Answer:
nth term = dn + (a - d) Where d is the difference between the terms, a is the first term and n is the term number.
Step-by-step explanation:
9*17 + (-6- 9)= 138
First find the common difference.
This can be found by subtracting the second term minus the
first term which in this case us 3 - (-6) or 3 + (+6) which is 9.
So we add 9 to reach the next term in this sequence.
Since this sequence isn't too long, continuing adding 9
until you reach the 17th term in this arithmetic sequence.
-6 ⇒ 1st term
3 ⇒ 2nd term
12 ⇒ 3rd term
21 ⇒ 4th term
30 ⇒ 5th term
39 ⇒ 6th term
48 ⇒ 7th term
57 ⇒ 8th term
66 ⇒ 9th term
75 ⇒ 10th term
84 ⇒ 11th term
93 ⇒ 12th term
102 ⇒ 13th term
111 ⇒ 14th term
120 ⇒ 15th term
129 ⇒ 16th term
138 ⇒ 17th term
By manually doing this, we found that our 17th term is 138.
A 0.143-Henry Inductor is connected in series with a variable resistor to a 208-volt 400-cycle source. For what value of capacitance will the current be (a) 1.04 ampere lagging and (b) 1.04 ampere leading?
Answer:
A.)359.2, B.)2.5 uf
Step-by-step explanation:
E / I = R
208 / 1.04 = 200 ohms
2*pi*f*L = Xl
6.28*400*.143 = 359.2 ohm
1 / (2*pi*f*Xc) = c
1 /(6.28*400*159.2) = 2.5 uf
The base of a rectangular prism has an area of 12 square cm. The height of the rectangular prism is 3. What is the volume in cubic cm of this rectangular prism
Answer:
volume = 36 cm³
Step-by-step explanation:
The volume of a rectangular prism = lwh
where
w = width
l = length
h = height
The base of a rectangular prism is a rectangle and the area of a rectangle is the product of length and width. Therefore,
base area of the rectangular prism = length × width
base area = lw
Base area of the rectangular prism = 12 cm²
Recall, the formula of the volume of a rectangular prism is the product of the length, width and height.
volume = lwh
substitute lw value in the formula above
volume = 12 × 3
volume = 36 cm³
4-3 times 54 divided by 9 (Explain)
Answer:
6
Step-by-step explanation:
4-3x54÷9
How I'd do it is separate it:
4-3=1
Then 1x54=54
Then 54/9=6
Answer:
6
Step-by-step explanation:
[tex]4-3*54/9\\4-3 =1\\1*54 =54 \\54/9 =6[/tex]
what is the area of a circle with a radius of 42 in use 3.14 for pi
Answer:
[tex] \boxed{Area \: of \: circle = 5538.96 {in}^{2}} [/tex]
Step-by-step explanation:
Radius (r) = 42 in.
Area of circle = πr²
= 3.14 × (42)²
= 3.14 × 1764
= 5538.96 in²
Suppose the nightly rate for a hotel in Rome is thought to be bell-shaped and symmetrical with a mean of 138 euros and a standard deviation of 6 euros. The percentage of hotels with rates between 120 and 144 euros is
Answer:
The percentage of hotels with rates between 120 and 144 euros is 84%.
Step-by-step explanation:
We know that the distribution of the nightly rate for a hotel in Rome is bell shaped with a mean of 138 euros and a standard deviation of 6 euros.
We want to know the proportion of hotels between 120 and 144 euros.
We can approximate the distribution to a normal distribution and calculate the z-score for both boundaries:
[tex]z_1=\dfrac{X_1-\mu}{\sigma}=\dfrac{120-138}{6}=\dfrac{-18}{6}=-3\\\\\\z_2=\dfrac{X_2-\mu}{\sigma}=\dfrac{144-138}{6}=\dfrac{6}{6}=1[/tex]
Then, we can calculate the proportion as the probability of having rates between 120 and 144:
[tex]P=P(120<X<144)=P(-3<z<1)\\\\P=P(z<1)-P(z<-3)\\\\P=0.8413-0.0013\\\\P=0.8400[/tex]
Then, we can conclude that the percentage of hotels with rates between 120 and 144 euros is 84%.
Suppose your marketing colleague used a known population mean and standard deviation to compute the standard error as 52.4 for samples of a particular size. You don't know the particular sample size but your colleague told you that the sample size is greater than 70. Your boss asks what the standard error would be if you quintuple (5x) the sample size. What is the standard error for the new sample size? Please round your answer to the nearest tenth.
Answer:
The new standard error is [tex]e_{new} = 23.4[/tex]
Step-by-step explanation:
From the question we are told that
The standard error is [tex]e = 52.4[/tex]
Generally the standard error is mathematically represented as
[tex]e = \frac{6}{\sqrt{n} }[/tex]
Where n is the sample size
for the original standard error we have
[tex]52.4 = \frac{6}{\sqrt{n} }[/tex]
Now sample size is quintuple
[tex]e_{new} = \frac{6}{\sqrt{5 * n} }[/tex]
[tex]but \ \ 52.4 = \frac{6}{\sqrt{n} }[/tex]
So [tex]e_{new} = \frac{52.4}{\sqrt{5} }[/tex]
[tex]e_{new} = 23.4[/tex]
The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11, while the number of 5th graders to that of the 6th graders was 13 to 9. By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?
Answer:
The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.
Step-by-step explanation:
I am going to say that:
x is the proportion of 5th graders.
y is the proportion of 6th graders.
z is the proportion of 7th graders.
The number of 6th graders in RSM summer camp to that of 7th graders was 4 to 11
This means that:
[tex]\frac{y}{z} = \frac{4}{11}[/tex]
So
[tex]11y = 4z[/tex]
[tex]y = \frac{4z}{11}[/tex]
The number of 5th graders to that of the 6th graders was 13 to 9.
This means that:
[tex]\frac{x}{y} = \frac{13}{9}[/tex]
[tex]9x = 13y[/tex]
[tex]x = \frac{13y}{9}[/tex]
All of them is 100%
This means that:
[tex]x + y + z = 1[/tex]
We need to find z.
[tex]y = \frac{4z}{11}[/tex]
[tex]x = \frac{13y}{9} = \frac{13*4z}{9*11} = \frac{52z}{99}[/tex]
Then
[tex]x + y + z = 1[/tex]
[tex]\frac{52z}{99} + \frac{4z}{11} + z = 1[/tex]
The lcm(least common multiple) between 11 and 99 is 99. Then
[tex]\frac{52z + 9*4z + 99z}{99} = 1[/tex]
[tex]187z = 99[/tex]
[tex]z = \frac{99}{187}[/tex]
[tex]z = 0.5294[/tex]
By what percent did the number of 7th graders exceed that of the number of 5th and 6th graders taken together ?
z(7th graders) is 52.94%.
x + y(5th and 6th graders) is 100 - 52.94 = 47.06%
52.94 - 47.06 = 5.88
The number of 7th graders exceed that of the number of 5th and 6th graders taken together by 5.88%.
During a typical Pennsylvania winter, I80 averages 1.6 potholes per 10miles. A certain county is responsible for repairing potholes in a 30-mile stretch of the interstate. LetXdenote the number of potholes thecounty will have to repair at the end of next winter.
(a) The distribution of the random variable X is (choose one)
(i) binomial
(ii) hypergeometric
(iii) negative binomial
(iv) Poisson.
(b) Give the expected value and variance of X.
(c)The cost of repairing a pothole is $5000. If Y denotes the county’s pothole repair expense for next winter, find the mean value and variance Y?
Answer:
a) (iv) Poisson.
b) E(X)=V(X)=λ=4.8
c) E(Y)=24,000
V(Y)=120,000,000
Step-by-step explanation:
We can appropiately describe this random variable with a Poisson distribution, as the probability of having a pothole can be expressed as a constant rate per mile (0.16 potholes/mile) multiplied by the stretch that correspond to the county (30 miles).
The parameter of the Poisson distribution is then:
[tex]\lambda=0.16\cdot 30=4.8[/tex]
b) The expected value and variance of X are both equal to the parameter λ=4.8.
c) If we define Y as:
[tex]Y=5000X[/tex]
the expected value and variance of Y are:
[tex]E(Y)=E(5,000\cdot X)=5,000\cdot E(X)=5,000\cdot 4.8=24,000\\\\\\ V(Y)=V(5000\cdot X)=5000^2\cdot V(X)=25,000,000\cdot 4.8=120,000,000[/tex]
Find the values of p for which the following integral converges:
∫[infinity]e 1/(x(ln(x))^p)dx
Input youranswer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all p, type an upper-case "D" in every blank.
Values of p are in the interval ,
For the values of p at which the integral converges, evaluate it. Integral =
Answer:
Step-by-step explanation:
Find the values of p for which the following integral converges:
∫[infinity]e 1/(x(ln(x))^p)dx
Input youranswer by writing it as an interval. Enter brackets or parentheses in the first and fourth blanks as appropriate, and enter the interval endpoints in the second and third blanks. Use INF and NINF (in upper-case letters) for positive and negative infinity if needed. If the improper integral diverges for all p, type an upper-case "D" in every blank.
Values of p are in the interval ,
For the values of p at which the integral converges, evaluate it. Integral =
Recall that
[tex]\int\limits^{\infty}_1 \frac{1}{x^p} dx[/tex]
converge if p > 1 and converge to [tex]\frac{1}{p-1}[/tex] and divertgent if p ≤ 1
Now, let u = Inx ⇒ du = 1/x dx
: e ≤ x ≤ ∞ ⇒ 1 ≤ u < ∞
⇒ [tex]\int\limits^{\infty}_e \frac{dx}{x(Inx)^p} = \int\limits^{\infty}_1 {x} \frac{du}{u^p}[/tex]
converge if p > 1 and converge to [tex]\frac{1}{p-1}[/tex] and divertgent if p ≤ 1
[tex]\text {Integral}=\frac{1}{p-1}[/tex]
Mme. Giselle's boutique in Cleveland, Ohio is planning to sell a Parisian frock. If the public view it as being the latest style, the frocks will be worth $10 comma 000. However, if the frocks are viewed as passe, they will be worth only $2 comma 000. If the probability that they are stylish is 10%, what is the expected value of the frocks? The expected value of the frocks (EV) is EVequals$ nothing. (Enter your response rounded to two decimal places.)
Answer:
the expected value of the frocks (EV) is 2800
Step-by-step explanation:
the expected value of the frocks= (probability of stylish* worth)+(probability of passe* worth)
If the public view it as being the latest style, the frocks will be worth $10,000.
if the frocks are viewed as passe, they will be worth only $2,000.
If the probability that they are stylish is 10%
probability of stylish = 10000
worth = 10%
probability of passe = 2000
[tex]=10 \%*10000+(1-10 \%)*2000\\\\=0.1\times 10000+(1-0.1)\times2000\\\\=1000+(0.9)\times2000\\\\=1000+1800\\\\=2800[/tex]
Therefore, the expected value of the frocks (EV) is 2800
Suppose that the probability of a drought in any independent year is 20%. Out of those years in which a drought occurs, the probability of water rationing is ten percent. However, in any year, the probability of water rationing is five percent.
Which of the following is true?
a. 0.01
b. 0.05
c. 0.30
d. 0.02
Answer:
the correct option is d. 0.02
Step-by-step explanation:
We have the following events:
x: A drought occurd
y: Water rationing.
Therefore, according to the plaster we have:
P [x] = 0.20
P [y | x] = 0.10
Now P [it is a drought and water rationing happens] =
P [x n y] = P [y | x] * P [x] = 0.10 * 0.20 = 0.02
Which means that the correct option is d. 0.02
does anyone know the answer for dis problem?
x = # of CDs Walter has
3x - number of CDs Brian has
144 - total
x + 3x = 144
4x = 144
x = 144/4
x = 36
Answer: D. 36
Answer:
D.36
Step-by-step explanation:
X+3X=144
4X=144 (THEN DIVIDE BOTH SIDES B 4)
X=144/4=36
Find the product (4x^2+2)(6x^2+8x+5)
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
[tex]= 24 {x}^{4} + 32 {x}^{3} + 32 {x}^{2} + 16x + 10 \\ [/tex]
Step-by-step explanation:
[tex](4 {x}^{2} + 2)(6 {x}^{2} + 8x + 5) \\ 4 {x}^{2} (6 {x}^{2} + 8x + 5) + 2(6 {x}^{2} + 8x + 5) \\ 24 {x}^{4} + 32 {x}^{3} + 2 0{x}^{2} + 12 {x}^{2} + 16x + 10 \\ = 24 {x}^{4} + 32 {x}^{3} + 32{x}^{2} + 16x + 10 \\ [/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Nancy has to cut out circles of diameter 1 3/ 7 cm from an aluminium strip of dimensions 7 1/ 7 cm by 1 3/ 7 cm . How many full circles can Nancy cut?
Answer:
Nancy can cut 6 full circles
Step-by-step explanation:
Length of aluminium strip = [tex]7 \frac{1}{7} cm[/tex]
Length of aluminium strip =[tex]\frac{50}{7} cm[/tex]
Breadth of aluminium strip =[tex]1 \frac{3}{7} cm[/tex]
Breadth of aluminium strip =[tex]\frac{10}{7} cm[/tex]
Area of strip = [tex]Length \times Breadth = \frac{50}{7} \times \frac{10}{7} =\frac{500}{49}[/tex]
Diameter of circle = [tex]1 \frac{3}{7} cm[/tex]
Diameter of circle = [tex]\frac{10}{7} cm[/tex]
Radius of circle =[tex]\frac{10}{ 7 \times 2}=\frac{10}{14} cm[/tex]
Area of circle =[tex]\pi r^2 = \frac{22}{7} \times (\frac{10}{14})^2=\frac{550}{343} cm^2[/tex]
No. of circles can be cut = [tex]\frac{\frac{500}{49}}{\frac{550}{343}}=6.3636[/tex]
So,Nancy can cut 6 full circles
Pls pls pretty pls do any of these whatever you know pls
Answer:
5) 8
6) True, a trapezium has at least 1 parallel side, and a parallelogram has 2.
7) I can't see where angle z is..., but x=42 and y= 96
Step-by-step explanation:
A rhombus has all sides of equal length, thus, if DC is 5, then all the other sides are also 5.
We see that AC is 6, and OC will be 3, or 6/2.
The pythagorean theorem shows that OD is 4, and BD is 8.
42+42=84
180-84=96
Answer:
5. BD = 8 cm
6. See explanation below.
7. x = 42; y = 96; z = 64
Step-by-step explanation:
5.
DC = 5 cm
The diagonals of a rhombus bisect each other, so since AC = 6 cm, OC = 3 cm.
The diagonals of a rhombus are perpendicular to each other, so triangle DOC is a right triangle with right angle DOC.
a^2 + b^2 = c^2
(DO)^2 + (OC)^2 = (DC)^2
(DO)^2 + (3 cm)^2 = (5 cm)^2
(DO)^2 + 9 cm^2 = 25 cm^2
(DO)^2 = 16 cm^2
DO = 4 cm
Since BD = 2DO,
BD = 2(4 cm) = 8 cm
Answer: BD = 8 cm
6.
There are different definitions of trapezium. In the U.S., trapezium is a quadrilateral, none of whose sides are parallel. According to the U.S. definition of trapezium, then, no parallelogram is a trapezium.
According to the UK definition of trapezium, a trapezium is a quadrilateral with at least 2 parallel sides. That means the other two sides may or may not be parallel. According to this definition, then a parallelogram is always a trapezium.
8.
Triangle ADB is isosceles with AD = AB. That meakes their opposite angles congruent.
x = m<ADB = 42
42 + 42 + y = 180
y = 96
In a kite, there are two pairs of congruent sides. DC = BC, so z = m<BDC
z + z + 52 = 180
2z = 128
z = 64
Help ASAP
Jamal and Diego both leave the restaurant at the same time, but in opposite directions. If Diego travels 7 mph faster than Jamal and after 4 hours they are 68 miles apart, how fast is each traveling?
Answer:
Jamal travels at a speed of 5 mph and Diego travels at a speed of 12 mph.
Step-by-step explanation:
Jamal's speed is of x mph.
Diego's speed is of (x + 7) mph.
Opposite directions.
This means that each hour, they will be x + x + 7 = 2x + 7 miles apart.
After 4 hours they are 68 miles apart, how fast is each traveling?
Using a rule of three.
1 hour - 2x + 7 miles apart.
4 hours - 68 miles apart.
[tex]4(2x + 7) = 68[/tex]
[tex]8x + 28 = 68[/tex]
[tex]8x = 40[/tex]
[tex]x = \frac{40}{8}[/tex]
[tex]x = 5[/tex]
Jamal travels at a speed of 5 mph and Diego travels at a speed of 12 mph.
The perimeter of a rectangle whose sides are lengths(3z+2) units and(2z+3)units
Answer:
P = 10z + 10 units.
Step-by-step explanation:
To find the perimeter of a rectangle, you can use the formula P = 2l + 2w.
If one side is '3z + 2' and the other is '2z + 3', we can plug these into the equation:
P = 2(3z + 2) + 2(2z + 3).
Distributing the 2's gives us:
P = 6z + 4 + 4z + 6
Combine like terms, resulting in the final answer:
P = 10z + 10 units.
If 20% of the people in a community use the emergency room at a hospital in one year, find
the following probability for a sample of 10 people.
a) At most three used the emergency room
b) Exactly three used the emergency room
c) At least five used the emergency room
Answer:
a) 87.91% probability that at most three used the emergency room
b) 20.13% probability that exactly three used the emergency room.
c) 3.28% probability that at least five used the emergency room
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they use the emergency room, or they do not. The probability of a person using the emergency room is independent of any other person. So we use the binomial probability distribution 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.
Sample of 10 people:
This means that [tex]n = 10[/tex]
20% of the people in a community use the emergency room at a hospital in one year
This means that [tex]p = 0.2[/tex]
a) At most three used the emergency room
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3)[/tex]
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{10,0}.(0.2)^{0}.(0.8)^{10} = 0.1074[/tex]
[tex]P(X = 1) = C_{10,1}.(0.2)^{1}.(0.8)^{9} = 0.2684[/tex]
[tex]P(X = 2) = C_{10,2}.(0.2)^{2}.(0.8)^{8} = 0.3020[/tex]
[tex]P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013[/tex]
[tex]P(X \leq 3) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 0.1074 + 0.2684 + 0.3020 + 0.2013 = 0.8791[/tex]
87.91% probability that at most three used the emergency room
b) Exactly three used the emergency room
[tex]P(X = 3) = C_{10,3}.(0.2)^{3}.(0.8)^{7} = 0.2013[/tex]
20.13% probability that exactly three used the emergency room.
c) At least five used the emergency room
[tex]P(X \geq 5) = 1 - P(X < 5)[/tex]
In which
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
From 0 to 3, we already have in a).
[tex]P(X = 4) = C_{10,4}.(0.2)^{4}.(0.8)^{6} = 0.0881[/tex]
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.1074 + 0.2684 + 0.3020 + 0.2013 + 0.0881 = 0.9672[/tex]
[tex]P(X \geq 5) = 1 - P(X < 5) = 1 - 0.9672 = 0.0328[/tex]
3.28% probability that at least five used the emergency room
If a rectangle has a width of 7 centimeters less than it’s length, and it’s area is 330 square centimeters. What are it’s length and width
Answer:
length 22 cmwidth 15 cmStep-by-step explanation:
If we assume the length and width are integer numbers of centimeters, we can look at the factors of 330:
330 = 1×330 = 2×165 = 3×110 = 5×66 = 6×55 = 10×33 = 11×30 = 15×22
The factors in this last pair differ by 7, so represent the width and length of the rectangle.
The rectangle's length and width are 22 cm and 15 cm, respectively.
Of 375 randomly selected students, 30 said that they planned to work in a rural community. Find 95% confidence interval for the true proportion of all medical students who plan to work in a rural community.
Answer:
The 95% confidence interval for the true proportion of all medical students who plan to work in a rural community is (0.0525, 0.1075).
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
For this problem, we have that:
[tex]n = 375, \pi = \frac{30}{375} = 0.08[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower limit of this interval is:
[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 - 1.96\sqrt{\frac{0.08*0.92}{375}} = 0.0525[/tex]
The upper limit of this interval is:
[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.08 + 1.96\sqrt{\frac{0.08*0.92}{375}} = 0.1075[/tex]
The 95% confidence interval for the true proportion of all medical students who plan to work in a rural community is (0.0525, 0.1075).
A recent survey was conducted to compare the cost of solar energy to the cost of gas or electric energy. Results of the survey revealed that the distribution of the amount of the monthly utility bill of a 3-bedroom house using gas or electric energy had a mean of $143 and a standard deviation of $8. If the distribution can be considered mound-shaped and symmetric, what percentage of homes will have a monthly utility bill of more than $135? Write your answer exclude the percentage. (Exp. if your answer is 12%, then input as 12)
Answer:
84.13.
Step-by-step explanation:
When the distribution is normal, we use the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.
For this question:
[tex]\mu = 143, \sigma = 8[/tex]
What percentage of homes will have a monthly utility bill of more than $135?
This is 1 subtracted by the pvalue of Z when X = 135. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{135 - 143}{8}[/tex]
[tex]Z = -1[/tex]
[tex]Z = -1[/tex] has a pvalue of 0.1587
1 - 0.1587 = 0.8413
84.13% of homes will have a monthly utility bill of more than $135. Excluding the percentage, the answer is 84.13.
what is the most abundant gas in the Earth's atmosphere?
Answer:
Nitrogen
Step-by-step explanation:
Nitrogen and oxygen are by far the most common; dry air is composed of about 78% nitrogen (N2) and about 21% oxygen (O2). Argon, carbon dioxide (CO2), and many other gases are also present in much lower amounts; each makes up less than 1% of the atmosphere's mixture of gases. Hope this helped!
A manufacturer of cheese filled ravioli supplies a pizza restaurant chain. Based on data collected from its automatic filling process, the amount of cheese inserted into the ravioli is normally distributed. To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 ravioli and measure the weight of cheese filling. They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams. What is the standard deviation of sample mean
Answer:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And the standard deviation for the sample mean would be given by:
[tex] \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3[/tex]
Step-by-step explanation:
For this case we know that the amount of cheese inserted into the ravioli is normally distributed. And we have the following info given;
[tex] \bar X =15[/tex] the sample mean
[tex]s= 1.5[/tex] the sample deviation
[tex] n=25[/tex] the sample size
And for this case we know that the sample size is large enough in order to apply the central limit theorem and the distribution for the sample mean would be given by:
[tex] \bar X \sim N(\mu, \frac{\sigma}{\sqrt{n}}) [/tex]
And the standard deviation for the sample mean would be given by:
[tex] \sigma_{\bar X}= \frac{1.5}{\sqrt{25}}= 0.3[/tex]
What is the sum of 7 3/5 and 2 4/5?
Step-by-step explanation:
[tex]7 \times \frac{3}{5} + 2 \times \frac{4}{5} \\ \frac{38}{5} + \frac{14}{5} \\ \frac{38 + 14}{5} \\ \frac{52}{5} \\ 10 \times \frac{2}{5} [/tex]
Answer:
Step-by-step explanation
7 [tex]\frac{3}{5}[/tex] + 2 [tex]\frac{4}{5}[/tex]
= 38/5 + 14/5
=52/5
The proportion of items in a population that possess a specific attribute is known to be 0.40. If a simple random sample of size 100 is selected and the proportion of items in the sample that contain the attribute of interest is 0.46, what is the sampling error?
Answer:
The sampling error = 0.06
Step-by-step explanation:
From the given information:
Let represent [tex]\beta[/tex] to be the population proportion = 0.4
The sample proportion be P = 0.46 &
The sample size be n = 100
The population standard duration can be expressed by the relation:
Population standard duration [tex]\sigma = \sqrt{\dfrac{\beta(1- \beta)}{n}}[/tex]
[tex]\sigma = \sqrt{\dfrac{0.4(1-0.4)}{100}}[/tex]
[tex]\sigma = \sqrt{\dfrac{0.4(0.6)}{100}}[/tex]
[tex]\sigma = 0.049[/tex]
The sample proportion = 0.46
Then the sampling error = P - [tex]\beta[/tex]
The sampling error = 0.46 - 0.4
The sampling error = 0.06
The radius of the inscribed circle is cm, and the radius of the circumscribed circle is cm.
The complete question is;
Instructions:Select the correct answer from each drop-down menu.
The side length of the square in the figure is 8 cm.
The radius of the inscribed circle is [ (32)^(1/2), 16, 4, 32 ] cm, and the radius of the circumscribed circle is [ (32)^(1/2), 2(32)^(1/2), (128)^(1/2), 128 ] cm.
Image is attached.
Answer:
Radius of inscribed circle = 4 cm
Radius of circumscribed circle = 32^(1/2) cm
Step-by-step explanation:
The square has a side of 8cm.
Thus,the diameter of the inscribed circle would be same as a side of the square.
So, if diameter = 8cm, then, radius of inscribed = 8/2 = 4cm
Now, to the circumscribed circle, the diagonal of the square would be the diameter of the circumscribed circle. It can be calculated with Pythagoreas theorem.
So, d² = 8² + 8²
d² = 64 + 64
d² = 128
d = √128
Expressing it in surd form gives;
d = √32 x √4
d = 2√32 cm
So radius of circumscribed circle = (2√32)/2 = √32 cm or 32^(1/2) cm
Answer:
4 and 32^1/2
Step-by-step explanation:
i just did it on plato :))
f(x) = x2 + 1
g(x) = 5-x
(f+g)(x) =
O x2 + x-4
x²+x+4
O x2-x+6
O x2 + x + 6
Answer:
[tex] \boxed{(f + g)(x) = {x}^{2} - x + 6} [/tex]
Given:
[tex]f(x) = {x}^{2} + 1 \\ \\ g(x) = 5 - x[/tex]
To Find:
[tex](f + g)(x) = f(x) + g(x)[/tex]
Step-by-step explanation:
[tex] = > f(x) + g(x) = ({x}^{2} + 1) + (5 - x) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 1 + 5 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} + 6 - x\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {x}^{2} - x + 6[/tex]
How do I find x to the nearest tenth?
Answer:
x=24.8
Step-by-step explanation:
When dots are printed from a laser printer to form letters, they must be close enough so that you do not see the individual dots of ink. To do this, the separation of the dots must be less than Raleigh's criterion of your eye at distances typical for reading Randomized Variables D 2.5 mm d-38 cm Take the pupil of the eye to be 2.5 mm in diameter and the distance from the paper to the eye as 38 cm. Find the minimum separation of two dots such that they cannot be resolved in cm. Assume a wavelength of 555 nm for visible light.
Answer:
The minimum separation is [tex]z = 1.0292 *10^{-4} \ m[/tex]
Step-by-step explanation:
From the question we are told that
The reading randomized variable are [tex]D= 2.5 \ mm[/tex] and [tex]d = 38 \ cm[/tex]
The diameter of the pupil is [tex]d = 2.5 \ mm = \frac{2.5}{1000} = 0.0025 \ m[/tex]
The distance from the paper is [tex]D = 38 \ cm = 0.38 \ m[/tex]
The wavelength is [tex]\lambda = 555 \ nm = 555 * 10 ^{-9} m[/tex]
Generally the Raleigh's equation for resolution is
[tex]\theta = 1.22 [\frac{\lambda}{D} ][/tex]
substituting values
[tex]\theta = 1.22 * \frac{555*10^{-9}}{0.0025}[/tex]
[tex]\theta = 2.7084*10^{-4} \ rad[/tex]
The minimum separation of two dots is mathematically represented as
[tex]z = \theta d[/tex]
substituting values
[tex]z = 2.7084*10^{-4} * 0.38[/tex]
[tex]z = 1.0292 *10^{-4} \ m[/tex]
Awnser on the lowest terms 2 hours 45 minutes + 3 hours 35 minutes
Step-by-step explanation:
2 hrs 45 min + 3 hrs 35 min
= 5 hrs 80 min
60 min = 1 hr
*80 min = 1 hr + 20 min
5hrs 80 min
= 5 hrs + 1 hr + 20 min
= 6 hrs 20 min
Answer:
6 hour 20 minutes
Step-by-step explanation:
Add the two time measurements separately.
2 hours + 3 hours = 5 hours
35 minutes + 45 minutes = 80 minutes
Now, simplify the measurements to the lowest terms. You can simplify the minutes by subtracting 60 from the value. 60 minutes is 1 hour. The number you get after subtracting is how many minutes there are.
80 - 60 = 20
80 minutes = 1 hour 20 minutes
Now add the two measurements together.
5 hours + 1 hour 20 minutes = 6 hour 20 minutes