What is the numerical solution to the equation five less than three times a number equals four more than eight times the numbers?
A. -9/5
B. 1/11
C. -1/5
D. 1/5

Answer:

A.

Step-by-step explanation:

We have AC = DF, ∠A =∠D, so

we need AB = DE.

We get SAS congruence.

It will take approximately 27 years to accumulate $100,000 in the savings account.

To calculate the time required, we can use the future value of an ordinary annuity formula. In this case, the annuity is the annual savings of $1,300, the interest rate is 5%, and the desired future value is $100,000. By plugging these values into the formula, we can solve for the number of periods (years) it will take to reach the target amount.

The formula is:

FV = P * ((1 + r)^n - 1) / r

Where FV is the future value, P is the annual payment, r is the interest rate, and n is the number of periods. Rearranging the formula to solve for n, we have:

n = log((FV * r / P) + 1) / log(1 + r)

Substituting the given values, we get:

n = log((100000 * 0.05 / 1300) + 1) / log(1 + 0.05)

Evaluating this expression, we find that n is approximately equal to 27. Therefore, it will take approximately 27 years to accumulate $100,000 in the savings account by saving $1,300 annually at an interest rate of 5%.

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According to the information we can infer that Jim is currently 42 years old.

To calculate how old is Joyce now let's start by assigning variables to the unknown ages:

Using the information given in the problem, we can create two equations:

This means that Jim's age when Joyce was K years old is equal to J - K. According to the statement, J is now twice this age. So we can write:

This means that when Joyce is J years old, their ages will add up to 63. So we can write:

Now we have two equations with two variables. We can use substitution to solve for one of the variables:

We can substitute this expression for J in equation 2: 2K + K = 63, which simplifies to 3K = 63. Therefore, K = 21.

So Joyce is currently 21 years old. To find Jim's age, we can use equation 1 and substitute K = 21:

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The sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

To find a sinusoidal function with the given attributes, we can use the general form of a sinusoidal function:

f(x) = A * sin(Bx + C) + D

where A represents the amplitude, B represents the frequency (related to the period), C represents the phase shift, and D represents the vertical shift.

Amplitude: The given amplitude is 10. So, A = 10.

Period: The given period is 5. The formula for period is P = 2π/B, where P is the period and B is the coefficient of x in the argument of sin. By rearranging the equation, we have B = 2π/P = 2π/5.

Midline: The given midline is y = 31, which represents the vertical shift. So, D = 31.

f(3) = 41: We are given that the function evaluated at x = 3 is 41. Substituting these values into the general form, we have:

41 = 10 * sin(2π/5 * 3 + C) + 31

10 * sin(2π/5 * 3 + C) = 41 - 31

10 * sin(2π/5 * 3 + C) = 10

sin(2π/5 * 3 + C) = 1

To solve for C, we need to find the angle whose sine value is 1. This angle is π/2. So, 2π/5 * 3 + C = π/2.

2π/5 * 3 = π/2 - C

6π/5 = π/2 - C

C = π/2 - 6π/5

Now we have all the values to construct the sinusoidal function:

f(x) = 10 * sin(2π/5 * x + (π/2 - 6π/5)) + 31

Simplifying further:

f(x) = 10 * sin(2π/5 * x - 2π/10) + 31

f(x) = 10 * sin(2π/5 * x - π/5) + 31

Therefore, the sinusoidal function that satisfies the given attributes is f(x) = 10 * sin(2π/5 * x - π/5) + 31.

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Answer:

\(n=5\)

Step-by-step explanation:

Given the following question:

\(0=n-5\)

To find the answer we simply add five on both sides because this is a one-step equation.

\(0=n-5\)
\(-5+5=0\)
\(0+5=5\)
\(5=n\)
\(n=5\)

Which means your answer is "n = 5."

Hope this helps.

Answer: sorry I dont know!

Step-by-step explanation:

Answer:

√12 = 3.46410161514

√50 = 7.07106781187

√84 = 9.16515138991

√200 = 14.1421356237

Step-by-step explanation:

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Answer:

w=-7/2z

Step-by-step explanation:

just ask

Step-by-step explanation:

\(5w + 9z = 2z + 3w\)

\(5w - 3w = 2z - (9z)\)

\(2w = - 7z\)

\(w = - 7z \div 2\)

\(w = - 7z \times \frac{1}{2} \\ \)

\(w = - \frac{7}{2} z \\ \)

The probability that the last two children to leave in the evening are 5 years old would be = 1/10

Probability is defined as the possible outcome of an event which may or may not occur.

The age range of children that attended daycare = 2,3,4,5,6

The of number of children per the age range given above = 3,2,1,3,1.

The total number of children = 3+2+1+3+1= 10

The probability of two children being 5 years = 3/10( first child)

3/9 = 1/3 ( second child)

For the two children = 1/3×3/10 = 1/10

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Answer:

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints.

Step-by-step explanation:

Line segment  is a line with two end points .

" Line is defined as the collection of points in one dimensional plane which has only one dimension  length which extends to infinity."

According to the question,

Definition of line segment :

In geometry, a line segment is a part of a line that is bounded by two distinct end points, and contains every point on the line between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints.

Hence, line segment  is a line with two end points .

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The angle of depression may be found by using this formula: tan y = opposite/adjacent. The opposite side in this case is usually the height of the observer or height in terms of location, for example, the height of a plane in the air. The adjacent is usually the horizontal distance between the object and the observer.

Answer:

1,000  

+ 900  

+ 20  

+ 0  

+   0.2

+   0.09

+   0.002

+   0.0003

Step-by-step explanation:

one thousand nine hundred twenty and two thousand nine hundred twenty-three ten-thousandths

Period of the functions: The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ). The period of the function f(t) = (7 cos t)² is given by 2π/b where b is the period of cos t.

We know that cos (t) is periodic and has a period of 2π.∴ b = 2π∴ The period of the function f(t) =

(7 cos t)² = 2π/b = 2π/2π = 1.

The period of the function f(t) = cos (2φt²/m) is given by T = √(4πm/φ) Hence, the period of the function f(t) =

cos (2φt²/m) is √(4πm/φ).

The function f(t) = (7 cos t)² is a trigonometric function and it is periodic. The period of the function is given by 2π/b where b is the period of cos t. As cos (t) is periodic and has a period of 2π, the period of the function f(t) = (7 cos t)² is 2π/2π = 1. Hence, the period of the function f(t) = (7 cos t)² is 1.The function f(t) = cos (2φt²/m) is also a trigonometric function and is periodic. The period of this function is given by T = √(4πm/φ). Therefore, the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

The period of the function f(t) = (7 cos t)² is 1, and the period of the function f(t) = cos (2φt²/m) is √(4πm/φ).

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To answer this question, we need to know that this is a problem of a linear function. If we see the problem, we have:

1. Mary is spending money at an average rate of $5 per day. In this case, it represents the slope of the line. The slope of the line is the rate of change of this function. Then, we have that the slope is m = -5 --$5 per day (because she is spending money. She is going to have less and less money as time passes.) The slope is given by the difference in the y-coordinates over the difference in the x-coordinates, or, in this case, change in money (y variable), and change in days (x variable). We are told that the amount left depends on the number of days (money is a dependent variable of time):

2. In the question, we are given a point of the function (14 days, $68) (see below in the graph.)

Therefore, we have the slope of the line, and also a point of the line. As a result, we can write the equation in the point-slope form of this situation as follows:

We have that:

m = -5

x1 = 14

y1 = 68

Then, we have the point-slope form for the situation:

And to find the slope-intercept form of the line, we need to simplify the previous expression as follows:

Then, we have:

1. First, apply the distributive property:

2. Now, add 68 to both sides of the equation:

The graph for this line is:

We can see the graph with the values of the x- and y-intercepts. In the beginning, Mary had $138, and after almost 28 days, at this rate, she will have no money with her.

In summary, we have that:

1. The equation in point-slope form is:

2. The equation in slope-intercept form is:

Answer:

median = 4.5

Step-by-step explanation:

the median is the middle value of the data set arranged in ascending order. If there is no exact middle value then it is the average of the values either side of the middle

express the values in ascending order ( smallest to largest )

2 , 3 , 4 , 5 , 6 , 8

           ↑

the middle is between 4 and 5 , then

median = \(\frac{4+5}{2}\) = \(\frac{9}{2}\) = 4.5

The value of cos θ is equal to 1/3 when sec θ= √6/2.

Since we are given the value of secant of theta, we can use the relationship between secant and cosine to find the value of cosine of theta.

Let's start by recalling the definitions of secant and cosine functions. The secant of an angle is defined as the reciprocal of the cosine of that angle.

In other words, secθ = 1/cosθ

Conversely, the cosine of an angle is defined as the reciprocal of the secant of that angle.

cosθ = 1/secθ

We are given that secθ= √6/2

We can use this value to find cosθ= 1/secθ

cosθ = 1 / (√6/2)

To simplify this expression, we can multiply both the numerator and denominator by 2/sqrt(6).

cosθ = ((2/√6) / (√6/2) * (2/√6))

cosθ = (2/√6) / 1

cosθ = (2/√6 * √6/√6)

cosθ = 2/6 = 1/3

Therefore, the value of cosθ is equal to 1/3 when secθ = sqrt(6)/2.

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Answer:

8

Step-by-step explanation:

8*8*8 = 512

or

8³ = 512

or

just punch it in a calculator

A six sided number cube will have the following numbers

1, 2 , 3 , 4 , 5 , 6

Total outcome = 6

Probability of rolling a 5

This implies that the possible out come of rolling a 5 because 5 only appears once

probability = possible outcome / total outcomes

probability of rolling a 5 = 1/6

The answer = 1/6

Here is the answer

I hope it helped you

Answer:

149.8 feet

Step-by-step explanation:

θ = Angle of elevation = 33°

The length of string Jaden lets out = Hypotenuse = 275 feet.

How high above the ground that the kite is flying = Opposite Side.

We are solving this question using the Trigonometric function of Sine

Sin θ = Opposite Side/Hypotenuse

Sin 33 = Opposite/275 feet

Cross Multiply

Sin 33 × 275 feet = Opposite

Opposite side(Height ) = 149.77573463 feet

Approximately to the nearest tenth = 149.8 feet

The amount of the refund Julia gets as a federal income tax will be $90.

It is given in the question:

Julia's gross pay = $500

federal income tax withholding from her pay was 13% of her gross pay

federal income tax she owes is = $495

To find out the refund we will first find the amount of Federal income which is 13% of the gross pay.

\(\rm federal \ amount =\dfrac{4500\times 13}{100} =585\)

The refund Julia will get will be

\(=585-495=90\)

Hence the amount of the refund Julia gets as a federal income tax will be $90.

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Solve for x means finding the value of x in an equation for which the equation holds true.

Solve for x is all related to finding the value of x in an equation of one variable that is x or with different variables like finding x in terms of y. When we find the value of x and substitute it in the equation, we should get L.H.S = R.H.S.

If I ask you to solve the equation 'x + 1 = 2' that would mean finding some value for x that satisfies the equation.

Do you think x = 1 is the solution to this equation? Substitute it in the equation and see.

1 + 1 = 2

2 = 2

L.H.S = R.H.S

That’s what solving for x is all about.

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The 4 tests for similar triangles are:-

AAA: Three pairs of equal angles.

SSS: Three pairs of sides in the same ratio.

SAS: Two pairs of sides in the same ratio and an equal included angle.

ASA: Two angles and the side included between the angles of one triangle are equal

What is AAA,SAS,ASA,SSS?

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the second triangle. 

According to the SAS rule, two triangles are said to be congruent if any two sides and any angle between the sides of one triangle are equal to the corresponding two sides and angle between the sides of the second triangle.

According to the ASA rule, two triangles are said to be congruent if any two angles and the side included between the angles of one triangle are equal to the corresponding two angles and side included between the angles of the second triangle.

According to the  AAA rule, "if in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion), and hence the two triangles are identical."

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1. The height of the density graph is given as follows: 0.25.

2. The probability of taking between 11 and 12.5 minutes is given as follows: 37.5%.

It is a distribution with two bounds, given by a and b, in which each possible outcome is equally as likely.

The bounds for this problem are given as follows:

a = 10, b = 14.

Hence the height is given as follows:

1/(b - a) = 1/4 = 0.25.

The probability of taking between 11 and 12.5 minutes is given as follows

(12.5 - 11)/(14 - 0) = 1.5/4 = 0.375 = 37.5%.

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Answer:

\(\left[\begin{array}{ccc}1&0\\0&4\end{array}\right]\) \(\left[\begin{array}{ccc}x\\y\end{array}\right]\) = \(\left[\begin{array}{ccc}5\\3\end{array}\right]\)

Step-by-step explanation:

A matrix is an algorithm that has many applications. It is composed of a series of numbers (typically coefficients of variables) organized in a pattern. When dealing with a matrix, one must always remember the rule (rows by columns). One such application is that a matrix can facilitate the process by which one solves a system of equations.

When given the following system:

y = 5

4x = 3

One can see that not all of the equations have all variables in them. Yet, bear in mind that any number times zero is zero, therefore, one can rewrite the equation such that it has all of the variables if one ensures that the coefficient of the missing variable is (0).

y + 0x = 5

0y + 4x = 3

Now organize this in the form of a matrix, the coefficients of the variable go in a (4 x 4) since there are now (4) elements. The variables are vertically arranged in a (2 x 1), and the equation results are also vertically arranged in a (2 x 1).

\(\left[\begin{array}{ccc}1&0\\0&4\end{array}\right]\) \(\left[\begin{array}{ccc}x\\y\end{array}\right]\) = \(\left[\begin{array}{ccc}5\\3\end{array}\right]\)

Algorithm is a set of instructions for solving a problem or performing a task, typically designed for a computer to follow.

An algorithm is essentially a step-by-step procedure for solving a problem or accomplishing a specific task. It is used in various fields, including mathematics, computer science, engineering, and many others. In computer science, algorithms are essential for software development and programming, as they provide a systematic approach to designing and implementing complex programs. The process of developing an algorithm typically involves breaking down a problem into smaller sub-problems, identifying the key steps required to solve each sub-problem, and then putting the steps together in the correct order to form a complete solution.

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Answer: $3,302.42 (rounded)

Step-by-step explanation:

52870.79(.0625)=3304.424375