Answer:
there are two solutions:
x=0
and
x=14
Step-by-step explanation:
lts suppose the numbers are x and x+2, so:
[tex]x(x+2)=8(x+(x+2))-16\\x(x+2)=8(2x+2)-16=16x+16-16=16x\\x^2+2x=16x\\x^2-14x=0\\x(x-14)=0\\x=0,~x=14[/tex]
Can someone help me with this problem
9514 1404 393
Answer:
x = 30°
Step-by-step explanation:
The lines will be parallel if and only if the sum of the marked angles is 180°:
4x +2x = 180°
6x = 180° . . . . . collect terms
x = 30° . . . . . . . divide by 6
Which of the following functions shows the reciprocal parent function, F(x) = 1, shifted left?
Answer:
G(x)=1/x+15
Step-by-step explanation:
.
She decides that ordering that many cars would not be economically feasible at this time and asks her sales manager to randomly choose one of the models for the sales lot. What is the probability that he chooses the 4-door, special edition model, with four-wheel drive?
The probability that he chooses the 4-door, special edition, four-wheel drive model is (44)=
P(4S4)=
Answer:
The probability that he chooses the 4-door, special edition, four-wheel drive model is P( 454) = 1 (Enter your answer as reduced fraction.) ...Step-by-step explanation:
The probability that he chooses the 4-door, special edition, four-wheel drive model is (44)=P(4S4)=Any two normal curves are the same except for their Multiple Choice standard deviations. means. standard deviations and means. standard deviations, means, skewness, and kurtosis.
Answer:
Standard deviation, means, skewness and kurtosis.
Step-by-step explanation:
Two normal curves may be same but they have different means, standard deviation and skewness. There can be different standard deviation for two curves and there is difference in skewness.
How many different committees can be formed from 12 teachers and 43 students if the committee consists of 3 teachers and 4 students?
The committee of 7 members can be selected in BLANK
different ways.
Answer:
27150200Step-by-step explanation:
Combination of 3 teachers out of 12:
12C3 = 12!/9!3! = 10*11*12/2*3 = 220Combination of 4 students out of 43:
43C4 = 43!/39!4! = 40*41*42*43/2*3*4 = 123410Total combinations:
220*123410 = 27150200What is the value of x if 2/ 3 - 2 = -4 ?
Answer:
x= -3
Step-by-step explanation:
(2x/3)-2=-4
Add 2 to both sides
2x/3=-2
multiply both sides by 3
2x=-6
divide both sides by 2
x= -3
Answer:
x = -3
Step-by-step explanation:
2x/3 - 2 = -4
Add 2 to both sides.
2x/3 = -2
Multiply both sides by 3/2.
x = -2 * 3/2
x = -3
15. Mark Twain one observed that the lower Mississippi River is very crooked and that over the years, as the bends and turns straighten out, the river gets shorter and shorter. Using numerical data about the length of the lower part of the river, he noticed that in the year 1700 the river was more than 1200 miles long, yet by the year 1875 it was only 973 miles long. Twain concluded that any person “can see that 742 years from now the lower Mississippi will be only a mile and three-quarters lone.” What is wrong with his inductive reasoning?
Answer:
Step-by-step explanation:
I'm sure he was making a joke at the expense of people who rely on mathematics rather than common sense. It is funny, but then Twain was a remarkably funny author..
The problem is that the comparison is apt using some sort of proportion, but it is absurd to think that the land holding the river would also shrink a proportional amount.
The river reached a minimum (presumably) in 1875 by cutting out all the loops that were there in 1700. The Mississippi was then a straight line from it's beginning to its delta on the gulf of Mexico. It could not get any shorter. Still, Twain managed to get laughs with his whimsical humor.
Thanks for posting. This made my evening.
Which of the following proportions is true?
10/40 = 8/36
8/18 = 6/16
9/15 = 44/50
12/18 = 16/24
Answer:
D. 12/18 = 16/24
Step-by-step explanation:
The method we must go about to solve this is finding the constant. For A, we can solve it by doing 10 divided by 8 (which is 1.25) and then 40 divided by 1.25 to see if it is 36. Alternatively, we can do 10 divided by 8 and then 40 divided by 36 to see if the constant is the same. It's up to you!
My answers:
A. No (constant varies)
B. No (constant varies)
C. No (constant varies)
D. Yes! Constant is 0.75
How to solve for D:
12/16 = 0.75
18/0.75 = 24 OR 18/24 = 0.75
I hope this helps! Please don't hesitate to reach out with more questions!
Hello!
10/40 = 8/36 ?
10 × 36 = 40 × 8
360 = 40 × 8
360 ≠ 320 => 10/40 ≠ 8/36
8/18 = 6/16 ?
8 × 16 = 18 × 6
128 = 18 × 6
128 ≠ 108 => 8/18 ≠ 6/16
9/15 = 44/50 ?
9 × 50 = 15 × 44
450 = 15 × 44
450 ≠ 660 => 9/15 ≠ 44/50
12/18 = 16/24 ?
12 × 24 = 18 × 16
288 = 18 × 16
288 = 288 => 12/18 = 16/24
Good luck! :)
circle A has a center of (2,3) and a radius of 5 and circle B has a center of (1,4) and a radius of 10. What steps will help show that circle A is similar to circle B
Answer:
12
Step-by-step explanation:
A(n) _____ is an expression that uses variables to state a rule.
plz help asap
Answer:
A FORMULA is an expression that uses variables to state a rule.
what is the value of -3^2+(4+7)(2)?
Answer:
[tex] { - 3}^{2} + (4 + 7)(2) \\ = - 9 + 22 \\ = 13[/tex]
Joe bikes at the speed of 30 km/h from his home toward his work. If Joe's wife leaves home 5 mins later by car, how fast should she drive in order to overtake him in 10 minutes.
Answer:
Joe's wife must drive at a rate of 45km/hour.
Step-by-step explanation:
We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.
Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.
Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:
[tex]2.5+0.5t[/tex]
Where t represents the time in minutes after his wife left the house.
And since we want to catch up in 10 minutes, Joe's distance from the house 10 minutes after his wife left will be:
[tex]2.5+0.5(10)=7.5\text{ km}[/tex]
Let s represent the wife's speed in km/min. So, her speed times 10 minutes must total 7.5 km:
[tex]10s=7.5[/tex]
Solve for s:
[tex]\displaystye s=0.75\text{ km/min}[/tex]
Thus, Joe's wife must drive at a rate of 0.75km/min, or 45km/hour.
Need help please....
Answer:
-14 x²
Step-by-step explanation:
10 x² - 24 x² = -14 x²
The answer is 14
if you multiply both P(x) and Q(x), the third part becomes 14x², so the coefficient of x² becomes 14.
Answered by GAUTHMATH
What is the expression (x+1)(x2+3x+2) as a polynomial in standard form?
Step-by-step explanation:
hope u like it.......
Suppose you just received a shipment of 14 televisions. Three of the televisions are defective. If two televisions are randomly selected , compute the probability that both televisions work. What is the probability at least one of the two televisions does not work?
Answer:
Probability of defective televisions : Now, If two televisions are randomly selected, then the probability that both televisions work. Hence, the probability that both televisions work is 0.5289 . Hence, the probability at least one of the two televisions does not work is 0.4711.
FastForward has net income of $19,090 and assets at the beginning of the year of $209,000. Its assets at the end of the year total $264,000. Compute its return on assets.
Given:
Net income = $19,090
Assets at the beginning of the year = $209,000.
Assets at the end of the year total = $264,000.
To find:
The return on assets.
Solution:
Formula used:
[tex]\text{Return of assets}=\dfrac{\text{Net income}}{\text{Average of assets at the beginning and at the end}}[/tex]
Using the above formula, we get
[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{20900+264000}{2}}[/tex]
[tex]\text{Return of assets}=\dfrac{19090}{\dfrac{473000}{2}}[/tex]
[tex]\text{Return of assets}=\dfrac{19090}{236500}[/tex]
[tex]\text{Return of assets}\approx 0.0807[/tex]
The percentage form of 0.0807 is 8.07%.
Therefore, the return on assets is 8.07%.
What is the sum?
8+(-12)
-20
4
ОО
20
1+1/2+1/4+1/8+1/16+1/32+1/64
if you continue adding on fractions according to this pattern, when will you reach a sum of 2?
Answer: You will never reach a sum of 2. You would need infinitely many terms to sum up.
============================================================
Explanation:
We have this sequence
1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, ...
which is geometric with the following properties
a = first term = 1r = common ratio = 1/2 = 0.5Notice how we multiply each term by 1/2 to get the next term. Eg: (1/4)*(1/2) = 1/8 or (1/16)*(1/2) = 1/32.
Since r = 0.5 is between -1 and 1, i.e. -1 < r < 1 is true, this means that adding infinite terms of this form will get us to approach some finite sum which we'll call S. This is because the new terms added on get smaller and smaller.
That infinite sum is
S = a/(1-r)
S = 1/(1-0.5)
S = 1/0.5
S = 2
So if we keep going with that pattern 1+1/2+1/4+... and do so forever, then we'll reach a sum of 2. However, we cannot go on forever since it's asking when we'll reach that specific sum. In other words, your teacher wants finitely many terms to be added.
In short, we'll never actually reach the sum 2 itself. We'll just get closer and closer.
Here's a list of partial sums
1+1/2 = 1.51+1/2+1/4 = 1.751+1/2+1/4+1/8 = 1.8751+1/2+1/4+1/8+1/16 = 1.93751+1/2+1/4+1/8+1/16+1/32 = 1.968751+1/2+1/4+1/8+1/16+1/32+1/64 = 1.9843751+1/2+1/4+1/8+1/16+1/32+1/64+1/128 = 1.99218751+1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256 = 1.99609375We can see that we're getting closer to 2, but we'll never actually get there. We'd need to add infinitely many terms to get to exactly 2.
Donald and Sara are surveying their neighbors about the community playground. Their questions, written on the survey, are below:
Donald: How many times do you visit the playground in a month?
Sara: Did you visit the playground this month?
Who wrote a statistical question and why?
Sara, because there will be variability in the responses collected
Donald, because every neighbor can give a different answer
Sara, because there can be only one answer to the question
Donald, because every neighbor will give the same answer
Answer:
B
Step-by-step explanation: Because Donald asks a more broad and open question which people could give different answers too
In a shipment of toys from a manufacturer, the probability that a toy is defective is
1
50
. If Marie selects 2 toys from a shipment, what is the probability that both toys are defective?
Answer:
The probability is 1/2500. (1/50)*(1/50)
Step-by-step explanation:
Which choice correctly shows the line y =
2x+3?
А
B
HN
N
1-3 -2 -1 1 2 3 4
-1
NH
-4 -3 -2 -1
1 2 3 4
D
c
2
1
1-3-2-1
1
2 3 4
-4 -3 -2
1 2 3
-1
-2
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24. What could be the 2-digit number? List all options.
Given:
The number 55 is attached to a two-digit number to its left and the formed 4-digit number is divisible by 24.
To find:
The 2-digit numbers.
Solution:
Let the two digit number be [tex]ab[/tex]. Then the 4 digit number will be [tex]55ab[/tex].
We know that the number [tex]55ab[/tex] lies in the range 5500 to 5599.
Now,
[tex]5500=229\times 24+4[/tex]
It means, [tex]5500-4=5496[/tex] is divisible by 24. So, the numbers lie in the range 5500 to 5599 and divisible by 24 are:
[tex]5496+24=5520[/tex]
[tex]5520+24=5544[/tex]
[tex]5544+24=5568[/tex]
[tex]5568+24=5592[/tex]
Therefore, the possible 2-digit numbers are 20, 44, 68, 92.
In the given figure, find m_RST, if m RSU = 43° and m_UST = 23°.
Answer:
66
Step-by-step explanation:
Add both of the angles given together
43 + 23
PLEASE BE RIGHT AND SOLVE PLEASE
Answer:
That transformation that happened was B rotation since b is rotated 180 degrees from A
Hope This Helps!!!
8. Calculate the Perimeter AND Area of
the RIGHT Triangle below.
17 m
10 m
21 m
Answer:
[tex]\text{Perimeter: }48\:\mathrm{m},\\\text{Area: }84\:\mathrm{m^2}[/tex]
Step-by-step explanation:
The area of a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] is given by:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex], where [tex]s=\frac{a+b+c}{2}[/tex]
Substituting [tex]a=21, b=17, c=10[/tex], we have:
[tex]A=\sqrt{24(24-21)(24-17)(24-10)},\\A=\sqrt{24(3)(7)(14)},\\A=\sqrt{7,084},\\A=\boxed{84\:\mathrm{m^2}}[/tex]
The perimeter of a polygon is given by the sum of its sides. Since the triangle has sides 10, 17, and 21, its perimeter is [tex]10+17+21=\boxed{48\:\mathrm{m}}[/tex].
by what number should 2/9 be divided to obtain 8/3
Answer:
[tex] \frac{1}{12} [/tex]
Step-by-step explanation:
[tex] \frac{2}{9} \div \frac{8}{3} \\ = \: \frac{1}{12}[/tex]
So, if you divide 2/9 by 1/12, you'll get 8/3
Answered by GAUTHMATH
Suppose the age that children learn to walk is normally distributed with mean 12 months and standard deviation 2.5 month. 34 randomly selected people were asked what age they learned to walk. Round all answers to 4 decimal places where possible.
Answer:
Step-by-step explanation:
a.) it's just mean, variance
so here it's just 12,6.25
b.) For the x bar thing just divide the variance by the number of people (mean stay the same)
the variance is then (2.5²/34)= .1838
which makes it (12,.1838)
c.) here we don't use x bar (and so it's normal (12,2.5²))
p(11.6) = (11.6-12)/(2.5)= -.16 = .4364
p(12.4)= (12.4-12)/2.5 = .16= .5636
.5636-.4364= .1272
d.) here we use x bar because it's asking for an average so it's normal (12, .1838)
same deal
p(11.6)=(11.6-12)/√.1838= -.93295= .1762
p(12.4)= (12.4-12)/√.1838= .93295= .8238
.8238-.1762= .6476
d.) no because they're probably IID
f.) It's average so here we use x bar
q1 is just the 25th percentile
the 25th percentile is -.6745
-.6745=(x-12)/(√.1838)= 11.711
q3 is the 75th percentile
.6745=(x-12)/√.1838
x=12.289
The interquartile range is just the difference between the two
12.289-11.711= .5784
Which of these is an example of technology?
an idea for a story
the first wheel ever built
an engineer
Answer:
the first wheel ever built
Answer:
The first wheel ever built
Step-by-step explanation
(*) Sorry for my late answer but I hope this helps others that are looking for this.
100% in the test :)
Feedback:Correct answer
Question 2 of 10
10.0 Points
3
Find the interquartile range for a data set having the five-number
summary: 4.6, 14.3, 19.7, 26.1, 31.2
A. 26.6
B. 11.8
C. 11.5
D. 15.1
Can someone help me solve this? Thanks!
9514 1404 393
Answer:
p(x) = x³ -3x²+4x -2
Step-by-step explanation:
When the polynomial has real coefficients, the complex roots come in conjugate pairs. You are given one root as 1+i, so there is another that is 1-i.
Each root r gives rise to a factor (x -r). Then the three roots tell you the factorization is ...
p(x) = (x -1)(x -(1+i))(x -(1-i))
The last two factors can be recognized as the factors of the difference of squares:
((x -1) +i)((x -1) -i) = (x -1)² -i²
= (x² -2x +1) -(-1) = x² -2x +2
Now the whole polynomial can be seen to be ...
p(x) = (x -1)(x² -2x +2) = x(x² -2x +2) -1(x² -2x +2)
p(x) = x³ -2x² +2x -x² +2x -2 . . . . eliminate parentheses
p(x) = x³ -3x²+4x -2