If a trapezoid has bases with lengths of 10 cm and 20 cm, and the height is 12 cm, what is the area
of the trapezoid?
Answer:
180
((10 + 20/2) * 12 = 180
Step-by-step explanation:
Step-by-step explanation:
Given;
b = 10cm
a = 20cm
h = 12cm
Area of trapezoid = 1/2 *h*(a+b)
= 1/2 *12* ( 20+10)
= 180cm^2
Find the volume of a cone that has a radius of 8 meters and a height of 9 meters. Use 3.14 for pi
Answer:
Volume of cone = 1/3 Area of base × height
= 1/3× πr² × h
= 1/3×3.14×8²×9
= 602.88 m³
Answer:
602.44 cubic meters[tex] \: [/tex]
Step-by-step explanation:
In the question, it is given that a cone has a radius of 8 meters and a height of 9 meters and we have to find the volume of the cone.
[tex] \: [/tex]
To Find the volume of the cone, we must know this formula :
[tex] \\{\longrightarrow{ \qquad{\underline{\boxed {\pmb{\frak { Volume_{(cone) }= \dfrac{1}{3} \: \pi {r}^{2}h }}}}}}} \\ \\[/tex]
Where,
r refers to the radius of the cone.h refers to the height of the cone.Now, we will substitute the values in the formula :
[tex] \\ {\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times {(8)}^{2} \times 9 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 64 \times 9 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 3.14 \times 576 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1}{3} \times 1808 .64 }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\sf { Volume_{(cone) }= \dfrac{1808 .64}{3} }}}}}}} \\ \\[/tex]
[tex]{\longrightarrow{ \qquad{{ {\pmb{\frak { Volume_{(cone) }= 602.88 }}}}}}} \\ \\[/tex]
Therefore,
The volume of the cone is 602.88 m³What if there were only 200 days in a year? How many people would need to be in a room before the probability that two people shared a birthday exceeded 50%?
According to the calculation, 301 people would be needed a room for the probability that two people shared a birthday to be higher than 50%.
ProbabilityTo determine, if there were only 200 days in a year, how many people would need to be in a room before the probability that two people shared a birthday exceeded 50%, the following calculation must be performed:
200 days / 200 people = 200 / 200 = 1300 / 200 = 1.5301 / 200 = 1,505Therefore, 301 people would be needed a room for the probability that two people shared a birthday to be higher than 50%.
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arrange in ascending order : 39, 31, 50, 18, 51, 63, 10, 34, 42, 89, 73, 11, 33, 31, 41, 25, 76, 13, 26, 23, 29, 30, 51, 91, 37, 64, 19, 86, 9, 20
Step-by-step explanation:
9, 10,11, 13,18,19,20,23,25,26,29,30,31,31,33,34,37,39,41,42,50,51,51,63,64,73,76,86,89,91
Answer:
9, 10, 11, 13, 18, 19, 20, 23, 25, 26, 29, 30, 31, 31, 33, 34, 37, 39, 41, 42, 50, 51, 51, 63, 64, 73, 76, 86, 89, 91
Santa seated his guests so that X number of people sat at each of Y number of tables. Mrs. Claus placed Y number of people at each table, but she had X number of tables. Compare the number of guests Santa and Mrs. Claus were able to seat.
Answer:
they are the same
Step-by-step explanation:
The number of guests seated were, in each case, ...
(guests per table) × (number of tables)
__
For Santa, this product is ...
X × Y
For Mrs. Claus, this product is ...
Y × X
The commutative property of multiplication tells you that ...
XY = YX
The numbers of guests were the same.
A right circular cylinder has a height of 2214 ft and a diameter 225 times its height.
What is the volume of the cylinder?
Enter your answer as a decimal in the box. Use 3.14 for pi and round only your final answer to the nearest hundredth.
Answer:
v = 3,463,118,874
Step-by-step explanation:
2214 * 225 = 498,510
diameter = 498,510
v = pi(d) * h
v = 3.14(498,510) * 2214
v = 1,564,191 * 2214
v = 3,463,118,874
A camera lens magnifies an object 10 exponent 3 times. The length of an object is
10 exponent -4 centimeter. What is its magnified length?
Answer:
10^3/10^-4
Step-by-step explanation:
FROM MATH MULLIGAN
What is Lens Focal Length
Focal length, usually represented in millimeters (mm), is the basic description of a photographic lens. It is not a measurement of the actual length of a lens, but a calculation of an optical distance from the point where light rays converge to form a sharp image of an object to the digital sensor or 35mm film at the focal plane in the camera. The focal length of a lens is determined when the lens is focused at infinity.
Lens focal length tells us the angle of view—how much of the scene will be captured—and the magnification—how large individual elements will be. The longer the focal length, the narrower the angle of view and the higher the magnification. The shorter the focal length, the wider the angle of view and the lower the magnification.
The magnified length of the object is 10⁻¹ m
What is magnified length?An image is said to be magnified when its size is greater than that of the object, and it is said to be diminished when its size is smaller than that of the object.
Given that,
A microscope magnifies an object 10³ times. The length of an object is 10⁻⁴ meters. The magnified length is:
10³ × 10⁻⁴ m
We can solve this by applying the Product of Powers Property. This property states that to multiply powers having the same base, we have to add the exponents.
10³ × 10⁻⁴ m
= 10³⁺⁽⁻⁴⁾ m
= 10³⁻⁴ m
= 10⁻¹ m
Hence, the magnified length is 10⁻¹ m.
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Oscar's spinner has scores from 1 to 4. The table shows the probabilities of scores 1, 2 and 3
1=0.1
2=0.5
3.0.1
4=?
Work out 4
given the room below describe how you would find the perimeter and area?
Perform the following
mathematical operation, and
report the answer to the
correct number of significant
figures.
45.2 x 0.035 =
Answer:
4
Step-by-step explanation:
45.2 x 0.035=1.582
"Significant figures are the number of digits in a value, often a measurement, that contribute to the degree of accuracy of the value. We start counting significant figures at the first non-zero digit." -Khan Academy. org > significant figures
Answer: 1.6 is the answer
Step-by-step explanation:
45.2 x 0.035 = 1.582
After you do that step Then you'll need to round 1.582 up in the tenths, and it should be 1.6!
Hope this helps
The problem is on the screenshot
Answer:
x=1 y=4
x=2 y=7
x=3 y=10
Step-by-step explanation:
To find the answer, you have to plug in the x-value for the equation to find y.
You will then find out that every time x increases by 1, y increases by 3.
Shaquil needs to borrow $400. the loan company charges him $80 in fees for the loan. shaquil calculates that the annual percentage rate (apr) on his loan is 250%. approximately what is the term of shaquil’s loan? a. 7 days b. 29 days c. 46 days d. 73 days please select the best answer from the choices provided a b c d
The term of shaquil's loan will be 29 days approximatly.
We have given that,
Principle amount (p) = $400
Rate (r)= 250% = 2.5
Interest = $80
t = time (in days) = t/365
What is the formula simple interest?
[tex]I=prt[/tex]
[tex]r=\frac{I}{rt}[/tex]
[tex]2.5 = \frac{80\times 365}{400\times t}[/tex]
[tex]t= \frac{80\times 365}{400\times 2.5}[/tex]
[tex]t=\frac{73}{2.5}\\ \\t=29.2[/tex]
t = 29.2
t = 29 days
Therefore option (B) is correct.
Therefore the term of shaquil's loan will be 29 days approximatly.
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Answer:
B.29 days
Step-by-step explanation:
Prove: An even times an even is
an even.
Answer: 4
Step-by-step explanation:
i just guessed and it was right, sorry i don't have a better explanation than that
what are the magnitude and direction of u+v+w ?
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°.
How to determine the magnitude and the direction of a resultantVectors are elements with two given characteristics: Magnitude and direction. A resultant is derived from the sum of vectors, the magnitude is the norm of a vector and the direction is the orientation of a vector. The resultant and its characteristics are described below:
Resultant[tex]\vec r = \left(\sum\limits_{i=1}^{n}x_{i}, \sum\limits_{i=1}^{n}y_{i}\right)[/tex] (1)
Magnitude[tex]\|\vec r\| = \sqrt{\left(\sum\limits_{i=1}^{n} x_{i}\right)^{2}+\left(\sum\limits_{i=1}^{n} y_{i}\right)^{2}}[/tex] (2)
Direction[tex]\theta = \tan^{-1}\frac{\sum\limits_{i=1}^{n}y_{i}}{\sum\limits_{i=1}^{n}x_{i}}[/tex] (3)
Where [tex]\theta[/tex] is resultant angle, measured in degrees.
If we know that [tex]\|\vec u\| = 90[/tex], [tex]\theta_{u} = 40^{\circ}[/tex], [tex]\|\vec v\| = 60[/tex], [tex]\theta_{v} = 20^{\circ}[/tex], [tex]\|\vec w\| = 40[/tex] and [tex]\theta_{w} = 30^{\circ}[/tex], then the resultant, its magnitude and its direction:
Resultant[tex]\vec r = (-90\cdot \cos 40^{\circ}-60\cdot \sin 20^{\circ}+40\cdot \cos 30^{\circ}, 40\cdot \sin 30^{\circ}+60\cdot \cos 20^{\circ}-90\cdot \sin 40^{\circ})[/tex]
[tex]\vec r = (-54.824, 18.531)[/tex]
Magnitude[tex]\|\vec r\| = \sqrt{(-54.824)^{2}+18.531^{2}}[/tex]
[tex]\|\vec r\| \approx 57.871[/tex]
Direction[tex]\theta = \tan^{-1} \left(\frac{18.531}{-54.824}\right)[/tex]
[tex]\theta \approx 198.676^{\circ}[/tex]
The magnitude and the direction of the resultant are approximately 57.871 and 198.676°. [tex]\blacksquare[/tex]
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Find the length indicated. Round answer to the nearest tenth.
Please and thank you so very much!!!!! See picture for the full problem.
Answer:
18.1
Step-by-step explanation:
All radii of a circle are congruent (same length), which means if we draw in a radius from the center to the end of the 16.3, it would be the same length of x.
Now we can use sa very simple theorem.... the pythagorean therom!
[tex]7.9^{2} + 16.3^{2} = x^{2} \\62.41 + 265.69 = x^{2} \\328.1 = x^{2} \\18.1 = x[/tex](rounded)
I hope this helps you.
a farmer receives 65% of proceeds of the sale of a crop of wheat. if the wheat is sold for $62,400. How much does he receive?
Answer:
40,560
Step-by-step explanation:
To find how much the farmer recives, we simply multiply:
62,400 * 65% = 40,560
Helppp plssssss!!!!!!
Find the surface area of the above solid.
O A 72 cm
O B 73 cm.
C. 70 cm
O a 62cm
Help quickly
Scientists are looking for a drone that crashed into a forest. They decide to use a map and conduct a
circular search to find the missing drone according to the equation y? + y2 - 12x - 4y + 24 = 0 in miles.
Which of the following statements are correct? Select all that apply.
A. The search radius is less than 5 miles.
B. The search radius more than 10 miles.
C. The search is centered on the map at point (12, -4).
D. The search is centered on the map at point (-2, -6).
E. The search is centered on the map at point (6, 2).
Select all the true statements about the following parallelogram
Answer:
it is D. and A.
Step-by-step explanation:
um because
Jeffrey is looking at a map of his town to help him get from his school to the library. If 1 inch is equal to 9 miles, and the distance on the map is 1/4
inch, how far is it to the library?
Answer:
2.25 miles
Step-by-step explanation:
1/4 of 9 is 2.25
Answer:
2.25 miles away
Step-by-step explanation:
first make 1/4 a percent
second set up a proportion
then solve the proportion and then you get 2.25 and add a label
Compare using >, < or =
7 x 5/4 _ 7
How do you know your answer is correct?
Choose 1 answer:
A. Because we are multiplying 7 by a fraction that is less than 1.
B. Because we are multiplying 7 by a fraction that is equal to 1
C. Because we are multiplying 7 by a fraction that is greater than 1.
I think the answer will be:
C but i not that sure
Answer:
C. Because we are multiplying 7 by a fraction that is greater than 1.
Step-by-step explanation:
- Sumin -
Find the volume of the cylinder. Explain or show your reasoning. All measurements are in centimeters
Answer:
200π cm³ (in term of π)
628 cm³ (when define π = 3.14)
Step-by-step explanation:
Given:
radius of circular base = 5height = 8Volume of Cylinder:
[tex]\displaystyle \large{V=\pi r^2h}[/tex]
If you notice, the volume of cylinder is area of circular base * height.
Input given information in the formula:
[tex]\displaystyle \large{V=\pi \cdot 5^2 \cdot 8}[/tex]
Evaluate:
[tex]\displaystyle \large{V=\pi \cdot 25 \cdot 8}\\\displaystyle \large{V=200 \pi}[/tex]
Since all measurements are in centimeters. Therefore, our unit is cm³ since we are finding volume which is three-dimensional.
Fact
cm is used for one-dimensional measurement such as line.cm² is used for two-dimensional measurement such as area.cm³ is used for three-dimensional measurement such as volume.However, you didn’t specific which π value/digit should we use so I’ll only put both solutions in where first being in term of π and second being 3.14.
Therefore, the volume is:
200π cm³628 cm³pls help me i have a 0 for math
Answer:3p
Step-by-step explanation:
405 0p x 7
The solution set of the system of inequalities below forms a triangle on the coordinate plane. What are the vertices of the triangle?
a.
(0,10), (3,4), (8,14)
c.
(-20,0),(1,0),(8/14)
b.
(0,0), (8,0), (8,14)
d.
(0,10),(3,4),(6,10)
i think its a but i may be rong if i am just know i tryed my vary best and that i am super sorry
Line A is perpendicular to Line B.
If the slope of Line A is 3
what is the slope of Line B?
Answer:
- 1/3
Step-by-step explanation:
m = slope of a line
Perpindicular slope = - 1/m
= - 1/3
Let slope of that line be m
We know product of slopes of two perpendicular line=-1
3m=-1m=-1/3Can someone help me understand how to solve 4 please. Would really appreciate it.
The length of RT from the figure is 8 units
Pythagoras theorem applicationIn order to find the measure of RT, we will use the pythagoras theorem. According to the theorem;
hypotenuse² = adjacent² + opposite²
From the given figure;
ST = hyp = 10
RS = adj = 6
Find RT
RT = √10² - 6²
RT = √100 - 36
RT = √64
RT = 8 units
Hence the length of RT from the figure is 8 units
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(Look at screenshot)
7. The graph represents the height of a passenger car on a ferris wheel, in feet, as a
function of time, in seconds.
Use the graph to help you:
a. Find H(0).
b. Does H(t)=0 have a solution? Explain how you know.
c. Describe the domain of the function.
d. Describe the range of the function.
Step-by-step explanation:
Use the graph to dtermine the answer for each part of question
a)
H(0) = 5b)
H(t) = 0 has no solution as its minimum value is 5 feetc)
The domain all positive rational numbers, since time is zero or positive.d)
The range changes between 5 and 55 feet, according to the graph.Answer:
a. 5 ft
b. No - see below
c. [0, ∞)
d. [5, 55]
Step-by-step explanation:
From inspection of the graph:
x-axis: t = time (in seconds)y-axis: H(t) = height (in feet)Part a
When H(0), t = 0 ⇒ y-intercept.
Therefore, from inspection of the graph, H(0) = 5 ft
Part b
H(t) = 0 does not have a solution as the curve never touches the y-axis (when y = 0).
Part c
Domain: set of all possible input values (x-values)
The domain is time (t) (x-axis), therefore the domain is [0, ∞)
Part d
Range: set of all possible output values (y-values)
From inspection of the graph, the lowest value of H(t) is 5 and the highest value of H(t) is 55. Therefore, the range is [5, 55]
Which of the following is a linear function?
A. y=1 over x
B. y=x²
C. y=x
D. y=√x
Answer:
C
Step-by-step explanation:
One day, a person went to a horse racing area. Instead of counting the number of humans and horses, he counted 74 heads and 196 legs. How many humans and horses were there?
A. 37 humans and 98 horses
B. 24 horses and 50 humans
C. 31 horses and 74 humans
D. 24 humans and 50 horses
Answer:
the answer is a
Step-by-step explanation:
Answer:
B. 24 horses and 50 humans
Step-by-step explanation:
74 x 2 = 148
196 - 148 = 48
48/2 = 24 (number of horses)
74 heads - 24 horses = 50 humans
