Note: Consider we need to find the solution of given equation.
Given:
The equation is
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
To find:
The solution of the equation.
Solution:
We have,
[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]
[tex]\dfrac{2+x^2}{2x}=\dfrac{11}{6}[/tex]
By cross multiplication, we get
[tex]6(2+x^2)=11(2x)[/tex]
[tex]12+6x^2=22x[/tex]
[tex]6x^2-22x+12=0[/tex]
[tex]2(3x^2-11x+6)=0[/tex]
Divide both sides by 2.
[tex]3x^2-11x+6=0[/tex]
Splitting the middle term, we get
[tex]3x^2-9x-2x+6=0[/tex]
[tex]3x(x-3)-2(x-3)=0[/tex]
[tex](x-3)(3x-2)=0[/tex]
Using zero product property, we get
[tex]x-3=0[/tex] and [tex]3x-2=0[/tex]
[tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex]
Therefore, the solutions of the given equation are [tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex].
Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).
Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
We are given the algebraic equation: 1/x+x/2=11/6
Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.
LCD(x,2,6) = 6x
Multiply all through the fractions by 6x
(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)
6 + 3x² = 11x
Rewriting the equation:
3x² - 11x + 6 = 0
Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0
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The mean volume for a bottle of cologne is 4 ounces and the standard deviation is 0.22 ounces. A random sample of 121 bottles is taken. What is the probability of obtaining a sample mean within 0.04 ounces of the population mean?
a. 0.9545
b. 0.0363
c. 0.3085
d. 0.5000
Answer:
The standard error of the mean is 0.02
Step-by-step explanation:
Here, we want to calculate the standard error of the mean.
Mathematically;
standard error of mean = SD/ √n
where SD is the standard deviation and n is the number of samples
From the question, SD = 0.22 and n = 121
Inserting this into the equation
Standard error of the mean = 0.22/√121
= 0.22/11 = 0.02
The probability of obtaining a sample mean is "0.9545".
According to the question,
Mean,
[tex]\mu = 4[/tex]
Standard deviation,
[tex]\sigma = 0.22[/tex]
Random sample,
[tex]n = 121[/tex]
By Central limit theorem,
→ [tex]\bar {x} \sim (4, \frac{0.22}{\sqrt{121} } )[/tex]
[tex]= 0.2[/tex]
Now,
→ [tex]P(|\bar{x} - \mu| \ \alpha \ 0.04) = P(-0.04 \ \alpha \ \bar{x} - \mu \ \alpha \ 0.04)[/tex]
[tex]= P(\frac{-0.04}{0.02} \ \alpha \ z \ \alpha \ \frac{0.04}{0.02} )[/tex]
[tex]= P(-2 \ \alpha \ z \ \alpha \ 2)[/tex]
[tex]= 0.9545[/tex]
Thus the above response i.e., "option a" is appropriate.
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Ms. Sunshine is going to bake cookies for her students. She wants each student to receive 2.5 cookies. If she has 25 students in her class, how many cookies does she need to bake?
Answer:
Ms. Sunshine needs to make 62.5 cookies.
Step-by-step explanation:
25 * 2.5 = 62.5
Find the slope of the line that passes through the points (5,2) and (6,10). *
Answer:
8
Step-by-step explanation:
[tex] \frac{10 - 2}{6 - 5} = 8[/tex]
Answer:
The slope of the line is 8
Step-by-step explanation:
Use this formula for calculating the slope with two points:
[tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
(5,2) = ([tex]x_{1}[/tex],[tex]y_{1}[/tex])
(6,10) = ([tex]x_{2}, y_{2}[/tex])
Substitute the points into the equation
10 - 2 = 8
-------- --- = 8
6 - 5 = 1
So the slope would be 8.
Write an expression in simplest form that represents the area of the banner
Answer:
Can I have a picture so I can give you one
Step-by-step explanation:
thank you
helpppp it’s my friends birthday
Place the following numbers from least to greatest.
4.14, 3.24, 3.14, 4.24
kelly flies a distance of 2,100 miles. The trip takes 4 2/3 hours.
What is the airplane's unit rate of speed in miles per hour?
Answer:
450 miles per hour
Step-by-step explanation:
Kelly flies at a distance of 2,100 miles
The time taken for the trip is 4 2/3 hours
Therefore the rate of speed can be calculated as follows
= 2,100 ÷ 4 2/3
= 2,100 ÷ 14/3
= 2100 × 3/14
= 150 × 3
= 450 miles per hour
Answer:
450
Step-by-step explanation:
If the Constant of Proportionality between X and Y is 12, which equation represents their relationship?
Answer:
y=12x 12=k k=constant of Proportionality
Step-by-step explanation:
Find the hypotenuse of a right triangle with a side of 6 and a side of 8.
(ONLY put the number of your answer.) *
Answer:
10 (can't just write a number bcs i couldn't send yoy if i won't write something else)
You are given a penny on January 1, two pennies on January 2, four pennies on January 3, and eight pennies on January 4, and so on. 1.
Assuming the pattern continues, how many pennies do you get on the following dates? January 5 January 10 January 31
Answer:
january 5 :12
january 10:22
Step-by-step explanation:
Answer:
16 pennies512 pennies1073741824 penniesStep-by-step explanation:
We can see a pattern:
Days >> Pennies1 >> 1= 2^02 >> 2= 2^13 >> 4 = 2^24 >> 8 = 2^3...n >> 2^(n-1)So
January 5 fall on n = 5, therefore 2^4 = 16 penniesJanuary 10 falls on n = 10, therefore 2^9 = 512 penniesJanuary 31 falls on n = 31, therefore 2^30 = 1073741824 penniesimagine you have to hunt find food to eat what kind of food will you find
Answer:
deer
Step-by-step explanation:
Answer:
hmm...wild dear and plants
Suppose X has a continuous uniform distribution over the interval [1.3, 6.2]. Round your answers to 3 decimal places.
Required:
a. Determine the mean of X.
b. Determine the variance of X
c. What is P(X < 3.7)?
Answer:
(a) 3.75
(b) 2.00083
(c) 0.4898
Step-by-step explanation:
It is provided that X has a continuous uniform distribution over the interval [1.3, 6.2].
(a)
Compute the mean of X as follows:
[tex]\mu_{X}=\frac{a+b}{2}=\frac{1.3+6.2}{2}=3.75[/tex]
(b)
Compute the variance of X as follows:
[tex]\sigm^{2}_{X}=\frac{(b-a)^{2}}{12}=\frac{(6.2-1.3)^{2}}{12}=2.00083[/tex]
(c)
Compute the value of P(X < 3.7) as follows:
[tex]P(X < 3.7)=\int\limits^{3.7}_{1.3}{\frac{1}{6.2-1.3}}\, dx\\\\=\frac{1}{4.9}\times [x]^{3.7}_{1.3}\\\\=\frac{3.7-1.3}{4.9}\\\\\approx 0.4898[/tex]
Thus, the value of P(X < 3.7) is 0.4898.
the tax on a purchase of $20 is 1.12. how much will tax be on a purchase of $45.50
Answer:
$ 1,593.75
Step-by-step explanation:
this is the advanced sale calculation if you wan a simple one i can write that in the comments! hope this help you! :D
please
help i’ve been stuck on
this all day
Answer:
CPB
Step-by-step explanation:
acute is less than 90 degrees and right is 90 degrees and obtuse is over 90 degrees
Answer: The answer is CPB
Simplify (10x^2− 8x − 1) + (4x^2− 8x − 5).
Answer: 14[tex]x^{2}[/tex] − 16x − 6
PLEASE HELP ME ITS URGENT
Just the first one
Answer:
m=-1/3
Step-by-step explanation:
7. What is the equation of the line that passes through (-1, -4) and (0,5)?
A.) y = 9x + 5 B.) y = 5x + 9 C.) y = -9x + 5 D.) y = -5x + 9 E.) none of these
1
Answer:
A)y=9x+5
Step-by-step explanation:
If x=-1, y=-4,
y=9*-1+5=(-9)+5=-4
If x=0, y=5,
y=9*0+5=5
There is a new truck worth $31,500 and it loses value at the rate of 2.7% per year.
1) Create an exponential model.
2) How much is the truck worth 5 years later?
3) How much is the truck worth 15 months later?
Answer:
For 2 it's 27,247 and for 3 it's 31393.86
Step-by-step explanation:
Given the following two equations determine if they are parallel, perpendicular, or neither.
3x + 6y = 30
4y + 2x = 9
Please show work!
Answer:
Parallel
Step-by-step explanation:
What you want to do first is to put both equations into the slope intercept form: y=mx+b.
In the first equation, you move the [tex]3x[/tex] to the right side of the equal sign by subtracting on both sides:
[tex]6y = -3x + 30[/tex]
Then you want to divide both sides by 6 to isolate y:
[tex]y = -\frac{1}{2}x + 5[/tex]
Next for the second equation, you do similar steps. You subtract [tex]2x[/tex] from both sides:
[tex]4y=-2x+9[/tex]
Then you want to divide both sides by '4' to isolate y:
[tex]y= -\frac{1}{2}x+\frac{9}{4}[/tex]
Now to check if the two equations are parallel, perpendicular, or neither, you compare the slopes 'm' which is the coefficient next 'x'. If two equations have the same slope, then they are parallel. If the slopes multiplied equal -1, then they are perpendicular. If the slopes are not the same or if the product of the slopes is not -1, then it is neither.
In the case of this problem, the slopes are the same, so the equations are parallel:
[tex]-\frac{1}{2} = -\frac{1}{2}[/tex]
Problems 4 (a and b), 6 (a,b, and c), 7 (a,b, and c), 8, and 9 (a,b, and c) Thank you so much!
For real help on this, people will receive more points to prevent point stealing.
Answer:
no problem glad to help
Find the slope. (4,2) (7, 6.5)
Answer:
B.
Step-by-step explanation:
m=y2-y1/x2-x1
6.5-2=4.5
7-4=3
4.5/3=1.5
the slope is 1.5
hope this helps :3
if it did pls mark brainliest
Yoooo who’s smart I need help in this ASAP
Answer:
3[tex]\sqrt[9]{Z}[/tex]²
Step-by-step explanation:
Expression -
(27[tex]\sqrt[3]{Z}[/tex]²) ^1/3
Transform the expression -
³[tex]\sqrt[3]{27}[/tex][tex]\sqrt[3]{Z}[/tex]²
Simplify - //Note: ignore the ' * '//
3[tex]\sqrt[3]{*}[/tex][tex]\sqrt[3]{z}[/tex]²
Simplify (Again) -
3[tex]\sqrt[9]{Z}[/tex]²
Solve the equation. Type just the numeral answer. Do NOT round your solution.
n
= -1.2
-1.5
n=
Answer:
-2.7
thats the answer but i cant submit without some words lol
Answer:
n= 1.8
Step-by-step explanation:
Solve the following expression:
n/-15 = -1.2
-Multiply -1.5 on both sides:
(-1.5) n/-1.5 = -1.2(-1.5)
n=1.8
Therefore, the final answer is n = 1.8.
Which of the following correctly represents the given data in the problem?
a = 24, g = 48, h = 22, i = 80
a = 22, c = 80, d = 24, i = 48
a = 24, b = 48, c = 22, i = 48
a = 24, c = 48, e = 22, i = 80
Answer:
D
Step-by-step explanation:
100% true
Answer:
It is D
Step-by-step explanation:
The modified expression x^3(2x+5)-4(2x+5) has two terms with a common factor of
Answer:
( 2 x +5) ( x ^3 − 4 )
Step-by-step explanation:
I dont think this the answer your looking for, however, if you work backwards from here by expanding, you might get what you want. :)
What is the slope of the line that passes through the points (−10,0) and (-13, 3)?
Answer:
-1
Step-by-step explanation:
To find slope
m=y2-y1
--------
x2-x1
m= 3-0
-----
-13-(-10)
m= 3
---
-3
m=-1
The sum of two numbers is 8 and
their difference is 2.
Answer:
The numbers are 3 and 5.
Step-by-step explanation:
Hope that helped.
Also can I please have Brainliest?
Only if I'm right of course
something divided by -7 that gives -4 PLEASE I NEED HEEELP
Answer:
28
Step-by-step explanation:
Just do -4 multiplied by -7 which is 28
When divided it gives you -4
Answer:
just look it up
Step-by-step explanation:
Safari, Ask what u need too, and that is it
2 1/8 and 17/8 are reciprocal numbers. True False
Answer:
False
Step-by-step explanation:
If make 2 1/8 into an improper fraction, it will be 17/8. a reciprocal is a flip of a number, so it is false.
please help me :(((((
Answer:
,hbdgyhy6jyiwci7oygiuhopuoyiudysrtaehsyrdutfihipj
Step-by-step explanation:
yugd oufygp8iuhyefyif hovujm
