Answer:
0.0918 = 9.18% probability that the battery life is at least 8.1 hours.
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.
Mean 7.5 hours
This means that [tex]\mu = 7.5[/tex]
Standard deviation 27 minutes.
An hour has 60 minutes, which means that [tex]\sigma = \frac{27}{60} = 0.45[/tex]
What is the probability that the battery life is at least 8.1 hours?
This is 1 subtracted by the p-value of Z when X = 8.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{8.1 - 7.5}{0.45}[/tex]
[tex]Z = 1.33[/tex]
[tex]Z = 1.33[/tex] has a p-value of 0.9082.
1 - 0.9082 = 0.0918
0.0918 = 9.18% probability that the battery life is at least 8.1 hours.
3. Two dice are rolled. What’s the conditional probability that both dice are 5’s if it’s known that the sum of points is divisible by 5?
Answer:
[tex]Pr =\frac{1}{3}[/tex]
Step-by-step explanation:
Given
[tex]S = \{(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)[/tex]
[tex](3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)[/tex]
[tex](5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)\}[/tex] --- sample space
First, list out all outcomes whose sum is divisible by 5
[tex]A = \{(4,6), (5,5),(6,4)\}[/tex]
So, we have:
[tex]n(A) = 3[/tex]
Next, list out all outcomes that has an outcome of 5 in both rolls
[tex]B = \{(5,5)\}[/tex]
[tex]n(B) =1[/tex]
The required conditional probability is:
[tex]Pr =\frac{n(B)}{n(A)}[/tex]
[tex]Pr =\frac{1}{3}[/tex]
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 70 mph. The westbound train travels at 90 mph. How long will it take for the two trains to be 192 miles apart.
Answer:
1.2 hours
Step-by-step explanation:
Recall :
Distance = speed * time
Let the time taken = x
Creating an equation for the question :
Distance of train A + Distance of train B = 192
70 * x + 90 * x = 192
70x + 90x = 192
160x = 192
x = 192 / 160
x = 1.2
It takes 1.2 hours to be 192 miles apart.
please help me find the area
Answer:
320 square feet.
Step-by-step explanation:
For the moment, let's put the square back in place. That would make the length 16 + 8 = 24 and the width 16.
L = 24
W = 16
Area = L * W
Area = 24 * 16
Area = 384
Now the next step is to take out the square. It is 8 * 8 = 64
The area of the figure = 384 - 64 = 320 square feet, and that's the answer.
Answer:
320 in^2
Step-by-step explanation:
we need to find the area of this figure
Firstly divide above picture in two parts
1st figure = (16*16)in.
2nd figure = (8*8)in.
Area of 1st figure = 16*16 = 256 in^2
Area of 2nd figure = 8*8 = 64 in^2
Area of whole figure = ( 256 + 64 )in^2
= 320 in^2
what is the area of Ghana?
Answer:
its 238,535km²
Step-by-step explanation:
i hope it helps alot
What is the area of Ghana?
ඞ Ghana covers an area of [tex]\sf\purple{238,535\: km²}[/tex].
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.}}}}}[/tex]
The store charges $2.50 for a bottle of soda and $1.25 for a bottle of water. Write an equation in standard form for the number of soda (s) and water (w) bottles that you can buy with $15. PLZ HELPPPP
Answer:
2.50 + 1.25= 3.75
15.00 - 3.75= 11.25
Step-by-step explanation:
2. The cost of oranges varies directly with the total mass bought. 2 kg of oranges costs $4.50. Describe the relationship between cost and mass in words. You may want to calculate a unit rate first.
Answer:
The relationship between the cost/mass is $2.25/kg.
Step-by-step explanation:
You first need to divide $4.50 / 2, to know what a single kilogram mass costs.
$4.50 / 2 = $2.25
Now that you have this unit rate $2.25, You can multiply/add it.
$4.50 + $2.25 is $6.75, + another $2.25 = $9.00, and so on.
I NEED HELP ASAP ⚠️⚠️
If 1 is a solution to g(x) = 0, what is the other solution?
9514 1404 393
Answer:
A. -1
Step-by-step explanation:
The table shows that g(x) = 0 for x = -1. (third row)
The other solution is x = -1.
Will Mark Brainlest help step by step. (The ratio of two men present age is 3:4 and this will be 7:9 after 4 years what are their present age)
Answer:
24 and 32
Step-by-step explanation:
Let their present ages be x and y
Therefore, x
[tex] \frac{x}{y} = \frac{3}{4} [/tex]
we have 4x = 3y
4x - 3y = 0......................(I)
After four years,
[tex] \frac{x + 4}{y + 4} = \frac{7}{9} [/tex]
we have, 9(x + 4) = 7(y + 4)
9x + 36 = 7y + 28
9x - 7y = -8 ........................(ii)
Solving (I) and (ii) simultaneously
4x - 3y = 0
9x - 7y = -8
multiply eqn I by 9 and equation (ii) by 4 and subtract result
36x - 27y = 0...............(iii)
36x - 28y = -32...........(iv)
subtracting (iv) from (iii) we have,
y = 32
substituting y back in equation (I)
4x - 3y = 0
4x -3(32) = 0
4x - 96 = 0
4x = 96
x = 24
Their ages are 24 and 32
There are 924 people in a theatre.
383 of the people are men.
356 of the people are women.
2
of the children are boys.
5
Work out how many girls are in the theatre
[tex]924 - (383 + 356 + 2 + 5 )[/tex]
Answer:
Step-by-step explanation:
total no. of people in the theatre = 924
men=383
women=356
boy children =2
doing workout 5
total=746
no. of girls= 924-746=178
Therefore, the number of girls are in the theatre are 178.
Use the graph of f(x) to estimate f(3).
Answer:
f(3) = -8
Step-by-step explanation:
f(3) means find the y value when x=3
Using the graph the y value when x =3 is -8
f(3) = -8
4x-1divide by 2=x+7
what is x
What is the area of the parallelogram below?
7 in2
14 in2
18 in2
28 in2
Answer:
14 (B)
Step-by-step explanation:
Area = L * h
L = 7 in^2
h = 2
Area = 7 * 2
Area = 14 in^2
Answer:
14
Step-by-step explanation:
Did lesson
Parrot eats only ........ products
Answer:
Maybe Plants products...
Find the indicated area of the sector surrounded in bold.
Answer:
75.36 yd² (≈ 75.4 yd²)
Step-by-step explanation:
GIVEN :-
Angle subtended by the arc at center of circle (θ) = 135°Radius of the circle = 8 ydTO FIND :-
Area of the sectorGENERAL FORMULAE TO BE USED IN THI QUESTION :-
Lets say there's an arc which subtends θ angle in the center of the circle & radius of the circle is 'r'.
Area of the sector = [tex]\frac{\theta}{360} \times \pi r^2[/tex]
SOLUTION :-
Area of the sector = [tex]\frac{\theta}{360} \times \pi r^2[/tex]
[tex]= \frac{135}{360} \times \pi (8)^2[/tex]
[tex]= \frac{3}{8} \times 64 \times 3.14[/tex]
[tex]= 3 \times 8 \times 3.14[/tex]
[tex]=75.36 \; yd^2[/tex]
Trong không gian Oxyz, cho a b c 2;2;0 , 2;2;0 , 2;2;2 .
Giá trị của a b c
bằng
Answer:
good question
Step-by-step explanation:
At Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice
cream alternating with layers of cake. If there are 8 flavors of ice cream, and we count
different cakes based on the order of ice cream layers from top to bottom:
a) how many different cakes can be made if flavors can be repeated?
Answer:
4096 different cakes can be made if flavors can be repeated.
Step-by-step explanation:
Since at Misu's Ice Cream Parlor, their famous 4-layer ice cream cake consists of four layers of ice cream alternating with layers of cake, if there are 8 flavors of ice cream, and we count different cakes based on the order of ice cream Layers from top to bottom, to determine how many different cakes can be made if flavors can be repeated, the following calculation must be performed:
8 x 8 x 8 x 8 = X
64 x 64 = X
4.096 = X
Therefore, 4096 different cakes can be made if flavors can be repeated.
2(x+3)=x-4
please help me <3
h(x)=6/(x-3), find h(5)
h(5) means the value of h(x) at x = 5. So what we have to do is to substitute x = 5 in the function.
We are given the function h(x) below:
[tex] \large{h(x) = \frac{6}{x - 3} }[/tex]
Substitute x = 5 in the equation.
[tex] \large{h(5) = \frac{6}{5 - 3} \longrightarrow \frac{6}{2} }[/tex]
Simplify in the simplest form.
[tex] \large{h(5) = \frac{3}{1} \longrightarrow 3}[/tex]
Thus h(5) is 3.
Answer
h(5) = 3Hope this helps! Let me know if you have any doubts.
What is the value of the upper quartile?
f(x) = 3x + 10
х
f(x)
-3
-2
-1
-4
There are two packs of hyenas that live just outside of a small town in Harar, Ethiopia. Each night, the
packs fight to determine which pack can go through the city gate. The city provides unlimited food and
water to any hyenas that enter.
Is there competition taking place in the scenario? *
2 points
Yes
No
Answer:
yes
Step-by-step explanation:
the packs are fighting for a common goal against each other
so they are competing
Please please help need today
Answer:
you need to zoom in i cant see plz :)
Step-by-step explanation:
HELP PLEASE WILL MARK BRAINLIEST ITS END BEHAVIOR OF A GRAPH
Which equation represents a circle with a center at (–3, –5) and a radius of 6 units?
Answer:
Step-by-step explanation:
The general equation of the circle is:
(x-h)²+(y-k)²=r²
(h, k)=(-3,-5) are the coordinates of the center of the circle.
r=6 is the radius
The equation of the circle is:
(x+3)²+(y+5)² = 36
Did I answer this correctly? Drag each tile to the correct box. Not all tiles will be used. Arrange the steps to solve this system of linear equations in the correct sequence.
Put the following in order:
A. Subtract 3x + 3y = -6 (obtained in step 1) from 2x – 3y = -9 (given) to solve for x.
B) Substitute the value of x in the first equation (x + y = -2) to get y = 1.
C) The solution for the system of equations is (-3, 1).
D) x = -15
E) The solution for the system of equations is (-15, 13).
F) Add 3x + 3y = -6 (obtained in step 1) to 2x – 3y = -9 (given), and solve for x.
G) x = -3
H) Substitute the value of x in the first equation (x + y = -2) to get y = 13.
J) Multiply the first equation by 3: 3(x + y) = 3(-2) 3x + 3y = -6.
Remember that only 5 can be used.
9514 1404 393
Answer:
your 3rd step should be x = -3
Step-by-step explanation:
When you combine the equations in step 2, you get ...
5x = -15
Dividing by 5 gives the solution for x:
x = -3
This is what your Step 3 should show. This is the value that is consistent with the remaining steps.
Answer:9514 1404 393
Step-by-step explanation:
Malik collects rare stamps and has a total of 212 stamps. He has 34 more domestic stamps than foreign stamps. Let x represent the number of domestic stamps and let y represent the number of foreign stamps.
How many foreign stamps does Malik have?
Answer:
answer in picture
c, b, d
Step-by-step explanation:
Please help me on this question. Thanks
Answer:
E. p - 7 + 7 = 22 + 7
Step-by-step explanation:
p - 7 + 7 = 22 + 7 ( -7 + 7 = 0)
p = 22 + 7
p - 7 = 22//
In a right triangle, angle C measures 40°. The hypotenuse of the triangle is 10 inches long. What is the approximate length of the side adjacent to angle C?
6.4 inches
7.7 inches
8.4 inches
13.1 inches
Answer:
The cosine function is: adjacent/hypotenuse = cos (40). We know the hypotenuse length is 10, so the equation is now adjacent/10 = cos (40). Solving for adjacent length we get 7.7 inches.
Answer:
the answer is B: 7.7 inches
Step-by-step explanation:
did the test go 100%
find the value of a and the value of b :
4x2 - 4x - 15 is a factor of 4x3 + ax2 + bx + 30.
Step-by-step explanation:
the answer is in the above image
pls give me BRAINLIEST
Write the slope-intercept form of the equation for the line.
Answer:
its 4/2 or simplified to 2/1
Step-by-step explanation:
mark me brainliest pls
