Archeologists found a previously unknown pyramid in Central America, shown in the figure. The media is interested in the volume of this pyramid. Find the volume of the pyramid.
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SOLUTION:
We are to find the volume of the given pyramid;
[tex]\text{Volume = }\frac{base\text{ area X height}}{3}[/tex][tex]\begin{gathered} \text{Length of the base square = 8 yd.} \\ \text{height of the pyramid = 3 yd.} \end{gathered}[/tex]The volume of the pyramid is;
[tex]\frac{8X8X3}{3}=64yd.^3[/tex]CONCLUSION:
The volume of the given pyramid is 64 cubic yards.
Related Questions
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. Round to four decimal places.
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To find the area under a normal distrubution curve use a z-score table, in the table you can identify the area under a z-score.
If you use the table for the z-score -1.82 you get the non-shaded area, but as the total area under the curve is 1 you subtract the value corresponding -1.82 from 1 to get the area of the shaded area
Area under -1.82:
Area of the shaded region:
[tex]1-0.0344=0.9656[/tex]Then, the area of the shaded region is 0.9656The function f(x) = x² - 6x+9 is shifted 5 units to the right to create g(x).What is g(x)?A. g(x) = (x - 5)^2 - 6(x - 5) +9B. g(x) = (x + 5)² - 6(x+5) +9C. g(x) = (x² - 6x +9) - 5D. g(x) = (x² - 6x + 9) + 5
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Solution:
Given the function:
[tex]f(x)=x^2-6x+9[/tex]To create g(x), the function f(x) is shifted 5 units to the right.
Firstly, the graph of f(x) is shown below:
To create g(x), we have
[tex]g(x)=(x-5)^^2-6(x-5)+9[/tex]The graph g(x) is shown below:
Hence, the g(x) function is expressed as
[tex]g(x)=(x-5)^2-6(x-5)+9[/tex]The correct option is A
Create an equation of a line that is perpendicular to y = 2 3 x − 3
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Given data:
The given equation of the line is y= 2x/3 -3.
The standard equation of the line is,
[tex]y=mx+c[/tex]Compare the above equation with the given equation.
[tex]m=\frac{2}{3}[/tex]The equation of the line perpendicular to the given line is,
[tex]\begin{gathered} y-b=-\frac{1}{(\frac{2}{3})}(x-a) \\ y-b=-\frac{3}{2}(x-a) \\ y=-\frac{3}{2}x+\frac{3a}{2}+b \end{gathered}[/tex]Thus, the equation of the line perpendicular to the given line is y=-3x/2 +3a/2 +b.
First solve for x, then use it to find all of the missing angle measurements
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The sum of interior angles of a triangle is 180 degrees
Here the interior angles are:
[tex](4x\text{ - 22) + (10x - 4) + (x + 11) = 180}[/tex]To find x, first open the parenthesis:
[tex]4x\text{ - 22 + 10x - 4 + x + 11 = 180}[/tex]Collect like terms:
[tex]4x\text{ + 10x + x -22 - 4 + 11 = 180}[/tex][tex]15x\text{ - 15 = 180}[/tex]Now add 15 to both sides:
[tex]15x\text{ - 15 + 15 = 180 + 15}[/tex][tex]15x\text{ = 195}[/tex]divide both sides by 15:
[tex]\frac{15x}{15}\text{ = }\frac{195}{15}[/tex][tex]\text{ x = 13}[/tex]Find the area of the radius Round to the nearest whole number
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Step-by-step explanation:
The formula of the area of a circle is A = πr² where A is the area and r is the radius of the circle.
To find the radius, you can follow the steps below:
Step 1) Substitute the value of the area (given) in the equation.
[tex]\begin{gathered} A=\pi\cdot r^2 \\ 9409\pi=\pi\cdot r^2 \end{gathered}[/tex]Step 2) Isolate r and solve the square root.
[tex]\begin{gathered} r^2=\frac{9404\pi}{\pi} \\ r^2=9404 \\ \sqrt[]{r^2}=\sqrt[]{9404} \\ r=97 \end{gathered}[/tex]Answer: The length of the radius is 97 centimeters.
When is the mean most useful in describing a set of data?when there is an outlierwhen the range is widewhen there are two or more modeswhen the range is narrow
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Solution
Step 1
The mean is the most useful in describing a set of data when range is wide.
Final answer
when the range is wide
Lisa is partitioning line segment a b so that a point C divides a line segment into the ratio 2 to 3 Nikki said that she can do the same thing but by multiplying point a by the fraction of 2/5 since this is the part to the whole ratio equivalent do you agree or disagree with Nikki justify your answer
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This is true because:
the ratio 2 to 3 = 2:3
Is equivalent to :
2/(3+2) = 2/5
If you want to express a ratio a:b as a fraction, you can always use this formula:
a:b = a/(a+b)
You can use the following formula:
If d(xp,yp) divides a line segment form A(x1,y1) to B(x2,y2) in the ratio a:b, then:
xp = x1 + a/(a+b) * (x2 - x1)
yp = y1 + a/(a+b) * (y2 - y1)
So:
xp = 1 + 2/5*(16-1) = 7
yp = 4 + 2/5*(14 - 4) = 8
What is the relationship between the two functions ( \small y=e^x and \small y= ln \small x) graphed below?
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y = e^x is the inverse of y = lnx
We know that the range of the inverse of a function is the domain of the original function. Looking at the graph, the domain of the y = e^x is (- infinity, infinity). We can see that the range of y = lnx is (- infinity, infinity). Thus, the answer is
y = e^x is the inverse of y = lnx
I’m struggling in math right now and could use some help
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Given:
There are given that the total population is 380000.
Explanation:
From the given statement:
The population of the city grows 6% each year.
Then,
From the formula to find the population after 10 years:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where,
[tex]\begin{gathered} P=380000 \\ r=6\%=0.06 \\ n=1 \\ t=10 \end{gathered}[/tex]Then,
Put all the values into the above formula:
So,
From the fromula:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ A=380000(1+\frac{0.06}{1})^{1(10)} \end{gathered}[/tex]Then,
[tex]\begin{gathered} A=380,000(1+\frac{0.06}{1})^{1(10)} \\ A=380,000(1.06)^{1(10)} \\ A=380,000(1.7908) \\ A=680504 \end{gathered}[/tex]Final answer:
Hence, the total population after 10 years is 680504.
suppose a bag if groceries costs $14.50 this year and the average annual rate of inflation over the last five years is 3%. if the inflation rate continues to be 3% per year, how much will the same bag of groceries cost 2 years from now? (round to the nearest $0.10)
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Let:
Op = Original price = $14.50
r = rate of inflation = 3% = 0.03
After the first year, the cost of the bag of groceries will be:
[tex]\begin{gathered} P1=Or+r\cdot Or \\ P1=14.50+0.03\cdot14.50=14.935 \end{gathered}[/tex]After the 2nd year, the cost will be:
[tex]\begin{gathered} P2=P1+rP1 \\ P2=14.935+0.03\cdot14.935=15.38 \end{gathered}[/tex]22. Find the difference between the volume of the cylinder and the volume of the rectangular box below. Round your answer to the nearest cubic Inch. (1) 26 (2) 68 (3) 47 (4) 52 (5) 38
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hello
to solve this question, we need to find the indivdual volumes and then find the difference between them.
1. let's find the volume of the cylinder first
[tex]\begin{gathered} v=\pi r^2h \\ \pi=3.14 \\ r=3in \\ h=7in \\ v=\pi r^2h \\ v=3.14\times3^2\times7 \\ v=3.14\times9\times7 \\ v=197.82in^3 \end{gathered}[/tex]volume of the cylinder is equal to 197.82in^3
next we solve the volume of the cubiod
[tex]\begin{gathered} v=l\times b\times h \\ l=5in \\ b=4in \\ h=8in \\ v=5\times4\times8=160in^3 \end{gathered}[/tex]the volume of the cubiod is equal to 160in^3
now we can proceed to find the difference (d) between the two figures
[tex]\begin{gathered} d=197.82-160 \\ d=37.82\approx38 \end{gathered}[/tex]the difference between the volume of two figures is approximately 38in^3
museum had a total of 224 visitors on Tuesday. Visitors older than 18 years paid $12 and visitors 18 years or younger paid $8 x+y=224 , 12x+8y=2520. How many visitors were 18 or younger ?
Answers
Answer
The visitors that were 18 years or younger = 42.
Explanation
Given that:
The total number of visitors on Tuesday = 224
The visitors older than 18 years paid $12
The visitors 18 years or younger paid $8
Representing visitors older than 18 years as x and visitors 18 years or younger paid $8 as y, the system of equations below were generated:
x + y = 224 , 12x + 8y = 2520
What to find:
The visitors that were 18 years or younger.
Step-by-step solution:
To get the visitors that were 18 years or younger, solve for y in the system of equation using the elimination method.
[tex]\begin{gathered} x+y=224----i\times12 \\ \\ 12x+8y=2520---ii \\ \\ Multiply\text{ }(i)\text{ }by\text{ }12 \\ \\ 12x+12y=2688----iii \\ \\ 12x+8y=2520---ii \\ \\ Now\text{ }substract\text{ }(ii)\text{ }from\text{ }(iii) \\ \\ 4y=168 \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }4 \\ \\ \frac{4y}{4}=\frac{168}{4} \\ \\ y=42 \end{gathered}[/tex]Therefore, the visitors that were 18 years or younger are 42.
To get visitors older than 18 years, that is to solve for x, substitute y as 42 into (i):
[tex]\begin{gathered} x+y=224-----i \\ \\ x+42=224 \\ \\ x=224-42 \\ \\ x=182 \end{gathered}[/tex]Hence, the number of visitors older than 18 years is 182.
this is product multiply and sum add from the diamond method
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Notice that:
[tex]\begin{gathered} 6\cdot4=24, \\ 6+4=10. \end{gathered}[/tex]Answer:
what would be 1,000% of 87
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We can do the next equivalences
87 -- 100%
x ---- 1000%
[tex]x=\frac{1000\cdot87}{100}=870[/tex]the answer is 870
ben and cam scuba diving.ben is 15.8 meters below the surface of the water.if he dives down the same distance again and then moved 12.4 meters towards the surface,what will his new position be?
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The surface of the water is at 0 meters.
Ben is 15.8 meters below the surface of the water.
if he dives down the same distance again then
15.8 meters + 15.8 meters = 31.6 meters below the surface
Then moved 12.4 meters towards the surface (means opposite direction so we need to subtract this distance)
31.6 meters - 12.4 meters = 19.2 meters below the surface
Therefore, the new position of Ben will be 19.2 meters below the surface.
Question: Nora needs to cut some equal pieces of yarn for her Science project. The piece of yarn she has is 67.6 inches long. Each piece of yarn must be 1.3 inches in lenght. How many pieces of yarn will Nora have.
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Nora will have 52 pieces of yarn
Here, we want to get the number of pieces of yam
What we have to do here is to divide the length of the entire yarn by the length of the individual piece
Mathematically, we have this as;
[tex]\frac{67.6\text{ inches}}{1.3\text{ inches}}\text{ = 52}[/tex]Which choices are equivalent to the expression below? Check all that apply.A.75B.C.D.E.F.
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SOLUTION
We want to find the expression equivalent to
[tex]5\sqrt{3}[/tex]we have
[tex]\begin{gathered} 5\sqrt{3} \\ =\sqrt{25}\times\sqrt{3} \\ =\sqrt{25\times3} \\ =\sqrt{75} \\ =\sqrt{25}\text{ . }\sqrt{3} \end{gathered}[/tex]hence the answers are options B and F
true or false? the order of an inequality remains the same if a positive number is multiplied or divided on both sides of the inequality
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Let's say the following inequality is multiplied by A>0:
[tex]\begin{gathered} 7>5 \\ \\ 7A>5A\text{ True} \end{gathered}[/tex]Notice that is the same as multiplying A by 7 and multiplying A by 5. When we multiply A by 7 the result is a number greater than when we multiply A by 5, since 7>5.
Thus, in this example, we see that the order of the inequality remains.
A different problem would be multiplying the inequality by a negative number. For example, let's multiply the original inequality by -1:
[tex]\begin{gathered} 7>5 \\ \\ -7>-5\text{ False} \end{gathered}[/tex]As we see, -7 is more negative than -5. Thus, -7 < -5. Then, multiplying by a negative number changes the order of the inequality.
The same happens when we divide by a positive number (the order is the same) or a negative number (the order is changed) since dividing would be the same as multiplying by a fraction.
Therefore, the statement "the order of an inequality remains the same if a positive number is multiplied or divided by on both sides of the inequality" is TRUE.
50å15 I need help pls
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50å15
[tex]50\sqrt[]{15}[/tex]in mr siegel class 15% of the students are in scrapbooking club and 45% are in the cooking club his remaining students are in the board game club whats the fraction form and decimal form
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In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
scrapbooking club = 15%
cooking club = 45%
board game club = ?
Step 02:
board game club = 100 - 15 - 45 = 40%
scrapbooking club:
fraction form = 15 / 100
decimal form = 0.15
cooking club:
fraction form = 45 / 100
decimal form = 0.45
board game club:
fraction form = 40 / 100
decimal form = 0.40
The full solution is:
scrapbooking club:
fraction form = 15 / 100
decimal form = 0.15
cooking club:
fraction form = 45 / 100
decimal form = 0.45
board game club:
fraction form = 40 / 100
decimal form = 0.40
17. A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches long, 9 inches wide, and 12 inches tall. Each notepad is in the shape of a cube with an edge length of 3 inches. What is the maximum number of notepads that will fit in 1 closed box? A. 10 B. 11 C. 12 D. 22 E. 36
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The volume of each box is:
[tex]V=\text{length}\cdot\text{width}\cdot\text{height}[/tex]Substituting with length = 9 in, width = 9 in, and height = 12 in, we get:
[tex]\begin{gathered} V=9\cdot9\cdot12 \\ V=972in^3 \end{gathered}[/tex]The volume of each notepad is:
[tex]V=\text{length}^3[/tex]Substituting with length = 3 in, we get:
[tex]\begin{gathered} V=3^3 \\ V=27in^3 \end{gathered}[/tex]The number of notepads that fit in 1 box is obtained dividing the volume of the box by the volume of each notepad, as follows:
[tex]\frac{972in^3}{27in^3}=36\text{ notepads}[/tex]I NEED ANSWERS NOT STEPS i already know the steps but the answer is wrong
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ANSWER
[tex]x=36.9\degree[/tex]EXPLANATION
To `find x, we have to apply the trigonometric ratios SOHCAHTOA for tangent:
[tex]\tan x=\frac{\text{opposite}}{\text{adjacent}}[/tex]Therefore, we have that:
[tex]\begin{gathered} \tan x=\frac{6}{8}=0.75 \\ x=\tan ^{-1}(0.75) \\ x=36.9\degree \end{gathered}[/tex]That is the answer.
Referring to the figure, segment AB and segment NM are the diameters of circle E. Find the angle of arc AC.
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Since AB and NM are the diameters, we can conclude that E is the central point. Therefore, the angle AEC (Central angle) is equal to the arc.
∠MEA, ∠AEC and ∠NEC are supplementary angles, therefore:
[tex]\begin{gathered} \angle MEA+\angle AEC+\angle NEC=180 \\ 55+\angle AEC+65=180 \\ 120+\angle AEC=180 \\ so\colon \\ \angle AEC=180-120 \\ \angle AEC=60 \\ _{\text{ }}Therefore\colon \\ AC=\angle AEC \\ AC=60 \end{gathered}[/tex]Answer:
60⁰
What is the intermediate step in the form (x+a)^2=b(x+a) 2 =b as a result of completing the square for the following equation?
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For this problem, we are asked to provide the intermediate step we obtain while completing the square for the following expression:
[tex]-6x^2-235=-48x+11[/tex]Completing the square means to transform the function into a expression such as:
[tex](a+b)^2=a^2+2\cdot a\cdot b+b^2[/tex]For this we will first change all the terms to the left side, as shown below:
[tex]\begin{gathered} 6x^2-48x+235+11=0 \\ 6x^2-48x+246=0 \end{gathered}[/tex]Since all three terms are divisible by 6, we need to use factorization to isolate the 6 from the equation:
[tex]6\cdot(x^2-8x+41)=0[/tex]Now, we need to rewrite the expression inside the parenthesis, such as we will obtain a form that is roughly equal to the perfect square we're looking for.
[tex]\begin{gathered} 6\cdot(x^2-2\cdot4\cdot x+41)=0 \\ 6\cdot(x^2-2\cdot4\cdot x+16+25)=0 \end{gathered}[/tex]Now, we need to remove the "25" from the parenthesis, for that we need to multiply the 6 by 25.
[tex]\begin{gathered} 6\cdot(x^2-2\cdot4\cdot x+16)+6\cdot25=0 \\ 6\cdot(x^2-2\cdot4\cdot x+16)+150=0 \\ 6\cdot(x^2-2\cdot4\cdot x+16)=-150 \end{gathered}[/tex]Now we can transform the parenthesis to the sum of two squares, where the term "a" is equal to x, and the "b" is equal to 4.
[tex]6\cdot(x^{}-4)^2=-150[/tex]PHU ME Humber. Round to the nearest tenth if necessary. 26% of 13 is what number? * 50 O 338 0 3.4 0 200
Answers
3.38
Explanation
Step 1
remember the percentage is a ratio to 100,so
[tex]26\rightarrow\frac{26}{100}=0.26[/tex]so, to find 26 % of any number just multiply by 0.26
so
[tex]\begin{gathered} 26\text{ \% of 13}\rightarrow0.26\cdot13=3.38 \\ \end{gathered}[/tex]so, the answer is 3.38
A recipe requires \frac{1}{4}1414 cup of water for each \frac{1}{3}1313 cup of milk. How many cups of water are needed for each cup of milk?
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1/4 cup of water----------------------->1/3 cup of milk
x cups of water------------------------> 1 cup of milk
using cross-multiplication:
[tex]\begin{gathered} \frac{\frac{1}{4}}{x}=\frac{\frac{1}{3}}{1} \\ solve_{\text{ }}for_{\text{ }}x\colon \\ x=\frac{\frac{1}{4}}{\frac{1}{3}} \\ x=\frac{3}{4} \end{gathered}[/tex]Answer:
3/4
QuestionA regular pyramid has a regular polygon base and athe baseover the center ofA. congruent polygonB. perpendicular line segmentC. circleD. vertex
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Given:
Information about a regular pyramid
To determine the answer based on the given choices, we note first that a regular pyramid has a regular polygon base and the vertex is directly above the center of its base. Therefore, the answer is: D. vertex
If a carpenter wants to make sure that the corner of a room is square and measures 9 At and 40 ft along the walls, how long should he make the diagonal?
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Answer:
The diagonal should be 41 ft long.
Step by step explanation:
A carpenter measures 9 ft and 40ft, to calculate the diagonal we can use the Pythagorean theorem:
[tex]\begin{gathered} a^2+b^2=c^2 \\ \text{where,} \\ a=9 \\ b=40 \end{gathered}[/tex]Substituting:
[tex]\begin{gathered} 9^2+40^2=c^2 \\ 81+1600=c^2 \\ c=\sqrt[]{1681} \\ c=41 \end{gathered}[/tex]The diagonal should be 41 ft long.
87 sit ups in 3 minutes Ratio: 87.3 Unit Rate: How many sit ups can he do in 1 minute
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We know that we can do 87 sit-ups in 3 minutes. To know the number of sit-ups he can do in 1 minute, we just have to divide 87/3
[tex]\frac{87}{3}=29[/tex]Hence, he can do 29 sit-ups in 1 minute.17. Is the parallelogram in #15 a rectangle, rhombus, or square?
Answers
This parallelogram is called RHOMBUS
Explanation:In the given shape, all sides have equal lengths, and opposite angles are equal. This parallelogram is called RHOMBUS.