Hello there. To solve this question, we need to analyze the probabilities for each case and see if the game is fair or not and also favorable to the player.
Sophia rolls a dice. If 5 turns up, she gets $2; If 6 turns up, she gets $3; If 2 turns up, she loses $10; She neither wins nor loses if any other face turns up.
First, let's remember something that will be important: a dice only haves 6 faces.
As we can see, she is winning (getting money) if 2 out of 6 faces turns up (5 and 6), and is losing if 1 out of 6 faces turns up (2). She is neither winning or losing if 3 out of 6 faces turns up (1, 3, 4).
About the fairness of the game, there are only 1 case she loses and 2 cases she wins something. We could only say the game is fair if the amount of winning cases were equal to the amount of losing cases. The game is not fair.
About being favorable, we'll consider it being unfavorable just the case that she loses money. The first and third cases, in which she gets money or doesn't get or lose money are favorable to her.
Since only 1 out of 6 faces makes her lose, then the game is favorable to the player.
Final answer: The game is not fair, but favorable to the player.
6. You deposit $1000 a year into an account. This account earns 8% interest compounded yearly,(20 points)a) how much will you have after 10 years?b) How much total money did you put in the account.c) How much total interest did you earn?
Compound interest formuae :
A = P ( 1+r/100)^ n or A = P( 1+i)^n or A = P ((1 + i )^n -1 )/i
we will use the highlighted formular due to compounded yearly statement on the question:
where A = Accumulated amount;
P = original amount invested/ (borrowed )
n = number of years
r = interest rate as a percentage
i = r/100
Answer to (a )
A = P ((1 + i )^n -1 )/i
where n = 10; i = 8/100 =0.08 ; P = 1000
A = 1000 ( 1 + (8/100))^10 -1)/ 0. 08
A =1000 ( 14.48)
A =$14486.56
b. 1000 X 10 = $12000
c. you earned interest of $14486 - $12000 = $2486
If I have 2 and a 1/2 bags of mortar
or every 100 cement blocks how many bags of water Mason needed for 350 blocks
The number of bags for 350 blocks is 8.75 bags
How to determine the number of bags for 350 blocks?From the question, we have the following parameters that can be used in our computation:
Bags of mortal = 2 and a 1/2 bags
Number of cements blocks = 100 blocks
The above parameters can be represented using the following ratio
Ratio = Bags of mortal : Number of cements blocks
Substitute the known values in the above equation, so, we have the following representation
Bags of mortal : Number of cements blocks = 2 and a 1/2 bags : 100 blocks
When the number of blocks is 350, we have the following equation
Bags of mortal : 350 = 2 and a 1/2 bags : 100 blocks
Express the ratio as fraction
Bags of mortal/350 = 2.5/100
Multiply both sides by 350
Bags of mortal = 350 * 2.5/100
Evaluate the products
Bags of mortal = 8.75
Hence, the number of bags is 8.75
Read more about ratio at
https://brainly.com/question/2328454
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Data with a correlation coefficient of 0.05 has a _[blank A]_ correlation, and data with a correlation coefficient of −0.80 has a _[blank B]_ correlation.Which answers provide the words that fill in the blanks in the previous sentence, in the correct order, to make it a true statement?Select two answers. Select one answer for the blank labeled "A," and select one answer for the blank labeled "B."
We have two correlations:
1) One with r = 0.05.
2) Another with r = -0.80.
The absolute value of r tells us how strong or weak is the correlation: strong correlation have values of |r| closer to 1, while weak correlations have values of |r| closer to 0.
The sign of r tells us if the correlation is positive or negative, independently of how strong it is.
Then, for a correlation with r = 0.05 we can conclude that it is a weak positive correlation.
For a correlation r = -0.80 we can conclude that it is a strong negative correlation.
Answer:
The correct options are
B: strong negative [second option]
A: weak positive [seventh option]
Use the distributive property of multiplication to find 6x14.
Answer
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Explanation
Distributive property is used to open brackets. For example, the expression
a (b + c) can be solved using the distributive property to multiply into the bracket.
a (b + c) = ab + ac
So,
6 × 14
= 6 × (7 + 7)
= (6 × 7) + (6 × 7)
= 42 + 42
= 84
Hope this Helps!!!
12.The graph of y=x + 3 is a vertical translation ofthe graph of y = x + 1, 2 units upward. Examine the intercepts of both linesand state another way that the geometric relationship between the two graphscan be described.
The graph of y=x + 3 is a vertical translation of
the graph of y = x + 1, 2 units upward. Examine the intercepts of both lines
and state another way that the geometric relationship between the two graphs
can be described.
we have
step 1
y=x+3
Find the x-intercepts
Value of x when the value of y is equal to zero
For y=0
0=x+3
solve for x
x=-3
step 2
y=x+1
Find the x-intercepts
Value of x when the value of y is equal to zero
For y=0
0=x+1
x=-1
step 3
The graph of y=x+3 is a horizontal translation 2 units at left of the graph of y=x+1
The rule is
(x,y) -------> (x-2,y)
A nurse measured The blood pressure of each person who visit a hair clinic and created a relative frequency histogram for the systolic blood pressure readings approximately what percentage of the people had a systolic blood pressure Reading between 110 and 139 inclusive
Given a relative frequency histogram for the systolic blood pressure readings.
We will find the percentage of the people who had a systolic blood pressure reading between 110 and 139
As shown:
The percentage of people who had a systolic blood pressure reading between 110 and 119 = 0.35
The percentage of people who had a systolic blood pressure reading between 120 and 129 = 0.25
The percentage of people who had a systolic blood pressure reading between 130 and 139 = 0.15
So, the answer will be = 0.35 + 0.25 + 0.15 = 0.75
So, the answer will be option 3) 75%
How many years will it take for an initial investment of $10,000 to grow to $25,000? Assume a rate of interest of 3% compounded daily.
The formula for compounded interest is the following:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Where A is the final amount, P is the principal, the initial investment, r is the annual rate of interest, n is how many times it is compounded per year and t is the time in years.
So, assuming the given rate of interest is annual, we have:
[tex]\begin{gathered} A=25000 \\ P=10000 \\ r=3\%=0.03 \\ n=365 \\ t=? \end{gathered}[/tex]Where we got n = 365 because it is compounded daily and there are 365 days in an year.
So let's start by solving for t:
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \frac{A}{P}=(1+\frac{r}{n})^{nt} \\ \log \frac{A}{P}=\log (1+\frac{r}{n})^{nt} \\ \log \frac{A}{P}=nt\log (1+\frac{r}{n}) \\ \frac{\log\frac{A}{P}}{n\log(1+\frac{r}{n})}=t \\ t=\frac{\log\frac{A}{P}}{n\log(1+\frac{r}{n})} \end{gathered}[/tex]Where the log base can be anyone, but it has to be the sme for both log.
Let's calculate the numerator and denominator separately first, using base 10:
[tex]\log _{}\frac{A}{P}=\log \frac{25000}{10000}=_{}\log 2.5=0.39794\ldots[/tex][tex]\begin{gathered} n\log (1+\frac{r}{n})=365\log (1+\frac{0.03}{365})=365\log (1+0.0000821918\ldots)= \\ =365\log (1.0000821918\ldots)=365\cdot0.000035694\ldots=0.013028\ldots \end{gathered}[/tex]Putting them together, we have:
[tex]t=\frac{\log\frac{A}{P}}{n\log(1+\frac{r}{n})}=\frac{0.39794\ldots}{0.013028\ldots.}=30.54\ldots\approx31[/tex]So, it will take between 30 and 31 years, closer to 31 years for it to grow to $25,000.
is the point (1,3) a solution to the linear equation 5x - 9y = 32?
We are given the following equation:
[tex]5x-9y=32[/tex]To determine if the point (1, 3) is a solution to this equation we will replace the given values since the point (1, 3) means that when x = 1, y = 3. Replacing in the equation:
[tex]5(1)-9(3)=32[/tex]Solving the operation we should get the same value on both sides of the equation:
[tex]\begin{gathered} 5-27=32 \\ -22\ne32 \end{gathered}[/tex]Since both sides are different this means that the point (1, 3) is not a solution to the equation.
Answer:
89
Step-by-step explanation:
hello. I need help with solving log6 129 on a calculator.
With the aid of a scientific calculator (most smart phones are equipped with one), you need to look out for the "LOG" button.
The button usually has the inscription shown as;
[tex]\text{Log}_{10}[/tex]Press the Second Function button and this key changes to;
[tex]\text{Log}_y[/tex]This second function button means,
"The log of x base y".
In this case it means, you take the log of 129, base 6.
The steps are;
[tex]\begin{gathered} (1)\text{Press 129} \\ (2)\text{Press Second Function button} \\ (3)\text{Press 6} \\ (4)\text{Press the "equal to" button} \end{gathered}[/tex]O 9,976 15) An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
An air-conditioning fan makes 125 revolutions per second. How many revolutions will it make if it runs for 30 minutes?
we know that
1 min=60 sec
we have
125 rev/sec
so
1 sec=1/60 min
substitute
125 rev/sec=125/ (1/60)=7,500 rev/min
Multiply by 30 min
7,500*30=225,000 rev
therefore
the answer is225,000 revolutionsThe perpendicular bisectors of triangle ABC intersect at point G and are shown in blue. Find BG
Answer:
9
Explanation:
A perpendicular bisector of a triangle is a line that is perpendicular to the side and passes through the midpoint of the triangle.
So when three perpendicular bisectors of the sides of a triangle meet at a point in a triangle, that point is called a circumcenter.
From the circumcenter theorem, we know that the circumcenter is equidistant from the vertices of a triangle, that is, the circumcenter is the same distance from each of the vertices of the triangle.
Looking at the given triangle, we can see that G is the circumcenter of the triangle because all the perpendicular bisectors DG, EG, and FG meet at this point.
We can see that AG is 9 which is the distance from vertex A to the circumcenter, G, since the circumcenter is equidistant from the vertices of a triangle according to the circumcenter theorem, therefore, BG will also be 9.
Solve 2(x-6)+7x = 5-3(x-2)
To solve x, let's eliminate the parenthesis first by multiplying 2 and -3 to it.
[tex]2x-12+7x=5-3x+6[/tex]Next, let's combine all like terms on either side. We will move -3x to the left side of the equation and -12 to the right side of the equation. Note that when a term crosses the equal symbol, the sign reverses. From -3x to +3x and from -12 to +12.
[tex]2x+7x+3x=5+6+12[/tex]Next, add the terms on both sides.
[tex]12x=23[/tex]Lastly, divide both sides by 12 to isolate x.
[tex]\begin{gathered} \frac{12x}{12}=\frac{23}{12} \\ x=\frac{23}{12} \end{gathered}[/tex]The value of x is 23/12.
Let's check if this is right by substituting the value of x to the equation.
[tex]\begin{gathered} 2(\frac{23}{12}-6)+7(\frac{23}{12})=5-3(\frac{23}{12}-2) \\ 2(-\frac{49}{12})+\frac{161}{12}=5-3(-\frac{1}{12}) \\ -\frac{98}{12}+\frac{161}{12}=5+\frac{3}{12} \\ \frac{63}{12}=\frac{63}{12} \\ \frac{21}{4}=\frac{21}{4} \end{gathered}[/tex]Since we got the same 21/4 on both sides of the equation, our x value 23/12 is correct.
Please be clear with the answer thank you bye-bye bye-bye
Solve the system of equations:
3x + 3y = 3
5x + y = 13
Solving the second equation for y:
y = 13 - 5x
Substituting in the first equation:
3x + 3(13 - 5x) = 3
Opeating:
3x + 39 - 15x = 3
Simplifying:
-12x + 39 = 3
Subtracting 39:
-12x = -36
Dividing by -12:
x = -36 / (-12)
x =3
Substituting in the equation for y:
y = 13 - 5(3)
y = -2
Answer: x = 3, y = -2
Answer: x = 3, y = -2
Step-by-step explanation:
e = radians. Identify the terminal point and tan e.O A. Terminal point: (33) tan = 13B. Terminal point: (1, 1); tan 6 = 73(1,1)tan 0 = 2C. Terminal point:; tane3D. Terminal point:
The correct answer is Option D
This following are the steps to take:
Step1: Convert the angle from radians to degrees
[tex]\begin{gathered} 1\pi radians=180^o \\ \text{Thus }\frac{\pi}{6}\text{ radians = }\frac{180^o}{6} \\ \text{ }\frac{\pi}{6}\text{ radians =}30^o \end{gathered}[/tex]Step 2: Draw a unit circle (with a radius of 1 unit), and show the line which forms angle 30 degrees with the x -axis
Step 3: Compute the values of the terminal points:
[tex]\begin{gathered} Th\text{e x-coordinate of the terminal point = 1 }\times cos30^0\text{ = }\frac{\sqrt[]{3}}{2} \\ Th\text{e y-coordinate of the terminal point = 1 }\times\sin 30^0\text{ = }\frac{1}{2} \\ \text{Thus the coordinates of ther terminal point = }(x,y)\text{ = (}\frac{\sqrt[]{3}}{2},\text{ }\frac{1}{2}\text{)} \end{gathered}[/tex]Step 4: Compute the values of the tangent of the angle:
[tex]\begin{gathered} \tan 30^0\text{ = }\frac{y}{x}=\frac{\frac{1}{2}}{\frac{\sqrt[]{3}}{2}}=\frac{1}{\sqrt[]{3}}\text{ } \\ \\ \tan 30^o=\frac{1}{\sqrt[]{3}}\text{ }\times\frac{\sqrt[]{3}}{\sqrt[]{3}}\text{ =}\frac{\sqrt[]{3}}{3} \\ \\ \tan 30^{o\text{ }}=\text{ }\frac{\sqrt[]{3}}{3} \end{gathered}[/tex]consider the equation -4x+3y=7. Assume that y is a function of x. rewrite the equation using function notation F(x)
Kellen earned $52.92 for waitressing at a burger restaurant on Friday night.if she waitressed for 4.5 hours,on average how much did she earn per hour?
Given data:
The amount Kellen earned in 4.5 hours is $52.92.
The expression for the given statement is,
[tex]\begin{gathered} 4.5\text{ hours=\$52.92} \\ 1\text{ hour= \$11.76} \end{gathered}[/tex]Thus, Kellen earned $11.76 per hour.
Each ticket to a matinee movie costs $8. Part A: Complete this table relating the number of movie tickets bought, m, to the total cost, c, of the tickets. m C 4 6 9 Part B: Write an equation that models this situation, using the variables m and c. Answer: Brandy thinks the number of movie tickets bought depends on the total cost of the movie tickets. Brandy's brother thinks the total cost of the movie tickets depends on the number of movie tickets bought Part C: Whose thinking is correct, Brandy's, her brother's, or both? Explain how you know.
Part A
Since each ticket costs $8, we need to add $8 for each plus ticket one buys:
[tex]\begin{gathered} 1\text{ ticket: \$}8 \\ 2\text{ tickets: \$}8+\text{ \$}8=\text{ \$}16 \\ 3\text{ tickets: \$}16+\text{ \$}8=\text{ \$}24 \\ 4\text{ tickets: \$}24+\text{ \$}8=\text{ \$}32 \\ 6\text{ tickets: \$}32+\text{ \$}16=\text{ \$}48 \\ 9\text{ tickets: \$}48+\text{ \$}24=\text{ \$}72 \end{gathered}[/tex]Therefore, we have:
Part B
Notice that, instead of summing (8+8+8+...) we can multiply $8 by the number of tickets bought m to obtain the total cost c.
Thus, we have:
[tex]c=m\times\text{ \$}8[/tex]Part C
The equation above (c = m x $8) shows that the total cost c depends on the number of tickets bought.
However, we write that relation in another way:
[tex]m=c\div\text{ \$}8[/tex]Thus, if we know the total cost, we can divide it by $8 to find the number of tickets bought. Then, we can say that the number of tickets boght m depends on the total cost c.
Therefore, both thoughts are correct.
Heather dropped a water balloon over the side of her school a height of 80 feet. The approximate height of the balloon at any point during it's fall can be represented by the following quadratic equation: h=-16t^2+80. About how long did it take for the balloon to hit the ground.A.1.73B.2.24C.2.45D.2.83
h = - 16t^ 2 + 80
[tex]h=-16t^2\text{ + 80}[/tex]The balloon will hit the ground when the height = 0
[tex]\begin{gathered} 0=-16t^2\text{ + 80} \\ \text{collect like terms} \\ \\ 16t^2\text{ = 80} \\ \text{Divide both sides by 16} \\ t^2\text{ = }\frac{80}{16} \\ t^2\text{ = 5} \\ t\text{ =}\sqrt[]{5} \\ t\text{ = 2.236} \\ t\text{ = 2.24} \end{gathered}[/tex]The correct option is B = 2.24
The rectangular rug has side lengths of 3 and 4 ft. What is the length of the diagonal? Draw a picture of the problem and solve. Round to the nearest tenth
ANSWER
The length of the diagonal is 5 ft
EXPLANATION
The diagram of the rug with the diagonal is:
The diagonal and the sides form a right triangle, so we can use the Pythagorean theorem to find x, the length of the diagonal:
[tex]\begin{gathered} x^2=3^2+4^2 \\ x=\sqrt[]{9+16} \\ x=\sqrt[]{25} \\ x=5 \end{gathered}[/tex]Simplify: 2x^2 + 19x + 35/2x^2 +11x +15 a) 7/3b) 19x + 35/11x + 15c) 2x + 7/2x + 3d) x + 7/x + 3
SOLUTION
We want to simplify
[tex]\frac{2x^2+19x+35}{2x^2+11x+15\text{ }}[/tex]Factorising the numerator and denominator, we have
[tex]\begin{gathered} \frac{2x^2+19x+35}{2x^2+11x+15\text{ }} \\ \frac{2x^2+14x+5x+35}{2x^2+6x+5x+15\text{ }} \\ \frac{2x(x+7)+5(x+7)}{2x(x+3)+5(x+3)} \\ \frac{(2x+5)(x+7)}{(2x+5)(x+3)} \end{gathered}[/tex]Canceling out the common factor which is
[tex]2x+5[/tex]We have our answer as
[tex]\frac{x+7}{x+3}[/tex]Hence the answer is option D
In the diagram below of circle A. diameter MP = 26. m_GAI = 30° and radiGA and Al are drawn.MАP30°G1if MG IP, find the area of the sector MAG in terms of me and approximateto the nearest hundredth.The area of the sector in terms of u isTTThe area of the sector rounded to the nearest hundredth isunitssquared.
To find the area of a sector of a circle in terms of π having the angle in degrees you use the next formula:
[tex]A=\frac{\theta}{360}\cdot\pi\cdot r^2[/tex]r is the radius
To find area of sector MAG:
1. Find the angle of the sector MAG.
The semicircle has an angle of 180° and it is divided into 3 sectors MAG, GAI, and IAP.
As the arcs MG and IP are congruents (have the same measure) the angles of the sectors MAG and IAP are also congruent.
[tex]\begin{gathered} m\angle\text{MAG}+m\angle\text{GAI}+m\angle\text{IAP}=180 \\ \\ m\angle MAG=m\angle IAP \\ m\angle GAI=30 \\ \\ 2m\angle MAG+m\angle GAI=180 \\ 2m\angle MAG+30=180 \end{gathered}[/tex]Use the equation above to find the measure of angle MAG:
[tex]\begin{gathered} 2m\angle MAG=180-30_{} \\ 2m\angle MAG=150 \\ m\angle MAG=\frac{150}{2} \\ \\ m\angle MAG=75 \end{gathered}[/tex]2. Find the area of sector MAG:
Angle 75°
radius= half of the diameter (26/2 = 13)
r=13
[tex]\begin{gathered} A=\frac{75}{360}\cdot\pi\cdot(13)^2 \\ \\ A=\frac{75}{360}\cdot\pi\cdot169 \\ \\ A=\frac{12675}{360}\pi \\ \\ A=\frac{845}{24}\pi \\ \\ A\approx35.21\pi \\ \\ A\approx110.61 \end{gathered}[/tex]The exact area of the sector MAG is 845/24 π units squared.
Rounded to the nearest hundredth 35.21 π units squared or 110.61 units squared
I'm terrible at explaining answers and this is one of them...
We see that the sign is a triangle and the area of a triangle is given by the expression:
[tex]A=\frac{1}{2}\text{base}\times height[/tex]base=36
height=32
Then,
[tex]\begin{gathered} A=\frac{1}{2}36\times32 \\ A=\frac{1152}{2}=576\text{ square inches} \end{gathered}[/tex]What is the volume of the cone when the radius is 10 and the height is 18
The volume of the cone is given by the formula:
12 1 point Which trig function should Sharlot use to find the measure of angle A ? C 1 B cosine 3 tangent 4 pythagorean theorem sine 6
using trigonometric ratio
[tex]\begin{gathered} \cos A=\frac{adjacent}{\text{hypotenuse}} \\ \cos A=\frac{5}{12} \end{gathered}[/tex]We have to use cosine to find angle A
insert the values given in the problem then scale up or down to find the missing value
Given the statements in the image, 2% of the fans implies that 2/100 of the fans in attendance equals to 120 teenagers. i.e,
[tex]\frac{2}{100}\text{ of fans }=120[/tex]Let the total number of fans equal to x. We have the following ratio:
[tex]\frac{2}{100}=\frac{120}{x}[/tex]To get x by scaling up our ratios, we multiply both numerator and denominator by a common factor of 60 to have:
It can be seen that:
[tex]\begin{gathered} 2\times60=120 \\ 100\times60=x \\ 6000=x \\ x=6000 \end{gathered}[/tex]Hence, the total number of people at the stadium is 6000.
Select all nat apply.Which steps are involved in multiplying fractions?Multip, the denominators togetherMultiply the numerators togetherCheck to see if the product can be simplifiedFind a common denominatorConvert the problem to a division problem
We want to list the steps involved in multiplying fractions;
Taking an example;
[tex]\frac{2}{3}\times\frac{3}{4}[/tex]First steps are;
- Multiply the numerators together
- Multiply the Denominators together
[tex]\begin{gathered} =\frac{2\times3}{3\times4} \\ =\frac{6}{12} \end{gathered}[/tex]Next is to;
Check to see if the product can be simplified;
[tex]\frac{6}{12}=\frac{1}{2}[/tex]So, we get the product to be;
[tex]\frac{1}{2}[/tex]in a 45-45-90 triangle, given the hypotenuse 9√2, find the leg of the triangle
Hypothenuse Z= 9√2
then
Z^2 = X^2 + X^2= 2X^2
(9√2)^2 = 2X^2
then
(9√2)/√2= X
cancel √2, then
9 = X
Then now find perimeter
Perimeter P= Z + X + X = 9√2 + 9 + 9 =
P = 9√2 + 18 = 9•(√2 + 2)
Answer is length of triangle= 9√2 + 18
Leg of triangle X= 9
Based on the end behavior, what is the graph of function R?
As given by the question
There are given that the function
[tex]f(x)=-x^3+3x^2+x-3[/tex]Now,
The graph of the given function is shown below:
Hence, the correct option is C.
Answer:
C
Step-by-step explanation:
Trust
D. 62B. 1811. Madison bought a sweater and a pair of jeans at the mall for $47. Thesweater cost $7 less than twice the cost of the jeans. How much did thesweater cost?c. $20A $29D. $13B. $27
Answer:
$29
Step-by-step explanation:
If Erik checks his pulse for 8 minutes, what is his rate if he counts 600 beats? beats per minute.
Given
Time taken by Erik to check his pulse = 8minutes
Count = 600 beats
To get his rate in beats per minute, you will use the formula:
Beat rate = Count (in beat)/Time taken (in minutes)
Sustitute the given paremeters into the formula given as shown:
Beat rate = 600beats/8minutes
Beat rate = 75beats per minutes
Hence his rate is 75 beats per minute.
form