By Green's theorem,
[tex]\displaystyle\int_{x^2+y^2=16}(3y-e^{\sin x})\,\mathrm dx+(7x+y^4+1)\,\mathrm dy[/tex]
[tex]=\displaystyle\iint_{x^2+y^2\le16}\frac{\partial(7x+y^4+1)}{\partial x}-\frac{\partial(3y-e^{\sin x})}{\partial y}\,\mathrm dx\,\mathrm dy[/tex]
[tex]=\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy[/tex]
The remaining integral is just the area of the circle; its radius is 4, so it has an area of 16π, and the value of the integral is 64π.
We'll verify this by actually computing the integral. Convert to polar coordinates, setting
[tex]\begin{cases}x=r\cos\theta\\y=r\sin\theta\end{cases}\implies\mathrm dx\,\mathrm dy=r\,\mathrm dr\,\mathrm d\theta[/tex]
The interior of the circle is the set
[tex]\{(r,\theta)\mid0\le r\le4\land0\le\theta\le2\pi\}[/tex]
So we have
[tex]\displaystyle4\iint_{x^2+y^2\le16}\mathrm dx\,\mathrm dy=4\int_0^{2\pi}\int_0^4r\,\mathrm dr\,\mathrm d\theta=8\pi\int_0^4r\,\mathrm dr=64\pi[/tex]
as expected.
Quadrilateral RSTV is dilated with respect to the origin by a scale factor of 1.5 to produce quadrilateral R'S'T'V' . Vertex R is located at (6, -9). Which ordered pair represents R' after the dilation?
Answer:
(9, -13.5)
Step-by-step explanation:
It's given in the question that a quadrilateral RSTV is dilated with a scale factor of 1.5 with respect to the origin to form R'S'T'V'.
Rule for dilation is,
(x, y) → (kx, ky)
where 'k' is the scale factor.
If vertex R of the quadrilateral is (6, -9),
By the given rule of dilation,
R(6, 9) → R'[(1.5 × 6), -(1.5 × 9)]
→ R'(9, -13.5)
Therefore, Option given in bottom right (9, -13.5) will be the answer.
Gail paid a total of $12,000 for stock that was $6 per share. If she sold all her shares for $18,000, how much profit on each share did she make?
A
$9
B
$3
С.
S2000
D
$6.000
Answer:
$3
Step-by-step explanation:
Given
Total Cost Price: $12,000
Unit Cost Price= $6
Total Selling Price = $18,000
Required
Determine the profit on each share
First, we need to determine the units of share bought;
Units = Total cost price / Unit Cost Price
[tex]Units = \frac{\$12000}{\$6}[/tex]
[tex]Units = 2000[/tex]
Next is to determine the selling price of each share; This is calculated as follows;
Unit Selling Price = Total Selling Price / Units Sold
[tex]Unit\ Selling\ Price = \frac{\$18000}{\$2000}[/tex]
[tex]Unit\ Selling\ Price = \$9[/tex]
The profit is the difference between the unit cost price and unit selling price
[tex]Profit = Unit\ Selling\ Price - Unit\ Cost\ Price[/tex]
[tex]Profit = \$9 - \$6[/tex]
[tex]Profit = \$3[/tex]
Is y = 8x -15 a function?
Answer:
Hey there!
A function only has one y value for every x value, so this is a function. Additionally, all linear equations (that are in the y=mx+b form) are functions.
Hope this helps :)
C-Spec, Inc., is attempting to determine whether an existing machine is capable of milling an engine part that has a key specification of 4 ± .003 inches. After a trial run on this machine, C-Spec has determined that the machine has a sample mean of 4.001 inches with a standard deviation of .002 inch. Calculate the Cpk for this machine.
Answer:
0.3333
Step-by-step explanation:
Given the following :
Sample mean(m) = 4.001 inch
Standard deviation(sd) = 0.002 inch
Key specification : = 4 ± .003 inches
Upper specification LIMIT ( USL) : (4 + 0.003) = 4.003 inches
Lower specification limit (LSL) : (4 - 0.003) = 3.997 inches
Cpk is found using the relation:
min[(USL - mean) / (3 * sd), (mean-LSL) / (3*sd)]
min[(4.003 - 4.001)/(3*0.002), (4.001 - 3.997)/(3*0.002)]
min[(0.002 / 0.006), (0.004 / 0.006)]
min[(0.33333, 0.66667)
Therefore Cpk = 0.3333
Because 0.33333<0.66667
2/5 × 3/7? please help
Answer:
[tex]\frac{2}{5}[/tex] • [tex]\frac{3}{7}[/tex] = [tex]\frac{6}{35}[/tex]
Answer: 0.171
Step-by-step explanation:
First, do 2/5 which would equal 0.4
Second, so 3/7 which would equal 0.428571428571429
Lastly multiply the two answers together to get 0.171428571428571
How do you find x when knowing the probability?
Answer:
x
Step-by-step explanation:
probability is the branch of mathematics concerning numeral descriptions of how likely an event is to occur or how likely it is that a proposition is true
)Patrick buys some bananas for 35%. He sells all the bananas for $40.60. Calculate profit
percentage. Show your working.
Answer:
40.60-35=5.6
Step-by-step explanation:
Profit is cost minus the amount you sold it for
What is 7 x -5?........
Answer:
-35
Step-by-step explanation:
7*5*(-1)
The solution to the expression 7 * -5 is -35
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
7 * -5
Evaluate all the products in the expression
so, we have the following representation
7 * -5 = -35/1
Evaluate all the quotients in the expression
so, we have the following representation
7 * -5 = -35
Lastly, we have
7 * -5 = -35
Hence, the solution is -35
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PLEASE HELP ASAP Madelyn drove a race car in a race. She averaged 55 mph and began the race 0.5 hours ahead of the other drivers. The variable d represents Madelyn's distance driven, in miles. The variable t represents the number of hours since the other drivers began to race. Which equation can be used to determine the distance Madelyn drove t hours into the race? d=55t−0.5 d=55(t+0.5) d=55(t−0.5) d = 55t + 0.5
Answer:
d=55(t+0.5)
Step-by-step explanation:
d=55(t+0.5)
Answer:
27.5
Step-by-step explanation:
Which of the following is a correct factorization of this trinomial?
-4x² +11x-6
A. -(4x+3)(x + 2). B. -4(x+3)(x + 2)
C. -(x+3)(x-4)
D. (-4x+3)(x-2)
Answer:
D
Step-by-step explanation:
Step 1: Find the factors of 4 and -6
-4x² +11x-6
-4x 3
1x -2
(This works because -4 x -2 multiple to 8 and 3 x 1 gives you 3 and when you add it up it gives you the 'b' term)
Step 2: Read the numbers from left to right starting from the top to bottom
(-4x+3)(1x-2)
Therefore the answer to the question is D.
Answer:
A
explain
= -4x^2-11x-6
= -4x^2-8x-3x-6
= -4x(x+2)-3(x+2)
= (x+2) (-4x-3)
= -(4x+3) (x+2)
How can a company use a scatter plot to make a future sales decision?
Answer:
Hope this helps :)
Step-by-step explanation:
A scatter plot is a two-dimensional diagram that displays individual data points based on the intersection of two variables, shown as vertical and horizontal axes. Individual data points or values are plotted at particular coordinates of the two variables being studied. Patterns of data points provide a visual representation of relationship between the two variables. A wide range of jobs and careers use this valuable analytical tool for data analysis and decision making.
My conclusion,
They help organize important data for future occurences.
What is the simplified form of the following expression? 2 StartRoot 18 EndRoot + 3 StartRoot 2 EndRoot + StartRoot 162 EndRoot
Answer: 2*√18 + 3*√2 + √162 = 18*√2
Step-by-step explanation:
I guess that the equation is:
2*√18 + 3*√2 + √162
And we want to simplify it.
first 18 = 9*2
then we can write:
2*√18 = 2*√(9*2) = 2*3*√2 = 6*√2
and 162/9 = 18
then we can write:
√162 = √(9*18) = √9*√18 = 3√18
now we can use the previous step: √18 = 3*√2
and:
√162 = 3*(3*√2) = 9*√2
now we can write our equation as:
6√2 + 3√2 + 9√2 = (6 + 3 + 9)√2 = 18*√2
And now we can not simplify it further more, so here we end.
Answer:
B. 18 sqrt 2
Step-by-step explanation:
This is the correct letter and answer on edge, if thats what youre using:)
A bus company has contracted with a local high school to carry 450 students on a field trip. The company has 18 large buses which can carry up to 30 students and 19 small buses which can carry up to 15 students. There are only 20 drivers available on the day of the field trip.
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
Determine the minimum cost of transporting all 450 students.
Answer:
Step-by-step explanation:
From the given information;
Let consider p to be the number of large buses and q to be the number of small buses.
The company has 18 large buses which can carry up to 30 students and 19 small buses which can carry up to 15 students.
The linear inequality represent the students with respect to the total students s:
30p + 15q ≥ 450 -----(1)
They are only 20 drivers available on the day of the field trip, therefore only 20 buses can be used. So,
p + q ≤ 20 ----- (2)
Also , There are only 19 small buses and 18 large buses:
∴
0 ≤ p ≤ 18
0 ≤ q ≤ 19
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day
In order to minimize the cost of transporting all 450 students, let z be the minimal cost. i.e
z = 225p + 100q
From equation 1 and 2 ; if we plot them graphically on the graph, the following points of intersection were obtained as shown in the sketch below, in which the shaded region lies the answer.
The point of intersection between equation (1) and (2) is (p,q) = (10,10)
From the critical point in the sketch of our graph attached below, the following values of z can be determined.
Point(s) Value for Z
(15,0) 15 × 225 = 3375
(18,0) 18 × 225 = 4050
(18,2) (18 × 225 )+ (2 × 100 ) = 4250
(10,10) (10 × 225) + (10 × 100) = 3250
Thus ; the minimum cost of transporting all 450 students = $3250
Use technology to solve the following problem: A certain car model has a mean gas mileage of 30 miles per gallon (mpg) with a standard deviation A pizza delivery company buys 42 of these cars. What is the probability that the average mileage of the fleet is greater than
Answer:
The answer is below
Step-by-step explanation:
The question is not complete, let me solve a question that is exactly like this one.
A certain car model has a mean gas mileage of 34 miles per gallon (mpg) with a standard deviation 5 mpg. A pizza delivery company buys 43 of these cars. What is the probability that the average mileage of the fleet is greater than 33.5 mpg?
Answer:
Given that the mean (μ) is 34 miles per gallon (mpg) with a standard deviation (σ) 5 mpg. The sample (n) is 43.
The z score is used in statistics to determine by how much the raw score is above or below the mean. It is given by:
[tex]z=\frac{x-\mu}{\sigma} \\for\ a \ sample\ size:\\z=\frac{x-\mu}{\sigma/\sqrt{n} }[/tex]
For the average mileage of the fleet is greater than 33.5 mpg (x > 33.5):
[tex]z=\frac{x-\mu}{\sigma/\sqrt{n} }\\z=\frac{33.5-34}{5/\sqrt{43} } =-0.66[/tex]
From the normal distribution table, The probability that the average mileage of the fleet is greater than 33.5 mpg = P(x > 33.5) = P(z > -0.66) = 1 - P(z < -0.66) = 1 - 0.2546 = 0.7454 = 74.54%
Translate verbal expression to an algebraic expression
8 times a number x is subtracted by 4
Answer:
8x - 4
Step-by-step explanation:
8x - 4
Translated algebraically expression is 8x-4
What is expression?
Expressions is the defined as mathematical statements that have a minimum of two terms containing variables or numbers.
Given verbal expression that,
8 times a number x is subtracted by 4
(1) Let x = the unknown number.
(2) "8 times a number of x" is translated algebraically as 8x
(3) "same number x is subtracted by 4" is translated algebraically as 8x -4
Putting analyses together translated algebraically into the following equation as the result : 8x-4
Learn more about algebraic expressions
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2. (1 pt) The following statement is true or false;
When we know the population standard deviation, o, we use a standard normal
distribution (z-score) to calculate the error bound EBM and construct the
confidence interval and when the population standard deviation, o, is unknown,
we use a Student's t distribution (t-score) to calculate the error bound EBM and
construct the confidence interval.
a. true
b. false
If you know the population standard deviation (sigma), then you use the Z distribution. If sigma is not known, then you use the T distribution.
Side note: Even if sigma is not known, you could use the Z distribution if the sample size n is greater than 30. If n > 30, then the T distribution is approximately about the same as the Z distribution.
1
Drag and drop the
labels to the correct
sides using Angle A
as a reference.
A
boy
3
4
hypotenuse
adjacent
opposite
5
6
hypotenuse goes to the line across from the right angle. adjacent is the bottom one. lastly opposite is the left one.
Step-by-step explanation:
Hi, there!!
According to the question, we should find the hypotenuse, adjacent, and opposite to the refrence angle A ,right.
so, let's simply work with it,
hypotenuse (h)= AC {side opposite to the 90° is always a hypotenuse}.
opposite (p)= BC { as the side opposite to the refrence angle is always perpendicular or opposite}
adjacent (b)= AB { as remaining side is always base or adjacent}
Hope it helps....
Evaluate the following expressions: 2(−1 + 3) − 7
Answer:
-3 is the answer.
Step-by-step explanation:
=2(-1+3)-7
=2(2)-7
=4-7
=-3
Hope it will help you :)
I WILL RATE YOUR BRAINLIEST Marius opened a savings account. The sequence {200, 208, 216.30, 225, …} describes the amount of interest he earns each year his account is active. If this pattern continues, how much total interest will Marius have earned by the 30th year the account is active?
Answer:
11,215Step-by-step explanation:
Given the sequence of interest earned by Marius on his savings account as
200, 208, 216.30, 225, …, the sequence of interest forms a geometric sequence since they have a common ratio.
[tex]r =\frac{T_2}{T_1}= \frac{T_3}{T_2}= \frac{T_4}{T_3}\\ r =\frac{208}{200}= \frac{216.30}{208}= \frac{225}{216.30} \approx 1.04[/tex]
To get how much total interest will Marius have earned by the 30th year the account is active, we will find the sum of the first 30 terms of the geometric sequence as shown.
[tex]S_n =\frac{ a(r^n-1)}{r-1} \ for \ r> 1\\ \\\\ n = 30, a = 200, r = 1.04\\S_{30} = \dfrac{ 200(1.04^{30}-1)}{1.04-1}\\\\S_{30} = \dfrac{ 200(3.243-1)}{0.04}\\\\S_{30} = \dfrac{ 200(2.243)}{0.04}\\\\S_{30} = \dfrac{ 448.6}{0.04}]\\\\S_{30} = 11,215[/tex]
Hence total interest that Marius will earn by the 30th year the account is active is 11,215.
the correct answer is
S30= 200(1-1.04^n)/1-1.04
i took the test
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answer:
154.2
Step-by-step explanation:
To find the average of the bowlers scores, you have to find the mean by adding the values and dividing by the number of values.
To find the bowlers average add the scores and divide by the number of games.
143+156+172+133+167/5=154.2 is the average score for the bowler.
Each side of a quilt square measures approximately 4.25 inches. If there are about 2.54 centimeters in 1 inch, how long is each side of the square in centimeters? Use complete sentences to explain your reasoning.
Answer: approximately 10.8 centimeters
Step-by-step explanation:
We have a square, where each side measures approx. 4.25 in
Now we know that 1in ≈ 2.54 cm
Then, in 4.25 in, we have 4.25 times 1 inch, so we have 4.25 times the length of 2.54 cm
So the approximate measure of the sides in centimeters is:
4.25*(2.54)cm = 10.8 cm
So we have that each side measures approximately 10.8 centimeters
determine the missing term x in the geometric sequence below
9,x,225
Answer:
45
Step-by-step explanation:
multiply 9 by 5 to get 45
then, multiply 45 by 5 to get 225
The geometric sequence is 5(previous number)
Consider these five values a population: 7, 4, 6, 4, and 7. Determine the mean of the population. (Round your answer to 1 decimal place.)
Answer:
[tex]Mean = 5.6[/tex]
Step-by-step explanation:
Given
[tex]7,4,6,4,7[/tex]
Required
Determine the mean
Mean is calculated as thus;
[tex]Mean = \frac{\sum x}{n}[/tex]
Where n is the number of observation;
In this case;
[tex]n = 5[/tex]
and [tex]\sum x[/tex] is the sum of the observations
The expression becomes
[tex]Mean = \frac{7+4+6+4+7}{5}[/tex]
[tex]Mean = \frac{28}{5}[/tex]
[tex]Mean = 5.6[/tex]
Hence, the mean of the population is 5.6
Write the following as an inequality: y is no greater than 4 but more than –2.
Answer:
Step-by-step explanation:
First lets focus on, y is no greater than 4,
y < 4
Now we focus on, more than –2,
y > -2
Combining these inequalities get us,
-2 < y < 4
Answer:
-2<y≤4
Step-by-step explanation:
An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of ^{14}\text{C} 14 C. Estimate the minimum age of the charcoal, noting that
An old campfire is uncovered during an archaeological dig. Its charcoal is found to contain less than 1/1000 the normal amount of [tex]^{14}\text{C}[/tex] . Estimate the minimum age of the charcoal, noting that [tex]2^{10} = 1024[/tex]
Answer:
57300 years
Step-by-step explanation:
Using the relation of an half-life time in relation to fraction which can be expressed as:
[tex]\dfrac{N}{N_o} = (\dfrac{1}{2})^{\frac{t}{t_{1/2}}[/tex]
here;
N represents the present atom
[tex]N_o[/tex] represents the initial atom
t represents the time
[tex]t_{1/2}[/tex] represents the half - life
Given that:
Its charcoal is found to contain less than 1/1000 the normal amount of [tex]^{14}\text{C}[/tex] .
Then ;
[tex]\dfrac{N}{N_o} = \dfrac{1}{1000}[/tex]
However; we are to estimate the minimum age of the charcoal, noting that [tex]2^{10} = 1024[/tex]
so noting that [tex]2^{10} = 1024[/tex], then:
[tex]\dfrac{1}{1000}> \dfrac{1}{1024}[/tex]
[tex]\dfrac{1}{1000}> \dfrac{1}{2^{10}}[/tex]
[tex]\dfrac{1}{1000}> (\dfrac{1}{2})^{10}[/tex]
If
[tex]\dfrac{N}{N_o} = \dfrac{1}{1000}[/tex]
Then
[tex]\dfrac{N}{N_o} > (\dfrac{1}{2})^{10}[/tex]
Therefore, the estimate of the minimum time needed is 10 half-life time.
For [tex]^{14}\text{C}[/tex] , the normal half-life time = 5730 years
As such , the estimate of the minimum age of the charcoal = 5730 years × 10
= 57300 years
If you randomly select a card from a well-shuffled standard deck of 52 cards, what is the probability that the card you select is a heart or Ace
Answer:
[tex]P(A\ or\ H) = \frac{4}{13}[/tex]
Step-by-step explanation:
Given
Number of Cards = 52
Required
Determine the probability of picking a heart or ace
Represent Ace with Ace and Heart = H
In a standard pack of cards; there are
[tex]n(A) = 4[/tex]
[tex]n(H) = 13[/tex]
[tex]n(A\ and\ H) = 1[/tex]
[tex]Total = 52[/tex]
Because the events are non mutually exclusive
[tex]P(A\ or\ H) = P(A) + P(H) - P(A\ and\ H)[/tex]
Where
[tex]P(A) = \frac{n(A)}{Total} = \frac{4}{52}[/tex]
[tex]P(H) = \frac{n(H)}{Total} = \frac{13}{52}[/tex]
[tex]P(A\ and\ H) = \frac{n(A\ and\ H)}{Total} = \frac{1}{52}[/tex]
Substitute these values in the above formula
[tex]P(A\ or\ H) = P(A) + P(H) - P(A\ and\ H)[/tex]
[tex]P(A\ or\ H) = \frac{4}{52} + \frac{13}{52} - \frac{1}{52}[/tex]
Take LCM
[tex]P(A\ or\ H) = \frac{4 + 13 - 1}{52}[/tex]
[tex]P(A\ or\ H) = \frac{16}{52}[/tex]
Reduce fraction to lowest term
[tex]P(A\ or\ H) = \frac{4}{13}[/tex]
Hence, probability of a heart or ace is 4/13
No, the graph suggests that the increase in adoptions from 2000 to 2005 was less significant than it actually is. No, the graph suggests that the increase in adoptions from 2000 to 2005 was more significant than it actually is. Yes, the graph fairly and accurately depicts the data in an objective manner.
Answer: No, the graph suggests that the increase in adoptions from 2000 to 2005 was more significant than it actually is
Step-by-step explanation:
Ok, in the graph we can see that the minimal value for the y-axis is y = 4000.
This means that the graph is like a "zoom" tath points to the tips of the boxes.
This makes the relative difference between the columns seems to be bigger than it actually is, so the correct answer would be:
"No, the graph suggests that the increase in adoptions from 2000 to 2005 was more significant than it actually is"
And remember that this happens for the people that only see the graph for a second and draw the conclusions (most of the people). While in the graph you can read all the information that you need to calculate exactly the relative change.
Need Help
Please Show Work
Answer:
18 - 8 * n = -6 * n
The number is 9
Step-by-step explanation:
Let n equal the number
Look for key words such as is which means equals
minus is subtract
18 - 8 * n = -6 * n
18 -8n = -6n
Add 8n to each side
18-8n +8n = -6n+8n
18 =2n
Divide each side by 2
18/2 = 2n/2
9 =n
The number is 9
━━━━━━━☆☆━━━━━━━
▹ Answer
n = 9
▹ Step-by-Step Explanation
18 - 8 * n = -6 * n
Simple numerical terms are written last:
-8n + 18 = -6n
Group all variable terms on one side and all constant terms on the other side:
(-8n + 18) + 8n = -6n + 8n
n = 9
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
A+B = 20
B+C= 30
C+ A= 40
C =?
55 I hope this helps you!
Alpha (a) is used to measure the error for decisions concerning true null hypotheses. What is beta (ß) error used to measure?
Answer:
Alpha (α) is used to measure the error for decisions concerning true null hypotheses, while beta (ß) is used to measure error for decisions concerning false null hypotheses.
Step-by-step explanation:
Suppose we have events X and Y.
1. If it is said that X equals Y, when X is actually not equal to Y, α is used in this case, the null hypotheses.
2. If X is said to not be equal to Y, when X is actually equal to Y, β is used in this case, the false null hypotheses.
