The original price of concert tickets before the addition of service fee is 42.93
PercentageAmount spent on tickets including service fee = 45.50Percentage if service fee = 6%Original cost before service fee = x45.50 = x + (6% of x)
45.50 = x + (0.06 × x)
45.50 = x + 0.06x
45.50 = 1.06x
x = 45.50/1.06
x = 42.9245283018867
Approximately,
x = 42.93
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PLEASE ANSWER PLEASE ANSWER
2. The spread of the Ebola virus in Africa in 2014 could be modeled by where C(1) represents the number of cases, and t represents the number of days since May 1, 2014). (source: http://www.geert.io/exponential-growth-of
ebola.html) a. [3 pts] Approximately how many cases were there on May 1, 2014 (round to two decimal places)?
b. [3 pts] How many cases were projected by November 24, 2014 (round to 2 decimal places)?
c. [4 pts] Find C(92) and explain what it means in the context of the problem.
(a) The number of cases on May 1, 2014, was approximately 188.59.
(b) The number of cases on November 24, 2014, was approximately 27107.76.
(c) C(92) = 1715.70.
This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.
Computed using the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
We are given that the spread of the Ebola virus in Africa in 2014 could be modeled by the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex], where C represents the number of cases and t represents the number of days since May 1, 2014.
(a) In the question, we are asked for the approximate number of cases on May 1, 2014.
Since, the date is May 1, 2014, t = 0.
Thus, the number of cases, C, can be calculated by putting t = 0, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(0) = 188.59e^{0.024*0}\\\Rightarrow C(0) = 188.59e^0\\\Rightarrow C(0) = 188.59[/tex]
Thus, the number of cases on May 1, 2014, was approximately 188.59.
(b) In the question, we are asked for the approximate number of cases on November 24, 2014.
Since, the date is November 24, 2014, t = 207.
Thus, the number of cases, C, can be calculated by putting t = 207, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(207) = 188.59e^{0.024*207}\\\Rightarrow C(207) = 188.59e^{4.968}\\\Rightarrow C(207) = 188.59*143.739121458\\\Rightarrow C(207) = 27107.76[/tex]
Thus, the number of cases on November 24, 2014, was approximately 27107.76.
(c) We are asked to find C(92).
This can be found by putting t = 92, in the exponential equation, [tex]C(t) = 188.59e^{0.024t}[/tex].
[tex]C(92) = 188.59e^{0.024*92}\\\Rightarrow C(92) = 188.59e^{2.208}\\\Rightarrow C(92) = 188.59*9.09750317953\\\Rightarrow C(92) = 1715.70[/tex]
Thus, C(92) = 1715.70.
This means that on the 92nd day from May 1, 2014, the number of Ebola cases in Africa was approximately 1715.70.
The complete question is:
"The spread of the Ebola virus in Africa in 2014 could be modeled by [tex]C(t) = 188.59e^{0.024t}[/tex] where C represents the number of cases and t represents the number of days since May 1, 2014. (source: http://www.geert.io/exponential-growth-of-ebola.html)
a. [3 pts] Approximately how many cases were there on May 1, 2014?
b. [3 pts] How many cases were projected by November 24, 2014?
c. [4 pts] Find C(92) and explain what it means in the context of the problem.
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The line segment AB has the endpoints (-21, -7) and (-6,3) Point C are partitions the line at a ratio of 4;1 What are the coordinates of point C?
The coordinates of point C are (-9, 1)
How to determine the coordinates of point C?The points are given as:
A = (-21, -7)
B = (-6, 3)
m : n = 4 : 1
The coordinates of point C is calculated as:
[tex]C = \frac{1}{m+n} *(mx_2 + nx_1, my_2+ ny_1)[/tex]
So, we have:
[tex]C = \frac{1}{4+1} *(4 * -6 + 1 * -21, 4 * 3+ 1 * -7)[/tex]
This gives
[tex]C = \frac{1}{5} *(-45, 5)[/tex]
This gives
C = (-9, 1)
Hence, the coordinates of point C are (-9, 1)
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A
C
Which choice correctly shows the line y
= -X?
NHH
1
-4-3-2-1 1 2 3 4
W23
-2
-3
31
2
1
#
B
D
31
21
2
1
-4-3-2-11 2 3 4
123
-2
The graph is shown in the attached image.
What is the unit price of a Mt. Dew if a six packs costs $2.70
Answer:
270 uits
Step-by-step explanation:
You are offered two different sales jobs. The first company offers a straight commission of 5% of the sales.
The second company offers a salary of $ 210 per week plus 2% of the sales. How much would you have to
sell in a week in order for the straight commission offer to be at least as good?
Answer:
The offers are equal at $7,000, after $7,000 more money will be made with a straight commission.
Step-by-step explanation:
.05x = .02x + 210 Subtract .02x from both sides.
.03x = 210 Divide both sides by .03
x = $7,000.
20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5)
20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5) = -115
Answer:
The simplified form of the above expressions solution is -115.
Step-by-step explanation:
Hello!20 x (-5) + 10x (-3) + (-5) × (-6)-(3x5).. given expression [tex] - 100 + 10( - 3) + ( - 5)( - 6) - 15 \\ - 100 - 30 + ( - 5)( - 6) - 15 \\ - 100 - 30 + 30 - 15 \\ - 130 + 30 - 15 \\ - 100 - 15 \\ - 115[/tex]_+_+_= 30
Use only
1,3,5,7,9,11,13,15
You can repeat it
Answer
1 possible solution:
(5x7) in the first blank
(-3!) in the second blank
(-1) in the third blank
Step-by-step explanation:
(5x7) + -(3!) + -(1) 3! equals 3x2x1 or 6
35 + (-6) + (-1)
Determine what type of model best fits the given situation:
Answer:
B. quadratic function graph
A jar of tickets for a drawing contains 22 winning tickets and 63 non-winning tickets. What are the odds against winning in the drawing? please help
Answer: 22/85
Step-by-step explanation:
Answer:
22/85
Step-by-step explanation:
Find the z-scores for the two normally distributed random variables, measured using different units of length.
a) x = 22 in, where X comes from N (15, 2.5)
b) y = 55.88 cm, where Y comes from N (38.1, 6.35)
Using the normal distribution, the z-scores are given as follows:
a) Z = 2.8.
b) Z = 2.8.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.Item a:
The parameters are:
[tex]\mu = 15, \sigma = 2.5[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{22 - 15}{2.5}[/tex]
Z = 2.8.
Item b:
The parameters are:
[tex]\mu = 38.1, \sigma = 6.35[/tex]
Hence the z-score is:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{55.88 - 38.1}{6.35}[/tex]
Z = 2.8.
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1. Based on the circular
angle below. What is the
best measurement
the angle?
for
a. less than 90°
b. more than 90°
C. more than 180°
d. less than 60°
Answer:
B. More than 90
Step-by-step explanation:
Hope this helps!
Evaluate the following expression when y=2.
9y−8y+2
Answer:4
Step-by-step explanation: 9y-8y+2, when y=2
9(2)-8(2)+2=
18-16+2
=4
Which expression is equivalent to √2+4?
OA. (2+4)²
OB. (2+4)²
OC. 6
D. 62
Find the equation of an ellipse satisfying the given conditions.
Foci: (-4, 0) and (4, 0); length of major axis: 14?
The equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
How to determine the ellipse equation?The given parameters are:
Foci: (-4, 0) and (4, 0)Length of major axis = 14The above means that:
c = 4 and
The semi-major axis, a = 7 i.e 14/2
Calculate b using
[tex]b = \sqrt{c^2 + a^2[/tex]
So, we have:
[tex]b = \sqrt{4^2 + 7^2[/tex]
[tex]b = \sqrt{65[/tex]
Square both sides
[tex]b^2 = 65[/tex]
The standard form of the ellipse is represented as:
[tex]\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1[/tex]
This gives
[tex]\frac{x^2}{7^2} + \frac{y^2}{65} = 1[/tex]
Evaluate
[tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
Hence, the equation of the ellipse is [tex]\frac{x^2}{49} + \frac{y^2}{65} = 1[/tex]
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Given AB=10cm, CD=11cm, and AD=39cm, find the length of BC
Answer:
BC = 18 cm
Step-by-step explanation:
As we can see from the diagram:
AB + BC + CD = AD
⇒ 10 cm + BC + 11 cm = 39 cm
⇒ BC + 21 cm = 39 cm
⇒ BC = 39 cm - 21 cm
⇒ BC = 18 cm
How many liters each of a 35% acid solution and a 80% acid solution must be used to produce 60 liters of a 65% acid solution? (Round to two decimal places if necessary.)
Solving a system of equations we will see that we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.
How many liters of each solution do we need to use?
First, we need to define the variables:
x = liters of the 35% acid used.y = liters of the 80% acid used.We know that we want to produce 60 liters of 65% acid, then we have the system of equations:
x + y = 60
x*0.35 + y*0.80 = 60*0.65
(in the second equation we wrote the percentages in decimal form).
To solve this we need to isolate one of the variables in one equation and then replace it in other one, isolating x we get:
x = 60 - y
Replacing that in the other equation:
(60 - y)*0.35 + y*0.80 = 60*0.65
y*(0.80 - 0.35) = 60*(0.65 - 0.35)
y*0.45 = 60*0.30
y = 60*0.30/0.45 = 40
So we need to use 40 liters of the 80% acid solution, and the other 20 liters are of the 35% acid solution.
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Which equations are examples of the Distributive Property of Multiplication over Addition? (Choose 2)
Answer: 5(5 + 9). This expression can be solved by multiplying 5 by both the addends. So, 5(5) + 5(9) = 25 + 45 = 70.
Step-by-step explanation:
Please help ASAP! Clear explanations are greatly appreciated!
Using a system of equations, it is found that her normal week is of €285.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
For this problem, the variables are given as follows:
Variable x: Her normal hours.Variable y: Her time and a half hours.The first equation, considering the first sentence, is given by:
x + 8y = 375.
The second equation, considering the second sentence, is given by:
x + 4y = 330.
Then the system is:
x + 8y = 375.x + 4y = 330.Multiplying the second equation by -2, the system is:
x + 8y = 375.-2x - 8y = -660.Adding the equations, we have that her normal week is given by:
x = 660 - 375 = €285.
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Evaluate 2-(-4)+(-y)2−(−4)+(−y)2, minus, left parenthesis, minus, 4, right parenthesis, plus, left parenthesis, minus, y, right parenthesis where y = 7y=7y, equals, 7.
(on khan academy)
The value of the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex] after substituting y = 7 is 108
Evaluation of ExpressionThe given expression is:
[tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex]
Simplifying the expression, we have:
[tex]2+4+y^2+4+y^2\\\\2y^2+10[/tex]
Substitute y = 7 into the simplified expression
[tex]2(7)^2+10\\\\=2(49)+10\\\\=98+10\\\\=108[/tex]
Therefore, after substituting y = 7, into the expression [tex]2-(-4)+(-y)^2-(-4)+(-y)^2[/tex], the resulting value is 108
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Answer: -1
Step-by-step explanation: khan academy
E and F are two events and that P(E)=0.2 and P(F/E)=0.6 what is P(E and F)
The probability of E and F expressed as P(E and F) equals;0.12
How to solve Conditional Probability?We are given;
P(E) = 0.2
P(F|E) = 0.6
Now, P(F/E) is known as conditional probability and it means the probability of event F given the probability of another event E. This can be expressed as; P(F|E) = P(E and F)/P(E)
Thus;
P(E and F) = 0.2 * 0.6
P(E and F) = 0.12
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Find all primes p, q such that p^2-p=37q^2-q
The pairs of prime numbers (p,q) such that p^2-p=37q^2-q is (43, 7)
How to determine the pairs of numbers?The expression is given as:
p^2 - p=37q^2 - q
The boundary or range of numbers of p and q is not given.
So, we make use of numbers between 2 (because 1 is not a prime number) and a very large number (say 1000000)
i.e. 2 ≤ p ≤ 1000000 and 2 ≤ b ≤ 1000000
Using the above range, we have the following program to determine the pairs of prime numbers (p, q).
for a in range(2,1000000):
for b in range(2,1000000):
if ((a* *2) - a) == (37 * (b* *2) - b):
print(str(a)+","+str(b))
The output of the above program is:
(43, 7)
The above represent all pairs of prime numbers (p,q) such that p^2 - p=37q^2 - q
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Find the surface area of the figure. For calculations involving π give both the exact value and an approximation to the nearest hundredth of a unit. Let r = 5 and h = 5
Answer:
100 pi = about 314.16
Step-by-step explanation:
the surface area of a cylinder: SA = 2πrh+2πr^2
we plug in the values of r and h, and get
SA = 50pi + 50pi = 100 pi, which is approximately 314.16
48.5 x 8.78
show your work ;)
How much would you need to deposit in an account in order to have $3000 in five years assume the account earns 6% interest compounded monthly
There are $2224.12 need to deposit in an account in order to have $3000 in five years.
What is future value?
Future value is the worth of a financial asset or investment on a specific future date. In other words, future value is the amount of money an investment will be worth, assuming a specific rate of return, after a specific amount of time (interest rate).
Given:
Future value = FV = $3000
Number of years = t = 5
Interest rate = r = 6% = 0.06
Compounding period = n = 12
We have to find the present value form given problem.
Consider, the Future value formula,
[tex]FV = PV(1 + \frac{r}{n})^n^*^t[/tex]
Plug the values in the above formula.
[tex]3000 = PV(1+\frac{0.06}{12})^1^2^*^5\\ 3000 = PV(1+0.005)^6^0\\3000 = PV(1.005)^6^0\\PV = 2224.11658[/tex]
PV = $2224.12
Hence, there are $2224.12 need to deposit in an account in order to have $3000 in five years.
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What is the measure of arc RT
The measure of arc RT is 156 degree.
Measure of arc RTGiven:
arc TRM=102°
Hence:
arc RST=2×1O2°
arc RST=204°
Measure of arc RT
arc RT= 2(180° - 102°)
arc RT = 2(78°)
arc RT = 156 degrees
Therefore the correct option is B.
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Which of the following sets of numbers could not represent the three sides of a triangle?
Answer:
Step-by-step explanation:
factor 18x^(2)+39x-15
Answer:
[tex]3(2x + 5)(3x - 1)[/tex]
Step-by-step explanation:
Hello!
We can first factor out the greatest common factor between the coefficients: 3.
[tex]f(x) = 18x^2 + 39x - 15[/tex][tex]f(x) = 3(6x^2 + 13x - 5)[/tex]Now, let's work with what we have inside the brackets.
Standard form of a quadratic: [tex]ax^2 + bx+ c = 0[/tex]
Given our equation: [tex]6x^2 + 13x - 5[/tex]
a = 6b = 13c = -5We need to find two numbers that add up to b (13) and multiply to ac (-30).
The two numbers are 15 and -2. Expand 13x to 15x and -2x and factor by grouping.
Factor by Grouping[tex]6x^2 + 13x - 5[/tex][tex]6x^2 -2x + 15x - 5[/tex][tex]2x(3x- 1) +5(3x - 1)[/tex][tex](2x +5)(3x - 1)[/tex]
Now, we simply add the other factor, 3, to the final factored form.
Factored Solution: [tex]3(2x + 5)(3x - 1)[/tex]
A solid cylinder of iron whose diameter is 18 cm and height 12 cm is melted and turned into a solid sphere. Find the diameter of the sphere so formed
Answer:
Diameter of sphere = 18 cm
Step-by-step explanation:
Volume of Cylinder and Sphere: Cylinder:Diameter = 18 cm
r = 18÷ 2 = 9 cm
h = 12 cm
[tex]\sf \boxed{\bf Volume \ of \ cylinder = \pi r^2h}[/tex]
= π * 9 * 9 * 12 cm³
Sphere:[tex]\sf \boxed{\text{\bf Volume of sphere = $\dfrac{4}{3} \pi r^3$}}[/tex]
Solid cylinder is melted and turned into a solid sphere.
Volume of sphere = volume of cylinder
[tex]\sf \dfrac{4}{3}\pi r^3 = \pi *9*9*12[/tex]
[tex]\sf r^{3}= \dfrac{\pi *9*9*12*3}{4*\pi }\\\\ r^{3}=9 * 9 *3 *3\\\\\\r = \sqrt[3]{9*9*9}\\\\ r = 9 \ cm\\\\diameter = 9*2\\\\\boxed{diameter \ of \ sphere = 18 \ cm}[/tex]
If you start at -4,3 move 8 units to the right and 10 units down, at what point on the graph would he end up? Which quadrant is the new point in?
Answer:
If you start at (-4,3) and move 8 units to the right and 10 units down, you would end up at the point (4,-7).
The point is located in the 3rd quadrant, where the x-coordinates are negative and the y-coordinates are negative.
It's important to note that moving 8 units to the right means moving to the positive direction on x-axis and moving 10 units down means moving to the negative direction on y-axis.
simplify. ((x/4)+(x/3))/(x/2)
Answer:
x/6
You're welcome! :)
Answer : 7/6
explanation is long