Answer:
747 samples
Step-by-step explanation:
Given:
Standard deviation = √125.44 = 11.2
Zcritical = 85℅
Margin of error, E = 0.59
The sample size, n required cnanbe obtained using the relation :
n = [(Zα/2 * σ) / E]²
Zcritical at 85% = 1.44
n = [(1.44 * 11.2) / 0.59]²
n = (16.128 / 0.59)²
n = 747.23
n = 747 samples
Given C(4, 3) and D(-4, -3) are two points on a circle, centered at the origin. Given
that CD is a diameter of the circle,
a) Find the radius of the circle.
b) State the equation of the circle
Answer:000
Step-by-step explanation:000
Evaluate the expression when a=-7 and y=3 3y-a
Answer:
3y-a
3.3-7
9-7
2
Step-by-step explanation:
first we have to do multiply by replacing the value of y and the subtract by using the value of a.
Hope this will be helpful for you
Construct the confidence interval for the population standard deviation for the given values. Round your answers to one decimal place. n=21 , s=3.3, and c=0.9
Answer:
The correct answer is "[tex]2.633< \sigma < 4.480[/tex]".
Step-by-step explanation:
Given:
n = 21
s = 3.3
c = 0.9
now,
[tex]df = n-1[/tex]
[tex]=20[/tex]
⇒ [tex]x^2_{\frac{\alpha}{2}, n-1 }[/tex] = [tex]x^2_{\frac{0.9}{2}, 21-1 }[/tex]
= [tex]31.410[/tex]
⇒ [tex]x^2_{1-\frac{\alpha}{2}, n-1 }[/tex] = [tex]10.851[/tex]
hence,
The 90% Confidence interval will be:
= [tex]\sqrt{\frac{(n-1)s^2}{x^2_{\frac{\alpha}{2}, n-1 }} } < \sigma < \sqrt{\frac{(n-1)s^2}{x^2_{1-\frac{\alpha}{2}, n-1 }}[/tex]
= [tex]\sqrt{\frac{(21-1)3.3^2}{31.410} } < \sigma < \sqrt{\frac{(21.1)3.3^2}{10.851} }[/tex]
= [tex]\sqrt{\frac{20\times 3.3^2}{31.410} } < \sigma < \sqrt{\frac{20\times 3.3^2}{10.851} }[/tex]
= [tex]2.633< \sigma < 4.480[/tex]
The firm has bonds with par value of 10,000,000 VND, coupon rate of 11%, annual interest payment, and the remaining maturity period is 07 years. If the bond's interest rate and current risk level have a return rate of 12%, what price should company C sell the bond in the present?
a.
10,000,000
b.
14,152,000
c.
12,053,000
d.
11,150,000
An online retailer processed 60 merchandise return requests from Wyoming and Montana in a day. Return requests from Montana were 5 times as many as those from Wyoming. How many return requests were from Wyoming?
A) 10
B) 25
C) 15
D) 20
E) 5
The number of merchandise return requests for Wyoming is equal to 10.
Let merchandise return requests from Wyoming be W.
Let merchandise return requests from Montana be M.
Given the following data;
Total number of merchandise return requests for W and M = 60Translating the word problem into an algebraic equation, we have;
[tex]W + M = 60[/tex] .....equation 1
[tex]M = 5W[/tex] ......equation 2
To find the value of W, we would solve the system of equations by using the substitution method;
Substituting eqn 2 into eqn 1, we have;
[tex]W + 5W = 60\\\\6W = 60\\\\W = \frac{60}{6}[/tex]
Wyoming, W = 10 merchandise return requests.
Therefore, the number of merchandise return requests for Wyoming is equal to 10.
Find more information: https://brainly.com/question/8409825
Can somebody help me to solve this?
Answer:
B
Step-by-step explanation:
Given
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{bc}[/tex] ( square both sides )
ab = bc ( divide both sides by b ) , then
a = c
Given
[tex]\sqrt{ac}[/tex] = [tex]\sqrt{4c^4}[/tex] ( square both sides )
ac = 4[tex]c^{4}[/tex] ( but a = c) , so
4[tex]c^{4}[/tex] = c² ( subtract c² from both sides )
4[tex]c^{4}[/tex] - c² = 0 ← factor out c² from each term on the left side
c²(4c² - 1) = 0 ← 4c² - 1 is a difference of squares
c²(2c - 1)(2c + 1) = 0
Equate each factor to zero and solve for x
c² = 0 ⇒ c = 0
2c - 1 = 0 ⇒ 2c = 1 ⇒ c = [tex]\frac{1}{2}[/tex]
2c + 1 = 0 ⇒ 2c = - 1 ⇒ c = - [tex]\frac{1}{2}[/tex]
But c > 0 , then c = [tex]\frac{1}{2}[/tex] → B
i need the answer no explanation
Answer:
the answer is option D because it cant be division or multiplication and minus does not work
Answer:
log 1/9 * log k
Step-by-step explanation:
[tex]\frac{1}{9} /k[/tex] = 1/9 * k/1 = 1/9 * k
Y= 2x - 3; Y = (1/2)x - 4
Answer:
(-2/3, -13/3)
Step-by-step explanation:
Given the expressions;
[tex]y= 2x - 3\\y = (\frac{1}{2} )x - 4[/tex]
Equating both expressions;
[tex]y=y\\2x-3=\frac{1}{2}x-4\\[/tex]
Collect the like terms:
[tex]2x-\frac{1}{2}x=-4+3\\\frac{3x}{2}=-1\\3x=-2\\x=\frac{-2}{3}[/tex]
Substitute [tex]x=\frac{-2}{3}[/tex] into any of the expressions to get 'y'
[tex]Recall\ y= 2x-3\\y=2(\frac{-2}{3} )-3\\y=\frac{-4}{3}-3\\y=\frac{-4-9}{3} \\y=\frac{-13}{3}[/tex]
Hence the solution to the equation is (-2/3, -13/3)
find the length of y, assume the triangles are similar
Answer:
y = 3.6
Step-by-step explanation:
Since the triangles are similar, we can write the following proportion:
[tex]\frac{y}{6.3} = \frac{2.4}{4.2} = \frac{2.8}{x}[/tex]
We don't need the fraction on the left because it is not necessary to solve for y. Instead, we can simplify the rest:
[tex]\frac{y}{6.3} = \frac{2.4}{4.2}[/tex]
[tex]\frac{y}{6.3} = \frac{0.4}{0.7}[/tex]
Now, we can cross-multiply:
[tex]0.7y = 6.3 * 0.4[/tex]
[tex]0.7y = 2.52[/tex]
[tex]y = 3.6[/tex]
Given:
The length of both triangle are in the same ratio,
2.4:2.8:y = 4.2:x:6.3
To find:
The value of 'y'
Steps:
Since 2.4 : y = 4.2 : 6.3, we can find the value of 'y'
2.4/y = 4.2/6.3
2.4 * 6.3 = 4.2 * y
15.12 = 4.2y
15.12/4.2 = y
3.6 = y
y = 3.6
Therefore, the value of y is 3.6
Happy to help :)
If you want help, feel free to ask
Use the figure to find x.
Answer:
[tex] x = 8.57[/tex]
Step-by-step explanation:
Here two triangles are given to us , which are attached to each other . Here we can use the concept of Trigonometry to find out the value of x. The angles of the triangle are 60° and 45° . Let the common side be p .
Step 1: Use the ratio of tan in upper triangle
[tex]\rm\implies tan60^o = \dfrac{perpendicular}{base} [/tex]
Substitute the respective values ,
[tex]\rm\implies \sqrt3=\dfrac{p}{7} [/tex]
Cross multiply ,
[tex]\rm\implies p = 7\sqrt3 [/tex]
Step 2: Use the ratio of cos in lower triangle
[tex]\rm\implies cos45^o = \dfrac{base}{hypontenuse} [/tex]
Substitute the respective values ,
[tex]\rm\implies \dfrac{1}{\sqrt2}=\dfrac{x}{7\sqrt3} [/tex]
Cross multiply ,
[tex]\rm\implies x= \dfrac{7\sqrt3}{\sqrt2} [/tex]
Put the approximate values of √2 and √3
[tex]\rm\implies x= \dfrac{7\times 1.732}{1.414} [/tex]
This equals to ,
[tex]\rm\implies \boxed{\blue{\rm \quad x = 8.57\quad}} [/tex]
Hence the value of x is 8.57 .
Answer:
The value of x is [tex]\frac{7\sqrt{6}}{2}[/tex]
Solution given:
AB=7
BD=x
<BAC=60°
<DBC=45°
In right angled triangle ABC
Tan 60°=opposite/adjacent
Tan 60°=BC/AB
Substitute value
[tex]\sqrt{3}[/tex]=[tex]\frac{BC}{7}[/tex]
BC=[tex]7\sqrt{3}[/tex]
again
againIn right angled triangle BCD
againIn right angled triangle BCDUsing Cos angle
Cos 45=adjacent/hypotenuse
Cos45°=BD/BC
Substituting value
[tex]\frac{\sqrt{2}}{2}=\frac{x}{7\sqrt{3}}[/tex]
Doing criss cross multiplication
[tex]\frac{\sqrt{2}}{2}*7\sqrt{3}=x[/tex]
x=[tex]\frac{7\sqrt{6}}{2}[/tex]
a site is 90m long and 45m wide what is the area of the site
Answer:4050m^2
Step-by-step explanation:
Assuming that the site is rectangular
Area= l x W
90 X 45
=4050
Answer:
1050m
How I got the answer: I assume the site is a rectangle so I'll use the formula for finding the area of a rectangle. Using the formula length times width I solved this problem. The length is 90m. The width is 45. When a question says x meters long it means the length is x meters. In other words long = length wide = width in a math problem. 90 times 40 is 1050m
which relation is a function?
Answer:
Choice A.
Step-by-step explanation:
Every other choice has multiple of the same x-values that have different corresponding y-values.
What type of object is pictured below?
O A. Point
O B. Ray
C. Segment
D. Line
Answer:
It is a ray because there are two points with a line passing through them which is extenging on one side but not on the other.
A company manufactures televisions. The average weight of the televisions is 5 pounds with a standard deviation of 0.1 pound. Assuming that the weights are normally distributed, what is the weight that separates the bottom 10% of weights from the top 90%?
Answer:
[tex]0.2564\text{ pounds}[/tex]
Step-by-step explanation:
The 90th percentile of a normally distributed curve occurs at 1.282 standard deviations. Similarly, the 10th percentile of a normally distributed curve occurs at -1.282 standard deviations.
To find the [tex]X[/tex] percentile for the television weights, use the formula:
[tex]X=\mu +k\sigma[/tex], where [tex]\mu[/tex] is the average of the set, [tex]k[/tex] is some constant relevant to the percentile you're finding, and [tex]\sigma[/tex] is one standard deviation.
As I mentioned previously, 90th percentile occurs at 1.282 standard deviations. The average of the set and one standard deviation is already given. Substitute [tex]\mu=5[/tex], [tex]k=1.282[/tex], and [tex]\sigma=0.1[/tex]:
[tex]X=5+(1.282)(0.1)=5.1282[/tex]
Therefore, the 90th percentile weight is 5.1282 pounds.
Repeat the process for calculating the 10th percentile weight:
[tex]X=5+(-1.282)(0.1)=4.8718[/tex]
The difference between these two weights is [tex]5.1282-4.8718=\boxed{0.2564\text{ pounds}}[/tex].
Answer:
0.2564
Step-by-step explanation:
90th percentile, we use the formula X=μ + Zσ,
Where u = mean and sigma = standard deviation and Z = 1.282
The mean is 5 and sigma = .1
X = 5+1.282(.1)
X = 5.1282
10th percentile, we use the formula X=μ + Zσ,
Where u = mean and sigma = standard deviation and Z = -1.282
The mean is 5 and sigma = .1
X = 5-1.282(.1)
X = 4.8718
The difference is
5.1282 - 4.8718
0.2564
Consumer products are required by law to contain at least as much as the amount printed on the package. For example, a bag of potato chips that is labeled as 10 ounces should contain at least 10 ounces.Assume that the standard deviation of the packaging equipment yields a bag weight standard deviation of 0.2 ounces. Assume the bag weight distribution is bell-shaped. Determine what average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.
Answer:
The average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802
Step-by-step explanation:
We are given that
Standard deviation, [tex]\sigma=0.2[/tex]ounces
We have to find the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag.
[tex]P(x\geq 10)=0.99[/tex]
Assume the bag weight distribution is bell-shaped
Therefore,
[tex]P(\frac{x-\mu}{\sigma}\geq 10)=0.99[/tex]
We know that
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Using the value of z
Now,
[tex]\frac{10-\mu}{0.2}=0.99[/tex]
[tex]10-\mu=0.99\times 0.2[/tex]
[tex]\mu=10-0.99\times 0.2[/tex]
[tex]\mu=9.802[/tex]
Hence, the average bag weight must be used to achieve at least 99 percent of the bags having 10 or more ounces in the bag=9.802
Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases. Suppose 13 samples are studied, and they can be considered to be independent for mutation. Determine the following probabilities.
(a) No samples are mutated.
(b) At most one sample is mutated.
(c) More than half the samples are mutated.
Round your answers to two decimal places (e.g. 98.76).
Answer:
a) 0.6730 = 67.30% probability that no samples are mutated.
b) 0.9436 = 94.36% probability that at most one sample is mutated.
c) 0% probability that more than half the samples are mutated.
Step-by-step explanation:
For each sample, there are only two possible outcomes. Either it is mutated, or it is not. The probability of a sample being mutated is independent of any other sample, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
Samples of rejuvenated mitochondria are mutated (defective) in 3% of cases.
This means that [tex]p = 0.03[/tex]
13 samples are studied
This means that [tex]n = 13[/tex]
(a) No samples are mutated.
This is P(X = 0). So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730[/tex]
0.6730 = 67.30% probability that no samples are mutated.
(b) At most one sample is mutated.
This is:
[tex]P(X \leq 1) = P(X = 0) + P(X = 1)[/tex]
So
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{13,0}.(0.03)^{0}.(0.97)^{13} = 0.6730[/tex]
[tex]P(X = 1) = C_{13,1}.(0.03)^{1}.(0.97)^{12} = 0.2706[/tex]
Then
[tex]P(X \leq 1) = P(X = 0) + P(X = 1) = 0.6730 + 0.2706 = 0.9436[/tex]
0.9436 = 94.36% probability that at most one sample is mutated.
(c) More than half the samples are mutated.
This is:
[tex]P(X > 6.5) = P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10) + P(X = 11) + P(X = 12) + P(X = 13)[/tex]
Then
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 7) = C_{13,7}.(0.03)^{7}.(0.97)^{6} \approx 0[/tex]
Using two decimal digits precision, all will be 0. So
0% probability that more than half the samples are mutated.
Suppose the daily customer volume at a call center has a normal distribution with mean 5,500 and standard deviation 1,000. What is the probability that the call center will get between 4,800 and 5,000 calls in a day
Answer:
0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set 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]
The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Mean 5,500 and standard deviation 1,000.
This means that [tex]\mu = 5500, \sigma = 1000[/tex]
What is the probability that the call center will get between 4,800 and 5,000 calls in a day?
This is the p-value of Z when X = 5000 subtracted by the p-value of Z when X = 4800. So
X = 5000
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5000 - 5500}{1000}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a p-value of 0.3085.
X = 4800
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{4800 - 5500}{1000}[/tex]
[tex]Z = -0.7[/tex]
[tex]Z = -0.7[/tex] has a p-value of 0.2420.
0.3085 - 0.2420 = 0.0665
0.0665 = 6.65% probability that the call center will get between 4,800 and 5,000 calls in a day.
Point P is plotted on the coordinate grid. If point S is 12 units to the left of point P, what are the coordinates of point S? On a coordinate grid from negative 12 to positive 12 in increments of 2, a point P is plotted at the ordered pair 6, negative 4. (6, −16) (−6, −16) (−6, −4) (6, 4)
9514 1404 393
Answer:
(−6, −4)
Step-by-step explanation:
Translating a point 12 units left subtracts 12 from its x-coordinate.
P(6, -4) +(-12, 0) = S(-6, -4)
Real life problem for (-10+-2)=12
Hello!
[tex]\bf [ (-10) + (-2) ] = 12 [/tex]
[tex]\bf [ (-10) - 2 ] = 12 [/tex]
[tex]\bf -10 - 2 = 12 [/tex]
[tex]\bf -12 ≠ 12 [/tex]
Answer: Wrong
Good luck! :)
How
many solutions are there to the equation below?
4(x - 5) = 3x + 7
A. One solution
B. No solution
O C. Infinitely many solutions
SUB
Answer:
A one solution
Step-by-step explanation:
4(x - 5) = 3x + 7
Distribute
4x - 20 = 3x+7
Subtract 3x from each side
4x-3x-20 = 3x+7-3x
x -20 = 7
Add 20 to each side
x -20+20 = 7+20
x = 27
There is one solution
Answer:
Step-by-step explanation:
Let's simplify that before we make the decision, shall we? We'll get rid of the parenthesis by distribution and then combine like terms.
4x - 20 = 3x + 7 and combining like terms and getting everything on one side of the equals sign:
1x - 27 = 0. Since that x has a power of 1 on it (linear), that means we have only 1 solution. If that was an x², we would have 2 solutions; if that was an x³, we would have 3 solutions, etc.
1289 +(-1236) + (2434) =
0 -1431
O 2345
O 2487
0 -1956
Answer:
This answer is 2487
which will be the third one
Hope this help
The delivery man checks his route for deliveries.
The map has a scale of 1:250,000.
The distance between the bakery and his last delivery is 35 cm
What is the actual distance?
km.
9514 1404 393
Answer:
87.5 km
Step-by-step explanation:
Actual distance is 250000×35 cm = 87.5×10^5 cm = 87.5 km
_____
There are 100 cm in 1 m, and 1000 m in 1 km, so 100,000 cm = 10^5 cm in 1 km
Is this true or false ??
=============================================================
Explanation:
We'll use these two properties of integrals [tex]\displaystyle \text{If f(x) is an even function, then } \int_{-a}^{a}f(x)dx = 2\int_{0}^{a}f(x)dx[/tex]
[tex]\displaystyle \text{If f(x) is an odd function, then } \int_{-a}^{a}f(x)dx = 0[/tex]
These properties are valid simply because of the function's symmetry. For even functions, we have vertical axis symmetry about x = 0; while odd functions have symmetry about the origin.
------------------------
Here's how the steps could look
[tex]\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}((ax^8+c)+bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\int_{-7}^{7}(ax^8+c)dx+\int_{-7}^{7}(bx)dx\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=\left(2\int_{0}^{7}(ax^8+c)dx\right)+(0)\\\\\\\displaystyle \int_{-7}^{7}(ax^8+bx+c)dx=2\int_{0}^{7}(ax^8+c)dx\\\\\\[/tex]
Therefore, the given statement is true. The values of a,b,c don't matter. You could replace those '7's with any real number you want and still end up with a true statement.
We can see that ax^8+c is always even, while bx is always odd.
------------------------
Side note:
For the second step, I used the idea that [tex]\int(f(x)+g(x))dx=\int f(x)dx+\int g(x)dx\\\\[/tex]
which allows us to break up a sum into smaller integrals.
Help what is this question
Answer:
0
Step-by-step explanation:
what is the quotient 3/8 ÷5/12
Answer:
9/10
Step-by-step explanation:
3/8 ÷5/12
Copy dot flip
3/8 * 12/5
Rewriting
3/5 * 12/8
3/5 * 3/2
9/10
Determine whether the following problem involves a permutation or combination. (It is not necessary to solve the problem.)
How many different -letter passwords can be formed from the letters S, T, U, W, X, Y, and Z if no repetition of letters is allowed?
The problem involves (combination or permiation) because the (order or number) of letters selected (does or does not) matter.
Answer:
Step-by-step explanation:
The order matters
stuwxyz is different than zyxwuts
You have 7 letters
The number of permutations is 7! which is 7*6*5*4*3*2*1 = 5040
answer this question
Answer:
(-2, 13) (-1,8) (0, 5) (1, 4) (2, 5) (3, 8)
(2.4 , 6) or (-0.4, 6)
Step-by-step explanation:
Graph y = 6 on top of y = [tex]x^{2}[/tex] -2x + 5 and use the points where the two lines meet.
Which of the following is the most accurate statement about statistics?
a) We can absolutely be 100% certain in accurately generalizing the characteristics of entire population based on the sample data
b) By analyzing data, we may be able to identify connections and relationships in our data
c) We can explore in the midst of variation to better understand our data
d) limited data or experience likely generates less confidence
e) Non of the above
Answer:
b) By analyzing data, we may be able to identify connections and relationships in our data.
Step-by-step explanation:
In statistics decisions are based on probability sampling distributions. As statics is collection and analysis of data along with its interpretation and presentation.plzz help with this question
Answer: 51 liters of fuel are required
Step by step: start by seeing how many times 476 can go into 1428
(1428/476=3)
Then take your sum of that and multiply it by 17 since that’s the number that correlates with 476
(17x3=51) therefore your answer is 51 liters
Find x and explain how you found x
Answer:
x=60
Step-by-step explanation:
There are different ways to find x but this is what I found easiest.
To solve first note that AOD and CFB are vertical angles; this means that they are congruent. AOD consists of two angles with the measurements of 90 and x. CFB consists of two angles with the measurements of 30 and 2x. So, to find x set add the adjacent angles and set them equal to the other pair of angles. The equation would be [tex]90+x=30+2x[/tex]. First, subtract x from both sides; this makes the equation [tex]90=30+x[/tex]. Then, subtract 30 from both sides. This gives the final answer, x=60.
