What is a simpler form of (3x+1)(x+4) ?

The standard form of a parabola is y = a(x - h)^2 + k, where (h,k) is the vertex of the parabola and "a" determines whether the parabola opens up (if a > 0) or down (if a < 0).

what is parabola?

A parabola is a U-shaped symmetrical curve. It is a type of conic section, formed by intersecting a cone with a plane parallel to its side. The shape of a parabola is determined by its equation, which can be written in standard form as y = ax^2 + bx + c, where a, b, and c are constants. The vertex of the parabola is located at the point (-b/2a, c - b^2/4a), and the axis of symmetry is a vertical line passing through the vertex. Parabolas have many applications in mathematics and physics, including in the design of reflective surfaces such as telescopes and satellite dishes.

what is symmetrical?

Symmetrical refers to having or exhibiting symmetry, which is a property of a shape or object that can be divided into two or more identical parts. When a shape or object is symmetrical, it looks the same on both sides of the line of symmetry. For example, a circle is symmetrical because any line passing through its center will divide it into two identical halves. A human face is also symmetrical because the left side and the right side are nearly identical. In mathematics, symmetry is an important concept that appears in various fields, including geometry, algebra, and calculus.

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Answer:

7:5 is another ratio equivalent to 56:40

Step-by-step explanation:

56/8 = 7

40/8 = 5

Answer:

hope this helps

Step-by-step explanation: an equivalent ratio in simplest form would be 7:5

this is found by dividing 56 by 8 which is 7 and 40 dividd by 8 which is 5

7:5

Answer:

2.5 hours

Step-by-step explanation:

The total amount of time studying by students who spent 1/2 an hour studying is the product of the number of students who spent 1/2 an hour studying by 1/2 an hour.

Hence, counting the number of dots on the point marked 1/2 gives the count of students who spent 1/2 an hour studying and multiply this number by 1/2.

Total amount of hours spent = 1/2 * 5 = 2.5 hours

Answer:

The incorrect comparison is D. -6 > -4

To show work:

-6 = -6

-4 = -4

-6 < -4 is incorrect, so D is incorrect.

The percentage of the population that did not believe the housing market would decrease within the next 5years (either unsure or thought it would increase) is 25.9%.

This refers to the supply & demand for houses usually in a particular country or region.

According to the attached pie chart, the percentage of people who did not believe that the housing market would decrease is:

= 20.4% + 5.5%

= 25.9%.

Therefore, the percentage of the population that did not believe the housing market would decrease within the next 5years is 25.9%.

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Answer:

a1 = 2

Step-by-step explanation:

what does a1 mean?

35, 32 29, 26, 23, 20 , 17, 14, 11, 8, 5, (2)

The equation of the tangent line to the Witch of Agnesi at a given point (x0, y0) is:  \(\(y - y_0 = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}(x - x_0)\)\)

The tangent lines to the curve called the Witch of Agnesi at a given point can be determined by finding the derivative of the curve and evaluating it at that point.

To find the equation of a tangent line, we need the derivative of the curve. The equation of the Witch of Agnesi is given by:

\(y = \frac{8a^3}{x^2 + 4a^2}\)

where 'a' is a constant that determines the shape of the curve.

Taking the derivative of y with respect to x, we can find the slope of the tangent line:

\(\frac{dy}{dx} = \frac{-64a^3x}{(x^2 + 4a^2)^2}\)

Let's assume we want to find the tangent lines at the point (x0, y0). We can substitute these coordinates into the derivative expression:

\(\frac{dy}{dx}\Bigr|_{x=x_0} = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}\)

This gives us the slope of the tangent line at the point (x0, y0).

Now, using the point-slope form of a line, we can write the equation of the tangent line:

\(y - y_0 = \frac{dy}{dx}\Bigr|_{x=x_0}(x - x_0)\)

Substituting the values we obtained earlier, the equation of the tangent line becomes:

\(y - y_0 = \frac{-64a^3x_0}{(x_0^2 + 4a^2)^2}(x - x_0)\)

This equation represents the tangent line to the Witch of Agnesi at the point (x0, y0).

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Answer:

Instructions are below.

Step-by-step explanation:

Giving the following information:

Fixed costs= 4,000 + 10,000= $14,000

Unitary variable cost= $5.5

Selling price= $7.2

To calculate the number of units to be sold to break-even, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 14,000 / (7.2 - 5.5)

Break-even point in units= 8,235 units

In dollars:

Break-even point (dollars)= fixed costs/ contribution margin ratio

Break-even point (dollars)= 14,000 / (1.7/7.2)

Break-even point (dollars)= $59,294

Now, imagine the company requires a profit of $50,000:

Break-even point in units= (fixed costs + desired profit) / contribution margin per unit

Break-even point in units= 64,000/1.7

Break-even point in units= 37,647 units

Break-even point (dollars)= (fixed costs + desired profit) / contribution margin ratio

Break-even point (dollars)= 64,000 / (1.7/7.2)

Break-even point (dollars)= $271,059

The most plausible (or valid) explanation regarding Kim and Larry's decision to focus on analyzing and forecasting mobile home shipments instead of vacancy rate would be option d:

They may think that obtaining data on mobile home shipments is easier as it is readily available online.

This explanation suggests that Kim and Larry chose to focus on mobile home shipments because they believe that obtaining data related to mobile home shipments is more accessible and readily available online. It implies that they may have faced difficulties in obtaining comprehensive or reliable data regarding the vacancy rate, which influenced their decision to shift their focus to a different variable for analysis and forecasting.

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The air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion.

According to Newton's Second Law of Motion, the rate of change of the airplane's momentum is equal to the sum of all the forces acting on the airplane. As the plane takes off and accelerates, the thrust of the engines acting in the forward direction causes the plane's momentum to increase. This increase in momentum results in an increase in air speed. The air resistance acting against the motion of the plane is another force that affects the plane's speed. As the plane accelerates, the air resistance increases, and the plane's speed decreases.

In summary, the air speed of a small airplane during the first 25 seconds of takeoff and flight can be modeled by Newton's Second Law of Motion, where the thrust of the engines and air resistance act as forces that influence the plane's air speed.

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Answer:

10b-2b-8x+14

(the last one)

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

6x + 8b = x + 5x + 8b

Answer:

2nd choice

When looking for common factors we are looking for the prime factors that are in common and then multiplying the prime factors together to get the GCF.

Step-by-step explanation:

The picture shows the choice that is being used to find the GCF.

Answer:

2nd choice

When looking for common factors we are looking for the prime factors that are in common and then multiplying the prime factors together to get the GCF.

Answer:

y = (- 2/3)x - 3

Step-by-step explanation:

y = mx + c

y = (- 2/3)x + c

- 1 = (- 2/3)(-3) + c

-1 = 2 + c

c = - 3

Therefore,

y = (-2/3)x - 3

Answer:

y = -2/3x - 3

Step-by-step explanation:

y = mx + b

y = y coordinate              → given: - 1

m = slope                        → given: - 2/3

x = x coordinate              → given: - 3

b = y intercept                 → need to find

y = -2/3x + b → -1 = -2/3(-3) + b

-1 = 2 + b

subtract 2 from both sides

-1 - 2 = 2 - 2 + b

-3 = b

y = -2/3x - 3

The solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

To solve the given differential equation

\(x^3y'''\ -\ 6y\ =\ 0,\)

we can use the method of power series. Let's assume a power series solution of the form

\(y(x)\ =\ \sum_{n=0}^{\infty} a_nx^n.\)

Differentiating y(x) with respect to x gives:

\(\[y'(x)\ =\ \sum_{n=0}^{\infty} n a_n x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+1) a_{n+1} x^n\]\)

Differentiating again gives:

\(\[y''(x)\ =\ \sum_{n=0}^{\infty} (n+1)na_{n+1}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)a_{n+2}x^n\]\)

Differentiating one more time gives:

\(\[y'''(x)\ =\ \sum_{n=0}^{\infty} (n+2)(n+1)na_{n+2}x^{n-1}\ =\ \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n\]\)

Substituting these expressions into the differential equation, we have:

\(\[x^3 \sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^n - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Rearranging the terms and combining like powers of x, we get:

\(\[\sum_{n=0}^{\infty} (n+3)(n+2)(n+1)a_{n+3}x^{n+3} - 6 \sum_{n=0}^{\infty} a_n x^n\ =\ 0\]\)

Now, let's equate the coefficients of like powers of x to zero:

For n=0:

\(\[(3)(2)(1)a_3 - 6a_0 = 0 \implies 6a_3 - 6a_0 = 0 \implies a_3 = a_0\]\)

For n=1:

\(\[(4)(3)(2)a_4 - 6a_1 = 0 \implies 24a_4 - 6a_1 = 0 \implies a_4 = \frac{1}{4}a_1\]\)

\(For \: n\geq 2:

\[(n+3)(n+2)(n+1)a_{n+3} - 6a_n = 0 \implies a_{n+3} = \frac{6a_n}{(n+3)(n+2)(n+1)}\]

\)

Now we can write the solution as:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{6a_{n-2}}{n(n-1)(n-2)}x^{n+3}\]

\)

Simplifying the series, we get:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_

1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]

\)

Therefore, the solution to the given differential equation is:

\(\[y(x)\ =\ a_0 + a_1x + \frac{1}{4}a_1x^4 + \sum_{n=2}^{\infty} \frac{2a_{n-2}}{(n-2)(n-1)}x^{n+3}\]\)

where a₀ and a₁ are arbitrary constants to be determined based on the initial conditions or boundary conditions given in the problem.

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Answer: 5/8

Step-by-step explanation:

Answer:

Smallest possible x = 98.

Step-by-step explanation:

4312 = 2 * 2 * 2 * 7 * 7 * 11

56 = 2 *2 * 2 * 7

154 = 2 * 7 * 11

Because the HCF is 14:-

x =   = 2 * 7 OR  2 * 7 * other prime number(s).

As there are 2 7's in the prime factors of 4312 there must also be another 7 in the prime factors of x.

x =  2 * 7 * 7 = 98.

Answer:

only one triangle can be formed ...

The numerical values of the areas, we would need to evaluate these integrals. However, without a specific context or requirement for the area calculation, it is not possible to provide an exact numerical answer in this format.

To find the area inside the larger loop and outside the smaller loop of the limaçon with the polar equation r = (1/2)cos(θ), we need to determine the range of θ values that correspond to the loops.

The equation r = (1/2)cos(θ) describes a cardioid with a loop. The loop occurs when cos(θ) = 0, which happens when θ = π/2 and θ = 3π/2.

The larger loop is traced when θ ranges from 0 to π/2, while the smaller loop is traced when θ ranges from π/2 to 3π/2.

To calculate the areas, we integrate the formula for the area enclosed by a polar curve:

A = (1/2) ∫[θ1,θ2] r^2 dθ

For the larger loop, the area is:

A1 = (1/2) ∫[0,π/2] [(1/2)cos(θ)]^2 dθ

For the smaller loop, the area is:

A2 = (1/2) ∫[π/2,3π/2] [(1/2)cos(θ)]^2 dθ.

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A(n) "correlational" design is used when the researcher wants to test a relationship between existing variables. This design aims to determine the degree to which two variables are related or associated with each other. In a correlational design, the researcher measures the variables of interest and examines the statistical relationship between them, typically using correlation coefficients.

On the other hand, a(n) "experimental" design is used when a researcher wants to test a causal link between variables. In an experimental design, the researcher manipulates one or more independent variables and measures the effect on a dependent variable. By controlling for confounding variables and using random assignment, an experimental design allows for causal inferences to be made.

It's important to note that while correlational designs can provide valuable insights into the relationships between variables, they do not establish causality. Experimental designs, on the other hand, provide stronger evidence for causal relationships by systematically manipulating variables.

A(n) \(\textbf{correlational}\) design is used when the researcher wants to test a relationship between existing variables.

A(n) \(\textbf{experimental}\) design is used when a researcher wants to test a causal link between variables.

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Answer:

m = 55

p=45

n = 135

Step-by-step explanation:

180 - 55 - 80 = 45

p = 45

55 = m

because ED and BC are parallel lines

80 + 55 = n

n = 135

The answer to the measure include the following:

This is referred to a polygon which consists of three edges and three vertices.

m=55 (alternate angle)

The sum of angles in a triangle is 180

Therefore 180 - 55 - 80 = 45

p = 45

Since 55 = m

ED and BC are parallel lines therefore:

80 + 55 = n

n = 135

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Answer:

\(12\) books

Step-by-step explanation:

\(62 \div 5 = 12remainder2\). Get rid of the the remainder (\(2\)) because it was specified that the books were split evenly, and then answer is \(12\).

For 8% p-value cutoff , Melissa should use 92% confidence interval

A confidence interval calculated for a treatment effect measure shows the range in which the true treatment effect is likely to fall.

A smaller sample size or higher variability will result in a wider confidence interval with a larger margin of error. The interval width is also influenced by the level of confidence. If you want a higher level of certainty, the interval should be wider.

The width of the confidence interval and the size of the p value are related.

The narrower the interval, the smaller the p value. The confidence interval, on the other hand, provides useful information about the likely magnitude of the effect under consideration as well as the accuracy of the estimate.

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Step-by-step explanation:

perimeter=2(l+b)

check the picture for more clarification

Given:

Total number of players = 15

Required players = 5

To find:

The number of ways to select 5 young women for the basketball team if 15 players try out?

Solution:

We know that, the total number of ways to select r items from n item is

\(^nC_r=\dfrac{n!}{r!(n-r)!}\)

The total number of ways to select 5 players from 15 is

\(^{15}C_5=\dfrac{15!}{5!(15-5)!}\)

\(^{15}C_5=\dfrac{15\times 14\times 13\times 12\times 11\times 10!}{5\times 4\times 3\times 2\times 1\times 10!}\)

\(^{15}C_5=\dfrac{15\times 14\times 13\times 12\times 11}{5\times 4\times 3\times 2\times 1}\)

\(^{15}C_5=3\times 7\times 13\times 11\)

\(^{15}C_5=3003\)

Therefore, coach Lewis can select 5 young women from 15 in 3003 ways.

a) The correct line chart for these time series data is Graph (iii).

b)  When a linear trendline is fitted to the data, it shows a positive linear trend.

(a) The correct line chart for these time series data is Graph (iii). From the chart, we can see that the average price per gallon of conventional regular gasoline has fluctuated over the 36-month period. It started around $2.27 per gallon and reached its peak around $3.90 per gallon before coming back down to around $3.56 per gallon at the end of the period.

(b) When a linear trendline is fitted to the data, it shows a positive linear trend. This indicates that, on average, the price of gasoline has been increasing over the 36-month period. The slope of the trendline provides an estimate of the average rate of increase per month, which can be used to forecast future prices.

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: The following table contains time series data for regular gasoline prices in the United States for 36 consecutive months: Month Price ($) Month Price ($) Month Price ($) 3.91 1 2.27 13 2.84 25 2 2.63 14 2.73 26 3.68 3 2.53 15 2.73 27 3.65 4 2.62 16 2.73 28 3.64 5 2.55 17 2.71 29 3.61 6 2.55 18 2.80 30 3.45 7 2.65 19 2.86 31 3.38 8 2.61 20 2.99 32 3.27 9 2.72 21 3.10 33 3.38 10 2.64 22 3.21 34 3.58 11 2.77 23 3.56 35 3.85 12 2.85 24 3.80 36 3.90 (a) Choose the correct line chart for these time series data. What interpretations can you make about the average price per gallon of conventional regular gasoline over these 36 months? (i) Price $ 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 i 3 Сл 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month (ii) Price $ 4.50 4.00 3.50 3.00 um Muuwi www 2.50 2.00 1.50 1.00 0.50 i 35 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month Price ($) 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month (iv) Price ($) 4.50 4.00 3.50 3.00 2.50 2.00 1.50 1.00 0.50 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Month - Select your answer Select your answer - Graph (1) Graph (ii) Graph (iii) Graph (iv) (b) Fit a linear trendline to the data. What does the trendline indicate about the price of gasoline over these 36 months? - Select your answer - - Select your answer Positive non-linear trend Positive linear trend Negative linear trend Negative non-linear trend

According to the information, the surface area of the pyramids is as follows: 1.377 inches², 2.208 inches², 3.160 inches².

To find the surface area of the pyramids we must perform the following mathematical operations.

A. Find the surface area of the base:

B. We must find the surface area of the faces:

1.

2.

3.

To find the total area of the total surface of the figures we must perform the following procedure:

C. Add the area of the base to the area of the faces:

1.

2.

3.

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We will determine the remaining almond flour as follows:

*First: We determine how much does 20% of it is:

So, 20% of almond flour is 18 pounds. Now, we subtract this amount from the total amount:

So, there are 72 pounds of almond flour left.