Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $15. For one performance, there were 65 tickets sold in all, and the total amount paid for them was $1500 . How many tickets of each type were sold?
The advance tickets were 35 in number and the same day ticket will be 30 in number.
What will be the number of tickets?To find out the number of the tickets sold we will give some notations so the notations are as follows:-
A= Cost of advance tickets=$30
S= cost of same-day ticket-=15
[tex]N_A=[/tex] Number of the advance tickets
[tex]N_S=[/tex]Number of same-day tickets.
The equations made by the given data will be:-
[tex]30N_A+15N_S=1500\\\\\\N_A+N_S=65[/tex]
By solving the above equations:-
[tex]N_S=30\ \ \ \ \ \ N_A=35[/tex]
Hence the advance tickets were 35 in number and the same day ticket will be 30 in number.
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Hello, help me please)
Answer:
Given equation:
[tex]10^{5x-2}=2^{8x-3}[/tex]
Take natural logs of both sides:
[tex]\implies \ln 10^{5x-2}= \ln 2^{8x-3}[/tex]
[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]
[tex]\implies (5x-2)\ln 10=(8x-3) \ln 2[/tex]
Expand brackets:
[tex]\implies 5x\ln 10 - 2\ln 10=8x \ln 2 -3 \ln 2[/tex]
Collect like terms:
[tex]\implies 5x\ln 10 - 8x \ln 2 =2\ln 10-3 \ln 2[/tex]
Factor left sides:
[tex]\implies x(5\ln 10 - 8 \ln 2) =2\ln 10-3 \ln 2[/tex]
[tex]\textsf{Apply log Power law}: \quad \ln_ax^n=n\ln_ax[/tex]
[tex]\implies x(\ln 10^5 - \ln 2^8) =\ln 10^2- \ln 2^3[/tex]
[tex]\textsf{Apply log Quotient law}: \quad \ln_a\frac{x}{y}=\ln_ax - \ln_ay[/tex]
[tex]\implies x\left(\ln\left(\dfrac{10^5}{2^8}\right)\right) =\ln\left(\dfrac{10^2}{2^3}\right)[/tex]
Simplify:
[tex]\implies x\left(\ln\left(\dfrac{3125}{8}\right)\right) =\ln\left(\dfrac{25}{2}\right)[/tex]
[tex]\implies x=\dfrac{\ln\left(\dfrac{25}{2}\right)}{\ln\left(\dfrac{3125}{8}\right)}[/tex]
[tex]\implies x=0.4232297737...[/tex]
In a particular region, for families with a combined income of $80,000 or more, 20% have no children, 30% have one child, 40% have two children, and 10% have three children. Use this information to construct the probability distribution for X, where x represents the number of children per family for this income group. Arrange x in increasing order and write the probabilities P(x) as decimals.
The probability distribution for x will be given below.
x 0 1 2 3
P(x) 0.20 0.30 0.40 0.10
What is a normal distribution?The Gaussian Distribution is another name for it. The most significant continuous probability distribution is this one. Because the curve resembles a bell, it is also known as a bell curve.
In a particular region, for families with a combined income of $80,000 or more, 20% have no children, 30% have one child, 40% have two children, and 10% have three children.
Let x be the number of children per family.
We have to construct a probability distribution for x from the given information.
x = 0, 1, 2, 3
For x = 0, the probability will be
P(x) = 20 / 100 = 0.20
For x = 1, the probability will be
P(x) = 30 / 100 = 0.30
For x = 2, the probability will be
P(x) = 40 / 100 = 0.40
For x = 2, the probability will be
P(x) = 10 / 100 = 0.10
Then the probability distribution for x will be given as
x 0 1 2 3
P(x) 0.20 0.30 0.40 0.10
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Sarah plays softball where a single is one base, a double is two bases, a triple is three bases, and a home run is four bases. In her last game, she only hit singles and triples, for a total of 14 bases. She had two more triples than singles. Choose the graph that best depicts this problem. graph the solution
Angle t= 37 degrees angle u=? Angle v= 63
Answer:
[tex]m <U = 80°[/tex]
Step-by-step explanation:
Before we start calculating we have to first note that the angles in a triangle always add up to 180°. Therefore in order to find the missing angle U we have to add both the angles we know, 37° and 63°, then subtract the sum from 180°
[tex]m < U = 180- (37 + 63) \\ \\ m < U = 180 - 100 \\ \\ m< U = 80[/tex]
i’m really stuck here
Answer:
sin(t) = 4*sqrt(5) / 21; cos(-t) = 19/21
Step-by-step explanation:
think of a right triangle with an adjacent leg a, opposite leg b, and hypotenuse c.
cos(t) = a/c = 19/21. so we can assume a=19 and c=21.
using Pythagorean's theorem, find b: b = sqrt(21^2 - 19^2) = 4*sqrt(5) or 8.944
since tan(t)> 0, b/a > 0 and a is positive so b must be positive. using this information, we know sin(t) = b/c = 8.944/21 or 4* sqrt(5) / 21
since cos x is an even function, cos(-x) = cos x so cos(-t) = cos(t) = 19/21
what is the angle in degrees between two consecutive spokes if there are 24 spokes in a wheel?
Answer:
15
Step-by-step explanation:
- 360 degrees in a complete circle you divide it by 24
360/24=15
How do I solve
[tex]2x^{2}+5x+2=0[/tex]
see the attachment...
hope it helps...!!!
Answer:
There are two solutions.
[tex]x_1 = -0.5\\x_2 = -2[/tex]
Step-by-step explanation:
Step 1
Use the formula of ax^2 + bx + c = 0 to find the coefficients.
[tex]a = 2\\b = 5\\c = 2[/tex]
Step 2
[tex]x=\frac{ (-b+/-sqrt(b^2-4ac))}{(2a)}\\x=\frac{ (-5 +/- sqrt(5^2-4*2*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(25-4*2*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(25-8*2))}{(2*2)}\\x=\frac{(-5 +/- sqrt(9))}{(2*2)}[/tex]
[tex]x = \frac{-5 +/- \sqrt{9} }{4}[/tex]
Step 3
[tex]9 = 3^2\\\sqrt{9} = \sqrt{3*3}\\\sqrt{3*3} = \sqrt{3^2}\\\sqrt{3^2} = 3[/tex]
Step 4
[tex]x_1=\frac{(-5+3)}{4} -- > x_2=\frac{(-5-3)}{4}\\x_1=\frac{(-5+3)}{4}\\x_1=\frac{-2}{4}\\x_1=-0,5[/tex]
[tex]x_2=\frac{(-5-3)}{4}\\x_2=\frac{(-8)}{4}[/tex]
[tex]x_2=-2[/tex]
Hope this helps.
Slope intercept form of an equation of a line
Answer:
Step-by-step explanation:
4a. yes: 5 = 3(2)-1 5 = 6 - 1 5 = 5
4b. No: 1 = 3(4) + 1
1 = 12 + 1
1 ≠ 13
4c. No; 1 = 3 - 3
1 ≠ 3
4d. yes; 7 = -3(5) + 22
7 = -15 + 22
7 = 7
4e. no; -8 = -2(-4)
-8 ≠ 8
4f. no; 8 = -2 + 11
8 ≠ 9
Graph: f(x) = (1/4)x
Step 1: Calculate the initial value of the function. f(0) =
Step 2: Plot the initial value of the function at (0, 1).
Step 3: Evaluate the function at two more points. f(1) = 1/4 f(-1) = 4
Step 4: Plot the points (1, 1/4) and (-1, 4)
Step 5: Identify the horizontal asymptote of the function. The asymptote is the line y = 0
Step 6: The smooth curve that includes these points and approaches the asymptote shows the graph of the function
The initial value of the function is f(0) = 1 and the graph of the function has been attached.
How to interpret graphs of functions?We are given the function f(x) = (1/4)ˣ
1) Now, the initial value of the function is;
f(0) = (1/4)⁰ = 1
2) The initial value of the function which is the coordinate (0, 1) can be plotted on the attached graph and the point is where the graph crosses the y-axis.
3) f(1) = (1/4)¹ = 1/4
4) The points (1, 1/4) and (-1, 4)
5) The horizontal asymptote will be a vertical line which will be the value of x when y = 0.
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PLEASE HELP ASAP *URGENT* 20 POINTS!!!!
Answer:
a5 = 122
Explanation:
Given:
a1 = 2an = -3aₙ₋₁ + 2Solve:
a1 = 2
a2 = -3a1+2 = -3(2)+2 = -4
a3 = -3a2 + 2 = -3(-4)+2 = 14
a4 = -3a3 + 2 = -3(14) + 2 = -40
a5 = -3a4 + 2 = -3(-40) + 2 = 122
Answer:
a₅ = 122
Step-by-step explanation:
What is a₅ for the sequence defined by:
[tex]\left\{\begin{array}{ccc}a_1=2\\a_n=-3a_{n-1}+2\\\end{array}\right\\\\\\\hrule[/tex]
Letting n=2:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{2-1}+2\\\\\\\\\Longrightarrow a_2=-3a_{1}+2\\\\\\\\\Longrightarrow a_2=-3(2)+2\\\\\\\\\therefore a_2=-4[/tex]
Letting n=3:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{3-1}+2\\\\\\\\\Longrightarrow a_3=-3a_{2}+2\\\\\\\\\Longrightarrow a_3=-3(-4)+2\\\\\\\\\therefore a_3=14[/tex]
Letting n=4:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{4-1}+2\\\\\\\\\Longrightarrow a_4=-3a_{3}+2\\\\\\\\\Longrightarrow a_4=-3(14)+2\\\\\\\\\therefore a_4=-40[/tex]
Letting n=5:
[tex]a_n=-3a_{n-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{5-1}+2\\\\\\\\\Longrightarrow a_5=-3a_{4}+2\\\\\\\\\Longrightarrow a_5=-3(-40)+2\\\\\\\\\therefore \boxed{\boxed{a_5=122}}[/tex]
If f is translated 4 units down to create g, which function represents g? A. g(x) = f(x) + 4 B. g(x) = f(x) - 4
Answer:
g(x) = f(x) - 4.
Step-by-step explanation:
4 down = -4
g(x) = f(x) - 4.
Bob walks dogs after school. He charges $43. 50 for 6 hours and $65.25.75 for 9 hours.
Enter an equation to represent the relationship. Let x represent the number of hours Bob works
and y represent the amount he charges.
The equation of the amount charged by Bob will be y = 7.25x.
What is an equation?
The equation in mathematics is the relationship between the variables and the number and establishes the relationship between the two or more variables.
Given that:-
Bob walks dogs after school. He charges $43. 50 for 6 hours and $65.25.75 for 9 hours.The equation will be generated as follow:-
6 hours = $ 43.50
1 hours = $ 7.25
9 hours = $ 65.2575
1 hours = $ 7.25
Let x represent the number of hours Bob works and y represent the amount he charges. The equation will be:-
y = 7.25x dollars.
Therefore the equation of the amount charged by Bob will be y = 7.25x.
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I really need help on this math problem, pls anyone that can help?!
Answer:
y = 3/2x + 6
Step-by-step explanation:
Equation of the given line
slope = rise/run = -2/3y-intercept = (0, -2)Equation is y = -2/3x - 2Perpendicular
Slope is the negative reciprocalm ⇒ -(1/[-2/3]) = 3/2Intersection point is (-2, 3)Using Point-slope equation
y - 3 = 3/2 (x + 2)y - 3 = 3/2x + 3y = 3/2x + 6WILL MARK BRAINLIEST 50 POINTS
Ben tracked the attendance in his class over a period of time and recorded the data in a frequency table.
Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots
The data recorded by Ben shows the attendance log of his classmates over a given period of time.
What is a Dot Plot?This refers to a simple chart that resembles a histogram that is used to represent small data.
Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,
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what is the sign of a times -b/b when a = 0 and b < 0?
The sign of a times -b/b when a = 0 and b < 0 is neutral neither negative nor positive .
What is a integers ?An integer is a whole number (not a fractional number) that can be positive, negative, or zero
As b<0 which means b would be negative.
So, -b/b gives a negative value.
Because if any of the either numerator or denominator is negative then the resulting value also be negative.
and if zero '0' is multiplied and number whether it is positive or negative the resulting value will be zero.
So, a* (-b/b)= 0* negative= negative zero, but zero is neither negative nor positive .
hence, the sign of a times -b/b is neutral neither negative nor positive .
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4. (1) Solve forx: 13 11 3x+16 65
Step-by-step explanation:
13113x+1665
_____________________________
Rewrite 13113 as 9 . 1457
Rewrite 1665 as 9 . 185
= 9 . 1457x + 9 . 185
=9(1457x + 185)
ANSWER THIS CORRECTLY FOR BRAINLIEST (algebra)
Answer:
267.95 cubic meters
Explanation:
volume of sphere: (4/3)π(radius)³
Here given:
radius: 4 meterVolume:
(4/3)π(radius)³insert values
(4/3)(3.14)(4)³simplify
(4/3)(3.14)(64)final answer
267.95 cm³Answer:
V = 267.95
Step-by-step explanation:
The equation to find the volume of a sphere is:
V = [tex]\frac{4}{3} \pi r^{3}[/tex]
r = radius
In the diagram of the question it shows that the radius is 4 m. Plug this into the equation:
[tex]V=\frac{4}{3} (3.14) (4)^{3}[/tex]
Use a calculator to find the answer and then round to two decimal points:
V = 267.95
Hope this helps!!
Jen spent $12 on school supplies. Percy spent 3 times as much on school supplies, and also bought a reusable water bottle for $6. How much money did Percy spend?
1 block is labeled Jen's purchase, 12 dollars. A rectangle divided into 4 blocks is labeled Percy's purchase. 1 of the blocks is labeled 6 dollars. 12 times 3 = 36. 36 minus 6 = 30.
What error did Percy make in his calculation? its C i guessed it correct
Answer:
12 * Answer:
12 x 3 = 36 + 6 = 42,
Step-by-step explanation:
Step-by-step explanation:
Find mKNL.
A. 264
B. 196
C. 184
D. 247
Applying the angle of intersecting secants and tangents theorem, m(KNL) is: A. 264°.
What is the Angle of Intersecting Secants and Tangents Theorem?The angle of intersecting secants and tangents theorem states that the angle formed outside a circle has a measure that equals 1/2 the positive difference of the measures of the intercepted arcs.
60 = 1/2(18x - 6 - 5x - 17) [angle of intersecting secants and tangents theorem]
Solve for x
2(60) = 13x - 23
120 = 13x - 23
120 + 23 = 13x
143 = 13x
x = 143/13
x = 11
m(KNL) = (18x - 6 + 5x + 17)
m(KNL) = 23x + 11
Plug in the value of x
m(KNL) = 23(11) + 11
m(KNL) = 264° (option A)
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A right triangular prism and its net are shown below.
(All lengths are in centimeters.)
Answer:
Below in bold.
Step-by-step explanation:
a) The rectangle in the middle of the net is 10 cm long.
A = 8
B = 3
C = 6
D = 10
b) Surface area
= 3*6 + 3*10 + 3*8 + 2 * 1/2 + 8 * 6
= 18 + 30 + 24 + 48
= 120 cm^2
[tex]sa = bh + ( b_{1} + b_{2} + b_{3})l[/tex]
[tex]sa = 6(8) + (6 + 8 + 3) \times 10[/tex]
[tex]sa = 48 + (17)(10)[/tex]
[tex]sa = 48 + 170[/tex]
[tex]sa = 220 \: {cm}^{2} [/tex]
The graph of y+21 > 6 is
Answer:
Image attached below.
Step-by-step explanation:
Hello!
First let's isolate y:
y + 21 > 6y > -15This means that we are looking at all the values on the coordinate plane that are above the line y = -15.
The red shaded region is the solution region. Note that -15 is not a solution of y > -15 (the dotted line indicates that).
What is the value of tan(60°)?
A
01
12
300
03
03
2.
В
60°
6
п
с
Answer:
√3 is the answer
Step-by-step explanation:
the value of tan60 is √3
A camera has a listed price of $615.99 before tax. If the sales tax rate is 9.25%, find the total cost of the camera with sales tax included. Round your answer to the nearest cent, as necessary.
Answer:
559.01 i think that is rounded correctly
Step-by-step explanation:
so it did $615.99 - 9.25% = 559.010925
Hope This Is Good And Helped Sorry If i Did It Worng
The rectangular prism below has a base area of 44 units2 and a height of 6 units. Find
its volume.
The volume of the rectangular prism given its base area and its height is 264 units³.
What is the volume?A rectangular prism is a three-dimensional object that has six faces, 12 sides and 6 vertices.
Volume = length x width x height
base area x height
44 x 6 = 264 units³
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the camera cost $540 if the sales tax is 7.2% what is the tax change and the total cost?
Answer:
38.88
Step-by-step explanation:
Convert the problem to an equation using the percentage formula: P% * X = Y.
P is 10%, X is 150, so the equation is 10% * 150 = Y.
Convert 10% to a decimal by removing the percent sign and dividing by 100: 10/100 = 0.10.
Given the following equation, what is the slope of the linear function?
Answer:
2/3
Step-by-step explanation:
The slope sits next to the x in the slope-intercept equation, y=mx+b. Slope is the m. In the equation in the problem y=2/3x-2.
The slope is 2/3.
Pam bought a pair of shoes on sale for $22.40. If this was 20%. Off the original price, find the original price of the shoes
Answer:
26.88
Step-by-step explanation:
20%*22.40=4.48
22.40+4.48=26.88
PLEASE HELP 20 POINTS!!
[tex]\text{First term,} ~a = 72\\\\\text{Common ratio,}~ r = \dfrac{-36}{72} =-\dfrac 12 \\\\\text{Sum of an infinite geometric series,}\\\\S_{\infty} = \dfrac a{1 - r}\\\\\\~~~~~= \dfrac{72}{1+ \dfrac 12}\\\\\\~~~~~=\dfrac{72 }{\tfrac 32}\\\\\\~~~~~=\dfrac{72 \times 2}3\\\\\\~~~~~=48[/tex]
Series: 72 - 36 + 18 - 9 +...
[tex]\sf S \infty \ =a_1 \ x \ \dfrac{1}{1-r}[/tex]
Identify the following
a1 = 72 - 36r = (18-9) ÷ (72-36) = 1/4Solve:
[tex]\rightarrow \sf S \infty \ =(72-36) \ x \ \dfrac{1}{1-\frac{1}{4} }[/tex]
[tex]\rightarrow \sf S \infty \ =48[/tex]
This series has a sum of 48.
URGENT!!!! What is the number of solutions in this system?
A None
B one
C Infinite
Answer:
C? Not 100% sure
Step-by-step explanation: