Zack fills two bird feeders with birdseed. Each bird feeder holds 2 1/2​ ​ cups of birdseed. Zack's scoop holds 1/4 cup. Write an expression for the number of scoops Zack needs to fill both feeders.

Answer:

3a² + ab + 4b²

Step-by-step explanation:

P - Q

= - 4a² - 2ab + 9b² - (- 7a² - 3ab + 5b² ) ← distribute parenthesis by - 1

= - 4a² - 2ab + 9b² + 7a² + 3ab - 5b² ← collect like terms

= 3a² + ab + 4b²

Answer:

3a² + ab + 4b²

Step-by-step explanation:

Combine like terms. Like terms have same variable with same power.

P - Q = -4a² - 2ab + 9b² - (-7a² - 3ab + 5b²)

To open the brackets, multiply each term of Q by (-1)

          = -4a² - 2ab + 9b² + 7a²+ 3ab - 5b²

-4a² and 7a² are like terms.

(-2ab) and  3ab  are like terms.

9b² and (-5b²) are like terms.

          = -4a² + 7a² -2ab + 3ab + 9b²- 5b²

          = 3a² + ab + 4b²

The expression is 723+189 and the solution is 912.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.

Here the given statement is  sum of 723 and 189 then the expression is

The word for sum is '+". Then,

=> 723+189

=> 912

Hence the expression is 723+189 and solution is 912.

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Answer:

c

Step-by-step explanation:

x=1 g(x)=-10

x=2 g(x)=-12

x=3 g(x)=-14

f(x)=x+4

=＞ g(x)=-2·(x+4)

Answer:

1/4

Step-by-step explanation:

Answer:

The answer is 9.625

Step-by-step explanation:

So what you have is the area and the base of the rectangle. To find the height, just divide 4 into 38.5

38.5 / 4 = 9.625

To double check just multiple 9.625 by 4

9.625 x 4 = 38.5

Hope this helps

The required value of y for the unit circle is: 2/3

The circle is defined as the locus of a point whose distance from a fixed point is constant i.e center (h, k).

The equation of the circle is given by:

(x - h)² + (y - k)² = r²

where:

h, k is the coordinate of the center of the circle on coordinate plane.

r is the radius of the circle.

Here,

Equation of the unit circle is given as,

x² + y² = 1

Now substitute the given value in the equation,

5/9 + y² = 1

y² = 1 - 5/9

y² = 4/ 9

y = √(4/9)

y = 2/3

Thus, the required value of y for the unit circle is 2/3

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It is a rectangular region with u and v values ranging from 1 to 2.

To find the Jacobian of the transformation x = 3u, y = 2uv, we need to compute the partial derivatives ∂x/∂u, ∂x/∂v, ∂y/∂u, and ∂y/∂v.

Given:

x = 3u

y = 2uv

Calculating the partial derivatives:

∂x/∂u = 3

∂x/∂v = 0 (since x does not depend on v)

∂y/∂u = 2v

∂y/∂v = 2u

Now, we can construct the Jacobian matrix J:

J = [∂x/∂u   ∂x/∂v]

   [∂y/∂u   ∂y/∂v]

Substituting the partial derivatives we calculated earlier:

J = [3   0]

   [2v  2u]

Therefore, the Jacobian of the transformation is:

J = [3   0]

   [2v  2u]

To sketch the region described by the inequalities g: 3 < 3u < 6, 2 < 2uv < 4, we can consider the ranges of u and v that satisfy these conditions.

From the inequality 3 < 3u < 6, we have:

1 < u < 2

From the inequality 2 < 2uv < 4, we can divide both sides by 2:

1 < uv < 2

Since u and v must both be greater than 1, we can determine the range of v:

1 < v < 2

Now, we can sketch the region in the u-v plane bounded by the conditions:

1 < u < 2

1 < v < 2

It is a rectangular region with u and v values ranging from 1 to 2.

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The area under the curve between z = −2.0 and z = −1.0 is 0.1359.

We can use tables to find the area under the normal curve between two values of z.

However, tables give areas from z = 0 to z = 3.9 (beyond which there is literally no change). But as the normal curve is symmetric at z = 0, we can use it to find between any two given z values.

For example, for the area under the curve between z = −2.0 and z = −1.0, we can take values for z = 2.0 and z = 1.0; their difference will give the area between z = −2.0 and z = −1.0.

From tables for z = 1.0, we have 0.8413 and for z = 2.0, we have 0.9772 and

Hence, the Area under the curve between z = −2.0 and z = −1.0 is 0.9772−0.8413 = 0.1359.

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Answer:

A) The number of wallpapers needed to cover the walls is 6 double roll wall papers

B) The number of wall paper border rolls needed is 3 rolls

Step-by-step explanation:

A) The given parameters are;

The dimensions of the room are 9 ft. by 12 ft. by 8 ft. high,

The area one double role wallpaper covers = 60 ft.²

Therefore, we have;

The area of the room wall = 12 × 8 × 2 + 9 × 8 × 2 = 336 ft²

The number of double rolls of wallpaper to be used = Area of wall/(area of wallpaper) = 336/60 = 5.6

Therefore, given that the wall papers are sold in single units, we round up to the next whole number of units to get;

The number of wallpapers needed to cover the walls = 6 double roll wall papers

B) The borders of a wallpaper are installed parallel (and installed along) to the ceiling line

Therefore, the amount of wallpaper border required is given as follows;

Wall paper border length required = 2 × Length of the room + 2 × Width of the room

∴ Wall paper border length required = 2 × 9 ft. + 2 × 12 ft. = 42 ft.

The size of each wall paper border sold = 5 yd. = 15 ft.

Therefore;

The number of wall paper border rolls required = 42 ft./(5 yd.) = 42 ft./(15 ft.) = 2.8 rolls

Therefore, we round up to get the number of wall paper border rolls needed as 3 rolls of wall paper borders.

The problem of unit root in standard regression and time-series models arises when a variable exhibits a non-stationary behavior, meaning it has a trend or follows a random walk. Unit root tests, such as the Dickey-Fuller and augmented Dickey-Fuller tests, are used to detect the presence of a unit root in a time series. These tests examine whether the coefficient on the lagged value of the variable is significantly different from one, indicating the presence of a unit root.

In standard regression analysis, it is typically assumed that the variables are stationary, meaning they have a constant mean and variance over time. However, many economic and financial variables exhibit non-stationary behavior, where their values are not centered around a fixed mean but instead follow a trend or random walk. This presents a problem because standard regression techniques may produce unreliable results when applied to non-stationary variables.

Time-series models, such as autoregressive integrated moving average (ARIMA) models, are specifically designed to handle non-stationary data. They incorporate differencing techniques to transform the data into a stationary form, allowing for reliable estimation and inference. Differencing involves computing the difference between consecutive observations to remove the trend or random walk component.

The Dickey-Fuller test and augmented Dickey-Fuller test are commonly used to detect the presence of a unit root in a time series. These tests examine the coefficient on the lagged value of the variable in a regression framework. The null hypothesis of the tests is that the variable has a unit root, indicating non-stationarity, while the alternative hypothesis is that the variable is stationary.

The Dickey-Fuller test is a simple version of the test that includes only a single lagged difference of the variable in the regression. The augmented Dickey-Fuller test extends this by including multiple lagged differences to account for potential serial correlation in the data. Both tests provide critical values that can be compared to the test statistic to determine whether the null hypothesis of a unit root can be rejected.

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Answer:

Step-by-step explanation:

First note that the triangles shown are isosceles triangles due to equality of two of their sides which is radius. So their baseline angles are equal

Since their middle angle are equal too, so their 3 angles are the same. It menas both triangles are similar.

However, we know two of three sides are equal, but the third should be also because of their similarity.

y+4 = 2y - 3

2y - y = 4 - 3

y = 4+3

y = 7

Therefore,

2y-3 = 2.7-3 = 14-3 = 11

Answer is 11 centimeters

Answer:

40

Step-by-step explanation:

Alternating angels are equal if 3 is equal to 40 then 7 must also be forty (this only applies since the lines are parallel)

Answer:

0.147

Step-by-step explanation:

This is rounded to the nearest thousandths place. 11 divided by 75 is 0.147.

Answer:

0.14666666 (or put the symbol for a repeating number on the first 6, that way you don't have to write all of the other sixes)

Hope this helps :)

Answer:

the answer it will be 4cm

Answer: 1.5

Step-by-step explanation:

Khan academy

The measure of angle ZXY of the rectangle WXYZ is 46°.

To find the measure of angle ZXY, we need to use the fact that quadrilateral WXYZ is a rectangle.

Given that m∠ZXW = x-11 and m∠WZX = x-9,

We can say that ∠WXZ = ∠XZY (Alternate Interior angles)

∠WZX + ∠XZY = 90 (all four angles of rectangle are equal to 90°)

x-9+x-11= 90

Simplifying the equation, we get:
2x = 90+20

x = 55

Now,

∠ZXY = ∠WZX (Alternate interior angles)

So, m∠ZXY = x-9 = 55-9 = 46

Therefore, the measure of the angle m∠ZXY is 46°.

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Answer:

it's c the slop is 3 your welcome

The circumference of a circle with a radius of 18 feet is 113.04 ft.

The distance around the circle's edge is referred to as the circumference. It is a basic characteristic of a circle and is incorporated into a number of geometric and trigonometric calculations.

C = 2πr, where C is the circumference, is a mathematical constant, and r is the circle's radius, is the formula for calculating a circle's circumference. An irrational number is one that contains an endless number of decimal places and cannot be stated as a ratio of integers. However, the value of is roughly 3.14 for the majority of practical purposes.

The circle's radius in the provided situation is 18 feet. We can use pi = 3.14 to determine the closest approximation for the circumference of this circle.

C = 2πr = 23.1418 = 113.04 feet.

  So ,the circumference of circle is 113.04 feet.

       Therefore, 113.04 feet is a circle's circumference with a radius of 18 feet.

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Answer:

A

Step-by-step explanation:

the order of letter should resemble the same shape

Dimensions of the parallelogram are:

Its perimeter is:

Its area is:

Perimeter is 2 times greater:

Area is 2*2 = 4 times greater:

Perimeter is 3 times greater:

Area is 3*3 = 9 times greater:

Perimeter is 2 times smaller:

Area is 2*2 = 4 times smaller:

It is false that the cost of two pounds of apple cast is more than $ 3.50.

Here to find the cost of the given quantity we need to find the cost of 1 unit i.e 1 pound in the given problem so that we can find the cost of given quantities. It is called a unitary method.

Given that  

Andrew buy 8 pounds of apples for $ 12.00  

Let 'x' be the cost of 1 pound of apples

By the given data,

=> 8x = $ 12

=> x = 12/8

=> x = 1.5  

The cost of 1 pound of apples = $ 1.5

Cost of 2 pounds apples = 2 × 1.5 = 3

Therefore,

It is false that the cost of two pounds of apple cast is more than $ 3.50.

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Answer:

Mean:

10.5+9.2+0+9.3+10.4+9.2=48.6

48.6 divded by 6 =8.1

Median is 9.3

Mode is 9.2

Step-by-step explanation:

To solve the problem of a vibrating string with damping using numerical methods and time steps, follow these steps:

1. Discretize the string into a set of points along its length.

2. Use a finite difference method, such as the central difference method, to approximate the derivatives in the equation.

3. Apply the difference equation to each point on the string, considering the damping force and given parameters.

4. Set up the initial conditions for the string's displacement and velocity at each point.

5. Iterate over time steps to update the displacements and velocities at each point using the finite difference equation.

6. Compute and store the values of the solution at selected points for analysis.

7. Compare the numerical solution with the analytical solution, if available, to assess accuracy.

8. Plot the results to visualize the behavior of the vibrating string over time.

9. If using MATLAB, write a script to implement the numerical method and generate plots.

Note: The specific equation and initial conditions are missing from the given question, so adapt the steps accordingly.

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Final Answer:

There are 0.036 decimeters in 3.6 millimeters.

Explanation:
To convert from millimeters to decimeters, we can use the following measurement conversion:

1 millimeter = 0.01 decimeters

So, to find out how many decimeters are in 3.6 millimeters, we can multiply 3.6 by 0.01:

3.6 * 0.01 = 0.036

Therefore, there are 0.036 decimeters in 3.6 millimeters.

To solve the equation \begin{equation}-\log{\left(x^2 - 15\right)} = \log{\left(2x\right)}\end{equation}, the following steps can be taken:

Apply the logarithmic identity log(a) = log(b) if and only if a = b to obtain the equation x^2 - 15 = 2x.

Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.

Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.

Use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero, to get x - 5 = 0 or x + 3 = 0.

Solve for x in each equation to obtain x = 5 or x = -3.

Therefore, the steps to solve the equation log(x^2 - 15) = log(2x) from 1 to 5 are:

Apply the logarithmic identity to get x^2 - 15 = 2x.

Move all the terms to one side of the equation to get x^2 - 2x - 15 = 0.

Factor the quadratic expression to obtain (x - 5)(x + 3) = 0.

Use the zero product property to get x - 5 = 0 or x + 3 = 0.

Solve for x in each equation to obtain x = 5 or x = -3.

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The sum of the infinite geometric series –288 –216 –144 –72 is -1152.

The sum of an infinite number of terms having a constant ratio between successive terms is called as infinite geometric series.

Given series, -288, -216, -144, -72, ...

The sum of the infinite geometric series can be calculated as:

Sum = \(\dfrac{a}{1 -r}\)

Here, 'a' is the first term of the series and 'r' is the common ratio.

a = -288

The common difference can be calculated as:

r = \(\dfrac{(-216)}{(-288)}\)

= \(\dfrac{3}{4}\)

Substitute the values in the sum formula:

Sum = \(\dfrac{-288}{1 - \dfrac{3}{4}}\)

It can be simplified as:

Sum =  -288 \(\times\) 4

             = -1152

So, the sum of the infinite geometric series is -1152.

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Answer:

Step-by-step explanation:

a. f(-3d) = (-3d)^2 - 2(-3d) - 8 = 9d^2 + 6d - 8

b. f(3) = (3)^2 - 2(3) - 8 = 9 - 8 - 8 = 1 - 8 = -7

c. f(2a - 1) = (2a - 1)^2 - 2(2a - 1) - 8 = 4a^2 - 4a + 1 -4a + 2 - 8 = 4a^2 - 8a - 5

d. g(5)= (2(5)+3)/(5^2 -2(5) + 1) = (10 + 3)/(25 - 10 + 1)= 13/15+1= 13/16

e. g(3x)= (2(3x) + 3))/((3x)^2 - 2(3x) + 1))= (6x + 3)/(9x^2 - 6x + 1)

f. g(-4a + 8) = (2(-4a + 8)) +  3/(-4a + 8)^2 - 2(-4a +8) +1))

         (-8a + 16 + 3)/(16a^2 - 32a + 64 + 8a - 16 + 1)

                    (-8a + 19)/(16a^2 - 24a + 49)

Answer:

l = 194999.45

Step-by-step explanation:

I'm going to assume that you meant 3.14 by 3,14.

336,765 = 3.14 × 0.55 × (l + 0.55)

336,765 ÷ (3.14 × 0.55) = l + 0.55

(336,765 ÷ (3.14 × 0.55)) - 0.55 = l

l = 194999.45

From the fundamental identities, we know that

By substituting this result into the given expression, we have

Now, by distributing sine of phi into the parentheses, we have

or equivalently,

Now, from the Pythagorean identity:

we can note that

Then, by substituting this result into our last result from above, we obtain

Therefore, the answer is:

Answer:

domain: x>=0

range: y>=1

Step-by-step explanation:

domain: x>=0

range: y>=1

A. We have the equation for the line of best fit: Q = -8p + 298, where Q represents the quantity of cables sold and p represents the price in dollars.

B. Rounding to the nearest whole cable, Alejandro would sell approximately 270 cables at a price of $3.65, according to the model.

To find an equation for the line of best fit, we can use the two given points (3.50, 270) and (4.75, 260).

In the first place, how about we decide the slant of the line:

slant = (change in amount)/(change in cost)

= (260 - 270)/(4.75 - 3.50)

= -10 / 1.25

= -8

Using the point-slope form of a linear equation, where (x1, y1) is one of the given points and m is the slope:

y - y1 = m(x - x1)

Plugging in the values (x1 = 3.50, y1 = 270) and the slope (m = -8):

Q - 270 = -8(p - 3.50)

Simplifying the equation:

Q - 270 = -8p + 28

Q = -8p + 298

Now we have the equation for the line of best fit: Q = -8p + 298, where Q represents the quantity of cables sold and p represents the price in dollars.

To predict the number of cables Alejandro would sell at a price of $3.65, we substitute p = 3.65 into the equation:

Q = -8(3.65) + 298

Q = -29.2 + 298

Q ≈ 269.8

Rounding to the nearest whole cable, Alejandro would sell approximately 270 cables at a price of $3.65, according to the model.

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