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1. Draw 16 stairs. Put them equally into 2 sets. How many stairs are in each set? ___

2. Round each number to the nearest 10. Then subtract : 497 - 315 is about: ___

3. Abel drew some Triangles. his drawing had 21 Vertices. How many triangles did he draw? write a division equation to answer the question: ___

If a line is drawn so that it passes through the point [tex](2,-1)[/tex] and [tex](0,5)[/tex] , then  slope of line is -3 .

What is Slope ?

The slope of a line is defined as measure of steepness and direction of  line. The slope of line in a plane help in predicting whether lines are parallel, perpendicular, or none without using a compass.

The slope of line passes through points [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] is calculated by formula ⇒ [tex]Slope = \frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex] ;

the points are given as  [tex](2,-1)[/tex] and [tex](0,5)[/tex]  ;

So , on substituting the values in the slope formula ,

we get ;

[tex]Slope = \frac{5 -(-1) }{0 -2 }[/tex] ;

= [tex]\frac{6}{-2}[/tex]

= -3 .

Therefore , the required slope of the line is -3 .

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Answer:

c

Step-by-step explanation:

The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c

Answer:

25%

Step-by-step explanation:

1 out of 4 chance = 25% chance to get 2

The height of the mt. Everest in miles exists 5.499 miles.

By changing the unit of measurement, a quality can be expressed differently. In contrast to distance, which can be stated in miles, kilometers, feet, or any other unit of length, time can also be expressed in minutes rather than hours.

By multiplying or dividing a number, a conversion factor can be used to change one set of units to another. The right conversion factor to an equal value must be used when a conversion is required. The correct conversion factor, for instance, is 12 inches to 1 foot when converting between inches and feet.

The height of the mt. Everest is : 29035 feet.

The unit conversion is given as :

5280 feet = 1 mile

1 feet = 1/5280 mile

So, 29035 feet =29035 × 1/5280 miles

29035 feet = 29035/5280 miles

29035 feet = 5.499 miles

So, the height of the mt. Everest in miles is 5.499 miles.

The complete question is:

In the Himalaya mountains along the border of Tibet and Nepal, mount Everest reaches a record height of 29,035 feet. how high is mt. Everest in miles? use the conversion equivalency of 1 mile = 5280 feet.

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Answer:  The height of the Mount Everest in miles is 5.499 miles

Step-by-step explanation:

1 miles = 5,280 feet

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The possible formula for the depth of water in tank is , D = 2.8 + 8 sin(π t/4) where t is time in hours.

Sinusoidally function, is defined as one of triagnometric function with a smooth, repetitive oscillation. "Sinusoidal" comes from "sine", function. We can write its equation in the following form y = A·sin(B(x - C)) + D

where, A --> amplitude

B--> period in form of pi

C--> phase or horizontal shift

D --> vertical shift

We have, the depth of water in a tank oscillates sinusoidally.

The smallest depth of water in tank = 6.6 feet

The largest depth of water in tank = 9.4 feet

We have to determine the formula of depth of water in tank as a function of time in hours .

For sinusoidal function,

Amplitude , A = average depth

= ( largest depth + smallest depth)/2

= (6.6 + 9.4)/2

= 16.0/2 = 8

Now, The period of 8 hours so, B = 2π/8

=> B = 45° = π/4

Also, upward shift , D is 9.4 - 6.6 = 2.8

Horizontal shift, C = 0

So, required function is D = 2.8 + 8 sin(π t/4) .

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Answer:

-5(x-21)(x-3)

Step-by-step explanation:

-5[tex]x^{2}[/tex] + 120x - 315 = -5([tex]x^{2}[/tex] - 24x + 63)

                           = -5([tex]x^{2}[/tex] - 3x - 21x + 63)

                           = -5[x(x-3) - 21(x-3)]

                           = -5[(x-21)(x-3)]

The process of simplify the equation is explained below.

The term equation is known as a mathematical statement that defines the equality between two expressions.

Here we have to define the process of simplifying the equation.

The first and foremost step is to remove parentheses and brackets by multiplying factors.

And then we have to use the exponent rule to remove grouping if the terms contain exponents.

Then we have to combine like terms by adding or subtracting coefficients.

Finally, we have to Combine the constants.

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Answer:

Step-by-step explanation:

The candies left for Kyla were 10 based on the amount given to her sister and friend from total 20 candies.

Firstly we will calculate the remaining candies from twenty after giving to her sister. Next calculation will be the final answer representing candies left for Kyla herself.

Remaining candies = total number of candies - 1/5×total candies

Keep the values in formula

Remaining candies = 20 - 1/5×20

Remaining candies = 20 - 4

Remaining candies = 16

Total candies for Kyla = remaining candies - 3/8×remaining candies

Candies for Kyla = 16 - 3/8×16

Candies for Kyla = 16 - 3×2

Candies for Kyla = 16 - 6

Candies for Kyla = 10

Thus, Kyla received 10 candies.

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Answer:

2) The estimated weight, in pounds, of the beaver on June 1.

Step-by-step explanation:

Given function:

[tex]w(t) = 29 + 0.0674t \quad t < 90[/tex]

where:

When t = 0:

[tex]\begin{aligned}\implies w(0)&=29+0.0674(0)\\&=29+0\\&=29\end{aligned}[/tex]

Therefore, the constant of the equation (29) is the estimated weight of the beaver, in pounds, when t = 0.

As t = 0 is June 1:

Answer: domain(-oo,oo). range= f(x) >-5

Step-by-step explanation:

Answer:

≈ 11.4 m

Step-by-step explanation:

The diagonal splits the rectangle into 2 right triangles , with legs 7 and 9 and the diagonal the hypotenuse.

Using Pythagoras' identity with h as the diagonal, then

h² = 7² + 9² = 49 + 81 = 130 ( take the square root of both sides )

h = [tex]\sqrt{130}[/tex] ≈ 11.4 m ( to the nearest tenth )

The interpretation of the slope is that the cost per minute is $2

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

C(m) = 2m + 15

Where

m = number of minutes

C(m) = cost function

The equation of a line can be represented as

y = mx + c

Where

Slope = m

By comparing the equations, we have the following

m = 2

This means that the slope is 2

And it means that the cost per minute is $2

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Answer:

No it does not equal a right triangle.

Answer:

Step-by-step explanation:

iF THERE MUST BE 4 PILES, and you have only 4 pennies, then there must be 1 penny in each pile.  

Answer:

40

Step-by-step explanation:

5 x 4 x 2 = 40

length x width x height = volume

A statement 'The lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.' is True.

We know that the formula for the lateral surface area of cone:

Area = π × radius × slant height

and the formula for the lateral surface area of cylinder:

Area = 2π × (radius) × (height)

Here we have been given a cone A with radius r and slant height 2h.

Using the above formula, the lateral surface area of cone A would be:

A1 =  π × r × 2h

A1 =  2π × r × h                    ..................(1)

Also, we have been given a cylinder B with radius r and height h.

Using the above formula, the lateral surface area of cylinder A would be:  

A2 =  2π × r × h                   ..............(2)

From (1) and (2) we can observe that,

A1 = A2

Therefore, the lateral surface area of cone A is exactly equal to the lateral surface area of cylinder B.

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Answer: [tex]6.04\ ft[/tex]

Step-by-step explanation:

Given

The fence has a length of 38 ft i.e. it is the circumference of the circular flower

The circumference of the circle is [tex]2\pi r[/tex]

Insert the values

[tex]\Rightarrow 2\pir=38\\\\\Rightarrow 2\times \dfrac{22}{7}\times r=38\\\\\Rightarrow r=\dfrac{38\times 7}{2\times 22}\\\\\Rightarrow r=\dfrac{266}{44}\\\\\Rightarrow r=6.04\ ft[/tex]

The largest radius of the garden is  [tex]6.04\ ft[/tex]

The solution of equation is ∅.

According to the mathematical definition of inequality, neither side is equal. When a relationship leads to a non-equal comparison between two expressions or numbers, it is known as an inequality in mathematics. The equal sign "=" in this statement can be replaced with any of the inequality symbols.

Given equation |x| + 7 < 4

subtract 7 from both sides

|x| + 7 - 7 < 4 - 7

|x| < -3

but |x| ≥ 0, for all real values,

so solution is ∅.

Hence the solution of equation is ∅.

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Answer:

23

Step-by-step explanation:

7(x+1) = 8(x-2)

7x+7 = 8x-16

x = 23

Answer:

Dylan has 5

Step-by-step explanation:

jessie 8+x

‘Dylan  x

so

8+x+x=18

2x=10

x=5

jessie has 13

dylan has 5

Answer:

C.) 13

Step-by-step explanation:

So, I'm going to break this down to the three sentences. If you look at the key words in each sentence, grammatically the last one stands out.

In the first sentence it is saying Jessie HAS 8 more pencils than Dylan

In the second sentence it is saying Together they HAVE a total of 18 pencils

In the third sentence it is asking How many pencils DID Dylan have

The word MORE implies in addition to. And this very well could mean at least. I believe the answer is 13.

Saying Dylan had 5 pencils (+ J's 8), would be 13

Saying Dylan had 8 pencils (+J's 8), would be 16

Both of which are not AT LEAST 18

Saying Dylan had 13 pencils (+J's 8), would be 21

If 10 is incorrect, your answer should be 13

The minimal number of employees who did not get their preferred shift that week was 20.

Out of 50, 40% are on the day shift = 0.4*50 = 20 & 60% are on the night shift = 30.

But, 80% of 50 prefer day shift = 0.8*50 = 20 & 20% of 50 prefer night shift = 10.

We need to find the minimum no. of people who did not get their desired shift. Since slots for the night shift(30) are greater than the people who desired it (10). We can assume that among those 30-night shift slots, 10 were occupied by the ones who wanted the night shift. So, whoever wanted the night shift got the night shift.

But, for the day shifts the no. of slots (20) is less than the number of people who desired it (40). So, there are going to be 20 people who did not get what they desired.

Thus, 20  is the minimum number of staff members who failed to receive her preference of shift that week.

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The additive inverse of 6 /- 5 is 6/5

We know that for any real number 'a' an additive inverse is a number 'b' such that a + b = 0

i.e., b = -a

An additive inverse of 'a' is -a.

The means, an additive inverse is nothing but changing sign + to - OR - to +

Here we have been given a rational number 6/(-5)

Let m be the additive inverse of number 6/(-5)

From the definition of additive inverse,

6/(-5) + m = 0

[6/(-5) + m] - 6/(-5) = -6/(-5)            

[6/(-5) - 6/(-5)] + m= -6/(-5)       ...........(associative property of addition)

0 + m =  6/5

m = 6/5

Hence, the additive inverse is 6/5

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Gary, Mary, and Rory have 96 candies altogether.

Let's assume that the original number of candies that Gary, Mary, and Rory had is "x".

After Gary gives Mary half of all his candies, he would have x/2 candies.

Then, after Mary gives Rory half of all the candies she has at the moment, she would have x/4 candies.

And then, after Rory gives Gary half of all the candies he (Rory) has at the moment, he would have x/8 candies.

Now, we know that Gary would have 12 more candies than he had originally, which means:

x/2 + x/8 = x/2 + x/4 - 12

We can combine like terms and simplify the equation:

x/2 + x/8 = x/4 + x/4 - 12

x/8 = 12

x = 8 * 12

x = 96

Thus, Gary, Mary, and Rory have 96 candies altogether.

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The rounding off of 34.171875 to the nearest 100th gives us= 34.17

The nearest hundredth should be the second digit after the decimal point. To round off any decimal figures, we need to see if the digit after the hundredth is greater than or equal to 5. If such is the case, then add 1 to the hundredth, or else remove the digits.

Here, the nearest hundredth digit is 7, and the digit after it (i.e, the third place after decimal) is smaller than 5. So, there is no need of adding an extra 1 to the hundredth. Now, after casting off the remaining digits, we get 34.17.

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Note: your teacher may not want you to enter "feet" and instead may just want the number only.

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Work Shown:

tan(angle) = opposite/adjacent

tan(40) = h/20

20*tan(40) = h

h = 20*tan(40)

h = 16.7819926 which is approximate

h = 16.8

The streetlamp is approximately 16.8 ft tall.

When using your calculator, make sure it's in degree mode. One way to check is to compute something like tan(45) and you should get 1 as a result.

An inequality involving absolute values that describes the range of possible thickness for the laminate.

(a) The range of possible thickness for the laminate is given by the tolerance of 0.004 in., so we can write an inequality involving absolute values as:

|h - 0.016| <= 0.004

(b) To solve the inequality, we need to consider two cases:

Case 1: h - 0.016 <= 0.004

             h <= 0.02

Case 2: h - 0.016 >= -0.004

             h >= 0.012

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Answer:

x^2-9

Step-by-step explanation:

-3 + 3 = 0 so the x terms cancel out.  This leaves you with only x^2-9