Answers
Answer:
a) The five ordered pairs are:-
(1,60) , (2,120) , (3,180) , (4,240) , (5,300)
b)When You divide the y value by x value for each ordered pair u find the slope.
c)The graph shows a proportional relationship.Because as x-value increases so does y-value.
d)Y=mx+b--> Y=60x (No y-intercept because it starts from 0)
e)If a person hiked for 9 hours then the distance would be 540. Because If u plug in the number of hours in the x value of the equatione then u will get 540. Here's the work:-
Y=60(9)
Y=540
Step-by-step explanation:
Hope it helps u. And if u get it right pls give me brainliest.
Related Questions
questions:
1. name two parallel lines___________________
2. Name the transversal lines________________
3. Name a pair of alternante exterior angles____________
4. Name an angle that is congruent to <2____________
5. Name an angle that is supplementary to <2________________________
Answers
Answer:
a and b c because it's crossing both lines a and b 1 and 5 4 is congruent to 21 is supplementary to 2 since they form a 180° angleWhich of the following ordered pairs satisfied the inequality 5x-2y<8
A) (-1,1)
B) (-3,4)
C) (4,0)
D) (-2,3)
Answers
Answer: A, B, and D
Step-by-step explanation:
Input the coordinates into the inequality to see which makes a true statement:
5x - 2y < 8
A) x = -1, y = 1 5(-1) - 2(1) < 8
-5 - 2 < 8
-7 < 8 TRUE!
B) x = -3, y = 4 5(-3) - 2(4) < 8
-15 - 8 < 8
-23 < 8 TRUE!
C) x = 4, y = 0 5(4) - 2(0) < 8
20 - 0 < 8
20 < 8 False
D) x = -2, y = 3 5(-2) - 2(3) < 8
-10 - 6 < 8
-16 < 8 TRUE!
An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 240240 engines and the mean pressure was 7.57.5 pounds/square inch (psi). Assume the population standard deviation is 1.01.0. The engineer designed the valve such that it would produce a mean pressure of 7.67.6 psi. It is believed that the valve does not perform to the specifications. A level of significance of 0.10.1 will be used. Find the P-value of the test statistic. Round your answer to four decimal places.
Answers
Answer:
p-value = 0.1213 (to 4-decimal places)
Step-by-step explanation:
Given:
N = 240
mean = 7.5
s = 1.0
Solution
With N=240 and using the central limit theorem, distribution can be approximated as normal.
Let
Null hypothesis H0, mu = 7.6
Alternate hypothesis, mu not equal to 7.6 (two-tail test)
for
Alpha = 0.1 (two sided)
Z = sqrt(N)(mean – mu)/s = sqrt(240)(7.5-7.6)/1.0 = -1.54919
p-value
= P(|Z|>1.54919)
= 2P(Z>1.54919)
= 2(1-P(Z<1.54919)
=2(1-0.9393) (using normal distribution table)
=0.12134
Since alpha = 0.1 < p-value (0.1213), H0 that mean = 7.6 is not rejected.
Which input value produces the same output value for the two functions on the graph?
Answers
Answer:
x=3
Step-by-step explanation:
To solve this problem, we should check the x coordinate of the point where both graphs intersect. Based on both graphs, they intersect at the point (3,-1). So, the input value for which both graphs have the same value is x=3.
Answer:
its x=-2
Step-by-step explanation:
cause i got it wrong and it said the answer was x=-2
The function s(V) = Negative RootIndex 3 StartRoot uppercase V EndRoot describes the side length, in units, of a cube with a volume of V cubic units. Jason wants to build a cube with a minimum of 64 cubic centimeters.
What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?
Answers
This question is incomplete
Complete Question
The function s(V) = ∛V describes the side length, in units, of a cube with a volume of V cubic units.
Jason wants to build a cube with a minimum of 64 cubic centimeters.
What is a reasonable range for s, the side length, in centimeters, of Jason’s cube?
a) s > 0
b) s ≥ 4
c) s ≥ 8
d) s ≥ 16
Answer:
b) s ≥ 4
Step-by-step explanation:
From the above question, we are given Volume of the cube = 64cm³
We are given the function
s(V) = ∛V
Hence,
The range for the side length s =
s(V) ≥ ∛V
s(V) ≥ ∛64 cm³
s(v) ≥ 4 cm
Therefore, the reasonable range for s, the side length, in centimeters, of Jason’s cube
Option b) s ≥ 4
Answer:
s≥ 4
Step-by-step explanation:
Find the unknown side length, x. Write your answer in simplest radical form.
A. 3
B. 34
C. 6.
D. 41
Answers
Answer:
√41
Step-by-step explanation:
Considering the sides with lengths 48 and 52 units, we would use Pythagoras theorem to find the third side. Let that side be t
52² = 48² + t²
t² = 52² - 48²
= 2704 - 2304
= 400
t = √400
= 20
Considering the next triangle with sides t (20 units) and 12 units, again using the theorem
20² = 12² + y²
where y is the third side
400 = 144 + y²
y² = 400 - 144
= 256
y = √256
= 16 units
Considering the triangle with two sides given as 5 and 13 units, the third side (which is part of the 16 units calculated earlier)
13² = 5² + u²
where u is the 3rd side
169 = 25 + u²
u² = 169 - 25
u² = 144
u = √144
u = 12
The other part of the side of that triangle
= 16 - 12
= 4
Considering the smallest triangle whose sides are x, 5 and 4,
x² = 5² + 4²
= 25 + 16
= 41
x = √41
Please do either 40 or 39
Answers
Answer:
y = 1.8
Step-by-step explanation:
Question 39).
Let the operation which defines the relation between a and b is O.
Relation between a and b has been given as,
a O b = [tex]\frac{(a+b)}{(a-b)}[/tex]
Following the same operation, relation between 3 and y will be,
3 O y = [tex]\frac{3+y}{3-y}[/tex]
Since 3 O y = 4,
[tex]\frac{3+y}{3-y}=4[/tex]
3 + y = 12 - 4y
3 + y + 4y = 12 - 4y + 4y
3 + 5y = 12
3 + 5y - 3 = 12 - 3
5y = 9
[tex]\frac{5y}{5}=\frac{9}{5}[/tex]
y = 1.8
Therefore, y = 1.8 will be the answer.
If ABCD is dilated by a factor of 2, the
coordinate of C'would be:
Answers
Answer:
(4, 4)
Step-by-step explanation:
All you really need to do is multiply C's original coordinates with the scale factor. So (2, 2), becomes (4, 4).
Answer:
( 4 , 4 )
Step-by-step explanation:
original C coordinates : ( 2 , 2 )
since the problem is telling us to dilate by the factor of 2 we multiply both 2's by 2.
( 2 ‧ 2 ) ( 2 ‧ 2 )
= ( 4 , 4 )
Please answer this correctly without making mistakes
Answers
Answer:
I believe 45.50
Step-by-step explanation: The locksmith is 18.3 miles W from furniture, the hotel is 27.2 E from furniture store so 18.3+27.2=45.50
Step by step is below
Hopefully this help you you
Have a great day :)
Find the surface area of the triangular prism (above) using its net (below).
Answers
Answer:
96 square units
Step-by-step explanation:
The surface area of the prism can be calculated using its net.
The net consists of 3 rectangles and 2 triangles.
The surface area = area of the 3 rectangles + area of the 2 triangles
Area of 3 rectangles:
Area of 2 rectangles having the same dimension = 2(L*B) = 2(7*3) = 2(21) = 42 squared units
Area of the middle triangle = L*B = 7*6 = 42 square units.
Area of the 3 triangles = 42 + 42 = 84 square units.
Area of the 2 triangles:
Area = 2(½*b*h) = 2(½*6*2) = 6*2
Area of the 2 triangles = 12 square units
Surface area of the triangular prism = 84 + 12 = 96 square units.
Answer:
It's 96 unit2
Step-by-step explanation:
I just do it in khan and it's correct
In a certain lake, trout average 12 in. in length with standard deviation 2.75 in. and the bass average 4 lb. in weight with standard deviation 0.8 lb. If Deion caught an 18-in trout and Keri caught a 6-lb bass, which fish was the better catch?
Answers
Answer:
The bass fish was the better catch
Step-by-step explanation:
From the question we are told that
The population mean for trout is [tex]\mu_1 = 12 \ in[/tex]
The standard deviation is [tex]\sigma_1 = 2.75 \ in[/tex]
The population mean for base is [tex]\mu _2 = 4 \ lb[/tex]
The standard deviation is [tex]\sigma_2 = 0.8 \ lb[/tex]
The number of trout caught [tex]x_1 = 18[/tex]
The number of bass caught [tex]x_2 = 6[/tex]
Generally z-value(standardized value ) for the of number trout caught is mathematically represented as
[tex]z_1 = \frac{x_1 - \mu_1}{\sigma_1 }[/tex]
substituting value
[tex]z_1 = \frac{18 - 12}{2.75 }[/tex]
[tex]z_1 = 2.18[/tex]
Generally z-value(standardized value ) for the of number bass caught is mathematically represented as
[tex]z_2 = \frac{x_2 - \mu_2}{\sigma_2 }[/tex]
substituting value
[tex]z_2 = \frac{6 - 4}{0.8 }[/tex]
[tex]z_2 = 2.5[/tex]
From our calculation we see that [tex]z_2 > z_1[/tex]
The fish that was the better catch is the bass fish
A table of values of a linear function is shown below. Find the output when the input is N. Type your answer in the space provide
Answers
Answer:
[tex] -3n - 7 [/tex]
Step-by-step explanation:
Considering the linear function represented in the table above, to find what output an input "n" would give, we need to first find an equation that defines the linear function.
Using the slope-intercept formula, y = mx + b, let's find the equation.
Where,
m = the increase in output ÷ increase in input = [tex] \frac{-13 - (-10)}{2 - 1} [/tex]
[tex] m = \frac{-13 + 10}{1} [/tex]
[tex] m = \frac{-3}{1} [/tex]
[tex] m = -3 [/tex]
Using any if the given pairs, i.e., (1, -10), plug in the values as x and y in the equation formula to solve for b, which is the y-intercept
[tex] y = mx + b [/tex]
[tex] -10 = -3(1) + b [/tex]
[tex] -10 = -3 + b [/tex]
Add 3 to both sides:
[tex] -10 + 3 = -3 + b + 3 [/tex]
[tex] -7 = b [/tex]
[tex] b = -7 [/tex]
The equation of the given linear function can be written as:
[tex] y = -3x - 7 [/tex]
Or
[tex] f(x) = -3x - 7 [/tex]
Therefore, if the input is n, the output would be:
[tex] f(n) = -3n - 7 [/tex]
i need help emergrncy shots fire shots fire we neeed all back ups
Answers
Answer:
a = 9h + bn
Step-by-step explanation:
total = $9 an hour + (bonus x number of items repaired)
The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a rectangular prism is the product of its base area and height, what is the height of the prism? PLEASE COMMENT, I Can't SEE ANSWERS CAUSE OF A GLITCH
Answers
Answer:
x + 1 - ( 4 / x³ + 3x² + 8 )
Step-by-step explanation:
If the volume of this rectangular prism ⇒ ( x⁴ + 4x³ + 3x² + 8x + 4 ), and the base area ⇒ ( x³ + 3x² + 8 ), we can determine the height through division of each. The general volume formula is the base area [tex]*[/tex] the height, but some figures have exceptions as they are " portions " of others. In this case the formula is the base area [tex]*[/tex] height, and hence we can solve for the height by dividing the volume by the base area.
Height = ( x⁴ + 4x³ + 3x² + 8x + 4 ) / ( x³ + 3x² + 8 ) = [tex]\frac{x^4+4x^3+3x^2+8x+4}{x^3+3x^2+8}[/tex] = [tex]x+\frac{x^3+3x^2+4}{x^3+3x^2+8}[/tex] = [tex]x+1+\frac{-4}{x^3+3x^2+8}[/tex] = [tex]x+1-\frac{4}{x^3+3x^2+8}[/tex] - and this is our solution.
Answer:
[tex]x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
Step-by-step explanation:
[tex]volume=base \: area \times height[/tex]
[tex]height=\frac{volume}{base \: area}[/tex]
[tex]\mathrm{Solve \: by \: long \: division.}[/tex]
[tex]h=\frac{(x^4 + 4x^3 + 3x^2 + 8x + 4)}{(x^3 + 3x^2 + 8)}[/tex]
[tex]h=x + \frac{x^3 + 3x^2 + 4}{x^3 + 3x^2 + 8}[/tex]
[tex]h=x +1 - \frac{4}{x^3 + 3x^2 + 8}[/tex]
QUESTION 4 (10 MARKS)
A retired couple requires an annual return of $2,000 from investment of $20,000. There are 3
options available:
(A) Treasury Bills yielding 9%;
(B) Corporate bonds 11%;
(C) Junk Bonds, 13%
How much should be invested in each to achieve their goal? Give 3 sets of options that can
achieve their goal.[10 Marks]
Answers
Answer:
A. $22,223
B. $20,000
C. $20,000
Explanation:
The annual return of the retired couple's investment is called the yield in percentage.
A. If they go for Treasury bills which has a yield of 9%, to attain a return of at least $2,000 their investment must exceed $20,000. 9% of 22,223 = $2,000.07
B. . If they go for Corporate bonds option which has a yield of 11%, to attain a return of at least $2,000; 11% of 20,000 = $2,200
C. . If they go for Junk bonds option which has a yield of 13%, to attain annual return of at least $2,000; 13% of $20,000= $2,600
In 2010 polls indicated that 75% of Americans favored mandatory testing of students in public schools as a way to rate the school. This year in a poll of 1,000 Americans 71% favor mandatory testing for this purpose. Has public opinion changed since 2010?
We test the hypothesis that the percentage supporting mandatory testing is less than 75% this year The p-value is 0.013
Which of the following interpretation of this p-value is valid?
A. The probability that Americans have changed their opinion on this issue since 2010 is 0.013.
B. There is a 1.3% chance that the null hypothesis is true.
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Answers
Answer:
C. If 75% of Americans still favor mandatory testing this year, then there is a 3% chance that poll results will show 72% or fewer with this opinion.
Step-by-step explanation:
Significance level or alpha level is the probability of rejecting the null hypothesis when null hypothesis is true. It is considered as a probability of making a wrong decision. It is a statistical test which determines probability of type I error. If the obtained probability is equal of less than critical probability value then reject the null hypothesis. In this question the sample of 1000 Americans is under test. It is the result of the poll that 75% still favor mandatory testing.
When doing blood testing for a viral infection, the procedure can be made more efficient and less expensive by combining partial samples of different blood specimens. If samples from five people are combined and the mixture tests negative, we know that all five individual samples are negative. Find the probability of a positive result for five samples combined into one mixture, assuming the probability of an individual blood sample testing positive for the virus is 0.06.
Answers
Answer: 0.271
Step-by-step explanation:
Probability of complement of an even is 1 decreased by the probability of the event
P(At least one) =1 - P(none)
The probability that of testing negative is 0.9 because the probability of testing positive is 0.1
P( at least one) = 1 - P(none) = 1 - (0.93^3) = 0.271
Ava wants to figure out the average speed she is driving. She starts checking her car’s clock at mile marker 0. It takes her 4 minutes to reach mile marker 3. When she reaches mile marker 6, she notes that 8 minutes total have passed since mile marker 0. What is the average speed of the car in miles per minute? What is an equation of the line that represents n, the number of mile marker passed, as a function of t, time in minutes? PLEASE HELP
Answers
Answer:
Below
Step-by-step explanation:
The average speed is given by the following formula:
● V = d/t
● d is the distance covered
● t is the time spent to cover the distance d
■■■■■■■■■■■■■■■■■■■■■■■
Ava takes 8 minutes to go from mile marker 0 to mile marker6.
● the distance Ava traveled is 6 miles
● the time Ava spent to reach mile marker 6 is 8 minutes
So the average speed of Ava is:
● V = 6/ 8 = 3/4 = 0.75 mile per min
●●●●●●●●●●●●●●●●●●●●●●●●
Let's The equation of the line that links the number of milemarkers (n) and the time (t).
Ava went from mile marker 0 to mile marker 6.
At t=0 Ava just started travelling from mile marker 0 to 1.
Afrer 8 minutes,she was at mile marker 6.
So 8 min => 6 mile markers (igonring mile marker 0 since the distance there was 0 mile)
6/8= 0.75
Then n/t = 0.75
● n = 0.75 * t
Let's check
● n= 0.75*4 = 3
That's true since after 4 minutes Ava was at mile marker 3.
What is the equation for the plane illustrated below?
Answers
Answer:
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Step-by-step explanation:
The general equation in rectangular form for a 3-dimension plane is represented by:
[tex]a\cdot x + b\cdot y + c\cdot z = d[/tex]
Where:
[tex]x[/tex], [tex]y[/tex], [tex]z[/tex] - Orthogonal inputs.
[tex]a[/tex], [tex]b[/tex], [tex]c[/tex], [tex]d[/tex] - Plane constants.
The plane presented in the figure contains the following three points: (2, 0, 0), (0, 2, 0), (0, 0, 3)
For the determination of the resultant equation, three equations of line in three distinct planes orthogonal to each other. That is, expressions for the xy, yz and xz-planes with the resource of the general equation of the line:
xy-plane (2, 0, 0) and (0, 2, 0)
[tex]y = m\cdot x + b[/tex]
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - x-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]y_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]y_{2} = 2[/tex], then:
Slope
[tex]m = \frac{2-0}{0-2}[/tex]
[tex]m = -1[/tex]
x-Intercept
[tex]b = y_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -(-1)\cdot (2)[/tex]
[tex]b = 2[/tex]
The equation of the line in the xy-plane is [tex]y = -x+2[/tex] or [tex]x + y = 2[/tex], which is equivalent to [tex]3\cdot x + 3\cdot y = 6[/tex].
yz-plane (0, 2, 0) and (0, 0, 3)
[tex]z = m\cdot y + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{y_{2}-y_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]y_{1}[/tex], [tex]y_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - y-Intercept, dimensionless.
If [tex]y_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]y_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
y-Intercept
[tex]b = z_{1} - m\cdot y_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the yz-plane is [tex]z = -\frac{3}{2}\cdot y+3[/tex] or [tex]3\cdot y + 2\cdot z = 6[/tex].
xz-plane (2, 0, 0) and (0, 0, 3)
[tex]z = m\cdot x + b[/tex]
[tex]m = \frac{z_{2}-z_{1}}{x_{2}-x_{1}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{1}[/tex], [tex]x_{2}[/tex] - Initial and final values for the independent variable, dimensionless.
[tex]z_{1}[/tex], [tex]z_{2}[/tex] - Initial and final values for the dependent variable, dimensionless.
[tex]b[/tex] - z-Intercept, dimensionless.
If [tex]x_{1} = 2[/tex], [tex]z_{1} = 0[/tex], [tex]x_{2} = 0[/tex] and [tex]z_{2} = 3[/tex], then:
Slope
[tex]m = \frac{3-0}{0-2}[/tex]
[tex]m = -\frac{3}{2}[/tex]
x-Intercept
[tex]b = z_{1} - m\cdot x_{1}[/tex]
[tex]b = 0 -\left(-\frac{3}{2} \right)\cdot (2)[/tex]
[tex]b = 3[/tex]
The equation of the line in the xz-plane is [tex]z = -\frac{3}{2}\cdot x+3[/tex] or [tex]3\cdot x + 2\cdot z = 6[/tex]
After comparing each equation of the line to the definition of the equation of the plane, the following coefficients are obtained:
[tex]a = 3[/tex], [tex]b = 3[/tex], [tex]c = 2[/tex], [tex]d = 6[/tex]
Hence, none of the options presented are valid. The plane is represented by [tex]3 \cdot x + 3\cdot y + 2\cdot z = 6[/tex].
Answer:
It is A 3x+3y+2z=6
Step-by-step explanation:
01:
Which expression can be used to model the phrase the sum of three and a number?
Answers
Answer:
3+x
Step-by-step explanation:
sum= addition
a number= a number
Answer:
3+x
eplanation
The winery sold 81 cases of wine this week. If twice
as many red cases were sold than white, how many
white cases were sold this week?
A. 32 cases
B. 61 cases
C. 27 cases
D. 54 cases
Answers
Answer:
Option (C)
Step-by-step explanation:
Let the red cases sold = r
and the number of white cases sold = w
Total number of cases sold by the winery = 81
r + w = 81 -------(1)
If number of red cases sold is twice of white cases sold,
r = 2w ------- (2)
By substituting the value of r from equation (2) to equation (1),
2w + w = 81
3w = 81
w = 27 cases
From equation (1),
r + 27 = 81
r = 54 cases
Therefore, number of white cases sold are 27 cases
Option (C) is he answer.
The range of f(x) = cos(x) is y ≤ 0
Answers
Answer:
Look at the image below↓
A city has a population of 240,000 people. Suppose that each year the population grows by 7.75%. What will the population be after 7 years?
round your answer to the nearest whole number.
people
Answers
Answer:
[tex]\large\boxed{\sf \ \ \ 404,699 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
At the beginning the population is 240,000
After 1 year the population will be
240,000*(1+7.75%)=240,000*1.0775
After n years the population will be
[tex]240,000\cdot1.0775^n[/tex]
So after 7 years the population will be
[tex]240,000\cdot1.0775^7=404699.058...[/tex]
So rounded to the nearest whole number gives 404,699
Hope this helps
Janet, an experienced shipping clerk, can fill a certain order in 14 hours. Jim, a new clerk, needs 15 hours to do the same job. Working together, how long will it take them to fill the order?
Answers
Answer:
7.24 hrs
Step-by-step explanation:
Janet can do the order in 14 hours.
In 1 hour, she can do 1/14 of the order.
Jim can do the order in 15 hours.
In 1 hour, he can do 1/15 of the order.
Let the total amount of time they take to do the job working together be x hours.
[tex]\frac{1}{14} x+\frac{1}{15}x =1[/tex]
[tex]\frac{29}{210} x=1[/tex]
[tex]\frac{210}{29}* \frac{29}{210} x=1*\frac{210}{29}[/tex]
[tex]x= 7.241379...[/tex]
EXAMPLE 4 Find ∂z/∂x and ∂z/∂y if z is defined implicitly as a function of x and y by the equation x6 + y6 + z6 + 18xyz = 1. SOLUTION To find ∂z/∂x, we differentiate implicitly with respect to x, being careful to treat y as a constant:
Answers
Answer:
see attachment
Step-by-step explanation:
We differentiate implicitly with respect to x taking y as a constant and we differentiate implicitly with respect to y taking x as a constant.
[tex]\rm \dfrac{\partial z}{\partial x} = - \dfrac{(x^5 + 3yz)}{z^5 + x} \ \ and \ \ \dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y}[/tex]
What is an implicit function?When in a function the dependent variable is not explicitly isolated on either side of the equation then the function becomes an implicit function.
The equation is given as [tex]\rm x^6 + y^6 + z^6 + 18xyz = 1.[/tex]
Differentiate partially the function with respect to x treating y as a constant.
[tex]\begin{aligned} \dfrac{\partial}{\partial x} x^6 + y^6 + z^6 + 18xyz &= 0\\\\6x^5 + 0 + 6z^5 \dfrac{\partial z }{\partial x} + 18y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\x^5 + z^5 \dfrac{\partial z }{\partial x} + 3y(z + x\dfrac{\partial z}{\partial x}) &= 0\\\\\dfrac{\partial z}{\partial x} &= - \dfrac{(x^5 + 3yz)}{z^5 + x} \end{aligned}[/tex]
Similarly, differentiate partially the function with respect to y treating x as a constant.
[tex]\begin{aligned} \dfrac{\partial}{\partial y} x^6 + y^6 + z^6 + 18xyz &= 0\\\\ 0 + 6y^5+ 6z^5 \dfrac{\partial z }{\partial y} + 18x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\y^5 + z^5 \dfrac{\partial z }{\partial y} + 3x(z + y\dfrac{\partial z}{\partial y}) &= 0\\\\\dfrac{\partial z}{\partial y} &= - \dfrac{(y^5 + 3xz)}{z^5 + y} \end{aligned}[/tex]
More about the implicit function link is given below.
https://brainly.com/question/6472622
Which of the following is equivalent to (3)/(x)=(6)/(x-4)
Answers
Answer:
[tex]3(x - 4) = 6x[/tex]Option A is the correct option.
Step-by-step explanation:
[tex] \frac{3}{x } = \frac{6}{x - 4} [/tex]
Apply cross product property:
[tex]3(x - 4) = 6 \times x[/tex]
[tex]3(x - 4) = 6x[/tex]
Hope this helps...
Best regards!!
Answer:
3 * (x - 4) = 6 * x.
Step-by-step explanation:
3 / x = 6 / (x - 4)
3 * (x - 4) = 6 * x
3x - 12 = 6x
6x = 3x - 12
6x - 3x = -12
3x = -12
x = -4.
Hope this helps!
Which correlation coefficient could represent the relationship in the scatterpot
Answers
Answer:
D. -0.98
Step-by-step explanation:
Well it is a negative correlation and it is really strong but it is impossible to go pasit -1.
Thus,
the answer is D. -0.98
Hope this helps :)
Answer:
D. -0.98
Step-by-step explanation:
The correlation is a negative if the Y value decreases as the x value increases. It is not -1.43 because it is not decraeseing that fast.
a) John is 3 years older than his brother Brian, the product of their ages is 54 i) Express this information in equation form ii) Show this information as a quadratic equation iii) Hence, solve the equation to find their individual ages.
Answers
Answer:
John is 9, Brian is 6.
Step-by-step explanation:
I)
Let [tex]J[/tex] represent John's age and [tex]B[/tex] represent Brian's age.
John is three years older than Brian. In other words:
[tex]J=B+3[/tex]
The product of their ages is 54. Or:
[tex]JB=54[/tex]
II)
Write this as a quadratic by substituting:
[tex]JB=54\\(B+3)B=54\\B^2+3B-54=0[/tex]
III)
Solve the quadratic:
[tex]B^2+3B-54=0\\B^2-6B+9B-54=0\\B(B-6)+9(B-6)=0\\(B+9)(B-6)=0\\B=-9, 6[/tex]
Since age cannot be negative, Brian must be 6 years old right now.
John is three year older, so John is 9.
Intelligence quotients (IQs) measured on the Stanford Revision of the Binet Simon Intelligence Scale are normally distributed with a mean of 100 and a standard deviation of 16. Determine the percentage of people who have an IQ between 115 and 140.
Answers
Answer:
the percentage of people who have an IQ between 115 and 140 is 16.79%
Step-by-step explanation:
From the information given:
We are to determine the percentage of people who have an IQ between 115 and 140.
i.e
P(115 < X < 140) = P( X ≤ 140) - P( X ≤ 115)
[tex]P(115 < X < 140) = P( \dfrac{X-100}{\sigma}\leq \dfrac{140-100}{16})-P( \dfrac{X-100}{\sigma}\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{140-100}{16})-P( Z\leq \dfrac{115-100}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq \dfrac{40}{16})-P( Z\leq \dfrac{15}{16})[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.9375)[/tex]
[tex]P(115 < X < 140) = P( Z\leq 2.5)-P( Z\leq 0.938)[/tex]
From Z tables :
[tex]P(115 < X < 140) = 0.9938-0.8259[/tex]
[tex]P(115 < X < 140) = 0.1679[/tex]
Thus; we can conclude that the percentage of people who have an IQ between 115 and 140 is 16.79%
Using the normal distribution, it is found that 82.02% of people who have an IQ between 115 and 140.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.In this problem:
The mean is of [tex]\mu = 100[/tex].The standard deviation is of [tex]\sigma = 15[/tex].The proportion of people who have an IQ between 115 and 140 is the p-value of Z when X = 140 subtracted by the p-value of Z when X = 115, hence:
X = 140:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{140 - 100}{16}[/tex]
[tex]Z = 2.5[/tex]
[tex]Z = 2.5[/tex] has a p-value of 0.9938.
X = 115:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{115 - 100}{16}[/tex]
[tex]Z = -0.94[/tex]
[tex]Z = -0.94[/tex] has a p-value of 0.1736.
0.9938 - 0.1736 = 0.8202.
0.8202 = 82.02% of people who have an IQ between 115 and 140.
More can be learned about the normal distribution at https://brainly.com/question/24663213
Which of the following is an example of a quadratic equation?
Answers
Answer:
C. x^2 - 64 = 0
hope this helps :)
Answer:
It's C
Step-by-step explanation:
It has a variable being squared