[tex] \begin{cases}\large\bf{\blue{ \implies}} \tt \: \frac{4}{9} \sf \: w \: = \: - 8 \\ \\ \large\bf{\blue{ \implies}} \tt \: \frac{4 \sf \: w}{9} \: = \: 8 \\ \\ \large\bf{\blue{ \implies}} \tt 4 \sf \: w \: = \: 9 \: \times \: 8 \\ \\ \large\bf{\blue{ \implies}} \tt 4 \sf \: w \: = \: 72 \\ \\ \large\bf{\blue{ \implies}} \tt \sf \: w \: = \: \cancel\frac{72}{4} \\ \\ \large\bf{\blue{ \implies}} \tt \sf \: w \: = \: 18 \end{cases}[/tex]
A university professor asked his class of 42 students when they had studied for his class the previous weekend. There responses were. please answer part a, b and c
ANSWERS:
a) 16 students
b) 25 students
c) 2 students
STEP BY STEP:
There are 42 students in total. This question can be solved by "Principal of Inclusion and Exclusion"
Question a)
The students that studied on Sunday in total with overlaps is 30. To figure out the students that ONLY studied on Sunday you need to first minus the overlaps in the combos:
the combos:
3, 10, 6, 2
Since the last combo included all of the other dates, we need to minus it:
1, 8, 4, 2
Now we can use the total of Sunday and minus the combos that includes Sunday:
30 - (4 + 2 + 8) = 16 students
Question b)
To figure out all the students that only studied on ONE day, not 2 not 3, just one day. We need to figure out the students that studied for Saturday and Friday using the same method before for figuring out Sunday:
Friday: 9 - 4 - 1 -2 = 2 students
Saturday: 18 - 1 - 2- 8 = 7 students
and now add them all together: 2 + 7 + 16 = 25 students
That is the total number of students that studied on one day.
Question c)
Now for the numbers of students that didn't study... We can just use the total to minus everything else!
42 - (25 + 1 + 4 + 8 + 2) = 2 students!!!
And thats all done! If you still don't get it, please ask!
Calculate the mean of: 4.6, 3, 8.1, 9, 12, 3, 9, 3.5, 7, 3
Given the functions below, find f(x) - g(x) f(x) = 3x^2 + 2x + 1 g(x) = x^2 - 6x + 3
Answer:
Here is your answer.....
Hope it helps....
The value of given function f(x) - g(x) is 2x² + 2x + 1.
What is function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.The characteristic that every input is associated to exactly one output defines a function as a relationship between a set of inputs and a set of allowable outputs.Given,
f(x) =3x² + 2x + 1
g(x) = x² - 6x + 3
f(x) - g(x) = ( 3x² + 2x + 1) - ( x²- 6x + 3)
= 3x² + 2x +1 - x² + 6x - 3
= 2x² +8x - 2
Therefore , the value of given function f(x) - g(x) is 2x² + 2x + 1.
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Select the correct answer from each drop-down menu.
The given composite shape has an area of (72,78,66,84) cm2 and a perimeter of (42,47,40,33) cm.
Answer:
78 cm²
42 cm
Step-by-step explanation:
To obtain the area of the shape given :
The figure is divide into three different rectanglular parts :
Recall, area of a rectangle = Length x width :
Rectangle 1 : 9* 6 = 54 cm²
Rectangle 2 = 6 * 2 = 12 cm²
Rectangle 3 = 4 * 3 = 12 cm²
Total area = (54 + 12 + 12). = 78 cm²
Perimeter = sun of the exterior sides of the shape
Perimeter = (9 + 8 + 3 + 4 + 3 + 6 + 3 + 6) = 42 cm
Can someone please help me with this.
Solve for X. Round to the nearest tenth, if necessary. Please help
Answer:
X=1.2/1.3
answérica is 1.25, depends on how you want to round
Step-by-step explanation:
Henry rolls a fair dice 42 times.
How many times would Henry expect to roll an odd number?
Answer:
You should get 21 odds
Step-by-step explanation:
There are 6 possible outcomes on a fair die
1,2,3,4,5,6
3 of the outcomes are odd
1,3,5
P(odd) = odd outcomes/ total = 3/6 =1/2
Rolling 42 times
number of times * P(odd)
42*1/2 = 21
You should get 21 odds
The edges of a rectangle solid have lengths 2x,3xand 5x.what is the total surface area of the solid ?
•30x^2
•60x^2
•62x^2
•30x^3
Answer:
30x³
Step-by-step explanation:
2x×3x=6x²
6x²×5x=30x³
(9,2) and (5,-4) find the slope of the line containing the pair of points
Answer:
3/2
Step-by-step explanation:
We can use the slope formula
m = (y2-y1)/(x2-x1)
= ( -4-2)/(5-9)
= -6/-4
=3/2
If x = y, then x – a = y – a represents the ________ property of equality.
Answer:
Subtractive Property of equality
Step-by-step explanation:
Since x = y, When you subtract anything from x, you must do the same to y for them to stay equal.
Answer:
Subtraction property of equality
Find the area of the triangle which the line 2x – 3y +6=0 forms with the coordinate axis.
2x-3y+6=0 has an x intercept of 2 and a y intercept of -3.
That means the 2 sides of the right triangle are 2 and -3
Area of triangle= 1/2×base×height
= 1/2×-3×2
=-3
∴ Area of the triangle=-3
The area of the asked triangle is 3 sq units.
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a triangle is formed by the line 2x – 3y +6=0 and the coordinate axis.
When we plot the graph of the line, we get, y-intercept = 2 and x-intercept = -3
Hence, the height and base of the triangle will be 2 and 3 respectively.
Area of a triangle = 1/2 (base) (height)
Area = 1/2 (2)(3)
Area = 3
Hence, the area of the asked triangle is 3 sq units.
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A scale drawing of a square desk is ¼ inch to 1 foot. The actual desk is 50 feet wide. What is the area of the desk in the model?
156.25 in2
40000 in2
625 in2
10000 in2
Answer:
Step-by-step explanation:
What is the point-slope form of a line with slope -3 that contains the point
(10, -1)?
Answer:
General equation of line:
[tex]{ \bf{y = mx + c}}[/tex]
Find y-intercept:
[tex]{ \tt{ - 1 = ( - 3 \times 10) + c}} \\ { \tt{c = 29}}[/tex]
Equation of line:
[tex]{ \bf{y = - 3x + 29}}[/tex]
In a tram, 12% of the passengers go without a ticket. What can be the largest number of passangers in the tram, if its not greater than 60
45 POINTS
Function: g(x) = 2x2 - 8
Answer:
f(x)= √ 1 2 x + 4 For x ≤ 0
Step-by-step explanation:
21. Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60%
solution. How many liters of each does he need make the needed 80 liters of 30% acid solution?
Gabe needs
liters of the 20% solution.
He also needs
liters of the 60% solution.
Let x be the amount (in liters) of 20% solution that Gabe uses, and y the amount (also in L) of the 60% solution.
He needs 80 L of 30% solution, so that
x + y = 80
0.20x + 0.60y = 0.30 (80) = 24
Solve for y in terms of x :
y = 80 - x
Substitute this into the second equation and solve for x :
0.20x + 0.60 (80 - x) = 24
0.20x + 48 - 0.60x = 24
24 = 0.40x
x = 60
Solve for y :
y = 80 - 60
y = 20
SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300. An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the 82% confidence interval to 25 points, how many students should the administrator sample
Answer:
The appropriate solution is "259".
Step-by-step explanation:
According to the question,
[tex]\sigma = 300[/tex]
[tex]M.E=25[/tex]
At 82% CI,
[tex]\alpha = 0.18[/tex]
Critical value,
[tex]Z_c=1.341[/tex]
Now,
The sample size will be:
⇒ [tex]n=(Z_c\times \frac{\sigma}{E} )^2[/tex]
By substituting the values, we get
[tex]=(1.341\times \frac{300}{25} )^2[/tex]
[tex]=(1.341\times 12)^2[/tex]
[tex]=259[/tex]
What is the constant of variation k of the direct variation y=KP through (-3, 2)
Answer:
isisis
Step-by-step explanation:
ISO’s
Answer:
-2/3
Answer: The constant of variation k for y = kx through (-3, 2) is k = -2/3.
what is proportion as applied in mathematics
Answer:
como se siente el actor al presentar la obra hola
...............................................................
Help please :) Whoever helps and gets answer correct gets Brainliest!
Answer:
1/8 is the slope
Step-by-step explanation:
Answer:
slope = 8
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{1}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 26) and (x₂, y₂ ) = (2, 34) ← 2 ordered pairs from the table
m = [tex]\frac{34-26}{2-1}[/tex] = [tex]\frac{8}{1}[/tex] = 8
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
5x – 4y = -4
Answer:
[tex]\boxed {\boxed {\sf y= \frac{5}{4}x+1}}[/tex]
Step-by-step explanation:
We are given the equation of a line and asked to put it into slope-intercept form.
Slope-intercept form is:
[tex]y=mx+b[/tex]
Where:
m= slope b= y-interceptIn order to put the equation into slope-intercept form, we have to isolate the variable y by performing the inverse operation.
[tex]5x-4y= -4[/tex]
5x is being added to -4y. The inverse of addition is subtraction, so subtract 5x from both sides of the equation.
[tex]5x-5x-4y=-4-5x[/tex]
[tex]-4y=-4-5x[/tex]
The variable y is being multiplied by -4. The inverse of multiplication is division. Divide both sides of the equation by -4.
[tex]\frac {-4y}{-4}=\frac{-4-5x}{-4}[/tex]
[tex]y= \frac{-4}{-4}+\frac{-5x}{-4}[/tex]
[tex]y=1+\frac{5}{4}x[/tex]
Rearrange the equation.
[tex]y= \frac{5}{4}x+1[/tex]
The fractions are completely simplified, so this is our final answer.
The equation of the line in slope-intercept form is [tex]\bold {y= \frac{5}{4}x+1}}[/tex].
The slope is 5/4 and the y-intercept is 1.
Please Help! What's the rule that represents the sequence 13, 27, 41, 55, ...?
Answer:
B
Step-by-step explanation:
an = a+(n-1)d
an=13+(n-1)14
d=14
Sudhanshu is solving a system representing a race between two remote control cars. The variable x is defined as time in seconds, and y is the distance in meters from the starting line.
Red car: y = 3 x + 5. Blue car: y = 4 x.
How many solutions should Sudhanshu find?
zero
one
two
infinite
Answer:
One
General Formulas and Concepts:
Algebra I
Slope-Intercept Form: y = mx + b
m - slope b - y-interceptSolving systems of equations
Step-by-step explanation:
Step 1: Define
Identify systems
y = 3x + 5
y = 4x
Step 2: Solve
If we compare the 2 lines, we can see that they both have a different slope. If they had the same slope but different y-intercepts, then they would be parallel and have no solution. We can also see that the 2 lines aren't the same. If they were, then they would have infinite solutions.
∴ the systems should have only one solution.
Answer:
B
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
9x – 15y = 135
Answer:
y=3/5x-9
Step-by-step explanation:
9x – 15y = 135
Subtract 9x from each side
9x -9x – 15y =-9x+ 135
-15y = -9x +135
Divide each side by -15
-15y/-15 = -9x/-15 +135/-15
y=3/5x-9
The California State University (CSU) system consists of 23 campuses, from San Diego State in the south to Humboldt State near the Oregon border. A CSU administrator wishes to make an inference about the average distance between the hometowns of students and their campuses. Describe and discuss several different sampling methods that might be employed. (Select all that apply.) There are no potential problems with self reporting of distances.
Answer:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
Step-by-step explanation:
1)The sample could be generated by taking a stratified random sample by taking a simple random sample from each of the 23 campuses and again asking each student in the sample to report the distance from their hometown to campus.
2)One could take a simple random sample of students from all students in the California State University system and ask each student in the sample to report the distance from their hometown to campus.
3)Certain problems arise with self reporting of distances, such as recording error or poor recall.
You have 8 quarts of milk. You need 1.25 cups to make one serving of deep fried chicken. How many servings can you make?
Answer: 25.6 servings (partial serving) / 25 servings (whole serving)
Step-by-step explanation:
Concepts:
As we can see from the question, there are two units applied. [Quarts] and [cups]; therefore, we need to do the unit conversion.
1 quart = 4 cups
Solve:
Step one: Convert quarts into cups
1 quart = 4 cups8 quarts = 4 × 8 = 32 cupsStep two: Divide the cups to find the number of servings
32 cups / 1.25 cups = 25.6 servings**Disclaimer** I am not sure about the rules that you apply in mathematics. Here, the answer is not an integer. I am concerned whether you would allow partial servings. In my understanding, the servings shall be a whole, thus should be rounded. However, if you are fine with decimals, then you have the choice.
Hope this helps!! :)
Please let me know if you have any questions
Let sin A = -5/13 with 270 degrees < A < 360 degrees and cos B = -15/17 with 90 degrees < B < 180 degrees find sin (A+B)
Answer:
Step-by-step explanation:
please help, will give brainliest!!!
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
y = x^2 -4
Exchange x and y
x = y^2 -4
Add 4 to each side
x+4 = y^2
Take the square root of each side
sqrt(x+4) = y
f^-1(x) = sqrt(x+4)
Answer:
f^-1(x) = sqrt(x+4)
Step-by-step explanation:
Find m These questions getting hard
Answer:
the
Step-by-step explanation:
it's fairly easy actually. You just have to use sin
