"One subtracted
from the
product of 4 and
a number is Il”

Answer:

If the animal gained weight, the signed number to represent the weight change would be positive. For example, if the animal gained 10 pounds, the signed number to represent the weight change would be +10. If the animal gained 20 pounds, the signed number would be +20.

Answer:

\(\textsf{13.}\quad(x+1)^2-\dfrac{y^2}{3}=1\)

\(\textsf{14.}\quad\dfrac{x^2}{16}-\dfrac{y^2}{65}=1\)

\(\textsf{15.}\quad y^2-\dfrac{x^2}{9}=1\)

\(\textsf{16.}\quad\dfrac{x^2}{36}-\dfrac{y^2}{64}=1\)

Step-by-step explanation:

\(\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of a vertical hyperbola}\\\\$\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center.\\ \phantom{ww}$\bullet$ $(h,k\pm a)$ are the vertices.\\\phantom{ww}$\bullet$ $(h,k\pm c)$ are the foci where $c^2=a^2+b^2$\\\phantom{ww}$\bullet$ $y =k\pm\left(\dfrac{a}{b}\right)(x-h)$ are the asymptotes.\\\end{minipage}}\)

\(\boxed{\begin{minipage}{7.4 cm}\underline{Standard equation of a horizontal hyperbola}\\\\$\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1$\\\\where:\\\phantom{ww}$\bullet$ $(h,k)$ is the center.\\ \phantom{ww}$\bullet$ $(h\pm a,k)$ are the vertices.\\\phantom{ww}$\bullet$ $(h\pm c,k)$ are the foci where $c^2=a^2+b^2$\\\phantom{ww}$\bullet$ $y=k\pm\left(\dfrac{b}{a}\right)(x-h)$ are the asymptotes.\\\end{minipage}}\)

Given:

As the y-values of the foci and vertices are the same, the hyperbola is horizontal (opening left and right).

The center (h, k) is the midpoint of the vertices.

Therefore, the center is (-1, 0) and so:

Use the formula for the vertices (h±a, k) to determine the value of a:

\(\begin{aligned}\implies h\pm a&=-2\\-1\pm a&=-2\\\pm a&=-1\end{aligned}\)                \(\begin{aligned}\implies h\pm a&=0\\-1\pm a&=0\\\pm a&=1\end{aligned}\)

Therefore:

Use the formula for the foci (h±c, k) to determine the value of c:

\(\begin{aligned}\implies h\pm c&=-3\\-1\pm c&=-3\\\pm c&=-2\end{aligned}\)                \(\begin{aligned}\implies h\pm c &=1\\-1\pm c&=1\\\pm c &=2\end{aligned}\)

Therefore:

To find b² use c² = a² + b² and the found values of a and c:

\(\begin{aligned}\implies c^2&=a^2+b^2\\2^2&=1^2+b^2\\4&=1+b^2\\b^2&=3\end{aligned}\)

Substitute the found values of h, k, a² and b² into the formula to create an equation of the hyperbola:

\(\implies\dfrac{(x+1)^2}{1}-\dfrac{(y-0)^2}{3}=1\)

\(\implies(x+1)^2-\dfrac{y^2}{3}=1\)

Given:

As the y-values of the foci and vertices are the same, the hyperbola is horizontal.

The center (h, k) is the midpoint of the vertices.

Therefore, the center is (0, 0) and so:

Use the formula for the vertices (h±a, k) to determine the value of a:

\(\begin{aligned}\implies h\pm a&=\pm4\\0\pm a&=\pm4\\\pm a&=\pm4\end{aligned}\)

Therefore:

Use the formula for the foci (h±c, k) to determine the value of c:

\(\begin{aligned}\implies h \pm c&=\pm9\\0\pm c&=\pm9\\\pm c&=\pm9\end{aligned}\)

Therefore:

To find b² use c² = a² + b² and the found values of a and c:

\(\begin{aligned}\implies c^2&=a^2+b^2\\9^2&=4^2+b^2\\81&=16+b^2\\b^2&=65\end{aligned}\)

Substitute the found values of h, k, a² and b² into the formula to create an equation of the hyperbola:

\(\implies\dfrac{(x-0)^2}{16}-\dfrac{(y-0)^2}{65}=1\)

\(\implies\dfrac{x^2}{16}-\dfrac{y^2}{65}=1\)

Given:

As the x-values of the vertices are the same, the hyperbola is vertical (opening up and down).

The center (h, k) is the midpoint of the vertices.

Therefore, the center is (0, 0) and so:

Use the formula for the vertices (h, k±a) to determine the value of a:

\(\begin{aligned}\implies k \pm a&=\pm1\\0\pm a&=\pm1\\\pm a&=\pm1\end{aligned}\)

Therefore:

Use the formula for the asymptotes to determine the value of b:

\(\begin{aligned}\implies k\pm\left(\dfrac{a}{b}\right)(x-h)&=\pm\dfrac{1}{3}x\\\\0\pm \left(\dfrac{1}{b}\right)(x-0)&=\pm\dfrac{1}{3}x\\\\\pm\dfrac{1}{b}x&=\pm\dfrac{1}{3}x\\\\\pm b&=\pm3\end{aligned}\)

Therefore:

Substitute the found values of h, k, a² and b² into the formula to create an equation of the hyperbola:

\(\implies\dfrac{(y-0)^2}{1}-\dfrac{(x-0)^2}{9}=1\)

\(\implies y^2-\dfrac{x^2}{9}=1\)

As the y-values of the vertices are the same, the hyperbola is horizontal.

The center (h, k) is the midpoint of the vertices.

Therefore, the center is (0, 0) and so:

Use the formula for the vertices (h±a, k) to determine the value of a:

\(\begin{aligned}\implies h \pm a&=\pm6\\0\pm a&=\pm6\\\pm a&=\pm6\end{aligned}\)

Therefore:

Use the formula for the asymptotes to determine the value of b:

\(\begin{aligned}\implies k \pm\left(\dfrac{b}{a}\right)(x-h)&=\pm\dfrac{4}{3}x\\\\0\pm \left(\dfrac{b}{6}\right)(x-0)&=\pm\dfrac{4}{3}x\\\\\pm \dfrac{b}{6}x&=\pm\dfrac{4}{3}x\\\\ \pm b&=\pm8\end{aligned}\)

Therefore:

Substitute the found values of h, k, a² and b² into the formula to create an equation of the hyperbola:

\(\implies \dfrac{x^2}{36}-\dfrac{y^2}{64}=1\)

Answer:

Either B or D

Step-by-step explanation:

Answer:

-110

Step-by-step explanation:

-70 + -40 = -110

Answer:

Justin's salary will be $1048 when he sells $3400 worth of merchandise.

Step-by-step explanation:

If the salesperson receives a monthly base pay and the commission on the sales expression that represents his monthly pay,

y = B + C(x)

Here y = Monthly pay

B = Base pay

C = percentage of commission

x = Amount of sales done

If he sells $500 worth of merchandise in a month, he earns $410,

410 = B + C(500) -----(1)

If he sells $900 worth of merchandise in a month, he earns $498,

498 = B + C(900) ------(2)

By subtracting equation (1) from equation (2),

498 - 410 = 900C - 500C

88 = 400C

C = \(\frac{88}{400}\)

C = 0.22

From equation (1),

410 = B + 0.22(500)

B = 410 - 110

B = $300

Therefore, expression for the monthly earning will be,

y = 300 + 0.22(x)

Justin's salary when he sells $3400 worth of merchandise in a month,

y = 300 + 0.22(3400)

y = 300 + 748

y = $1048

Therefore, Justin's salary will be $1048.

The equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

To determine the solutions to the equation log₂(x - 1) = x³ - 4x, we can set the two expressions equal to each other:

log₂(x - 1) = x³ - 4x

Since we know that the graphs of the two functions intersect at the points (2, 0) and (1.1187, -3.075), we can substitute these values into the equation to find the solutions.

For the point (2, 0):

log₂(2 - 1) = 2³ - 4(2)

log₂(1) = 8 - 8

0 = 0

The equation holds true for the point (2, 0), so (2, 0) is one solution.

For the point (1.1187, -3.075):

log₂(1.1187 - 1) = (1.1187)³ - 4(1.1187)

log₂(0.1187) = 1.4013 - 4.4748

-3.075 = -3.0735 (approx.)

The equation is not satisfied for the point (1.1187, -3.075), so (1.1187, -3.075) is not a solution.

Therefore, the equation log₂(x - 1) = x³ - 4x has one solution at x = 2.

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The volume of the solid is (32/15)πp³.

The region bounded by the parabola 4py = x² and the square root function y = √4px is a shape that looks like a sideways "U". To find the volume of the solid obtained by rotating this region around the x-axis, we use the method of cylindrical shells.

The radius of each cylindrical shell is given by r = y = √(4px). The height of each cylindrical shell is given by h = dx. The volume of each cylindrical shell is given by V = 2πrhdx = 2πx(4px)^(1/2)dx. To find the total volume, we integrate V with respect to x from 0 to 4p.

∫[0,4p] 2πx(4px)^(1/2)dx

= (32/15)πp³

Therefore, the volume of the solid is (32/15)πp³.

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The area of the composite figure is 28 square miles, which is option A. So, the correct option is A.

To find the area of the composite figure, we need to add the areas of the two shapes. The figure is made up of a rectangle and a triangle.

The rectangle has a length of 7 miles and a width of 4 miles, so its area is 7 x 4 = 28 square miles. The triangle has a base of 4 miles and a height of 3 miles, so its area is 1/2 x 4 x 3 = 6 square miles.

Adding these two areas together gives us a total area of 28 + 6 = 34 square miles. However, we need to subtract the overlap area of the two shapes, which is 6 square miles.

Therefore, the final area of the composite figure is 34 - 6 = 28 square miles, which is option A.

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Answer:

\(y = 40\cdot k\)

Step-by-step explanation:

Let suppose that each bus has the same capacity and exists a direct proportionality between the amount of people that is transported and the number of buses:

\(y \propto x\)

\(y = k \cdot x\)

Where \(k\) is the proportionality constant, which is equivalent to the maximum capacity of each bus. In that case, the quantity of people that is transported on 40 buses is:

\(y = 40\cdot k\)

Answer:

The first answer is ''y=45 x''

1800 people for the second one

Answer:

b

Step-by-step explanation:

because

Answer:

A

Step-by-step explanation:

Using the altitude- on- hypotenuse theorem

(leg of big Δ )² = (part of hypotenuse below it ) × ( whole hypotenuse) , so

x² = 4 × (4 + 8) = 4 × 12 = 48 ( take square root of both sides )

x = \(\sqrt{48}\) = \(\sqrt{16(3)}\) = 4\(\sqrt{3}\) → A

Answer:

1.4 people out of 10

Step-by-step explanation:

Just divide it by 10

Answer:

only 4 people

Answer:

"what are angles"

Step-by-step explanation:

En la geometría euclidiana, un ángulo es la figura formada por dos rayos, llamados lados del ángulo, que comparten un punto final común, llamado vértice del ángulo. Los ángulos formados por dos rayos se encuentran en el plano que contiene los rayos. Los ángulos también se forman por la intersección de dos planos. Estos se llaman ángulos diedros

There are 4,651,200 different committees that can be formed with 3 managers and 6 engineers selected without replacement from a pool of 10 managers and 20 engineers.

To determine the number of different committees that can be formed, we need to calculate the combination of managers and engineers that can be selected.

The number of ways to select 3 managers from 10 managers can be calculated using the combination formula:

C(n, r) = n! / (r!(n - r)!)

where n is the total number of managers and r is the number of managers to be selected.

In this case, we have n = 10 and r = 3, so the number of ways to select 3 managers from 10 is:

C(10, 3) = 10! / (3!(10 - 3)!) = 10! / (3!7!) = (10 * 9 * 8) / (3 * 2 * 1) = 120.

Similarly, the number of ways to select 6 engineers from 20 engineers can be calculated as:

C(20, 6) = 20! / (6!(20 - 6)!) = 20! / (6!14!) = (20 * 19 * 18 * 17 * 16 * 15) / (6 * 5 * 4 * 3 * 2 * 1) = 38,760.

To find the total number of different committees possible, we multiply the number of ways to select managers and engineers:

Total number of committees = C(10, 3) * C(20, 6) = 120 * 38,760 = 4,651,200.

Therefore, there are 4,651,200 different committees that can be formed with 3 managers and 6 engineers selected without replacement from a pool of 10 managers and 20 engineers.

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Step-by-step explanation:

if you follow me I will give your answer

Answer:

Step-by-step explanation:

The frequency table shows that there is a relationship between buying a hot dog and buying a drink at a baseball game. The huge 70.2% is evidence of this.

The frequency table is meant to show the relationship between variables. Of all the values provided, the relationship with the highest percentage is 70.2%.

This shows that the number of people who purchased a hot dog while also purchasing a drink constituted the highest number. None of the figures come close to this one. So, there is a strong relationship between the variables.

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Answer:

is not

Step-by-step explanation:

ANSWER

x = 15, y = 30

EXPLANATION

We want to solve the system of equations by substitution method.

We have that:

y = x + 15

y = 2x

Substitute the value of y in the second equation into the first:

=> 2x = x + 15

Collect like terms:

2x - x = 15

x = 15

Recall that:

y = 2x

=> y = 2(15)

y = 30

The solution to the system of equations is: x = 15, y = 30

Answer:

41.667

Step-by-step explanation:

Cⁿ₁ is always positive, then the second term has negative sign.

What does binomial expansion mean?

Theorem that states that any power of a binomial (a + b) can be expanded as a specific sum of products (aibj), such as (a + b)2 = a2 + 2ab + b2.

The i-th term of the binomial expansion \((x- y)^{n}\)

Ti = nCi - 1 . (x)ⁿ+¹⁺i  . (-y)i - 1

For any n, when i=2,

T₂ = nC₂₋₁  . xⁿ⁺¹⁻² . (-y)²⁻¹  = -Cⁿ₁ xⁿ⁻¹ . y

Given that is consistently positive, the second term has a negative sign.

Cn1 is consistently positive, and the second term is always negative.

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For displaying the ratings of a movie on a scale of 1-5 stars with the number of votes for each rating, a bar graph is generally more appropriate than a histogram.

A bar graph is used to represent categorical data, where each category (in this case, the rating) is shown on the x-axis, and the corresponding frequency or count (number of votes) is represented on the y-axis. The bars in a bar graph are usually separated and do not touch each other since the categories are distinct.

On the other hand, a histogram is used to display the distribution of continuous data. It divides the data into intervals or bins on the x-axis and represents the frequency or count of data points falling within each interval on the y-axis. Histograms are useful for visualizing the shape, center, and spread of data.

Since movie ratings on a scale of 1-5 stars are discrete and categorical, a bar graph would be the appropriate choice. Each rating (category) will have its own separate bar, and the height of each bar will represent the number of votes received for that rating.

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Answer: 8 hours

Step-by-step explanation:  240 mph ÷ 30 = 8 hours

Answer:4

Step-by-step explanation:

Just look at it. Pretty sure it's 4. .-.

The dimensions 36 x 27 inches are too small to allow a 48-inch piece of glass to fit through it.

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Answer:

98

Step-by-step explanation:86+86=172

368-172=196

196/2=98

The total interest that must be paid is $101.32.

Based on the information, you would need to pay a total interest amount of $101.32.

First, let's calculate the interest charges for each month:

Month 1:

Interest charge = (0.010111 * $3300) = $33.4363

Month 2:

New balance = $3300 + $33.4363 = $3333.4363

Interest charge = (0.010111 * $3333.4363) = $33.7707

Month 3:

New balance = $3333.4363 + $33.7707 = $3367.207

Interest charge = (0.010111 * $3367.207) = $34.1167

Now, if the account is paid off within the 3-month period, all interest charges are canceled. However, since the payment is made 1 day late, the interest for that extra day is not canceled.

Total interest amount = $33.4363 + $33.7707 + $34.1167

= $101.3237

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Answer:

8p²q²r² - 7p²q²r² + q²r²

Step-by-step explanation:

The pattern in y = x² exhibits a nonlinear increase in y as x increases, forming a U-shaped curve, while the pattern in y = 15 + x shows a linear increase in y as x increases at a constant rate.

The patterns in the equations y = x² and y = 15 + x differ in terms of the direction of change. In the equation y = x², the pattern shows an increase in y as x increases.

As x increases from negative to positive values, the corresponding y values also increase, forming a symmetric U-shaped curve. The rate of increase for y becomes steeper as x moves further away from zero.

On the other hand, in the equation y = 15 + x, the pattern shows a linear increase in y as x increases. As x increases, the corresponding y values increase in a straight line.

The rate of increase for y remains constant at one unit per increase in x. This linear pattern reflects a constant upward shift of the graph as x increases.

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The equation of the tangent plane at P0 is 0x + 0y + 0z = 0, which simplifies to 0 = 0. The equation indicates that the tangent plane is degenerate and effectively reduces to a point at P0. The coordinates of P0 and the components of the direction vector is (x - 3)/(72π + 72) = (y - 4)/54 = z/(6e + 12).

To find the equations for the tangent plane and the normal line at the point P0(3, 4, 0) on the surface −2cos(πx) + 6x^2y + 2exz + 3yz = 220, we'll follow a step-by-step process.

Step 1: Determine the partial derivatives of the surface equation with respect to x, y, and z.

The partial derivatives are:

∂f/∂x = 2πsin(πx) + 12xy + 2ez

∂f/∂y = 6x^2 + 3z

∂f/∂z = 2ex + 3y

Step 2: Evaluate the partial derivatives at the point P0(3, 4, 0) to obtain the slope of the tangent plane.

Substituting the coordinates of P0 into the partial derivatives:

∂f/∂x at P0 = 2πsin(3π) + 12(3)(4) + 2e(3)(0) = 72π + 72

∂f/∂y at P0 = 6(3^2) + 3(0) = 54

∂f/∂z at P0 = 2e(3) + 3(4) = 6e + 12

The slope of the tangent plane at P0 is given by the vector (∂f/∂x at P0, ∂f/∂y at P0, ∂f/∂z at P0).

Step 3: Write the equation for the tangent plane.

The equation of a plane is of the form Ax + By + Cz = D. To find the coefficients A, B, C, and D, we use the slope vector and the coordinates of the point P0:

A(x - x0) + B(y - y0) + C(z - z0) = 0

A(3 - 3) + B(4 - 4) + C(0 - 0) = 0

0 + 0 + 0 = 0

Therefore, the equation of the tangent plane at P0 is 0x + 0y + 0z = 0, which simplifies to 0 = 0. The equation indicates that the tangent plane is degenerate and effectively reduces to a point at P0.

Step 4: Determine the direction vector of the normal line.The direction vector of the normal line is parallel to the gradient vector of the surface equation at P0. The gradient vector is given by (∂f/∂x at P0, ∂f/∂y at P0, ∂f/∂z at P0).

Step 5: Write the equation for the normal line.

The equation of a line is of the form (x - x0)/A = (y - y0)/B = (z - z0)/C, where A, B, and C are the components of the direction vector.

Using the coordinates of P0 and the components of the direction vector, we have:

(x - 3)/(∂f/∂x at P0) = (y - 4)/(∂f/∂y at P0) = (z - 0)/(∂f/∂z at P0)

Substituting the values we calculated earlier:

(x - 3)/(72π + 72) = (y - 4)/54 = z/(6e + 12)

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To find the estimated project completion time for the given project activities, we need to first calculate the earliest start and earliest finish times and then the latest start and latest finish times.

Using the activity times given, we can calculate the earliest start and earliest finish times for each activity as follows: Activity A: Earliest start time = 0

Earliest finish time = 1

Activity B: Earliest start time = 2

Earliest finish time = 5

Activity C: Earliest start time = 5

Earliest finish time = 11

Activity D: Earliest start time = 11

Earliest finish time = 17

Activity E: Earliest start time = 5

Earliest finish time = 8 Activity F:

Earliest start time = 8

Earliest finish time = 17

Now we can calculate the latest start and latest finish times for each activity using the backward pass.

Latest finish time = 5

Latest start time = 2

Activity A: Latest finish time = 1

Latest start time = 0

Now we can calculate the slack time for each activity as follows:Activity A:

Slack time = 0

Activity B: Slack time = 0

Activity C: Slack time = 0

Activity D: Slack time = 0

Activity E: Slack time = 3

Activity F: Slack time = 0

The critical path for this project is A -> C -> D, since these activities have zero slack time. Therefore, the estimated project completion time is 17 units of time.

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