The expected value for player A is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]The expected value of player B is:
[tex]\begin{gathered} (\frac{1}{2}\times\frac{1}{2}\times2)-(1\times\frac{1}{2}\times\frac{1}{2}) \\ =(\frac{1}{4}\times2)-(1\times\frac{1}{4}) \\ =(\frac{1}{2})-(\frac{1}{4}) \\ =\frac{1}{4} \end{gathered}[/tex]a sign says that the price marked on all mysic equipment is 30% off the original price. You buy an electric guitar for the sale price of $315. b. How much money did you save off the original price of the guitar?
30% off the prices means that the there is a discount of 30% on the original price.
If 30% discount is given, then it means that the new cost price will be = 100% -30% the original price
=> 70% the original price
Since the Electric Guitar was sold at $315
Then it means that 70% the original price = $315
Let the original price be P
then 70% of P = $315
[tex]\begin{gathered} 70percent=\frac{70}{100}\text{ = 0.7} \\ \end{gathered}[/tex]70% of P = 0.7 x P = 0.7P
Question A.
We can then obtain P, the original price by equatin to $315
=> 0.7P = $315
To get P, divide both sides by the coefficient of P
[tex]\frac{0.7p}{0.7}=\frac{315}{0.7}[/tex]P = $450
Orignal Price of Guitar = $450
Question B
Amount saved = Original Price - Selling Price
Amount saved = $450 -$315
=> Amount saved = $135
Paul is driving his car. At the end of two hours he has driven 68 miles, then at the end of 4 hours he has driven 132 miles. What is his average rate of change?_(blank)_miles per hourType your numerical answer below.
This problem describes two points in a route of 4 hours. He went through 68 miles after the first two hours, and 132 miles after 4 hours of driving. We need to calculate the average rate of change.
The average rate of change is the division between the total distance and the time it took to travel that distance, so we have:
[tex]r=\frac{132}{4}=33\text{ miles per hour}[/tex]The average rate of change is equal to 33 miles per hour.
Explain how you know and i'll mark as brainlist.
Answer: They have the same area.
Step-by-step explanation:
Here you just have to count the small squares.
In the blue shape, you can see there are 16 small squares.
And in the green shape, there is also 16 squares.
And the small squares are all equal.
So they both have the same area.
The length of a rectangular rug is 4 less than twice its width. The perimeter of the rug is 34 feet. What is the area?
My first step is always to draw a picture
We are told the length is 4 less than twice the width
l = 2w-4
We are told the perimeter is 34
P =2(l+w)
Substitute the first equation in for l
P = 2( 2w-4 + w)
Combine like terms
34 = 2( 3w-4)
Distribute the 2
34 = 6w -8
Add 8 to each side
34+8 = 6w-8+8
42 = 6w
Divide by 6
42/6 = 6w/6
7 =w
Now we can find l
l = 2w-4 = 2(7) -4 = 14-4 = 10
The question asks for the area
A = l*w = 10 *7 = 70
round to the nearest whole number. 65.73
66
1) To round it off to the nearest whole number, let's consider that:
65.73 is > 65.5 then we can round it up
2) Hence, 65.73 after rounding it up is 66 and that's the answer.
Find the equation of the line that passes through the points (2,13) & (-1,-2)
The two endpoints of a line are given, and to find the equation we need to express it in the slope-intercept form written as follows;
y = mx + b, where m is the slope and b is the intercept of y.
To calculate the slope, we use the formular;
[tex]undefined[/tex]I'll send pic of equation
Given the following functions:
f(x) = 3x
g(x) = x + 4
h(x) = x^2 - 1
Before simplifying g(f(-1)), let's first determine f(-1).
f(x) = 3x
f(-1) = 3(-1)
f(-1) = -3
g(x) = x + 4
g(f(-1)) = (-3) + 4
= -3 + 4
g(f(-1)) = 1
Therefore, the answer is 1.
Donovan has 5 times as many as red fish as he does blue fish and half as many gray fish as blue fish. How many total fish (F) does Donovan have?answer optionsF = 6x + 1/2xF = 1/2x + 5 + xF = 6 + 1/2xF = 5x + 1/2x
Donavan has 6x + 1/2 x total number of fishes.
Let Donovan has x number of blue fishes.
Hence the number of red fishes = 5x
The number of gray fishes = 1/2 of x = 1/2 x
Total number of fishes = red + blue + gray = 5x + x + 1/2 x = 6 + 1/2 x
For something like an equation to have any importance, the coefficient involving at least any variable must not be 0. In actuality, the following equation would either be inconsistent (for b ≠ 0) and have no solution, or full n-tuples are solutions, as was mentioned for one variable, if any variable does actually have a zero coefficient.
A regular polynomial over such a field, from which the coefficients are drawn, can also be equalized to zero to produce a linear equation. Since linear equations typically do a good job of representing non-linear systems, they are used extensively in all branches of mathematics as well as in physics and engineering.
Therefore we can infer that Donavan has 6x + 1/2 x total number of fishes.
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i inserted a picture of the question which is question 7, i can give you the answer to the previous question which is question 6 if it helps
The first thing we have to know is that the trinomial (polynomial of three terms) is called a perfect square trinomial, the polynomial that when factorized gives us a perfect squared expression in the following way
[tex]a^2+2ab+b^2=(a+b)^2[/tex][tex]\begin{gathered} w^2-3w=350 \\ a=1 \\ 2ab=-3 \\ b=-\frac{3}{2} \\ b^2=\frac{9}{4} \end{gathered}[/tex][tex]\begin{gathered} w^2-3w-\frac{9}{4}=350-\frac{9}{4} \\ w^2-3w-\frac{9}{4}=347.75 \\ (w-\frac{3}{2})^2=347.75 \end{gathered}[/tex][tex](w-\frac{3}{2})^2-\frac{1409}{4}=0\to\text{answer}[/tex]Consider the following word problem:Eleanor is working her way through school. She works two part-time jobs for a total of 22 hours a week. Job A pays $6.40 per hour, and Job B pays $6.60 per hour.How many hours did she work at each job the week that she made $143.60.Step 1 of 2: Use the variables x and y to set up two equations to solve the given problem.
Let
x ------> number of hours Job A
y -----> number of hours Job B
we have that
x+y=22 ------> x=22-y ------> equation 1
6.40x+6.60y=143.60 ------> equation 2
Solve the system of equations
substitute equation 1 in equation 2
6.40(22-y)+6.60y=143.60
solve for y
140.8-6.40y+6.60y=143.60
0.20y=143.60-140.8
0.20y=2.8
y=14 hours
so
x=22-14=8
therefore
number of hours Job A was 8andnumber of hours Job B was 14QuesQuestion 3 (1 point)Let sin (47) = 0.7314. Enter an angle (B), in degrees, where cos (B) = 0.7314.Answer:Blank 1:Next PageBack
Solution
Let sin (47) = 0.7314. Enter an angle (B), in degrees,
[tex]sin(47)=0.7314[/tex]where cos (B) = 0.7314 means
[tex]\begin{gathered} sin(A)=cos(90-A) \\ let\text{ A = 47} \\ sin(A)=cos(90-47) \\ sin(A)=cos43 \end{gathered}[/tex]since the vaule of sin(A) = 0.7314
Hence the cos(B) = cos43 = 0.7314
The angle of B = 43°
marks LXL Search topics and skills Q Q Welcome, Learning Diagnostic Analytics Recommendations Skill plans 4 Math Language arts of Science Social studies GA Stan Eighth grade > T.11 Volume of cones YYR The volume of this cone is 2,110.08 cubic centimeters. What is the radius of this cone? Use a 3.14 and round your answer to the nearest hundredth. 14 cm centimeters Submit
EXPLANATION
The radius of a cone is given by the following relationship:
[tex]\text{Volume}=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]We have Volume=V= 2,110.08 cm^3 and the height is h=14cm
Replacing terms:
[tex]2,110.08=\frac{1}{3}\cdot\pi\cdot r^2\cdot14[/tex]Multiplying both sides by 3:
[tex]2,110.08\cdot3=\pi\cdot r^2\cdot14[/tex]Dividing both sides by 14*pi:
[tex]\frac{2,110.08\cdot3}{14\cdot\pi}=r^2[/tex]Applying the square root to both sides:
[tex]\sqrt[]{\frac{2,110.08\cdot3}{14\cdot\pi}}=r[/tex]Switching sides:
[tex]r=\sqrt[]{\frac{2,110.08\cdot3}{14\cdot3.14}}[/tex]Simplifying:
[tex]r=\sqrt[]{144}[/tex]Simplifying:
[tex]r=12[/tex]The answer is r=12 centimeters
Write the expression in simplest form.[tex] \sqrt{49 {x}^{5} } [/tex]
Answer:
[tex]=7x^2\sqrt[]{x}[/tex]Explanation:
Given the expression:
[tex]\sqrt{49x^5}[/tex]First, the expression can be rewritten in the form below:
[tex]\begin{gathered} =\sqrt[]{49\times x^5} \\ By\text{ multiplication of surds: }=\sqrt[]{mn}=\sqrt[]{m}\times\sqrt[]{n} \\ =\sqrt[]{49^{}}\times\sqrt[]{x^5} \end{gathered}[/tex]Next, we simplify:
[tex]\begin{gathered} =\sqrt[]{7^2}\times\sqrt[]{x^4\times x} \\ =7\times\sqrt[]{x^4}\times\sqrt[]{x} \\ =7\times x^2\times\sqrt[]{x} \end{gathered}[/tex]The simplest form of the expression is:
[tex]=7x^2\sqrt[]{x}[/tex]Drag each shape to the correct location on the table. Each shape can be used more than once, but not all shapes will be used.
Consider the given square pyramid.
Vertical cross-section ⇒
Isosceles triangle, figure 5Horizontal cross-section ⇒
Square, figure 4Vertical cross-section through base and two lateral faces ⇒
Isosceles trapezoid, figure 1
Answer:
In the image
Hope this helps!
Step-by-step explanation:
According to one study, an average payout for slots machines is 84 cents on each dollar. What is the percent return on every dollar spent in playing slots?The percent return on every dollakspent in playing slots is %.
Given that the average payout for slots machines is 84 cents on each dollar.
We know that
[tex]100\text{ cents = 1 dollar}[/tex]The cost of return for every dollar spent is 100-84=16 cents.
The percent return on every dollar spent in playing slots is
[tex]=\frac{16}{\text{one dollar}}\times100=\frac{16}{100}\times100=16\text{ \%.}[/tex]The percent return on every dollar spent in playing slots is 16%.
The one-to-one functions g and h are defined as follows.g(x) = 4x - 3h={(-6, 3), (-4, 7), (3, -8), (6, 4)Find the following
It is given that
[tex]g(x)=4x-3[/tex]Now to find the inverse of g
Let
[tex]\begin{gathered} y=4x-3 \\ 4x=y+3 \\ x=\frac{y+3}{4} \end{gathered}[/tex]So
[tex]g^{-1}(x)=\frac{x+3}{4}[/tex]Now we know that
[tex](g^{-1}.g)(x)=\text{ x}[/tex]So
[tex](g^{-1}.g)(2)=2[/tex]And since
[tex]h(-6)=3[/tex]So
[tex]h^{-1}(3)=-6[/tex]Figure DEFG is a parallelogram.If m
Given
DEFG is a parallelogram and
Answer
Since adjacent angles of parallelogram are supplementary
D+E = 180
30 + E = 1`80
E = 180- 30 = 150
Solve the absolute value equation. 20x - 19 = 0
To solve this absolute value equation, we can use find the solutions as follows taking into account the definition of absolute value, then, we have:
[tex]|20x-19|=0\Rightarrow20x-19=0,or-(20x-19)=0[/tex]Now, we can solve both equations to find the solution(s):
First case:
[tex]20x-19=0\Rightarrow20x=19\Rightarrow x=\frac{19}{20}[/tex]Second case:
[tex]-(20x-19)=0\Rightarrow-20x+19=0\Rightarrow-20x=-19\Rightarrow x=-\frac{19}{-20}\Rightarrow x=\frac{19}{20}[/tex]Then, both solutions are the same, because of the absolute rule (this is the point when y = 0, that is the x-intercept for this function.)
Therefore, the solution set is {19/20}.
Points XX and ZZ are on a number line, and point YY partitions \overline{XZ}
XZ
into two parts so that the ratio of the length of \overline{XY}
XY
to the length of \overline{YZ}
YZ
is 5:75:7.
The coordinate of XX is 1.31.3, and the coordinate of YY is 3.83.8. What is the coordinate of ZZ?
If a point divides two other points in any ratio m : n, then the coordinate of the point dividing the given two points can be known using section formula. The coordinate of the point ZZ on the number line is (4.06, 8.46).
What is section formula?Section formula is used in Coordinate geometry to find the ratio between two points on a line given one another point on the line.
Given that,
The ratio XZ : XY : YZ = 5 : 75 : 7
The coordinates of XX are (1.31, 3) and of YY are (3.83, 8).
Since YY is partitions the point XX and ZZ. In order to find the the coordinates of ZZ section formula can be used as below,
x = (m₁x₂ + m₂x₁) ÷ (m₁ + m₂) and y = (m₁y₂ + m₂y₁) ÷ (m₁ + m₂)
Here, m₁ : m₂ is equal to XY : YZ which can be known from the given ratio as,
XY : YZ = 75 : 7
=> m₁ : m₂ = 75 : 7
=> m₁ = 75 and m₂ = 7.
Suppose the coordinates of XX, YY and ZZ are (x₁, y₁), (x, y) and (x₂, y₂) respectively.
Substitute the respective values in the section formula to get,
3.83 = (75x₂ + 7 × 1.31) ÷ (75 + 7)
=> (75x₂ + 7 × 1.31) = 82 × 3.83
=> 75x₂ = 82 × 3.83 - 7 × 1.31
=> x₂ = (82 × 3.83 - 7 × 1.31) ÷ 75
=> x₂ = 4.06
And,
8 = (75y₂ + 7 × 3) ÷ (75 + 7)
=> (75y₂ + 7 × 3) = 82 × 8
=> 75y₂ = 82 × 8 - 7 × 3
=> y₂ = (82 × 8 - 7 × 3) ÷ 75
=> y₂ = 8.46
Thus, ( x₂, y₂) is equal to (4.06, 8.46).
Hence, the coordinate of ZZ is given by (4.06, 8.46).
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If LM = 14 and MN = 11, what is KM?Write your answer as a whole number or as a decimal rounded to the nearest hundredth
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
LM = 14
MN = 11
KM = ?
Step 02:
We must apply the triangle rules to find the solution.
Pythagoras Theorem
LM² = LN² + MN²
(14)² = LN² + (11)²
(14)² - (11)² = LN²
[tex]LN\text{ = }\sqrt[]{196-121}[/tex]LN = 8.66
[tex]\frac{LN}{MN}=\frac{KN}{LN}[/tex][tex]\frac{8.66}{11}=\frac{KN}{8.66}[/tex]8.66 * 8.66 = 11 * KN
6.818 = KN
KM = KN + MN
KM = 6.818 + 11 = 17.818
The answer is:
The value of KM is 17.82
what is the profit in dollar and cents that the store makes per sweater?p=26s
Given the expression:
[tex]p=26s[/tex]if 'p' represents the profit in dollar and 's' represents the number fo sweaters that the store sells, then we have that the store makes 26 dollars per sweater.
We can see this since the equation is the same as a linear function with rate of change m:
[tex]y=mx[/tex]Which of the percentage of the female population is made up by the age of group 5- 9?
Given,
The data of the male and female for different age group is shown in question tab.
Required:
The percentage of the female population is made up by the age of group 5- 9.
From the given data,
It is clearly seen that the percentage of female for 5 - 9 age group is 11%.
Hence, the percentage is 11%.
What is the domain of the function shown below? f(x) = log, (x-3) O A. All real numbers greater than 0 O B. All real numbers O c. All real numbers greater than 3 D. All real numbers greater than or equal to -2
Given the function:
[tex]f(x)=\log _5(x-3)[/tex]the domain of the function is all the possible values of x that can be substituted into the function f(x)
for the log functions:
x - 3 > 0
x > 3
So, the domain of the function is all real numbers greater than 3
so, the answer will be option C
help i can’t understand this work and i need the answer
[tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]is equivalent expression of [tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]
What is Expression?An expression is combination of variables, numbers and operators.
The given expression is
[tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]
The power of whole term is multiplied with power of each term
[tex]x^{\frac{1}{2}} y^{\frac{3}{2}} xy^{8}[/tex]
When variables are same the powers will be added
[tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]
Hence, [tex]x^{\frac{3}{2}} y^{\frac{19}{2}}[/tex]is equivalent expression of [tex]\sqrt{xy^{3} }(x^{\frac{1}{2}}y^{4} )^{2}[/tex]
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hey, can someone please help me? i really need it!
Iterative rule for the sequence 7,21 , 63,189
It is a geometry sequence, it solution is going to be:
[tex]a_n=a_0*number^{n-1}[/tex]In this case
[tex]\begin{gathered} a_0=7\text{ } \\ number\text{ is going to be } \\ number=3 \end{gathered}[/tex]Sustituing:
[tex]a_n=7*(3)^{n-1}[/tex]This is the answer, so when n=1
[tex]\begin{gathered} a_1=7*(3)^{1-1}=7 \\ a_2=7(3)^{2-1}=7*3=21 \end{gathered}[/tex]Which transformation produces a similar but incongruent figure?
Similar means that the figure has the same shape, but not neccesarily the same size. It is said, also, that it is incoungruent, so it definetly doesn't have the same size. A transformation that gives you a similar but incongruent figure is a dialation, rotation and/or translation. I'll do a drawing to illustrate:
Notice that I've done the three of them. I have the same figure, smaller, in another position and rotated.
6(x-1)=3x+6+3x what is the solution?Many solution No solution or One solution
To solve this equation, we can follow the next steps:
First: we can sum similar terms like 3x + 3x.
6(x - 1) = 3x + 3x + 6
6(x - 1) = 6x + 6
Then, solve 6(x-1) using the distributive property:
6x - 6 = 6x + 6
Subtract 6x from both sides of the equation:
6x - 6x - 6 = 6x - 6x + 6
0 - 6 = 6
-6 = 6
Since the result is not congruent, we can say that this equation has no solution.
Make the following conversions. Round your answers to 2 decimal places, if necessary.7 feet 6 inches toa. Inches: in.b. Feet: ft
So we need to express 7 ft 6 in in inches and in feet. For this purpose is important to remember this relation:
[tex]1ft=12in[/tex]So in a we need to express 7ft 6in in inches. This means we must convert the 7ft into inches and then add the result to 6in. If we use the rule of thre we get:
[tex]\begin{gathered} 1ft\rightarrow12in \\ 7ft\rightarrow x \\ \text{Where }x=\frac{7ft\cdot12in}{1ft}=84in \end{gathered}[/tex]Then we get:
[tex]7ft+6in=84in+6in=90in[/tex]So the answer to part a is 90in.
For part b we can take the result of part a and convert it into feet. Using the rule of three again we get:
[tex]\begin{gathered} 12in\rightarrow1ft \\ 90in\rightarrow x \\ \text{Where }x=\frac{90in\cdot1ft}{12in}=7.5ft \end{gathered}[/tex]Then the answer to part b is 7.5ft.
how do I find the linear change
In order to find the rate of change of the given line, use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]where (x1,y1) and (x2,y2) are two points of the line.
From the given graph you can select any pair of points, for example:
(x1,y1) = (2,400)
(x2,y2) = (4,1200)
replace the values of the previous coordinates in the formula for m:
[tex]m=\frac{1200-400_{}}{4-2}=\frac{800}{2}=400[/tex]Hence, the rate of change is 400
Which of the following is the value of y that solves the system of equations shown below?
(1) -5
(3) 6
3x + 4y = 16
(2) 8
(4) -2
x + y =16
Answer:
(4) -2
Explanation:
Given the system of equations:
[tex]\begin{gathered} 3x+4y=16 \\ x+y=6 \end{gathered}[/tex]Set x as the subject in the second equation: x=6-y
Substitute x=6-y into the first equation:
[tex]\begin{gathered} 3x+4y=16 \\ 3(6-y)+4y=16 \\ 18-3y+4y=16 \\ y=16-18 \\ y=-2 \end{gathered}[/tex]The value of y that solves the system of equations is -2.