Answer:
[tex]Cost = 338500[/tex]
Step-by-step explanation:
Given
Startup = $116000
Cost per item = $25
Equation: 25q + 116000
Required
Determine the cost of producing 8900 items
The question implies that q = 8900
To solve further, we have to substitute 8900 for q in the given equation
Equation = 25q + 116000 becomes
[tex]Cost = 25 * 8900 + 116000[/tex]
[tex]Cost = 222500 + 116000[/tex]
[tex]Cost = 338500[/tex]
Hence, the cost of producing 8900 items is $338500
A survey of 500 randomly selected adults found that 57% say that they would take a ride in a fully self-driving car. The 95% confidence interval for the true proportion of all adults who would take a ride in a full self-driving car is found to be (0.5266, 0.6134). Can we conclude that the majority of all adults would take a ride in a fully self-driving car?
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
No; The data does not include all adults, so we cannot make a conclusion about the population.
No; The confidence interval limits are not large enough to determine that a majority rely only on cellular phones. The proportion would need to be much greater than 50%, and the one above is only slightly larger.
Yes; Since the proportion of adults who said yes is 57%, and this is higher than 50%, we can conclude that a majority would take a ride in a fully self-driving car.
Answer:
Yes; Since the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
Step-by-step explanation:
From the question we are told that
The sample size is n = 500
The sample proportion is [tex]\r p = 0.57[/tex]
The 95% confidence interval is (0.5266, 0.6134)
Looking at the 95% confidence level interval we see that the sample proportion is within the interval and given that the confidence interval limits are both greater than 50%, we can reasonably conclude that more than half of all adults would take a ride in a fully self-driving car.
The solutions to the equation $(x+1)(x+2) = x+3$ can be written in the form $m+\sqrt n$ and $m-\sqrt n$, where $m$ and $n$ are integers. What is $m+n$?
Answer:
1
Step-by-step explanation:
Hello, please consider the following.
First, we develop and move everything to the left side, then we solve the equation, using the discriminant.
Finally, we get the expression of the two solutions and we can conclude.
[tex](x+1)(x+2)=(x+3)\\\\<=> x^2+3x+2-x-3=0\\\\<=>x^2+2x-1=0\\\\\Delta=b^2-4ac=4+4=8\\\\x_1=\dfrac{-2-\sqrt{8}}{2}=\dfrac{-2-2\sqrt{2}}{2}=-1-\sqrt{2}\\\\x_2=\dfrac{-2+\sqrt{8}}{2}=-1+\sqrt{2}[/tex]
So, m=-1 and n = 2
m+n = -1 + 2 = 1
Thank you
The value of m + n is 1.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 4 - 9 is an equation.
We have,
(x + 1)(x + 2) = x + 3
x² + 2x + x + 2 = x + 3
x² + 3x + 2 - x - 3 = 0
x² + 2x - 1 = 0
This is in the form of ax² + bx + c = 0
a = 1, b = 2, and c = -1
Now,
Using the determinant.
x = -b ± √(b² - 4ac) / 2a
x = -2 ± √(4 + 4) / 2
x = (-2 ± 2√2) / 2
x = (-1 ± √2)
x = -1 + √2
x = -1 - √2
Now,
The solutions can be written in the form of (m + √n) and (m - √n).
This means,
m + √n = -1 + √2
m - √n = -1 - √2
m = -1 and n = 2
Now,
m + n
= -1 + 2
= 1
Thus,
m + n is 1.
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Starting with x1 = 2, find the third approximation x3 to the root of the equation x3 − 2x − 2 = 0.
Answer:
0.8989
Step-by-step explanation:
Using the Newton's Raphson approximation formula.
Xn+1 = Xn - f(Xn)/f'(Xn)
Given f(x) = x³-2x+2
f'(x) = 3x²-2
If the initial value X1 = 2
X2 = X1 - f(X1)/f'(X1)
X2 = 2 - f(2)/f'(2)
f(2) = 2³-2(2)+2
f(2) = 8-4+2
f(2) = 6
f'(2) = 3(2)²-2
f'(2) = 10
X2 = 2- 6/10
X2 = 14/10
X2 = 1.4
X3 = X2 - f(X2)/f'(X2)
X3 = 1.4 - f(1.4)/f'(1.4)
f(1.4) = 1.4³-2(1.4)+2
f(1.4) = 2.744-2.8+2
f(1.4) = 1.944
f'(1.4) = 3(1.4)²-2
f'(1.4) = 3.880
X3 = 1.4- 1.944/3.880
X3 = 1.4 - 0.5010
X3 = 0.8989
Hence the value of X3 is 0.8989
A research center claims that % of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of adults in that country, % say that they would travel into space on a commercial flight if they could afford it. At , is there enough evidence to reject the research
Complete Question
A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At , is there enough evidence to reject the research center's claim
Answer:
Yes there is sufficient evidence to reject the research center's claim.
Step-by-step explanation:
From the question we are told that
The population proportion is p = 0.30
The sample proportion is [tex]\r p = 0.34[/tex]
The sample size is n = 700
The null hypothesis is [tex]H_o : p = 0.30[/tex]
The alternative hypothesis is [tex]H_a : p \ne 0.30[/tex]
Here we are going to be making use of level of significance = 0.05 to carry out this test
Now we will obtain the critical value of [tex]Z_{\alpha }[/tex] from the normal distribution table , the value is [tex]Z_{\alpha } = 1.645[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{ \r p - p }{ \sqrt{ \frac{ p (1-p)}{n} } }[/tex]
substituting values
[tex]t = \frac{ 0.34 - 0.30 }{ \sqrt{ \frac{ 0.30 (1-0.30 )}{ 700} } }[/tex]
[tex]t = 2.31[/tex]
Looking at the values of t and [tex]Z_{\alpha }[/tex] we see that [tex]t > Z_{\alpha }[/tex] hence the null hypothesis is rejected
Thus we can conclude that there is sufficient evidence to reject the research center's claim.
3(2+7) - 9 x 7 = 3+8 x 2 x 2 - 4 = 16 ÷ 2 x 5 x 3 ÷ 6 = Please answer! ✨✨
Answer:
At first, we have 3 expressions that are equal.
[tex]3(2+7) - 9 \cdot 7= 3+8 \cdot 2 \cdot 2 - 4[/tex]
[tex]6+21 - 63= 3+32 - 4[/tex]
[tex]-36=31[/tex]
[tex]-36\neq 31[/tex]
This is not true.
Which statements about the dilation are true? Check all that apply. Triangle X prime Y prime Z prime. Point X prime is 2 units from the center of dilation C and point Z prime is 3 units from the center of dilation. Triangle X Y Z. Point X is 5 units from point C and point Z is 7.5 units from point C. The center of dilation is point C. It is a reduction. It is an enlargement. The scale factor is 2.5. The scale factor is Two-fifths.
Answer:
I only know two right answers.
A: The center of dilation is point C.
C: It is an enlargement.
E: The scale factor is 2/5.
Step-by-step explanation:
These two answers are correct because When you look in the center you see a C.
You tell if it is a reduction because the pre image is small but the image is big.
The center of dilation is point C.
It is an enlargement.
The scale factor is 2/5
The correct options are D, F, H.
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during a dilatation.
Given:
The transformation of the figure is dilation.
The figure is given in the attached image.
From the diagram:
The center of dilation is point C.
It is an enlargement.
The scale factor is 2/5
Therefore, all the correct statements are given above.
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23. f(x) is vertically shrank by a factor of 1/3. How will you represent f(x) after transformation?
A. f(3x)
B. 3f(x)
C. 13f(x)
D. f(13x)
Answer:
Step-by-step explanation:
vertical stretching / shrinking has the following transformation.
f(x) -> a * f(x)
when a > 1, it is stretching
when 0< a < 1, it is shrinking.
when -1 < a < 0, it is shringking + reflection about the x-axis
when a < -1, it is stretching + reflection about the x axis.
Here it is simple shrinking, so 0 < a < 1.
I expect the answer choice to show (1/3) f(x).
However, if the question plays with the words
"shrink by a factor of 1/3" to actually mean a "stretching by a factor of three", then B is the answer (stretch by a factor of three).
Help!!!!!!! Thank you!!!!!!!
Answer:
D
Step-by-step explanation:
The ratio of yellow paint to blue paint is 4:3. We can make the largest amount of green paint by using all of the 20 quarts of yellow paint so we have to solve for x in 4:3 = 20:x, since 4 * 5 = 20, 3 * 5 = x so we use 15 qts of blue paint, therefore we will have 20 + 15 = 35 qts of green paint.
Answer:
D
Step-by-step explanation:
Consider the functions
JIGO
For the x-values given in the table below, determine the corresponding values of six) and plot each point on the graph...
Х
-1
0
1
2
G(x)
Answer:
g(x) = 4, 6, 9, 13.5 for the x-values given
Step-by-step explanation:
The table and graph are attached.
-7y=-91 show your work
Answer:
[tex] \boxed{ \bold{\sf{y = 13}}}[/tex]Step-by-step explanation:
[tex] \sf{ - 7y = - 91}[/tex]
Divide both sides of the equation by -7
⇒[tex] \sf{ \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} }[/tex]
Calculate
⇒[tex] \sf{y = 13}[/tex]
Hope I helped!
Best regards!!
Answer:
[tex] \boxed{\sf y = 13} [/tex]
Step-by-step explanation:
Solve for y:
[tex] \sf \implies - 7y = - 91[/tex]
Divide both sides of -7y = -91 by -7:
[tex] \sf \implies \frac{ - 7y}{ - 7} = \frac{ - 91}{ - 7} [/tex]
[tex] \sf \frac{ - 7}{ - 7} = 1 : [/tex]
[tex] \sf \implies y = \frac{ - 91}{ - 7} [/tex]
[tex] \sf \implies y = \frac{ \cancel{ - 7} \times 13}{ \cancel{ - 7}} [/tex]
[tex] \sf \implies y = 13[/tex]
WILL GIVE BRAINLEST PLEASE!!!!!!!! Jenny has some tiles in a bag. The tiles are of three different colors: purple, pink, and orange. Jenny randomly pulls a tile out of the bag, records the color, and replaces the tile in the bag. She does this 50 times. The results are recorded in the given table: Color of Tile Purple Pink Orange Number of times the tile is drawn 6 18 26 What is the experimental probability that Jenny will pull out a purple tile? fraction 6 over 50 fraction 44 over 50 fraction 6 over 44 fraction 18 over 44
Answer:
6/50
Step-by-step explanation:
There are 50 tiles
6 purple
18 pink
26 orange
P( purple) = purple/ total
= 6/50
Help Please. Whoever answers it right with an explanation will get brainliest
Answer:
The answer is
ab( 11 + 9b)( a - 3b)Step-by-step explanation:
11a³b - 24a²b² - 27ab³
To factor the expression
First factor ab out
That's
ab ( 11a² - 24ab - 27b²)
Factor the terms in the bracket
Write - 24ab as a difference
That's
ab ( 11a² + 9ab - 33ab - 27b²)
Factor out a from the expression
ab [ a( 11a + 9b) - 33ab - 27b²) ]
Factor -3b from the expression
That's
ab [ a( 11a + 9b) - 3b( 11a + 9b) ]
Factor out 11a + 9b from the expression
We have the final answer as
ab( 11 + 9b)( a - 3b)Hope this helps you
What is the answer and how is this solved?
Answer:
Sum : 65
Step-by-step explanation:
In this notation, n is our starting value, and hence we start at 3 and go to 7. Given the set of values : { 3, 4, 5, 6, 7 }, we can substitute in our expression " 4n - 7 " for n and solve. The sum of these values is our solution.
4( 3 ) - 7 = 12 - 7 = 5,
4( 4 ) - 7 = 16 - 7 = 9,
4( 5 ) - 7 = 20 - 7 = 13,
Our remaining values for n = 6 and n = 7 must then be 17 and 21. This is predictable as we have an arithmetic series here, the common difference being 4. As you can see 9 - 5 = 4, 13 - 9 = 4, 17 - 13 = 4, 21 - 17 = 4.
Therefore we have the series { 5, 9, 13, 17, 21 }. This adds to an answer of 65.
In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft. For a group of 1013 adults, the mean of those who do not worry about identify theft is closest to ________.
Answer: 669
Step-by-step explanation:
Given, In a Gallup poll of randomly selected adults, 66% said that they worry about identity theft.
i.e. The proportion of adults said that they worry about identity theft. (p) = 0.66
Sample size : n= 1013
Then , Mean for the sampling distribution of sample proportion = np
= (1013) × (0.66)
= 668.58 ≈ 669 [Round to the nearest whole number]
Hence, the mean of those who do not worry about identify theft is closest to 669 .
Classify the following random variable according as either discrete or continuous. The temperature in degrees Celsius on January 1st in a certain city
A continuous
B discrete
Answer:
continuous
Step-by-step explanation:
A quantity like temperature is a continuous random variable. A continuous random variable is different from a discrete random variable because it can take on many values infinitely.
From the question, measuring the Temperature in degrees can take on many different values because there are an uncountable number of possible temperatures that could be taken.
The revenue, cost, and profit functions for a line of cell phone cases is shown. Identify the location on the profit function where the profit from sales of the phone cases is a maximum.
Answer:
approximately x = 38
Step-by-step explanation:
The maximum profit is the vertex of the profit graph parabola. The maximum occurs at approximately x = 38.
The solution is x = 38
The location on the profit function parabola where the profit from sales of the phone cases is a maximum is given by x = 38
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
Let the revenue, cost, and profit functions for a line of cell phone cases be given as two parabolic functions R ( x ) and P ( x )
The maximum profit is given by the parabolic function R ( x )
The profit is represented by = y
The price per phone is represented by = x
Now , when y is maximum ,
The value of y = $ 2,250,000
The value of x when y = $ 2,250,000 is x = 38
So , the value of x from the parabola where profit is maximum is x = 38
Therefore, the value of x = 38
Hence , the value of x from the function is x = 38
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IQ tests are scaled so that the mean score in a largepopulation should be μ =100. We suspect that the very-low-birth-weight population has mean score less than100. Infants weiging less than 1500 grams at birth are classed as "very low birth weight". Low birth weight carriesmany risks. One study followed 113 male infants with very low birth weight to adulthood. At age 20, the mean IQ score for these men was (x bar=87.6.) Iq scores vary Normally with standard deviation σ=15. Give a 95% confidence interval for the mean IQ score at age 20 for allvery-low-birth-weight males. Use the four-step process for confidence interval.
Answer:
The 95% confidence interval is [tex]84.83< \mu < 90.37[/tex]
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 113[/tex]
The sample mean is [tex]\= x = 87.6[/tex]
The standard deviation is [tex]\sigma = 15[/tex]
Given that the confidence level is 95% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 95[/tex]
[tex]\alpha = 5\%[/tex]
[tex]\alpha = 0.05[/tex]
Next we obtain the critical value of [tex]\frac{\alpha }{2}[/tex] from the normal distribution table, the value is
[tex]Z_{\frac{ \alpha }{2} } = 1.96[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{ \sigma}{ \sqrt{n} }[/tex]
=> [tex]E = 1.96 * \frac{ 15}{ \sqrt{113} }[/tex]
=> [tex]E = 2.77[/tex]
The 95% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
substituting values
[tex]87.6 - 2.77< \mu < 87.6 + 2.77[/tex]
[tex]84.83< \mu < 90.37[/tex]
Please answer quick!!!
Find the interquartile range of the data set represented by this box plot.
30
56
20
10
Answer:
A. 30
Step-by-step explanation:
The interquartile range for a box and whiskers plot, is the value from the right side of the box minus the value of the left side of the box.
In this case at the far right side of the box it is at 130, at the far left side of the box it is at 100.
130-100=30
Answer:
[tex]\huge\boxed{IQR = 30}[/tex]
Step-by-step explanation:
Q1 = 130 (Left hand edge of the box)
Q3 = 100 (Right Hand edge of the box)
Interquartile Range = Q3-Q1
IQR = 130-100
IQR = 30
A project has an initial cost of $40,000, expected net cash inflows of $10,000 per year for 8 years, and a cost of capital of 14%. What is the project's NPV? (Hint: Begin by constructing a time line.) Do not round intermediate calculations. Round your answer to the nearest cent.
Answer:
50k
Step-by-step explanation:
Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of α= 0.01.
Internet Users 80.3 78.2 56.4 67.6 77.7 38.6
Award Winners 5.6 9.3 3.2 1.6 10.9 0.1
Required:
a. Construct a scatterplot.
b. Determine the null and alternative hypotheses.
c. The test statistic is:_________
d. The P-value is:_________
Answer:
There is not sufficient evidence to support a claim of linear correlation between the two variables.
Step-by-step explanation:
(a)
The scatter plot for the provided data is attached below.
(b)
The hypothesis to test significance of linear correlation between the two variables is:
H₀: There is no linear correlation between the two variables, i.e. ρ = 0.
Hₐ: There is a significant linear correlation between the two variables, i.e. ρ ≠ 0.
(c)
Use the Excel function: =CORREL(array1, array2) to compute the correlation coefficient, r.
The correlation coefficient between the number of internet users and the award winners is,
r = 0.786.
The test statistic value is:
[tex]t=r\sqrt{\frac{n-2}{1-r^{2}}}[/tex]
[tex]=0.786\times\sqrt{\frac{6-2}{1-(0.786)^{2}}}\\\\=2.5427\\\\\approx 2.54[/tex]
Thus, the test statistic is 2.54.
(d)
The degrees of freedom is,
df = n - 2
= 6 - 2
= 4
Compute the p-value as follows:
[tex]p-value=2\cdot P(t_{n-2}<2.54)=2\times 0.032=0.064[/tex]
*Use a t-table.
p-value = 0.064 > α = 0.05
The null hypothesis will not be rejected.
Thus, it can be concluded that there is not sufficient evidence to support a claim of linear correlation between the two variables.
Simplify -(7/x-2)+(2x/x) Simplify your answer as much possible
Answer:
[tex]\dfrac{2x-11}{x-2}[/tex]
Step-by-step explanation:
Simplify the fractions, then add.
[tex]-\dfrac{7}{x-2}+\dfrac{2x}{x}=\dfrac{-7}{x-2}+2=\dfrac{-7}{x-2}+\dfrac{2(x-2)}{x-2}\\\\=\dfrac{2x-4-7}{x-2}=\boxed{\dfrac{2x-11}{x-2}}[/tex]
_____
Note that this comes with the restriction that x ≠ 0.
is -54 rational number whole number or integersis
Answer:
-54 is a integer and rational number
Step-by-step explanation:
Evaluate the expression 8p6
Answer:
Evaluate 8P6 P 6 8 using the formula nPr=n!(n−r)! P r n = n ! ( n - r ) ! . 8!(8−6)! 8 ! ( 8 - 6 ) ! Subtract 6 6 from 8 8 . 8!(2)! 8 ! ( 2 ) ! Simplify 8!(2)! 8 !
Step-by-step explanation:
evaluate" usually means to put a value in for the variable, but you don't give us a value for p. also, it is unclear if you ...
The value of the expression [tex]^8P_6[/tex] is 20160.
What is permutation?A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order.
The value of the expression is calculated as:-
[tex]^8P_6=\dfrac{8!}{8!-6!}=\dfrac{8!}{2!}[/tex]
[tex]^8P_6 =\dfrac{8\times 7\times 6\times 5\times 4\times 3\times 2}{2}[/tex]
[tex]^8P_6[/tex] = 20160
Hence, the value is 20160.
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Malia measures the longer side of a dollar bill using a ruler at school. Which of the following is most likely the quantity she measured?
Answer:
6.14 inches
Step-by-step explanation:
The one side of the dollar bill is 6.14 inch. The 6.14 inches of the dollar approximates the 156.1 mm. When Malia measures the longer side of a dollar bill from her rule it will be approximately 6.14 inches in length. The ruler normally has inches and cm sides. Very few rulers have mm scales. The most probable scale that malia would have measure is in inches.
A plan for a dog park has a grassy section and a sitting section as shown in the figure. Which equation can be used to find the area of the grassy section?
Answer:
[tex]Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Step-by-step explanation:
The grassy area is that of a trapezoid, so recall the formula for the area of a trapezoid:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height[/tex]
where:
Base stands for the larger base (in our case the dimension "B" in the attached image)
base stands for the shorter base parallel to the largest Base (in our case the dimension "b" in the attached image)
and
height stands for the distance between bases (in our case the dimension "h" in the attached image.
Therefore the formula for the area of the grassy section becomes:
[tex]Area=\frac{1}{2} (Base\,+\,base)\,height\\Area=\frac{1}{2} (B\,+\,b)\,h[/tex]
Answer:
1/2 (b+b) h
here is the actual picture
Triangle+ Triangle + Triangle = 30 Triangle + circle + circle = 20 Circle + Square + Square = 13 Triangle + circle x half square = ?
Answer:
Below
Step-by-step explanation:
Let T be triangle, C the circle and S the square.
● T + T + T = 30
● 3T = 30
Divide both sides by 3
● 3T/3 = 30/3
● T = 10
So the triangle has a value of 10.
●30 T + C + C = 20C + S + S = 13T +C ×S/2
Add like terms together
●30 T + 2C = 20C +2S= 13T + C×S/2
Replace T by its value (T=10)
● 300 + 2C = 20C + 2S = 130 + C×S/2
Take only this part 20C + 2S = 130 + C × S/2
● 20C + 2S = 130 + C×S/2 (1)
Take this part (300+2C = 20C+2S) and express S in function of C
● 20C + 2S = 300 + 2C
Divide everything by 2 to make easier
● 10 C + S = 150+ C
● S = 150+C-10C
● S = 150-9C
Replace S by (5-9C) in (1)
● 20C + 2S = 130 + C×S/2
● 20C + 2(150-9C) = 130 +C× (150-9C)/2
● 20C + 300-18C= 130 + C×(75-4.5C)
● 2C + 300 = 130 + 75 -4.5C^2
● 2C +300-130 = 75C - 4.5C^2
● 2C -75C + 170 = -4.5C^2
● -73C + 170 = -4.5C^2
Multiply all the expression by -1
● -4.5C^2 +73C+ 170= 0
This is a quadratic equation, so we will use the discriminant method.
Let Y be the discriminant
● Y = b^2-4ac
● b = 73
● a = -4.5
● c = 170
● Y = 73^2 - 4×(-4.5)×170= 8389
So the equation has two solutions:
● C = (-b +/- √Y) /2a
√Y is approximatively 92
● C = (-73 + / - 92 )/ -9
● C = 18.34 or C = -2.11
Approximatively
● C = 18 or C = -2
■■■■■■■■■■■■■■■■■■■■■■■■■
● if C = 18
30T + 2C = 300 + 36 = 336
● if C = -2
30T + 2C = 300-4 = 296
Use Green’s theorem to evaluate line integral along curve C ∮_c〖( 3ydx+2xdy )〗, C : The boundary of 0≤x≤π,0≤y≤sin x
Answer:
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy} = \boxed{\bold{2}}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]
Derivative Rule [Basic Power Rule]:
Integration
IntegralsIntegration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]
Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]
Multivariable Calculus
Partial Derivatives
Vector Calculus
Circulation Density:
[tex]\displaystyle F = M \hat{\i} + N \hat{\j} \rightarrow \text{curl} \ \bold{F} \cdot \bold{k} = \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y}[/tex]
Green's Theorem [Circulation Curl/Tangential Form]:
[tex]\displaystyle \oint_C {F \cdot T} \, ds = \oint_C {M \, dx + N \, dy} = \iint_R {\bigg( \frac{\partial N}{\partial x} - \frac{\partial M}{\partial y} \bigg)} \, dx \, dy[/tex]
Step-by-step explanation:
Step 1: Define
Identify given.
[tex]\displaystyle \oint_C {3y \, dx + 2x \, dy}[/tex]
[tex]\displaystyle \text{Region:} \ \left \{ {{0 \leq x \leq \pi} \atop {0 \leq y \leq \sin x}} \right.[/tex]
Step 2: Integrate Pt. 1
Define vector functions M and N:Step 3: Integrate Pt. 2
We can evaluate the Green's Theorem double integral we found using basic integration techniques listed above:
[tex]\displaystyle \begin{aligned}\oint_C {3y \, dx + 2x \, dy} & = - \int\limits^{\pi}_0 \int\limits^{\sin x}_0 {} \, dy \, dx \\& = - \int\limits^{\pi}_0 {y \bigg| \limits^{y = \sin x}_{y = 0}} \, dx \\& = - \int\limits^{\pi}_0 {\sin x} \, dx \\& = \cos x \bigg| \limits^{x = \pi}_{x = 0} \\& = \boxed{\bold{2}}\end{aligned}[/tex]
∴ we have evaluated the line integral using Green's Theorem.
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Topic: Multivariable Calculus
Unit: Green's Theorem and Surfaces
What are the approximate solutions of the graphed function?
Answer:
x = -2.6, x = 2.6
Step-by-step explanation:
The graph crosses the x-axis at approximately 2.6 and -2.6.
The required approximate solution of the function graphed is x = -2.6 and 2.6.
Given that,
A graph of a function is plotted, and the solution of the function is to be determined.
What are functions?
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
What is a graph?The graph is a demonstration of curves that gives the relationship between the x and y-axis.
Here, the solution of the function is that value of x where the function terminates to zero, So the given curve terminates to zero at two places at x = -2.6 and x = 2.6 from the observation of the graph.
Thus, the required approximate solution of the function graphed is x = -2.6 and 2.6.
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A plot of land has vertices as follows, where each coordinate is a measurement in feet. Find the perimeter of the plot of land. (1,7),(7,7),(7,1),(1,1) please help and explain how to do this type of thing because i am lost
Answer:
Perimeter of ABCD = 36 ft
Step-by-step explanation:
Given:
A (1,7)
B (7,7)
C (7,1)
D (1,1)
Find:
Perimeter of ABCD
Computation:
Distance between two point = √(x1-x2)² + (y1-y2)²
So,
AB = √(1-7)²+(7-7)²
AB = 6 ft
BC = √(7-7)²+(7-1)²
BC = 6 ft
CD = √(7-1)²+(1-1)²
CD = 6 ft
DA = √(1-1)²+(1-7)²
DA = 6 ft
Perimeter of ABCD = AB + BC + CD + DA
Perimeter of ABCD = 6 + 6 + 6 +6
Perimeter of ABCD = 36 ft
The perimeter of the plot is the sum of side length of the plot of land.
The perimeter of the plot is 24 feet.
Represent the vertices as follows:
[tex]W = (1,7)[/tex]
[tex]X = (7,7)[/tex]
[tex]Y = (7,1)[/tex]
[tex]Z = (1,1)[/tex]
First, we calculate the side length using the following distance formula:
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]WX = \sqrt{(1- 7)^2 + (7- 7)^2} = \sqrt{36} = 6[/tex]
[tex]XY = \sqrt{(7- 7)^2 + (7- 1)^2} = \sqrt{36} = 6[/tex]
[tex]YZ = \sqrt{(7- 1)^2 + (1- 1)^2} = \sqrt{36} = 6[/tex]
[tex]ZW = \sqrt{(1- 1)^2 + (1- 7)^2} = \sqrt{36} = 6[/tex]
The perimeter (P) is then calculated as follows:
[tex]P = WX + XY + YZ + ZW[/tex]
So, we have:
[tex]P = 6 + 6 + 6 + 6[/tex]
[tex]P = 24[/tex]
Hence, the perimeter of the plot of land is 24 feet.
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A manager from a certain well known department store found out the money their customers carry into the store is normally distributed with a mean of $258 dollars and a standard deviation of $35. In a sample of 76 Americans who walked into that store find the probability that a random customer will have more than $260 in his or her wallet
Answer:
0.30924
Approximately ≈ 0.3092
Step-by-step explanation:
To solve for this question, we use the formula:
z = (x - μ)/σ
where x is the raw score
μ is the sample mean
σ is the sample standard deviation.
From the question,
x is the raw score = 260
μ is the sample mean = population standard deviation = 258
σ is the sample standard deviation
= σ/√N
N = 76 samples
σ = Population standard deviation
= 35/√76
= 4.0146919966
Hence,
z = (x - μ)/σ
= 260 - 258/ 4.0146919966
= 0.4981702212
Approximately = 0.498
We find the Probability using z score table for normal distribution
P(x = z) = P( x = 260)
= P( z = 0.498)
= 0.69076
The probability that a random customer will have more than $260 in his or her wallet is calculated as:
P(x>Z) = 1 - P( z = 0.498)
P(x>Z) = 1 - 0.69076
P(x>Z) = 0.30924
Approximately ≈ 0.3092
