5. Miguel plans on retiring in 16 years, and he wants to double his money by that time. He's contacted various banks, looking for a CD that compounds interest monthly, and to calculate what annual interest rate he needs, he is using the Rule of 72.

Part I: What is the rule of 72? To represent the annual interest rate, use r. ​

A)

I) 114.31

ii)114

iii) 114, 107

B)

x frequency

90-99: 1

100-109: 5

110-119: 2

120-129: 1

130-139: 2

Step-by-step explanation:

A x. f. fx

97. 1. 97

100. 1. 100

103. 1. 103

105. 1. 105

107. 2. 214

108. 1. 108

114. 2. 228

115. 1. 115

122. 1. 122

137. 1. 137

139. 1. 139.

13 1468

I) mean: £fx. =. 1468

£f. 13

= 114.3076

=114.31 to 2 decimal places

Ii) median: 97,100,103,105,107,107,108,114,114,115,122,137,139

:• median= 108

III) mode = 107,114

Answer:

19 km/h

Step-by-step explanation:

average speed = total distance / total time

in this case it will be 57/3 = 19 km/h

To find the orthogonal projection of a vector onto a subspace, we can use the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ,

where A is a matrix whose columns span the subspace, and u is the vector we want to project.

In this case, the subspace W is spanned by the vector v = [0, 0, 0, 1].

Let's calculate the orthogonal projection of u onto W using the formula:

A = [v]

The transpose of A is:

Aᵀ = [vᵀ].

Now, let's substitute the values into the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ

= v⁻¹[vᵀ]u

= [v][(vᵀv)⁻¹vᵀ]u

Substituting the values of v and u:

v = [0, 0, 0, 1]

u = [1, 0, 0, 0]

vᵀv = [0, 0, 0, 1][0, 0, 0, 1] = 1

[(vᵀv)⁻¹vᵀ]u = (1⁻¹)[0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 0]

Therefore, the orthogonal projection of u onto the subspace W is [0, 0, 0, 0].

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Answer: 18 mega rolls

Step-by-step explanation:                      

Answer:

the second one is a better deal.

Step-by-step explanation:

first deal:

6 rolls for 9.24

9.24/6 = 1.54

1.54$ per roll

second deal:

18 rolls for 27.54

27.54/18 = 1.53

1.53$ per roll

the second one is one cent cheaper

Answer:

C

Step-by-step explanation:

the domain is the set of numbers that can be x values. in this case, the equation is linear so any number you plug in for x will give you a y value

Six and forty-seven thousandths.

or six point zero four seven.

the answer depends on what you have to write.

Hope this helps!

Answer:

u should put this also in English then type it in so it will translate

Add the 3 republican amounts: 38 + 104 + 44 = 186

Divide by total people: 186/651 = 0.285714

Multiply by 100: 0.285714 x 100 = 28.5714%

Round to nearest tenth = 28.6%

Total of Same column: 104 + 87+90 = 281

Divide by total people: 281/651 = 0.431644

Multiply by 100: 0.431644 x 100 = 43.1644%

Round to nearest tenth = 43.2%

Republicans that said the same = 104

Total republicans = 38 + 104 + 44 = 186

Percentage = (104/186) x 100 = 55.9%

Answer:

-528/25

Step-by-step explanation:

The required area of Fiona's circle is49π. Option D is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Where h, k is the coordinate of the center of the circle on a coordinate plane and r is the radius of the circle.

The radius of Fiona's circle is half of the diameter, which is 14/2 = 7 meters.

The formula for the area of a circle is A = πr², where A is the area and r is the radius.

Substituting the value of the radius in the formula, we get:

A = π(7)² = 49π

So, the area of Fiona's circle is 154 square meters, if we use the value of π as 3.14.

Therefore, the answer is 49.

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The possible coordinates of point A are (-1, -2) and (-1, 4)

what are coordinates ?

Coordinates are sets of values that locate a point in a given space or plane. In mathematics, coordinates are commonly used to locate points on a graph, such as the Cartesian plane, which has two axes, the x-axis and y-axis, with perpendicular lines representing different values. The coordinates of a point are typically represented as an ordered pair, (x, y), where x represents the horizontal distance from the origin along the x-axis and y represents the vertical distance from the origin along the y-axis.

According to the question:

We know that the x-coordinate of point A is -1. Let's assume the y-coordinate of point A to be y.

Using the distance formula, we can find the distance between points A and B:

\(distance = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)}\)

\(5 =\sqrt{((3 - (-1))^2 + (1 - y)^2)}\)

Simplifying the equation, we get:

\(25 = 16 + (1 - y)^2\)

\(9 = (1 - y)^2\)

\(\±3 = 1 - y\)

\(y = -2 or 4\)

Therefore, the possible coordinates of point A are (-1, -2) and (-1, 4).

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The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.

To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.

Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.

To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.

Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.

Therefore, the slope of the line that divides the region into two equal areas is 5.

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Answer:

M=77

Step-by-step explanation:

Do you need work?

Answer:

The width would be 8 inches

Step-by-step explanation:

50% of 16 is 8

Display ads sold on a cost per thousand impressions (CPM) basis often focus on reaching a large audience or maximizing brand exposure.

Cost per thousand impressions (CPM) is a common pricing model used in digital advertising, where advertisers pay for every one thousand times their ad is displayed to users.

In this model, the focus is on the number of impressions or views rather than the actual performance or engagement with the ad. As a result, display ads sold on a CPM basis often prioritize reaching a large audience and maximizing brand exposure.

By selecting a CPM pricing model, advertisers aim to increase their ad's visibility and generate brand awareness among a wide range of users.

They are interested in getting their message in front of as many people as possible, regardless of whether those users interact with the ad or take any specific action.

CPM-based display ads are commonly used for branding campaigns, where the primary goal is to create brand recognition, increase visibility, and establish a presence in the minds of potential customers.

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f(x) = 1 + 7x + 49x^2/2! + 343x^3/3! + ...

The Taylor series for f(x) = e^7x (centered at c = 0) is given by the above equation.

The Taylor series formula is a way of expressing a function as an infinite sum of terms. This sum can be made up of the derivatives of the function evaluated at a single point.

The formula for Taylor series is as follows:

f(x) = f(c) + f'(c)(x-c) + f''(c)(x-c)^2/2! + ... where c is the center of the series and f', f'', f''', and so on, represent the first, second, third, and so on, derivatives of the function f(x).

For f(x) = e^7x and c = 0, we will first find the derivatives of f(x):

f(x) = e^7x

f'(x) = 7e^7x

f''(x) = 49e^7x

f'''(x) = 343e^7x

...

and so on.

Evaluating these derivatives at c = 0:

f(0) = e^0 = 1

f'(0) = 7e^0 = 7

f''(0) = 49e^0 = 49

f'''(0) = 343e^0 = 343

...

and so on.

Substituting these values into the Taylor series formula:

f(x) = 1 + 7x + 49x^2/2! + 343x^3/3! + ...

The Taylor series for f(x) = e^7x (centered at c = 0) is given by the above equation.

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Step-by-step explanation:

photos explain. in the second photo, A didnt start at 0 so it looked not accurate

The shapes of the curves in the AS/AD (Aggregate Supply/Aggregate Demand) model are based upon the relationship between the price level and the output level in an economy.

The AD curve shows the relationship between the overall price level and the quantity of goods and services demanded by all buyers in an economy. It has a negative slope, indicating that as the price level increases, the quantity of goods and services demanded decreases.

The AS curve shows the relationship between the overall price level and the quantity of goods and services that firms are willing and able to supply. In the short run, the AS curve is upward sloping, indicating that as the price level increases, firms are willing to supply more output due to higher profits. In the long run, the AS curve becomes vertical, indicating that the level of output is determined by the factors of production and technology, not the price level.

Thus, the shapes of the curves in the AS/AD model are based on the behavior of buyers and sellers in an economy and their response to changes in the overall price level.

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Answer:

true

Step-by-step explanation:

because there's less humidity

The negation of the proposition posed the statement is:

"Every student in this class has seen a computer."

The negation of the proposition "There is a student in this class who has never seen a computer" can be expressed using quantifiers as follows:

∀ x ∈ S, ∃ y ∈ C (x has seen y)

This means "For all students x in the class S, there exists a computer y in the set of computers C such that x has seen y."

In English, the negation of the proposition can be expressed as "Every student in this class has seen a computer."

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Answer:

x=-\(\frac{3+-\sqrt{41} }{8}\)

Step-by-step explanation:

We can use the quadratic formula here. We then plug in the values.

Answer:456

Step-by-step explanation:

First you grab the crabby patty formula and then you decide that by 3 multiply it by 6 then after all of that you do the equation 64%78+4637=456 so that’s how I got my answer.

Answer:

The answer is 9.45

Step-by-step explanation:

2.7*3.5=9.45

Answer:

( x − 3 ) ( x + 5 )

Step-by-step explanation:

HAVE A NICE DAY

Answer:

B

Step-by-step explanation:

; factor the left side of the equation

; (x−3) (x+5) = 0

set factors equal to 0

x − 3 = 0

or

x + 5 = 0

; so, x = 3  or  x = −5

Answer:

Step-by-step explanation:

40

Answer:

40

Step-by-step explanation:

 20              

20

+-----

zero plus zero is zero

two plus two is four

40

The given statement, "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is False.

Explanation: Null space is a linear algebra term used to refer to the set of all vectors that are mapped to the null vector. The solution of Ax=0 is also referred to as the null space or kernel of A. Since the matrix is of size 4x4 and non-zero, it must have at least one non-zero eigenvalue. Any non-zero vector multiplied by this non-zero eigenvalue will result in a non-zero vector, even if it is in the nullspace of the matrix. Because of this, a non-zero 4 x 4 matrix's nullspace can have four or fewer linearly independent vectors.

Hence, the statement "The nullspace of a nonzero 4 x 4 matrix cannot contain a set of four linearly independent vectors" is false.

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The sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

What is sampling distribution ?

An example of a sampling distribution is a probability distribution of a statistic that is derived from repeated sampling of a particular population.            

                         It depicts a spectrum of potential results for a statistic, such as the mean or mode of a variable, for a population.

Given,

Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325.

Simulation A will consist of 1500 trials with a sample size of 100.

Simulation B will consist of 2000 trials with a sample size of 50.

Center for Simulation A and Simulation B will be roughly equal.  

Overall Sample size of Simulation A will be

  = 1500 * 100  = 150000

Overall Sample size of Simulation B will be

 = 2000 *  50  =  100000

Hence, the sample size for Simulation A is greater than then the sample size for Simulation B and the variability of Simulation A will be less then the variability of Simulation B.  

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The complete question is -

In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?

A) The centers will roughly be equal, and the variabilities will roughly be equal.

B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.

C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.

D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.

E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.

Answer:

The algebraic equation for the given sentence is

3x - 8 = 25