if z3=x3 y2, dxdt=3, dydt=2, and z>0, find dzdt at (x,y)=(4,0).

Answer:

y = 3x - 2

Step-by-step explanation:

See the attached worksheet.  Look for an equation of the form y=mx+b, where m is the slope and b is the y-intercept.  The slope of the line can be determined by taking two points on the line to calculate the Rise/Run.  The points selected for this example are (0,-2) and (2,4).  This makes the Rise/Run (6/2), or 3.  The y-intercept, b, is -2 as per point (0,-2).

The equation for this (non)-prependicular line is thus y = 3x - 2.

Answer:

20 units I believe

Step-by-step explanation:

20 units

Answer:   C. 20 units

2021 edg

Step-by-step explanation:

To have exactly 3 kings in a hand, we need to choose 3 kings out of 4 and 2 non-kings out of 48. This can be done in 4512 ways.


To calculate the number of hands containing exactly 3 kings, we need to use the concept of combinations. We know that there are 4 kings in a deck of 52 cards. To choose 3 kings out of 4, we can use the combination formula, also known as "n choose k," which is written as nCk.

So, the number of ways to choose 3 kings out of 4 is 4C3 = 4.

Next, we need to choose 2 non-kings out of the remaining 48 cards. This can be done using the combination formula again. The number of ways to choose 2 non-kings out of 48 is 48C2 = 1128.

Now, we can use the multiplication principle to find the total number of hands containing exactly 3 kings. We multiply the number of ways to choose 3 kings by the number of ways to choose 2 non-kings:

Total number of hands = 4C3 * 48C2 = 4 * 1128 = 4512.

Therefore, there are 4512 hands that contain exactly 3 kings when 5 cards are randomly chosen from a standard deck.

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Answer:

V = 126 cm³

Step-by-step explanation:

the figure is made up of 2 cuboids ( flat one on the left and upright one on the right )

the volume (V) of a cuboid is calculated as

V = lbh ( l is length, b is breadth, h is height )

cuboid on left has l = 7 , b = 6 and h = 1 , then

V = 7 × 6 × 1 = 42 cm³

upright cuboid has l = 7 , b = 3 and h = 4 , then

volume = 7 × 3 × 4 = 84 cm³

Then volume of figure is the sum of the 2 volumes calculated

V = 42 + 84 = 126 cm³

Answer:

126 cm^3

Step-by-step explanation:

In order to find the volume of a cuboid the formula is:

l × w × h

In this case, we actually have two cuboids making up this one figure. Thus you can them apart into two cuboids.

I take one cuboid with the measurements of 9 by 7 by 3 and calculate the volume below:

\(9*7*3=63\)

Similarly, the other cuboid will have measurements of 3 by 3 by 7(the reason why h is 3 is that I chose to include the bottom half of the width of the cuboid). Now calculate your volume for the second cuboid:

\(3*3*7=63\)

Now add both volumes together and you  get 126 cm^3

Answer:

x = 80

Step-by-step explanation:

if ray RU bisects <QRS that means it divided the angle into two equal parts

then we can write the following equation to find the value of x:

<SRU = <QRU

50 = (x/2 + 10) subtract 10 from both sides

40 = x/2 multiply both sides with 2

80 = x

<QRS = 100 because it's the sum of <SRU and <QRU

Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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The length of the line segment defined by two endpoints; negative 3 comma 10 to 4 comma negative 1 as required in the task content is; 13.04.

It follows from the task content that the length of the line segment whose endpoints are as given in the task content is to be determined.

Recall; The length of a line segment whose endpoints are defined by; (x1, y1) and (x2, y2) is given as;

Length = √{ (y2 - y1)² + (x2 - x1)² }

Therefore, since the given endpoints are; (-3, 10) and (4, -1), it follows that the length of the line segment in discuss is;

Length = √{ (-1 - 10)² + (4 - (-3))² }

Length = √(121 + 49)

Length = √170

Length = 13.04.

Ultimately, the length of the line segment as required is; 13.04.

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To calculate the value of X that Ellen should deposit in the bank, we need to determine the present value of the future payments that will accumulate to $50,000 in six years.

Using the formula for compound interest, the present value can be calculated as follows:

PV = X/(1 + r)^1 + X/(1 + r)^2 + X/(1 + r)^3,

where r is the annual interest rate (5%) expressed as a decimal.

To find the value of X, we set the present value equal to $50,000 and solve for X:

50,000 = X/(1 + 0.05)^1 + X/(1 + 0.05)^2 + X/(1 + 0.05)^3.

Once we determine the value of X, we can proceed to the next step.

For the second part of the question, after four years, the bank raises the interest rate to 6%.

From year four to year six, Ellen's money will continue to accumulate interest.

To find the amount donated, we calculate the future value of the remaining amount after deducting the down payment of $50,000:

Remaining amount = X/(1 + 0.06)^2 + X/(1 + 0.06)^3 + X/(1 + 0.06)^4.

The donated amount is then the difference between the remaining amount and the total accumulated after six years.

By evaluating these expressions, we can determine the value of X and the amount donated by Ellen.

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Answer:

b.

Step-by-step explanation: because when you are figuring out if it is that number it shold be the answer.

Answer:

15.4 ft

Step-by-step explanation:

\sin A = \frac{\text{opposite}}{\text{hypotenuse}}=\frac{9.7}{x}

sinA=

hypotenuse

opposite

​

=

x

9.7

​

\sin 39=\frac{9.7}{x}

sin39=

x

9.7

​

x\sin 39=9.7

xsin39=9.7

Cross multiply.

\frac{x\sin 39}{\sin 39}=\frac{9.7}{\sin 39}

sin39

xsin39

​

=

sin39

9.7

​

Divide each side by sin 39.

x=\frac{9.7}{\sin 39}=15.4135\approx 15.4\text{ feet}

x=

sin39

9.7

​

=15.4135≈15.4 feet

Type into calculator and round to the nearest tenth of a foot.

Answer:

Step-by-step explanation:

92 -- 2*2*23

146 ---2*73

Answer:

2

Step-by-step explanation:

Hey there!

The equation is asking us, c x c = 4

What is c?

Well the only number that is equal to 4 when you square it is 2

Answer:

20

Step-by-step explanation:

The simplified expression for (f ∘ g)(x) is 2 + x (option d).

To find and simplify (f ∘ g)(x), we need to substitute the expression for g(x) into f(x) and simplify.

Given:

f(x) = log₃(9x)

g(x) = \(3^x\)

Substituting g(x) into f(x):

(f ∘ g)(x) = f(g(x)) = log₃\((9 * 3^x)\)

Now, we simplify the expression:

log₃\((9 * 3^x)\) = log₃(9) + log₃\((3^x)\)

Since logₓ(a * b) = logₓ(a) + logₓ(b), we have:

log₃(9) + log₃\((3^x)\) = log₃\((3^2)\) + x

Using the property logₓ\((x^a)\) = a * logₓ(x), we get:

log₃\((3^2)\) + x = 2 * log₃(3) + x

Since logₓ\((x^a)\) = a, where x is the base, we have:

2 * log₃(3) + x = 2 + x

Therefore, (f ∘ g)(x) simplifies to:

(f ∘ g)(x) = 2 + x

So, the correct answer is (d) 2 + x.

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Complete Question:

Given f(x)=log₃(9x) and g(x)=\(3^x\). Find and simplify (f ∘ g)(x)

(a) 2x

(b) x

(c) \(27^x\)

(d) 2+x

(e) None of these.

Answer:

Step-by-step explanation: 737/ 11= 67

sooooo 67 x 5= 335

Over the interval [-3, 1], the local minimum is 0,  Over the interval [-1, 0], the local maximum is 4.39,  Over the interval [0, 3], the local minimum is -32.

By plot the function on a graphing tool and visually identify the local minimum and maximum values over the specified intervals .A function that is continuous for an interval [a,b], a is not equal to b, then there is a local maximum and minimum if:

Local maximum: f(d) > f(x), ∀ x ≠ d, a ≤ d ≤ b

Local minimum: f(c)< f(x), ∀ x ≠ to c, a≤c≤b

we can proceed to solve each question:

Over the interval [-3, 1], the local minimum is 0,

since f(-2) < f(x), ∀ x ≠ -2,-3 ≤ x ≤ -1 .

Over the interval [-1, 0], the local maximum is 4.39,

since f(-0.8) > f(x), ∀ x ≠ -0.8, -1 ≤ x ≤ -1.

Over the interval [0, 3], the local minimum is -32,

since f(-2) < f(x), ∀ x ≠ -2.0 ≤ x ≤3.

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Answer:

0

4.39

-32

Step-by-step explanation:

on edge

Answer:

He traveled 520 miles

Step-by-step explanation:

8 x 65 = 520

Answer: 520 miles

Step-by-step explanation:

Data: Juan drove 8 hours

Drove at an average Speed of 65 mph

Miles driven=x

Only step: Multiply 65 by 8 which is 520

Explanation: Since Juan drove at an average speed of 65 miles per hour, that means he drove 65 mile for every hour he drove. So since he drove for 8 hours, you multiply 8 hours by 65 miles so that you get get the total amount of hours driven by him.

Don't forget to add "Miles" to the end of your answer because most math teachers tend to want that in an answer like this.

I hope this helps(Mark brainiest if you want to, thanks)

Answer:

20%

Step-by-step explanation:

Step 1: Find the decrease in consumption

10kg - 8kg = 2kg

So the family decrease their consumption of sugar by 2kg

Step 2: We have to find what percent did the family reduce their sugar consumption

We can divide how much they reduced by with the original amount

2kg/10kg = 1/5 kg or 20%

Therefore the family reduced the consumption of sugar by 20$

Answer:

It will take him

\( \frac{1}{2} \)

of a minute to fill the bottle.

Step-by-step explanation:

I'm really not sure this is right but..

we can solve using proportions. Cross-multiply and divide.

\(\frac{ \frac{1}{3} of \: a \: water \: bottle}{\frac{1}{6} minute} \: = \frac{ \frac{3}{3} of \: a \: water \: bottle}{x} \\ \\ \frac{ \frac{1}{6} }{ \frac{1}{3} } = \frac{ \frac{1}{3} x}{ \frac{1}{3} } \\ \\ \frac{1}{2} = x\)

a) expenses increased overall by 47.76%. ; b)  average rate of increase is 8.67%. ; c)  expenses in 2017 were  €2,273.13.

a) The overall increase in expenditure can be found using the formula:

Overall increase = (1 + i₁) × (1 + i₂) × ... × (1 + iₙ) - 1

where i₁, i₂, ..., iₙ are the increases in each year.In this case, the increases are 10%, 12%, 8%, 3%, and 8%.

Substituting these values, we get:

Overall increase = (1 + 0.1) × (1 + 0.12) × (1 + 0.08) × (1 + 0.03) × (1 + 0.08) - 1

≈ 47.76%

Hence, the expenses increased overall by approximately 47.76%.

b) The average rate of increase can be found by taking the nth root of the overall increase formula:

Average rate of increase = [(1 + i₁) × (1 + i₂) × ... × (1 + iₙ)]^(1/n) - 1

where n is the number of years.

In this case, n = 5, so substituting the values of the increases, we get:

Average rate of increase = [(1 + 0.1) × (1 + 0.12) × (1 + 0.08) × (1 + 0.03) ×\((1 + 0.08)]^(1/5)\)- 1

≈ 8.67%

Hence, the average rate of increase is approximately 8.67%.

c) To find the expenses in 2017, we can use the following formula:

New amount = Initial amount × \((1 + r)^t\)

where r is the rate of increase and t is the number of years.In this case, we want to find the expenses in 2017 given that they were €1,500 in 2012.

We know that the average rate of increase over the years was 8.67%.

The time period is 5 years (from 2012 to 2017).

So, substituting the values, we get:

New amount = 1500 × \((1 + 0.0867)^5\)

≈ €2,273.13

Hence, the expenses in 2017 were approximately €2,273.13.

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Answer:

a)  (2 x 1000) + (5 x 100)

b)  5^4 × 2²

c)  ??

Step-by-step explanation:

b) 2500 = 25 x 100

25 = 5 x 5

100 = 25 x 4 = 5 x 5 x 2 x 2

Answer:

G is equal to (8, -11)

Step-by-step explanation:

We are given the midpoint and one end of the line segment.  We can find the other end of it by taking the distance from H to M, doubling it, and adding that to H:

\(G(x, y) = H(x, y) + 2(M(x, y) - H(x, y))\\\\G_x = H_x + 2(M_x - H_x)\\G_x = -4 + 2(-6 - (-4))\\G_x = -4 + 2(-2)\\G_x = -4 - 4\\G_x = 8\\\\G_y = H_y + 2(M_y - H_y)\\G_y= 3 + 2(- 3 - 4)\\G_y= 3 - 6 - 8\\G_y = -11\)

So the coordinates of endpoint G are (8, -11)

Answer: The answer is the number of each type of topping ordered.

The predicted values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350, therefore, the correct option is IC.

Given,

Mean of X = 600

Standard deviation of X = 10

Mean of Y = $5000

Standard deviation of Y = 1000

Correlation r= 0.9

Future value of X = 595

Z score of X = (X- Mean of X) / Standard deviation of X= (595-600) / 10 = -0.5

Using the formula, Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (-0.5) * 1000 = $4750

The predicted value of Y for X = 595 is $4750.

Now, to find the values of A, B, C, and D; we need to calculate the Z score of X = 615 and find the corresponding predicted value of Y.

Z score of X = (X- Mean of X) / Standard deviation of X= (615-600) / 10 = 1.5

Predicted y = average of y+ r* (Z score of X)* standard deviation of y

Predicted y = $5000 + 0.9 * (1.5) * 1000 = $6350

The predicted value of Y for X = 615 is $6350.

Hence, the values of A, B, C, and D are: A = 595B = -0.5C = 600D = $6350

Therefore, the correct option is IC.

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The correlation coefficient between the number of questions right and the number of questions wrong is -2.

The correlation coefficient measures the strength and direction of the linear relationship between two variables. In this case, the variables are the number of questions right and the number of questions wrong for each student.

To calculate the correlation coefficient, you need to have data for both variables for each student. Let's assume we have the following data for three students:
Student 1: 8 right, 2 wrong
Student 2: 5 right, 5 wrong
Student 3: 2 right, 8 wrong
Step 1: Calculate the mean of the number of questions right (meanX) and the mean of the number of questions wrong (meanY). In our example:
meanX = (8 + 5 + 2) / 3 = 5
meanY = (2 + 5 + 8) / 3 = 5
Step 2: Calculate the deviations from the mean for both variables. This is done by subtracting the mean from each individual value.
For student 1:
deviationX = 8 - 5 = 3
deviationY = 2 - 5 = -3
For student 2:
deviationX = 5 - 5 = 0
deviationY = 5 - 5 = 0
For student 3:
deviationX = 2 - 5 = -3
deviationY = 8 - 5 = 3
Step 3: Calculate the product of the deviations for each student.
For student 1:
product of deviations = deviationX * deviationY = 3 * -3 = -9
For student 2:
product of deviations = deviationX * deviationY = 0 * 0 = 0
For student 3:
product of deviations = deviationX * deviationY = -3 * 3 = -9
Step 4: Calculate the sum of the product of deviations.
sum of products of deviations = (-9) + 0 + (-9) = -18
Step 5: Calculate the standard deviation of the number of questions right (sdX) and the standard deviation of the number of questions wrong (sdY). This is done by taking the square root of the sum of the squares of the deviations from the mean divided by the number of data points minus 1.
In our example:
sdX = √[((3^2) + (0^2) + (3^2)) / (3 - 1)] = √[(9 + 0 + 9) / 2] = √[18 / 2] = √9 = 3
sdY = √[((-3^2) + (0^2) + (3^2)) / (3 - 1)] = √[(9 + 0 + 9) / 2] = √[18 / 2] = √9 = 3
Step 6: Calculate the correlation coefficient (r). This is done by dividing the sum of the product of deviations by the product of the standard deviations.
In our example:
r = sum of products of deviations / (sdX * sdY) = -18 / (3 * 3) = -18 / 9 = -2
The correlation coefficient between the number of questions right and the number of questions wrong is -2. The negative sign indicates a negative linear relationship, meaning that as the number of questions right increases, the number of questions wrong decreases, and vice versa.

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Answer:

x^2 - 6x + 8 = 0

Step-by-step explanation:

Answer:

(x-3)^2 = 17

Step-by-step explanation:

Plato/Edmentum

Answer:

5643/494-6494_x error45H5Y09B9,Gn94365

Step-by-step explanation:

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