Given: An investment of $20000 for 5 years at an interest rate of 6.5%.
Required: To determine the accumulated value if the money is compounded monthly.
Explanation: The formula for compound interest is as follows-
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Here, n=12 as the money is compounded monthly in a year. Also
[tex]\begin{gathered} P=20000 \\ t=5 \\ r=\frac{6.5}{100} \\ =0.065 \end{gathered}[/tex]Substituting the values into the formula as-
[tex]A=20000(1+\frac{0.065}{12})^{12\times5}[/tex]Further solving-
[tex]A=27,656.35[/tex]Final Answer: The accumulated value is $27,656.35
FINANCE Yetunde is purchasing a refrigerator, which costs $950. The store has a finance option: pay 10% now, and pay the remaining balance
in one year, with a 5% annual simple interest rate applied to the remaining balance.
How much will she pay up front if she uses the finance option? $
How much interest will she pay at the end of one year? $
What is the total cost of the refrigerator after using the one-year finance option? $
What is the total cost of the refrigerator if she pays the balance and interest at 6 months? $
S
1. The amount that Yetunde will pay upfront if she uses the finance option is $95.
2. The interest she will pay at the end of one year is $42.75.
3. The total refrigerator cost after using the one-year finance option is $992.75.
4. The total cost of the refrigerator if she pays the balance and interest at 6 months is $971.375.
What is a finance charge?A finance charge is the interest cost added to the amount borrowed or used for credit purchases.
Cost of the refrigerator = $950
Finance Option: Initial deposit = 10% = $95 ($950 x 10%)
Balance to be financed = $855 ($950 - $95)
Simple Interest rate = 5%
Simple interest amount = $42.75 ($855 x 5%)
The total cost with finance option is $992.75 ($950 + $42.75)
Simple interest amount at 6 months = $21.375 ($42.75/2)
The total cost at 6 months = $971.375 ($950 + $21.375)
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Solve 2x2 + x - 4=0.X2+be += 0DONEIntro
a box has the dimensions of 5, 2x, and 6x. Find a total area of all faces of this box
The total area of the box is 10
Total area
Total area means the area including the base(s) and the curved part. It is the total area covered by the surface of the object.
Given,
A box has the dimensions of 5, 2x, and 6x.
Here we need to find the total area of all faces of this box.
Basically, area is the total area occupied by the surface.
To find the total area of the box, we have to add the all the side values.
So, when we add the side value, then we get,
=> Total area = 5 + 2x + 6x
=> 8x + 5
=> 8x = 5
=> x = 5/8
Here we removed the negative sign because the area doesn't take the negative value.
So, the side values are
=> 2x = 2 (5/8) = 5/4
=> 6x = 6(5/8) = 15/4
Now, we have to find the total area as,
=> 5 + 5/4 + 15/4
=> 5 + 20/4
=> 5 + 5
=> 10
Therefore, the total area of the box is 10.
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Josephine can correct her students’ test papers in 7 hours, but if her teacher’s assistant helps, it would take them 5 hours. How long, in hours and minutes, would it take the assistant to do it alone. Write in mixed units
Answer: it will take the assistant to do it alone 17 1/2 hours
Explanation:
Let x represent the number of hours it will take the assistant to do it alone. This means that the unit work rate per hour is 1/x
If Josephine can correct her students’ test papers in 7 hours, it means that the unit work rate per hour is 1/7
If both of them can do the job in 5 hours, it means that their combined unit rate is 1/5
Since the rates are independent, it means that
1/x + 1/7 = 1/5
The lowest common multiple of the denominators is 35x. Multiplying through by 35x, we have
35 + 5x = 7x
7x - 5x = 35
2x = 35
x = 35/2 = 17/2
it will take the assistant to do it alone 17 1/2 hours
Marisa's hair grew 1 1/4 inches in 2 months. How many inches will her hair grow in 1 month?
Answer:
5/8 of an inch.
Step-by-step explanation:
based on the graph what is the solution to the system of the equation?
The graph cross at (2, 1) . Therefore, the solution of the of the system of equation is (2, 1). x = 2 and y = 1.
The population of the city of Woodville is growing in a constant rate the expression 35,000+2400 X model would real population which three statements are correct
The expression is,
38000+2400x.
The x represents the number of year.
38,000 represents the current population.
2400 represents the yearly growth.
Thus, option (a), (c) and (d) are the correct solution.
Rewrite the given standard form linear equation using function notation. Identify the slope, y-intercept, and z
-intercept. Sketch the graph of the linear equation.
-5x +9y = 45
Writing f as a function of z, the equivalent function notation form of the equation is:
Part 1
[tex]-5x+9y=45 \\ \\ 9y=5x+45 \\ \\ y=\frac{5}{9}x+5 \\ \\ \therefore f(x)=\frac{5}{9}x+5[/tex]
Part 2
Correct.
Part 3
Correct.
Part 4
Correct.
6. A poll was taken of 14,502 working adults aged 40-70 to determine their level of education. The participants were classified by sex and by level of education. The results are shown below. Education Level Male Female Total High School or Less 3618 3117 6735 Bachelor's Degree 2860 3762 6622 Master's Degree 574 476 1050 Ph.D. 41 54 95 Total 7093 7409 14,502 A person is selected at random. Compute the following probabilities. (a) What is the probability that the selected person does not have a Ph.D.? (b) What is the probability that the selected person does not have a Master's degree? (c) What is the probability that the selected person is female or has a Master's degree? (d) What is the probability that the selected person is male or has a Ph.D.?
Okay, here we have this:
We need to calculate the probability that the selected person is female or has a Master's degree, so according with this we obtain the following information:
The number of female is 7409, and the number of male with a master's degree is 574, so finally we obtain the following probability:
[tex]\begin{gathered} p=\frac{7409+574}{14502} \\ p=\frac{7983}{14502} \\ p\approx0.5505 \\ p=55.05\text{ percent} \end{gathered}[/tex]Finally we obtain that the percentage is %55.05.
Urgent!! Math work in image!! Urgent help!!
The TV would not fit as the TV is too tall option (C) is correct after applying the concept of the ratio.
What is the ratio?It is described as the comparison of two quantities to determine how many times one obtains the other. The proportion can be expressed as a fraction or as a sign: between two integers.
The aspect ratio is:
= 4:3
Multiply by 16 to the above ratio:
= 64: 48
The height in the area = 47"
But from the aspect ratio the height of the TV = 48"
Thus, the TV would not fit as the TV is a too tall option (C) is correct after applying the concept of the ratio.
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Heather decorated her house for a birthday party. She had 30 balloons to hang in three different rooms?
Which expression represents the total number of balloons if each room had an equal number of balloons as shown in the image?
A. 10x3
B. 3x10
C. 5x6
D. 6x5
Option A, which is 10×3, represents the total number of balloons if each room had an equal number of balloons as shown in the image.
What is meant by expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.As an illustration, the phrase x + y is one where x and y are terms with an addition operator in between. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables.An expression is 3x - 2. On the other hand, an equation is when two independent expressions are linked together by an equal to sign. For instance, an equation is when 3x - 2 = 5 + x.To learn more about expression refer to:
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Write the equation of the line, with the given properties, in slope-intercept form. Slope = -7, through (-5,7)
the general equation of a line is
[tex]y=mx+b[/tex]where m is the slope an b an initial point
we can replace m=-7 and (x,y)=(-5,7) to find b an creat the equation for this case
[tex]\begin{gathered} (7)=(-7)(-5)+b \\ 7=35+b \\ b=-28 \end{gathered}[/tex]and the equation is
[tex]y=-7x-28[/tex]Type in the value ol 29 С A 21 20 B sin A= COSA = tanA= sinC = cosC =
Given,
The measure of side AC is 29.
The measure of side AB is 20.
The measure of side BC is 21.
The angle ABC is right angle.
The expression of sin in trigonometric ratio is,
[tex]\begin{gathered} \sin \text{ A=}\frac{\text{side opposite to angle A}}{\text{Hypotenuse}} \\ \sin \text{ A=}\frac{21}{29} \\ \sin \text{ C=}\frac{\text{side opposite to angle C}}{\text{Hypotenuse}} \\ \sin \text{ C=}\frac{20}{29} \end{gathered}[/tex]The expression of cos in trigonometric ratio is,
[tex]\begin{gathered} \cos \text{ A=}\frac{\text{side adjacent to angle A}}{\text{Hypotenuse}} \\ \cos \text{ A=}\frac{20}{29} \\ \cos \text{ C=}\frac{\text{side adjacent to angle C}}{\text{Hypotenuse}} \\ \cos \text{ C=}\frac{21}{29} \end{gathered}[/tex]The expression of tan in trigonometric ratio is,
[tex]\begin{gathered} \tan \text{ A=}\frac{\text{side opposite to angle A}}{\text{side adjacent to angle A}} \\ \tan \text{ A=}\frac{21}{20} \\ \tan \text{ C=}\frac{\text{side opposite to angle C}}{\text{side adjacent to angle C}} \\ \tan \text{ C=}\frac{20}{21} \end{gathered}[/tex]Hence, the value of sin A is 21/29, cos A is 20/29 , tan A is 21/20 and the value of
I need help with part "C" and "D"
3x²cos( x³ ) and 3sin²( x ) cos( x ) are the derivatives of the composite functions f(x) = sin(x³) and f(x) = sin³(x) respectively.
What are the derivative of f(x) = sin(x³) and f(x) = sin³(x)?Chain rule simply shows how to find the derivative of a composite function. It states that;
d/dx[f(g(x))] = f'(g(x))g'(x)
Given the data in the question;
f(x) = sin(x³) = ?f(x) = sin³(x) = ?First, we find the derivate of the composite function f(x) = sin(x³) using chain rule.
d/dx[f(g(x))] = f'(g(x))g'(x)
f(x) = sin(x)
g(x) = x³
Apply chain rule, set u as x³
d/du[ sin( u )] d/dx[ x³ ]
cos( u ) d/dx[ x³ ]
cos( x³ ) d/dx[ x³ ]
Now, differentiate using power rule.
d/dx[ xⁿ ] is nxⁿ⁻¹
cos( x³ ) d/dx[ x³ ]
In our case, n = 3
cos( x³ ) ( 3x² )
Reorder the factors
3x²cos( x³ )
Next, we find the derivative of f(x) = sin³(x)
d/dx[f(g(x))] = f'(g(x))g'(x)
f( x ) = x³
g( x ) = sin( x )
Apply chain rule, set u as sin( x )
d/du[ u³ ] d/dx[ sin( x )]
Now, differentiate using power rule.
d/dx[ xⁿ ] is nxⁿ⁻¹
d/du[ u³ ] d/dx[ sin( x )]
3u² d/dx[ sin( x )]
Replace the u with sin( x )
3sin²(x) d/dx[ sin( x )]
Derivative of sin x with respect to x is cos (x)
3sin²( x ) cos( x )
Therefore, the derivatives of the functions are 3x²cos( x³ ) and 3sin²( x ) cos( x ).
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The directions are with the pic below. I have to send an additional pic. All wouldn’t fit on the page.
Given:
We get the points A(-1,-2) , K(-2, 2) and M(0,2).
Aim:
We need to find the new figure which is obtained by rotating the given figure by 90-degree counterclockwise.
Explanation:
Recall that when we rotate the point (x,y) 90 degrees counterclockwise then the image of the point (x,y) can be written as follows.
[tex](x,y)^{\prime}\rightarrow(-y,x)[/tex]The image of point A(-1, -2).
[tex]A(-1,-2)\rightarrow A^{\prime}(-(-2),-1)[/tex][tex]A(-2,-2)\rightarrow A^{\prime}(2,-1)[/tex]The image of point K(-2,2)
[tex]K(-2,2)\rightarrow K^{\prime}(-(2),-2)[/tex][tex]K(-2,2)\rightarrow K^{\prime}(-2,-2)[/tex]The image of point M(0,2).
[tex]M(0,2)\rightarrow M^{\prime}(-(2),0)[/tex][tex]M(0,2)\rightarrow M^{\prime}(-2,0)[/tex]Mark points A'(2,-1), K'(-2,-2), and M'(-2,0) on the graph and join all points.
Final answer:
The new figure is
Nikki has rowing lessons every four days and tennis every 7 days. If she had both lessons on the last day of the previous month, when will she have both lessons on the same day of the current month?
we know that
Nikki has rowing lessons every four days
so
4 8 12 16 20 24 28
and
tennis every 7 days
7 14 21 28
therefore
She will have both lessons again the day 28 of the current month
Solve each of these systems of equations. You may use either the substitution or elimination method.2x+y=15x+6y =4
Answer:
x=2/7 and y=3/7
Explanation:
Given the systems of equations:
[tex]\begin{gathered} 2x+y=1 \\ 5x+6y=4 \end{gathered}[/tex]We use the substitution method to solve.
Step 1: Make y the subject in the first equation.
[tex]\begin{gathered} 2x+y=1 \\ y=1-2x \end{gathered}[/tex]Step 2: Substitute y into the second equation.
[tex]\begin{gathered} 5x+6y=4 \\ 5x+6(1-2x)=4 \\ 5x+6-12x=4 \\ 5x-12x=4-6 \\ -7x=-2 \\ x=-\frac{2}{-7} \\ x=\frac{2}{7} \end{gathered}[/tex]Step 3: Solve for y
[tex]\begin{gathered} y=1-2x \\ =1-2(\frac{2}{7}) \\ =1-\frac{4}{7} \\ y=\frac{3}{7} \end{gathered}[/tex]Therefore, x=2/7 and y=3/7.
One afternoon you picked 6/8 of a pound of strawberries that night you ate 3/6 of what you picked
Given :
the amount of picked strawberries = 6/8 pounds
you ate 3/6 of what you picked.
so, the amount is eaten =
[tex]\frac{6}{8}\times\frac{3}{6}[/tex]cross out the number 6
so, the answer will be = 3/8 pounds
Find the values of x that make mlln
Answer:
4x² = 100° (corresponding angles)
x² = 100÷4
= 25
x = √25
= 5°
Find the perimeter of the triangle whose vertices are
(-2, 4), (-2, 1), (-4,-2).
The sum of the length of the sides is the perimeter of the triangle.
The perimeter of the triangle is 5[tex]\sqrt{10}[/tex] + [tex]\sqrt{13}[/tex].
How to find the perimeter of a triangle?The sum of the length of the sides is the perimeter of the triangle.
d = [tex]\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}[/tex]
Lets take (-2, 4) and (-2, 1).
[tex]d = \sqrt{(-2+2)^2 + (1 - 4)^2}\\\\d = \sqrt{0 + -3^2} \\\\d = \sqrt{9} \\[/tex]
d = 3
Now, let's take the points (-2, 1) and (-4,-2).
d = [tex]\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}[/tex]
[tex]d = \sqrt{(-4+2)^2 + (-2-1)^2}\\\\d = \sqrt{-2^2 + -3^2} \\\\d = \sqrt{4 + 9} \\[/tex]
d = [tex]\sqrt{13}[/tex]
Now, let's take the points (-2, 4) and (-4,-2).
d = [tex]\sqrt{(x^2 - x^1)^2 + (y^2 - y^1)^2}[/tex]
[tex]d = \sqrt{(-4+2)^2 + (-2-4)^2}\\\\d = \sqrt{-2^2 + -6^2} \\\\d = \sqrt{4 + 36} \\[/tex]
d = 40 = 2[tex]\sqrt{10}[/tex]
The sum of the length of the sides is the perimeter of the triangle d= 3 + [tex]\sqrt{13}[/tex] + 2[tex]\sqrt{10}[/tex]
The perimeter of the triangle is 5[tex]\sqrt{10}[/tex] + [tex]\sqrt{13}[/tex].
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Solve: 82 ÷ 3 Follow the steps for long division. Write the number that should appear in the letter blank to solve the problem. Write the remainder in the box represented as "R:" in the image. And i need it now please
Answer:27 R1
Step-by-step explanation:2 7
3 8 2
- 6
2 2
- 2 1
1
For her 9th birthday, Cindy
wanted to buy her class
number nine donuts. If each
number donut costs $1.09 and
she has 22 students in
her class, how much will
she spend on donuts?
Answer:
23.98 dollars
Step-by-step explanation
Multiply 22 x 1.09
Answer:
$23.98
Step-by-step explanation:
If there's 22 students to serve, Cindy needs to take the price of one donut ($1.09) and multiply that by 22.
22 x 1.09 = 23.98
A parabola has a directrix of y=1 and a focus of (1,12). Which statement is true?A)The parabola opens upward.B)The parabola opens downward.C)The parabola opens to the left.D)The parabola opens to the right.
1) Since the directrix is y=1 and the focus (1,12) We can write that, using the distance formula:
[tex]\begin{gathered} \sqrt[]{(y-1)^2}=\sqrt[]{(x-1)^2+(y-12)^2} \\ (y-1)^2=(x-1)^2+(y-12)^2 \\ y^2-2y+1=x^2-2x+1+y^2-24y+144 \\ -2y+1=x^2-2x+1-24y+144 \\ -2y+24y=x^2-2x+145 \\ -22y=x^2-2x+145 \\ y=\frac{x^2-2x+145}{22} \\ \\ y=\frac{x^2-2x+145}{22} \end{gathered}[/tex]2) Then we can state that the correct option is A the parabola opens upward.
The accompanying table shows the median household income (in dollars) for 25 randomly selected regions. Complete parts (a) through (g) below.B!: Click the icon to view the table of data.(a) Construct a frequency distribution. Use a first class having a lower class limit of 35,000 and a class width of 5000.IncomeFrequency
Step 1:
Draw a table with class intervals to construct the frequency distribution table.
Step 2:
Choose a lower class and a class interval.
Lower class limit = 35,000
Class interval = 5000
Step 3:
Get the smallest and largest values from the table
Smallest value = 39712
Largest value = 67729
Step 4:
Draw the table using the class interval.
a) Frequency distribution table
Help please
Stem: 6, 7, 8, 9
Leaf: 8, 579, 02, 2667
Questions: What score represents the median of this data? What score represents the mode of this data? What is the mean of this data? If you use the mean, median, or mode to describe this data, which one would be the most misleading?
1. The score that represents the median is 81.
2. The score that represents the mode is 96.
3. The score that represents the mean is 84.2.
4. The mode will be the most misleading since it's far away from the mean and median.
What is a mean?The stem and leaf plot data are 68, 75, 77, 79, 80, 82, 92, 96, 96, and 97.
A mean simply means the average of a set of numbers. The mean will be:
= Sum of all data values / Number of values
= 842 / 10
= 84.2
The mode is the number that occurs most and this will be 96.
The median is the number in the middle. This will be:
= (80 + 82)/2
= 162/2
= 81
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Is 8 a solution of the equation x+6=−2?
In the accompanying table, the random variable x represents the number of televisions in a household in a certain country. Determine whether or not the table is a probability distribution. If it is a probability distribution, find its mean and standard deviation.xP(x)00.0310.1220.2430.3140.1850.12
For the table to be a complete probability distribution we need to check that the addition of the probabilities (P(x)) is equal to 1.
[tex]0.03+0.12+0.24+0.31+0.18+0.12=1[/tex]As it is equal to one, we can be certain that no household has more than 6 TVs. The function P(x) is indeed a probability distribution
Now, we need to find its mean and standard deviation
[tex]\begin{gathered} \operatorname{mean}=\mu=\sum ^{}_{}xP(x) \\ \Rightarrow\mu=0\cdot0.03+1\cdot0.12+2\cdot0.24+3\cdot0.31+4\cdot0.18+5\cdot0.12 \\ \Rightarrow\mu=2.85 \end{gathered}[/tex]And the Standard Deviation is:
[tex]SD=\sigma=\sqrt[]{\sum^{}_{}}P(x)(x-\mu)^2[/tex]Then, in our case:
[tex]\begin{gathered} \sigma=\sqrt[]{0.03(-2.85)^2+0.12(-1.85)^2+0.24(-0.85)^2+0.31(0.15)^2+0.18(1.15)^2+0.12(2.15)^2} \\ \Rightarrow\sigma=1.2757\ldots \end{gathered}[/tex]The Empire State building in New York City is approximately 1250 ft tall. How many U.S. dimes would be in a stack of the same height? Each dime is 1.35 mm thick.
Answer:
It is necessary to stack 277778 dimes.
Step-by-step explanation:
The height of the Empire State building in meters is 1250 * 0,30 = 375 meters.
I need help answering this please ! The calculator has to be In degree mode and the second picture is used to help you find the answer
A) AB is a side and not an angle. A side is a length, an angle is a junction of two lines.
B) You are given a side, AC and two angles, Angles B and C
C) Angles and lines are named according to their oppositeness. Angle A is opposite to side a.
[tex]\frac{\sin A}{BC}=\frac{\sin B}{AC}=\frac{\sin C}{AB}=\frac{\sin A}{BC}=\frac{\sin50}{12}=\frac{\sin 62}{AB}[/tex]D) To find AB, we crossmultiply with the expression in the middle of the equation. This gives:
[tex]AB\text{ = }\frac{\text{12 sin 62}}{\sin 50}=13.8313[/tex]Line AB is 13.83 to the nearest hundredth
3x+1x2+5x+6=ax+2+bx+3
Answer: If you have an equation of the form "ax2 + bx + c = 0".
x2 = 3x -1, x2 - 3x + 1 = 0, a=1, b=-3, c=1.
Step-by-step explanation:
