Answers
Answer:
Refraction is what happens when light passes through some medium and changes it's direction because of it. For instance, when light travels through a lens light is bent as it goes from air to glass and back to air again. :)
Related Questions
the figure below shows segments AC and EF which intersect at point B.
Answers
Answer:
Choice 3
Step-by-step explanation:
For some reason it doesn't let me put more details
Answer: C) ∠ A FB ≅ ∠CEB
Step-by-step explanation:
We can prove that Δ ABF ≅ ΔCBE by Angle-Angle (AA) Congruency Theorem.
∠ABF ≡ ∠CBE Vertical Angles Postulate
∠AFB ≡ ∠CEB Alternate Interior Angles Postulate
∠FAB ≡ ∠ECB Alternate Interior Angles Postulate
We only need two of the above statements/reasons above to prove AA Congruency Theorem.
Point M is in the exterior of an angle AOB, ray OC is a bisector of this angle. Prove, that the measure of angle MOC is equal to one-half the sum of the measures of angles AOM and BOM.
Answers
Answer:
see the prove below
Step-by-step explanation:
We have to prove that MOC=(AOM+BOM)/2
Let Angle AOM=x and AOC=y . => AOB=2y ( because OC is the bisector of AOB)
So MOC= AOM+AOC=x+y
BOM=AOB+AOM=2y +x
AOM+BOM= x+2y+x=2y+2x
(AOM+BOM)/2= (2y+2x)/2=x+y=MOC
The statement is proved
The arithmetic mean (average) of four numbers is 85. If the largest of these numbers is 97, find the mean of the remaining three numbers. I cannot solve this. Please help on it.
Answers
Answer:
81
Step-by-step explanation:
Let's do this systematically:
Four numbers: a, b, c, d
Whose mean is 85: [tex]\frac{a + b + c + d}{4} = 85[/tex]
Whose largest number is 97: [tex]\frac{a + b + c + 97}{4} = 85[/tex]
Lets solve for the other numbers:
a+b+c+97 = 85*4 = 340
340 - 97 = 243
a+b+c = 243
at this point it doesn't matter what the numbers are, they just need to add up to 243.
We can do 243÷3=81, which is our answer
what is the solution to 0.5(5x+1)=3
Answers
0.5(5x+1) = 3
= 2.5x + 0.5 = 3
= 2.5x = 3 - 0.5
= 2.5x = 2.5
= x = 1
Hope it helped !!!
Comments below
Answer:
1
Step-by-step explanation:
Divide each term by
0.5 and simplify.
Divide each term in
0.5 ( 5 x + 1 ) = 3 by 0.5 . 0.5 ( 5 x + 1 ) 0.5
= 3 0.5 Cancel the common factor of 0.5 . 5 x + 1 = 3 0.5 Divide 3 by 0.5 .
5 x + 1 = 6
Move all terms not containing
x
to the right side of the equation.
Subtract 1 from both sides of the equation.
5 x = 6 − 1 Subtract 1 from 6 . 5 x = 5
Divide each term by
5 and simplify.
Divide each term in 5 x = 5 by 5 . 5 x 5 = 5 5
Cancel the common factor of 5 .
Cancel the common factor.
5 x 5 = 5 5 Divide x by 1 . x = 5 5 Divide 5 by 5 .
x = 1
Determine if the function defines an inner product on R3, where u = (u1, u2, u3) and v = (v1, v2, v3). (Select all that apply.) u, v = 5u1v1 + 2u2v2 + u3v3
Answers
Answer:
u1v1 + u2v2 + u3v3
Step-by-step explanation:
Inner product is a method of multiplying vectors, with the outcome being a scalar. \
u = (u1, u2, u3) and v = (v1, v2, v3)
Inner product = u.v = (u1, u2, u3). (v1, v2, v3)
= u1v1 + u2v2 + u3v3
Describe the process of dividing a fraction by a fraction.
Answers
Answer: okay here we go.....you ready????
Step-by-step explanation: So to divide a fraction, to make it easier, we do first fraction multiplied by second one, but the second fraction is flipped over when multiplied, the reciprocal, basically, and nothing else changes!
Hi there!
example of fraction:
5/9*4/9
1.Reverse the middle fraction around:
[tex]4/9=9/4[/tex]
2.Reverse the * into multiplication:
[tex]\frac{4}{9}[/tex]·[tex]\frac{9}{4}[/tex]
3.Multiply the two terms:
[tex]\frac{4}{9}[/tex]·[tex]\frac{9}{4}=1\frac{1}{4}[/tex]
HELP! WILL GIVE BRAINLIEST!! EASY! GIVE LONG DETAILED ANSWER!
Answers
Answer:
x² + 2x + y² + 4y = 20
(x² + 2x + 1) - 1 + (y² + 4y + 4) - 4 = 20
(x + 2)² + (y + 4)² - 5 = 20
(x + 2)² + (y + 4)² = 25
Therefore, the center is (-2, -4) and the radius is √25 = 5.
Find the value of x. Please help! Thanks.
Answers
Answer:
[tex]\huge\boxed{x=\sqrt{30}}[/tex]
Step-by-step explanation:
ΔABC and ΔBDC are similar (AAA).
Therefore the corresponding sides are in proportion:
[tex]\dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]
substitute
[tex]AC=7+3=10\\{BC}=x\\CD=3[/tex]
[tex]\dfrac{10}{x}=\dfrac{x}{3}[/tex] cross multiply
[tex](10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=\sqrt{30}[/tex]
I NEED HELP PLEASE, THANKS! :)
Find the sum of the first 5 terms of the geometric series. 8 – 16 + 32 – ... 87
86
88
89
Answers
Answer: c) 88
Step-by-step explanation:
8, -16, 32, ...
We can see that each previous term is multiplied by -2
so the next two terms will be 32(-2) = -64 and -64(-2) = 128
So the first 5 terms of the sequence is: 8, -16, 32, -64, 128
Add the positive numbers and the negative numbers, then find their sum.
8 + 32 + 128 = 168
-16 + (-64) = -80
Sum = 88
A soda factory has a special manufacturing line to fill large bottles with 2 liters of their beverage. Every process is computerized. However, it doesn't always fill exactly 2 liters. It follows a normal distribution, witha mean of 1.98 liters and a variance of 0.0064 liters. If the amount of soda in a bottle is more than 1.5 standard deviations away from the mean, then it will be rejected. Find the probability that a randomly selected bottle is rejected.
A 0
B 0.04
C 0.07
D 0.13
E 0.
Answers
Answer:
[tex] z= \frac{2.1-1.98}{0.08}= 1.5[/tex]
And we can use the normal standard table and the complement rule and we got:
[tex]P(z>1.5)= 1-P(Z<1.5) =1- 0.933= 0.067 \approx 0.07[/tex]
And the best answer would be:
C 0.07
Step-by-step explanation:
Let X the random variable who represent the amount of soda filled in large bottles and we know this:
[tex]\mu = 1.98, \sigma =\sqrt{0.0064}= 0.08[/tex]
And we want to find this probability:
[tex] P(X> \mu +1.5 \sigma = 1.98 +1.5*0.08 =2.1)[/tex]
And for this case we can use the z score formula given by:
[tex] z=\frac{X -\mu}{\sigma}[/tex]
And replacing we got:
[tex] z= \frac{2.1-1.98}{0.08}= 1.5[/tex]
And we can use the normal standard table and the complement rule and we got:
[tex]P(z>1.5)= 1-P(Z<1.5) =1- 0.933= 0.067 \approx 0.07[/tex]
And the best answer would be:
C 0.07
The Jones family and the Connor family both bought the same boxed package of sugar cubes at the store, in which the cubes were arranged in 5 layers. After drinking of 61 cups of tea, the Joneses found that they were out of sugar. The Connors' sugar box was enough to last them through 88 cups of tea. Both families put either 2 or 3 pieces of sugar per cup. How many sugar cubes were in the box?
Answers
Answer:
180
Step-by-step explanation:
At the beggining, it says they are stacked in 5 layers which means the number of cubes is divisible by 5.
If the number of cubes equals x:
The least amount of sugar cubes the Jones family could have used is [tex]61*2[/tex] which equals 122. The most they couldve used is [tex]61*3[/tex] which equals 183.
Based on the information from the Jones family, x is between 122 and 183.
Based on the information from the Connor's, x is between 176 and 264.
Based on the information from both, x is between 176 and 183. The only number that is divisible by 5 between those numbers is 180 cubes.
Find the position function of a particle moving along a coordinate line that satisfies the given conditions. 2sint-cost
Answers
Answer:
the position of a particle moving at a coordinate say(y) will satisfy the given conditions t=0 (say) if y=2sint-cost
Step-by-step explanation:
Clearly by the above we can see that if y=2sint-cost at t=0, then y=-1 because at t=0 sint vanishes and leaves us with only cost and at t=0 cos0=1
Suppose you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. If you randomly guess on all 30 questions, what is the probability you pass the exam (correctly guess on 60% or more of the questions)? Assume none of the questions have more than one correct answer (hint: this assumption of only 1 correct choice out of 4 makes the distribution of X, the number of correct guesses, binomial). What is the expected number of correct guesses, from problem #19? What is the standard deviation, ? (Remember that X is a binomial random variable!) What would be considered an unusual number of correct guesses on the test mention in problem number 19 using ?
Answers
Answer:
(a) The probability you pass the exam is 0.0000501.
(b) The expected number of correct guesses is 7.5.
(c) The standard deviation is 2.372.
Step-by-step explanation:
We are given that you take a 30-question, multiple-choice test, in which each question contains 4 choices: A, B, C, and D. And you randomly guess on all 30 questions.
Since there is an assumption of only 1 correct choice out of 4 which means the above situation can be represented through binomial distribution;
[tex]P(X =x) = \binom{n}{r}\times p^{r}\times (1-p)^{n-r} ; x = 0,1,2,3,......[/tex]
where, n = number of trials (samples) taken = 30
r = number of success = at least 60%
p = probbaility of success which in our question is the probability
of a correct answer, i.e; p = [tex]\frac{1}{4}[/tex] = 0.25
Let X = Number of questions that are correct
So, X ~ Binom(n = 30 , p = 0.25)
(a) The probability you pass the exam is given by = P(X [tex]\geq[/tex] 18)
Because 60% of 30 = 18
P(X [tex]\geq[/tex] 18) = P(X = 18) + P(X = 19) +...........+ P(X = 29) + P(X = 30)
= [tex]\binom{30}{18}\times 0.25^{18}\times (1-0.25)^{30-18} + \binom{30}{19}\times 0.25^{19}\times (1-0.25)^{30-19} +.......+ \binom{30}{29}\times 0.25^{29}\times (1-0.25)^{30-29} + \binom{30}{30}\times 0.25^{30}\times (1-0.25)^{30-30}[/tex]
= 0.0000501
(b) The expected number of correct guesses is given by;
Mean of the binomial distribution, E(X) = [tex]n \times p[/tex]
= [tex]30 \times 0.25[/tex] = 7.5
(c) The standard deviation of the binomial distribution is given by;
S.D.(X) = [tex]\sqrt{n \times p \times (1-p)}[/tex]
= [tex]\sqrt{30 \times 0.25 \times (1-0.25)}[/tex]
= [tex]\sqrt{5.625}[/tex] = 2.372
Please answer this correctly
Answers
Answer:
12.5
Step-by-step explanation:
This is the answer!
Answer:
50%
Step-by-step explanation:
Total Cards = 4
6 or even cards = 2
P( 6 or even) = 2/4
=> 1/2
In %age:
50%
Write the recursive sequence for: 64, 16, 4, 1, ...
Answers
Answer:
Use the formula
a
n
=
a
1
r
n
−
1
to identify the geometric sequence.
Step-by-step explanation:
a
n
=
64
4
n
−
1 hope this helps you :)
Answer: The answer is in the steps.
Step-by-step explanation:
f(1)= 64
f(n)=1/4(n-1) n in this case is the nth term.
(3a^3-5b^3)+blank a^3+blank b^3=(a^3+b^3)
Answers
Answer:
(3a³-5b³)+ (-2)a³ +6b³=(a³+b³)
Step-by-step explanation:
First, lets remove the brackets. There is no "-" before the brackets, so we can just remove them at all.
3a³-5b³+ ...a³ +...b³=a³+b³
Now we can joint similar monoms (with variable a) ( and with variable b) in the left side of equation
3a³+...a³ -5b³ +...b³=a³+b³
Now we can notice that 3a³+...a³=a³ (1) and
-5b³ +...b³=b³ (2)
Lets find deduct 3a³ from both sides of (1)
...a³= a³-3a³
...a³= -2a³ So instead ... we have to type -2 (-2 is negative sowe type -2 in brackets).
Similarly lets add 5b³ to both sides of (2)
-5b³ +...b³=b³
-5b³ +5b³ +...b³=b³+5b³
...b³=6b³ So instead ... we have to type 6.
please simplify this
Answers
Answer:
(√77) / 22
Step-by-step explanation:
To rationalize the fraction we must multiply the entire fraction by √11 / √11. Note that the 2 is not important because it's not a radical. This gives us √77 / 22.
The value of 82 is between which two integers?
Answers
Hey there!
Let's look at the squares of all of our answer options. We will compare them to eighty two to see which it belongs in.
A. 36 and 49.
B. 49 and 64.
C. 64 and 81.
D. 81 and 100
As you can see, 82 is in between 81 and 100, so the answer is D. 9 and 10.
Also, the square root of 82 is about 9.05, and this fits our answer.
Have a wonderful day!
The value of √82 is between 9 and 10 integers.
What is Number system?A number system is defined as a system of writing to express numbers.
We need to find the value of √82 is between which two integers.
The value of √82 is 9.05
Square root of eighty two is nine point zero five
9.05 is in between 9 and 10
Nine point zero five is between nine and ten.
Hence, the value of √82 is between 9 and 10 integers.
To learn more on Number system click:
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A large mixing tank initially contains 1000 gallons of water in which 30 pounds of salt have been dissolved. Another brine solution is pumped into the tank at the rate of 4 gallons per minute, and the resulting mixture is pumped out at the same rate. The concentration of the incoming brine solution is 2 pounds of salt per gallon. If represents the amount of salt in the tank at time t, the correct differential equation for A is:__________.A.) dA/dt = 4 - .08AB.) dA/dt = 8 -.04AC.) dA/dt = 4-.04AD.) dA/dt = 2-.04AE.) dA/dt = 8-.02A
Answers
Answer:
(B)[tex]\dfrac{dA}{dt}=8-0.004A[/tex]
Step-by-step explanation:
Volume of fluid in the tank =1000 gallons
Initial Amount of Salt in the tank, A(0)= 30 pounds
Incoming brine solution of concentration 2 pounds of salt per gallon is pumped in at a rate of 4 gallons per minute.
Rate In=(concentration of salt in inflow)(input rate of brine)
[tex]=(2\frac{lbs}{gal})( 4\frac{gal}{min})=8\frac{lbs}{min}[/tex]
The resulting mixture is pumped out at the same rate, therefore:
Rate Out =(concentration of salt in outflow)(output rate of brine)
[tex]=(\frac{A(t)}{1000})( 4\frac{gal}{min})=\frac{A}{250}[/tex]
Therefore:
The rate of change of amount of salt in the tank,
[tex]\dfrac{dA}{dt}=$Rate In-Rate out\\\dfrac{dA}{dt}=8-\dfrac{A}{250}\\\dfrac{dA}{dt}=8-0.004A[/tex]
A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,048, $154,144). Give a practical interpretation of the interval.
a) 90% of the sampled CEOs have salaries that fell in the interval $139,048 to $154,144b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144. c) 90% of all CEOs in the electronics industry have salaries that fall between $139,048 to $154,144d) We are 90% confident that the mean salary of the sampled CEOs falls in the interval $139,048 to $154,144.
Answers
Answer:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
Step-by-step explanation:
Confidence interval:
Confidence level of x%
We build from a sample.
Between a and b.
Intepretation: We are x% sure that the population mean is between a and b.
In this question:
90%
45 CEO's
Between ($139,048, $154,144).
So
We are 90% sure that the mean salary of all CEO's falls within this interval.
The correct answer is:
b) We are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,048 to $154,144.
V’s Warehouse has a market value of $880,000. The property in V’s area is assessed at 35% of the market value. The tax rate is $58.90 per $1,000 of assessed value. What is V’s property tax?
Answers
Answer:
$18,141.20
Step-by-step explanation:
The assessed value is $880,000 × 0.35.
The tax will be ...
(58.90/1000) × (0.35 × $880,000) = $18,141.20
PLEASE HELPP! f(x)= -3x + 3
Which of the graphs represent the inverse of the function F??
Answers
Answer:
Answer is Y
Step-by-step explanation:
In the diagram below,DE and EF are tangent to 0.What is the measure of DGF?
Answers
Answer: 245
Step-by-step explanation:
Answer:
The answer is D
Step-by-step explanation:
What is the measure of angle S?
480
56°
930
101°
Answers
Answer:
m∠s = 93°
Step-by-step explanation:
We know that any quadrilateral's sum of angles adds up to 360°. In that case,
360 - (56 + 132 + 79) = m∠s
m∠s = 93°
Answer:
S° = 93 °
Step-by-step explanation:
[tex]The- diagram- is- a- trapezoid (quadrilateral)\\Sum- of- angles-in a- quadrilateral = 360\\ 132\° + 56\° + 79\° + x\° = 360\° \\267\° + x\° = 360\° \\x = 360 \° - 267 \° \\x\° = 93\°[/tex]
Choose the correct simplification of the expression (7x - 3)
(4x2 – 3x - 6). (1 point)
Answers
Answer:
Step-by-step explanation:
hello,
I assume that you want to develop the expression
[tex](7x-3)(4x^2-3x-6)=7x(4x^2-3x-6)-3(4x^2-3x-6)\\= 28x^3-21x^2-42x-12x^2+9x+18\\\\=28x^3-33x^2-33x+18[/tex]
hope this helps
3) BRAINLIEST & 10 + POINTS! :)
Answers
Answer:
33,175.21/radians/sec
Step-by-step explanation:
22 rev/sec x 60sec/1 min x 4ft x2 pi/1 rev
22 x 60 = 1320
1320 x 4 = 5280
2 x pi = 6.2831853072
5280 x 6.2831853072= 33,175.218421884
Please answer this correctly
Answers
Answer:
40%
Step-by-step explanation:
The numbers that are not even are 5 and 7.
2 numbers out of 5.
2/5 = 0.4
P(not even) = 40%
Answer:
[tex]40\%[/tex]
Step-by-step explanation:
5 and 7 are not the numbers
There are 5 numbers in the spinner
[tex]p = \frac{2}{5} \\ = \frac{2 \times 20}{5 \times 20} \\ = \frac{40}{100} \\ = 40\%[/tex]
PLEASE HELP ME OUT
Move point b to different locations in the coordinate plane. What do you notice about the relationship between BG and GF? Explain in terms of <BGF
Answers
Answer:
BG is always perpendicular to GF. The measure of angle BGF is always 90 degree
Step-by-step explanation:
Answer:
is always perpendicular to . The measure of is always 90°.
Step-by-step explanation:
Plato Awnser
Which graph represents the function y = 2x - 4?
Answers
Answer:
The second graph on the top
Step-by-step explanation:
As the last number says it would cross the y axis at -4 and go up two over one so 1,-2 then 2,0 3,2 4,4 etc.
The x-intercept of y = 2x - 4 is (2,0) thus the third graph represents the function y = 2x - 4.
What is a linear function?A straight line on the coordinate plane is represented by a linear function.
A linear function always has the same and constant slope.
The formula for a linear function is f(x) = ax + b, where a and b are real values.
As per the given function,
y = 2x - 4
At x = 0, y = -4 thus (0,-4) will be the y-intercept.
At y = 0, 2x - 4 = 0 or x = 2 thus (2,0) will be the x-intercept.
The line passing through (2,0) and (0,-4) is shown in the third graph.
Hence "The x-intercept of y = 2x - 4 is (2,0) thus the third graph represents the function y = 2x - 4".
For more about the linear function,
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Suppose you are managing 16 employees, and you need to form three teams to work on different projects. Assume that all employees will work on a team, and that each employee has the same qualifications/skills so that everyone has the same probability of getting choosen. In how many different ways can the teams be chosen so taht the number of employees on each project are as follows:
a. 5
b. 1
c. 10
Answers
Answer:
4380 ways
Step-by-step explanation:
We have to form 3 project of 16 employees, they tell us that the first project must have 5 employees, therefore we must find the number of combinations to choose 5 of 16 (16C5)
We have nCr = n! / (R! * (N-r)!)
replacing we have:
1st project:
16C5 = 16! / (5! * (16-5)!) = 4368 combinations
Now in the second project we must choose 1 employee, but not 16 but 11 available, therefore it would be to find the number of combinations to choose 1 of 11 (11C1)
2nd project:
11C1 = 11! / (1! * (11-1)!) = 11 combinations
For the third project we must choose 10 employees, but since we only have 10 available, we can only do a combination of this, since 10C10 = 1, therefore:
3rd project: 1 combination
The total number of combinations fro selecting 16 employees for each project would be:
4368 + 11 + 1 = 4380 combinations, that is, there are 4380 different ways of forming projects with the given conditions.
