Answer:
A. TRUE
Step-by-step explanation:
To determine if two triangles are congruent, we need to establish the facts that the three angles and three side lengths of one is congruent to corresponding angles and side lengths of the other triangle.
The diagram given only tells us the angle measure of the two triangles which are congruent to each other. The side length wasn't given. Therefore, the triangles may not be congruent.
A robot that makes _/6 of a boat per day will make 5 boats in 6 days
Suppose that on the average, 7 students enrolled in a small liberal arts college have their automobiles stolen during the semester. What is the probability that less than 1 student will have his automobile stolen during the current semester
Answer:
[tex]P(x>1)=0.9927[/tex]
Step-by-step explanation:
From the question we are told that:
Mean [tex]\=x =7[/tex]
Generally the Poisson equation for \=x is mathematically given by
[tex]P(x>1)=1-P(x \leq 1)[/tex]
Therefor
[tex]P(x>1)=1-(\frac{e^{-7}*7^0}{0!}+{\frac{e^{-7}*7^1}{1!})[/tex]
[tex]P(x>1)=1-(9.1*10^{-4}+6.3*10^{-3})[/tex]
[tex]P(x>1)=1-(7.3*10^{-3}[/tex]
[tex]P(x>1)=0.9927[/tex]
In a right triangle, the lengths of the two legs are 8 cm and 10 cm respectively. Find the hypotenuse of the triangle.
9 cm
10.5 cm
12 cm
12.8 cm
12.8, pythagorean theorem.
Combine as indicated by the signs. Write answer In descending powers of x.
X+6/x^28x+15+3x/x+5-x-3/x+3
= ?
Answer:
Step-by-step explanation:
Can someone give me the letter to all answers 1-4 or at least one 3
Answer:
hello there here are your answers:
1) a- 12, 18, 24, 30, 36
2) b- 31
3) a-communitive property of addition
4) a- 6a
Step-by-step explanation:
1: go through all the numbers and add 6 like 12+6=16 etc.
2: the common difference is 4 so 27+4 =31
3: communitive property because you can change the number in any order and still get the same sum
4: 6a because only 24ab has a b in it
Find the domain.
p(x) = x^2+ 2
Answer:
The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.
Interval Notation:
( − ∞ , ∞ )
Set-Builder Notation:
{ x | x ∈ R }
Step-by-step explanation:
hope that helps bigger terms
PLEASE HELP ASAP! So the answer I got for this problem is 50.26. Can someone make sure that is the correct answer? Please let me know how to solve this problem if it is wrong.
Answer:
Step-by-step explanation:
every thing looks good, except the question says "round" and soooooo, if you are rounding to the 2nd decimal place, then the next two decimal places are 54, or 50.2654 so, to round that, round up , so your final answer would look like 50.27 :) see?
9514 1404 393
Answer:
50.24 inches (or 50.2 inches)
Step-by-step explanation:
The formula for circumference in terms of radius is ...
C = 2πr
Using the given values for radius and for pi, the circumference is ...
C = 2(3.14)(8 in) = 50.24 in
__
Additional comment
If you use a more accurate value of pi, the rounded value is 50.27 in. That is not the value requested by this problem. It helps to follow directions.
If you like, you can round to 50.2, since only one decimal place is required in the result.
Factor 2x2+25x+50. Rewrite the trinomial with the x-term expanded, using the two factors.
9514 1404 393
Answer:
rewrite: 2x^2 +5x +20x +50factored: (x +10)(2x +5)Step-by-step explanation:
I find this approach the most straightforward of the various ways that trinomial factoring is explained or diagramed.
You want two factors of "ac" that have a total of "b". Here, that means you want factors of 2·50 = 100 that have a total of 25. It is helpful to know your times tables.
100 = 1·100 = 2·50 = 4·25 = 5·20 = 10·10
The sums of these factor pairs are 101, 52, 29, 25, and 20. We want the pair with a sum of 25, so that's 5 and 20.
The trinomial can be rewritten using these factors as ...
2x^2 +5x +20x +50
Then it can be factored by grouping consecutive pairs:
(2x^2 +5x) +(20x +50) = x(2x +5) +10(2x +5) = (x +10)(2x +5)
_____
Additional comment
It doesn't matter which of the factors of the pair you write first. If our rewrite were ...
2x^2 +20x +5x +50
Then the grouping and factoring would be (2x^2 +20x) +(5x +50)
= 2x(x +10) +5(x +10) = (2x +5)(x +10) . . . . . same factoring
13, 5, 4, 9, 7, 14, 4 The deviations are _____.
A. "5, -3, -4, 0, 1, 6, 4"
B."5, -3, -4, 1, -1, 6, -4"
C."6, -3, -4, 1, 2, 6, -4"
D."-5, 3, 4, -1, 1, 6, 4 "
Answer:
B."5, -3, -4, 1, -1, 6, -4"
Step-by-step explanation:
We are given that
13,5,4,9,7,14,4
We have to find the deviation.
Mean=[tex]\frac{sum\;of\;data}{total\;number\;of\;data}[/tex]
Using the formula
[tex]Mean,\mu=\frac{13+5+4+9+7+14+4}{7}[/tex]
[tex]Mean,\mu=\frac{56}{7}=8[/tex]
Deviation=[tex]x_i-\mu[/tex]
[tex]x_i-\mu[/tex]
13 5
5 -3
4 - 4
9 1
7 -1
14 6
4 - 4
Hence, option B is correct.
solve the inequality 4t^2 ≤ 9t-2 please show steps and interval notation. thank you!
Answer: [tex]t\in [\dfrac{1}{4},2][/tex]
Step-by-step explanation:
Given
Inequality is [tex]4t^2\leq9t-2[/tex]
Taking variables one side
[tex]\Rightarrow 4t^2-9t+2\leq0\\\Rightarrow 4t^2-8t-t+2\leq0\\\Rightarrow 4t(t-2)-1(t-2)\leq0\\\Rightarrow (4t-1)(t-2)\leq0[/tex]
Using wavy curve method
[tex]t\in [\dfrac{1}{4},2][/tex]
Find the prime factorisation of each of the following numbers, leaving your answer in index notation..
(e) 117 800
plzz answer quick
Answer:
3x3x13 and 2 x 2 x 2 x 2 x 2 x 5 x 5
Step-by-step explanation:
Explain why the following function is not piecewise continuous
9514 1404 393
Answer:
the function has no finite limit at the left end of the interval (5, ∞)
Step-by-step explanation:
In order for the function to be piecewise continuous, it must have finite limits at the endpoints of each of the subintervals. Here, the function goes to infinity as x → 5+, so has no finite limit there.
Which expression is equivalent to v2/3v2? 1/4 6v2 v2 v2/2
Answer:
Step-by-step explanation:
[tex]2^{1/2} - 2^{-1/3} = 2^{1/2 + 1/3} = 2^{3/6} = 2^{1/2} = \sqrt{2}[/tex]
Answer:
[tex]\sqrt[6]{2}[/tex]
Step-by-step explanation:
2 ^ 1/2 ÷ 2 ^ 1/3
We know that a^b ÷ a^ c = a^(b-c)
2 ^ (1/2 -1/3)
2^ (3/6 - 2/6)
2 ^ 1/6
[tex]\sqrt[6]{2}[/tex]
Questions 24-25. In 1963, postage was 5 cents per ounce. In 1981, postage was 18 cents per ounce.
If the trend had continued through to 2015, what would the postage per ounce be?
(round to the nearest central
The answer posted "42.55" is incorrect.
Answer:
The postage per ounce would be of $2.02.
Step-by-step explanation:
Exponential model:
The postage, in t years after 1963, follows the following format:
[tex]P(t) = P(0)(1+r)^t[/tex]
In which P(0) is the initial value and r is the growth rate, as a decimal.
In 1963, postage was 5 cents per ounce.
This means that [tex]P(0) = 5[/tex]
So
[tex]P(t) = P(0)(1+r)^t[/tex]
[tex]P(t) = 5(1+r)^t[/tex]
In 1981, postage was 18 cents per ounce.
This means that [tex]P(1981 - 1963) = P(18) = 18[/tex]. We use this to find r. So
[tex]P(t) = 5(1+r)^t[/tex]
[tex]18 = 5(1+r)^{18}[/tex]
[tex](1+r)^{18} = \frac{18}{5}[/tex]
[tex]\sqrt[18]{(1+r)^{18}} = \sqrt[18]{3.6}[/tex]
[tex]1 + r = (3.6)^{\frac{1}{18}}[/tex]
[tex]1 + r = 1.0738[/tex]
So
[tex]P(t) = 5(1.0738)^t[/tex]
If the trend had continued through to 2015, what would the postage per ounce be?
2015 - 1963 = 52, so this is P(52).
[tex]P(52) = 5(1.0738)^{52} = 202[/tex]
202 cents, so $2.02.
solve the system of equation — 3х + бу = 9
5х + 7y = -49
Answer:
y = 64/3
x = -119/3
Step-by-step explanation:
3х + 6у = 9 => 5*3x+5*6у = 9*5 => 15x+30у=45 (1)
5х + 7y = -49 => 3*5x + 3*7y = -49*3 => 15x+21y=-147 (2)
(1)-(2) => 9y = 192 => y = 64/3
x = -119/3
Using law of sines please show process and answer
Hello,
[tex]\widehat{A}=180^o-24.4^o-103.6^o=52^o\\\\\dfrac{sin(24.4^o)}{37.3} =\dfrac{sin(103.6^o)}{c} \\\\\\c=87.760246\approx{87.8}\\\\\\\dfrac{sin(52^o)}{a} =\dfrac{sin(24.4^o)}{37.3} \\\\\\a=71.1510189...\approx{71.2}\\[/tex]
1.6000×6+787838837÷748+783998-8387=
2.45000÷45×463×6377+6388-894=
Solve using the elimination method
x + 5y = 26
- X+ 7y = 22
Answer:
[tex]x=6\\y=4[/tex]
Step-by-step explanation:
Elimination method:
[tex]x+5y=26[/tex]
[tex]-x+7y=22[/tex]
Add these equations to eliminate x:
[tex]12y=48[/tex]
Then solve [tex]12y=48[/tex] for y:
[tex]12y=48[/tex]
[tex]y=48/12[/tex]
[tex]y=4[/tex]
Write down an original equation:
[tex]x+5y=26[/tex]
Substitute 4 for y in [tex]x+5y=26[/tex]:
[tex]x+5(4)=26[/tex]
[tex]x+20=26[/tex]
[tex]x=26-20[/tex]
[tex]x=6[/tex]
{ [tex]x=6[/tex] and [tex]y=4[/tex] } ⇒ [tex](6,4)[/tex]
hope this helps...
Answer:
x = 6, y = 4
Step-by-step explanation:
x + 5y = 26
- x + 7y = 22
_________
0 + 12y = 48
12y = 48
y = 48 / 12
y = 4
Substitute y = 4 in eq. x + 5y = 26,
x + 5 ( 4 ) = 26
x + 20 = 26
x = 26 - 20
x = 6
Use reduction of order to find a second linearly independent solution
(2x+5)y′′−4(x+3)y′+4y=0,x>−52,y1=e2x
Given that exp(2x) is a solution, we assume another solution of the form
y(x) = v(x) exp(2x) = v exp(2x)
with derivatives
y' = v' exp(2x) + 2v exp(2x)
y'' = v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)
Substitute these into the equation:
(2x + 5) (v'' exp(2x) + 4v' exp(2x) + 4v exp(2x)) - 4 (x + 3) (v' exp(2x) + 2v exp(2x)) + 4v exp(2x) = 0
Each term contains a factor of exp(2x) that can be divided out:
(2x + 5) (v'' + 4v' + 4v) - 4 (x + 3) (v' + 2v) + 4v = 0
Expanding and simplifying eliminates the v term:
(2x + 5) v'' + (4x + 8) v' = 0
Substitute w(x) = v'(x) to reduce the order of the equation, and you're left with a linear ODE:
(2x + 5) w' + (4x + 8) w = 0
w' + (4x + 8)/(2x + 5) w = 0
I'll use the integrating factor method. The IF is
µ(x) = exp( ∫ (4x + 8)/(2x + 5) dx ) = exp(2x - log|2x + 5|) = exp(2x)/(2x + 5)
Multiply through the ODE in w by µ :
µw' + µ (4x + 8)/(2x + 5) w = 0
The left side is the derivative of a product:
[µw]' = 0
Integrate both sides:
∫ [µw]' dx = ∫ 0 dx
µw = C
Replace w with v', then integrate to solve for v :
exp(2x)/(2x + 5) v' = C
v' = C (2x + 5) exp(-2x)
∫ v' dx = ∫ C (2x + 5) exp(-2x) dx
v = C₁ (x + 3) exp(-2x) + C₂
Replace v with y exp(-2x) and solve for y :
y exp(-2x) = C₁ (x + 3) exp(-2x) + C₂
y = C₁ (x + 3) + C₂ exp(2x)
It follows that the second fundamental solution is y = x + 3. (The exp(2x) here is already accounted for as the first solution.)
What do you add to 2 7/8 to make 5
Answer:
2 1/8
Step-by-step explanation:
7/8 is the same as 0.875 and therefore you need 0.125 also known as 1/8 to make it a whole number. When you add it to the already existing whole 2 you get three. Subtract three from five to make two which is what you need to add on top to finally get 5.
4. One in four people in the US owns individual stocks. You randomly select 12 people and ask them if they own individual stocks. a. Find the mean, variance, and standard deviation of the resulting probability distribution. (3pts) b. Find the probability that the number of people who own individual stocks is exactly six. (3pts) c. Find probability that the number of people who say they own individual stocks is at least two. (3pts) d. Find the probability that the number of people who say they own individual stocks is at most two. (3pts) e. Are the events in part c. and in part d. mutually exclusive
Answer:
a. The mean is 3, the variance is 2.25 and the standard deviation is 1.5.
b. 0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.
c. 0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.
d. 0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two
e. Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they own stocks, or they do not. The probability of a person owning stocks is independent of any other person, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
One in four people in the US owns individual stocks.
This means that [tex]p = \frac{1}{4} = 0.25[/tex]
You randomly select 12 people and ask them if they own individual stocks.
This means that [tex]n = 12[/tex]
a. Find the mean, variance, and standard deviation of the resulting probability distribution.
The mean of the binomial distribution is:
[tex]E(X) = np[/tex]
So
[tex]E(X) = 12(0.25) = 3[/tex]
The variance is:
[tex]V(X) = np(1-p)[/tex]
So
[tex]V(X) = 12(0.25)(0.75) = 2.25[/tex]
Standard deviation is the square root of the variance, so:
[tex]\sqrt{V(X)} = \sqrt{2.25} = 1.5[/tex]
The mean is 3, the variance is 2.25 and the standard deviation is 1.5.
b. Find the probability that the number of people who own individual stocks is exactly six.
This is P(X = 6). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 6) = C_{12,6}.(0.25)^{6}.(0.75)^{6} = 0.0401[/tex]
0.0401 = 4.01% probability that the number of people who own individual stocks is exactly six.
c. Find probability that the number of people who say they own individual stocks is at least two.
This is:
[tex]P(X \geq 2) = 1 - P(X < 2)[/tex]
In which
[tex]P(X < 2) = P(X = 0) + P(X = 1)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]
[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]
[tex]P(X < 2) = P(X = 0) + P(X = 1) = 0.0317 + 0.1267 = 0.1584[/tex]
0.1584 = 15.84% probability that the number of people who say they own individual stocks is at least two.
d. Find the probability that the number of people who say they own individual stocks is at most two.
This is:
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{12,0}.(0.25)^{0}.(0.75)^{12} = 0.0317[/tex]
[tex]P(X = 1) = C_{12,1}.(0.25)^{1}.(0.75)^{11} = 0.1267[/tex]
[tex]P(X = 2) = C_{12,2}.(0.25)^{2}.(0.75)^{10} = 0.2323[/tex]
[tex]P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0317 + 0.1267 + 0.2323 = 0.3907[/tex]
0.3907 = 39.07% probability that the number of people who say they own individual stocks is at most two.
e. Are the events in part c. and in part d. mutually exclusive
Both cases include one common outcome, that is, 2 people owning stocks, so the events are not mutually exclusive.
If today is Friday, tomorrow will be Saturday
Answer:
Yes
Step-by-step explanation:
Yesterday would be Thursday and the day after next would be Sunday
evaluate expression when a=5 b= -3
6a-b
We deposit $12000 into an account carning 3 % interest compounded continuously, How many years will it take
for the account to grow to $16800? Round to 2 decimal places,
Answer:
The answer is 13.33 year
Step-by-step explanation:
P = $12000
Rate = 3%
Amount = $16800
so,
I = A-P
= $16800 - $12000
= $4800
So,
T = (I × 100)/P×R
= (4800×100)/P×R
= 480000/($12000×3)
= 480000/36000
= 480/36
= 13.33 year
SCC U of 1 pt 3 of 1 1.2.11 Assigned Media A rectangle has a width of 49 centimeters and a perimeter of 216 centimeters. V The length is cm.
Answer:
The length is of 59 cm.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with width w and length l is given by:
[tex]P = 2(w + l)[/tex]
Width of 49 centimeters and a perimeter of 216 centimeters:
This means that [tex]w = 49, P = 216[/tex]
The length is cm.
We have to solve the equation for l. So
[tex]P = 2(w + l)[/tex]
[tex]216 = 2(49 + l)[/tex]
[tex]216 = 98 + 2l[/tex]
[tex]2l = 118[/tex]
[tex]l = \frac{118}{2}[/tex]
[tex]l = 59[/tex]
The length is of 59 cm.
Which is the graph of f(x) = 4(1/2)^x
Answer:
B.
Step-by-step explanation:
f(x) = 4(1/2)^x
Let's find the value of the function for x = 0 and for x = 1.
f(0) = 4(1/2)^0 = 4(1) = 4
f(1) = 4(1/2)^1 = 4(1/2) = 2
The only graph that has both points (0, 4) and (1, 2) is the second graph.
Answer: B.
Is the random variable described discrete or continuous? The amount of rain during the next thunderstorm.
Answer:
continuous
rain does not fall in specific units like 1 inch , 2 inches etc... but 1.23456 etc..
Step-by-step explanation:
Find the range of the data set represented by this box plot.
25
70
20
60
Answer:
D. 60
Step-by-step explanation:
Range is the difference between the maximum value and the minimum value.
The minimum value is at the extreme end of the whisker of the box plot to your left = 65
The maximum value is at the extreme end of the whisker of the box plot to your right = 125
Range = 125 - 65 = 60
Consider the exponential function f(x) = One-fifth(15x). What is the value of the growth factor of the function?
Answer:
15
Step-by-step explanation:
Yellowstone National Park is a popular held trip destination. This year the senior class at
High School A and the senior class at High School B both planned trips there. The senior
class at High School A rented and filed 2 vans and 3 buses with 153 students. High
School Brented and nited il vans and 10 buses with 534 students. Every van had the
same number of students in it as did the buses. Find the number of students in each van
and in each bus.
Van: 39
Bus: 18
Van: 21
Bus: 21
o
Van: 27
Bus: 19
.
Van: 18
Bus: 39
Answer:
Who was the first president of United States?