Mathematics College

Mason earns $70,000 per year and puts 7% of his earnings into a savings account. What is the total amount in Mason's account after 1 year if the interest rate is 3%?
 A. $147
B. $72,100
C. $5,047
 D. $2,100

Answers

Answer 1
The answer is B. $5,047.
Answer 2

Annual income of Mason is 70,000 dollars.

He saves 7% of his annual earnings into a saving account.

So, his savings would be 7% of 70,000 = 0.07 x 70,000 = 4,900 dollars.

The saving account gives an interest rate of 3% per annum.

So the interest accrued on 4900 dollars over the year would be 3% of 4,900 = 0.03 x 4,900 = 147 dollars.  

Total amount in the saving account would be sum of principal amount and interest accrued.

Total balance = principal amount + interest accrued.

Total balance = 4900 + 147 = 5,047 dollars.

Hence, option C is correct i.e. 5,047 dollars.

Related Questions

list all the possible whole number length and width of rectangles that darla can cut from the 400 square inch piece of paper

Answers

The possible dimension are :

400 = 1 x 400
400 = 2 x 200
400 = 4 x 100
400 = 5 x 80
400 = 8 x 50
400 = 10 x 40
400 = 16 x 25
400 = 20 x 20

A Fermi estimate is an estimate of a very large number found by using geometry to estimate measurements of a real-world objects

True
or
False

Answers

False. A Fermi estimate doesn't rely on geometry. It's a method for approximating large numbers using basic assumptions and math.

False. A Fermi estimate is not reliant on geometry to estimate measurements of real-world objects.

Instead, it's a method for making quick, rough approximations of quantities or numbers, especially when precise data is unavailable or impractical to obtain. Named after physicist Enrico Fermi, this approach involves breaking down complex problems into simpler components, making reasonable assumptions, and using basic mathematics to arrive at an estimate.

While geometry might be employed in some cases, Fermi estimates primarily focus on leveraging broad understanding and educated guesses to reach ballpark figures rather than precise calculations based on specific measurements.

Q # 1 solve the problem

Answers

 For this case we have the following variables:
  x = the number of adult tickets
  y = the number of children's tickets
  We write the inequality:
  8x + 6y <= 172
  The solution is the set of points that belong to the region shaded in the graph.
  Answer: 
  8x + 6y <= 172 
  see attached image.


The solution is shown in the graph attached.

Explanation:

I am goind to teach you how to get that solution.

1) Restricctions: both x and y cannot be negative, i.e. x ≥ 0 and y ≥ 0

⇒ the solution is on the first quadrant.

2) Using the prices of the tickets, $ 8 for adults, and $ 6 for children, the linear equation for the costs is: cost = 8x + 6y.

3) Since the radio station is willing to spend a maximum of $ 172 you have the final restriction:

⇒ 8x + 6y ≤ 172.

4) Then the solutions that meet the three restrictions (x ≥0, y ≥ 0, and 8x + 6y ≤ 172) is found graphically by drawing the line 8 x + 6y = 172

5) To draw the line 8x + 6y = 172, use the axis intercepts:

x = 0 ⇒ y = 172/6 = 86/3 ⇒ point (0, 86/3)

y = 0 ⇒ x = 172/8 = 86/4 ⇒ point (86/4, 0)

6) Once you have the line you shade the region that is between the line and the two axis. That region contain of the possible solutions.

a _____ is a list of things where each thing appears only once and Order matters

Answers

Answer: Permutation

Permutation is a way, in which a set or number of things can be ordered or arranged. It is a listing where order matters and each thing in the list of things appears only once.

 In Mathematics, permutation is the action of changing the arrangement of a set of items. .It is also called an "arrangement number" or "order 

Two urns contain white balls and yellow balls. The first urn contains 5 white balls and 8 yellow balls and the second urn contains 9 white balls and 2 yellow balls. A ball is drawn at random from each urn. What is the probability that both balls are white?

Answers

About 31.5% when rounded. 

This is because you have to start with the probability of each urn. The first urn has 13 total balls (5 white and 8 yellow). Since 5 of them are white, the odds of pulling a white ball are 5/13. Then find the same for the second urn (9 white and 2 yellow). Therefore there are 11 total balls and 9/11 chance of getting a white one. After finding both, multiply them together to get the answer.

[tex] \frac{5}{13} [/tex] * [tex] \frac{9}{11} [/tex] = [tex] \frac{45}{143} [/tex] = 31.5%
For the first urn:

p(white ball) = 5/13

For the second urn:

p(white ball) = 9/11

Since the two drawings are independent events, the probability of both happening is the product of the individual probabilities.

p(drawing two white balls) = 5/13 * 9/11 = 45/143

Find the perimeter and the area of a rectangle measuring 8 1/4 yd long by 4 1/8 yd wide

Answers

8.25 * 4.125 = 34.03125 square yards

perimeter = 2 * 8.25 + 2 * 4.125 =
16.50 + 8.25 =
24.75 yards


hey can you please help me posted picture of question

Answers

Option A is the correct answer.

The cubic parent function is y = x³ , with no coefficients multiplied to x and with number added to or subtracted from x. Other cubic functions are a modified form of parent cubic function.

So, the answer is y = x³

Write each of the following expressions without using absolute value. |z−7|−|z−9|, if z<7

Answers

Here is one way.

[tex]\left\{ \begin{array}{rcl}-2&\mbox{for}&z < 7\\2(z-8)&\mbox{for}&7\le z\le9\\2&\mbox{for}&9 < z\end{array}\right\,[/tex]

Corey drew 8 shapes. Four are squares, two are triangles, and the rest are parallelogram. Write two fractions that name the part of the shapes that are quadrilaterals

Answers

The part of the shapes that are quadrilaterals are represented as
6(4 squares and 2 parallelograms) out of 8

6/8 = 3/4

The two fractions are 6/8 and 3/4.

Find the length of CE

Answers

we know that
CE=CD+DE

in the right triangle EDF
cos 38°=EF/DE-----> DE=EF/cos 38°-----> DE=17/cos 38°----> DE=21.57 units

∠FDE=90-38----> 52°
∠BDC=∠FDE------> vertical angles
so
∠BDC=52°

in the right triangle BDC
cos 52°=BD/CD-------> CD=BD/cos 52°----> CD=10/cos 52°---> CD=16.24

CE=CD+DE----> CE=16.24+21.57----> CE=37.81 units

the answer is
the length of CE is 37.81 units

mean median mode range on 83 75 74 40 85 64 23 68

Answers

In the given set, the mean is 64, the median is 66, there is no mode, and the range is 62.

To find the mean, median, mode, and range of the given set of numbers: 83, 75, 74, 40, 85, 64, 23, 68.

1. Mean:

[tex]\[ \text{Mean} = \frac{\text{Sum of all numbers}}{\text{Total number of numbers}} \][/tex]

[tex]\[ \text{Mean} = \frac{83 + 75 + 74 + 40 + 85 + 64 + 23 + 68}{8} \][/tex]

[tex]\[ \text{Mean} = \frac{512}{8} \][/tex]

[tex]\[ \text{Mean} = 64 \][/tex]

2. Median:

The median is the middle number when the numbers are arranged in ascending order.

Arranging the numbers in ascending order: 23, 40, 64, 68, 74, 75, 83, 85

Since there are 8 numbers, the median is the average of the two middle numbers:

[tex]\[ \text{Median} = \frac{64 + 68}{2} \][/tex]

[tex]\[ \text{Median} = 66 \][/tex]

3. Mode:

The mode is the number that appears most frequently.

In this set, there is no number that appears more than once.

So, there is no mode.

4. Range:

The range is the difference between the largest and smallest numbers.

[tex]\[ \text{Range} = \text{Largest number} - \text{Smallest number} \][/tex]

[tex]\[ \text{Range} = 85 - 23 \][/tex]

[tex]\[ \text{Range} = 62 \][/tex]

So, for the given set of numbers, the mean is 64, the median is 66, there is no mode, and the range is 62.

Nina wants to put color tiles on a square three color tiles fit across the top of the square how many rows and Columns of the squares will Nina need how many color tiles will she use in all

Answers

Nina will need 3 columns,3 rows and she will use 9 squares in all. 
Hope that helped

what number is the opposite of 890

Answers

-890 is your answer . Any positive number is the negative of it .

The opposite of 890 is -890, which means -890 added to 890 equals zero.

The opposite of a number is defined as a number that, when added to the original number, results in zero. To find the opposite of a number, you simply change its sign. If the number is positive, the opposite is negative, and if the number is negative, the opposite is positive. Therefore, the opposite of 890 is -890.

Which of the following statements is true? If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are proportional. If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. If two polygons are similar, then the corresponding sides are congruent and the corresponding angles are proportional. None of the choices are correct.

Answers

Final answer:

The correct statement is that if two polygons are similar, their corresponding sides are proportional while their corresponding angles are congruent. Similar polygons have the same shape but can have different sizes, and this applies across various geometrical figures and principles, like the Pythagorean theorem in the context of right triangles.

Explanation:

The correct statement among the given options is: If two polygons are similar, then the corresponding sides are proportional and the corresponding angles are congruent. When polygons are similar, this means their shapes are geometrically the same but they may differ in size. The ratios of the lengths of corresponding sides of similar polygons are equal, which is true for any pairs of similar polygons, not just triangles. The corresponding angles, on the other hand, are congruent, which means they have the same measure in both polygons.

To explain this concept, we use different examples in geometry. For instance, in similar triangles, not only are the three angles in one triangle congruent to the three angles in the other, but also the sides are proportional, which can be expressed as the ratio of any two corresponding sides in the two triangles being equal. This proportional relationship is a key characteristic of similarity in geometry.

Moreover, a statement like the Pythagorean theorem applies to right triangles, stating that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This theorem is connected to similarity because one can generate a family of similar right triangles by scaling a single right triangle.

write the ratio 41 to 100 as a percent

Answers

Answer:

[tex]41\%[/tex]

Step-by-step explanation:

we have the ratio

[tex]\frac{41}{100}[/tex]

To write as percent, multiply the ratio by 100

so

[tex]\frac{41}{100}*100=41*100/100=41\%[/tex]

what is 0.0003840 expressed in scientific notation

Answers

You can write the fraction 0.0003840 a number of ways.
  0.0003840 = 0.003840/10 = 0.03840/100 = 0.3840/1000 = 3.840/10000

The one we're interested in is the last one, which has one non-zero digit to the left of the decimal point. The power of 10 in the denominator is the 4th power (the number of zeros is 4). 10^4 in the denominator is equivalent to multiplying by 10^(-4) in the numerator.

Expressed in scientific notation,
[tex]0.0003840=3.840 \cdot 10^{-4}[/tex]

0.0003840

Written in scientific notation!

Move the decimal point.

.00384 x 10^1

.0384 x 10^2

.384 x 10^3

3.84 x 10^4

38.4 x 10^5


kirsten has an area of 70 square feet for a flower garden she plants 5 varieties of flowers equally in her garden which ratio shows the square feet per flower type

Answers

The Ratio of the square feet to the per flower type is 14 : 1.

What is Ratio?

A Ratio shows the relative size of two or more value.

According to the question,

Area of a flower garden = 70 square feet

Number of flower plants varieties = 5

Formula for Perimeter of square = 4a where 'a' is sides of a square

4(a) = 70

a=70/4

a=15

To find the Ratio of the square feet to the per flower type

70 : 5

14 : 1.

Hence,  the Ratio of the square feet to the per flower type is 14:1

To learn more about Ratio here

https://brainly.com/question/1363102

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describe how a company that produce earphones can design a survey

Answers

First of all this survey need to be anonymous. The company need to know the population whom the survey is addressed. So, I think the following questions can be a good example:

1. Where do you usually use earphones? (Please select all that apply)

library 
home
transportation
kitchen
driving/riding
Other

2. What are the purposes you use earphones? (Please select all that apply)  learn language
listen to music
watch video
privacy concerns(show ‘don’t bother me’)
for beauty
Other

3. What kind of earphones you like the most?
 
circumaural
supra-aural
earbuds
in-ear 

4. What are the reasons make you like the earphone you chose in question 3? (Please select all that apply)
 
appearance
comfortability
function(plays music well) 
brand 
price 
portability 
Other

5. Have you ever felt vulnerable or unsafe while wearing headphones and listening to music because you are not as aware of your surroundings?
 
yes 
no

which of the following is equal to the rational expression when x does not equal to 5 or -1
(x-7)(x+1)/(x+1)(x-5)
a- x+1/x-5
b-x-7/x+1
c- x+1/x-7
d- x-7/x-5

Answers

The answer is D. You can cancel the (x+1) on the top and bottom because they are the same number. 

The expression that is equal to the rational expression when x does not equal to 5 or -1 is; (x - 7)/(x -5)

How to simplify Algebraic Expressions?

We want to simplify the algebraic expression;

(x - 7)(x + 1)/(x + 1)(x - 5)

Now, looking at the given expression, we see that (x + 1 ) is common to both numerator and denominator and as such they will cancel out to leave us with;

(x - 7)/(x -5)

Read more about Algebraic expressions at; https://brainly.com/question/4344214

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Which conversion requires multiplication? Use the metric table to help answer the question.

Answers

Any conversion that goes down to a smaller value 

Ex: Kilometer to meter will be x1000
meter to centimenter is x100

BUT going up will be division
Meter to kilometer is /1000

Answer:

centimeters to kilometers

Step-by-step explanation:

Find the volume of the given prism round it to the nearest tenth, 6 cm, 3.9 cm, 13.2 cm

Answers

The volume of a rectangular prism is the product of its dimensions.
  (6 cm)*(3.9 cm)*(13.2 cm) ≈ 308.9 cm³

find the center and radius of the circle (x+8)^2+(y-2)^2=25

Answers

The circle equation is in the format: (x – h)^2 + (y – k)^2 = r^2
The center is at the point (h,k) and the radius is r

In the equation (x+8)^2+(y-2)^2=25,

Center = (-8, 2)
Radius = 5

Hope this helps. :)

The students at Porterville Elementary sold raffle tickets, each for the same price, for a fundraiser. The equation below shows how much money was raised with the tickets sold. $1,760 = $20t. What is the unit rate in the equation above?

Answers

The "unit rate" appears to be $20 per ticket.

Q # 15 please solve

Answers

The give line is a horizontal line, i.e. parallel to x-axis.

The slope of a parallel line is always 0, and the equation of the horizontal line can be expressed as:

y = c

where c is the x-intercept.

So 2nd option is the correct answer

HELP
Given right triangle ABC.

In the given right triangle, find the length of the hypotenuse, AB, if BC = 6 and AC = 5.
A.5
B.√36
C.√61
D.√11

Answers

Use the Pythagorean Theorem:
 A²+B²=C²
 6²+5²=C²
36+25=C²
       61=C²
    √61=C
So the answer is C.

Answer:

Correct answer is option C (√61)

Step-by-step explanation:

in this question we have given a right triangle in which

∠C=[tex]90^{0}[/tex]

BC = 6 and AC = 5

we have to find the length of the hypotenuse, AB=?

To find the the hypotenuse we will apply Pythagoras theorem (According to Pythagoras theorem, "in a right angle triangle, square of hypotenuse is equal to the sum of square of other two sides")

In ΔABC by Pythagoras theorem

[tex]AB^{2}=AC^{2}+BC^{2}[/tex]...................(1)

put values of BC and AC in equation 1

[tex]AB^{2}=5^{2}+6^{2}[/tex]

[tex]AB^{2}=25+36[/tex]

[tex]AB^{2}=61[/tex]

AB=√61

A combination lock requires 4 selections of numbers, each from 1 to 20. • how many different combinations are there? • suppose that the lock is constructed in such a way that no number maybe used twice. how many different combinations are possible?

Answers

NUmber of combination = 20 x 19 x 18 x 17 = 116 280

Answer:  116 280

Hey can you please help me posted picture of question

Answers

The correct answer is the option C, which is:

 C. G(x)=x-6

 The explanation is shown below:

 You have that the patern function of the linear function is: F(x)=x. By definition, the patern function is the most basic function in the families of functions. If you have the linear function f(x)=x and you shifted it 6 units down, the function will be: f(x)=x-6, which inficates the it moves 6 units on the –y axis. Therefore, as you can see, the correct answer is the option mentioned above (The option C).

Nadine has 3 yard of ribbon to wrap birthday party favors if each favor use 1/5 yards of ribbon how many favors can nadine wrap

Answers

I think the answer is 15 Hope this helps

the expression sinx + cotx cosx can be simplified to___. A. cotx B. cscx C. cosx sinx D. secx

Answers

[tex]\sin x+\cot x\cos x=\sin x+\dfrac{\cos x}{\sin x}\cos x=\dfrac1{\sin x}(\sin^2x+\cos^2x)=\csc x[/tex]

Answer:

Solution-

∵ cotx = (cosx÷sinx)

∴ The given expression can be written as

sinx + cotx·cosx = sinx + ( cosx÷ sinx).cosx

⇒sinx +(cosx)²÷sinx = [ (sinx)² + (cosx)²] ÷ sinx

⇒ 1÷ sinx = cosecx = cscx

using the identity (sinx)²+(cosx)²=1

∴ option B is correct.


the quotient of a number and 9 is equal to the same number decreased by 40. what is the number

Answers

Quotient is the result of dividing two numbers.

x= the unknown number

The equation is x divided by 9 equals x minus 40.


x/9= x - 40
multiply both sides by 9

(9)(x/9)= (9)(x - 40)
x= 9x - 360

subtract 9x from both sides
-8x= -360

divide both sides by -8
x= 45


ANSWER: The number is 45.

Hops this helps! :)
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