find the value of
\( {3}^{2} {}^{x + 1} \)
if x=1​

Answer:

d) (6, 0)

Step-by-step explanation:

y = -2/12 = -1/6x - 4 = y

New line = y = -1/6x + 6

Plug and test!

0 = -1/6(6) + 6

0 does indeed equal 0

Answer: 50.26548 (50.27)

Step-by-step explanation:

Circumference = 2 x π x r(radius)

Diameter = 2 x r(radius)

C = π x 16 = 50.26548

Answer:

Step-by-step explanation:

This is more physics than math, but since "The book of nature is written in the language of mathematics"...

Anyway, the one-dimesional motion equation you want to use here resembles the quadratic we use to model parabolic motion. It is

\(v^2=v_0^2+2a\)Δx

where v is the final velocity of the firefighter, v₀ is the initial velocity of the firefighter, a is -9.8 m/s/s (negative because the motion is in the downward direction), and Δx is -34 m. This is also negative because where the firefighter lands is below the point at which he started. This is important, because if you leave the 34 as positive, you end up with a negative radicand...and that's not gonna work. Filling in the formula:

\(v^2=(7.5)^2+2(-9.8)(-34)\)

Paying close attention to significant digits here is important (at least it is when I teach physics in school!). Since there are 2 significant digits in 7.5, we need 2 in the product. 7.5 squared is 56.25 which will round to 56. Then on the right side of the plus sign, we need 2 significant digits as well since the number 2 is part of the equation. We don't count it as significant if it is part of the equation. 2(-9.8)(-34) = 666.4 but that will round to 670. NOW, since the rules for significant digits are different in multiplication and addition, you have to round each first, then take the square root of the sum, rounding at the end. In this case we will round to the place that holds the least significance between the 2 numbers. In our case that is the tens place, since the tens place is less significant than is the 1's place. The number 7 is in the tens place. (Following that rule is super tricky, and also quite maddening!)

What we have here is

\(v^2=56+670\) and

\(v=\sqrt{56+670}\)

That leaves us with

v = 26.94438j

But don't forget we round that to the tens place which comes out in the end, finally, to

v = 30 m/s

Answer:

97271.1577

Step-by-step explanation:

multiply 3374.60 by 2882.45%

The lower outlier boundary is 76.5 and the upper outlier boundary is 136.5.

Given information:Three quartiles for systolic blood pressure in a sample of 1213 women between the ages of 20 and 29 were Q-99,Q2 = 103, and Qs = 114. Part 1 of 3 Find the IQR. 1QR - 15We are required to find the interquartile range (IQR) of blood pressure in women.Interquartile range (IQR) is the difference between the upper quartile and lower quartile. It is given by the formula:IQR = Q3 - Q1Where Q1 and Q3 are the first and third quartiles respectively.

Substituting the values of Q1 and Q3 in the above formula,IQR = Q3 - Q1 = 114 - 99 = 15Hence, the interquartile range is 15. The IQR for the blood pressure in women is 15.Part 2 of 3 Find the upper and lower outlier boundaries.Outliers are the values that lie outside the range of (Q1 - 1.5*IQR, Q3 + 1.5*IQR). The lower outlier boundary is the minimum value in the data set that is not an outlier. The upper outlier boundary is the maximum value in the data set that is not an outlier. Therefore, we need to find the lower and upper outlier boundaries. Lower outlier boundary = Q1 - 1.5*IQRUpper outlier boundary = Q3 + 1.5*IQRSubstituting the given values in the above formulas,Lower outlier boundary = Q1 - 1.5*IQR= 99 - 1.5*15 = 76.5Upper outlier boundary = Q3 + 1.5*IQR= 114 + 1.5*15 = 136.5Therefore, the lower outlier boundary is 76.5 and the upper outlier boundary is 136.5.

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Answer:

Step-by-step explanation:

Answer:

the anser wouold be 5

Step-by-step explanation:

1 is too small 25 is too big 313 is out rageesty to big

When parallel parked along a curb, the front and rear bumpers of your vehicle must be no more than 12 inches or one foot away from other vehicles. This distance is to ensure that there is enough space for other vehicles to maneuver around your car and to prevent any accidental collisions or damage.

It is important to note that this distance may vary depending on local laws and regulations, so it is always best to check with your local authorities for specific guidelines. In addition, it is crucial to use your mirrors and signals when parallel parking to ensure that you are not blocking traffic or causing any hazards on the road. By following these guidelines and being mindful of others on the road, you can safely and effectively parallel park your vehicle.

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The point on the curve where the tangent line has a slope of 1/2 is (x, y) = (27, -1).

As we know, x = 6t² + 3 and y = t³ - 9

Let's find dx/dt using the first equation.  

We have:

dx/dt = 12t

Now, let's find dy/dt using the second equation. We have:

dy/dt = 3t²

Next, we'll calculate dy/dx. We know that dy/dx = dy/dt ÷ dx/dt.

So we get: dy/dx = dy/dt ÷ dx/dt= 3t² ÷ 12t= t ÷ 4

The slope of the tangent line is 1/2, so we set t/4 = 1/2 and solve for t.t/4 = 1/2t = 2

We must find x and y values that correspond to t = 2. We have:

x = 6t² + 3= 6(2²) + 3

= 27y = t³

- 9= 2³

- 9= -1(x, y)

= (27, -1)

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The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b. This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

To find the equation for the tangent plane to the graph of the function f(x, y) = 2e^x - y at a given point (x0, y0), we need to calculate the partial derivatives of f with respect to x and y at that point.

The partial derivative of f with respect to x, denoted as ∂f/∂x or fₓ, represents the rate of change of f with respect to x while keeping y constant. Similarly, the partial derivative of f with respect to y, denoted as ∂f/∂y or fᵧ, represents the rate of change of f with respect to y while keeping x constant.

Let's calculate these partial derivatives:

fₓ = d/dx(2e^x - y) = 2e^x

fᵧ = d/dy(2e^x - y) = -1

Now, we have the partial derivatives evaluated at the point (x0, y0). Let's assume our point of interest is (a, b), where a = x0 and b = y0.

At the point (a, b), the equation for the tangent plane is given by:

z - f(a, b) = fₓ(a, b)(x - a) + fᵧ(a, b)(y - b)

Substituting fₓ(a, b) = 2e^a and fᵧ(a, b) = -1, we have:

z - f(a, b) = 2e^a(x - a) - (y - b)

Now, let's substitute f(a, b) = 2e^a - b:

z - (2e^a - b) = 2e^a(x - a) - (y - b)

Rearranging and simplifying:

z = 2e^a(x - a) - (y - b) + 2e^a - b

The final equation for the tangent plane to the graph of f at the point (a, b) is z = 2e^a(x - a) - y + 2e^a - 2b.

This equation represents the plane that is tangent to the graph of f at the specified point (a, b).

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The exact values of the trigonometric functions of a vector are listed below:

sin θ = - 7√58 / 58

cos θ = - 3√58 / 58

tan θ = 7 / 3

cot θ = 3 / 7

sec θ = - √58 / 3

csc θ = - √58 / 7

In this problem we find the coordinates of the terminal end of a vector, whose trigonometric functions are now defined:

P(x, y) = (x, y)

sin θ = y / √(x² + y²)

cos θ = x / √(x² + y²)

tan θ = y / x

cot θ = x / y

sec θ = √(x² + y²) / x

csc θ = y / √(x² + y²)

If we know that x = - 3 and y = - 7, then the exact values of the trigonometric functions are, respectively:

sin θ = - 7 / √[(- 3)² + (- 7)²]

sin θ = - 7 / √58

sin θ = - 7√58 / 58

cos θ = - 3√58 / 58

tan θ = 7 / 3

cot θ = 3 / 7

sec θ = - √58 / 3

csc θ = - √58 / 7

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The equation model of the given statement in question is 6 + 7× x.

The model of equation is defined as the model of the given situation in the form of an equation using constants and variables.

In math, it deals with numbers of operations given according to the statements. The four major arithmetic operators are, addition, subtraction, multiplication, and division.

Given that;

6 is added to product of a number and 7

Now,

Let, the number multiplied by 7 be x,

=7*x

6 is added to the product;

= 6 + 7 × x

Therefore, the equation of model will be given as 6 + 7 × x;

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Answer:

D

Step-by-step explanation:

Answer:

The answer would be D)

Step-by-step explanation:

Hope this helps :)

\( \frac{2}{5} + \frac{3}{10} - \frac{7}{9} \\ = \frac{2 \times 18 + 3 \times 9 - 7 \times 10}{90} \\ = \frac{36 + 27 - 70}{90} \\ = \frac{ - 7}{90} \)

\( \frac{ - 7}{90} \)

Answer:

5

52

52

52 +

52 + 10

52 + 103

52 + 103

52 + 103 −

52 + 103 − 9

52 + 103 − 97

52 + 103 − 97

52 + 103 − 97

52 + 103 − 97 =

52 + 103 − 97 = 90

52 + 103 − 97 = 902×18+3×9−7×10

52 + 103 − 97 = 902×18+3×9−7×10

52 + 103 − 97 = 902×18+3×9−7×10

52 + 103 − 97 = 902×18+3×9−7×10 =

52 + 103 − 97 = 902×18+3×9−7×10 = 90

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 =

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90}

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90−7

52 + 103 − 97 = 902×18+3×9−7×10 = 9036+27−70 = 90−7 Answer:\frac{ - 7}{90} 90−7

Answer:-56x

Step-(7x-4)(7x-4)

49x^2-28x-28x+16by-step explanation:

The value of missing number that makes the expression a perfect square is,

⇒ 56

We have to given that,

An expression is,

⇒ 49x² - _x + 16

Now, We can find the missing number that makes the expression a perfect square.

Since, We know that,

⇒ (a + b)² = a² + 2ab + b²

Now, We can simplify as,

⇒ 49x² - _x + 16

⇒ (7x)² - 2×4×7x + (4)²

⇒ (7x)² - 56x + (4)²

⇒ 49x² - 56x + 16

Thus, The value of missing number is,

⇒ 56

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The simpler form of the expression −3(−4y^3)7y is 12y^4.

To combine like terms and simplify the expression −3(−4y^3)7y, we follow these steps:

Multiply the coefficients outside the parentheses:
-3 * -4 = 12

Multiply the variables inside the parentheses:
y^3 * y = y^4

Combine the results from steps 1 and 2:
12y^4

The simpler form of the expression −3(−4y^3)7y is 12y^4.

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The given procedure does not result in a binomial distribution because it does not satisfy the criteria of having only two possible outcomes and independent trials.

No, this procedure does not result in a binomial distribution. In order for a distribution to be binomial, it must meet four criteria: (1) there must be a fixed number of trials; (2) the trials must be independent; (3) there must be only two possible outcomes (i.e., success or failure); and (4) the probability of success must remain the same in all trials.

In the given procedure, there are more than two possible outcomes (i.e., the different TV shows that the college students can choose) and the trials are not independent. Therefore, the procedure does not satisfy two of the four criteria necessary for a binomial distribution.

A binomial distribution can be described by the formula:

\(P(x) = nCx * p^x * (1 - p)^(n - x)\)

where n is the number of trials, x is the number of successes, and p is the probability of success. Since the given procedure does not meet the criteria for a binomial distribution, this formula does not apply.

The given procedure does not result in a binomial distribution because it does not satisfy the criteria of having only two possible outcomes and independent trials.

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Answer:

185 is the square root of 34225

Step-by-step explanation:

hope you understood!!

Answer:The distance is 10.8

Step-by-step explanation:

The mean is 65 inches and the standard deviation is 3 inches.

Given,

In a group of women, the distribution of heights is roughly normal. Women who are shorter than 62 inches in height make up 16% of the population.

The empirical rule, less than μ - σ of 16% of the data is accurate.

P (x < μ - σ) = 16%

μ - σ = 62 → (I)

Approximately 97.5% of the women are under 71 inches in height,

P (x < μ + 2σ) = 97.5%

μ + 2σ = 71 → (II)

By solving (I) & (II);

μ - σ = 62

μ + 2σ = 71

3σ = 9

σ = 3

From (I);

μ - σ = 62

μ - 3 = 62

μ = 65

Hence, Mean = 65 inches

            Standard deviation = 3 inches

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The distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector.

To find the distance between the point P(2, 6, -4) and the line defined by the parametric equations r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩, we can use the formula for the distance between a point and a line in three-dimensional space.

The formula for the distance between a point and a line is given by:

d = ||PQ||/||v||

where PQ is the vector connecting the point P to any point Q on the line, v is the direction vector of the line, and || || represents the magnitude of a vector.

Let's first find the direction vector of the line. By examining the parametric equations, we can see that the direction vector of the line is v = ⟨1, 4, -2⟩.

Now, we need to find the vector PQ connecting the point P(2, 6, -4) to any point Q on the line. We can represent PQ as the difference between the coordinates of P and Q:

PQ = ⟨2 - 1, 6 - 3t, -4 - 1, 4t, -4 - 3, -2t⟩ = ⟨1, 6 - 3t, -5, 4t, -7, -2t⟩

Next, we calculate the magnitude of PQ:

||PQ|| = √(1^2 + (6 - 3t)^2 + (-5)^2 + (4t)^2 + (-7)^2 + (-2t)^2)

= √(1 + 36 - 36t + 9t^2 + 25 + 16t^2 + 49 + 4t^2)

= √(29t^2 - 36t + 111)

Finally, we calculate the magnitude of the direction vector v:

||v|| = √(1^2 + 4^2 + (-2)^2) = √(1 + 16 + 4) = √21

Now we can substitute these values into the formula for the distance:

d = ||PQ||/||v|| = (√(29t^2 - 36t + 111))/√21

To find the minimum distance between the point P and the line, we need to minimize the function d with respect to t. We can accomplish this by finding the critical points of the function and determining the value of t that gives the minimum distance.

Taking the derivative of d with respect to t and setting it equal to zero, we have:

d' = (29t - 18)/(√21(√(29t^2 - 36t + 111))) = 0

Solving for t, we get:

29t - 18 = 0

29t = 18

t = 18/29

By substituting this value of t into the formula for d, we can find the minimum distance between the point P and the line.

d = (√(29(18/29)^2 - 36(18/29) + 111))/√21

Simplifying this expression will give us the final value of the distance.

In summary, the distance between the point (2, 6, -4) and the line r(t) = ⟨1, 3t, 1, 4t, 3, -2t⟩ can be calculated using the formula d = ||PQ||/||v||, where PQ is the vector connecting the point P to any point Q on the line, and v is the direction vector

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Answer:

Hi again

Its your 3rd option

Step-by-step explanation:

Answer:

Step-by-step explanation:

Option 3 is correct just got the test!

To find the general solution of the given differential equation, let's follow the procedures developed in this chapter. The differential equation is y′′−2y′+y=x^2e^x.

Step 1: Solve the homogeneous equation
To start, let's find the solution to the homogeneous equation y′′−2y′+y=0. The characteristic equation is r^2-2r+1=0, which can be factored as (r-1)^2=0. This gives us a repeated root of r=1.

The general solution to the homogeneous equation is y_h=c_1e^x+c_2xe^x, where c_1 and c_2 are constants.

Step 2: Find a particular solution
To find a particular solution to the non-homogeneous equation y′′−2y′+y=x^2e^x, we can use the method of undetermined coefficients. Since the right side of the equation is a polynomial multiplied by an exponential function, we assume a particular solution of the form y_p=(Ax^2+Bx+C)e^x, where A, B, and C are constants to be determined.

Differentiating y_p twice, we have y_p′′=(2A+2Ax+B)e^x and y_p′=(2A+2Ax+B)e^x+(Ax^2+Bx+C)e^x.

Substituting these derivatives into the original differential equation, we get:
(2A+2Ax+B)e^x-2[(2A+2Ax+B)e^x+(Ax^2+Bx+C)e^x]+(Ax^2+Bx+C)e^x=x^2e^x.

Simplifying the equation, we have 2Ax^2e^x+(2B-4A+2A)x+(B-2B+C+2A)=x^2e^x.

By comparing coefficients, we can determine the values of A, B, and C:
2A=1 (from the coefficient of x^2e^x)
2B-4A+2A=0 (from the coefficient of xe^x)
B-2B+C+2A=0 (from the constant term)

Solving these equations, we find A=1/2, B=1, and C=-2.

Therefore, a particular solution to the non-homogeneous equation is y_p=(1/2)x^2e^x+x^e^x-2e^x.

Step 3: Write the general solution
The general solution to the non-homogeneous equation is the sum of the homogeneous solution and the particular solution:
y=y_h+y_p=c_1e^x+c_2xe^x+(1/2)x^2e^x+x^e^x-2e^x.

So, the general solution of the given differential equation is y=c_1e^x+c_2xe^x+(1/2)x^2e^x+x^e^x-2e^x.

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Answer:

\(A' = (3,-1)\)

\(B' = (4,1)\)

\(C' = (5,-2)\)

Step-by-step explanation:

Given

\(A = (1,3)\)

\(B = (-1,4)\)

\(C = (2,5)\)

Rotation: 90 degrees clockwise

Required

Determine A'B'C'

When a point \(P (x,y)\) is rotated 90 degrees in the clockwise direction, the new coordinates is: \(P' (y, -x).\)

So, we have:

\(A = (1,3)\)

\(B = (-1,4)\)

\(C = (2,5)\)

Becomes

\(A' = (3,-1)\)

\(B' = (4,1)\)

\(C' = (5,-2)\)

There are approximately 11.25 cups of granulated sugar in a 5 pound bag.

To determine the number of cups of granulated sugar in a 5 pound bag, we can use the conversion factor of 2.25 cups per pound.

First, we multiply the number of pounds (5) by the conversion factor:

5 pounds * 2.25 cups/pound = 11.25 cups

Therefore, there are approximately 11.25 cups of granulated sugar in a 5 pound bag.

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r = lim_{n->inf} |a_{n+1}/a_n|

r = lim_{n->inf} |11(n+1)/(n+1)^2| * |n^2/11n|

r = lim_{n->inf} |11/n+1|

Since the limit is zero, the series converges for all values of x, so the radius of convergence is infinity.

x = 1:

∑ 11n / n^2 = 11 * π^2 / 6 => converges

x = -1:

∑ (-11)^n / n^2 => converges by the alternating series test

Therefore, the interval of convergence is [-1,1].

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Answer:

C. 25% is correct answer

Table 1 compares characteristics of women based on their alcohol intake. It includes the mean age of mothers at birth for nondrinkers (28.2 ± 4.4 years) and drinkers (30.1 ± 4.4 years). The table does not provide the p-value or the specific test statistic used for comparison.

In Table 1, the characteristics of women are compared based on their intake of alcohol. The table provides information on two groups: non-drinkers and drinkers. The following variables are presented:

Mean age of mother at birth (years): The mean age of mothers at birth is reported for both nondrinkers (28.2 + 4.4 years) and drinkers (30.1 + 4.4 years). The values indicate the average age of mothers in each group.

Test Statistic: This column represents the statistical test used to compare the two groups based on the given variable. The specific test used is not mentioned in the provided information.

P value: The p-value indicates the statistical significance of the observed differences between the two groups. It is used to determine if the differences observed are likely to occur by chance. However, the actual p-value is not provided in the given information.

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Answer:

Step-by-step explanation:

Binomial distribution:  \(X \sim B(n,p)\)

where n is the number and p is the probability

Given:

\(X \sim B(12,0.8)\)

P(X ≥ 10) = 1 - P(X ≤ 9)

              = 1 - 0.4416542515...

              = 0.5583 (4 dp)

The lifetime cost of Ellen's dishwater is $1,030.44

What is Number system?

A system of writing to express the number is called number system.

Given that;

Cost of dishwasher before sales tax 9.22% is = $315

And, Sales tax = 9.22%

Hence, Total cost = 315 *( 1 + 0.0922) = 315 * 1.0922 = 344.043

And, Average of 10 times per week for the next 6 years before replacing it.

Since, There are 52 weeks in a year.

So, Average uses is calculated as,

10  * 52  * 6 = 3120

Since, cost for water = $0.09

Cost for electricity = $0.13

Total cost per uses = $0.22

Hence, Cost of uses = 0.22 * 3120 = $686.40

Now, Purchase cost = $344.043

And, Cost of uses =  $686.40

Hence, Lifetime cost =  $344.043 + $686.40 = $1,030.443

So, The lifetime cost of Ellen's dishwater is $1,030.44.

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