Answer: 107.67°C
Step-by-step explanation:
I guess that we could do a Taylor expansion around the point (2, 1)
Remember that a Taylor expansion around the point (a, b) is:
[tex]T(x,y) = T(a, b) + \frac{dT(a,b)}{dx}(x - a) + \frac{dT(a,b)}{dy}(y - b) + .....[/tex]
Where the latter terms need higher orders of the derivates of T, so we can not find them, regardless of that, this expansion will be accurate near the point (a, b),
Then, using this, we can write our expanssion as:
T(x,y) = 107 + 9*(x - 2) - 8*(y - 1)
Now we evaluate this in x = 2.03 and y = 0.95
T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8*(0.95 - 1) = 107.67
Then a good estimation of the temperature at the point (2.03,0.95) is 107.67°C
The estimate of the temperature of the unevenly heated metal plate at temperature at the point (2.03,0.95) is;
T(2.03, 0.95) = 107.67 °C
Formula for taylor expansion around a point (a, b) is given as;
T(x, y) = T(a,b) + [tex]\frac{dT(a,b)}{dx}[/tex](x - a) + [tex]\frac{dT(a,b)}{dy}[/tex](y - b) + ....
We are given;
T(2,1) = 107
T'x(2,1) = [tex]\frac{dT(a,b)}{dx}[/tex] = 9
T'y(2,1) = [tex]\frac{dT(a,b)}{dy}[/tex] = −8
Plugging in the relevant values into our taylor expansion above gives;
T(x, y) = 107 + 9(x - 2) - 8(y - 1)
Now, we want to estimate the temperature at the point (2.03, 0.95).
Thus, we will plug in x = 2.03 and y = 0.95 to get;
T(2.03, 0.95) = 107 + 9(2.03 - 2) - 8(0.95 - 1)
T(2.03, 0.95) = 107 + 0.27 + 0.4
T(2.03, 0.95) = 107.67 °C
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Which functions have an axis of symmetry of x = -2? Check all that apply. A. f(x) = x^2 + 4x + 3 B. f(x) = x^2 - 4x - 5 C. f(x) = x^2 + 6x + 2 D. f(x) = -2x^2 - 8x + 1 E. f(x) = -2x^2 + 8x - 2
Answer:
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Step-by-step explanation:
The axis of symmetry is found by h = -b/2a where ax^2 +bx +c
A. f(x) = x^2 + 4x + 3
h = -4/2*1 = -2 x=-2
B. f(x) = x^2 - 4x - 5
h = - -4/2*1 = 4/2 =2 x=2 not -2
C. f(x) = x^2 + 6x + 2
h = -6/2*1 = -3/2 = x=-3/2 not -2
D. f(x) = -2x^2 - 8x + 1
h = - -8/2*-2 = 8/-4 =-2 x=-2
E. f(x) = -2x^2 + 8x - 2
h = - 8/2*-2 = -8/-4 =2 x=2 not -2
Answer:
Hey there! The answer to this question is
A. f(x) = x^2 + 4x + 3
D. f(x) = -2x^2 - 8x + 1
Please answer this correctly
Please help me !!!!!
Answer:
11.5
Step-by-step explanation:
Put the numbers in order from smallest to largest
2,2,6,9,9,11,11,12,32,43,46,54,54,59
The median is the middle number
There are 14 numbers so the middle is between 7 and 8
2,2,6,9,9,11,11, 12,32,43,46,54,54,59
Take the average of the 7th and 8th numbers
(11+12)/2 = 11.5
The median is 11.5
Answer: 11.5
Step-by-step explanation:
The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.
Ordering the data from least to greatest, we get:
2 2 6 9 9 11 11 12 32 43 46 54 54 59
As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:
Median= 11+12/2=11.5
Determine the sum of the arithmetic series 6 + 11 + 16 +......
91.
Answer:
873
Step-by-step explanation:
so the equation is: 5x+1
sum is:
[tex] \frac{first \: one \: + \: last \: one}{2} \times quantity \: of \: terms \\ [/tex]
we have 6( 5×1+1) to 91 (5×18+1)
so we have 18 terms
then:
[tex] \frac{91 + 6}{2} \times 18 = 873[/tex]
Please answer this correctly
Assuming the coin is not weighted and is a fair and standard coin - the chance of flipping head is 1/2. You can either flip head or tails, there are no other possible outcomes.
Solve of the following equations for x: x + 3 = 6
Answer:
X = 3Step-by-step explanation:
[tex]x + 3 = 6[/tex]
Move constant to R.H.S and change its sign:
[tex]x = 6 - 3[/tex]
Calculate the difference
[tex]x = 3[/tex]
Hope this helps...
Good luck on your assignment..
Add the two rational expressions: (x/x+1)+(2/x)
6th grade math, help me please :)
Answer:
(14,4) (21, 6) (28,8) If they had six losses, they would have 21 wins
Step-by-step explanation:
According to the information given, for every 7 wins, they lose 2 games. That means in order to finish the table, we have to find multiples of 7 and 2. If they won 14 games, they would have 4 losses. This is because since 14 is twice the value of 7, they would have lost twice the number of games.
The next would be 21 wins since 7x3 is 21 and 6 losses since 2x3 is 6
The last one would be 28 wins (7x4) and 8 losses (2x4)
If they had six losses, they would have 21 wins
Please answer this correctly
Answer:
1/8
Step-by-step explanation:
Total cards = 8
Card with 4 = 1
P(4) = 1/8
which set of fractions is ordered from least to greatest 7/8 5/11 2/3
Answer:
5/11, 2/3, 7/8
Step-by-step explanation:
you can just do the numerator divided by the denominator to get a decimal, which can help you rank the fractions easier. hope this helps
Calculate sales tax using the following information: Taxable amount of the sale: $ 142 Sales tax percentage: 7 % What is the amount of the sales tax? Round the answer to the nearest cent (hundredths).
Answer:
Step-by-step explanation:
142(.07)= 9.94 amount of the sales tax
$142+9.94= $151.94
the linear equation y=2x represents the cost y of x pounds of pears. which order pair lies on the graph of the equation? A. (2,4) B. (1,0) C.(10,5) D. (4,12)
Answer:
A. (2, 4)
Step-by-step explanation:
The ordered pairs represent (x, y). Since you have y =2x, this is the same as ...
(x, 2x)
That is, the second number in the pair needs to be twice the first number in the pair. Since you know your times tables, you know that this is not the case for (1, 0), (10, 5) or (4, 12). Those values of x would give (1, 2), (10, 20), (4, 8).
It is the case that you have (x, 2x) for (2, 4).
The point (2, 4) lies on the graph of y = 2x.
Betty can mow a lawn in 60 minutes. Melissa can mow the same lawn in 30 minutes. How long does it take for both Betty and Melissa to mow the lawn if they are working together? Express your answer as a reduced fraction.
Answer:
20 minutes
Step-by-step explanation:
Melissa works as fast as two Bettys, so working together, they get the job done at the rate 3 Bettys could do it. That time is (60 minutes)/3 = 20 minutes.
Working together, Betty and Melissa can mow the lawn in 20 minutes.
_____
You can also think in terms of mowing rates as lawns per minute. The total mowing rate is ...
Betty's rate + Melissa's rate = (1/60 lawns/min) +(1/30 lawns/min)
= (1/60 +2/60) lawns/min = 1/20 lawns/min
The inverse rate is then ...
20/1 min/lawn
Together, they take 20 minutes to mow 1 lawn.
A boat that can travel 18 mph in still water can travel 21 miles downstream in the same amount of time that it can travel 15 miles upstream. Find the speed (in mph) of the current in the river.
Hey there! I'm happy to help!
We see that if the river isn't moving at all the boat can move at 18 mph (most likely because it has an engine propelling it.)
We want to set up a proportion where our 21 miles downstream time is equal to our 15 miles upstream time so we can find the speed. A proportion is basically showing that two ratios are equal. Since our downstream distance and upstream distance can be done in the same amount of time, we will write it as a proportion.
We want to find the speed of the river. We will use r to represent the speed of the river. When going downstream, the boat will go faster, so it will have a higher mph. So, our speed going down is 18+r. When you are going upstream, it's the opposite, so it will be 18-r.
[tex]\frac{distance}{speed} =\frac{21}{18+r} = \frac{15}{18-r}[/tex]
So, how do we figure out what r is now? Well, one nice thing to know about proportions is that the product of the items diagonal from each other equals the product of the other items. Basically, that means that 15(18+r) is equal to 21(18-r). This is a very nice trick to solve proportions quickly. We see that we have made an equation and now we can solve it!
15(18+r)=21(18-r)
We use the distributive property to undo the parentheses.
270+15r=378-21r
We subtract 270 from both sides.
15r=108-21
We add 21 to both sides.
36r=108
We divide both sides by 36.
r=3
Therefore, the speed of the river is 3 mph.
You also could have noticed that 18mph to 21 mph is +3, and 18mph to 15 mph -3 in -3 mph, so the speed of the river is 3 mph. That would have been a quicker way to solve it XD!
Have a wonderful day!
Write an equation that represents the relationship.Please help!
Answer:
n = r - 2.5
Step-by-step explanation:
We have the following data:
7 4.5
8 5.5
10 7.5
12 9.5
Now, what we will do is what happens if we subtract each one:
7 - 4.5 = 2.5
8 - 5.5 = 2.5
10 - 7.5 = 2.5
12 - 9.5 = 2.5
The difference is always kept constant, therefore the equation would be:
n = r - 2.5
I need help asap I don't understand this
Answer:
[tex]\boxed{\sf \ \ \ a=-2, \ b = 1 \ \ \ }[/tex]
Step-by-step explanation:
Hello,
saying that the function is continuous means that you cannot have a "jump" in the graph of the function
so we want
a*(-3)+b=7 and a*4+b=-7
it comes
(1) -3a + b = 7
(2) 4a + b = -7
(2)-(1) gives 4a + b + 3a - b =7a = -7-7 = -14
so a = -14/7 = -2
we replace in (1)
b = 7 + 3*(-2) = 7 - 6 = 1
hope this helps
A line with points (-4.0) and (-3.1)
has a slope of?
Slope is the change in y over the change in x
Slope = (1-0) /( -3 - -4)
Slope = 1/1
Slope = 1
What is the value of x?
Answer:
x=98°
Step-by-step explanation:
The angles of a triangle must equal 180°.
To get the third angle (G) you must do: 180°-53°-45°
That will give you 82°
Anglr G and angle x create a straight line which is 180°.
so to get the answer you must do 180°-G=x
180°-82°=98°
Therefore x=98°
Suppose you are looking for a house to purchase, and have a maximum price you can afford. To help decide which neighborhoods to shop for a home in, which is most useful to you?a. the mean house priceb. the median house pricec. the mode house priced. the SD of the house pricee. the range of the house price
Answer:
Mean
Step-by-step explanation:
-Mean is the average calculated by adding up all the prices and dividing them by the number of prices.
-Median is the middle value in the group of prices after they are organized from the lowest to the highest.
-Mode is the price that is repeated more frequently in the data set.
-SD refers to the quantity of variation between the prices.
-The range is the difference between the highest and the lowest price.
According to this, the answer is that the most option is the mean house price because it indicates the center of the values and it allows to get an overall idea of the prices which would allow you to have a clear view about the neighborhoods where you can shop for a home in.
The other options are not right because the median would indicate the middle value and the mode the most repeated value but they don't necessarily provide an exact image of the prices as for example, the most repeated value does not necessarily reflects the values of all the houses in the neighborhood. Also, SD calculates the variation and the range calculates the difference between prices which doesn't provide a clear picture about the neighborhoods where you can afford a house.
An article reported that for a sample of 52 kitchens with gas cooking appliances monitored during a one-week period, the sample mean CO2 level (ppm) was 654.16, and the sample standard deviation was 165.4.
Required:
a. Calculate and interpret a 9596 (two-sided) confidence interval for true average C02 level in the population of all homes from which the sample was selected.
b. Suppose the investigators had made a rough guess of 175 for the value of s before collecting data. What sample size would be necessary to obtain an interval width of 50 ppm for a confidence level of 95%?
Answer:
a) [tex]654.16-2.01\frac{165.4}{\sqrt{52}}=608.06[/tex]
[tex]654.16+2.01\frac{165.4}{\sqrt{52}}=700.26[/tex]
b) [tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
So the answer for this case would be n=189 rounded up to the nearest integer
Step-by-step explanation:
Part a
[tex]\bar X=654.16[/tex] represent the sample mean
[tex]\mu[/tex] population mean (variable of interest)
s=165.4 represent the sample standard deviation
n =52represent the sample size
The confidence interval for the mean is given by the following formula:
[tex]\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (1)
The degrees of freedom aregiven by:
[tex]df=n-1=52-1=51[/tex]
Since the Confidence is 0.95 or 95%, the significance [tex]\alpha=0.05[/tex] and [tex]\alpha/2 =0.025[/tex], and the critical value would be [tex]t_{\alpha/2}=2.01[/tex]
Now we have everything in order to replace into formula (1):
[tex]654.16-2.01\frac{165.4}{\sqrt{52}}=608.06[/tex]
[tex]654.16+2.01\frac{165.4}{\sqrt{52}}=700.26[/tex]
Part b
The margin of error is given by this formula:
[tex] ME=z_{\alpha/2}\frac{s}{\sqrt{n}}[/tex] (a)
And on this case we have that ME =25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:
[tex]n=(\frac{z_{\alpha/2} s}{ME})^2[/tex] (b)
The critical value for this case wuld be [tex]z_{\alpha/2}=1.960[/tex], replacing into formula (b) we got:
[tex]n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189[/tex]
So the answer for this case would be n=189 rounded up to the nearest integer
i need help please!!!
Answer:
1 = 95
2 = 77
3 = 85
4 = 103
Step-by-step explanation:
Inscribed angles are half their arc that their 2 lines intersect.
Select the correct answer from each drop-down menu.
The given equation has been solved in the table.
Answer: a) additive inverse (addition)
b) multiplicative inverse (division)
Step-by-step explanation:
Step 2: 6 is being added to both sides
Step 4: (3/4) is being divided from both sides
It is difficult to know what options are provided in the drop-down menu without seeing them. If I was to complete a proof and justify each step, then the following justifications would be used:
Step 2: Addition Property of Equality
Step 4: Division Property of Equality
The life of light bulbs is distributed normally. The standard deviation of the lifetime is 25 hours and the mean lifetime of a bulb is 510 hours. Find the probability of a bulb lasting for at most 552 hours.
Answer:
The probability of a bulb lasting for at most 552 hours.
P(x>552) = 0.0515
Step-by-step explanation:
Step(i):-
Given mean of the life time of a bulb = 510 hours
Standard deviation of the lifetime of a bulb = 25 hours
Let 'X' be the random variable in normal distribution
Let 'x' = 552
[tex]Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628[/tex]
Step(ii):-
The probability of a bulb lasting for at most 552 hours.
P(x>552) = P(Z>1.63)
= 1- P( Z< 1.63)
= 1 - ( 0.5 + A(1.63)
= 1- 0.5 - A(1.63)
= 0.5 -A(1.63)
= 0.5 -0.4485
= 0.0515
Conclusion:-
The probability of a bulb lasting for at most 552 hours.
P(x>552) = 0.0515
What is the volume of this aquarium?
Answer:
4,224 in ^3
Step-by-step explanation:
5184-960 (subtract the cut-out from the entire shape)
me Left:1:23:57
Mandeep Sharma: Attempt 1
Question 1 (2 points)
A scientist records the internal temperature of a kiln that has been turned off for maintenance after
a limestone calcination reaction as 794 °C. He then leaves the room to allow the kiln cool further.
The room temperature is 25°C. An equation that models the temperature of the cooling kiln (T in °C,
t in min) is as follows:
T(t) = 1.0.73l/3.7 + 25
How fast is the reaction cooling rate (%T lost/min) to the nearest whole number?
Your Answer:
Answer
Answer:
c and I will talk to you later today or tomorrow morning and then I will
Step-by-step explanation:
email to you later today to see you and the kids are doing well and that you
Identify which quadrant of the coordinate plane the point (−3, 15) lies in.
Answer:
Quadrant II.
Step-by-step explanation:
Quadrant | has positive x and y coordinates.
Quadrant || has negative x and positive y coordinates.
Quadrant ||| has negative x and y coordinates.
Quadrant |V has positive x and negative y coordinates.
Since -3 is negative and 15 is positive, the answer is Quadrant II.
Express it in slope-intercept form
Answer:
Step-by-step explanation:
Can u help me
Answer:
cant see the picture
Step-by-step explanation:
In 1998, the average price for bananas was 51 cents per pound. In 2003, the following 7 sample prices (in cents) were obtained from local markets:
50, 53, 55, 43, 50, 47, 58.
Is there significant evidence to suggest that the average retail price of bananas is different than 51 cents per pound? Test at the 5% significance level.
Answer:
[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]
The degrees of freedom are given by:
[tex]df=n-1=7-1=6[/tex]
The p value for this case would be given:
[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]
The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51
Step-by-step explanation:
Info given
50, 53, 55, 43, 50, 47, 58.
We can calculate the sample mean and deviation with this formula:
[tex]\bar X=\frac{\sum_{i=1}^n X_i}{n}[/tex]
[tex]s=\sqrt{\frac{\sum_{i=1}^n (X_i -\bar X)^2)}{n-1}}[/tex]
represent the mean height for the sample
[tex]s=5.014[/tex] represent the sample standard deviation for the sample
[tex]n=7[/tex] sample size
represent the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level for the hypothesis test.
t would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value
Hypothesis to test
We want to test if the true mean is equal to 51, the system of hypothesis would be:
Null hypothesis:[tex]\mu = 51[/tex]
Alternative hypothesis:[tex]\mu \neq 51[/tex]
The statistic is given by:
[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex] (1)
Replacing we got:
[tex]t=\frac{50.857-51}{\frac{5.014}{\sqrt{7}}}=-0.075[/tex]
The degrees of freedom are given by:
[tex]df=n-1=7-1=6[/tex]
The p value for this case would be given:
[tex]p_v = 2*P(t_6 <-0.075)=0.943[/tex]
The p value for this case is lower than the significance level so then we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly different from 51
given that 3*6=12 and 2*5=9, then a*b may be defined as
Answer:
I noticed a pattern:
3 * 2 + 6 = 12 and 2 * 2 + 5 = 9
This means that a*b = 2a + b.
What is the value of the angle marked with xxx?
Answer:
Here you go!! :)
Step-by-step explanation:
Given that the sides of the quadrilateral are 3.3
The measure of one angle is 116°
We need to determine the value of x.
Value of x:
Since, the given quadrilateral is a rhombus because it has all four sides equal.
We know the property that the opposite sides of the rhombus are equal.
The measure of the opposite angle is 116°
x = measure of opposite angle
x = 116°
Then, the value of x is 116°
Therefore, the value of x is 116°
Answer:
In the diagram, the measurement of x is 87°
Step-by-step explanation:
In this diagram, this shape is a quadrilateral. This quadrilateral in this picture is known as rhombus. In a rhombus, the consecutive angles are supplementary meaning they have a sum of 180°. Consecutive means the angles are beside each other. So, we will subtract 93 from 180 to find the value of x.
180 - 93 = 87
The measurement of x is 87°