We want to find the probability that the two students chosen for the duet are boys. We will find that the probability that both students chosen for the duet are boys is 0.458
If we assume that the selection is totally random, then all the students have the same probability of being chosen.
This means that, for the first place in the duet, the probability of randomly selecting a boy is equal to the quotient between the number of boys and the total number of students, this is:
P = 11/16
For the second member of the duet we compute the probability in the same way, but this time there is one student less and one boy less (because one was already selected).
Q = 10/15
The joint probability (so both of these events happen together) is just the product of the individual probabilities, this will give:
Probability = P*Q = (11/16)*(10/15) = 0.458
So the probability that both students chosen for the duet are boys is 0.458
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Which ordered pair is a solution to the system of inequalities?
y > –x
y ≤ x + 1
A) (0,5)
B) (4,–1)
C) (1,3)
D) (–4,0)
9514 1404 393
Answer:
B) (4,–1)
Step-by-step explanation:
A graph can help you figure this out. The point (4, -1) is in the doubly-shaded area, so is a solution to this system.
==========================================================
Explanation:
Choice A can be ruled out because
[tex]y \le x+1\\\\5 \le 0+1\\\\5 \le 1\\\\[/tex]
which is false.
Choices C and D are similar, so they can be ruled out as well.
---------------------
Choice B is the answer because it makes both inequalities true.
If we plug the coordinates of (4,-1) into the first inequality, we get
[tex]y > -x\\\\-1 > -4[/tex]
which is a true statement because -1 is to the right of -4 on the number line.
Now try the other inequality
[tex]y \le x+1\\\\-1 \le 4+1\\\\-1 \le 5\\\\[/tex]
that's true also. So again, (4,-1) makes both inequalities true, and that's why choice B is the answer.
construct a 3×3 matrix aij=3j-2i Hellpppp ASAP
[tex]a_{ij}=3j-2i[/tex] is the formula for (i, j )-th entry (row i, column j ) of the matrix. So the matrix would be
[tex]\begin{bmatrix}3\times1-2\times1&3\times2-2\times1&3\times3-2\times1\\3\times1-2\times2&3\times2-2\times2&3\times3-2\times2\\3\times1-2\times3&3\times2-2\times3&3\times3-2\times3\end{bmatrix} = \begin{bmatrix}1&4&7\\-1&2&5\\-3&0&3\end{bmatrix}[/tex]
If 1100 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box. Round to two decimal places if necessary.
volume= a^2 * h
area= a^2+4ah
take the second equation, solve for h
4ah=1100-a^2
h=1100/4a -1/4 a now put that expression in volume equation for h.
YOu now have a volume expression as function of a.
take the derivative, set to zero, solve for a. Then put that value back into the volume equation, solve for Volume.
Cited from jiskha
КУ
11
10
A
9
8
7 구
6
5
4
A А
C
3
B'
2
1
B
C с
-6 -5 -4 -3 -2 -1
1 2 3 4 5 6
A ABC is dilated about the origin./
What scale factor was used to make the image A A'B'C?
Answer:
3
Step-by-step explanation:
The dilation factor is 3
A store has x packages of 4 markers and y packages of 12 markers. The store has a total of 192 markers in
stock. If there are 21 packages of 4 markers in the store, how many packages of 12 markers are there?
Sh363gdbzej3yve truly urban urge Heydyeh hdye
in order for the parallelogram to be rhombus x=?
Answer:
14
Step-by-step explanation:
The angles created by the diagonals of a rhombus add up to 360 meaning each one is 90 degrees
5x+20 = 90
subtract 20 from both sides
5x = 70
divide by 5 on both sides
x=14
Books, and then you have 44+45x=?
Answer:
45x=-44
x=-44/45
Step-by-step explanation:
is this a free question?
Joe used a project management software package and has determined the following results for a given project.: Expected completion time of the project = 22 days Variance of project completion time = 2.77 What is the probability of completing the project over 20 days?
Answer:
0.1151 = 11.51% probability of completing the project over 20 days.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Expected completion time of the project = 22 days.
Variance of project completion time = 2.77
This means that [tex]\mu = 22, \sigma = \sqrt{2.77}[/tex]
What is the probability of completing the project over 20 days?
This is the p-value of Z when X = 20, so:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{20 - 22}{\sqrt{2.77}}[/tex]
[tex]Z = -1.2[/tex]
[tex]Z = -1.2[/tex] has a p-value of 0.1151.
0.1151 = 11.51% probability of completing the project over 20 days.
Jacob bought a magazine for $2.80 and three candy bars. Write an expression for how much Jacob paid.
Answer:
total = 2.8 + 3x
x is the price of the candy bars
i have 6 one, 7 tens and 14 hundreds. what number am i?
Answer:
Step-by-step explanation:
6×1 = 6
7×10 = 70
14×100 = 1400
6+70+1400 = 1476
Answer:
1,476
Step-by-step explanation:
I hope this helps you out! (please give me brainliest)
(Use Pascal's triangle to expand each binomial. (x – 5y)^5
The n-th row in Pascal's triangle tells you the coefficients of terms in the expansion of (a + b)ⁿ. Starting with n = 0,
1
1 … 1
1 … 2 … 1
1 … 3 … 3 … 1
1 … 4 … 6 … 4 … 1
1 … 5 … 10 … 10 … 5 … 1
In more concrete terms, this translates to
(x - 5y)⁵ = 1 x ⁵ (-5y)⁰ + 5 x ⁴ (-5y)¹ + 10 x ³ (-5y)² + 10 x ² (-5y)³ + 5 x ¹ (-5y)⁴ + 1 x ⁰ (-5y)⁵
Simplify:
(x - 5y)⁵ = x ⁵ - 25x ⁴y + 250x ³y ² - 1250x ²y ³ + 3125xy ⁴ - 3125y ⁵
What is the distance between the following points?
WILL GIVE BRAINLIEST
Answer:
D.√85
Step-by-step explanation:
We can find the distance between two points using the distance between two points formula
Distance between two points formula:
d = √(x2 - x1)² + (y2 - y1)²
Where the x and y values are derived from the given points
We are given the two points (-2,7) and (7,9)
Using these points let's define the variables ( variables are x1, x2, y1, and y2)
Remember points are written as follows (x,y)
The x value of the first point is -2 so x1 = -2
The x value of the second point is 7 so x2 = 7
The y value of the first point is 7 so y1 = 7
The y value of the second point is 9 so y2 = 9
Now that we have defined each variable let's find the distance between the two points
We can do this by substituting the values into the formula
Formula: d = √(x2 - x1)² + (y2 - y1)²
Variables: x1 = -2, x2 = 7, y1 = 7, y2 = 9
Substitute values in formula
d = √(7 - (-2))² + (9 - 7)²
Evaluation:
The two negative signs cancel out on 7-(-2) and it changes to +7
d = √ (7+2)² + (9-7)²
Add 7+2 and subtract 9 and 7
d = √ (9)² + (2)²
Simplify exponents 9² = 81 and 2² = 4
We then have d = √ 81 + 4
Finally we add 81 and 4
We get that the distance between the two points is √85
Please help explanation if possible
Answer:
140-5x
Step-by-step explanation:
x would be the number of minutes
for eg, after 1 min, the temperature of the steak would be 140-5(1) = 135
not sure how to explain this, but its basically the start temperature - change
Last year, Singh had $20,000 to invest. He invested some of it in an account that paid 7% simple interest per year, and he invested the rest in an account that paid 6% simple interest per year. After one year, he received a total of $1280 in interest. How much did he invest in each account?
Answer:
8000 and 12000 respectively
Step-by-step explanation:
Let the amount invested in first account be x and y be the amount invested in the second account.
ATQ, x+y=20000 and 1280=(7/100)*x+(6/100)*y
x=8000 and y=12000.
In GeoGebra, display the slope of AB and the slope of the perpendicular line passing through C. Use this to verify your responses in parts B and C. Then move points A, B, and C on the grid to several different locations, and record the slopes of the two lines and the coordinates of A, B, and C.
Answer:
plato screenshot!
Step-by-step explanation:
I don't personally know *how* to find the answers, but here's the screenshot of the suggested answer on Plato
Answer:
A B Slope of C Slope of Line Through C
(−5,4) (−1,−1) −1.25 (1,2) 0.8
(−5,4) (−3, 5) 0.5 (−2, 1) −2
(−4, 1) (−3, 5) 4 (−2, −2) −0.25
(−5, −2) (−1, 1) 0.75 (−4, 3) −1.33
(−5, −2) (1, −1) 0.17 (−3, 1) −6
Step-by-step explanation:
that way you can copy and paste each one but Plato
Given the function f ( x ) = { 6 x − 4 x < 0 6 x − 8 x ≥ 0 Calculate the following values: f ( − 1 ) = f ( 0 ) = f ( 2 ) =
Answer:
[tex]f(-1) = -10[/tex]
[tex]f(0) =- 8[/tex]
[tex]f(2) = 4[/tex]
Step-by-step explanation:
Given
[tex]f(x) = 6x - 4[/tex] --- [tex]x < 0[/tex]
[tex]f(x) = 6x - 8<0[/tex] -- [tex]x \ge 0[/tex]
Solving (a); f(-1)
Here [tex]x= -1[/tex]
[tex]-1 < 0[/tex], so:
[tex]f(x) = 6x - 4[/tex]
[tex]f(-1) = 6 *-1 -4[/tex]
[tex]f(-1) = -10[/tex]
Solving (b); f(0)
Here [tex]x = 0[/tex]
[tex]0 \ge 0[/tex], so:
[tex]f(x) = 6x - 8[/tex]
[tex]f(0) = 6*0 - 8[/tex]
[tex]f(0) =- 8[/tex]
Solving (c) f(2)
Here [tex]x = 2[/tex]
[tex]2 \ge 0[/tex], so:
[tex]f(x) = 6x - 8[/tex]
[tex]f(2) = 6*2 - 8[/tex]
[tex]f(2) = 4[/tex]
A rocket is fired upward with an initial velocity v of 100 meters per second. The quadratic function S(t)=-5t^2+100t can be used to find the height s of the rocket, in meters, at any time t in seconds. Find the height of the rocket 7 seconds after it takes off. During the course of its flight, after how many seconds will the rocket be at a height of 450 meters?
The rocket will be at the height of 450metres at 13.16secs and 6.84secs
Given the expression modeled by the height S(t)=-5t^2+100t where
t is the time taken by the rocket to take off
s is the height traveled by rocket
In order to find the height of the rocket 7 seconds after it takes off, we will substitute t = 7 into the equation
S(7) = -5(7)²+100(7)
S(7) = -5(49)+700
S(7) = -245+700
S(7) = 455metres
Hence the height of the rocket 7 seconds after it takes off is 455metres
Given that S = 450m, we can also get the time taken by the rocket at this height.
Recall that S(t)= -5t²+100t
450 = -5t²+100t
Rearrange
-5t²+100t - 450 = 0
5t²-100t + 450 = 0
Divide through by 5
t²-20t + 90 = 0
On factorizing above equation;
t= 10+√10 or t=10−√10
t = 10+3.1623 or 10 - 3.1623
t = 13.16 and 6.84secs
Hence the rocket will be at the height of 450metres at 13.16secs and 6.84secs
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4) In a clinical test with 2353 subjects, 1136 showed improvement from the treatment.
Answer:
1217
Step-by-step explanation:
Given
[tex]Subjects = 2353[/tex]
[tex]Improvement = 1136[/tex]
Required
The number that didn't improve --- missing from the question.
Let the unimproved be represented as x.
So, we have:
[tex]x + Improvement = Subjects[/tex]
Substitute known values
[tex]x + 1136 = 2353[/tex]
Solve for x
[tex]x =- 1136 + 2353[/tex]
[tex]x =1217[/tex]
A 90% confidence interval is (35 45). What is the margin of error?
A.5
B.4.5
C.9
D.10
Answer:
option a 5......
...
I hope it's correct
Marie's backyard deck cost $68.29 per square meter to build. The deck is 9 meters wide and 9 meters long. How much did it cost to build the deck?
$5531.49
(9×9)×$68.29
i 0 -i
8. If P=0 -i i
-i i 0
pois ecual to
then PQ is equal to
and Q=00
i -i.
(-2 2
1 -1
1
2 -2
-1
1
(1)
(
2)
-1
2 -2
-1 1
(3)
1 0 0
0 1 0
0 0 1
(4)
Answer:
-2 maybe
Step-by-step explanation:
Answer:
-2
Step-by-step explanation:
pls help Describe how to find the product of the two terms 3x^2y^5 and 4x^3y^7
Answer:
12 x^5y^12
Step-by-step explanation:
3x^2y^5 * 4x^3y^7
Multiply the constants
3*4 = 12
Multiply the x terms
x^2 * x^3
We know a^b* a^c = a^(b+c)
x^(2+3) = x^5
Multiply the y terms
y^6 * y^7 = y&(5+7) = y^12
Put them back together
12 x^5y^12
If a < 0 and b > 0, then which of the following is true?
Select one:
a. a + b > 0
b. a + b < 0
c.
a + b = 0
d.
The relationship between a and b cannot be determined.
Answer:
d. The relationship between a and b cannot be determined.
Step-by-step explanation:
Given
[tex]a < 0[/tex]
[tex]b > 0[/tex]
Required
Which is true
To do this, we test each of the options using assumed values
[tex]a + b > 0[/tex]
Let:
[tex]a = -5[/tex] [tex]b= 1[/tex]
So:
[tex]-5 + 1 > 0[/tex]
[tex]-4 > 0[/tex] --- false
[tex]a + b < 0[/tex]
Let:
[tex]a = -5[/tex] [tex]b= 7[/tex]
So:
[tex]-5 + 7 < 0[/tex]
[tex]2 < 0[/tex] --- false
[tex]a + b = 0[/tex]
Let:
[tex]a = -5[/tex] [tex]b= 7[/tex]
So:
[tex]-5 + 7 = 0[/tex]
[tex]2 = 0[/tex] --- false
Hence, the relationship is not specific and cannot be determined
find the angle and area of shaded region
Area of shaded region = 1/2(πr²)
= 1/2(22/7×3×3)
= 99/7
= 99/7×2
= 198/7 cm^2
Thats the total area of the shaded region
Must click thanks and mark brainliest
Which statement explains how you could use coordinate geometry to prove that quadrilateral ABCD is a square
Answer:
Prove that all sides are congruent and that the slopes of consecutive sides are opposite reciprocals. Step-by-step explanation: In order to two segmets to be perpendicular, the slope of both lines must be opposite and reciprocals, having a 90° interception and forming a square.
A superhero can fly from New York to Los Angeles in 30 minutes. The distance from New York to Los Angeles is approximately 2,450 miles.
How many miles per hour is the superhero flying?
Work Shown:
30 min = 30/60 = 0.5 hours
distance = rate*time
rate = distance/time
rate = (2450 miles)/(0.5 hours)
rate = (2450/0.5) mph
rate = 4900 mph
For the sake of comparison, a typical commercial passenger jet can reach max speeds of about 600 mph.
The faces of all prisms are _____________.
triangles
circles
parallelograms
trapezoids
Last week, you spoke with 800 customers in 40 hours."
Employee: "That is an average of __________ customers every 30 minutes."
Answer:
10 customers
Step-by-step explanation:
Hi!
Each hour has 60 minutes, so two half hour (30 minute) blocks. Thus, 1 hour = 2 half hours, so 40 hours = 80 half hours.
800 customers in 80 half hours, divide that:
800 customers / 80 half hours = 10 customers / half hour
So, your answer is 10 customers every half hour, or 10 customers every 30 minutes.
Average is [tex]10[/tex] customers per hour
Average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list.
Total number of customers [tex]=800[/tex]
Total number of hours [tex]=40[/tex]
[tex]=40\times 60[/tex]
[tex]=2400[/tex] minutes
Average (in every [tex]30[/tex] minutes) [tex]=[/tex] Total number of customers [tex]\div[/tex] Total number of hours
[tex]=\frac{800}{2400 \div 30}[/tex]
[tex]=10[/tex] customers per hour
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Surface area of the below shape
Solve all of the equations below and add all of the solutions to those equations to get your answer.
10x4x2=
8x4x2=
10x8=
(10x8)-(7x6)=
7x2x2=
6x2x2=
7x6=
Choose the slope-intercept form of 3x + 2y = 5.
3.
у==x
5
2.
O
O y=-x+
5
0
5
v=-x+
O
yox
5
3
Answer:
y = -3x/2 + 5/2
Step-by-step explanation:
Well, basically what you do is modify it so that y is on one side.
3x+2y = 5
2y = 5-3x
y = (5-3x)/2
y = 5/2 -3x/2
So, the answer is the second option.
Answer:
B
Step-by-step explanation:
3x + 2y = 5
Our goal is this form:
y = mx + b
- move 3x to right anc change its sign
2y = -3x + 5
- divide each member by 2
y = -3/2 x + 5/2
