Answer:
Step-by-step explanation:
In double angle, sin2x = sin(x+x) = sinxcosx+cosxsinx
sin2x = 2sinxcosx ... 1
Applying this formula to prove that sin(4x) = 4 sinx cosx(1 − 2sin2x is shown below;
sin(4x) = sin(2x+2x)
= sin2xcos2x+cox2xsin2x
sin4x = 2sin2xcos2x ..2
also cos2x = cos(x+x) = cosxcox-sinxsinx
cos 2x = cos²x - sin²x ...3
Substituting equation 1 and 3 into 2, we will have;
sin4x = 2(2sinxcosx(cos²x - sin²x ))
sin4x = 4sinxcosx(cos²x - sin²x )
From sin²x+cos²x =1; cos²x = 1-sin²x
Substituting the expression into the resulting equation will give;
sin4x = 4sinxcosx(1-sin²x - sin²x )
sin4x = 4sinxcosx(1-2sin²x) Verified!
In the search to determine if car 1 is slower to accelerate than car 2, the mean time it takes to accelerate to 30 miles per hour is recorded (Note: a car is slower to accelerate if it takes more time to accelerate). Twenty trials of the acceleration time for each car are recorded, and both populations have normal distributions with known standard deviations. What are the hypotheses used in this test
Answer:
Step-by-step explanation:
The happiest used in a test in statistics are the null and the alternative hypothesis. The null hypothesis is usually the default statement while the alternative hypothesis is thevopposite of the null hypothesis.
In this case study, the null hypothesis is u1 = u2: the average mean time it takes to accelerate to 30 miles per hour for car 1 is the same as that for car 2.
The alternative hypothesis is u1 > u2: the mean time it takes to accelerate to 30 miles per hour is greater than that for car 2 thus car 1 is slower to accelerate as it takes more time.
please I need help with this question!
The weight of adult males in Boston are normally distributed with mean 69 kilograms and variance 25 kilograms.
I. what percentage of adult male in Boston weigh more than 72 kilograms?
ii. what must an adult male weigh in order to be among the heaviest 10% of the population?
Thank you in advance!
Answer:
lmkjhvjgcfnhjkhbmgnc gfghh
Step-by-step explanation:
what is the length of a hypotenuse of a triangle if each of its legs is 4 units
Answer:
[tex]\boxed{c = 5.7 units}[/tex]
Step-by-step explanation:
Using Pythagorean Theorem:
=> [tex]c^2 = a^2+b^2[/tex]
Where c is hypotenuse, a is base and b is perpendicular and ( a, b = 4)
=> [tex]c^2 = 4^2+4^2[/tex]
=> [tex]c^2 = 16+16[/tex]
=> [tex]c^2 = 32[/tex]
Taking sqrt on both sides
=> c = 5.7 units
Answer:
5.65 unitsStep-by-step explanation:
Given,
Base ( b ) = 4 units
Perpendicular ( p ) = 4 units
Hypotenuse ( h ) = ?
Now,
Using Pythagoras theorem to find length of hypotenuse:
[tex] {h}^{2} = {p}^{2} + {b}^{2} [/tex]
Plugging the values
[tex] {h}^{2} = {4}^{2} + {4}^{2} [/tex]
Evaluate the power
[tex] {h}^{2} = 16 + 16[/tex]
Calculate the sum
[tex] {h}^{2} = 32[/tex]
[tex]h = \sqrt{32} [/tex]
[tex]h = 5.65 \: units[/tex]
Hope this helps..
Best regards !!
The Sugar Sweet Company is going to transport its sugar to market. It will cost $3500 to rent trucks, and it will cost an additional $150 for each ton of sugar transported. Let C represent the total cost (in dollars), and let S represent the amount of sugar (in tons) transported. Write an equation relating C to S. Then use this equation to find the total cost to transport 17 tons of sugar.
Answer:
C = $6050
Equation:
To write the equation, we have to remember that C is the total cost, so that means the equation should end in "= C". S is the amount of sugar, so the equation would look something like this:
[tex]3500+150(S)=C[/tex]
3500 is at the beginning since that is the cost for the trucks, and each ton of sugar costs $150, and that would get multiplied by S amount of sugar, to get the total cost, C.
Solving the equation
To solve the equation when S = 17, we simply have to plug in S as 17 into our equation we wrote above.
[tex]3500+150(17)=C[/tex]
150 * 17 is 2550, and 3500 + 2550 is 6050, which is C.
Our answer is: C = $6050
limit xtens to 0 x^2logx^2 what is the ans of interminate forms?
Rewrite the limit as
[tex]\displaystyle\lim_{x\to0}x^2\log x^2=\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}[/tex]
Then both numerator and denominator approach infinity (with different signs, but that's not important). Applying L'Hopital's rule, we get
[tex]\displaystyle\lim_{x\to0}\frac{\log x^2}{\frac1{x^2}}=\lim_{x\to0}\frac{\frac2x}{-\frac2{x^3}}=\lim_{x\to0}-x^2=\boxed{0}[/tex]
Translate into an algebraic expression and simplify if possible. The value of a number whose units digit is x and whose tens digit is three more than the units digit.
Answer: 11x + 30
Step-by-step explanation: Algebraic expression is a way of use letters to express relationships between algarisms.
For this question:
Units digit = x
Tens digit = 10(x + 3)
The number in question is:
10(x + 3) + x
10x + 30 + x
To simplify, add, subtract, multipy or divide similar terms:
As x is of the first order:
10x + x + 30
11x + 30
The simplified algebraic expression is 11x + 30
Pick two cards at random from a well-shuffled deck of 52 cards (pick them simultaneously so they are not the same card). There are 12 cards considered face cards. There are 4 cards with the value 10. Let X be the number of face cards in your hand. Let Y be the number of 10's in your hand. Explain why X and Y are dependent.
Answer:
The variables X and Y are dependent.
Step-by-step explanation:
The variable X denotes number of face cards . That is it can take values,
X = {0, 1, 2 }
Compute the probability for all he values of X as follows:
P [X = 0] = P (None of the 12 card is chosen in either draw)
= (40/52)×(39/51)
= 1560/2652
= 0.5882
P [X = 1] = P (One of the card is face card is selected)
= 2×(40/52)×(12/51)
= 960/2652
= 0.3619
P [X = 2] = P (Two of the 12 card is chosen in the draw)
= (12/52)×(11/51)
= 132/2652
= 0.0498
The variable Y denotes number of cards numbered 10 . Thus, it can take values:
Y = {0, 1, 2 }
P [Y = 0] = P (None of the 4 card is chosen in either draw)
= (48/52)×(47/51)
= 2256/2652
= 0.8507
P [Y = 1] = P (One of the 4 card is chosen in either draw)
= 2×(4/52)×(48/51)
= 384/2652
= 0.1448
P [Y = 2] = P (Two of the 4 card is chosen in the draw)
= (4/52)×(3/51)
= 12/2652
= 0.0045
Now compute the probability of (X and Y).
P [X = 0 and Y = 0] = P(None of the 16 card is chosen in either draw)
= (36/52)×(35/51)
= 1260/2652
= 0.4751
The variables X and Y are independent if,
P [X = 0 and Y = 0] = P [X = 0] × P [Y = 0]
= P [X = 0] × P [Y = 0]
= 0.8507 × 0.5882
= 0.5204
The two values are not equal.
Hence, the variables X and Y are not independent.
Solve 2x2 – 6x + 10 = 0 by completing the square.
Answer: x = 6.32 or -0.32
Step-by-step explanation:
2x² - 6x + 10 = 0
No we divide the expression by 2 to make the coefficient of x² equals 1
We now have
x² - 3x + 5 = 0
Now we remove 5 to the other side of the equation
x² - 3x = -5
we add to both side square of half the coefficient of x which is 3
x² - 3x + ( ⁻³/₂)² = -5 + (⁻³/₂)²
(x - ³/₂)² = -5 + ⁹/₄
Resolve into fraction
(x - ³/₂)² = ⁻¹¹/4
Take the roots of the equation
x - ³/₂ = √¹¹/₄
x - ³/₂ = √11/₂
x = ³/₂ ± 3.32/₂
= 3+ 3.32 or 3 - 3.32
= 6.32 or - 0.32
The random variable x is the number of houses sold by a realtor in a single month at the Sendsom's Real Estate office. Its probability distribution is as follows:
Houses Sold (x) Probability P(x)
0 0.24
1 0.01
2 0.12
3 0.16
4 0.01
5 0.14
6 0.11
7 0.21
Find the mean of the given probability distribution.
A. μ = 3.35
B. μ = 3.50
C. μ = 3.60
D. μ = 3.40
Answer:
C. μ = 3.60
Step-by-step explanation:
Two tables have been attached to this response.
One of the tables contains the given data and distribution with two columns: Houses Sold and Probability
The other table contains the analysis of the data with additional columns: Frequency and Fx
=> The Frequency(F) column is derived from the product of the probability of each item in the Houses sold column and the total number of houses sold (which is 28). For example,
When the number of houses sold = 0
F = P(0) x Total number of houses sold
F = 0.24 x 28 = 6.72
When the number of houses sold = 1
F = P(1) x Total number of houses sold
F = 0.01 x 28 = 0.28
=> The Fx column is found by multiplying the Frequency column by the Houses Sold column. For example,
When the number of houses sold = 0
Fx = F * x
F = 6.72 x 0 = 0
Now to get the mean, μ we use the relation;
μ = ∑Fx / ∑F
Where;
∑Fx = summation of the items in the Fx column = 100.8
∑F = summation of the items in the Frequency column = 28
μ = 100.8 / 28
μ = 3.60
Therefore, the mean of the given probability distribution is 3.60
The mean of the discrete probability distribution is given by:
C. μ = 3.60
What is the mean of a discrete distribution?The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability.
In this problem, the table x - P(x) gives each outcome and their respective probabilities, hence, the mean is:
[tex]E(X) = 0(0.24) + 1(0.01) + 2(0.12) + 3(0.16) + 4(0.01) + 5(0.14) + 6(0.11) + 7(0.21) = 3.6[/tex]
Hence option C is correct.
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Change -4Y - 3X = -8 to the slope-intercept form of the equation of a line.
Answer:
y=-3/4x+2
Step-by-step explanation:
Add +3x both sides.
Divide each side by -4
-8/-4=2
Slope = -3/4
Y-intercept= 2
The diagram shows a right triangle and three squares. The area of the largest square is 55 units.
Which could be the areas of the smaller squares?
Choose all answers that apply:
A
12 and 43
B
14 and 40
16 and 37
Answer:
It's 12 and 43
Step-by-step explanation:
A square is a plane shape with equal length of sides, while a right triangle is a triangle that has one of its angles to be [tex]90^{o}[/tex]. Thus, the areas of the smaller squares could be:
A. 12 and 43
A square has equal length of sides, so that its area is given as:
Area of a square = length x length
= [tex]l^{2}[/tex]
For the largest square its area = 55 [tex]units^{2}[/tex], so that:
Area = [tex]l^{2}[/tex]
⇒ 55 = [tex]l^{2}[/tex]
l = [tex]\sqrt{55}[/tex]
Now applying the Pythagoras theorem to the right triangle, we have:
[tex]/Hyp/^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
where hypotenuse = [tex]\sqrt{55}[/tex]
([tex]\sqrt{55}[/tex][tex])^{2}[/tex] = [tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex]
[tex]/Adj 1/^{2}[/tex] + [tex]/Adj 2/^{2}[/tex] = 55
Therefore, the addition of the areas of the smaller squares should be equal to that of the largest square.
Thus from the theorem above, the areas of the smaller squares could be 12 and 43.
i.e 12 + 43 = 55
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Need help with graphing
subtract 2-3/4-1 1/10=
Answer:
23/20
Step by step Explanation
Answer:
3/20Step-by-step explanation:
[tex]2-\frac{3}{4}-1\frac{1}{10}=x\\x=2-\frac{3}{4}-\frac{11}{10}\\\mathrm{Convert\:element\:to\:fraction}:\quad \:2=\frac{2}{1}\\x=\frac{2}{1}-\frac{3}{4}-\frac{11}{10}\\1,\:4,\:10\\\mathrm{Prime\:factorization\:of\:} ;\\1=1\\4=2\times \:2\\10=2\cdot \:5\\\mathrm{Multiply\:the\:numbers:}\:2\times \:2\times \:5=20\\Adjust\: fractions\: based\: on\: their\: LCM ;\\\frac{2}{1}=\frac{2\times \:20}{1\times \:20}=\frac{40}{20}\\\\\frac{3}{4}=\frac{3\times \:5}{4\times \:5}=\frac{15}{20}\\[/tex]
[tex]\frac{11}{10}=\frac{11\times \:2}{10\times \:2}=\frac{22}{20}\\\mathrm{Since\:the\:denominators\:are\:equal,\\\:combine\:the\:fractions}:\\\quad \frac{a}{c}\pm \frac{b}{c}=\frac{a\pm \:b}{c}\\\\\mathrm{Subtract\:the\:numbers:}\:40-15-22=3\\\\x=\frac{3}{20}[/tex]
There are 45 balloons: 15 are blue; 20 are green; 10 are red. 3 balloons are selected for the float. Leaving your answers in combinatorics format, how many ways can all 3 be selected such that they are the same color.
Answer: Required number of ways = 1715
Step-by-step explanation:
Given, there are 45 balloons: 15 are blue; 20 are green; 10 are red.
3 balloons are selected for the float.
Number of combinations to select r things out of n things : [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]
So, the number of ways to select 3 ballons such that they are the same color = (Ways to select all blue ) x (Ways to select all green ) x (Ways to select all red)
[tex]^{15}C_3+^{20}C_3+^{10}C_3\\\\=\dfrac{15!}{12!\times3!}+\dfrac{20!}{17!\times3!}+\dfrac{10!}{7!\times3!}\\\\=\dfrac{15\times14\times13}{6}+\dfrac{20\times19\times18}{6}+\dfrac{10\times9\times8}{6}\\\\=455+1140+120\\\\=1715[/tex]
Hence, Required number of ways = 1715
Stella bought a dinette set on sale for $725. The original price was $1,299. To the nearest tenth of a percent, what was the rate of discount?
Answer:
40%
Step-by-step explanation:
1299-725= 574
574/1299 x 100 = 44.19%
The rate of discount on the dinette set = 44.2%.
What is a discount?Often, goods are sold at a price that is lower than their marked price. The price at which the good is sold is called the selling price and the difference between the marked price and the selling price is the discount.
Discount = Marked Price - Selling Price.
Rate of Discount = Discount/Marked Price * 100%.
How to solve the given question?In the question, we are given that Stella bought a dinette set on sale for $725. The original price was $1,299.
We are asked to calculate the rate of discount on the dinette set.
The marked price of the dinette set = $1299.
The selling price of the dinette set = $725.
∴ The discount on the dinette set = the marked price of the dinette set - the selling price of the dinette set = $1299 - $725 = $574
∴ The rate of discount on the dinette set = the discount on the dinette set/the marked price of the dinette set *100%
or, The rate of discount on the dinette set = 574/1299 * 100%
or, The rate of discount on the dinette set = 0.4418 * 100%
or, The rate of discount on the dinette set = 44.18% ≈ 44.2% (to the nearest tenth of a percent)
∴ The rate of discount on the dinette set = 44.2%.
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Lisa is 34 years old. Two years ago, she was twice as old as her brother. How old is her brother now?
Answer:
18
Step-by-step explanation:
Two years ago, Lisa was 34 - 2 = 32 years old. If she was twice as old as her brother, he was 32 / 2 = 16 years old at that time. His age now will be 16 + 2 = 18.
CAN ANYONE HELP ME PLEASE? Two numbers total of 52 and have a difference of 30. Find the two numbers. The larger number is ? and the smaller number is ?
Answer:
41 and 11.
Step-by-step explanation:
Let's say the 2 numbers are x and y.
Since they add up to 52, x + y = 52.
Seeing as the difference is 30, x - y = 30 assuming x is the larger number.
We have left:
x + y = 52
x - y = 30
By solving these simultaneous equations (adding the 2 equations together for instance), we are left with 2x = 82
Therefore x = 41.
Since x + y = 52
41 + y = 52
Therefore y = 11
Therefore we have: the larger number is 41 and the smaller number is 11.
The diameter of ball bearings produced in a manufacturing process can be explained using a uniform distribution over the interval 3.5 to 4.75 millimeters. What is the probability that a randomly selected ball bearing has a diameter greater than 4.4 millimeters?
Answer:
The probability is 0.28
Step-by-step explanation:
Here, we want to calculate the probability that the ball bearing randomly selected has a diameter greater then 4.4 mm
I.e P(X> 4.4)
P(X>4.4) = (4.75-4.4)/(4.75-3.5) = 0.35/1.25 = 0.28
i will give brainliest and 50 points pls help ASAP
Answer:
answer is 2.3 hope you get the answer
Find the measure of angle angle AGE in the figure below. Enter only the number.
Help please!
Answer:
AGE = 129 degrees
Step-by-step explanation:
Two angles whose sum is 180° are called supplementary angles. The measure of ∠AGE in the given figure is 129°.
What are supplementary angles?Two angles whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles. That means, that if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
In the given figure, line segment CE is a straight line. Therefore, the sum of the angles formed on the same side of the line will be a linear pair.
Thus, the measure of the angles can be rewritten as,
∠AGC + ∠AGE = 180°
51° + ∠AGE = 180°
∠AGE = 180° - 51°
∠AGE = 129°
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To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called:____________
Answer:
Convenience sampling.
Step-by-step explanation:
To gather information on customer satisfaction, a researcher goes into each store and interviews six randomly selected customers at each store. This sampling technique is called convenience sampling.
Convenience sampling can be defined as a sampling method which involves the researcher selecting or collecting data that is easily available or choosing the individuals who are easiest to reach in a population. It is a type of non-probability method of sampling where the first or easiest available data source is being used by the researcher without other requirements.
In this scenario, to gather information on customer satisfaction, the researcher went to the store most likely situated in a shopping mall to collect data from six (6) customers in each stores.
Some of the advantages of convenience sampling are low cost, data are collected quickly, lesser rules etc.
Suppose you just flipped a fair coin 8 times in a row and you got heads each time! What is the probability that the next coin flip will result in a heads
Answer:
The probability is 1
Step-by-step explanation:
Given
Number of flips = 8
Outcomes = 8 heads
Required
Probability of getting a head in the next row
This problem can be attributed to experimental probability and it'll be solved using experimental probability formula, which goes as follows;
[tex]Probability = \frac{Number\ of\ Occurence}{Total\ Trials}[/tex]
Let [tex]P(Head)[/tex] represents the probability of getting a head in the next row;
[tex]P(Head)= \frac{Outcome\ of\ head}{Total\ Flips}[/tex]
[tex]P(Head)= \frac{8}{8}[/tex]
[tex]P(Head)= 1[/tex]
Hence, the probability of obtaining a head in the next flip is 1
Please help. I’ll mark you as brainliest if correct! Don’t understand this math problem.
Answer:
work is pictured and shown
Answer:
Infinitely many solutions.
Step-by-step explanation:
To solve the system of equation using the substitution method, the problem has already given us a solution for x:
x = -4y - 9
Using this, we can plug that into the first equation and solve for y:
3x + 12y = -27
3(-4y - 9) + 12y = -27
-12y - 27 + 12y = -27
-27 = -27
The fact that our solution indicate -27 = -27 means that these two equations have infinitely many solutions for the value y. This simply means that no matter what we put in for y, the statement will always be true.
Notice that these two equations are in fact the same equation:
x = -4y - 9 ==> x + 4y = -9 ==> 3x + 12y = -27
Since these two equations are the same, then there are infinitely many solutions.
I'm not sure quite what they want for the form in terms of y, but let's solve for y since they already solved for x:
x = -4y - 9
x + 9 = -4y
y = (-1 / 4) (x + 9)
Cheers.
I NEED THE ANSWER AS SOON AS POSSIBLE PLEASE!!
Answer:
[tex]\Large \boxed{\sf \ \ 4\sqrt{a^2+b^2} \ \ }[/tex]
Step-by-step explanation:
Hello,
You can use Pythagoras in the 4 right triangles.
For one triangle it comes [tex]\sqrt{a^2+b^2}[/tex].
Then for the polygon it gives [tex]4\cdot \sqrt{a^2+b^2}[/tex].
Hope this helps.
Do not hesitate if you need further explanation.
Thank you
A Cepheid variable star is a star whose brightness alternately increases and decreases. For a certain star, the interval between times of maximum brightness is 5.7 days. The average brightness of this star is 5.0 and its brightness changes by ±0.25. In view of these data, the brightness of the star at time t, where t is measured in days, has been modeled by the function B(t) = 5.0 + 0.25 sin 2πt 5.7 .Find the rate of change of the brightness after t days.
Correct expression of B(t) is;
B(t) = 5.0 + 0.25 sin(2πt/5.7)
Answer:
B'(t) = (5π/57)cos(2πt/5.7)
Step-by-step explanation:
We are given;
B(t) = 5.0 + 0.25 sin(2πt/5.7)
Now the rate of change of the brightness after t days is simply the derivative of B(t)
Thus;
B'(t) = 0 + [{0.25 cos(2πt/5.7)} × (2π/5.7)]
This leads to;
B'(t) = (0.5π/5.7)cos (2πt/5.7)
Simplifying this further gives;
B'(t) = (5π/57)cos(2πt/5.7)
Find the distance between the points (–9, 0) and (2, 5). Find the distance between the points (–9, 0) and (2, 5).
Answer:
sqrt( 146)
Step-by-step explanation:
To find the distance, we use the following formula
d = sqrt( ( x2-x1) ^2 + ( y2-y1) ^2)
sqrt( ( -9-2) ^2 + ( 0-5) ^2)
sqrt( ( -11) ^2 + ( -5) ^2)
sqrt( 121+25)
sqrt( 146)
Probability equation need help again. worded problem-the table below displays the number of siblings for students. at one school. Find the probability that a randomly selected students has 2 siblings.
Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.18.
1. Which of the following is a type I error?
a. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
b. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
c. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
d. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
2. Which is the following is a type II error?
a. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
b. Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
c. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
d. Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
Answer:
Type I error: Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
Type II error: Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
Step-by-step explanation:
We are given the following hypothesis below;
Let p = proportion of people who write with their left hand
Null Hypothesis, [tex]H_0[/tex] : p = 0.18 {means that the proportion of people who write with their left hand is equal to 0.18}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.18 {means that the proportion of people who write with their left hand is different from 0.18}
Type I error states that we would reject the null hypothesis given the fact that the null hypothesis was actually true. Or in other words, the probability of rejecting a true hypothesis.
So, according to our question, Type I error is to Reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually 0.18.
Type II error states that we would accept the null hypothesis given the fact that the null hypothesis was actually false. Or in other words, the probability of accepting a false hypothesis.
So, according to our question, Type II error is Fail to reject the claim that the proportion of settled malpractice suits is 0.18 when the proportion is actually different from 0.18.
need help thanksssss
Before we can find any of the three items mentioned, we need the height. The diameter is 10, so the radius is 5. A right triangle with hypotenuse 13 and leg 5 forms. The height is h. Use the pythaogrean theorem to solve for h
5^2+h^2 = 13^2
25+h^2 = 169
h^2 = 169-25
h^2 = 144
h = sqrt(144)
h = 12
The height is 12. We now have enough info to find the volume, the lateral area and surface area.
-------------------------------------------------------------------
Volume
V = (1/3)*pi*r^2*h
V = (1/3)*3.14*5^2*12
V = 314 cubic cm
-------------------------------------------------------------------
Lateral Area
LA = pi*r*L
LA = 3.14*5*13
LA = 204.1 square cm
-------------------------------------------------------------------
Surface Area
SA = 2*pi*r + pi*r*L .... note how we add on the lateral area to the bottom circular area
SA = 2*3.14*5 + 3.14*5*13
SA = 235.5 square cm
A train travels 45 feet in 1/10 if a second. How far will it travel in 3.5 seconds
Answer:
1575 ft
Step-by-step explanation:
Convert 1/10 to decimal to make the math simpler.
1/10 = 0.1
Divide 3.5 by 0.1.
3.5/0.1 = 35
Multiply 35 by 45.
35 × 45 = 1575
The train will travel 1575 feet in 3.5 seconds.
The distance covered by the train in 3.5 seconds will be 1575 feet.
What is speed?The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.
We know that the speed formula
Speed = Distance/Time
A train travels 45 feet in 1/10 in a second.
Then the speed will be
Speed = 45 / (1/10)
Speed = 45 x 10
Speed = 450 feet per second
The distance covered by the train in 3.5 seconds will be
Distance = 450 x 3.5
Distance = 1575 feet
More about the speed link is given below.
https://brainly.com/question/7359669
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