Step-by-step explanation:
Given:
Deposit P = $9000Interest rate r = 5% = 0.05Time t = 1 yearNumber of compounds n = 4A. Find the value of one year
[tex]A = P(1 + r/n)^{nt} = 9000(1+0.05/4)^4=9458.51[/tex]B. Use the future value formula for simple interest to determine the effective annual yield
[tex]A=P(1+rt)\\[/tex][tex]r=(A/P-1)/t[/tex][tex]r=(9458.51/9000-1)/1=0.0509[/tex] r = 5.1%Answer:
A) $9458.51
B) 5.09% (2 d.p.)
Step-by-step explanation:
Part ACompound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $9000r = 5% = 0.05n = 4 (quarterly)t = 1 yearSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=9000\left(1+\frac{0.05}{4}\right)^{4 \times 1}[/tex]
[tex]\implies \sf A=9000(1.0125)^4[/tex]
[tex]\implies \sf A=9458.508032...[/tex]
Therefore, the value of the account after 1 year is $9458.51.
Part BSimple Interest Formula
A = P(1 + rt)
where:
A = final amountP = principalr = interest rate (in decimal form)t = time (in years)Given:
A = $9458.51P = $9000t = 1 yearSubstitute the given values into the formula and solve for r:
[tex]\implies \sf 9458.51=9000(1+r(1))[/tex]
[tex]\implies \sf 9458.51=9000(1+r)[/tex]
[tex]\implies \sf \dfrac{9458.51}{9000}=1+r[/tex]
[tex]\implies \sf r=\dfrac{9458.51}{9000}-1[/tex]
[tex]\implies \sf r=0.050945...[/tex]
[tex]\implies \sf r=5.0945... \%[/tex]
Therefore, the effective annual yield is 5.09% (2 d.p.).
According to a 2014 Pew Research poll, 58% of Americans believe in Hell. Suppose a random sample of 100 Americans is obtained and the number of Americans who believe in Hell is recorded. Can this binomial experiment be approximated using a normal distribution? Be sure to demonstrate your conclusion numerically.
Testing the conditions, we get that [tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.
For each person sampled, there are only two possible outcomes. Either they believe in Hell, or they do not. The probability of a person believing in hell is independent of any other person, which means that the binomial distribution is used to solve this question.
Binomial distribution:
Probability of x successes on n trials, with p probability.
If [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex], it can be approximated to the normal distribution.
In this problem:
Sample of size 100, thus [tex]n = 100[/tex].58% believe in Hell, thus [tex]p = 0.58[/tex].Then
[tex]np = 100(0.58) = 58 \geq 10[/tex]
[tex]n(1 - p) = 100(0.42) = 42 \geq 10[/tex]
[tex]np = 58 \geq 10[/tex] and [tex]n(1 - p) = 42 \geq 10[/tex], thus, this binomial experiment can be approximated using a normal distribution.
A similar problem is given at https://brainly.com/question/24261244
Click on the greatest amount of rainfall.
Answer:
Click on the 2
Step-by-step explanation:
( p + 6 ) + ( 8p + 2 )
Answer:
9p+8
Step-by-step explanation:
p+8p= 9p
6+2= 8
9p+8
Answer:
Step-by-step explanation:
(p+6) + (8p+2)
(p+8p) + (6+2)
9p + 8
please help !!! thank you :)
Answer:
12
Step-by-step explanation:
2 ( - 2x + 6 )
= 2 ( - 2x ) + 2 ( 6 )
= - 4x + 12
I’m a little lost on this
Zahid and nasir had 7350 game cards. Zahid gave 520 cards to nasir. Now zahid had 4 times as many games cards as nasir. How many game cards did zahid bave at first?
Answer:
Zahid had/has 31480 cards
7350 + 520= 7870
7870 times 4 = 31480
Step-by-step explanation:
Hope this helps
can i get braineist
Answer:
Step-by-step explanation:
Zahid and nasir had game cards= 7350
Zahid gave cards =520
Total cards left= 7350 - 520= 6830
Let
Zahid =x
Nasir = 4x
x+4x=6830
5x=6830
x=6830/5=1366
Zahid=1366
Nasir=4x=4(1366)=5464
Check
Zahid=1366+520=1886
Nasir=5464
Zahid+Nasir=1886+5464=7350
solve. −3.1=−3.5x−4.6
Answer:
x = 0.428571 repeating
Step-by-step explanation:
Answer:
-0.428571 repeating
Step-by-step explanation:
add 4.6 both sides
1.5 = -3.5x
divide -3.5 both sides
-0.428571 repeating
find the value of each of the following a) 6+14÷7_2×3
Answer:
48
Step-by-step explanation:
6 + 14 ÷ 7
= 8
= 8 _ 2× 3
= 8_ 6
=8×6
=48
Write 1000 as a power of 10
3/4 x 5/8 in simplest form
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Triangle ABC is defined by the points A(3,8), B(7,5), and C(2,3).
Create an equation for a line passing through point A and perpendicular to BC.
y=
X +
Reset
Next
Answer:
y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{31}{2}[/tex]
Step-by-step explanation:
Calculate the slope m of BC using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = B (7, 5 ) and (x₂, y₂ ) = C (2, 3 )
[tex]m_{BC}[/tex] = [tex]\frac{3-5}{2-7}[/tex] = [tex]\frac{-2}{-5}[/tex] = [tex]\frac{2}{5}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{2}{5} }[/tex] = - [tex]\frac{5}{2}[/tex] , then
y = - [tex]\frac{5}{2}[/tex] x + c ← is the partial equation
To find c substitute A (3, 8 ) into the partial equation
8 = - [tex]\frac{15}{2}[/tex] + c ⇒ c = 8 + [tex]\frac{15}{2}[/tex] = [tex]\frac{16}{2}[/tex] +[tex]\frac{15}{2}[/tex] = [tex]\frac{31}{2}[/tex]
y = - [tex]\frac{5}{2}[/tex] x + [tex]\frac{31}{2}[/tex] ← equation of perpendicular line
The equation for a line passing through point A and perpendicular to BC is 2y = -5x +31 or y = -2.5x +15.5.
What is the equation of a Straight Line ?The equation of the straight line is represented by
y = mx+c
where m is the slope , and c is the intercept on y axis.
The equation of the line BC for points B(7,5), and C(2,3) is
y- y' = m(x-x')
m = 2/5
and c =
y-5 = (2/5)x - (14/5)
y = (2/5)x+(11/5)
The slope of the line perpendicular rot this line is given by
as the product of two perpendicular lines should be -1
m = -5/2
y = (-5/2)x +c
8 = (-15/2) + c
8 +(15/2) = 0
31/2 = c
Therefore the equation for a line passing through point A and perpendicular to BC is
2y = -5x +31
To know more about equation of a Straight Line
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The functions f and g are defined as follows.
f(x)=-3x-1
3
g(x)=2x? +2
Find f (2) and g(-2).
Simplify your answers as much as possible.
__________
[tex] \: [/tex]
f(x) = -3x - 1
g(x) = 2x + 2
Soo :
f(2) :f(2) = -3(2) - 1
f(2) = -6 - 1
f(2) = -7✔
.
g(-2) ;g(-2) = 2(-2) + 2
g(-2) = -4 + 2
g(-2) = -2✔
which is equivalent to 2 5/6?
A. 5/3
B. 12/5
C. 7/6
D. 17/6
(IF YOU ARE ABLE TO, PLEASE PROVIDE AN EXPLANATION FOR THE ANSWER)
a line passes through the point of (4,2) and has a slope of -5/4
Answer:
y = -5/4x + 7
Step-by-step explanation:
y = -5/4x + b
2 = -5/4(4) + b
2 = -5 + b
7 = b
Which is the label of the ordered pair (1,3)?
1. V
2.W
3.X
4. Y
5. Z
Answer:
dude. its 4.Y
This question in algebraic expression and number form : the difference between 20 and x
Answer: Let the numbers be x and y.
x+y = 20 …(1)
x-y = 10 …(2)
Add (1) and (2)
2x = 30, or x = 15, and so y = 5.
The product of the two numbers = xy = 15*5 = 75.
Step-by-step explanation:
Someone please please help!
Answer:
C.
Step-by-step explanation:
After the given, you need another pair of congruent angles to prove the triangles congruent by AAS. Those angles you need are vertical angles, so they are congruent.
Answer: C.
Use the functions f(x) and g(x). to evaluate below.
Given the graph and the table of functions, f(x) and g(x), the following evaluated:
a. f(0) = 9
b. g(2) = -3
c. f(-1) = 5
Given the functions, f(x) and g(x), the following can be evaluated:
a. Find f(0):
Using the table given, what we need to determine is the of the output, f(0) that an input value, x = 0, will give.
From the table, we see that when x = 0, f(x) =9.Therefore,
f(0) = 9
b. Find g(2):
From the graph, find the corresponding value of g(x) that corresponds with x = 2.
From the graph, when x = 0, g(x) = -3Therefore,
g(2) = -3
c. Find f(-1):
From the table, find the corresponding value of f(x) that corresponds with x = -1.
From the table, when x = -1, f(x) = 5Therefore,
f(-1) = 5
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Show that (1 + 2V3)2 = 13 +4V3
7. Trading volume on the New York Stock Exchange is heaviest during the first half hour (early morning) and last half hour (late afternoon) of the trading day. The early morning trading volumes (millions of shares) for 13 days in January and February are shown here (Barron’s, January 23, 2006; February 13, 2006; and February 27, 2006). 214 163 265 194 180 202 198 212 201 174 171 211 211 The probability distribution of trading volume is approximately normal. a) Compute the mean and standard deviation to use as estimates of the population mean and standard deviation. b) What is the probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares? c) What is the probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares?
In this problem, first we find the sample mean and the standard deviation, and then, we use the normal distribution. Then, we get that:
a) The mean is of 199.69 and the standard deviation is of 25.02.
b) 0.2148 = 21.48% probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares.
c) 0.1131 = 11.31% probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares.
In a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.Item a:
The mean is the sum of all observations divided by the number of observations, thus:
[tex]\mu = \frac{214 + 163 + 265 + 194 + 180 + 202 + 198 + 212 + 201 + 174 + 171 + 211 + 211}{13} = 199.69[/tex]
The standard deviation is given by the square root of the sum of the difference squared between each observation and the mean, divided by the number of values. Thus:
[tex]\sigma = \sqrt{\frac{(214-199.69)^2 + (163-199.69)^2 + (265-199.69)^2 + (194-199.69)^2 + ... + (211-199.69)^2}{13}} = 25.02[/tex]
The mean is of 199.69 and the standard deviation is of 25.02.
Item b:
This probability is the p-value of Z when X = 180, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{180 - 199.69}{25.02}[/tex]
[tex]Z = -0.79[/tex]
[tex]Z = -0.79[/tex] has a p-value of 0.2148.
0.2148 = 21.48% probability that, on a randomly selected day, the early morning trading volume will be less than 180 million shares.
Item c:
This probability is 1 subtracted by the p-value of Z when X = 230, thus:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{230 - 199.69}{25.02}[/tex]
[tex]Z = 1.21[/tex]
[tex]Z = 1.21[/tex] has a p-value of 0.8869.
1 - 0.8869 = 0.1131
0.1131 = 11.31% probability that, on a randomly selected day, the early morning trading volume will exceed 230 million shares.
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Heyyyyyy help meeeeeeee
Answer:
1.25 or 1 1/4
Step-by-step explanation:
1 ounce is 0.0625 pounds
therefore 20 oz = 1.25 or 1 1/4
The cost c, for manufacturing x flags is given by c=x? -24x +39. Find the number of flags manufactured if the cost is $120.
The number of flags are 0
(Simplify your answer.)
9514 1404 393
Answer:
27
Step-by-step explanation:
You want to find x when c = 120.
120 = x^2 -24x +39
x^2 -24x -81 = 0 . . . . . . subtract 120 to put in standard form
(x -27)(x +3) = 0 . . . . . .factor it
Solutions are ...
x = 27, x = -3 . . . . . values of x that make the factors zero
The number of flags manufactured for a cost of $120 is 27 flags.
By which rule are these triangles congruent?
Answer:
S, S, S
Step-by-step explanation:
hey guys pls help me i need to submit this before 1hr .graphing an inverse function.y = 4x + 12 using the x values (-2,-1, 0, 1 and 2).
Answer:
4, 8, 12, 16, 24
Step-by-step explanation:
Replace the x with the x values starting at -2 and use the equation with the new x value.
E.g.
x = -2
y = 4 * -2 + 12
y = 4
Sorry if my explanation isn't the best.
Help or no if so thanks<3
solve pls brainliest
Answer:
y = 1.28
Step-by-step explanation:
Hi there!
[tex]10.24=8y[/tex]
To solve for y, divide both sides by 8:
[tex]\displaystyle \frac{10.24}{8} =\displaystyle \frac{8y}{8} \\\\1.28=y[/tex]
Therefore, y = 1.28.
I hope this helps!
Answer:
= 1 . 2 8
Step-by-step explanation:
10.24 =8y
10.24 = 8y
8 8
What is the system of measurement used most often in the United States?
customary
converted
metric
similar
Answer:
metric po
Step-by-step explanation:
measurements and metric units of measure
please just work out the last one. thank you if u can do all
I made an f in math last year
Answer:
a) 1.8
b) 11.8
c) 23.6
Step-by-step explanation:
1) 2.4+1.6+3.2+0.3+1.5=9
you divide 9 by 5 because that is the number of elements in the data.
9/5=1.8
2) the total would be 50 more because 5*10=50.
50+9=59
59/5=11.8
3) i think this question is referencing the previous question.
59*2=118
118/5=23.6
A person flying a kite has released 176 m of string . the string makes an angle of 27 degrees with the ground . how high is the kite? how far away is the kite horizontally? answer to the nearest meter
Answer:
80 m High and 157 m away
Step-by-step explanation:
Cos(27)=x/176
x= 156.8 m
Sin(27) = y/176
y = 80
hey can u please help i will give brainliy if u get it right :)
9514 1404 393
Answer:
400 minutes
Step-by-step explanation:
The cost of the first plan is ...
A = 14 + 0.15m . . . . . . . . where m is the number of minutes used
The cost of the second plan is ...
B = 30 + 0.11m
The costs will be equal when ...
14 +0.15m = 30 +0.11m
0.04m = 16 . . . . . . . . . . . . . subtract 14+0.11m from both sides
m = 400 . . . . . . . . . . . . . . . divide by 0.04
The plans will have the same cost for 400 minutes of calls.