Answer:
30% is the correct answer.
Step-by-step explanation:
Total number of boys = 2
Total number of girls = 3
Total number of students = 5
To find:
Probability that the pianist will be a boy and the alternate will be a girl?
Solution:
Here we have to make 2 choices.
1st choice has to be boy (pianist) and 2nd choice has to be girl (alternate).
[tex]\bold{\text{Required probability }= P(\text{boy as pianist first}) \times P(\text{girl as alternate})}[/tex]
Formula for probability of an event E is given as:
[tex]P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}[/tex]
For [tex]P(\text{boy as pianist})[/tex], number of favorable cases are 2 (total number of boys).
Total number of cases = Total number of students i.e. 5
So, [tex]P(\text{boy as pianist})[/tex] is:
[tex]P(\text{boy as pianist}) = \dfrac{2}{5}[/tex]
For [tex]P(\text{girl as alternate})[/tex], number of favorable cases are 3 (total number of girls).
Now, one boy is already chosen as pianist so Total number of cases = Total number of students left i.e. (5 - 1) = 4
[tex]P(\text{girl as alternate}) = \dfrac{3}{4}[/tex]
So, the required probability is:
[tex]\text{Required probability } = \dfrac{2}{5}\times \dfrac{3}{4} = \dfrac{3}{10} = \bold{30\%}[/tex]
Answer:
30% A
Step-by-step explanation:
The first side of a triangle measures 3 in. less than the second side, the third side is 2 in. more than the first side, and the perimeter is 20 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.
Answer:
P = 3x - 4
Step-by-step explanation:
Side 1 = x - 3
Side 2 = x
Side 3 = 2 + (Side 1) = 2 + x - 3 = x - 1
Perimeter = 20 in
Perimeter = Side 1 + Side 2 + Side 3
Perimeter = (x - 3) + (x) + (x - 1)
Perimeter = x - 3 + x + x - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 3 - 1
Perimeter = 3x - 4
P = 3x - 4
A museum curator is hanging 7 paintings in a row for an exhibit. There are 4 Renaissance paintings and 3 Baroque paintings. From left to right, all of the Renaissance paintings will be hung first, followed by all of the Baroque paintings. How many ways are there to hang the paintings
Answer:
144 ways
Step-by-step explanation:
Number of paintings = 7
Renaissance = 4
Baroque = 3
We are hanging from left to right and we will first hang Renaissance painting before baroque painting.
For Renaissance we have 4! Ways of doing so. 4 x3x2x1 = 24
For baroque we have 3! Ways of doing so. 3x2x1 = 6
We have 4!ways x 3!ways
= (4x3x2x1) * (3x2x1) ways
= 144 ways
Therefore we have 144 ways to hang the painting.
What are the zeros of the quadratic function represented by this graph?
У
A
6
2
X
-6
- 2
6
2-
-6-
A.
1 and 3
OB.
-3 and -1
C.
-3 and 1
D. -1 and 3
Look where the parabola crosses the x axis. This is where the x intercepts are located. The term "x intercept" is the same as "root" and also the term "zero".
A population consists of 100 elements. We want to draw a simple, random sample of 20 elements from this population. On the first selection, the probability of any particular element being selected is ____.
Answer:
1/5Step-by-step explanation:
Probability is the likelihood or chance that an event will occur.
Probability = expected outcome of event /total outcome
Since the population consists of 100 elements, the total outcome of event = 100.
If random sample of 20 element is drawn from the population, the expected outcome = 20
On the first selection, the probability of any particular element being selected = 20/100 = 1/5
What is the name of a number that can be written in the form a + bi where a and b are nonzero real
numbers? (1 point)
a pure imaginary number
an imaginary unit
a real number
a complex number
Answer:
Complex numbers
Step-by-step explanation:
Given
[tex]a + bi[/tex]
Required
Determine the type of number in that form
Numbers written in [tex]a + bi[/tex] are referred to as complex numbers
Where [tex]a \neq 0[/tex]; [tex]b\neq 0[/tex] and [tex]i = \sqrt{-1}[/tex]
Note that a and b can either integers or non integers and a and be can also be positive or negative
The following are valid examples of complex numbers
[tex]2 + 3i[/tex]
[tex]2.4 - 5i[/tex]
[tex]-3 - i[/tex]
and lots more..
bananas cost $4 and apples close 0.60$ each if b represents the number of bunches of bananas and a represents the number of apple which of the following expressions represents the total cost? 1 4.60(b+a) 2 4b + 0.60 3 4.60 + a 4 4.60ab
Answer:
4b + .60a
Step-by-step explanation:
b represents the number of bunches of bananas
a represents the number of apple
Multiply the cost by the number purchased of each item and add them together
4b + .60a
Answer:
[tex]\huge\boxed{\$ (4 b + 0.60 a)}[/tex]
Step-by-step explanation:
Bananas represented by b
1 banana costs $4 so b bananas will cost $ 4 b
Apples represented by a
1 apples costs 0.60 $ so a apples will cost $ 0.60 a
Totally, they will cost:
=> $ (4 b + 0.60 a)
{4.OA.A.3} There are 1,492 chairs in the auditorium. Ms. Jones wants to put them into 10 rows. If she splits the chairs evenly into 10 rows, how many chairs will Ms. Jones have left over?
Answer:
2 chairs will be left over.
Step-by-step explanation:
Given that
There are a total of 1492 chairs.
which are to divided in 10 rows evenly.
To find:
Number of chairs left ?
Solution:
Let the number of chairs in each row = [tex]x[/tex]
There are 10 rows so number of chairs in rows = 10[tex]x[/tex]
Let the number of chairs left = [tex]y[/tex]
Total number of chairs =10[tex]x[/tex] + [tex]y[/tex] = 1492
The above equation is like:
Divisor [tex]\times[/tex] Quotient + Remainder = Dividend
So, we have to find the remainder in this question where we are given Divisor and Dividend.
10 [tex]\times[/tex] 149 + 2 = 1492
So, dividing 1492 with 10, we get remainder as 2.
Hence, 2 chairs will be left.
in the diagram, find the values of a and b.
Answer:
m∠a = 67° , m∠b = 42°Step-by-step explanation:
∠a is alternate interior angle to ∠ECD
∠b is alternate interior angle to ∠BCD
so:
If AB || CD then:
m∠a = m∠ECD = 25° + 42° = 67°
m∠b = 42°
A man claims to have extrasensory perception (ESP). As a test, a fair coin is flipped10 times and the man is asked to predict the outcome in advance. He gets 7 out of10 correct. What is the probability that he would have done at least this well if hehad no ESP?
Answer:
I would say 70%
Step-by-step explanation:
He got 7 of of 10 (7/10 = 70%) right so I would say he would do just as well without ESP since it doesn't exist.
Consider population data with μ = 30 and σ = 3. (a) Compute the coefficient of variation. (b) Compute an 88.9% Chebyshev interval around the population mean. Lower Limit Upper Limit
Answer:
A. 10%
B. Lower limit= 21
Upper limit = 39
Step-by-step explanation:
Mean = 30
SD = 3
a. COV = SD/|x| × 100
= 3/30 × 100
= 10%
= 0.1
B. For 88.9 chevbychev interval:
= (1 - 1/K²) = 0.889
= 1/K² = 1 - 0.889
= 1/K² = 0.111
= K² = 1/0.111
= K² = 9
= K = √9
K = 3
Lower limit = 30 - 3(3)
Lower limit = 21
Upper limit = 30 + 3(3)
Upper limit = 39
Therefore lower limit is 21 and upper limit is 39
The Colonel spots a campfire at a bearing N 59∘59∘ E from his current position. Sarge, who is positioned 242 feet due east of the Colonel reckons the bearing to the fire to be N 34∘34∘ W from his current position.
Determine the distance from the campfire to each man, rounded to the nearest foot.
Colonel is about............................ feet away from the fire
Sarge is about............................... feet away from the fire
Answer:
i. Colonel is about 201 feet away from the fire.
ii. Sarge is about 125 feet away from the fire.
Step-by-step explanation:
Let the Colonel's location be represented by A, the Sarge's by B and that of campfire by C.
The total angle at the campfire from both the Colonel and Sarge = [tex]59^{0}[/tex] + [tex]34^{0}[/tex]
= [tex]93^{0}[/tex]
Thus,
<CAB = [tex]90^{0}[/tex] - [tex]59^{0}[/tex] = [tex]31^{0}[/tex]
<CBA = [tex]90^{0}[/tex] - [tex]34^{0}[/tex] = [tex]56^{0}[/tex]
Sine rule states;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
i. Colonel's distance from the campfire (b), can be determined by applying the sine rule;
[tex]\frac{b}{Sin B}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{b}{Sin 56^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{b}{0.8290}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
b = [tex]\frac{0.8290*242}{0.9986}[/tex]
= 200.8993
Colonel is about 201 feet away from the fire.
ii. Sarge's distance from the campfire (a), can be determined by applying the sine rule;
[tex]\frac{a}{Sin A}[/tex] = [tex]\frac{c}{Sin C}[/tex]
[tex]\frac{a}{Sin 31^{0} }[/tex] = [tex]\frac{242}{Sin 93^{0} }[/tex]
[tex]\frac{a}{0.5150}[/tex] = [tex]\frac{242}{0.9986}[/tex]
cross multiply,
a = [tex]\frac{0.5150*242}{0.9986}[/tex]
= 124.8073
Sarge is about 125 feet away from the fire.
domain and range A) D: (–7, –2], (–1, 3] R: (–10, 9.2] B) D: [–7, –2], [–1, 3] R: [–10, 9.2] C) D: (–7, 3] R: (–10, 9.2] D) D: (–7, –2), (–1, 3) R: (–10, 9.2)
Answer:
[tex]\Large \boxed{\mathrm{C) \ D: (-7, 3] \ R: (-10, 9.2]}}[/tex]
Step-by-step explanation:
The domain is the set of all possible x values.
The range is the set of all possible y values.
For the domain, we observe the graph, the graph will contain all the x values shown on the x-axis.
[tex]\mathrm{D= (-7,3] }[/tex]
For the range, we observe the graph, the graph will contain all the y values shown on the y-axis.
[tex]\mathrm{R= (-10,9.2] }[/tex]
Solve the equation for solutions in the interval [0, 2 π). Use algebraic methods and give exact values. Support your solution graphically. cos2x = 0
Answer:
45° or 135°
Step-by-step explanation:
Cos 2x = 0
2x = cos^-1 0
2x = 90° or 270°
x= 45° or 135°
Answer:
Step-by-step explanation:
● cos 2x = 0
We khow that Pi/2 equals 0.
So
● 2x = Pi/2 or 2x= -Pi/2
Then:
● x = Pi/4 or x = -Pi/2
So the solutions are:
● x = Pi/4 + 2×k×Pi
● or x = -Pi/4 + 2×k×Pi
Where k is an integer
The picture below has a graphical solution
● Pi/4 is approximatively 0.785 and -Pi/4 is approximatively -0.785
● the output of both Pi/4 and -Pi/4 is 0
So our answer was righr
PLEASE HELP!
Suppose there is a strong positive correlation between mand n. Which of the
following must be true?
A. An increase in m causes n to increase.
B. When m increases, n tends to decrease.
C. When m increases, n tends to increase.
D. An increase in m causes n to decrease.
Answer:
A an increase in m cause n to increase
Step-by-step explanation:
a positive correlation means they will travel in the same direction when one is affected.
Answer:
Option A: An increase in m causes n to increase.
Step-by-step explanation:
A Positive correlation is a relationship between two variables in which both variables move with the same ratio. A positive correlation exists when one variable increases as the other variable increases, or vice-versa.
A perfect positive correlation means that both variables move by the exact same percentage.
Therefore, if there is a strong positive correlation between m and n then V increases and, w tends to increase.
Hope this helped :)
What is the lateral area of the drawing is it a 200 km.b. 425.c.114d.1021km
Answer:
114 km
Step-by-step explanation:
Each side is an isosceles trapezoid, so ED=2 since you would need to add 2 to each end of the bottom line to get the top line. Now use Pythagorean Theorem to get ED^2+AD^2=AE^2. Plug in your numbers to solve for AE. This is the height of each trapezoid. Then use your formula for the area of a trapezoid, (B1+B2)h/2, to get the area of each side, then multiply by 4 to get the lateral area since there are 4 sides. Remember lateral area is just the sides, then surface area is when you include the area of the two bases.
find out what's wrong with this graph
Answer:
The y-axis is upside down, meaning that instead of the values increasing as they go up, they decrease.
PLEASE HELP ME!!! The students in Suzanne's school are painting a rectangular mural outside the building that will be 15 feet by 45 feet. To prepare they are create a scale drawing that represents 20% of the given dimensions. What is the length and width of the scale drawing?
Answer:
length of scale drawing = 9 feet
width of scale drawing = 3 feet
Step-by-step explanation:
Actual dimension 15 feet by 45 feet.
length = 45 feet
width = 15 feet
Dimension on drawing is 20% of actual dimension.
20% = 20/100
Thus,
20% of 15 feet = 20/100 * 15 feet = 3 feet
20% of 45 feet = 20/100 * 45 feet = 9 feet
Thus, length of scale drawing = 9 feet
width of scale drawing = 3 feet
point a is at (6,-6) and point c is at (-6, -2)
Find the cooridantes of point b on AC such that AB=3/4 AC
Answer:
(-3,-3)
B=(6-9,6+3)
15 POINTS AND BRAINLIEST JUST HELP ME PLZZZZZ 4x^2 + 28x + 49 = 0 Rewrite equation (x + __ )^2 = __
Answer:
[tex]\boxed{(x+7)^2 =-3x^2-14x}[/tex]
Step-by-step explanation:
[tex]4x^2 + 28x + 49 = 0[/tex]
[tex]\sf Subtract \ 3x^2 \ and \ 14x \ from \ both \ sides.[/tex]
[tex]4x^2 + 28x + 49 -3x^2-14x= 0-3x^2-14x[/tex]
[tex]x^2 + 14x + 49 = -3x^2-14x[/tex]
[tex]\sf Factor \ left \ side \ of \ the \ equation.[/tex]
[tex](x+7)^2 =-3x^2-14x[/tex]
Answer:
(x+7)² = -3x² -14x
Step-by-step explanation:
4x^2 + 28x + 49 = 0
Subtract 3x² and 14x from each sides.
x^2 + 14x + 49 = -3x² -14x
Next step will be factoring.
(x+7)² = -3x² -14x
On the maturity date of a $10,800, 6-month, 8% note, the borrower sends a check that includes the principal and all of the interest due on the note. What is the amount of the borrower's check?
Answer: $ 11,232.00
Step-by-step explanation:
Given: Amount = $ 10,800
Interest Rate = 8% =0.08
Time in Months= 6.00
Formula :
Interest on Note = (Amount)× (Interest Rate) × ((Time in Months) /12)
= (10800)× (0.08)× (6/12)
= $432
The amount of the borrower's check =(Amount + Interest on Note)
= $ (10,800+432)
= $ 11,232.00
Hence, The amount of the borrower's check = $ 11,232.00
In rectangle ABCD, point E lies half way between sides AB and CD and halfway between sides AD and BC. If AB=10 and BC=2, what is the area of the shaded region? Answer as a decimal, if necessary. Little confused on this one.
Answer:
10 units²
Step-by-step explanation:
Consider the unshaded region to consists of 2 triangles, ∆AED and ∆BEC, which are both of equal dimensions. Their bases and heights are both the same. Both triangles are embedded inside a rectangle ABCD.
Area of the shaded region = Area of rectangle - area of the 2 triangles.
Area of rectangle = l*w
l = 10
w = 2
[tex] Area_R = 10*2 = 20 units^2 [/tex]
Area of the 2 triangles = 2(½*b*h)
b = 2
h = 5
[tex]Area_T = 2(\frac{1}{2}*2*5)[/tex]
[tex] Area_T = 1*2*5 = 10 units^2 [/tex]
Area of shaded region = 20 - 10 = 10 units²
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle. y = x2 − 4x y = 3x
Answer:
Hello your question is incomplete attached is the missing part the second curve ; y = 3x is incomplete so i would solve the problem taking the second curve as ; y = 3x + 8 ( giving you the general methodology )
answer : y = ( 5,32) , x = ( -1,8 )
area of shaded region = 90.673
Step-by-step explanation:
The given curves ; [tex]y = x^2 - 4x\\y = 3x +8[/tex]
solving the above curves simultaneously
[tex]x^2-4x = 3x + 8[/tex]
x^2 - 7x - 8 = 0
( x + 1 )(x - 8 ) = 0
hence X = ( -1 , 8 )
Therefore y = 3x + 8
when x = -1 , y = -3 + 8 = 5
when x = 8 , y = 24 + 8 = 32
hence y = ( 5, 32 )
attached below is the sketched region
Integrating the curves to determine the shaded area in respect to x = ( -1, 8)
∫ [( 3x +8 ) - ( x^2 - 4x ) ] dx
∫ ( -x^2 +7x + 8 ) dx
= { - x^3/3 + 3x^2 + 8x }
= { - 8^3/3 + 3(64) + 64} - { -1^3/3 + 3 - 8 }
= {-170.66 + 192 + 64 } - { -1/3 - 5 }
= -170.66 + 192 + 64 + 5.333 = 90.673 ( area of the shaded region )
Find a • b. a = 5i + 7j, b = -4i + 3j (5 points)
<1, 10>
<-20, 21>
1
41
Answer:
[tex]a\cdot b[/tex] = 1
Step-by-step explanation:
Given that,
Vector [tex]a=5i+7j[/tex]
Vector [tex]b=-4i+3j[/tex]
We need to find [tex]a{\cdot} b[/tex] means the dot product of a and b. So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)[/tex]
We know that,
[tex]i{\cdot}i, j{\cdot}j,k{\cdot}k=1\ \text{and}\ i{\cdot}j= j\cdot i=0[/tex]
So,
[tex]a{\cdot} b=(5i+7j){\cdot} (-4i+3j)\\\\=5i{\cdot}(-4i)+5i{\cdot} 3j+7j\cdot(-4i)+7j\cdot 3j\\\\=-20+21\\\\=1[/tex]
So, the value of [tex]a\cdot b[/tex] is 1.
Answer:
1
Step-by-step explanation:
Emile is a long-distance trucker. In one week he drives miles from his home in Fort Lauderdale, FL, to Benson, NC. He then drives miles to Barstow, CA, and continues driving miles to Bakersfield, CA. From there, Emile drives miles to Seattle, WA. Estimate the total distance Emile travels by first rounding each distance to the nearest hundred. Do not put units in your answer.
Answer:
Estimated total distance is 1,900 miles.
Step-by-step explanation:
We begin by adding each distance traveled by Emile:
1. Fort Lauderdale, FL, to Benson, NC = 748 miles
2. Barstow, CA, to Bakersfield, CA = 130 miles
3. Bakersfield, CA. to Seattle, WA = 1030 miles
Total miles = 1,908.
Therefore, in one week Emile's total distance to the nearest hundred is 1,900.
Note: the distances where gotten via Google Map.
Find the missing term in the
geometric sequence.
13,[ ? ],208
Answer:
110.5
Step-by-step explanation:
208=13+(3-1)d
208=13+2d
-13. -13
195=2d
÷2. ÷2
97.5=d. (d means difference)
13(first term)+97.5=110.5
Answer: 676
Step-by-step explanation: r/13=208/r
r²=2704
r=52
13x52=676
Suppose you have read two different books on world war 2 and each book has different arguments about how the war started which of the following sources provides the best support for the authors arguments
Answer:
Well this is my opinion I would try to compared both them and see if they have something familiar in their arguments. If not I would try to view their different point of view and write your own opinion about it. I would check out another book about the World War 2 because there's infinite of books about it.
3
Select the correct answer.
Which equation represents the line that is parallel to y= 2 and passes through (-1,-6)?
OA x=-1
OB
X= 2
OCy= -6
OD. y= 2x - 4
Reset
Next
Hey there! I'm happy to help!
Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.
We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.
If the line we are looking for is flat; it stays at the same y-value the entire time. We see that the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.
I hope that this helps! Have a wonderful day!
Answer:
Lines that are parallel have the same slopes because they are increasing or decreasing at the same rate and therefore will never bump into each other.
We see that y=2 has a slope of 0 because there is no x that we can see in the equation. This is just a flat line.
If the line we are looking for is flat; it stays at the same y-value the entire time. We see that the y-value for this line of ours is -6. Therefore, the answer is C. y=-6.
Step-by-step explanation:
; ) BELIEVE IN YOURSELF!!!!!!!!!!!!!!!!!
The Bookstall Inc. is a specialty bookstore concentrating on used books sold via the Internet. Paperbacks are $1.35 each, and hardcover books are $3.50. Of the 60 books sold last Tuesday morning, 55 were paperback and the rest were hardcover. What was the weighted mean price of a book? (Round your answer to 2 decimal places.)
Answer:
dddddd okaksy ogvurn
Step-by-step explanation:
d
1.
The ratio of the numbers of sides of two regular polygons is 1:2 .If each interior angle of the first
polygon is 1200 then the measure of each interior angle of the second polygon
is
(1)1400
(2)1350
(3)1500
(4)1600
first polygon
ext. angle=180°-120°
=60°
[tex]ext \: ang = \frac{360}{n} [/tex]
n=360°/60°
n=6
second polygon
n=2(6)=12
ext. ang= 360°/n = 360°/12° = 30°
int. ang = 180°-30°= 150°
answer is C
If the ratio of the numbers of sides of two regular polygons is 1:2 and each interior angle of first angle is 120° then the measure of each interior angle of the second polygon is 150° which is option 3).
What is regular polygon?A regular polygon is a polygon whose all sides are equal to each other.
How to find interior angle?We have been given ratio of sides of two polygon that is 1:2 and the interior angle of first polygon that is 120 degrees.
Exterior angle will be 180-120=60°
We know that exterior angle =360/n where n is the sides of the polygon.
60=360/n
n=360/60
n=6
Number of sides of other polygon=2*6=12
Exterior angle=360/n
=360/12
=30
Interior angle=180-30=150°
Hence the interior angle of the second polygon is 150 degrees.
Learn more about regular polygon at https://brainly.com/question/1592456
#SPJ2
State the correct polar coordinate for the graph shown:
Answer:
Solution : ( - 8, - 5π/3 )
Step-by-step explanation:
There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. For r < 0 we have the coordinates ( - 8, 60° ) and ( - 8, - 300° ) . - 300° in radians is - 5π/3, and hence our solution is option d. But let me expand on how to receive the coordinates. Again r is the directed distance from the pole, and theta is the directed angle from the positive x - axis.
So when r is either negative or positive, we can tell that this point is 8 units from the pole. Therefore - r = - 8 in both our second cases ( we are skipping the first two cases for simplicity ). For r < 0 the point will lay on the ray pointing in the opposite direction of the terminal side of theta.
Our first coordinate is ( - 8, 60° ). Theta will be 2 / 3rd of 90 degrees, or 60 degrees, for - r. Respectively the remaining degrees will be negative, 360 - 60 = 300, - 300. Our second point for - r will thus be ( - 8, - 300° ) . - 300° = - 5π/3 radians, and our coordinate will be ( - 8, - 5π/3 ).
