Answer:
hello,
a) answer: 600
b) answer: 840
Step-by-step explanation:
a)
20=2²*5,25=5²,30=2*3*5,40=2³*5
l.c.m(20,25,30,40)=2³*3*5²=8*3*25=800
b)
24=2³*3, 42=2*3*7,35=5*7
l.c.m=(24,42,35)=2³*3*5*7=840
Describe the system of equations
How many solutions does this system have.
Answer:
Step-by-step explanation:
One solution, at the point of intersection, (3,3)
Define percent in terms of ratios
Find f(0) and then find the equation of the given linear function.
x 1 2 3 4
f(x) 6 10 14 18
f(0) =
f(x) =
Answer:
f(0) = 2
f(x) = 4x + 2
Step-by-step explanation:
You can see that the consecutive x-values are producing y-values that increase by 4 each time. Since the change in y is the same every time, we know this is a linear graph because in a continuous linear graph the slope does not change.
We can use the equation for a line: y = mx + b,
where m is the slope and b is the y-intercept.
The slope [m] is calculated by [change in y]/[change in x]. The y-values are increasing by 4 each time x increases by 1. m = 4/1 = 4.
Once we have found the slope, we can find the value for f(0). The line graph has a positive slope, so to find the value at x=0, we would subtract 4, moving backwards along the line.
6-4 = 2
The y-intercept on a line is the y-value for which x = 0. In this case we have already solved for the y-intercept, f(0) = 2.
Now plug the values into the formula.
y = mx + b
The value of f(0) is 2.
The equation of this linear function is y = 4x + 2
What is a function?A function is defined as a relation between a set of inputs having one output each.
The inputs are called domain of the function.
The outputs are called the range of the function.
We have,
x = 1, 2, 3, 4
f(x) = 6, 10, 14, 18
The f(x) values are the values we get when we substitute x values.
There is a difference of 4 in the f(x) values.
10 - 6 = 4
14 - 10 = 4
18 - 14 = 4
Since the difference between the values of f(x) is same, the given function is a linear function.
The equation of this linear function will be in the form of:
y = mx + c
m = slope
c = y-intercept
Find m.
Choose any two points as: (1, 6) and (2, 10)
m = 10-6 / 2-1 = 4/1= 4
Find c.
x = 0 in y-intercept and choosing any point = (1, 6)
So,
6 = 4 + c
c = 6 - 4 = 2
Now,
The equation of this linear function:
y = 4x + 2
f(0) = 4 x 0 + 2 = 0 + 2 = 2
Thus,
The value of f(0) is 2.
The equation of this linear function is y = 4x + 2
Learn more about functions here:
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Brenda wants to buy a sweater that costs 138 Croatian kuna (form of money in Croaita). She has $20.
$1 = 6 Croatian kuna
Fill in the blank.
$20 = (blank) Croatian kuna
Does Brenda have enough money to buy the sweater?
Answer:
She only has 120 croat
Step-by-step explanation:
We can use a ratio to solve
She only has 20 dollars
1 dollar 20 dollars
---------- = --------------
6 croat x croat
6*20 = x
120 =x
120croat
She does not have enough money
She needs 138 croat
Answer:
120 croatian kuna
Step-by-step explanation:
One of the problems encountered by corporations in America is finding an adequate number of employees who want to move into management. Recent surveys of workers in America taken by the Department of Labor in Washington D. C. revealed that only 20% of employees would like to move into management and be the boss. Suppose that a random sample of 75 U.S. workers was taken and each person was asked whether or not they would like to move into management. Find the probability that at least 18 of the 75 sampled employees would like to move into management.
Answer:
0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x successes on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
20% of employees would like to move into management and be the boss.
This means that [tex]p = 0.2[/tex]
Sample of 75:
This means that [tex]n = 75[/tex]
Mean and standard deviation:
[tex]\mu = E(X) = np = 75(0.2) = 15[/tex]
[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{75*0.2*0.8} = 3.4641[/tex]
Find the probability that at least 18 of the 75 sampled employees would like to move into management.
Using continuity correction, this is [tex]P(X \geq 18 - 0.5) = P(X \geq 17.5)[/tex], which is 1 subtracted by the p-value of X = 17.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{17.5 - 15}{3.4641}[/tex]
[tex]Z = 0.72[/tex]
[tex]Z = 0.72[/tex] has a p-value of 0.7642.
1 - 0.7642 = 0.2358
0.2358 = 23.58% probability that at least 18 of the 75 sampled employees would like to move into management.
Pls help with this question. No links.
Answer:
i hope it's helpful for youThe time for a visitor to read health instructions on a Web site is approximately normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes. Suppose 64 visitors independently view the site. Determine the following: a. The expected value and the variance of the mean time of the visitors. b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes c. The value exceeded by the mean time of the visitors with probability 0.01.
Answer:
a) The mean is 10 and the variance is 0.0625.
b) 0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.
c) 10.58 minutes.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Normally distributed with a mean of 10 minutes and a standard deviation of 2 minutes.
This means that [tex]\mu = 10, \sigma = 2[/tex]
Suppose 64 visitors independently view the site.
This means that [tex]n = 64, = \frac{2}{\sqrt{64}} = 0.25[/tex]
a. The expected value and the variance of the mean time of the visitors.
Using the Central Limit Theorem, mean of 10 and variance of (0.25)^2 = 0.0625.
b. The probability that the mean time of the visitors is within 15 seconds of 10 minutes.
15 seconds = 15/60 = 0.25 minutes, so between 9.75 and 10.25 seconds, which is the p-value of Z when X = 10.25 subtracted by the p-value of Z when X = 9.75.
X = 10.25
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{10.25 - 10}{0.25}[/tex]
[tex]Z = 1[/tex]
[tex]Z = 1[/tex] has a p-value of 0.8413.
X = 9.75
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{9.75 - 10}{0.25}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a p-value of 0.1587.
0.8413 - 0.1587 = 0.6826.
0.6826 = 68.26% probability that the mean time of the visitors is within 15 seconds of 10 minutes.
c. The value exceeded by the mean time of the visitors with probability 0.01.
The 100 - 1 = 99th percentile, which is X when Z has a p-value of 0.99, so X when Z = 2.327.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]2.327 = \frac{X - 10}{0.25}[/tex]
[tex]X - 10 = 2.327*0.25[/tex]
[tex]X = 10.58[/tex]
So 10.58 minutes.
Determine the probability of landing on tails at most 33 times if you flip a fair coin 80 times. Round your answer to the nearest tenth.
Answer:
0.0728177272
Step-by-step explanation:
Given :
Number of flips = 80
Probability of landing on tail at most 33 times ;
Probability of landing on tail on any given flip = 1 / 2 = 0.5
This a binomial probability problem:
Hence ;
P(x ≤ 33) = p(x=0) + p(x=1) +... + p(x = 33)
Using a binomial probability calculator :
P(x ≤ 33) = 0.0728177272
A paint manufacturer knows that ultraviolet light can degrade many types of paint. It wants to know which paint composition has the least amount of degradation under ultraviolet light. Three different paint compositions were tested. A wall in a windowed hallway of a paint manufacturing plant was divided into 18 sections, and each of the sections was randomly assigned to one of the three paint compositions. The wall sections were painted and then left to be exposed to sunlight. After 18 months of sunlight exposure, the walls were analyzed to determine the degree of change in pigment of the paint, and the results were compared between paint compositions. What are the individuals in this experiment?
This question uses the experimental study concept.
Doing this, we have that the walls analyzed are the individuals.
First, the concept of experimental study is presented:
Experimental study: In an experimental study, there is an intervention in the individuals, and it's effect is studied.In this question:
There is an intervention in the walls, they are painted, using three different paint compositions, and then they are exposed to sunlight, and after that the walls were analyzed, to study the degree of change in pigment of the paint, being compared between different paint compositions.
Thus, since the intervention was in the walls, they are the individuals in this experiment.
A similar question is found at https://brainly.com/question/24321224
The legs of a right triangle are 10 and 12. What is the length of the hypotenuse in simplest radical form?
A. 2√61
B. 4√17
C. 3√7
D. 5√13
Answer:
2 * sqrt(61)
Step-by-step explanation:
a = 10
b = 12
c = ?
c^2 = a^2 + b^2
c^2 = 10^2 + 12^2
c^2 = 100 + 144
c^2 = 244
c^2 = 4 * 61
sqrt(c^2) = sqrt(4) * sqrt(61)
c = 2 * sqrt(61)
Help me to answer this.
Answer:
no solution
Step-by-step explanation:
Consider the phrase "the sum of 3 times a number and the quotient of the number and 4." Let’s break it down. You want the sum of two values. The first value is 3 times a number. What expression represents 3 times a number?
9514 1404 393
Answer:
3x
Step-by-step explanation:
If x represents the number, then "3 times a number" is 3x.
__
Additional comment
"The quotient of the number and 4" is x/4.
The sum of those two expressions is ...
3x + x/4
Please help below with prob Stats
Answer:
te qif y btubf
Step-by-step explanation:
The scores on a standardized test are normally distributed with a mean of 80 and standard
deviation of 5. What test score is 0.9 standard deviations above the mean?
Answer:
84.5
Step-by-step explanation:
Given :
Mean μ = 80
Standard deviation, σ = 5
Z = number of standard deviations from the mean, Z = 0.9
Teat score, x
Using the Zscore formula :
Zscore = (x - μ) / σ
Plugging in our values :
0.9 = (x - 80) / 5
Cross multiply
0.9 * 5 = x - 80
4.5 = x - 80
4.5 + 80 = x
x = 84.5
Test score = 84.5
Which of the following is the solution set of 6x + 5 = -29? {-4}
Answer:
[tex]{ \tt{6x + 5 = - 29}} \\ { \tt{6x = - 36}} \\ { \tt{x = - 6}}[/tex]
Can someone help me? I am struggling and I would be so happy if any of you helped me. Thank you for your help.
Answer:
mean=256229+253657+218747+246163+235626+288694+316265+196721+285077+215152+253291+315011+199901+265443+291806+303556+215359+258554+293658+289935÷21
=5198845÷21
=247564.0
=247564 to the next whole number
B.6 times
Simplify
x * x^5 / x^2 * x
Hari earns Rs 4300 per month. He spends 80% from his income. How much amount does he save in a year?
Answer:
Hari saves $ 10,320 in a year.
Step-by-step explanation:
Given that Hari earns $ 4300 per month, and he spends 80% from his income, to determine how much amount does he save in a year, the following calculation must be performed:
100 - 80 = 20
4300 x 0.20 x 12 = X
860 x 12 = X
10320 = X
Therefore, Hari saves $ 10,320 in a year.
Find the sum of the geometric series given a1=−2, r=2, and n=8.
A. -510
B. -489
C. -478
D. 2
Answer:
A. -510
Step-by-step explanation:
We are given the variable values:
a = -2r = 2n = 8Geometric series formula:
[tex]s = \frac{a( {r}^{n} \times - 1) }{r - 1} [/tex]
Plugging in values we have:
[tex]s = \frac{ - 2( {2}^{8} - 1) }{2 - 1} [/tex]
Simplifying the equation we are left with:
[tex] \frac{ - 2(255)}{1} = - 510[/tex]
6. Solve for x: 3|x - 7| = 15
Please give steps! ❤️
3 | x - 7 | = 15
Divide both sides by 3
3 | x - 7 | ÷ 3 = 15 ÷ 3
| x - 7 | = 5
_________________________
" Reminder "
| a | = t ===》 a = + t OR a = - t
__________________________
| x - 7 | = 5
x - 7 = 5 ====》 x = 12
OR
x - 7 = - 5 ===》 x = 2
someone please help
Answer:
28
Step-by-step explanation:
78
If 4 gallons of gasoline cost $13.76, how much will 11 gallons of gasoline cost?
Answer:
x=37.84
Step-by-step explanation:
We can write a ratio to solve
4 gallons 11 gallons
--------------- = ----------------
13.76 x dollars
Using cross products
4x = 11*13.76
4x=151.36
Divide by 4
4x/4 = 151.36/4
x=37.84
Write the point-slope form of an equation of the line through the points (-2, 6) and (3,-2).
Answer:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
Step-by-step explanation:
Hi there!
Point-slope form: [tex]y-y_1=m(x-x_1)[/tex] where [tex](x_1,y_1)[/tex] is a point and [tex]m[/tex] is the slope
1) Determine the slope
[tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-2, 6) and (3,-2):
[tex]m=\frac{\displaystyle -2-6}{\displaystyle 3-(-2)}\\\\m=\frac{\displaystyle -8}{\displaystyle 3+2}\\\\m=-\frac{\displaystyle 8}{\displaystyle 5}[/tex]
Therefore, the slope of the line is [tex]-\frac{\displaystyle 8}{\displaystyle 5}[/tex]. Plug this into [tex]y-y_1=m(x-x_1)[/tex]:
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
2) Plug in a point [tex](x_1,y_1)[/tex]
[tex]y-y_1=-\frac{\displaystyle 8}{\displaystyle 5}(x-x_1)[/tex]
We're given two points, (-2, 6) and (3,-2), so there are two ways we can write this equation:
[tex]y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x-(-2))\\\\y-6=-\frac{\displaystyle 8}{\displaystyle 5}(x+2)[/tex]
OR
[tex]y-(-2)=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)\\y+2=-\frac{\displaystyle 8}{\displaystyle 5}(x-3)[/tex]
I hope this helps!
If (-3)^-5 = 1/x, what is the value of x?
Answer:
-243
Step-by-step explanation:
(-3) (-3) (-3) (-3) (-3) = - 243
[tex]\frac{1}{-243 }[/tex]
A bag contains 9 red balls numbered 1, 2, 3, 4, 5, 6, 7, 8, 9 and 6 white balls numbered 10, 11, 12, 13, 14, 15. One ball is drawn from the bag. What is the probability that the ball is white, given that the ball is even-numbered
Answer:
3/ 7
Step-by-step explanation:
We know that it is an even ball
2,4,6,8,10,12,14 are even balls
2,4,6,8 are red and 10,12,14 are white
P ( white) = white even / total even
= 3/ 7
HELP PLEASE I DONT KNOW THIS ONE
Answer:
-3x^2 +7x -4
-------------------------------
(x-3)(x-2)(x+3)
Step-by-step explanation:
2 3x
-------- - ----------
X^2-9 x^2 -5x+6
Factor
2 3x
-------- - ----------
(x-3)(x+3) (x-3)(x-2)
Get a common denominator
2 (x-2) 3x(x+3)
-------- - ----------
(x-3)(x+3)(x-2) (x-3)(x-2)(x+3)
2x-4 - (3x^2 -9x)
-------------------------------
(x-3)(x-2)(x+3)
Distribute
2x-4 - 3x^2 +9x
-------------------------------
(x-3)(x-2)(x+3)
Combine like terms
-3x^2 +7x -4
-------------------------------
(x-3)(x-2)(x+3)
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{gold}{Answer \red{:)}}}}}}}}[/tex]
[tex]\sf{\dfrac{2}{ x^2-9}-\dfrac{3x}{x^2-5x+6}}[/tex] [tex]\sf{\dfrac{2}{ (x)^2-(3)^2}-\dfrac{3x}{x^2-2x-3x+6} }[/tex] [tex]\sf{\dfrac{2}{(x+3)(x-3)}-\dfrac{3x}{x(x+2)-3(x+2)} }[/tex][tex]\sf{\dfrac{2}{(x+3)(x-3)}-\dfrac{3x}{(x+2)(x-3)}}[/tex][tex]\sf{\dfrac{2(x-2)-3x(x+3)}{(x+3)(x-2)(x-3)} }[/tex] [tex]\sf{\dfrac{2x-4-(3x^2-9x)}{(x+3)(x-2)(x-3) }}[/tex] [tex]\sf{\dfrac{2x-4-3x^2+9x}{(x+3)(x-2)(x-3) }}[/tex] [tex]\sf{\dfrac{-3x^2+7x-4}{(x+3)(x-2)(x-3) }}[/tex][tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
[tex]\sf{ }[/tex]
The function f(x)=log4x is dilated to become g(x)=f(13x).
What is the effect on f(x)?
Answer:
f(x) is compressed horizontally
Step-by-step explanation:
Given
[tex]f(x) = \log(4x)[/tex]
[tex]g(x) = f(13x)[/tex]
Required
The effect on f(x)
[tex]g(x) = f(13x)[/tex] implies that f(x) is horizontally compressed by 13.
So, we have:
[tex]f(13) = \log(4 * 13x)[/tex]
[tex]f(13) = \log(52x)[/tex]
So:
[tex]g(13) = \log(52x)[/tex]
Find the sample correlation coefficient for the following data.
X Y
3 8
7 12
5 13
9 10
11 17
13 23
19 39
21 38
a. .8911.
b. .9132.
c. .9822.
d. .9556.
Answer:
quneotentendeiporoqenouteetendxdin
Step-by-step explanation:
Find the formula for the geometric sequence 4, 20, 100, 500, ...
Answer:
2500
Step-by-step explanation:
it is a geometric progression
r=5
The geometric sequence 4, 20, 100, 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].
What is the geometric sequence?A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant.
This ratio is known as a common ratio of the geometric sequence.
The given geometric sequence 4, 20, 100, 500.
The common difference between the geometric sequence is;
[tex]\rm \dfrac{a_2}{a_1}=\dfrac{20}{4} =5\\\\ \dfrac{a_3}{a_2}=\dfrac{100}{20} =5\\\\ \dfrac{a_4}{a_3}=\dfrac{500}{100} =5\\\\[/tex]
The formula geometric sequence is;
[tex]\rm a_n = a_1 \times r^{n-1}\\\\ a_n = 4 \times 5^{n-1}[/tex]
Where a1 is the first term and r is the common difference of the given geometric sequence.
Hence, the geometric sequence 4, 20, 100, and 500 is [tex]\rm a_n = 4 \times 5^{n-1}[/tex].
Learn more about geometric sequence here;
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Write 4 with denominator 5
Answer:
4/5
Step-by-step explanation:
I'm not exactly sure what this question is asking but I'm guessing it's asking to create a fraction with the numerator as 4 and denominator as 5.
