Distribute 3x ( -x + 4).​

The area of this figure is the sum of areas of the right triangle and the semi-circle

Area of the triangle = 1/2 * base * height

The base = 6 feet

The height = 8 feet

So the area of the triangle is:

Now let us find the area of the semi-circle

Area of semi-circle = 1/2 * 3.14 * r^2

Since the diameter of the semi-circle is 8 feet and the radius is 1/2 the diameter

So the radius = 8/2 = 4 ft

Area of semi-circle is:

Let us add the two areas to find the area of the figure

Area of the figure = 24 + 25.12 = 49.12 square feet

The missing is 49.12

Given:

The rate of change in volume = 12 cubic feet per minute.

We need to find the rate of change of radius at radius = 6 feet.

Consider the formula to find the volume of the sphere.

Differentiate with respect to t.

Dividing both sides by 144pi, we get

Hence the radius of the balloon increases by 0.03 feet per minute.

Answer:

I believe it is y=1/4x.

Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)

Answer:

the x

Step-by-step explanation:

Looking at the x in an equation can reveal its shape. A linear graph can look like y=x, y=mx, y=mx+b (m being any number).

When you look at graphs that aren't linear, the x doesn't stand alone in the equation.

Parabolas have a y=x^2 equation. Cubic graphs are y=x^3. They have something attached to the x.

To see all the different kinds of equations and what their graphs look like you can search up "parent functions" and all the basic formulas show up.

Answer:171x+8

Step-by-step explanation:

3x^3+12x^2x+8

=27x+144x+8

=171x+8

Answer:

I think the answer is O

a) The dimensions of the missing face is 10 x 5 cm.

b) The four edges that the missing face can be attached are: A, B, C and H.

The net of a given shape is the figure formed when all its surfaces are spread out on a 2 dimensional plane. The shape is reproduced when the net is folded as require.

A cuboid if a 3 dimensional shape that is produced from a rectangle. Such that it has length, width and height.

In the given net of a cuboid, it can be deduced that;

a. The dimension of the missing face is that similar to F, such that it is 10 x 5 cm.

b. The four edges that the missing face could be attached to should be A, B, C and H. This is the closed end of the cuboid.

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The following values can be placed in order from lowest to highest to represent a profit-maximizing firm in the short run that chooses to remain open while losing money: marginal revenue, marginal cost, total cost, total revenue.

In the short run, a profit-maximizing firm may choose to remain open even if it is losing money. This is because the firm has fixed costs that cannot be immediately adjusted, such as rent, equipment, and salaries. In this situation, the firm's goal is to minimize losses and maximize profits as much as possible. To determine whether to remain open or shut down, the firm compares its marginal revenue and marginal cost. If marginal revenue is greater than marginal cost, the firm will continue to operate. However, if marginal cost is greater than marginal revenue, the firm will shut down. Total cost and total revenue are also important factors to consider, as they determine the overall profitability of the firm.

In summary, a firm in this situation would prioritize minimizing losses over maximizing profits and would consider marginal revenue, marginal cost, total cost, and total revenue when making the decision to remain open or shut down.

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To make a decision for the hypothesis test, we need to analyze the ANOVA summary table for the test of significance of the overall regression model.

From the table, we can see that the regression sum of squares (SS) is given as 20, and the residual sum of squares (SS) is given as 400. We also know that the total sum of squares (SS) is the sum of the regression SS and the residual SS.

Since the degrees of freedom (df) for the regression model is equal to the number of predictor variables (k) minus 1 (k - 1), and the df for the residual is the total sample size (n) minus the number of predictor variables (k), we can calculate the df for the regression and the residual.

Given that the sample size (n) is 45 and the number of predictor variables (k) is 4, we can calculate:

df for regression = k - 1 = 4 - 1 = 3

df for residual = n - k = 45 - 4 = 41

Next, we need to calculate the mean square (MS) for the regression and the residual by dividing the SS by their respective degrees of freedom.

MS for regression = SS for regression / df for regression = 20 / 3

MS for residual = SS for residual / df for residual = 400 / 41

Finally, we can calculate the F-statistic by dividing the MS for regression by the MS for residual.

F = (MS for regression) / (MS for residual)

Now, we can compare the calculated F-statistic to the critical F-value at the given significance level (α = 0.05). If the calculated F-statistic is greater than the critical F-value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

Without the information of the critical F-value or the calculated F-statistic, we cannot make a definitive decision or final conclusion for the hypothesis test. Please provide the necessary values, and I will be able to help you with the decision and conclusion.

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Let's start solving the expression using the product to sum formulae.

Here's the given expression,

\[\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3}\]

Using the product-to-sum formula,

\[\sin A \cos B=\frac{1}{2}[\sin (A+B)+\sin (A-B)]\]

Applying the above formula in the first term,

\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3} &= \frac{1}{2} \left[\sin \left(\frac{x}{3}+\frac{2 x}{3}\right)+\sin \left(\frac{x}{3}-\frac{2 x}{3}\right)\right] \\&= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]\end{aligned}\]

Using the product-to-sum formula,

\[\cos A \sin B=\frac{1}{2}[\sin (A+B)-\sin (A-B)]\]

Applying the above formula in the second term,

\[\begin{aligned}\cos \frac{x}{3} \sin \frac{2 x}{3}&= \frac{1}{2} \left[\sin \left(\frac{2 x}{3}+\frac{x}{3}\right)-\sin \left(\frac{2 x}{3}-\frac{x}{3}\right)\right] \\ &= \frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right]\end{aligned}\]

Substituting these expressions back into the original expression,

we have\[\begin{aligned}\sin \frac{x}{3} \cos \frac{2 x}{3}+\cos \frac{x}{3} \sin \frac{2 x}{3} &= \frac{1}{2} \left[\sin x+\sin \left(-\frac{x}{3}\right)\right]+\frac{1}{2} \left[\sin x-\sin \left(\frac{x}{3}\right)\right] \\ &=\frac{1}{2} \sin x + \frac{1}{2} \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\\ &= \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)\end{aligned}\]

Therefore, the given expression can be written in terms of a single trigonometric function as:

\boxed{\sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right)}

Hence, the required expression is \sin x - \frac{1}{2} \sin \left(\frac{x}{3}\right). The solution is complete.

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Answer:

The equation of the circle is (x-2)^2+(y-1)^2=13

Step-by-step explanation:

Answer: 4 horas

Step-by-step explanation:

Una semana (de lunes a viernes) contiene 5 días

Si se entrena 1 hora por día:

1 x 5 = 5 horas (total de horas de entrenamiento de lunes a viernes)

Ese total más el número de horas que se entrena el sábado (x) dividido por 6 (numero de días en la semana incluyendo sábado) debe ser igual a el promedio de horas entrenadas en los 6 días (1.5)

(5+x) /6 =1.5

Despajando x:

5+x =1.5 x 6

5+x =9

x =9-5

x = 4 horas

If f(x) = x - 5, then

f(h) = h - 5

f(x + h) = (x + h) - 5

(f(x + h) - f(x))/h = (((x + h) - 5) - (x - 5))/h

(f(x + h) - f(x))/h = (x + h - 5 - x + 5)/h

(f(x + h) - f(x))/h = h/h

(f(x + h) - f(x))/h = 1

since h ≠ 0.

The expressions of the functions are:

f(h) = h - 5

f(x + h) = x + h - 5

[f(x + h) - f(x)] / h = 1

Given the function f(x) = x - 5, let's calculate the following expressions:

f(h):

To find f(h), we substitute h into the function:

f(h) = h - 5

f(x + h):

To find f(x + h), we substitute (x + h) into the function:

f(x + h) = (x + h) - 5

= x + h - 5

[f(x + h) - f(x)] / h:

To find [f(x + h) - f(x)] / h, we substitute (x + h) and x into the function:

[f(x + h) - f(x)] / h = [(x + h) - 5 - (x - 5)] / h

= (x + h - x + 5 - 5) / h

= h / h

= 1

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The equation of the linear trendline is y = 18.1x + 51.97

The linear trendline is the line which best minimizes the sum of squared error for the data. The linear trendline is usually written in slope-intercept form ; mx+b.

m= slope of the equation

b = Intercept

The equation of the trendline obtained using a regression calculator is y = 18.1x + 51.97. With a slope value of 18.1 and intercept value of 51.97.

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Answer:

Discriminant= b²-4ac

a = 9 b = -3 and c = -2

Discriminant = (-3)² - 4(9)(-2)

= 9+72

Discriminant = 81

Ans = 81

The method that cannot be used to show congruency of two triangles is the method of "angle-angle-angle" (AAA).

The AAA method states that if the corresponding angles of two triangles are congruent, then the triangles themselves are congruent. However, this method is not valid for proving congruency because it does not take into account the lengths of the sides of the triangles.

To prove congruency, we typically use one of the following valid methods:

Side-Side-Side (SSS): If the three sides of one triangle are congruent to the corresponding three sides of another triangle, then the triangles are congruent.

Side-Angle-Side (SAS): If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Angle-Side-Angle (ASA): If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Side-Angle-Angle (SAA): If two angles and a non-included side of one triangle are congruent to two angles and a non-included side of another triangle, then the triangles are not necessarily congruent. This method alone is not sufficient to prove congruency.

Therefore, the method that cannot be used to show congruency of two triangles is the Angle-Angle-Angle (AAA) method.

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The number of randomly presented items that children can repeat immediately after the items are presented is called their immediate memory span or short-term memory capacity.

The number of randomly presented items that children can repeat immediately after the items are presented is called their immediate memory span or short-term memory capacity.

The capacity of short-term memory is limited and varies from person to person and depending on the complexity of the information being presented.

The typical range of immediate memory span for children is around 5 to 9 items, with older children and adults having a slightly larger capacity.

However,

Some individuals with exceptional memory abilities, such as memory athletes, can recall significantly more items in short-term memory.

Factors that can affect short-term memory capacity include the nature of the items being presented their familiarity or meaningfulness, the duration of the presentation and the individual's level of attention and working memory capacity.

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Answer: D) On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (1, negative 1).

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the right of the line is shaded.

Suppose there is inequality given as: y ≥ f(x)

The region it covers is the region of value pairs (x,y) for which this inequality holds true.

We've to draw the region covered by it.

For a function y = f(x), there is y > f(x) on one side of the graph of the function y = f(x) in XY plane, and on other side there is y < f(x).

A manufacturing machine has two processes. One of them is repeated 4 times and the second only once. The entire cycle can take no longer than 3 minutes.

Let t be the time of the first process in minutes

s be the time of the second process in minutes

we know that the time of the first process multiplied by 4 (because is repeated 4 times) plus the time of the second process multiplied by 1 (because is repeated only once) must be less than or equal to 3 minutes

So, The inequality that represents this situation is

\(4t + s\leq 3\)

The y-intercept of the solid line is the point (0,3)

The x-intercept of the solid line is the point (0.75,0)

The slope of the solid line is negative m=-4

On a coordinate plane, a solid straight line has a negative slope and goes through (0, 3) and (1, negative 1). Everything to the right of the line is shaded.

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Answer: The absolute value inequality will be |x| ≥ -2.

Step-by-step explanation: gl :)

Answer:

more simple here da answer but this answer is from the person above i just putted the answer

The absolute value inequality will be |x| ≥ 6

Answer:

A. 40°

Step-by-step explanation:

∠Z=∠Y (base ∠ of isosΔ)

    = 60°

∠X=180-60-60(∠ sum of Δ)

    =40°

Answer:

A

Step-by-step explanation:

z = y                                  Both are opposite equal sides

z = 70                                From the first statement.

y = 70                                Given

x = 180 - z - y                    A triangle has 180 degrees

x = 180 - 70 - 70

x = 40

The probability distribution for daily sales:X = $0, P(X = $0) = 0.3X = $50,000, P(X = $50,000) = 0.0333 X = $100,000, P(X = $100,000) = 0.0444 and  the mean daily sales is approximately $5,333.33, and the standard deviation is approximately $39,186.36.

To find the probability distribution for daily sales, we need to consider the different possible outcomes and their probabilities.

Let's define the random variable X as the daily sales.

The possible values for X are:

- No sale: $0

- One sale: $50,000

- Two sales: $100,000

Now, let's calculate the probabilities for each outcome:

1. No sale:

The probability of contacting one customer and not making a sale is 1/3 * 0.9 = 0.3.

2. One sale:

The probability of contacting one customer and making a sale is 1/3 * 0.1 = 0.0333.

3. Two sales:

The probability of contacting two customers and making two sales is 2/3 * 2/3 * 0.1 * 0.1 = 0.0444.

Now we can summarize the probability distribution for daily sales:

X = $0, P(X = $0) = 0.3

X = $50,000, P(X = $50,000) = 0.0333

X = $100,000, P(X = $100,000) = 0.0444

To find the mean and standard deviation of the daily sales, we can use the formulas:

Mean (μ) = Σ(X * P(X))

Standard Deviation (σ) = sqrt(Σ((X - μ)^2 * P(X)))

Let's calculate the mean and standard deviation:

Mean (μ) = ($0 * 0.3) + ($50,000 * 0.0333) + ($100,000 * 0.0444) = $5,333.33

Standard Deviation (σ) = sqrt((($0 - $5,333.33)^2 * 0.3) + (($50,000 - $5,333.33)^2 * 0.0333) + (($100,000 - $5,333.33)^2 * 0.0444)) ≈ $39,186.36

Therefore, the mean daily sales is approximately $5,333.33, and the standard deviation is approximately $39,186.36.

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Answer:

6 times

Step-by-step explanation:

\( \frac{1}{6} \times 36 = 6\)

The area of the triangle whose vertices are (-3, 5), (3, -6), and (7, 2) is 14.

To find the area of a triangle given the coordinates of its vertices, we can use the formula:

Area = 1/2 * |(x1y2 + x2y3 + x3y1) - (y1x2 + y2x3 + y3x1)|

where (x1,y1), (x2,y2), and (x3,y3) are the coordinates of the three vertices.

Substituting the given coordinates, we get:

Area = 1/2 * |(-3*-6 + 32 + 75) - (5*3 - (-6)7 + 2(-3))|

= 1/2 * |(-18 + 6 + 35) - (15 + 42 - 6)|

= 1/2 * |23 - 51|

= 1/2 * |-28|

= 14

Therefore, the area of the triangle is 14 square units.

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Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

x = 5

Step-by-step explanation:

4x - 3 = 2x + 7

Add 3 to both sides.

4x = 2x + 10

Subract 2x from both sides.

2x = 10

Divide both by 2.

Final Answer: 5

If you wanted to check your answer, you can plug in 5 from the x's

4(5) - 3 = 2(5) + 7

17 = 17

Answer: X = 5

Step-by-step explanation: The target should be to reduce the equations to having either one term or polynomial on each side, starting with the right side. First, start with subtracting 2x from each side. Then, add three to both sides. Finally, divide both sides. You can also double-check the answer by substituting.

4x - 3 = 2x + 7

2x - 3 = 7 (Subtracted 2x)

2x = 10 (Added 3 to both sides)

10/2 (Divide both sides)

X = 5

4(5) - 3 = 2(5) + 7

17 = 17

In a simple linear regression model, the coefficient of the independent variable (x) in the estimated sample regression equation indicates the change in the predicted value of the dependent variable (y) when x increases by one unit. This coefficient is also known as the slope of the regression line. Therefore, to calculate the predicted value of y, we multiply the coefficient by the value of x and add the intercept.

In a simple linear regression model, the coefficient that indicates the change in the predicted value of y when x increases by one unit is the "slope coefficient" or the "regression coefficient" (usually denoted as b1). This coefficient represents the relationship between the independent variable x and the dependent variable y.

The linear regression equation is given as:

y = b0 + b1 * x

Where:
- y is the predicted value of the dependent variable
- b0 is the intercept coefficient (where the line intersects the y-axis)
- b1 is the slope coefficient (the change in y when x increases by one unit)
- x is the independent variable

In this equation, b1 indicates the change in the predicted value of y when x increases by one unit.

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