Using the together rate, it is found that it would take each person working individually 27 and 29 hours to paint the house.
What is the together rate?The together rate is the sum of each separate rate.
In this problem, we have that the rates are given as follows:
The together rate is 1/14.The separate rates are 1/d and 1/(d-2).Hence:
[tex]\frac{1}{d} + \frac{1}{d - 2} = \frac{1}{14}[/tex]
[tex]\frac{d - 2 + d}{d(d - 2)} = \frac{1}{14}[/tex]
d² - 2d = 28d - 28.
d² - 30d + 28 = 0
(d - 29)(d - 0.96) = 0.
Both d and d - 2 have to be positive, hence the solution is d = 29, and it would take each person working individually 27 and 29 hours to paint the house.
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Quick algebra 1 questions for 50 points!
Only answer if you know the answer, quick shout-out to Yeony2202, tysm for the help!
The cost per person if number of students is 100 given the inverse variation is $46.75
Inverse variationCost per person = CNumber of students = nC = k / n
where,
k = constant of proportionality
If n = 55 and C = $85
C = k / n
85 = k / 55
85 × 55 = k
4,675 = k
Find C if n = 100
C = k / n
= 4,675 / 100
C = $46.75
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Answer:
C = $46.75
Step-by-step explanation:
85 × 55 = k
4,675 = k
4675/100=46.75
therefore the answer is 46.75
the graph of y =-3x+4 is
Answer:
Step-by-step explanation:
hello :
The graph of y =-3x+4 is the line
the market price of article is rs 3000. a discount of 30% was agreed. find the sale price of the article and the amount of discount.
Answer: 2400
Step-by-step explanation:
3000 x 20/100 = 600
Discount = 600
Sale price of the article: 3000-600 = 2400
6. a. Sixty students in a class took an examination in Physics and Mathematics. If 17 of them passed Physics only, 25 passed in both Physics and Mathematics and 9 of them failed in both subjects, find i. the number of students who passed in Physics ii. the probability of selecting a student who passed in Mathematics 17
Let [tex]C[/tex] be the set of all students in the classroom.
Let [tex]P[/tex] and [tex]M[/tex] be the sets of students that pass physics and math, respectively.
We're given
[tex]n(C) = 60[/tex]
[tex]n(P \cap M') = 17[/tex]
[tex]n(P \cap M) = 25[/tex]
[tex]n((P \cup M)') = n(P' \cap M') = 9[/tex]
i. We can split up [tex]P[/tex] into subsets of students that pass both physics and math [tex](P\cap M)[/tex] and those that pass only physics [tex](P\cap M')[/tex]. These sets are disjoint, so
[tex]n(P) = n(P\cap M) + n(P\cap M') = 25 + 17 = \boxed{42}[/tex]
ii. 9 students fails both subjects, so we find
[tex]n(C) = n(P\cup M) + n(P\cup M)' \implies n(P\cup M) = 60 - 9 = 51[/tex]
By the inclusion/exclusion principle,
[tex]n(P\cup M) = n(P) + n(M) - n(P\cap M)[/tex]
Using the result from part (i), we have
[tex]n(M) = 51 - 42 + 25 = 34[/tex]
and so the probability of selecting a student from this set is
[tex]\mathrm{Pr}(M) = \dfrac{34}{60} = \boxed{\dfrac{17}{30}}[/tex]
HELP ASAP
You work at a canning factory that's producing cans for a new brand of soup. You need to decide what size the cans should be. The soup cans can have a radius of either 2 in, 2.5 in, 3 in, or 3.5 in. The cans need to hold a volume of exactly 90 in3. The company wants the cans to be no more than 5 inches tall, and it wants the cans to have the greatest lateral surface area possible so it can print more information on the side of the cans.
To solve this problem, you will fill in this table with the surface area and volume of each cylinder:
a. First, calculate the height each can must be, given the radius and volume.
b. Now calculate the lateral surface area for each possible can.
c. Based on the requirements for the can, which can should you make?
Answer:
The answers are in the image
Step-by-step explanation:
The solution is in the attached image
Can anyone please help me with this i am stuck and i really need help.Explain how u got the answer
The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively
What is a kite?A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.
The given figure is a kite with two intersecting lines that are perpendicular to each other.
Since the lines are perpendicular to each other, hence;
m<1 = 90 degrees
For the measure of m<2
m<2 + 90 + 27 =180
m<2 + 117 = 180
m<2 = 180 - 117
m<2 = 63degrees
Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees
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Which is the completely factored form of 12x4 + 39x3 + 9x2?
3x2(x – 3)(4x – 1)
3x2(x + 3)(4x + 1)
3x(x + 3)(4x + 1)
3x(x – 3)(4x + 1)
Answer:
The second option, 3x^2(x+3)(4x+1)
Step-by-step explanation:
Factor out the common term, which is 3x^2
This then becomes 3x^2(4x^2+13x+3)
Factor the inside term and it becomes
(3x^2)(x+3)(4x+1)
Lesson 13:Find a Sequence
Describe a sequence of reflections, rotations, and translations that takes ABCD onto
A'B'C'D'.
The sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
How to Identify the Transformation?
We want to find the transformation that maps Quadrilateral ABCD onto Quadrilateral A'B'C'D'.
Looking at the given image, the sequence of transformation will be;
Rotate 120 degrees Counterclockwise around B, then Translate B to B' and reflect over segment BA.
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Fill in the table using this function rule.
The complete table is
x y
-1 -2
0 3
1 8
2 13
How to complete the table?
The function is given as:
y = 5x + 3
On the table, we have
x = -1, 0, 1 and 2
Using the above values, we have:
y = 5(-1) + 3 = -2
y = 5(0) + 3 = 3
y = 5(1) + 3 = 8
y = 5(2) + 3 = 13
So, the complete table is
x y
-1 -2
0 3
1 8
2 13
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David has kept track of his family’s grocery bills for the past 10 weeks, as shown in the table.
Week 1 2 3 4 5 6 7 8 9 10
Bill ($) 92 106 129 115 100 84 110 156 98 87
Would you choose to use a histogram, a circle graph, or a line graph to display the data? Explain your choice. Then make a display.
The best option that would be used to show the data would be the line graph.
Why the line graph is the bestThe reason I chose the line graph is that it would show us the trend in the data. This is in a way that we would see the periods there was a high bills.
Also the line graph is very simple to understand. The relationship and the changes in the data is easily seen.
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A dog gave birth to 9 puppies, of which 2 are brindle. What is the ratio of brindle puppies to non-brindled puppies?
Answer:
2:7
Step-by-step explanation:
If 2 of the puppies are brindle that leaves 7 that are not out of the nine making the ratio 2:7.
PLEASE HELP!!! I'LL MARK AS BRAINLIEST TO THE FIRST PERSON THAT CAN ANSWER!!!
When two exponents with the same base are multiplied together, this reflects the _______ of powers property.
Solve each of the following equations show the solution on a number line check your answers 5-|n-1|=-2
n=8
n=-6
What is a number line?A number line is a horizontal line with evenly spaced number increments. The numbers on the line will determine how the number on the line can be answered.
The numbers on the number line increase as one moves from left to right and decrease as one moves from right to left.
Solution for the above equation 5-|n-1|=-2What is the modulus?A modulus function is a function that returns the absolute value of a number or variable. It yields the magnitude of the number of variables. It is also known as an absolute value function. This function's output is always positive, regardless of the input.
Open modulus with a positive sign.
5-|n-1|=-2
-|n-1|=-2-5
n+1= 7
n= 8
Open modulus with a negative sign.
5-|n-1|=-2
-|n-1|=-2-5
n-1= -7
n= -6
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What is the scale factor of this dilation? Triangle A B C. Side A C is 8, C B is 10, A B is 6. Triangle A prime B prime C prime. Side A prime C prime is 4, C prime B prime is 5, B prime A prime is 3. One-fifth One-half 1 2
Answer:
The scale factor from the original triangle to the image is 1/2. The scale factor from the image to the original is 2.
Step-by-step explanation:
I make a sketch of the information. Look at the corresponding sides. Side AC on the big triangle is 8 and A'C' is 4. It is half of the size of the large triangle. That is true for each pair of sides.
If I went the other way, the original sides are twice as big as the images sides.
Help, please. I just need an answer, so if anyone is bored, for the love of god please...
Answer:B & E
Step-by-step explanation:
We can first rearrange the function to isolate y. Then, we can find the slope as the function is in the form y=mx+b.
[tex]3x-4y=7\\-4y=-3x+7\\y=\frac{3}{4}x-\frac{7}{4}[/tex]
Since parallel lines have the same slope, we can put the slope of 3/4 into the point slope form to get the answer.
For reference, the point-slope form is [tex]y-y_1=m(x-x_1)[/tex]
[tex]y+2=\frac{3}{4}(x+4)\\y+2=\frac{3}{4}x+3\\y=\frac{3}{4}x+1[/tex]
The first line is found in option E, so option E is one of the correct options.
We can also move the x to the other side, as two of the 5 options have both variables on the left (B and C).
[tex]-\frac{3}{4}x+y=1[/tex]
If we multiply the whole equation by -4, we can get rid of the fraction.
[tex]-4(-\frac{3}{4}x+y)=-4(1)\\3x-4y=-4[/tex]
Hence, option B is also correct.
HELPPPP PLSSSSSSSS
-----
Answer:
Translation of 3 units to the left.
Vertical stretch by a factor of 2.
Translation of 5 units down.
Step-by-step explanation:
Transformations
For a > 0
[tex]f(x+a) \implies f(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]
[tex]y=a\:f(x) \implies f(x) \: \textsf{stretched parallel to the y-axis (vertically) by a factor of}\:a[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]
Parent function:
[tex]y=x^2[/tex]
Translate 3 units left
Add 3 to the variable of the function
[tex]\implies y=(x+3)^2[/tex]
Stretch vertically by a factor of 2
Multiply the whole function by 2:
[tex]\implies y=2(x+3)^2[/tex]
Translate 5 units down
Subtract 5 from the whole function:
[tex]\implies y=2(x+3)^2-5[/tex]
Please see the attached graphs for the final transformed function (as well as the graphed steps).
Answer:
a) vertical expansion by a factor of 2; translation 3 units left and 5 units down
b) see attached
Step-by-step explanation:
a.Describing transformations is all about matching patterns. The elements of the transformed function are matched with the elements of a transformation.
Vertical scalingA function is scaled vertically by multiplying each function value by some scale factor. In generic terms, the function f(x) is scaled vertically by the factor 'c' in this way:
original function: f(x)scaled by a factor of 'c': c·f(x)If we want the function f(x) = x² scaled vertically by a factor of 2, then we have
f(x) = x² . . . . . . . original function
2·f(x) = 2x² . . . . scaled vertically by a factor of 2
On a graph, each point is vertically twice as far vertically from some reference point (the vertex, for example) as it is in the original function graph.
Horizontal translationA function is translated to the right by 'h' units when x is replaced by (x -h).
original function: f(x)translated h units right: f(x -h)If we want the function f(x) = x² translated right by 3 units, we will have ...
f(x) = x² . . . . . . . . . . . original function
f(x -3) = (x -3)² . . . . . .translated right 3 units
Note that translation left by 3 units would give ...
f(x -(-3)) = f(x +3) = (x +3)² . . . . translated left 3 units
On a graph, each point of the left-translated function is 3 units left of where it was on the original function graph.
Vertical translationA function is translated upward by 'k' units when k is added to the function value.
original function: f(x)translated k units up: f(x) +kThe value of k will be negative for a translation downward.
If we want the function f(x) = x² translated down by 5 units, we will have ...
f(x) = x² . . . . . . . . . . . original function
f(x) = x² -5 . . . . . . . . .translated down 5 units
Combined transformationsUsing all of these transformations at once, we have ...
f(x) = x² . . . . . . . . . . . . . . . . . original function
c·f(x -h) +k = c·(x -h)² +k . . . scaled by 'c', translated h right and k up
Compare this to the given function:
y = 2(x +3)² -5
and we can see that ...
c = 2 . . . . . . vertical scaling by a factor of 2h = -3 . . . . . translation 3 units leftk = -5 . . . . . translation 5 units downThis is the pattern matching that is described at the beginning.
__
b.When graphing a transformed function, it is often useful to start with a distinctive feature and work from there. The vertex of a parabola is one such distinctive feature.
TranslationThe transformations move the vertex 3 units left and 5 units down from its original position at (0, 0). The location of the vertex on the transformed function graph will be at (x, y) = (-3, -5).
Vertical scalingThe graph of the parent function parabola (y= x²) goes up from the vertex by the square of the number of units right or left. That is, 1 unit right or left of the vertex, the graph is 1 unit above the vertex. 2 units right or left, the graph is 2² = 4 units above the vertex.
The scaled graph will have these vertical distances multiplied by 2:
±1 unit horizontally ⇒ 2·1² = 2 units vertically; points (-4, -3), (-2, -3)±2 units horizontally ⇒ 2·2² = 8 units vertically; points (-5, 3), (-1, 3)The graph of the transformed function is shown in blue in the attachment.
__
Additional comment
The vertical scale factor 'c' may have any non-zero value, positive or negative, greater than 1 or less than 1. When the magnitude is less than 1, the scaling is a compression, rather than an expansion. When the sign is negative, the graph is also reflected across the x-axis, before everything else.
Please help me with this
Answer:
altitude: 16 cmbase: 12 cmStep-by-step explanation:
The given relation can be used with the formula for the area of a triangle to give an equation for the altitude or base.
SetupLet b represent the length of the base. Then the altitude (height) is (b+4). The area formula tells us the area is ...
A = 1/2bh
Using given values, the equation becomes ...
96 = 1/2b(b +4)
SolutionSimplifying the equation and multiplying by 2, we have ...
192 = b² +4b
Adding (4/2)² = 4 will complete the square.
196 = b² +4b +4 = (b +2)²
Taking the square root gives ...
14 = b +2 . . . . . . we are not interested in the negative root
12 = b . . . . . . . . subtract 2
16 = b+4 . . . . . find the altitude
The base is 12 cm; the altitude is 16 cm.
A city architect is designing a parking garage at city hall. the garage layout is in the shape of a rectangle. the width of the
garage is x + 15, where x is measured in feet. the length of the garage is 49 feet less than 2 times the width. the square
footage (area) that the parking garage covers should be 162 more than 27 times the garage's perimeter. find the length an
width of the parking garage that fits these requirements.
part a
The measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.
How to determine the dimensionsFrom the information given, we have the following proofs;
Width, w = x+15 Length, l = 2(x+15) - 49Length, l = 2x + 30 - 49
Length = 2x - 19
The formula for perimeter of a rectangle is given as;
Perimeter = 2( length + width)
Substitute the expressions into the formula
Perimeter = 2 ( x+ 15 + 2x - 19 )
Perimeter = 2 (3x - 4)
Perimeter = 6x - 8
We have that the area is 162 more than 27 times the perimeter, which is Area = 27 (perimeter )+ 163
Area = 27(6x-8) + 162
Expand the bracket
Area= 162x - 216 + 162
Area = 162x - 54
But we know that
Area = length × width
Substitute the expressions
Area = (x+15)(2x-19)
Area = 2x² - 19x +30x - 285
Area = 2x² + 11x - 285
Equate the two formulas for area
162x - 54 = 2x² +11x - 285
Collect like terms
2x² + 11x - 285 - 162x + 54 = 0
2x² - 151x - 231 = 0
Solve the quadratic equation
(2x + 3)(x-77) = 0
Let's solve for x
x - 77 = 0
x = 77
The expression for the width;
Width = x+15
Width = 77 + 15
Width = 92 feet
The expression for the length
Length = 2(x+15) - 49
Length = 2 ( 77 + 15) - 49
Length = 154 + 30 - 49
Length = 184 - 49
Length = 135 feet
Thus, the measure of the length and width of the rectangle is given as 135 feet and 92 feet respectively.
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(4x⁴-4x²-x-3) ÷ (2x²-3)
so far i have 2x²+1+?/2x²-3
what is the question mark?
Answer:
[tex]2x^2+1-\dfrac{x}{2x^2-3}[/tex]
Step-by-step explanation:
Use the long division method to divide polynomials:
[tex]\large \begin{array}{r}2x^2\phantom{)))))}+1\phantom{)}\\2x^2-3{\overline{\smash{\big)}\,4x^4-4x^2-x-3\phantom{)}}}\\\underline{-~\phantom{(}(4x^4-6x^2)\phantom{-b))))))}}\\0+2x^2-x-3\phantom{)}\\\underline{-~\phantom{()}(2x^2\phantom{))))}-3)}\\-x\phantom{))))))}\end{array}[/tex]
Therefore:
[tex]\dfrac{4x^4-4x^2-x-3}{2x^2-3}=2x^2+1-\dfrac{x}{2x^2-3}[/tex]
Here is a list of numbers: 2 , 8 , 1 , 7 , 4 , 10 , 1 , 15 , 20 State the median.
Answer:
7
Step-by-step explanation:
1, 1, 2, 4, 7, 8, 10, 15, 20
median = 7
Which of the following is equal to the expression below?
(4^-5)^3
A. -4^2
B. 1/4^15
C. -4^15
D. 1/4^2
Answer: B
Step-by-step explanation:
[tex](4^{-5})^3=4^{-15}=\frac{1}{4^{15}}[/tex]
7/11 = x/9
Round your answer to the nearest tenth.
The solution to the given fraction 7/11 = x/9 to the nearest tenth is 5.7
Fraction7/11 = x/9
cross product7 × 9 = 11 × x
63 = 11x
divide both sides by 11x = 63/11
x = 5.72727272727272
Approximately,
x = 5.7
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PLEASE HELP
place the figure in a coordinate plane and find the indicated length a square with side length n; Find the length of the diagonal
Thanks
For the square with side length n, the diagonal measures:
[tex]d = \sqrt{2} *n[/tex]
How to get the length of the diagonal?The sidelength of the square is n, and we want to get the length of the diagonal d.
Notice that the diagonal is the hypotenuse of a right triangle whose catheti measure n.
Then we can use the Pythagorean theorem, which says that the square of the hypotenuse is equal to the sum of the squares of the cathetus;
[tex]d^2 = n^2 + n^2\\\\d^2 = 2n^2\\\\d = \sqrt{2n^2} \\\\d = \sqrt{2}*n[/tex]
That is the length of the diagonal.
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Drag the tiles to the correct boxes to complete the pairs. Suppose you roll a fair six-sided die. Then you roll a fair eight-sided die. Match each probability to its correct value. the probability that both numbers are odd numbers and their product is greater than 10 the probability that the second number is twice the first number the probability of getting numbers whose sum is a multiple of 4 the probability that the sum of the two numbers is greater than 11 the probability that the second number rolled is less than the first number arrowRight arrowRight arrowRight arrowRight arrowRight
The probability will be:
Case 1 matches with 5/48.
Case 2 matches with 1/12.
Case 3 matches with 1/4.
Case 4 matches with 1/8.
Case 5 matches with 5/16.
How to illustrate the probability?We have a total sample space of six-sided die and an eight sided die.
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(2,7),(2,8)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(3,7),(3,8)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(4,7),(4,8)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(5,7),(5,8)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6),(6,7),(6,8)
Case 1: The Probability that both numbers are odd numbers and their product is greater than 10. are: (3,5),(3,7),(5,3),(5,5),(5,7)
And the total number of outcomes are: 48.
The required probability is 5/48.
Case 2: The probability that the second number is twice the first number are:
(1,2),(2,4),(3,6),(4,8)
And the total number of outcomes are 48.
So, the required probability is 1/12.
Case 3: The probability of a number whose sum is a multiple of 4 are:
(1,3),(1,7),(2,2),(2,6),(3,1),(3,5),(4,4),(4,8),(5,3),(5,7),(6,2),(6,6).
And the total number of outcomes are: 48.
The required probability is 12/48 = 1/4
Case 4: The probability that the sum of two numbers is greater than 11.
(4,8),(5,8),(6,7),(6,8),(5,7),(6,6)
And a total number of outcomes are 48.
So, the required probability is 6/48 = 1/8.
Case 5: The probability that the second number rolled is less than the first number are:
(2,1),(3,1),(3,2),(4,1),(4,2),(4,3),(5,1),(5,2),(5,3),(5,4),(6,1),(6,2),(6,3),(6,4),(6,5)
And the total number of outcomes are: 48.
The required probability is 15/48 = 5/16.
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what is 4x-5/3+2x=7+2/9x+2
Simplifying the expression gives 36x^2 - 82x - 10 = 0
How to simplify the expressionGiven the expression;
4x-5/3+2x=7+2/9x+2
[tex]\frac{4x - 5}{3 + 2x} = \frac{9}{9x + 2}[/tex]
Cross multiply
[tex]4x - 5( 9x + 2) = 9 (3 + 2x)[/tex]
Expand the bracket
[tex]36x^2 + 8x - 45x - 10 = 27x + 18x[/tex]
Collect like terms
36x^2 + 8x - 45x - 27x - 18x = 0
Add the like terms
36x^2- 82x - 10 = 0
Thus, simplifying the expression gives 36x^2- 82x - 10 = 0
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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match each expression to make pairs of equivalent expressions.
The equivalent expressions indicated are;
1) 1/a^6b^4
2) a^6/b^6
3) a^6/b^5
4) b^6/a^6
5) a^5b^3
What is the result of the equivalent expressions?
We have to note that when we talk about the equivalent expressions, we mean the expressions that we have to get from each other when we carry out a little computational work on the original expression.
Thus, the equivalent expression has shown that the expression that is in the bracket is the same as the original expression by the use of the laws of exponents.
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Which systems of equations have no real number solutions? Check all that apply.
Oy=x² + 4x + 7 and y = 2
□ y=x²-2 and y=x+5
-Oy=-x²-3 and y = 9 + 2x
y=-3x-6 and y = 2x² - 7x
y=x² and y = 10 - 8x
Answer + Step-by-step explanation:
Recall That the number of solution
of a quadratic equation ax² + bx + c = 0
depends on the discriminant b² - 4ac :
if b² - 4ac > 0 , the equation has two distinct solutions.
if b² - 4ac = 0 , the equation has only one solution.
if b² - 4ac < 0 , the equation has no solutions.
=======================================
System 1 :
y = x² + 4x + 7 and y = 2
⇔ x² + 4x + 7 = 2
⇔ x² + 4x + 5 = 0
→ b² - 4ac = 4² - 4×1×5 = 16 - 20 = -4 < 0
Then the quadratic equation has no solutions
Therefore the system has no solutions.
System 2 :
y = x² - 2 and y = x + 5
⇔ x² - 2 = x + 5
⇔ x² - x - 7 = 0
→ b² - 4ac = (-1)² + 4×7 = 29 > 0
Then the quadratic equation has two solutions
Therefore the system has two solutions.
System 3 :
y = -x² - 3 and y = 9 + 2x
⇔ -x² - 3 = 9 + 2x
⇔ -x² - 2x - 12 = 0
→ b² - 4ac = (-2)² - 4×(-1)×(-12) = 4 - 48 = -44 < 0
Then the quadratic equation has no solutions
Therefore the system has two solutions.
System 4 :
y = -3x - 6 and y = 2x² - 7x
⇔ -3x - 6 = 2x² - 7x
⇔ 2x² - 4x + 6 = 0
→ b² - 4ac = (-4)² - 4×(2)×(6) = 16 - 48 = -32 < 0
Then the quadratic equation has no solutions
Therefore the system has two solutions.
System 5 :
y = x² and y = 10 - 8x
⇔ x² = 10 - 8x
⇔ x² + 8x - 10 = 0
→ b² - 4ac = 8² - 4×1×(-10) = 64 + 40 = 104 > 0
Then the quadratic equation has two solutions
Therefore the system has two solutions.
There are 26 prize tickets in a bowl, labeled A to Z. What is the probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen? Does this represent an independent or dependent event? Explain.
Using it's concept, there is a 0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
For the first ticket, since 5 out of 26 letters are vogal, the probability is:
5/26.
For the second ticket, since there is no replacement, the probability is:
4/25.
The probability of both tickets is:
[tex]p = \frac{5}{26} \times \frac{4}{25} = 0.0308[/tex]
0.0308 = 3.08% probability that a prize ticket with a vowel will be chosen, not replaced, and then another prize ticket with a vowel will be chosen. Since the letter is not replaced, the number of outcomes change, hence they are dependent.
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An architect wants an artistic flair to the house he is building, so he designs windows that are three fourths of a circle in shape. The builder is making trim for the windows and needs to know the length of the arc of the outer rim of the window. If the central angle is 270 degrees, and the radius of the partial circle is 30 inches, how much trim is needed for each window? Round your answer to the nearest inch, and enter the number only.
The amount of rim needed for each window is 141.4 in
How to find the length of the outer rim?Since the outer rim is the length of an arc, we use the formula for length of an arc of a circle.
What is an arc?An arc is part of section of the circumference of a circle
What is the length of an arc?So, length of arc, L = Ф/360 × 2πR where
Ф = central angle of arc and R = radius of circle.Gven that for the window rim
Ф = angle of the rim = 270° and R = radius of the rim = 30 inSubstituting the values of the variables into the equation for L, we have
L = Ф/360 × 2πR
L = 270°/360° × 2π × 30 in
L = 3/4 × 2π × 30 in
L = 3/2 × π × 30 in
L = 3 × π × 15 in
L = 45π in
L = 141.37 in
L ≅ 141.4 in
So, the amount of rim needed for each window is 141.4 in
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A square has a perimeter of 12x 52 units. which expression represents the side length of the square in units?
Answer:
X
Step-by-step explanation:
KHAN ACADEMY