Answer:
i think the 2nd one
Step-by-step explanation:
Answer:
y = x+40
Step-by-step explanation:
First, calculate the rate of the rate by using the slope formula, \(m = \frac{y_1-y_2}{x_1-x_2}\).
m = (50-47)/(10-7) = 3/3 = 1
Now plug m = 1 into the slope-intercept form, y = mx+b. Also plugin y = 42 and x = 2 in other to find the y-intercept (b).
42 = 1(2)+b
42-2 = b
b = 40
Replace b with 40 in the slope-intercept formula.
y = x+40
Please answer number 19 please I beg you!
Answer:
147,000,000
Step-by-step explanation:
152,000,000+147,000,000=299,000,000
Step-by-step explanation:
299,000,000-152,000,000=Male
Male=147,000,000
=1.47×10'8
In the month of March the Digby Corporation received and delivered orders of 152,000 units at a price of $15.00 for revenue of $2.280mil for their product Dixie. Digby uses the accrual method of accounting and offers 30 day credit terms. By the end of May Digby had collected payments of $2.280mil for the March deliveries. How much of the collected $2.280mil should Digby show on the March 31st income statement and how much on the May 31st income statement?
Select 1:
A) $2.280mil in March;
$0 in May
B) $1.140mil in March;
$1.140mil in May
C) $0.752mil in March;
$1.528mil in May
D) $0 in March;
$2.280mil in May
Digby Corporation should show $0 on the March 31st income statement and $2.280 million on the May 31st income statement.
Digby Corporation uses the accrual method of accounting, which means revenue is recognized when it is earned, regardless of when the payment is received. In this case, the revenue of $2.280 million was earned in March when the deliveries were made, even though the payments were collected later.
On the March 31st income statement, Digby should not show any of the collected $2.280 million since the payments were not received by that date. The income statement for March will only reflect the revenue earned and any expenses incurred during that month.
On the May 31st income statement, Digby should show the full $2.280 million as revenue since the payments were collected by that date. The income statement for May will reflect the revenue earned in March, as well as any additional revenue and expenses for the month of May.
Therefore, the correct answer is:
D) $0 in March;
$2.280 million in May.
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1 point
6. At five below there is a discount of $5 for every 4 items you buy. If the
receipt show discount of $20 how many items did you buy?*
HINT: This problem is similar to #6, page 90
O A You bought 20 items
B You bought 15 items
C You bought 16 itmes
D You bought 8 items
c. 5x4=20
4x4=16 items.
In the following diagram triangle ABC is drawn, with A(-7,-4), B(8,2) and C(-6,8).(a) determine the slope of line AB in simplest form.(b) draw the line that passes through C and is perpendicular to line AB. Write it's equation in point-slope form (c) If point D lies at the intersection of line AB with the line you drew in (b), mark D and state its coordinates.(d) what kinds of triangles are triangle CBD and CAD? Why)
Given are the points of the vertices of the triangle.
A ( -4 , -7 )
B ( 8, 2 )
C ( -6, 8 )
Required:
a) slope of line AB
b) equation of the line that passes through C and is perpedicular to AB
c) coordinates of D which is the intersection of AB and the line that passes through C
d) the kind of triangle CBD and CAD
Solution :
a) slope of line AB
A ( -4 , -7 )
B ( 8, 2 )
\(\text{slope = }\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-7)}{8-\text{ (-4)}}=\frac{9}{12}=\frac{3}{4}\)b) equation of the line that passes through C and is perpedicular to AB.
The slopes of two perpendicular lines are negative reciprocals of each other. Therefore, the slope of the line that passes through C ( -6, 8 ) is
\(\text{slope}=-\frac{4}{3}\)The point-slope form of a line is :
\(y-y_1=m(x-x_1)\)where m is the slope = -4/3
at point C ( -6, 8)
\(\begin{gathered} y-8\text{ = -}\frac{4}{3}(x-(-6)) \\ y-8=-\frac{4}{3}(x+6) \end{gathered}\)c) coordinates of D which is the intersection of AB and the line that passes through C
Equation of line AB : Let's take point A ( -4 , -7 ) and slope is 3/4 . Using the point intercept form:
\(\begin{gathered} y-(-7)\text{ = }\frac{3}{4}(x-(-4)) \\ y+7=\frac{3}{4}(x+4) \\ 4\cdot\lbrack y+7\text{ = }\frac{3}{4}(x+4)\rbrack\cdot4 \\ y+28=3(x+4) \\ y+28=3x+12 \\ 3x-y-16=0 \end{gathered}\)Equation of the line that passes through C:
\(\begin{gathered} y-8=-\frac{4}{3}(x+6) \\ 3\cdot\lbrack y-8=-\frac{4}{3}(x+6)\rbrack\cdot3 \\ y-24=-4(x+6) \\ y-24=-4x+24 \\ 4x+y-48=0 \end{gathered}\)The point of intersection of line
\(\begin{gathered} a_1x+b_1y+c_1=0\text{ } \\ \text{and} \\ a_2x+b_2y+c_2=0\text{ } \\ is \\ (x,y)=\lbrack\frac{b_1c_2-b_2c_1}{a_1_{}b_2-a_2b_1},\frac{a_2c_1-a_1_{}c_2}{a_1b_2-a_2b_1}\rbrack \end{gathered}\)\(\begin{gathered} AB\text{ : }3x-y-16=0\text{ } \\ a_1=3 \\ b_1=-1 \\ c_1=-16 \end{gathered}\)\(\begin{gathered} C\colon\text{ }4x+y-48=0 \\ a_2=4 \\ b_2=1 \\ c_2=-48 \end{gathered}\)The point of intersection, D:
\(\begin{gathered} D(x,y)=\lbrack\frac{b_1c_2-b_2c_1}{a_1b_2-a_2b_1},\frac{a_2c_1-a_1c_2}{a_1b_2-a_2b_1}\rbrack \\ D(x,y)=\lbrack\frac{(-1)(-48)-(1)(-16)}{(3)(1)-(4)(-1)},\frac{(4)(-16)-(3)(-48)}{(3)(1)-(4)(-1)}\rbrack \\ D(x\mathrm{}y)=\lbrack\frac{48+16}{3+4},\frac{-64_{}+144}{3+4}\rbrack=\lbrack\frac{64}{7},\frac{80}{7}\rbrack \\ D(xy)=D(\frac{64}{7},\frac{80}{7}) \end{gathered}\)d) the kind of triangle CBD and CAD
Both triangles are right triangle , since sline CD is perpendicular to line AB
If noah eats 1/3 of an apple in 1/6 mintues how much willi it take to eat a full apple.
Answer:
30 Minutes
Step-by-step explanation:
1/6 = 10 minutes
so if he eats a third every ten minutes then it will take him 30 minutes
Find the volumes of the pyramid and triangular pyramid.
Answer:
1) Volume of triangular pyramid = 33 cm³.
2) Volume of triangular prism = 99 cm³
Step-by-step explanation:
1) Volume of a triangular pyramid is given as;
V_py = ⅓Ah
Where A is area of base and h is height
We see from the diagram that;
A = 11 cm²
h = 9 cm
Thus; V_py = ⅓ × 11 × 9 = 33 cm³
2) Volume of triangular prism is given by;
V_pr = ½bhl
Where;
½bh is area of triangular cross section
l is length
We see from the diagram that ½bh = 11 cm² and L = 9 cm
Thus;
V_pr = 11 × 9 = 99 cm³
HELPPP
Verify that csc theta cos theta tan theta=1
Answer:
See Explanation
Step-by-step explanation:
\( \csc \theta \: \cos \theta \: \tan \theta = 1 \\ \\ LHS = \csc \theta \: \cos \theta \: \tan \theta \: \\ \\ = \frac{1}{ \sin \theta} \: \times \cancel{ \cos \theta }\: \times \frac{ \sin \theta}{ \cancel{ \cos \theta }} \\ \\ = \frac{1}{ \cancel{ \sin \theta}} \: \times \cancel{ \sin \theta} \\ \\ = 1 \\ \\ = RHS \\ \\ hence \: proved\)
Answer:
a) Only the first one is an identity.
Step-by-step explanation:
1). 8 cos O tan O csc O = 8 simplifies to:
cos O tan O csc O = 1
cos O * (sin O / cos O) * (1 /sin O)
= cos O sin O / cos O sin O
= 1
So it is identity.
2) 13 sec^2 O/ cos^2 O - tan^2 O / cos^2O
= 13 sec^2 O - tan^2 O / cos^2 O
Now sec^2 O = 1 + tan^2 O, so we have:
(13( 1 + tan^2 O) - tan^2 O) / cos^2 O
= (12 tan^2 O + 13) / cos^2 O
This is not always = 2 so its not an identity.
Step-by-step explanation:
The spinner above is used in a game. What is the theoretical probability of the given event with one spin?
P(a multiple of 3)
a.
Three-fourths
c.
StartFraction 3 Over 8 EndFraction
b.
One-fourth
d.
0
Please select the best answer from the choices provided
The correct answer is option d. The theoretical Probability of spinning a multiple of 3 with one spin is 0.
The theoretical probability of an event, we need to identify the number of favorable outcomes (the desired event) and the total number of possible outcomes.
In this case, the event is spinning a multiple of 3 on the spinner. Let's examine the possible outcomes and identify the favorable outcomes:
Possible outcomes on the spinner: {1, 2, 3, 4, 5, 6}
Favorable outcomes (multiples of 3): {3, 6}
The total number of possible outcomes is 6, and the number of favorable outcomes is 2.
The theoretical probability of spinning a multiple of 3 can be calculated as:
P(multiple of 3) = (Number of favorable outcomes) / (Total number of possible outcomes)
P(multiple of 3) = 2 / 6
Simplifying the fraction, we get:
P(multiple of 3) = 1 / 3
Therefore, the correct answer is option d. The theoretical probability of spinning a multiple of 3 with one spin is 0.
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The probability that a house in an urban area will be burglarized is 15%. If 30 houses are randomly selected, what is the mean of the number of houses burglarized?
The mean of the number of houses burglarized in this sample is 4.5 based on probability.
The probability of a house in an urban area being burglarized is 15%. This means that out of every 100 houses, 15 will be burglarized.
If 30 houses are randomly selected, we can use the binomial distribution to find the mean number of houses burglarized. The formula for the mean of a binomial distribution is:
Mean = n * p
where n is the number of trials (in this case, 30) and p is the probability of success (in this case, 0.15).
Substituting these values, we get:
Mean = 30 * 0.15
Mean = 4.5
Therefore, the mean number of houses burglarized out of 30 randomly selected houses is 4.5. Note that this is an expected value and may not represent the actual number of houses burglarized in any particular sample of 30 houses.
To find the mean of the number of houses burglarized, we can use the formula:
Mean = (Probability of success) x (Number of trials)
In this case:
- Probability of success (a house being burglarized) is 15%, or 0.15 as a decimal.
- Number of trials (randomly selected houses) is 30.
Using the formula, we get:
Mean = (0.15) x (30) = 4.5
So, the mean of the number of houses burglarized in this sample is 4.5.
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Simplify the expression: (9t+5)+(3t-6) HELPPPP
Answer:
12t - 1
Step-by-step explanation:
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!5
Answer:
C
Step-by-step explanation:
I may be wrong...
Sooo sorry if I am
Nora s a race car driver. during a race the first pit stop took 8.352 seconds and the second pit stop took 8.025 seconds. how much faster was the second pit stop
The second pit stop was 0.327 seconds faster than the first pit stop which is the difference between both time
What is the Subtraction operation?
Subtraction is a mathematical operation that deducts the right-hand operand from the left-hand operand.
for example 4 -2 = 2
We have been given that during a race the first pit stop took 8.352 seconds and the second pit stop took 8.025 seconds.
To determine how much faster the second pit stop.
We need to calculate the difference between the first pit stop and the second pit stop of time.
the difference = Time of first pit stop - Time of second pit stop
the difference = 8.352 - 8.025
the difference = 0.327 second
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What is 7/8 pound divided by 1/4 pound?
Answer:
3.5 pounds
Step-by-step explanation:
7/8 / 1/4 =7/8*4=7/2=3.5
A right cylindrical container
can hold 64T cubic meters of
liquid when full. The height
of the container is 4 meters.
What is the radius, r, of the
container in meters?
4 m
The radius of the container is approximately 7.98 meters. The container can hold 64T cubic meters of liquid when full, which means that:
V = 64T
We are also given that the height of the container is 4 meters, which means that: h = 4
Substituting these values into the formula, we get:
64T = πr^2(4)
Simplifying the equation, we get:
16T = πr^2
Dividing both sides by π, we get:
r^2 = (16T)/π
Taking the square root of both sides, we get:
r = √((16T)/π)
Now we just need to substitute the given value of T to find the radius:
r = √((16 x 1000)/π)
r ≈ 7.98 meters
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can y’all help me please
Answer:
it would be 3rd one
Step-by-step explanation:
(2a)3 = (8a)3
(4b)3=64b3
simplify= (8ab)3
HELP! brainliest will be given
Answer:
A
Step-by-step explanation:
y = 2x
inverse is found:
x = 2y
y = x/2
Those are not the same
Find the average value of the function f(x) = (x + 2) on the interval [0, 3].
The average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
Calculate the definite integral of the function over the interval [a, b], then divide it by the interval's length (b - a), in order to determine the average value of a function f(x) over the interval.
Given that the interval is [0, 3] and the function f(x) = (x + 2), we have:
= (1/3) × [1/2 x² + 2x] evaluated from x=0 to x=3
= (1/3) × [(1/2 × 3² + 2×3) - (1/20² + 20)]
= (1/3) × [(9/2 + 6) - 0]
= (1/3) × (21/2)
= 7/2
Therefore, the average value of the function f(x) = (x + 2) on the interval [0, 3] is 7/2.
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Let R(x)=3x3+2x2+x and S(x)=4x2+1. Find R(x)+S(x).
The function R(x) + S(x) exists given by \(3x^3+6x^2+x+1\).
What is a function?An expression, rule, or law that describes a relationship between one variable (independent variable) and another variable (dependent variable) exists named a function.
Let the functions be \(R(x)=3x^3+2x^2+x\) and \(S(x)=4x^2+1.\)
Adding both of the equations, we get
\($R(x)+S(x)=(3x^3+2x^2+x) +(4x^2+1)\)
simplifying both of the equations we get
\($R(x)+S(x)=3x^3+2x^2+x+4x^2+1\)
\(=3x^3+6x^2+x+1\)
Therefore, the function R(x) + S(x) exists given by \(3x^3+6x^2+x+1\).
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Shirley, a recent college graduate, excitedly described to her older sister the $1,800 sofa, table, and chairs she found today. However, when asked she could not tell her sister which interest calculation method was to be used on her credit-based purchase. Calculate Zhe monthly payments and total cost for a bank loan assuming a one-year repayment period and 13.5 percent interest. Now, assume the store uses the add-on method of interest calculation. Calculate the monthly payment and total cost with a one-year repayment period and 11.5 percent interest. Using the information above, how much interest will Shirley "save" or be rebated if she can repay the loans after six months? Click on the table icon to view the MILPF table For a bank loan assuming a one-year repayment period and 13.5% interest, the monthly payment is $ (Round to the nearest cent.)
The monthly payment for a bank loan assuming a one-year repayment period and 13.5% interest is To calculate the monthly payment for a bank loan, we can use the formula:
Monthly payment = Total cost / Number of months
Given that the total cost is $1,800 and the repayment period is one year (12 months), we can substitute these values into the formula:
Monthly payment = $1,800 / 12 = $
Now, let's calculate the total cost for the bank loan:
Total cost = Monthly payment * Number of months
Total cost = $ * 12 = $
For the add-on method of interest calculation with a one-year repayment period and 11.5% interest, the monthly payment is $ (main answer).
The add-on method of interest calculation involves adding the interest to the principal amount and then dividing it by the number of months.
Given that the total cost is $1,800 and the repayment period is one year (12 months), we can calculate the interest as follows:
Interest = Total cost * Interest rate
Interest = $1,800 * 11.5% = $
Now, let's calculate the new principal amount:
New principal amount = Total cost + Interest
New principal amount = $1,800 + $ = $
Finally, we can calculate the monthly payment:
Monthly payment = New principal amount / Number of months
Monthly payment = $ / 12 = $
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What is the distance between -3 and 12?
Answer:
-15
Step-by-step explanation:
The required solution is 15.
It is required to find the solution.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
By the distance formula we get,
Distance between -3 and 12 is
=12-(-3)
=15
Therefore, the required solution is 15.
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Dave is driving from Portola Ave. To Springs Street. Portola Ave. Is marked as "A" and Springs Street is marked as "E".
He takes 3 miles to go to the ice store. (C)
He drives back to Portola Ave. Where his house is.
From A to C is 6 miles
After a few hours he drives to the market (D)
he spends 25 minutes there and drives back home which is 24 miles.
He stops by a gas station (B) when he goes back home. He takes 10 minutes there.
Then when he’s home, he packs items which takes 55 minutes.
Then he drives to springs street (E)
This takes 40 miles.
He realized that he forgot something at the market, so he drives back to the market which is 5 miles away.
Then he drives back to Springs Street
After he enters the airport (E) he takes 25 minutes to have his luggage checked and boards the plane. Then the plane immediately takes off.
It is 12:45pm when Dave is about to go the ice store.
When he rests for a few hours after coming back from ice store he rests for 2 hours.
What time does the plane take off?
When he rests for a few hours after coming back from ice-store he rests for 2 hours the time the plane takes off is 9:10 pm.
Total distance traveled is 151 miles.
Dave spends 25 + 10 + 55 + 25 = 115 minutes (or 1 hour and 55 minutes) on stops.
Dave rests for 2 hours.
To calculate the time the plane takes off, we need to add up all the time Dave spends on driving, stops, and rests, and then add that time to the time he starts (12:45 pm).
Time to drive from A to C and back to A: 2 * 6 / 60 = 0.2 hours
Time to drive from A to C to D to B to A: (6 + 24 + 24 + 3) / 60 = 0.95 hours
Time to drive from A to C to D to home to E to market to E: (6 + 24 + 24 + 40 + 5 + 5) / 60 = 2.33 hours
Time to rest: 2 hours
Total time spent: 0.2 + 0.95 + 2.33 + 1.92 = 5.4 hours
Time of departure: 12:45 pm + 5.4 hours = 6:25 pm
Adding 45 minutes for the luggage check and boarding, the plane takes off at 6:25 pm + 0.45 hours = 7:10 pm
Adding another 2 hours for the time zone difference, the plane takes off at 7:10 pm + 2 hours = 9:10 pm.
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Which of the following is a distinguishing characteristic of a Keynesian cross diagram?
A. real GDP on the horizontal axis
B. a flat line
C. 45-degree line
D. several different Phillips curves
Answer:
45 degree line
Step-by-step explanation:
A distinguishing characteristic of a Keynesian cross diagram is the 45-degree line.
The Keynesian cross diagram is a simple graphical representation of the relationship between aggregate expenditure and real GDP in an economy. It shows the equilibrium level of real GDP where aggregate expenditure equals real GDP, and helps to illustrate the effects of changes in aggregate expenditure or other factors on the economy.
The 45-degree line in the Keynesian cross diagram represents the level of real GDP where aggregate expenditure equals real GDP, or where there is equilibrium in the economy. Points below the 45-degree line indicate that aggregate expenditure is less than real GDP, while points above the 45-degree line indicate that aggregate expenditure is greater than real GDP. The slope of the aggregate expenditure function determines the sensitivity of real GDP to changes in aggregate expenditure.
chris has been given a list of bands and asked to place a vote. his vote must have the names of his favorite and second favorite bands from the list. how many different votes are possible?
There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.
To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.
Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.
Therefore, the number of different votes possible is m * (m-1) / 2.
In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.
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SET AT 100 POINTS AND BRAINLIEST PERIMETER ON A CORDINENTAL PLANE
A student has a rectangular bedroom. If listed as ordered pairs, the corners of the bedroom are (18, 25), (18, −11), (−19, 25), and (−19, −11). What is the perimeter in feet?
73 feet
146 feet
36 feet
37 feet
Answer:
146 feet is the correct option
Answer: 146
Step-by-step explanation:
just filling in so you can give other brainliest
it can be shown that y1=e3x and y2=e−7x are solutions to the differential equation y′′ 4y′−21y=0 on the interval (−[infinity],[infinity]). find the wronskian of y1,y2 (note the order matters)
The Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.
To find the Wronskian of y1 = e^(3x) and y2 = e^(-7x), we can use the formula for calculating the Wronskian of two functions. Let's denote the Wronskian as W(y1, y2).
The formula for calculating the Wronskian of two functions y1(x) and y2(x) is given by:
W(y1, y2) = y1(x) * y2'(x) - y1'(x) * y2(x)
Let's calculate the derivatives of y1 and y2:
y1(x) = e^(3x)
y1'(x) = 3e^(3x)
y2(x) = e^(-7x)
y2'(x) = -7e^(-7x)
Now, substitute these values into the Wronskian formula:
W(y1, y2) = e^(3x) * (-7e^(-7x)) - (3e^(3x)) * e^(-7x)
= -7e^(3x - 7x) - 3e^(3x - 7x)
= -7e^(-4x) - 3e^(-4x)
= (-7 - 3)e^(-4x)
= -10e^(-4x)
So, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) is W(y1, y2) = -10e^(-4x).
Note that the order of the functions matters in the Wronskian calculation. If we were to reverse the order and calculate W(y2, y1), the result would be the negative of the previous Wronskian:
W(y2, y1) = -W(y1, y2) = 10e^(-4x).
Since the Wronskian is a constant value regardless of the interval (-∞, ∞) in this case, we can evaluate it at any point. For simplicity, let's evaluate it at x = 0:
W(y1, y2) = 10e^(0)
= 10
Therefore, the Wronskian of y1 = e^(3x) and y2 = e^(-7x) on the interval (-∞, ∞) is W(y1, y2) = 10.
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Sandra calculated the missing side length of one of these triangles using the Pythagorean Theorem. Which triangle is it?
Four triangles A, B, C, D are shown from left to right. Triangle A has two sides labeled 6 each, and the included acute angle is shown. Triangle B has one side labeled as 2 and the other as 3, and the included obtuse angle is shown. Triangle C has one side labeled as 6 and the other as 7, and the included acute angle is shown. Triangle D has one side labeled as 2 and the other as 3, and the included right angle is shown.
A
B
C
D
Which issue is least likely arise in machine learning (ml) and artificial intelligence (ai)?
The issue of too many proficient business-savvy programmers is least likely to arise in machine learning(ml) and artificial intelligence(ai).
What is machine learning?
The process by which computers learn to recognize patterns, or the capacity to continuously learn from and make predictions based on data, then make adjustments without being specifically programmed to do so, is known as machine learning (ML), a subcategory of artificial intelligence.
The operation of machine learning is quite complicated and varies according to the task at hand and the algorithm employed to do it. However, at its foundation, a machine learning model is a computer that analyzes data to spot patterns before using those realizations to better fulfill the work that has been given to it. Machine learning can automate any task that depends on a set of data points or rules, even the more difficult ones.
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What is the answer to 6=1-c
Answer: c=-5
Step-by-step explanation: first you have to rearrange terms
6=1-c
6=-c+1
second you have subtract 1 on both sides
6=-c+1
6-1= -c+1-1
third and final you have to Simplify
5=-c
c=-5
4. Determine the maximum rate of change of f at the given point P and the direction in which it occurs (a) f(x,y) = sin(xy), P(1,0) (b) f(x,y,z) = P(8,1.3)
5. Show that a function f decreases most rapidly at x in the direction opposite to the gradient (that is, in the direction of −∇f(x)) and that the maximum rate of decrease equals −|∇f|
4. (a) The maximum rate of change of f(x, y) = sin(xy) at point P(1, 0) is 1 and it occurs in the direction of the positive y-axis.
(b) The maximum rate of change of f(x, y, z) = P(8, 1.3) is -∇f(x) and it occurs in the direction opposite to the gradient vector ∇f.
4. (a) To find the maximum rate of change at point P(1, 0) for f(x, y) = sin(xy), we first calculate the partial derivatives with respect to x and y: ∂f/∂x = ycos(xy) and ∂f/∂y = xcos(xy). Evaluating these partial derivatives at P(1, 0), we get ∂f/∂x = 0 and ∂f/∂y = 1. The maximum rate of change is given by √((∂f/∂x)^2 + (∂f/∂y)^2), which equals 1. The direction of maximum rate of change is in the positive y-axis direction.
(b) To show that the function f decreases most rapidly at x in the direction opposite to the gradient ∇f(x), we consider the directional derivative in the direction of −∇f(x). The directional derivative is given by the dot product of the gradient ∇f(x) and the unit vector in the opposite direction −∇f(x)/|∇f(x)|. The maximum rate of decrease is equal to the magnitude of the negative gradient vector −|∇f(x)|.
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25-26 pls someone help me out.
Answer:
C. 8, H. 6x^2+43x+55
Step-by-step explanation:
You're looking for a value that will make x-2=6, since you add exponents. So W^8/W^-2 is equal to 1/W^6. Since 8-2=6.
A= length * width
(2x+11)(3x+5), foil it out by taking 2x(3x+5), then 11(3x+5).
6x^2+10x+33x+55, combine like terms
6x^2+43x+55
Answer:
26. H: \(6x^2+43x+55\)
Step-by-step explanation:
\(( 2x + 11 ) ( 3x + 5 )\)
\(6x^2+43x+55\)