suppose you plunk $5000 into a one-year certificate of deposit (CD) that pays simple interest at 3% per annum. The interest you earn after one year would be $150:​

Let [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex] be the nonzero rows of [tex]$R$[/tex] starting from the 1st row to the [tex]k[/tex]th row.

Step 1: We want to show that

R(R)= span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]

For any vector [tex]v $$\in \mathcal{R}(R)$$[/tex], We may write

v= [tex]$$c_{1} \boldsymbol{r}_{1}+c_{2} \boldsymbol{r}_{2}+\cdots+c_{k} \boldsymbol{r}_{k}+c_{k+1} \mathbf{0}+\cdots+c_{m} \mathbf{0}$$[/tex]

Then v= [tex]$$c_{1} r_{1}+c_{2} r_{2}+\cdots+c_{k} r_{k}$$[/tex]

So [tex]v[/tex] belongs to span{ [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]}

Thus R(R)[tex]\leq[/tex] Span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]

But trivially,

span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]≤ span{[tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex], 0, . . . , 0} = R(R),

span [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]=R(R)

Step 2: We want to show that  [tex]$\boldsymbol{r}_{1}, \ldots, \boldsymbol{r}_{k}$[/tex]are linearly independent. Suppose otherwise,

then we can write

[tex]$$c_{1} \boldsymbol{r}_{i_{1}}+\cdots+c_{\ell} \boldsymbol{r}_{i_{\ell}}=\mathbf{0}$$[/tex]

From Steps 1 and 2, we have proven that the nonzero rows of R form a basis for the row space.

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Answer:

K = 17

Based on the given conditions, formulate: 

51 / 3 = k

Swap the sides : k = 51 / 3

Cross out the common factor: k = 17

Answer:

Step-by-step explanation:

Find the roots of x^2-25=0 by solving for x.

Add 25 to both sides

x^2=25

Square root both sides

x=-5

x=5

Answer:

x=5;x=-5

Step-by-step explanation:

It was right for me

Answer:

It is the first graph

Step-by-step explanation:

The line under the > and < sign means that it must include the 3 and the 0.  The closed circle is showing that the 3 and 0 or included.

The surface area of a rectangular prism is found as 150 square inches.

A rectangular prism is a polyhedron in geometry that has two parallel and congruent bases. It also goes by the name cuboid. Six faces make up a rectangular prism, and each face has a rectangle shape and twelve edges.

Actually, prisms get their name from the way their faces are shaped. Therefore, a rectangular prism is just a prism with rectangular faces. Although it is a closed, three-dimensional object, two rectangles serve as its foundation.

Calculation for the surface area of rectangular prism-

Height of a rectangular prism => H = 4 inches

Width of a rectangular prism => B = 9 inches

Length of a rectangular prism => L = 3 inches

Surface area of a rectangular prism = 2(LB + BH + HL)

                                                           = 2(9×3 + 9×4 + 4×3)

                                                           = 150

Therefore, the surface area of a rectangular prism is found as  150 square inches.

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The y-intercept of the function f(x) is (0, 10/3)

The function is given as:

[tex]f\left(x\right)=\frac{30}{1+2^{3-x}}[/tex]

As x approaches infinity, we have:

[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-x}}[/tex]

This gives

[tex]\lim_{x \to \infty} \frac{30}{1+2^{3-\infty}}[/tex]

[tex]\lim_{x \to \infty} \frac{30}{1+2^{-\infty}}[/tex]

Evaluate

[tex]\lim_{x \to \infty} \frac{30}{1}[/tex]

[tex]\lim_{x \to \infty} 30[/tex]

As x approaches negative infinity, we have:

[tex]\lim_{x \to -\infty} \frac{30}{1+2^{3+x}}[/tex]

This gives

[tex]\lim_{x \to -\infty} \frac{30}{\infty}[/tex]

Evaluate

[tex]\lim_{x \to -\infty} 0[/tex]

Hence, the limits of the function are [tex]\lim_{x \to \infty} 30[/tex] and [tex]\lim_{x \to -\infty} 0[/tex]

Remove the denominator

f(x) = 30

Also, set the numerator to 0

f(x) = 0

Hence, the horizontal asymptotes are y = 30 and y = 0

Set x = 0

[tex]f\left(0\right)=\frac{30}{1+2^{3-0}}[/tex]

Evaluate

[tex]f\left(0\right)=\frac{30}{9}[/tex]

Divide

[tex]f\left(0\right)=\frac{10}3[/tex]

Hence, the y-intercept is (0, 10/3)

The numerator of f(x) is 30.

In (b), we have

The horizontal asymptotes are y = 30 and y = 0

This means that the horizontal asymptotes and the numerator are the same

See attachment for the graph of f(x)

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Answer:

Option A.

Step-by-step explanation:

Demonstration

[tex]y=\frac{7}{4} x+7[/tex]

for x = -4

[tex]y=\frac{7}{4} (-4)+7=-\frac{28}{4} +7=-7+7=0[/tex]

for x= 0

[tex]y=\frac{7}{4}(0) +7=0+7=7[/tex]

for x= 4

[tex]y=\frac{7}{4} (4)+7=\frac{28}{4} +7=7+7=14[/tex]

Hope this helps

Answer:

(3, 2 )

Step-by-step explanation:

given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

( [tex]\frac{x_{1}+x_{2} }{2}[/tex] , [tex]\frac{y_{1}+y_{2} }{2}[/tex] )

here (x₁, y₁ ) = (2, 3 ) and (x₂, y₂ ) = (4, 1 ) , then

midpoint = ( [tex]\frac{2+4}{2}[/tex] , [tex]\frac{3+1}{2}[/tex] ) = ( [tex]\frac{6}{2}[/tex] , [tex]\frac{4}{2}[/tex] ) = (3, 2 )

The volume of the rectangular prism is 8 1 / 8 units³

volume of a rectangular prism = lwh

where

Therefore,

volume of a rectangular prism = base area × height

volume of a rectangular prism = 16 1 / 4 × 1 / 2

volume of a rectangular prism = 65 / 4 × 1 / 2

volume of a rectangular prism =  65 / 8

volume of a rectangular prism =  8 1 / 8 units³

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The average daily balance for the month was $84.21, and the finance charge for the month was $30.13.

Given that Sally's balance on her credit card is $75.00 on the first day of August, and she makes a payment of $18.00 on August 17 and a new purchase of $41.00 on August 29, and the annual interest rate is 21.25%, to determine what is Sally's average daily balance and finance charge for the month of August, the following calculation must be made:

Therefore, the average daily balance for the month was $84.21, and the finance charge for the month was $30.13.

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Answer:

Original equation:

y = a sin(b(θ -c)) + d

a = vertical dilation (stretch) of the amplitude

b = horizontal compression (shrink) of the period

c = horizontal shift (left/right)

d = vertical shift (up/down)

Your function is:

y = 3 sin(3θ + π) - 2

First, put it into the general from by factoring out the three in the argument of the sine:

y = 3 sin(3(θ + π/3)) - 2

a = vertical (amplitude) dilation = 3

b = horizontal (period) compression = 2π/period = 3

c = horizontal shift = π/3 to the left

d = vertical shift = -2

Answer:

680

Step-by-step explanation:

Factorize the numerator and denominator. You'll see that they both have a factor of 4 that can be canceled. The introduce a factor of 3 to change the denominator to 36.

[tex]\dfrac{28}{48} = \dfrac{4\times7}{4\times12} = \dfrac7{12} = \dfrac{3\times7}{3\times12} = \boxed{\dfrac{21}{36}}[/tex]

Answer:

Step-by-step explanation:

hello :

P(E and F)=0.7×0.6 =0.42

The central tendency researcher use to describe these data is "mode".

The value that appears most frequently in a data set is called the mode. One mode, several modes, or none at all may be present in a set of data. The mean, or average of a set, and the median, or middle value in a set, are two more common measurements of central tendency.

Calculation of mode is done by-

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Answer:

Rectangular Prism

Step-by-step explanation:

We usually see building shaped as a 3D rectangle. If this is the type of building you are talking about, we use a rectangular prism in order to build the building with correct measurements.

The parameters of the sinusoidal function graphs can be found from the coordinates of the given locations.

First graph;

a. Amplitude = 0.5

b. The period = 2•π

c. The horizontal shift = 1

d. The vertical shift = π/4

Second graph;

a. Amplitude = 2

b. The period = π

c. The horizontal shift = -π/4

d. The vertical shift = -2

First graph;

a. The amplitude is half the distance between the y-value peak point and the y-value of a throw (lowest point) on the graph.

The coordinate of a peak point in the first graph is (0, -1.5)

The coordinate of a throw point is (π/2, -2.5)

Therefore;

Amplitude = (-1.5 - (-2.5)) ÷ 2 = 0.5

b. The period is the number of cycles per second, we have;

From the graph, we have;

Therefore;

The frequency = 1/π cycle per unit length

c. The horizontal shift is the distance from the closet intersection of the midline and the rising region of the graph and the y-axis.

Therefore;

The horizontal shift = (-π/2)/2 = -π/4

d. The vertical shift is the distance from the horizontal axis to the midline of the graph.

By observation, the midline is y = -2

Therefore;

Second Graph;

For the second graph, we have;

a. Amplitude = (3 - (-1))/2 = 2

b. Frequency = 1/(2×(5•π/4 - π/4)) = 1/(2•π)

Therefore;

c. Horizontal shift = Distance between x-coordinate of the intersection of the midline and the graph and the x-coordinate of the closest peak.

Therefore;

d. Vertical shift = (3 + (-1))/2 = 1

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By using Binomial Distribution the probability that exactly 6 workers take the bus to work is 0.001.

When every experiment shares the probability of achieving a given value, the number of trials or observations is summarised using the binomial distribution.

The likelihood of observing a specific percentage of successful occurrences in a specific number of trials is determined by the binomial distribution.

The formula for binomial distribution is-

[tex]P(X=x)={ }^{n} C_{k} p^{k}(1-p)^{n-k}[/tex]

'p' is the probability of success,

(1-p) is probability of failure,

'n' is the number of workers,

'k' is number of given workers.

According to the question,

Calculate the probability of success as;

[tex]p=\frac{15}{100}=0.15[/tex]

The, the probability of the failure becomes;

[tex](1-p)=1-0.15=0.85[/tex]

Put above two value in formula of binomial theorem to get the value.

[tex]{ }^{10} C_{6}(0.15)^{6}(0.85)^{4}=0.001[/tex]

Therefore, the probability that exactly 6 workers take the bus to work is 0.001.

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Circumference = 10π in, Area = 25π in²

Circumference = 19 π in, Area = 90. 25 π in²

Area = 225 π in²

Circumference = 16π

It is important to note that the formula for area and circumference are;

Area = πr^2

Circumference = 2πr

For the first column, we have

radius = 5in

Substitute the values of the radius into the formula

Circumference = 2 × π × 5

Circumference = 10π in

The area;

Area = π × 5 × 5

Area = 25π in²

For the second column,

radius = 9. 5 in

Substitute the values of the radius into the formula

Circumference = 2 × π × 9. 5

Circumference = 19 π in

Area = π × 9. 5 × 9. 5

Area = 90. 25 π in²

For the third column

radius = 15in

Substitute the values of the radius into the formula

Area = π × 15 × 15

Area = 225 π in²

For the fourth column

radius = 8 in

Substitute the values of the radius into the formula

Circumference = 2 × π × 8

Circumference = 16π

From the solved solution, we can see that the shape is a circle.

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If the growth rate is 0.469 per member per day and in the beginnning there are 5 members then the population size after eight days is 108.42.

Given growth of population of protozoa 0.469 per member per day and population in beginninng is 5 members.

We have to find the population afte eight days.

First of all we have to find the function or equation showing sum of population after t days.

Because it is given that the rate is 0.469 per member per day it means it is like compounding.

The equation which shows the sum after compounding is P[tex](1+r)^{n}[/tex]

where P is the amount in beginning, r is the rate and n is the number of years.

In this problem the equation will be 5[tex](1+0.469)^{t}[/tex] where t is number of days.

We have to put the value of t=8 to find the population after 8 days=

=5[tex](1.469)^{8}[/tex]

=5*21.68

=108.42

Hence the population of protozoa after 8 days is 108.42.

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The standard error of the mean, rounded to the nearest hundredth is 0.27

The standard error of the mean (SEM) calculates how big of a difference there is between the mean of a sample and the mean of the population.

The square root of the sample size is divided by the standard deviation in order to obtain  the Standard error of mean.

Always, standard error of mean will be smaller than standard deviation.

But a statistical inference based on the sampling distribution is part of the Standard error of mean definition.

According to the question,

Population Mean=56.7

Standard Deviation=4.3

Sample Size=260

Standard Error of mean=4.3/[tex]\sqrt{260}[/tex]

                                       =4.3/16.1245

                                       =0.27

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Answer:

0.27

Step-by-step explanation:

Plato/Edmentum

P ( work/ senior ) = 0.14

The attached table

required

P ( work/ senior )

This is calculated using:

P ( work/ senior ) = n ( work/ senior )/ n ( senior ).

n ( work/ senior ) = 5

n ( senior ) = 25 + 5 + = 35

So:

P ( work/ senior ) = 5/35

P ( work/ senior ) = 0.14

Add 25+5+5 (because that is all the numbers in the 'Seniors' row) and then take the 5 that is in the 'Work' column and put that over 25. (5/25 fraction as a percent is 14).

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Use elimination

(1)×5 and (2)×4

(3)-(4)

Putting in eq(1)

x + 4y = 16 __(1)

3x + 5y = 27 __(2)

Multiply the 1st equation by 3

3x + 12y = 48 __(3)

Solving (2) and (3)

3x + 12y = 48

3x + 5y = 27

__________

(-) (-) (-)

7y = 21

So, y = 3

By, putting the value of y = 3 in equation 1

x + 4(3) = 16

x + 12 = 16

x = 16 - 12

x = 4

The value of x = 4 and y = 3

Hope it helps you any confusions you may ask!

Mark up = $66

Mark up on selling price = 37%

Selling price = 37%

Selling price x Mark up percentage = Mark up

Selling price x 37% = 66

Selling price = $178.38

Cost = Selling price - Mark up

= 178.38-66

= $112.38

Cost as a percentage of selling price = Cost / Selling price

= 112.38/178.38

= 63%

The selling charge is how much a purchaser pays for a product or service. it is able to range relying on how tons consumers are inclined to pay, how a whole lot the seller is inclined to just accept, and the way competitive charge is in comparison to other businesses inside the marketplace.

A sale rate is the discounted rate at which goods or services are being offered. This rate is normally offered for a restrained period of time, usually to spur income all through a slow duration or to sell off excess stock. the discount is advertised as a percentage discount from the ordinary listing charge.

Fee rate: the quantity paid to purchase a piece of writing or the fee at which an editorial is made is known as its cost charge. The value fee is abbreviated as C.P. selling price: The rate at which an editorial is sold is called its selling rate. The promoting price is abbreviated as S.P.

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The minimum value of c = 7x + 8y is 42. The minimum value is obtained at point (6, 0).

To calculate the minimum value of the given equation w.r.t the given constraints(inequalities), the steps are:

Step 1: Identify the system of inequalities in the given constraints

Step 2: Graph those inequalities

Step 3: Identify the maximum and minimum values of x and y that satisfy the given inequalities

Step 4: Then, with the obtained coordinates solve the given equation to get the minimum value.

The given equation is C = 7x + 8y, and the constraints list is

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

Graphing these inequalities and shading the region that satisfies the given inequalities.

So, from the graph,

the x-values that satisfy all the given inequalities are [6, ∞]

the y-values that satisfy all the given inequalities are [0, ∞]

So, the required coordinate is (6, 0). By this, we can calculate the minimum value of the given equation C = 7x + 8y

Then,

C = 7(6) + 8(0) = 42 + 0 = 42

Thus, the minimum value of the given equation is 42.

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Disclaimer: The given question is incomplete. Here is the complete question.

Question: What is the minimum value of c = 7x 8y, given the constraints on x and y listed below?

2x + y ≥ 0

x + y ≥ 6

x ≥ 0

y ≥ 0

Mathew's speed of 100 m/min, and the distance of 10 m. east to which he is blown by the wind gives the angle in degrees Mathew is blown off his path as approximately 2.86°.

The given parameters are;

Speed at which Mathew is flying = 100 m/min

Distance and direction in which the strong wind blows him = 10 m. east

Time it takes the wind to deflect Mathew by 10 m. = 2 minutes

Therefore;

Speed and direction of the wind = 10/2 m/min east

Speed and direction of the wind = 5 m/min east

Mathew's flight path can be represented using a vector diagram (please see attached drawing)

Distance Mathew travels in 2 minutes = 100 m/min × 2 minutes = 200 m.

Tangent of the angle by which Mathew is off his flight path, A, can be found as follows;

tan(A) = 10/200 = 1/20

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The angle of elevation of 61° and 72° with the height of the tower being 553.3 m. gives Vic's distance from Dan as approximately 356 meters.

Location of Vic relative to the tower = South

Vic's sight angle of elevation to the top of the tower = 61°

Dan's location with respect to the tower = West

Dan's angle of elevation in order to see the top of the tower = 72°

Height of the tower = 553.3m

[tex]tan( \theta) = \frac{opposite}{adjacent} [/tex]

[tex]tan( 61 ^{ \circ}) = \frac{553.3}{ Vic' s\: distance \: to \: tower} [/tex]

[tex]distance = \frac{553.3}{tan ( {61}^{ \circ} )} = 306.7[/tex]

Similarly, we have;

[tex] Dan's distance = \frac{553.3}{tan ( {72}^{ \circ} )} = 179.8[/tex]

Given that Vic and Dan are at right angles relative to the tower (Vic is on the south of the tower while Dan is at the west), by Pythagorean theorem, the distance between Vic and Dan d is found as follows;

Therefore;

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There are 109 terms in given series.

According to the statement

we have given that the sum of series is AP series and

This is 19 20.5 22 23.5 ... 181

And the sum of series is 10,900

Now, we have to find the number of terms in the series.

Then we use the summation formula which is

S = n/2 (a + L)

Substitute the all given values in it like

L = 181

A = 19 and S= 10,900

then

10,900= n/2(19+181)

10,900= n/2(200)

After solve the equation for n

10,900= 100n

n = 10,900 / 100

n = 109

There are 109 terms in given series.

So, There are 109 terms in given series.

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