The rental cost of each movie is $4.50
The rental cost of each video game is $5.75
Explanation:let the cost of one movie = m
let the cost of one video games = v
1st month:
Number of movies = 5
number of video games = 6
Total cost of both = $57
Total cost = cost of one movie(Number of movies ) + cost of one video (Number of video games)
57 = m(5) + v(6)
57 = 5m + 6v ...equation 1
2nd month:
Number of movies = 3
number of video games = 2
Total cost of both = $25
Total cost = cost of one movie(Number of movies ) + cost of one video (Number of video games)
25 = m(3) + v(2)
25 = 3m + 2v ...equation 2
57 = 5m + 6v ...equation 1
25 = 3m + 2v ...equation 2
Using elimination method:
To eliminate v, we would multiply equation 2 by 3:
3(25) = 3(3m) + 3(2v) ...equation 2
75 = 9m + 6v ...equation 2
57 = 5m + 6v ...equation 1
subtract equation 1 from 2:
75 - 57 = 9m - 5m + 6v - 6v
18 = 4m + 0
18 = 4m
m = 18/4
m = 4.5
Substitute for m in any of the equation:
Using eqauation1: 57 = 5m + 6v
57 = 5(4.5) + 6v
57 = 22.5 + 6v
57 - 22.5 = 6v
34.5 = 6v
v = 34.5/6
v = 5.75
The rental cost of each movie is $4.50
The rental cost of each video game is $5.75
If there are four independent events E1, E2, E3, and E4, then the probability P(E1 and E2 and E3 and E4) equals ____________________.
Answer:
The probability of having all four events is;
[tex]P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]Explanation:
Given that there are four independent events E1,E2,E3 and E4.
[tex]E_1,E_2,E_3,E_4[/tex]The probability of having all the four events;
[tex]P(E_1-and-E_2-and-E_3-and-E_4)[/tex]would be the product of the probability of each of the events;
[tex]P(E_1-and-E_2-and-E_3-and-E_4)=P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]Therefore, the probability of having all the four events is;
[tex]P(E_1)\times P(E_2)\times P(E_3)\times P(E_4)[/tex]A survey of 130 freshmen business students at a local university produced the results listed below. How many students took only psychology?
We could draw the following Venn's diagram to solve this problem.
So, after drawing this diagram, we notice that the number of students that took only psychology were 9.
What is the relative value of F(x) when the value of x is close to 2 for the function F(x) = 1/x+2, whose graph is shown below?A. A very large numberB. ZeroC. A very small numberD. Either a very large number or a very small number
Answer:
D. Either a very large number or a very small number
Explanation:
Given the function:
[tex]F(x)=\frac{1}{x+2}[/tex]As can be seen from the graph, the point x=2 is an asymptote of the function.
Thus, the relative value of F(x) when the value of x is close to 2 is either a very large number or a very small number.
Option D is correct.
Based on sample data, newborn males have weights with a mean of 3242.4 g and a standard deviation of 844.4 g. Newborn females have weights with a mean of 3095.9 g and a standard deviation of 508.6 g. Who has the weight that is more extreme relative to the group from which they came: a male who weighs 1700 g or a female who weighs 1700 g?
The formula for calculating z score is expressed as
z = (x - μ)/s
where
x is the sample mean
μ is the mean
s is the sample standard deviation
Considering the newborn males,
x = 1700
μ = 3242.4
s = 844.4
Thus,
z = (1700 - 3242.4)/844.4
z = - 1.83
Considering the newborn females,
x = 1700
μ = 3095.9
s = 508.6
Thus,
z = (1700 - 3095.9)/508.6
z = - 2.74
The most extreme value is the z score that is furthest from zero. It is z = - 2.74. Thus, the female who weighs 1700 g is more extreme relatively
Since the z score for the male is z = - 1.83 and the z score for the female is z = - 2.74, the female has the weight that is more extreme.
7 m The side lengths of the base of a triangular prism are 7 meters, 5 meters, and 8 meters. The height of the prism is 12.5 meters. 12.5 m 6 m What is the lateral surface area of the prism in square meters? 5 m
Given a triangular prism with side lengths of the base as a, b, and c, and height h, then the lateral surface area, A is given by
[tex]A=(a+b+c)h[/tex]In our case,
[tex]a=5m,b=6m,c=7m,\text{ and }h=12.5m[/tex]Hence,
[tex]A=(5+6+7)12.5=18\times12.5=225m^2[/tex]Therefore, the lateral surface area in square meters is 225
Use the number line to determine if each number is a solution . And don't worry this is just a practice :)
what value of x makes this equation true?[tex]12x - 15 = 6 - 3x[/tex]
The value of x that makes the equation true is;
[tex]x\text{ = }\frac{7}{5}[/tex]Here, we want to get the value of x that makes the equation true
All have to do here is to solve the equation for x
We have this as follows;
[tex]\begin{gathered} 12x-15\text{ = 6-3x} \\ 12x\text{ + 3x = 6 + 15} \\ 15x\text{ = 21} \\ x\text{ = }\frac{21}{15} \\ \\ \text{ x = }\frac{7}{5} \end{gathered}[/tex]5/12×6/34 pls help me
The given numerical expression can be simplified as a fraction as 5/68 .
The given expression is 5/12 × 6/34
This is a multiplication of fractions.
therefore here we will multiply the numerators and divide it by the product of the denominators.
5/12 × 6/34
or , (5×6) ÷ (12×34)
or, 30 ÷ 408
or, 5 / 68
therefore the required expression is 5 / 68
Expressions are statements in mathematics that include variables, numbers, or both, as well as at least two terms connected by an operator. Addition, subtraction, multiplication, and division are examples of mathematical operations.
Expressions can be classified into two categories in mathematics: algebraic expressions, which also contain variables, and numerical expressions, which only contain numbers. It seems like a fixed amount of money.
A variable is a symbol without a known value. One constant, one variable, or a collection of variables and constants multiplied or divided can make up a term. The coefficient in an equation is a number that is further multiplied by a variable.
To learn more about expression visit:
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Instructions: Find the missing length indicated.x=Check81225X
Given: A right triangle is given, and an altitude is drawn to the hypotenuse of the triangle.
Required: To determine the missing side x.
Explanation: The given triangle is as follows-
Let the side of the triangle be as shown in the figure. Now triangle ABD is a right-angled triangle. Hence, by Pythagoras theorem, we have-
[tex]\begin{gathered} BD^2=AB^2+AD^2 \\ (225)^2=x^2+y^2\text{ ...}(1) \end{gathered}[/tex]Similarly, triangles ABC and ADC are right-angled triangles. Thus-
[tex]\begin{gathered} y^2=z^2+(144)^2\text{ ...}(2) \\ x^2=(81)^2+z^2\text{ }...(3) \end{gathered}[/tex]Equations (1), (2), and (3) represent equations in 3 variables. Hence solving equations (1) and (2) by substituting the value of y from equation (2) into equation (1) as follows-
[tex]\begin{gathered} x^2+z^2+(144)^2=(225)^2 \\ x^2+z^2=(225+144)(225-144) \\ x^2+z^2=369\times81 \\ x^2+z^2=29889\text{ ...}(4) \end{gathered}[/tex]Now, we can solve equations (3) and (4) for x as follows-
[tex]x^2+x^2+z^2=6561+z^2+29889[/tex]Further solving for x as-
[tex]\begin{gathered} 2x^2=36450 \\ x=\sqrt{18225} \\ x=\pm135\text{ units} \end{gathered}[/tex]Since the side of a triangle can't be negative. Hence, x=135 units.
Final Answer: The length of the missing side is-
[tex]x=135\text{ units}[/tex]Ahmad is putting 11 colored light bulbs into a string of lights. There are 5 green light bulbs, 4 yellow light bulbs, and 2 red light bulbs. How many distinct ordersof light bulbs are there if two light bulbs of the same color are considered identical (not distinct)?
So, we have a total of 11 light bulbs. 5 are green, 4 are yellow and two are red. In cases in which the light bolbs are considered identical, we use the following math formula:
[tex]N=\frac{n!}{n_g!n_{y!}n_r!}[/tex]In which n is the total, 11. ng is thee number of green lightbulbs, ny the number of the yellow ones, and nr the number of the reds. So:
[tex]\begin{gathered} N=\frac{11!}{5!4!2!} \\ N=\frac{11\cdot10\cdot9\cdot8\cdot7\cdot6\cdot5!}{5!\cdot24\cdot2} \\ N=11\cdot10\cdot9\cdot7 \\ N=6,930 \end{gathered}[/tex]So, Ahmad has 6,930 distinct orders
How do I simplify -88/4
Determine if the expression s3+s2+s5/4 is a polynomial or not. If it is a polynomial state the type and degree of the polynomial
Given the algebraic expression
[tex]s^3+s^2+s^{\frac{5}{4}}[/tex]For the algebraic expression to be classified as a polynomial, all expressions must have a non-negative integer exponent.
From the given expression, we can see that the last term doesn't obey this rule (an exponent that is in fraction term).
Hence, the expression given is not a polynomial.
ProbabilityHello need help Thank you. A phone number in Cameroon consists of 9 digits. From the theoretical capacity of the Cameroonian telephone network, say whether the 4 current operators (CAMTEL MTN, NEXTTEL and ORANGE) can meet a demand for 150 million subscriptions. 1) How many different ways can you arrange four people in four numbered chairs? 2)How many ways can you distribute 10 balloons to 3 children, 4 for the first and 3 for each of the other two?
Answer:
1) 24
2)66
Explanation:
1) How many different ways can you arrange four people in four numbered chairs?
Answer: we have 4 people ands 4 chairs, so we use the factorial of 4 to find the number of ways that we can arrenge the people:
[tex]4!\text{ = 4}\cdot3\cdot2\cdot1=24[/tex]we can arrange 4 people in 4 chairs in 24 different ways
2)How many ways can you distribute 10 balloons to 3 children?
To distribute "n" objects to "r" people (in this case n=10, and r = 3) we use the following combinarions formula:
[tex]C(n+r-1,r-1)[/tex]substituting our values we get:
[tex]C(10+3-1,3-1)[/tex][tex]C(12,2)[/tex]and since C(a,b) is defined as:
[tex]C(a,b)=\frac{a!}{b!(a-b)!}[/tex]For C(12,2) we get the following:
[tex]C(12,2)=\frac{12!}{2!(12-2)!}[/tex]which simplifies to:
[tex]C(12,2)=\frac{12!}{2!(10)!}=66[/tex]We can distribute 10 balloons to 3 people in 66 ways
The table below shows the value for the function y=f(x)If g(x)=1/2 which of the following are solutions to g(x) select all that applyA (-3,5.5)B(-1,-2)C(0,4)D (5,-8)
So we have a table of values that associate x values with a function f(x). The pairs (x,y) are solutions to the equation y=f(x) and they are:
[tex]\begin{gathered} (-3,5) \\ (-1,-4) \\ (0,2) \\ (5,-8) \\ (6,3) \end{gathered}[/tex]If we define a new function g(x)=(1/2)*f(x) its solutions will be those of f(x) but with their y values divided by 2. Then the solutions to g(x) are:
[tex]\begin{gathered} (-3,\frac{5}{2})=(-3,2.5) \\ (-1,-\frac{4}{2})=(-1,-2) \\ (0,\frac{2}{2})=(0,1) \\ (5,-\frac{8}{2})=(5,-4) \\ (6,\frac{3}{2})=(6,1.5) \end{gathered}[/tex]Then the only option with a solution to g(x) is the second option (-1,-2).
Which of the following is a simplified version of 11 + 4(x + 3) = 10? A 4x + 4 = 10 B В 4x + 23 = 10 15x + 3 = 10 15x + 45 = 10
11 + 4(x + 3) = 10
Apply distributive property:
11+ 4(x)+4(3) = 10
11+ 4x+12 = 10
Combine like terms:
4x+11+12 = 10
4x +23 = 10
kiran ran 1/5 the length of the road which is 9 miles how many miles did he run?
Answer:0.02
Step-by-step explanation:
After 3 hours, they are ____ miles apart. (Round to the nearest mile as needed.)
Since Mike drove at 65 mph for 3 hours, we have that he traveled:
[tex]3\cdot65=195\text{ miles}[/tex]for Sandra, we have the following:
[tex]3\cdot70=210\text{ miles}[/tex]notice that both trajectories with the distance apart segment form a right triangle, then, using the pythagoren theorem, we get:
[tex]x=\sqrt[]{(210)^2+(195)^2}=\sqrt[]{44100+38025}=\sqrt[]{82125}\approx287\text{ miles}[/tex]therefore, Sandra and Mike are approximately 287 miles apart after 3 hours
sin(??? ) O A. O V3 ОВ. 2 Oc. O D.
The correct option is D
[tex]-\frac{1}{2}[/tex]Explanation:[tex]\sin(\frac{7\pi}{6})=-\frac{1}{2}[/tex]The numbers of products a store sold on 4 consecutive days were x,x+5,x+3 and x+12. if the daily average of the products sold was 13. What is the value of x?
Answer:
x = 8
Step-by-step explanation:
average is calculated as
average = [tex]\frac{sum}{count}[/tex]
given daily average is 13 , then
[tex]\frac{x+x+5+x+3+x+12}{4}[/tex] = 13 ( multiply both sides by 4 to clear the fraction )
4x + 20 = 52 ( subtract 20 from both sides )
4x = 32 ( divide both sides by 4 )
x = 8
g(x) = 2x + 3, find g(a + 1). *
ANSWER:
g(a+1) = 2a + 5
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]g(x)=2x+3[/tex]Replacing, when x is a + 1:
[tex]\begin{gathered} g(a+1)=2\cdot(a+1)+3 \\ g(a+1)=2a+2+3 \\ g(a+1)=2a+5 \end{gathered}[/tex]3. B 8 cm 9 cm D F 5 cm x cm A CITO 4 CM Α' ο cm D' F O 75 cm o Scale Factor: Scale Factos
Scale factor on a map
question number 2! I already have the answer of the number one
If we have f(x) = sin(x), then:
[tex]f(2x)=\sin2x[/tex]f(2x) = sin(2x) is a vertical shrink if we compare it with f(x) = sin(x). Then, the graph of each function is:
I need to find how much does is his monthly payment.
The total amount Christian will pay is given by:
[tex]A=P(1+rt)[/tex]where P is the principal, r is the interes rate and t is the time. In this case we have that P=15000, r=0.07 and t=2. Then we have:
[tex]\begin{gathered} A=15000(1+0.07(2)) \\ A=17100 \end{gathered}[/tex]Hence he will pay $17,100 in total. Now, to find the monthly amount we divide the total by the number of months; in this case 24:
[tex]\frac{17100}{24}=712.50[/tex]Therefore he will pay $712.50 each month.
A chemist is using 328 milliliters of a solution of acid and water. If 13.7% of the solution is acid how many milliliters of acid are there? Round to nearest tenth
Hello
Let's find 13.7% of 328
[tex]\begin{gathered} \frac{13.7}{100}=\frac{x}{328} \\ x=\frac{13.7\times328}{100} \\ x=44.94 \end{gathered}[/tex]From the calculation above, 44.94mL of acid is present in the solution
find the volume of a right rectangular prism with the following measurements by multiplying The edge lengths. length 3/4 width 1/2 heigth 2/3
Explanation
The volume of a rectangular prism is given by:
[tex]\text{Volume}=\text{ length}\cdot width\cdot height[/tex]then,Let
length= 3/4
width=1/2
heigth=2/3
Now, replace,
[tex]\begin{gathered} \text{Volume}=\text{ length}\cdot width\cdot height \\ \text{Volume}=(\frac{3}{4}\cdot\frac{1}{2}\cdot\frac{2}{3}) \\ \text{Volume}=\frac{3\cdot1\cdot2}{4\cdot2\cdot3}=\frac{1}{4} \\ \text{Volume}=\frac{1}{4}\text{cubic units} \end{gathered}[/tex]I hope this helps you
Consider the following data set where “x” is a positive integer: {x+2, x+4, x-4, x-3, x+6} Which of the following statements are true? Select all that apply.A. The mode is x-4B. The median is x+2C. The mean is x+1D. None of above
Before start analyzing the mode, median and mean of the data set, we must organize it from lowest to highest:
{x+2, x+4, x-4, x-3, x+6}
↓
{x-4, x-3, x+2, x+4, x+6}
ModeThe mode is the most frequently repeated data. Since every data appears just one time, then this set has not mode.
MedianThe median is the data that is in the center. We find it just by counting the same numbers from left to right and from right to left:
The median is x+2
MeanThe mean is given by the addition of all the data, and the division by the number of data.
there are 5 values, then we should divide their sum by 5:
[tex]\begin{gathered} \frac{(x-4)+(x-3)+(x+2)+(x+4)+(x+6)}{5} \\ =\frac{x-4+x-3+x+2+x+4+x+6}{5} \\ =\frac{5x+5}{5}=x+1 \end{gathered}[/tex]The mean is x+1
ANSWERS: B and CSolve: x^3= -65 This is for homework
Step 1
Solve the equation by graphing
You can rewrite the equation as
[tex]x^3+65=0[/tex]step 2
Using a graphin calculator as Desmos
x=-4.021
The solution is x=-4.021
-
what is 8 × 2000? and
simple, it's a multiplication
I multiply the number of atoms with the weight of each one to find the total weight of the gas
[tex](5.04\times10^{23})\times(1.67\times10^{-24}^{})[/tex]We group
[tex](5.04\times1.67)\times(10^{23}\times10^{-24})[/tex]and solve
[tex]\begin{gathered} (8.4168)\times(10^{-1}) \\ =0.84168 \end{gathered}[/tex]the result is: 0.84 grams
What effect does changing the function f(x)=3sin(x)+1to the function g(x)=3sin(x4)+2 have on the graph of f(x)?
Step 1
The parent function f(x) is given as;
[tex]f(x)=3\sin (x)+1[/tex]If we transform the function by adding 1 to it we will have;
[tex]\begin{gathered} f(x)=3\sin (x)+1+1 \\ f(x)=3\sin (x)+2 \end{gathered}[/tex]We have the following graph;
which means when you add 1 to the to get f(x)=3sin(x)+2, the function is shifted up by 1 unit.
Step 2
If the function is further transformed to;
[tex]f(x)=3\sin (\frac{x}{4})+1[/tex]we will have the graph below;
This means that the graph stretches horizontally by a factor of 4.
Therefore the changes f(x) passes through to g(x) are;
[tex]\begin{gathered} f(x)=2\sin (\frac{x}{4})+1_{}--(A\text{ horizontal stretch by a factor of 4)} \\ g(x)=2\sin (\frac{x}{4})+2---(A\text{ shift up by 1 unit)} \end{gathered}[/tex]Answer; The graph is stretched horizontally by a factor of 4 and shifted up by 1 unit.
Calculator 5 ft С A window in the shape of a parallelogram has the dimensions given What is the area of this window?A.20 ftB.24 ftC.28 ftD.40 ft
Area of a parallelogram = b x h