Answer:
Find the linearization L(x,y) of the function at each point. f(x,y) = x2 + y2 + 1 a. (4,0) b. (2,0) a. L(x,y) = Find the linearization L(x,y,z) of the function f(x,y,z) = 1x2 + y2 +z2 at the points (7,0,0), (3,4,0), and (4,4,7). The linearization of f(x,y,z) at (7,0,0) is L(x,y,z)= (Type an exact answer, using radicals as needed.)
Height of a tree increases by 2.5 feet each growing season. Quadratic, linear or exponential?
Answer:
Linear
Step-by-step explanation:
Given
Height of a tree grows by 2.5 feet
Required
Determine the type of relationship
Take for instance, the height of the tree at year 1 is x
At year 2, it will be x + 2 * 1
At year 3, it will be x + 2 * 2
At year 4, it will be x + 2 * 3
Following same pattern
At year n, it will be x + 2 *(n - 1)
Hence, growth rate = x + 2(n -1)
From the list of given options, the correct answer is Linear because the derived formula above is an example of a linear equation
What is the rate of change from x = 0 to x = pi over 2 ? (6 points) trig graph with points at: (0, negative 4) and (pi over 2, 0) and (pi, 4) and (3 pi over 2, 0) and (2 pi, negative 4)
Answer:
Rate of Change : 8 / π
Step-by-step explanation:
To determine this rate of change, we have to first consider the points at x = 0 and x = π / 2.
When x = 0, f( x ) = - 4,
When x = π / 2, f( x ) = 0
Remember that rate of change is represented by a change in y / change in x. Therefore,
( 0 - ( - 4 ) ) / ( π / 2 - 0 ),
( 0 + 4 ) / ( π / 2 ),
4 / π / 2 = 8 / π
Therefore the rate of change from x = 0 ➡ x = π / 2 will be 8 / π.
10-
What is the equation of the line that is perpendicular to
the given line and passes through the point (2, 6)?
8-
(2,6)
-6
O x = 2
4
O x = 6
-2
-10 -3 -6 -22
2
4
B
8
10
X
O y = 2
O y = 6
(-34)
(814)
8
WO
Answer:
x = 2
Step-by-step explanation:
This blue line seems to be horizontal, and so a line perpendicular would have to be vertical. The only vertical line that passes through (2, 6) would be x = 2.
The equation of the line perpendicular to the given line and passes through the point (2, 6) is x = 2.
What is the Equation of line in Slope Intercept form?Equation of a line in slope intercept form is y = mx + b, where m is the slope of the line and b is the y intercept, which is the y coordinate of the point where it touches the Y axis.
Given is a line that passes through the points (-8, -4) and (8, -4).
This line is parallel to the X axis.
A line parallel to X axis has the equation y = b.
The y coordinate is -4 throughout the line.
So equation of the line is y = -4.
A line perpendicular to the given line will be parallel to Y axis.
Parallel lines to Y axis has the equation of the form x = a.
Line passes through the point (2, 6).
x coordinate will be 2 throughout.
So the equation of the perpendicular line is x = 2.
Hence the required equation is x = 2.
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find x, if sq.root(x) +2y^2 = 15 and sq.root(4x) - 4y^2=6
Answer:
Example: solve √(2x−5) − √(x−1) = 1
isolate one of the square roots:√(2x−5) = 1 + √(x−1) square both sides:2x−5 = (1 + √(x−1))2 ...
expand right hand side:2x−5 = 1 + 2√(x−1) + (x−1) ...
isolate the square root:√(x−1) = (x−5)/2. ...
Expand right hand side:x−1 = (x2 − 10x + 25)/4. ...
Multiply by 4 to remove division:4x−4 = x2 − 10x + 25.
Answer:
Step-by-step explanation:
ewrerewrwrwerrwer
A study claimed residents in a suburb town spend at most 1.9 hours per weekday commuting to and from their jobs. A researcher believed commute times were now different and wants to test this claim by sampling 14 adults. Sample statistics for these 14 adults are: X = 2.2 $=0.7 Can the researcher support the claim that mean commuting time is more than 1.9 hours ? Test using a =.01.
Answer:
There is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours
Step-by-step explanation:
From the question we are told that
The population mean is [tex]\mu = 1.9 \ hr[/tex]
The sample mean is [tex]\= x = 2.2[/tex]
The standard deviation is [tex]\sigma = 0.7[/tex]
The sample size is [tex]n = 14[/tex]
The level of significance is [tex]\alpha = 0.01[/tex]
The null hypothesis is [tex]H_o : \mu = 1.9 \ hr[/tex]
The alternative hypothesis is [tex]H_a : \mu > 1.9 \ hr[/tex]
Generally the test statistics is mathematically represented as
[tex]t = \frac{\= x - \mu }{ \frac{\sigma}{ \sqrt{n} } }[/tex]
[tex]t = \frac{ 2.2 - 1.9 }{ \frac{0.7 }{ \sqrt{14} } }[/tex]
[tex]t = 1.6036[/tex]
The p-value is obtained from the z-table, the value is
[tex]p-value = P(t > 1.6036) = 0.054401[/tex]
Looking at the value of [tex]p-value \ and \ \alpha[/tex] we see that [tex]p-value > \alpha[/tex]
So we fail reject the null hypothesis
Hence we can conclude that there is no sufficient evidence to support the claim that mean commuting time is more than 1.9 hours
Which of the functions below could have created this graph?
O A. F(x) = -x' +5x° +7
O B. F(x) = 2x2 - 4x2 +4
O C. F(x)=x2+x+3
O D. F(x) = -5x – 2x+5
Answer:
[tex] \boxed{f(x) = 2 {x}^{9} - 4 {x}^{2} + 4}[/tex]
Option B is the correct option
Step-by-step explanation:
By looking at the end behavior , we can say that the degree of the polynomial must be odd and leading coefficient will be positive.
Thus , the correct choice is B.
Hope I helped!
Best regards!
The polynomial function that could have created the given curve on the xy-plane is [tex]f(x)= 2x^9-4x^2+4[/tex]
What are polynomial function?Polynomial functions aree function having a leading degrees of 3 and greater.
The nature of the curve on the xy-plane depends on its end behaviour. From the given graph, the end behaviour shows that the equivalnt function has a positive leading coefficient and an odd degree.
From the listed option, the function that satisfies both criteria is [tex]f(x)=2x^9-4x^2+4[/tex].
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Test scores in a Test were normally distributed with a mean of 75 and a standard deviation of 10. Carl scored 90 in the Test . What is the z-score of Carl’s test score?
Answer:
Z-score = 1.5
Step-by-step explanation:
Z-score = (x-mean)/standard deviation
= (90-75)/10
= 1.5
find the 11th termm of the arithmetic sequence with first term 3 and common difference -2
Answer:
-17
Step-by-step explanation:
a=3, d=-2
11th term= a + 10d
11th term= 3 + 10(-2)
= 3 + (-20)
= 3 - 20
= -17
Find the length of AC¯¯¯¯¯¯¯¯ A. 211.63 B. 44.98 C. 9.35 D. 207
Answer:
Step-by-step explanation:
tanθ= opp / adj
tan(12) = AC/44
now
AC = tan(12)/44
AC = ...
use calculator to find the value
I just broke mine
Help me please I need answers
Answer:
[tex]\huge \boxed{\mathrm{\$ \ 7,533.33}}[/tex]
Step-by-step explanation:
There are 12 months in one whole year.
In one year, the person earns $96,600 with bonus.
The person gets a bonus of $6,200 during Christmas.
96,600 - 6,200 = 90,400
The person earns $90,400 yearly.
[tex]\frac{90,400}{12}[/tex] = 7,533.3333
Each month, the person earns $7,533.33, to the nearest cent.
Heeeellllllppppp?????
9514 1404 393
Answer:
-1
Step-by-step explanation:
We notice that we want term a1 and have terms a17 and a33. These terms (every 16-th term) form an arithmetic sequence. The middle term (a17) is the average of the other two, so we have ...
a17 = (a1 +a33)/2
2a17 -a33 = a1 = 2(10) -21 = -1
a1 = -1
_____
Additional comment
You could go to the trouble to find the general term of the sequence.
an = a1 +d(n -1)
a17 = a1 + d(17 -1) = 10
a33 = a1 + d(33 -1) = 21
Subtracting the first equation from the second, we have ...
16d1 = 11
d1 = 11/16
Using the first equation, we find ...
a1 +(11/16)(17 -1) = 10
a1 = 10 -11 = -1 . . . . same as above.
The distance a race car travels is given by the equation, [tex]d=v_{0} t+\frac{1}{2} at^{2}[/tex], where [tex]v_{0}[/tex] is the initial speed of the race car, a is the acceleration and t is the time traveled. Near the beginning of a race, the driver accelerates for 9 seconds at a rate of [tex]4m/s^{2}[/tex]. The driver's initial speed was 75 m/s.
Find the driver's average speed during the acceleration.
Step-by-step explanation:
here's the answer to your question
Select the correct answer from each drop-down menu.
A cross section is the intersection of a
Solid or point and a plane or plane. Helpp
Answer:
solid, plane
Step-by-step explanation:
A cross section is the intersection of a solid and a plane.
Answer:
A cross section is the intersection of a solid and a plane.
Step-by-step explanation:
Got this right on plato, hope it helps :P
y varies directly as z, y=180, z=10 , find ywhen z=14
Step-by-step explanation:
To find the value of y when z = 14 we must first find the relationship between them
The statement
y varies directly as z is written as
y = kz
where k is the constant of proportionality
when y = 180
z = 10
180 = 10k
Divide both sides by 10
k = 18
The formula for the variation is
y = 18z
When z = 14
y = 18(14)
y = 252Hope this helps you
In your own words tell how you can use the number line to add and subtract integers.
Answer:
We can use number lines for adding as well as subtracting integers. For doing this:
1. First mark the first integer on the number line.
2. Now to add a positive integer to this number, move to the right on the number line from this number.
3. In case you have to add a negative integer, move to the left on the number line from this number.
4. Subtracting an integer means adding its opposite and hence, if you have to subtract a positive integer from this number, move to the left on the number line from this number.
5. But if you have to subtract a negative integer from this number, move to the right on the number line from this number.
<3
The values of 9’s in 9905482
Answer:
9,905,482=
Million place
9,905,482=
one hundred thousandth
There are four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag. Which expression represents the probability of randomly selecting a blue marble, replacing it, and then randomly selecting a red marble? StartFraction 4 over 10 EndFraction (StartFraction r over 10 EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction 4 over 10 r EndFraction) StartFraction 4 over 10 + r EndFraction (StartFraction r over 10 + r EndFraction) StartFraction 4 over 10 r EndFraction (StartFraction r over 10 r EndFraction)
Answer:
4/ (10+r) * r/ (10+r)
Step-by-step explanation:
four blue marbles, an unknown number of red (r) marbles, and six yellow marbles in a bag = 4+r+6 = 10+r marbles
P( blue) = blue marbles / total marbles
= 4/ (10+r)
Then replace
P( r) = red marbles / total marbles
= r/ (10+r)
P( blue replace ,red) =P ( blue ) * P(red)
= 4/ (10+r) * r/ (10+r)
= 4r / ( 10+r) ^2
Answer:
C. 4/10+r (r/10+r)
Step-by-step explanation:
EDG20
find the derivative by using product rule and distribution
pls help quickly and show work
Answer:
Below
Step-by-step explanation:
First method:
● f(x)= (x^3-2x+1)×(x-3)
● f'(x)= (x^3-2x+1)' ×(x-3) + (x^3-2x+1)×(x-3)'
●f'(x)= (3x^2-2)×(x-3) + (x^3-2x+1) × 1
●f'(x) = 3x^3-9x^2-2x+6 + x^3-2x+1
● f'(x)= 4x^3-9x^2-4x+7
■■■■■■■■■■■■■■■■■■■■■■■■■■
Second method:
●f(x) = (x^3-2x+1)×(x-3)
●f(x) = x^4-3x^3 -2x^2+6x+x-3
●f(x) = x^4-3x^3-2x^2+7x-3
●f'(x) = 4x^3-9x^2-4x+7
We got the same result using both methods.
v divided by 5 is equal to 60.
Answer:
[tex]\boxed{v=300}[/tex]
Step-by-step explanation:
Hey there!
To find v we’ll set up the following,
v ÷ 5 = 60
To get v by itself we’ll do
5*60 = 300
v = 300
Hope this helps :)
Bob Nale is the owner of Nale's Texaco GasTown. Bob would like to estimate the mean number of litres (L) of gasoline sold to his customers. Assume the number of litres sold follows the normal distribution with a standard deviation of 18 L. From his records, he selects a random sample of 18 sales and finds the mean number of litres sold is 56.
a. What is the point estimate of the population mean? (Round the final answer to the nearest whole number.)
The point estimate of the population mean is
litres.
b. Develop a 80% confidence interval for the population mean. (Round the final answers to 3 decimal places.)
The 80% confidence interval for the population mean is between
and
.
c. Interpret the meaning of part (b).
If 100 such intervals were determined, the population
mean
would be included in about
intervals.
Answer:
a
The point estimate of the population mean is [tex]\= x = 56[/tex]
b
The 80% confidence level is [tex]50.57 < \mu < 61.43[/tex]
c
There is 80% confidence that the true population mean lies within the confidence interval.
Step-by-step explanation:
From the question we are told that
The sample size is n = 18
The standard deviation is [tex]\sigma = 18 \ L[/tex]
The sample mean is [tex]\= x = 56[/tex]
Generally the point estimate of the population mean is equivalent to the sample mean whose value is [tex]\= x = 56[/tex]
Given that the confidence interval is 80% then the level of significance is mathematically represented as
[tex]\alpha = 100 - 80[/tex]
[tex]\alpha = 20 \%[/tex]
[tex]\alpha = 0.20[/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} } = 1.28[/tex]
Generally the margin of error is mathematically evaluated as
[tex]E = Z_{\frac{\alpha }{2} } * \frac{\sigma }{\sqrt{n} }[/tex]
=> [tex]E = 1.28 * \frac{18 }{\sqrt{18} }[/tex]
=> [tex]E = 5.43[/tex]
Generally the 80% confidence interval is mathematically represented as
[tex]\= x - E < \mu < \= x + E[/tex]
=> [tex]56 - 5.43 < \mu < 56 + 5.43[/tex]
=> [tex]50.57 < \mu < 61.43[/tex]
The interpretation is that there is 80% confidence that the true population mean lies within the limit
Find the value of 21 - 18 \ 3•2
18
1/2
2
9
Answer:
use m a t h w a y
Step-by-step explanation:
A movie theater is having a special. If a group of four pays $7.25 each for tickets, each person can get popcorn and a drink for $5.75. Use the expression 4(5.75 + 7.25) to find the total cost for 4 friends.
Answer:
The price for 4 people is 52 dollars.
4 × (5.75 + 7.25) = 52
The total cost including drink and popcorn is $52 according to a given condition.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Cost of movie ticket = $7.25/person
Cost of popcorn and drink = $5.75/person
Total cost per person = 5.75 + 7.25 = $13
Now,
Number of people = 4
So,
4(5.75 + 7.25) = 4(13) = $52
Hence "The total cost including drink and popcorn is $52 according to a given condition".
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Three-fourths (x minus 8) = 12
Answer:
x=24
Step-by-step explanation:
3/4(x-8)=12
3/4x-24/4=12
3/4x=18
18 dived by 3/4
x=24
your welcome :)
1. Find the 4th term for the sequence with formula tn= n² + 1
Answer:
17
Step-by-step explanation:
T4 = 4² + 1
T4 = 4² + 1 = 17
Yip yip that's all
PLEASE HELP
4/9w = -8
Show your work in details if you can, I have a hard time understanding this.
[tex] \begin{cases}\large\bf{\blue{ \implies}} \tt \: \frac{4}{9} \sf \: w \: = \: - 8 \\ \\ \large\bf{\blue{ \implies}} \tt \: \frac{4 \sf \: w}{9} \: = \: 8 \\ \\ \large\bf{\blue{ \implies}} \tt 4 \sf \: w \: = \: 9 \: \times \: 8 \\ \\ \large\bf{\blue{ \implies}} \tt 4 \sf \: w \: = \: 72 \\ \\ \large\bf{\blue{ \implies}} \tt \sf \: w \: = \: \cancel\frac{72}{4} \\ \\ \large\bf{\blue{ \implies}} \tt \sf \: w \: = \: 18 \end{cases}[/tex]
3. Convert 10% into fraction.
1/10 to get your answer
10÷100=
0.1=1/10
A truck can be rented from Company A for $120 a day plus $0.80 per mile. Company B charges $50 a day plus $0.90 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same.
Answer:
700 miles driven in a day
Step-by-step explanation:
Create an equation to represent the situation, where x is the number of miles.
0.8x + 120 = 0.9x + 50
Solve for x:
120 = 0.1x + 50
70 = 0.1x
700 = x
So, the rental costs will be the same at 700 miles driven in a day.
What is 28% of 58?
Hhhhhhh
Answer:
16.24
Step-by-step explanation:
of means multiply
28% * 58
Change to decimal form
.28 * 58
16.24
Answer:
[tex]\Large \boxed{\mathrm{16.24}}[/tex]
Step-by-step explanation:
[tex]28\% \times 58[/tex]
[tex]\displaystyle \sf Apply \ percentage \ rule : a\%=\frac{a}{100}[/tex]
[tex]\displaystyle \frac{28}{100} \times 58[/tex]
[tex]\sf Multiply.[/tex]
[tex]\displaystyle \frac{1624}{100} =16.24[/tex]
look at the image below
Answer:
16
Step-by-step explanation:
volume= Length x width x height
Answer:
Volume: [tex]1/3\times Area\; of\; base\;\times height[/tex]
[tex]= 1/3\times2\times 2\times 4[/tex]
[tex]=16/3\; ft^{3}[/tex]
[tex]=5.3\; ft^{3}[/tex]
OAmalOHopeO
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.