Answer:
The total amount in 7 years is: $958.62
Step-by-step explanation:
Recall the formula for compound interest:
[tex]A=P\,(1+\frac{r}{n} )^{n\,t}[/tex]
where:
A is the Accrued value (total in the account including accumulated interest), and in our case the unknown.
P is the Principal (amount initially deposited), and in our case $700.
r is the annual percent rate (but in decimal form) in our case 0.045
n is the number of compoundings done per year, and in our case 12 since it is compounded monthly
t is the time in years of the deposit.
Then the formula becomes:
[tex]A=P\,(1+\frac{r}{n} )^{n\,t}\\A=700\,(1+\frac{0.045}{12} )^{12\,*\,7}\\A=958.61657[/tex]
which can be rounded to the cents: $958.62
Lucy obtains a 1-year payday loan for $5000.00 at 12% interest compounded monthly. To get the loan, she
also pays an origination fee of $125.00. What is the total cost of the loan to Lucy? Enter your answer as a
dollar amount, such as: 1400.68.
Answer:
$5759.12
Step-by-step explanation:
$5759.12
At the end of the year, the compound interest on her loan is: $5000(1+0.1212)12=$5000(1.01)12≈$5634.12. To pay off the loan at the end of the year, she pays 5634.12+125=$5759.12.
Bisi leaves 5km from school. She walks 1km at 4km/h and travels the rest of the way by bus at 16km/h . what is the average speed for the whole distance
Answer:
1/2 hour
Step-by-step explanation:
I am assuming you meant "lives 5km"
The first km would take 1/4 an hour because she is going 4km/h for one hour. One hour she would go 4km but we only need 1 mile so it would be cut to a fraction.
The same fraction goes for the bus. 4 is 1/4 of 16 so you would have to add them together and have 1/2 and hour to get home.
The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.917 g and a standard deviation of 0.303 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 37 cigarettes with a mean nicotine amount of 0.872 g. Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 37 cigarettes with a mean of 0.872 g or less.
Answer:
[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]
And we can find this probability to find the answer:
[tex] P(z<-0.903)[/tex]
And using the normal standar table or excel we got:
[tex] P(z<-0.903)=0.1833 [/tex]
Step-by-step explanation:
Let X the random variable that represent the amounts of nocatine of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0.917,0.303)[/tex]
Where [tex]\mu=0.917[/tex] and [tex]\sigma=0.303[/tex]
We have the following info from a sample of n =37:
[tex] \bar X= 0.872[/tex] the sample mean
And we want to find the following probability:
[tex] P(\bar X \leq 0.872)[/tex]
And we can use the z score formula given by;
[tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
And if we find the z score for the value of 0.872 we got:
[tex] z = \frac{0.872-0.917}{\frac{0.303}{\sqrt{37}}}= -0.903[/tex]
And we can find this probability to find the answer:
[tex] P(z<-0.903)[/tex]
And using the normal standar table or excel we got:
[tex] P(z<-0.903)=0.1833 [/tex]
What is the midpoint of Line segment A B ?
point F
point G
point H
point I
Answer:
the answer is Point G
Write a matrix equation for the given systems of equations.
2x-6y-2z = 1
3y - 2z = -5
2y + 2z = -3
Answer:
[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]
Step-by-step explanation:
Given system of equations are
2x-6y-2z = 1
3y - 2z = -5
2y + 2z = -3
given
2 x - 6 y - 2 z = 1
0 x + 3 y - 2z = -5
0 x +2y + 2 z = - 3
The Matrix form of the given system of equations
A X = B
[tex]\left[\begin{array}{ccc}2&-6&2\\0&3&-2\\0&2&2\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]= \left[\begin{array}{ccc}1\\-5\\-3\end{array}\right][/tex]
For each problem clearly describe the conditional distribution of each coordinate given the others. Then describe the procedure for running Gibbs sampling to sample from the joint distribution. Assume that Gibbs sampling works for continuous densities as well as discrete distributions. Guess the conditional from the structure of the joint distribution. Avoid doing integration as much as possible. Use your knowledge of the all the named one dimensional distributions/ densities.
a. Sample from the mixed joint pmf/pdf:
f(p, n) = p(1 - p)^-1, 0
Answer:
Step-by-step explanation:
Identify the like terms in the algebraic expression 2x/5-5.2y+2.2+x/3
Question:
Identify the like terms in the algebraic expression
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Answer:
The like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
Step-by-step explanation:
Given:
[tex]\frac{2x}{5} -5.2y +2.2 + \frac{x}{3}[/tex]
Required:
Identify the like terms
To solve this, we need to understand what like term is all about.
Like term simply refer to terms or entities that have the same variable and exponents (power)
From the expression above, there are two variables;
x and y.
To get the like terms of x and/or y;
we simply look for another occurrence of x and/or y in the expression; and this occurrence must have the same exponent as x and/or y.
For x
[tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex] have the same variable and exponent; Hence, they are like terms
There's only one occurrence of variable y;
Conclusively, the like terms in the given expression are [tex]\frac{2x}{5}[/tex] and [tex]\frac{x}{3}[/tex]
2x/5 and -5.2y
hope this helps
Please answer this correctly
Answer:
13 2/3 cm
Step-by-step explanation:
To find the perimeter, add up all the sides
2 1/2 + 3 1/3+ 4 1/2 + 3 1/3
Add up the whole numbers
2+3+4+3 = 12
Add up the fractions
1/2+1/3+1/2+1/3
2/2 + 2/3
1 +2/3
Put them together
12+1+2/3
13 2/3
Answer: 13 2/3 cm
Step-by-step explanation:
1. Turn mixed fractions into improper fractions:
2 1/2 = 5/2
3 1/3 = 10/3
3 1/3 = 10/3
4 1/2 = 9/2
2. Formula for perimeter: left side + right side + upper base + lower base
3. Put your numbers in replace: 10/3 + 10/3 + 5/2 + 9/2
4. Solve: 41/3
5. Simplify into mixed fraction: 41/3 = 13 2/3
6. Don't forget to add the unit!
What is the vertex of the graph of f(x) = |x-13[ + 11?
оооо
о(-11, 13)
о(-13, 11)
О(11, 13)
О (13, 11)
Answer:
(13, 11)
Step-by-step explanation:
The vertex of g(x) = |x| is (0, 0).
When the function is transformed to ...
f(x) = g(x -h) +k
the vertex is moved to (h, k).
Here, we have (h, k) = (13, 11), translating the function to ...
f(x) = |x -13| +11
and moving the vertex to (13, 11).
Answer:
D. (13, 11)
Step-by-step explanation:
EDGE 2020 :)
Please help ;-; what is the answer?
Answer:
5.7
Step-by-step explanation:
The altitude divides right triangle ABC into similar right triangles ADB and BDC. The ratios of short leg to long leg will be proportional in these similar triangles, so you have ...
AD/BD = BD/CD
Cross multiplying gives ...
AD·CD = BD²
(x+3)(2x+3) = 5²
2x² +9x = 16 . . . . . perform the multiplication, subtract 9
2(x² +4.5x) = 16
2(x² +4.5x +2.25²) = 16 +2(2.25²) . . . . . add 2(2.25²) to complete the square
2(x +2.25)² = 26.125 . . . . . write as a square
x +2.25 = √13.0625 . . . . . .divide by 2, take the positive square root
x = -2.25 +√13.0625 . . . . subtract 2.25 to find x
We want the value of CD, so ...
CD = 2x +3 = 2(-2.25 +√13.0625) +3
CD = -1.5 +2√13.0625 ≈ 5.7284
The length of CD is about 5.7 units.
A firm can produce only 2500 units per month. The monthly total cost is given by C(x) = 400 + 200x dollars, where x is the number produced. If the total revenue is given by R(x) = 350x − 1 100 x2 dollars, how many items, x, should the firm produce for maximum profit?
Answer:
2500
Step-by-step explanation:
Monthly total cost, C(x) = 400 + 200x dollars
Monthly total revenue, R(x) = [tex]350x -\dfrac{1}{100}x^2[/tex] dollars
Profit = Revenue - Cost
[tex]=R(x)-C(x)\\=(350x -\dfrac{1}{100}x^2)-(400 + 200x)\\=350x -\dfrac{1}{100}x^2-400 - 200x\\P(x)=150x-\dfrac{1}{100}x^2-400[/tex]
To determine how many items, x, the firm should produce for maximum profit, we maximize P(x) by taking its derivative and solving for its critical points.
[tex]P(x)=150x-\dfrac{1}{100}x^2-400\\P'(x)=150-\dfrac{x}{50}\\\\$Set $ P'(x)=0\\150-\dfrac{x}{50}=0\\150=\dfrac{x}{50}\\$Cross multiply\\x=150*50\\x=7500[/tex]
Next, we check if the point x=7500 is a maxima or a minima.
To do this, we find the second derivative of P(x).
[tex]P''(x)=-\dfrac{1}{50} $ which is negative[/tex]
Hence, the point x=7500 is a point of maxima. However, since the firm can only produce 2500 units per month.
Therefore, the company needs to produce 2500 units to maximize profit.
(3x+12)+x=180 Find the value of x.
Answer:
x =42
Step-by-step explanation:
(3x+12)+x=180
Combine like terms
4x +12 = 180
Subtract 12 from each side
4x +12-12=180-12
4x = 168
Divide by 4
4x/4 =168/4
x =42
Answer:
x=42
Step-by-step explanation:
180-12=168
168 divided by 4 = 42
x=42
A hotel wants to know if there's a relationship between gender and the way customers make room reservations. A manager takes a random sample of 160 reservations. She records whether they were made by a man or a woman, and also records how the reservation was made. She gets the following data: Phone 28 Men Women Fax 9 12 Email 37 29 45 Perform a chi-square significance test of association with a = .05. Be sure to include your null and alternative hypotheses, a justification for the use of this test, your test statistic calculations, your P-value, and your conclusion.
Answer:
Step-by-step explanation:
Here,
H_o: The way of reservation is independent of gender.
H_a: The way of reservation is not independent of gender.
We use a chi square test because we can calculate the expected frequencies for this chart.
Doing an Expected Value Chart,
33.7625 9.7125 30.525
39.2375 11.2875 35.475
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 4.482385929
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 3
b = 2
df = 2
Thus, the critical value is
significance level = 0.05
chi^2(critical) = 5.991464547
Also, the p value is
P = 0.106331579
Thus, comparing chi^2 and chi^2(critical) [or, p and significance level], we FAIL TO REJECT THE NULL HYPOTHESIS.
Thus, there is no significant evidence that the way of reservation is dependent of gender. [CONCLUSION]
What is the square root of -1?
–i
i
–1
1
Answer:
[tex]i[/tex]
Step-by-step explanation:
[tex]\sqrt{-1} =i[/tex]
[tex]i[/tex] is an imaginary number that represents the square root of -1.
a number,x, rounded to 1 significant figure is 40 write down the error interval for x
Answer:
Error interval is [tex]35\leq x< 45[/tex]
Step-by-step explanation:
Given: A number x becomes 40 if it is rounded to 1 significant figure
To find: error interval for x
Solution:
In the given question, an error interval is the range of values that a number x can be equal to before it is rounded to 1 significant figure.
As a number x becomes 40 if it is rounded to 1 significant figure, error interval is [tex]35\leq x< 45[/tex].
A number x in this interval becomes equal to 40 if it is rounded to 1 significant figure.
daryl hit a home run 8 out of 32 times.if he is at bat 224 times how many home runs will he hit
Answer:
56 out of 224 times
Step-by-step explanation:
8 out of 32 = 1 out of 4
56 out of 224 = 1/4
Answer:56
Step-by-step explanation:
The radius of a circle is 1 meter. What is the area of a sector bounded by a 135º arc?
Answer:
d=2
Step-by-step explanation:
Shape: Circle
Solved for diameter
Radius: 1
Formula: d=2r
Formula: Radius
Answer: 2
Hope this helps.
Find the length of the portion of the line y = 4 that lies inside a circle of radius 7
centered at the origin
Answer: 2sqrt(33)
Step-by-step explanation:
We want to find the length of the line y = 4 in the circle x^2+y^2=49.
Substitute y = 4 to get x^2 = 33, so x = sqrt(33) or -sqrt(33).
That means the total length is sqrt(33) * 2 = 2sqrt(33).
Hope that helped,
-sirswagger21
The approximate length of the portion of the line is 11.49.
Circle centered at (h,k) with radius r is [tex](x-h)^{2} + (y-k)^{2}=r^{2}[/tex]
A circle of a radius 7 centered at the origin:
[tex]x^{2} +y^{2}=49[/tex] ......... (i)
[tex]y=4[/tex] ..........(ii)
We have a circle and a line. We need to find the points of
intersection and find the distance between those two points.
Replace y with 4 in the 1st equation and solve for x.
[tex]x^{2} +4^{2} =49\\x^{2} =49-16\\x^{2} =33\\[/tex]
[tex]x=[/tex] ±[tex]\sqrt{33}[/tex]
We have the 2 values of x where the line intersects the circle.
Plug those into one of the original equations to find the associated
y values.
[tex]\sqrt{33} ^{2} +y^{2} =49\\y^{2}=49-33\\y=4[/tex]
Two points on the circle are [tex](\sqrt{33} , 4)[/tex] and [tex](-\sqrt{33} , 4)[/tex]
Using the distance formula:-
[tex]=\sqrt{(4-4)^{2}+(-\sqrt{33}-\sqrt{33)} ^{2} } \\=\sqrt{(2\sqrt{33}) ^{2} } \\=2\sqrt{33}\\[/tex]
≈ 11.49
Therefore, the length of the portion of the line is approximately 11.49.
For more information:
https://brainly.com/question/24214108
94 cities were surveyed to determine sports teams. 26 had baseball, 23 had football, 22 had basketball, 12 baseball and football, 13 had baseball and basketball, 14 had football and basketball, and 7 had all three.A) How many had only a basketball team?B) How many had baseball or football?C) How may had baseball or football, but not basketball?
Answer:
A) 2
B) 33
C) 13
Step-by-step explanation:
Baseball =26
Football = 23
Basketball = 22
Baseball and Football (BF) = 12
Baseball and basketball (BK) = 13
Football and basketball (FK) = 14
All three (BFK) = 7
A) The total number of cities that have basketball teams is given by the cities with basketball only, added to the cities with basketball and football and cities with basketball and baseball, minus the cities with all three sports:
[tex]22=K+BK+FK-BFK\\22=K+13+14-7\\K=2[/tex]
B) The total number of cities with baseball of football is given by sum of the cities with either sport, minus the number of cities with both sports:
[tex]B\ or\ F = 23+22-12\\B\ or\ F =33[/tex]
C) If 22 cities have basketball and only 2 have basketball only, 20 cities have basketball and either baseball, football or all three sports. The number of cities with baseball or football, but not basketball is:
[tex](B\ or\ F)\cap (not\ K) = 33-20=13[/tex]
A teacher needs to cut pieces of yarn, each 3/4 yards in length. How many
pieces can he cut from a string of yarn that is 6 yards long?
Answer:
8 pieces
Step-by-step explanation:
Take 6 yds and divide by the length of each piece
6 ÷ 3/4
Copy dot flip
6 * 4/3
24/3
8
We can get 8 peices
Find in degrees the numeric value of the acute angle of rotation that eliminates the product term from the equation 7x2+24xy−34x+24y−185=07x2+24xy−34x+24y−185=0
Rotating the graph of [tex]Ax^2+Bxy+Cy^2+Dx+Ey+F=0[/tex] with [tex]B\ne0[/tex] counterclockwise by [tex]\theta[/tex] eliminates the [tex]xy[/tex] term, where [tex]\cot2\theta=\frac{A-C}{B}.[/tex] Plugging in, we have [tex]\cot2\theta=\frac{7}{24},[/tex] since [tex]C=0.[/tex] Solving, we have [tex]\theta=\frac{1}{2}\cot^{-1}(\frac{7}{24})\approx\boxed{36.9^\circ}.[/tex]
Suppose that you are testing the hypotheses Upper H 0: pequals0.16 vs. Upper H Subscript Upper A: pnot equals0.16. A sample of size 350 results in a sample proportion of 0.21. a) Construct a 90% confidence interval for p. b) Based on the confidence interval, can you reject Upper H 0 at alphaequals0.10? Explain. c) What is the difference between the standard error and standard deviation of the sample proportion? d) Which is used in computing the confidence interval?
Answer:
Given:
Sample size, n = 350
Sample proportion, P' = 0.21
H0 : p = 0.16
Ha : p ≠ 0.16
a) A 90% confidence interval for P.
Significance level = 1 - confidence interval = 1 - 0.90 = 0.10
For Z critical, we have:
Z critical = [tex] Z_0_._1_/_2 = Z_0_._0_5 = 1.645 [/tex] (using z table)
Standard error, S.E = [tex] \sqrt{\frac{P'(1 - P')}{n}} = \sqrt{\frac{0.21(1 - 0.21)}{350}} = 0.02177 [/tex]
Margin of error, E = 1.645 * 0.02177 =0.03581
The 90% confidence interval =
0.21 ± 0.03581
The lower limit: 0.21 - 0.03581 = 0.17419
The upper limit: 0.21+0.03581 =0.24581
b) Based on the confidence interval at significance level = 0.10,
We reject null hypothesis, H0, since 0.16 is not cointained in the confidence interval. We conclude that p ≠ 0.16.
c) Standard error is based on sample proportion p^ while standard deviation is based on hypothesized proportion Po.
d) Standard error is used to compute the confidence interval.
Mary is building a sandcastle with rectangular prism molds. One mold is 4 inches long, 6 inches wide, and 2 inches tall. The other mold is 3 inches long, 5 inches wide, and 1 inch tall. If she creates a castle by stacking these molds on top of each other, what volume of sand will be contained in her castle?
Answer:
63 cubic inches
Step-by-step explanation:
You have to first find the volume of each mold:
6 × 4 × 2= 48 cubic inches
3 × 5 × 1= 15 cubic inches
Add these two volumes together to find the overall volume of the whole sand castle.
48+15= 63 cubic inches
Answer:
The whole castle can hold 63 in² of sand.
Step-by-step explanation:
First, find the volume of the first mold.
V = whl Substitute
V = (6)(2)(4) Multiply
V = 48 in²
Now, find the volume of the second mold.
V = whl Substitute
V = (5)(1)(3) Multiply
V = 15 in²
Add together both volumes to find the volume of the whole castle.
48 + 15 = 63 in²
A local hamburger shop sold a combined total of 621 hamburgers and cheeseburgers on Friday there were 71 more cheeseburgers old and hamburgers how many hamburgers were sold on Friday
What is imaginary 34
Answer:
raising a number to the 34th power
Step-by-step explanation:
A Florida neighborhood is comprised of a total of 250 houses of which 12% are in foreclosure. A random sample of 91 homes from this neighborhood was selected. The standard error of the proportion is ________.
Answer:
the standard error of the proportion is 0.0272
Step-by-step explanation:
We have that if the sample size is greater than 5% of the entire population, a finite population correction factor (fpc) is multiplied with the standard error :
fpc = [tex]\sqrt{\frac{N -n}{N -1} }[/tex]
We know that N = 250 n = 91, replacing:
fpc = [tex]\sqrt{\frac{250 - 91}{250 -1} }[/tex]
fpc = 0.799
Now, the formula would then be:
SE = [tex]\sqrt{\frac{p * (1 -p)}{n} }[/tex]*fpc
Now replacing, knowing that p = 0.12
SE= [tex]\sqrt{\frac{0.12 * (1 - 0.12)}{91} }[/tex]*0.799
SE = 0.0272
So the standard error of the proportion is 0.0272
What’s the correct answer for this question?
Answer:
[tex] \frac{11}{24} [/tex]
Answer:
D. 11/24
Step-by-step explanation:
Total students' reading preferences = 240
Using electronic device = 110
Probability of having electronic device = 110/240
= 11/24
plifying a Radical
Find the values for a, b, and c that complete the simplificatio
12.95
Y Z
12
y8 .y . z. z = x y z Syz
a =
I
b =
Answer: answer is D
Step-by-step explanation:
Answer: The correct answer is 6,4,2
Step-by-step explanation: Doing a 100 point giveaway stay tuned!
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answer:
A. [tex]F(x) = (\frac{3}{4}x )^2-1[/tex]
Step-by-step explanation:
The correct answer is "A," because the function F(x), shifted downwards 1 unit. This means that the function has to have a -1 being subtracted. Note that when the number in front of x is less than one, the function widens. In this case, [tex]\frac{3}{4}[/tex] is less than one, making it grow bigger as shown on the graph above.
A piece of wire is 290 cm long.
Dawid cuts three 25 cm lengths off the wire.
He then cuts the rest of the wire into as many 30 cm lengths as possible.
Work out how many 30 cm lengths of wire Dawid cuts.
Answer:
8
Step-by-step explanation:
(290-25)/30
265/30
8 and 5/6
so how many full 30 cm lengths?
8
Answer:
7
Step-by-step explanation:
3 × 25 = 75cm
He cuts 75cm of 290cm so the remaining length is 290 - 75 = 215 cm
→ He then cuts the rest of the wire into as many 30 cm lengths as possible.
215 ÷ 30 = 7.17
