Find the lateral area and the surface area of the composite solid. Keep answer in exact form.
10 cm
12 cm
1
1
1
1
32 cm
10 cm
Lateral Area
Surface Area
Answers
Answer:
a) Lateral area of the solid = 2011.43 [tex]cm^{2}[/tex]
b) Surface area of the solid = 2544 [tex]cm^{2}[/tex]
Step-by-step explanation:
a) Lateral area of the figure = 2[tex]\pi[/tex]rh
where; r is the radius of the cylinder, and h is its height.
Lateral area of the figure = 2 x [tex]\frac{22}{7}[/tex] x 10 x 32
= 2011.43 [tex]cm^{2}[/tex]
b) The surface area = 2[tex]\pi[/tex]r(r + h) - 2([tex]\frac{1}{2}[/tex] x b x h)
= 2[tex]\pi[/tex]r(r + h) - (b x h)
The height of the isosceles triangle can be determined by applying the Pythagoras theorem to have,
[tex]10^{2}[/tex] = [tex]6^{2}[/tex] + [tex]h^{2}[/tex]
100 = 36 + [tex]h^{2}[/tex]
[tex]h^{2}[/tex] = 100 - 36
= 64
h = [tex]\sqrt{64}[/tex]
= 8
h = 8 cm
The surface area of the solid = 2 x [tex]\frac{22}{7}[/tex] x 10 (10 + 32) - 12 x 8
= 2640 - 96
= 2544
The surface area of the solid is 2544 [tex]cm^{2}[/tex].
Related Questions
Select all statements below that are true about the box plots shown.
1) The interquartile range for the cars going North is higher than the interquartile range for the cars going South.
2) The median speed for the cars going North is higher than the median speed for the cars going South.
3) The interquartile range for the cars going South is 9.
4) The interquartile range for the cars going North is 27.
5) The maximum speed for the cars going North is higher than the maximum speed for the cars going South.
6. The lower quartile for the cars going North is lower than the lower quartile for the cars going South.
Answers
In other words, choices 2 and 4 are false while everything else is true.
==========================================================
Explanation:
The boxplot, or box-and-whisker plot, is a visual way to display a five number summary. Recall that the five items of a five number summary are:
MinQ1MedianQ3MaxThe min and max are exactly what they sound like: They're the smallest and largest values. Visually, this means they are the left and right most edges of the whiskers. This assumes that there are no outliers on either side.
The visual representation of Q1 and Q3 are the left and right edges of the box in that order. The gap between them is the IQR (interquartile range). The wider the box, the larger the IQR will be. The diagram shows the north cars have a larger IQR compared to the south ones.
Choice 1) is one of the answers since it is a true statement.
-------------------
The median is visually shown as a vertical line somewhere inside the box. It doesn't have to be at the exact midpoint of the left and right edges. We could have the median be closer to the left edge for instance, as the north cars boxplot shows.
Choice 2 is false because the diagram shows that the cars going south have a higher median speed, due to that lower vertical line being more to the right compared to the upper vertical line. In other words, the median speed of the cars going south is 64 mph while the median speed of the cars going north is 62 mph.
-------------------
Choice 3 is a bit tricky since the left edge of the blue box isn't lined up with a value on the number line. But it appears to be halfway between 58 and 60, so it seems like Q1 = 59 for the southbound cars. The value of Q3 for the southbound cars is Q3 = 68. The IQR is therefore,
IQR = Q3 - Q1 = 68-59 = 9
It's very likely that choice 3 is true
-------------------
For the northbound cars, we have
Q1 = 56
Q3 = 71 (assuming the right edge of the green box is exactly in the middle of the tickmarks of 70 and 72)
So,
IQR = Q3 - Q1 = 71 - 56 = 15
We don't get a result of 27, so choice 4 is not a true statement.
-------------------
Choice 5 is a true statement. The max speed of the northbound cars is larger than the max of the southbound cars. This is because the right tip of the north's whisker is further to the right compared to the south's corresponding whisker.
-------------------
The lower quartile is another name for "Q1" or "first quartile". So we'll be looking at the left edges of each box. The northbound cars have a smaller Q1 value because
Q1 = 56 for northbound cars
Q1 = 59 (or somewhere between 58 and 60) for southbound cars
Therefore, choice 6 is true.
PLEASE HELPPP 7TH GRADE MATHHHH!! WILL GIVE BRAINLIEST!! NEED RN PLEASE
Driving down the highway in separate vehicles, two friends realized that there were mile markers along each side of the road. They counted ten green markers for every mile they traveled. They also counted 8 yellow markers for each green marker. They text to each other their observations and wondered who was driving faster. Dev said he saw 110 green markers in 20 minutes. Mike said she saw 88 yellow markers in 2 minutes. Based on their observations, who is traveling faster?
Answers
Answer:
Mike
Step-by-step explanation:
Mike is the traveling faster.
Which type of function is shown in the table below ?
X Y
0 1
1 4
2 16
3 64
Answers
Answer:
The answer is linear.
Step-by-step explanation:
The x int is being added by 1 while the y int is subtracting 1
What is the value of [ 3 × ( 8 − 2 ) ] + 5 ?
Answers
simplify 0.75 : 2 5/16
Answers
To start this is a ratio, and the goal is to get at least 1 to be a whole number so first lets get the number below 1 to 1.
0.75 : 2 5/16 ---> (x1.3333 on both sides) ---> 1 : 3 1/12.
Next, if needed for your answer, lets get the other number to be a whole number as well. We can do this my multiplying both sides by 12 since the fraction on 3 1/12 is 1/12.
1 : 3 1/12 --> (x12 on both sides) ---> 12 : 37
Your final answer will either be 1 : 3 1/12 or 12 : 37, depending on the formatting expected for your homework assignment.
Solve the following equation for x 2log: 2x = 2 Describe what method you used to solve the problem and why?
Answers
Answer:
look at the picture i sent
can someone plz help
Answers
What is the measure of the angle in standard position 30 330 -60 -30
Answers
I am doing this fr a meme so whoever responds is cool and I will mark brailiest
Answers
Answer:
Step-by-step explanation:
yesssss
Plz help me well mark brainliest if you are correct!!...
Answers
Answer:
2/B
Step-by-step explanation:
The base is 9 and the height is 4.
Question 3 of 11 Lucy asked 5 friends how many books they each read last month. She put her data in a table and found the total books read. Friend Ben Ann Dan Ellie Caty Total Number of books 0 0 3 3 10 Find the mean and the median of the data set. Determine which of these values is greater. A. The median, 3, is greater than the mean, 2. B. The median, 4, is greater than the mean, 0. . C. The mean, 3. is greater than the median, 2 D. The mean, 4, is greater than the median, 3.
Answers
Step-by-step explanation:
mean = 0 + 0 + 3 + 3 + 10 ÷ 5
= 16 ÷ 5
= 3.2
median = 3
The price of a ticket to attend a show is $28.50. In addition to the ticket price, Laurence had to pay a service fee of 10% and a sales tax
of 6%. The service fee and sales tax are each applied to the original price of the ticket
How much did Laurence pay in total?
Enter your answer in the box.
Answers
Answer:
HI!!
Step-by-step explanation:
What’s the correct answer?????
Correct answer gets brainlest
Answers
Answer:
B. $14
Step-by-step explanation:
starting amount: $8 per hour
8x35 weeks=280
8x0.05=0.4
8+0.4=8.40
8.40x35=294
294-280= 14
OR
8x35 weeks=280
280x0.05= 14
3100 people attended a football game. If 5% of the people who attended were teenagers, how many teenagers attended the game?
Answers
Answer:
155 are teenagers
Step-by-step explanation:
3100 -5%= 2945
2945-3100=155
Find the GCD of 36,72 and 576
Answers
Answer:
36
Step-by-step explanation:
1×36
36×2
36×16
aaaaaaaaaaaaaaaaaaaaaa
Suppose the sphere below with radius r has a surface area equal to 45 units
Find the surface area of the sphere with twice the radius.
Answers
Answer:
180 units 2 ............
6)
Which polynomial is in standard form?
A)
3m3 + 2m? - m + 2
B)
8m3 + 6m2 + 2 - m
C)
-m” + 2m - m
– m2 + 1
D)
mº + 6m3 - 3m4 - 8
Answers
Answer:
D is the answer of this question
Identify the constant of proportionality in the graph.
A) 60
B) 120
C) 180
D) 240
Answers
Answer:
A) 60
Step-by-step explanation:
Find two points that intersect with the grid.
(0,0) and (1, 60)
Subtract the second y value from the first y value. Do the same to the X-values.
Write this as a fraction with the y values over the x-values.
60-0= 60
-------------
1 - 0 = 1
60/1 = 60
Which rule defines Sn for a Subscript n Baseline = 5 (three-fourths) Superscript n? S Subscript n Baseline = 15 (three-fourths) Superscript n S Subscript n Baseline = 5 (three-fourths) Superscript n S Subscript n Baseline = 15 (1 minus (three-fourths) Superscript n) S Subscript n Baseline = 5 (1 minus (three-fourths) Superscript n)
ANSWER: C
Answers
Answer:
C
Step-by-step explanation:
Answering your question so it will not get removed.
The correct option for the question is C. [tex]S_{n}[/tex] = 15 [ 1 - [tex](3/4)^{n}[/tex] ]
What is a Geometric progression?If in a sequence of terms, each succeeding term is generated by multiplying each preceding term with a constant value, then the series is referred to as a geometric progression. (GP), while the constant value is called the common ratio.
Conclusion: The nth term from the end of the GP with the last term l and common ratio r = l/ [r(n – 1)]. The sum of infinite, i.e. the sum of a GP with infinite terms is S∞= a/(1 – r) such that 0 < r < 1.
[tex]a_{n}[/tex] = 5[tex](3/4)^{n}[/tex]
[tex]S_{n}[/tex]= Σ[tex]a_{n}[/tex]
[tex]S_{n}[/tex] = ∑5[tex](3/4)^{n}[/tex]
= 5∑[tex](3/4)^{n}[/tex]
= 5 [ 3/4 + [tex](3/4)^{2}[/tex] + ......+ [tex](3/4)^{n}[/tex]]
=5 [ 3/4 * { 1- [tex](3/4)^{n}[/tex]} / 1 - 3/4 ]
[tex]S_{n}[/tex] = 15 [ 1 - [tex](3/4)^{n}[/tex] ]
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WILL
GIVE
BRAINLIST
...
.
Answers
3. 8.F.1.3
Which of the following equations represents
a linear function?
A. y = 3x2
B. y = 2-
C. y = 4x+6
D. y = -x + 3
Answers
The ordered pairs (12, 32). (x, 40), (18,48), (21, y) represent a proportional
relationship. Find the values of x and y. Select the two correct answers.
Answers
Answer:
x= 17
y=62
Step-by-step explanation:
3 less than the quotient of 18 and a number n
Answers
Answer:
(18÷n)-3
Step-by-step explanation:
The equation is above. There is no answer to the equation because we don't have a full equation to solve. Unless the question includes the answer to the equation, we can't fully solve it. But I believe that's the answer that you are looking for.
A rectangular prism has a 192 cubic inches.
Answers
Answer:
6
Step-by-step explanation:
Volume of Rectangular Prism: (l)(w)(h)
8 x 4 x ? = 192
32 x ? = 192
/32 /32
height = 6
To check work:
(8)(4)(6) = 192
What is the solution to the equation below round your answer to two decimal decimal places 5+6•log2 x=14
A. x=1.62
B. x=2.83
C. x=2.42
D. x=2.25
Answers
Answer:
x=2.83
Step-by-step explanation:
The solution to the equation, rounded to two decimal places, is x = 2.83.
The correct answer is option B: x = 2.83.
To solve the equation 5 + 6·log2(x) = 14 and round the answer to two decimal places, we can follow these steps:
1. Subtract 5 from both sides of the equation: 6·log2(x) = 9.
2. Divide both sides of the equation by 6: log2(x) = 9/6.
3. Simplify the right side: log2(x) = 1.5.
To find the value of x, we need to rewrite the equation in exponential form.
Remember that log2(x) = y is equivalent to [tex]2^y= x[/tex].
4. Rewrite the equation in exponential form: [tex]2^{1.5} = x[/tex].
5. Calculate the value of [tex]2^{1.5}[/tex] using a calculator or by approximating: x ≈ 2.83.
To learn more about the equation;
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please help me!!!!!!! find the surface area of this figure ?
show your work.
Answers
Answer:
[tex] 93 \: {in}^{2} [/tex]
Step-by-step explanation:
Surface area of the figure
[tex] = \frac{1}{2} \times 6 \times 7 + 3 \times \frac{1}{2} \times 6 \times 8 \\ \\ = 3 \times 7 + 3 \times 3 \times 8 \\ \\ = 21 + 72 \\ \\ = 93 \: {in}^{2} [/tex]
Researchers wish to examine the effectiveness of a new weight-loss pill. A total of 200 obese adults are randomly assigned to one of four conditions: weight-loss pill alone, weight-loss pill with a low-fat diet, placebo pill alone, or placebo pill with a low-fat diet. The weight loss after six months of treatment is recorded in pounds for each subject. To analyze this data, you would use __________.
a. a z-test
b. a t-test
c. an ANOVA F test
d. a Chi-square test
Answers
Answer:b
Step-by-step explanation:
To analyze this data, you would use An ANOVA F test.
What is a normal distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range, while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the center
The study involves comparing the weight loss of four groups of participants (weight-loss pill alone, weight-loss pill with a low-fat diet, placebo pill alone, or placebo pill with a low-fat diet) after six months of treatment. ANOVA (Analysis of Variance) is a statistical method used to analyze the differences among means of two or more groups.
In this case, ANOVA can be used to determine if there are significant differences in weight loss among the four treatment conditions.
A t-test or z-test would be appropriate if there were only two groups being compared.
A chi-square test is used to analyze categorical data, which is not applicable in this scenario where the data is continuous.
Therefore, an ANOVA F test would be used.
Learn more about normal distribution here:
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Ryan has homework in six subjects. He is deciding what order to complete them in
Answers
HOW DO YOU SOLVE IT PLEASE 20/3 = 10/9 x
Answers
Answer:
!! , ' !!!
Step-by-step explanation:
ꜰɪʀꜱᴛ! ᴄᴏᴍʙɪɴᴇ ᴍᴜʟᴛɪᴘʟɪᴇᴅ ᴛᴇʀᴍꜱ ɪɴᴛᴏ ᴀ ꜱɪɴɢʟᴇ ꜰʀᴀᴄᴛɪᴏɴ:
/ = /
/ = / ᴊᴜꜱᴛ ʟɪᴋᴇ ᴛʜᴀᴛ!
ꜱᴇᴄᴏɴᴅ! ᴍᴜʟᴛɪᴘʟʏ ᴀʟʟ ᴛᴇʀᴍꜱ ʙʏ ᴛʜᴇ ꜱᴀᴍᴇ ᴠᴀʟᴜᴇ ᴛᴏ ᴇʟɪᴍɪɴᴀᴛᴇ ꜰʀᴀᴄᴛɪᴏɴ ᴅᴇɴᴏᴍɪɴᴀᴛᴏʀꜱ!! ᴇᴀꜱʏ ᴘᴇᴀꜱʏ:
/ = /
9⋅/= 9⋅/ ꜱᴇᴇ ᴇᴀꜱʏ ᴘᴇᴀꜱʏ!!
! :
9⋅/=!!!
ᴀʟᴍᴏꜱᴛ ᴅᴏɴᴇ!!
ꜰᴏᴜʀᴛʜʟʏ!! ᴍᴜʟᴛɪᴘʟʏ ᴛʜᴇ ɴᴜᴍʙᴇʀꜱ (ᴊᴜꜱᴛ ᴛʜᴀᴛ ꜱɪᴍᴘʟᴇ!):
9⋅/
˜”*°•.˜”*°• Which Would equal 60=10x!! •°*”˜.•°*”˜
ꜰɪꜰᴛʜ!! ᴅɪᴠɪᴅᴇ ʙᴏᴛʜ ꜱɪᴅᴇꜱ ᴏꜰ ᴛʜᴇ ᴇQᴜᴀᴛɪᴏɴ ʙʏ ᴛʜᴇ ꜱᴀᴍᴇ ᴛᴇʀᴍ:
60/10 = 10x/10
ʟᴀꜱᴛʟʏ!!! ꜱɪᴍᴘʟɪꜰʏʏ:
=6
ᴛʜᴇɴ ʏᴏᴜ ɢᴇᴛ ʏᴏᴜʀ ᴀɴꜱᴡᴇʀʀ!!
x=6 ʕ ˵• ₒ •˵ ʔ
ᴀɴʏᴡᴀʏꜱ ᴛᴏᴏᴅʟᴇꜱ!!
ʜᴀᴠᴇ ᴀɴ ᴀᴍᴀᴢɪɴɢ ɴɪɢʜᴛ ᴏʀ ᴅᴀʏ!
ꜰʀᴏᴍ ʏᴏᴜʀ ᴏɴᴇ ᴀɴᴅ ᴏɴʟʏ ᴘɪɴᴋʏ ʕ ﾟ ● ﾟʔ
Find the degree of the polynomial 7x⁴– 25x + 3x⁷
Answers
Answer:
The degree of the polynomial is equal to 7.
Step-by-step explanation:
The given polynomial is :
7x⁴– 25x + 3x⁷
We need to find the degree of the polynomial.
We know that,
Degree of the polynomial = The highest sum of exponents for anyone monomial.
In this case, the powers of x are 4,1 and 7.
Out of these three, the exponent of x is 7 which is highest.
Hence, the degree of the polynomial is equal to 7.