nple
If a pyramid has a square base with side lengths and height h, which
formula represents the volume of the pyramid?
Since the base of the pyramid is a square, the area of the base is
Abase = SXS = 5².
The volume of a pyramid is one-third the product of base area and
height, so the volume of this pyramid is
Key Term
Cavalieri's principle is applicable to all three-dimensional shapes, including
and
Cavalieri's principle implies that a tilted cone (or pyramid) has exactly the same
as an upright cone (or pyramid) with same base and
height.
The formulas for the volumes of a cone and a pyramid are applicable even if their shapes are not upright.
Summary
What is the relationship between the volume of a rectangular prism and a pyramid with the same base area
and height?
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2 half dollars just mean a dollar. In that case, that's 10 dimes. (10*10=100)

Answer:

10 dimes

Step-by-step explanation:

So in order to get this answer we first must know that...

1 half dollar = 50 cents

1 dime = 10 cents

So...

5 dimes = 50 cents

2 half dollars = 100 cents aka $1

10 dime = 100 cents aka $1

Therefore we can use our common sense to figure out that 2 half dollars is 10 dimes.

Answer:

Step-by-step explanation:

( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] )

( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )

d = [tex]\sqrt{(x_{2} -x_{1} )^2+(y_{2} -y_{1} )^2}[/tex]

~~~~~~~~~~~~~~~

A ( 3 , 6 )

B ( 0 , 1 )

C ( 4 , 0 )

AB = [tex]\sqrt{(0-3)^2 + (1-6)^2}[/tex] = 3√5 ≈ 6.71

AC = [tex]\sqrt{(4-3)^2 + (0-6)^2 }[/tex] = √37 ≈ 6.08

BC = [tex]\sqrt{(4-0)^2 + (0-1)^2 }[/tex] = √17 ≈ 4.12

AB ≠ AC ≠ BC ⇒ Δ ABC is a scalene triangle

Answer: x=-16

Step-by-step explanation:

g^-1 is the inverse of the g(x) graph meaning that the x and g(x) values of the g(x) graph switch places. So in the table when  x=-2 g(x)=-16

Answer:10,600 to 16,400

Step-by-step explanation:

First you subtract the margin of error to find  the least amount of hours.

6.75 - 1.45 = 5.3 x 2,000(people) = 10,600 (least amount of hours)

Then you add the margin of error to find the most amount of hours.
6.75 + 1.45 = 8.2 x 2,000(people) = 16,400 (most amount of hours)

The margin of error just shows that people spent at least 5.3 and at most 8.2 hours at the park.

You multiply those numbers with how many people went to the park. 2,000

That means the answer is C: 10,600 TO 16,400.

Plus.....I took the test and got it right!

Answer:

49.57

Step-by-step explanation:

0.7 can go into 34.7 49 times. 0.7*49=37.3

34.7-34.3=0.4 and 0.4/0.7 is 4/7 or 0.57...

So 49+.57=49.57

The probability of selecting four cards of the same suit is 0.0106.

A probability is a number that reflects the chance or likelihood that a particular event will occur.

Given that, four cards are selected at random without replacement from a well-shuffled deck of 52 playing cards

No. of cards for each suit = 13

Total types of four suits = 4(hearts, spades, diamond, clubs)

Probability = (conditional case)/(total case)

So, total number of conditional case = No. of case of selecting all 4 cards of hearts suit + no. of case of selecting all 4 cards of spades suit + no. of case of selecting all 4 cards of clubs suit + no. of case of selecting all 4 cards of diamonds suit

= 13C4 + 13C4 + 13C4 + 13C4

= 4*13C4 = 4*13!/9!4! = 4*13*12*11*10*9!/9!*4*3*2*1 = 2860

Total number of cases = 52C4 = 52!/48!4! = 270725

So, probability of getting all 4 cards of the same suit =

2860/270725

​= 0.0106.

Hence, The probability of selecting four cards of the same suit is 0.0106.

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Answer:

Step-by-step explanation:

Find the slope of PQ

[tex]\frac{9 - (-1)}{5-0}=\frac{10}{5}[/tex] or just [tex]2[/tex]

The perpendicular slope is the negative reciprocal

Use a slope of [tex]-\frac{1}{2}[/tex]

Use the point-slope form of a equation and point P to find a new equation in slope-intercept form

[tex](y- (-1))=-\frac{1}{2}(x-0)[/tex]

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

Subtract the 1 from both sides of the equation

[tex]y=-\frac{1}{2}x-1[/tex]

Answer:3

Step-by-step explanation: 3x3=9

Answer:

3

Step-by-step explanation:

√9

=√3²

=√(3²)

=3

{as square root =1/2, 2*1/2 = 1}

By evaluating the exponential equation, we will see that the amount owed after 6 years is $8551.56

The formula we need to use is the exponential equation:

A = P*(1 + r/n)^(n*t)

Where:

P is the initial amount, here we know that it is $5,300

r is the rate, in this case is 8%, but it needs to be written as a decimal, so we have r = 0.08

t is the variable, this time is the time in years, we want to find the amount owed after 6 years, so t = 6

n is how many the the rate applies on one unit of t, in this case the rate is monthly, and there are 12 months on a year, so n = 12.

Replacing all that in the given formula we will get:

A = $5,300*(1 + 0.08/12)^(12*6) = $8551.56

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The length of the segment BD is 2.4 units and that of AB is 4 units.

According to the question,

We have the following information:

We have a figure of triangle in which there are two right-angled triangles.

Now, we can find the length of the segment BD and AB using the Pythagoras theorem.

Using it in triangle BDC:

[tex]BC^{2} = CD^{2} + BD^{2}[/tex]

Putting the values of BC and CD:

3*3 = 1.8*1.8+[tex]BD^{2}[/tex]

9 = 3.24+[tex]BD^{2}[/tex]

Subtracting 3.24 from both sides:

9-3.24 = [tex]BD^{2}[/tex]

[tex]BD^{2}[/tex] = 5.76

BD = 2.4 units

Now, using the same theorem in triangle BDA:

[tex]AB^{2} = BD^{2}+ AD^{2}[/tex]

[tex]AB^{2}[/tex] = 5.76+3.2*3.2

[tex]AB^{2}[/tex] = 5.76+10.24

[tex]AB^{2}[/tex] = 16

AB = 4 units

Hence, the length of the segment BD is 2.4 units and that of AB is 4 units.

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Answer:

milk

Step-by-step explanation:

To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .

In the question ,

it is given that ,

the each serving should not be larger than  8oz .

let the number of Ounces of Brand A food = x , and

let the number of ounces of brand B = y ,

So , x + y ≤ 8

Brand A has 3 units of Nutrient 1 and 4 units of Nutrient 2 , and

Brand B has 5 units of Nutrient 1 and 2 units of Nutrient 2 ,

So , 3x + 5y ≥ 29 ,

and 4x + 2y ≥ 20,

and x , y ≥ 0  .

given, that

cost of Brand A = 5 cents/ounce

cost of Brand B = 7 cents/ounce

So , the cost equation is c(x) = 5x + 7y ,

drawing the given inequalities on the graph ,

From the graph given below , we find that the vertices of the feasible region are ,

(2,6) , (5.5,2.5) , (3,4)

Substituting the points in the cost equation , we get

For point (2,6) , C = 5(2) + 7(6) = 10 + 42 = 52

For point (3,4), C = 5(3) + 7(4) = 15 + 28 = 43

For point (5.5,2.5) , C = 5(5.5) + 7(2.5) = 45 ,

the minimum cost is at point (3,4) ,

So , 3 ounces of Brand A and 4 ounces of Brand B should be used .

Therefore , To meet the given requirements 3 ounces of Brand A and 4 ounces of Brand B should be served , the minimum cost is $43 .

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The distance between the points (-4, -5) and (8, 0) is 13 units

The coordinates of the first point = (-4, -5)

The coordinates of the second point = (8, 0)

The distance between the two points d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Where d is the distance between two points

[tex](x_1,y_1)[/tex] is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The distance between the two points = [tex]\sqrt{(8--4)^2+(0--5)^2}[/tex]

= [tex]\sqrt{12^2+5^2}[/tex]

Find the square of each term

= [tex]\sqrt{144+25}[/tex]

Add the terms together

= [tex]\sqrt{169}[/tex]

Find the square root of the number

= 13 units

Hence, the distance between the points (-4, -5) and (8, 0) is 13 units

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y = -1/3 x + 5 this equation represents the given graph.

How do you plot points on graph ?

Proof :

(0, 5) and ( 15, 0) these are the points where the graph is plotted.

y = -1/3 x + 5

put x= 0 and find y

y = 0 + 5

y = 5

put y = 0 and find x

0 = -1/3 x + 5

-5 = -1/3 x

x = 15

So, now we get the same points i.e, (0, 5) and ( 15, 0) as plotted in the given graph.

Hence, we can say that  y = -1/3 x + 5 this equation represents the given graph.

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The percent change in the number of pounds that Jake can lift is 80%.

From the information illustrated, Jake could lift 25lbs and one month later he could lift 45lbs.

The percentage change will be:

= Change in pounds / Original pounds × 100

= (45 - 25) / 25 × 100

= 20 / 25 × 100

= 4 / 5 × 100

= 80%

The percentage change is 80%.

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The perimeter of the triangle is, 8x + 3y +1.

What is perimeter?

A perimeter is a closed path that encloses, surrounds, or delimits a one-dimensional length, a two-dimensional shape, or both. The circumference of a circle or an ellipse is its perimeter. There are numerous practical uses for calculating the perimeter.

Let, the side lengths of the triangle are (7x - 4), (x + 3) and (3y + 2).

Since the perimeter is the sum of all side lengths.

So,

Perimeter = (7x - 4) + (x + 3) + (3y + 2)

                 = 7x - 4 + x + 3 + 3y + 2

Perimeter = 8x + 3y + 1

Hence, the perimeter of the triangle is, 8x + 3y + 1.

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(x-2)9

9x-18

good luck <33

Answer: 42 km of 120km is 35%

Step-by-step explanation: 42 ÷ 120 is 0.35 then you move decimal 2 places right to get percent.

The height of the kite is approximately 112.763 meters above the ground.

The situation is represented by the following geometric diagram, a right triangle with a known hypotenuse (r), in meters, and a known acute angle (θ), in degrees. The height of the kite (h), in meters, is represented by the leg opposite to the acute angle and can be found by trigonometric functions:

sin θ = h / r

h = r · sin θ

h = 120 · sin 70°

h ≈ 112.763 m

The height of the kite is approximately 112.763 meters.

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Answer:

2m Wide

Step-by-step explanation:

The three ordered pairs for the equation y = -4x+3 are (0,3), (1,-1) and (2,-5).

According to the question,

We have the following equation:

y = -4x+3

We have to find the three ordered pairs when the values of x are given in the table.

When x = 0, we have the following value of y:

y = -4*0+3

y = 3

When x = 1:

y = -4*1+3

y = -4+3

y = -1

When x = 2:

y = -4*2+3

y = -8+3

y = -5

Hence, the three ordered pairs for the equation y = -4x+3 are (0,3), (1,-1) and (2,-5).

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The x- and y- intercepts of then graph of; -2x + y = 22 as required in the task content are; -11 and 22 respectively.

It follows from the task content that the x- and y-intercepts of the graph of the equation; -2x + y = 22 are to be determined.

Recall that the y-intercept of a graph refers to the value of y when x = 0.

Therefore; we have;

-2(0) + y = 22;

y = 22.

Recall that the x-intercept of a graph refers to the value of x when y = 0;

-2x + 0 = 22

x = 22/-2

x = -11.

On this note, it follows that the x-intercept of the graph is at x = -11 while the y-intercept is at; y = 22.

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All apply values to the equation are:

0 ⇒ A

π/3 ⇒ B

5π/3 ⇒ E

What is an equation?

A formula known as an equation shows the equality of two expressions by joining them with the equals sign =.

Main Body:

∵ 0 ≤ x ≤ 2π is the domain for angle x

∴ 0 ≤x/2  ≤ π is the domain of angle

∵ sin(x/2) + cos(x) - 1 = 0

→ To solve the equation we should use the rule of cosine double angle

∵ cos(x) = 1 - 2 sin²(x/2)

→ Substitute it in the equation above

∴ sin(x/2) + (1 - 2 sin²(x/2) = 0

∴ sin(x/2) + 1 - 2 sin²(x/2) = 0

→ Add the like terms

∴ sin(x/2) + (1 - 1) - 2 sin²(x/2) = 0

∴ sin(x/2) - 2 sin²(x/2) = 0

→ Take sin(x/2) as a common factor

∴ sin(x/2) [1 - 2sin(x/2)] = 0

→ Equate each factor by 0

∵ sin(x/2) = 0

→ The value of sine equal zero on the x-axis

∴ x/2 = 0, π, 2π

∵ The domain of x/2  is 0 ≤ (x/2) ≤ π

∴  x/2 = 0 and π ⇒ 2π refused because ∉ the domain

→ Multiply both sides by 2 to find x

∴ x = 0 and 2π

∵ 1 - 2sin(x/2) = 0

→ Subtract 1 from both sides

∴ - 2sin(x/2) = -1

→ Divide both sides by -2

∴ sin(x/2) = 1/2

→ The sine is positive in the 1st and 2nd quadrants

∴ (x/2) lies on the 1st OR 2nd quadrants

∵ (x/2) = sin⁻¹(1/2)

∴ (x/2) =  π/6 =  ⇒ 1st quadrant

→ Multiply both sides by 2

∴ x = π/3

∵ (x/2) = π -π/6  = 5π/6 ⇒ 2nd quadrant

→ Multiply both sides by 2

∴ x = 5π/3

∴ The values of x are 0,π/3 , 5π/3 , 2π

Hence  apply values are:

0 ⇒ A

π/3⇒ B

5π/3⇒ E

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Carlos harvests cassavas at a constant rate. He needs 353535 minutes to harvest a total of 151515 cassavas.

The ratio of the change in dependent values or outputs to the change in independent values or inputs is known as the rate of change. The change, which also refers to the function's slope, represents the shift in values between two points on a coordinate plane. The formula for the rate of change is (y2 - y1)/, where y stands for the dependent variable and x for the independent variable (x2 - x1).

Given:

Carlos gives  353535 minutes to harvest a total of 151515 cassavas.

Find:

We have to find the total number of cassavas.

Solution:

Carlos harvests cassava at constant rate is 353535 minutes per 151515 cassavas

= 151515/353535

= 0.429

A formula for the quantity of cassava (C) that Carlos harvests each time (T).

This means that after 353535 minutes, 151515 cassavas have been harvested, after 700000 minutes, 300000 cassavas, and so on.

Hence, the required constant rate is 0.429T.

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Answer:

Side YZ

Step-by-step explanation:

think of the triangles as mirrors of each other

and pay attention to the symbols that correspond from side to side, and angle to angle

The value of h in a regular polygon of 16 sides is 37.3.

According to the question,

We have the following information:

A regular polygon has 16 sides. And one of its angles measures (5h − 29)°.

We know that following formula is used to find the sum of interior angles of a polygon:

(n-2)*180 where n is the number of sides of a polygon

(16-2)180

14*180

2520°

Now, in this polygon, there are 16 sides. So, there will be 16 angles.

Now, to find the measurement of one angle, we will divide total sum by number of angles.

One angle = 2520/16

One angle = 157.5°

Now, we have the following expression:

5h-29 = 157.5

5h = 157.5+29

5h = 186.5

h = 186.5/5

h = 37.3

Hence, the correct option is B (the second one).

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Answer: The quotient is x²- 1

Answer:

  c ≈ 14.76

Step-by-step explanation:

In right triangle ABC, you have short sides a=7 and b=13. You want the length of the hypotenuse, 'c'.

The Pythagorean theorem tells you the relationship between the sides of a right triangle is ...

  c² = a² +b²

Filling in the given values, we have ...

  c² = 7² +13² = 49 +169 = 218

  c = √218 ≈ 14.7648

Rounding to hundredths, we have ...

  c ≈ 14.76

__

Additional comment

Your posted question asks for the value of C (capitalized). That refers to the right angle, so its value is C = 90°. It is always helpful if you ask for what you really want to know.

Answer:

Its 12.5 miles per hour.

Step-by-step explanation:

Distance covered by cyclist=3.75 miles. Time =0.3 hours. Speed =3.75÷0.3=12.5

hope this helps

Answer:

0.4 miles per hour

Step-by-step explanation:

Distance covered= 5.83 miles

Time taken to cover the distance =0.4 hours

[tex] speed \: = \frac{distance}{time} [/tex]

[tex] = \frac{5.83}{0.4} [/tex]

=14.575 ~=14.5 miles per hour

If the rate (speed) = 14.575 miles per hour

Distance = 5.5 miles

[tex]time = \frac{distance}{speed} [/tex]

[tex] = \frac{5.5}{14.575} [/tex]

=0.337 ~= 0.4 hours