A scientist makes $150,000 per year. She deposits 5% of her yearly income in a travel savings account. How much money should she have in her savings account by the the end of the year in dollars and cents?

Answer:

Let's solve your equation step-by-step.

3x−31=x+59

Step 1: Subtract x from both sides.

3x−31−x=x+59−x

2x−31=59

Step 2: Add 31 to both sides.

2x−31+31=59+31

2x=90

Step 3: Divide both sides by 2.

2x

2

=

90

2

x=45

Answer:

x=45

Step-by-step explanation:

Answer:

x=45

Step-by-step explanation:

3x - 31 = x + 59

Both side -x

3x-x-31=x-x+59

3x-x -31=59

Both side +31

2x-31+31=59+31

2x=90

Both side divide 2

x=45

This statement must be true as RT + TW = WX + TW, which is correct option (A).

Two triangles are said to be congruent if their corresponding sides and angles are equal.

SSS stands for Side-Side-Side criterion. According to this, two triangles are congruent if three sides of a triangle are equal to the corresponding sides of the other triangle.

Since RT ≅ WX, RT and WX are represent congruent

So we can say that for all kinds of reasons, they are absolutely equal.

Given that, we can substitute RT with WX in the equations and solve them to check which one is valid. The valid equation will be to true statement.

For RT + TW = WX + TW

Substitute RT = WX in the equation

RT + TW = WX + TW

WX + TW = WX + TW

Subtract TW from both sides of the equation

WX + TW - TW = WX + TW -TW

WX = WX

Since RT ≅ WX,

Therefore RT and WX are exactly equivalent and interchangeable as a result, the equation WX = WX is true..

Hence, this statement must be true as RT + TW = WX + TW

Learn more about of congruent triangles here:

brainly.com/question/4364353

#SPJ6

Answer:

A

Step-by-step explanation:

Given a parabola in standard form, y = ax² + bx + c ( a ≠ 0 ), then

minimum/ maximum value is the y- coordinate of the vertex.

The x- coordinate of the vertex is

\(x_{vertex}\) = - \(\frac{b}{2a}\)

y = x² - \(\frac{5}{3}\) x + \(\frac{31}{36}\) ← is in standard form

with a = 1 and b = - \(\frac{5}{3}\) , thus

\(\frac{x}{vertex}\) = - \(\frac{-\frac{5}{3} }{2}\) = \(\frac{5}{6}\)

Substitute this value into y

y = (\(\frac{5}{6}\) )² - \(\frac{5}{3}\) (\(\frac{5}{6}\) ) + \(\frac{31}{36}\)

   = \(\frac{25}{36}\) - \(\frac{25}{18}\) + \(\frac{31}{36}\) = \(\frac{1}{6}\)

Since a > 1 then the vertex is a minimum, thus

minimum value = \(\frac{1}{6}\) → A

Answer:

1001

Step-by-step explanation:

Answer:

1001 (A)

Step-by-step explanation:

In an incidence geometry with the additional axiom that every line has exactly three points lying on it, the minimum number of points required is 4.

This is because a line must have at least two-points to exist, and if it has only two points, it is not possible to have another point lying on it (since every line must have exactly three points).

Hence, there must be at least 4-points to create two lines such that each line contains exactly three points.

Also, with 4 points, it is possible to create 6 lines such that each line contains exactly 3 points, forming a configuration known as the Fano-plane, which is the smallest example of an incidence geometry that satisfies the given axiom.

Learn more about geometry:

https://brainly.com/question/28359671

#SPJ4

The circumference of the circle is 62.8 feet.

In geometry, the circumference of a circle or ellipse is referred to as its perimeter (from the Latin circumference, meaning "carrying around").

The diameter of the circle = 20 ft

radius (r) = 20 ÷ 2 = 10 ft

Circumference = 2πr = 2 × 3.14 × 10 = 62.8 feet.

For the second problem

The circumference is 17 feet

∴2πr=17

or, 2r = 17 ÷ 3.14 = 5.414... ≈5.41 feet

Hence the diameter is 5.41

To learn more about circumference visit:

https://brainly.com/question/4268218

#SPJ1

In this case, Asset A has a return of 16% and represents 60% of the portfolio, while Asset B has a return of 22% and represents 40% of the portfolio. The correlation between Asset A and B is given as 0.93.

To calculate the expected return of the portfolio, we use the following formula:

Expected Return = (Weight of Asset A * Return of Asset A) + (Weight of Asset B * Return of Asset B) + (2 * Weight of Asset A * Weight of Asset B * Correlation between A and B * Standard Deviation of Asset A * Standard Deviation of Asset B)The expected return for a portfolio composed of two assets, A and B, can be calculated using the weighted average of the individual asset returns, considering their respective weights in the portfolio.

By plug in the given values and performing the calculations, we can determine the expected return for the portfolio comprised of 60% Asset A and 40% Asset B.

Learn more about plug here

brainly.com/question/30262705

#SPJ11

The value of M and N from the given expression is -10 and -21 respectively

Sum of functions is the addition of expression. Given the expression below;

M = 5(x + 1) and;

N = (6x - 3)

Take the difference of the expressions

M - N = 10

Substitute

5(x+1) - (6x-2) = 10

Expand the expression to have:

5x + 5 -6x + 2 = 10
5x - 6x + 5 + 2 = 10
-x + 7 = 10
-x = 10 - 7
-x = 3
x = -3

Determine the value of M

M = 5x + 5
M = 5(-3) + 5
M = -15 + 5
M = -10

Determine the value of N

N = 6x - 3
N = 6(-3) - 3
N = -18 - 3
N = -21

Hence the value of M and N from the given expression is -10 and -21 respectively

Learn more on sum of expression here: https://brainly.com/question/2164351

#SPJ1

The statement that is true about qualitative analysis is: there are no universally adopted rules for analyzing qualitative data.

Qualitative analysis is a research method that involves analyzing non-numerical data, such as text, images, or audio, to identify patterns and themes. One key characteristic of qualitative analysis is that it is often undertaken concurrently with data collection, rather than after all the data has been gathered. This allows researchers to adjust their approach and ask follow-up questions based on emerging findings. Unlike quantitative analysis, there are no universally adopted rules for analyzing qualitative data, and methods may vary depending on the researcher's perspective and goals.

Learn more about qualitative analysis

https://brainly.com/question/29082855

#SPJ4

the volume of the solid obtained by rotating the rectangle with width a and height x about the x-axis is (2π/3) a^3

Assuming you meant "a rectangle with width x", we can find the volume of the solid obtained by rotating this rectangle about the x-axis using the method of cylindrical shells.

Consider a thin vertical strip of width dx at a distance x from the y-axis. The length of this strip is the height of the rectangle, which is x. When this strip is rotated about the x-axis, it sweeps out a cylindrical shell of radius x and thickness dx. The volume of this cylindrical shell is given by 2πx(x dx) = 2πx^2 dx.

To find the total volume of the solid, we integrate the volume of each cylindrical shell from x = 0 to x = a, where a is the width of the rectangle. Therefore, the volume of the solid is given by:

V = ∫ 2πx^2 dx (from x = 0 to x = a)

V = [2π/3 x^3] (from x = 0 to x = a)

V = (2π/3) a^3

To learn  more about volume visit:

brainly.com/question/28058531

#SPJ11

Answer:

-0.9

Step-by-step explanation:

hope this helps lovely! lmk if you need an explanation!

The maximum possible side length of the base of the building is; C: 71 feet.

The given parameters of the new building in the shape of a square pyramid that is to be constructed are as follows:

Base is expressed as b

Slant height (l) is expressed as 5b

The lateral surface area of the square pyramid is calculated from the formula given as;

LSA = 2bl

Thus, the lateral surface area is expressed as;

L = 2 * b * 5b

L = 10b²

The total surface area is calculated using the formula:

T = L + b²

Thus, plugging in the value of 10b² for L gives the total surface area as;

T = 10b² + b²

T = 11b²

The maximum surface area is 50,000 square feet and so we can find b from the following expression;

11b² = 50000

Divide both sides of the equation by 11 to get;

b² = 50000/11

b = √(50000/11)

b =  71 feet to the nearest foot.

Read more about Pyramid side length at; https://brainly.com/question/22744289

#SPJ1

To find an explicit formula for the nth term of the sequence satisfying\(\(a_1 = 0\) and \(a_n = 2a_{n-1} + 1\) for \(n \geq 2\),\)  we can use recursive formula to generate the terms of the sequence.

Given:

\(\(a_1 = 0\)\\\(a_n = 2a_{n-1} + 1\) for \(n \geq 2\)\)

Using the recursive formula, we can generate the terms of the sequence as follows:

\(\(a_2 = 2a_1 + 1 = 2(0) + 1 = 1\)\\\(a_3 = 2a_2 + 1 = 2(1) + 1 = 3\)\)

\(\(a_4 = 2a_3 + 1 = 2(3) + 1 = 7\)\\\(a_5 = 2a_4 + 1 = 2(7) + 1 = 15\)\)

From the pattern, we observe that the nth term of the sequence is given by \(\(2^{n-2} - 1\).\)

Therefore, the explicit formula for the nth term of the sequence satisfying \(\(a_1 = 0\) and \(a_n = 2a_{n-1} + 1\) for \(n \geq 2\) is: \\\\\a_n = 2^{n-2} - 1.\]\)

To know more about sequence visit-

brainly.com/question/32355325

#SPJ11

Answer:

The random process described is a symmetrical random walk.

A symmetrical random walk is a mathematical model that represents a series of steps taken in either a forward (+1) or backward (-1) direction, each with equal probability. Starting from point zero, the process involves taking a certain number of steps. The outcome at each step is independent of previous steps, making it a stochastic process. The key characteristic of a symmetrical random walk is that, on average, the process remains centered around its starting point. This means that over a large number of steps, the expected displacement from the starting point approaches zero.

Learn more about: Random walks  

brainly.com/question/28534847

#SPJ11

Answer:

number 6 is −5/6=1

Step-by-step explanation:

Draw each interval on the real line.

From the figure, the intersection of the intervals is the common interval to both and the union is the interval in either of them or in both.

Answer: meters: 3 6 9 12

            Millimeters: 6,000 7,000 9,000

Step-by-step explanation:

Your adding by 3 in meters and then after 7,000 you have 9,000 then 10,000

I hope this helped!

Answer: 1: 6, 2: 7, 3: 9000, 4: 10

im sure thats it

Step-by-step explanation:

The probability that, out of a random sample of 10 internet users, 6 are concerned about the privacy of their e-mail can be calculated using the binomial probability formula.

The binomial probability formula allows us to calculate the probability of a specific number of successes (concerned internet users) in a given number of trials (random sample of 10 internet users), given the probability of success in a single trial (95% or 0.95 in this case).

Using the binomial probability formula, we can calculate the probability as follows:

\(P(X = 6) = C(n, x) * p^x * (1 - p)^(n - x)\)

P(X = 6) is the probability of exactly 6 internet users being concerned about privacy,

n is the total number of trials (10 in this case),

x is the number of successful trials (6 in this case),

p is the probability of success in a single trial (0.95 in this case), and

C(n, x) is the number of combinations of n items taken x at a time.

Plugging in the values, we have:

\(P(X = 6) = C(10, 6) * 0.95^6 * (1 - 0.95)^(10 - 6)\)

Calculating this expression will give us the probability that exactly 6 out of the 10 internet users in the random sample are concerned about the privacy of their e-mail.

Learn more about binomial probability here:

https://brainly.com/question/12474772

#SPJ11

Answer:

y=-4/3x + 22/3

This line goes through both points

Let me know if you need any more help! :)

Answer:

x=.3 or 3/10

Step-by-step explanation:

to solve for x, we need to separate it

so, we add 13 to the left side

40-11x=x

then add 11x to the right side so we have different coefficients on each side to solve for x

40=12x

then we divide 40/12 to get what x equals

we get

x= 0.3 or 3/10

hope this helped!

Answer:

x=10/3

Step-by-step explanation:

27 - 11x = x - 13

27+13=x+11x

40=12x

x=40/12

x=10/3

Answer:

Three inches because its half of six

Answer:

8

Step-by-step explanation:

x=pizza

y= breadsticks

3x+2y=30

2x+3y=25

first we myltiply the top equation with 3 and then w emultiply the lower equation with -2 so it is

9x+6y=90

-4x-6y= -50

now we can add them together and the y contracts

5x=40

now we divide it by 5

x=8

So pizza costs 8

Answer: $310.31

Step-by-step explanation:

Invested amount (P) = $302

Interest rate (r) = 3.3% per year

Period = 10 months

Recall, simple interest formula :

A = P(1 + rt) where ; A = final amount

Interest = 3.3% = 3.3/ 100 = 0.033

A = $302 ( 1 + 0.033(10/12))

A = $302 (1 + 0.033(0.8333333))

A = $302 ( 1 + 0.0275)

A = $302 ( 1. 0275)

A = $310.305

A = $310.31

Answer:

6 + 30

Step-by-step explanation:

6(1+5)

6 + 30

= 36

we have to add 7775000 to make 7800000 from 25000 which is calculated by using Substraction method.

Subtraction in mathematics is the process of subtracting one integer from another. In other terms, the result of subtracting two from five is three. After addition, subtraction is usually the second process you learn in math class.Subtraction is the action or procedure of determining the difference between two quantities or figures. The phrase "taking away one number from another" is also used to describe the process of subtracting one number from another.

Distance to be covered altogether= 7800000 m
THE distance has covered= 25000 m.

We can calculate the thousands needs to be added in 25000 to make it 7800000 by using Substraction method:-

7800000-25000= 7775000m

hence, to make 7800000 from 25000 we have to add 7775000.

To know more about Substraction method go through:-

https://brainly.com/question/17301989

#SPJ4