Mathematics High School

Which of the following would triple the volume of the Egyptian square-based Pyramid below?

A. Multiply only the height by 3.

B. Add 3 to each dimension of the Pyramid.

C. Multiply every dimension of the Pyramid by 3.

D. Add 3 to the slant height.

Answers

Answer 1

Final answer:

To triple the volume of a square-based Egyptian pyramid, you must multiply every dimension of the pyramid by 3. This is because volume is proportional to all three dimensions of the shape, and changing just one dimension won't achieve the desired effect.

Explanation:

The question asks which action would triple the volume of a square-based Egyptian pyramid. The volume (V) of a pyramid is calculated using the formula V = (1/3) × base area × height. To triple the volume, you would need to triple the factor of each dimension because volume is a three-dimensional measurement, and changing one dimension alone would not be sufficient.

Option A suggests multiplying only the height by 3, but this would not triple the volume as the base area remains the same. Option B suggests adding 3 to each dimension, but adding a constant to linear dimensions does not maintain a proportional relationship to volume.

Option D suggests adding 3 to the slant height, which does not directly correlate to the volume. Therefore, option C is correct: Multiplying every dimension of the Pyramid by 3 would indeed triple the volume because changing each dimension equally maintains the proportion. This is similar to how if a block's dimensions were doubled (2L × 2L × 2L), the new volume would be 8 times the original (8L³).

Related Questions

A normal distribution has a mean of 0.40 and standard deviation of 0.028. What percentage of observations will lie between 0.372 and 0.428?

Answers

Solution:
To evaluate for P(0.372<x<0.428) we shall proceed as follows:
z-score is given by:
z=(x-μ)/σ
thus when x=0.372:
z=(0.372-0.4)/0.028
z=-1
thus
P(x<0.372)=P(z<-1)=0.1587

when x=0.428
z=(0.428-0.4)/(0.028)=1
P(x<0.428)=P(z<1)=0.8413
thus
P(0.372<x<0.428) =P(z<1)-P(z<-1)=0.8413-0.1587=0.6826
Final answer:

To find the percentage of observations between two values in a normal distribution, we can convert the values to z-scores and use a z-table to find the corresponding areas. In this case, the percentage of observations between 0.372 and 0.428 is 68.26%.

Explanation:

To find the percentage of observations that will lie between 0.372 and 0.428 in a normal distribution with a mean of 0.40 and standard deviation of 0.028, we need to find the area under the curve between these two values.

Using a standard normal distribution table or z-table, we can convert the values to z-scores by subtracting the mean and dividing by the standard deviation. The z-score for 0.372 is (0.372 - 0.40) / 0.028 = -1, and the z-score for 0.428 is (0.428 - 0.40) / 0.028 = 1.

By looking up the corresponding area for these z-scores in the z-table, we find that the area to the left of -1 is 0.1587 and the area to the left of 1 is 0.8413. To find the percentage between -1 and 1, we subtract the smaller area from the larger area: 0.8413 - 0.1587 = 0.6826 or 68.26%.

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Consider the function f(x)=(x-9)/(x^3-81x)

Find the vertical asymptote(s) of f(x)

Answers

Answer:

Its A

x=0, -9

Step-by-step explanation:

just got it correct

Final answer:

The function f(x)=(x-9)/(x^3-81x) has three vertical asymptotes at x = 0, x = 9, and x = -9.

Explanation:

To find the vertical asymptote(s) of the function f(x) = (x-9)/(x^3-81x), we need to determine the values of x for which the denominator equals zero. Setting the denominator equal to zero and solving for x, we get:

x^3 - 81x = 0x(x^2 - 81) = 0x(x - 9)(x + 9) = 0

Therefore, the function has three vertical asymptotes at x = 0, x = 9, and x = -9.

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A city has a population of 260,000 people. Suppose that each year the population grows by 6.75% . What will the population be after 7 years? Use the calculator provided and round your answer to the nearest whole number.

Answers

Final answer:

The population of the city after 7 years will be approximately 393,574.

Explanation:

To find the population after 7 years, we'll use the formula for exponential growth:

P = P0(1 + r)t

Where P is the future population, P0 is the initial population, r is the growth rate as a decimal, and t is the number of years.

In this case, P0 = 260,000, r = 6.75% = 0.0675 (decimal form), and t = 7.

Plugging in these values, we have:

P = 260,000(1 + 0.0675)7

Using a calculator, the population after 7 years is approximately 393,574.

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Daniel is setting up rows for a concert. He decides to put 9 chairs in each row. There are 45 chairs. Let x represent the number of rows of chairs. Which equation can be used to find the number of rows of chairs Daniel needs to set up?

Answers

9x=45
*divide 45 by 9 which is 5
x=5
hope this helps!

Megan consumed 3.5 gallons of water in one day. How many milliliters are equal to 3.5 gallons, if 1 liter equals 1,000 milliliters and 1 gallon = 3.785 liters?

Answers

First, find how many milliliters there are in 1 gallon. 3.785 x 1,000 = 3,785
There are 3,785 milliliters in one gallon.

Then, multiply that by 3.5    3,785 x 3.5 = 13,247.5   

There are 13,247.5 ml in 3.5 gallons

Answer:

There are 13,247.5 ml in 3.5 gallon

BRAINLIESTTT ASAP!

please help

Answers

Width = x
Length = 2x+1

1/2 the permiter = l + w

1/2 perimeter = 176 /2 = 88
 so we have x + 2x+1 = 88

combine like terms:
3x +1 = 88

subtract 1 from both sides:
3x = 87
 divide both sides by 3
x = 87 / 3 = 29

with = 29 feet
 length = 29 x 2 = 58 +1 = 59 feet

check: 59 +59 +29+29 = 176


A florist earns a profit of $2.00 on each bunch of carnations, $3.00 on each bunch of lilies and $1.00 on a bunch of roses. On a particular day, she sold 46 bunches of flowers and made a profit of $82.00. She sold twice as many bunches of roses as bunches of lilies.

Answers

its your mom cause she was at my house


jk its b. love yah


Simplify the function f(x)= 1/2 (27) 2x/3. Then determine the key aspects of the function

Answers

The given expression is:

[tex]f(x)= \frac{1}{2}(27)^{ \frac{2x}{3} } \\ \\ f(x)= \frac{1}{2}((27)^{ \frac{2}{3} })^{x} \\ \\ f(x)= \frac{1}{2}(9)^{x} [/tex]

From the above equation, we can answer all the 4 questions.

a) Initial value occurs when x = 0

So,

[tex]f(0)= \frac{1}{2}(9)^{0}= \frac{1}{2} [/tex]

So, the Initial value of the function is 1/2.

b) Simplified Base:
The base of an exponential function is the term which contains the exponent.
From the simplified equation, we can see that the base has been simplified and is equal to 9.

So, the simplified base is 9

c) Domain:
From the equation we can see that there is no such value which makes the function undefined. So all reall numbers are included in the Domain.

So, Domain is Set of All real numbers. 
In Interval notation this can be expressed as: (-∞,∞)

d) Range:
Range is the set of all y values that a function can take. Since the graph is not shifted vertically up or down, the range will be the set of all real numbers greater than zero.

So, Range is equal to All real numbers greater than 0.
In Interval notation, this can be expressed as (0,∞)

Answer:

The last one is y>0

please help asap 50 pts

Answers

(-2,-3) is the vertex. Since it is the lowest point, it is the minimum.

The vertex is always the lowest or highest point:

When a parabola looks like a smiley face, it has a minimum (like this one).

When a parabola looks like a frowning face, it has a maximum.

The coordinate for the vertex is (-2, -3).

So, your answer is C.

An alloy of copper is 10% copper and weighs 25 pounds. A second alloy is 18% copper. How much (to the nearest lb.) of the second alloy must be added to the first alloy to get a 13% mixture.

Answers

You need 15 pounds of copper to get a 13% mixture

You choose a marble at random from a bag containing 8 brown marbles 6 yellow marbles and one purple marble. You replace the marble and then choose again.find p (both yellow)

Answers

Pick 1: 6 yellow out of 15 total marbles = 6/15 = 2/5
Pick 2: 6 yellow out of 15 total marbles = 6/15 = 2/5

Pick 1 AND Pick 2
   2/5     x       2/5    = 4/25

Frazier has $1,200 in savings. He works because he is saving money for college, and he earns $9 an hour. If Frazier saves 25 percent of his net pay, after 20 percent is taken out for tax, identify the expression which represents Frazier's savings.

A) 1.8x + 1,200
B) 3.6x + 1,200
C) 7.2x + 1,200
D) 9x + 1,200

Answers

the correct answer is A..!! I think...:(



Answer:  The correct option is (A) [tex]1.8x+1200.[/tex]

Step-by-step explanation:  Given that Frazier is saving money for college and has $1200 in savings. He earns $9 per hour. He saves 25% of his net pay after 20% taken out for tax.

We are to identify the expression that represents Frazier's savings.

Let, x represents the number of hours for which Frazier works.

So, the net pay of Frazier = $ 9x.

Since 20% of the net pay is taken out for tax, so total pay of Frazier after taking out tax is given by

[tex]I_t=9x-20\%\times 9x=9x-\dfrac{20}{100}\times 9x=9x-\dfrac{9x}{5}=\dfrac{36x}{5}.[/tex]

Now, Frazier's savings from his net pay is given by

[tex]I_s=25\%\times \dfrac{36x}{5}=\dfrac{25}{100}\times \dfrac{36x}{5}=\dfrac{9x}{5}=1.8x.[/tex]

Since Frazier has $1200 already in savings, so the equation representing Frazier's savings will be

[tex]1.8x+1200.[/tex]

Thus, the required equation is [tex]1.8x+1200.[/tex]

Option (A) is CORRECT.

will give brainiest if correct

A. 69.1
B. 20.9
C. 22.4
D. 67.6

Answers

I think it's D. But I'm not sure if my math was correct
Using sin law;

sin A/ a = sinB/ b

where A = C or 90 degrees; a = 21
B = ? , b = 8

solving for b;
sin(90) / 21 = sin(B) / 8 ; B = 22.39 degrees

Total angle of triangle = 180

180 - 90 - 22.39 = x
x = 67.607 degrees

Anyone know this? Will give brainiest

Answers

I believe the answer is C,
Hope this helps

WILL MAKE BRAINLIEST!!!!!!!The arc length of a sector is equal to twice the radius. Express the arc length s as a function of the area a of the sector.
s=

Answers

The area of a circular sector is . 

==>  
Since r = s/2, it follows that , or , or 
.

The arc length as a function of the area of the sector is  l=2√A.

What is the area of a sector?

Area of a sector = 1/2 * arc length(l) * radius(r)

[tex]A=[/tex] [tex]\frac{1}{2} l*r[/tex]......(1)

It is given that the arc length of a sector is equal to twice the radius.

This means [tex]l=2r\\[/tex]

So, [tex]r=\frac{l}{2}[/tex]

Putting the value of r in (1)

[tex]A = \frac{l^{2} }{4}[/tex]

[tex]l^{2} =4A[/tex]

[tex]l=2\sqrt{A} \\[/tex]

So, the required function is l=2√A

Hence, the arc length as a function of the area of the sector is  l=2√A.

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A town has a population of 13000 and grows at 4.5% every year. What will be the population after 13 years, to the nearest whole number?

Answers

23,039. 
y=13,000(1.045)^t
t=13
You get 1.045 because you add 1+ the percentage in decimal form.

Answer:

population after 13 years is around 23,039

Step-by-step explanation:

A town has a population of 13000 and grows at 4.5% every year.

Population growth is given by [tex]y=a(1+r)^t[/tex]

y is the population after t years

'a' is the initial population= 13000

'r' is the rate of growth=4.5%= 0.045

t is the number of years=13

[tex]y=a(1+r)^t[/tex]

[tex]y=13000(1+0.045)^13[/tex]

y=23,038.54

A number cube numbered from 1 to 6 is rolled. what is the probability of the number cube showing a 5 or an even number?

Answers

The probability would be 4/6 but if it is a simplified answer then you would get 2/3.

A bag contains 6 red, 7 blue, and 5 green coins. If 3 coins are randomly selected in succession, what is the probability of selecting a red coin, then a blue coin, and then a green coin, if replacement occurs each time?

Answers

Total coins = 6 + 7 + 5 = 18
Red = 6
Blue = 7
Green = 5

P(Red, then blue, then green) = (6/18)(7/18)(5/18) = 35/972

Answer: 35/972
[tex]|\Omega|=18^3=5832\\ |A|=6\cdot7\cdot5=210\\\\ P(A)=\dfrac{210}{5832}=\dfrac{35}{972}\approx3.6\%[/tex]

simplify 15r+7r+9r-7s

Answers

yo edges a** 56789123456

15r + 7r + 9r - 7r
 12r      +    2r
         14r
_____________________

12r + 2r = simplified

answer is 14r

______________________

Hope this helps,
QueenBeauty666

Use the x-intercept method to find all real solutions of the equation. x^3-9x^2+20x-12=0

Answers

For this case we have the following function:
 x ^ 3-9x ^ 2 + 20x-12 = 0
 Rewriting we have:
 (x-6) * (x-2) * (x-1) = 0
 Therefore, the solutions are given by:
 Solution 1:
 x-6 = 0
 x = 6
 Solution 2:
 x-2 = 0
 x = 2
 Solution 3:
 x-1 = 0
 x = 1
 Answer:
 x = 6
 x = 2
 x = 1

Answer:

D= 1,2,or 6

Step-by-step explanation:

How do you simplify # (x+3)/(x^2+7x+12)#?

Answers

hey friend your answer



hope it is helpful
By using the method of factorization

Jacob drove from town a to town b at an average rate of x miles per hour, then returned along the same route at y miles per hour. if he then drove back to town b at z miles per hour along the same route, what was jacob's average rate of speed for the entire trip, in miles per hour?

Answers

The answer is 1,000 miles

can someone please explan how I got this wrong?
Solve for x in the triangle
using laws of cosine

Answers

[tex]\bf \textit{Law of Cosines}\\\\ c^2 = a^2+b^2-(2ab)cos(C)\implies c = \sqrt{a^2+b^2-(2ab)cos(C)} \\\\\\ \cfrac{a^2+b^2-c^2}{2ab}=cos(C)\implies cos^{-1}\left(\cfrac{a^2+b^2-c^2}{2ab}\right)=\measuredangle C\\\\ -------------------------------\\\\ \begin{cases} x=24\\ a=25\\ b=19 \end{cases}\implies cos^{-1}\left(\cfrac{25^2+19^2-24^2}{2(25)(19)}\right)=\measuredangle x \\\\\\ cos^{-1}\left( \cfrac{41}{95} \right)=\measuredangle x\implies 64.432194^o\approx \measuredangle x[/tex]

Complete the equation of the line through (-6,5) and (-3,-3) Use exact numbers. y=

Answers

(-6,5) and (-3,-3) 
slope = (5+3)/(-6 + 3) = 8/-3 = -8/3

y = mx + b
b = y - mx
b = -3 - (-8/3)(-3)
b = -3 - 8
b = -11

equation
y = -8/3 x - 11

hope it helps

The equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.

What is the equation of a line passing through two points?

Let the equation of the line pass through (x₁, y₁) and (x₂, y₂).

Then the equation of the line is given as,

[tex]\rm (y - y_2) = \left (\dfrac{y_2 - y_1}{x_2 - x_1} \right ) (x - x_2)[/tex]

The points are given below.

(-6,5) and (-3,-3)

Then the equation of the line passing through the points (-6,5) and (-3,-3) will be

[tex]\rm (y + 3) = \left (\dfrac{-3-5}{-3+6} \right ) (x + 3)[/tex]

Simplify the equation, then the equation of the line will be

y + 3 = -(8/3)(x + 3)

y = -(8/3)x - 8 - 3

y = -(8/3)x - 11

Then the equation of the line passing through the points (-6,5) and (-3,-3) will be y = -(8/3)x - 11.

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The path of a rocket ship is given by the parametric equations x(t)=3t and y(t)=4t^2+1, where t is the time in seconds after launch. Where is the ship after 10 seconds?
A.) (3,4)
B.) (3,5)
C.) (30,401)
D.) (30,501)

Answers

x(t)=3t
y(t)=4t^2+1

Time (seconds):

Where is the ship after 10 seconds?
t=10→Position: Point: P=(x(t), y(t))=(x(10), y(10))=?

t=10→x(10)=3(10)→x(10)=30
t=10→y(10)=4(10)^2+1=4(100)+1=400+1→y(10)=401

Position: P=(x(10), y(10))=(30, 401)

Answer: Option C.) (30, 401) 

Selecting a red pen and then a blue pen, when selecting 2 pens from a bag of 10 red pens

Answers

What? That’s not possible because there’s no blue pens. If that’s the awnser?

In the expansion of (3a + 4b)8, which of the following are possible variable terms? Explain your reasoning. a2b3; a5b3; ab8; b8; a4b4; a8; ab7; a6b

Answers

Answers are: 
a^5b^3
b^8
a^4b^4
a^8
ab^7
(there are 5 answers)

==================================================

The exponents for the variable terms must add to 8, which is the original outer exponent of the expression given (3a+4b)^8

For something like a^8, we don't have any other exponent so we don't have to worry about it. If you wanted, you can think of a^8 as a^8b^0 and then note how 8+0 = 8. So the rule still applies

For ab^7, we would write it as a^1b^7 and the rule works here as well (1+7 = 8). 

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

Something like a^2b^3 is a non-answer because the exponents add to 2+3 = 5
Same goes for ab^8 = a^1b^8 because we have the exponents add to 1+8 = 9
And for a^6b = a^6b^1 we have the sum of exponents being 6+1 = 7

The [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms and this can be determined by using the arithmetic operations.

Given :

Expression  ---  [tex]\rm (3a + 4b)^8[/tex]

The following calculation can be used in order to determine the possible variables from the given expression.

The given expression can be written as:

[tex]\rm (3a + 4b)^8=(3a+4b)^2(3a+4b)^2(3a+4b)^2(3a+4b)^2[/tex]

[tex]\rm (3a + 4b)^8=(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)(9a^2+16b^2+12ab)[/tex]

Now, further simplify the above expression.

[tex]\rm (3a + 4b)^8=(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)(81a^4+144a^2b^2+108a^3b+144a^2b^2+256b^4+192a^3b+108a^3b+192ab^3+144a^2b^2)[/tex]

So, from the above calculation, it can be concluded that [tex]a^5b^3[/tex], [tex]ab^8[/tex], [tex]b^8[/tex], [tex]a^4b^4[/tex], [tex]a^8[/tex], and [tex]ab^7[/tex] are the possible variable terms.

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What is the value of x?
28
47
56
33

Answers

The answer is:  " 47 " .
______________________________________________________
                       →   " x = 47 "  .
______________________________________________________
Explanation:
______________________________________________________
Note:   The "vertex" is "floating around" inside the circle.  


Answer:

47

Step-by-step explanation:

Fifty-eight boys were asked if they play football and/or baseball. Thirty-one of them said they do not play baseball. Sixteen of them said they play football. Twenty of them said they do not play baseball or football.

Enter your answers in the boxes to complete the two-way table based on the given data.

Answers

The two-way table is attached.

We start out placing 31 in the Total column beside the Don't Play Baseball row.  We then place 16 in the Total row under the Play Football column.  20 goes in the Don't Play Baseball row under the Don't Play Football column.

Since there are 31 people that do not play baseball, and 20 of them don't play football, this leaves us with 31-20=11 that do not play baseball and play football.

There are 58 people total, so this goes in the Total row under the Total column.

There are 58 people, and 31 of them do not play baseball; this leaves us 58-31=27 total that play baseball.

16 total people play football, and 11 of them don't play baseball.  This leaves us 16-11=5 people that play football and play baseball.

There are 58 people, and 16 of them play football; this leaves us 58-16=42 total that don't play football.

42 people don't play football, and 20 of them don't play baseball; this leaves us 42-20=22 people that don't play football and play baseball.

5 people play baseball and play football, and 22 people play baseball and don't play football; this gives us 5+22=27 people total that play baseball.

If you answer 110 questions and get a 94% how many did you get wrong

Answers

STEP 1:
Set up a ratio.

x= number correct out of 110

x/110= 94/100
cross multiply

(x * 100)= (110 * 94)
100x= 10,340

divide both sides by 100
x= 103.4


STEP 2:
subtract number correct in step 1 from total number of questions

=110 - 103.4
=6.6 questions wrong


ANSWER: There were exactly 6.6 questions wrong on the test. Since you cannot have a partial question (unless otherwise stated), but only whole questions, round up to 7 whole questions wrong.

Hope this helps! :)
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