2 rowing teams are having a race. Boat a had a head start crossing the start line first & traveling at a speed of 3 meters per second. Boat b waited and crossed the start line 6 seconds after boat a. The speed of boat b was 4.8 meters per second.

6 weeks from now, you will have $215 in your bank account

The given parameters are:

b = 60 + (20+6)w

When the account balance is $215, we have

60 + (20+6)w = 215

Subtract 60 from both sides

(20+6)w = 155

This gives

26w = 155

Divide both sides by 26

w = 5.96

Approximate

w = 6

Hence, 6 weeks from now, you will have $215 in your bank account

Read more about linear equations at:

https://brainly.com/question/14323743

#SPJ1

Answer: 2,916 inches³

Step-by-step explanation:

The volume of a box is:

= Length * Width * Height

But all of these have to have the same units for it to work. This means that the height of the box will have to be converted to inches :

1 ft is 12 inches so:

= 1¹/₂ * 12

= 3/2 * 12

= 18 inches

Volume is therefore:

= 18 * 9 * 18

= 2,916 inches³

Explanation:

Here is the solution to the given problem:

Journal entries for Elite Electronics, Inc. are given below:

a) Write-off of a customer balance of $250 from a prior year which is not collectible:

General Journal Debit Credit

Allowance for doubtful accounts $250

Accounts receivable $250

b(1) Reversal of the write-off the $250 customer account:

General Journal Debit Credit

Accounts receivable $250

Allowance for doubtful accounts $250

b(2) Receipt of cash of $250 from the customer:

General Journal Debit Credit

Cash $250

Accounts receivable $250

Therefore, the journal entries for Elite Electronics, Inc. are given below:

Journal entry for the write-off of a customer account that is uncollectible:

Allowance for doubtful accounts $250

Accounts receivable $250

Journal entry for the reversal of the write-off $250 customer account:

Accounts receivable $250

Allowance for doubtful accounts $250

Journal entry for the receipt of cash of $250 from the customer:

Cash $250

Accounts receivable $250

Learn more about Debit-Credit here:

https://brainly.com/question/13290364

#SPJ11

Consequently, 15 is the third partial total of the sequence.

The area of mathematics known as arithmetic deals with the mathematical study of numbers and the numerous procedures that can be performed on them. Addition, subtraction, multiplication, and division are the fundamental mathematical processes. The icons listed above stand in for these processes.

The given series is an arithmetic series with first term a1 = 2 and common difference d = 3.

To find the third partial sum, we need to add the first three terms of the series:

S₃ = 2 + 5 + 8

S₃ = 15

Therefore, the third partial sum of the series is 15.

To know more about Arithmetic visit:

brainly.com/question/11559160

#SPJ1

The eigenvalues of the coefficient matrix A is λ = 5 ± 6i

An eigenvector corresponding to the eigenvalue with a positive imaginary part is v = k(3 + 2i, 1)

The general solution can be expressed as

X(t) = e^(5t) × (C1 × cos(6t) + C2 × sin(6t)) × (3 + 2i, 1)

Given,  dx/dt = 7x + 13y and dy/dt = -2x + 9y.

Eigenvalues of the coefficient matrix A:

The coefficient matrix A is:

\(A = \left[\begin{array}{cc}7&13\\-2&9\end{array}\right]\)

To get the eigenvalues, we have to solve the characteristic equation.

| (7 - λ) (9 - λ) - (-2)(13) | = 0

63 - 7λ - 9λ +λ² + 26 =0

λ² - 16λ + 89 =0

Solving this equation, we get the eigenvalues λ = 5 ± 6i.

The positive imaginary part eigenvalue λ = 5 + 6i. Let v be the eigenvector now we have to solve the system (A - λI)v = 0.

| (2 - 6i)  13     | |x| = |0|

|  -2      (4 - 6i)| |y| = |0|

After solving this system, we get an eigenvector v = k(3 + 2i, 1), where k is a constant.

The general solution of the given system:

The general solution can be expressed as

X(t) = e^(5t) × (C1 × cos(6t) + C2 × sin(6t)) × (3 + 2i, 1)

Where C1 and C2 are constants.

Learn more about Eigenvalues here

brainly.com/question/16945116

#SPJ4

Answer:

\((f-g)(x)=-7x-3\)

Step-by-step explanation:

a. Using the calculated z-score, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

b. The appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

(a) To find the probability that a randomly chosen bolt has a width between 941 and 957 mm, we can use the z-score formula and the standard normal distribution.

First, let's calculate the z-scores for the given values using the formula:

z = (x - μ) / σ

where:

For x = 941:

z₁ = (941 - 952) / 10 = -1.1

For x = 957:

z₂ = (957 - 952) / 10 = 0.5

Next, we need to find the probabilities corresponding to these z-scores using a standard normal distribution table or a calculator.

Using the standard normal distribution table, we find:

P(z < -1.1) ≈ 0.135

P(z < 0.5) ≈ 0.691

Since we want the probability of the width falling between 941 and 957, we subtract the two probabilities:

P(941 < x < 957) = P(-1.1 < z < 0.5) = P(z < 0.5) - P(z < -1.1) ≈ 0.691 - 0.135 = 0.5558

Therefore, the probability that a randomly chosen bolt has a width between 941 and 957 mm is approximately 0.5558.

(b) To find the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749, we need to find the z-score corresponding to this probability.

Using a standard normal distribution table or calculator, we find the z-score corresponding to a cumulative probability of 0.8749 is approximately 1.15.

Now, we can use the z-score formula to find the value of C:

z = (x - μ) / σ

Substituting the known values:

1.15 = (C - 952) / 10

Solving for C:

C - 952 = 1.15 * 10

C - 952 = 11.5

C ≈ 963.5

Therefore, the appropriate value for C such that a randomly chosen bolt has a width less than C with probability 0.8749 is approximately 963.5 mm.

Learn more on probability here;

https://brainly.com/question/24756209

#SPJ4

Answer:

fuimaa

Step-by-step explanation:

The first 3 terms of the sequence using the expression are -5, -4 and -1

From the question, we have the following sequence that can be used in our computation:

n(n – 2) – 4

This means that

T(n) =  n(n – 2) – 4

Set n = 1, 2 and 3

So, we have

T(1) =  1 * (1 – 2) – 4 = -5

T(2) =  2 * (2 – 2) – 4 = -4

T(3) =  3 * (3 – 2) – 4 = -1

Hence, the first 3 terms of the sequence using the expression are -5, -4 and -1

Read more about sequence at

https://brainly.com/question/30499691

#SPJ1

Step-by-step explanation:

\( \tan(2x) = 1.5\)

Take the arc tangent,

\( \tan {}^{ - 1} ( \tan(2x) ) = \tan {}^{ - 1} (1.5) \)

\(2x = 56.3\)

\(x = 28.15\)

b.

\((3 \cos(x) + 1)(2 \cos(x) + 3) = - 2\)

\(6 \cos {}^{2} (x) + 11 \cos(x) + 3 = - 2\)

\(6 \cos {}^{2} (x) + 11 \cos(x) + 5 = 0\)

\(6 \cos {}^{2} (x) + 6 \cos(x) + 5 \cos(x) + 5 = 0\)

\(6 \cos(x) ( \cos(x) + 1) + 5( \cos(x) + 1) = 0\)

\((6 \cos(x) + 5)( \cos(x) + 1) = 0\)

Set each factor equal to zero.

\(6 \cos(x) + 5 = 0\)

\(6 \cos(x) = - 5\)

\( \cos(x) = - \frac{5}{6} \)

\(x = \cos {}^{ - 1} ( \frac{5}{6} ) \)

\(x = 146.4\)

For the second factor,

\( \cos(x) + 1 = 0\)

\( \cos(x) = - 1\)

\(x = 180\)

So the answer for the second one is

146.4 and 180.

Answer:Step 3

Step-by-step explanation:

61 is the sum of two consecutive integers (-6,-5 ) and (5,6).

According to Pierr De Fermat any whole number writteen as the sum of four or less square numbers.

So 61 is the whole number so we can write in the sum of squares,

Now we know even+odd=odd so that let a and a+1 integer , according to Pierr De Fermat we can write,

a²+(a+1)²=61;

⇒a²+a²+2a+1=61

⇒2a²+2a-60=0

⇒a²+a-30=0 (∵divided by 2)

⇒a²+6a-5a-30=0

⇒a(a+6)-5(a+6)=0

⇒(a+6)(a-5)=0

⇒a+6=0 or a-5=0 ⇒a=-6 or a=5

If a=-6 then a+1=-6+1=-5.

if a=5 then a+1=5+1= 6.

so 61= (-6)²+(-5)² and 61= 6²+5².

To know more about Consecutive Integers, Here

https://brainly.com/question/29354311

#SPJ4

Answer:

Step-by-step explanation:

4.5 %

Answer:

B-12

Step-by-step explanation:

Answer:

B) 12

Step-by-step explanation:

Set x equal to zero and you get y= 12

It would be  31 Thai baht per US dollar. the correct answer is B

To determine the number of Thai baht per US dollar, we need to calculate the exchange rate between the British pound and the Thai baht and between the British pound and the US dollar, and then convert from baht to US dollars.

Given the information provided:

1 British pound = US $1.25

1 British pound = 39 Thai baht

To find the exchange rate between the Thai baht and the US dollar, we can divide the exchange rate between the British pound and the Thai baht by the exchange rate between the British pound and the US dollar.

Exchange rate (Thai baht per US dollar) = (Exchange rate British pound to Thai baht) / (Exchange rate British pound to US dollar)

Exchange rate (Thai baht per US dollar) = 39 Thai baht / US $1.25

Exchange rate (Thai baht per US dollar) ≈ 31 Thai baht per US dollar

Therefore, the correct option is B) 31 Thai baht per US dollar.

To learn more about exchange rate here

brainly.com/question/14231622

#SPJ11

Answer:

\( \boxed{Values \: true \: of \: 'x' \: for \: equation \: {x}^{2} + 2x = 24 \: is \: -6 \: and \: 4} \)

Step-by-step explanation:

\( = > {x}^{2} + 2x = 24 \\ \\ = > {x}^{2} + 2x - 24 = 0 \\ \\ = > {x}^{2} + (6 - 4)x - 24 = 0 \\ \\ = > {x}^{2} + 6x - 4x - 24 = 0 \\ \\ = > x(x + 6) - 4(x + 6) = 0 \\ \\ = > (x + 6)(x - 4) = 0 \\ \\ = > x + 6 = 0 \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: \: x - 4 = 0 \\ \\ = > x = - 6 \: \: \: \: \: \: \: \: \: \: and \: \: \: \: \: \: \: \: \: x = 4\)

Values true of 'x' for equation x² + 2x = 24 is -6 and 4

Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of kids and y represent the number of adults that can be invited to the park.

Since the family has at most $190 to spend, hence:

8x + 4y ≤ 190    (1)

Also, the maximum number of invites is 35 people. This is represented by the equation:

x + y ≤ 35       (2)

Graphing equation 1 and equation 2 using geogebra online graphing

We have the solution as:

(0, 35), (23.75, 0) and (12.5, 22.5)

Since the number of people must be a whole number, the possible solutions are:

0 children and 35 adults or 23 children and 0 adults or 12 children and 22 adults

The number formed by the digits 16, 06, and 68 is 160668, which is determined by concatenating them in the given order.

To determine the number formed by the given digits, we concatenate them in the given order. Starting with the first digit, we have 16. The next digit is 06, and finally, we have 68. By combining these three digits in order, we get the number 160668.

When concatenating the digits, the position of each digit is crucial. The placement of the digits determines the resulting number. In this case, the digits are arranged as 16, 06, and 68, and when they are concatenated, we obtain the number 160668. It's important to note that the leading zero in the digit 06 does not affect the value of the resulting number. When combining the digits, the leading zero is preserved as part of the number.

Therefore, the number formed by the digits 16, 06, and 68 is 160668.

LEARN MORE ABOUT concatenating here: brainly.com/question/32230816

#SPJ11

Using the t-distribution, it is found that the data does not provide convincing evidence that the mean number is greater when the coupons were addressed to a female.

At the null hypothesis, it is tested if there is no difference, that is, the mean is of 0, hence:

\(H_0: \mu = 0\)

At the alternative hypothesis, it is tested if the mean number is greater for females, that is, the mean is greater than 0, hence:

\(H_1: \mu > 0\)

The test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

The parameters are:

In this problem, the parameters are given as follows:

\(\overline{x} = 1.5, \mu = 0, s = 4.75, n = 50\).

Hence, the test statistic is given by:

\(t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}\)

\(t = \frac{1.5 - 0}{\frac{4.75}{\sqrt{50}}}\)

t = 2.23

Considering a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.01 and 50 - 1 = 49 df, the critical value is given by \(t^{\ast} = 2.4\).

Since the test statistic is less than the critical value for the right-tailed test, the data does not provide convincing evidence that the mean number is greater when the coupons were addressed to a female.

More can be learned about the t-distribution at https://brainly.com/question/26454209

Farmer brown had ducks and cows having a total of 13 heads and 46 feet, which means there are 10 cows and 3 ducks.

This is an algebraic problem that can be solved using a system of equations.

Let x be the number of cows and y be the number of ducks. We know from the problem statement that:

x + y = 13 (the number of heads)

4x + 2y = 46 (the number of feet)

We can use the first equation to solve for one of the variables in terms of the other.

For example, if we subtract y from both sides of the equation we get:

x = 13 - y

We can substitute this expression for x into the second equation:

4(13 - y) + 2y = 46

Simplifying, we get:

52 - 4y + 2y = 46

which gives us:

-4y = -6

then we get:

y=3

Now we can use this value of y to solve for x in terms of y:

x = 13 - y

x = 13 - 3

x = 10

Therefore, there are 10 cows and 3 ducks.

Solve more problems on algebraic problem at : https://brainly.com/question/15167098

#SPJ4

Answer:

Step-by-step explanation:

B

Answer:

B. The graph curves away from its sum

Step-by-step explanation:

A convergent infinite geometric series, the graph of the series curves away from the sum, the correct option is B.

A sequence of numbers such that the consecutive term is increasing or decreasing by a fixed ratio is called a geometric series.

The standard equation for geometric series is

Tₙ = a₁ rⁿ⁻¹

The sum of an infinite geometric series is given by

S = a₁/(1-r)

where a₁ is the first term and r is the common ratio.

The graph of an infinite series curves away from its sum.

To know more about Geometric Series

https://brainly.com/question/4617980

#SPJ5

Given:

Polynomial is \(3x^2+15x-56\).

To find:

The sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form.

Solution:

The sum of given polynomial and the square of the binomial (x-8) is

\(3x^2+15x-56+(x-8)^2\)

\(=3x^2+15x-56+x^2-2(x)(8)+8^2\)    \([\because (a-b)^2=a^2-2ab+b^2]\)

\(=3x^2+15x-56+x^2-16x+64\)

On combining like terms, we get

\(=(3x^2+x^2)+(15x-16x)+(-56+64)\)

\(=4x^2-x+8\)

Therefore, the sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form is \(4x^2-x+8\).

Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To determine when tan(theta) is undefined on the unit circle, we need to remember the definition of the tangent function.
Tangent is defined as the ratio of the sine and cosine of an angle. Specifically, tan(theta) = sin(theta)/cos(theta).

Now, we know that cosine can never be equal to zero on the unit circle, since it represents the x-coordinate of a point on the circle and the circle never crosses the x-axis. Therefore, the only way for tan(theta) to be undefined is if the cosine of theta is equal to zero.
There are two values of theta on the unit circle where cosine is equal to zero: pi/2 and 3pi/2.

At theta = pi/2, we have cos(pi/2) = 0, which means that tan(pi/2) = sin(pi/2)/cos(pi/2) is undefined.
Similarly, at theta = 3pi/2, we have cos(3pi/2) = 0, which means that tan(3pi/2) = sin(3pi/2)/cos(3pi/2) is also undefined.
Therefore, the answer is option C: theta = pi/2 and theta = 3pi/2.

To know more about theta visit:-

https://brainly.com/question/21807202

#SPJ11

The equation of the line that is parallel to 2y = 3x - 1 and passes through the point (4, 2) is: y = (3/2)x - 4

To find the equation of a straight line that is parallel to the line 2y = 3x - 1, we need to remember that parallel lines have the same slope.

First, let's rearrange the given equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept:

2y = 3x - 1

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

So the slope of this line is 3/2.

Now, if we want to find the equation of a line that is parallel to this line, we just need to use the same slope. Let's call the new line y = mx + b, where m is the slope we just found and b is the y-intercept we need to find.

So the equation of the parallel line is:

y = (3/2)x + b

To find the value of b, we need to use a point on the line. Let's say we want the line to go through the point (4, 2):

2 = (3/2)(4) + b

2 = 6 + b

b = -4

So the equation of the line that is parallel to 2y = 3x - 1 and passes through the point (4, 2) is: y = (3/2)x - 4

To know more about   straight line, here

https://brainly.com/question/25969846

#SPJ4

There are 1820 different groups of applicants for 4 management trainee positions, 126 different groups of trainees consisting entirely of women, and a 0.0692 probability that the trainee class will consist entirely of women.

The number of different groups of applicants that can be selected for the four management trainee positions can be calculated using the combination formula:

nCr = n! / (r! * (n-r)!)

where n is the total number of applicants (16 in this case) and r is the number of positions to be filled (4 in this case).

So the number of different groups of applicants that can be selected is:

16C4 = 1820

Therefore, there are 1820 different groups of applicants that can be selected for the four management trainee positions.

The number of different groups of trainees that would consist entirely of women can be calculated using the combination formula again, but this time we are selecting all 4 positions from the 9 female applicants:

9C4 = 126

Therefore, there are 126 different groups of trainees that would consist entirely of women.

Assuming that all groups of four are equally likely to be selected, the probability that the trainee class will consist entirely of women can be calculated by dividing the number of different groups of trainees that consist entirely of women (126) by the total number of different groups of applicants (1820):

Probability = 126 / 1820 = 0.0692

So the probability that the trainee class will consist entirely of women is 0.0692 (rounded to four decimal places).

To know more about Probability:

https://brainly.com/question/11234923

#SPJ4

The counterclockwise circulation around c is 12 and the outward flux through c is zero.

Green's theorem is a useful tool for calculating the circulation and flux of a vector field around a closed curve in two-dimensional space.

In this case,

we have a field f=(7x−4y)i+(9y−4x)j and

a square curve c bounded by x=0, x=4, y=0, y=4.

To find the counterclockwise circulation, we can use the line integral of f along c, which is equal to the double integral of the curl of f over the region enclosed by c.

The curl of f is given by (0,0,3), so the line integral evaluates to 12.

To find the outward flux, we can use the double integral of the divergence of f over the same region, which is equal to zero since the divergence of f is also zero.

To learn more about : circulation

https://brainly.com/question/30619471

#SPJ11

Answer:

x= 100

Step-by-step explanation:

x/5 = 20

multiply both the sides by 5 we get

5× x/5 = 20×5

x = 100