Will has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. If Ashley has 30 stamps and she has a third as many as Carlton has, how many stamps are in Will’s collection?

The partial derivatives are:

fx = z/y

fy = z/x

fz = ln(xy)

To find the partial derivatives of f(x, y, z) = z(ln(xy)) with respect to x, y, and z, we can use the product rule and chain rule as follows:

fx = ∂f/∂x = z(1/y) * y = z/y

fy = ∂f/∂y = z(1/x) * x = z/x

fz = ∂f/∂z = ln(xy)

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Answer: 486 mm^2

Step-by-step explanation:

Area of parallelogram = base x height

area = 27 x 18 = 486 mm^2

Answer:

it is 486mm

Step-by-step explanation:

i just took the test and this is right. i hope this helps :)

Answer:

The formula for this problem is D = √((y₂ - y₁)² + (x₂ - x₁)²))

So plug in the variables and solve.

D = √((6-1)2 + (14-2)2))D = √( 25 + 144 )D = √169D = 13

I hope this helps love! :)

Step-by-step explanation:

can u mark me  as a brill please

The correct answer is b. we know the standard deviation of the population.

The Nearly Normal condition, also known as the Central Limit Theorem, states that the sampling distribution of the sample mean tends to be approximately normal, even if the population distribution is not normal, under certain conditions. One way to meet the Nearly Normal condition is by knowing the standard deviation of the population.

When the standard deviation of the population is known, the sample size does not have to be large for the sampling distribution of the sample mean to be approximately normal. This is because the standard deviation provides information about the variability of the population, allowing for a more accurate estimation of the sample mean distribution.

While the other options (a, c, and d) may be relevant in specific scenarios, they are not directly related to meeting the Nearly Normal condition as defined by the Central Limit Theorem.

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Step-by-step explanation:

Given \:number (m) = £ 490Givennumber(m)=£490

Increase (g) = 11\%Increase(g)=11%

\begin{gathered} \red{ Required \:number } \\= m\Big( \frac{(100+g)}{100} \Big)\\= 490\Big(\frac{100+11}{100}\Big)\\= 490 \times \frac{111}{100} \\= 490 \times 1.11 \\= £ 543.9 \end{gathered}

Requirednumber

=m(

100

(100+g)

)

=490(

100

100+11

)

=490×

100

111

=490×1.11

=£543.9

Therefore.,

\red{ Required \:number }\green { = £ 543.9}Requirednumber=£543.9

•••♪

Answer:

£543.90

Step-by-step explanation:

You have to add 2 and nothing

Answer:

31.5 cm

Step-by-step explanation:

scale of an architecture is ratio of size of drawing to size of actual object.

Given size of football field is 160 feet by 360 feet

Given that on map shortest side is 14

since value of shortest side is 160 feet

then

scale defined for this football filed will be

scale = size of shortest side on model/size of shortest side of actual football field

scale = 14/160

Given that scale will remain same for longer side as

14/160= size of longer side on model/size of longer side of actual

14/160 =  size of longer side on model/360

thus,

size of longer side on model = (14/160) * 360

size of longer side on model = 14*360/160 = 31.5

Thus, the other side of model that is longer side is 31.5 cm

The 95% confidence interval for the average score is [34.18, 95.82]. Therefore, the correct option is (B) [34.18, 95.82].

Given that: Sample of 16 students revealed that they score, on average, 65 percent. And previous semesters, the population standard deviation is thought to be 53 percent.

To find: The 95% confidence interval for the average score.

Here, the sample size is 16, which is less than 30. Hence, we can use the t-distribution to estimate the population parameter.

The formula for the confidence interval is given by:(x‾ - t_(α/2) * (s/√n), x‾ + t_(α/2) * (s/√n)).

Here, n = 16 (sample size)x‾ = 65 (sample mean)σ = 53 (population standard deviation).

We need to find the t-value corresponding to 95% confidence level and 15 degrees of freedom.α = 1 - 0.95 = 0.05 (as 95% confidence interval is given)So, α/2 = 0.025 (two-tailed test)At 15 degrees of freedom, the t-value for 0.025 is 2.131.

Confidence interval = (x‾ - t_(α/2) * (s/√n), x‾ + t_(α/2) * (s/√n))(65 - 2.131 * (53/√16), 65 + 2.131 * (53/√16))= (34.18, 95.82)Therefore, the correct option is (B) [34.18, 95.82].

To find the 95% confidence interval for the average score we have used the formula:(x‾ - t_(α/2) * (s/√n), x‾ + t_(α/2) * (s/√n)).

Here, n = 16 (sample size)x‾ = 65 (sample mean)σ = 53 (population standard deviation)We need to find the t-value corresponding to 95% confidence level and 15 degrees of freedom.α = 1 - 0.95 = 0.05 (as 95% confidence interval is given)So, α/2 = 0.025 (two-tailed test).

At 15 degrees of freedom, the t-value for 0.025 is 2.131.Confidence interval = (x‾ - t_(α/2) * (s/√n), x‾ + t_(α/2) * (s/√n))(65 - 2.131 * (53/√16), 65 + 2.131 * (53/√16))= (34.18, 95.82)

The 95% confidence interval for the average score is [34.18, 95.82]. Therefore, the correct option is (B) [34.18, 95.82].Note: The general formula for the confidence interval in case of a small sample (n < 30) is(x‾ - t_(α/2) * (s/√n - 1), x‾ + t_(α/2) * (s/√n - 1))Where n is the sample size, x‾ is the sample mean, s is the sample standard deviation, α is the significance level, and t_(α/2) is the critical value of t at α/2 with n - 1 degrees of freedom.

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The dimension of the sidewalk is length 29.8 cm and the height 31.8 cm.

Given,

The side of square base of pyramid x.

Height 2 centimeters greater than the length of each side of its square base=x+2

Volume of pyramid=297cubic cm

We have to calculate the dimensions

Volume=1/3 a²h

a is the side length.

h is height of pyramid.

297=x²(x+2)/3

891=x³+2x²

891=x²(x+2)

x²=891, x+2=891

x=29.8, x+2=891,x=889

Hence length of base the pyramid is 29.8 cm and height is 31.8cm

A three dimensional shape can be defined as a solid figure or an object or shape that has three dimensions—length, width, and height.

A pyramid (from Greek: pyrams) is a structure with triangular outside surfaces that converge to a single step at the summit, giving the shape the shape of a pyramid in the geometric sense.

A pyramid's base can be trilateral, quadrilateral, or any polygon shape. A pyramid, as a result, has at least three exterior triangle surfaces (at least four faces including the base).

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Answer:

0.02

Step-by-step explanation:

The amount of each quarterly payment, rounded, for a $30,000 loan with a 6% annual interest rate to be paid off in 10 equal quarterly payments is $2,803 (option B).


To calculate the amount of each quarterly payment, we need to use the formula for calculating the equal payments on an installment loan. In this case, the loan amount is $30,000, the annual interest rate is 6%, and the loan term is 10 quarters.

Using the formula, we can determine that the amount of each quarterly payment is approximately $2,803. This amount is rounded to the nearest whole number, as specified in the question. Therefore, option B, $2,803, is the correct answer. The other options (A, C, and D) are not applicable to the calculation based on the given information.

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To find the fraction of the students in the class that like either basketball and soccer, we have to sum

We use the following property

Let's do it

The complement of this fraction represents the students that like basketball AND soccer.

Hence, the answer is

The Maclaurin series through degree 4 of f(x)=(1+x)^(-4/3) is approximately 1 - (4/3)x + (14/9)x^2 - (56/27)x^3 + (208/81)x^4.

To find the Maclaurin series of f(x)=(1+x)^(-4/3), we start by using the formula for the Maclaurin series of a function f(x) centered at x=0:

f(x) = ∑[n=0 to infinity] f^(n)(0) * x^n / n!

where f^(n)(0) represents the nth derivative of f(x) evaluated at x=0.

We begin by finding the first few derivatives of f(x):

f(x) = (1+x)^(-4/3)

f'(x) = (-4/3)(1+x)^(-7/3)

f''(x) = (28/9)(1+x)^(-10/3)

f'''(x) = (-224/27)(1+x)^(-13/3)

f''''(x) = (2912/81)(1+x)^(-16/3)

Evaluating these derivatives at x=0, we get:

f(0) = 1

f'(0) = -4/3

f''(0) = 14/9

f'''(0) = -56/27

f''''(0) = 208/81

Substituting these values into the Maclaurin series formula, we get:

f(x) ≈ 1 - (4/3)x + (14/9)x^2 - (56/27)x^3 + (208/81)x^4

This gives us the Maclaurin series through degree 4 of f(x)=(1+x)^(-4/3).

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How to solve your question

Solve for y:

-y = 3 y

Subtract 3 y from both sides:

-y - 3 y = 3 y - 3 y

-y - 3 y = -4 y:

-4 y = 3 y - 3 y

3 y - 3 y = 0:

-4 y = 0

Divide both sides of -4 y = 0 by -4:

(-4 y)/(-4) = 0/(-4)

(-4)/(-4) = 1:

y = 0/(-4)

0/(-4) = 0:

Answer: | y = 0

Answer:

C

Step-by-step explanation:

The total profit function, P(t), is: P(t) = -e^(-t^2) - 10000 + e^(-9) dollars

a) To find the total profit function, we need to integrate the given profit rate function, P'(t), with respect to time, t.

∫P'(t) dt = ∫te^(-t^2) dt

Let's integrate using the substitution method:

Let u = -t^2

Then, du = -2t dt

Rewriting the integral in terms of u:

∫te^(-t^2) dt = -∫e^u du

Integrating:

∫te^(-t^2) dt = -∫e^u du = -e^u + C = -e^(-t^2) + C

Since we're given that the total profit in the third year is $10,000, we can find the value of C:

-10000 = -e^(-3^2) + C

Solving for C:

C = -10000 + e^(-9)

(b) In the long run, as t approaches infinity, the term e^(-t^2) becomes negligibly small. This is because the exponential function decays rapidly as the exponent becomes more negative. Consequently, the total profit function approaches a constant value of -10000 + e^(-9) dollars.

In other words, in the long run, the total amount of profit stabilizes and reaches a steady state of approximately -10000 + e^(-9) dollars. This indicates that the growth of profit from the new technology eventually levels off and does not increase significantly beyond this value.

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Answer:

y = -4 - 1/3x

Step-by-step explanation:

x + 3y = -12

-x              -x

3y = -12 - x

divide all by 3, to isolate the y

y = -4 - 1/3x

Thus, the integral of xe^yds on the circle from (2,0) to (5,4) is equal to 207/8 e^4 - 23/8.

To solve this problem, we will use the line integral formula:
∫(P dx + Q dy) = ∫(P(x,y) dx + Q(x,y) dy)

where P and Q are the x and y components of the vector field F(x,y) = (xe^y, 0).

First, we need to parameterize the given circle. We can do this by using the parametric equations:

x = 2 + 3t
y = 4t

where 0 ≤ t ≤ 1.

Next, we can compute the differential ds:

ds = √(dx^2 + dy^2) = √(9 + 16) dt = 5 dt

Now, we can substitute the parametric equations and ds into the line integral formula:

∫(P dx + Q dy) = ∫(xe^y dx) = ∫(xe^y dx/dt dt) = ∫((2+3t)e^(4t) 3 dt)

Evaluating the integral gives:

∫(xe^yds) = ∫((2+3t)e^(4t) 3 dt) = 207/8 e^4 - 23/8

Therefore, the integral of xe^yds on the circle from (2,0) to (5,4) is equal to 207/8 e^4 - 23/8.

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Answer:

A

A would be the best answer since it asking how much did it change.

Answer:

Reduction

Step-by-step explanation:

In this problem, there are 2 triangles: the solid lines represent the preimage and the dotted lines represent the image. All of the vertices of the dotted lines are inside the solid line. This means that the preimage is larger than the image. If the preimage is larger, then a reduction has occurred.

There are 2 ways to tell that this is a reduction. The simplest is to just say that the image is inside the preimage and therefore smaller. More mathematically, you could also see that all of the coordinate pairs are closer to the origin by a scale factor of 2/3. Thus, the triangle must be smaller and reduced.

The number of teams formed by the total number of students will be 4.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that centre, Middle School is having a pie eating contest and needs a team consisting of 5 people from Mrs Brown's classroom. There are 20 students in Mrs Brown's classroom.

The number of teams will be calculated as,

N = 20 / 5

Therefore, the number of teams formed by the total number of students will be 4.

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Answer:

Mary ran the farthest

Step-by-step explanation:

Look at Diagram :)

As the Diagram shows, Mary ran the farthest!

Hope this Helps!

Answer:

Step-by-step explanation:

Given function

From the table we get the function g(x), use pairs (1, 10) and (3, 14)

The slope:

The y-intercept:

The function g(x) is found as:

The y- intercept of f (x) is subtracted from the y-intercept of g (x):

Answer:

(the answer is • -4)

...

Answer:

x = -2

Step-by-step explanation:

-6x + 6 = -4x-2
add 6 to both sides and you get

-6x = -4x +4

add 4x to both sides and you get

-2x = 4

divide by -2

x = -2

Evening alexisann,

Let's Move all terms containing x to the left side of the equation.

which gives us -2x + 6 = -2

Next, Move all terms not containing x to the right side of the equation.

-2x = -8

Then we divide each term in -2x = -8 by -2 and simplify to get the following:

X=4

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Length of YZ = 29.5

Two triangles are similar if their corresponding angles are equal and their corresponding sides are within the same ratio (or proportion). Similar triangles will have the same shape, but not necessarily the same size.

Given,

∵ ABCD ~ WXYZ

∴ By the figure ΔADC ~ ΔYWZ

∴ AD/DC = WZ/YZ

AD = 8, DC = 4, and WZ = 59

⇒ 8/4 = 59/YZ

⇒ 2 = 59/YZ

⇒ 2YZ = 59

⇒ YZ = 29.5

Hence, 29.5 is the length of YZ.

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The cost of 250 bricks, delivered to a worksite, is $170. The cost of 400 bricks delivered is $245 and the cost to have 320 bricks will delivered $217.6 .

The cost of 250 bricks, delivered to a worksite, is $170.

So , we can calculate the single brick cost need to divide 170/250=0.68

Single brick cost is 0.68

The cost of 400 bricks delivered is $245.  In this case a single brick cost is 0.6125

The answers is different from the first answer we can calculate  320  brick cost 320×0.68=217.6

The following equation is used to calculate the Cost Per Brick. To calculate the cost per brick, divide the total cost of the bricks by the number of bricks. Bricks in 1 cubic Feet (cft) = Volume of brickwork/ Volume of one brick with mortar. Thus, thumb rule formula: No. of bricks in wall per Cubic Feet= (Area in Cft × 14).

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Answer:

\(n=3.875\)

Step-by-step explanation:

First, we can expand the brackets:

\(-(5n-9)+3n=-2(5n-20)\) (given)

\(-5n+9+3n=-10n+40\)

\(-2n+9=-10n+40\) (combine like-terms)

\(8n=31\)

\(n=3.875\)

Hope this helps :)

Answer:

answer and explanation in the pics above

hope it helps

Answer:

500 meters above sea level

Step-by-step explanation:

600-100 = 500

Answer:

362

Step-by-step explanation:

Answer:

\(x - 12 \\ coefficent = 1 \\ constant = - 12 \\ thnk \: you\)