The volume of the cone is 4.2 units cube.
How to find the volume of a cone?The volume of a cone can be calculated as follows:
Therefore,
volume of a cone = 1 / 3 πr²h
where
r = radius of the coneh = height of the coneTherefore,
r = 1.5 units
h = 1.8 units
volume of a cone = 1 / 3 × 22 / 7 × (1.5)² × 1.8
volume of a cone = 1 / 3 × 89.1 / 7
volume of a cone = 89.1 / 21
volume of a cone = 4.24285714286
volume of the cone = 4.2 units cube
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In triangle ABC, m∠B = (15x − 19)° and the measure of the exterior angle to ∠B is (9x − 17)°. Find m∠B.
116°
71°
64°
9°
Angle B, in the triangle ABC is solved to be 116 degrees
How to find angle BAngle B is solved using the concept of triangles and exterior angle relationship. This helps to know that addition of exterior angle to ∠B to angle B results to 180 degrees. Hence we have that:
exterior angle to ∠B + ∠B = 180
given data:
∠B = (15x − 19)°
exterior angle to ∠B is (9x − 17)°
plugging in gives
9x − 17 + 15x − 19 = 180
9x + 15x = 180 + 19 + 17
24x = 216
x = 9
For m∠B = (15x − 19)°
= 15 * 9 - 19
= 116 degrees
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How do the two plotted values compare, and what is their relationship to zero? The values are the same, and they have different distances to zero. The values are the same, and they are both three and one half units from zero. The values are opposites of each other and have different distances to zero. The values are opposites of each other, and they are both three and one half units from zero.
The correct statement regarding the values is given as follows:
The values are opposite from each other, and they are both 5/2 units from zero.
What is the absolute value function?The absolute value function is defined by the following piecewise rule, depending on the input of the function:
|x| = x, x ≥ 0.|x| = -x, x < 0.It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.
The values for this problem are given as follows:
-5/2.5/2.The numbers are the same, with the opposite signal, hence they are opposites.
Additionally, both numbers have the same absolute value of 5/2, hence they are both at a distance of 5/2 units from the origin.
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Destiny has $500 in her bank account . Each month. she adds 100 more
Answer:
Within one year, she'll have:
500 + 100 × 12 which is $1,700.
Quite unsure as the question seems incomplete. But based on the given details, here's your answer..
A charity is raising money by selling two thousand raffle tickets for $2 each. There is one grand prize worth $500, three secondary prizes worth $200 each, and eight third level prizes worth $20 each. What is the expected value of a $2 ticket? Answer is negative $1.358 but how do you calculate that?
The expected value of a $2 ticket is $0.63
How to determine the expected value of a $2 ticketTo calculate the expected value of a $2 ticket, we need to multiply the probability of winning by the value of the prize, then sum those products:
The Probability of winning the grand prize = 1/2000
Product: (1/2000) x $500 = $0.25
The Probability of winning a secondary prize: 3/2000
Product: (3/2000) x $200 = $0.30
The Probability of winning a third level prize: 8/2000
Product: (8/2000) x $20 = $0.08
The sum of the products:
$0.25 + $0.30 + $0.08 = $0.63
So the expected value of a $2 ticket is $0.63, meaning that on average, a person can expect to win $0.63 for every $2 they spend on a ticket.
The charity is expected to make a profit, which is why the answer is negative.
That is -$2 + $0.63 = -$1.37
So the expected profit for the charity per ticket sold is -$1.37, which is approximately the same as the given answer of negative $1.358(rounding off)
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Ocean waves move in parallel lines toward the shore. The figure shows the path that a windsurfer takes across several waves. For this exercise, think of the windsurfer's wake as a line. If m∠1 = (8x + 5y)° and m∠2 = (8x + y)°, find x and y.
78°
Answer:
x = 9.75 and y = 0
Step-by-step explanation:
Since the path of the windsurfer crosses both angles, we can use the fact that the sum of the angles around a point is 180 degrees to set up an equation:
m∠1 + m∠2 + m∠3 = 180°
We know that m∠1 = (8x + 5y)° and m∠2 = (8x + y)°. We can also see from the diagram that m∠3 = 180° - 78° = 102°. Substituting these values into the equation, we get:
(8x + 5y)° + (8x + y)° + 102° = 180°
Simplifying and solving for x and y, we get:
16x + 6y = 78°
8x = 78° - 6y
x = (78° - 6y)/8
We can substitute this expression for x into one of the earlier equations to solve for y:
8[(78° - 6y)/8] + y = 78°
78° - 6y + y = 78°
-5y = 0
y = 0
Now that we know y = 0, we can substitute this value into the equation we found for x:
x = (78° - 6(0))/8 = 9.75
Ceci was feeding her guinea pig fluffles 30 grams of food each day and she needs to reduce the food by 15%. How many grams of food should Fluffles get each day?
Ceci should give Fluffles 26 grams of food each day after the 15% reduction.
Given that the original amount of food: 30 grams/day
Now, calculate the 15% reduction:
30 grams/day x 0.15 = 4.5 grams/day
Subtract the reduction from the original amount:
30 grams/day - 4.5 grams/day = 25.5 grams/day
Round the answer to the nearest gram:
25.5 grams/day ≈ 26 grams/day
Thus, she should give Fluffles 26 grams of food each day after the 15% reduction.
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Please see attachment below!
Answer:
5cm
Step-by-step explanation:
According to Pythagoras Theorem:
a^2+b^2=c^2
Given,
a=3, b=4, c=x
3^2+4^2=x^2
9+16=x^2
25=x^2
25 sqrt= 5
Therefore the answer is 5cm.
In AKLM, m = 63 inches, m/K=24° and m/L=42°. Find the length of 1, to
the nearest inch.
The length of side l of the triangle using sine rule is: 46 inches
How to use sine rule?Sine rule is used to show the relationship between the sides and angles of a triangle. It is given as:
a/sinA = b/sinB = c/sinC
Where A, B, C are the angles and a, b and c are the opposite sides to the angles.
Thus:
63/sin 114 = l/sin 42
(63 * sin 42)/sin 114 = 46 inches
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A square pyramid has a base length of 6 inches and a height of 8 inches.
What is the volume of this pyramid?
Enter your answer in the box.
The volume of the pyramid will be equal to 96 in^3.
We are given that square pyramid has a base length of 6 inches and a height of 8 inches.
Suppose that the height of the pyramid is of h units, then:
[tex]v = \dfrac{l \times w \times h}{3} \: \rm unit^3[/tex] is the volume of that pyramid.
The base is a rectangle with length = L units, and width = W units, thus its area is:
[tex]b = l \times w\: \rm unit^2[/tex]
Therefore, the volume of the pyramid;
V = 1/3 a^2 h
V = 1/3(6^2)(8)
V = 1/3(36)(8)
V = 96 in^3
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A plane intersecting a cylinder
forms a rectangular cross-section
Which describes how the plane
intersects the cylinder?
Answer: A cylindric section is the intersection of a plane with a right circular cylinder.
If we cut a cylinder perpendicularly to its base, the figure formed is a rectangle with a length equal to the height of the cylinder and a length equal to its diameter.
HELP ASAP PLEASE! Find the probability that a point chosen randomly inside the rectangle is in each given shape. Round to the nearest tenth of a percent.
After considering all the given options we conclude that the probability of selecting a point inside the rectangle randomly falls outside the triangle, which is Option B.
The probability regarding a point selected randomly within the rectangle is in the square is given by the ratio of the area of the square to the area of the rectangle.
The evaluated area regarding the given square is
4² = 16 sq units.
The area of the rectangle is 12 x 8 = 96 sq units. Then , after evaluation the probability regarding a specified point taken randomly inside the rectangle is in the square is
16/96
= 1/6
= 0.1667 or 16.7%
The probability concerning a point taken randomly within the rectangle is outside the triangle is given by subtracting the area of the triangle from the area of the rectangle and then dividing by the area of the rectangle.
The area of the triangle is
(1/2) x base x height
= (1/2) x 4 x 5
= 10 sq units.
Then, the probability that a point chosen randomly inside the rectangle is outside the triangle is
(12 x 8 - 10)/(12 x 8)
= 94/96
= 0.9792 or 97.9%
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The following is a list of movie tickets sold each day for 10 days.
7, 18, 23, 41, 34, 12, 48, 65, 57, 52
Which of the following intervals are appropriate to use when creating a histogram of the data?
0 – 9, 10 – 19, 20 – 29, 30 – 39, 40 – 50
0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74
0 – 15, 15 – 20, 20 – 35, 35 – 60, 60 – 75
0 – 20, 20 – 40, 40 – 60, 60 – 80
The appropriate intervals to use when creating a histogram of the data are:
0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74.
Given information:
The following is a list of movie tickets sold each day for 10 days.
7, 18, 23, 41, 34, 12, 48, 65, 57, 52.
When creating a histogram, you want to group the data into intervals or bins.
The intervals should be chosen so that they are of equal size, and they should also include all the data values.
In this case, the data values range from 7 to 65, so we need to choose intervals that cover this range.
The appropriate intervals to use when creating a histogram of the data are:
0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74
These intervals capture the range of values in the data set and have equal widths, making it easy to create a histogram.
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shawn deposits $100 every year into a savings account that pays interest at a rate of 3.5% per year, compounded annually. How much money will there be in his account at the end of 4 years
A-214.25
B-210.62
C-207
D-270
The amount of money that should be in the account at the end of 4 years of investment would be = $114.
How to calculate the amount of money in a given account?To calculate the total amount of money that will be in an account at the end of a given time can be calculated using the given formula below;
Simple interest = principal× time×rate/100
where;
principal = $100
rate = 3.5%
time = 4 years
simple interest = 100×3.5×4/100
= 14
Therefore the total amount of money that will be in the account at the end of 4 years = 100+14 = $114.
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What is 6 [4(-5)^n-1] n=1 equal to
The value of 6 [4(-5)^n-1] when n is 1 is 24
What is substitution of variable?This simply means replacing a known value for an unknown value in an expression.
For example, 5x²+2 , the value of the expression when x is -2 is solved by substituting -2 for x in the expression.
5x²+2 = 5(-2)² +2
= 5×4 +2
= 20+2
= 22
Similarly, the value of 6 [4(-5)^n-1] when n= 1 can be calculated by substituting 1 for n in the expression.
6 [4(-5)^n-1] = 6(4(-5)^1-1)
= 6(4(5)^0)
= 6 × 4 × 1
= 24
Therefore the value of 6 [4(-5)^n-1] when n= 1 is 24
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NO LINKS!! URGENT HELP PLEASE!!!
Find an equation of the circle that has center C(7, -2) and is tangent to the line y = 5
Answer:
[tex](x-7)^2+(y+2)^2=49[/tex]
Step-by-step explanation:
A tangent of a circle is a straight line that touches the circle at only one point.
Since the circle is tangent to the horizontal line y = 5, the distance between the center of the circle and the line y = 5 is equal to the radius of the circle.
Given the center of the circle is C(7, -2), the y-coordinate of the center is y = -2. Therefore, the radius of the circle is the difference between y = 5 and y = -2:
[tex]\implies r=5-(-2)=7[/tex]
The equation of a circle is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where (h, k) is the center and r is the radius.
Substitute the given center (7, -2) and found radius, r = 7, into the equation of circle:
[tex](x-7)^2+(y-(-2))^2=7^2[/tex]
Simplify:
[tex](x-7)^2+(y+2)^2=49[/tex]
Therefore, the equation of the circle that has center C(7, -2) and is tangent to the line y = 5 is:
[tex]\boxed{(x-7)^2+(y+2)^2=49}[/tex]
One particular 13-foot tall cone of dry sand has a base diameter of 38.2 feet. To the nearest tenth of a degree, what is the angle of repose of this type of dry sand?
A different conical pile of the same type of sand as before (which will have the same angle of repose) is 10 feet tall. What is the diameter of the cone’s base?
Answer:
Step-by-step explanation:
34.0 degrees, 29.6 feet in Diameter.
This is a right triangle trigonometry question.
Use half of the diameter to form the base of the triangle (19.3 ft) with a height 0f 13.
Use Inverse Tangent function to find the angle of repose
round to 34.0
then use the angle of repose to solve trigonometric function of the tangent for the radius of the other cone.
switch denominator and tangent
multiply by 2 to get diameter of second cone
14.82*2≈29.6
Determine if the following is traversable. Then trace the object. If the network is not traversable, say why.
In the realm of computer networking, a traversable network is a structure in which any message or packet can be efficiently transmitted from one node to another without impediment.
What is the traversable network?Essentially, this implies that all nodes within the network are interconnected, devoid of any isolated segments that could impede data transmissions.
It should be noted that to ensure a network's traversability, several paths may be established between two given nodes or it might connect each node to a key switch or hub for communication purposes. Designing a topology with reliability and expedience at the core is essential for facilitating successful functioning, as traversable networks allow for information and resources to be sent swiftly - and without potential delay or loss. An overview was given based on the information.
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Four friends attend the cinema and buy tickets using this offer.
"Buy 3 tickets and get a ticket free."
They each pay £6.30
How much does a ticket cost?
Answer: The cost of a single ticket is £6.30.
Step-by-step explanation: The group bought 4 tickets and got one for free, which means they paid for 3 tickets. If each of them paid £6.30, then the total amount paid is 4 x £6.30 = £25.20.
To find the cost of a single ticket, we can divide the total paid by the number of tickets bought, which is 4:
£25.20 ÷ 4 = £6.30
Therefore, the cost of a single ticket is £6.30.
Use decomposition to find the area of the figure.
10 yd
8 yd
The area is
13 yd
square yards.
Answer:
The area is 92 square yards.
Step-by-step explanation:
We can decompose this figure into a rectangle and a triangle.
First, we can find the area of the rectangle.
A(rect) = length × width
A(rect) = 10 × 8
A(rect) = 80 yd²
Next, we can find the area of the triangle.
A(triangle) = (1/2) × base × height
[tex]A(\text{triangle}) = \dfrac{1}{2} \, (13 - 10) \times 8[/tex]
[tex]A(\text{triangle}) = \dfrac{3}{2} \times 8[/tex]
[tex]A(\text{triangle}) = 12 \text{ yd}^2[/tex]
Finally, we can add the two shapes' areas to get the area of the entire figure.
A = A(rect) + A(triangle)
A = 80 yd² + 12 yd²
A = 92 yd²
Answer: 92 yd²
Step-by-step explanation:
Decomposition means to break the shape into parts, but it's not necessary to break apart.
This is a trapezoid turned sideways A=1/2(b1+b1)h
b1=10
b2=13
h=8
A=1/2(10+13)8 =92 yd²
if you decompose, you can make the top a triangle and bottom a rectangle.
A(triangle) = 1/2(b)(h) b=3 h=8
1/2(b)(h)
= 12
A(rectangle)=bh b=10 h=8
=10*8
=80
Add the 2 and you get 92 again
Solve the following for θ, in radians, where 0≤θ<2π.
cos^2(θ)+7cos(θ)+4=0
Select all that apply:
4.03
2.65
1.65
2.25
1.43
The range of the cosine function is [-1, 1], there are no real solutions for θ in the given range.
We have,
We can solve the given quadratic equation for cos(θ) using the quadratic formula:
cos(θ) = (-b ± sqrt(b^2 - 4ac)) / 2a
Here, a = 1, b = 7, and c = 4.
Substituting these values, we get:
cos(θ) = (-7 ± √(7² - 4(1)(4))) / 2(1)
cos(θ) = (-7 ± √(41)) / 2
Since 0 ≤ θ < 2π, we need to consider only the solutions that lie in this range.
Using a calculator, we get:
cos(θ) ≈ -3.03 or -0.65
Since the range of the cosine function is [-1, 1], there are no real solutions for θ in the given range.
Therefore,
None of the given options (4.03, 2.65, 1.65, 2.25, 1.43) is correct.
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A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 90% confidence if (a) she uses a previous estimate of 0.58? (b) she does not use any prior estimates? refer to picture to view the table of critical values. (a) n = ? (Round up to the nearest integer.). b.) n=?
If she uses a previous estimate of 0.58, n = 733
If she does not use any prior estimates, n = 752
How to solve for the estimatesHere, E is given as 0.03
For 90% confidence level, Z* = 1.645
Using formula for margin of error we have
0.03 = 1.645 x (√0.58(1 - 0.58) / n)
n = 733
without prior estimates the value of p = 0.5
Then we have
0.03 = 1.645 x (√0.5(1 - 0.5) / n)
n = 752
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The variables x and y vary inversely. Use x=−3 and y=4 to write an equation relating x and y. Then find y when x=6 .
Step-by-step explanation:
If x and y vary inversely, we can write the equation:
xy = k
where k is a constant of proportionality. To solve for k, we can use the values x = -3 and y = 4:
(-3)(4) = k
-12 = k
So the equation relating x and y is:
xy = -12
To find y when x = 6, we can plug in these values and solve for y:
(6)y = -12
y = -2
So when x = 6, y = -2.
If the mass of a solid is 25 g and its volume is 50 cm³, what is its density?
Answer:
0.2 because Density = Mass / Volume
Density = 25 / 50
Density= 0.2 g/cubic cm
Question 10 of 25
Suppose g(x) = f(x-1)-5. Which statement best compares the graph of
g(x) with the graph of f(x)?
A. The graph of g(x) is shifted 1 unit left and 5 units down.
B. The graph of g(x) is shifted 1 unit left and 5 units up.
C. The graph of g(x) is shifted 1 unit right and 5 units down.
D. The graph of g(x) is shifted 1 unit right and 5 units up.
SUBMI
The graph of g(x) = f(x - 1) - 5 is: C: The graph of g(x) is shifted 1 unit right and 5 units down.
How to Interpret Transformed Functions?Some of the terminologies in shifting of functions are:
1. Shift graph functions y = f(x) to the left: This means that we will be adding inside the function.
y= f(x + b) , where b is constant
2. Shift graph function y = f(x) to the right means that we will be subtracting inside the function
y = f(x - b)
3. To shift graph function y = f(x) up by b units means that we would be adding outside the function:
y = f(x) + b
4. To shift graph down by b units means that we would be subtracting outside the function:
y = f(x) - b
Therefore, by the definition we can say that the graph of g(x) = f(x-1)-5 is the graph of f(x) 1 units to the right and 5 units down.
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Four functions are given below. Either the function is defined explicitly, or the entire graph of the function is shown.
For each, decide whether it is an even function, an odd function, or neither.
Answer:
Step-by-step explanation:
even function is symmetric along the y-axis
the y-axis acts like a mirror
f(x) = f(-x) for any real x
odd function is similar to even function except
one side is up-side-down. (rotational symmetric by 180 degree)
odd function is nice property since the definite integral
from -a to a always equals to 0
f(x) = -f(-x) for any real x
top-left:
even
top-right:
odd
bottom-left:
Neither
bottom-right:
odd
Rick wants to determine if there is a correlation between the age and the cost of a used car.
What can be interpreted from this data?
There is no correlation between age and the cost of a used car
What can be interpreted from the scatter plotFrom the question, we have the following parameters that can be used in our computation:
The scatter plot
Where
x = Age
y = cost of used car
From the graph, we can see that
The points on the graph are scattered and they do not follow a definite pattern
This means that the scatter plot shows no correlation
And as such the correct option is (d)
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What is the nth term of the quadratic sequence -4,-1,4,11,20
Answer:
76
Step-by-step explanation:
the second number = the first one + 3
the third number = the second one + 5
the fourth number = the third one + 7
the fifth number = the fourth one + 9
because of this, we can know that we add an odd number to the left number
so
sixth = 20+11=31
seventh = 31+13=44
eighth = 44+15=59
ninth = 59+17=76
A soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
28.26 gallons
113.04 gallons
211.38 gallons
845.54 gallons
Therefore, after the water cooler is fully filled, there will be about 211.38 gallons of water inside.
What is a gallon?Eight pints or 4.564 liters make up a gallon, a unit of liquid or dry capacity.
The cylinder's diameter is specified as 3 feet, so its radius must be half that, or 1.5 feet. The cylinder is described as having a height of 4 feet.
When we enter these values into the formula, we obtain:
V is equal to (1.5)2(4) = 28.26 cubic feet.
We are aware that one cubic foot contains about 7.48 gallons of water. Therefore, we need to multiply the volume of the cylinder by 7.48 to get how many gallons of water are in the water cooler when it is fully filled.
The result of multiplying 28.26 by 7.48 is:
211.38 liters
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Point A is the center of this circle.
The ratio of the lengths of
to
is 2 : 1.
The required ratio of the lengths EF and AD is 2:1 for the given circle.
Given that a circle A with points B, C, D, E, F, and I on its circumference.
A chord of the circle is a line that connects any two locations on the circumference of any circle. The circle chords are BC, EF, and HI in this case.
The radius of the circle is defined as the line connecting center A with any point on the circle's perimeter. AD indicates the radius of the circle.
The diameter of the circle is any chord that passes through the center of the circle. The diameters of the circle are represented by EF and HI.
A diameter is usually twice as long as a radius.
As a result, the diameter-to-radius ratio will be 2:1.
Therefore, the required ratio of the lengths EF and AD is 2:1
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The missing figure has been attached below.
Find the area of the shaded sector of the circle to the nearest tenth
Answer:
Area of shaded portion= (θ/360º) × πrr
32/360°×22/7×3cm×3cm
(Simplify)
=2.514cm×cm
To nearest tenth= 2.500cm×cm
