Answer:
CI = $182.25
Step-by-step explanation:
Compound interest formula:
[tex]Compound \space\ Interest= P(1 + \frac{r}{100})^{n} - P[/tex] ,
where P is the principal amount ($4000), r is the interest rate (2%), and n is the time period (2 years and 3 months = 2.25 years).
Using formula:
CI = [tex]4000(1 + \frac{2}{100} )^{2.25} - 4000[/tex]
CI = $182.25
\Triangle X Y Z is shown. Angle X Z Y is 63 degrees. The length of X Z is 2.7 and the length of X Y is 2.8.
Law of sines: StartFraction sine (uppercase A) Over a EndFraction = StartFraction sine (uppercase B) Over b EndFraction = StartFraction sine (uppercase C) Over c EndFraction
Which is the approximate measure of angle Y? Use the law of sines to find the answer.
52°
59°
64°
67°
in the game of roulette, a player can place a $ 7 bet on the number 28 and have a 1/38 probability of winning. if the metal ball lands on 28, the player gets to keep the $7 paid to play the game and the player is awarded $245. otherwise, the player is awarded nothing and the casino takes the player's $7. what is the expected value of the game to the player? if you played the game 1000 times, how much would you expect to lose?
Answer: The player expects to lose 184.21 dollars.
=========================================================
Explanation:
X = net winnings in dollars
Ignore the "28" because it's really not that relevant here. All we care about is the probability 1/38 which is the probability of winning money. The probability of losing money is 1 - (1/38) = 37/38. Put another way: there's 1 way to win, and 37 ways to lose.
If the player wins, then they walk away with 7+245 = 252 dollars
If the player loses, then their "winnings" is -7
So either X = 252 or X = -7 are the only two options.
Let's form a table showing those options with their corresponding probabilities.
[tex]\begin{array}{|c|c|} \cline{1-2}X & P(X)\\\cline{1-2}252 & 1/38\\\cline{1-2}-7 & 37/38\\\cline{1-2}\end{array}[/tex]
Now multiply each X value and P(X) value across the rows.
252*(1/38) = 6.631579
-7*(37/38) = -6.815789
These values are approximate.
[tex]\begin{array}{|c|c|c|} \cline{1-3}X & P(X) & X*P(X)\\\cline{1-3}252 & 1/38 & 6.631579\\\cline{1-3}-7 & 37/38 & -6.815789\\\cline{1-3}\end{array}[/tex]
Add up the results of the third column
6.631579 + (-6.815789) = -0.18421
This represents the net winnings for any average spin of the wheel. The player unfortunately expects to lose, on average, about $0.18421 or 18.421 cents per spin.
Do this 1000 times and the player should expect to lose about
1000*(0.18421) = 184.21 dollars
Keep in mind that due to the random nature of roulette wheel, the player may get lucky or their luck may be worse than what is described. The idea is that over the long run, the average should be somewhat close to losing 184.21 dollars.
Another way to think of it could be to have 1000 players doing the same game (rather than have 1 person play the same game 1000 times). Some players may get lucky, while others may not get so lucky. But their collective average should be losing that $184.21
Question 7 of 10
Classify the following triangle. Check all that apply.
Answer:
A,C,E
(if you find a better answer choose that.)
Step-by-step explanation:
This one has two acute angles and one obtuse.
This one is a scalene.
So, tick A,C,E
Fill in the blanks below.
Find the slope of the line passing through the points (8,5) and (8,-4).
Step-by-step explanation:
please mark me as brainlest
For what values of x is the following polynomial expression undefined?
x^2+4x+32/x^2−x−10∗2x^2+4x^3/x^2+3x÷x^2+3x+2/x
The values of x for which the expression [tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]is undefined are 0,[tex]\sqrt{41} /2[/tex] and imaginary numbers.
Given Expression :x^2+4x+32/x^2−x−10∗2x^2+4x^3/x^2+3x÷x^2+3x+2/x
We have to find out those values of x for which the expression does not exists.
[tex](x^{2} +4x+32)/(x^{2} -x-10)(2x^{2} +4x^{3} )+4x^{3} /x^{2} +3x/x^{2} +3x+2/x[/tex]
We have to take LCM of the expression which is equal to [tex]x^{3}(x^{2}-x-10)(2x^{2} +4x^{3})[/tex]
LCM is the smallest positive integer that is divisible by both the numbers whose LCM is found.
and it is present in the denominator.
Expression if exists cannot take denominator equal to 0.
So, by putting LCM equal to zero we find
x=0,x=imaginary numbers and x=[tex]\sqrt{41} /2[/tex].
Hence the given expression have not take values of x=0,[tex]\sqrt{41} /2[/tex], imaginary number.
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41% of adults say cashews are their favorite kind of nut. You randomly select 12 adults and ask each to name his or her favorite nut. Find the probability that the number who say cashews are their favorite nut is (a) exactly three, (b) at least four, and (c) at most two. If convenient, use technology to find the probabilities.
The probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
41% of adults say cashews are their favorite kind of nut.
P = 41% = 0.41
Q = 1 - P = 1 - 0.41 = 0.59
n = 2
From the binomial distribution:
[tex]\rm P(X = r) = C(n, r) P^r(1-P)^{n-r}[/tex]
a) Exactly three
[tex]P(X=3) = C(12, 3) (0.41)^3(0.59)^9[/tex]
P(X = 3) = 0.131
b) At least four:
P(X≥4) = P(X=4)+ P(X=5)+ P(X=6)+..............+ P(X=13)
[tex]\rm P(X\geq 4)=C(12, 4) (0.41)^4(0.59)^9+C(12, 5) (0.41)^5(0.59)^8+...............+C(12, 3)(0.41)^3(0.59)^9[/tex]
P(X ≥ 4) = 0.795
c) At most two:
P(X≤2) =P(X=0)+ P(X=1)+ P(X=2)
[tex]\rm =C(12, 0) (0.41)^0(0.59)^12+C(12, 1) (0.41)^1(0.59)^1^1+C(12, 2)(0.41)^2(0.59)^1^0[/tex]
P(X ≤ 2) = 0.0733
Thus, the probability for part (a) is 0.131, for part (b) is 0.795, for part (c) is 0.0733.
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1. What is pi?
2. And why is it important?
Answer:
pi [π] is the ratio of a circle's circumference to its diameter, and it is constant [meaning it is always the case] for all circles.
{this is a long number, 3.141592653589793238... is not even the full length, but 3.14 [or 3.14159] is typically used for estimation}
The significance of pi is typically centered in math--it can be used to find values that we don't know of circles. There are other areas of math that have been related back to the value of pi--which is incredible, and genuinely relevant.
We can find pi in the shape of rivers, physics--including waves--DNA
[+ anywhere there is a circle]
hope this helps!! :)
Answer:
ratio of circle's circumference to diameter
it is constant
Addison and Kelsey are running on a path modeled by x2 + y2 – 14x – 16y – 287 = 0, where the distance is in meters. What is the maximum distance between the runners at any given time?
20 meters
32 meters
40 meters
140 meters
Answer:
40 meters
Step-by-step explanation:
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
Given that, Addison and Kelsey are running on a path modeled by x² + y² - 14x - 16y - 287 = 0.
What is a circle equation?The equation of circle provides an algebraic way to describe a circle, given the center and the length of the radius of a circle. The equation of a circle is different from the formulas that are used to calculate the area or the circumference of a circle.
The standard equation of a circle with center at (x1,y1) and radius r is (x-x1)²+(y-y1)²=r²
Here, the circular path is modeled by x² + y² - 14x - 16y - 287 = 0
We complete the squares to place it in the standard format, thus:
x² - 14x + 49 + y² - 16y +64 = 287+49+64
⇒ (x-7)² + (y-8)² = 400
⇒ (x-7)² + (y-8)² = 20²
So, r² = 20²
⇒ r = 20 meters
Maximum distance = d = 2r
= 40 meters
The maximum distance between the runners at any given time 40 meters. Therefore, option C is the correct answer.
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If AABC= ADEF, which congruences are true by CPCTC? Check all that
apply.
∠A ≅ ∠D , BC≅ EF , AC ≅ DF , option B , C , F are the correct answer.
What is CPCTC ?CPCTC stands for corresponding parts of congruent triangles are congruent .
This means when two triangles are congruent then the corresponding sides are also congruent.
In the given triangles , Δ ABC ≅ ΔDEF
∠A ≅ ∠D
BC≅ EF
AC ≅ DF
Therefore option B , C , F are the correct options
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Find the equation of a line containing the points (−2,−4) and (1,−3).
The earnings for a cashier at the local grocery store varies directly with how many hours she works. If the cashier is paid $524 for a 40 hour work week, how many hours would it take for him to make 720.50? Enter the number only.
Using proportions, it is found that it would take 55 hours for him to make $720.50.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
He is paid $524 for a 40 hour work week, hence per hour he earns?
r = 524/40 = $13.1.
The amount of hours he would need to make $720.50 is given by:
h = 720.50/13.1 = 55.
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Which expression is equivalent?
Answer:
Last one/D 9^9/5/5^9/10
Step-by-step explanation:
On a unit circle, Ø = 60°. Identify the terminal point and Tan Ø
The terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
What is angle measurement?An angle measure is the measurement of the angle created by two rays or arms at a shared vertex in geometry. A protractor is used to measure angles in degrees (°).
Given;
Ø = 60°
Let's assume the value of r = 1 units
The terminal points are;
x= rcosΘ
x=1 × cos 60°
x=0.5
y=rsinΘ
y=rsin60°
y = 0.86
The terminal points when the value of r is 1 will be 0.5 and 0.86.
The value of the tan for the given value of the angle;
Tan 60° = 1.732
Hence, the terminal points when the value of r is 1 will be 0.5 and 0.86 and the value of tan 60 will be 1.732.
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What is the surface area of the cylinder below?
Answer:
Surface Area = 378.25
Step-by-step explanation:
Comment
It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.
Area lids
diameter = 11.4
radius = d/2
radius = 11.4/2
radius = 5.7
Area = pi * r^2
Area = (3.14 * 5.7^2) * 2 There are 2 lids.
Area = 102.01 yd^2
Area body
This is found by finding the circumference of the lid and multiplying by the height
Circumference
C = 2*pi*r
2*r = the diameter
2*r = 11.4
C = 3.14*11.4
C = 35.80
Area body
Area body = C* h
h = 7.8
Area body = 35.80 * 7.8
Area body = 279.24
Total Area = 102.01 + 279.24 = 378.25
10,000,000,000 is which power of ten? 21 -1 10 100
Answer:
10
Step-by-step explanation:
There are ten zeros therefore in standard form it is 1 x 10 to the power of 10 or [tex]10_{12}[/tex]
Based on the circle graph,how many pounds of milk and eggs does the average American consume each year?PLEASE EXPLAIN IMAGE IS PROVIDED
E.300
F.368
G.460
H.552
About 492 pounds of milk and egg were consumed each year
Pie charts and percentagesGiven the following parameters from the chart
Total consumption = 1640 pounds per person
The percentage of milk and egg = 100 -(38 + 10 + 10 +8 + 4)
The percentage of milk and egg = 30%
Determine the amount consumed each year
Amount of milk and egg consumed = 30% of 1640
Amount of milk and egg consumed = 492 pounds
Hence about 492 pounds of milk and egg were consumed each year
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1
2
3
at
4
927
5
6
Which graph represents g(x)?
7
8
The graph of f(x) = x² is translated to form g(x) = (x - 5)² + 1. What does the graph look like?
6
10
Two trains leave station 416 miles apart. One train is traveling 90 miles per hour while the other is traveling 70 miles per hour. How long will it take the two trains to meet
Answer:
2.6 hours
Step-by-step explanation:
Let t be the time that the trains meet.
[tex]90t = 416 - 70t[/tex]
[tex]160t = 416[/tex]
[tex]t = 2.6[/tex]
What is the slope of the line that passes through the points (6, 2) and (4, 10)? −4 −14 14 4
Answer:
-4
Step-by-step explanation:
The equation for slope is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
m: Slope
(6, 2) = [tex](x_1, y_1)[/tex]
(4, 10) = [tex](x_2, y_2)[/tex]
Substitute these values into the equation:
[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]
Therefore the slope is -4.
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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the slope of the line that passes through the points? 2 points given
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract
[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate
[tex]\bf{-4}[/tex]
[tex]\rule{300}{1.7}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Slope\;-4}[/tex]
[tex]\boxed{\bf{aesthetic\not101}}[/tex]
There are nine baseball players in the cafeteria The number of baseball players is one less than twice the number of golfers find the number of golfers
Using a system of equations, it is found that the number of golfers in the cafeteria is of 5.
What is a system of equations?A system of equations is when two or more variables are related, and equations are built to find the values of each variable.
In this problem, the variables are:
Variable x: Number of baseball players.Variable y: Number of golf players.The number of baseball players is one less than twice the number of golfers, hence:
x = 2y - 1.
Since x = 9:
9 = 2y - 1
2y = 10
y = 5.
There are 5 golfers in the cafeteria.
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Use the given sample data to find Q3.
49 52 52 52 74 67 55 55
The given sample data the Q3=61
We begin by ordering the data from smallest to largest.
Next, find the median of the data.
The data set has 8 values, so the two middle values are 52 and 55.
49 52 52 52 55 55 67 74
What is the formula for the median?Median = (52 + 55) / 2
Median= 53.5
The third quartile (Q3) is the 25th percentile or the median of the upper half of the data.
To find the median of all the values that lie above 53.5.
Q3 = (55 + 67)/ 2
Therefore the Q3=61
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i give brainliest to first person who gets it correct
Answer:
(-4,-3)
Step-by-step explanation:
The point where those 2 equations intersect is (-4,-3)
there are 48 tables at a school.
3/8 of the tables are in the dining hall.
the rest are shaded equally between 5 classrooms.
how many tables are in the main hall
Total: 48
DIning Hall: 48(3/8)=18
so theres 30 left for the classes
30/5(#of classes)=6 per class
At 50 minutes how far is the winning runner use ur equations
Answer:
3.5 km
Step-by-step explanation:
in a study of birth orders and intelligence, IQ test were given to 18 and 19 years old men to estimate the size of difference, if any, between the main IQs of firstborn sons and second born sons. The following data for 10 firstborn sons and 10 second born sons are consistent with the means and standard deviation's reported in the article. It is reasonable to assume that the samples come from populations that are approximately normal. First born numbers are 107, 113, 84, 126, 99, 95, 98, 109, 91, 90. Second born numbers are 112, 92, 102, 86, 97, 106, 105, 116, 109, 95. construct a 95% confidence interval for the difference in mean IQ between first born and second born sons. Let them one denote the main IQ of firstborn sons.
In a study of birth orders and intelligence, IQ tests were given to 18 and 19 years old men to estimate the size of the difference, we have that [tex]|t|=0.618\leq t_c =2.101[/tex] and for this reason, we cannot reject the null hypothesis.
What are the Test Statistics?Null and Alternative Hypotheses
[tex]H_o: \mu_{1} = \mu_{2}\\\\Ha: \mu_1 \neq \mu_2 .[/tex]
Since the population standard deviations are unknown, we will apply a t-test on the means of the two populations, using two independent samples.
The degrees of freedom are df = 18, and the significance threshold is set at alpha = 0.05, based on the data presented. If we assume that the population variances are the same, we can calculate the degrees of freedom in this way:
The rejection region for this two-tailed test is R = \{t : |f| > 2.101}
Therefore the Test Statistics is
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
[tex]t= \frac{X 1 -X 2 }{\frac{\sqrt{ (n_1 -1)s_1 ^ 2 +(n_2 -1)s_2 ^2}} {n_1 +n_2 -2} (( 1/n_1 + 1 n_2 )}}[/tex]
t=0.618
In conclusion. we have that [tex]|t|=0.618\leq t_c =2.101[/tex]
For this reason, we cannot reject the null hypothesis.
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Please help, will give the brainliest!
(J) 80 • 125
(K) (80+65) • 125
(L) (65 • 80) + (80 • 60)
M (65•80)+(80•60)
N (65•80)+ 1/2 (125 • 100)
Answer:
option N is the correct option, apply Formula of area of rectangle and triangle by splitting figure into 2 parts
Write an equation of the line that passes through a pair of points: On a coordinate plane, a line goes through (4, 1) and (5, 2). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 Please select the best answer from the choices provided A B C D
Answer:
b. y = x - 3
Step-by-step explanation:
The general form of the equation of the line is y = mx + c.
1) Find for m (gradient) using the following formula:
m = y2 - y1 / x2 - x1
Substitute the values into it and solve for m.
m = 2 - 1 / 5 - 4
m = 1 / 1
m = 1
2) Substitute into m of the y = mx + c.
y = 1x + c
3) Choose one the coordinates that the line goes through ((4, 1) or (5, 2)) to find c (y-intercept). I will choose (4, 1). Then, substitute your chosen coordinates into your newfound equation (y = 1x + c)
1 = 1(4) + c
1 = 4 + c
1 - 4 = c
-3 = c
Substitute -3 in place of c.
y = 1x - 3, which can be simplified to y = x - 3. Therefore, the correct choice is b.
I need help with my geometry proof homework from 2-3
Answer: Tbh i don’t know anything besides that all the angles are equal to another and you have to prove it. I would just say: “90 degrees = 90 degrees
Sorry mate I can’t help
Step-by-step explanation:
What is the square root of -1? Complex numbers
Answer:
The square root of -1 is i
Step-by-step explanation:
"i" is the imaginary unit and represents the value of sqrt -1
Which of the following best describes the expression below when i = √-1?
3+4i
A. Complex number
B. Real number
C. Irrational number
D. Rational number
The answer is A. Complex number
