Answers
Hence, the area of the sector is 12.5pie inches squared.
Related Questions
The odds of winning a raffle are 1:9. The probability of winning a carnival game is 0.15. Does the raffle or the carnival game give you a better chance of winning? Explain. The probability of winning the raffle is %. The probability of winning the carnival game is %. So, the gives you a better chance of winning.
Answers
the probability of winning the raffle is 1/9 which is equal to 0.11 approximately
the probability of winning the carnival game is 0.15
in percentage
probability of winning the raffle is 11/100
which implies 11 success out of 100 attempts
probability of winning the carnival game is 15/100
which implies 15 possiblities out of 100 trials
thus the carnival game gives a better chance because it has more amount successful outcomes compared to the raffle
Identify the variable and the constant in the expression below.18 +tVariable:Constant
Answers
From the expression 18 + t, the constant is 18 and the variable is t.
If you deposit $100 each month into an IRA earning 2.3% interest, how much will you have in the account after 17 years? Round your answer to the nearest cent.
Answers
Given:
The amount deposited each month, d=$100.
The rate of interest, R=2.3%.
The number of years after which the balance in the account is calculated, N=17.
The formula for the balance in the acoount after N years is,
[tex]P_N=\frac{d((1+\frac{r}{k})^{Nk}-1)}{(\frac{r}{k})}\text{ ---(1)}[/tex]Here, r is the interest rate in decimal form and k is the number of compounding periods in one year.
Since deposit is made every month, we use monthly compounding, k=12.
The rate of interest in decimal form is,
[tex]r=\frac{R}{100}=\frac{2.3}{100}=0.023[/tex]Now, substitute the known values in equation (1).
[tex]\begin{gathered} P_{17}=\frac{100((1+\frac{0.023}{12})^{17\times12}-1)}{(\frac{0.023}{12})}\text{ } \\ P_{17}=\frac{100((1+\frac{0.023}{12})^{204}-1)}{(\frac{0.023}{12})}\text{ } \\ P_{17}=24934.19 \end{gathered}[/tex]Therefore, after 17 years, the balance in the account will be $24934.19, to the nearest cent.
table below shows the circumstances of a tree trunk as the tree ages. which statement describes the rate of change shown in the table?
Answers
Remember that
the arte of change is the the same that the slope
so
we take two points
(4,6) and (7,9)
m=(9-6)/(7-4)
m=3/3
m=1 in/year ------> rate of change
the equation is slope intercept form is
y=mx+b
we have
m=1 -
point (4,6)
substitute
6=1(4)+b
b=2
y=x+2
Verify the other ordered pairs with the equation
For x=11 ------> y=11+2=13 is ok
For x=16 -----> y=18 is ok
For x=22 -----> y=24 is ok
therefore
the answer is option AThe probability of choosing two green balls without replacement is 111, and the probability of choosing one green ball is 13.What is the probability of drawing a second green ball, given that the first ball is green?
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given probabilities
[tex]\begin{gathered} Pr(2\text{ greens\rparen}=\frac{1}{11} \\ Pr(one\text{ green\rparen}=\frac{1}{3} \end{gathered}[/tex]STEP 2: Write the probability formula for probability of second green given first green
[tex]\begin{gathered} Pr(G2|G1)=\frac{Pr(2\text{ greens\rparen}}{Pr(one\text{ green\rparen}} \\ =\frac{1}{\frac{11}{\frac{1}{3}}}=\frac{1}{11}\div\frac{1}{3}=\frac{1}{11}\times\frac{3}{1}=\frac{3}{11} \end{gathered}[/tex]Hence, the answer is 3/11
Write the equation In vertex form describe the transformation of the parents function y= x^2
Answers
Given:
[tex]\frac{(x-3)(x+2)}{(x+1)(x-3)}[/tex]Find-:
State any restriction on the variable
Explanation-:
Simplify the expression
[tex]\begin{gathered} =\frac{(x-3)(x+2)}{(x+1)(x-3)} \\ \\ =\frac{x+2}{x+1} \end{gathered}[/tex]Denominal is not equal to zero then
[tex]\begin{gathered} x+1\ne0 \\ \\ x\ne-1 \end{gathered}[/tex]So the function restricts at x=1.
One day, Jada takes home $90.45 after working h hours and after paying the bus fare. Write an equation to represent this situation.
Answers
The equation to represent this situation is t = b + h*p + 90.45.
It is given in the question that:-
Amount of money Jada takes home = $ 90.45
Number of hours Jada worked = h
We have to write an equation to represent the situation.
According to the data given in the question, we can write,
Total money with Jada = Bus fare + number of hours Jada worked*price per hour of working + amount of money Jada takes home
Let the bus fare be b.
The Total money with Jada be t.
Price per hour = p
Hence, we can write,
t = b + h*p + 90.45
To learn more about equation, here:-
https://brainly.com/question/10413253
#SPJ1
Learning Page? QUESTIONA certain brand of coffee comes in two sizes. An 11.5-ounce package costs $4.24. A 27.8-ounce package costs $9.98.Find the unit price for each size. Then state which size is the better buy based on the unit price.Round your answers to the nearest cent.74°FComputing unit prices to find the better buyStartUnit price for the 11.5-ounce package: $ per ounceUnit price for the 27.8-ounce package: $per ounceThe better buy:OO EXPLANATION0The 11.5-ounce packageThe 27.8-ounce packageNeither (They have the same unit price)I need help with this math problem
Answers
TEXPLANATION
For the 11.5-ounce package that costs $4.24. The unit price per pound is
[tex]unit\text{ price}=\frac{cost}{quantity}=\frac{4.24}{11.5}=0.37[/tex]For the 27.8-ounce package that costs $9.98.
[tex]unit\text{ price}=\frac{9.98}{27.8}=0.36[/tex]Answer: Box A = 0.37, Box B= 0.36. The better buy is the 27.8-ounce package
Express (81^1/2) ^5 in simplest radical form
Answers
1) Let's simplify this expression, making use of the properties of the exponents.
2) So we can write it out:
[tex]\begin{gathered} (a^b)^c=a^{bc} \\ (81^{\frac{1}{2}})^5=((9^2)^{\frac{1}{2}})^5=(9^{\frac{2}{2}})^5=9^5 \end{gathered}[/tex]Note that we rewrote 81 as power and then applied the property of the exponents
convert 4x + y equals negative 1 from standard form to slope intercept form
Answers
Given data:
The given expression is 4x+y=-1.
The given expression can be written as,
y=-4x-1.
Here, slope is -4, and y-intercept is -1.
Thus, the slope intercept form is y=-4x-1.
Which of the following is the product of the rational expressions shown here?Х/x-2•3/x-2A. X+3/2x -4B. 3x/x^2- 4x + 4c. 3x/x^2-4
Answers
Step 1: Write out the expression
[tex]undefined[/tex]the elevator in an office building starts at ground level and goes up at a speed of 6 feet per second for 7.5 second then it goes down at a speed of 10 feet per second for 8 seconds what is the elevators elevation now
Answers
when it is going up
[tex]x=16\cdot7.5=120[/tex]so when it stops, it has a elevation of 120 feet
[tex]x=120-10\cdot8=40[/tex]so the final elevation is 40 feet
The principle is borrow a simple interest rate R for a period of time
Answers
Simple interest = Principal x Rate x Time : 100
Simple interest = 7000 x (0.04) x 1
Simple interest = $280
Answer: $280
Solve the following quadratic equation for all values of x in simplest form. 6- 2.r? = -2
Answers
EXPLANATION
Given the equation 6 - 2x^2 = -2
Adding -6 to both sides
6 - 6 - 2x^2 = -2 -6
Simplifying:
-2x^2 = -8
Dividing both sides by -2:
x^2 = -8/-2
Simplifying the fraction:
x^2=4
Applying the square root to both sides:
[tex]x_1,x_2=\pm\sqrt[]{4}[/tex]Solving the square root:
[tex]x_1,x_2=\pm2[/tex]The answer is +- 2
#4 DLet ZD be an acute angle such that sin D = 0.19. Use a calculator to approximate the measure of ZD to the nearest tenthof a degree.m/D
Answers
Given that
angle D=?
[tex]Sin(D)=0.19[/tex]Solving for D
[tex]D=ArcSin(0.19)[/tex][tex]D=0.19116[/tex]Round to the nearest tenth
measure angle D = 0.2
) I want another BMW i-8 that costs $98,316.00 for 5 years at an APR of 1.02%. What is my monthly payment?
Answers
$1681.76
Explanation
Step 1
Let
M = the total monthly mortgage payment.
P = the principal loan amount=98316
Annual Percentage Rate=1.02%=0.0102
montly rate=0.0102/12=0.00085
n = number of payments over the loan’s lifetime=5*12=60 months
then
[tex]M=P(\frac{r(1+r)^n}{(1+r)^n-1})[/tex]then, replace
[tex]\begin{gathered} M=98310(\frac{0.0102(1+0.0102)^{60}}{(1+0.0102)^{60}-1}) \\ M=98310(\frac{0.018}{1.0102^{60}}) \\ MonthlyPayment=$1,681.76$ \end{gathered}[/tex]I hope this helps you
Mr. Gordon’s science class is studying blood types. The table below shows the probability that a person living in the US has a particular blood type. The probability of having a blood type: O= 9/20; A= 41/100; B= 1/10; and AB= 1/25What is the probability that three students selected randomly from the class will have A, B, and AB blood, respectively?A.) 41/25,000 or 0.16%B.) 41/2500 or 1.64%C.) 43/25,000 or 0.17%D.) 43/135 or 31.9%
Answers
Given the probability of having a blood type:
O = 9/20
A = 41/100
B = 1/10
AB = 1/25
Let's find the probability that three students selected at random from the class will have A, B, and AB blood respectively.
Let's first verify if the events are mutually dependent or independent:
[tex]\begin{gathered} \frac{9}{20}+\frac{41}{100}+\frac{1}{10}+\frac{1}{25} \\ \\ \frac{5(9)+1(41)+10(1)+4(1)}{100} \\ \\ \frac{45+41+10+4}{100} \\ \\ =\frac{100}{100} \\ \\ =1 \end{gathered}[/tex]Since the total probability is 1, the events are mutually independent.
Since the events are mutually independent, to find the probability a randomly selected student will have A, B, and AB blood respectivel, we have:
[tex]\begin{gathered} P(A)*P(B)*P(AB) \\ \\ =\frac{41}{100}*\frac{1}{10}*\frac{1}{25} \\ \\ =\frac{41*1*1}{100*10*25} \\ \\ =\frac{41}{25000} \\ \\ =0.00164\approx0.16\text{ \%} \end{gathered}[/tex]Therefore, the probability that three students selected randomly from the class will have A, B, and AB respectively is 41/25,000 or 0.16%
ANSWER:
A.) 41/25,000 or 0.16%
find the distance of (-3, -5) and (4,4)
Answers
√130
1) To find the distance between two points. We can use a formula derived from the Pythagorean Theorem:
[tex]d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]In this case,
[tex]d=\sqrt[]{(4+3)^2+(4+5)^2}=\sqrt[]{130}[/tex]So the distance between those two points is √130
An object is launched at 19.6 meters per second (m/s) from a 58.8-meter tallplatform. The equation for the object's height s at time t seconds after launch is s(t) =-4.9t^2 +19.6t+ 58.8, where s is in meters.a) When does the object strike the ground?b) What is the initial height of the object?c) What is the maximum height of the object?
Answers
Solution
Step 1
[tex]s(t)\text{ = -4.9t}^2+19.6t+58.8[/tex]a)
The object strike the ground at s(t) = 0
[tex]\begin{gathered} s(t)=\text{-4.9t}^2\text{+19.6t+58.8} \\ \\ -4.9t^2\text{{}+19.6t+58.8 = 0} \end{gathered}[/tex][tex]\begin{gathered} \mathrm{Multiply\:both\:sides\:by\:}10 \\ -4.9t^2\cdot \:10+19.6t\cdot \:10+58.8\cdot \:10=0\cdot \:10 \\ -49t^2+196t+588=0 \\ t_{1,\:2}=\frac{-196\pm \sqrt{196^2-4\left(-49\right)\cdot \:588}}{2\left(-49\right)} \\ t_{1,\:2}=\frac{-196\pm \:392}{2\left(-49\right)} \\ Separate\:the\:solutions \\ t_1=\frac{-196+392}{2\left(-49\right)},\:t_2=\frac{-196-392}{2\left(-49\right)} \\ \mathrm{The\:solutions\:to\:the\:quadratic\:equation\:are:} \\ t=-2,\:t=6 \\ t\text{ cannot be negative} \\ t\text{ = 6 seconds} \end{gathered}[/tex]b)
The initial height = 58.8
c)
[tex]\begin{gathered} At\text{ maximum height, }\frac{ds(t)}{dt}=0 \\ \\ s(t)\text{ =}-4.9t^2+19.6t+58.8 \\ \\ \frac{ds(t)}{dt}=\text{ -9.8t + 19.6} \\ \\ -9.8t\text{ + 19.6 = 0} \\ \\ 9.8t\text{ = 19.6 } \\ \\ t\text{ =}\frac{19.6}{9.8}=2\text{ seconds} \\ \\ Maximum\text{ height =}-4.9\times2^2+19.6\times2+58.8 \\ \\ =-2^2\times \:4.9+39.2+58.8 \\ =78.4 \\ Maximum\text{ height = 78.4} \end{gathered}[/tex]What is the volume of the compositefigure shown? Use 3.14 for 1.
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first, we find the volume of cone
[tex]V=\frac{\pi\cdot r^2\cdot h}{3}=\frac{\pi\cdot2^2\cdot6}{3}=\frac{\pi\cdot4\cdot6}{3}=\frac{\pi\cdot24}{3}=8\pi[/tex]then, we find the volume of the semisphere
[tex]V=\frac{2}{3}\cdot\pi\cdot r^3=\frac{2}{3}\cdot\pi\cdot2^3=\frac{2}{3}\cdot\pi\cdot8=\frac{16}{3}\pi[/tex]so the volume of figure is:
[tex]V=8\pi+\frac{16}{3}\pi=\frac{40}{3}\pi=\frac{40}{3}(3.14)=\frac{125.6}{3}=41.87[/tex]answer: 41.87 in^3
Flashdance Furniture Company ordered 25 sofas at a list price of $1,950 each. The company received a 24% trade discount, plus an additional 5% off (after the tradediscount) if the final invoice was over $30,000. What was the wholesale price paid by the company?$30,678.54$35,197.50$37,123.90$38,348.62None of these choices are correct.
Answers
I'll solve this problem using proportions
1950 x 25 = $48750
Original price = $48750
Considering the 5% discount
48750 ------------------- 100
x ------------------- 5
x = (5 x 48750)/100
x = 2437.5
Price = 48750 - 2437.5
= 46312.5
46312.5 ------------------- 100
x ------------------ 24
x = (24 x 46312.5) / 100
x = 1111500/100
x = 11115
Final price = 46312.5 - 11115
= $ 35197.5
The second choice is the correct solution.
For each problem below, solve theequation for the missing variable.Then, use that equation to find themissing quantity in the situation. Showall steps.Question 3
Answers
Solution:
To find the area, A, of a triangle, the formula is
[tex]\begin{gathered} A=\frac{1}{2}bh \\ A\text{ is the area } \\ b\text{ is the base} \\ h\text{ is the height} \end{gathered}[/tex]Given that;
[tex]\begin{gathered} A=84\text{ m}^2 \\ h=12\text{ m} \end{gathered}[/tex]Substitute the values of the variables into the formula above
[tex]\begin{gathered} A=\frac{1}{2}bh \\ 84=\frac{1}{2}\times b\times12 \\ 84=6b \\ b=\frac{84}{6} \\ b=14\text{ m} \end{gathered}[/tex]Hence, the measure of the base, b is 14 m
6x+8=28 find the value of X
Answers
Give the equation for a circle with the given center and radius.Center at (-1, 3), radius = 4A. (x+3)2+(y−1)2=4B. (x−1)2+(y+3)2=16C. (x+1)2+(y−3)2=16D. (x−3)2+(y+1)2=4Don't need explanation just answer!
Answers
ANSWER:
C. (x + 1)² + (y − 3)² =16
STEP-BY-STEP EXPLANATION:
We have that the equation of the circle has the following structure:
[tex]\begin{gathered} \left(x−a\right)^2+\left(y−b\right)^2=r^2 \\ \\ \text{ Where \lparen a, b\rparen is the center and r is the radius.} \end{gathered}[/tex]We replace the center and the radius and we are left with the following:
[tex]\begin{gathered} \left(x-(-1)\right)^2+\left(y-3\right)^2=4^2 \\ \\ \left(x+1\right)^2+\left(y-3\right)^2=16 \end{gathered}[/tex]This means that the correct answer is C. (x + 1)² + (y − 3)² =16
Solve the following system of linear equations using elimination. 3r- y=5 x=y=1
Answers
3x - y = 5 Equation l
x - y = 1 Equation ll
By elimination
-Multiply equation l by -1
-3x + y = -5
x - y = 1
-2x = -4
Solve for x
x = -4/-2
x = 2
-Find y
2 - y = 1
-y = 1 - 2
-y = -1
y = -1/-1
y = 1
Solurtion: x = 2, y = 1
malfunctioned and ruined 13 half gallons. If the remaining ice cream is sold for $4.02 per half gallon, how many half gallons did the store buy if they made a profit of $72.70
Answers
Given:
malfunctioned and ruined 13 half gallons.
Which name would represent the angle shown in yellow? D A
Answers
We can name an angle with the 3 letters of the points that define it, being the vertex the point that is written in the middle of the 3 letters.
In this case, the yellow angle is defined by the points I, A and B, where A is the vertex of the angle.
Then, we can name the angle as It can also happens that more of 3 points can be use to define and angle, but it is not the case for the yellow angle in this example.
Answer:
the lemur population on an island is declining at a rate of 2.3% per year. the population was 3,700 in the year 2008. what is the best prediction of the population in the year 2017? round to the nearest whole number.
Answers
Given:
2008 : 3,700 population
decrease of 2.3% per year.
100% - 2.3% = 97.7%
2017 - 2008 = 9 years
3,700 * (0.977)^9 = 3000.9088
The lemur population in 2017 will be 3000.9088
Solve this system of equations. Fill in the blank with the correct point. a=-b + 5 2b+a=11
Answers
Answer:
The solution to the system of equations is:
a = -1
b = 6
Explanation:
Given the system of equations:
a = -b + 5 .............................................................(1)
2b + a = 11 ............................................................(2)
Substituting the expression for a in equation (1) into equation (2), we have:
2b + (-b + 5) = 11
2b - b = 11 - 5
b = 6
Using this value of b in equation (1), we have:
a = -6 + 5
= -1
Therefore,
a = -1
b = 6
Hello can you help me? I want to know if I did this correctly. A - 624B - 729C - 652D - 843
Answers
Remember that
The area of a triangle is equal to
A=(1/2)(b)(h)
In this problem
b=36 km
h=XU
step 1
Find the length segment XU
In the right triangle XWU
we have
sin(67)=XU/WU -----> by opposite side divided by the hypotenuse
XU=WU*sin(67)
XU=44*sin(67)
XU=40.50 KM
step 2
Find the area
A=(1/2)(36)(40.50)
A=729 Km2option B