Answer:
Not perpendicular and not parallel.
Step-by-step explanation:
The equations are not perpendicular because the slopes of the two lines are not negative reciprocals.
The equations are not parallel because the slopes of the two lines are not equal.
There are 35 students in art class and 57 students in dance class. Find the number of students who are either in art class or in dance class. Find
When two classes meet at different hours and 12 students are enrolled in both activities. ( 2marks)
When two classes meet at the same hour. ( 2 marks)
Answer:
a. 80 students
b. 92 students
Step-by-step explanation:
Represent arts students with A and Dance students with D.
So, we have,
n(A) = 35
n(D) = 57
Required
Determine n(A or D)
Solving (a):
Here, we have:
n(A and D) = 12
n(A or D) is calculated as thus:
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 12
n(A or D) = 80
b. From the given details
n(A and D) = 0 because both students are not mixed up as in (a) above
Using the same formula as (a).
n(A or D) = n(A) + n(D) - n(A and D)
n(A or D) = 35 + 57 - 0
n(A or D) = 92
Which of the following is the equation of the line that is parallel to
y= 3/5x+ 8 and goes through point (-10,4)?
Select one:
a. y = 5/3x + 20 2/3
b. y=-5/3x – 12 2/3
c.y= 3/5x + 10
d. y = -3/5x-2
Answer:
C
Step-by-step explanation:
We want to write the equation of a line that is parallel to:
[tex]y=\frac{3}{5}x+8[/tex]
And also passes through (-10, 4).
Remember that parallel lines have the same slope.
The slope of our old line is 3/5.
Therefore, the slope of our new line is also 3/5.
We know that it passes through (-10, 4). So, we can use the point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
Where m is the slope and (x₁, y₁) is a point.
So, let's substitute 3/5 for m and let (-10, 4) be our (x₁, y₁). This yields:
[tex]y-(4)=\frac{3}{5}(x-(-10))[/tex]
Simplify:
[tex]y-(4)=\frac{3}{5}(x+10)[/tex]
Distribute on the right:
[tex]y-4=\frac{3}{5}x+6[/tex]
Add 4 to both sides:
[tex]y=\frac{3}{5}x+10[/tex]
So, our answer is C.
And we're done!
Step-by-step explanation:
Hey there!
The equation of a st.line passing through point (-10,4) is ;
(y-y1)= m1(x-x1) [one point formula]
Put all values.
(y - 4) = m1( x + 10)..........(i)
Another equation is; y = 3/5 + 8.............(ii)
From equation (ii)
Slope (m2) = 3/5 [ By comparing equation with y = mx+c].
As per the condition of parallel lines,
Slope of equation (i) = slope of equation (ii)
(i.e m1 = m2 )
Therefore, the value of m1 is 3/5.
Putting value of slope in equation (i).
[tex](y - 4) = \frac{3}{5} (x + 10)[/tex]
[tex](y - 4) = \frac{3}{5} x + \frac{3}{5} \times 10[/tex]
[tex](y - 4) = \frac{3}{5} x + 6[/tex]
[tex]y = \frac{3}{5} x + 10[/tex]
Therefore the required equation is y = 3/5x + 10.
Hope it helps...
Determine whether the lines are parallel, perpendicular, or neither. EM has the
slope of 5/6 and TC has the slope of 6/5
Answer:
Not sure, not good with lines, but I think I did it correctly. EM = Neither TC= Perpendicular.
Two points that are on the same line are called what?
A
coplanar
B
collinear
C
supplementary
D
parallel
Answer:
That would be B Collinear
Answer:
B: Collinear
Step-by-step explanation:
Let's look at the answer choices, shall we?
-Coplanar is two lines or points on the same plane.
-Supplementary is where two angles measure to 180 degrees
- Parallel lines are where two lines have the same slope and will never intersect
The only other option is collinear, which happens to have the definition of two points on the same line.
Please help me answer this question:
Answer:
Total area = 141,
the trapezoid = 117, the triangle=24
. A triangle has one angle measuring 3x degrees. A second angle measures 2x+20 degrees and the third angle measures 4x-20 degrees. What is the value of x
Answer:
Step-by-step explanation:
You know that all of the angles of a triangle have to add to equal 180°.
Therefore, (3x)+(2x+20)+(4x-20)= 180°
If you combine like terms you get:
9x=180°
Divide both sides by 9 to get:
X=20
The norman h.s. math club has twice as many male members as female members twenty percent of the male members and 30 female members participated in a math contest. What fraction of those members participating in the math contest were female? express your answer as a common fraction
Answer:
[tex]\frac{3}{7}[/tex]
Step-by-step explanation:
20% male and 30% female. 20% + 30%= 50% It is asking us what members participating was female. *50% out of 100%
> [tex]\frac{30}{70}[/tex] reduce or divide by 10 we get our fraction and answer, [tex]\frac{3}{7}[/tex].
Once cup of instant rice makes 1.5 cups of cooked rice. How many cups of cooked rice will 3 cups of instant rice make?
Answer:
2
Step-by-step explanation:
If 1 = 1.5
2 = 3
That is the answer
Answer: 3 cups will make 4.5 cups of cooked rice.
Step-by-step explanation: 3 * 1.5
Given m || n, find the value of x and y.
(3x-4)
(6x-5)
Answer:
X=21 and Y=121
Step-by-step explanation:
With these types of problems, we need to know our vertical angles and that lines are 180° when two angles on a line are next to each other.
To solve this problem algebraically we want to add (3x-4) and (6x-5) together so that they equal 180. The reason we do this is that they lie on the same line which is 180°. The equation would look like [tex]3x+6x-5-4=180[/tex]. We then want to add like terms which will leave us with [tex]9x-9=180[/tex]. Now we want to get 9x by itself by adding 9 on each side which leaves us with [tex]9x=189[/tex]. To isolate x we need to divide on each side by 9 which finally leaves us with [tex]x=21[/tex]
Now that we have the value of x (21) we can now utilize our knowledge of vertical angles (angles that are completely across and equal to one another.) We can find y by doing this equation: [tex]y=6x-5[/tex] and with the value of x found we can plug in the value to get [tex]y=6(21)-5[/tex] which simplifies to [tex]y=126-5[/tex] then to [tex]y=121[/tex].
The biggest zucchini from Joe’s Farm is 2. 5/8 pounds,which is 1 1/12 pound more than the average weight from his farm.what is the average weight of zucchini’s from his farm?
Answer:
1 13/ 24
Step-by-step explanation:
2-1=1
5/8 - 1/12=26/48 =13/24
How much is 2/3 - 1/6 =
Answer:
1/2
Step-by-step explanation:
First create like dominators
2/3 -1/6 = 4/6 - 1/6
simplify using subtraction
4/6 - 1/6 = 3/6
Simplify the answer
3/6 = 1/2
Answer:
1/2
Step-by-step explanation:
2/3 - 1/6
Subtract the two fractions:
2/3 - 1/6 = 1/2
The answer we get is:
1/2
Divide the numerator by the denominator for the decimal form:
1 ÷ 2 = 0.5
0.5 is our decimal form.
1/2 and 0.5 are our answers.
Hope you learned from this answer!
I buy a printer for $125 and ink cartridges cost $15 each. Explain the relationship between the cost of ink cartridges and the total cost.
Answer:
125+15c=t
Step-by-step explanation:
Every cartridge is worth $15, so that would be 15c aka 15 x however many cartridges you purchase. Then the printer is $125, and its not changing so there will be no variable. Put those two amounts together and you'll get the total cost. (Hopefully I explained this well enough.)
which is the equation of the line that passes through the points (-4,-8) and (1,3)
Answer:
−5x+13y=84
Step-by-step explanation:
I hope this is good :)
Someone plz help me
Answer:
The first order.
Step-by-step explanation:
What do these symbols mean?
The funny shaped line is a square root, meaning what times itself (so for example, 3 x 3) gets that number. So the square root of 9=3.
The small 2 in the top right of the big numbers means square. The opposite. This means multiply that big number by itself twice. If the small number was say, 7, you would multiply the big number by itself 7 times. A common mistake is propel multiply the big number by the small number. The square used in these is 2 to the power of 3, the small number. This means you do 2x2x2, as the small 3 determines how many time you multiply the big number, 2. The result of 2x2x2=8.
The fraction is 11/9. The 9 means how many parts are in a whole number. The 11 means how many of those parts you actually have. Like a pizza-if you had a pizza (the whole) split into 7 parts, 7 would be your bottom number (as the 9 is here). If you are 4 parts and were left with 3 parts, 3 would be your top number (as the 11 is here). Seeing as 11 is bigger than 9, you have to imagine 2 pizzas. Each is split into 9, and you have 11 parts altogether. Thsi is 1 whole pizza and 2 extra parts, making the fraction 1 and 2/9. This is jaut another way to write 11/9 but I find it easier to look at.
The answer?
So. We have established that 11/9 = 1 & 2/9
And that 2 cubed (with the small 3 on it) = 8.
Amd the square roots of 5, 11 and 20 are approximately (Not exactly, but close enough) the following:
5. 2.2
11. 3.3
20. 4.4
So this leaves us a bunch of numbers to put in order from smallest to largest. This is fairly easy. It's not the second one. 8>3.3. It's not the third one. 8>2.2. It's not the fourth one. 1 & 2/9 may be smaller than 8, but 2.2 isn't. So this leaves the first order.
*Note that the symbol > means greater than or bigger than. So 8>2 means 8,is bigger than 2.
NEED HELP PLEASEE!!!!!
Answer:
x=1
Step-by-step explanation:
i believe its asking at which point is the output the same and when x=1 they both output 3
Simplify 3-8 divided by 3-2
Answer:
-5
Step-by-step explanation:
[tex] \frac{3 - 8}{3 - 2} [/tex]
[tex] \frac{ - 5}{1} [/tex]
[tex] - 5[/tex]
A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 31% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled and asked if they believe their company president has low ethical standards and their years of experience at the company. Could the probability distribution for the number of years of experience be modelled by a binomial probability distribution?
Answer:
Explained below.
Step-by-step explanation:
A Binomial experiment has the following properties:
There are a fixed number of trials (n). Each trial are independent of the others. Each trial has only two outcomes: Success and Failure Each trial has the same probability of success (p).If a random variable X is used in an experiment and the experiment has all the above mentioned properties, then the random variable X is known as a binomial random variable.
The number of employees selected is, n = 20.
Every employees response is independent of the others.
Each employees response is either: Yes or No.
The probability of an employee responding as "yes" is, p = 0.31.
Thus, the experiment being performed is a binomial experiment.
So, the probability distribution for the number of employees believing their company president has low ethical standards can be modelled by a binomial probability distribution.
But the number of years of experience cannot be modelled by a binomial probability distribution. Because every employee will have different answer for this question.
Classify the following triangle. Check all that apply.
A. Right
B. Acute
C. Equilateral
D. Scalene
E. Obtuse
F. Isosceles
true or false? y=x^2 - 1 defines y as a function of x
Answer:
true
Step-by-step explanation:
it equals to
x1= -1
and
x2= 1
Answer:
Step-by-step explanation:
y=x²-1 is not a function for every value of y , x has more than one value
ex: if x=-1 , y=(-1)²-1 then y=0
if x=1 then y=0
f(x) = x^3 translate 3 units left translate 1 unit down
Answer:
the function would look like: f(x)=(x³+3)-1
the graph would literally look like the cubic parent graph, just shifted 3 left and 1 down
Which of the following list contains exactly 2 composite numbers and 2 prime numbers?
Corey earned
$3,200 working over the summer. If he
made $400 each week, how many weeks
did he work? How many weeks would he
need to work to earn $6,400? $8,800?
Answer:
He would need to work 8 weeks for 2300, 16 for 6400, and 22 for 8800
Step-by-step explanation:
You have to divide 3,200 by 400 since thats how much he makes in a week
that gives you 8
and you do the same for the rest
equation:
money wanted/400=weeks
Answer:)
he work for 8 weeks to earn 3,200
he needs to work 8 more weeks to earn 6,400
he needs to work 14 more weeks to earn 8,800
Step-by-step explanation:
2. Find the distance between (-2,1) and (3,4).
Answer:
[tex]\sqrt{34}[/tex] or 5.83095
Step-by-step explanation:
Use the distance formula [tex]\sqrt{(x_{2}-x_{1} )^{2}+(y_{2}-y_{1} )^2 }[/tex]
Make sure to round the answer appropriately if not asked for in square root form!!
A = 2/3 * (B + C)
Solve for C
Ming li spent $15 at the movies. She then earned $30 babysitting. She spent $12 at the bookstor. She now has $18 left. How much money did ming li have to begin woth
Answer:
$15
Step-by-step explanation:
30 - (12+15)
30-27=3
18-3=15
Hope this helps ;)
I need help with 20 please thank you.
Answer:
IM BACK!!!!
The answer is *DRUMROLLLLLLLL* B
jk
its 1 lol
Step-by-step explanation:
Plug in -8 to x and you end up multiplying -8 by 1/2 which is pretty simple but the Muhammad ibn Musa al-Khwarizmi guy invented Algebra, Gottfried Wilhelm Leibniz invented functions, and Brahmagupta of India invented addition, so thanks to them, you can solve this question. -8 times 1/2 is -4 and -4 plus 5 equals 1.
Hope this helps
Expand the expression
3(x-6)
Answer:
3x-3(6) = 3x-18
Step-by-step explanation:
What is the answer to 6x + 7= -x + 70
Answer:
x = 9
Step-by-step explanation:
6x + 7 = -x + 70
~Subtract 7 to both sides
6x = -x + 63
~Add x to both sides
7x = 63
~Divide 7 to both sides
x = 9
Best of Luck!
Which of the following expressions is not equivalent to -4.5 • -8?
-8 • -4.5
8 • 4.5
(8)(-4.5)
(4.5)(8)
Answer: (8)(-4.5)
Step-by-step explanation:
If you were to multiply-4.5 • -8 that would equal a positive number but if you were to divide (8)(-4.5) it would equal a negative number
Answer:
(8)(-4.5)
Step-by-step explanation:
please mark brainliest
The concentration of particles in a suspension is 50 per mL. A 5 mL volume of the suspension is withdrawn. a. What is the probability that the number of particles withdrawn will be between 235 and 265? b. What is the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52? c. If a 10 mL sample is withdrawn, what is the probability that the average number per mL of particles in the withdrawn sample is between 48 and 52? d. How large a sample must be withdrawn so that the average number of particles per mL in the sample is between 48 and 52 with probability 95%?
Answer:
(a) 0.6579
(b) 0.2961
(c) 0.3108
(d) 240
Step-by-step explanation:
The random variable X can be defined as the number of particles in a suspension.
The concentration of particles in a suspension is 50 per ml.
Then in 5 mL volume of the suspension the number of particles will be,
5 × 50 = 250.
The random variable X thus follows a Poisson distribution with parameter, λ = 250.
The Poisson distribution with parameter λ, can be approximated by the Normal distribution, when λ is large say λ > 10.
The mean of the approximated distribution of X is:
μ = λ = 250
The standard deviation of the approximated distribution of X is:
σ = √λ = √250 = 15.8114
Thus, [tex]X\sim N(250, 250)[/tex]
(a)
Compute the probability that the number of particles withdrawn will be between 235 and 265 as follows:
[tex]P(235<X<265)=P(\frac{235-250}{15.8114}<\frac{X-\mu}{\sigma}<\frac{265-250}{15.8114})[/tex]
[tex]=P(-0.95<Z<0.95)\\=P(Z<0.95)-P(Z<-0.95)\\=P(Z<0.95)-[1-P(Z<0.95)]\\=2P(Z<0.95)-1\\=(2\times 0.82894)-1\\=0.65788\\\approx 0.6579[/tex]
Thus, the value of P (235 < X < 265) = 0.6579.
(b)
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{5}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{5}})[/tex]
[tex]=P(-0.28<Z<0.28)\\=P(Z<0.28)-P(Z<-0.28)\\=P(Z<0.28)-[1-P(Z<0.28)]\\=2P(Z<0.28)-1\\=(2\times 0.64803)-1\\=0.29606\\\approx 0.2961[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.2961[/tex].
(c)
A 10 mL sample is withdrawn.
Compute the probability that the average number of particles per mL in the withdrawn sample is between 48 and 52 as follows:
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{10}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{10}})[/tex]
[tex]=P(-0.40<Z<0.40)\\=P(Z<0.40)-P(Z<-0.40)\\=P(Z<0.40)-[1-P(Z<0.40)]\\=2P(Z<0.40)-1\\=(2\times 0.65542)-1\\=0.31084\\\approx 0.3108[/tex]
Thus, the value of [tex]P(48<\bar X<52)=0.3108[/tex].
(d)
Let the sample size be n.
[tex]P(48<\bar X<52)=P(\frac{48-50}{15.8114/\sqrt{n}}<\frac{\bar X-\mu}{\sigma/\sqrt{n}}<\frac{52-50}{15.8114/\sqrt{n}})[/tex]
[tex]0.95=P(-z<Z<z)\\0.95=P(Z<z)-P(Z<-z)\\0.95=P(Z<z)-[1-P(Z<z)]\\0.95=2P(Z<z)-1\\P(Z<z)=\frac{1.95}{2}\\\\P(Z<z)=0.975[/tex]
The value of z for this probability is,
z = 1.96
Compute the value of n as follows:
[tex]z=\frac{\bar X-\mu}{\sigma/\sqrt{n}}\\\\1.96=\frac{48-50}{15.8114/\sqrt{n}}\\\\n=[\frac{1.96\times 15.8114}{48-50}]^{2}\\\\n=240.1004\\\\n\approx 241[/tex]
Thus, the sample selected must be of size 240.