For f(x,y), find all values of x and y such that fx(x,y) = 0 and fy(x,y) = 0 simultaneously.

f(x,y) = ln(x^4+y^4+52)
(x,y) = (______)

If Aldrin drove a distance of 16 km and his cousin rode 12 km, how fast did Aldrin drive is: 24 kilometers per hours.

Let x+6 represent Aldrin

Let x represent Aldrin brother

Hence:

16/x+16=12/x

16x=12(x+6)

16x=12x+72

Collect like terms

4x=72

Divide both side by 4x

x=72/4

x=18

Hence:

x+6 where x=18

18+6=24  kilometers per hours

Therefore If Aldrin drove a distance of 16 km and his cousin rode 12 km, how fast did Aldrin drive is: 24 kilometers per hours.

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The coefficient of\(x^{k} y^{n-k}\) in the expansion of (xy)ⁿ is C(n, k), which is the binomial coefficient for choosing k elements out of n.

To find the coefficient of a specific term in the expansion of a binomial raised to a power, you can use the binomial theorem. In this case, we want to find the coefficient of the term with the term with \(x^{k} y^{n-k}\).

The binomial theorem states that for any real numbers a and b, and a non-negative integer n, the expansion of (a + b)ⁿ can be written as:

(a + b)ⁿ = C(n, 0) ×aⁿ ×b⁰ + C(n, 1) × \(a^{n-1}\)× b¹ + C(n, 2)× \(a^{n-2}\) ×b² + ... + C(n, n-1) ×a¹ × \(b^{n-1}\) + C(n, n) × a⁰ × bⁿ

where C(n, k) represents the binomial coefficient, which is given by:

C(n, k) = n! / (k! × (n - k)!)

In this case, we have (xy)ⁿ, so a = x, b = y, and we're looking for the term with \(x^{k} y^{n-k}\), which corresponds to the term with C(n, k) × \(a^{k}\) × \(b^{n-k}\). Therefore, the coefficient of \(x^{k} y^{n-k}\) in the expansion of (xy)ⁿ is given by C(n, k).

Therefore, the coefficient of\(x^{k} y^{n-k}\) in the expansion of (xy)ⁿ is C(n, k), which is the binomial coefficient for choosing k elements out of n.

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Answer:

the aa similarity postulate

Step-by-step explanation:

no sides are given and we can not simply assume the sides are congruent, however we do know two of the angles on both triangles are the same allowing us to know that the third therefore must also be the same.

both traingles share angle MAN

and AMN and ABC are equal so therefore

angle ANM and ACB must also be the same

The equation is: y = -3/4x (in slope-intercept form) or y + 3 = -3/4(x - 4) (in point-slope form).

The correct statements are:

The slope-intercept form is expressed as y = mx + b [m is the slope, b is the y-intercept].

The point-slope form is expressed as y - b = m(x - a) [(a, b) is a point on the line, while m is the slope of the line].

Given the table:

x   |  y  

-8   6

4    -3

8    -6

Use two points, (-8, 6) and (4, -3), to find the slope:

Slope (m) = change in y / change in x = (-3 - 6) / (4 - (-8))

m = -9/12

m = -3/4

To find the y-intercept, substitute (x, y) = (4, -3) and m = -3/4 into y = mx + b:

-3 = -3/4(4) + b

-3 = -3 + b

-3 + 3  = b

b = 0

To write the equation in slope-intercept form, substitute m = -3/4 and b = 0 into y = mx + b:

y = -3/4x - 0

y = -3/4x

To write the equation in point-slope form, substitute m = -3/4 and (a, b) = (4, -3) into y - b = m(x - a):

y + 3 = -3/4(x - 4).

Therefore, we can conclude that:

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Answer:

what language is that??

Step-by-step explanation:

Answer:

use area

Step-by-step explanation:

we can't use volume here since we are dealing with the outside part only

so area of a cylinder is =πr²h

our r represents the radius which is diameter/2

r=7.5/2

=3.75m

our h represents height which is 12.5m

so put in our formula

area = π×(3.75)²×(12.5)

=552.2330836m³

that's it dear

give my answer a brainliest

Answer:

Median: 75

Mode: 50

Mean: ≈ 75.4

Range: 50

Step-by-step explanation:

Arrange the numbers in order:

50, 50, 70, 80, 88, 90, 100

There is no exact middle number.

\(70 + 80 = 150\\150/2 = 75\)

The median is about 75.

50, 50, 70, 80, 88, 90, 100

"50" appears the most.

The mode is 50.

Add all numbers in the set.

\(100+88+50+50+90+70+80 = 528\)

Divide by the number of values in the set.

\(528/7 = 75.4285714286\)

75.4285714286 ≈ 75.4

The mean is about 75.4.

Subtract the smallest number in the data set from the largest number in the data set.

\(100-50=50\)

The range is 50.

Brainilest appreciated.

Answer:

Step-by-step explanation:

\(17. (a^{m})^{n}=a^{m*n}\\\\a^{m}*a^{n}=a^{m+n}\\\\-3k^{2}*(4k^{5})^{3}=-3k^{2}*4^{3}*k^{5*3}\\\\ = -3k^{2}*64*k^{15}\\\\= (-3)*64*k^{2+15}\\\\= - 192k^{17}\)

\(19. \dfrac{a^{m}}{a^{n}}=a^{m-n}\\\\\\\dfrac{(-7p^{4})*(-8p^{5})}{2p^{3}}= \dfrac{(-7)*(-8)*p^{4}*p^{5}}{2p^{3}}\\\\\\=(-7)*(-4)*p^{4+5-3} \\\\= 28p^{6}\\\)

\(20)\dfrac{15a^{16}b^{11}}{(3a^{4}b^{2})^{3}}=\dfrac{15a^{16}b^{11}}{3^{3}*a^{4*3}*b^{2*3}}\\\\\\=\dfrac{15a^{16}b^{11}}{27*a^{12}*b^{6}}\\\\=\dfrac{5*a^{16-12}*b^{11-6}}{9}\\\\\\=\dfrac{5a^{4}b^{5}}{9}\)

Answer:

2.) s = 32

3.) y=10, x=80

Step-by-step explanation:

3.) x=y=90

10+80=90

80/8=10, so 80 is 10 times bigger

Assuming that the rates are constant, we can see that Tom can paint the fence in 7.5 hours.

Here we will use equations of the form:

(rate at which person x paints)*(time) = 1 fence painted.

We know that Chuck can paint a fence in 5 hours, then if C is the rate (assuming this is constant), we can write:

C*5 hours = 1 fence

C = (1/5) fences per hour.

And let's say that Tom's rate is T.

When they work together, the rate is:

(C + T)

And they can paint the fence in 3 hours, then:

(C + T)*3 hours = 1 fence

Replacing the value of T we will get:

( 1/5 fences per hour + T)*3 hours = 1 fence

1/5 fences per hour + T = 1/3 fences per hour.

T = (1/3 - 1/5) fences per hour

T = (5/15 - 3/15) fences per hour

T = 2/15 fences per hour.

Then Tom paints the fence in:

(15/2) hours = 7.5 hours.

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Considering the probability space whose outcomes are these random permutations and a random variable X defined on this probability space such X = 1 when the product xyz is even and X = 0 when that product is odd. E[X] = \[\frac{53}{63}\]

To find the expected value of the random variable X given the permutation of 10 decimal digits, we will determine the probability of the random variable X being odd or even. If the product xyz is odd, then X is odd, otherwise X is even.

Let A be the event that x is odd, B be the event that y is odd and C be the event that z is odd. The probability of A occurring is:

P(A) = \[\frac{5}{9}\] since there are 5 odd digits out of the 9 remaining after any digit is chosen as the first digit in x. Similarly, P(B) = \[\frac{4}{7}\] since there are 4 odd digits out of the 7 remaining after any digit is chosen as the first digit in y. Also, P(C) = \[\frac{3}{6}\] since there are 3 odd digits out of the 6 remaining after any digit is chosen as the first digit in z.

Therefore, P(A ∩ B ∩ C) is the probability of the product being odd which is given as:

P(A ∩ B ∩ C) = P(A) × P(B) × P(C) = \[\frac{5}{9}\] × \[\frac{4}{7}\] × \[\frac{3}{6}\] = \[\frac{10}{63}\]

Thus, the probability of the product being even is:

P(A ∩ B ∩ C)¯ = 1 − P(A ∩ B ∩ C) = 1 − \[\frac{10}{63}\] = \[\frac{53}{63}\]

Therefore, the expected value of X is given as:

E[X] = (0 × \[\frac{10}{63}\]) + (1 × \[\frac{53}{63}\]) = \[\frac{53}{63}\]

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Hector and Gabrielle will have $638.45 in their savings account after two years of earning 13% interest compounded annually. They will be able to spend up to this amount on their trip.

To solve this problem, we need to use the formula for compound interest:

A = \(P(1 + r/n)^{(nt)\)

where:

A = the final amount

P = the initial deposit

r = the annual interest rate as a decimal

n = the number of times interest is compounded per year

t = the time in years

In this case, we have:

P = $500.00

r = 13% = 0.13 (as a decimal)

n = 1 (compounded annually)

t = 2 years

So, we can plug these values into the formula:

A = $500.00(1 + 0.13/1)²

A = $500.00(1.13)²

A = $500.00(1.2769)

A = $638.45

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Answer:

Yes

Step-by-step explanation:

Anything muliplied by zero end up equalling zero. So with this in mind we can put 0 in for x and find out what each eqautian equals.

2(0) + 6(0) = 0; Once we multiply both sides we end up adding 0 and 0, so it equals 0

9(0) = 0

Since, 0 = 0 they are both equal.

Hope this helps!

Answer:

it would b 2 in half cups of powder

Let x represent the first integer.

Let y represent the second integer.

Let z represent the third integer.

From the information given,

the sum of the three integers is 380. This means that

x + y + z = 380

The sum of the first and second integers exceeds the third by 74. This means that

x + y = z + 74

The third integer is 62 less than the first. This means that

z = x - 62

We would substitute z = x - 62 into the first and second equations. We have

For the first equation,

x + y + x - 62 = 380

By collecting like terms, we have

x + x + y = 380 + 62

2x + y = 442

For the second equation,

x + y = x - 62 + 74

By collecting like terms,

x - x + y = - 62 + 74

y = 12

Subctituting y = 12 into 2x + y = 442, we have

2x + 12 = 442

2x = 442 - 12 = 430

x = 430/2

x = 215

z = x - 62 = 215 - 62

z = 153

Thus, the integers are 215, 12 and 153

Answer:

Step-by-step explanation:

Answer:

3.7

Step-by-step explanation:

Absolute value is defined as the following:

\(\displaystyle{|x| = \left \{ {x \ \ \ \left(x > 0\right) \atop -x \ \left(x < 0\right)} \right. }\)

In simpler term - it means that for any real values inside of absolute sign, it'll always output as a positive value.

Such examples are |-2| = 2, |-2/3| = 2/3, etc.

Answer: 3/4 *3/4 *3/4 = 27/64 this is the proabability that is DOES snow every day. 1-27/64 = 37/64 this is the proabability that is DOES NOT snow EVERY day. 1/(4^3) = 1/64 IS the probability that is does not snow AT ALL for the 3 days.

Step-by-step explanation:

George spend 5 hours driving on the Interstate if George spent two more hours on the Interstate than on the highway.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let's suppose the George spend x hours on the interstate and (x+2) hours on the highway.

570 = 75x + 65(x-2)

570 = 75x + 65x -130

700 = 140x

x = 5 hours

Thus, George spend 5 hours driving on the Interstate if George spent two more hours on the Interstate than on the highway.

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Disjoint events are events that cannot happen at the same time. Two events A and B are independent if the occurrence of A does not affect the probability of B happening, and vice versa. Mathematically, this can be written as P(A and B) = P(A)P(B).

In the case of disjoint events, P(A and B) = 0 because they cannot occur at the same time. Therefore, the condition for A and B to be independent is that either P(A) = 0 or P(B) = 0, since any non-zero probability for either event would make the product P(A)P(B) also non-zero.

Two disjoint events are independent if and only if at least one of them has zero probability.

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Slot machines are a real-world example of a variable ratio schedule.

A variable-ratio schedule in operant conditioning is a partial reinforcement schedule where a response is reinforced after an arbitrary number of responses. 1 A consistent, high rate of response is produced by this schedule. A reward based on a variable-ratio schedule is one that can be found in gambling and lottery games.

The individual will continue to engage in the target behavior in variable ratio schedules because he is unsure of how many responses he must give before receiving reinforcement. This leads to highly stable rates and increases the behavior's resistance to extinction.

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The area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis is 2.08 square units.

We have been given parametric equations x = t^2 − 3t, y = √t

We need to find the area enclosed by the curve x = t^2 − 3t, y = √t and the y-axis.

Consider x = 0

So, t^2 − 3t =  0

t(t - 3) = 0

t = 0   or  t = 3

Let f(t) =  t^2 − 3t and g(t) = t

Differentiate the curve f(t) with respect to t.

f'(t) = 2t - 3

NWe know that the formula to find the area under the curve.

A = ∫[a to b] g(t)f'(t) dt

here, a = 0 and b = 3

so, A = ∫[0 to 3] √t (2t - 3) dt

A = ∫[0 to 3] (2t√t - 3√t) dt

A = ∫[0 to 3] (2t^(3/2) - 3t^(1/2)) dt

A = [4/5 t^(5/2) - 2 t^(3/2)]_[t = 0, t = 3]

A = 4/5 3^(5/2) - 2 3^(3/2) - 0 + 0

A = 4/5 3^(5/2) - 2 3^(3/2)

A = 6√3 /5

A = 2.08

Therefore,  the area of the curve is 2.08 square units.

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Answer:

By plotting points A', B' and C' we can get the dilated image A'B'C'.

Step-by-step explanation:

Let the point P is origin (0, 0), segment AB lies on the x-axis and segment PC on the y-axis,

Coordinates of A, B and C will be (1, 0), (2, 0) and (0, 2).

When triangle ABC is dilated by a scale factor 4 about the origin,

Rule for dilation;

(x, y) → (4x, 4y)

New coordinates of the points A, B and C will be,

A(1, 0) → A'(4, 0)

B(-2, 0) → B'(-8, 0)

C(0, 2) → C'(0, 8)

Answer:

Correct

Step-by-step explanation:

New coordinates of the points A, B and C will be,

A(1, 0) → A'(4, 0)

B(-2, 0) → B'(-8, 0)

C(0, 2) → C'(0, 8)

Answer:

Is it .04

Step-by-step explanation:

Answer:

x=-3

Step-by-step explanation:

x=-12/4 divide both sides by 4

Answer:

x = -3

Step-by-step explanation:

Let's solve your equation step-by-step.

4x=−12

Step 1: Divide both sides by 4.

4x/4 = -12/4

x=−3

The value of the integral is 512/15. To evaluate the integral S4 0 (4-t)√t dt, we can use integration by substitution. Let u = √t, then du/dt = 1/(2√t), which implies that dt = 2u du.

Substituting u = √t and dt = 2u du, the integral becomes:

S4 0 (4-t)√t dt = S4 0 (4-t) u * 2u du = 2 S2 0 (4-u²) u² du

Now, we can expand the integrand and integrate term by term:

2 S2 0 (4-u²) u² du = 2 [∫4 0 u² du - ∫4 0 u⁴ du]

= 2 [(u³/3) |4 0 - (u⁵/5) |4 0]

= 2 [(64/3 - 64/5) - (0 - 0)]

= 2 [(320/15) - (64/15)]

= 2 [(256/15)]

= 512/15

Therefore, the value of the integral is 512/15.

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Answer:

(∠C) ≅ (∠B)

∴ tan(∠B) = tan(∠C) and

Slope AB = Slope BC

Step-by-step explanation:

Part A:

To explain why the slope from point from A to B is the same with the slope from B to C with similar triangles we have;

The angle between segment AB and the vertical is the same as the angle between segment BC and the vertical - (corresponding angles)

The angle between segment AB and the horizontal is the same as the angle between segment BC and the horizontal - (corresponding angles)

The length of a segment opposite to the angle between segment AB and the horizontal is the as the length of a segment opposite to the angle between segment BC and the horizontal

Therefore, the triangle formed by A, B and the point of intersection of the vertical line from A with the horizontal line from B is congruent to the triangle formed by B, C and the point of intersection of the vertical line from B with the horizontal line from C

Which gives the angle with the horizontal at C (∠C) is congruent to the angle with horizontal B (∠B)

The slope AB = tan(∠B)

Slope BC = tan(∠C)

(∠C) ≅ (∠B)

Therefore, tan(∠B) = tan(∠C) and slope AB = Slope BC.

Answer:

Step-by-step explanation:

the answer is 5]

Lucas bought 6 scarves and 4.8 hats.

Lucas has $100 to spend on scarves (X) and hats (Y).

Each scarf costs $7 and each hat costs $11.

If Lucas buys two or more scarves, he gets one scarf for free.

If he buys 4.8 hats, how many scarves does Lucas consume?

Let us suppose that Lucas buys x scarves and y hats.

He has to satisfy the following conditions:Cost of x scarves = 7x Cost of y hats = 11y

His budget is $100.

Therefore, 7x + 11y = 100 ----------- (1)

If Lucas buys two or more scarves, he gets one scarf for free.

In other words, if he buys n scarves, then he pays for (n-1) scarves.

Hence, if Lucas buys 2 scarves, he gets 1 for free and he pays for only one.

Therefore, cost of 2 scarves = 7(2-1) = $7

Similarly, if Lucas buys 3 scarves, he gets 1 for free and he pays for only two.

Therefore, cost of 3 scarves = 7(3-1) = $14 And so on...

We can write this information in a table:

Let us assume that Lucas buys n scarves. He gets (n/2) scarves for free.

Total cost of n scarves is given by:C(n) = 7(n - n/2) + 11y ----------- (2)

Since he buys 4.8 hats, we can write:y = 4.8

Therefore, equation (1) becomes:7x + 11(4.8) = 1007x = 100 - 11(4.8)7x = 45.6x = 6.51

Thus, Lucas bought 6 scarves and 4.8 hats.

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