The fraction 7 8 is really close to 1 , so Yvonne could estimate that she needs approximately yards of fabric per dress. So, to make 5 dresses she would need approximately yards of fabric.

Answer:

We have that the sum of two numbers  is 9

this can be written as:

x + y  = 9

where x is the larger number.

Now we want to write:

"the difference between one more than the larger number and twice the smaller number"

First, remember that the difference between A and B is:

A - B

Then "the difference between one more than the larger number and twice the smaller number"

is:

"one more than the larger number" = ( x + 1)

"twice the smaller number" = 2*y

the difference between these is:

(x + 1) - 2*y

Now we can simplify:

We know that:

x + y = 9

then:

y = 9 - x

replacing that in the equation:

(x + 1) - 2*y

we would get:

x + 1 - 2*(9 - x)

x + 1  -18 + 2x

(x + 2x) + (1 - 18)

3x - 17

This means that we can write:

"the difference between one more than the larger number and twice the smaller number"

as: 3x - 17

Answer:

  A.  f(0) = 4

  B.  f(6) = 8

Step-by-step explanation:

When evaluating a piecewise function, the fist step is to determine the applicable domain. Then the function defined for that domain is the one that is used for the evaluation.

x = 0 is in the domain x < 5, so the applicable function is f(x) = x+4.

  f(0) = 0 +4 = 4

__

x = 6 is in the domain 5 ≤ x < 7, so the applicable function is f(x) = 8.

  f(6) = 8

Answer:

Matrix with 1 row and 3 columns consisting of elements 17, 13, and 21.

Step-by-step explanation:

This is because the table shows the number of houses available in each city and the columns represent the number of houses of each type (1-bedroom, 2-bedroom, and 3-bedroom). The row for Miami corresponds to the numbers 17, 13, and 21, indicating the availability of 17 1-bedroom houses, 13 2-bedroom houses, and 21 3-bedroom houses in Miami.

The coordinates of Z' are (3, 4)

The given parameters are:

W(-2, -3) X(-2, 1) Y(4, 1) and Z(4, -3).

The rotation is given as:

90° counter-clockwise

The rule of the above rotation is:

(x, y) = (-y, x)

For point Z, we have

Z'= (3, 4)

Hence, the coordinates of Z' are (3, 4)

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The $1314^\text{th}$ digit past the decimal point is 2.

To find the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$, we can use long division to compute the decimal expansion of the fraction.

The long division of $\frac{5}{14}$ is as follows:

```

0.35    <-- Quotient

-----

14 | 5.00

   4.2    <-- Subtract: 5 - (14 * 0.3)

   -----

     80   <-- Bring down the 0

     70    <-- Subtract: 80 - (14 * 5)

     -----

     100   <-- Bring down the 0

      98    <-- Subtract: 100 - (14 * 7)

      -----

       20   <-- Bring down the 0

       14    <-- Subtract: 20 - (14 * 1)

       -----

        60   <-- Bring down the 0

        56    <-- Subtract: 60 - (14 * 4)

        -----

         40   <-- Bring down the 0

         28    <-- Subtract: 40 - (14 * 2)

         -----

         120   <-- Bring down the 0

         112    <-- Subtract: 120 - (14 * 8)

         -----

           80   <-- Bring down the 0

           70    <-- Subtract: 80 - (14 * 5)

           -----

           ...

```

We can see that the decimal expansion of $\frac{5}{14}$ is a repeating decimal pattern with a repeating block of digits 285714. Therefore, the $1314^\text{th}$ digit past the decimal point is the same as the $1314 \mod 6 = 0^\text{th}$ digit in the repeating block.

Since $1314 \mod 6 = 0$, the $1314^\text{th}$ digit past the decimal point in the decimal expansion of $\frac{5}{14}$ is the first digit of the repeating block, which is 2.

So, the $1314^\text{th}$ digit past the decimal point is 2.

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Answer:

Slope of the line, m = 4/3

Step-by-step explanation:

Given;

4x - 1 = 3y + 5

Make y the subject

4x - 1 = 3y + 5

4x - 3y = 5 + 1

4x - 3y = 6

-3y = 6 - 4x

Divide both sides by -3

y = (6 - 4x) / -3

y = -2 + 4/3x

Slope intercept form is given by

y = mx + b

Where,

m = slope

y = - 2 + 4/3x

m = 4/3

Slope of the line, m = 4/3

Answer:

Above answer is INCORRECT.

The CORRECT answer is 2/3

Step-by-step explanation:

The function represents the difference h(x) is x^2+7x.

You know that the area of Rectangle A is given by

\(f(x) = 4x^2 + 6x\)

And the area of Rectangle B is given by

\(g(x) = 3x^2 - x\)

Therefore, to find the function representing the difference, you need to subtract the functions f(x) and g(x).

The way in which two things are being compared is not the same or the fact of not being the same.

Then, you get this function h(x)

\(h(x)=f(x)-g(x)\\h(x)=4x^2 + 6x-(3x^2 - x)\\h(x)=4x^2+6x-3x^2+x\\h(x)=x^2+7x\)

Therefore the function represents the difference h(x) is x^2+7x.

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Answer: D

Step-by-step explanation:

Answer:

Option (C)

Step-by-step explanation:

To determine the population we use the formula,

\(P_n=P_0(1+r)^{n}\)

Where \(P_n\) = final population

\(P_0\) = Initial population

r = percentage growth

Now we substitute these values in the formula,

\(7921=7547(1+r)^1\)

\(\frac{7921}{7547}=(1+r)\)

r = 1.0496 - 1

r = 0.0496

r = 0.05

Therefore, percentage growth of the population of Stark county is 5%.

Option (C). will be the answer.

Answer:

2(1/5)

Step-by-step explanation:

7(1/5) - 3(11/5)

= {(35 + 1)/5} - {(14+11)/5}

= (36/5) - (25/5)

Take the LCM of the denominator 5 and 5 is 5 as common.

= (36*1 - 25*1)/5

= (36 - 25)/5

= 11/5

= 2(1/5) → [Mixed fraction] Ans.

Please let me know if you have any other questions.

Answer:

50 days

Step-by-step explanation:

40×300=1200

1200-700

500

so 1 day is 10 . 50 days is 500

The number of days he was absent from work will be 50 days

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that a man gets Rs. 40 for every day he works, but is fined Rs. 10 for every day he is absent If he got Rs. 700 at the end of 30 days.

The number of days he was absent from work will be calculated as below:-

40×300 = 1200

             = 1200-700

             = 500

1 day is 10 then 50 days is 500. Therefore, the number of days he was absent from work will be 50 days

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Answer:

it's a linear problem

Step-by-step explanation:

0=1

1=2

2=3

3=4

4=5

5=6

6=7

7=8

8=9

9=10

Answer:

Number of more red cup = 1.5 cups

Step-by-step explanation:

Given:

Number of white cup = 4

Number of red cup = 6

Number of more white cup = 1

Find:

Number of more red cup

Computation:

Number of more red cup = Number of more white cup x [Number of red cup / Number of white cup]

Number of more red cup = 1 [6/4]

Number of more red cup = 1.5 cups

The connection that will have the same constant of proportionality will likewise have a slope of 3, and the constant of proportionality is 3.

We must first obtain the equation of the line before we can get the proportionality constant for the given graph.

Y = mx + b is the standard equation for a line.

With reference to the coordinates (0, 0) and (2, 6)

Get the "m" slope.

\(m = \frac{(6 -0)}{2-0} \\\\m = \frac{6}{2} \\\\m= 2\)

The y-intercept is 0 since the line traveled through the origin.

Obtain the necessary equation:

y = mx + b

y = 3x + 0

y = 3x

The proportionality constant is determined by the equation to be 3. The slope of the connection, which will have the same proportionality constant, will be 3.

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Answer:

180°

Step-by-step explanation:

Answer:

The answer is (3×7) + (12×2) .

\((3 \times 7) + (12 \times 2)\)

\( = 21 + 24\)

\( = 45\)

Answer:

A) Yes, m=-3 and b = -3

Step-by-step explanation:

The m is the slope of the line and the b is the y-intercept. We can see that the y-intercept is at -3, so that means D and B are not the answer. This leaves us with A and C. The slope of the line is going down instead of up, meaning that the slope of the line is negative. This means that C is not the answer.

Therefore, the answer is A, m= -3 and b= -3.

Given the following, Mass of the wooden rod, m = 0.180 kgLength of the wooden rod, l = 1.25 m Distance of the spot on the rod from the axis of rotation, r = 0.95 m(a) What is the angular acceleration of the rod after it is released?The angular acceleration, α = ?

The moment of inertia, I of a rod pivoted at one end, having length L and mass M is given by;I = (1/3)ML²Substitute the given values,

I = (1/3) x 0.180 kg x (1.25 m)²

I = 0.0478 kg m²

The torque,

τ = Iα

We know that torque, τ = FrWhere, F is the force applied at a perpendicular distance r from the axis of rotationOn releasing the wooden rod, the force of gravity acting on it provides the torque around the pivot.

Thus,τ = Frg, where g is the acceleration due to gravityτ = Iαα = (τ/I)α = (mgr)/Iα = (0.180 kg x 9.81 m/s² x 1.25 m)/(0.0478 kg m²)α = 94.8 rad/s²

The angular acceleration of the rod is 94.8 rad/s².(b) What is the linear acceleration of a spot on the rod that is 0.95 m from the axis of rotation.

The linear acceleration,

a = ?a = rαa = (0.95 m) x (94.8 rad/s²)

a = 90.06 m/s²

The linear acceleration of the spot is 90.06 m/s².(c) At what location along the rod should a die be placed (figure 11-9) so that the die just begins to separate from the rod as it falls?The location of the die along the rod, x = ?We know that the force applied at the point, x, on the rod is equal to the weight of the rod that is acting on this point. We can use this fact to determine the location of the die.x is such that

mg = Fg = ma

Where,Fg is the force acting on the die,mg is the weight of the rodma is the force acting on the die, which is equal to

FgFg = mgFg = 0.180 kg x 9.81 m/s²

Fg = 1.764 N

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Explanation:

The point (3,a) means that x = 3 and y = a pair up together

Plug in those values and compute 'a'

y = 9-4x

a = 9-4(3)

a = 9-12

a = -3

The point (3, a) updates to (3, -3)

The point (3, -3) is on the line y = 9-4x

The number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

Specify the correct number from the list below that corresponds to the appropriate null and alternative hypotheses for this problem.

It should be noted that the null hypothesis suggests that there's no statistical relationship between the variables.

The alternative hypothesis is different from the null hypothesis as it's the statement that the researcher is testing.

In this case, the number that corresponds to the null hypothesis and the alternative hypothesis will be 3 and 6 respectively.

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If there is a positive correlation between x and y in the regression equation y = bx + a, then b > 0.

In the regression equation, y = bx + a, a positive correlation between x and y indicates that as the value of x increases, the value of y also increases, and vice versa. The correlation between these two variables is represented by the coefficient b in the equation.

A positive correlation means that b > 0, as a positive value for b will result in y increasing when x increases. On the other hand, if b < 0, it would indicate a negative correlation, meaning that y would decrease as x increases.

The constant term a in the equation represents the y-intercept or the value of y when x is equal to zero. It does not directly affect the correlation between x and y, so it can be either positive (a > 0) or negative (a < 0) depending on the specific data being analyzed. The value of a will only shift the position of the regression line on the graph, while the slope (b) determines the direction of the correlation between the variables.

In conclusion, if there is a positive correlation between x and y in the regression equation y = bx + a, then b > 0. The values of a > 0 or a < 0 are not directly related to the correlation between x and y.

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The graph of g(x) is the graph of f(x) stretched vertically and reflected over the axis.

The correct option is C.

We can compare the graphs of two functions f(x)=x² and g(x)=-2/3 x² by determining their vertices, domain, range, axis of symmetry, and shape of the graphs. The vertex of f(x)=x² is at the origin (0,0), which means that the parabola opens upward and is symmetrical around the y-axis.

The domain is all real numbers, and the range is y≥0. The axis of symmetry is the y-axis. On the other hand, the vertex of g(x)=-2/3 x² is also at the origin, and it opens downward. It is also symmetrical around the y-axis. The domain is all real numbers, and the range is y≤0.

The axis of symmetry is the y-axis, just like f(x).It is important to remember that g(x) is the negative of f(x), which indicates that g(x) is reflected across the x-axis. Furthermore, the stretch factor is 2/3, which makes the graph of g(x) flatter than the graph of f(x) and it is  stretched vertically and reflects over x axis(option c).

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Answer:

Step-by-step explanation: T20 = (-1)^20 3520(c)^15(d)^20

= 35c20c^15 d^20

The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose.

The steepest angle at which unconsolidated granular material remains stable is known as the angle of repose. This angle varies depending on the properties of the granular material such as size, shape, and degree of consolidation. The angle of repose is a critical factor in many fields such as engineering, geology, and agriculture. For example, in civil engineering, the angle of repose is essential in designing stable slopes and retaining walls. In agriculture, it is crucial for understanding the flow and distribution of granular materials such as seeds, fertilizers, and grains. In general, the angle of repose for unconsolidated granular materials ranges from 25 to 45 degrees, but it can be higher for certain materials such as sand, or smaller for cohesive soils.
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The answer is , the determinant of the given matrix is:

det = x * ((3q+b) * 2r + 2q * (3r+c)) + (3p+a) * (y * 2r + 2q * z) + 2p * (y * (3r+c) + (3q+b) * z)

To compute the determinant of the given matrix:

\(\left[\begin{array}{ccc}-x&3p+a&2p\\-y&3q+b&2q\\-z&3r+c&2r\end{array}\right]\)

You can use the property that if you multiply any row (or column) of a matrix by a scalar, the determinant is also multiplied by that scalar.

In this case, we can multiply the second row by -1:

\(\left[\begin{array}{ccc}-x&3p+a&2p\\y&-3q-b&-2q\\-z&3r+c&2r\end{array}\right]\)

Now, we can expand the determinant using the first row:

det = -x * (-1)⁽¹⁺¹⁾ * det of the minor matrix + (3p+a) * (-1)⁽¹⁺²⁾ * det of the minor matrix + 2p * (-1)⁽¹⁺³⁾ * det of the minor matrix

Since the determinant of the 2 × 2 minor matrix is just the product of its diagonal elements minus the product of its off-diagonal elements, we have:

det = -x * ((-1) * (-(3q+b) * 2r - 2q * (3r+c))) + (3p+a) * ((-1) * (-y * 2r - 2q * (-z))) + 2p * ((-1) * (-y * (3r+c) - (-(3q+b)) * (-z)))

Simplifying further:

det = x * ((3q+b) * 2r + 2q * (3r+c)) + (3p+a) * (y * 2r + 2q * z) + 2p * (y * (3r+c) + (3q+b) * z)

Therefore, the determinant of the given matrix is:

det = x * ((3q+b) * 2r + 2q * (3r+c)) + (3p+a) * (y * 2r + 2q * z) + 2p * (y * (3r+c) + (3q+b) * z)

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∫_A^B ∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr dθ.

This represents the full iterated integral for F_sav over the given solid cylinder.

(a) The iterated integral for F_sav with the given limits of integration is as follows:

∫∫∫_W (10%)(x^2 + y^2 + z^12) dz dr dθ,

where the limits of integration are A = 0, B = C = 0, D = 6, and E = -1.

(b) To evaluate the integral, we begin with the innermost integration with respect to z. Since z ranges from -1 to 6, the integral becomes:

∫∫_D^E (10%)(x^2 + y^2 + z^12) dz.

Next, we integrate with respect to r, where r represents the radial distance from the z-axis. As the solid cylinder is centered about the z-axis and has a base radius of 6, r ranges from 0 to 6. Thus, the integral becomes:

∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr.

Finally, we integrate with respect to θ, where θ represents the angle around the z-axis. As the cylinder is symmetric about the z-axis, we integrate over a full circle, so θ ranges from 0 to 2π. Hence, the integral becomes:

∫_A^B ∫_B^C ∫_D^E (10%)(x^2 + y^2 + z^12) dz dr dθ.

This represents the full iterated integral for F_sav over the given solid cylinder.

The problem asks for the iterated integral of F_sav over the solid cylinder W. To evaluate this integral, we use the cylindrical coordinate system (r, θ, z) since the cylinder is centered about the z-axis. The function inside the integral is 10% times the sum of squares of x, y, and z^12. By integrating successively with respect to z, r, and θ, and setting appropriate limits of integration, we obtain the final iterated integral. The integration limits are determined based on the given dimensions of the cylinder.

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Answer:

The slope is 6

Step-by-step explanation:

f(x)=2(3x-7)

Distribute the 2

f(x)=2*3x-2*7

f(x) = 6x -14

This is in slope intercept form

y = mx+b  where m is the slope and b is the y intercept

The slope is 6 and the y intercept is -14

The slope is 6

Answer: slope =1/2  y intercept (0,6)

Step-by-step explanation: use the slope and y intercept form y=mx + b