Find f(2) if f(x) = (x + 1)2

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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Answer:

The answer would be $6,700

A form of digital television that works with digital broadcast signals, transmitting digital sound, supporting wide screens, and providing high resolutions is High-Definition Television (HDTV).

HDTV is a type of television broadcasting that utilizes digital signals, allowing for superior picture and sound quality compared to traditional analog television. It supports wide screens, providing an aspect ratio of 16:9, which is ideal for displaying content in widescreen formats. HDTV also offers high resolutions, typically 720p or 1080i/p, resulting in sharper and more detailed images on compatible high-definition displays. With its digital nature, HDTV brings improved audiovisual experiences to viewers, enhancing their overall television-watching experience.

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No, a fraction is not a term. The distributive property can be applied to fractions because it is a general mathematical principle.

A fraction is not considered a term in the traditional sense. It is a mathematical expression that represents division. However, the distributive property can still be applied to fractions because the property itself is a fundamental rule of arithmetic that extends beyond specific types of expressions.

The distributive property states that for any real numbers a, b, and c:

a × (b + c) = (a × b) + (a × c).

When working with fractions, we can apply the distributive property as follows:

Let's consider the expression: a × (b/c).

We can rewrite this as: (a × b)/c.

Now, let's distribute the 'a' to 'b' and 'c':

(a × b)/c = (a/c) × b.

In this step, we applied the distributive property to the fraction (a/c) by treating it as a whole.

Although fractions represent division, we can still use the distributive property because it is a general mathematical principle that allows for manipulating expressions involving addition, subtraction, multiplication, and division.

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Answer:

B

Step-by-step explanation:

If you see two negatives next to each other, just think of them as adding. So add 8 and 7, you get 15.

Answer:

1

Step-by-step explanation:

m=2

3m²- 2m- 7

3(2)² -2(2) -7

3(4)- 4- 7

12- 4- 7= 1

When the speed of the body is doubled, it will travel a distance of 2 times the original distance d.

When the speed of a body moving on a rough surface is doubled, the distance it will travel can be calculated using the equation for distance traveled with constant deceleration. The initial speed of the body is doubled, so the final speed will be 2u. The deceleration on the rough surface remains the same. Let's denote the original distance traveled as d1 and the distance traveled after doubling the speed as d2.

To calculate d2, we can use the equation:

d2 = (v_f^2 - u^2) / (2a)

where:

v_f is the final speed (2u, in this case)

u is the initial speed

a is the deceleration

Since the body stops after traveling a distance d1, the final speed v_f will be 0. Substituting the values into the equation, we have:

0 = (2u)^2 - u^2 / (2a)

Simplifying the equation:

0 = 4u^2 - u^2 / (2a)

0 = 3u^2 / (2a)

Now, let's solve for d2:

d2 = (2u)^2 / (2a)

d2 = 4u^2 / (2a)

d2 = 2u^2 / a

Therefore, when the speed of the body is doubled, it will travel a distance of 2 times the original distance d.

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If the speed of a body moving on a rough surface is doubled, how far will it travel?

If y = sin(1+x^3), then dy/dx is equivalent to 3x^2cos(1+x^3).

To find the derivative dy/dx of y = sin(1+x^3), we apply the chain rule. The derivative of the outer function sin(u) with respect to u is cos(u), and the derivative of the inner function 1+x^3 with respect to x is 3x^2. Therefore, by applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function, resulting in dy/dx = 3x^2cos(1+x^3).

If y = (1+cos^2x)^3, then dy/dx is equivalent to -6cosx sinx (1+cos^2x)^2.

To find the derivative dy/dx of y = (1+cos^2x)^3, we apply the chain rule. The derivative of the outer function (1+u)^3 with respect to u is 3(1+u)^2, and the derivative of the inner function cos^2x with respect to x is -2cosx sinx. Therefore, by applying the chain rule, we multiply the derivative of the outer function by the derivative of the inner function, resulting in dy/dx = -6cosx sinx (1+cos^2x)^2.

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Answer:

6÷1×2+1×3

5/6

i think that is

Answer:

5/6

Step-by-step explanation:

Well you need to make their denominators same by multiplying numerator and denominators by same number like I have shown below:

\( \frac{1}{3} \times \frac{2}{2} + \frac{1}{2} \times \frac{3 }{3} = \frac{2}{6} + \frac{3}{6} = \frac{5}{6} \)

Hope it helps

please mark me brainliest

Based on the given information, the researcher should not reject the null hypothesis if using an alpha level of 0.05.

In hypothesis testing, the null hypothesis is typically assumed to be true until there is sufficient evidence to reject it. To determine whether to reject the null hypothesis, researchers often compare the calculated F-value from an ANOVA test with the critical F-value. The critical F-value is based on the significance level (alpha) chosen for the test. In this case, the given F-value is 3.47 with degrees of freedom (3, 32), indicating that there are three groups and a total of 32 observations. To make a decision, the researcher needs to compare the calculated F-value to the critical F-value. If the calculated F-value is greater than the critical F-value, the null hypothesis is rejected. However, if the calculated F-value is less than or equal to the critical F-value, the null hypothesis is not rejected. Since the critical F-value corresponding to alpha = 0.05 is not provided in the question, we cannot determine whether the null hypothesis should be rejected.

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The equation of tangent to a curve  corresponding to the given value of the parameter x = t⁵ + 1, y = t⁶ + t; t = 1 is y = 7x/5 - 4/5

The equation of tangent to a curve is the equation of the line that touches the curve at one point.

To find an equation of the tangent to the curve at the point corresponding to the given value of the parameter.

x = t⁵ + 1, y = t⁶ + t; t = 1, we proceed as follows.

We know that the tangent to the curve is the derivative dy/dx.

Now dy/dx = dy/dt ÷ dx/dt

x = t⁵ + 1

So, differntiating, we have

dx/dt = d(t⁵ + 1)/dt

= dt⁵/dt + d1/dt

= 5t⁴ + 0

= 5t⁴

Also, y = t⁶ + t

differentiating, we have that

dy/dt = d(t⁶ + t)/dt

= dt⁶/dt + dt/dt

= 6t⁵ + 1

= 6t⁵ + 1

Since dy/dx = dy/dt ÷ dx/dt, substituting the values of the variables into the equation, we have that

dy/dx = dy/dt ÷ dx/dt

dy/dx = (6t⁵ + 1) ÷ 5t⁴

At t = 1, we have that

dy/dx = (6t⁵ + 1) ÷ 5t⁴

dy/dx = (6(1)⁵ + 1) ÷ 5(1)⁴

dy/dx = (6(1) + 1) ÷ 5(1)

= (6 + 1) ÷ 5

= 7/5

Now, we know that the equation of the tangent is the equation of a straght line.

So, using the equation of a straight line in slope-point form, we have that

(y - y')/(x - x') = dy/dx

Now, y' = y at t = 1

So,y = t⁶ + t

y = 1⁶ + 1

= 1 + 1

= 2

Also, x' = x at t = 1

So,x =  t⁵ + 1

x =  1⁵ + 1

= 1 + 1

= 2

Since

Substituting the values of the variables into the equation, we have that

(y - y')/(x - x') = dy/dx

(y - 2)/(x - 2) = 7/5

Cross-multiplying,we have that

5(y - 2) = 7(x - 2)

5y - 10 = 7x - 14

5y = 7x - 14 + 10

5y = 7x - 4

y = 7x/5 - 4/5

So, the equation is y = 7x/5 - 4/5

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Answer:

For a problem like this there is no one solution.  It is an inequality.  When you graph it you would start with the Y-intercept at (0,10) then you move down 2 on the y axis and move the the right 1 on the x axis as that is your slope.  Do that a couple times until you can connect the dots.  You will draw a solid line to connect, and shade everything to the left and below the line.  Everything in the shaded area are the potential solutions for the inequality.

To your question about (0, -4) that would be in the solution set.

I hope this helps

Answer:

Step-by-step explanation:

n x 5

The value of the given Matrices,

A^2 = [1  2b  0  b]

A^3 = [1  3b  0  0]

A^5 = [1   5b   0   0]

To compute A^2 and A^3, the given matrices are A=[1, b, 0, 1] and A=[2, 2, 0, 0].

The first row: 1, b.

The second row: 0, 1.

The first row: 2, 2.

The second row: 0, 0.

A^2 = A × A

A^2 = [1    b    0    1] × [1    b    0    1]

A^2 = [1 + b * 0    1 * b + b * 1    0 + 0   1 * 0 + b * 1]

A^2 = [1   2b   0   b]

A^3 = A × A^2

A^3 = [1    b    0    1] × [1    2b    0    0]

A^3 = [1 + 0 * 0    b + 1 * 2b    0 + 0    1 * 0 + b * 0]

A^3 = [1  3b  0  0]

For predict A^5, we can compute A^4 and A^5.

A^4 = A^2 × A^2

A^4 = [1  2b  0  0] × [1  2b  0  0]

A^4 = [1 + 2b * 0  1 * 2b + 2b * 1  0 + 0  1 * 0 + 2b * 0]

A^4 = [1   4b   0   0]

A^5 = A^4 × A

A^5 = [1   4b   0   0] × [1   b   0   1]

A^5 = [1 + 4b * 0   1 * b + 4b * 1   0 + 0   1 * 0 + b * 0]

A^5 = [1   5b   0   0]

To predict A^n, let us look at A^2 and A^3.

A^2 has 1's at [1][1] and [2][2], while A^3 has 1's at [1][1], [2][2], and [3][3].

Therefore, A^n will have 1's at the diagonal starting from [1][1] until [n][n]. The off-diagonal elements in the matrices will have a multiple of b, based on the row and column.

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Answer:

original price $450 saved $145 the percent its sold for is 70%

The recursive formula of the sequence 7, 10, 13, 16 is \(a_n = a_{n-1} + 3\).

The explicit formula of the sequence -8, -13, -18, -23 is a(n) = -8 + (n-1)(-5).

What is recursive formula?

A recursive formula is one that defines each term in a sequence by reference to the one before it (s). The following parameters are defined using the recursive formulas:

In order to find the recursive formula we first need to calculate the difference between each term. So,

Second term - First term = 10 - 7 = 3

Therefore the recursive formula is \(a_n = a_{n-1} + 3\)

In order to find the explicit formula we first need to calculate the difference between each term. So,

Second term - First term = -13 - (-8) = -5

Therefore the explicit formula is  a(n) = -8 + (n-1)(-5).

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Answer:

B, 49π ft²

Step-by-step explanation:

Formula: Area of Circle = r²π

Step 1:

Radius = Diameter/2

14/2 = 7

Step 2:

Find the area of the circle using the formula.

7²π = 49π

Answer: 49π ft²

Answer:

I think; 1400 m

I hope I helped you^_^

Answer:

wait I am solving this

Step-by-step explanation:

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Answer:

8/3  or 2   2/3

Step-by-step explanation:

so we take 3/4 and flip it. 2 x 4/3= 8/3  or   2    2/3

Hope this helps :3

The Quotient is 8/3.

One of the four fundamental mathematical operations, along with addition, subtraction, and multiplication, is division. Division is the process of dividing a larger group into smaller groups so that each group contains an equal number of things.

Given:

2 divided by 3/4

As, division is not possible in fraction so we will perform the multiplication

= 2  ÷ 3/4

= 2 x 4/3

= 8/3

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The missing part of the equation is \(-7.0\times10^4 s^2kg⋅m^2 / 1000000.\)

To fill in the missing part of the equation, let's analyze the given information and the desired conversion. The equation is:

\((-7.0\times 10^4 s^2g⋅m^2)\cdot \pi = ? s^2kg\cdot m^2\)

In this equation, we have a quantity expressed in\(s^2g\cdot m^2\) units on the left-hand side. To convert it to \(s^2kg\cdot m^2\) units, we need to multiply it by a conversion factor.

To perform the conversion, we can use the fact that 1 kg is equal to 1000 g. Therefore, the conversion factor we need is:

1 kg / 1000 g

To ensure that the units cancel out correctly, we need to square this conversion factor because we have \(s^2g\cdot m^2\) on the left-hand side. So the missing part of the equation is:

\((-7.0\times 10^4 s^2g\cdot m^2)\cdot \pi = (-7.0\times 10^4 s^2g\cdot m^2)\cdot (1 kg / 1000 g)^2\)

Simplifying this expression, we get:

\((-7.0\times10^4 s^2g\cdot m^2)\cdot \pi = -7.0 \times10^4 s^2kg\cdot m^2 / 1000000\)

Therefore, the missing part of the equation is \(-7.0 \times 10^4 s^2kg\cdot m^2 / 1000000.\)

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Answer:

y = - 4x - 7

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = - 4, thus

y = - 4x + c ← is the partial equation

To find c substitute M(- 2, 1) into the partial equation

1 = 8 + c ⇒ c = 1 - 8 = - 7

y = - 4x - 7 ← equation of line

Answer: 2 quarters, a dime and a nickel

Step-by-step explanation: There are multiple ways to do this, but with a single dollar it would be 100(cents in a dollar) divided by the 65%. The 65% is just 65/1, which is 65 cents. Almost any coins that add to 65 cents will work.

The logarithmic form is written as logₐ(X)=b. It is a rearrangement of the exponential form, aᵇ=X.

What is Logarithmic Form?

The logarithmic form is written as logₐ(X)=b. It is generally the rearrangement of the exponential form, aᵇ=X. Any exponential equation can be written as a logarithm. The logarithmic form is mostly used to calculate an exponent of an equation. The logₐ(X)=b. is read as “log base a of X equals b“.

The logarithmic form is simply a rearrangement of an equation written in exponential form. The same numbers are used but they are written in a different order. The word log is written which implies that the logarithm function is being used.

Therefore, If the logarithmic form is logₐ(X)=b. then it is a rearranged as the exponential form as aᵇ=X.

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Answer:

15%

Step-by-step explanation:

0.15 x 100 = 15%

Answer:

  190 square units

Step-by-step explanation:

The area of a rectangular prism can be found using the formula ...

  A = 2(LW +H(L +W))

  A = 2(3·5 +10(3 +5)) = 2(15 +80) = 190

The area is 190 square units.

To find the union and intersection of the intervals I₁ = (-2, 2] and I₂ = [1, 5), let’s consider the overlapping values and the combined range.

The union of two intervals includes all the values that belong to either interval. Taking the union of I₁ and I₂, we have:

I₁ U I₂ = (-2, 2] U [1, 5)

To find the union, we combine the intervals while considering their overlapping points:

I₁ U I₂ = (-2, 2] U [1, 5)
= (-2, 2] U [1, 5)

So the union of the intervals I₁ and I₂ is (-2, 2] U [1, 5).

Now let’s find the intersection of the intervals I₁ and I₂, which includes the values that are common to both intervals:

I₁ ∩ I₂ = (-2, 2] ∩ [1, 5)

To find the intersection, we consider the overlapping range between the two intervals:

I₁ ∩ I₂ = [1, 2]

Therefore, the intersection of the intervals I₁ and I₂ is [1, 2].


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The simplest form of the given ratio 32 min : 36 min is equal to  

option a. 8 : 9.

Ratio  is equal to

32 min : 36 min

Factors of 32 are = 1, 2, 4, 8, 16, 32

Factors of 36 are = 1, 2, 3, 4, 6, 9, 12, 18, 36

Greatest common factor of 32 and 36 is equal to 4

Simplest form of the given ratio is equal to

32 min : 36 min

= ( 8 × 4 ) min : ( 9 × 4 ) min

'4' get cancelled with other we get,

= 8 min : 9 min

Therefore, the simplest form of the given ratio by taking out common factors is equal to option a. 8 : 9 .

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The statsmodels ols() method is used on an exam scores dataset to fit a multiple regression model using exam4 as the response variable. exam1, exam2, and exam3 are used as predictor variables. the general form of this model is,

The general form of a multiple regression model using exam1, exam2, and exam3 as predictor variables and exam4 as the response variable is:

exam4 = beta_0 + beta_1 * exam1 + beta_2 * exam2 + beta_3 * exam3

where beta_0 is the intercept term and beta_1, beta_2, and beta_3 are the coefficients for exam1, exam2, and exam3, respectively. These coefficients represent the change in the response variable (exam4) for a one-unit change in the predictor variables, holding all other predictor variables constant.

The statsmodels ols() method can be used to fit this multiple regression model to a dataset. The ols() method stands for "ordinary least squares," which is a method for estimating the parameters (i.e., the beta coefficients) in a linear regression model. To use the ols() method, you will need to specify the predictor variables and the response variable as input variables and provide the data for these variables as a Pandas DataFrame. You can then call the fit() method on the ols() object to fit the model to the data.

here, we have,

For example, if your data is stored in a Pandas DataFrame called "df," you could fit a multiple regression model using exam1, exam2, and exam3 as predictor variables and exam4 as the response variable with the following code:

import statsmodels.formula.api as smf

model = smf.ols(formula='exam4 ~ exam1 + exam2 + exam3', data=df)

results = model.fit()

Once the model is fit, you can access various summary statistics and parameters of the model using the results object. For example, you can access the coefficients of the model using the params attribute, like this:

beta_0 = results.params[0]

beta_1 = results.params[1]

beta_2 = results.params[2]

beta_3 = results.params[3]

You can also use the summary() method on the results object to get a summary of the model fit, including the R-squared value, the F-statistic, and the p-values for the coefficients.

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The total number of ways to fit 1 X 1 X 2 sized dominoes into a domino of dimensions 2 X 2 X N is \(2^{(N/2)\)if N is even, and \(2^{((N-1)/2)\) if N is odd.

We can approach this problem by considering the number of possible positions for the dominoes in the 2 X 2 X N domino.

First, note that the dominoes are 1 X 1 X 2 in size, which means that they can only be placed in the 2 X 2 face of the larger domino.

Let's consider the placement of the first domino. It can be placed either horizontally or vertically in the 2 X 2 face of the larger domino. If it is placed horizontally, then the remaining space in the 2 X 2 face can accommodate one more horizontal domino or two vertical dominoes. If it is placed vertically, then the remaining space can accommodate two horizontal dominoes or one more vertical domino.

Let's assume that we start by placing the first domino horizontally. Then, the remaining space can accommodate one more horizontal domino or two vertical dominoes. If we place another horizontal domino, then the remaining space can only accommodate two vertical dominoes. Therefore, we can only place two horizontal dominoes in this case.

If we place the second domino vertically instead, then the remaining space can accommodate two horizontal dominoes or one more vertical domino. If we place another vertical domino, then the remaining space can only accommodate two horizontal dominoes. Therefore, we can only place two vertical dominoes in this case.

Therefore, the possible combinations are as follows:

If N is even: There are N/2 possible positions for the dominoes in each of the N/2 layers of the larger domino. Each layer can accommodate two horizontal dominoes or two vertical dominoes. Therefore, the total number of combinations is 2^(N/2).

If N is odd: We can place one horizontal domino in the first layer, and then proceed as if N were even. Therefore, the total number of combinations is 2^((N-1)/2).

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