Which of the following is the formula for the volume of a pyramid with base area B and height h?

A. [tex]V=\frac{1}{3} Bh[/tex]
B. [tex]V=Bh[/tex]
C. [tex]V=\frac{1}{3} Bh^2[/tex]
D.[tex]V=-\frac{1}{3} Bh[/tex]

Answer:

Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.

Step-by-step explanation:

The volume is given in terms of x as  [tex]V(x)=x^3-6x^2+8x[/tex].

We factor the GCF to get;

[tex]V(x)=x(x^2-6x+8)[/tex].

We split the middle term of the trinomial in the parenthesis.

[tex]V(x)=x(x^2-4x-2x+8)[/tex].

We now factor the expression within the parenthesis by grouping;

[tex]V(x)=x[x(x-4)-2(x-4)][/tex].

[tex]V(x)=x(x-2)(x-4)[/tex].

Since the width of the box is [tex]x-2[/tex] units, the linear expression for the height and length is [tex]x(x-4)[/tex]

Either the height is [tex]x[/tex] and the length is [tex]x-4[/tex] or the other way round.

Answer:

a) 864,000,000,000      8.64E11

b) 8,640,000,000           8.64E9

c) 86,400,000,000,000     8.64E13

d) 864,000,000,000,000    8.64E14

Step-by-step explanation:

A scientific notation is a way to represent very large values into the decimal form.

Steps to write in scientific notation:

Move the decimal to left before first digit of the given number.

Find the number of times decimal is moved to left.

Put that number in the exponent of e.

So, matching:

a) 864,000,000,000      8.64E11

b) 8,640,000,000           8.64E9

c) 86,400,000,000,000     8.64E13

d) 864,000,000,000,000    8.64E14

Answer:

False

Step-by-step explanation:

The surface area of the cone is

[tex]V=\pi r^2 +\pi rl[/tex]

[tex]SA=\pi r^2 +\pi\times r\times 2r[/tex]

[tex]SA=\pi r^2 +2\pi\times r^2[/tex]

[tex]SA=3\pi r^2[/tex]

The surface area of the cylinder is:

[tex]SA=2\pi r^2 +2\pi rh[/tex]

[tex]SA=2\pi r^2 +2\pi\times r\times r[/tex]

[tex]SA=4\pi r^2 [/tex]

Answer:

6 feet

D

Step-by-step explanation:

Givens

l = 10

h = 8

w = ?

Formula

l^2 = h^2 + w^2

Solution

10^2 = 8^2 + w^2

100 = 64 + w^2

100 - 64 = 64 - 64 + w^2

w^2 = 36

sqrt(w^2) = sqrt(36)

w = 6 feet.

Answer:

There are 38 dimes, 22 nickels and 16 quarters.

Step-by-step explanation:

Let n, d and q represent the # of nickels, dimes and quarters respectively.

Then n + d + q = 76

The value of a nickel is $0.05; that of a dime is $0.10, and that of a quarter is $0.25.

Thus, the value of n nickels is $0.05n (and so on).

The total value of the coins is $0.05n + $0.10d + $0.25q = $8.90.

d = n + q allows us to eliminate d.

First, n + d + q = 76 becomes n + (n + q) + q = 76, and second:

$0.05n + $0.10(n + q) + $0.25q = $8.90.  Here we have succeeded in eliminating d from two different equations, and now we have these two different equations in two unknowns (n and q), which is solvable.

Simplifying both equations, we get:

2n + 2q = 76 and

5n + 10n + 10q + 25q = 890, or 15n + 35q = 890

Let's use the substitution method of solving linear equations:

Rewrite 2n  + 2q = 76 as n + q = 38, or n = 38 - q.  Substituting this result into the second equation, we get:

15(38 - q) + 35 q = 890, or

  570 - 15q + 35q = 890, or

   570 + 20 q = 890.  Then 20q = 890 - 570 = 320, and q = 320/20 = 16.

There are 16 quarters.  Thus, the number of nickels is n = 38 - 16 = 22.

Finally, since n + d + q = 76, 22 + d + 16 = 76, or:

22 + d = 60, or d = 60 - 22 = 38.

There are 38 dimes, 22 nickels and 16 quarters.

Answer:

Approximately 485 meters

Step-by-step explanation:

We can first construct a right triangle, using the 500 m length of hill as our hypotenuse. Using the fact that the cosine of an angle is the ratio of the adjacent side to the hypotenuse, we see that

[tex]\cos{15^\circ}=\frac{x}{500}[/tex]

where x is the horizontal distance covered. Solving for x, we find this horizontal distance to be

[tex]x=500\cos{15^\circ}\approx500(0.97)=485[/tex]

so our answer is approximately 485 m.

Answer:

The solution to this system is (-2, 1, -3).

Step-by-step explanation:

Let's eliminate variable x first.  Combine the first two equations, obtaining:

3x - 0y + 2z  = -12.

Now subtract the third equation from this result:

 3x - 0y + 2z  = -12

-(3x −   y −   z =  −4)

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

           y + 3z  = -8

Similarly, combine the second and third original equations to eliminate x again.  To do this, subtract  2(x + y + z = -4) from the first equation:

2x−y+z=−8

-2x - 2y - 2z = 8

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

    -3y - z = 0

Now we have eliminated x completely, and find from -3y - z = 0 that z = -3y.  Substitute this -3y for z in the equation y + 3z  = -8 found above:

y + 3(-3y)  = -8.  Then y - 9y = -8, and so y must = 1.  From -3y - z = 0, substituting 1 for y, we find that z = -3(1), or z = -3.

Finally, subst. 1 for y and -3 for z in the second equation:

x + 1 - 3 = -4

So, x - 2 = -4, and thus x must be -2.

The solution to this system is (-2, 1, -3).

Answer:

The maximum value of g(x) = 2/3 at x = 0

Step-by-step explanation:

* Lets find the maximum value of a function using derivative of it

- The function g(x) = 2/(x² + 3)

- 1st step use the negative power to cancel the denominator

∴ g(x) = 2(x² + 3)^-1

- 2nd use derivative of g(x) to find the value of x when g'(x) = 0

* How to make the derivative of a function

# If f(x) = a(h(x))^n, then f'(x) = an[h(x)^(n-1)](h'(x))

∵ [tex]g(x)=2(x^{2}+3)^{-1}[/tex]

∴ [tex]g'(x) = 2(-1)(x^{2}+3)^{-2}(2x)=-4x(x^{2}+3)^{-2}[/tex]

# Put g'(x) = 0

∴ [tex]-4x(x^{2}+3)^{-2}=0====\frac{-4x}{(x^{2}+3)^{2}}=0[/tex]

∴ [tex]-4x=(0)(x^{2}+3)^{2}====-4x = 0[/tex]

∴ x = 0

* The maximum value of g(x) at x = 0

- Substitute the value of x in g(x)

∴ g(0) = 2/(0 + 3) = 2/3

* The maximum value of g(x) = 2/3 at x = 0

Answer:

False

Step-by-step explanation:

we know that

In this problem the vertical distance is equal to 12 ft (the horizontal distance must be equal to the vertical distance, by angle of 45 degrees)

so

The length of the ladder is equal to

Applying Pythagoras Theorem

[tex]L=\sqrt{12^{2}+12^{2}} \\ \\L=\sqrt{288}\ ft\\ \\L=16.97\ ft[/tex]

Answer:

16%

Step-by-step explanation:

The Empirical rule says that 68% of a normal distribution lies between -1 and +1 standard deviations.

That means that 32% lies outside of ±1 standard deviations.

Since the normal curve is symmetrical, that means 16% is less than -1 standard deviation and 16% is greater than +1 standard deviation.

So the answer is 16%.

Heather and her lab partners found that the probability of the weight of a US quarter being below one standard deviation from the mean is 16%.

Heather and her lab partners need to find the probability that the weight of a US quarter is below one standard deviation from the mean. Since the weight of a quarter follows a normal distribution, we use the property of the normal distribution to find this probability.

In a normal distribution:

Therefore, the probability of a weight being below one standard deviation from the mean is 16%. This is calculated by taking half of the remaining probability outside the 68%, which is (100% - 68%) ÷ 2 = 16%.

Answer:

[tex]\boxed{\text{274.5 cm; }71.3^{\circ}}[/tex]

Step-by-step explanation:

If we open the surface of the pole and lay it flat, we will get a rectangle with the red stripe as a diagonal.

l = 260 cm.

The width of the rectangle is enough for two revolutions (i.e., twice the circumference).

w = 2C = 2 × 2πr = 4π × 14/2 = 28π cm = 87.96 cm

Length of stripe

The stripe is the diagonal of the rectangle.

d² = 260² + (28π)² = 67 600 + 87.96² = 67 600 + 7738 = 75 338

d = √(75 338) = 274.5 cm

Angle with horizontal

tanθ = 260/(28π) = 260/87.96 =2.956

θ = arctan2.956

θ = 71.3°

The stripe is [tex]\boxed{ \text{274.5 cm}}[/tex] long and the angle with the horizontal is [tex]\boxed{71.3^{\circ}}[/tex].

Final answer:

The red stripe on the barber pole is approximately 520.8 cm long and makes an angle of about 71.1 degrees with the horizon.

Explanation:

The problem describes a cylinder (barber pole) with a helical stripe wrapping around it. To find the length of the stripe, we need to construct a right-angled triangle by unwrapping the helix. One side of the triangle is the height of the pole (260 cm), and the other side is the circumference of the pole multiplied by the number of revolutions (2).

First, calculate the circumference using the diameter given:

The length of the stripe is then the hypotenuse of the right triangle, which can be found using the Pythagorean theorem:

For the angle with the horizon, θ, we use the tangent function:

The angle with the horizon is approximately 71.1 degrees. So, the length of the stripe is about 520.8 cm, and it makes an angle of roughly 71.1° with the horizon.

Answer:

  it depends

Step-by-step explanation:

The endpoints of the hypotenuse are insufficient to specify a right triangle. The perimeter can range from twice the distance between these points, about 18.868 units, to 1+√2 times the distance between these points, about 22.776 units.

___

In the attached figure, the colored numbers are the total length of the two legs of that color. The hypotenuse and its length are in black.

_____

The distance between two points is given by the formula ...

  d = √((x2-x1)^2 +(y2 -y1)^2)

The perimeter will be the sum of the distances between pairs of points that define the vertices of the triangle. We need to know the third vertex to answer the question precisely.

Answer:

Option C

Step-by-step explanation:

The standard form of equation of a cirle is:

(x-h)^2+ (y-k)^2=r^2

In the given question as the point is given and the radius of circle is given:

So,

(h,k)=(2,-1)

and

r=3

Here,

h=2

k= -1

Putting the values of h,k and r in standard form

(x-2)^2+ (y-(-1))^2=(3)^2

(x-2)^2+ (y+1)^2=(3)^2

So the equation of circle is:

(x-2)^2+ (y+1)^2=9(3)^2

Option C is the correct answer ..

Answer:

141.12 cm^2

Step-by-step explanation:

   Since the area of a trapezoid is the average of the bases multiplied by the height, we can just plug these numbers into the equation! Since the average of 10.2 and 12.2 is 11.2, and the height is 12.6, we multiply them to get the area to be 141.12 cm^2.

Answer:

141.12cm^2

Step-by-step explanation:

I do not know if this is the correct way to do it, but I split the trapezoid in half, then putting it on top of each other to create a rectangle, which is (10.2cm+12.2cm)(12.6cm/2)

Final answer:

The probability of choosing all boys for the classroom responsibilities from a classroom of 11 boys and 14 girls is calculated using combinatorial probability, which is the ratio of the number of ways to choose 4 boys out of 11 to the total number of ways to choose 4 students out of 25.

Explanation:

The probability that all four students chosen at random from a classroom of 11 boys and 14 girls will be boys is a classic example of a combinatorial probability question.

First, we calculate the total number of ways to choose 4 out of 25 students, which is the combination of 25 students taken 4 at a time. This is given by the binomial coefficient 25 choose 4, which is calculated as 25! / (4! * (25-4)!).

Next, we calculate the total ways to choose 4 out of the 11 boys, which is the combination of 11 boys taken 4 at a time, given by 11 choose 4, calculated as 11! / (4! * (11-4)!).

The probability is the ratio of the number of favorable outcomes (only boys chosen) to the total number of outcomes. Therefore, the probability is (11 choose 4) / (25 choose 4).

Answer:

L = 10, w = 17

Step-by-step explanation:

Area of a rectangle is A = Lw.  We are told that the width is 3 less than twice the length, so we will change the width into some expression in terms of the length.

w = 2L - 3 and

length = L.

Filling in the area formula now, knowing that the area is given as 170:

170 = (2L - 3)(L) so

[tex]170=2L^2-3L[/tex]

Get everything on one side of the equals sign and throw it into the quadratic formula to factor it and solve for the values of L.  When we do this we get that L = 10 and L = -8.5

Since the 2 things in math that will NEVER EVER be negative are time and distance/length measures, it is safe to disregard the -8.5.  Therefore,

if L = 10, then

w = 2(10) - 3 and

w = 17

Answer:

7

5

27.5

Step-by-step explanation:

edgu 2020

Answer:first 7 then 5 and 27.5 used the other person and got it right on edge:)

Step-by-step explanation:

Answer:

x = 58.0

Step-by-step explanation:

We can use the inverse of cos to solve for x once you set up the equation

[tex]cosx = \frac{9}{17}[/tex]

This is as 9 is the adjacent side and 17 is the hypotenuse of the triangle.

We can then solve for x using the inverse of cos

[tex]x= cos^{-1} (\frac{9}{17} )[/tex]

When plugged into a calculator you get

x= 58.03 degrees

this rounds to 58.0 degrees

The probability that at least three out of five randomly picked buttons are black is approximately 0.6614.

To find the probability that at least three out of five randomly picked buttons are black, we can consider the different combinations of buttons that satisfy this condition.

There are two cases where at least three buttons are black:

1. Exactly 3 buttons are black.

2. All 5 buttons are black.

Let's calculate the probabilities for each case:

1. Exactly 3 buttons are black:

  This can happen in [tex]\( \binom{4}{3} \)[/tex] ways (choosing 3 black buttons) multiplied by [tex]\( \binom{5}{2} \)[/tex] ways (choosing 2 brown buttons).

  Probability of this case:

[tex]\[ P(\text{3 black}) = \frac{\binom{4}{3} \times \binom{5}{2}}{\binom{9}{5}} \][/tex]

2. All 5 buttons are black:

  This can happen in [tex]\( \binom{4}{5} = 0 \)[/tex] ways (because there are only 4 black buttons).

The probability that at least three buttons are black is the sum of the probabilities of these two cases.

[tex]\[ P(\text{at least 3 black}) = P(\text{3 black}) + P(\text{5 black}) \]\[ P(\text{at least 3 black}) = \frac{\binom{4}{3} \times \binom{5}{2}}{\binom{9}{5}} + 0 \][/tex]

[tex]\[ P(\text{at least 3 black}) = \frac{\frac{4!}{3!(4-3)!} \times \frac{5!}{2!(5-2)!}}{\frac{9!}{5!(9-5)!}} \]\[ P(\text{at least 3 black}) = \frac{\frac{4 \times 5}{3!} \times \frac{5 \times 4}{2!}}{\frac{9 \times 8 \times 7 \times 6 \times 5}{5!}} \][/tex]

[tex]\[ P(\text{at least 3 black}) = \frac{\frac{4 \times 5}{6} \times \frac{5 \times 4}{2}}{\frac{9 \times 8 \times 7 \times 6 \times 5}{5 \times 4 \times 3 \times 2 \times 1}} \]\[ P(\text{at least 3 black}) = \frac{\frac{20}{6} \times \frac{20}{2}}{\frac{3024}{120}} \][/tex]

[tex]\[ P(\text{at least 3 black}) = \frac{\frac{100}{6}}{\frac{3024}{120}} \]\[ P(\text{at least 3 black}) = \frac{100 \times 120}{6 \times 3024} \]\[ P(\text{at least 3 black}) = \frac{1000}{1512} \][/tex]

[tex]\[ P(\text{at least 3 black}) ≈ 0.6614 \][/tex]

Answer:

The elevation of Mt. Wilson is 16,160.10 ft

Step-by-step explanation:

Let

x-----> represent the elevation of Mt. Wilson

y ----> represent the elevation of Snow Crest

we know that

y=x+11,990.21 ----> linear equation that represent this situation

we have that

y=28,150.31 ft ----> see the attached figure

substitute in the linear equation and solve for x

28,150.31=x+11,990.21

x=28,150.31-11,990.21=16,160.10 ft

Answer:

the answer is 18 birds and 5 cats

Step-by-step explanation:

the easiest way i did this was that i used a calculator and kept subtracting 8.5 untill i reached a number that was completely divisable by 5, i subtracted 8.5 five times which got the total down to 90$ and since each bird is 5$ you can just divide which means there was a total of 18 bird and 5 cats on Tuesday

To find out how many birds were at the shelter on Tuesday, we set up and solved a system of linear equations involving the total daily care costs and the total number of animals. By substituting and simplifying, we found the number of birds among the 23 animals.

The question involves solving a system of linear equations to find out how many birds were at the shelter on Tuesday, given the daily care costs for birds and cats, the total cost for Tuesday, and the total number of birds and cats. We use the information that the shelter spends $5.00 per day to care for each bird and $8.50 per day to care for each cat, with a total expenditure of $132.50 for 23 birds and cats together.

Let x be the number of birds and y be the number of cats. Therefore, we have two equations:

From the second equation, we can isolate one variable, say x = 23 - y. Substituting this into the first equation gives us:

5(23 - y) + 8.5y = 132.50

After simplifying, we find the value of y, and then substitute back to find x, which represents the number of birds. This method of solving the system of equations is straightforward and efficient for this problem.

Answer:

(x - 5)² + (y + 3)² = 16

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

here (h, k) = (5, - 3) and r = 4, so

(x - 5)² + (y - (- 3))² = 4², that is

(x - 5)² + (y + 3)² = 16

Answer:

7569 meters cubed

Step-by-step explanation:

first: make the improper fractions to a fraction greater than one.

11 3/5= 58/5

12 1/2 = 145/2

9=9

then you have to multiply them all together

cross multiply 58/5 and 145/2...you should get 841. Now multiply 841 and 9...you should get 7569 meters cubed.

*When VOLUME of a RECTANGLE is given, make sure to MULTIPLY the HIEGHT, WIDTH and the LEGNTH.

Answer:

7569³m

Step-by-step explanation:

Answer:

(4,3)

Step-by-step explanation:

Given

x^2+y^2=25

x-y^2=-5

In order to solve the equations, from equation 2 we get

-y^2= -5-x

y^2=5+x

Putting the value of y^2 in equation 1

x^2+5+x=25

x^2+5-25+x=0

x^2+x-20=0

x^2+5x-4x-20= 0

x(x+5)-4(x+5)=0

(x+5)(x-4)=0

So

x+5=0  x-4=0

x=-5   x=4

Now for x=-5

x^2+y^2=25

(-5)^2+y^2=25

25+y^2=25

y^2=25-25

y^2=0

so Y=0  

And for x = 4

x^2+y^2=25

(4)^2+y^2=25

16+y^2=25

y^2=25-16

y^2=9

y= ±3

So the solution to the system of equations is

(-5,0) , (4,3), (4,-3)

The only solution that belongs to first quadrant is (4,3)

Answer:

(4,3)

Step-by-step explanation:

solve the simultaneous equations

x²+y²=25.........................(i)

x-y²= -5.............................(ii) ⇒make y² the subject of the equation;

y²=x+5.................................(iii)

Substitute equation (iii) in (i)

x² + x+5 =25

x²+x=25-5

x²+x-20=0..........solve for the quadratic equation

x(x-4)+5(x-4)=0

(x-4)(x+5)=0

x-4=0

x=  4 or

x+5=0

x=  -5

finding value of y

if y²=x+5 then;

when x=4, y²=4+5=9⇒y=√9 = ±3...................y= ±3

when x= -5  , y²= -5+ 5=0............... y=0

Coordinates = (4,3) and (-5,0)

Coordinates that lie in the 1st quadrant is (4,3)

Answer:

Black

Step-by-step explanation:

Black-White-Yellow-Brown

Also can you please rate this as the most brainliest because I need it to level up?

The length AB of the triangle is 31.2 inches.

The side AB of the triangle can be found using sine rule for triangles as follows:

Using sine law,

a / sin A = b / sin B = c / sin C

Hence,

22 / sin 43 = AB / sin 75

cross multiply

AB sin 43 = 22 sin 75

divide both sides by sin 43

AB = 22 sin 75 / sin 43

AB = 21.2503681784 / 0.68199836006

AB = 31.1629271154

AB = 31.2 inches

learn more on triangle here: https://brainly.com/question/24225878

#SPJ1

Answer: $1980

Step-by-step explanation:

Well, based off of the question being asked, I assume that you will need to pay $11 for 90 square footage of tiling, and then the same for the other square footage of tiling. Therefore your answer will be $1980. If you are looking for the equation, it is (11x90)=990   (990)2 = 1980

you do not need to multiply 11 by 90 again because you already know the answer.

Answer:

$110

Step-by-step explanation:

We are given that

Cost of 1 square yard of floor tile =$11

We have to find the cost of 90 square feet of tile.

To find the cost of 90 square feet we will convert it into square yard.

We know that

9 square foot=1 square yard

1 square foot=[tex]\frac{1}{9}[/tex]

90 square feet=[tex]\frac{1}{9}\times 90=10[/tex] square yard

By unitary method

Cost 1 square yard=$11

Cost of 10 square yard=[tex]11\times 10=[/tex]$110

Hence, the cost of 90 square feet to tile a bathroom=$110

Answer:

1 5/9

hope it helped

Step-by-step

divide 5 1/4 by 3 3/8 to get 1 5/9

Step-by-step answer:

The maximum and minimum values are the positive sum and difference of the two magnitudes.  The magnitude of u+v can range between these two limits, namely 5+4=9, and 5-4=1.

Therefore among the given choices, the possible values of u+v are 1 unit and 9 units.  11 and 13 are greater than the maximum so do not apply.

Answer:

1 unit

9 units

Step-by-step explanation:

PLATO

Answer:

The side length of the smaller pyramid is 3/4 the side length of the larger pyramid.

Step-by-step explanation: