A saw mill cuts boards that are 16 ft long. After they are cut, the boards are inspected and

rejected if the length has a percent error of 1. 5% or more. The saw mill also cuts boards that are 10, 12, and 14 feet long. An inspector rejects a board that

was 2. 3 inches too long. What was the intended length of the board?

The volume of the pyramid as calculated from the data given is found to be as 21.33 cubic units .

The distance from a corner to the center is 8 , and from the corner to the top of the pyramid is 8, because it is given that the tringles are equilateral.

so the height becomes,

√3a/2 = 4√3

The area of the hexagon is calculated using the formula ,

=3√3/2 x a²

=3√3/2 x 64

= 963√3

=332.553 square units.

Volume of a pyramid is calculated as ,

1/3 x base x height

= 1/ 3 x 8 x 8

= 1/3 x 64

=21.33 cubic units answer.

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The graph of the variation of the height of a person on the Ferris wheel with time, created with MS Excel is attached

The values of the constants in the sinusoidal function, h = a + b·(c·t) are;

a = 30

b = -20

c = π/1.5

A sinusoidal function is a periodic, oscillatory function, that is based on the sine (or cosine) trigonometric ratios.

The diameter of the Ferris wheel = 40 m

The location of the axle above the ground = 30 m

The time it takes to make a complete a rotation = 3 minutes

The formula for modelling the elevation or height, h, of a person above the ground is presented as follows;

h = a + b·cos(c·t)

The details in the question is that at time, t = 0, the person enters the wheel at the lowest point.

Therefore;

At t = 0, h = 30 - 40/2 = 10

h = 10 = a + b·cos(c × 0) = a + b·cos(0) = a + b

a + b = 10

Whereby the height of the axis of the wheel above the ground is a constant, for visibility in the analysis, let the constant a represent the constant height of the axis from the ground, we get;

a = 30

a + b = 10, therefore;

b = 10 - a

b = 10 - 30 = -20

b = -20

At t = 1.5 minutes, the location on the wheel the person enters is at the maximum height on the wheel = 30 + 20 = 50

50 = a + b·cos(1.5·c)

50 = 30 - 20 × cos(1.5·c)

20 × cos(1.5·c) = 30 - 50 = -20

cos(1.5·c) = -1

cos(π) = -1

Therefore; 1.5·c = π

c = π/1.5

The equation is therefore;

h = 30 - 20·cos((π/1.5)·t)

a = 30, b = -20, c = π/1.5

Please find attached a graph showing the variation of height with time of the motion on a Ferris created with MS Excel

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Suzy randomly picks marbles from a bag containing 13 identical marbles. The possible outcomes of the given probability if she selects 9 marbles is:

259,459,200.

Randomness is commonly used to refer to an event's apparent or actual lack of pattern or predictability. Random events, symbols, or steps frequently occur in no particular order and do not adhere to any recognizable pattern or combination.

Germanic in origin, Randon is a name for boys. With a name that means "wolf shield," you can inspire baby Randon to embrace their sense of adventure. something or someone that is suspiciously out of the ordinary, unidentified, or unknown. a peculiar or erratic individual or thing. Something that is random lacks structure, direction, or intent. Like the random selection of lottery numbers or unplanned random events, it occurs entirely by chance.

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The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.

It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Hence, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Consequently, it follows that the greatest possible quotient as required is; 25.

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Answer:

25.5

Step-by-step explanation:

first find the area od the rectangle than the triangle.

to find the area count the number of squares and use A=b*h

than do the same for the triangle using A=.5*b*h

15=3*5

10.5=.5*3*7

10.5+15=25.5

Right angled triangle is formed by the points (3, 2), (-2, -3) and (2,3).

Let the given points be,

A = (3, 2), B = (-2, -3) and C = (2, 3)

The formula for the distance between two points:

The length of the line segment bridging two points on a plane is known as the distance between the points.

The formula to find the distance between the two points is usually given by [tex]D = $$\sqrt{\left(X_2-X_1\right)^2+\left(Y_2-Y_1\right)^2}$$[/tex].

Therefore,

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), B = [tex](x_{2} , y_{2} )[/tex] = (-2, -3)

[tex]& \mathrm{AB}=\sqrt{(3+2)^2+(2+3)^2}=\sqrt{50}=5 \sqrt{2}[/tex]  units

B = [tex](x_{1} , y_{1} )[/tex] = (-2, -3), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{BC}=\sqrt{(-2-2)^2+(-3-3)^2}=\sqrt{52}=2 \sqrt{13}[/tex]  units

A = [tex](x_{1} , y_{1} )[/tex] = (3, 2), C = [tex](x_{2} , y_{2} )[/tex] = (2, 3)

[tex]& \mathrm{AC}=\sqrt{(3-2)^2+(2-3)^2}=\sqrt{2}[/tex]  units

By using the Pythagorean theorem:

According to Pythagoras's Theorem in a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides.

Now, we can see that,

[tex]& (2 \sqrt{13})^2=(5 \sqrt{2})^2+(\sqrt{2})^2 \\[/tex]

[tex]& \mathrm{BC}^2=\mathrm{AB}^2+\mathrm{AC}^2[/tex]

Therefore, the given triangle is a right angled triangle.

Therefore, option(A) s correct.

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What type of triangle do the points (3, 2), (-2, -3) and (2,3) form a triangle? If so, name the type.

A. right triangle

B. equilateral triangle

C. isosceles triangle

D. none of these

Answer:

a= -2,3*4,-1

b=u

c=w

Step-by-step explanation:

Answer:

sum up the numbers and divide by the numbers of values.

80+84+79+44+87+73+89+90+82+89+93+97+77+71 / 14

1135/14

= 81•1 is the mean

The division technique can be used to evaluate the given expression

12.75÷1. 5

The division formula is used for splitting a number into equal parts. Symbols that we use to indicate division are  (÷) and (/).

“p divided by q” can be written as: (p÷q) or (p/q).

The method of verification can be expressed as:

Dividend = (Divisor × Quotient) + Remainder.

The given equation is:12.75÷1.5

We'll first write the above decimal numbers in fractional form.

12.75÷1.5

1275/100÷15/10

2. Now we'll divide it further.

⇒1275/100÷15/10

⇒1275/100×15/10

⇒1275/10×15

⇒225/10×3

⇒88/10

3. And finally, we'll write our quotient in decimal form.

⇒88/10

⇒8.8

ㅤ

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The result of the operation between two mixed numbers are listed below:

Mixed numbers are real numbers with special notation to transform improper fractions into a combination of integers and fractions. That is:

a b / c = a + b / c

Where a, b, c are integers and c is a non-zero number.

The procedure to simplify the operation is described below:

Case 1

1 3 / 8 ÷ 1 4 / 9

(1 + 3 / 8) ÷ (1 + 4 / 9)

(11 / 8) ÷ (13 / 9)

(11 / 8) / (13 / 9)

99 / 104

Case 2

2 1 / 3 ÷ 1 3 / 4

(2 + 1 / 3) ÷ (1 + 3 / 4)

(7 / 3) ÷ (7 / 4)

(7 / 3) / (7 / 4)

28 / 21

4 / 3

Case 3

4 1 / 5 ÷ 3 1 / 2

(4 + 1 / 5) ÷ (3 + 1 / 2)

(21 / 5) ÷ (7 / 2)

42 / 35

6 / 5

Case 4

5 1 / 5 ÷ 2 1 / 2

(5 + 1 / 5) ÷ (2 + 1 / 2)

(26 / 5) ÷ (5 / 2)

(26 / 5) / (5 / 2)

52 / 25

Case 5

9 1 / 2 ÷ 9 4 / 6

(9 + 1 / 2) ÷ (9 + 4 / 6)

(19 / 2) ÷ (58 / 6)

114 / 106

57 / 53

Case 6

2 2 / 10 ÷ 6 2 / 3

(2 + 2 / 10) ÷ (6 + 2 / 3)

(22 / 10) ÷ (20 / 3)

(22 / 10) / (20 / 3)

(66 / 200)

33 / 100

Case 7

2 1 / 4 ÷ 4 1 / 2

(2 + 1 / 4) ÷ (4 + 1 / 2)

(9 / 4) ÷ (9 / 2)

(9 / 4) / (9 / 2)

18 / 36

1 / 2

Case 8

2 2 / 3 ÷ 1 2 / 3

(2 + 2 / 3) ÷ (1 + 2 / 3)

(8 / 3) ÷ (5 / 3)

(8 / 3) / (5 / 3)

8 / 5

Case 9

5 3 / 5 ÷ 1 2 / 5

(5 + 3 / 5) ÷ (1 + 2 / 5)

(28 / 5) ÷ (7 / 5)

(28 / 5) / (7 / 5)

28 / 7

4

Case 10

4 2 / 3 ÷ 3 1 / 2

(4 + 2 / 3) ÷ (3 + 1 / 2)

(14 / 3) ÷ (7 / 2)

(14 / 3) / (7 / 2)

28 / 21

4 / 3

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Answer:

2 x 13 x 9 = 234 cm3 is your answer.

Step-by-step explanation:

Whenever given 3 side lengths of a rectangular prism you ALWAYS have to multiply those in order to get the volume..

3 quarts is equal to approximately 285 centilitres.

To Calculate this we have:

3 quarts is equal to 3 x 0.95 liters = 2.85 liters.

1 litre is equal to 100 centilitres, so 2.85 litres is equal to 2.85 x 100 = 285 centilitres.

Therefore, 3 quarts is equal to approximately 285 centilitres.

In detail, a quart is a unit of measurement in the Customary System Units and is defined as a quarter of a gallon. 1 quart is equal to 0.95 litres. To find out how many centilitres are in 3 quarts, we need to multiply the number of quarts (3) by the conversion factor (0.95 litres per quart). This gives us 2.85 litres. Since 1 litre is equal to 100 centilitres, we can multiply 2.85 litres by 100 to get 285 centilitres. Therefore, 3 quarts is equal to approximately 285 centilitres.

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Answer:

12.25

Step-by-step explanation:

Solution for What is 35 percent of 35:

35 percent *35 =

( 35:100)*35 =

( 35*35):100 =

1225:100 = 12.25

Now we have: 35 percent of 35 = 12.25

Question: What is 35 percent of 35?

Percentage solution with steps:

Step 1: Our output value is 35.

Step 2: We represent the unknown value with x.

Step 3: From step 1 above, 35 = 100%

Step 4: Similarly, x = 35%

Step 5: This results in a pair of simple equations:

35 = 100% (2)

x = 35% (2)

Step 6: By dividing equation 1 by equation 2 and noting that both the RHS (right hand side) of both equations have the same unit (%); we have

[tex]\frac{35}{x} =\frac{100}{35}[/tex] (with % for 100 and 35)

Step 7: Again, the reciprocal of both sides gives

[tex]\frac{x}{35} =\frac{35}{100}[/tex]

⇒ x=12.25

Therefore, 35% of 35  is 12.25

The graph of the inequality system is attached. The coordinate of a point in the solution set is (-1, 2).

In order to graph the system of inequalities graphically, consider the equation of each inequality.

y = x – 1

y = x - 4

Choosing a few values of x, plot the graph for each equation. Shade the area bounded by the line based on the inequality. If the inequality is less than, shade the area right to the line and if the inequality is greater than, shade the area left to the line. Hence, y < x – 1 is represented by red area and y > x – 4 is represented by blue area. The overlapping shaded area contains the coordinates that represent the solution of the inequality system. The coordinate of a point in the solution set is (-1, 2).

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Answer:

3/2

Step-by-step explanation:

3/2 is in the simplest form; it can't be decreased any more.

Answer:

10

Step-by-step explanation:

no explanation just math-way

The length and width of the rectangle will be 2 and 8x + 12

Area of rectangle = 16x + 24.

A rectangle is a four-sided geometric shape having opposite sides that are equal in length and four right angles. The length and width of the rectangle are its opposing sides.

A rectangle's area is found by multiplying its length and width together, so:

Area = length x width

Calculating the length and width of the rectangle -

Factoring out 2 from the equation -

Therefore -

2 (8x+12)

Since, the area is the length times width, thus -

2 x (8x+12)

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The given sequence represents the sales of a product over time. The sum of the first 6 terms is 693.75, which is calculated by multiplying each term in the sequence by its respective exponent.

The sum of the first 6 terms of the geometric sequence is calculated as follows:

[tex]a_1 = 125 \left(\frac{1}{5}\right)^{1-1} = 125 \\[/tex]

[tex]a_2 = 125 \left(\frac{1}{5}\right)^{2-1} = 25 \\[/tex]

[tex]a_3 = 125 \left(\frac{1}{5}\right)^{3-1} = 5 \\a_4 = 125 \left(\frac{1}{5}\right)^{4-1} = 1 \\a_5 = 125 \left(\frac{1}{5}\right)^{5-1} = \frac{1}{5} \\a_6 = 125 \left(\frac{1}{5}\right)^{6-1} = \frac{1}{25} \\[/tex]

Total sum = 125 + 25 + 5 + 1 +[tex]\frac{1}{5} + \frac{1}{25}[/tex] = 693.75

The geometric sequence a_n=12[tex]5\left(\frac{1}{5}\right)^{n-1}[/tex]represents the sales of a product over time, where n is the number of years after its release. The sum of the first 6 terms is calculated by multiplying each term in the sequence by its respective exponent. This gives us the following 6 terms: a_1 = 125, a_2 = 25, a_3 = 5, a_4 = 1, a_5 = 1/5, and a_6 = 1/25. The sum of these 6 terms is 693.75.

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Answer:

28 cm^2

Step-by-step explanation:

a^+21^2=36^2

a^2+441=1225

a=28

Plotting method is the graphical representation of mathematical expression.

A plot is a graphical representation of a list of data. Besides, a plot is the graphical analysis of mathematical expressions and equations because plot can show the relationship between two or more variables. There are many plotting methods such as hand plotting method, computer aided plotting method and so on.

At first, we need to choose the coordinate system by which we plot the point.

suppose we choose a XY coordinate plane. At first identify the horizontal or X axis and vertical or Y axis.

besides, we need to determine the required value that will be plotted on the plan.

if we have a list of X and Y value then find the value of X on the x axis and next find the value of Y on the Y axis.

we will notice some points for every pair of x and y value. Finally, we will join the points to achieve a required shaped graph.

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It’s angle 1 and angle 8

The pair of angles that are formed on the other side of the pearl lines, but on the opposite side of the transversal

goodluck

this is your proper answer

hii, how are you

Answer:

15

Step-by-step explanation:

Answer:

7

Step-by-step explanation:

So first you substitute A in

15-|-4(2)|

Then you multiply first because of GEMDAS or PEMDAS

15-|-8|

And because absolute value means how far away it is from 0, -8 is 8 away from 0 , thus |-8| is 8. So we simplify the equation

15-8

=7

Answer:

The equation for the volume of a sphere is [tex]\frac{4}{3}\pi r^{2}[/tex]. Substitute the variables with the given numbers to get [tex]\frac{4}{3}\pi 9^2[/tex]. Simplify the equation to get 3053.63.

Function 3x²+24x-6 does not belong with the other three

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

From the option we have to simplify each function

a. f(x)=3x²+6x-24

b. f(x)=3x²+24x-6

c. f(x)=3(x-2)(x+4)

=3(x²+4x-2x-8)

=3x²+6x-24

d. f(x)=3(x+1)²-27

3(x²+1+2x)-27

3x²+3+6x-27

3x²+6x-24

So function 3x²+24x-6 does not belong with the other three

Hence, function 3x²+24x-6 does not belong with the other three

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Answer:

Nonlinar assosion

Step-by-step explanation:

Answer:

Its B

Step-by-step explanation:

Answer: 1/36

Step-by-step explanation: 2/9 x 1/8 =2/72 = 1/36

Answer:y=1.19x

Step-by-step explanation: Since each pound of tomato costs 1.19, you multiple the price by the amount of pounds to get the total cost.

7 gallons of 76% solution contain 0.76×(7 gal) = 5.32 gal of sugar

10 gal of c% solution (c for concentration) contain c/100×(10 gal) = c/10 gal of sugar

(for example, if you have 10 gal of 50% solution, then it contains 50/10 = 5 gal of sugar)

Mixing the two gives a new solution with a total volume of 17 gal. If its concentration ends up at 64%, then it must contain 0.64×(17 gal) = 10.88 gal of sugar. This means

(sugar in 76% solution) + (sugar in c% solution) = 10.88 gal

5.32 gal + c/10 gal = 10.88 gal

c/10 gal = 5.56 gal

c = 50.56 ≈ 51

which makes the answer A.

Answer:

d. 56

Equation:

Let x = the percent of the 10 gallon sugar solution

10x + 76(7) = 64(10 + 7)

10x + 532 = 1088

10x = 1088 - 532

10x/10 = 556/10

x = 55.6

55.6 is closest to 56, therefore, the answer is 56%