sides. Opposite sides are parallel and congruent. A rhombus, rectangle, square can all be considered a parallelogram.

A rhombus have four congruent sides and opposite sides are parallel. All squares are rhombi, but not all rhombi are squares. Square is the most specific shape. All sides of the square must be equal and all angles must be 90°.

We can say all squares are rhombus, all rhombi are parallelograms, all parallelograms are quadrilaterals.

So the correct order from least to most specific according to shape is Quadrilateral, parallelogram, rhombus, square.

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Answer:

None of them?

Step-by-step explanation:

2 yards = 6 feet

6 feet = 72 inches

3 yard = 9 feet

9 feet = 108 inches

4 yards = 12 feet

12 feet = 144 inches

5 yards = 15 feet

15 feet = 180 inches

Step 1: Calculate the normal usage for the coming month. Since normal usage is one case of 12 cans per week and the coming month is expected to be very busy, requiring 50 percent more tomato juice than normal, the normal usage for the coming month can be calculated by multiplying 12 cans per week by 4 weeks, then multiplying that number by 1.5, which gives us a total of 72 cans.

Step 2: Calculate the desired ending inventory for the coming month. The desired ending inventory for the coming month is 18 cans.

Step 3: Calculate the quantity to order. To calculate the quantity to order, we need to subtract the quantity on hand (6 cans) and the desired ending inventory (18 cans) from the normal usage (72 cans). This gives us a total of 48 cans to order.

Step 4: Calculate the number of cases to order. To calculate the number of cases to order, divide the quantity to order (48 cans) by 12 cans per case, which gives us 4 cases.

Therefore, Harvey's Restaurant should order 4 cases of tomato juice today in order to meet the expected demand for the coming month.

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Answer:

3.333

Step-by-step explanation:

[tex]3x - 6 = 4[/tex]

Add 6 to both sides of the equation

[tex]3x - 6 + 6 = 4 + 6[/tex]

[tex]3x = 10[/tex]

Divide both sides by 3

3x/3= 10/3

x = 3.333

Answer:

20.199

Step-by-step explanation:

ln (3x – 6) = 4

ln(3x-6)=2^2

x=2+e^4/3    

x=20.199

Answer: y=-1/2,7

Step-by-step explanation: The y intercept is at 0,7 and th eslope is going down 1 right 2

The equation of the line that is parallel to this line and passes through the point (6, -3) is y = x/2.

The equation of the line that is perpendicular to this line and passes through the point (6, -3) is y = -2x + 9.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

From the information provided above, we have the following slope and data points on the line:

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ 1/2 = 1/2

At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - (-3) = 1/2(x - 6)

y + 3 = x/2 - 3

y = x/2 - 3 + 3

y = x/2

In Mathematics, a condition that must be met for two lines to be perpendicular is given by:

m₁ × m₂ = -1

1/2 × m₂ = -1

m₂ = -2

At data point (6, -3), a linear equation of this line can be calculated by using the point-slope form as follows:

y - (-3) = -2(x - 7)

y + 3 = -2(x - 6)

y = -2x + 12 - 3

y = -2x + 9.

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Answer:4x−6

That's one

Answer: $350

Step-by-step explanation: