Answer:
[tex]\large \boxed{3.4 \times 10^{10}\text{ ergs }}[/tex]
Step-by-step explanation:
[tex]\begin{array}{rcl}\log E & = & 11.8 + 1.5M\\& = & 11.8 + 1.5 \times 8.3\\& = & 11.8 + 12.45\\& = & 24.25\\E & = & e^{24.25}\\& = & \mathbf{3.4 \times 10^{10}} \textbf{ ergs}\\\end{array}\\\text{ The energy released was $\large \boxed{\mathbf{3.4 \times 10^{10}}\textbf{ ergs }}$}[/tex]
A bag contains five white balls and four black balls. Your goal is to draw two black balls. You draw two balls at random. Once you have drawn two balls, you put back any white balls, and redraw so that you again have two drawn balls. What is the probability that you now have two black balls? (Include the probability that you chose two black balls on the first draw.)
Answer:
Probabilty of both Black
= 1/6
Step-by-step explanation:
A bag contains five white balls and four black balls.
Total number of balls= 5+4
Total number of balls= 9
Probabilty of selecting a black ball first
= 4/9
Black ball remaining= 3
Total ball remaining= 8
Probabilty of selecting another black ball without replacement
= 3/8
Probabilty of both Black
=3/8 *4/9
Probabilty of both Black
= 12/72
Probabilty of both Black
= 1/6
Farah is x years old. Ibtisam is 3 years younger than Farah. Muna is twice as old as Ibtisam. Write and expression in terms of x, for
(a) Ibtisam's age,
(b) The sum of their three ages, giving your answer in its simplest form.
Answer:
Farah: x
Ibtisam: x-3
Muna: 2(x-3) or 2x-6
Sum of all their ages: 4x-6
Step-by-step explanation:
Farah is x, so we don't need an expression for that.
Ibtisam is 3 years younger than Farah, which means that we need to subtract 3 from Farah, and that would be Ibtisam's age. x-3.
Muna is 2 TIMES Ibtisam's age, so we need to multiply whatever expression taht was used for Ibtisam by 2. Put brackets around the equation with 2 outside: 2(x-3). Solve and you get 4x-6
Now, you have all their ages in expression form, now you need to simplify by adding:
x+x+2x-6
We cannot simplify -6, so we put that aside. Add all the x's and you get 4x, insert the minus 6 at the end:
4x-6
Hope this helps!
--Applepi101
Answer:
a) X -3
b) 4x - 9
Step-by-step explanation:
a) Farah's age is X so Ibtisam will be X - 3 old since he is 3years younger than Farah
b) Farah is X years old
Ibtisam is X - 3 years old
Muna is 2(X -3) since she is 2 times older than Ibtisam.
the sum of Thier ages will be
X + X -3 + 2(x-3)
= 2x - 3 + 2x - 6
= 4x - 9
13% of a sample of 200 students do not like ice cream. What is the 95% confidence interval to describe the total percentage of students who do not like ice cream?
The 95% confidence interval is (8.3%,17.7%), and the correct option is C.
------------------------------------------
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
------------------------------------------
13% of a sample of 200 students do not like ice cream.
This means that [tex]\pi = 0.13, n = 200[/tex]
------------------------------------------
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
------------------------------------------
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 - 1.96\sqrt{\frac{0.13*0.87}{200}} = 0.083[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.13 + 1.96\sqrt{\frac{0.13*0.87}{200}} = 0.177[/tex]
------------------------------------------
As a percentage:
0.083x100% = 8.3%0.177x100% = 17.7%Thus, the 95% confidence interval is (8.3%,17.7%), and the correct option is C.
A similar problem is given at https://brainly.com/question/22223066
Find the probability of winning a lottery with the following rule. Select the winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Complete Question
Find the probability of winning a lottery with the following rule. Select the six winning numbers from 1, 2, . . . ,34 . (In any order. No repeats.)
Answer:
The probability is [tex]P(winning ) = 7.435 *10^{-7}[/tex]
Step-by-step explanation:
From the question we are told that
The total winning numbers n = 34
The total number to select is r = 6
The total outcome of lottery is mathematically represented as
[tex]t_{outcome}) = \left n } \atop {}} \right. C_r[/tex]
[tex]t_{outcome}) = \frac{n! }{(n-r )! r!}[/tex]
substituting values
[tex]t_{outcome}) = \frac{ 34 ! }{(34 - 6 )! 6!}[/tex]
[tex]t_{outcome}) = \frac{ 34 ! }{28 ! 6!}[/tex]
[tex]t_{outcome}) =1344904[/tex]
The number of desired outcome is
[tex]t_{desired} = 1[/tex]
this is because the desired outcome is choosing the six winning number
The probability of winning a lottery is mathematically represented as
[tex]P(winning ) = \frac{t_{desired}}{t_{outcome}}[/tex]
substituting values
[tex]P(winning ) = \frac{1}{1344904 }[/tex]
[tex]P(winning ) = 7.435 *10^{-7}[/tex]
Please answer this correctly without making mistakes
Step-by-step explanation:
Option A and B are the correct answer because it equal to 688.5 and 688.05
Answer:
it is 1377/2 and 688 1/17 thats the answer
Step-by-step explanation:
PLEASE HELP!
Determine which of the following points lies on the graph of y=[tex]\sqrt{x} x+4[/tex]
I have been working on this all morning. I have used different calculators and the answers that I am getting do not match any of the choices I am given on my homework. I can choose from (0,4), (5,3), (-3,0), and (12,5).
Answer:
-
Step-by-step explanation:
Forget using calculators.
Test each point by plugging its coordinates into the equation, and checking if the equation holds true.
Don't bother testing (-3,0), because you can't take the square root of -3.
10a+5(a-3)=15 I don’t know the answer I keep checking and it’s wrong
Answer:
[tex]10a + 5(a - 3) = 15 \\ 10a + 5a - 15 = 15 \\ 15a = 30 \\ a = \frac{30}{15} \\ a = 2 \\ 10 \times 2 + 5(2 - 3) = 15 \\ 20 + - 5 = 15 \\ 15 = 15 \\ lhs = rhs\\ thank \: you[/tex]
Answer: a = 2
Solve:
Given
10a + 5 (a - 3) = 15
Expand parentheses and apply the distributive property
10a + 5 · a - 5 · 3 = 15
10a + 5a - 15 = 15
Combine like terms
(10a + 5a) - 15 = 15
15a - 15 = 15
Add 15 on both sides
15a - 15 + 15 = 15 + 15
15a = 30
Divide 15 on both sides
15a / 15 = 30 / 15
[tex]\boxed{a=2}[/tex]
Check:
Left-hand side = 10a + 5 (a - 3)
Left-hand side = 10(2) + 5 (2 - 3)
Left-hand side = 20 + 5(-1)
Left-hand side = 20 - 5
Left-hand side = 15
Right-hand side = 15
15 = 15, therefore, [tex]\boxed{a=2}[/tex] would make the equation true.
Hope this helps!! :)
Please let me know if you have any questions
1.3 is 10% of what number
Answer:
33.33 percent
Step-by-step explanation:
Answer:
13
Step-by-step explanation:
Make a proportion
part/whole = part/whole
1.3/x=10/100
130=10x
x=13
Two numbers, if the first one increases by 1, and the second one decreases by 1, then their product increases by 2020. If the first number decreases by 1, and the second one increases by 1, what value does the product decrease?
Answer:
The product decreases 2022.
Step-by-step explanation:
(x + 1)(y - 1) = xy + 2020
xy - x + y - 1 = xy + 2020
-x + y = 2021
(x - 1)(y + 1) = xy + x - y - 1
+ 2021 = -x + y
----------------------------------
(x - 1)(y + 1) + 2021 = xy - 1
(x - 1)(y + 1) = xy - 2022
The product decreases 2022.
can anyone ans this question
Answer:
Question 1: the angle of y is the same as 49 degrees.
So, y = 49 degrees.
y + x = straight line
=> Straight line = 180 degrees
=> 49 + x = 180
=> 49 - 49 + x = 180 - 49
=> x = 131
Answer to Question 1:
x = 131 degrees
y = 49 degrees
Question 2: Angle x is the same as 119 degrees
x + y = straight line
=> Straight line = 180 degrees
=> 119 + y = 180
=> 119 - 119 + y = 180 - 119
=> y = 61
y + z = straight line
=> Straight line = 180 degrees
=> 61 + z = 180
=> 61 - 61 + z = 180 - 61
=> z = 119
Answer to Question 2:
x = 119 degrees
y = 61 degrees
z = 119 degrees
which function defins (g-f) (x)
Answer:
(g÷f) (x) (1.8) ³x²+⁷x+2
Step-by-step explanation:
Im glad to help you
Find the length of DM
Answer:
67
Step-by-step explanation:
DM=JM-JD=84-17=67
Answer:
Step-by-step explanation:
How many variables terms are in the expression 3xcube y+5xsquare+y+9
Answer: Please Give Me Brainliest, Thank You!
2
Step-by-step explanation:
There are two variables here, X and Y
Find and interpret a 95% confidence interval to estimate the average number of bolts per box for all boxes in the population. Round to 3 decimal places.
Complete Question
The complete question is shown on the first uploaded image
Answer:
The 95% confidence interval is [tex]49.85 < \mu < 54.15[/tex]
This means that there is 95% chance that the true population mean is within this interval
Step-by-step explanation:
From the question we are told that
The sample size is n = 30
The sample mean is [tex]\= x = 52[/tex]
The population standard deviation is [tex]\sigma = 6[/tex]
Given that the confidence level is 95% then the level of confidence is evaluate as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table , the values is
[tex]Z_{\frac{\alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically represented as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
substituting values
[tex]E = 1.96 * \frac{ 6 }{\sqrt{30} }[/tex]
[tex]E = 2.147[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]52 - 2.147 < \mu < 52 + 2.147[/tex]
[tex]49.85 < \mu < 54.15[/tex]
What are the Links of two sides of a special right triangle with a 306090° and a Hypotenuse of 10
Answer:
Step-by-step explanation:
60°=2×30°
one angle is double the angle of the same right angled triangle.
so hypotenuse is double the smallest side.
Hypotenuse=10
smallest side=10/2=5
third side =√(10²-5²)=5√(2²-1)=5√3
What types of concurrent constructions are needed to find the incenter of a triangle?
A. intersection of the lines drawn from each vertex of the triangle and perpendicular to its opposite side
B. intersection of the lines drawn to the midpoint of each side of the triangle to its opposite vertex
C. intersection of the lines drawn perpendicular to each side of the triangle through its midpoint
D. intersection of the lines drawn to bisect each vertex of the triangle
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places. 800 grams = ______ pounds 700 grams = _____ pounds
Answer:
800= about 1.76 lbs
700= about 1.54 lbs
(there are about 453.5 grams in a pound
Step-by-step explanation:
Answer:
800 grams = 1.76 pounds
700 grams = 1.54 pounds
Step-by-step explanation:
i googled it
Convert 0.450 to a proper fraction
Answer:
9/20
Step-by-step explanation:
450/1000
this is not the answer, because it is not simplified
so here we have to find common factor and simplifying
________________________________________________
450/1000 is simplified to 9/20, and it can no longer be simplified.
Help question 25 pleasee
Answer:
4b³ + 11b² - 6b + 13
Step-by-step explanation:
Subtract like terms.
6b³ - 2b³ = 4b³
3b² - (-8b²) = 3b² + 8b² = 11b²
0 - 6b = -6b
8 - (-5) = 13
All together, the difference is 4b³ + 11b² - 6b + 13.
1500 to the nearest hundred
Answer:
1500.
There is no need to round here, it is already exact.
I really need help with this one
A plane traveled 4425 miles with the wind in 7.5 hours and 3675 miles against the wind in the same amount of time. Find the speed of the plane in still air and the speed of the wind.
Answer:
540 and 50 respectively
Step-by-step explanation:
Let the speed of plane in still air be x and the speed of wind be y.
ATQ, (x+y)*7.5=4425 and (x-y)*7.5=3675. Solving it, we get x=540 and y=50
A house m by m is surrounded by a walkway m wide. 27 9 1.8 a) Find the area of the region covered by the house and the walkway. b) Find the area of the walkway.
Answer:
A. 385.56 square meters.
B. 142.56 square meters.
Step-by-step explanation:
A house 27m by 9m is surrounded by a walkway 1.8m wide.
a) Find the area of the region covered by the house and the walkway.
b) Find the area of the walkway.
Let
Length of the house=l=27m
Width of the house=w=9m
Wideness of the walkway=x=1.8m
Area of the region covered by the house and the walkway
=( L + 2*x) * (w + 2*x)
= (27+2*1.8)*(9+2*1.8)
=(27+3.6)*(9+3.6)
=(30.6)*(12.6)
=385.56 square meters.
b) Area of the walkway
= (L + 2*x)*(w + 2*x) - l*w
= (27+2*1.8)*(9+2*1.8) - 27*9
=(27+3.6)*(9+3.6) - 243
=(30.6)*(12.6) - 243
=385.56 - 243
=142.56 square meters.
A random sample of 149 recent donations at a certain blood bank reveals that 76 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of appropriate hypotheses using a significance level of 0.01. Would your conclusion have been different if a significance level of 0.05 has been used?
Answer:
Yes it suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood.
Well if a significance level of 0.05 is used it will not affect the conclusion
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 149[/tex]
The number that where type A blood is k = 76
The population proportion is [tex]p = 0.40[/tex]
The significance level is [tex]\alpha = 0.01[/tex]
Generally the sample proportion is mathematically represented as
[tex]\r p = \frac{k}{n}[/tex]
=> [tex]\r p = \frac{76}{149}[/tex]
=> [tex]\r p = 0.51[/tex]
The Null hypothesis is [tex]H_o : p = 0.41[/tex]
The Alternative hypothesis is [tex]H_a : p \ne 0.40[/tex]
Next we obtain the critical value of [tex]\alpha[/tex] from the z-table.The value is
[tex]Z_{\alpha } = Z_{0.01} = 1.28[/tex]
Generally the test statistics is mathematically evaluated as
[tex]t = \frac{\r p - p }{ \sqrt{ \frac{p(1-p)}{n} } }[/tex]
substituting values
[tex]t = \frac{0.51 - 0.40 }{ \sqrt{ \frac{0.40 (1-0.40 )}{149} } }[/tex]
[tex]t =2.74[/tex]
So looking at the values for t and [tex]Z_{0.01}[/tex] we see that [tex]t > Z_{0.01}[/tex] so we reject the null hypothesis. Which means that there is no sufficient evidence to support the claim
Now if [tex]\alpha = 0.05[/tex] , the from the z-table the critical value for [tex]\alpha = 0.05[/tex] is [tex]Z_{0.05} = 1.645[/tex]
So comparing the value of t and [tex]Z_{0.05} = 1.645[/tex] we see that [tex]t > Z_{0.05}[/tex] hence the conclusion would not be different.
Can I have somebody answer a few more of the questions that I need please and this one too?
Answer:
x > 22
Step-by-step explanation:
Hey there!
Well to solve,
52 - 3x < -14
we need to single out x
52 - 3x < -14
-52 to both sides
-3x < -66
Divide both sides by -3
x > 22
The < changes to > because the variable number is a - being divided.
Hope this helps :)
Answer:
x > 22
Step-by-step explanation:
First, rearrange the equation
52 - 3 × x - (-14) < 0Then, pull out the like terms:
66 - 3xNext, apply algebra to the equation by dividing each side by -3. It should now look like this: x > 22.
Therefore, the solution set of the inequality would be x > 22.
Twelve dieters lost an average of 13.7 pounds in 6 weeks when given a special diet plus a "fat-blocking" herbal formula. A control group of twelve other dieters were given the same diet, but without the herbal formula, and lost an average of 10.7 pounds during the same time. The standard deviation of the "fat-blocker" sample was 2.6 and the standard deviation of the control group was 2.4. Find the 95% confidence interval for the differences of the means.
Answer:
The 95% confidence interval is [tex]0.88 < \mu_1 - \mu_2 < 5.12[/tex]
Step-by-step explanation:
From the question we are told that
The sample mean for fat-blocking [tex]\= x_1 = 13.7[/tex]
The sample size for fat-blocking [tex]n = 12[/tex]
The standard deviation for fat-blocking is [tex]\sigma_1 = 2.6[/tex]
The sample mean for control group is [tex]\= x _2 = 10.7[/tex]
The sample size for control group is [tex]n_2 = 12[/tex]
The standard deviation for control group is [tex]\sigma _2 = 2.4[/tex]
Given that the confidence level is 95% then the level of significance can me mathematically evaluated as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5 \%[/tex]
[tex]\alpha =0.05[/tex]
Generally the degree of freedom is mathematically represented as
[tex]df = n_1 + n_2 - 2[/tex]
substituting values
[tex]df = 12 +12 - 2[/tex]
[tex]df = 22[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] at a degree of freedom of 22 form the students t-distribution , the value is
[tex]t_{\frac{\alpha }{2}, df } = 2.074[/tex]
Generally the margin of error is mathematically represented as
[tex]E = t_{\frac{\alpha }{2}, df } * \sqrt{ \frac{\sigma^2_1 }{n_1 } + \frac{\sigma^2_2 }{n_2 } }[/tex]
substituting values
[tex]E = 2.07 4 * \sqrt{ \frac{ 2.6^2 }{12 } + \frac{2.4^2 }{12 } }[/tex]
[tex]E = 2.12[/tex]
the 95% confidence interval for the differences of the means is mathematically represented as
[tex]\= x_1 - \= x_2 - E < \mu_1 - \mu_2 < \= x_1 - \= x_2 + E[/tex]
substituting values
[tex]13.7 - 10.7 - 2.12 < \mu_1 - \mu_2 < 13.7 - 10.7 + 2.12[/tex]
[tex]0.88 < \mu_1 - \mu_2 < 5.12[/tex]
Estimate the product of 0.235 and 13.467 to the nearest hundredth. Round each value to the nearest hundredth before multiplying. Your final answer should also be rounded to the nearest hundredth.
Answer:
0.235 = 0.24
13.467 = 13.47
0.24+13.47=13.71
Mr Makgato sells his car for R42 000.00. The total commission is 7.2% of the selling price of which the broker receives 2 thirds and the salesperson receives the rest. How much does the broker receive?
Answer:
2016
Step-by-step explanation:
using USA dollars:
$42000 x .072 (7.2%) = 3024 total commission
3024 x 2/3 = 2016 brokers amount
The 1991 Tractor has a horse power of 195, which is five less than four times the horsepower of the Cinderella's carriage. What was the horsepower of the carriage?
Answer:
The horsepower of the carriage is 50
Step-by-step explanation:
Let the horsepower of the carriage=x
ATQ, 195+5=4x, x=50.
Given: AABC, AC = 5
m C = 90°
m A= 22°
Find: Perimeter of AABC
A
C
B
9514 1404 393
Answer:
perimeter ≈ 12.4 units
Step-by-step explanation:
The side adjacent to the angle is given. The relationships useful for the other two sides are ...
Tan = Opposite/Adjacent
Cos = Adjacent/Hypotenuse
From these, we have ...
opposite = 5·tan(22°) ≈ 2.02
hypotenuse = 5/cos(22°) ≈ 5.39
Then the perimeter is ...
P = a + b + c = 2.02 + 5 + 5.39 = 12.41
The perimeter of ∆ABC is about 12.4 units.