Answer:
6.2
Step-by-step explanation:
to fine the mean of numbers
1) add the given no.........3+5+6+7+9+6+8 which is 44
2)divide the result by the amount of the numbers....44/7
the answer will be 6.285.....
Use what you know about decomposing fractions to write 11/10 as a mixed number.
Help please :(
Answer:
11/10 is 1 1/10
Step-by-step explanation:
which of the following statements must br true about this diagram exterior and interior angles
Answer:
C: w > y
D: w > x
E: x + y = w
help me please pls this ur really hard help
The IQR is used as a measure of variation when the distribution is ----------------.
Answer:
variability
Step-by-step explanation:
simplify the algebraic expression
6•4-12÷2+3(x-5)
Answer:
9(x-5)
Step-by-step explanation:
- First multiply 6 and 4
-Then subtract by 12
-Add 3
-Leave the variable and number that are in paranthese
At a university, the percentages of Distinction", "Merit", and Pass' in students are 10%, 20%
70%, respectively. The probability that a D. M. P student obtain a scholarship are 0.8.0.3 and
0.05, respectively. What are the proportions of D. M. P student among scholarships?
Answer:
63% of all undergraduates receive at least one grant or scholarship.
Step-by-step explanation:
Scholarships and grants, which covered 31% of cost, and parent income and savings, which covered 30%, are the top two sources of funding. The share of cost paid from other resources are 14% from student borrowing, 13% from student income and savings, 10% from parent borrowing, and 2% from friends and family.
y=??
length =?
width =?
9514 1404 393
Answer:
y = 12 -x0 ≤ y ≤ 12Step-by-step explanation:
The perimeter of a rectangle is given by ...
P = 2(L +W) . . . . . where L and W represent the length and width
Filling in the given values, we have ...
24 = 2(y +x)
Solving for y, we get ...
12 = y + x . . . . . divide by 2
y = 12 -x . . . . . . subtract x
The length y is the difference between 12 and the width x.
__
We want both x and y to be non-negative, so possible values of y range from 0 to 12.
Given f(x) = 3sqrt(2x-1).
6(2x-1)^2-3
What is lim f(x)?
Answer:
[tex]\displaystyle 51[/tex]
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringFunctionsFunction NotationAlgebra II
Piecewise functionsCalculus
Limits
Right-Side Limit: [tex]\displaystyle \lim_{x \to c^+} f(x)[/tex]Limit Rule [Variable Direct Substitution]: [tex]\displaystyle \lim_{x \to c} x = c[/tex]
Limit Property [Addition/Subtraction]: [tex]\displaystyle \lim_{x \to c} [f(x) \pm g(x)] = \lim_{x \to c} f(x) \pm \lim_{x \to c} g(x)[/tex]
Limit Property [Multiplied Constant]: [tex]\displaystyle \lim_{x \to c} bf(x) = b \lim_{x \to c} f(x)[/tex]
Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle f(x) = \left \{ {{3\sqrt{2x - 1}, \ x \leq 2} \atop {6(2x - 1)^2 - 3, \ x > 2}} \right.[/tex]
Step 2: Solve
Substitute in function [Limit]: [tex]\displaystyle \lim_{x \to 2^+} 6(2x - 1)^2 - 3[/tex]Factor: [tex]\displaystyle \lim_{x \to 2^+} 3[2(2x - 1)^2 - 1][/tex]Rewrite [Limit Property - Multiplied Constant]: [tex]\displaystyle 3\lim_{x \to 2^+} 2(2x - 1)^2 - 1[/tex]Evaluate [Limit Property - Variable Direct Substitution]: [tex]\displaystyle 3[2(2 \cdot 2 - 1)^2 - 1][/tex]Simplify: [tex]\displaystyle 51[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Limits
Book: College Calculus 10e
If events A and B are independent, what must be true?A.) P(AB) = P(B)
B.) P(A/B) = P(A)
C.) P(A) = P(B)
D.) OP(AB) = P(BIA)
Answer:
B.) P(A/B) = P(A)
Step-by-step explanation:
If two events, A and B are independent:
We have that:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Since they are independent:
[tex]P(A \cap B) = P(A)P(B)[/tex]
Then
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{P(A)P(B)}{P(A)} = P(B)[/tex]
So
[tex]P(B|A) = P(B)[/tex], or either:
[tex]P(A|B) = P(A)[/tex], and thus, the correct answer is given by option B.
Solve the following equation for
a
a. Be sure to take into account whether a letter is capitalized or not.
Answer:
6/5 n = a
Step-by-step explanation:
n = 5/6a
Multiply each side by 6/5
6/5 n = 6/5 * 5/6a
6/5 n = a
The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.09 kWh. A previous study found that for an average family the variance is 5.76 kWh and the mean is 16.6 kWh per day. If they are using a 98% level of confidence, how large of a sample is required to estimate the mean usage of electricity
Answer:
A sample of 3851 is required.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.98}{2} = 0.01[/tex]
Now, we have to find z in the Z-table as such z has a p-value of .
That is z with a pvalue of , so Z = 2.327.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Variance is 5.76 kWh
This means that [tex]\sigma = \sqrt{5.76} = 2.4[/tex]
They would like the estimate to have a maximum error of 0.09 kWh. How large of a sample is required to estimate the mean usage of electricity?
This is n for which M = 0.09. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]0.09 = 2.327\frac{2.4}{\sqrt{n}}[/tex]
[tex]0.09\sqrt{n} = 2.327*2.4[/tex]
[tex]\sqrt{n} = \frac{2.327*2.4}{0.09}[/tex]
[tex](\sqrt{n})^2 = (\frac{2.327*2.4}{0.09})^2[/tex]
[tex]n = 3850.6[/tex]
Rounding up:
A sample of 3851 is required.
Solve for x and simplify answer as much as possible
Answer:
[tex]x=-1[/tex]
Step-by-step explanation:
[tex]4=6+2x[/tex]
Flip the equation:
[tex]2x+6=4[/tex]
Subtract 6 from both sides:
[tex]3x+6-6=4-6[/tex]
[tex]2x=-2[/tex]
Divide both sides by 2:
[tex]2x/2=-2/2[/tex]
[tex]x=-1[/tex]
Answer:
x= -1
Step-by-step explanation:
firstly group the like terms
4-6=2x
-2=2x
divide both sides by 2
-2/2=2x/2
-1=x
therefore x is -1
Marquise has 200200200 meters of fencing to build a rectangular garden.
The garden's area (in square meters) as a function of the garden's width xxx (in meters) is modeled by:
A(x)=-x^2+100xA(x)=−x
2
+100xA, left parenthesis, x, right parenthesis, equals, minus, x, squared, plus, 100, x
WHAT IS THE MAXIMUM AREA POSSIBLE SQUARE METERS
Hence the maximum possible area is 2500 square meters
Given the area of the rectangular garden expressed as;
[tex]A(x)=-x^2+100x\\[/tex]
The maximum area occurs when dA(x)/dx = 0
[tex]\frac{dA(x)}{dx} = -2x + 100\\0= -2x + 100\\ 2x = 100\\x = \frac{100}{2}\\x = 50[/tex]
Next is to get the maximum area possible. Substitute x = 50 into the original function as shown;
[tex]A(50)= -50^2 + 100(50)\\A(50) = -2500+5000\\A(50) = 2500[/tex]
Hence the maximum possible area is 2500 square meters
Learn more here: https://brainly.com/question/17134596
2500 square meters
This question was on Khan Academy and I got it correct
The radius of a sphere is increasing at a rate of 3 mm/s. How fast is the volume increasing when the diameter is 60 mm
Answer:
The volume is increasing at a rate of 33929.3 cubic millimeters per second.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere of radius r is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In this question:
We have to derivate V and r implicitly in function of time, so:
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
The radius of a sphere is increasing at a rate of 3 mm/s.
This means that [tex]\frac{dr}{dt} = 3[/tex]
How fast is the volume increasing when the diameter is 60 mm?
Radius is half the diameter, so [tex]r = 30[/tex]. We have to find [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = 4\pi (30)^2(3) = 33929.3[/tex]
The volume is increasing at a rate of 33929.3 cubic millimeters per second.
What is the slope of the line in the graph?
Answer:
The slope of this line is 1 and the equation for the line is y=x+1
Step-by-step explanation:
So take 2 points passing through the the line (0,1), (-1,0)
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
First, let's find what m is, the slope of the line...
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,1), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=1.
Also, let's call the second point you gave, (-1,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-1 and y2=0.
Now, just plug the numbers into the formula for m above, like this:
m=
0 - 1
-1 - 0
So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:
y=1x+b
Now, what about b, the y-intercept?
To find b, think about what your (x,y) points mean:
(0,1). When x of the line is 0, y of the line must be 1.
(-1,0). When x of the line is -1, y of the line must be 0.
Because you said the line passes through each one of these two points, right?
Now, look at our line's equation so far: y=x+b. b is what we want, the 1 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,1) and (-1,0).
So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.
You can use either (x,y) point you want..the answer will be the same:
(0,1). y=mx+b or 1=1 × 0+b, or solving for b: b=1-(1)(0). b=1.
(-1,0). y=mx+b or 0=1 × -1+b, or solving for b: b=0-(1)(-1). b=1.
In both cases we got the same value for b. And this completes our problem.
The equation of the line that passes through the points
(0,1) and (-1,0)
is
y=x+1
I need help ASAP is anyone available
Answer:
C
Step-by-step explanation:
The graph has asymptotes at x = 2 and x = -1 corresponding to the denominator of option C.
Rachel and Hugo sorted 236 crayons into boxes for a local arts project. Each box had 10 crayons. How many crayons were left over?
Help please lol
Answer:
6
Step-by-step explanation:
236/10 = 23 remainder 6, so 6 crayons is the answer
Perform the indicated operation.
h(x) = x² + 3x
g(x) = -x +4
Find h(g(-x)
A. X^4-11x^2+28
B. -x^2-3x+4
C. X^2+11x+28
D. -x^2+3x+4
Answer:
C
Step-by-step explanation:
g(-x) = x+4, h(g(-x))=h(x+4)=(x+4)^2+3(x+4)=x^2+11x+28
please help!!!
find the inverse of f(x)=2/3x+6
find f^-1(4)
Answer:
-3
Step-by-step explanation:
y = 2/3x +6
Exchange x and y
x = 2/3y +6
Solve for y
x-6 = 2/3y+6-6
x-6 = 2/3 y
Multiply each side by 3/2
3/2(x-6) = 3/2*2/3y
3/2x - 9 = y
The inverse is 3/2x -9
f^-1(x) = 3/2x-9
Let x = 4
f^-1(4) = 3/2(4)-9
= 6-9
= -3
Y^2-Y/Y answer please
Answer:
y - 1
Step-by-step explanation:
y^2 - y / y
Cancel out the numerator with the denominator, so cancel out the y's to get:
y - 1
Remember that there is a "hidden" 1 in front of the y. Meaning that it is "-1."
Can anyone help with this question?
x-intercept = (2, 0)
y-intercept = (0, 7.5)
Step-by-step explanation:
The x-intercept can be found by setting y = 0. Thus,
[tex]15x + 4(0) = 30 \Rightarrow x = 2[/tex]
Therefore, the x-intercept is (2, 0).
The y-intercept can be found by setting x = 0:
[tex]15(0) + 4y = 30 \Rightarrow y = 7.5[/tex]
Therefore, the y-intercept is at (0, 7.5)
The graph of the parent function f(x) = |x| is dashed and the graph of the transformed function g(x) = |x – h| is solid.
Use the slider to change the value of h. How does changing the value of h affect the vertex?
Positive values of h shift the graph .
Negative values of h shift the graph
9514 1404 393
Answer:
positive: rightnegative: leftStep-by-step explanation:
In the transformed function f(x-h), the value of h is the right shift of the parent function.
For h positive, shift is to the right.
For h negative, shift is to the left.
Changing the value of h shifts the graph horizontally. Positive values of h shift the graph to the right. Negative values shift left.
Note: there is a minus sign in front while the value of h is positive, i.e. |x - 5| is shifted 5 units to the right, and |x - (-5)| = |x + 5| is shifted 5 units to the left.
A jar contains 8 red marbles, 5 blue marbles and 3 green marbles. Christopher wins if he picks a red marble and Janet wins if he doesn’t pick a red marble. Is this game fair? Why or why not?
No, the game is not fair because Janet has a higher probability of winning than Christopher.
No, the game is not fair because Christopher has a higher probability of winning than Janet.
Yes, the game is fair because Christopher and Janet do not have an equal probability of winning.
Yes, the game is fair because Christopher and Janet have an equal probability of winning.
Answer:
Yes, the game is fair because Christopher and Janet have an equal probability of winning.
Step-by-step explanation: Christopher - Red marble=8
Janet - blue + green= 5+3= 8
Student Engineers Council at an Indiana college has one student representative from each of the five engineering majors (civil, electrical, industrial, materials, and mechanical). Compute how many ways a president, a vice president, and a secretary can be selected.
Answer:
A president, a vice president, and a secretary can be selected in 60 ways.
Step-by-step explanation:
The order in which the people are chosen is important(first president, second vice president and third secretary), which means that the permutations formula is used to solve this question.
Permutations formula:
The number of possible permutations of x elements from a set of n elements is given by the following formula:
[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]
In this question:
3 students from a set of 5, so:
[tex]P_{(5,3)} = \frac{5!}{2!} = 5*4*3 = 60[/tex]
A president, a vice president, and a secretary can be selected in 60 ways.
simplify the expression: (3x+y2)
please help me to solve
We have to,
Simplify the expression,
→ (3x + y²)
Now remove brackets in expression,
→ (3x + y²)
→ 3x + y²
Therefore, 3x + y² is simplest form.
Suppose an airline policy states that all baggage must be box-shaped with a sum of length, width, and height not exceeding 144 in. What are the dimensions and volume of a square-based box with the greatest volume under these conditions?
Answer:
110592 in³
Step-by-step explanation:
Since baggage should take the shape of a box; with the sum of it's dimension not exceeding 144 ;
Dimensions of a box : length, width, height
If ; l + w + h = 144
Greatest volume is obtained when the dimension is equal : such that l = w = h
Hence, each dimension becomes ; 144 / 3 = 48 in
Volume of box = length * width * height
Volume = 48 * 48 * 48
Volume = 48³ = 110592
Which answer choice correctly identifies the extraneous information in the problem?
Anna babysat 2 children on Saturday night. She charges $8 an hour to babysit. She wants to save the money she earns babysitting to buy a stereo system that cost $225. If Nina babysat for 5 hours, how much money did she earn?
Answer: $40 / $80
Step-by-step explanation: 40$ if it's $8 for BOTH per hour, or if it's $8 for ONE per hour it's $80
Find the length of the line in cm.
PLEASE HELP
Answer:
60cm
Step-by-step explanation:
12x-10x=120
2x=120
x=60
Answer:
60 cm
Step-by-step explanation:
We know that 12x - 10x = 120.
We simplify that to 2x = 120.
That way, x = 60.
The length of the line is 60 cm.
Will give brainliest answer
Answer:
[tex]d=-18[/tex]
Step-by-step explanation:
The only way we can achieve an extraneous solution is by squaring both sides. Example:
[tex]\sqrt{-1}=x, \\\sqrt{-1}^2=x^2,\\1=x^2,\\x=1\text{ [extraneous]}[/tex]
Square both sides of the equation:
[tex]\sqrt{\frac{1}{2}y-1}^2=(\frac{3}{4}y+d)^2[/tex]
Substitute [tex]y=20[/tex]:
[tex]9=(15+d)^2[/tex]
Expand the right side using [tex](a+b)^2=a^2+2ab+b^2[/tex]:
[tex]9=15^2+2(15)(x)+x^2,\\x^2+30x+225=9[/tex]
Subtract 9 from both sides:
[tex]x^2+30x+216=0[/tex]
Factor:
[tex](x+12)(x+18)=0,\\\begin{cases}x+12=0, x=\boxed{-12},\\x+18=0,x=\boxed{-18}\end{cases}[/tex]
Substitute both solutions to see which work:
[tex]\sqrt{\frac{1}{2}(20)-1}=(\frac{3}{4}(20)+d), \\\\d=-12\checkmark\\d=-18\times[/tex]
The solution [tex]d=-18[/tex] yields [tex]3=-3[/tex] which does not work and therefore is extraneous.
How to solve
(2.31*10^-6)+(3.41*10^3)