Answer: The required solution of the given system is
(x, y) = (3, 1) and (4, 0).
Step-by-step explanation: We are given to solve the following system of equations :
[tex]x+y=4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\y=x^2-8x+16~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)[/tex]
From equation (i), we have
[tex]x+y=4\\\\\Rightarrow y=4-x~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(iii)[/tex]
Substituting the value of y from equation (iii) in equation (ii), we get
[tex]y=x^2-8x+16\\\\\Rightarrow 4-x=x^2-8x+16\\\\\Rightarrow x^2-8x+16-4+x=0\\\\\Rightarrow x^2-7x+12=0\\\\\Rightarrow x^2-4x-3x+12=0\\\\\Rightarrow x(x-4)-3(x-4)=0\\\\\Rightarrow (x-3)(x-4)=0\\\\\Rightarrow x-3=0,~~~~~~~x-4=0\\\\\Rightarrow x=3,~4.[/tex]
When, x = 3, then from (iii), we get
[tex]y=4-3=1.[/tex]
And, when x = 4, then from (iii), we get
[tex]y=4-4=0.[/tex]
Thus, the required solution of the given system is
(x, y) = (3, 1) and (4, 0).
you flip a spinner that has 4 differently colored regions (red, white, blue, green) all equal in area, and toss 1 die and count the dots on top (1 thourgh 6 possible). How many color-dot outcomes are possible?
Answer:
24 ways
Step-by-step explanation:
Two different events
1) flip a spinner with 4 different colors regions.
2) tossing a die with 6 outcomes
to calculate number of colored dots possible
note here both action are independent of each other
by the principal of counting we can say
if an act is performed in m ways and another act can be performed in n ways the both the act simultaneously can be performed in [tex]m\times n[/tex] ways.
here act 1 has m=4 ways and act n= 6 ways
hence number of ways of getting colored dots = [tex]4\times6[/tex] ways
= 24 ways
The total number of possible outcomes when flipping a spinner with 4 differently colored regions and tossing a die is 24, calculated by multiplying the number of possible outcomes from the spinner (4) and the die (6).
Explanation:The subject of the question is the calculation of possible outcomes in a probability scenario involving a spinner and a die. A spinner with 4 differently colored areas can give 4 outcomes (red, white, blue, green), and tossing a die can result in 6 outcomes (1, 2, 3, 4, 5, 6).
To find the total number of possible outcomes, we simply multiply the number of possible outcomes from the spinner and the die: 4 (from the spinner) times 6 (from the die).
So, there are 24 color-dot outcomes possible when flipping a spinner with 4 differently colored areas and tossing a die.
Learn more about Probability here:https://brainly.com/question/32117953
#SPJ3
Gold used to make jewerly is often a blend of gold, silver, and copper. Consider three alloys of these metals. The first alloy is 75% gold, 5% silver, and 20% copper. The second alloy is 75% gold, 12.5% silver, and 12.5% copper. The third alloy is 37.5% gold and 62.5% silver. If 100 g of the first alloy costs $2500.40, 100 g of the second alloy costsnbsp $ 2537.75, and 100 g of the third alloy costs $ 1550.00, how much does each metal cost?
Answer:
Gold - $33, Silver - $5, Copper - $0.02
Step-by-step explanation:
Let $x be the price of one gram of gold, $y - price of 1 g of silver and $z - price of 1 g of copper.
1. The first alloy is 75% gold, 5% silver, and 20% copper, so in 100 g there are 75 g of gold, 5 g of silver and 20 g of copper. If 100 g of the first alloy costs $2500.40, then
75x+5y+20z=2500.40
2. The second alloy is 75% gold, 12.5% silver, and 12.5% copper, so in 100 g there are 75 g of gold, 12.5 g of silver and 12.5 g of copper. If 100 g of the first alloy costs $2537.75, then
75x+12.5y+12.5z=2537.75
3. The third alloy is 37.5% gold and 62.5% silver, so in 100 g there are 37.5 g of gold and 62.5 g of silver . If 100 g of the first alloy costs $1550.00, then
37.5x+62.5y=1550.00
Solve the system of three equations:
[tex]\left\{\begin{array}{l}75x+5y+20z=2500.40\\75x+12.5y+12.5z=2537.75\\37.5x+62.5y=1550.00\end{array}\right.[/tex]
Find all determinants
[tex]\Delta=\|\left[\begin{array}{ccc}75&5&20\\75&12.5&12.5\\37.5&62.5&0\end{array}\right] \|=28125\\ \\
\Delta_x=\|\left[\begin{array}{ccc}2500.40&5&20\\2537.75&12.5&12.5\\1550.00&62.5&0\end{array}\right] \|=928125\\ \\
\Delta_y=\|\left[\begin{array}{ccc}75&2500.40&20\\75&2537.75&12.5\\37.5&1550&0\end{array}\right] \|=140625\\ \\
\Delta_z=\|\left[\begin{array}{ccc}75&5&2500.40\\75&12.5&2537.75\\37.5&62.5&1550\end{array}\right] \|=562.5\\ \\[/tex]
So,
[tex]x=\dfrac{\Delta_x}{\Delta}=\dfrac{928125}{28125}=33\\ \\\\y=\dfrac{\Delta_y}{\Delta}=\dfrac{140625}{28125}=5\\ \\\\z=\dfrac{\Delta_z}{\Delta}=\dfrac{562.5}{28125}=0.02\\ \\[/tex]
Jerry spent ¾ of his allowance on baseball cards. If he was given S20, how mch did he spend on baseball cards.
Answer:
$15
Step-by-step explanation:
He had $20 and he spent [tex]\frac{3}{4}[/tex] of that in baseball cards, that is
[tex]20*\frac{3}{4}= \frac{20*3}{4} = \frac{60}{4} = 15.[/tex]
So, he spent $15 in baseball cards.
Why do you think students have difficulty understanding the concept of a mathematical function?
Answer:
Because they have never had to express one quantity in terms of another. The idea of such a relationship is completely new, as is the vocabulary for expressing such relationships.
Step-by-step explanation:
"Function" is a simple concept that says you can relate two quantities, and you can express that relationship in a number of ways. (ordered pairs, table, graph)
The closest experience most students have with functions is purchasing things at a restaurant or store, where the amount paid is a function of the various quantities ordered and the tax. Most students have never added or checked a bill by hand, so the final price is "magic", determined solely by the electronic cash register. The relationship between item prices and final price is completely lost. Hence the one really great opportunity to consider functions is lost.
Students rarely play board games or counting games (Monopoly, jump rope, jacks, hide&seek) that would give familiarity with number relationships. They likely have little or no experience with the business of running a lemonade stand or making and selling items. Without these experiences, they are at a significant disadvantage when it comes to applying math to their world.
Inâ 2001, the population in a town was 11% more than it was in 2000. If the population was 25,570 in 2002 which was 10% more than 2001 find the population in 2000
write the number (Round to the nearest wholeâ number.)
Answer: There was population of 22808 in 2000.
Step-by-step explanation:
Since we have given that
Population was in 2002 = 25,570
According to question, the population in 2002 was 10% more than 2001.
So, the population in 2001 was
[tex]25570=P_1(1+\dfrac{r}{100})\\\\25570=P_1(1+\dfrac{10}{100})\\\\25570=P_1(1+0.1)\\\\25570=P_1(1.01)\\\\\dfrac{25570}{1.01}=P_1\\\\25316.8\approx 25317=P_1[/tex]
Now, we have given that
In 2001, the population in a town was 11% more than it was in 2000.
So, population in 2000 was
[tex]25317=P_0(1+\dfrac{r}{100})\\\\25317=P_0(1+\dfrac{11}{100})\\\\\25317=P_0(1+0.11)\\\\25317=P_0(1.11)\\\\P_0=\dfrac{25317}{1.11}\\\\P_0=22808[/tex]
Hence, there was population of 22808 in 2000.
Provide a counterexample:
If a and b are integers where a is divisible by b and b is divisible by a, then a = b.
Answer:
[tex]a=2 \quad \text{and} \quad b=-2[/tex]
Step-by-step explanation:
Take [tex]a=2 \quad \text{and} \quad b=-2[/tex], note that
[tex]2=(-1)\cdot(-2)[/tex]
hence b divides a. On the other hand, we have that
[tex]-2=(-1)\cdot2[/tex]
which tells us that a divides b. Moreover, [tex]a=2 \neq -2=b[/tex].
What is the median for the set of data? Ages Stem Leaves
1 0, 3, 6
2 0, 1, 3, 7, 7, 8, 9
3 0, 2, 3, 3, 3, 3, 8, 9
4 6, 6, 6, 8 1|0 = 10 years old
30
31
32
33
Answer:
This is a stem leaf data, in which the stem generally stands for the "tens" place value while the leaf stands for the "ones" place value.
Expand the data, and find the median by finding the middle number:
10, 13, 16, 20, 21, 23, 27, 27, 28, 29, 30, 32, 33, 33, 33, 33, 38, 39, 46, 46, 46, 48
There are 22 numbers in all. To find the Median when there is a even amount of numbers, Find the two middle numbers, and find the mean of the two numbers:
(32 + 30)/2 = (62)/2 = 31
31 is your answer.
~
U = {a, b, c, d, e, f, g} A = {a, c, e, g} B = {a, b, c, d} Find A ∩ B
[tex]A\cap B=\{x:x\in A \wedge x\in B\}[/tex]
[tex]\large\boxed{A\cap B=\{a,c\}}[/tex]
A programmer plans to develop a new software system. In planning for the operating system that he will​ use, he needs to estimate the percentage of computers that use a new operating system. How many computers must be surveyed in order to be 95% confident that his estimate is in error by no more than four percentage points question marks? Assume that nothing is known about the percentage of computers with new operating systems.
Answer:
n = 601
Step-by-step explanation:
Since we know nothing about the percentage of computers with new operating system, we assume than 50% of the computers have new operating system.
So, p = 50% = 0.5
q = 1 - p = 1 - 0.5 = 0.5
Margin of error = E = 4 percentage points = 0.04
Confidence Level = 95%
z value associated with this confidence level = z = 1.96
We need to find the minimum sample size i.e. n
The formula for margin of error for the population proportion is:
[tex]E=z\sqrt{\frac{pq}{n}}[/tex]
Re-arranging the equation for n, and using the values we get:
[tex]n=(\frac{z}{E} )^{2} \times pq\\\\ n=(\frac{1.96}{0.04})^{2} \times 0.5 \times 0.5\\\\ n = 601[/tex]
Thus, the minimum number of computers that must be surveyed is 601
What is the condition on the probability of success p that will guarantee the histogram of a binomial distribution is symmetrical about x=n/2. Justify your answer.
Answer:
The probability of success is 1/2.
Step-by-step explanation:
The histogram of a binomial distribution has a mode of n×p. For that to be n/2, the value of p must be 1/2.
Find x.
A.4
B.18
C.12
D.38
The inside angle is half the outside angle.
2x +2 = 76 /2
2x +2 = 38
Subtract 2 from each side:
2x = 36
Divide both sides by 2:
x = 36 /2
x = 18
The answer is B.
If possible, find the solution of y=x+2z
z=-1-2x
x=y-14
A. No solution
B.(11,-14,7)
C.(-4,10,7)
D.(3,4,0)
Answer:
C. (-4,10,7)
Step-by-step explanation:
Use the first equation to substitute for y in the last equation:
x = (x +2z) -14
14 = 2z . . . . . . add 14-x
7 = z . . . . . . . . divide by 2
Now, find x:
7 = -1 -2x . . . . substitute for z in the second equation
8/-2 = x = -4 . . . . . add 1, divide by -2
Finally, find y:
y = -4 +2(7) = 10 . . . . . substitute for x and z in the first equation
The solution is (x, y, z) = (-4, 10, 7).
Answer:
C
Step-by-step explanation:
EDGE
A bit out of practice, but how to go about finding the origin and vertix of this equation
9x^(2)+16y^(2)=144
Answer:Explained Below
Step-by-step explanation:
The given equation is similar to an ellipse which is in the form of
[tex]\frac{x^2}{a^2}[/tex]+[tex]\frac{y^2}{b^2}[/tex]=1
where
2a=length of major axis
2b=length of minor axis
Here after rearranging the given equation we get
[tex]\frac{x^2}{\frac{144}{9}}[/tex]+[tex]\frac{y^2}{\frac{144}{16}}[/tex]=1
[tex]\frac{x^2}{16}[/tex]+[tex]\frac{y^2}{9}[/tex]=1
[tex]\frac{x^2}{4^2}[/tex]+[tex]\frac{y^2}{3^2}[/tex]=1
therefore its origin is (0,0)
and vertices are[tex]\left ( \pm4,0\right )[/tex]&[tex]\left ( 0,\pm3\right )[/tex]
We can find origin by checking what is with x in the term [tex]\left ( x-something\right )^{2}[/tex]
same goes for y
for [tex]\left ( x-2\right )^{2}[/tex] here 2 is the x coordinate of ellipse
and for vertices Each endpoint of the major axis is vertices and each endpoint of minor axis is co-vertices
what is minimum spanning tree
Answer:
Given an unguided connected graph, an extension tree of this graph is a subgraph which is a tree that connects all vertices. A single graph may have different extension trees. We can mark a weight at each edge, which is a number that represents how unfavorable it is, and assign a weight to the extension tree calculated by the sum of the weights of the edges that compose it. A minimum spanning tree is then an extension tree with a weight less than or equal to each of the other possible spanning trees. Generalizing more, any non-directional graph (not necessarily connected) has a minimal forest of trees, which is a union of minimal extension trees of each of its related components.
Find the standard deviation. Round to the nearest tenth. 1, 2, 11, 8, 16, 16,20, 16, 18 OA. 6.5 O B. 6.9 O C. 1.5 ? D. 7.4
Answer:
A. 6.5
Step-by-step explanation:
First we find the average [tex]\bar{x}[/tex] of the 9 data:
[tex]\bar{x} =\frac{\sum_{x=1}^{n}x_{i}}{n}[/tex]
Where n is the data number, that in this case is 9.
[tex]\bar{x} =\frac{1+ 2+ 11+ 8+ 16+ 16+20+ 16+ 18}{9}=12\\[/tex]
The formula of the standard deviation [tex]\sigma[/tex] is:
[tex]\sigma=\sqrt{\frac{\sum_{x=1}^{n}(x_{i}-\bar{x})^{2}}{n}}[/tex]
We replace the data and find the value of the standard deviation:
[tex]\sigma=\sqrt{\frac{(1-12)^{2}+(2-12)^{2}+(11-12)^{2}+(8-12)^{2}+(16-12)^{2}+(16-12)^{2}+(20-12)^{2}+(16-12)^{2}+(18-12)^{2}}{9}}[/tex]
[tex]\sigma=\sqrt{\frac{(-11)^{2}+(-10)^{2}+(-1)^{2}+(-4)^{2}+(4)^{2}+(4)^{2}+(8)^{2}+(4)^{2}+(6)^{2}}{9}}=6,54[/tex]
We approximate the number and the solution is 6,5
1. A 20 kg object is thrown with an initial upward velocity of 2 m/s. If air resists motion of the object by 4 N for each m/s, what is the terminal velocity of this object? (Hint: use the model developed in Day 10 Lecture notes)
Answer:
49 m/s
Step-by-step explanation:
We don't know what your model is, so we'll solve this based on the balance of forces. Air resistance exerts an upward force of ...
(4 N/(m/s))v
Gravity exerts a downward force of ...
(20 kg)(9.8 m/s²) = 196 N
These are balanced (no net acceleration) when ...
(4 N/(m/s))v = 196 N
v = (196 N)/(4 N/(m/s)) = 49 m/s
The terminal velocity is expected to be 49 m/s.
a slice of bread has 1.5 g of fat, 19 g carbohydrate and 4 g protein. how many kcal in the slice? please show all of you work in a dimensional analysis format.
Answer:
The answer is 105.5 kcal/slice of bread.
Step-by-step explanation:
The kcal per gram of:
protein = 4kcal/g.carbohydrate = 4kcal/g.fat = 9kcal/g.Now, you have:
1.5 g of fat + 19g of carbohydrate + 4g of protein = 1 slice of bread.If we multiply the amount of components by his kcal:
1.5g * 9kcal/g + 19g * 4kcal/g + 4g * 4kcal/g;Now gram/gram = 1, and we can cancel the grams in the equation:
1.5* 9kcal + 19 * 4kcal + 4 * 4kcal = 105.5kcal;Finally, the result of the kcal of the slice bread is:
105.5 kcal/slice of bread.An insurance company found that 9% of drivers were involved in a car accident last year. If seven drivers are randomly selected, find the probability that exactly two of them were involved in a car accident last year.
Answer: 0.1061
Step-by-step explanation:
Given : An insurance company found that 9% of drivers were involved in a car accident last year.
Thus, the probability of drivers involved in car accident last year = 0.09
The formula of binomial distribution :-
[tex]P(X=x)^nC_xp^x(1-p)^{n-x}[/tex]
If seven (n=7) drivers are randomly selected then , the probability that exactly two (x=2) of them were involved in a car accident last year is given by :-
[tex]P(X=2)=^7C_2(0.09)^2(1-0.09)^{7-2}\\\\=\dfrac{7!}{2!5!}(0.09)^2(0.91)^{5}=0.106147867882\approx0.1061[/tex]
Hence, the required probability :-0.1061
The student council at a college is made up of four freshmen, five sophomores, six juniors, and seven seniors. A yearbook photographer would like to line up two council members from each class for a picture. How many different pictures are possible if each group of classmates stands together?
Answer:
7257600
Step-by-step explanation:
Number of freshmen in the student council= 4
Number of sophomores in the student council= 5
Number of juniors in the student council= 6
Number of seniors in the student council= 7
Ways of choosing council members
⁴C₂×⁵C₂×⁶C₂×⁷C₂
[tex]^4C_2=\frac{4!}{(4-2)!2!}\\=\frac{24}{4}=6\\\\^5C_2=\frac{5!}{(5-2)!2!}\\=\frac{120}{12}=10\\\\^6C_2=\frac{6!}{(6-2)!2!}\\=\frac{720}{48}=15\\\\^7C_2=\frac{7!}{(7-2)!2!}\\=\frac{5040}{240}=21[/tex]
⁴C₂×⁵C₂×⁶C₂×⁷C₂=6×10×15×21=18900
Ways of lining up the four classes=4!=1×2×3×4=24
Ways of lining up members of each class=2⁴=2×2×2×2=16
Pictures are possible if each group of classmates stands together
⁴C₂×⁵C₂×⁶C₂×⁷C₂×4!×2⁴
=18900×24×16
=7257600
There are 453600 possible different pictures
How to determine the number of different pictures?
The given parameters are:
Freshmen = 4
Sophomores = 5
Juniors = 6
Seniors = 7
Two council members are to be selected from each group.
So, the number of ways this can be done is:
n = ⁴C₂×⁵C₂×⁶C₂×⁷C₂
Apply combination formula, and evaluate the product
n = 18900
Each group are to stand together.
There are 4! ways to arrange the 4 groups.
So, the total number of pictures is:
Total = 4! * 18900
Evaluate the product
Total = 453600
Hence, there are 453600 possible different pictures
Read more about combination at:
https://brainly.com/question/11732255
Write an equation of the circle with center (4,5) and radius 9.
Answer:
I'm going to write both of these because maybe you have a fill in the blank question. I don't know.
[tex](x-4)^2+(y-5)^2=9^2[/tex]
Simplify:
[tex](x-4)^2+(y-5)^2=81[/tex]
Step-by-step explanation:
[tex](x-h)^2+(y-k)^2=r^2[/tex] is the equation of a circle with center (h,k) and radius r.
You are given (h,k)=(4,5) because that is the center.
You are given r=9 because it says radius 9.
Let's plug this in.
[tex](x-4)^2+(y-5)^2=9^2[/tex]
Simplify:
[tex](x-4)^2+(y-5)^2=81[/tex]
Answer:
(x-4)^2 + (y-5)^2 = 9^2
or
(x-4)^2 + (y-5)^2 =81
Step-by-step explanation:
The equation for a circle is (x-h)^2 + (y-k)^2 = r^2
Where (h,k) is the center and r is the radius
(x-4)^2 + (y-5)^2 = 9^2
or
(x-4)^2 + (y-5)^2 =81
On a recent road trip, it took John 3.53.5 h to drive from a suburb of Phoenix to a small town outside of Yuma. According to his dashboard computer, he averaged 8585 mph on the drive. John's friend in Yuma is European, and he asked for the distance that John drove in kilometers. How far did John drive in kilometers?
Answer:
He drove approximately 478.78 km
Step-by-step explanation:
We know that,
Distance = Speed × time,
Given,
Time taken by john in driving = 3.5 hours,
His average speed = 85 mph,
So, the total distance he drove = 3.5 × 85 = 297.5 miles,
Since, 1 miles = 1.60934 km,
Thus, the total distance he drove = 1.60934 × 297.5 = 478.77865 km ≈ 478.78 km
The lifetime of an alkaline battery is exponentially distributed with a mean of 20 a) What is the probability that the battery will last between 10 and 15 hours?
Answer: 0.1342
Step-by-step explanation:
The cumulative distribution function for exponential distribution is :-
[tex]P(x)=1-e^{\frac{-x}{\lambda}}[/tex], where [tex]\lambda [/tex] is the mean of the distribution.
Given : [tex]\lambda =20[/tex]
Then , the probability that the battery will last between 10 and 15 hours is given by :-
[tex]P(10<x<15)=P(15)-P(10)\\\\=1-e^{\frac{-15}{20}}-(1-e^{\frac{-10}{20}})\\\\=-e^{-0.75}+e^{-0.5}=0.13416410697\approx0.1342[/tex]
Hence, the probability that the battery will last between 10 and 15 hours = 0.1342
The probability that the battery will last between 10 and 15 hours is 18.13%.
Explanation:In order to find the probability that the battery will last between 10 and 15 hours, we need to use the exponential distribution. The exponential distribution is defined by the formula P(X
For this problem, the mean is 20, so λ = 1/20. Plugging in the values, we get P(10
Therefore, the probability that the battery will last between 10 and 15 hours is 18.13%.
2. A random sample of 30 households was selected as part of a study on electricity usage, and the number of kilowatt-hours (kWh) was recorded for each household in the sample for the March quarter of 2017. The average usage was found to be 375kWh. From past years in the March quarter the population standard deviation of the usage was 81k Assuming the standard deviation is unchanged and that the usage is normally distributed ; A. Determine the interval of 95% confidence for the average kilowatt-hours for the population. B. Determine the 99% confidence interval. C. With a confidence level of 90%, what would the minimum sample size need to be in order for the true mean of the heights to be less than 20kWh from the sample mean? (This would mean an error amount of 20kWh.)
Answer:
Step-by-step explanation:
Given that n =30, x bar = 375 and sigma = 81
Normal distribution is assumed and population std dev is known
Hence z critical values can be used.
For 95% Z critical=1.96
Margin of error = [tex]1.96(\frac{81}{\sqrt{30} } )=29[/tex]
Confidence interval = 375±29
=(346,404)
B) 99% confidence
Margin of error = 2.59*Std error =38
Confidence interval = 375±38
=(337, 413)
C) For 90%
Margin of error = 20
Std error = 20/1.645 = 12.158
Sample size
[tex]n=(\frac{81}{12.158} )^2\\=44.38[/tex]
Atleast 44 people should be sample size.
To determine the confidence intervals for the average kilowatt-hours, a formula is used that includes the sample mean, Z-values, population standard deviation, and sample size. For a 95% confidence level, the interval is 324.95 to 425.05 kWh, and for a 99% confidence level, the interval is 311.01 to 438.99 kWh. To have a confidence level of 90% with a maximum error amount of 20kWh, the minimum sample size required is approximately 35 households.
Explanation:A. Determine the interval of 95% confidence for the average kilowatt-hours for the population:
To determine the interval of 95% confidence, we can use the formula:
95% confidence interval = sample mean ± (Z-value) * (population standard deviation / √sample size)
Substituting the given values, we have:
95% confidence interval = 375 ± (1.96) * (81 / √30) = 324.95 to 425.05 kWh
B. Determine the 99% confidence interval:
Using the same formula, but with a Z-value of 2.57 (corresponding to 99% confidence), we have:
99% confidence interval = 375 ± (2.57) * (81 / √30) = 311.01 to 438.99 kWh
C. Minimum sample size for a confidence level of 90% and an error amount of 20kWh:
To determine the minimum sample size, we can rearrange the formula for the confidence interval and solve for the sample size:
Sample size = ((Z-value) * (population standard deviation / error amount))^2
Substituting the given values, we have:
Sample size = ((1.645) * (81 / 20))^2 = 34.64 or approximately 35 households
Learn more about Confidence intervals here:https://brainly.com/question/34700241
#SPJ3
Suppose you are asked to find the area of a rectangle that is 2.1-cm wide by 5.6-cm long. Your calculator answer would be 11.76 cm2. Now suppose you are asked to enter the answer to two significant figures. (Note that if you do not round your answer to two significant figures, your answer will fall outside of the grading tolerance and be graded as incorrect
Answer:
12 cm²
Step-by-step explanation:
Length of rectangle = 5.6 cm
Width of rectangle = 2.1 cm
Area of rectangle = Length of rectangle×Width of rectangle
⇒Area of rectangle = 5.6×2.1
⇒Area of rectangle = 11.76 cm²
11.76 has 4 significant figures in order to write this term in 2 significant terms we round of the term
The last digit in the decimal place is 6. Now, 6≥5 so we round the next digit to 8 we get
11.8
Now the last digit in the decimal place is 8. Now, 8≥5 so we round the next digit to 2 we get
12
∴ Hence the area of the rectangle when rounded to 2 significant figures is 12 cm²
Use Stokes' Theorem to evaluate S curl F · dS. F(x, y, z) = 5y cos(z) i + ex sin(z) j + xey k, S is the hemisphere x2 + y2 + z2 = 4, z ≥ 0, oriented upward. Step 1 Stokes' Theorem tells us that if C is the boundary curve of a surface S, then curl F · dS S = C F · dr Since S is the hemisphere x2 + y2 + z2 = 4, z ≥ 0 oriented upward, then the boundary curve C is the circle in the xy-plane, x2 + y2 = 4 Correct: Your answer is correct. seenKey 4 , z = 0, oriented in the counterclockwise direction when viewed from above. A vector equation of C is r(t) = 2 Correct: Your answer is correct. seenKey 2 cos(t) i + 2 Correct: Your answer is correct. seenKey 2 sin(t) j + 0k with 0 ≤ t ≤ 2π.
By Stokes' theorem, the integral of the curl of [tex]\vec F[/tex] across [tex]S[/tex] is equal to the integral of [tex]\vec F[/tex] along the boundary of [tex]S[/tex], call it [tex]C[/tex]. Parameterize [tex]C[/tex] by
[tex]\vec r(t)=2\cos t\,\vec\imath+2\sin t\,\vec\jmath[/tex]
with [tex]0\le t\le2\pi[/tex]. So we have
[tex]\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S=\int_C\vec F\cdot\mathrm d\vec r[/tex]
[tex]=\displaystyle\int_0^{2\pi}(10\sin t\cos 0\,\vec\imath+e^{2\cos t}\sin0\,\vec\jmath+2\cos t\,e^{2\sin t}\,\vec k)\cdot(-2\sin t\,\vec\imath+2\cos t\,\vec\jmath)\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^{2\pi}-20\sin^2t\,\mathrm dt[/tex]
[tex]=\displaystyle-10\int_0^{2\pi}(1-\cos2t)\,\mathrm dt=\boxed{-20\pi}[/tex]
The problem makes use of Stokes' theorem to evaluate a given field over a hemisphere. We established the boundary curve of the surface and described it using a vector equation.
Explanation:This problem can be solved using Stokes' theorem which asserts that the magnetic field flux through a surface is related to the circulation of the field encircling that surface. Stokes' theorem can be written in this form ∫ S curl F · dS = ∫ C F · dr. Given the field F(x, y, z) = 5y cos(z) i + ex sin(z) j + xey k and the hemisphere S defined by x² + y² + z² = 4, z ≥ 0, we need to look for its boundary curve C. C here is the circle in the xy-plane defined by x² + y² = 4, z = 0. We can describe this boundary using a vector equation r(t) = 2 cos(t) i + 2 sin(t) j + 0k with 0 ≤ t ≤ 2π.
Learn more about Stokes' theorem here:https://brainly.com/question/35538480
#SPJ3
find the value of solid cylinder figure not including cut out: cylinder is 9.7 ft in height, 7 feet in base length, with 4 ft hole cut out.
Answer:
251.28 cubic feet
Step-by-step explanation:
The height of the cylinder is 9.7 ft.
The base length is 7 feet. So, the radius(R) = [tex]\frac{7}{2} = 3.5 feet[/tex]
The length of 4 feet cylinder cut out. So, the radius of the cut cylinder (r) = [tex]\frac{4}{2} = 2 feet[/tex]
We have to find the volume of solid cylinder figure without cutting part.
= Volume of the whole cylinder - Volume of the hole cut
We know that volume of a cylinder is [tex]\pi *r^2*h[/tex]
Using this formula,
= [tex]\pi *R^2*h - \pi *r^2*h[/tex]
= [tex]\pi h [R^2 - r^2][/tex]
Here π = 3.14, R = 3.5, r = 2 and h = 9.7
Plug in these values in the above, we get
= [tex]3.14*9.7 [3.5^2 - 2^2]\\= 30.458[12.25 - 4]\\= 30.458[8.25]\\= 251.2785 ft^3[/tex]
When round of to the nearest hundredths place, we get
So, the volume of solid cylinder figure not including cut out= 251.28 cubic feet
Scor Question Help 4.D.49 You can afford monthly payments of $500. If current mortgage rates are 2.83% for a 15-year fixed rate loan, how much can you afford to borrow? If you are required to make a 10% down payment and you have the cash on hand to do it, how expensive a home can you afford? (Hint: You will need to solve the loan payment formula for P.) How much can you afford to borrow? S(Round to the nearest dollar as needed.) orary cess esources 6ew
Answer:
No down payment = $73 267; 10 % down payment = $81 408
Step-by-step explanation:
1. With no down payment
The formula for a maximum affordable loan (A) is
A = (P/i)[1 − (1 + i)^-N]
where
P = the amount of each equal payment
i = the interest rate per period
N = the total number of payments
Data:
P = 500
APR = 2.83 % = 0.0283
t = 15 yr
Calculations:
You are making monthly payments, so
i = 0.0283/12 = 0.002 358 333
The term of the loan is 15 yr, so
N = 15 × 12 = 180
A = (500/0.002 3583)[1 − (1 + 0.002 3583)^-180]
= 212 014(1 - 1.002 3583^-180)
= 212 014(1 - 0.654 424)
= 212 014 × 0.345 576
= 73 267
You can afford to spend $73 267 on a home.
2. With a 10 % down payment
Without down payment, loan = 73 267
With 10 % down payment, you pay 0.90 × new loan
0.90 × new loan = 73 267
New loan = 73267/0.90 = 81 408
With a 10 % down payment, you can afford to borrow $81 408 .
Here’s how it works:
Purchase price = $81 408
Less 10 % down = -8 141
Loan = $73 267
And that's just what you can afford.
A poll asked the question, "What do you think is the most important problem facing this country today?" Twenty percent of the respondents answered "crime and violence." The margin of sampling error was plus or minus 4 percentage points. Following the convention that the margin of error is based on a 95% confidence interval, find a 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters.
Answer: (16%, 24%)
Step-by-step explanation:
The confidence interval for proportion is given by :-
[tex]p\pm E[/tex]
Given : Significance level : [tex]\alpha=1-0.95=0.05[/tex]
The proportion of the respondents answered "crime and violence." : p=0.20
Margin of sampling error : [tex]E=\pm0.04[/tex]
Now, the 95% confidence interval for the proportion of the population that would respond "crime and violence" to the question asked by the pollsters is given by :-
[tex]0.20\pm 0.04\\\\=0.20-0.04,\ 0.20+0.04\approx(0.16,0.24)[/tex]
In percentage, [tex](16\%,24\%)[/tex]
Hence, the 95% confidence interval for the percentage of the population that would respond "crime and violence" to the question asked by the pollsters =(16%, 24%)
The 95% confidence interval for the population that would answer "crime and violence" to the poll question, given a sample proportion of 20% and a margin of error of 4%, is between 16% and 24%.
Explanation:This question is about constructing a confidence interval based on poll data, a mathematical and statistical concept. The poll indicates that 20% of respondents believe the most pressing issue in the country today is "crime and violence", with a margin of error of ±4%. A 95% confidence interval for the population proportion can be constructed by adding and subtracting the margin of error from the sample proportion.
So in this case, we can calculate the low and high end of the interval as follows:
Low end = 20% - 4% = 16% High end = 20% + 4% = 24%So, we can be 95% confident that the true population proportion that would respond "crime and violence" to the question lies somewhere between 16% and 24% based on this poll.
Learn more about Confidence interval here:https://brainly.com/question/34700241
#SPJ3
A real estate firm owns the Kasumba Garden Apartments which consists of 90 apartments. At $350 per month every apartment can be rented. However, for each $10 per month increase there will be two vacancies with no possibility of filling them. The firm wants to receive $31 980 per month from rents. What rent should be charged for each apartment?
Answer:
The rent should be $ 390 or $ 410.
Step-by-step explanation:
Given,
The original monthly rent of an apartment = $350,
Also, the original number of apartment that could be filled = 90,
Let the rent is increased by x times of $ 10,
That is, the new monthly rent of an apartment =( 350 + 10x ) dollars
Since, for each $10 per month increase there will be two vacancies with no possibility of filling them.
Thus, the new number of filled apartments = 90 - 2x,
Hence, the total revenue of the firm = ( 90 - 2x )(350 + 10x ) dollars,
According to the question,
( 90 - 2x )(350 + 10x ) = 31,980
[tex]90(350)+90(10x)-2x(350)-2x(10x)=31980[/tex]
[tex]31500+900x-700x-20x^2=31980[/tex]
[tex]-20x^2+200x+31500-31980=0[/tex]
[tex]20x^2-200x+480=0[/tex]
By the quadratic formula,
[tex]x=\frac{200\pm \sqrt{(-200)^2-4\times 20\times 480}}{40}[/tex]
[tex]x=\frac{200\pm \sqrt{1600}}{40}[/tex]
[tex]x=\frac{200\pm 40}{40}[/tex]
[tex]\implies x=\frac{200+40}{40}\text{ or }x=\frac{200-40}{40}[/tex]
[tex]\implies x=6\text{ or } x =4[/tex]
Hence, the new rent of each apartment, if x = 6, is $ 410,
While, if x = 4, is $ 390
Sophia has 16 plants and one window. Only five plants can be placed in the window at any given time. If each of the 16 plants spends the same amount of time in the window during an eight-hour period of sunlight, what is the greatest number of minutes in the sun that is possible per plant?
Answer:
120 minutes
Step-by-step explanation:
Total plants are 16 and only 5 can be placed in one go. so total number of rounds for the plants will be: 16/5 = 3.2 rounds ≅ 4 rounds
As there are four rounds to go in 8 hours, so the time for 1 round will be: 8/4 = 2 hours.
Therefore, 2 hours or 120 minutes of sunlight are possible for one plant ..
Answer:
The answer is actually 150 minutes.
Step-by-step explanation: