Answer:
Step-by-step explanation:
It is given that the base edge of the regular triangular pyramid is b=10 cm and altitude of the base h =8.66 cm. The slant height of the pyramid is k=8 cm.
Now, the lateral surface area of the pyramid is given as:
[tex]LSA={\frac{3}{2}}(b)(k)[/tex]
Substituting the given values, we have
[tex]LSA=\frac{3}{2}(10)(8)[/tex]
[tex]LSA=120cm^2[/tex]
Thus, the Lateral surface area of the pyramid is [tex]120cm^2[/tex].
Now, the surface area is given as:
[tex]SA=\frac{1}{2}bh+LSA[/tex]
[tex]SA=\frac{1}{2}bh+120[/tex]
[tex]SA=\frac{1}{2}(10)(8.66)+120[/tex]
[tex]SA=43.3+120[/tex]
[tex]SA=163.3cm^2[/tex]
Thus, the surface area of the pyramid will be [tex]163.3cm^2[/tex].
The Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
What is a pyramid?A polyhedron that has a polygonal base and triangles for sides, is a pyramid.
The lateral area of the pyramid is equal to the area of its three triangular lateral faces is;
[tex]\rm Lateral \ Area=3 \times \dfrac{1}{2}\times b \times k\\\\ Lateral \ Area=3 \times \dfrac{1}{2}\times 10 \times 8\\\\ Lateral \ Area=120[/tex]
The surface area of the pyramid is;
[tex]\rm Surface \ area=\dfrac{1}{2}bh + Lateral \ area\\\\Surface \ area=\dfrac{1}{2}\times 10 \times 8.66 +120\\\\Surface \ area=43.3+120\\\\Surface \ area=163.3 \ cm^3[/tex]
Hence, the Lateral area is 120 cubic cm, and the Surface area of the pyramid is 163.3 cubic cm.
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In the united states, 20 ounces of a beverage that is 25% ethanol contains __________ ounces of alcohol
Easy math problem, please help.
O is the center of the circle. Assume that lines that appear to tangent are tangent. What is the value of x?
A. 56
B. 62
C. 248
D. 304
Answer:
Option A is correct that is x° = 56°
Step-by-step explanation:
Let Given Lines are tangents.
So we use a result which states that Tangents are perpendicular with radius at point of contacts.
⇒ ∠ B = ∠ D = 90°
Angle sum property of Quadrilateral = 360°
⇒ ∠A + ∠B + ∠O + ∠D = 360
x + 90 + 124 + 90 = 360
x + 304 = 360
x = 360 - 304
x = 56
Therefore, Option A is correct that is x° = 56°
Can anybody help me with this question(#6)? It’s over systems word problems. ASAP!
At a local baseball game there are 3 hot dog vendors. collectively the vendors sold 1,700 hot dogs. if vendor a sold 456, vendor b sold 607, and vendor c sold 637, what percentage of the total did each vendor sell? (round to the nearest percent.) a) 26 percent, 40 percent, 44 percent b) 45 percent, 37 percent, 18 percent c) 27 percent, 36 percent, 37 percent d) 30 percent, 35 percent, 35 percent
Answer:
c) 27 percent, 36 percent, 37 percent
Step-by-step explanation:
Given,
Hot dogs sold by,
Vendor a = 456
Vendor b = 607
Vendor c = 637,
Total hot dogs = 1700,
Thus, the percentage of the hot dogs sold by a = [tex]\frac{\text{Hot dog sold by a}}{\text{Total hot dogs}}\times 100[/tex]
[tex]=\frac{456}{1700}\times 100[/tex]
[tex]=\frac{456}{17}[/tex]
= 26.82%
≈ 27%
Similarly,
Percentage of the hot dogs sold by a
[tex]=\frac{607}{1700}\times 100[/tex]
[tex]=\frac{607}{17}[/tex]
= 35.71%
≈ 36%
Percentage of the hot dogs sold by a
[tex]=\frac{637}{1700}\times 100[/tex]
[tex]=\frac{637}{17}[/tex]
= 37.47%
≈ 37%
Hence, OPTION c) is correct.
PLS HELP ME ASAP ON THIS,
YOU NEED TO FIND THE DOMAIN AND RANGE
AND CIRCLE WHAT BEST ANSWERS THEQUESTION
(Random answers gets moderated.)
Leo has 100 coins in his piggy bank. All coins are either nickels, or dimes, or quarters. There are as many nickels as dimes and quarters together. How much money are nickels in Leo's piggy bank worth?
Answer:
33
Step-by-step explanation:
Express answer in exact form.
A segment of a circle has a 120 arc and a chord of 8in. Find the area of the segment.
10 POINTS!!! FULL ANSWER IN STEP BY STEP FORMAT!!
The mathematics department of a college has 1414 male professors, 99 female professors, 99 male teaching assistants, and 1111 female teaching assistants. if a person is selected at random from the group, find the probability that the selected person is a professor or a male.
I think the answer is Probability is (1513+99)/(1414+99+1111+99)=1612/2723
Is -5/0 undefined. And why is it or why is it not.
-5/0 is undefined.
The reason why division by zero is undefined is because there is no real number that can be multiplied by 0 to get -5.
In essence, the division operation asks how many times the denominator can be contained within the numerator. Since nothing times zero gives any number other than zero, this question has no answer.
Moreover, division by zero is not allowed in the real number system because it can lead to logical contradictions and undefined behavior.
There are 1760 yards yards in a mile. what fraction of a mile is represented by 1100 yards yardsâ?
To find the fraction of a mile represented by 1100 yards, divide 1100 yards by 1760 yards (the total number of yards in a mile). The fraction is 0.625.
Explanation:To find the fraction of a mile represented by 1100 yards, we need to divide 1100 yards by the total number of yards in a mile, which is 1760 yards. We can set up a proportion with the fraction we're looking for, x, in the numerator and 1760 in the denominator:
1100 yards / 1760 yards = x / 1 mile
Since the denominator on the left side is the same as the denominator on the right side, we can cross-multiply and solve for x:
x = 1100 / 1760
x = 0.625
Therefore, the fraction of a mile represented by 1100 yards is 0.625.
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(5.4+3)×(6−2) help plzzz
Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units. What is the length of AC?
A. 5 units
B. 6 units
C. 10 units
D. 12 units
Answer:
D. 12 on edge
Step-by-step explanation:
How many zeros does the function f(x) = 4x^11 − 20x^7 + 2x^3 − 15x + 14 have?
I'm between 3 & 11.
If a square has a perimeter of 40 yards, what is the length of one side of the square?
Conor buys 75 tokens for games at the arcade. the price to play each game is 3 tokens. if conor has already played x games, which expression is equivalent to the number of tokens that remain?
Answer:
y = 75 - 3x
Step-by-step explanation:
Let the number of token left = y
total number of token bought = 75
Number of games played by Conor = x
It is given for playing one game, the price = 3 token
Therefore for playing x games, the price is = 3x
Therefore, the number of tokens left with Conor is given by
y = 75 - 3x
Thus, the expression that is equivalent to the number of remaining tokens is
y = 75 - 3x
Write the equation in standard form for the circle with radius 3 centered at the origin
Quadrilateral ABCD is a parallelogram. DE = 6.1 cm and m∠DAB = 120°. What is BC? cm What is m∠BCD? ° What is AB? cm What is EB? cm
There are six important properties of parallelograms to know:
1) Opposite sides are congruent (AB = DC and AD=BC).Answer: check
Step-by-step explanation:
done
What is the least common multiple (LCM) of 8 and 10?
Answer:
LCM (8,10) = 2 × 2 × 2 × 5 = 40
Step-by-step explanation:
Least common multiple is the smallest number that is multiple of both the given numbers.
Example: LCM of 2 and 3 is 6 .
6 is a multiple of both 2 and 3 .
Given numbers are 8 and 10
First write both in factor form,
⇒ 8 = 2 × 2 × 2
⇒ 10 = 2 × 5
We find LCM by writing common terms one times and multiplying all terms together,
Here, 2 is common to both 8 and 10 so we write it once only.
Thus, LCM (8,10) = 2 × 2 × 2 × 5 = 40.
Quickly
Which coordinates represent a translation of B(–4, 1) 3 units to the right and 2 units down?
To translate point B(−4, 1) 3 units to the right and 2 units down, you add 3 to the x-coordinate and subtract 2 from the y-coordinate, resulting in the new coordinates B' = (−1, −1).
The coordinates that represent a translation of B(−4, 1) 3 units to the right and 2 units down can be found by adding 3 to the x-coordinate and subtracting 2 from the y-coordinate of point B. The new coordinates will be:
B' = (−4 + 3, 1 − 2)
So, the new coordinates would be B' = (−1, −1).
The length of a rectangle is five times its width. if the area of the rectangle is 320 m2 , find its perimeter. m
Final answer:
To find the perimeter of the rectangle, first find the dimensions using the given information and the formula. Then, use the formula for perimeter to calculate the final result.
Explanation:
To find the perimeter of the rectangle, we need to first find the dimensions of the rectangle. Let the width of the rectangle be w. According to the given information, the length of the rectangle is 5 times its width, so the length can be represented as 5w. The area of the rectangle is given as 320 m², so we can set up the equation:
w * 5w = 320
Simplifying this equation, we have:
5w² = 320
Dividing both sides of the equation by 5, we get:
w² = 64
Taking the square root of both sides, we find:
w = 8
So, the width of the rectangle is 8 meters. The length can be found by multiplying the width by 5:
length = 5 * 8 = 40 meters
The perimeter of the rectangle is calculated using the formula: Perimeter = 2*length + 2*width. Substituting the values we found:
Perimeter = 2*40 + 2*8
Calculating this expression, we get:
Perimeter = 80 + 16 = 96 meters
Suppose that on a particular computer, it takes the merge sort algorithm a total of 60 seconds to sort an array with 60,000 values. approximately how long will it take the algorithm to sort an array with 120,000 values? round to the nearest second.
Given:
CDKM is a parallelogram,
DA
⊥
CK
, DK – CD = 7
CA = 6, AK = 15
Find: CD and DK
In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
What is Pythagoras theorem?Pythagoras theorem says that in a right angle triangle the square of hypotenuse side is equal to the sum of square of other two legs of right angle triangle.
The quadrilateral CDKM is a parallelogram. In this parallelogram, the side DA is perpendicular to the side CK.
The difference of the side DK and CD is,
[tex]DK - CD = 7\\DK=7+CD[/tex]
The length of the line segment CA and AK is 6 units and 15 units respectively.Then by the Pythagoras theorem,
[tex](AD)^2=(CD)^2-(AC)^2\\(AD)^2=(CD)^2-(6)^2[/tex] ....1
Again by using the Pythagoras theorem
[tex](AD)^2=(Dk)^2-(AK)^2\\(AD)^2=(DK)^2-(15)^2[/tex]
Put the value of (AD)², from equation 1 in the above equation as,
[tex](CD)^2-6^2=(DK)^2-(15)^2\\(CD)^2-36=(DK)^2-225[/tex]
Put the value of DK in the above equation as,
[tex](CD)^2-36=(7+CD)^2-225\\(7+CD)^2-(CD)^2=225-36\\(CD)^2+14CD+49-(CD)^2=189\\CD=10[/tex]
Hence, the value of DK is,
[tex]DK=7+10DK=17[/tex]
Hence, In the parallelogram CDKM the value of the line segment CD and DK is 10 units and 17 units.
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Iven 5 different letters, how many different ways can you arrange 3 of them (whether they spell a word or not)
The number of different ways you can arrange 3 out of 5 letters is 10.
Explanation:To find the number of different ways you can arrange 3 out of 5 letters, you can use the formula for combinations. The formula for combinations is given by nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items being chosen at a time.
In this case, n = 5 and r = 3. So the number of different ways to arrange 3 out of 5 letters is 5C3 = 5! / (3!(5-3)!) = 10.
Therefore, there are 10 different ways you can arrange 3 out of the 5 letters.
A student invests $500 for 3 years in a savings account that earns 4% interest per year. No further deposits or withdrawals were made during this time. Which does NOT yield the correct balance in the account at the end of the 3 years? Please show work for the answer! A)500(1.04)^3 B)500(1-.04)^3 C)500(1+.04)(1+.04) D)500+500(.4)+520(.04)+540.8(04)
Answer:
he`s right its a or b
i'm going with b
Step-by-step explanation:
In ∆ABC, ∠BAC= 80°, ∠ABC=60°, a = 7, b = x.
Find x. (accurate to 3 significant figures)
The value of x = .
It takes a girl 55 minutes to deliver the papers on her route. if her brother helps, it takes only 20 minutes. how long would it take her brother to deliver the papers by himself? if necessary, round to 1 decimal place.
Answer- 31.11 minutes
Let 'T' be the total number of newspapers.
Newspapers distributed by girl alone in 55 minutes = T
Newspapers distributed by girl alone in 1 minute = T/55
Newspapers distributed by girl and boy in 20 minutes = T
Newspapers distributed by girl and boy in 1 minutes = T/20
Newspapers distributed by boy alone in 1 minute = T/20 - T/55 = 7T/220
On solving, total time taken by boy to distribute newspapers = 31.11 minutes
How many permutations exist of the letters a, b, c, d taken four at a time?
There are 24 permutations of the letters a, b, c, d taken four at a time, calculated using the formula 4!.
Explanation:The question revolves around finding the number of permutations of the letters a, b, c, d taken four at a time. To solve this, we need to understand that a permutation represents the arrangement of all members of a set in every possible order.
In the case of the letters a, b, c, d, we want to arrange them in all possible ways where order matters and taking all four at a time. The formula to calculate permutations is P(n, r) = n! / (n-r)!, where n is the total number of items to choose from, and r is the number of items to choose. However, since we are taking all four letters each time, we are essentially looking for 4!, which simplifies to 4*3*2*1.
Therefore, 4! equates to 24. This means there are 24 possible ways to arrange the letters a, b, c, d when taking all four at a time. It's an excellent exercise to manually write out all of these permutations to get practical experience with the concept.
HELPPPPPPPPPPPP and explain
The tax rate is 3.9%
What is the tax on 42$?
Round to the nearest hundredth
To calculate the tax on $42 at a 3.9% rate, first convert the percentage to a decimal (0.039) then multiply the amount by the tax rate. The result is approximately $1.64.
Explanation:The problem involves calculating the tax on a certain amount using a specified tax rate. In this case, the tax rate is given as 3.9% and the amount is $42.
You calculate the tax by multiplying the tax rate by the amount.
First, convert the percentage into a decimal by dividing by 100: 3.9 ÷ 100 = 0.039.
Next, multiply the amount by the tax rate: $42 x 0.039 = $1.638.
Therefore, the tax on $42 at a rate of 3.9% is approximately $1.64, when rounded to the nearest hundredth.
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The tax on $42 with a 3.9% tax rate is approximately $1.64 when rounded to the nearest hundredth.
Explanation:To find the tax on $42 with a tax rate of 3.9%, we need to multiply the total amount by the tax rate. First, turn the percentage into a decimal by dividing 3.9 by 100, which gives us 0.039. After that, you multiply $42 by 0.039. This results in approximately $1.64, which we round to the nearest hundredth as per the instructions, thus our answer is $1.64.
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