If the base and height of the triangle that forms its base are 18 units and 12 units respectively then the height of the pyramid is 21 units.
The formula for the volume of a triangular pyramid is:
V = (1/3) * base area * height
We are given that the volume of the pyramid is 756 units^3, the base of the pyramid is a triangle with base length 18 units and height 12 units, so its area is:
A = (1/2) * base * height = (1/2) * 18 * 12 = 108 units^2
Substituting the given values into the formula for the volume of a pyramid, we get:
756 = (1/3) * 108 * h
Multiplying both sides by 3 and dividing by 108, we get:
h = 756 / 36 = 21
Therefore, the height of the pyramid is 21 units.
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What is the side lengths of a a and b. What is the value of x?
(3x)^2+(6x)^2=40^2
If a lobster travels 5 miles each year how many years will it take the lobster to travel 39. 5 miles
It will take 7.9 years for the lobster to travel 39.5 miles
What is Word Problem?Word problem is usually made up of a few sentences describing a situation that needs to be solved through mathematics
How to determine this
If a lobster travels 5 miles each year
i.e 5 miles = 1 years
How many years will it take the lobster to travel 39.5 miles
Let x represent the number of years the lobster travel
For lobster to travel 39.5 miles,
i.e 39.5 miles = x years
To calculate the number of years
When 5 miles = 1 year
39.5 miles = x
x = 39.5 miles * 1 year/5 miles
x = 39.5 years/5
x = 7.9 years
Therefore, it will take 7.9 years for the lobster to travel 39.5 miles
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I NEED HELP ASAP
i am in need of help quickly
Answer:
25ft
Step-by-step explanation:
An ice field is melting at the rate M (t)=4-(sin t)³ acre-feet per day, where t is measured in
days. How many acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the
beginning of day 4 (t = 3) ?
(A) 10.667
(B) 10.951
(C) 11.544
(D) 11.999
A 11.544 acre-feet of this ice field will melt from the beginning of day 1 (t = 0) to the beginning of day 4 (t = 3). So, correct option is C.
To solve the problem, we need to integrate the given rate of melting with respect to time over the interval [0,3] to find the total amount of ice that melts during this time.
First, we can simplify the given rate of melting by using the identity: sin³(t) = (3sin(t) - sin(3t))/4
So, M(t) = 4 - (3sin(t) - sin(3t))/4 = 16/4 - 3sin(t)/4 + sin(3t)/4 = 4 - 0.75sin(t) + 0.25sin(3t)
Integrating this expression with respect to t over the interval [0,3], we get:
[tex]\int\limits^3_0[/tex] M(t) dt = [tex]\int\limits^3_0[/tex] (4 - 0.75sin(t) + 0.25sin(3t)) dt
= [4t + 0.75cos(t) - (1/3)cos(3t)]|[0,3]
= (12 + 0.75cos(3) - (1/3)cos(9)) - (0 + 0.75cos(0) - (1/3)cos(0))
= 11.544
Therefore, the answer is (C) 11.544.
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what are the first four terms of the geometric sequence a2= 11, and a3=-121.
The first four terms of the geometric sequence are -1, 11, -121, and -1210.
We have,
To find the first four terms of the geometric sequence, we need to determine the common ratio, r, and then use it to calculate the other terms.
We can start by using the formula for the nth term of a geometric sequence:
an = a1 x r^(n - 1)
where an is the nth term, a1 is the first term, r is the common ratio, and n is the position of the term we want to find.
Since we are given a2 and a3, we can use them to form two equations:
a2 = a1 x r
a3 = a1 x r²
We can then solve for a1 and r:
a1 = a2 / r = 11 / r
r = a3 / a2 = -121 / 11
Substituting these values into the formula for the nth term, we get:
an = (11 / r) x (-121 / 11)^(n - 2)
Simplifying this expression, we get:
an = -11 x 11^(n - 2)
Now we can calculate the first four terms:
a1 = 11 / r = 11 / (-121 / 11) = -1
a2 = 11
a3 = -121
a4 = -11 x 11^(4 - 2) = -1210
Therefore,
The first four terms of the geometric sequence are:
-1, 11, -121, -1210
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The circle graph describes the distribution of preferred transportation methods from a sample of 300 randomly selected San Francisco residents.
circle graph titled San Francisco Residents' Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent
Which of the following conclusions can we draw from the circle graph?
Bus is the preferred transportation for 25 residents.
Bicycle is the preferred transportation for 48 residents.
Together, Streetcar and Cable Car are the preferred transportation for 42 residents.
Together, Walk and Streetcar are the preferred transportation for 165 residents.
The correct conclusions which can we draw from the circle graph is,
⇒ Together, Walk and Streetcar are the preferred transportation for 165 residents.
Given that;
The circle graph describes the distribution of preferred transportation methods from a sample of 300 randomly selected San Francisco residents.
And, Circle graph titled San Francisco Residents Transportation with five sections labeled walk 40 percent, bicycle 8 percent, streetcar 15 percent, bus 10 percent, and cable car 27 percent.
Hence, For Walk and Streetcar;
(40 + 15)% of 300
55% of 300
55/100 x 300
55 x 3
165
Thus, The correct conclusions which can we draw from the circle graph is,
⇒ Together, Walk and Streetcar are the preferred transportation for 165 residents.
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Graphing Quadratic Equations
The quadratic equation is solved and the graph is plotted
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = - ( x + 3 )² + 4
The given quadratic function is in vertex form:
y = a(x - h)² + k
where (h, k) is the vertex
Comparing with the given function y = -(x + 3)² + 4, we can see that h = -3, k = 4, and a = -1
Therefore, the vertex of the parabola is (-3, 4)
The axis of symmetry is the vertical line that passes through the vertex. Since the vertex is (-3, 4), the equation of the axis of symmetry is x = -3
Hence, the axis of symmetry is x = -3 and the vertex is (-3, 4)
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Select the correct answer.
If a group of distinct objects can be arranged in 120 different ways, how many objects are there?
O
O
A. 3
O
B. 4
OC. 5
D. 6
Answer: C. 5
Step-by-step explanation:
I will give Brainlest and 100 points to first correct answer
Answer:
The Clean & Bright box holds more detergent than the Soapy Suds box.
Step-by-step explanation:
The volume of the Soapy Suds Box is:
8 x 13 x 9 = 936 cubic inches
The volume of the Clean & Bright Box is:
13 x 12 x 8 = 1248 cubic inches
Therefore, the Clean & Bright box holds more detergent than the Soapy Suds box.
Help me with this question I begg
Answer:x= 39 , y= -6
Step-by-step explanation:
we have y = -6 (1)
x = -8y-9 (2)
Let (1) replace (2)
x = -8(-6)-9
x = 48-9 = 39
So x=39 , y=-6
Triangle ABC has vertices with A(x,3), B(-3,-1), C(-1,-4). Determine and state a value of x that would make triangle ABC a right triangle. Justify why trinagle ABC is a right angle
The value of x that would make triangle ABC a right triangle is x= 2. The justification is that the product of the slopes of two perpendicular lines is -1/2, and when the points are plugged into the distance formula, the sides satisfy the Pythagorean theorem.
To determine a value of x that would make triangle ABC a right triangle, we need to check if the square of the length of any two sides equals the square of the length of the third side.
We can use the distance formula to find the lengths of the sides of the triangle
AB = √((x + 3)² + 4²)
BC = √(2² + 3²)
CA = √((x + 1)² + 1²)
To make triangle ABC a right triangle, we need to find a value of x that satisfies the Pythagorean theorem
AB² + BC² = CA²
[(x + 3)² + 4²] + [2² + 3²] = [(x + 1)² + 1²]
Simplifying this equation yields
x² + 2x - 8 = 0
Solving for x, we get
x = 2 or x = -4
So, if x = 2 or x = -4, then triangle ABC is a right triangle.
To justify this, we can find the slopes of the line segments connecting the vertices of the triangle
mAB = (3 - (-1)) / (x - (-3)) = 4 / (x + 3)
mBC = (-4 - (-1)) / (-1 - (-3)) = -3/2
mCA = (3 - (-4)) / (x + 1 - (-1)) = 7 / (x + 2)
When x = 2, we get
mAB = 4/5
mBC = -3/2
mCA = 7/3
mAB * mBC = -2/5
mBC * mCA = -7/6
mCA * mAB = 14/15
when x = 2, triangle ABC is right triangle.
When x = -4, we get
mAB = 4/(-1) = -4
mBC = -3/2
mCA = 7/(-3) = -7/3
mAB * mBC = 6
mBC * mCA = 14/3
mCA * mAB = 7/2
when x = -4, triangle ABC is not a right triangle.
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What is the area of this figure?
Answer: 288
Step-by-step explanation:
2 × 6 × 2 × 4 × 3=288
The radius of Circle Upper A is 6 mm. The radius of Circle Upper B is 3 mm greater than the radius of Circle Upper A. The radius of Circle Upper C is 5 mm greater than the radius of Circle Upper B. The radius of Circle Upper D is 3 mm less than the radius of Circle Upper C. What is the area of each circle? How many times greater than the area of Circle Upper A is the area of Circle Upper D ?
The area of Circle D is 3.36 times greater than the area of Circle A.
What is circle?
A circle is a geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center.
We are given the following information about the radii of the four circles:
The radius of Circle A is 6 mm.
The radius of Circle B is 3 mm greater than the radius of Circle A, so it is 6 + 3 = 9 mm.
The radius of Circle C is 5 mm greater than the radius of Circle B, so it is 9 + 5 = 14 mm.
The radius of Circle D is 3 mm less than the radius of Circle C, so it is 14 - 3 = 11 mm.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
Therefore, we can calculate the areas of the four circles as follows:
The area of Circle A = π(6)² = 36π mm².
The area of Circle B = π(9)² = 81π mm².
The area of Circle C = π(14)² = 196π mm².
The area of Circle D = π(11)² = 121π mm².
To find out how many times greater the area of Circle D is than the area of Circle A, we can divide the area of Circle D by the area of Circle A:
Area of Circle D / Area of Circle A = (121π) / (36π) = 3.36
Therefore, the area of Circle D is 3.36 times greater than the area of Circle A.
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your summer job pays you $20 an hour (y=20x) and work every week between 5 to 20 hours
The solution is: y = 30x, is the equation for total pay (y) as a function of total hours worked (x).
Here, we have,
Because we are talking about over 8 hours.
The question states that you get 30$ per hour for overtime hours.
That means if you work over 8 hours your dollars per hour increases to 30.
So because the amount of dollars increases to 30 you can infer that all you have to do is make the same equation as the 20 dollar's per hour equation.
Except you put 30 making it y = 30x.
Hence, The solution is: y = 30x, is the equation for total pay (y) as a function of total hours worked (x).
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complete question:
A company pays $20 per hour for up to 8 hours of work, and $30 per hour for overtime hours (hours beyond 8 hours). For up to 8 hours worked, the equation for total pay (y) for hours worked (x) is y = 20x. For over 8 hours worked, what is the equation for total pay (y) as a function of total hours worked (x)?
100 POINTS!!!
Students were asked to prove the identity (cot x)(cos x) = csc x − sin x. Two students' work is given.
Student A
Step 1: cosine x over sine x times cosine x equals cosecant x minus sine x
Step 2: cosine squared x over sine x equals cosecant x minus sine x
Step 3: 1 minus sine squared x over sine x equals cosecant x minus sine x
Step 4: 1 over sine x minus sine squared x over sine x equals cosecant x minus sine x
Step 5: csc x − sin x = csc x − sin x
Student B
Step 1: cotangent x times cosine x equals 1 over sine x minus sine x
Step 2: cotangent x times cosine x equals 1 over sine x minus sine squared x over sine x
Step 3: cotangent x times cosine x equals 1 minus sine squared x over sine x
Step 4: cotangent x times cosine x equals cosine squared x over sine x
Step 5: cotangent x times cosine x equals cosine x over sine x times cosine x
Step 6: cot x cos x = cot x cos x
Part A: Did either student verify the identity properly? Explain why or why not.
Part B: Name two identities that were used in Student A's verification and the steps they appear in.
Neither student's work properly verifies the identity and csc x = 1/sin x, sin² x + cos² x = 1 are the two identities that were used in Student A's verification.
Part A:
Both Student A and Student B did not verify the identity properly. Student A started with the correct expression, but then manipulated it incorrectly.
In Step 1, multiplying cosine x over sine x times cosine x does not equal cosecant x minus sine x.
In Step 2, dividing cosine squared x by sine x also does not equal cosecant x minus sine x. Student B also started with the correct expression, but made a mistake in Step 2.
Subtracting sine squared x over sine x from 1 does not equal 1 over sine x minus sine squared x over sine x.
Therefore, neither student's work properly verifies the identity.
Part B:
Identity 1: csc x = 1/sin x
Student A uses this identity in Step 4 when they rewrite 1/sin x as csc x.
Identity 2: sin² x + cos² x = 1
Student A uses this identity in Step 3 when they rewrite cos² x as 1 - sin²x.
Hence, neither student's work properly verifies the identity and csc x = 1/sin x, sin² x + cos² x = 1 are the two identities that were used in Student A's verification.
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What are the answers?
According to the information, the view from above would have 8cm on each side and 6cm on each section of the base. On the other hand, the side view would be 4cm high in the roof part and 4cm in the wall part and 8cm in the base.
How to identify the correct measurements?To identify the correct measurements we must see the measurements in meters that the construction has. In this case the measurements are in meters, to make a scale model we must express each meter in 2cm. So, we must multiply the numbers of each section by 2 and put the expression "cm" to refer to the fact that they are centimeters. According to the above:
The view from above would have 8cm on each side and 6cm on each section of the base. On the other hand, the side view would be 4cm high in the roof part and 4cm in the wall part and 8cm in the base.
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Find z₁ X 2₂ for z₁ = 9 (cos 225° + i sin 225°) and z2 = 3 (cos 45° + i sin 45°). Express the product in
a + bi form.
Answer:
-3+0i
Step-by-step explanation:
have a good day :)
The International Space Station orbits the Earth at a height of 250 miles.
What is the height of the International Space Station in kilometres?
Use 8 kilometres equals 5 miles.
km?
Using unit conversions, the height of the International Space Station in kilometers is 400 kilometers.
What is unit conversion?Unit conversion enables the conversion of one unit to another.
Division and multiplication operations are heavily deployed in unit conversions.
These two basic mathematical operations help create the conversion factors for unit conversions.
The orbiting height of the International Space Station = 250 miles
5 miles = 8 kilometers
250 miles = 250 x 8/5 kilometers
= 400 kilometers
Thus, a height of 250 miles is the same as a height of 400 kilometers.
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150° arc of a circle has a length of 23.6 feet what is the radius of a circle
Answer:
The answer for the radius is approximately 18ft
Step-by-step explanation:
23.6ft=0/360×2pir
23.6=150/360×22/7×r
23.6=3300r/2520
cross multiply
23.6×2520=3300r
59472=3300r
divide both sides by 3300
3300r/3300=59472/3300
r=18.02
r≈18ft
The point D is plotted on the coordinate grid below. Plot the point D’, the reflection of D over the y-axis
The reflection of D (-1, 6) over the x - axis D' is(-1, -6)
What do you mean by reflection in a graph ?A reflection is a transformation representing a flip of a figure. Figures may be reflected in a point, a line, or a plane.
When reflecting a figure in a line or in a point, the image is congruent to the preimage.
A reflection maps every point of a figure to an image across a fixed line.
We have the coordinates of D is (-1, 6)
(x, y) => (x, -y)
We apply this reflection, we get:
and the reflection will be D' (-1 , -6)
Hence, The reflection of D (-1, 6) over the x - axis D' is (-1, -6)
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The given question is incomplete, complete question is:
The point D (-1, 6) is plotted on the coordinate grid below. Plot the point D’, the reflection of D over the y-axis
In 2010,musa got 750 bags of coffee from his farm in 2011 his yield reduced by 30%,2012 it rose up by 15% over that of 2011 a bag of coffee weighs 55kg and he paid 7900shs per tonne in 2010 thereafter the price per tone increased each year by 10% find his earnings from coffee for each of the three years hence their total income
Musa's earnings for the three years were approximately 325,875 shs, 250,951.25 shs, and 317,389.78 shs, and their total income was approximately 894,216.03 shs.
How to solve for the earningsFirst, let's find the number of bags of coffee for each year:
2010: 750 bags
2011: 750 - 0.3 * 750 = 750 - 225 = 525 bags
2012: 525 + 0.15 * 525 = 525 + 78.75 = 603.75 bags (rounding to 604 bags)
Now, let's find the total weight of coffee for each year in tonnes (1 tonne = 1000 kg):
2010: 750 * 55 kg = 41,250 kg = 41.25 tonnes
2011: 525 * 55 kg = 28,875 kg = 28.875 tonnes
2012: 604 * 55 kg = 33,220 kg = 33.22 tonnes
Next, let's find the price per tonne for each year:
2010: 7900 shs
2011: 7900 * 1.1 = 8690 shs
2012: 8690 * 1.1 = 9559 shs
Finally, let's calculate Musa's earnings for each year and their total income:
Earnings 2010: 41.25 * 7900 = 325,875 shs
Earnings 2011: 28.875 * 8690 = 250,951.25 shs
Earnings 2012: 33.22 * 9559 = 317,389.78 shs
Total income: 325,875 + 250,951.25 + 317,389.78 ≈ 894,216.03 shs
So, Musa's earnings for the three years were approximately 325,875 shs, 250,951.25 shs, and 317,389.78 shs, and their total income was approximately 894,216.03 shs.
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At Regan's Closet, 7/12 of the clothes are white and another 1/8 are black. What fraction of the clothes are either black or white?
The fraction of cloths which are either black or white is 17/24.
Given that, Regan has 7/12 of the clothes are white and another 1/8 are black.
We need to find the fraction of the clothes are either black or white,
To find the same, we need to simply add both the fractions,
7/12 + 1/8 = 14 + 3 / 24
= 17/24
Hence, the fraction of cloths which are either black or white is 17/24.
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The table shows the running time for different movies.
Create a line plot to display the data. To create a line plot, hover over each number on the number line. Then click and drag up to plot the data.
Answer:
Step-by-step explanation:
a teacher surveyed his class about how many wore watches and how many wore rings. the venn diagram shows her results. if a person from the class is randomly selected, what is the probability that person wears a watch given that they wear a ring?
The probability of selecting a person who wears a watch given that they wear a ring is 2/5 or 0.4.
From the Venn diagram, we can see that there are 10 people who wear rings, 2 of whom also wear watches. This means that the probability of randomly selecting a person who wears a ring is 10 out of the total number of people in the class. That is:
P(Ring) = 10 / (10+2) = 10/12
Similarly, we can find the probability of selecting a person who wears both a watch and a ring. From the diagram, we can see that there are 4 such people. Thus,
P(Watch and Ring) = 4 / (10+2) = 4/12
Using the formula for conditional probability, we get:
P(Watch|Ring) = P(Watch and Ring) / P(Ring)
Substituting the values we obtained earlier, we get:
P(Watch|Ring) = (4/12) / (10/12) = 4/10 = 2/5 or 0.4
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You have $11. 40 to buy drink boxes for the football team. Each drink box costs $0. 40 How many drink boxes can you buy? Should you expect to get change when you pay for the drink boxes? If so, how much?
The total number of boxes purchased using $11.40 and the remaining expected changed money received is 28 boxes and $0.20 respectively.
Total amount of money to buy drink boxes = $11.40
Cost of each drink box = $0.40
Number of drink boxes bought
= $11.40 ÷ $0.40/drink box
= 28.5 drink boxes
Since you cannot buy a fractional part of a drink box.
Round down to the nearest whole number.
Here, 28 drink boxes can be bought with the available money.
To determine expect change,
Subtract the total cost of the drink boxes from the amount of money available.
$11.40 − ($0.40/drink box × 28 drink boxes)
= $11.40 − $11.20
= $0.20
The amount of change is $0.20.
Therefore, the number of boxes bought with given amount is 28 boxes and the remaining expected amount of money received is $0.20 .
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Use the distributive property to fill in the blanks below
2 X (1+6) = (2 X _) + (2 X _)
Using the distributive property, the filled expression is 2 X (1+6) = (2 X 1) + (2 X 6)
Completing the expressionFrom the question, we have the following parameters that can be used in our computation:
2 X (1+6) = (2 X _) + (2 X _)
The distributive property states that
a * (b + c) = ab + ac
So, we have
2 X (1+6) = (2 X 1) + (2 X 6)
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can some one help me? i'll give you my discord to help with more im failing math
Answer:
Angle BAC
Step-by-step explanation:
The actual angle letter (in this case A) is ALWAYS in the center. The first and last letters are the ends of the lines that make the angle (B and C). You can put the first and last letters as BAC OR CAB, because either way you are describing the same angle.
I hope this helps :)
Express the function graphed on the axes below as a piecewise function.
The piecewise function in the graph is:
f(x) = 3 if -8 < x < - 2
f(x) = -0.5x + 5 for -2 < x - 6
How to define the piecewise function?First we can see a constant segment at y = 3 that starts at x = -8 and ends at x = -2
So we have:
f(x) = 3 if -8 < x < - 2
Then we have a line that starts at x = -2, and ends at x = 6
We can see that the y-intercept is 5, then we can write:
y = ax + 5
It also passes through (4, 3), replacing that:
3 = a*4 + 5
3 - 5 = a*4
-2 = a*4
-2/4 = a
-0.5 = a
Then the second part is:
f(x) = -0.5x + 5 for -2 < x - 6
The piecewise function is:
f(x) = 3 if -8 < x < - 2
f(x) = -0.5x + 5 for -2 < x - 6
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A carnival game uses this spinner to determine prizes. If each player spins the wheel once, how many players would you expect to spin beofre someone wins $500?
The number of players expect to spin before someone wins $500 in the game is equal to 16.
Number of times each player spin the wheel = once
Expected number of players who would spin the wheel before someone wins $500.
Calculate the probability of winning $500 on a single spin
And then use the formula for the expected value of a geometric distribution.
At the spinner, there are 16 equal sections.
And one of these sections is labeled with $500.
The probability of winning $500 on a single spin is,
P(winning $500) = 1/16
Next, use the formula for the expected value of a geometric distribution,
Expected value = 1 / P(winning)
Here, the probability of winning is 1/16,
so the expected value is equal to,
Expected value = 1 / (1/16)
= 16
Therefore, expected number of players spinning the wheel before someone wins $500 in this carnival game is 16.
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does anybody understand this problem? please help i’ll award whatever the things are
In the triangle the value of JL is 14.
Let us find the value of KJ which is hypotenuse
8²+6²=KJ²
64+36=KJ²
KJ=10
From the triangle KLM
tan 45= opposite side/adjacent side
1=6/ML
ML=6
So JL = 8+6
=14
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