Answer:
30/420 or 1/14
Step-by-step explanation:
3*2*7/5*7*12= 30/420 simplify the you get 1/14
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
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
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
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
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.
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.
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.
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.
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.
How to solve
(2.31*10^-6)+(3.41*10^3)
The IQR is used as a measure of variation when the distribution is ----------------.
Answer:
variability
Step-by-step explanation:
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.
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)
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
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
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
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
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.
help me please pls this ur really hard help
Given an equation in point-slope form, explain how to determine the coordinates of its y-intercept.
Given an equation or graph of a line, describe how to write an equation of a parallel line that goes through a given point.
Given an equation or graph of a line, describe how to write an equation of a perpendicular line that goes through a given point.
IF POSSIBLE ANSWER ALL 3, BUT IF YOU ONLY KNOW ONE FEEL FREE TO ANSWER ONLY ONE. WILL GIVE BRAINLIEST
Hi there!
Given an equation in point-slope form, explain how to determine the coordinates of its y-intercept.
The y-intercept of a line occurs when x=0. Replace x with 0 in the equation and solve for y to find the y-intercept.Given an equation or graph of a line, describe how to write an equation of a parallel line that goes through a given point.
Determine the slope of the line. In slope-intercept form [tex]y=mx+b[/tex], the slope would be [tex]m[/tex], and in point-slope form [tex]y-y_1=m(x-x_1)[/tex], the slope would be [tex]m[/tex] as well. Given a graph, it would be necessary to solve for the slope. Find two points and plug them into the equation [tex]m=\frac{\displaystyle y_2-y_1}{\displaystyle x_2-x_1}}[/tex] as [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] to solve for the slope.Parallel lines always have the same slope. Now that we've just solved for the slope, plug it into [tex]y=mx+b[/tex].Now, all that's left to solve in the equation is [tex]b[/tex]. Plug the given point into [tex]y=mx+b[/tex] along with the slope and solve for [tex]b[/tex].Plug both the slope and y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation.Given an equation or graph of a line, describe how to write an equation of a perpendicular line that goes through a given point.
Determine the slope of the line.Perpendicular lines always have slopes that are negative reciprocals. To determine the slope of a perpendicular line, take the slope from step 1 and find its negative reciprocal. For example, the negative reciprocal of 2 is -1/2. Plug this slope into [tex]y=mx+b[/tex].Now, all that's left to solve in the equation is [tex]b[/tex]. Plug the given point into [tex]y=mx+b[/tex] along with the slope and solve for [tex]b[/tex].Plug both the slope and the y-intercept back into [tex]y=mx+b[/tex] to achieve the final equation.I hope this helps!
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
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.
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:
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."
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.
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
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.
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
A data set includes 103 body temperatures of healthy adult humans having a mean of 98.5°F and a standard deviation of 0.61°F. Construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. What does the sample suggest about the use of 98.6°F as the mean body temperature? What is the confidence interval estimate of the population mean μ?
Answer:
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.3ºF and 98.7ºF. 98.6°F is part of the confidence interval, which means that the sample suggests that this is a correct measure.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.99}{2} = 0.005[/tex]
Now, we have to find z in the Z-table as such z has a p-value of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.005 = 0.995[/tex], so Z = 2.575
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.
[tex]M = 2.575\frac{0.61}{\sqrt{103}} = 0.2[/tex]
The lower end of the interval is the sample mean subtracted by M. So it is 98.5 - 0.2 = 98.3ºF.
The upper end of the interval is the sample mean added to M. So it is 98.5 + 0.2 = 98.7ºF.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is between 98.3ºF and 98.7ºF. 98.6°F is part of the confidence interval, which means that the sample suggests that this is a correct measure.
