The area of a surface between a plane and a cylinder is evaluated using the integral [tex]\int\limits \int\limits^{}_D {\sqrt{(\frac{dz}{dx})^2 + (\frac{dz}{dy})^2 + 1} } \, dA[/tex]. So, the area of the given surface is [tex]\frac{4\pi}{3}\sqrt{14}[/tex]
Given that
[tex]x + 2y + 3z =1[/tex]
[tex]x^2 + y^2 = 4[/tex]
Make z the subject in [tex]x + 2y + 3z =1[/tex]
[tex]3z = 1 - x - 2y[/tex]
[tex]z = \frac{1}{3}(1 - x - 2y)[/tex]
The surface area is calculated using the formula:
[tex]Area = \int\limits \int\limits^{}_D {\sqrt{(\frac{dz}{dx})^2 + (\frac{dz}{dy})^2 + 1} } \, dA[/tex]
Where: [tex]dA = rdr \times d\theta[/tex]
[tex]z = \frac{1}{3}(1 - x - 2y)[/tex]
Calculate [tex]\frac{dz}{dx}[/tex]
[tex]\frac{dz}{dx}= \frac{1}{3}(0 - 1 - 2 \times 0)[/tex]
[tex]\frac{dz}{dx}= \frac{1}{3}(0 - 1 - 0)[/tex]
[tex]\frac{dz}{dx}= \frac{1}{3}(- 1)[/tex]
[tex]\frac{dz}{dx}= -\frac{1}{3}[/tex]
Calculate [tex]\frac{dz}{dy}[/tex]
[tex]\frac{dz}{dy}= \frac{1}{3}(0 - 0 - 2 \times 1)[/tex]
[tex]\frac{dz}{dy}= \frac{1}{3}(- 2)[/tex]
[tex]\frac{dz}{dy}= -\frac{2}{3}[/tex]
Because the plane is inside [tex]x^2 + y^2 = 4[/tex], then the region of z is:
[tex]D = \{(r,\theta) | 0 \le r \le \sqrt{4}, 0 \le \theta \le 2\theta\}[/tex]
[tex]D = \{(r,\theta) | 0 \le r \le 2, 0 \le \theta \le 2\theta\}[/tex]
[tex]Area = \int\limits \int\limits^{}_D {\sqrt{(\frac{dz}{dx})^2 + (\frac{dz}{dy})^2 + 1} } \, dA[/tex] becomes
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{(\frac{-1}{3})^2 + (\frac{-2}{3})^2 + 1} } \, dA[/tex]
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{\frac{1}{9} + \frac{4}{9} + 1} } \, dA[/tex]
Take LCM
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{\frac{1+4+9}{9}} } \, dA[/tex]
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\sqrt{\frac{14}{9}} } \, dA[/tex]
Evaluate the square root of 9
[tex]Area = \int\limits^{2\pi}_0 \int\limits^{2}_0 {\frac{\sqrt{14}}{3} } \, dA[/tex]
Remove the constant
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 \int\limits^{2}_0 { dA}[/tex]
Recall that: [tex]dA = rdr \times d\theta[/tex]
So, we have:
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 \int\limits^{2}_0 { rdr \times d\theta}[/tex]
Integrate
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { \frac{r^2}{2} |\limits^{2}_0 \ d\theta}[/tex]
Expand
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { \frac{2^2 - 0^2}{2} \ d\theta}[/tex]
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { \frac{4}{2} \ d\theta}[/tex]
[tex]Area = \frac{\sqrt{14}}{3}\int\limits^{2\pi}_0 { 2 \ d\theta}[/tex]
Integrate
[tex]Area = \frac{\sqrt{14}}{3}[2\pi]|\limits^{2\pi}_0[/tex]
Expand
[tex]Area = \frac{\sqrt{14}}{3}[2 \times 2\pi - 0][/tex]
[tex]Area = \frac{\sqrt{14}}{3}[4\pi - 0][/tex]
[tex]Area = \frac{\sqrt{14}}{3}[4\pi][/tex]
[tex]Area = \frac{4\pi}{3}\sqrt{14}[/tex]
Hence, the area of the surface is: [tex]\frac{4\pi}{3}\sqrt{14}[/tex]
Read more about the area of a surface between a plane and a cylinder at:
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Determine the domain and range of the following function. Record your answers in set notation. The domain is {x∈R| x≠−5}, and the range is {y∈R| y≠−2}. The domain is {x∈R| x≠−2}, and the range is {y∈R| y≠−5}. The domain is all real numbers, and the range is all real numbers as well. The domain is {x∈R| x≠−3}, and the range is {y∈R| y≠−5}.
Answer:
Option (2)
Step-by-step explanation:
Domain of a function is represented by the set of x-values (Input values) and Range of the function is represented by the set of y-values (Output values)
From the graph attached,
Given function is,
[tex]f(x)=\frac{x^2-x-6}{x+2}[/tex]
Domain of this function will be {x ∈ R | x ≠ -2}
[Since, point x = -2 doesn't lie on the given graph]
Range of the function will be {y ∈ R | y ≠ -5}
Therefore, Option (2) will be the correct option.
Answer:
the correct answer is A
Step-by-step explanation:
just did it on edg
HELP ME PLEASE
(The problem is in the picture)
Answer:
Hey there!
In this expression, 5k and -6 are terms, not factors.
In this expression, 5 and k are factors, so the last option is correct.
Let me know if this helps :)
Answer:
5 and k are factors.
Step-by-step explanation:
A factor would be a value or variable which is multiplied by something else. It is 'a part' of the product.
In [tex]5k-6[/tex], 5 and k are being multiplied by each other. This would mean that 5 and k are factors.
Option E should be the correct answer.
A survey of over 25,000 Americans aged between 18 and 24 years revealed the following: 88.1% of the 12,678 females and 84.9% of the 12,460 males had high school diplomas.
a) Do the data suggest that females are more likely to graduate from high school than males? Test at a significance level of 5%.
b) Set-up a 95% confidence interval for the difference in the graduation rates between females and males.
c) State the assumptions and conditions necessary for the above inferences to hold.
Answer:
(a) Yes, the data suggest that females are more likely to graduate from high school than males.
(b) A 95% confidence interval for the difference in the graduation rates between females and males is [0.024, 0.404] .
Step-by-step explanation:
We are given that a survey of over 25,000 Americans aged between 18 and 24 years revealed the following: 88.1% of the 12,678 females and 84.9% of the 12,460 males had high school diplomas.
Let [tex]p_1[/tex] = population proportion of females who had high school diplomas.
[tex]p_2[/tex] = population proportion of males who had high school diplomas.
(a) So, Null Hypothesis, [tex]H_0[/tex] : [tex]p_1\leq p_2[/tex] {means that females are less or equally likely to graduate from high school than males}
Alternate Hypothesis, [tex]H_A[/tex] : [tex]p_1 > p_2[/tex] {means that females are more likely to graduate from high school than males}
The test statistics that will be used here is Two-sample z-test statistics for proportions;
T.S. = ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of females having high school diplomas = 88.1%
[tex]\hat p_2[/tex] = sample proportion of males having high school diplomas = 84.9%
[tex]n_1[/tex] = sample of females = 12,678
= sample of males = 12,460
So, the test statistics =
= 7.428
The value of the standardized z-test statistic is 7.428.
Now, at a 5% level of significance, the z table gives a critical value of 1.645 for the right-tailed test.
Since the value of our test statistics is more than the critical value of z as 7.428 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.
Therefore, we conclude that females are more likely to graduate from high school than males.
(b) Firstly, the pivotal quantity for finding the confidence interval for the difference in population proportion is given by;
P.Q. = [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ~ N(0,1)
where, [tex]\hat p_1[/tex] = sample proportion of females having high school diplomas = 88.1%
[tex]\hat p_2[/tex] = sample proportion of males having high school diplomas = 84.9%
[tex]n_1[/tex] = sample of females = 12,678
[tex]n_2[/tex] = sample of males = 12,460
Here for constructing a 95% confidence interval we have used a Two-sample z-test statistics for proportions.
So, 95% confidence interval for the difference in population proportions, ([tex]p_1-p_2[/tex]) is;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level
of significance are -1.96 & 1.96}
P(-1.96 < [tex]\frac{(\hat p_1-\hat p_2)-(p_1-p_2)}{\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < 1.96) = 0.95
P( [tex]-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < [tex]{(\hat p_1-\hat p_2)-(p_1-p_2)}[/tex] < [tex]1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
P( [tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] < ([tex]p_1-p_2[/tex]) < [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ) = 0.95
95% confidence interval for ([tex]p_1-p_2[/tex]) = [[tex](\hat p_1-\hat p_2)-1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] , [tex](\hat p_1-\hat p_2)+1.96 \times {\sqrt{\frac{\hat p_1(1-\hat p_1)}{n_1}+\frac{\hat p_2(1-\hat p_2)}{n_2}} }[/tex] ]
= [ [tex](0.881-0.849)-1.96 \times {\sqrt{\frac{0.881(1-0.881)}{12,678}+\frac{0.849(1-0.849)}{12,460}} }[/tex] , [tex](0.881-0.849)+1.96 \times {\sqrt{\frac{0.881(1-0.881)}{12,678}+\frac{0.849(1-0.849)}{12,460}} }[/tex] ]
= [0.024, 0.404]
Therefore, a 95% confidence interval for the difference in the graduation rates between females and males is [0.024, 0.404] .
(c) The assumptions and conditions necessary for the above inferences to hold are;
The data must follow the normal distribution.The sample must be taken from the population data only or the sample represents the population data.Daniel is starting his own sewing business. Daniel has calculated that he needs to earn $360 per week to support his family. If he knows he will only be able to work 30 hours per week, what is the minimum amount of dollars per hour will he need to charge his customers?
Answer:
$12 the hour
Step-by-step explanation: $360 divided by 30 is 12, meaning he will need to make a minimum of 12 an hour to support his family.
Answer:
12
Step-by-step explanation:
A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data?
Answer:
Step-by-step explanation:
Given that:
A set of numbers is transformed by taking the log base 10 of each number. The mean of the transformed data is 1.65. What is the geometric mean of the untransformed data.
To obtain the geometric mean of the untransformed data,
X = set of numbers
N = number of observations
Arithmetic mean if transformed data = 1.65
Log(Xi).... = transformed data
Arithmetic mean = transformed data/ N
Log(Xi) / N = 1.65
(Πx)^(1/N), we obtain the antilog of the aritmétic mean simply by raising 10 to the power of the Arithmetic mean of the transformed data.
10^1.65 = 44.668359
Use the diagram to find the angle measures of the triangle. Recall that the sum of the angle measures of a triangle is 180°. (2+4) 3 (x + 4) =
Answer: 45 45 90
Step-by-step explanation:
A bowl holds the pieces of fruit shown below. The image shows 8 apples and 7 oranges. If Jasmine correctly writes the fraction of fruit that are apples, which of the following would be the numerator of the fraction?
Answer:
8+7=15 therefore 8
5
Step-by-step explanation:
The numerator from the fraction of apple fruits to total fruits is 8
How to find fraction of apples to total fruits?
Number of apples = 8Number of oranges = 7Total fruits = apples + oranges
= 8 + 7
= 15
Fraction of apple fruits to total fruits = Number of apples / Total fruits
= 8/15
Therefore, the numerator from the fraction of apple fruits to total fruits is 8
Learn more about fraction:
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The temperature at the point (x, y, z) in a substance with conductivity K = 4.5 is u(x, y, z) = 5y2 + 5z2. Find the rate of heat flow inward across the cylindrical surface y2 + z2 = 7, 0 ≤ x ≤ 2.
Answer:
The rate of the heat flow = 1260 π
Step-by-step explanation:
From the information given :
k = 4.5
u(x,y,z) = 5y² + 5z²
Surface cylinder:
y² +z² = 5, 0 ≤ x ≤ 2
[tex]\mathtt{\overline F = \bigtriangledown u = -k(0,10y, 10z )}[/tex]
[tex]\mathtt{\overline F = -4.5(0,10y, 10z )}[/tex]
[tex]\mathtt{\overline F = (0,-45y, -45z ) \ --- (1)}[/tex]
Now parameterizing the surface by :
x = u , y = [tex]\mathtt{\sqrt{7} \ cos \ t}[/tex] , z = [tex]\mathtt{\sqrt{7} \ sin \ t}[/tex]
0 ≤ x ≤ 2 , 0 ≤ t ≤ 2π
[tex]\mathtt{{ \left. \begin{array}{1} \overline{r_y} = (1,0,0) } \\ \\ \overline{r_t} = (0, \ - \sqrt{7}\ sin \ t, \sqrt{7} \ cos \ t) \end{array} \right\} = r_u \times r_t}[/tex]
[tex]\mathtt{\overline r_u \times \overline r_t = ( -0, - \sqrt{7} \ cos \ t , - \sqrt{7} \ sin \ t) --- (2)}[/tex]
Taking integral of both equations; we have:
[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} (0, -45y, -45 z) (0, - \sqrt{7} \ cos \ t, - \sqrt{7} \ sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= \int ^{2}_0 \int ^{2 \pi}_{0} ( 45\sqrt{7} \ y\ cos \ t+ 45 \sqrt{7} \ z \ sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= 45\sqrt{7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (( \sqrt{7} \ cos \ t)cos \ t + (\sqrt{7} \ \ sin \ t) sin \ t) \ dtdu}[/tex]
[tex]\mathtt{= 45\times {7}\ \int ^{2}_0 \int ^{2 \pi}_{0} (1) \ dtdu}[/tex]
= 315 × (2) × (2π)
= 1260 π
If 2(x+7)+x=20 what does x equal?
Start by distributing the 2 through both terms inside the parentheses.
This gives us 2x + 14 + x = 20.
Now subtract 14 from both sides to get 2x + x = 6.
Now combine like terms on the left to get 3x = 6.
Now, dividing both sides by 3, we find that x = 2.
Determine the measure of the central angle for a regular
7-sided polygon, round answers to one decimal place.
Select one:
a. 25.7°
b. 51.4°
c. 61.4°
d. 62.2°
Answer:
B
Step-by-step explanation:
If the figure is regular, then everyone of the central angles are equal. They add up to 360 degrees.
x + x + x + x + x + x + x = 360 Combine
7x = 360 Divide by 7
x = 360/7
x = 51.43
FUNNY ONE ANSWER ! !!!!!!!!!
Answer: trapezoid
Step-by-step explanation: A trapezoid is a quadrilateral
with exactly one pair of parallel sides.
Also, quadrilaterals are two-dimensional shapes.
So it's impossible that's its 3-d.
Answer:
A. trapezoid
Step-by-step explanation:
You please help me with this problem I’ll give you brainless
Answer:
C
Step-by-step explanation:
-27 -(-38)
when you subtract a negative it turns into addition
-27+38
Answer:
c) -27 +38
Step-by-step explanation:
the reason is because when a number is in parentheses, especially if they are negatives, they become the opposite which in this case is + so -(-38) can be the same as saying -1 × -38 and since they are both negatives, the sign becomes positive and it's just 38 while the 27 isn't affected because there's nothing in front of it I hope I helped.
Statistical Quality Control Stat class
1) For a single-sampling plan for attributes, what do the following symbols represent?
a. N
b. n
c. c
d. d
2) For a double-sampling plan for attributes, what do the following symbols represent?
a. n1
b. n2
c. c1
d. c2
e. d1
f. d2
Answer:
Step-by-step explanation:
In a single - sampling plan, when a decision on acceptance / rejection of the lot is made on the basis of only one sample, Then , the acceptance plan is said to be a single sampling plan. The single sampling plan is known as the most common and easiest sampling plan
The following symbol representation can be written as follows:
a. N → Lot size from which the sample is drawn
b. n → sample size
c. c → acceptance number
d. d → number of defectives in the sample
For example:
if we take a randomized sample of size 'n' from the Lot size.
The next step will be to inspect all items in the sample to find the defectives 'd'
The decision rule is that:
If the number of defectives is less than or equal to acceptance number, then answer is YES i.e d ≤ c, Then , we accept the Lot
If the number of defectives is not less than or equal to acceptance number, then the answer is NO . Then , we reject the Lot.
So if we reject, we either do 100% inspection or return the lot to the supplier.
In a double sampling plan , the decision on acceptance/rejection of the Lot is based on two samples.
The following symbol representation can be written as follows:
a. n1 → number of size of sample 1
b. n2 → number of size of sample 2
c. c1 → acceptance number for sample 1
d. c2 → acceptance number for sample 2
e. d1 → number of defectives in sample 1
f. d2 → number of defectives in sample 2
A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4. A die is selected at random and rolled four times. You are told that two rolls were 1's and two were 4's. Find the probability the die chosen was green.
Answer:
The probability the die chosen was green is 0.9
Step-by-step explanation:
From the information given :
A bag contains two six-sided dice: one red, one green. The red die has faces numbered 1, 2, 3, 4, 5, and 6. The green die has faces numbered 1, 2, 3, 4, 4, and 4.
SO, the probability of obtaining 4 in a single throw of a fair die is:
P (4 | red dice) = [tex]\dfrac{1}{6}[/tex]
P (4 | green dice) = [tex]\dfrac{3}{6}= \dfrac{1}{2}[/tex]
A die is selected at random and rolled four times.
When the die is selected randomly; the probability of the first die must be equal to the probability of the second die = [tex]\dfrac{1}{2}[/tex]
The probability of two 1's and two 4's in the first dice can be calculated as:
[tex]= \begin {pmatrix} \left\begin{array}{c}4\\2 \end{array}\right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^4[/tex]
[tex]=\dfrac{4!}{2!(4-2)!}\times (\dfrac{1}{6})^4[/tex]
[tex]=\dfrac{4!}{2!(2)!}\times (\dfrac{1}{6})^4[/tex]
[tex]=\dfrac{4\times 3 \times 2!}{2!(2)!}\times (\dfrac{1}{6})^4[/tex]
[tex]=\dfrac{12}{2 \times 1}\times (\dfrac{1}{6})^4[/tex]
[tex]= 6 \times (\dfrac{1}{6})^4[/tex]
[tex]= (\dfrac{1}{6})^3[/tex]
[tex]= \dfrac{1}{216}[/tex]
The probability of two 1's and two 4's in the second dice can be calculated as:
[tex]= \begin {pmatrix} \left\begin{array}{c}4\\2 \end{array}\right \end {pmatrix} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
[tex]= \dfrac{4!}{2!(4-2)!} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
[tex]= \dfrac{4!}{2!(2)!} \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
[tex]= 6 \times \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} ^2 \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
[tex]= \begin {pmatrix} \dfrac{1}{6} \end {pmatrix} \times \begin {pmatrix} \dfrac{3}{6} \end {pmatrix} ^2[/tex]
[tex]= \dfrac{9}{216}[/tex]
∴ The probability of two 1's and two 4's in both dies
= P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )
The probability of two 1's and two 4's = [tex](\dfrac{1}{216} \times \dfrac{1}{2} )+ ( \dfrac{9}{216} \times \dfrac{1}{2})[/tex]
The probability of two 1's and two 4's = [tex]\dfrac{1}{432}+ \dfrac{1}{48}[/tex]
The probability of two 1's and two 4's = [tex]\dfrac{5}{216}[/tex]
Using Bayes Theorem; the probability that the die was green can be computed as follows:
P(second die (green) | two 1's and two 4's ) = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's)
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{\dfrac{1}{2} \times \dfrac{9}{216} }{\dfrac{5}{216}}[/tex]
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{\dfrac{1}{48} }{\dfrac{5}{216}}[/tex]
P(second die (green) | two 1's and two 4's ) =[tex]\dfrac{1}{48} \times \dfrac{216}{5 }[/tex]
P(second die (green) | two 1's and two 4's ) = [tex]\dfrac{9}{10}[/tex]
P(second die (green) | two 1's and two 4's ) = 0.9
∴
The probability the die chosen was green is 0.9
The quadratic $10x^2+100x+1000$ can be written in the form $a(x+b)^2+c$, where $a$, $b$, and $c$ are constants. What is $a+b+c$?
Answer:
765
Step-by-step explanation:
Hello, please consider the following.
[tex]10x^2+100x+1000=10(x^2+10x+100)\\\\=10((x+5)^2-25+100)\\\\=10(x+5)^2+750[/tex]
So, a = 10, b = 5, c = 750 and the sum is 765.
Thank you
A teacher covered the exterior of a rectangular prism-shaped box that measured 8 inches by 9 inches by 10 inches using one sheet of. ... by 9 inches by 10 inches using one sheet of rectangular-shaped wrapping paper that measured 2 feet by 3 feet. ... How many square inches of wrapping paper were left over?
Answer:
380 square inches
Step-by-step explanation:
Step 1
We find the Surface Area of the Rectangular Prism
The Rectangular Prism has the dimensions of Length × Width × Height = 8 inches by 9 inches by 10 inches
Surface Area of a Rectangular Prism = 2(WL+ HL + HW)
Where W = Width = 9 inches
L = Length = 8 inches
H = Height = 10 inches
Surface Area of the Rectangular Prism = 2(9 × 8 + 10 × 8 + 9 × 10)
= 2(72 + 80 + 90)
= 2(242)
= 484 square inches.
Step 2
Find the area of the Rectangular shaped wrapping paper
The wrapping paper has dimensions :
2 feet by 3 feet
We have to convert to inches first
1 foot = 12 inches
2 feet = 2 × 12 inches = 24 inches
3 feet = 3 × 12 inches = 36 inches
Area of the Rectangular shaped wrapping paper = Length × Width
= 24 inches × 36 inches
= 864 square inches
Step 3
We calculate the amount of square inches of wrapping paper left.
The Amount left over = Area of Rectangular wrapping paper - Area of Rectangular prism
= 864 square inches - 484 square inches
= 380 square inches.
Therefore, the square inches of wrapping paper left over is 380 square inches.
Multiply.
(y- 4z) (4y - 7)
Simplify your answer
Answer:
4y²-7y+16yz+28z
Step-by-step explanation:
4y²-7y+16yz+28z
The owner of Maumee Ford-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year.
Car Age (years) Selling Price ($000)
1 9 11.1
2 5 9.5
3 13 4.4
4 17 4.4
5 7 8.0 6
6 12.0 7
7 10.6
8 14 8.1
9 12 8.1
10 17 4.8
11 4 12.5
12 4 10.7
a. Determine the regression equation. Use the rounded slope value to compute the y-intercept. (Round your answers to 3 decimal places. Negative amounts should be indicated by a minus sign.)
a = ___
b = ___
b. Estimate the selling price (in dollars) of a 7-year-old car. (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
$____
c. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount. Omit the "$" sign in your response.)
For each additional year, the car decreases $ ___ in value.
(Scroll Down for Answer!)
Answer:
b= - 1.26317
a = 17.237
b. The selling price (in dollars) of a 7-year-old car
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1263.17 $ decreases per year
Step-by-step explanation:
Let y be the selling price in thousands and x be the age in years
Car Age Selling Price
(years) ($000) XY X²
X Y
1 9 11.1 99.9 81
2 5 9.5 47.5 25
3 13 4.4 57.2 169
4 17 4.4 74.8 289
5 7 8.06 56.42 49
6 1 2.07 2.07 1
7 1 0.6 0.6 1
8 14 8.1 113.4 196
9 12 8.1 97.2 144
10 17 4.8 81.6 289
11 4 12.5 50 16
12 4 10.7 42.8 16
∑ 97 84.33 723.49 1276
The estimated regression line of Y on X is
Y= a +bX
and the two normal equations are
∑ y= na + b∑X
∑XY= a∑X + b∑X²
Now
X`= ∑X/n = 97/12= 8.083
b= n∑XY - (∑X)(∑Y)/ n∑ X²- (∑X)²
b= 723.49 - (97)(84.33)/ 12(1276) - (97)²
b= -7456.52/ 5903
b= - 1.26317
a= Y`- b X`
a= 7.0275 - (-- 1.26317)8.083
a = 17.237
Y = 17.237 - 1.26317 X
y= - 1.26317 X + 17.237
b. The selling price (in dollars) of a 7-year-old car
y = - 1.26317 (7) + 17.237
y= 8.39481
y = 8394.81 dollars
C. For each additional year, the car decreases $ ___ in value.
1.26317 *1000= 1263.17 $ decreases per year
janice published a novel. Last month the book sold 1364 copies, earning Janice a total of $1579.16. This month the book sold 1347 copies. How much should Janice expect to receive in royalties this month?
[tex]\$1562.52[/tex]
Unitary MethodThe unitary method is a methodology for solving problems that involves first determining the value of a single unit and then multiplying that value by the required value. The unitary method is used to calculate the value of a single unit from a given multiple.
Number of books sold last month [tex]=1364[/tex]
Total amount earned [tex]=\$1579.16[/tex]
So,
Price of each book [tex]=\frac{1579.16}{1364}[/tex]
[tex]=\$1.16[/tex]
Number of books sold this month [tex]=1347[/tex]
Total amount earned [tex]=1.16\times 1347[/tex]
[tex]=\boldsymbol{\$1562.52}[/tex]
Find out more information about unitary method here:
https://brainly.com/question/12116123?referrer=searchResults
i need help with this can someone help me
Answer:
a. 7(3) - 20 = 1°
b. 9 cm
c. Aly is correct
Step-by-step explanation:
Answer:
a. ZWY
b. 9cm
c. Aly's solution is correct
Step-by-step explanation:
a. YW bisects the whole angle, thus angle XWY and angle ZWY are same
NOTE: REMEMBER TO WRITE THE LETTER ACCORDINGLY
b. the two triangles are congruent by AAS (angle-angle-side) thus the two legs of the the triangles are also congruent. when one is 9cm, the other is also 9cm.
c. Since the triangles are congruent, their sides also congruent.
7x-20=2x-5
7x-2x=-5+20
5x=15
x=3
This is same as Aly's solution
What is the decision regarding the differences between the observed and expected frequencies if the critical value of the chi-square is 9.488 and the computed chi-square value is 6.079 g
Answer:
Accept the null hypothesis if it is two tailed test.
Step-by-step explanation:
The null hypotheses can only be accepted if it is a two tailed test and calculated chi square must be less than the critical value of chi square.
Then the difference between the the observed and expected frequencies will be zero.
where
H0 : σ²-σ²= 0 Ha: σ²-σ²≠0
For this the critical region would be greater than the calculated value of chi square. If so we will accept the null hypothesis and reject the alternative hypothesis.
which property is represented by 5+8(-8)=-8+5?
indentity, associative, commutative, distributive
Answer:
The Commutative property is represented by 5 + (-8) = -8 + 5.
Step-by-step explanation:
We are the following the following expression below;
5 + (-8) = -8 + 5
Identity property;This property says that is any number is added to 0, then the result is the number itself, i.e.;
2 + 0 = 2 or (-7) + 0 = -7.
Associative property;Suppose there are three numbers; a, b and c.
So, this property hold the condition that; a + (b + c) = (a + b) + c
If we add the second and third numbers and then add the first number to it or if we add the first and second numbers and then add the third number to it, the result will be the same.
Commutative property;Suppose there are two numbers 6 and 8.
This property states that if we add 6 + 8 or 8 + 6, both are equal, i,e;
6 + 8 = 8 + 6
14 = 14.
Distributive property;This property states the following condition;
a [tex]\times[/tex] (b + c) = (a [tex]\times[/tex] b) + (a [tex]\times[/tex] c)
So, 5 + (-8) = -8 + 5 is represented by the commutative property.
The volume of a sphere is 36ft. What is the radius
Answer:
r≈2.05
Step-by-step explanation:
Answer:3
Step-by-step explanation:
What is the ratio 18 to 27 written as a fraction and lowest terms
Step-by-step explanation:
18:27
=18/27
=2/3 or 2:3
Represent the following sentence as an algebraic expression, where "a number" is the
letter x.
Twice a number.
Answer:
[tex]x = 2a[/tex]
Step-by-step explanation:
Required
Represent twice a number is x as an algebra
Given that the number is a;
Then
[tex]Twice\ a\ number = 2 * a[/tex]
[tex]Twice\ a\ number = 2a[/tex]
Also,
[tex]Twice\ a\ number = x[/tex]
So, we have that
[tex]x = 2a[/tex]
Hence, the algebraic representation of the given parameters is
[tex]x = 2a[/tex]
A bag contains 4 red marbles, 6 blue marbles, and 7 green marbles. What is the probability of choosing a blue marble when one marble is drawn?
Answer:
Probabilty of selecting a blue marble if one marble is drawn
= 0.3529
Step-by-step explanation:
A bag contains 4 red marbles, 6 blue marbles, and 7 green marble.
Total number of marbles
=4 red+ 6 blue+7 green
= 17 marbles in total
Probabilty of selecting a blue marble if one marble is drawn
= Number of blue marble/total number of marble
Probabilty of selecting a blue marble if one marble is drawn
= 6/17
Probabilty of selecting a blue marble if one marble is drawn
= 0.3529
cos2A is equivalent to: A. sin2A−cos2A B. sin2A+cos2A C. cos2A−sin2A D. cosA−sinA
Answer:
C. [tex]cos^2A -sin^2A[/tex]
Step-by-step explanation:
Given:
[tex]cos2A[/tex]
To find:
The given expression is equivalent to:
A. [tex]sin^2A-cos^2A[/tex]
B. [tex]sin^2A+cos^2A[/tex]
C. [tex]cos^2A -sin^2A[/tex]
D. [tex]cosA-sinA[/tex]
Solution/Proof:
First of all, let us have a look at the compound angle formula for [tex]cos(X+Y)[/tex].
Compound angle means in which there is sum of two angles given.
In the above we are having X+Y i.e. sum of two angles X and Y. So it is compound angle.
The compound angle formula for cosine is given as:
[tex]\bold{cos(X+Y)=cosXcosY-sinXsinY}[/tex]
Here, let us put X = Y = A
[tex]cos(A+A)=cosAcosA-sinAsinA\\\Rightarrow \bold{cos(2A)=cos^2A-sin^2A}[/tex]
So, cos2A is equivalent to [tex]cos^2A -sin^2A[/tex].
Correct answer is:
Option C. [tex]cos^2A -sin^2A[/tex]
Help plzdont get this
Answer:
$3.
Step-by-step explanation:
All you have to do is 9/3 = 3.
find the perimeter of the garden that has the side length of 4.3m, 8.7m and 10m
WHAT IS THE EQUATION FOR INVERSE PROPORTION?
Answer: Hi!
The equation for inverse proportion is x y = k or x = k/ y.
When finding the value of the constant k, you can use the known values and then use this formula to calculate all of the unknown values.
Hope this helps!