Answer:
Approximately $594.38
Step-by-step explanation:
Use the formula: y = a(1 + r)^t
a is the initial amount
r is the percent of interest in decimal form
t is the time in years
y is the money after t years
Substitute the values given in the problem into the equation:
400(1+0.02)^20
Use a calculator or solve manually
Around 594.38
Write the number five and a quarter million in figures.
Answer:
5 and a 250,000
Step-by-step explanation:
A quarter million = 1,000,000 · [tex]\frac{1}{4}[/tex] = 250,000
Answer:
It is: 5,250,000
Algebra 2 help needed image below
Answer:
8x + 100
Step-by-step explanation:
Your answer is correct! But because the equation is already set to "y =", you do not need the "f(x)" in your equation.
A company makes Citi bikes. 95% (i.e., 0.95) pass final inspection. Suppose that 5 bikes are randomly selected. ( use binomial distribution formula ) do I need to use a factorial symbol V! When showing steps by step
a) What is the probability that exactly 4 of these 5 sports bikes pass final inspection?
b) What is the probability that less than 3 of these 5 sports bikes pass final inspection?
I got disconnected with my tutor
Using the binomial distribution, it is found that the probabilities are given as follows:
a) 0.2036 = 20.36%.
b) 0.0011 = 0.11%.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.The values of the parameters are given as follows:
p = 0.95, n = 5.
Item a:
The probability is P(X = 4), hence:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 4) = C_{5,4}.(0.95)^{4}.(0.05)^{1} = 0.2036[/tex]
Item b:
The probability is P(X < 3), hence:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2).
Then:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{5,0}.(0.95)^{0}.(0.05)^{5} \approx 0[/tex]
[tex]P(X = 1) = C_{5,1}.(0.95)^{1}.(0.05)^{4} \approx 0[/tex]
[tex]P(X = 2) = C_{5,2}.(0.95)^{2}.(0.05)^{3} = 0.0011[/tex]
Then:
P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0 + 0 + 0.0011 = 0.0011.
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If REX ~ ROB, find the value of a.
Answer: 8
Step-by-step explanation:
As corresponding sides of similar triangles are proportional,
[tex]\frac{RX}{RB}=\frac{XE}{BO}\\\\\frac{6}{15}=\frac{a}{20}\\\\a=20\left(\frac{6}{15} \right)=\boxed{8}[/tex]
Choose the single logarithmic expression that is equivalent to the one shown. log6 25 − log6 5
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(25) - log_{6}(5) [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) {}^{2} - log_{6}(5) [/tex]
[ property : x² = 2 log x ]
[tex]\qquad \tt \rightarrow \: 2 \: log_{6}(5) {}^{} - log_{6}(5) [/tex]
[tex]\qquad \tt \rightarrow \: log_{6}(5) [/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
How do I get this answer?
Answer:
Step-by-step explanation:
Several trig identities are involved in the proof of this. This is the order in which they are used.
cos(2x) = cos²(x) -sin²(x)cos²(x) +sin²(x) = 1cos(x) = 1/sec(x)ProofStarting with the left side, we can transform it into the right side.
[tex]2\cos(2x)=2(\cos^2(x)-\sin^2(x)) = 2(\cos^2(x)-(1-\cos^2(x)))\\\\=2(2\cos^2(x)-1)=2\left(\dfrac{2}{\sec^2(x)}-\dfrac{\sec^2(x)}{\sec^2(x)}\right)\\\\=\boxed{\dfrac{4-2\sec^2(x)}{\sec^2(x)}}[/tex]
A group fitness gym classifies its fitness class attendees by class type and member status. The marketing team has gathered data from a random month, in which there
were 2039 class attendees. The data is summarized in the table below.
Class Type and Member Status of Class
Attendees
Class Type
Barre
Boot Camp
Boxing
Spinning
Yoga
Member
.240
204
288
191
177
Non-Member
185
155
234
271
94
What is the probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class?
Enter a fraction or round your answer to 4 decimal places, if necessary.
The probability that a class attendee is a non-member of the gym and is attending a barre class or is a member of the gym and is attending a boot camp class is 0.009.
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The marketing team has gathered data from a random month, in which there were 2039 class attendees.
The probability that a class attendee is a non-member of the gym and is attending a barre class
= 185/2039
= 0.09
The probability that a class attendee is a member of the gym and is attending a boot camp class
= 204/2039
= 0.10004
The probability for both the event would be
= 0.09 x 0.10004
= 0.009
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any solutions will each system of linear equations have? Match the systems with the correct number of
Solutions
Based on the information given, the correct options will be
y = x + 6 and 3x - 3y = -18 .... Infinitely many solutions.
y = -2x + 5 and 2x + y = -7 .... No solution.
y = -4x + 11 and -6x + y = 11 ... One solution.
Solving equations
y = -4x + 11 ....... equation i
-6x + y = 11 ...... equation ii
Put equation i into ii.
-6x + y = 11
-6x + (-4x + 11) = 11
-6x - 4x + 11 = 11
-6x - 4x = 11 - 11
-10x = 0
x = 0
Therefore, x = 0 and y = 11. This gives a solution for each variable.
y = -2x + 5 ..... i
2x + y = -7 ..... ii
Put equation I into ii
2x + y = -7
2x + (-2x + 5) = -7
2x - 2x = -7 - 5
0 = -12
This indicates no solution.
y = x + 6 ..... i
3x - 3y = -18 ..... ii
Put equation I into ii
3x - 3y = -18
3x - 3(x + 6) = -18
3x - 3x - 18 = -18
3x - 3x = - 18 + 18
0 = 0
This implies that there are infinitely many solutions.
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A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 65% salt and Solution B is 80% salt. She wants to obtain 120 ounces of a mixture that is 70% salt. How many ounces of each solution should she use?
The Rainbow Motor Motel is a 50-room facility with a restaurant to accommodate its guests. The motel is open 365 days a year, even on leap years; as Lurena Boucha, the proprietor, closes down the facility every February 29, her birthday, for an all day celebration of four years of successful operations. On the average, 98% of the rooms are available for sale. For the year just ended, the actual number of rooms sold totaled 15,000 and the number of guests for the year totaled 20,000. The projected occupancy rate for the next year is 82% of the available rooms based on past experience. The food information is as follows:
Sales $150,000, Beg Inventory 8,000, Purchases $70,000, Ending Inventory, $ 13,000 Consumption by employees (free of charge) $3,000, Number of checks 64,139. Cost of sales ?
From the information given, the cost of sales is $65,000. See the explanation below.
What is the definition of cost of sales?Add your initial inventory to the purchases made over the time period, remove that amount from your ending inventory, and that is your cost of sales.
Cost of Sales = (Bi + P) - Ei
Where Bi is Beginning Inventory
P is Purchases; and
Ei is Ending Inventory.
So the derivation of the solution above is?Beginning Inventory = 8,000
(add) Purchase = 70,000
Bi + P = 78,000
Ending Inventory = 13,000
Cost of sales = 78,000 - 13,000
= $65,000
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D
4
3
2
1
-5 -4 -3 -2 -1 0
1
2
GO
-4
-5
A
1
2
3 4 5 Match the graph with its equation
This graph represents the equation y = -3
Triangle X Y Z is shown. The length of X Z is 12, the length of Y Z is 11, and the length of Y X is 6.
A scalene triangle has the lengths 6, 11, and 12. Keyla uses the law of cosines to find the measure of the largest angle. Complete her work and find the measure of angle Y to the nearest degree.
1. 122 = 112 + 62 − 2(11)(6)cos(Y)
2. 144 = 121 + 36 − (132)cos(Y)
3. 144 = 157 − (132)cos(Y)
4. −13 = −(132)cos(Y)
According to law of cosines if the lengths of triangle are 12,11,6 then the angle will be 114=157-132cos(Y)
Given the length of XZ is 12, length of YZ is 11 and the length of YX=6.
According to law of cosines the angle of a triangle when the length of sides are given can be written as:
[tex]c^{2} =a^{2} +b^{2} -2abcosd[/tex]
where c is the side opposite to the angle which we have to find and a and b are the rest sides.
We have to put the values of sides in the above law:
[tex]12^{2} =6^{2} +11^{2} -2*6*11cosY[/tex]
144=36+121-132 cos Y.
Hence the angle can be written as 144=36+121-132 cos Y.
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can someone help me
Answer:
See Pictures
Step-by-step explanation:
Name the corresponding part if polygon WXYZ ≅ polygon PQRS.
Question: QP =
The corresponding part of PQ is WX
How to determine the corresponding parts?The congruent statement is given as:
polygon WXYZ ≅ polygon PQRS.
This means that the corresponding points are:
W and P, X and Q, Y and R, Z and S
When two points Q and P are joined together, we have:
polygon WX ≅ polygon PQ
Hence, the corresponding part of PQ is WX
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Determine whether each set of data can be modeled by an exponential function. If so, find the exponential
function that fits the data.
Answer: The data cannot be modeled by an exponential function because the data is for a linear function (as there is a constant increase in f(x) each time x increases by 1)
Given log base 2 =1/6, what is log base 4
Answer:
log x to the base 2 +log x to the base 4 =2
or log x/ log 2+ log x /lig 4 =2
or log x /log2 + log x /2.log 2 = 2
or log x/log 2(1+1/2)= 2
or log x/log 2 = 4/3
or 3.log x =4.log2
or logx^3=log 2^4
or x^3= 2^4
or x =(2)^4/3 or 2.(2)^1/3 ,Answer.
hope this helps
Step-by-step explanation:
Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation and in set
builder form using a compound inequality.
Note: To type in the sign, type <= or use the Math Quill by clicking the yellow arrow.
Answer:
Domain: Interval notation is [tex](-3, 4][/tex], set builder is [tex]\{x|-3 < x\leq4 \}[/tex]Range: Interval notation is [tex][0, 3)[/tex], set builder is [tex]\{y|0\leq y < 3\}[/tex]Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
In the figure shown below, AC is parallel to DE with transversal BF
Determine the values of x and y
PLEASE SHOW WORK FOR THIS!
x=_______
y=_______
Answer:
X = 142°Y = 38°Given - AC is parallel to DE
angle 3y + 28 = angle X ( Vertically opposite angles are equal).
3y + 28 = X
X + Y = 180° ( supplementary angles).
3y - X = (-28)
Solving both the equation we get
multiply eq 1 with 3
3x + 3y = 540
-X + 3y = (-28)
subtracting
4x = 568
x = 142°
3y + 28 = 142
3y = 142 - 28
3y = 114
y = 38°
If f(x) = 2x+6 and g(x)= x3 what is (g f)(0)?
Answer:
[tex]27[/tex]
Step-by-step explanation:
[tex]g(f(0))=g(2(0)+3)=g(3)=3^3=27[/tex]
HELP me find percentage qwq
Answer:
option B or 40%
Step-by-step explanation:
Well if 14/35 of the class is male. You divide 14 by 35. And after using calculator I see the answer is 40% of the class is male.
Thank
Quadrilateral WXYZ has vertices W(2, 10), X(10, 10), (10,2), and Z(2, 2). Determine if quadrilateral WXYZ is a rhombus.
A. No, quadrilateral WXYZ is not a rhombus.
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
C. Yes, quadrilateral WXYZ is a rhombus because the slopes of the diagonals are perpendicular.
D. There is not enough information to determine.
Please select the best answer from the choices provided
Answer:
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
Step-by-step explanation:
1) according to the given coordinates the equations of the sides are:
YZ: y=2; WZ: x=2; WX: y=10; XY: x=10. It means
2) YZ⊥WZ; YZ⊥XY; WX⊥XY; WX⊥WZ. To the additional, WX=WZ=YZ=XY, then
3) the given quadrilateral is sqare (rhombus with angles m∠=90°).
4) finally, the correct answer is
B. Yes, quadrilateral WXYZ is rhombus because the sides are perpendicular.
Which ordered pair is a solution of the equation?
y=4x−7
Answer:
Unknown
Step-by-step explanation:
Hi! so you didn't add the ordered pair options but I will do my best :) so if you see the ordered pair (0.7) that could definitely be a solution because using the slope intercept form equation you gave I know that's our y Intercept. the slope is 4/1 so moving up 4 and to the right 1 or down 4 and to the left 1 on a graph could show you more points! If you don't want to draw it you could use Desmos and just put this equation in or give me the ordered pairs and I will give you your answer!
hope this helps :)
Assume that 900 births are randomly selected and 4 at the births are girls. Use subjective judgment to describe the number of girls as significantly high, significantly low, or neither
The number of girls are significantly low.
What is Probability ?Probability is the study of likeliness of an event to happen.
It is given that
900 births are randomly selected
The probability of birth of a boy or a girl is 1/2 = 0.5
Total chances of a girl is 900 * 0.5 = 450
The birth of girl observed is 4
Therefore the number of girls are significantly low.
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What should you substitute for y in the second equation (bottom equation) in order to solve the system by the substitution method?
Answer:
C. 3x - 9
Step-by-step explanation:
3x – y = 9 ___(1)
8x – 4y = 0 ___(2)
From (1) eq.
3x – y = 9
– y = 9 – 3x
y = - (-3x + 9)
y = 3x – 9
Hence, 3x - 9 should be substituted in the second equation to get the required answer.
Answer:
c
Step-by-step explanation:
solve for y in the first equation
y = 3x - 9
when you substitute, you will get a value of 9 for x and 18 for y
The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours. Daryl plans to be gone at least 6 hours, and he has a plant outside. If he wants the plant to remain in temperatures above -10° should Daryl move the plant to a warmer location before leaving
The inequality equation will be -5x + 20 < -10.
What is inequality?Inequality is defined as an equation that does not contain an equal sign.
The weather report says the temperature is 20°c and will drop 5°c per hour for the next 6 hours.
Daryl plans to be gone at least 6 hours, and he has a plant outside.
If he wants the plant to remain in temperatures above -10° should Daryl move the plant to a warmer location before leaving will be
The inequality equation will be
-5x + 20 < -10
where x is the number of hours.
Then we have
-10 < -5x + 20
5x > 30
x > 6 hours
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Ms. Jerome wants to buy identical boxes of art supplies for her 25
students. If she can spend no more than $375 on art supplies,
what inequality describes the price can she afford for each
individual box of supplies, b?
The inequality describes the price $375 she can afford for 25
individual box of supplies will be $375 ≥ 25x.
What is inequality?An inequality is comparison of two values, showing if one is less than, greater than, or simply not equal to another value.
Let the price of each box is $x.
The inequality describes the price can she afford for each
individual box of supplies will be $375 ≥ 25x.
Therefore inequality is $375 ≥ 25x.
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Evaluate the piecewise-defined function for the indicated values. I’m just unsure of how to solve when the value isn’t given directly. Namely, how to solve for b through d
The value of the function at t=0 is 9 , 6<x<7 is -t+5, 1<n<2 is 9, for [tex]m^{2} +1[/tex] is 9.
Given function which is 9 for 0 to 5 , -t+5 for 5 to 8 and [tex]\sqrt{t-1}[/tex] for 8<t<11.
A) We have to find the function at t=0 which is 9 because it lies between 0<=t<5.
B) In this we have to find the value of the function when x=t lies between 6 and 7. is -t+5.
C) In this we have to find the value of Q(n) when n lies between 1 and 2 and the value becomes 9 because it lies between 0 and 5.
D) In this we have to find the function at [tex]m^{2} +1[/tex] when m belongs to [tex]\sqrt{7} and \sqrt{10}[/tex] the value of m lies between 2 and 4 and the value of m square +1 lies between 3 and 5. Hence the value of function at m square plus one is 9.
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Given: A = { -1,5,6} B = {-1,2,3,4,6,8} Find the union of sets A and B.
Step-by-step explanation:
{-1,2,3,4,5,6,8} is the answer
Find the value of x.
2x
70
120
In a certain Algebra 2 class of 26 students, 16 of them play basketball and 9 of them
play baseball. There are 5 students who play both sports. What is the probability that
a student chosen randomly from the class plays basketball or baseball?
Answer:
.7692307692 or 10/26
Step-by-step explanation:
You solve this problem by finding the total number of sports playing students and dividing it by the total, in this case 26. Since we know there are 5 students that play both sports, you subtract that 5 from the total number of basketball plyers and baseball players, so 16-5=11 and 9-5=4, then add those together, so 11+4=15. From there you add back in the students that play both which is 5, so 15+5=20. 20/26 is your answer.
