You have $4000 to invest. If you'd like to earn exactly $638
in interest each year, how much should you invest in each of
two accounts, one that earns 8% per year and one that
earns 21% per year. (Round your answer to the nearest
dollar)
8%: $
21%: $

Answer:

3.60$

Step-by-step explanation:

if we bought 3 pens that would equal 1.20$ so we add 1.20$ to 2.40$ we get 3.60$

Answer:

Step-by-step explanation:

To prove that [tex]w_1,\dots w_n[/tex] form a basis for W, we must check that this set is a set of linearly independent vector and it generates the whole space W. We are given that T is an isomorphism. That is, T is injective and surjective. A linear transformation is injective if and only if it maps the zero of the domain vector space to the codomain's zero and that is the only vector that is mapped to 0. Also, a linear transformation is surjective if for every vector w in W there exists v in V such that T(v) =w

Recall that the set [tex]w_1,\dots w_n[/tex] is linearly independent if and only if  the equation

[tex]\lambda_1w_1+\dots \lambda_n w_n=0[/tex] implies that

[tex]\lambda_1 = \cdots = \lambda_n[/tex].

Recall that [tex]w_i = T(v_i)[/tex] for i=1,...,n. Consider [tex]T^{-1}[/tex] to be the inverse transformation of T. Consider the equation

[tex]\lambda_1w_1+\dots \lambda_n w_n=0[/tex]

If we apply [tex]T^{-1}[/tex] to this equation, then, we get

[tex] T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) =T^{-1}(0) = 0[/tex]

Since T is linear, its inverse is also linear, hence

[tex]T^{-1}(\lambda_1w_1+\dots \lambda_n w_n) = \lambda_1T^{-1}(w_1)+\dots +  \lambda_nT^{-1}(w_n)=0[/tex]

which is equivalent to the equation

[tex]\lambda_1v_1+\dots +  \lambda_nv_n =0[/tex]

Since [tex]v_1,\dots,v_n[/tex] are linearly independt, this implies that [tex]\lambda_1=\dots \lambda_n =0[/tex], so the set [tex]\{w_1, \dots, w_n\}[/tex] is linearly independent.

Now, we will prove that this set generates W. To do so, let w be a vector in W. We must prove that there exist [tex]a_1, \dots a_n[/tex] such that

[tex] w = a_1w_1+\dots+a_nw_n[/tex]

Since T is surjective, there exists a vector v in V such that T(v) = w. Since [tex]v_1,\dots, v_n[/tex] is a basis of v, there exist [tex]a_1,\dots a_n[/tex], such that

[tex]a_1v_1+\dots a_nv_n=v[/tex]

Then, applying T on both sides, we have that

[tex]T(a_1v_1+\dots a_nv_n)=a_1T(v_1)+\dots a_n T(v_n) = a_1w_1+\dots a_n w_n= T(v) =w[/tex]

which proves that [tex]w_1,\dots w_n[/tex] generate the whole space W. Hence, the set [tex]\{w_1, \dots, w_n\}[/tex] is a basis of W.

Consider the linear transformation [tex]T:\mathbb{R}^2\to \mathbb{R}^2[/tex], given by T(x,y) = T(x,0). This transformations fails to be injective, since T(1,2) = T(1,3) = (1,0). Consider the base of [tex]\mathbb{R}^2[/tex] given by (1,0), (0,1). We have that T(1,0) = (1,0), T(0,1) = (0,0). This set is not linearly independent, and hence cannot be a base of [tex]\mathbb{R}^2[/tex]

k=2

Step-by-step explanation:

since all the base are 10 you use the powers to solve it.

so it would be -3+1+k=-3=-3

Answer:

k = -1

Step-by-step explanation:

I did the test, good luck! :)

Answer:

3  ≥ x

Step-by-step explanation:

-24 ≤x-3-8x

Combine like terms

-24 ≤-3-7x

Add 3 to each side

-24+3≤-3+3-7x

-21 ≤-7x

Divide by -7, remembering to flip the inequality

-21 /-7 ≥ -7x/-7

3  ≥ x

Answer:

y = x/60

Step-by-step explanation:

y = kx

k = y / x = 10/600 = 1/60

y = x/60

[tex]y[/tex] is directly proportional to [tex]x[/tex] when [tex]x=600[/tex] and [tex]y=10[/tex] then the formula for [tex]y[/tex] in terms of [tex]x[/tex] is given  as  [tex]y=\frac{1}{60} x[/tex] .

We say that, [tex]y[/tex] and [tex]x[/tex] are directly proportional, if  [tex]\frac{y}{x} =k[/tex]  or [tex]y=kx[/tex].

So,

According to the question;

[tex]x=600[/tex]

[tex]y=10[/tex]

From the above statement;

[tex]\frac{10}{600} =k[/tex]

[tex]k = \frac{1}{60}[/tex] ,

So,

[tex]y[/tex] in terms of [tex]x[/tex] is given by,

[tex]y=\frac{1}{60} x[/tex]

Hence, we can say that [tex]y[/tex] is directly proportional to [tex]x[/tex] when [tex]x=600[/tex] and [tex]y=10[/tex] then the formula for [tex]y[/tex] in terms of [tex]x[/tex] is given  as  [tex]y=\frac{1}{60} x[/tex] .

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Answer:

  A:  y= -4/3x+120

Step-by-step explanation:

The blue line on the plot has a y-intercept of +120, matching choices A and B only.

The line has a negative slope, matching choice A. If you count grid squares, you find the slope is -40/30 = -4/3, also matching choice A.

Answer:

 A:  y= -4/3x+120

Answer:

Step-by-step explanation:

If you don't consider how the wood might be cut, or how the tray might be assembled, you can look only at the area requirements.

A tray that is 10.5 inches square will have an area of ...

  (10.5 in)^2 = 110.25 in^2

That base will have a perimeter that is 4×10.5 in = 42 in. If the perimeter piece(s) are 2 inches high, the area of the sides of the tray will be ...

  (42 in)(2 in) = 84 in^2

Then the total area of wood required for the proposed tray is ...

  110.25 in^2 +84 in^2 = 194.25 in^2

__

The area of the wood Stephan has is ...

  A = LW = (18 in)(12 in) = 216 in^2 . . . . . . more than required

__

Stephan does have enough wood to make the tray, because he has 216 square inches, which is more than he needs to make the tray, 194.25 square inches.

Answer:

C

Step-by-step explanation:

Since the output is just the input multiplied by 3, the output will be 15.4*3=46.2, or answer choice C. Hope this helps!

Answer:

C. 46. 2

Step-by-step explanation:

All you need to do is multiply 15.4 by 3, like so:

15.4 · 3 = 46.2

Answer:

Mean, Median

Step-by-step explanation:

Outliers affect the mean because it is not resistant to outliers. They will affect the sum and therefore the mean.

The solution is, Mean, Median.

i.e. The outlier of a data set causes the Mean (mean/median) to be greater than the Median (mean/median) when the outlier is in the upper part of the data set.

In statistics and probability theory, the median is the value separating the higher half from the lower half of a data sample, a population, or a probability distribution. For a data set, it may be thought of as "the middle" value.

here, we have,

we know that,

Outliers affect the mean because it is not resistant to outliers.

They will affect the sum and therefore the mean.

so, we get,

The outlier of a data set causes the Mean (mean/median) to be greater than the Median (mean/median) when the outlier is in the upper part of the data set.

hence, The solution is, Mean, and, Median.

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Answer:

:v What??

jwkwlwmwbwjqkq

.........

.

........

..

Answer:

0.04

Step-by-step explanation:

Standard deviations== square root of variance define as spread.

Standard deviations square = variance

[0.2]^2= 0.04

Answer:

5

Step-by-step explanation:

4 people you didnt kill and that were already there and you

can i have brainliest if i got it right pls

Answer:

31

Step-by-step explanation:

there were 34 people and you killed 30. the other people would have gotten scared and ran away leaving you with 30 other bodies in the room

Answer:

Several ways, take the diameter and divide it by half.

Take the circumference "C" and r = C/2π

Step-by-step explanation:

Answer:

The answer is 4

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

A correlation coefficient a numerical measure of change of two variables, but it is often a sample from a data set. Considering there is no change between our x and y variables that align in our change, the correlation coefficient I thought it would be is 0, but answering C.4 got an 100% on the Edge Test.

Answer:

B is the answer for but I don't now about others thank you

Answer:

YOU MAY NEED TO CHAN

Step-by-step explanation:

Phil would need to save for at least 6 weeks to have enough money to buy the bike.

Phil saves one-quarter of his pay each week, which is:

1/4 x £240 = £60

Let's assume it takes him n weeks to save enough to buy the bike. Then, the amount he saves in n weeks is:

n x £60 = £349

We can solve for n by dividing both sides by £60:

n = £349 / £60

n ≈ 5.82

Since we can't have a fraction of a week, Phil would need to save for 6 weeks to have enough money to buy the bike.

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Answer:

a bc they are parallel

Step-by-step explanation:

Answer:

460

Step-by-step explanation: multiply all numbers to get your answer

Answer:

2.09, 2.59, 2.9

Step-by-step explanation:

Answer:

2.09, 2.59, 2.9

Step-by-step explanation:

hope this helps have a wonderful day

Answer:

[tex] Range =1.41-0.66 = 0.75[/tex]

[tex] \bar X = 1.171 W/Kg[/tex]

[tex] s^2 = 0.0607[/tex]

And taking the square root we got the sample deviation:

[tex] s = \sqrt{0.0607}= 0.246 W/kg[/tex]

Step-by-step explanation:

For this case we have the following datset given:

0.83 1.39 1.39 1.03 0.66 1.26 1.39 1.18 1.41 1.19 1.15

We need to find the range, and the range is defined by:

[tex] Range = Max -Min[/tex]

And replacinng we got:

[tex] Range =1.41-0.66 = 0.75[/tex]

Then we can find the sample variance, but firt we need to find the sample mean with this formula:

[tex]\bar X = \frac{\sum_{i=1}^n X_i}{n}[/tex]

And replacing we got:

[tex] \bar X = 1.171 W/Kg[/tex]

Now we can find the sample variance with this formula:

[tex] s^2 = \frac{\sum_{i=1}^n (X_i -\bar X)^2}{n-1}[/tex]

And replacing we got:

[tex] s^2 = 0.0607[/tex]

And taking the square root we got the sample deviation:

[tex] s = \sqrt{0.0607}= 0.246 W/kg[/tex]

Answer:

65

Step-by-step explanation:

Order the numbers in order

Find the middle number

Since there were 2, find the average

Answer:65

Step-by-step explanation:

median is the middle

there is 2 and they are 50 and 80

add it up and divide by 2

Answer:

1/20 of a gallon

Step-by-step explanation:

If she divides 1/4 into 5 glasses, the answer would be 0.05, or 1/20 gallons, if its right please give 5 stars

Answer:

<1 = <5 is True

<2 = <4 is True

<2 = <7 is False

<3 and <6 are not a linear pair

<4 and <5 are not supplementary angles

m<5 is 75°

m<11 is 75°

m<16 is 65°

Answer:

30

Step-by-step explanation:

If these two shapes are similar, then ratios of corresponding sides will stay constant. Therefore:

[tex]\dfrac{g}{45}=\dfrac{50}{75}[/tex]

Multiply both sides by 45:

[tex]g=\dfrac{50\cdot 45}{75}=30[/tex]

Hope this helps!

Answer:

The area of base is 47.1 m² or 15π m².

Step-by-step explanation:

Given that the formula of volume of cylinder is V = πr²h where πr² is the base area of cylinder so you have to substitute the following values into the formula :

[tex]v = \pi \times {r}^{2} \times h[/tex]

Let v = 315π,

Let h = 21,

[tex]315\pi = \pi {r}^{2} \times 21[/tex]

[tex]\pi {r}^{2} = 315\pi \div 21[/tex]

[tex]\pi {r}^{2} = 15\pi[/tex]

[tex]base \: area = 15\pi \: {m}^{2} [/tex]

[tex]base \: area = 47.1 \: {m}^{2} (3s.f)[/tex]

Answer:

a

Step-by-step explanation:

Answer:

10 and 5

Step-by-step explanation:

Answer:

43.125

Step-by-step explanation:

From trigonometry;

Tan87.4 =height of monument / 25

Height of monument = 25 * Tan 87.4

= 25 * 1.525

=38.125 ft

There is an extra substention of 5ft we add that

38.125 + 5 = 43.125 ft