Answer:The first issue one most notice is the words “at least” We are trying to find the probability of at least 2 girls.
The five possible outcomes for girls are 0,1,2,3,4. The odds of 1 girl out of 4 is .25 and the odds of 1 boy out of 4 is .25 (same as the odds of 3 out of 4 girls). Therefore the odds of 1 OR 3 girls must be .5 because 1 girl and 3 girls each has a .25 probability. If the probability of (1 OR 3 girls) equals .5, then the probability of 2 girls must be a different number.
The probability of 2 or more girls, is the sum of the probability of 4 girls (.06125)(—-.5 to the 4th power—— ), plus the probability of 3 girls (.25)——(the same as the probability of 1 boy)—- plus the probability of 2 girls. Since we know the probability of zero boys is .0625 (again, .5 to the 4th power) and the probability of 1 boy is .25 (the same as the probability of 3 girls )———then the probability of 2 girls is ((1 minus (the sum of the probability of 0 OR 1 boys) plus the (sum of the probability of 3 or 4 girls)), or 1-((.0625+.25)+(.0625+.25)), or .375. We had to derive the probability of two from the other known probabilities. Therefore .375+.25+.0625=.6875 is the probability of both AT LEAST 2 girls and also NO MORE than 2 boys. Notice this adds up to 1.375 because the probability of the central number 2 (i.e., .375) appears on both sides.
prove that [tex]2/\sqrt{3} cosx + sin x= sec(\pi /6-x)[/tex]
Answer:
sec(π/6 - x) = R.H.S = 2/(√3cosx + sinx) = L.H.S.
Step-by-step explanation:
sec(π/6 - x) = 1/cos(π/6 - x)
Using compound angle formula,
cos(A - B) = cosAcosB + sinAsinB where A = π/6 and B = x.
So, cos(π/6 - x) = cos(π/6)cosx + sin(π/6)sinx , cosπ/6 = √3/2 and sinπ/6 = 1/2
cos(π/6 - x) = cosπ/6cosx + sinπ/6sinx = (√3/2)cosx + (1/2)sinx
sec(π/6 - x) = 1/cos(π/6 - x)
= 1/(√3/2)cosx + (1/2)sinx = 2/(√3cosx + sinx)
= L.H.S
So, sec(π/6 - x) = R.H.S = 2/(√3cosx + sinx) = L.H.S
Helppp thank you!!!!!
Answer:
D
Step-by-step explanation:
x is greater than 12:
[tex]x>12 \text{ or } 12<x[/tex]
and x is less than or equal to 3 times the value of y:
[tex]12<x\leq 3y[/tex]
We can divide everything by 3:
[tex]4<\frac{x}{3} \leq y[/tex]
this graph shows the solution to which inequality (3 3) (-3 -1)
Answer:
B
Step-by-step explanation:
since the graph shows dotted line the sign has to be < or > so C and D eliminated from your answer
y>2/3 x +1 is your answer (B)
Answer:
[tex] \boxed{y > \frac{2}{3} x + 1}[/tex]Option B is the correct option.
Step-by-step explanation:
point ₁ ( - 3 , - 1 ) x₁ = - 3 , y₂ = - 1
point ₂ ( 3 , 3 ). x₂ = 3 , y₂= 3
Now, let's find the slope:
Slope ( m ) = [tex] = \frac{y2 - y1}{x2 - x1} [/tex]
[tex] = \frac{3 - ( - 1)}{3 - ( - 3)} [/tex]
[tex] = \frac{3 + 1}{3 + 3} [/tex]
[tex] = \frac{4}{6} [/tex]
[tex] = \frac{2}{3} [/tex]
At ( 3 , - 1 )
y = mx + c , where m is the gradient / slope amd c is called the intercept on y-axis
[tex] - 1 = \frac{2}{3} \times ( - 3) + c[/tex]
Solve for c
[tex] - 1 + 2 = c[/tex]
[tex]c = 1[/tex]
Since, The red line is dotted line. Therefore it does not include the equal to part. And the shaded region is upper part. Hence, ' > ' should be used.
The answer would be:
[tex]y > \frac{2}{3} x + 1[/tex]
Hope I helped!
Best regards!
-3x+2y=6 Find the intercepts. Show your work.
Answer:
The x-intercept is (-2,0)
The y-intercept is (0,3)
Step-by-step explanation:
An x-intercept is the point when the graph crosses the x-axis. In other words, the y-coordinate of the x-intercept is 0 (since it lays on the x-axis). In other words, to solve for the x-intercept(s), plug in 0 for y and solve for x:
[tex]-3x+2y=6\\-3x+2(0)=6\\-3x=6\\x=-2[/tex]
So, the x-intercept is (-2,0).
Likewise, the y-intercept is the point when the graph crosses the y-axis. Because it's on the y-axis, the x-coordinate value would be 0. Thus, to find the y-intercept, plug in 0 for x and solve for y:
[tex]-3x+2y=6\\-3(0)+2y=6\\2y=6\\y=3[/tex]
Thus, the y-intercept is (0,3).
There are 100 prize tickets in a bowl, numbered 1 to 100. What is the probability
that an even numbered prize ticket will be chosen at random, not replaced, then an
odd numbered prize ticket will be chosen? Does this represent an independent or
dependent event? Explain.
Answer:
25/99; Dependent event
Step-by-step explanation:
This is the probability that an even ticket will be chosen out of 100 tickets times the probability that an odd ticket will be chosen out of the remaining 99 tickets.
There 50 even out of 100 to start off with. After 1 even is chosen there are still 50 odd but only 99 more tickets.
(50/100)(50/99)=2500/9900= 25/99
This is a dependent event because an odd number should come after the even number only.
Answer:
25/99
Dependent event
Step-by-step explanation:
1. Multiply the possibilities
There are 50 even numbers out of 100 numbers. If one even number is drawn and not replaced, that would leave the odd ticket to be drawn out of 99 tickets. Because an even number was drawn first, all 50 odd numbers would remain.
[tex]\frac{50}{100}[/tex] · [tex]\frac{50}{99}[/tex] = [tex]\frac{2500}{9900}[/tex]
Simplify
[tex]\frac{2500}{9900}[/tex] = [tex]\frac{25}{99}[/tex]
2. This is a dependent event because the chances of an odd number being drawn was altered. If the even ticket was replaced, the probability of the odd number being drawn would not have been affected.
Which pairs of polygons are congruent?
Answer:
pair3
Step-by-step explanation:
it is when they have same number of sides .
Answer:
1 and 3.
Step-by-step explanation:
Pair 1 and pair 3.
If we reposition one of them we see that it exactly fits onto the other.
Alan travels eight and two thirds kilometers to get to school. He ran one and ten elevenths kilometers and walked the rest. How many kilometers were left to walk?
Answer:
4 and 34/63
Step-by-step explanation:
we know that he has to walk 8 and 2 thirds of an kilometer to school. so far he has ran 1 10/11 of a kilo.
To solve this you would have to divide 8 2/3 by 1 10/11.
you would have to make them into improper fractions so 26/3 divided by 21/11
your answer will be 4 34/63
Alan covers he distance by walking is 6+25/33 km.
what is distance?distance is a scaler quantity which means it only have magnitude and no direction if any person or any thing moves from place A to B then it will show the distance between A and B
Given that Alan's school a distance is 8+2/3 km which is 26/3 km,
and he ran one and ten elevenths kilometers
means 1+10/11 = 21/11 km
and walks rest
let distance covered by walking be x
total distance for Alan school = distance covered by running + distance covered by walking
26/3 = 21/11 +x
x = 26/3 - 21/11
x = 223/33 = 6+25/33
Hence rest walking distance for Alan is 6+25/33
Learn more about Distance
https://brainly.com/question/15317318
#SPJ3
zero of the function f(x)=3x/x2-9
Answer:
It should equal zero or seven. I think is zero
Please help correct answer gets brainliest.
Answer:
C. The charge of each minute of a call is $0.40
Step-by-step explanation:
We look at the point (1, 0.4)
We know that our x = 1 is 1 minute of the call.
We know that y = 0.4 is the cost when 1 minute of the call has elapsed.
Therefore, our answer is C.
Answer:
Step-by-step explanation:
The answer is (c)
The price goes up $0.40 every minute Greg is on a call.
If the production rate is 975 brownies per hour at a bakery, how many brownies will be produced in an 8 hour shift?
Answer:
[tex]\large \boxed{\mathrm{7800 \ brownies}}[/tex]
Step-by-step explanation:
975 brownies are produced per 1 hour.
To find how many brownies are produced in 8 hours, multiply the brownies amount by the hours.
975 × 8 = 7800
7800 brownies will be produced in an 8 hour shift.
Answer:
the answer is 7800
Step-by-step explanation:
975 brownies are created per 60 minutes.
To discover what number of brownies are created in 8 hours, duplicate the brownies sum continuously.
975 × 8 = 7800
7800 brownies will be created in a 8 hour move.
Tres amigos quieren abrir una empresa dedicada al reciclaje de plasticos. Para eso deben contar con $72.000. Uno de los amigos aporto 1/3 de dinero necesario para abrirla, el segundo aporto una cantidad equivalente a los 5/6 del resto.¿cuanto dinero aporto el tercer amigo?¿Cual de los tres hizo el mayor aporte?¿cuanto mas puso en relación con que el que aporto menos?
Answer:
a) ¿cuanto dinero aporto el tercer amigo?
= $ 8,000
b) ¿Cual de los tres hizo el mayor aporte?
El segundo amigo hizo la mayor contribución.
c)¿cuanto mas puso en relación con que el que aporto menos?
El tercer amigo hizo la menor contribución
Step-by-step explanation:
De la pregunta, se nos dice:
Dinero total requerido: $ 72,000
El primer amigo contribuyó: 1/3 si el dinero era necesario
Por lo tanto, el primer amigo contribuyó:
1/3 × $ 72 000 = $ 24 000
El segundo amigo contribuyó con 5/6 del resto
La fracción que representa el resto = 1 - 1/3 = 2/3
Por lo tanto, el segundo amigo contribuyó = 5/6 de 2/3 = 5/6 × 2/3 = 5/9
La fracción de la cantidad de dinero que contribuyó el segundo amigo = 5/9
Por lo tanto, la cantidad que contribuyó el segundo amigo =
5/9 × $ 72 000 = $ 40 000.
a) ¿cuanto dinero aporto el tercer amigo?
Esto se calcula como:
$ 72,000 - ($ 24,000 + $ 40,000)
$ 72 000 - $ 64 000
= $ 8,000
Por lo tanto, el tercer amigo aportó $ 8,000.
b) ¿Cual de los tres hizo el mayor aporte?
Del cálculo anterior:
El primer amigo = $ 24,000
Segundo amigo = $ 40,000
Tercer amigo = $ 8,000
Por tanto, el segundo amigo hizo la mayor contribución.
c) ¿cuanto mas puso en relación con que el que aporto menos?
Del cálculo anterior:
El primer amigo = $ 24,000
Segundo amigo = $ 40,000
Tercer amigo = $ 8,000
Por lo tanto, el tercer amigo hizo la menor contribución.
collen family plans to paint the window of their house. her father will paint twice as many window as her mother, and collen and her 2 brothers will paint an equal number of the rest of the windows
Answer:
21 windows
Step-by-step explanation:
colleen's family plans to paint the windows of their house. her father will paint twice as many windows as her mother, and Colleen and her 2 brothers will paint an equal number of the rest of the windows. Colleen decided to do her own share and her mother's share and paints 7 window, which is one less than her father's share. how many windows are in their house?
Answer: Let the number of window Colleen father would paint be x while that of her mother be y. Since her father will paint twice as many window as her mother, therefore the number of windows painted by the father x = 2y
Let the number of windows each painted by Colleen and her 2 brothers be z since they would paint the same number of windows. The total number of windows to be painted = 2y + y + z + z + z = 3y + 3z = 3(y + z).
Then number of windows needed to be painted by Colleen and her mother is given as z + y. Since Colleen painted 7 windows as her share and her mother share i.e. y + z = 7
Therefore the total number of windows = 3(y + z) = 3(7) = 21 windows
Dante is baking two different recipes, cookies and brownies. The cookie recipe requires 1.5 cups of sugar, and the brownie recipe requires 1.25 cups of sugar. Write an addition equation to represent the total amount of sugar Dante needs. Enter your answer as an addition equation, like this: 42+(-53)=-11
Answer:
2.75 cups of sugar
Step-by-step explanation:
Hello!
To find the total amount of sugar Dante needs we need to add the amount need for each recipe
Cookie recipe needs 1.5 cups
Brownie recipe needs 1.25 cups
1.5 + 1.25 = 2.75 cups of sugar
The answer is 2.75 cups of sugar
Hope this helps!
Answer:
the answer is 1.5+1.25=1.75
Step-by-step explanation:
i just added them together
your welcome ( it also depends on how many times he uses the recipes)
Question 13 of 25
Which of the following is a correct name for a side of the given angle?
D
E
A. Point E
B. ED
C. DE
D. Point D
Last week, 17 employees exceeded their sales quota, 13 employees met their sales quota, and 3 employees didn't meet their sales quota. Express the number of employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota. Question 11 options: A) 3:13 B) 16:17 C) 17:16 D) 17:33
Answer:
17:16
Step-by-step explanation:
Number of employees exceeded their sales quota = 17
Number of employees met their sales quota = 13
Number of employees didn't exceed their sales quota = 3
Now, we need to find the ratio of the number employees who exceeded their sales quota to the number of employees who didn't exceed their sales quota.
PlZ HELP NOW ASAP!!!
Answer:
x=33
Step-by-step explanation:
x for ?
sinx=opposite/hypotenuse
sinx=162.5/298=0.54530201
convert to degrees using arcsin(0.54530201)= 33.043
33 degrees rounded to the nearest ones
Pete earns graduated commission on his sales each month. He earns 7% commission on the first $35,000 in sales and 9% on anything over that. If Pete had $43,000 in sales this month, how much commission did he earn?
a. $2,610
b. $3,170
c. $3,870
d. $6,880
Please select the best answer from the choices provided A B C D
Answer:
b.$3170
Step-by-step explanation:
43,000-35,000=8,000
SO you would find 9% commission on 8,000
8,000x.09=720
then, you would find his normal commission if he only made 35,000
so you would do 35,000x.07=2450
you would, then, add the two together to get his entire commission, which is $3170
Answer:
b
Step-by-step explanation:
How many solutions does the following equation have? 4(y-30)=4y+124(y−30)=4y+12
Answer:
A. No solution
Step-by-step explanation:
Choose 1 answer:
A. No solutions
B. Exactly one solution
C. Infinitely many solutions
Solution
Given:
4(y-30)=4y+12
Open parenthesis
4y-120=4y+12
Collect like terms
4y-4y=12+120
0=142
There is no solution to the equation, therefore, the answer is A
Which recrusive formula can be used to generate the sequence shown, where f(1)=5 and n>=1 5,-1,-7,-13,-19
Answer:
a_n = 11 - 6n
Step-by-step explanation:
you can observe every next element is smaller then the previous one by 6
a_n = 5 - 6*(n-1)
a_n = 5 - 6n + 6
a_n = 11 - 6n
solve for x 3(x+2) = 12
Answer:
x=2
Step-by-step explanation:
3(x+2) = 12
Divide by 3
3/3(x+2) = 12/3
x+2 = 4
Subtract 2 from each side
x+2-2 = 4-2
x =2
Answer:
The value of x is equal to 2.
Step-by-step explanation:
3(x + 2) = 12
Distribute 3 to (x + 2)
3x + 6 = 12
Subtract 6 from both sides of the equation.
3x = 6
Divide 3 on both sides of the equation.
x = 2
The value of x is 2
Please help!
Match each system on the left with the number of solutions that it has on the right.
Answer:
1. No solution
2. Infinitely many solutions
3. Infinitely many solutions
4. One solution
Step-by-step explanation:
1.
x=y-3
2x-2y=6
Substitute x=y-3 in (2)
2(y-3)-2y=6
2y-6-2y=6
2y-2y=6+6
0=12
No solution
2.
5x+2y=-7
10x+4y=-14
Multiply (1) by 2 and (2) by 1
10x+4y=-14
10x+4y=-14
Subtract (3) from (4)
0+0=0
0=0
Infinitely many solutions
3.
y=2x+1
4x-2y=-2
Substitute y=2x+1 into (2)
4x-2(2x+1)=-2
4x-4x-2=-2
4x-4x=-2+2
0=0
Infinitely many solutions
4.
9x+6y=15
2y= -1+3x
From 2
2y+1-3x=0
-3x+2y=-1
9x+6y=15 (1)
-3x+2y=-1 (2)
Multiply (2) by 3
-9x+6y=-3
9x+6y=15
Subtract (3) from (1)
9x-(-9x)=15-(-3)
9x+9x=15+3
18x=18
x=18/18
=1
x=1
Substitute x=1 into (1)
9x+6y=15
9(1)+6y=15
9+6y=15
6y=15-9
6y=6
y=6/6
=1
One solution
Please answer this now with correct answer
Answer:
483.56 square milimeters
Step-by-step explanation:
In the above question, we obtain the following information:
Slant height = 15mm
Radius = 7mm
π = 3.14
Since we are given the slant height ,
the formula for surface area of a cone = πrl + πr²
= πr (l + r)
= 3.14 × 7(15 + 7)
= 3.14 × 7( 22)
= 21.98(22)
= 483.56 square milimeters
2 + 8(x + 2) = 52
a 3
b 1
C2
d 4
Step-by-step explanation:
[tex]2 + 8(x + 2) = 52 [/tex]
[tex]2 + 8x + 16 = 52[/tex]
[tex]8x + 18 = 52[/tex]
[tex]8x = 52 - 18[/tex]
[tex]8x = 32[/tex]
[tex]x = \frac{34}{8} [/tex]
[tex]x = 4.25[/tex]
Hope it helps u
If each of the 4 shelves holds 14 movies, how many movies does Betty have on her shelving unit? Show your work.
Answer:
62
Step-by-step explanation:
4x + 6
4(14) + 6 (substituting x = 14)
56 + 6
62
which of the following graphs dont belong and why?
Answer:
Upper Right
Step-by-step explanation:
All of them have different dips, therefore the one facing in a different direction must be the odd one out.
Answer:
top right graph
Step-by-step explanation:
3 of the 4 graphs start at negative infinity for negative x, and approach infinity as x approaches infinity.
The top right graph starts at infinity for negative x and approaches negative infinity as x approaches infinity.
Answer: top right graph
name four points that are not coplanar
Answer: U, W, Z and Y
Step-by-step explanation:
4 points are not coplanar if there does not exist any plane that contains the 4 points.
So, a plane is formed by a line and one point outside of it.
Then, we want to select the last point in such a way that it lies outside of the plane generated by the first 3 points selected.
For example:
If first we select Point U and Point W, we will have a line, as shown in the image.
Now we can select the Point Z, that is outside the line, and now we have the plane M that you can see in the image.
Now we need to select a point that is not in the plane, the only two options are Point X and Point Y, we can select any of those two, let's take the Point Y.
So, here we have that:
Points U, W, Z and Y are not coplanar.
Express 0.00013745 to 3 significant figures.
Answer:
0.000137
To 1 significant figure: 0.0001
To 2 significant figures: 0.00014
To 3 significant figures: 0.000137
To 4 significant figures: 0.0001375
To 5 significant figures: 0.00013745
Plz HELP !!!!! I would appreciate it!!!
Answer/Step-by-step explanation:
a. The sides of ∆ABC can be labelled as follows, taking θ as the reference point.
Adjacent = side AB
Opposite = side BC
Hypotenuse = side AC
b. I. "<B is an acute angle" => FALSE. It is a right angle (90°)
II. "The side opposite to <C is BC" => FALSE. The side opposite to <C is AB.
III. The side adjacent to <A is AB => TRUE
IV. The side opposite to <B is not the longest. => FALSE. It is the hypotenuse and the longest side.
c. Cos θ = [tex] \frac{adjacent}{hypotenuse} = \frac{AB}{AC} [/tex]
Tan θ = [tex] \frac{opposite}{adjacent} = \frac{BC}{AB} [/tex]
d. Sin C = [tex] \frac{opp}{hypo} = \frac{AB}{AC} [/tex]
Cos C = [tex] \frac{adjacent}{hypotenuse} = \frac{BC}{AC} [/tex]
Tan C = [tex] \frac{opp}{adjacent} = \frac{AB}{BC} [/tex]
100 2/3 as a decimal
Answer:
100.66 is the decimal.
Step-by-step explanation:
100⅔ = 302/3
302 ÷ 3 = 100.66 to infinity.
convert American $553 in Nepal rupees
Answer:
65,994.52 Nepalese Rupee
Step-by-step explanation:
using conversion rate 1 usd = 119.74 nepalese rupee
553*119.74
