Determine how many terms of the following convergent series must be summed to be sure that the remainder is less than 10-1 in magnitude. 31– 1)* k! k =0 The number of terms that must be summed is (Simplify your answer.)

Answer:

d trust me

Step-by-step explanation:

Answer:

Graph D

Step-by-step explanation:

Passes both Horizontal and Vertical line tests.

The columns of a matrix are dependent if there exists a vector combination that results in a vector of zeroes.

This can be tested using a vector V of coefficients, such that:

\(MV = 0\)

If this is true, then the columns of M are dependent. To illustrate this with an example, consider a 3x3 matrix:

\(M = [[a, b, c], [d, e, f], [g, h, i]]\)

To find the vector combination V that results in a vector of zeroes, we can use Gaussian elimination to reduce the matrix to row echelon form:

\(M = [[1, 0, -c/a], [0, 1, -f/e], [0, 0, 0]]\)

From this, we can deduce the vector combination V:

\(V = [1, -(c/a)*(f/e), 1]\)

Therefore, the columns of M are dependent.

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A numeric variable is used with the VAR statement.

Given statement,

What type of variable is analyzed using a PROC TTEST? That is, what type of variable do we use with the VAR statement,

Here, we use;

→ Numeric Variable

Hence, a Numeric Variable type of variable is analyzed using a PROC TTEST.

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Answer:

8! 8x8=64 lol

Step-by-step explanation:

Hope this helps, And have a good day!

Based on the provided information of speed, A) Beth gets to San Francisco first. B) The first to arrive has to wait for 20 minutes for the second to arrive.

A) To find out who gets to San Francisco first, we need to calculate the time it takes for each of them to travel the distance of 400 miles.

For Brian, we use the formula time = distance / speed:

time = 400 miles / 50 mph = 8 hours

So Brian will arrive in San Francisco at 4:00 p.m. (8:00 a.m. + 8 hours).

For Beth, we use the same formula:

time = 400 miles / 60 mph = 6.67 hours

So Beth will arrive in San Francisco at 3:40 p.m. (9:00 a.m. + 6.67 hours).

Therefore, Beth gets to San Francisco first.

B) To find out how long the first to arrive has to wait for the second, we subtract the arrival time of the first from the arrival time of the second:

wait time = 4:00 p.m. - 3:40 p.m. = 0.33 hours = 20 minutes

So the first to arrive has to wait for 20 minutes for the second to arrive.

Note: The question is incomplete. The complete question probably is: Brian leaves Los Angeles at 8:00 a.m. to drive to San Francisco, 400 miles away. He travels at a steady speed of 50 mph. Beth leaves Los Angeles at 9:00 a.m. and drives at a steady speed of 60 mph. A) Who gets to San Francisco first? B) How long does the first to arrive have to wait for the second?

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The length of the shortest straight  is approximately 28.01 ft.

What is the right triangle?

A right triangle is" a type of triangle that has one angle measuring 90 degrees (a right angle). The other two angles in a right triangle are acute angles, meaning they are less than 90 degrees".

To find the length of the shortest straight beam,we can use the Pythagorean theorem.

Let's denote the length of the beam as L and  a right triangle formed by the beam, the wall, and the ground. The wall is 28 ft tall, and the distance from the wall to the building is 1 ft.

Using the Pythagorean theorem,

\(L^2 = (28 ft)^2 + (1 ft)^2\)

Simplifying the equation:

\(L^2 = 784 ft^2 + 1 ft^2\\ L^2 = 785 ft^2\)

\(L = \sqrt{785}ft\)

Calculating the value of L:

L ≈ 28.01 ft

Therefore, the length of the shortest straight beam  is approximately 28.01 ft.

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Answer:

62 mph

Step-by-step explanation:

The region bounded by the x-axis, the lines x = -3 and x = 0, and the function y = f(x) = (x+3)2 can be calculated using the limit of sums approach.

On the x-axis, we define small subintervals of width x between [-3, 0]. In the event that there are n subintervals, then x = (0 - (-3))/n = 3/n.

Rectangles within each subinterval can be used to roughly represent the area under the curve. Each rectangle has a height determined by the function f(x) and a width of x.

The area of each rectangle is f(x) * x = (x+3)2 * (3/n).

The total area is calculated by taking the limit and adding the areas of each rectangle as n approaches infinity:

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Ali and Leila are analyzing the following points. Ali thinks that most of the points are in quadrant 2 because there are many x-values that are negative. Leila disagrees. Ali is correct because all of the negatives are mostly in quadrant 2

This is further explained below.

Generally, The plane is segmented into four infinite areas known as quadrants by the axes of a two-dimensional Cartesian system, with each quadrant being bordered by two half-axes.

In conclusion, The following points are being discussed and analyzed by Ali and Leila.

Because there are a lot of x-values that are negative, Ali believes that the majority of the points are in quadrant 2 because of this. Leila disagrees. Because the majority of the negatives are located in the second quadrant, Ali is accurate.

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Answer:

\(\text{g}^{-1}(x)=\boxed{\dfrac{x-13}{2}}\)

\(\left(\text{g}^{-1} \circ \text{g}\right)(-4)=\boxed{-4}\)

\(h^{-1}(9)=\boxed{-3}\)

Step-by-step explanation:

To find the inverse of function g(x) = 2x + 13, begin by replacing g(x) with y:

\(y=2x+13\)

Swap x and y:

\(x=2y+13\)

Rearrange to isolate y:

\(\begin{aligned}x&=2y+13\\\\x-13&=2y+13-13\\\\x-13&=2y\\\\2y&=x-13\\\\\dfrac{2y}{2}&=\dfrac{x-13}{2}\\\\y&=\dfrac{x-13}{2}\end{aligned}\)

Replace y with g⁻¹(x):

\(\boxed{\text{g}^{-1}(x)=\dfrac{x-13}{2}}\)

\(\hrulefill\)

As g and g⁻¹ are true inverse functions of each other, the composite function (g⁻¹ o g)(x) will always yield x. Therefore, (g⁻¹ o g)(-4) = -4.

To prove this algebraically, calculate the original function g at the input value x = -4, and then evaluate the inverse function of g at the result.

\(\begin{aligned}\left(\text{g}^{-1} \circ \text{g}\right)(-4)&=\text{g}^{-1}\left[\text{g}(-4)\right]\\\\&=\text{g}^{-1}\left[2(-4)+13\right]\\\\&=\text{g}^{-1}\left[5\right]\\\\&=\dfrac{(5)-13}{2}\\\\&=\dfrac{-8}{2}\\\\&=-4\end{aligned}\)

Hence proving that (g⁻¹ o g)(-4) = -4.

\(\hrulefill\)

The inverse of a one-to-one function is obtained by reflecting the original function across the line y = x, which swaps the input and output values of the function. Therefore, (x, y) → (y, x).

Given the one-to-one function h is defined as:

\(h=\left\{(-3,9), (1,0), (3,-7), (5,2), (9,6)\right\}\)

Then, the inverse of h is defined as:

\(h^{-1}=\left\{(9,-3),(0,1),(-7,3),(2,5),(6,9)\right\}\)

Therefore, h⁻¹(9) = -3.

15/19 + 14/19 = 29/19

Step-by-step explanation:

Add the number of balls in the basket together.

Subtract the number of white balls from the sample space ( the total amount of balls) your answer is written over the sample space and the same process is done for the green ball

Answer:

Step-by-step explanation:

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Answer=4/5

The fraction of his original money does he have left = 4/5 .

What is a fraction in math?

A boy has = 800 and spends = 160

800-160=640

640/800=64/80

64/80=16/20

16/20=4/5

Therefore, his original money left =4/5

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Answer:

8.5% tax rate

Step-by-step explanation:

17/200= 0.085 = 8.5%

Answer:

240

Step-by-step explanation:

Answer:

240

Step-by-step explanation:

Answer:

x = 4

y = 12

Step-by-step explanation:

Replace all occurrences of y with 3x in each equation.

7x = 28

y = 3x

Divide each term in 7x = 28 by 7 and simplify.

x = 4

y = 3x

Replace all occurrences of x with 4 in each equation.

y = 12

x = 4

The solution to the system is the complete set of ordered pairs that are valid solutions.

(4,12)

The result can be shown in multiple forms.

Point Form:

(4,12)

Equation Form:

x = 4,y = 12

Hope I helped <3

In conclusion, we cannot apply Rolle's Theorem to the function g on the interval (0,k) for any value of k.

To show that g satisfies the hypotheses of Rolle's Theorem on the interval (0,k), we need to verify that:
1. g is continuous on [0,k]
2. g is differentiable on (0,k)
3. g(0) = g(k)

Since g(x) = (22/3)x - 22, it is a polynomial function, and therefore it is both continuous and differentiable on any interval. So, the first two conditions are satisfied.

Now, we need to find the value of k that satisfies the third condition:
g(0) = g(k)
(22/3)(0) - 22 = (22/3)k - 22
0 = (22/3)k
k = 0

Since k cannot be equal to 0 (because the interval is (0,k)), there is no value of k that satisfies the third condition.

Therefore, g does not satisfy the hypotheses of Rolle's Theorem on the interval (0,k) for any value of k.

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Approximately 9.4 seconds after diving, the sky diver's velocity will be 59 meters per second.  

The velocity function for a sky diver falling near the Earth's surface is given by the exponential function \(v(t) = 71 - 71e^(-0.19t)\), where t represents the time after diving measured in seconds.

To find the number of seconds after diving when the sky diver's velocity is 59 meters per second, we need to solve the equation:

\(59 = 71 - 71e^{(-0.19t)}\)

Let's solve it step by step:

Subtracting 71 from both sides:

\(-12 = -71e^{(-0.19t)}\)

Dividing both sides by -71:

\(e^{(-0.19t)} = \frac{12}{71}\)

Taking the natural logarithm (ln) of both sides to eliminate the exponential:

\(ln(e^{(-0.19t)}) = ln(\frac{12}{71})\\-0.19t = ln(\frac{12}{71})\)

Now, we can solve for t by dividing both sides by -0.19:

\(t =\frac{ln(\frac{12}{71})}{-0.19}\)

Using a calculator or a software, we find:

t ≈ 9.356 seconds (rounded to three decimal places)

Therefore, approximately 9.4 seconds after diving, the sky diver's velocity will be 59 meters per second.  

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Answer:

Step-by-step explanation:

-1

Answer:

\(\frac{12}{16} =\frac{16-x}{12}\) → \(144=256-16x\)

\(16x=256-144\)

\(16x=112\) → \(x=7\)

OAmalOHopeO

Performing a change of scale we will see that the actual distance is 4 miles.

We know that the scale is:

3/4 inch = 2 miles.

And the distance that Nicole found on the map is (1 + 1/2) inches.

We can rewrrite the scale as:

1 inch = (4/3)*2 miles

1 inch = (8/3) miles.

Then the actual distance will be:

distance = (1 + 1/2) inches = (1 + 1/2)*(8/3) miles = 4 miles.

The correct option is A.

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Three methods for determining the volume of geometric shapes are the formula method, the displacement method, and the integral method.

The formula method is commonly used for basic geometric shapes such as cubes, rectangular prisms, cylinders, and spheres. These shapes have well-defined formulas for calculating their volumes, such as V = l x w x h for a rectangular prism or V = πr²h for a cylinder. This method is straightforward and easy to use, but it may not be applicable to irregular or complex shapes.

The displacement method involves immersing the shape in a liquid and measuring the amount of liquid displaced. The volume of the shape is then equal to the volume of the liquid displaced. This method is useful for irregular shapes that cannot be easily measured using traditional formulas. However, it requires careful measurements and may not be practical for large or delicate objects.

The integral method is a mathematical technique that uses calculus to determine the volume of a shape. It is particularly suited for complex three-dimensional objects that cannot be easily measured or calculated using other methods. By breaking down the shape into infinitesimally small elements and integrating their volumes, the total volume of the shape can be accurately determined. This method is highly precise but requires advanced mathematical knowledge and computational tools.

In conclusion, while the formula method and the displacement method are useful for simple and irregular shapes respectively, the integral method is expected to be the most precise for determining the volume of geometric shapes. It can handle complex shapes and provide accurate results, albeit requiring advanced mathematical skills and tools.

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Answer:

x = 5

Step-by-step explanation:

4x - 5x + 1 = -4

4x - 5x = -4-1

-x = -5

x = 5

Hope this helped

Brainliest is Appreciated.

The length of the rectangular flower whose area is 60 sq. meters garden is 10 meters.

Let's assume the width of the rectangular flower garden is x meters. According to the given information, the length is 4 meters more than the width, so the length can be represented as (x + 4) meters.

The area of a rectangle is calculated by multiplying its length and width. In this case, we know that the area is 60 square meters, so we can set up the following equation:

Area = Length × Width 60 = (x + 4) × x

Expanding the equation, we get: 60 = x² + 4x

Rearranging the equation to the standard quadratic form, we have

x² + 4x - 60 = 0

x² + 10x - 6x - 60 = 0

x(x + 10) - 6(x+ 10) = 0

(x - 6)(x+ 10) = 0

x - 6 = 0 or x + 10 = 0

x = 6 or x = -10

we find that the solutions are x = 6 and x = -10. Since the width cannot be negative, we discard the negative value.

Therefore, the width of the garden is 6 meters.

The length, we can substitute the width value into the expression for the length:

Length = Width + 4 = 6 + 4 = 10 meters.

Hence, the length of the garden is 10 meters.

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Answer:

y=5x+31

Step-by-step explanation:

y=mx+b

1=(-6*5)+b

1=-30+b

31=b

y=5x+31

(5*-6)+31

-30+31

1

you can also graph a line on desmos

Answer:

90

Step-by-step explanation:

Answer:

9×3+11 = 27 I think hope it helps

Answer:

Step-by-step explanation:

The statement that best compares the theoretical and experimental probability of landing on blue is:

The theoretical probability of landing on blue is one fourth, and the experimental probability is 35%.

Theoretical probability is the probability of an event occurring based on the assumption that the spinner is fair, and the experimental probability is the probability of an event occurring based on the data collected from the spins.

Since the spinner has four equal sections, the theoretical probability of landing on any section is 1/4 or 25%. Therefore, the theoretical probability of landing on blue is 1/4 or 25%.

On the other hand, the experimental probability is the number of times an event occurs, divided by the total number of trials.

In this case, the experimental probability of landing on blue is 7/20 or 35%.

So the theoretical probability of landing on blue is one fourth or 25% and the experimental probability is 35%.

The estimated p-value is approximately 0.313.

To estimate the value for the sample statistic and the p-value, we can calculate the sample proportions and perform a hypothesis test using those estimates.

Given the following information from the study:

- Sample size of men (group 1): n1 = 989

- Sample size of women (group 2): n2 = 1012

- Number of men owning a smartphone: x1 = 688

- Number of women owning a smartphone: x2 = 671

We can estimate the sample proportions for each group:

p^1 = x1 / n1 = 688 / 989 ≈ 0.6955 (rounded to four decimal places)

p^2 = x2 / n2 = 671 / 1012 ≈ 0.6624 (rounded to four decimal places)

The estimated difference in sample proportions is:

p^1 - p^2 ≈ 0.6955 - 0.6624 ≈ 0.0331 (rounded to four decimal places)

To test the hypothesis of no difference in proportions, we can conduct a two-proportion z-test. The test statistic can be calculated as:

z = (p^1 - p^2) / sqrt((p^1 * (1 - p^1) / n1) + (p^2 * (1 - p^2) / n2))

Plugging in the estimated values, we have:

z = (0.6955 - 0.6624) / sqrt((0.6955 * (1 - 0.6955) / 989) + (0.6624 * (1 - 0.6624) / 1012))

Calculating this expression, we find:

z ≈ 1.0084 (rounded to four decimal places)

To find the p-value, we can compare the test statistic to a standard normal distribution. Since the alternative hypothesis is two-sided (p1 ≠ p2), we need to find the probability of observing a test statistic as extreme as the one calculated.

Using a standard normal distribution table or software, we find that the probability of observing a test statistic as extreme as 1.0084 (in both tails) is approximately 0.313. This is the p-value.

Therefore, the estimated p-value is approximately 0.313.

Please note that these are estimated values, and the actual values may differ slightly when performing the calculations with more decimal places or using statistical software.

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Answer:subtraction

Step-by-step explanation:

4x^5-8x-3x^2-- - 8x-9

gives you 4x^5-3x^2-9

-8x- -8× cancel out