The surface area of the cylinder is 16.125π cm², which is closest to option D) 19.55π cm².
To find the surface area of a cylinder, we need to calculate the sum of the areas of its two bases and its lateral surface.
The formula for the lateral surface area of a cylinder is given by:
[tex]\[ LSA = 2 \pi r h \][/tex]
where [tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height of the cylinder.
Given that the diameter of the cylinder is 1.5 centimeters, the radius [tex]\( r \)[/tex] is half of that, which is [tex]\( \frac{1.5}{2} = 0.75 \)[/tex] centimeters.
The height of the cylinder is given as 5 centimeters.
Substituting these values into the formula for the lateral surface area:
[tex]\[ LSA = 2 \pi (0.75) (5) \][/tex]
[tex]\[ LSA = 15 \pi \][/tex]
Now, we need to find the area of the two bases of the cylinder. Since the cylinder has two circular bases, we can find their combined area using the formula for the area of a circle:
[tex]\[ A_{\text{base}} = \pi r^2 \][/tex]
[tex]\[ A_{\text{base}} = \pi r^2 \][/tex]
[tex]\[ A_{\text{base}} = \pi (0.75)^2 \][/tex]
[tex]\[ A_{\text{base}} = \pi (0.5625) \][/tex]
[tex]\[ A_{\text{base}} = 0.5625 \pi \][/tex]
The total surface area is the sum of the lateral surface area and the areas of the two bases:
[tex]\[ \text{Total Surface Area} = LSA + 2A_{\text{base}} \][/tex]
[tex]\[ \text{Total Surface Area} = 15 \pi + 2(0.5625 \pi) \][/tex]
[tex]\[ \text{Total Surface Area} = 15 \pi + 1.125 \pi \][/tex]
[tex]\[ \text{Total Surface Area} = 16.125 \pi \][/tex]
[tex]\[ \text{Total Surface Area} = 16.125 \pi \][/tex]
Therefore, the surface area of the cylinder is 16.125π cm².
The closest option is D) 19.55π cm².
do y’all know what these symbols are called ??
Answer:
They are called tie's
Step-by-step explanation:
They basically mean to carry the note out longer so instead of it being 4 beats its now 8
Hope that helped!
There are a total of 15 dimes and quarters in a covered cup. The value of all 15 coins totals 2.85
Answer:
There are 6 dimes and 9 quarters.
Step-by-step explanation:
Represent the number of dimes and the number of quarters by d and q.
Then d + q = 15, or q = 15 - d.
Also, ($0.25)q + ($0.10)d = $2.85, or 5q + 2d = 57.
Substituding 15 - d for q, we get 5(15 - d) + 2d = 57, or
75 - 5d + 2d = 57, or
75 - 3d = 57, or
3d = 18. Thus, there are 6 dimes. Since q = 15 - d, q = 15 - 6 = 9.
There are 6 dimes and 9 quarters.
The number of dimes and quarters totaling $2.85 are 6 dimes and 9 quarters.
To solve this, we can set up two equations based on the number of coins and their total value.
Let's denote the number of dimes as d and the number of quarters as q. The value of a dime is $0.10, and the value of a quarter is $0.25. We know there are 15 coins in total, which gives us the first equation:
d + q = 15
The second equation is based on the total value of the coins:
0.10d + 0.25q = 2.85
To solve the system of equations, we can use substitution or elimination. Multiplying the second equation by 10 gives us:
d + 2.5q = 28.5
Subtracting the first equation from this results in:
1.5q = 13.5
Dividing by 1.5 gives us the number of quarters:
q = 9
Substituting q = 9 into the first equation gives us the number of dimes:
d + 9 = 15
d = 6
Therefore, there are 6 dimes and 9 quarters in the cup.
Which equation is equivalent to 2x + 10 = 6
A)
2x = 4
x + 5 = 3
(
x + 10 = 3
2x + 6 = 10
Help??????????????????(
Step-by-step explanation:
Tn = n² - 3
Now
the first three terms
t1 = 1² - 3 = 1 - 3= -2
t2 = 2² - 3= 4 - 3 = 1
t3 = 3² - 3 = 9 - 3 = 6
----------------
The first three terms are -2 , 1 , 6
and
tenth term
t10= 10² - 3= 100-3 = 97
Hope it will help you :))
Answer:
-2, 1, 6 and the 10th is 97
Step-by-step explanation:
to find the terms, in a row, replace n with 1
nth = 1^2 -3 -2 is the answer (1^2) is 1 -3 = -2
then replace the n with 2, 3, 4 etc till you have your sequence
nth = 2^2 -3 1 is the answer (2^2) is 4 -3 = 1
nth = 3^2 -3 6 is the answer (3^2) is 9-3 = 6
nth = 4^2 -3 13 is the answer (4^2) is 16-3 = 13
nth = 5^2 -3 22 is the answer (5^2) is 25-3 = 22
etc to 10
nth = 10^2 -3 97 is the answer (10^2) is 100 - 3 = 97
sequence is -2, 1, 6, 13, 22, . . . . 97
M is the centroid of the triangle.
CM=7, PM=10, & BQ=18
BM=[? ]
Answer:
The length of the BM is 6 unit.
Step-by-step explanation:
Given : M is the centroid of the triangle. CM=7, PM=10, & BQ=18
To find : The value of BM ?
Solution :
Refer the attached figure below.
The centroid of a triangle is the point of intersection of its medians.
M is the centroid and the centroid divide the line in 1:2 ratio.
So, M divide BQ in 1:2 ratio and the total length of BQ is 18.
BM is one third of 18.
i.e. [tex]BM=\frac{18}{3}[/tex]
[tex]BM=6[/tex]
Therefore, the length of the BM is 6 unit.
Answer: BM=6
Step-by-step explanation:
Explain how to add fractions with the same denominator. Use
3/8 + 2/8 as an example. Use the words numerator and
denominator in your response.
Step-by-step explanation:
To add fractions with the same demonator for example 3/8 + 2/8 you would add 3 +2 = 5 The numerator would be 5 and the demonator would stay the same. You would get an answer of 5/8
Answer:
Step-by-step explanation:
[tex]\frac{3}{8}+\frac{2}{8}=\frac{3+2}{8}\\\\=\frac{5}{8}[/tex]
If two fractions have same denominator, add the numerator and write the common denominator.
Solve for j . −1/3=/j4−10/3
Answer:
j = 12
Step-by-step explanation:
Solve for j by simplifying both sides of the equation, then isolating the variable.
e price of an item yesterday was 130. Today, the price rose to 221. Find the percentage increase
Answer:
70
Step-by-step explanation:
The explanation is in the picture
please rate and mark as brainliest
Three students take equivalent stress tests. Which is the highest relative score (meaning which
has the largest z score value)?
a. A score of 144 on a test with a mean of 128 and a standard deviation of 34
b. A score of 90 on a test with a mean of 86 and a standard deviation of 18
c. A score of 18 on a test with a mean of 15 and a standard deviation of 5
B is the correct answer with the explanation of a score of 90 on a test with a mean of 86 and a standard deviation of 18.
The highest relative score is of the student with a score of 18 on a test with a mean of 15 and a standard deviation of 5
What is z-score?Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values.
Given that, three students take equivalent stress tests, we need to calculate the highest relative score among them,
Z-score = X-μ / σ,
X = observed value, μ = mean and σ = standard deviation
a) A score of 144 on a test with a mean of 128 and a standard deviation of 34 :-
Z-score = X-μ / σ
Z-score = 144-128 / 34 = 0.47
b) A score of 90 on a test with a mean of 86 and a standard deviation of 18 :-
Z-score = X-μ / σ
Z-score = 90-86 / 18 = 0.22
c) A score of 18 on a test with a mean of 15 and a standard deviation of 5 :-
Z-score = X-μ / σ
Z-score = 18-15 / 5 = 0.6
Hence, the highest relative score is of the student with a score of 18 on a test with a mean of 15 and a standard deviation of 5
Learn more about z-score, click;
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What is the product of 3x(x2 + 4)?
O x² + 3x +4
O 3x3 + 4
O 3x3 + 12x
3x² + 12x
Answer:
3x³ + 12x
Step-by-step explanation:
Given
3x(x² + 4) ← multiply each term in the parenthesis by 3x
= 3x³ + 12x
Answer:
3x^3 +12x
Step-by-step explanation:
3x^3 +12x
The measurement of one angle of a right triangle is 43° what is the measurement of the third angle
During a solo competition for playing the flute, Sandra was given the following scores by four of the five judges:
6, 8, 9, and 8. What score would the fifth judge need to give her so that her average score from the five judges
was 8.0?
Answer: she needs a 9 from the fifth judge
Step-by-step explanation: so you have 5 judges and to get a perfect score you need 8. when you multiply the amount of judges by the score of 8 you get 40 witch is 100%, and when you add 6+8+9+8 you get 31 so there is 9 missing to get 40 so the answer is 9.
HELP HElp help HELp HElp please fast give 10 points
Answer:
y = 2x + 3
Step-by-step explanation:
its quizzizz you need fast
15x + 35 = 65 * what does X=
A. x = 2
B. x = -2
C. x = 5
D. x = 50
Answer:
A
Step-by-step explanation:
15x+35=65
15x=30
x=2
Answer: X= 2
Step-by-step explanation:
We know that 15 + 35 = 50.
But we still need to figure out the X, out of the options multiply it by 2 will get you 30. If we have 30 then we can complete our equation.
15x2 = 30 + 35 = 65
Hope this helps :D
Does the function model exponential growth or decay? h(t)=0.25\cdot 1.5^th(t)=0.25⋅1.5 t
Answer
Answer:
growth
Step-by-step explanation:
srry im late
When graphed, the three lines y = -x + 2, y = 2x − 1, and y = x − 2 intersect in such a way that they form a triangle.
What are the coordinates of the three vertices of this triangle?
A.
(2, 0), (0, 2), and (-1, -3)
B.
(0, 2), (2, 0), and (1, -1)
C.
(1, 1), (2, 0), and (-1, -3)
D.
(1, 1), (0, 2), and (-1, -3)
E.
(2, 0), (1, -1), and (-1, -3)
The answer is C
Insert y=X-2 into the equation y=-X+2
You will get the point (2,0)
Insert y=2X-1 into the same equation
you will get the point (1,1).
Without solving for the last point
you will realize that your answer is C
Note: This approach is appropriate for solving objective questions
Select the equivalent expression
In triangle ABC, a = 4, b = 6, and cos C = − 1/4. What is the length of side c?
(1)8
(2)2√7
(3)2√10
(4)4
The length of side c would be 8.
Step-by-step explanation:
Given that,
a = 4
b = 6
cosC = -1/4
If we are given two sides and angle, the law of Cosines can be used to find the third side:
[tex]c^{2} = a^{2} + b^{2} - 2ab (cos(c))[/tex]
By inserting the values in the formula, we get
[tex]c^{2} = 4^{2} + 6^{2} - 2.4.6 (-\frac{1}{4} )[/tex]
[tex]c^{2} = 16 + 36 + 12[/tex]
[tex]c^{2} = 64[/tex]
[tex]\sqrt{c^{2} } = \sqrt{64}[/tex]
c = 8.
Therefore, the length of side c would be 8.
The length of side [tex]\( c \)[/tex] is 8. The option (1) is correct.
To find the length of side [tex]\( c \)[/tex] in triangle ABC given [tex]\( a = 4 \), \( b = 6 \)[/tex], and [tex]\( \cos C = -\frac{1}{4} \),[/tex] we use the cosine rule:
[tex]\[ c^2 = a^2 + b^2 - 2ab \cos C \][/tex]
Substitute the given values:
[tex]\[ c^2 = 4^2 + 6^2 - 2 \cdot 4 \cdot 6 \cdot \left(-\frac{1}{4}\right) \][/tex]
[tex]\[ c^2 = 16 + 36 + 12 \][/tex]
[tex]\[ c^2 = 64 \][/tex]
Now, take the square root of both sides to find [tex]\( c \):[/tex]
[tex]\[ c = \sqrt{64} \][/tex]
[tex]\[ c = 8 \][/tex]
Therefore, the length of side [tex]\( c \)[/tex] is 8.
Each letter of the word PROBABILITY is written on an individual card, each of which
is the same size, and all are put in a bag. A card is drawn without looking. A card is
drawn without looking. Find P(Letter A or Vowel)
Mutually Exclusive Event
O Inclusive Event
Independent Event
Dependent Event
Answer:
Independent event
Step-by-step explanation:
Please match the answer to the question.
Question 3 options:
-5
-8
+4
+5
+8
1.
profit of $5
2.
depth of 8ft
3.
increase of 8 degrees F
4.
loss of $5
5.
height of 4ft
Answer:
see below
Step-by-step explanation:
1. profit of 5 means a gain of 5 +5
2 depth of 8ft means down 8 -8
3 increase of 8 degrees means a gain of 8 +8
4 loss of 5 dollars means negative -5
5 height of 4 ft means we go up +4
what is 527.79 rounded to the nearest thousandth?
I looked it up and it said it was just 527.79, but when i put my answer in it said it was wrong so im really confused.
527.79
there is no because just round and try this I think it might work i dont know
A large box contains buttons with pictures of animals.
There are four different animals. A button is drawn and replaced. In 100 trials, 35 buttons with cats were drawn.
What is the probability that the next button will be a different animal?
A.
The experimental probability is 35%.
B.
The experimental probability is 65%.
C.
The theoretical probability is 35%.
D.
The theoretical probability is 65%.
Answer: its B
Step-by-step explanation:
You have to subtract 100 and 35. You get 65. Its also a experimental probability.
EE
Solve the system of equations.
y= 2x + 4
y = x2 + x - 2
A. (-2, 0) and (3, 10)
B. (2,0) and (-3,-10)
C. (-3,-10) and (-2,0)
D. (-3, 10) and (2,0)
Answer:
A
Step-by-step explanation:
Given the 2 equations
y = 2x + 4 → (1)
y = x² + x - 2 → (2)
Substitute y = x² + x - 2 into (1)
x² + x - 2 = 2x + 4 ( subtract 2x + 4 from both sides )
x² - x - 6 = 0 ← in standard form
(x - 3)(x + 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 3 = 0 ⇒ x = 3
x + 2 = 0 ⇒ x = - 2
Substitute these values into (1) for corresponding values of y
x = 3 : y = 2(3) + 4 = 6 + 4 = 10 ⇒ (3, 10 )
x = - 2 : y = 2(- 2) + 4 = - 4 + 4 = 0 ⇒ (- 2, 0 )
Which is the best estimate of the sum of the fractions 5/12+5/9
Answer:
0.926
Step-by-step explanation:
5/12 as a decimal is 0.416 and
5/9 as a decimal is 0.5 repeating
You just have to turn the fraction into a decimal and
add those together.
So your final equation would be 0.416+0.5
Answer:
35/36
Step-by-step explanation:
The least common denominator for both 12 and 9 is 36.
5 3 = 15
— X —
12 3 = 36
5 4 = 20
– X
9 4 = 36
15+20 = 35
so, 35/36
Hope this help, have a great day, and Stay Safe.
:)
4c = 3 C =
please help me I am late for hw and ned this question done asap
Answer:
4c=4 c=3/4
Step-by-step explanation:
Consider U = {x\x is a positive integer greater than 1}.
Which is an empty set?
{xx € U and 2x is prime}
{xlx EU and 2x is prime}
{XX € U and 1/2x can be written as a fraction}
{x|x € U and 2x can be written as a fraction}
Considering U = {x l x is a positive integer greater than 1} the empty set will be,
⇒ { X ∈ U and 2x is prime}
What are prime numbers?Prime numbers refers to a whole number more than 1 whose only factors are 1 and itself.
Now, A whole number that may be split evenly into another number by multiplication is referred to as a factor.
2, 3, 5, 7, 11, 13, 17, 19, 23 and 29 are the first few prime numbers.
Here, The number 2 is the only prime even number and hence no other prime number will be fall as an even number or a product from multiplication by 2.
Hence, Considering U = {x l x is a positive integer greater than 1} the empty set will be,
⇒ { X ∈ U and 2x is prime}
Learn more about prime numbers at:
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From a standard deck of 52 cards, what is the probability of picking a 6 at random from the deck?
Answer:
Only 4 out of 52 cards are 6.
4/52 = 1/13
Probability is 4/13
Answer:
4/52 or 1/13
Step-by-step explanation:
There are 4 of each card in a deck except for Jokers. Therefore, the answer is 4/52 or 1/13
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True or false: opposite angles of a square are supplementary angles
Answer:
True
Step-by-step explanation:
Supplementary angles are those that sum up to 180 degrees. A square is a polygon with all its angles measuring 90 degrees. This means that opposite angles are both 90 degrees. And, since 90 + 90 = 180, that means that a square's opposite angles are supplementary.
Hope this helps!
Answer:
True
Step-by-step explanation:
Supplementary angles add up to 180
All angles in a square are 90.
Opposite angles add up to 180°
What is the graph to the piecewise defined function g(x) = { x+4, -5<=x<=-1
2-x, -1<=x<=5?
Answer:
third graph, see attached in case the order changes
Step-by-step explanation:
g(x) = { x+4, -5<=x<=-1
2-x, -1<=x<=5
The graph will change at -1, so we can eliminate the first graph
It changes completely so we can eliminate the second graph
From -5 to -1 the slope is positive 1 so it will increase from left to right
The last graph decreases, so it has a negative slope at -5. We can eliminate the last graph
That leaves us the third graph
g(x) = x+4, -5《x《-1
At x = -5, g(x) = -1
At x = -1, g(x) = 3
g(x) = 2-x, -1《x《5
At x = -1, g(x) = 3
At x = 5, g(x) = -3
On the last day of April 2009, the price of a share of stock in a major entertainment corporation was $5.36. Over the next 4 years, the annual growth rate was 4.15%. The growth in the price of this stock can be modeled by the function where P represents the price, in dollars, and t represents the number of years since the last day in April 2009. Which function can be used to represent the price of a share of stock in this entertainment corporation on the last day in June 2011?
Answer:
Hence After 2 years from 2009 to 2011 THe price for share of stock will be 5.8141 $
Step-by-step explanation:
Given:
Initial price=$5.36
Rate=4.15 %
To Find:
Function which represents the growth price for stock market?
Solution:
As the function is growing one and with same rate and depends upon the time period ,
So the exponential function as
[tex]P=A(1+R)^t[/tex] will the required function ,
So P will be price of stock at t time period with R as rate for function.
A be the previous year price
From 2009 to 2013 rate is 4.15 %
we have to find price after 2 years
So t=2 , A at 2009 =5.36$
So P at 2011 will be given by,
[tex]P=A(1+R)^t[/tex]
[tex]P=5.36(1+0.0415)^2[/tex]
[tex]P=5.36(1.0415)^2[/tex]
[tex]P=5.8141 $[/tex]