kaiden and her brother both open savings accounts. each begin with a balance of zero dollars. for every two dollars that kaiden saves in her account, her brother saves five dollars. if kaiden saves 300 dollars how much did her brother save

Answer:

Tn = -4n²+40n+36

Step-by-step explanation:

A general quadratic sequence, Tn = an²+bn+c, where n is the term of the sequence.

So, when n = 1, Tn = 72, which means T1 = a+b+c=72.

when n = 2, Tn = 100, which means T2= 4a+2b+c = 100

when n = 3, Tn = 132, which means T3 = 9a+3b+c = 132.

Now, use a calcaulatot to solve the 3 variable simultaneous equation. According to my calculator, a = -4, b = 40, c = 36.

Hence, you a, b, and c in the Tn equation given above.

Therefore, Tn = -4n²+40n+36

Answer:

13 , 6.

Step-by-step explanation:

A equation is given to us and we need to find out the value of x . The given equation to us is ,

[tex]\sf\implies \dfrac{ x -9}{\sqrt{x+3}}= 1 [/tex]

Cross multiply ,

[tex]\sf\implies x - 9 =\sqrt{ x +3} [/tex]

Squaring both sides ,

[tex]\sf\implies (x - 9)^2 = x + 3 [/tex]

Simplify the whole square ,

[tex]\sf\implies x^2+9^2-2.9.x = x +3 \\ [/tex]

[tex]\sf\implies x^2+81 - 18x = x -3[/tex]

Add 3 and subtract x on both sides ,

[tex]\sf\implies x^2 -18x-x +81-3=0[/tex]

Simplify ,

[tex]\sf\implies x^2 -19x +78=0 [/tex]

Split the middle term of the quadratic equation,

[tex]\sf\implies x^2-13x-6x+78=0 [/tex]

Take out common ,

[tex]\sf\implies x( x -13)-6(x-13)=0[/tex]

Take out ( x -13 ) as common ,

[tex]\sf\implies ( x -13)(x-6)=0 [/tex]

Equate both factors to 0 ,

[tex]\sf\implies \boxed{\pink{\sf x = 13,6}}[/tex]

Hence the value of x is 13 or 6 .

Answer:

Step-by-step explanation:

If the slope is 2, which it is, it was found in this manner:

[tex]m=\frac{12-8}{4-2}\frac{inches}{min} =\frac{4}{2}\frac{inches}{min} =2 \frac{inches}{min}[/tex]

Because the slope is positive, it is interpreted as the height of the water increasing at a constant rate of 2 inches per minute.

Answer:

(x-2), (x+2), (3x-5)

Step-by-step explanation:

Factors of 3: ±1, ±3

Factors of 20: ±1, ±2, ±4, ±5, ±10, ±20

Possible factors of the polynomial: ±1, ±2, ±3, ±4, ±5, ±10, ±20, .... (there's a lot more but you probably do not need to list them all)

Pick a number to divide the polynomial by (I picked 2)

(3x³-5x²-12x+20)÷(x-2) = 3x²+x-10

So (x-2) is a factor of f(x) = 3x³-5x²-12x+20

Factor 3x²+x-10 = (3x-5)(x-2) these are the other factors of f(x) = 3x³-5x²-12x+20

Answer:

The value is [tex]t = 2.705[/tex].

Step-by-step explanation:

In this question, we have to find the critical value for the t-distribution, with 40 degrees of freedom, and a 99% confidence level.

99% confidence level:

We have to find a value of T, which is found looking at the t table, with 40 degrees of freedom(y-axis) and a two-tailed value of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.705.

The value is [tex]t = 2.705[/tex].

Answer:

Step-by-step explanation:

The expression is too close together. Can you space them out?

Answer:

d) -216x^9y^18

Step-by-step explanation:

Answer:

[tex]x^\frac{2}{3}[/tex]

Step-by-step explanation:

Using the power of power rule (multiply the exponents)

[tex]x^\frac{4}{3}[/tex] × [tex]^\frac{1}{3}[/tex]       [tex]x^\frac{2}{3}[/tex] × [tex]^\frac{1}{3}[/tex]

[tex]x^\frac{4}{9}[/tex]            [tex]x^\frac{2}{9}[/tex]

When exponents are multiplied, add the answers:

x ^ ( 4/9 + 2/9 )

x ^ ( 6/9 )

x ^ ( 2/3 )

Given:

Scale factor of map is:

1 decimeter = 11.5 kilometers

The distance between M and N on the map is 235 decimeters.

To find:

The Actual distance between M and N.

Solution:

Scale factor of map is:

1 decimeter = 11.5 kilometers

Using this scale factor, we get

235 decimeter = 235 × 11.5 kilometers

235 decimeter = 2702.5 kilometers

235 decimeter = [tex]2702\dfrac{1}{2}[/tex] kilometers

Therefore, the points M and N are [tex]2702\dfrac{1}{2}[/tex] kilometers apart.

Answer:

the domain of f/g consists of numbers x for which g(x) IS NOT EQUAL 0 that are in the domain of both f(x) and g(x)

Step-by-step explanation:

The denominator of a rational function can't be zero (see the first row in the attached table)

The required fill in the blanks is ≠ , f(x) and g(x).

It is required to fill in the blanks.

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The domain of f/g consists of numbers x for which g(x) IS NOT EQUAL 0 that are in the domain of both f(x) and g(x).

The domain of (f/g) (x) consists of all x-values that are in the domain of both f and g, where g(x) ≠ 0. Both f and g have domain all real numbers.

Therefore, the required fill in the blanks is ≠ , f(x) and g(x).

Learn more about  function here:

brainly.com/question/24240489

#SPJ2

Answer:

i THINK its A. 4(n-3) -6n

Step-by-step explanation:

Have a wonderful day!!

Answer:

C

Step-by-step explanation:

3.5x4.1x0.5 = 7.175 7.175x7.2=51.66

Answer:

51.66 In³

Step-by-step explanation:

This is a right angle triangular prism ....Hence ...

V=BA×H

BA= ½×4.1 in×3.5 In

BA= 7.175 In²

H= 7.2 In

V=7.175in² × 7.2In

V= 51.66 In³

Answer:

$785.17

Step-by-step explanation:

Given data

PV is the loan amount

PMT is the monthly payment

i is the interest rate per month in decimal form (interest rate percentage divided by 12)

n is the number of months (term of the loan in months)

PMT =$700

n = 10 years

i = 0.89%

The formula for the loan amount is

Answer:

0.8 = 80% probability that they did in fact study for the test.

Step-by-step explanation:

Conditional Probability

We use the conditional probability formula to solve this question. It is

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]

In which

P(B|A) is the probability of event B happening, given that A happened.

[tex]P(A \cap B)[/tex] is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: Passed the exam.

Event B: Studied.

Probability of passing the test:

80% of 60%(Studied).

30% of 100 - 60 = 40%(did not study). So

[tex]P(A) = 0.8*0.6 + 0.3*0.4 = 0.6[/tex]

Probability of passing the test studying:

80% of 60%, so:

[tex]P(A \cap B) = 0.8*0.6 = 0.48[/tex]

Find the probability that they did in fact study for the test with this knowledge in hand.

[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.48}{0.6} = 0.8[/tex]

0.8 = 80% probability that they did in fact study for the test.

Answer:

9

Step-by-step explanation:

f(3) = 2(3) + 3

= 9

Answer:

[tex]{ \tt{f(x) = 2x + 3}}[/tex]

f(3) means x = 3, substitute for x as 3 :

[tex]{ \tt{f(3) = 2(3) + 3}} \\ = 6 + 3 \\ = 9[/tex]

Answer:

209

Step-by-step explanation:

Given the following:

[tex]a_{1} = 17\\d=6[/tex]

The nth term of an arithmetic sequence is expressed as:

[tex]a +(n-1)d[/tex]

a is the first term = 17

d is the common difference =6

Get the 33rd term:

[tex]n=33\\a_{33}=17+(33-1)*6\\a_{33} =17+32(6)\\a_{33}=17+192\\a_{33}=209[/tex]

Hence the 33rd term is 209

Answer:

c. The interquartile range offers a measure of income inequality among California residents.

Step-by-step explanation:

The range is the midspread which measures statistical dispersion. This is also known as H-spread which is equal to the difference between 75th percentile and 25th percentile. In the given scenario the interquartile range offers measure of income inequality among California residents.

Answer:

I hope option D is write

I hope you help

Answer:

B. 32°

Step-by-step explanation:

The reference angle for 212°

=212°-180°

=32°

Hope it is helpful to you

Answer:

= 3v^2 x^27

Step-by-step explanation:

Apply exponent rule:   aa = a^2

VV = V^2

=3V^2x^24x^3

Simplify x^24 x^3 :  x^27

= 3v^2 x^27

Answer:

largest 4 digit number × largest 3 digit number

=9999 × 999

(10000-1)×(1000-1) = (a-b)(c-b)= ac-ab-bc+b^2

10000000-10000-1000+1 = 9989001

Answer:

[tex]E.G=\$2[/tex]

Step-by-step explanation:

Sample size 52 card

Pay for J or Q [tex]=\$17[/tex]

Pay for King or Ace [tex]=\$5[/tex]

Pay for others [tex]=-\$2[/tex]

Therefore

Probability of drawing J or Q

[tex]P(J&Q)=\frac{8}{52}[/tex]

Probability or drawing King or Ace

[tex]P(K or A)=\frac{8}{52}[/tex]

Probability or drawing Other cards

[tex]P(O)=\frac{36}{52}[/tex]

Therefore

Expected Gain is mathematically given as

[tex]E.G=\sum_xP(x)[/tex]

[tex]E.G=17*\frac{8}{52}+5*\frac{8}{52}+(-2)*\frac{36}{52}[/tex]

[tex]E.G=\$2[/tex]

Answer:

The country's debt is $ 48,543.68 per person.

Step-by-step explanation:

Given that at the end of a year, the gross debt of a country stood at about $ 15 trillion, to determine this amount in dollars per person, assuming that the population of the country is about 309 million, the following calculation must be done:

15 trillion = 15,000,000,000,000

15,000,000,000,000 / 309,000,000 = X

15,000,000 / 309 = X

48,543.68 = X

Therefore, the country's debt is $ 48,543.68 per person.

Answer:

Step-by-step explanation:

(6+8i)(3-2i)

use FOIL

18 - 12i + 24i - (16[tex]i^{2}[/tex])

18 + 12i - (-16)

18 + 12i + 16

34 + 12i

Answer:

1

4

3

6

2

5

Step-by-step explanation:

Too lazy to explain 6 factorings on mobile. Trust me if it pleases you.

Step-by-step explanation:

side² is the formula to find area of square.

mark as brainliest

Answer:

x = ±i(√6 / 2)

General Formulas and Concepts:

Pre-Algebra

Algebra I

Algebra II

Imaginary root i

Step-by-step explanation:

Step 1: Define

Identify

2x² + 3 = 0

Step 2: Solve for x

Step-by-step explanation:

Given:

[tex]\vec{a} = 5\hat{\textbf{i}} + 4\hat{\textbf{j}}[/tex]

[tex]\vec{b} = 5\hat{\textbf{i}} - 5\hat{\textbf{j}}[/tex]

Then

[tex]2\vec{a} = 2(5\hat{\textbf{i}} + 4\hat{\textbf{j}})[/tex]

[tex]\:\:\:\:\:\:= 10\hat{\textbf{i}} + 8\hat{\textbf{j}}[/tex]

[tex]3\vec{b} = 3(5\hat{\textbf{i}} - 5\hat{\textbf{j}})[/tex]

[tex]\:\:\:\:\:\:= 15\hat{\textbf{i}} - 15\hat{\textbf{j}}[/tex]

Therefore,

[tex]2\vec{a} - 3\vec{b} = (10 - 15)\hat{\textbf{i}} + (8 - (-15))\hat{\textbf{j}}[/tex]

[tex]= -5\hat{\textbf{i}} + 23\hat{\textbf{j}}[/tex]

To find the magnitude,

[tex]|2\vec{a} - 3\vec{b}| = \sqrt{(-5)^2 + (23)^2}= 23.54[/tex]

Answer:

The correct answer is "0.43".

Step-by-step explanation:

According to the question,

The probability of boat accessories sale,

= 0.3

The probability of sale in Portland store,

= 0.35

now,

The probability that the decision was signed somewhere at Portland shop will be:

= [tex]\frac{P(boat \ acessories \ sale\times P(sale \ in \ Portland \ store)}{P(boat \ accessories \ sale)}[/tex]

By substituting the values, we get

= [tex]\frac{ 0.3\times 0.35}{( 0.2\times 0.5 + 0.3\times 0.35 + 0.25\times 0.15)}[/tex]

= [tex]\frac{0.105}{0.1+0.105+0.0375}[/tex]

= [tex]0.43[/tex]

Answer:

it seems as it is adding .15 every time so the next 3 would be .05 .20 and .65