Suppose you invest a certain amount of money in account that earns 3% annual interest. You also invest that same amount + $2000 that earns 4% annual interest. If the total interest from both accounts at the end of the year is $535, how much has been invested in each account?

Answer:

Hello,

Answer 2

Step-by-step explanation:

7=2*0+7

9=2*1+7

11=2*2+7

13=2*3+7

15=2*4+7

17=2*5+7

y=2*x+7

An other way:

[tex]points\ ( 0,7)\ and\ (1,9)\\\\\Delta\ y=9-7=2\\\Delta\ x=1-0=1\\\\\\y-7=(x-0)*2\\\\y=2x+7\\[/tex]

The complete equation is [tex]y = 2x+7[/tex].

An equation is a condition on a variable such that two expressions in the variable should have equal value.

Substitution means replacing the variables (letters) in an algebraic expression with their numerical values.

According to the question.

We have a table which shows the relation between x and y.

Let the missing term be a and b.

The the given equation becomes

[tex]y = ax + b[/tex]

For finding the value of a and b.

Substitute x = 0 and y = 7 in equation y = ax + b.

[tex]\implies 7 = a(0) + b\\\implies b = 7[/tex]

Again, substitute  x = 1 and y = 9 in the equation y = ax+ b

[tex]\implies 9 = a(1) +b\\\implies 9 = a + 7\\\implies a = 2[/tex]

substitute the value of a and b in the equation y = ax + b.

[tex]\implies y = 2x+ 7[/tex]

Therefore, the complete equation is [tex]y = 2x+7[/tex].

Find out more information about equation and substitution here:

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Answer:

Step-by-step explanation:

(-1) × 1 = -1

Answer:

-1

Step-by-step explanation:

anything times 1 =1. except 0.

Answer:

see explanation

Step-by-step explanation:

Using the Sine rule in all 3 questions

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

(2)

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values

[tex]\frac{45}{sin133}[/tex] = [tex]\frac{c}{sin26}[/tex] ( cross- multiply )

c × sin133°  = 45 × sin26° ( divide both sides by sin133° )

c = [tex]\frac{45sin26}{sin133}[/tex] ≈ 27.0 ( to the nearest tenth )

(4)

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] , substitute values

[tex]\frac{19}{sinB}[/tex] = [tex]\frac{30}{sin97}[/tex] ( cross- multiply )

30 sinB = 19 sin97° ( divide both sides by 30 )

sinB = [tex]\frac{19sin97}{30}[/tex] , then

∠ B = [tex]sin^{-1}[/tex] ( [tex]\frac{19sin37}{30}[/tex] ) ≈ 38.9° ( to the nearest tenth )

(6)

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex], substitute values

[tex]\frac{18}{sin102}[/tex] = [tex]\frac{xAB}{sin45}[/tex] ( cross- multiply )

AB sin102° = 18 sin45° ( divide both sides by sin102° )

AB = [tex]\frac{18sin45}{sin102}[/tex] ≈ 13.0 ( to the nearest tenth )

Answer:

C is correct

Step-by-step explanation:

10/12=0.83...

2/3=0.66...

2/3<10/12

Answer:

C

Step-by-step explanation:

Why the others are incorrect:

A: [tex]\frac{2}{10} > \frac{3*2}{5*2}[/tex] → [tex]\frac{2}{10} > \frac{ 6}{10}[/tex] This statement/comparison is false

B : [tex]\frac{2*2}{4*2} > \frac{4}{8}[/tex] → [tex]\frac{4}{8} > \frac{4}{8}[/tex] This statement/comparison is false

D:[tex]\frac{9}{12} < \frac{3*2}{6*2}[/tex] → [tex]\frac{9}{12} < \frac{6}{12}[/tex] This statement/comparison is false

C: [tex]\frac{2*4}{3*4} < \frac{10}{12}[/tex] → [tex]\frac{8}{12} < \frac{10}{12}[/tex] This statement/comparison is true

[tex]\\ \Large\sf\longmapsto 11+12[/tex]

[tex]\\ \Large\sf\longmapsto 23[/tex]

[tex]\boxed{\Large{\sf P(G)=\dfrac{No\:of\:green\:marbles}{Total\:marbles}}}[/tex]

[tex]\\ \Large\sf\longmapsto P(G)=\dfrac{11}{23}[/tex]

Answer:

11/23

Step-by-step explanation:

11 green marbles and 12 orange marbles = 23 marbles

P(green) = green marbles / total marbles

               = 11/23

Answer:

B is the answer

Step-by-step explanation:

hope it helps

Answer:

16 cents per pound

Step-by-step explanation:

Take the cost and divide by the number of pounds

96 cents / 6 lbs

16 cents per pound

Answer:

More points are needed to determine the correlation.

Answer:

its d

Step-by-step explanation:

;)

Answer:

the area should be 3 centimeters around the square

Step-by-step explanation:

Answer:

A the input x=3 goes to two different output values

Step-by-step explanation:

This is not a function

x = 3 goes to two different y values

x = 3 goes to t = 10 and y = 5

Answer:

y=-2x-7

Step-by-step explanation:

after putting the choices with the question in a graph I found that that ones stays in a line with the question

Brainliest please!!

Answer:

[tex]M_{st} = (\frac{-2+4}{2}, \frac{-4+6}{2})[/tex]  

[tex]M_{st}=(\frac{2}{2}, \frac{2}{2} )[/tex]

[tex]M_{st}=(1, 1)[/tex]

[tex]M_{cd}=(\frac{-6+4}{2} , \frac{10-8}{2} )[/tex]

[tex]M_{cd}=(\frac{-2}{2} , \frac{2}{2} )[/tex]

[tex]M_{cd}=(-1, 1)[/tex]

Answer:

The expected number of items that will be classified into group 1 is 100.

Step-by-step explanation:

For each observation, there are only two possible outcomes. Either it will be classified into group 1, or it will not. The probability of an observation being classified into group 1 is independent of any other observation, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

400 observations

This means that [tex]n = 400[/tex]

Four mutually exclusive groups. The probability of a randomly selected item being classified into any of the four groups is equal.

This means that [tex]p = 0.25[/tex]

Then the expected number of items that will be classified into group 1 is

[tex]E(X) = np = 400*0.25 = 100[/tex]

100 is the answer.

Answer:

136 cm²

Step-by-step explanation:

Surface area = 2(lw+wh+hl)

l = 7

w = 2

h = 6

so,

2(7×2+2×6+7×6)

= 136 cm²

Answer:

136 cm^2

Step-by-step explanation:

L 7cm

W 6cm

D 2cm

7 x 6 + 6 x 2 + 2 x 7 (x 2) = 68 x 2 = 136cm^2

Answer:

I believe the red one is the first image then the blue then the green because they show the prime sign

Step-by-step explanation:

9514 1404 393

Answer:

  0.17 and 0.18

Step-by-step explanation:

Usually, a question like this asks for two integer values that bound the root. Here, those would be 0 and 1.

  √(3/100) = (√3)/10 ≈ 0.17320508...

You can truncate this at any point to find a number lower than √.03, then add 1 to that value's least-significant digit to find a number higher than √.03.

For example, if we use 4 digits, the two numbers bounding the root could be ...

  0.1732 and 0.1733

Answer:

It's yes

Step-by-step explanation:

Answer:

yep

Step-by-step explanation:

number is even, so it can be evenly divided by 2. :)

9514 1404 393

Answer:

Step-by-step explanation:

The coefficient of a term is its constant multiplier. The exponent is the power to which the base is raised.

The term 4·b^(-3) has an exponent of -3, a base of b and a coefficient of 4.

The exponent is -3; the coefficient is 4.

Answer:

exponent = -3           coefficent = 4

Step-by-step explanation:

Answer:

38%

Step-by-step explanation:

First determine her savings

560-347.49

212.51

Then divide by the total amount

212.51/560

.379482143

Change to percent form

37.948%

Answer:

38%

Step-by-step explanation:

[tex]560.00-347.49=212.51\\212.51\div560.00==38[/tex]

Answer:

Hello,

Step-by-step explanation:

u(i) is the ith term of the a.s

a is the first term and d the common difference

for n in {1,2,3...}: u(n)=a+(n-1)*d

u(1)=a+0*d=a

u(2)=u(1)+d=a+d=a+1*d

u(3)=u(2)+d=a+1*d+d=a+2*d

...

u(20)=a+19*d

Answer:

a+19d

Step-by-step explanation:

edmentum

Answer:

Hello,

Step-by-step explanation:

[tex]u_1\ is\ the \ first\ term\ of\ the\ gp\\q\ is \ the\ common\ ratio\\\\\\\boxed{u_n=u_1*\dfrac{q^n-1}{q-1} }[/tex]

Step-by-step explanation:

The prime 43 appears in the sixth twin-prime pair 41, 43. As a sum of four or fewer squares: 43 = 32 + 32 + 52 = 12 + 12 + 42 + 52 = 32 + 32 + 32 + 42. ... As a difference of two squares: 43 = 222 − 212.

Answer:

C. (-3x+15)/2

Step-by-step explanation:

y = (15-2x)/3

To find the inverse, exchange x and y

x = (15-2y)/3

Solve for y

Multiply each side by 3

3x = (15-2y)/3 *3

3x= 15-2y

Subtract 15 from each side

3x-15 = 15-2y-15

3x-15 = -2y

Divide by -2

(3x-15)/-2 = -2y/-2

(-3x+15)/2 = y

Answer:

C.I = (0.259,1.175) -> Fail to Reject H0  

Step-by-step explanation:

Answer:

y=2x-5

Step-by-step explanation:

By using two-points form:

y-y1/y2-y1=x-x1/x2-x1

p(x1,y1)=(4,3)

p(x2,y2)=(2,-1)

Subtitute points in formula:

y-3/-1-3=x-4/2-4

y-3/-4=x-4/-2

y-3/-2=x-4/-1

1(y-3)=2(x-4)

y-3=2x-8

y=2x-8+3

y=2x-5

Note:if you need to ask any question please let me know.

Answer:189 cm

Step-by-step explanation:

the area of a perimeter is 2L+2w while l is length and w is width

in this case, 121/2 is the length and 102/3 is the width.

using the formula it should be

121/2 x 2 +102/3 x

= 121 + 68

=189 cm

i hope this helps.

Explanation:

Stella can move 1 box for every 4 boxes Michael moves.

She moves 10 boxes, so that must mean Michael moved 40 boxes (since 4*10 = 40).

Put another way, the ratio 1:4 bumps up to the equivalent form 10:40 after multiplying both parts by 10. The first value of each ratio is the amount of boxes Stella moves, and the second part is what Michael moves.

You could also solve it like this

1/4 = 10/x

1*x = 4*10

x = 40

In the second step, I used cross multiplication.