Answer:
Step-by-step explanation:
Arithmetic sequence:
a = first term = 4
d = common difference = second term - first term
= 9 - 4
d = 5
[tex]\sf t_n =a +(n -1)*d[/tex]
= 4 + (n - 1) *5
= 4 + 5n - 5
= 5n -1
Check; n= 1 , first term = 5*1 - 1 = 5 - 1 = 4
n = 2, second term = 5*2 - 1 = 10 -1 = 9
n = 3, third term = 5*3 - 1 = 15 - 1 = 1
The next term, fifth term = 5*5 - 1
= 25 - 1
= 24
Anthony is planning a trip using a map with the scale of 1 cm to 15 miles it’s a destinations 15 cm away on the map how far away in Miles as the destination
The distance of Miles' destination is 225 miles.
What is the distance of the destination?A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The map is a scale drawing of a larger town. The scale drawing is reduced by constant dimensions.
Actual distance = (15 x 15) / 1 = 225 miles
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A number of friends decided to go on a picnic and planned to spend rs. 96 on eatables. four of them, however, did not turn up. as a consequence, the remaining ones had to contribute rs. 4 each extra. the number of those who attended the picnic was
The number of those who attended the picnic was 8.
Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = [tex]ax^{2} + bx + c[/tex] = 0 where a, b, c, ∈ R and a ≠ 0.
Such questions are best examples of quadratic equations where the unknown is simply assumed to be a variable which when substituted according to the conditions yield a quadratic equation which can easily be solved.
Let x represent the whole population.
Total Spending = Rs. 96
Thus, each individual's contribution is equal to 96/x.
Four people did not show up causing
others to contribute Rs. 4 extra.
So the given condition can be written as
96/(x-4) – 96/x = 4
=>96x – 96(x-4) = 4x(x-4)
=> 96x -96x + 384 = 4x2 – 16x
=> 4x2 – 16x – 384 = 0
=> x2 – 4x – 96 = 0
=> (x – 12)(x + 8) = 0
=> x = 12 or x = -8 (neglect)
So x = 12
x-4 = 8 ( because four of them did not turn up)
∴ The number of those who attended the picnic was 8.
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Keilantra has a toy car collection of 400 toy cars. She keeps 268 of the toy cars on her
wall. What percentage of Keilantra's toy car collection does she keep on her wall?
Answer:
15
I
Submit Answer
MacBook Air
33
attempt 1 out of 2
4
Answer:
67%
Step-by-step explanation:
268 ÷ 400 = 0.67 = 67%
[tex]\huge\boxed{67\%}[/tex]
This can be solved just with division.
[tex]\dfrac{268\ \text{cars on the wall}}{400\ \text{total cars}}=0.67[/tex]
Multiply the result by [tex]100[/tex] to get a percentage.
[tex]0.67=\boxed{67\%}[/tex]
A math teacher randomly assigns seats in the classroom to students each quarter. Each student randomly chooses their row number out of a hat. In the classroom, there are 4 desks in each row and 27 students in your class. What is the probability that you and your 3 friends will get to sit together in the same row?
Using the combination formula, it is found that the probability that you and your 3 friends will get to sit together in the same row is given by:
[tex]p = \frac{1}{17550}[/tex].
We do not consider the order, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
4 students will be taken from a set of 27, hence the number of ways they can sit is given by:
[tex]C_{27,4} = \frac{27!}{4!23!} = 17550[/tex]
Only one outcome is desired, hence the probability is given by:
[tex]p = \frac{1}{17550}[/tex].
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Write as an equation: The product of a number and 12 is 78.
A. 12n=78
12
n
=
78
B. n+12=78
n
+
12
=
78
C. 12−n=78
12
−
n
=
78
D. 12=78n
A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?
A glass contains alcohol and water in the ratio 1:4. A second glass contains the same quantity of liquid, but this time the ratio of alcohol to water is 2:3. Each glass is emptied into a third glass. What is the ratio of alcohol to water in the final mixture?
Answer:
3:7
Step-by-step explanation:
So to solve this problem, you have to understand what the ratio 1:4 and 2:3 means. The 1:4 ratio in the first equation means that for "each unit of alcohol" there is 4 of those units of water. So let's say I had 2 gallons of alcohol and mixed it with 8 gallons of water. This means for each gallon of alcohol, there is 4 gallons of water, or in other words a 1:4 ratio. This can be described as a percentage as well. For each 5 gallons there are 4 gallons of water, and 1 gallon of alcohol or 20% is alcohol. So let's just say that x=alcohol and y=water, this means that: [tex]x+y=c[/tex] where c is the total amount in the glass. This means that: [tex]x=0.20c[/tex]
Let's do the same thing to the second equation. the ratio means that for every 2 units of alcohol there are 3 units of water. This means for every 5 gallons of the mixture there is 2 units of alcohol which is 40%. In this case let's also say that j=alcohol and k=water. This means that: [tex]j+k=c[/tex] and that: [tex]j=0.40c[/tex].
So if we're going to add the two glasses, we simply add the two sides, and get: [tex]j+x+k+y=2c[/tex]. Now remember how can can express j and x in terms of c, since it's a certain percentage of c (the entire thing). This means that we get: [tex](0.4c+0.2c)+x+k=2c[/tex] Now we can add like terms to get the equation: [tex]0.6c+y+k=2c[/tex]. We can find how much 0.6c is to 2c by dividing the 2, in doing so we get that 0.6c/2c = 0.3, or in other words the 0.6c is only 30% of the final mixture, and since the 0.6c represents the alcohol in this mixture, that means that's the percentage of alcohol. To write this as a ratio, this means for every 3 units of alcohol, there is 7 units of water, because 3/10 = 30%.
Answer:
3 : 7
Step-by-step explanation:
We can do this question using a easier way.
For example, A glass contains sugar and water, the ratio to sugar to water is 2 : 5. And the second glass's sugar to water is 2 : 3. The mixture of the first glass is 200 mL. The mixture of the second glass is the same as the first glass.
This kind of glass question, is very important to Math.
Try using this to solve this question.
calls arrive at lynn ann fish's hotel switchboard at a rate of 2.0 per minute. the average time to handle each is 10 seconds. there is only one switchboard operator at the current time. the poisson and negative exponential distributions appear to be relevant in this situation. what is the probability, as a percent, that the operator is busy
The probability that the operator is busy is 33.33% if the call rate is 2 per minute and average time to handle is 10 seconds.
Given rate of calls 2 per minute and average time to handle a call is 10 seconds.
We have to find the probability that the operator is busy.
Probability is the chance of happening an event among all the events possible. The value of probability lies between 0 and 1.
Probability= number of items/ total items
If rate is 2 per minute then the customers handled in 1 hour=2*60=120
The average time to handle a call=10 seconds.
Therefore customers to be handled in 1 hour=360 (10*6*60)
Probability that the operator is busy is as under:
Probability=λ/μ
=120/360
=1/3
=1/3*100
=33.33%
Hence the probability that the operator is busy is 33.33%.
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The perimeter of the rectangle below is 130 units. Find the length of side VY.
Write your answer without variables.
Y
4y
V
5y + 2
X
W
VY
Answer:
VY = 28 units
Step-by-step explanation:
the perimeter (P) of a rectangle is calculated as
P = 2 ( length + breadth )
given P = 130 , then
2(5y + 2 + 4y) = 130 ( divide both sides by 2 )
9y + 2 = 65 ( subtract 2 from both sides )
9y = 63 ( divide both sides by 9 )
y = 7
Then
VY = 4y = 4 × 7 = 28
As strange as it may seem, it is possible to give a precise-looking verbal definition of an integer that, in fact, is not a definition at all. The following was devised by an English librarian, G. G. Berry, and reported by Bertrand Russell. Explain how it leads to a contradiction. Let [tex]n[/tex] be “the smallest integer not describable in fewer than [tex]12[/tex] English words.” (Note that the total number of strings consisting of [tex]11[/tex] or fewer English words is finite.)
Worth 10 points.
YOUR ANSWER MUST BE UNIQUE
The statements hold the contradiction, just by confusion in keep meaning of statements and get confused with "12" which is string in quotes
Let be “the smallest integer not describable in fewer than English words.” (Note that the total number of strings consisting of or fewer English words is finite.)
What do you mean by contradiction?
Contradiction means that couple of statements that opposes each other.
Here,
The statement says let n be “the smallest integer not describable in fewer than English words.” which implies that n is connected with string mentioned in "" quotes, which is not a definition but contain 11 words in the quotes.
and another statement - Note that the total number of strings consisting 11 or fewer English words is finite which implies that:
the limit of words inside the quotes ≤ 11 words
Thus, strings implies in quotes is simple meaning with 11 word in it
While in statement in brackets implies the limit of words as a string should be ≤ 11. the string "12" create the contradiction in minds.
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Of the cartons produced by a company, 5% have a puncture, 8% have a smashed corner, and 0.4% have both a puncture and a smashed corner. Find the probability that a randomly selected carton has a puncture or a smashed corner.
The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.
In this problem, the events are:
Event A: Puncture.
Event B: Smashed corner.
The "or" probability is given by:
[tex]P(AUB)=P(A)+P(B)-P(A[/tex]∩[tex]B)[/tex]
5% have a puncture, hence [tex]P(A)=0.05[/tex]
8% have a smashed corner, hence [tex]P(B)=0.08[/tex]
0.4% have both a puncture and a smashed corner, hence[tex]P(AUB)=0.004[/tex]
Then:
[tex]P(AUB)=0.05+0.08-0.004= 0.126[/tex]
Therefore, The probability that a randomly selected carton has a puncture or a smashed corner is 12.6%.
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17-19, deal with the ambiguous SSA. For each, find all possible solutions and sketch the triangle(s) in each case
The possible solutions using the Sine Law are given as follows:
Triangle A:
B = 50.26°
C = 79.74°
Triangle B:
B = 62.79°
C = 70.21°
What is the sine Rule?
The sine law asserts that the ratio of a triangle's side length to the sine of the opposing angle is the same for all three sides. The sine rule is another name for it.
What is the explanation for the above solution?Triangle A
Given the sine law:
a/SinA = b/SinB
Hence
Sin B = (b/a) SinA
Sin B = 15/10 (Sin 50)
Sn B = (15/10) * 0.766
Sin B = 1.5 * 0.766
B = Sin⁻1 (1.14)
B = 50.26°
Hence, C =
180 - B - A
= 180 - 50.26 - 50
C = 79.74°
Solution B
Given the sine law:
a/SinA = b/SinB
Hence
Sin B = (b/a) SinA
Sin B = 2/1.6 (Sin 47)
Sn B = 1.25 * 0.73
Sin B = 0.9125
B = Sin⁻1 (0.9125)
B = 62.79°
Hence,
C = 180 - 62.79 - 47
C = 70.21°
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Suppose the round-trip airfare between Philadelphia and Los Angeles a month before the departure date follows the normal probability distribution with a mean of $387.20 and a standard deviation of $68.50. The interval around the mean that contains 95% of the airfares is ________.
The interval around the mean that contains 95% of the airfare is (250.2,524.2).
Normal Distribution is bell shaped and symmetrical in nature.
We use standard normal to find probabilities of normal distribution
Normal distributions have key characteristics that are easy to spot in graphs: The mean, median and mode are exactly the same. The distribution is symmetric about the mean—half the values fall below the mean and half above the mean. Diagram below shows standard normal figure.
In a normal distribution, 95% of the values fall between mean±2*sd
Give: mean=387.20
sd=68.50
So the interval around the mean that contains 95% of the airfare is (250.2,524.2).
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Find the value of x.
[tex]x + 4x + 4x + 135 + 135 = 540[/tex]
[tex]9x + 270 = 540[/tex]
[tex]9x = 540 - 270 \\ 9x = 270[/tex]
[tex]x = \frac{270}{9} = 30[/tex]
There were some people on a train
17 get off the train at the first stop and 22 people get on the train
Now there are 66 people on the train
How many people were on the train to begin with
Can someone give me the answer to this?
[tex]\frac{FI}{IG}=\frac{14}{28}=\frac{1}{2}\\\\\frac{FE}{EH}=\frac{12}{26}=\frac{6}{13}[/tex]
So, IE is not parallel to GH.
3 quick algebra 1 questions for 50 points!
Only answer if you know the answer, shout-out to subtomex0, tysm for the help!
The range of the function across the domain is {18, 2, -6}
The range of the functionThe function is given as:
f(x) = -2x + 12
The domain is given as:
{-3, 5, 9}
So, we have:
f(-3) = -2*-3 + 12 = 18
f(5) = -2*5 + 12 = 2
f(9) = -2*9 + 12 = -6
Hence, the range of the function across the domain is {18, 2, -6}
The value of the functionThe function is
f(x) = 3x - 11
To calculate f(4), we have:
f(4) = 3 * 4 - 11
Evaluate
f(4) = 1
Hence, the value of f(4) is 1
The value of the functionThe function of the graph is given as:
w(x)
To calculate w(2), we check the corresponding point on the graph where x = 2
From the graph, we have:
w(2) = 5
Hence, the value of w(2) is 5
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Answer:
1. f(4) = 1
2. range: {18, 2, -6}
3. w(2) = 5
Step-by-step explanation:
Question 1
[tex]\textsf{Given}: \quad f(x)=3x-11[/tex]
To find f(4) substitute x = 4 into the given function:
[tex]\begin{aligned}\implies f(4) & = 3(4)-11\\& = 12-11\\& = 1\end{aligned}[/tex]
Question 2
Domain: set of all possible input values (x-values)
Range: set of all possible output values (y-values)
[tex]\textsf{Given}: \quad b(x)=-2x+12[/tex]
To find the range of the given function for the domain {-3, 5, 9} simply input these values of x into the function:
[tex]\implies b(-3)=-2(-3)+12=18[/tex]
[tex]\implies b(5)=-2(5)+12=2[/tex]
[tex]\implies b(9)=-2(9)+12=-6[/tex]
Therefore, the range of the given function is {18, 2, -6}.
Question 3
Given: The graph of function w(x)
To find w(2) simply find the y-value of the point on the graph where x = 2:
Find x = 2 on the x-axis. Trace vertically until you meet the line. Trace horizontally to the y-axis to find the corresponding value of y.Therefore, w(2) = 5
(bus, cab, or train) to school, and in the evening he has the same 333 choices for his trip home.
The probability that he will use both bus and the train among bus, cab, train is 0.11.
Given There are 3 choices to people each among bus, cab, train for his trip home.
Probability is the likeliness of happening an event among all the events possible. The value of probability lies between 0 and 1. The formula to calculate probability is as under:
Probability= number of things/ total things.
The value of probability cannot be negative.
Number of buses=3
Number of cab=3
Number of train=3
Probability that he will go through train and bus is 3/9*3/9
=9/81
=1/9
=0.11
Hence the probability that he will travel with bus and train is 0.11.
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Question is incomplete as it includes:
What is the probability that he will use both train and bus?
32. Find the ratio of the side lengths of the small triangle to the large
triangle.
3/10
6/20
3/2
2/3
Answer:
2/3
Step-by-step explanation:
that the ratio of that number
Look At The Graph. How many nails are less than 1 1/2 inches long?
A)7
B)17
C)6
D)15
Answer:
D 15
Step-by-step explanation:
Count all of the x's less than 1 1/2 = 15
This table shows the scores that Mario had on his last five math tests.
Which statement does NOT describe this set of data?
A. The mode is 85.
B. The mean is greater than the median.
C. The median is 81.
D. The mode and the median are equal.
Answer:
Step-by-step explanation:
its A i just did it lol
The height of an
equilateral triangle is
11√12. What is a side
of the triangle?
Answer:
I don't know the answer
Step-by-step explanation:
it's hard solve it for me
If two triangles are congruent which of the following statements must be true
The statement which must be true are Options B, C and D
which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.
What are congruent triangles?Congruent triangles are triangles that have corresponding sides, angles which are all equal in measure.
They can be rotated and turned to be look be identical.
Thus, the statement which must be true are Options B, C and D
which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.
The complete question is
If two triangles are congruent which of the following statements must be true? CHECK ALL THAT APPLY
A. The triangles have the same size but not the same shape.
B. The triangles have the same size and shape
C. The corresponding sides of the triangles are congruent.
D. The corresponding angles of the triangles are congruent.
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What is the domain of function m based on the graph?
Answer:
let why is equal to FX b and function with an independent variable X and dependent variable y if a function of f provide a way to successfully produced the single value using for the prepos a value of x then the chosen X value is called belong to domain f
Can someone solve it step by step for me please?
The second highest point measured above sea level is the summit of
Kangchenjunga which is 8,586m above sea level and the lowest point is
challenger deep at the bottom of Mariana Trench which is 10,911 m below
the sea level. What is the vertical distance between these two points? Collect
some more information about these two points and present them withimages
Answer:
To find the vertical distace between both points you will have to add both. 8,586+10,911= 19 497.
Hence, the vertical distance is 19,497 feet.
Here is a picture:
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A standard deck of cards contains 52 cards. Of these cards there are 13 of each type of suit (hearts, spades, clubs, diamonds) and 4 of each type of rank (A - K). Two cards are pulled in order from this deck of 52 playing cards. What is the probability that the cards will be two 10's?
A) 1/663
B) 9/26
C) 1/252
D) 1/221
The probability of drawing two 10's is P = 1/221, so the correct option is D.
How to find the probability?
We know that in the deck of 52 cards, we have 4 10's.
Then, the probability of drawing the first 10 is:
p = 4/52.
At this point, we have 3 10's in the deck, and a total of 51 cards (because we already took one 10).
The probability of getting another is:
q = 3/51
The joint probability (of getting both 10's, one after the other) is given by the product of the individual probabilities:
P = p*q = (4/52)*(3/51) = (1/13)*(1/17) = 1/221
Then the correct option is D.
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Find the radius of the given circle with the given central angle and arc length. Round your answer to the nearest tenth.
Show work for full credit.
130*
19.6 cm
Answer: 8.6
Step-by-step explanation:
[tex]19.6=2\pi r\left(\frac{130}{360} \right)\\\\r=\frac{19.6}{2\pi \left(\frac{130}{360} \right)}\\\\r \approx 8.6[/tex]
In the following exercises, multiply the binomials. Use any method.
254. (10a − b)(3a − 4)
Answer:
Hence the expression [tex]$$(10a-b)(3a-4)=30a^2-3ab-40a+4b$$[/tex]
Step-by-step explanation:
Explanation
The given expression is (10a-b)(3 a-4).We have to multiply the given expression.Multiply the (10a-b) by -4, multiply the (10 a-b) by 3a then add like terms.[tex]$$\begin{matrix}{} & {} & {} & {} & 10a & - & b \\ \times & {} & {} & {} & 3a & - & 4 \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}{} & {} & {} & - & 40a & + & 4b \\ 30{{a}^2} & - & 3ab & {} & {} & {} & {} \\ \end{matrix}$$[/tex]
___________________
[tex]$$\begin{matrix}30{{a}^2} & - & 3ab & - & 40a & + & 4b \\ \end{matrix}$$[/tex]
Find the tangent of angle Θ in the triangle below.
Answer: 4/3
Step-by-step explanation:
[tex]\tan \theta=\frac{20}{15}=\boxed{\frac{4}{3}}[/tex]
From the diagram below, if the sides AD = 3 and DC = 27, and BD = X + 3, find x.
Select one:
a.
36
b.
9
c.
16
d.
6
Answer: d. 6.
Step-by-step explanation:
AD=3 DC=27 BD=x+3 x>0 x=?
1. Consider triangle ABD:
It's rectangular (∡ADB=90°). ⇒
AB²=(x+3)²+3²=(x+3)²+9.
2. Consider triangle BDC:
It's rectangular (∡BDC=90°). ⇒
BC²=(x+3)²+27²=(x+3)²+729.
3. Consider triangle ABC:
It's rectangular (∡ABC=90°).
AC=AD+CD=3+27=30. ⇒
AC²=AB²+BC²
(x+3)²+9+(x+3)²+729=30²
2*(x+3)²+738=900
2*(x²+6x+9)+738=900
2x²+12x+18+738=900
2x²+12x-144=0 |:2
x²+6x-72=0
D=324 √D=18
x₁=-12 ∉ 'cause x>0
x₂=6.