Explanation
We are given the following:
[tex]\begin{gathered} Bag=\begin{cases}{2\text{ }blue\text{ }marbles} \\ {1\text{ }white\text{ }marbles} \\ {1\text{ }red\text{ }marbles}\end{cases} \\ Total\text{ }marbles=2+1+1=4 \end{gathered}[/tex]We are required to determine the following probabilities:
[tex]\begin{gathered} (a)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }red \\ (b)\text{ }a\text{ }red,\text{ }then\text{ }white \\ (c)\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue,\text{ }then\text{ }a\text{ }blue \end{gathered}[/tex]We know that probability is calculated as:
[tex]Prob.=\frac{Number\text{ }of\text{ }required\text{ }outcome}{Number\text{ }of\text{ }possible\text{ }or\text{ }total\text{ }outcome}=\frac{n(E)}{n(S)}[/tex]For Question A:
We can determine the probability of a blue, then a red as:
[tex]\begin{gathered} P(blue\text{ }and\text{ }red)=P(Blue)\times P(Red) \\ =\frac{2}{4}\times\frac{1}{4}=\frac{2}{16}=\frac{1}{8} \\ \therefore P(blue\text{ }and\text{ }red)=\frac{1}{8} \end{gathered}[/tex]For Question B:
We can determine the probability of a red, then white as:
[tex]\begin{gathered} P(red\text{ a}nd\text{ w}h\imaginaryI te)=P(Red)\times P(Wh\imaginaryI te) \\ =\frac{1}{4}\times{}\frac{1}{4}=\frac{1}{16} \\ \operatorname{\therefore}P(red\text{ a}nd\text{ w}h\imaginaryI te)=\frac{1}{16} \end{gathered}[/tex]For Question C:
We can determine the probability of a blue, then blue, then blue as:
[tex]\begin{gathered} P(blue,blue,blue)=P(blue)\times P(blue)\times P(blue) \\ =\frac{2}{4}\times\frac{2}{4}\times\frac{2}{4}=\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2}=\frac{1}{8} \\ \therefore P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]Hence, the answers are:
[tex]\begin{gathered} (a)\text{ }P(blue\text{ }and\text{ }red)=\frac{1}{8} \\ \\ (b)\text{ }P(red\text{ a}nd\text{ w}h\mathrm{i}te)=\frac{1}{16} \\ \\ (c)\text{ }P(blue,blue,blue)=\frac{1}{8} \end{gathered}[/tex]For a football game, 5,600 tickets were sold. The price for each adult ticket is $27.25, and the price for each childrens ticket is $12.00. The total revenue for the game was $117,311.50. How many children's tickets were sold for the football game?
We have a problem that can be solved with a system of equations.
First we need to identify the equations of the system.
We have two unknown variables, the number of adult's tickets sold and the number of children's tickets sold. Let's call them:
- number of adult's tickets sold: x
- number of children's tickets sold: y.
The total number of tickets sold, 5600, is the sum of these:
[tex]x+y=5600_{}[/tex]And since the prices are 27.25 (adult) and 12.00 (children), the total revenue (117311.50) will be the sum of these prices multiplyied by the number of tickets of each of them:
[tex]27.25x+12.00y=117311.50[/tex]So, the system of equations is:
[tex]\begin{gathered} _{}x+y=5600_{} \\ 27.25x+12.00y=117311.50 \end{gathered}[/tex]Since we want y the number of children's tickets sold, we can solve for the other varible, x, in one equation, and substitute into the other.
Solving in the first equation, we have:
[tex]\begin{gathered} x+y=5600 \\ x=5600-y \end{gathered}[/tex]And substituting into the other:
[tex]\begin{gathered} 27.25x+12.00y=117311.50 \\ 27.25(5600-y)+12.00y=117311.50 \\ 27.25\cdot5600-27.25y+12.00y=117311.50 \\ 152600-15.25y=117311.50 \\ -15.25y=117311.50-152600 \\ -15.25y=-35288.50 \\ y=\frac{-35288.50}{-15.25} \\ y=2314 \end{gathered}[/tex]Since y is the number of children's tickets sold, then the number of children's tickets sold is 2314.
If f(x) = 6x + 8(x + 2), find f-1(x).f-1(x) = (x - 16)/14f-1(x) = x +16/14f-1(x) = -x - 16/14f-1(x) = -x + 16/14
SOLUTION:
We want to find the inverse of f(x);
[tex]f(x)=6x+8(x+2)[/tex]We solve for x;
[tex]\begin{gathered} y=6x+8(x+2) \\ y=6x+8x+16 \\ y=14x+16 \\ y-16=14x \\ x=\frac{y-16}{14} \\ interchange\text{ }y\text{ }and\text{ }x \\ f^{-1}(x)=\frac{x-16}{14} \end{gathered}[/tex]Thus the answer is OPTION A
Identify any congruent figures in the coordinate plane. Explain. This is a fill in the blank question based off of the options that are listed down below!
Solution
For this case we can conclude the following:
triangle HJK ≅ triangle QRS because one is rotation of 90º about the origin of the other
Rectangle DEFG ≅ rectangle MNLP because one is a translation of the other
triangle ABC ≅ no given figure because one is not related by rigid motions of the other
I'll show you the picture of the question I'm struggling with
The proportion of the first row with the second row is
[tex]\frac{7}{12}=\frac{8}{16}=\frac{6}{12}=\frac{10}{20}=\frac{2}{4}=\frac{1}{2}[/tex]that is, we have the proportionality 1:2, which correspond to the pink square.
-16 = m - 3 solve m
m = -13
Explanations:-16 = m - 3
Add 3 to both sides of the equation
-16 + 3 = m - 3 + 3
-13 = m
m = -13
4/8=28/x show your work
Given:
[tex]\frac{4}{8}=\frac{28}{x}[/tex]Simplify the equation,
[tex]\begin{gathered} \frac{4}{8}=\frac{28}{x} \\ 4x=28(8) \\ 4x=224 \\ x=\frac{224}{4} \\ x=56 \end{gathered}[/tex]Answer: x = 56.
Solve each system by elimination 10x-2y= -44x+5y= -19
10x - 2y = -4 ==== (1)
4x + 5y = -19 ==== (2)
To solve the system we should make the coefficients of y have the same values to eliminate it, then
Multiply equation (1) by 5 and equation (2) by 2
5(10x) - 5(2y) = 5(-4)
50x - 10y = -20 ===== (3)
2(4x) + 2(5y) = 2(-19)
8x + 10y = -38 ===== (4)
Now add equations (3) and (4) to eliminate y
(50x+8x) + (-10y + 10y) = (-20 + -38)
58x + 0 = -58
58x = -58
Divide both sides by 58 to find x
x = -1
Substitute the value of x in equation (1) or (2) to find the value of y
4(-1) + 5y = -19
-4 + 5y = -19
Add 4 to both sides
-4 + 4 + 5y = -19 + 4
0 + 5y = -15
5y = -15
Divide both sides by 5 to find y
y = -3
The solution of the system is (-1, -3)
solve the system of equations by graphing. y = -5x + 4 andy = 3x + 4
1) To solve this System of Solutions graphically, we'll need to plot those lines described by those respective equations.
2) Let's set two tables
y=-5x +4
x | y
1 -1 ( 1,-1)
2 -6 ( 2,-6)
3 -11
y=3x + 4
x | y
1 | 7 ( 1,7)
2 |10 ( 2,10)
3 | 13
2.2 Let's plot those equations and interpret the results:
3) As these lines have point (0,4) as their common point. Therefore we can state that the solution for this consistent system is S=(0,4)
The circle below has center S. Suppose that m QR = 84°. Find the following.
Given:
[tex]\text{m}\hat{\text{QR}}=84^{\circ}[/tex]b) To find:
[tex]\angle QSR[/tex]We know that,
[tex]\hat{QR}=\angle QSR=84^{\circ}[/tex]Thus, the answer is,
[tex]\angle QSR=84^{\circ}[/tex]a) To find:
[tex]\angle QPR[/tex]We know that,
[tex]\begin{gathered} \angle QPR=\frac{1}{2}\angle QSR \\ \angle QPR=\frac{1}{2}(84^{\circ}) \\ \angle QPR=42^{\circ} \end{gathered}[/tex]Thus, the answer is,
[tex]\angle QPR=42^{\circ}[/tex]Patios Plus sold an outdoor lighting set for $119.95. The Markup on the set was $25.99. Find the selling price as a percent of cost. Round to the nearest percent
The selling price as a percent of the cost is given by the ratio between the selling price and the the cost. The selling price is given, which is $119.95 the cost is given by the difference between the selling price and the Markup($25.99). Combining all those informations in an equation, we have
[tex]\frac{119.95}{119.95-25.99}=1.27660706684\ldots[/tex]To write this as a percentage, we just multiply the ratio by 100.
[tex]1.27660706684\ldots\times100=127.660706684\ldots\approx128[/tex]The selling price is 128% of the cost.
How to: determine if the side lengths could form a triangle. use an inequality to prove your answer
We need to simply use the triangle inequality Theorem, This theorem state that the sum of the two side lengths of a triangle must always be greater than the third side.
Now let's check from the given lengths
16 + 21 = 37 and 37 is less than 39 which is the third side
Hence, it cannot form a triangle
Solve for x and simplify your solutions:x^2 = 63Select ALL the correct answers.answer choices include:18√79√7-3√73√7-18√7-9√7
In order to find the correct answers, let's simplify the equation by calculating the square root of both sides of the equation:
[tex]\begin{gathered} x^2=63\\ \\ x=\pm\sqrt{63}\\ \\ x=\pm\sqrt{3^2\cdot7}\\ \\ x=\pm3\sqrt{7} \end{gathered}[/tex]Therefore the correct options are 3√7 and -3√7.
Please give me an explanation and the answers on question 3
We will illustrate on how to find the inverse function.
First, recall that the inverse function is a function that given the output of a function, it will give you back the input out of which that output came from.
when athe function has a formula, we can follow some steps to find the inverse function. Suppose we are given the function
[tex]f(x)=3x+5[/tex]Now, we first change f(x) with the letter y. So we get
[tex]y=3x+5[/tex]now, we interchange variables x and y. So we get
[tex]x=3y+5[/tex]Finally we solve this equation for y. We will first subtract 5 on both sides and then divide both sides by 3. So we get
[tex]y=\frac{x\text{ -5}}{3}[/tex]and now we replace the y with the symbol of the inverse function. So we have that
[tex]f^{\text{ -1}}(x)=\frac{x\text{ -5}}{3}[/tex]Given the recursive formula shown, what are the first 4 terms of the sequence? A) 5, 25, 100, 400B) 5, 14, 60, 236C) 5, 25, 125, 625D) 5, 20, 80, 320
SOLUTION:
Step 1:
In this question, we have the following:
Step 2:
Given:
[tex]\begin{gathered} f(n)=5,\text{ if n =1,} \\ f(n)\text{ = 4 f(n-1) if n > 1} \end{gathered}[/tex][tex]\begin{gathered} f(1)\text{ = 5} \\ f(2)\text{ = 4 f(2-1) = 4 x f(1) = 4 x 5 = 20} \\ f(3)\text{ = 4f(3-1) =4 x f(2) = 4x20 = 80} \\ f(4)\text{ = 4 f(4-1)=4xf(3) = 4 x 80 = 320} \\ \text{Hence, the first 4 terms of the sequence are:} \\ 5,\text{ 20, 80 , 320 --- OPTION D} \end{gathered}[/tex]Question 4 When changing 67,430,000 to scientific notation, how many places is the decimal point mc 5 07
Observe that the given number is 67,430,000.
If we express it as a scientific notation, then we would have to move the decimal point 7 spots to the left.
[tex]6.743x\times10^{-7}[/tex]Therefore, the answer is 7.solve the following system y=5x-33x-8y=24
The given system is
[tex]\mleft\{\begin{aligned}y=5x-3 \\ 3x-8y=24\end{aligned}\mright.[/tex]We can multiply the first equation by 8, then we sum and solve for x.
[tex]\mleft\{\begin{aligned}8y=40x-24 \\ 3x-8y=24\end{aligned}\rightarrow3x=40x\mright.[/tex]Then we, solve for x.
[tex]\begin{gathered} 40x-3x=0 \\ 27x=0 \\ x=\frac{0}{27}=0 \end{gathered}[/tex]Now we use this value to find y.
[tex]\begin{gathered} 3x-8y=24 \\ 3(0)-8y=24 \\ -8y=24 \\ y=\frac{24}{-8}=-3 \end{gathered}[/tex]Therefore, the solution of the system is x = 0 and y = -3.what is the smallest angle of rotational symmetry of a pentagon
Answer:
72°
Step-by-step explanation:
Origin is completely 360° and its divided into 5 sides. So,360÷5=72°
PerioAlgebra 2NameUsing Linear Equations to Solve Problems Date1) The chess club is selling popcorn balls for $1.00 and jumbo candy bars for$1.50 each. This week they have made a total of $229 and have sold 79popcorn balls. How many candy bars have they also sold?
The popcorn balls cost $1.00 each
Jumbo candy bars cost $1.50 each
This week they have made a total of $229 and have sold 79
popcorn balls.
First, let's make a function with includes this information.
Let's say that popcorn balls are x and Jumbo candy bars are y.
So the function would be
1.00x+ 1.50y = 229
We already have the x value which represents the total of popcorn balls sold this week, so replace this value in the function:
1.00x+ 1.50y = 229
1.00(79)+ 1.50y = 229
79.00 + 1.50y = 229
Solve the equation for y to find the total of candy bars sold.
79 + 1.50y = 229
1.50y = 229 - 79
1.50y = 150
y = 150/1.50
y = 100
So the have sold 100 candy bars this week
Amer class, Mrs. Sandoval picked up several piece of paper containing students' work from SHAVN ELLA LEVI 263.140)14) + 2(3.4)() 602.86 units 21314)(a)) 2512 unit 23.425) - 2/3 4729 RUBY KATRINA LORENZO 22 28.141815) 218.1489 663.12 units 2[3.2) 203.4)(48) + 213.)(4) 30144 units Which student found the total surface area of a cylinder with a height that was two times greater than its radius? O Ruby O Lorenzo O Ella O Levi
we know that
the total surface of a cylinder is equal to
[tex]SA=2B+Ph[/tex]where
B us the area of the circular base
P is the circumference of the circular base
h is the height of the cylinder
we have
h=2r
so
[tex]B=\pi\cdot r^2[/tex][tex]P=2\pi\cdot r^{}[/tex]substitute
[tex]SA=2(\pi\cdot r^2)+(2\pi\cdot r)\cdot h[/tex]substitute the value of h
[tex]\begin{gathered} SA=2(\pi\cdot r^2)+(2\pi\cdot r)\cdot2r \\ SA=2\pi r^2+4\pi r^2 \\ SA=6\pi r^2 \end{gathered}[/tex]therefore
the answer is Rudybecauser=4 and h=8A team digs 12 holes every 20 hours, what is the unit rate?
The unit rate = 0.6 holes per hour
Explanation:Number of holes dug by the team = 12
Total time taken = 20 hours
The unit rate = (Number of holes) / (Time)
The unit rate = 12/20
The unit rate = 0.6 holes per hour
what is an equation of the line that passes through the point (-2,-3) and is parallel to the line x+3y=24
Solve first for the slope intercept form for the equation x + 3y = 24.
[tex]\begin{gathered} \text{The slope intercept form is }y=mx+b \\ \text{Convert }x+3y=24\text{ to slope intercept form} \\ x+3y=24 \\ 3y=-x+24 \\ \frac{3y}{3}=\frac{-x}{3}+\frac{24}{3} \\ y=-\frac{1}{3}x+8 \\ \\ \text{In the slope intercept form }y=mx+b,\text{ m is the slope. Therefore, the slope of} \\ y=-\frac{1}{3}x+8,\text{ is }-\frac{1}{3}\text{ or } \\ m=-\frac{1}{3} \end{gathered}[/tex]Since they are parallel, then they should have the same slope m. We now solve for b using the point (-2,-3)
[tex]\begin{gathered} (-2,-3)\rightarrow(x,y) \\ \text{Therefore} \\ x=-2 \\ y=-3 \\ \text{and as solved earlier, }m=-\frac{1}{3} \\ \\ \text{Substitute the values to the slope intercept form} \\ y=mx+b \\ -3=(-\frac{1}{3})(-2)+b \\ -3=\frac{2}{3}+b \\ -3-\frac{2}{3}=b \\ \frac{-9-2}{3}=b \\ b=-\frac{11}{3} \end{gathered}[/tex]After solving for b, complete the equation.
[tex]y=-\frac{1}{3}x-\frac{11}{3}\text{ (final answer)}[/tex]Find the solution of the system of equations. 2x + 3y=-4 , x + 9y = 13
(-5, 2)
1) Solving this Linear System with the method of Addition/Elimination:
2x + 3y=-4
x + 9y = 13 x-2 Multiply the whole equation by -2
2x +3y = -4
-2x -18y= -26
--------------------
-15y= -30
15y= 30 Divide both sides by 15
y = 2
2) Plug into the simpler equation y=2
x +9y = 13
x + 9(2) = 13
x +18 = 13
x =13-18
x= -5
3) So the answer is (-5, 2)
Let f(x)=x2-2 and g(x)=9-X. Perform the composition or operation indicated.(fg)(-7)
Given the functions below
[tex]\begin{gathered} f(x)=x^2-2 \\ g(x)=9-x \end{gathered}[/tex]We are to find (fg)(-x)
SOLUTION
First of all, we have to get (fg)(x)
[tex](fg)(x)=(x^2-2)(9-x)[/tex]Expand the function
[tex]\begin{gathered} (fg)(x)=x^2(9-x)-2(9-x) \\ (fg)(x)=9x^2-x^3-18+2x \\ \therefore(fg)(x)=-x^3+9x^2+2x-18 \end{gathered}[/tex]Let us now solve for (fg)(-7)
[tex]\begin{gathered} (fg)(-7)=-(-7)^3+9(-7)^2+2(-7)-18 \\ (fg)(-7)=343+441-14-18=752 \end{gathered}[/tex]Hence,
[tex](fg)(-7)=752[/tex]
(40s + 100t) + 6 distributive property to write the products in standard form
The given expression is
[tex](40s+100t)\div10[/tex]We will use the distributive property to solve it
Divide each term in the bracket by 10
[tex]\frac{40s}{10}+\frac{100t}{10}[/tex]Simplify each term
[tex]\begin{gathered} \frac{40s}{10}=4s \\ \\ \frac{100t}{10}=10t \\ \\ 4s+10t \end{gathered}[/tex]The answer in standard form is 4s + 10t
If f(x) = 2x + 3 and g(x) = 4x - 1, find f(4).A. 11B. 15C. 5D.17
You have the following expression for the function f(x):
f(x) = 2x + 3
In order to calculate the value of f(4), just replace x=4 into the function f(x) and simplify it:
f(4) = 2(4) + 3
f(4) = 8 + 3
f(4) = 11
Hence, the answer is:
A) 11
7. In physics, the equation PV = nRT is called the ideal gas law. It is used toapproximate the behavior of many gases under different conditions. Whichequation is solved for T?
ANSWER:
[tex]\frac{PV}{nR}=T[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]PV=nRT[/tex]We solve for T:
[tex]\begin{gathered} \frac{PV}{nR}=T \\ T=\frac{PV}{nR} \end{gathered}[/tex]Therefore, the correct answer is option 2.
There are 4 options on the dessert menu at a restaurant. Bill and Laura like all of the choices equally, so theyeach choose a dessert at random from the menu. What is the probability that Bill will choose apple pie andLaura will choose strawberry cheesecake for dessert? Express your answer as a decimal. If necessary, roundyour answer to the nearest thousandth.O 0.083O 0.250 0.938O 0.063
So Bill and Laura like all of the choices equally. This means that the probability of each of them choosing one out of the four is the same for each options. So this probability is 1 out of 4: 1/4. So the probability of Bill choosing apple pie is 1/4 and that of Laura choosing strawberry cheesecake is also 1/4. The probability of both making those choices at the same time is given by the product of the mentioned probabilities. Then the probability we are looking for is:
[tex]\frac{1}{4}\cdot\frac{1}{4}=\frac{1}{16}=0.063[/tex]Then the answer is the fourth option.
Find at least three solutions to the equation y = 3x - 1, and graph the solutions as points on the coordinate plane.Connect the points to make a line. Find the slope of the line.
To find a solution to the equation y = 3x - 1, we have to replace a variable by a number and compute the other variable.
Assuming x = 0, then
y = 3(0) - 1
y = 0 - 1
y = -1
Then, the point (0, -1) is a solution
Assuming x = 1, then
y = 3(1) - 1
y = 3 - 1
y = 2
Then, the point (1, 2) is a solution
Assuming x = 2, then
y = 3(2) - 1
y = 6 - 1
y = 5
Then, the point (2, 5) is a solution
In the next graph, the solutions and the line are shown
The slope of the line that passes through the points (x1, y1) and (x2, y2) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Replacing with points (0, -1) and (1,2) we can compute the slope, as follows:
[tex]m=\frac{2-(-1)}{1-0}=3[/tex]convert the rectangular equation to polar form.Assume a > 0x=18
To convert a rectangular equation to polar forma, we use
[tex]x=r\cos (\theta),y=r\sin (\theta)[/tex]In the equation x=18, we only have x, so
[tex]\begin{gathered} 18=r\cos (\theta) \\ r=\frac{18}{\cos(\theta)}=18\sec (\theta) \end{gathered}[/tex]Multiply.
7.
-2 7
-5 -6
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Write your answer in simplest form solve this
The simplest form of 7 × (-2/-5) × (7/-6) is - 49/15.
Multiplication of fractions:A whole number or another fraction is produced when one fraction is multiplied by another fraction. We all know that a fraction has two components: a numerator and a denominator. In order to multiply any two fractions, we must multiply the numerators and denominators, respectively.
Here we have
=> [tex]7. \frac{-2}{-5} .\frac{7}{-6}[/tex]
Can be multiplied as given below
=> [tex]7 \times\frac{-2}{-5} \times\frac{7}{-6}[/tex]
=> [tex]7 \times\frac{1}{5} \times\frac{7}{-3}[/tex]
=> [tex]-\frac{49}{15}[/tex]
Therefore,
The simplest form of 7 × (-2/-5) × (7/-6) = -49/15
Learn more about Fractions at
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