Answer:
4
Step-by-step explanation:
Pluto has a circumference of about 7,232,000 meters.Give the circumference of Pluto in scientific notation
Final answer:
The circumference of Pluto is 7,232,000 meters, which is represented as 7.232 × 10⁶ meters in scientific notation.
Explanation:
To express the circumference of Pluto in scientific notation, you start by placing the decimal after the first non-zero digit and count the number of places the decimal has moved. The circumference of Pluto is 7,232,000 meters. In scientific notation, this is written as 7.232 × 10⁶ meters.
Here is a step-by-step breakdown of the conversion process:
Identify the first non-zero digit in 7,232,000, which is 7.Place the decimal point after this digit to get 7.232Count how many places you moved the decimal point; in this case, it is 6 places to the left.Write the number as a product of the first part and 10 raised to the power of the number of decimal places moved, which is 106.The final answer in scientific notation is 7.232 × 10⁶ meters.Remember, scientific notation is useful for expressing very large or very small numbers in a simplified format.
Se lanza un objeto desde una plataforma.
Su altura (en metros), xxx segundos después del lanzamiento, está modelada por:
h(x)=-5x^2+20x+60h(x)=−5x
2
+20x+60h, left parenthesis, x, right parenthesis, equals, minus, 5, x, squared, plus, 20, x, plus, 60
¿Cuál es la altura del objeto en el momento del lanzamiento?
La altura inicial del objeto lanzado desde una plataforma es de 60 metros, representando la altura de la plataforma. Esto se obtiene al evaluar h(x) cuando x = 0.
La altura del objeto en el momento del lanzamiento se refiere al valor de la función h(x) cuando x = 0, ya que x representa el tiempo en segundos después del lanzamiento. Para determinar la altura inicial, simplemente sustituimos x = 0 en la función h(x):
h(0) = -5(0)^2 + 20(0) + 60 = 60
Por lo tanto, la altura inicial del objeto en el momento del lanzamiento es de 60 metros.
En términos físicos, esto tiene sentido, ya que el término cuadrático (-5x^2) representa la aceleración debida a la gravedad, y el término lineal (20x) representa la velocidad inicial. Cuando x = 0, no ha pasado tiempo después del lanzamiento, y la altura es simplemente la altura inicial de la plataforma, que es 60 metros.
En resumen, la altura del objeto en el momento del lanzamiento es de 60 metros.
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The object will land on the ground 6 seconds after launch.
To determine when the object will land on the ground, we need to find the time [tex]\( x \)[/tex] when the height [tex]\( h(x) \)[/tex] is zero. The height of the object is given by the equation:
[tex]\[ h(x) = -5x^2 + 20x + 60 \][/tex]
Set [tex]\( h(x) = 0 \)[/tex] to find the time when the object lands on the ground:
[tex]\[ -5x^2 + 20x + 60 = 0 \][/tex]
This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \),[/tex] where [tex]\( a = -5 \), \( b = 20 \),[/tex] and [tex]\( c = 60 \).[/tex] We can solve this using the quadratic formula:
[tex]\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \][/tex]
Substitute the values of [tex]\( a \), \( b \),[/tex] and [tex]\( c \)[/tex] into the formula:
[tex]\[ x = \frac{-20 \pm \sqrt{20^2 - 4(-5)(60)}}{2(-5)} \][/tex]
Simplify inside the square root:
[tex]\[ x = \frac{-20 \pm \sqrt{400 + 1200}}{-10} \][/tex]
[tex]\[ x = \frac{-20 \pm \sqrt{1600}}{-10} \][/tex]
[tex]\[ x = \frac{-20 \pm 40}{-10} \][/tex]
This gives us two solutions:
[tex]\[ x = \frac{-20 + 40}{-10} = \frac{20}{-10} = -2 \][/tex]
[tex]\[ x = \frac{-20 - 40}{-10} = \frac{-60}{-10} = 6 \][/tex]
Since time [tex]\( x \)[/tex] cannot be negative, we discard [tex]\( x = -2 \).[/tex] Therefore, the object will land on the ground [tex]\( 6 \)[/tex] seconds after launch.
So, the object will land on the ground 6 seconds after launch.
The translated question is:
An object is launched from a platform. Its height (in meters), x seconds after the launch, is modelled by:
[tex]h(x)=-5x^2+20x+60[/tex]
How many seconds after launch will the object land on the ground?
Darren invests $4,500 into an account that earns 5% annual interests. How much will be in the account after 10 years if the interest rate is compounded annually, quarterly, monthly, or daily? Which compounded interest rate should Darren choose?
We have been given that Darren invests $4,500 into an account that earns 5% annual interests. We are asked to find the amount in his account after 10 years, if the interest rate is compounded annually, quarterly, monthly, or daily.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
[tex]5\%=\frac{5}{100}=0.05[/tex]
When compounded annually, [tex]n=1[/tex]:
[tex]A=4500(1+\frac{0.05}{1})^{1\cdot 10}[/tex]
[tex]A=4500(1.05)^{10}[/tex]
[tex]A=4500(1.6288946267774414)[/tex]
[tex]A=7330.025820498\approx 7330.03[/tex]
When compounded quarterly, [tex]n=4[/tex]:
[tex]A=4500(1+\frac{0.05}{4})^{4\cdot 10}[/tex]
[tex]A=4500(1.0125)^{40}[/tex]
[tex]A=4500(1.6436194634870132)[/tex]
[tex]A=7396.28758569\approx 7396.29[/tex]
When compounded monthly, [tex]n=12[/tex]:
[tex]A=4500(1+\frac{0.05}{12})^{12\cdot 10}[/tex]
[tex]A=4500(1.00416666)^{120}[/tex]
[tex]A=4500(1.64700949769)[/tex]
[tex]A=7411.542739605\approx 7411.54[/tex]
When compounded daily, [tex]n=365[/tex]:
[tex]A=4500(1+\frac{0.05}{365})^{365\cdot 10}[/tex]
[tex]A=4500(1.0001369863013699)^{3650}[/tex]
[tex]A=4500(1.6486648137656943695)[/tex]
[tex]A=7418.9916619456\approx 7419.00[/tex]
Since amount earned will be maximum, when interest is compounded daily, therefore, Darren should use compounded daily interest rate.
The three lines represent the number of hot dogs eaten by three contestants at a hot dog eating competition. Which contestant was eating at the slowest rate?
Answer:
Contestent K
Step-by-step explanation:
The contestant who was eating at the slowest rate will be in line K.
What is a linear equation?A relationship between two or more parameters that, when shown on a graph, produces a linear model. The degree of the variable will be one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The three lines represent the number of hot dogs eaten by three contestants at a hot dog eating competition.
The diagram is shown below.
From the diagram, we can observe that for the same run, the rise of line K will be the least.
The contestant who was eating at the slowest rate will be in line K.
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-4x - 2y = -2
X - 2y = 9
What is the result of subtracting the second equation from the first
Answer: -5x= -11
Step-by-step explanation:
Final answer:
Subtracting equations to find the value of x.
Explanation:
The result of subtracting the second equation from the first is:
Subtract every corresponding term:
-4x - 2y - (x - 2y) = -2 - 9
-4x - 2y - x + 2y = -11
-5x = -11
x = 11/5 or 2.2
In order for you to answer the following question correctly, please use the images down below:
Complete the two-column proof of the Segments of Chords Theorem.
Please correct me for any of the answers I got wrong.
AEC is congruent to DEB should be the answer for 5.
ALSO...
You're proving that EB * EA = EC * ED, so the 7th blank should be "EB * EA = EC * ED"
Otherwise, everything else is good.
- Tony had 4 equal sets of sports
cards. He gave his friends 5 cards.
Now he has 31 cards. How many
cards were in each set?
Answer:
9 cards
Step-by-step explanation:
he originally had 36 cards before giving 5 away, 36 divided by 4 is 9
Final answer:
Tony originally had 9 cards in each of the 4 equal sets before he gave 5 cards away.
Explanation:
The question asks how many cards were in each set originally when Tony had 4 equal sets of sports cards, gave away 5 cards, and now has 31 cards left. To find the number of cards in each set, we add back the 5 cards Tony gave away to the total number he has left, which gives us 31 + 5 = 36 cards. Since these 36 cards were divided into 4 equal sets, we divide 36 by 4 to find the number of cards in each set. Therefore, each set originally had 36 / 4 = 9 cards.
The rectangle below has an area of x2 - 4x - 12 square meters and a length of x + 2 meters.
What expression represents the width of the rectangle?
X+2
Width
x² - 4x – 12
Width =
meters
Answer:
w=(x-6)
Step-by-step explanation:
x^2-4x-12=(x + 2)(w)
a=wl (area equals width times length)
x^2-4x-12=(x + 2)(w)
(x-6)(x+2)=(x + 2)(w)
(x-6)=w
The table gives a set of outcomes and their probabilities. Let A be the event "the outcome is divisible by 9". Find P(A).
Answer:
0.15
Step-by-step explanation:
The only outcome that is divisible by 9 is 9 itself. At this point, the probability is 0.15. Hope this helps!
I FAILED and lost Leo Murillo Find the correct result. 1+4=5 2+5=12 3+6=21 5+8=_________ If your answer is wrong, upload this on your timeline. GAME?
Answer:
Step-by-step explanation:
45
Answer:
34
Step-by-step explanation:
1+4=5 2+5=12 3+6=21 5+8= ??
It is noticed that the previous solution is added to the unknowns and the cycle continues.
The previous solution is 5 which is added to 2 and 5 to give 12
5+2+5=12
12 is then added to the next set of unknowns 3+6 to give 21
12+3+6=21
21 is then added to the 5+8 to give 34
21+5+8= 34
When trying to find the probability of rolling an even number on a number cube with numbers 1 through 6, how many desired outcomes are there?
Answer:
3
Step-by-step explanation:
3 even numbers 2,4,6
or 1/2
or 50%
Mike bought a soft drink for 3 dollars and 4 candy bars. He spent
a total of 19 dollars. How much did each candy bar cost ?
Answer: each candy bars costs 4 dollars
Step-by-step explanation:
subtract 3 from 19 then divide the answer by 4
Each candy bar equalled 4 dollars.
19-3= 16
16 divided by 4 (candy bars) = 4
Brian is buying T-shirts for the marching band. He knows that at parades the band forms 24 rows. Each row has 13 students. If T-shirts come in boxes of 100, how many boxes of T-shirts should Brian buy?
Answer:
4 boxes (Brainliest Please)
Step-by-step explanation:
You have to find the amount of students
24 X 13 = 312
You have to get enough for everybody so you need 400 shirts so that everyone can get one.
400 / 100
4 boxes
When using Cramer's Rule to solve a system of equations, if the determinant of the coefficient matrix equals zero and at least one numerator determinant is zero, then the system _____________________.
A. is consistent
B. is dependent
C. is inconsistent
D. has no solution
Answer:
B. is dependent
Step-by-step explanation:
The denominator determinant will be zero when the coefficients of the variables are dependent. One of the numerator coefficients will be zero when the coefficients involved are dependent. Hence using Cramer's Rule will result in the ratio 0/0 when the system is dependent.
___
The ratio will be 1/0 if the system is inconsistent (has no solution).
What is the area of this parallelogram to 2 significant figures?
Answer:
Step-by-step explanation:
Area of a parellogram is bh but a parellogram with its adjacent sides equal is a rhombus and rhombuses area us 1/2diagonal1×diagonal2 also diagonal of a parellogram bisect each other so diagonal will be 8cm and 14cm diagonal of a parellogram divides it into two congruent triangle vertically opposite angles are equal all non zero numbers are significant if zero is between two numbers its significant if zero is after decimal and the number less than zero than the zeroes are insignificant like in 0.0820 but the zeroes after decimal are significant
But zeroes after no decimals are not significant like 100 the powers tens are irrelevant like 10^3 has only one significant figure
Sorry don't know answer but hopes this helps so sorry
A circle graph titled Education Level. 13 percent is some high school, 26 percent is completed high school, 27 percent is some college, 34 percent is completed college. This graph shows the results of 150 people surveyed. How many people completed college? people
Answer:
51
Step-by-step explanation:
Just did it on edgu
Final answer:
Based on the circle graph, 34 percent of the 150 surveyed people completed college, which translates to 51 individuals.
Explanation:
The question asks how many people completed college based on a circle graph showing the education levels of 150 surveyed individuals. To answer this, we use the percentage given for those who completed college and apply it to the total number surveyed. With 34 percent having completed college, we calculate the number of people by multiplying 34 percent (or 0.34 as a decimal) by the total survey number, 150 people.
The calculation is as follows: 0.34 × 150 = 51. Therefore, 51 people surveyed completed college.
Where does photosynthesis take place
Answer:chloroplast
Step-by-step explanation:It’s takes place inside plant cells in small things called “chloroplast”
What is the area of the rectangle 21 m 33 m 21 m
The area of a rectangle with dimensions 21 m by 33 m is 693 square meters, calculated by multiplying the length and width.
The area of a rectangle is calculated by multiplying the length by the width. In the case of a rectangle with dimensions 21 m by 33 m, the formula to find the area A is:
A = length x width
So, the area of the rectangle is:
A = 21 m x 33 m
A = 693
Hence, the area of the rectangle is 693 square meters.
On the spring an entire field of flowering trees blossoms. The population of focusts consuming these Flowers rapidly increases as the trees blossom The relationship between the elapsed time in weekssince the beginning of spring, and the total number of focusts N(t) is modeled the following function N(t) = 300 * (49/16) ^ t Complete the following sentence about the rate of change of the locust population. Round your answer to two decimal places. On the spring an entire field of flowering trees blossoms. The population of focusts consuming these Flowers rapidly increases as the trees blossom The relationship between the elapsed time in weekssince the beginning of spring, and the total number of focusts N(t) is modeled the following function N(t) = 300 * (49/16) ^t Complete the following sentence about the rate of change of the locust population. Round your answer to two decimal places.
Answer:.5
Step-by-step explanation:
.5
What is the slope of the graphed line ?
Answer:
you cannot see the graph
Step-by-step explanation:
1/3
The slope is determined by change in y / change in x.
Here we can see that it takes 3 blocks from (1,1) until the line is on an integer, (4,2) and that y increases by one while x increases by 3.
Choose the right answer. Plane A leaves Tulsa at 2:00 p.m., averaging 300 mph and flying in a northerly direction. Plane B leaves Tulsa at 2:30 p.m., averaging 225 mph and flying due east. At 5:00 p.m., how far apart will the planes be?
Plane A and Plane B will be approximately 1061.21 miles apart at 5:00 p.m
Given: Speed of plane A is 300 mph and B is 225 mph. Plane A leave at 2 pm and B leaves at 2:30 pm
To find: distance between them at 5 pm
We know that [tex]\text{speed} = \frac {\text{distance}}{\text{time}}[/tex]
So, we can find distance travelled by plane A by 5 pm [tex]= 300 \times 3 = 900[/tex] miles
To calculate distance travelled by plane B we need to find the time plane B has flied between 2:30 and 5 pm. We can see that the plane flew for 2 hours and 30 mins. We can write 2 hours 30 mins as 2.5 hours.
So, distance travelled by plane B by 5 pm [tex]= 225 \times 2.5 = 562.5[/tex] miles
Since plane A is moving in north and plane B is moving in east, it forms a right angled triangle with 900 miles and 562.5 miles as its perpendicular and base.
To find distance between the planes we can use Pythagoras theorem:
[tex]\text{hypotenuse} = \sqrt{ \text{(perpendicular)}^2 + \text{(base)}^2} \\\text{hypotenuse} = \sqrt{ 900^2 + 562.5^2}\\\text{hypotenuse} = \sqrt{810000 + 316406.25}\\\text{hypotenuse} = \sqrt{1126406.25} \approx 1061.21\\[/tex]
Therefore, the planes will be approximately 1061.21 miles apart at 5:00 p.m.
Un supermercado lanza una promoción para agradecer la fidelidad de sus clientes así: cada que 33 personas pasen por la caja registradora se le regala al cliente de turno un descuento del 50% en sus compras y, cada que pasen 44 personas, al cliente de turno se le obsequiará un televisor LCD de 32 pulgadas. ¿Cada cuántos clientes se ganan los dos premios es una misma compra? A. 77 clientes. B. 88 clientes. C. 99 clientes. D. 132 clientes.
Answer: La respuesta es cada 132 clientes
Lo que hice fue poner la parte de 33 y 44 sumándose entre si:
33+33=66+33=99+33=132 etc
44+44=88+44=132 etc
Y si te diste cuenta concuerdan los dos en 132
Espero que te sirva
Aplicando el mínimo común múltiplo, se encuentra que a cada 132 clientes se ganan los dos premios es una misma compra, opción D.
Los clientes que ganan el descuento de 50% son los múltiplos de 33.Los clientes que ganan el televisor LCD de 32 pulgadas son los múltiplos de 44.Para ver los que ganam ambos, hay que ver lo mínimum común múltiplo de 33 y 44, o sea:
33 - 44|2
33 - 22|2
33 - 11|3
11 - 11|11
1
mcm(33,44) = 2x2x3x11 = 132
O sea, cada 132 clientes se ganan los dos premios es una misma compra, opción D.
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A ribbon is 3 2/3 yards long. Mae needs to cut the ribbon into pieces that are 2/3 yard long.
I need help with this. :)
Answer:
5.5 pieces (it can also be 5 if you dont have 5.5)
Step-by-step explanation:
3 and 2/3 divided by 2/3 is 5 and a half
(please give brainliest if it helps you)
The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What are the expected value and the standard error for a labor participation rate in the company's sample?
Answer:
Expected value=77 people
Standard error=0.0040
Step-by-step explanation:
-Given the proportion is, p=0.67
-The expected value can be calculated as:
[tex]Expected \ Value=np\\\\=120\times 0.637\\\\=76.44\approx 77[/tex]
#The standard deviation is calculated as:
[tex]\sigma_p=\sqrt{\frac{p(1-p)}{n}}\\\\=\sqrt{\frac{0.637(1-0.637)}{120}}\\\\=0.0439[/tex]
#We use this calculated standard deviation to calculate the standard error:
[tex]SE=\frac{\sigma_p}{\sqrt{n}}\\\\=\frac{0.0439}{\sqrt{120}}\\\\=0.0040[/tex]
Hence, the sample has an expected value of approximately 77 people and a standard error of 0.0040
What is the input value for which
f(x)=−3
Answer:
Every value of x.
Step-by-step explanation:
The function is a zero-order polynomial, whose value remains constant for all value of x.
Garrett's family is going to relax at the beach all day! In preparation, Garrett made s
sandwiches for them to eat when they get hungry. Garrett put 3 slices of turkey and 3 slices
of ham on each sandwich.
Pick all the expressions that represent how many slices of meat Garrett used on the
sandwiches.
6s
3 + 3 + S
9s
3s + 3s
Answer:
6s
3s + 3s
Step-by-step explanation:
Consider the equation below. log Subscript 4 Baseline (x + 3) = log Subscript 2 Baseline (2 + x) Which system of equations can represent the equation? y 1 = StartFraction log (x + 3) Over log 4 EndFraction, y 2 = StartFraction log (2 + x) Over log 2 EndFraction y 1 = StartFraction log x + 3 Over log 4 EndFraction, y 2 = StartFraction log 2 + x Over log 2 EndFraction y 1 = StartFraction log 4 Over log 2 EndFraction, y 2 = StartFraction log (x + 3) Over log (2 + x) EndFraction y 1 = StartFraction log x + 3 Over 4 EndFraction, y 2 = StartFraction log 2 + x Over 2 EndFraction
Answer:
A
Step-by-step explanation:
just took the quiz on edgen
The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.
What is the definition of a logarithm?Exponents can also be written as logarithms. The other number is equal to a logarithm with a number base. It's the exact inverse of the exponent function.
The property of the logarithm is found as;
[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)}[/tex]
Given equation;
[tex]\rm log_4(x+3) = log_2(2+x)[/tex]
LHS;
[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_4(x+3) \\\\ y_1 = \rm y_1 = \frac{log(x+3)}{log 4}[/tex]
RHS;
[tex]\rm log_b(a) = \frac{log_x(a)}{log_x(b)} \\\\ \rm log_2(2+x) \\\\ y_2 = \frac{log(2+x)}{log 2}[/tex]
The system of equations that can represent the equation is,[tex]\rm y_1 = \frac{log(x+3)}{log 4} , y_2 = \frac{log(2+x)}{log 2}[/tex].Option A is correct.
Hence, option A is correct.
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Belinda may choose one of two options for the method in which she may be awarded a money prize. OPTION A: Spin a spinner twice. The spinner is divided into four equally-sized sectors numbered 1, 3, 4, and 5. If the sum of the two spins is greater than 6, Belinda is awarded $8. Otherwise, she must pay $2. OPTION B: Flip a coin three times. If heads appears twice, Belinda is awarded $10. Otherwise, she must pay $2. Belinda chooses the option with the greater mathematical expectation. How much more money can Belinda expect to make by choosing this option over the other option?
Answer:
Belinda can expect to make $1 more with option B.
Step-by-step explanation:
The expected value for every option is calculated as:
[tex]E(x)=x_1*p(x_1)+x_2*p(x_2)[/tex]
Where [tex]x_1[/tex] and [tex]x_2[/tex] are the posibles money prize and [tex]p(x_1)[/tex] and [tex]p(x_2)[/tex] are their respective probabilities.
Option A:
Belinda has 12 possibilities: 1-3, 1-4, 1-5, 3-1, 3-4, 3-5, 4-1, 4-3, 4-5, 5-1, 5-3 and 5-4
From that 12 possibilities, there are 6 that have a sum greater than 6. That possibilities are: 3-4, 3-5, 4-3, 4-5, 5-3 and 5-4
So, the probability that the sum of the two spins is greater than 6 is:
[tex]P=\frac{6}{12} = 0.5[/tex]
At the same way the probability that the sum of the two spins is lower or equal than 6 is 0.5.
So, the expected value for this option is:
[tex]E_A(x)=(8*0.5)+((-2)*0.5)=3[/tex]
Option B:
Belinda has 8 possibilities: HHH, HHT, HTH, HTT, THH, THT, TTH and TTT
Where T means Tails and H means Heads.
Form that 8 possibilities, there are 4 which heads appear twice. That possibilities are: HHH, HHT, HTH and THH.
So, the probability that head appear twice is:
[tex]P=\frac{4}{8}=0.5[/tex]
At the same way, the probability that head doesn't appear or appear once is equal to 0.5
So, the expected value for this option is:
[tex]E_B(x)=(10*0.5)+((-2)*0.5)=4[/tex]
Finally, Belinda can expect to make $1 more with option B.
[tex]E_A(x)-E_B(x)=4-3=1[/tex]
Belinda can expect to make [tex]\( \frac{9}{8} \)[/tex] more units of currency (dollars) by choosing Option A over Option B.
To find the option with the greater mathematical expectation, we need to calculate the expected value (or mean) for each option.
Option A:
Step 1:
- The spinner has numbers 1, 3, 4, and 5.
- There are a total of 16 possible outcomes when spinning the spinner twice (4 outcomes for each spin).
- We need to find the probability of getting a sum greater than 6 and multiply it by $8, and then find the probability of getting a sum less than or equal to 6 and multiply it by -$2.
Step 2:
Let's calculate the probabilities:
1. Probability of getting a sum greater than 6:
- Possible outcomes: (3, 4), (3, 5), (4, 3), (4, 4), (4, 5), (5, 3), (5, 4), (5, 5) (total of 8 outcomes)
- Probability: [tex]\( \frac{8}{16} = \frac{1}{2} \)[/tex]
- Winning amount: $8
2. Probability of getting a sum less than or equal to 6:
- Possible outcomes: (1, 1), (1, 3), (1, 4), (1, 5), (3, 1), (4, 1), (5, 1) (total of 7 outcomes)
- Probability: [tex]\( \frac{7}{16} \)[/tex]
- Losing amount: -$2
Step 3:
Now, we calculate the expected value for Option A:
[tex]\[ \text{Expected value (Option A)} = (\text{Probability of winning}) \times (\text{Winning amount}) + (\text{Probability of losing}) \times (\text{Losing amount}) \][/tex]
[tex]\[ \text{Expected value (Option A)} = \left( \frac{1}{2} \right) \times (8) + \left( \frac{7}{16} \right) \times (-2) \][/tex]
[tex]\[ \text{Expected value (Option A)} = 4 - \frac{7}{8} \][/tex]
[tex]\[ \text{Expected value (Option A)} = \frac{29}{8} \][/tex]
Option B:
Step 1:
- There are 2 ways to get heads twice out of 3 coin flips: (HHH, HHT, HTH, THH)
- There are a total of 8 possible outcomes when flipping a coin three times.
- We need to find the probability of getting heads twice and multiply it by $10, and then find the probability of not getting heads twice and multiply it by -$2.
Step 2:
Let's calculate the probabilities:
1. Probability of getting heads twice:
- Possible outcomes: (H, H, T), (H, T, H), (T, H, H) (total of 3 outcomes)
- Probability: [tex]\( \frac{3}{8} \)[/tex]
- Winning amount: $10
2. Probability of not getting heads twice:
- Possible outcomes: (H, H, H), (T, T, T), (T, T, H), (T, H, T), (H, T, T), (H, T, H) (total of 5 outcomes)
- Probability: [tex]\( \frac{5}{8} \)[/tex]
- Losing amount: -$2
Step 3:
Now, we calculate the expected value for Option B:
[tex]\[ \text{Expected value (Option B)} = (\text{Probability of winning}) \times (\text{Winning amount}) + (\text{Probability of losing}) \times (\text{Losing amount}) \][/tex]
[tex]\[ \text{Expected value (Option B)} = \left( \frac{3}{8} \right) \times (10) + \left( \frac{5}{8} \right) \times (-2) \][/tex]
[tex]\[ \text{Expected value (Option B)} = \frac{30}{8} - \frac{10}{8} \][/tex]
[tex]\[ \text{Expected value (Option B)} = \frac{20}{8} \][/tex]
Step 4:
To find out which option has the greater mathematical expectation, we compare the expected values of Option A and Option B:
[tex]\[ \text{Expected value (Option A)} = \frac{29}{8} \approx 3.625 \][/tex]
[tex]\[ \text{Expected value (Option B)} = \frac{20}{8} = 2.5 \][/tex]
Since [tex]\( \frac{29}{8} \)[/tex] is greater than [tex]\( \frac{20}{8} \)[/tex], Belinda should choose Option A.
To find out how much more money she can expect to make by choosing Option A over Option B, we calculate the difference in expected values:
[tex]\[ \text{Difference} = \text{Expected value (Option A)} - \text{Expected value (Option B)} \][/tex]
[tex]\[ \text{Difference} = \frac{29}{8} - \frac{20}{8} \][/tex]
[tex]\[ \text{Difference} = \frac{29}{8} - \frac{20}{8} = \frac{9}{8} \][/tex]
[tex]\[ \text{Difference} = \frac{9}{8} \][/tex]
Belinda can expect to make [tex]\( \frac{9}{8} \)[/tex] more units of currency (dollars) by choosing Option A over Option B.
The area of a square equals the square of a length of the side of the square. The perimeter of a square equals the sum of the lengths of all four sides. The sum of the areas of two squares is 65, while the difference in their areas is 33. Find the sum of their perimeters.
We can call the areas of the squares x and y. x+y=65 and x-y=33.
x would have an area of 49 and y has an area of 16.
Each side of x would be 7 and each side of y would be 4.
Mrs. Lia has 19 pounds of modeling clay. She divides the clay into 1/2
pound blocks.
If Mrs. Lla sets aside 9 of the blocks and gives the rest to the students in her art class, how many 1/2 pound
blocks of clay does Mrs. Lia glve to her class?