Patricia has $34,000 to invest. She invests some at 17% and the balance at 20%. Her total annual interest income is $6245. Find the amount invested at each rate

Step-by-step explanation:

here's the answer to your question

In this question first you should find profit amount by using formula and you should use profit amount in profit percentage formula then you should calculate it

Answer:

The 13th term is 81x + 59.

Step-by-step explanation:

We are given the arithmetic sequence:

[tex]\displaystle -3x -1, \, 4x +4, \, 11x + 9 \dots[/tex]

And we want to find the 13th term.

Recall that for an arithmetic sequence, each subsequent term only differ by a common difference d. In other words:

[tex]\displaystyle \underbrace{-3x - 1}_{x_1} + d = \underbrace{4x + 4} _ {x_2}[/tex]

Find the common difference by subtracting the first term from the second:

[tex]d = (4x+4) - (-3x - 1)[/tex]

Distribute:

[tex]d = (4x + 4) + (3x + 1)[/tex]

Combine like terms. Hence:

[tex]d = 7x + 5[/tex]

The common difference is (7x + 5).

To find the 13th term, we can write a direct formula. The direct formula for an arithmetic sequence has the form:

[tex]\displaystyle x_n = a + d(n-1)[/tex]

Where a is the initial term and d is the common difference.

The initial term is (-3x - 1) and the common difference is (7x + 5). Hence:

[tex]\displaystyle x_n = (-3x - 1) + (7x+5)(n-1)[/tex]

To find the 13th term, let n = 13. Hence:

[tex]\displaystyle x_{13} = (-3x - 1) + (7x + 5)((13)-1)[/tex]

Simplify:

[tex]\displaystyle \begin{aligned}x_{13} &= (-3x-1) + (7x+5)(12) \\ &= (-3x - 1) +(84x + 60) \\ &= 81x + 59 \end{aligned}[/tex]

The 13th term is 81x + 59.

sin(x+y) - sin(x-y) - 1 = cos(2x)

sin(90) - sin(x-y) - 1 = cos(2x)

1 - sin(x-(90-x)) - 1 = cos(2x)

-sin(2x-90) = cos(2x)

-1*(sin(2x)cos(90) - cos(2x)sin(90)) = cos(2x)

-1*(sin(2x)*0 - cos(2x)*1) = cos(2x)

-1*(0 - cos(2x)) = cos(2x)

-1*(-cos(2x)) = cos(2x)

cos(2x) = cos(2x)

This confirms the identity is true.

Notice that throughout this proof, I only changed the left hand side.

On the 5th line, I used the identity sin(A-B) = sin(A)cos(B)-cos(A)sin(B).

Answer:

Range = maximum number - minimum number

Range = 99 - 62 = 37

Answer:

37

Step-by-step explanation:

The range is the difference between the highest number and the smallest number.

Looking at the stem and leaf plot we can identify the largest and smallest number

Largest number: 99

Smallest number: 62

If range = largest number - smallest number then range = 99 - 62 = 37

Answer:

90 degrees

Step-by-step explanation:

see image

make x A

y B

z C

AB=3 (given)

AC=9 (given)

measure of angel B or y, is 90

if

x= A

y= C

z= B

then the hypotenuse would be shorter than one of the legs

3<9

so B has to be the right angle (90 degrees)

Answer:

Triangle ACB =~ triangle DFE, by adding 6 units to each side of both triangles their relationship will not change. They are still similar.

Step-by-step explanation:

The answer isn't great in all honesty but it's been a long time since I took geometry and I don't 100% remember the proper way of stating it. Though I am 100% sure they stay similar.

Sorry couldn't be of more help but figured something was better then nothing

Answer:

see below

Step-by-step explanation:

The domain is the values that the input takes

The values go from 0 to 7

0≤x≤7

This is the time from the initial launch until the object hits the ground

Answer: 5

Step-by-step explanation:

⇒ (x - 4) = 1

⇒ x = 1 + 4

⇒ x = 5

Therefore value of x = 5

Answered by Gauthmath must click thanks and mark brainliest

Answer: (0, -3/7)

Step-by-step explanation:

The Y-intercept would be the value of y when x is at 0, which is when the Y axis is intercepted. -3/7 is the starting position of the function when the the X = 0.

Answer:

the answer is 21

Step-by-step explanation:

Answer:

a)139°

Step-by-step explanation:

two co interior angles make one opposite exterior angle

49+90=139°

Answer:

x = 1 và 2       x= 1 and 2

Step-by-step explanation:

Đầu tiên trừ đi 1 để được 2x-3 nhỏ hơn -1 sau đó bạn lập phương trình bằng 2x-3 = -1 và 2x-3 = 1 để nhận được kết quả cuối cùng là 1 và 2 do đó x = 1 và 2

First subtract 1 to get 2x-3 is less then -1 then you let the equation equal 2x-3=-1 and 2x-3=1 to get a final answer of 1 and 2 therefore x=1 and 2

Answer:

x=2 is incorrect

Step-by-step explanation:

Y(2)=(3/4)*x^2=(3/4)*4=3

Answer:

a) 16, 19, 22, 25, 28, 31, 34, 37, 40

b) 1, 3, 9, 27, 81, 243, 729, 2187

a) Add 3 on every number.

b) Multiply every number by 3.

Answer:

The average, mode, and median of the results are 5, meaning that half of the time the quarter will land on heads.

Step-by-step explanation:

The required dot plot shows the result of the experiment performed by flipping a quarter 21 times.

In an experiment, a student is to flip a quarter 10 times and record the number of times heads appears. A group of students performs the experiment 21 times, with these results. 6 4 5 6 5 6 4 6 2 4 3 4 5 7 5 8 7 5 3 5 5.

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,

Statistics is the study of mathematics that deals with relations between comprehensive data.

Here,
The dot plot has been made, for the number of outcomes and their frequencies. The dot plot gives the info about the mean mode and median.

Thus, the required a dot plot showing the result of the experiment performed by flipping a quarter 21 times.

Learn more about arithmetic here:

brainly.com/question/14753192

#SPJ2

Answer:

Step-by-step explanation:

Given equation of the quadratic function is,

y = x² + 5x - 7

Convert this equation into vertex form,

y = x² + 2(2.5x) - 7

  = x² + 2(2.5x) + (2.5)² - (2.5)² - 7

  = (x + 2.5)²- 6.25 - 7

  = (x + 2.5)² - 13.25

Therefore, vertex of the function is → (-2.5, -13.25)

For the solutions,

y = 0

(x + 2.5)² - 13.25 = 0

x = (±√13.25) - 2.5

x = (±3.64) - 2.5

x = 1.14, -6.14

Solutions → (-6.14, 0) and (1.14, 0)

Answer:

11

Step-by-step explanation:

If the set of numbers are not in least to greatest first set them up into their positions. But since this set is already in least to greatest we can go to the next step.

6, 7, 10, 12, 12, 13

Cross off all numbers until you get to the middle:

6, 7, 10, 12, 12, 13

Find the mean of the numbers in the middle:

10 + 12 = 22

22 / 2 = 11

The answer is 11

Hope this helped.

Answer:

11

Step-by-step explanation:

10+12=22

22÷2=11

median is equal to the middle number after being arranged in ascending order.

please check the attachment for solutions

Answer:

That is the graph for y = -|x| + 3

Answer:

My best guess rn is the first option

Step-by-step explanation:

the last dude had it close but it was basically flipped as you can tell.

The answer is (C) [tex]R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]

We need to make [tex]R_2[/tex] the subject of the formula [tex]R_T=\frac{R_1R_2}{R_1+R_2}[/tex]

First remove the denominator by multiplying both sides by the binomial [tex](R_1+R_2)[/tex]

[tex]R_T\times (R_1+R_2)=\frac{R_1R_2}{R_1+R_2}\times(R_1+R_2)\\\\R_TR_1+R_TR_2=R_1R_2[/tex]

Arrange all terms containing [tex]R_2[/tex] on one side

[tex]R_1R_2-R_TR_2=R_TR_1[/tex]

Factor out [tex]R_2[/tex] from the LHS

[tex]R_2(R_1-R_T)=R_TR_1[/tex]

Finally, divide both sides by the binomial [tex](R_1-R_T)[/tex] to leave [tex]R_2[/tex]

[tex]R_2(R_1-R_T)\times\frac{1}{(R_1-R_T)}=R_TR_1\times\frac{1}{(R_1-R_T)}\\\\R_2=\frac{R_TR_1}{(R_1-R_T)}[/tex]

Learn more about change of subject of formula here: https://brainly.com/question/343660

Answer:

s(2) = 17 cm

Step-by-step explanation:

We are told that the velocity function is;

v(t) = 6t² + 4t − 5 cm/sec

Integral of velocity gives distance.

Thus;

s(t) = ∫v(t) = ∫6t² + 4t − 5

s(t) = 2t³ + 2t² - 5t + c

We are told that s(0)=3 cm

Thus;

s(0) = 2(0)³ + 2(0)² - 5(0) + c = 3

Thus; c = 3

Thus;

s(t) = 2t³ + 2t² - 5t + 3

At t = 2 secs

s(2) = 2(2)³ + 2(2)² - 5(2) + 3

s(2) = 17 cm

Answer:

[tex]z=14.4[/tex]

Step-by-step explanation:

One is given the following equation:

[tex]24=\frac{z}{0.6}[/tex]

Use inverse operations to solve this equation. Multiply both sides of the equation by (0.6) to undo the division of (0.6).

[tex]24=\frac{z}{0.6}[/tex]

[tex](0.6)(24)=z[/tex]

Simplify,

[tex](0.6)(24)=z[/tex]

[tex]z=14.4[/tex]

Answer:

I think b no. is the correct answer

Answer:

D. (5, –23)

Step-by-step explanation:

The vertex is in essence the turning point of the parabola y = x² − 10x + 2

the x coordinate of the turning point =  

                                                        =  

                                                        =  5

when x = 5, y = (5)² - 10(5) + 2

                     = -23

Thus coordinate or vertex is ( 5, -23)

5 right 23 down

Step-by-step explanation:

10 % of 2700 = 270

so he had 2970 rupee

20% of 2970 = 594

so customer have to pay 2970 + 594 = 3564

Answer:

4/10 : 1/25

4/10 / 1/25 = 4/10 x 25/1 = 100/10 = 10.

10 can also be written as 10:1, so A is correct.

Hope this helps!