a) The probability that a student will study and will pass is 0.765.
b) The probability that a student will pass is 0.715.
What is probability?
Simply put, probability is the likelihood that something will occur. When how an event will turn out is not known, one can discuss the likelihood of several outcomes.
Define some events -
A: A student studies.
B: A student will pass.
Given that P(A)=0.85 and
P(B|A)=1-P([tex]\bar{B}[/tex]|A)
=1-0.10
=0.90
a) P(a student will study and will Pass)= P(A∩B)
= P(A)·P(B|A)
= 0.85×0.90
= 0.765
b) Given that P( student will either study or pass), the probability is -
=P(A∪B)= 0.8 then P(a student will pass)
=P(B)
It is known that P(A∪B)= P(A)+P(B)-P(A∩B)
Then P(B)=P(A∪B) -P(A) +P(A∩B)
=0.8-0.85 + 0.765
=0.715
Therefore, the probabilities are 0.765 and 0.715.
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help? anyone? please
Answer:
Step-by-step explanation:
Perimeter is the addition of all the sides.
So in this question, if you add up all the sides :
14x + 8x +7x +12
Simplify by adding all terms with x :
29x + 12
(As you can not add a number constant to a variable )
The rectangular floor of a classroom is 24 feet in length and 40 feet in width. A scale drawing of the floor has a length of 6 inches. What is the area, in square inches, of the floor in the scale drawing?
HURRY! :D
The area of the floor in the scale drawing is 60 inches².
What is a rectangle?A rectangle is a two-dimensional shape where the length and width are different.
The area of a rectangle is given as:
Area = Length x width
We have,
Actual rectangle:
Length = 24 feet
Width = 40 feet
Scale rectangle:
Length = 6 inches
Width = 40/4 = 10 inches
The area of the scaled rectangle.
= Length x Width
= 6 x 10
= 60 inches²
Thus,
The area of the scaled rectangle is 60 inches².
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help me out thankyou
Answer: A
Step-by-step explanation:
I took the test
A math class has 3 girls and 5 boys in the seventh grade and 3 girls and 3 boys in the eighth grade. The teacher randomly selects a seventh grader and an eighth grader from the class for a competition. What is the probability that the students she selects are both boys? Write your answer as a fraction in simplest form.
answer:
5/3 m
Step-by-step explanation:
because 3/3=1 so teacher choose boys
Need help with this triangle measure please.
I also need explanation. Thank you-----
Please help if you can or and know how to do this pls! Can
Answer:
m<1=50
m<2=130
m<3=50
m<4=130
m<5=40
m<6=40
m<7=90
m<8=140
Step-by-step explanation:
25 PTS WILL GIVE BRAINLY LINKS REPORTED
Each statement describes a transformation of the graph of f(x) = x. Which statement correctly describes the graph of g(x) if g(x) = f(x - 11)?
A.
It is the graph of f(x) translated 11 units to the left.
B.
It is the graph of f(x) where the slope is increased by 11.
C.
It is the graph of f(x) translated 11 units to the right.
D.
It is the graph of f(x) translated 11 units up.
The Answer is D
I REALLY hope this helps :D
It is the graph of f(x) translated 3 units down.
Answer:
D
Step-by-step explanation:
Because f(x) translated 3 down
How do you find the missing side of a 30 60 90 triangle?
A 30-60-90 triangle is a right triangle where the three interior angles are 30°, 60°, and 90°.
Let, the shorter leg of a 30 60 90 triangle is equal to a. Then:
The second leg is equal to a√3;The hypotenuse is 2a;The area is equal to a²√3/2; andThe perimeter equals a(3 + √3).If we know the shorter leg length, we can find out that:
Longer leg= √3 times of shorter leghypotenuse= twice the shorter legIn the 30 60 90 triangles :
For angles, the ratio is 1:2:3 (30°: 60°: 90°)For sides, the ratio is 1 : √3: 2Read more about the right triangle:
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What is the value of sin cos theta?
If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2
We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.
And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.
Given that sinθ⋅cosθ = 1/2
2(sinθ⋅cosθ) = 1 .........(1)
We know that trigonometric identity,
sin(2θ) = 2 sinθ cosθ
so equation (1) becomes,
sin(2θ) = 1
We know that sin(π/2) = 1
Comparing with equation sin(2θ) = 1 we get,
2θ = π/2
θ = π/4
Using trigonometric table,
sin(π/4) = 1/√2
and cos(π/4) = 1/√2
The value of sinθ+cosθ would be,
sin(π/4) + cos(π/4)
= (1/√2) + (1/√2)
= 2/√2
= √2
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The complete question is:
If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ
What is the volume of the pyramid?
A solid oblique pyramid has an equilateral triangle as a
base with an edge length of 4/3 cm and an area of 12
3 cm?
A. 12/3 cm3
B. 16/3 cm3
C. 24/3 cm3
D. 32/3 cm3
Answer:
B 16/3
Step-by-step explanation:
on edg
The volume of the pyramid shown is 16√3 cm³.
What is Volume?Volume of a three dimensional shape is the space occupied by the shape.
Given a solid oblique pyramid.
It has an equilateral triangle as a base with an edge length of 4√3 cm and an area of 12√3 cm².
Volume of the pyramid = 1/3 × base area × height
Base area = 12√3 cm²
Height = 4√3 × tan (30°) = 4√3 × 1/√3 = 4
Volume = 1/3 × 12√3 × 4
= 16√3 cm³
Hence the volume is 16√3 cm³.
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I got this from Khan Academy.
The function which has greater slope is Function 2.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx where, m is the slope
Given:
Function 1:
y = -2x + 10
and Function 2:
Slope = (5-10)/( 2-0) = -5/2
So, the Equation of line
(y - 10) = -5/2 (x -0)
y - 10 = -5/2x
y = -5/2x + 10
y= -2.5x +10
So, the slope of Function 1 is greater than slope of function 2.
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Can someone show me step by step what to do next please I’m confused?!!! Please anyone
Answer:
You need to combine like terms
what is 12/7 please help and i will be very happy
Answer:
12/7 is a improper fraction
Step-by-step explanation:
as a decimal it is 1.71428571429 and as a mixed number it is 1 5/7
Answer:
its gonna be 1 5/7
Step-by-step explanation:
7 goes into 12 1 time and there is 5 left over so thats gonna be 1 and 5/12 or
1 5/12
Harry kept a weather journal. The sun was shining four out of five days. On what percent of the days was the sun shining?
Answer:
80%
Step-by-step explanation:
divide the number of days that there was sun (4) by the total number fo days (5), then multiply by 100 to get to a percent.
if you have any questions, leave them in the comments and i will try to answer them, if this helped, please give brainliest.
Answer:
50
Step-by-step explanation:
Find all of the solutions for the following equation.
Answer:
3 tan theta=root 3
tan theta=root 3/3
tan theta=0.57
Step-by-step explanation:
Everyone at Lorenzo's school wore either red or green for school spirit day. 738 students wore red and 162 students wore green. What percentage of the students wore red?
Answer:
Given that ,
738 students wore red while 162 students wore green.
Therefore , total number of students ,
[tex]\dashrightarrow \: 738 + 162 \\ \dashrightarrow \: 900[/tex]
Now , 738 students out of 900 wore red.
So , percentage of students who wore red ,
[tex]\dashrightarrow \: \frac{738}{9\cancel{00}} \times \cancel{100} \\ \\ \dashrightarrow \: \cancel\frac{738}{9} \\ \\ \dashrightarrow \: 82\%[/tex]
hope helpful :-;
ALGEBRA 2 NEED HELP ASAP
The rule for g(x) = f(x-1)-3 is g(x) = (x-1)⁶-3(x-1)³ - 1
How to write the rule for g(x) = f(x-1)-3?A function is an expression, rule, or law that defines a relationship between an independent variable and a dependent variable. Based on the information given, we can see that the variables that are illustrated in the question are f and g.
In order to write the rule for g(x) = f(x-1)-3 when f(x) = x⁶ - 3x³ + 2, replace x with x-1 in f(x) and subtract 3. That is:
g(x) = f(x - 1) - 3
g(x) = (x-1)⁶ - 3(x - 1)³ + 2 - 3
g(x) = (x-1)⁶ - 3(x - 1)³- 1
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What is the Vertex of the graph?
options:
(1,1)
(-1,1)
(0,1)
(1,0)
Answer:
Step-by-step explanation:
(-1, 1): You can see that a vertical line through x = -1 is the center line (axis of symmetry) of this parabolic graph. The vertex lies 1 unit above the x-axis: y = 1.
What is 24.21 written in expanded form?
Answer:
(2 x 10) + (4 x 1) + (2 x 0.1) + (1 x 0.01)
Step-by-step explanation:
The expanded form of 24.21 = (20 + 4 + 0.2+ 0.01)
The expanded form of an equation requires writing out the place value term of each digit of the number given :
24.21 :
Tens digit = 2 × 10 = 20
Unit digit = 4 × 1 = 4
Tenth digit = 2 × 0.1 = 0.2
Hundredth digit = 1 × 0.01 = 0.01
Hence, the expanded form of the number is :
(20 + 4 + 0.2+ 0.01)
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Solve
the equation 2y" + 3y' - 5y = 0
Answer:
y= ae^pi + C2e ^ -1/2 pi
Step-by-step explanation:
i couldnt type out symbols, hope this helps
(2⋅3) 2 −5 2 =
PLEASE HELP!
Answer: -40
Step-by-step explanation:
This answer is only correct if that last number is 52. So if the last number is something other than 52 then the answer is wrong,
Which probability indicates that an event will likely occur?
ОО
A
O
4
Answer:
The answer is c- 1/2
Step-by-step explanation:
how do you find LCM? please give a good explanation!
Answer:
72xy1
Step-by-step explanation:
becuz the multiple of 9,6 and 24 is 72 and the multiple of x is 1x which is just x and the multiple of y is 1y
How many pounds of walnuts that cost $0.80 per pound must be mixed
with 8 pounds of cashews that costs $1.25 per pound to make a mixture of
nuts that costs $1.00 per pound?
Answer:
kt 5.20 yes
Step-by-step explanation:
5.20
Step-by-step explanation:
The Yellow Cab Company charges just $1.25 per mile, but it costs $6.00 to get in the cab. Express Cab charges no fee to get in the cab, but $2.00 per mile for the ride. For what number of miles is the cost the same?
Answer: 8 miles
Step-by-step explanation:
1.25m+6=2m
--1.25m. -1.25m
6=.75
6/.75m=8 mile
s
Find Arc measure of ABC
Answer:
268°
Step-by-step explanation:
[tex] In\: \odot O, [/tex] AB is diameter.
So, [tex] \widehat{AB} \:\&\: \widehat {BA}[/tex] are semicircular arcs.
[tex] \therefore m\widehat {AB} =m\widehat {BA} = 180\degree [/tex]
[tex] \because \: m\widehat {BC} = m\widehat {BA} - m\widehat {CA} [/tex]
[tex] \therefore \: m\widehat {BC} = (180-92)\degree [/tex]
[tex] \therefore \: m\widehat {BC} =88\degree [/tex]
[tex] \because m\widehat {ABC} = m\widehat {AB}+m\widehat {BC} [/tex]
[tex] \therefore m\widehat {ABC} = 180\degree+88\degree [/tex]
[tex] \therefore m\widehat {ABC} = 268\degree [/tex]
2. A recent study of 35 students determined that the mean number of hours per week they played video games was 16.6 hours. The standard deviation of the population was 2.8 hours. Find a 95% confidence interval of the population mean.
According to a recent study of 35 students,Population-wide, there was a 2.8-hour standard deviation. 16.60 is the population mean's 95% confidence interval.
What means 95% confidence interval?A Confidence Interval is a zone created using sampled data from a population (sample space) that has a fixed size and follows a specific probability distribution. The interval is built to include a selected population statistic with a certain probability. A range of values above and below the point estimate, within which the true value in the population is likely to reside with 95% confidence, is known as a 95% confidence interval. 5% of the time, the true result might not fall inside the confidence interval.A confidence interval that includes the value of no difference between treatments denotes that there is no statistically significant difference between the therapy under consideration and the control.The result is that P([sample mean] - margin of error [sample mean] + margin of error) = 0.95.To learn more about confidence interval refer to :
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Example 2: An object is thrown upward from the top of a building, where h is the height of the object in metres and t is the time in seconds. The graph below represents the relationship between height and time.
a) What is the maximum height of the object above
the ground?
b) After how many seconds does the object reach this
maximum height?
c) From the moment the object was thrown, how much
time would it take for it to reach he ground?
d) How tall is the building?
The answers are given as 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m
What is a curve in a graph?A curve is defined as a smoothly- flowing continuous line that has bent. It does not have any sharp turns. The way to identify the curve is that the line bends and changes its direction at least once. Curve of the graph is a pictorial representation of a particular function.
Given : A object is thrown from the top of the building thus by observing the graph we derive the following information
1) Maximum height = 165 m
2) The object reaches maximum height at t=3 seconds
3) The time it took to reach the ground is 9 seconds
4) The building is 120 m tall
Hence, the answers are 1) 165 m 2)3 seconds 3) 9 seconds 4)120 m
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A triangle is placed in a semicircle with a radius of 2 yd, as shown below. Find the area of the shaded region. Use the value 3.14 for pie, and do not round your answer. Be sure to include the correct unit in your answer.
Answer:
[tex]A_s=2.28yd^2[/tex]
Step-by-step explanation:
From the question we are told that:
Radius [tex]r=2yd[/tex]
Pie [tex]\pi=3.14[/tex]
Generally the equation for Area of the shaded part [tex](A_s)[/tex] is mathematically given by
[tex]A_s=Area\ of\ semi-circle(A_c)-Area\ of\ triangle(A_t)[/tex]
Generally the equation for Area of semi-circle is mathematically given by
[tex]A_c=\frac{1}{2}\pi r^2[/tex]
[tex]A_c=\frac{1}{2}*(3.14) (2)^2[/tex]
[tex]A_c=6.28yd^2[/tex]
Generally the equation for Area of triangle is mathematically given by
[tex]A_t=\frac{1}{2} base*height[/tex]
[tex]A_t=\frac{1}{2} (2+2)*2[/tex]
[tex]A_t=4yd^2[/tex]
Therefore Area of the shaded part [tex](A_s)[/tex]
[tex]A_s=A_c-A_t[/tex]
[tex]A_s=6.28yd^2-4yd^2[/tex]
[tex]A_s=2.28yd^2[/tex]
A 20% acid solution is mixed with a 70% acid solution to get 50 liters of a 40% solution.
How much of the 70% solution is used?
A)30 liters
B)20 liters
C)25 liters
x = liters of solution at 20%
y = liters of solution at 70%
[tex]\begin{array}{lcccl} &\stackrel{liters}{quantity}&\stackrel{\textit{\% of liters that is}}{\textit{acid only}}&\stackrel{\textit{liters of}}{\textit{acid only}}\\ \cline{2-4}&\\ \textit{Sol'n at 20\%}&x&0.2&0.2x\\ \textit{Sol'n at 70\%}&y&0.7&0.7y\\ \cline{2-4}&\\ mixture&50&0.4&20 \end{array}~\hfill \begin{cases} x + y = 50\\\\ 0.2x+0.7y=20 \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\stackrel{\textit{using the 1st equation}}{x+y=50\implies x=50-y}\hspace{5em}\stackrel{\textit{substituting on the 2nd equation}}{0.2(50-y) + 0.7y=20} \\\\\\ 10-0.2y+0.7y=20\implies -0.2y+0.7y=10\implies 0.5y=10 \\\\\\ y=\cfrac{10}{0.5}\implies \boxed{y=20}[/tex]