Which pyramid has a greater volume and how much greater is its volume?
8 in.
8 in
6 in.
Mark this and return
4 in.
10 in.
The volume of the pyramid on the left is greater by 8 in.³.
The volume of the pyramid on the left is greater by 24 in.³.
The volume of the pyramid on the right is greater by 8 in.³
The volume of the pyramid on the right is greater by 24 in."
9 in.
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Answer:

63

Step-by-step explanation:

So just find the area of the carpet:

9 * 7 = 63

You do know that to get to the fifth term from the second term you had to add the common difference 3 times. (adding ones takes you to the 3d term, adding twice takes you to the 4th term, and adding 3 times takes you to the 5th term.

An arithmetic sequence is a sequence where each term increases by adding/subtracting some constant k. This is in contrast to a geometric sequence where each term increases by dividing/multiplying some constant k. Example: a1 = 25. a(n) = a(n-1) + 5.

nth term=a+(n-1)d

Where a is the first term and d is the common difference.

Now,

2nd term=a+(2–1)d=a+ d——————(1)

5th term=a+(5–1)d=a+4d—————-(2)

Now, we take (2)-(1):

5th term-2nd term=(a+4d)-(a+ d)

5th term-2nd term=3d

So:

d=(5th term-2nd term)/3

Now as all the terms are known we can find out the common difference

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Answer:

  5.846∠-25.704°

Step-by-step explanation:

The sum is easily found using an appropriate calculator.

  2∠30° +5∠-45° ≈ 5.846∠-25.704°

__

If you have a less-capable calculator, you can add the rectangular coordinates and convert the result to polar form

  2∠30° +5∠-45° = (2cos(30°), 2sin(30°) +(5cos(-45°), 5sin(-45°))

  = (√3, 1) +(5/2√2, -5/2√2) = (5/2√2 +√3, 1 -5/2√2)

The magnitude is the root of the sum of squares of these values:

  |sum| = √(29+5(√6 -√2)) ≈ 5.846

The angle is the arctangent of the ratio of the second value to the first.

  ∠sum = arctan((1 -5/2√2)/(5/2√2 +√3)) ≈ -25.704°

Then the sum of the two numbers is about 5.846∠-25.704°.

The values of x, y , and z in the matrix equation is 3, 4, 0 respectively.

The solution of the matrix equation is calculated by applying Cramer's rule as shown below;

[ 1     1     -1 ]  [ 7 ]

[ 2    3     0 ] [ 18 ]

[ -5   -7    -1 ] [ -43 ]

The determinant of the matrix is calculated as follows;

[ 1     1     -1 ]  

[ 2    3     0 ]

[ -5   -7    -1 ]

Δ = 1 (-3 - 0) - 1(-2 - 0 )  - 1(-14 + 15)

Δ = -2

The x determinant of the matrix is calculated as follows;

[ 7     1     -1 ]  

[ 18    3     0 ]

[ -43   -7    -1 ]

Δx = 7 (-3 - 0) - 1 (-18 - 0 )  - 1(-126 + 129)

Δx = -6

The y determinant of the matrix is calculated as follows;

[ 1     7     -1 ]  

[ 2    18     0 ]

[ -5   -43   -1 ]

Δy = 1 (-18 - 0 )   - 7(-2 - 0 )  -1(-86 + 90)

Δy = -8

The z determinant of the matrix is calculated as follows;

[ 1     1     7 ]  

[ 2    3    18 ]

[ -5   -7   -43]

Δz = 1 (-129 + 126) - 1(-86 + 90) + 7(-14 + 15)

Δz = 0

The values of x, y , and z is calculated as;

x = Δx/Δ = -6/-2 = 3

y = Δy/Δ = -8/-2 = 4

z = Δz/Δ = 0/-2 = 0

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Answer: the answer would be C

Yes, the television is approximately 8 inches shorter than the space.

Step-by-step explanation: My name is Ebenezer Haile

Answer:

Given the information you provided, we can model cellular phone usage over time with an exponential growth model. An exponential growth model follows the equation:

`y = a * b^(x - h) + k`

where:

- `y` is the quantity you're interested in (cell phone usage),

- `a` is the initial quantity (34 million in 1995),

- `b` is the growth factor (1.22, representing 22% growth per year),

- `x` is the time (the year),

- `h` is the time at which the initial quantity `a` is given (1995), and

- `k` is the vertical shift of the graph (0 in this case, as we're assuming growth starts from the initial quantity).

So, our specific model becomes:

`y = 34 * 1.22^(x - 1995)`

To find the cellular usage in 2003, we plug 2003 in for x:

`y = 34 * 1.22^(2003 - 1995)`

Calculating this out will give us the cellular usage in 2003.

Let's calculate this:

`y = 34 * 1.22^(2003 - 1995)`

So,

`y = 34 * 1.22^8`

Calculating the above expression gives us:

`y ≈ 97.97` million.

So, the cellular phone usage in 2003, according to this model, is approximately 98 million.

Answer:

I think it is d or a. I might be wrong sorry

Step-by-step explanation:

Answer:

a. quotient refers to division

9514 404 393

Answer:

  128/7 ≈ 18.29

Step-by-step explanation:

The average rate of change is the slope of the line between the two points. That is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (251 -123)/(14 -7) = 128/7 = 18 2/7 ≈ 18.29

The average rate of change is 128/7 ≈ 18.29.

the SOLUTION

From this equation, we can know that the axis of symmetry will pass through the point (x= -2), and the maximum point is at point (-2,8)

From the graph plot above, the blue line at (x= -2) represents the plot of the line of symmetry and the highlighted black point (-2,8) represents where the maximum point will occur for the function.

The total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

From the figure, the area of triangles can be calculated using the:

Area = (1/2)height×base length

Area of three triangle = 1/2(4×6) + 1/2(6×4) + 1/2(4×6)

Area of three triangle = 1/2(24×3) = 36 square units

Area of the figure = area of three triangle + area of the rectangle

= 36 + 6×4

= 60 square units

Thus, the total area of the three triangles is square units is 36 and the area of the figure is square units is 60.

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Answer: Well first one chocolate souffles uses 3 eggs and each lemon maringue uses 4

Step-by-step explanation: First what i did was look at the question and it shows that there is two sets, so you have to plug in some random numbers and i started at o and if you do 8*1 you would have 1 egg per each souffles and you would have 28 eggs left and that won't work because 28/3 gives some long and then i tried 2... and 8*2 is 16 so you would have 20 eggs left and of course another long answer. But if you try three, 8*3 it gives you 24 so 36-24 and you get 12 and 3*4 is 12.. so then i plugged the same numbers in for the second part.. 3*2=6 and 4*2=8 and 6+8=14

if you need better more im here to help... have a good dayy!! (✿◡‿◡)

Answer:

Step-by-step explanation:

The system of equations with no solution is:

y + 3x = -7

4z - 2y = 10

The system of equations with exactly one solution is:

y = 6z+8

y = 6x-4

y = 3x + 2

2z-y = 5

y=-2z+8

The system of equations with infinitely many solutions is:

4z + y = 8

Answer:

\(\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}\)

Step-by-step explanation:

Given

\(\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}\)

Required

Fill in the gaps

Going by the given parameters, we have that

\(\frac{4x+2}{x^{2}-9+8 } = \frac{A}{()(x-1)} + \frac{B}{()(x-8)}\)

\(x^2 - 9x + 8\), when factorized is \((x-1)(x-8)\)

Hence; the expression becomes

\(\frac{4x+2}{(x-1)(x-8)} = \frac{A}{(x-8)(x-1)} + \frac{B}{(x-1)(x-8)}\)

Combine Fractions

\(\frac{4x+2}{(x-1)(x-8)} = \frac{A + B}{(x-8)(x-1)}\)

Simplify the denominators

\(4x + 2 = A + B\)

By direct comparison

\(A = 4x\)

\(B = 2\)

Hence, the complete expression is

\(\frac{4x+2}{x^2 - 9x + 8} = \frac{4x}{(x-8)(x-1)} + \frac{2}{(x-8)(x-1)}\)

Answer:4x+2/x2−9x+8 = −6/7(x−1) + 34/7(x−8)

The ratio between the number of red gummy bears to the number of yellow gummy bears is of:

20/23.

The ratio between the number of red gummy bears and the number of yellow gummy bears is obtained applying the proportions in the context of the problem.

To obtain the ratio between two amounts A and B, you need to divide the first amount by the second amount. The result of this division will give you the ratio of the two amounts.

The amounts for this problem are given as follows:

Hence the ratio between these two amounts is given as follows:

20/23.

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\(\large\texttt{Answer\::}\)

pls refer to the explanation !

\(\large\texttt{Calculations\::}\)

\(\textsf{Area of a circle : $A=\pi r^2$}\)

We're asked to use 3.14 for pi , so we'll do just that .

We have the diameter , so we divide it by 2 to find the radius (remember , the radius is 1/2 of the diameter).

Plug in :

A=3.14*(7)²

A=3.14*49

Multiply :

A=153.86 inches²

\(\footnotesize\texttt{hope\:helpful~}\)

Answer:

Step-by-step explanation:

Given:

Use the area of the circle formula.

AREA OF THE CIRCLE FORMULA:

\(\Longrightarrow: \sf{A=\pi r^2}\)

\(\Longrightarrow: \sf{\pi =3.14}\)

\(\Longrightarrow: \sf{r=\dfrac{14}{2}=7}\)

\(\Longrightarrow: \sf{3.14*7^2}\)

Use the order of operations.

PEMDAS stands for:

BODMAS stands for:

\(\sf{3.14*7^2}\)

First, solve exponents.

\(\Longrightarrow: \sf{7^2=7*7=49}\)

\(\Longrightarrow: \sf{3.14*49}\)

Then, multiply.

\(\sf{3.14*49=\boxed{\sf{153.86}}\)

Solutions:

\(\Longrightarrow: \boxed{\sf{153.86\ in^2}}\)

I hope this helps, let me know if you have any questions.

The equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

To find the equation of a line that passes through the point (-1, 3) with a slope of 1, we can use the point-slope form of a linear equation.

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.

Using the given point (-1, 3) and slope 1, we substitute these values into the point-slope form equation:

y - 3 = 1(x - (-1))

Simplifying:

y - 3 = x + 1

Now, we can rewrite the equation in the standard form:

y = x + 4

Therefore, the equation of the line that passes through the point (-1, 3) with a slope of 1 is y = x + 4.

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Answer: 40 mph

Step-by-step explanation: let s = speed in traffic

(s+17) = out of traffic

:

Write a time equation; time = dist/speed

traffic time + normal speed time = 4 hrs

46%2Fs + 80%2F%28%28s%2B17%29%29 = 4

multiply by s(s+17) to cancel the denominators

46(s+17) + 80s = 4s(s+17)

46s + 782 + 80s = 4s^2 + 68s

126s + 782 = 4s^2 + 68s

Arrange as a quadratic equation on the right

2s^2 - 29s - 391 = 0

Use the quadratic formula a=2; b=-29; c=-391

I got a positive solution of

s = 23 mph in traffic

:

:

:

Check this by finding the actual times. Normal speed: 23 + 17 = 40 mph

46/23 = 2 hrs in traffic

80/40 = 2 hrs at normal speed

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

total time 4 hrs

0 = 4s^2 + 68s - 126s - 782

4s^2 - 58s - 782 = 0

simplify, divide by 2

so  the answer is 40mph

Answer:

x = 38

Step-by-step explanation:

The external angle of a circle = ½ of the difference of the measures of the intercepted arcs. Thus:

m<S = ½(arc UV - arc TW)

34 = ½[(3x - 2) - (x + 6)]

34 = ½[3x - 2 - x - 6] (distributive property)

Add like terms

34 = ½[2x - 8]

Multiply both sides by 2

2*34 = 2x - 8

68 = 2x - 8

68 + 8 = 2x - 8 + 8

76 = 2x

Divide both sides by 2

76/2 = 2x/2

38 = x

x = 38

The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Consecutive terms in this sequence differ by p.

First term: p

Second term: p + p = 2p

Third term: 2p + p = 3p

and so on. It follows that the n-th term satisfies

np = 336

Presumably you meant to say the "sum of the first n terms" is 7224, which is to say

p + 2p + 3p + … + np = 7224

which can be rewritten as

p (1 + 2 + 3 + … + n) = 7224

p (n (n + 1)/2) = 7224

n (n + 1) p = 14,448

Substitute the first equation in the second one and solve for n :

336 (n + 1) = 14,448

n + 1 = 43

n = 42

Now solve for p :

42p = 336

p = 8

To find the probability that Naomi selects both white balls, we need to consider the total number of possible outcomes and the number of favorable outcomes.

Total number of outcomes:

Naomi selects 2 balls without replacement, so the total number of outcomes is the number of ways she can choose 2 balls out of the total number of balls in the bag. This can be calculated using combinations:

Total outcomes = C(20, 2) = (20!)/(2!(20-2)!) = (20 * 19)/(2 * 1) = 190

Number of favorable outcomes:

Naomi needs to select 2 white balls. There are 2 white balls in the bag, so the number of favorable outcomes is the number of ways she can choose 2 white balls out of the 2 white balls in the bag:

Favorable outcomes = C(2, 2) = 1

Probability = Favorable outcomes / Total outcomes = 1/190

Therefore, the correct answer is (G) 1/190.

The volume of the pyramid is 576 cubic inches.

To find the volume of a square base pyramid, you can use the formula:

Volume = (1/3) x base area x height

In this case, the side of the square base is given as 12 inches, and the height is given as 12.5 inches.

First, calculate the base area of the pyramid:

Base area = side²

= 12²

= 144 square inches

Now, substitute the values into the volume formula:

Volume = (1/3) x 144 x 12.5

Volume = 576 cubic inches

Therefore, the volume of the pyramid is 576 cubic inches.

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Answer:

a)  \(Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}\)

b)  \(n=24\)

Step-by-step explanation:

From the question we are told that:

Rate r=90 units per hour

Setup cost =20

Operating Cost =26

Units=40000

Generally the equation for Total cost is mathematically given by

\(Total Cost=20n+\frac{(\frac{40000}{90}*26)}{n}\)

\(T_n=20n+\frac{11556}{n}\\\\T_n=\frac{20n^2+11556}{n}.....equ 1\)

Differentiating

\(T_n'=\frac{n(40n)-(40n^2+11556)}{n_2}\\\\T_n'=\frac{20n^2-11556}{n^2}.....equ 2\)

Equating equ 1 to zero

\(0=\frac{20n^2+11556}{n}\)

\(n=24\)

Therefore

Substituting n

For Equ 1

\(T_n=\frac{20(24)^2+11556}{24}\)

F(n)>0  

For Equ 2

\(T_n'=\frac{20(24)^2-11556}{24^2}\)

F(n)'<0

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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To graph the function g(x) = 7x + 10, we shift the graph of f(x) = 7x vertically by adding a constant term of +10. This means every y-coordinate on the graph increases by 10 units. The slope of the line remains the same at 7. The resulting graph is a straight line passing through (0, 10) with a slope of 7.

To graph the function g(x) = 7x + 10, you need to make the following change to the graph of f(x) = 7x:
1. Translation: The graph of f(x) = 7x can be shifted vertically by adding a constant term to the equation. In this case, the constant term is +10.
Here's how you can do it step by step:
1. Start with the graph of f(x) = 7x, which is a straight line passing through the origin (0,0) with a slope of 7.
2. To shift the graph vertically, add the constant term +10 to the equation. Now, the equation becomes g(x) = 7x + 10.
3. The constant term of +10 means that every y-coordinate of the points on the graph will increase by 10 units. For example, the point (0,0) on the original graph will shift to (0,10) on the new graph.
4. Similarly, if you take any other point on the original graph, such as (1,7), the corresponding point on the new graph will be (1,17) since you add 10 to the y-coordinate.
5. Keep in mind that the slope of the line remains the same, as only the y-values are affected. So, the new graph will still have a slope of 7.
By making this change, you will have successfully graphed the function g(x) = 7x + 10.

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Answer: (6,11π/6).

Step-by-step explanation:We need to find the radius r and the angle θ. Remember that r2=x2+y2, so

because of the signs of x and y, our angle is in quadrant IV. Therefore, we find that θ=11π/6.

So the final answer is (6,11π6).

Answer:

the cooking club made 8 pies

Step-by-step explanation:

first do 60 divided by 5 to find the total number of pies you get 12

then since the cafetria donates four pies and the cooking club makes the rest,  you do 12-4=8

There were 11 pies cooked in all by the club to earn money for the basketball game.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

Given, The Cooking Club made some pies to sell at a basketball game to raise money for the new math books. The cafeteria contributed four pies to the sale.

Each Pie cut into four pieces

Since there were 60 pieces of pie

The total number of pies sell at a basketball game =  60/4

The total number of pies sell at a basketball game = 15

Also, given there were four pies donated by Cafeteria

Thus,

Total pie basketball team made = 15 - 4

Total pie basketball team made = 11

Therefore, the Total number of pies made by the club to raise funds for the basketball game is 11.

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It should be noted that experimental probability is based on past observations and might not accurately predict future events.

It has been established that experimental probability is based on past observations or on historical data.

To determine the experimental probability of the high temperature being over 75 degrees on June 23rd, one would basically gather historical data of high temperatures on June 23rd from previous years. Then, one would calculate the proportion of times the temperature was over 75 degrees.

For example, if one had data for the past 10 years and on 7 of those years the temperature was over 75 degrees on June 23rd, the experimental probability would be 7/10 or 0.7 (or 70%).

Therefore, it's always a good idea to consult meteorological sources or weather forecasts for the most up-to-date and accurate information.

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