Can someone explain this

The value of the expression is 9y⁵z³/x⁶

Note that index forms are described as mathematical forms of writing numbers that are large or too small in more convenient forms.

The rules of index forms are;

From the information given, we have that;

(y³z⁻¹) (3x⁻³y/z⁻²)²

expand the bracket, we get;

(y³z⁻¹) 9x⁻⁶y²/z⁻⁴

Take the inverse exponent of the denominator

(y³z⁻¹) 9x⁻⁶y²z⁴

Now, add the exponents

9x⁻⁶y³⁺²z⁻¹⁺⁴

9x⁻⁶y⁵z³

Then, we have;

9y⁵z³/x⁶

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The approximate diameter of the garden is 12.82 feet.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.

Here, we have

Given: A circular garden has a circumference of 40.25 feet.

We have to find the diameter of the garden.

The formula for the circumference of a circle is given as 2πr.

We have to find the radius of the circular garden

Hence: 2πr = 40.25m

π = 3.14

To find the radius, the formula would be given as

r = C/2π

Where C = Circumference of the circle

r = (40.25/2)x 3.14

r = 63.195

d =  C/π

d = 40.25/3.14

d = 12.82

Hence, the approximate diameter of the garden is 12.82 feet.

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Using the method of conversion,

The patient will take 6 teaspoons of the elixir and 2 tablespoons of the elixir as prescribed by the physician.

Conversion means changing a particular unit of measurement into another so that the values or the measurements are in a single unit which then allows us to solve the problem or the sum easily. Both the base units compared should be same.

This helps to reduce the complications that are created in a question.

Now here in the question,

We have 1 ounce of elixir.

Now to convert 1 ounce in 1 teaspoon we need to multiply the value by 6.

Similarly in order to convert 1 ounce into tablespoon, we need to multiply it by 2.

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Answer:

The angles are congruent, the two that are touching, m<s

Step-by-step explanation:

Answer:

The formula for the volume of a cylinder is:

V = πr^2h

where V is the volume, r is the radius, and h is the height.

Substituting the given values, we get:

V = π(7ft)^2(31ft)

V = π(49ft^2)(31ft)

V = 49π(31ft^3)

V ≈ 15,067.05 cubic feet (rounded to two decimal places)

Therefore, the volume of the silo is approximately 15,067.05 cubic feet.

The following statements are true about parallelograms: diagonals bisect each other, opposite sides are congruent, opposite angles are congruent and opposite angles are supplementary.

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are supplementary to the transversal on the same side. 360 degrees is the total of all interior angles.

A parallelepiped is a three-dimensional shape with parallelogram-shaped faces. The base (one of the parallel sides) and height (the distance from top to bottom) of the parallelogram determine its area. A parallelogram's perimeter is determined by the lengths of its four sides.

The properties of a parallelogram are shared by the shapes of a square and a rectangle.

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Answer:

[tex]sin( \alpha ) = \frac{12}{13} [/tex]

[tex] \cos( \alpha ) = \frac{5}{13} [/tex]

[tex] \tan( \alpha ) = \frac{12}{5} [/tex]

It follows that:

[tex] \cot( \alpha ) = \frac{5}{12} [/tex]

[tex] \sec( \alpha ) = \frac{13}{5} [/tex]

There are 8 possible outcomes and we need to find the probability of having at least two male children.

Out of the 8 outcomes, there are 3 outcomes where all children are female (FFF, probability = 1/8) and 3 outcomes where there is exactly one male child (FMF, FFM, MFF, probability = 3/8).

Therefore, the probability of having at least two male children is the complement of these outcomes, which is 1 - (1/8 + 3/8) = 4/8 or 1/2.

So the probability of selecting a family with at least two male children is 1/2 or 0.5.

The probability of selecting a family with at least two male children is 3/8.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

Example:

The probability of getting a head in tossing a coin.

P(H) = 1/2

We have,

There are 8 equally likely outcomes, and we want to find the probability of selecting a family with at least two male children.

There are three outcomes that satisfy this condition:

MMM, MMF, and MFM.

The probability of each of these outcomes is:

MMM: (1/2) x (1/2) x (1/2) = 1/8

MMF: (1/2) x (1/2) x (1/2) = 1/8

MFM: (1/2) x (1/2) x (1/2) = 1/8

So the total probability of selecting a family with at least two male children is:

1/8 + 1/8 + 1/8 = 3/8

Therefore,

The probability of selecting a family with at least two male children is 3/8.

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Answer:32

Step-by-step explanation:

Jackson will have earned $72 in interest at the end of 3 years.

Jackson saves $25 per month for 12 months:

$25 * 12 months = $300 per year

Now, let's calculate the total amount saved at the end of each year:

Year 1: $300

Year 2: $300 + $300 = $600

Year 3: $300 + $600 = $900

Next, we'll apply the 4% interest rate compounded annually to the final yearly balance:

Year 1: $300 * (1 + 0.04) = $300 * 1.04 = $312

Year 2: $600 * (1 + 0.04) = $600 * 1.04 = $624

Year 3: $900 * (1 + 0.04) = $900 * 1.04 = $936

So, the total amount Jackson will save at the end of 3 years is:

$312 (Year 1) + $624 (Year 2) + $936 (Year 3) = $1,872

Total deposited:

$300 + $600 + $900

= $1,800

Total interest earned:

$1,872  - $1,800

= $72

So, Jackson will have earned $72 in interest at the end of 3 years.

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Answer:

Step-by-step explanation:

,mnlnnl;

The rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the annual rate of change between 1992 and 2006, we can use the formula:

r = [tex](V2/V1)^{1/n}[/tex] - 1

where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.

r = -0.0839

Therefore, the annual rate of change between 1992 and 2006 is -0.0839.

To express the rate of change in percentage form, we can multiply the result from part A by 100:

r = -0.0839 x 100

r = -8.39%

Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.

To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.

From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:

where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.

V = 11792.51

Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).

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Answer:

y = 150x + 3000

Step-by-step explanation:

We can express the cost (y) as a linear function of heater quantity (x) by writing the equation in the slope-intercept form (y = mx + b), where m is the slope (in this case change in cost / change in heater quantity) and b is the y-intercept (when x = 0).

To find the slope (m), we can use the slope formula, which is

[tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex], where x1 and y1 are one point and x2 and y2 are the other point.

If we allow (30, 7500) to represent x1 and y1 and (40, 9000) to represent x2 and y2, our slope is:

[tex]m=\frac{9000-7500}{40-30}\\ \\m=\frac{1500}{10}\\ \\m=150[/tex]

Now, we can find the y-intercept by plugging in the slope and one of the points and solving for b:

[tex]7500=150(30)+b\\7500=4500+b\\3000=b[/tex]

Thus, our equation where y (cost) is a function of x (heater quantity) is y = 150x + 3000

Answer:

The total volume, in cubic feet, of the three boxes is 144 cubic feet.

Chain of thought:

1. Volume = base x height

2. Box 1: Volume = 16 sq feet x 3 feet = 48 cubic feet

3. Box 2: Volume = 16 sq feet x 3 feet = 48 cubic feet

4. Box 3: Volume = 16 sq feet x 5 feet = 80 cubic feet

5. Total Volume of three boxes = 48 + 48 + 80 = 144 cubic feet

To find the value of tan(-284°24'), we can use the fact that the tangent function has period π, which means that:

tan(x) = tan(x + nπ)

where n is any integer. We can use this fact to convert the angle -284°24' to an equivalent angle between 0° and 360°:

-284°24' = -360° + 75°36' = 75°36'

Now, we need to find the reference angle, which is the acute angle between the terminal side of the angle and the x-axis. Since 75°36' is in the second quadrant (where the tangent function is positive), the reference angle is:

75°36' - 180° = -104°24'

Finally, we can use the identity:

tan(-θ) = -tan(θ)

to find the value of tan(-104°24'):

tan(-104°24') = -tan(104°24')

We can use a calculator to find that:

tan(104°24') ≈ 2.3835

Therefore:

tan(-284°24') ≈ -2.3835 (rounded to the nearest ten-thousandth)

So, the value of tan(-284°24') to the nearest ten-thousandth is -2.3835.

Using area formula,

a. Area of the trapezium = 47.5m².

b. Area of parallelogram = 54inches².

The area of a thing is the amount of space it occupies in two dimensions. It is a way to count how many unit squares completely round the surface of a closed figure. The standard unit of area is the square unit, which is usually expressed as square inches, square feet, etc.

a. Sides of the trapezium are, a = 5m and b = 14m.

Height, h = 5m.

Area of the trapezium = (a+b)/2 × h

= (5 + 14)/2 × 5

= (19× 5)/2

= 95/2

= 47.5m².

b. Height of parallelogram = 6inches.

Base of parallelogram = 9inches.

Area = b × h

= 6 × 9

= 54inches².

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The 5-digit number that can be formed is 100,000.

5-digit numbers using 0,1,,2,3,4,5,6,7,8,9,

 We can use any of the 10 numbers to form a 5-digit number

The first place, there can be any of the 10 numbers

       In the second place, there can be any of the 10 numbers

       In the third place, also there can be any of the 10 numbers and so on.

       Therefore we have:

   10×10×10×10×10 = 100,000 digits

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The 999th digit to the right of the decimal point is 9.

Decimal expansion is the representation of a number in decimal form. In decimal expansion, a number is represented using the base-ten positional notation system, where each digit represents a multiple of a power of ten.

For example, the decimal expansion of the number 1234.5678 is:

which simplifies to:

1000 + 200 + 30 + 4 + 0.5 + 0.06 + 0.007 + 0.0008 = 1234.5678

The decimal expansion of a number can be finite or infinite, and it may or may not be a repeating decimal. A repeating decimal is a decimal that has a repeating pattern of digits after the decimal point. For example, the decimal expansion of 1/3 is 0.3333..., with the digit 3 repeating infinitely.

To find the 999th digit to the right of the decimal point, we need to determine the repeating block of digits in the decimal expansion of 9/23.

The remainder when 9 is divided by 23 is 9, so we can start the long division as follows:

         0.3913043478260869565217...

         --------------------------------

23 |    9.00000000000000000000

           - 6

          --------

                30

               -23

               -----

                   7

                    ...

We can see that the decimal expansion of 9/23 repeats after 22 digits, since the remainder becomes 7, which is the same as the remainder we obtained after dividing 9 by 23.

Therefore, the 999th digit to the right of the decimal point is the same as the (999 mod 22)th digit, which is the 9th digit in the repeating block of digits:

0.3913043478260869565217...

9

So the 999th digit to the right of the decimal point is 9.

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The proof for the above question are given above accordingly.

10) Since OA ⊥ OC; and

OB ⊥ OD (Given)
Thus,

∠AOC = 90°;  perpendicular bisector theorem

∠BOD = 90°; perpendicular bisector theorem

Therefore,

90° Less ∠1 = ∠BOC; and

90° less ∠3 = ∠BOC,

Thus,

∠1≅∠3 - subtraction theorem of congruence

11)

Since ∠A is complimentary to ∠ ADB; Given.....1

and ∠C is complimentary to ∠CDB - Given. .....2
Where DB  bisects ∠ADC, thus,

∠DBC = 90° ----Line bisector theorem .......3
∠BDC = 90° -----Line bisector theorem........4

From 1 and 2 above, we know that:

∠A + ∠ADB = 90°
∠C + ∠CDB = 90°, thus,


Since

∠A + ∠ADB + ∠DBA = 180° - Sum of Angles in a triangle; and

∠C + CDB + ∠BDC = 180° - Sum of angles in a triangle, we can state that

∠A ≅∠C.

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Answer:

367

Step-by-step explanation:

Places in the alphabet:
T=20, H=8, E=5, R=18, E=5. 20+8+5+18+5=56. THERE=56
A=1, R=18, E=5. 1+18+5=24. ARE=24
S=19, O=15, M=13, E=5. 19+15+13+5=52. SOME=52
S=19, A=1, N=14, D=4, W=23, I=9, C=3, H=8, E=5, S=19. 19+1+14+4+23+9+3+8+5+19=105. SANDWICHES=105
O=15, N=14. 15+14=29. ON=29
T=20, H=8, E=5. 20+8+5=33. THE=33
S=19, H=8, E=5, L=12, F=6. 19+8+5+12+6=49. SHELF=49
56+24+52+19+105+29+33+49=367

Answer:

150 men and 252 women

Step-by-step explanation:

            Men : Women = 5 : 9

Number of men = 5x

Number of women = 9x

42 women left the museum.

Number of remaining women = 9x - 42

              New ratio = 2 : 3

                      [tex]\dfrac{5x}{9x -42}=\dfrac{2}{3}\\\\\\\bf Cross \ multiply,[/tex]

                          3*5x  = 2*(9x - 42)

                          15x     = 2*9x - 2*42

                              15x = 18x - 84

                  18x - 84 = 15x

Add 84 to both the sides,

                         18x = 15x + 84

Subtract 15x from both sides,

                18x - 15x = 84

                         3x = 84

Divide both sides by 3,

                            x = 84 ÷ 3

                            x =  28

Number of men = 5 * 28 = 140

Number of women = 9*28 = 252

Rule 1: The output is the square of the input. For example, if the input is 3, then the output would be 9 (3 squared).

Rule 2: The output is 90 greater than the input. For example, if the input is 3, then the output would be 93 (3 + 90).

These are the two rules you've provided, and they describe how to calculate the output (y) based on the input (x).
Rule 1: The output is the square of the input.
In this rule, when you have an input value (let's call it x), you square it (multiply it by itself) to get the output value (y). Mathematically, this can be written as:
[tex]y = x^2[/tex]
Rule 2: The output is 90 greater than the input.
In this rule, when you have an input value (x), you add 90 to it to get the output value (y).

Mathematically, this can be written as:
y = x + 90.

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Number of math textbooks is 110 and number of history textbooks is 330 were sold when a textbook store sold a combined total of 440 math and history textbooks in a week.

There are two categories of textbooks. Let "x" stand for the quantity of math textbooks and "y" for the quantity of history textbooks.

A textbook store sold a combined total of 440 math and history textbooks in a week.

Equation,

x + y = 440

The number of math textbooks sold was three times the number of history textbooks sold.

x = 3y

Substituting the values in equation x + y = 440,

3y + y = 440

4y = 440

y = [tex]\frac{440}{4}[/tex]

y = 110

Number of math textbooks = 110

Number of history textbooks:

3y

3 × 110

330

Number of math textbooks is 110 and number of history textbooks is 330 were sold when a textbook store sold a combined total of 440 math and history textbooks in a week.

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Answer:

308 yards^2

Step-by-step explanation:

Area = length * width

Length = 20

Width = 15.4

20 * 15.4 = 308

Answer: 308 yards

Step-by-step explanation:

The probability of there being no defects in the entire shipment is 0.2075.

What is probability?

Probability can be used to calculate an event's probability. It can only be used to assess the possibility that an event will occur. A scale from 0 to 1, where 0 is impossible and 1 is a particular occurrence.

We are given that out of the 400 components, 68 are defective and 332 are non-defective computer components.

A random sample of 25 is taken.

So,

⇒ Probability (Defects in the shipment) =  [tex]\frac{68}{400}[/tex]

⇒ Probability (Defects in the shipment) = 0.17

Thus,

⇒ Probability (No Defects in the shipment) =25 * (1 - 0.17)

⇒ Probability ( No Defects in the shipment) = 25 * (0.83)

⇒ Probability ( No Defects in the shipment) = 0.2075

Hence, the probability of there being no defects in the entire shipment is 0.2075.

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Answer:

90

Step-by-step explanation:

We can translate this into the following equation:

x - 0.4x = 54

Simplifying the left side of the equation, we get:

0.6x = 54

Dividing both sides by 0.6, we get the following:

x = 90

Therefore, 90 is the number decreased by 40% leaving 54.

Given triangle is not a right angle triangle.

What is Pythagoras theorem?

For any right angle triangle,

Hypotenuse ²= Base²+Height ²

To determine whether the any triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the sides of the triangle as follows,

a = 14

b = 10

c = 4√19

Then we can check whether the Pythagorean theorem holds for these values:

c² = (4√19)² = 16×19 = 304

a²+ b² = 14²+ 10² = 196 + 100 = 296

Since c² is not equal to a² + b², the triangle is not a right triangle. Therefore, the answer is no, the given triangle is not a right angle triangle.

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Answer:

D. 4 units

Step-by-step explanation:

Similar figures have corresponding lengths in proportion.

[tex]\frac{4x}{2x}=\frac{x+1}{x} \\ \\ 2=1+\frac{1}{x} \\ \\ 1=\frac{1}{x} \\ \\ x=1[/tex]

Therefore, the height of Figure 1 is 4.

The function of the sequence is T(n) = n² + n and it is quadratic

The domain of the graph is [0, 18]

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

Step          Cells

1                 2

2                6

3                12

From the table, we have

T(n) = n * (n + 1)

This gives

T(n) = n² + n

Hence, the function is T(n) = n² + n

The sequence T(n) = n² + n is a quadratic sequence

This is the set of the x values

From the graph, we have

x = 0 to 18

So, we have

Domain = [0, 18]

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sin60=√3/2 = x/12

x=√3×12/2

x=√3×6

x=6√3