Kathleen successfully solved the system of equations 4.2 + 3y = 15 and -- 5x – 2y = -24 by multiplying each equation by a constant and adding the two equations together to eliminate
the x-terms. She then solved for y and substituted the value of y back into one of the equations and solved for a. What could she have multiplied each equation by, and what was her final answer?

It would take about 2.6 years for the value of the account to reach $5,920, assuming no deposits or withdrawals are made.

We can use the formula for compound interest to solve the problem;

A = \(P(1+r/n)^{(nt)}\)

where;

A is the amount after t years

P is principal (the initial amount invested)

r is annual interest rate (as a decimal)

n is number of times the interest is compounded per year

t is the time in years

In this case, we know that;

P = $4,900

r = 0.03 (3% expressed as a decimal)

n = 12 (interest is compounded monthly)

A = $5,920

We can solve for t by plugging in these values and solving for t;

$5,920 = $4,900\((1+0.03/12)^{12t}\)

Divide both sides by $4,900;

1.20918367347 = \((1+0.03/12)^{12t}\)

Take the natural logarithm of both sides;

ln(1.20918367347) = ln(\((1+0.03/12)^{12t}\))

Use the property of logarithms that allows us to bring the exponent down;

ln(1.20918367347) = 12t ln(1 + 0.03/12)

Divide both sides by 12 ln(1 + 0.03/12)

t = ln(1.20918367347) / (12 ln(1 + 0.03/12))

t ≈ 2.6 years

Therefore, it would take about 2.6 years.

--The given question is incomplete, the complete question is

"Ella invested $4,900 in an account paying an interest rate of 3% compounded monthly. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $5,920?​"--

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The volume of the rectangular prism is 208cm³

Volume' is a mathematical quantity that shows the amount of three-dimensional space occupied by an object or a closed surface. The unit of volume is in cubic units such as m3, cm3, in3 etc. Sometimes, volume is also termed capacity.

The volume of a rectangular a prism is expressed as base area × height. The base area is a rectangle and the area of a rectangle is Length × width

length = 2cm

width = 13 cm

height = 8cm

base area = 13× 2 = 26cm²

Volume of the prism = 26× 8 = 208cm³

Therefore the volume of the rectangular prism is 208cm³.

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Answer:

1460

Step-by-step explanation:

rounding to the nearest ten, that is nearest to 1456 which would be 1460 (hope this helps! ) ♡

Answer:

1460

Step-by-step explanation:

Original number is 1 4 5 6

To round to the nearest ten, look at the digit in the 10's place and the digit immediately to the right of it

The digit in the tens place is 5

If the digit to the immediate right of this digit is 5 or greater, round the digit in the tens place up by one digit and set the immediate right digit to 0

So 5 rounds up to 6

The 6 to the immediate right(units place becomes 0)

1 4 5 6 rounded to nearest ten==> 1 4 6 0

Answer:

-5.55

Step-by-step explanation:

-1 3/4 = -1.75

-1.75 + (-3.8) = -1.75 - 3.8 = -5.55

I hope this helped and please mark me as brainliest!

The solution for the given expression is 16.

There are different power rules, see some them:

1. Multiplication with the same base: you should repeat the base and  add the exponents.

2. Division with the same base: you should repeat the base and  subctract the exponents.

3.Power. For this rule, you should repeat the base and multiply the exponents.

4. Zero Exponent. When you have an exponent equals to zero, the result must be 1.

First, you apply the Power Rules - Power for  \((\frac{2^2x^2y}{xy^3} )^2}\). For this rule, you should repeat the base and multiply the exponents. Thus, the result will be:\(\frac{16x^4y^2}{x^2y^6}\).

After that, you should apply the  Power Rules - Division . For this rule, you should repeat the base and  subctract the exponents. Thus, the result will be:\(\frac{16x^2}{y^4}\).

Now, you should replace the variable x by 4 and the variable y by 2. Thus, the result will be:\(\frac{16*4^2}{2^4}=\frac{16*16}{16} =16*1=16\)

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Answer:

A

Step-by-step explanation:

The sum of the decimal values given is 0.93

Simplifying the decimal values can be done thus :

Both values are in two decimal places, hence we can multiply by 100 to obtain a whole number .

0.36*100 = 36

0.57*100 = 57

Adding the whole numbers :

__36

+_57

_____

__93

Dividing the sum by 100 to convert to an equivalent decimal value,

Therefore, the required value is 0.93

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Step-by-step explanation:

212 sit-ups = 8 minutes

1 minutes = 212÷8

1 minutes = 26.5

The equation of the rational function with the given features is given as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

A rational function is a fraction, in which both the numerator and the denominator contain instances of the variable x.

Considering the x-intercepts, the numerator of the function is defined as follows:

y = a(x + 4)(x + 1)

y = a(x² + 5x + 4).

Considering the y-intercept at (0,4), the leading coefficient a is given as follows:

a = 4.

The vertical asymptotes determine the zeros of the denominator, which is given as follows:

(x + 2)(x - 3) = x² - x - 6.

Hence the function is defined as follows:

F(x) = [4(x² + 5x + 4)]/(x² - x - 6).

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The answer that correctly describes the data shown by the box plot is (B) "The interquartile range is 4 and the range is 10." (option-b)

The box plot provides a graphical representation of data that shows the distribution of a dataset, including the median, quartiles, and any outliers. Here, we need to compute the interquartile range (IQR) and range based on the information given in the box plot.

The IQR is the difference between the third quartile (Q3) and the first quartile (Q1). Looking at the box plot, we can see that Q1 is 3 and Q3 is 7. Therefore, the IQR is 7 - 3 = 4.

The range is the difference between the maximum and minimum values of the dataset. Looking at the box plot, we can see that the minimum is 0 and the maximum is 10. Therefore, the range is 10 - 0 = 10.

None of the other options (A), (C), or (D) accurately reflects the IQR and range of the dataset shown.(option-b).

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Answer:

The Answer is D

Step-by-step explanation:

A survey of every 10th person leaving a large shopping mall. I hope im right this question was tricky though. Hope it helps :)

Answer:

1. 7

2. 5

3. 6

4. Start at the number 34. count back 1 at a time 28 times. then you will get your answer to 34-28 which is 6.

Step-by-step explanation:

have a great day! feel free to mark as brainliest. :)

Answer:

3

Step-by-step explanation:

Set equation to 9 to find x:

9=5x-6

+6 +6

15=5x

x=3

Answer:

Step-by-step explanation:

Area of semi-circle is \(\frac{\pi r^2}{2}\) ≈ \(\frac{22}{7}\) × 4² ÷ 2 ≈ 25 cm²

Area of square is 8² = 64 cm²

Total area is 25 + 64 = 89 cm²

2/5 > 1/2

2/5 = 4/10, 1/2 = 5/10

A is not the answer.

2/5 < 1/2

B is the answer.

2/5 = 1/2

C is not the answer.

Let me know if this is the correct answer. :)

Answer:

10 years old

Step-by-step explanation:

lets break it down:

6 more means +6

four times means *4

so if her son is x years old, she is 4x+6

since we know she's 46, we know that 4x+6=46

now we just solve the equation

4x+6=46

-6 on both sides

4x=40

/4 on both sides

x=10

Answer:

P is 250% of Q

Step-by-step explanation:

50/100 Q  =   20/100P            Multiply both sides by 100

50Q = 20 P                              Divide by 20

50/20 Q = P

2.5 Q = P

So P is 2.5 times the size of Q.

2.5 as a percent is 250 %

A good estimate for the area of a circle if the radius is 4 meters is D. 50.2m²

It is important to note that the area of a circle is calculated as πr².

In this case, r = radius

The radius is given as 4 meter.

Therefore, the area of the circle will be:

Area = πr²

Area = 3.14 × 4²

Area = 3.14 × 16

Area = 50.24m²

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Answer:

72; Proofs attached to answer

Step-by-step explanation:

Proofs attached to answer

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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Answer:

x=2

Step-by-step explanation:

1/16 x 2=1/8

X=2

Hope this helps

also if u click the crown it marks brainliest but you can only do it when two people answer.

I just wanted to say that just incase u didnt know because I didnt know lol

The 100th derivative of P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷) will be zero.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given:

A polynomial,

P(x) = (x+x⁵+x⁷)¹⁰(1+x²)¹¹(x³+x⁵+x⁷).

To find the degree:

(x⁷)¹⁰(x²)¹¹(x⁷) = x⁹⁹.

The polynomial has a degree of 99.

If we think about it intuitively,

Therefore, if we were to multiply it all out,

the leading word would be x⁹⁹.

The term's first derivative is 99x⁹⁸,

followed by 99(98)x⁹⁷,

and 99(98)(97)x⁹⁶.

And finally,

the 99th derivative is 99×98×97×96×...4×3×3×2×1× (x⁰)

=99!

So, the 100th derivative will be zero.

Therefore, by the 100th derivative, all terms will cancel out.

100th derivative will be zero.

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Answer: The determinant of the given matrix is -75e^24x.

Step-by-step explanation:

To evaluate the determinant of a matrix containing functions, we can use a method called Laplace Expansion. This method involves taking the determinant of the matrix by expanding it along its first row.

Using Laplace Expansion, the determinant of the given matrix can be calculated as follows:

|e^5x 3^2x 3e^6x 5e^3x| = e^5x(3^2x5e^3x - 3e^6x3^2x) = e^5x(45e^9x - 27e^12x) = e^5x(18e^12x) = 18e^17x = -75e^24x.

Therefore, the determinant of the given matrix is -75e^24x.

Answer: -21

Step-by-step explanation:

Answer:

5778

Step-by-step explanation:

1+2+3+4+5+....+105+106+107

The sequence of numbers (1, 2, 3, … , 107) is arithmetic and when we are looking for the sum of a sequence, we call it a series. Thanks to Gauss, there is a special formula we can use to find the sum of a series:

S=n(n+1)/2=11556÷2=5778

S is the sum of the series and n is the number of terms in the series, in this case, 107

There are other ways to solve:

This is an arithmetic series, for which the formula is:

S = n[2a+(n-1)d]/2

where a is the first term, d is the difference between terms, and n is the number of terms.

For the sum of the first 107 whole numbers:

a = 1, d = 1, and n = 107

Therefore, sub into the formula:

S = 107[2(1)+(107-1)(1)]/2 =

107(2+106)/2=107*108/2=5778

so she blow out 5778 candless during her lifetime