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IAn Individual Retirement Account (IRA) has $22,000 in it, and the owner decides not to add any more money to the account other than interest earned at 8%compounded daily. How much will be in the account 29 years from now when the owner reaches retirement age?There will be in the account.(Round to the nearest cent. Use a 365 day year.)
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Given:
[tex]\begin{gathered} \text{Principal (P)= \$22000} \\ \text{Rate of interest= 8\%} \\ n=29\text{ years} \end{gathered}[/tex][tex]\begin{gathered} \text{Amount in the account after 9 years=}P(1+\frac{r}{365})^{365\times n} \\ =22000(1+\frac{8}{100\times365})^{365\times29} \\ =22000(1+0.0002)^{10585} \\ =22000(8.3044) \\ =\text{ \$182696}.80 \end{gathered}[/tex]Amount in the account after 29 years is $182696.80
congruent sides are marked on the figure to the right. Find the values of x and y.
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You can identify that the triangle ACD is divided into two different triangles. These triangles are ABD and BCD.
Notice that the triangle BCD has two congruent sides. Therefore, it is an Isosceles triangle.
The triangle ABD has three congruent sides. This means that it is an Equilateral triangle. The measure of each interior angle of and Equilateral triangle is:
[tex]60\degree[/tex]Therefore, you can determine that:
[tex]x=60\degree[/tex]Let's assume that ABD is a Right triangle. Then:
[tex]ADC=90\degree[/tex]Since the other triangle C has twol equal angles:
[tex]m\angle BDC=y=90\degree-60\degree[/tex]Therefore:
[tex]y=30\degree[/tex]The answer is:
[tex]\begin{gathered} x=60\degree \\ y=30\degree \end{gathered}[/tex]el valor de 1 décimo es menor que el vamos de 3 décimas.?
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Cuando expresas un valor decimal en fracciones lo haces utilizando al 10 como denominador de la misma, entonces
1 décimo en fracciones es:
[tex]\frac{1}{10}[/tex]3 décimas corresponde entonces a
[tex]\frac{3}{10}[/tex]Al expresar estos valores utilizando cifras, el denominador 10 de la fracción indica que el numerador se encuentra en el primer lugar detrás de la coma decimal, entonces
[tex]\frac{1}{10}=0.1[/tex]y
[tex]\frac{3}{10}=0.3[/tex]Al organizar estos valores tienes que tener en cuanta la posición decimal en la que se encuentran. Si ambos se encuentran en la misma posición, entonces no debes tomar ninguna consideración y puedes ordenarlos siguiendo la mísma lógica que cuando ordenas números enteros.
Es decir, si al ordenar los enteros obtienes que:
0, 1, 2, 3
Cuando los divides por diez, simplemente corres la coma un lugar a la izquierda pero no cambias el orden de los valores, entonces:
0.0, 0.1, 0.2, 0.3
Dónde puedes ver que 0.1 es más cercano a 0 que 0.3, en otras palabras, 0.1 (una décima) es menor que 0.3 (tres décimas)
the verticles of a triangle are located at (2,0), (5,0) and (5,5). which best describes the triangle?
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Answer:
Right scalene
E Y2-yi X2-X1 Find the slope of the line that passes through these two points. Simplify completely. (2, -3) (5,6) m = [?] Enter
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Given:
Two given points are,
[tex]\begin{gathered} (x_1,y_1)=(2,-3) \\ (x_2,y_2_{})=(5,6) \end{gathered}[/tex]THe objective is to find the value of slope, (m).
The formula to find the slope is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Now, substitute the given values in the above slope formula.
[tex]\begin{gathered} m=\frac{6-(-3)}{5-2} \\ m=\frac{6+3}{5-2} \\ m=\frac{9}{3} \\ m=3 \end{gathered}[/tex]Hence, the slope of the line is 3.
Write and solve an inequality for each of the word problems.A person does door to door sales and earns a salary of $1500 per month plus 6.5% of the sales. What must the sales be if the person has a monthly income of at least $3,350.
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Explanation
Let the sales be represented by x
Since the person earns 6.5% of the sales, this becomes;
[tex]\frac{6.5}{100}\times x=0.065x[/tex]Recall that at least implies greater than or equal to in inequality. Therefore, the equation becomes;
[tex]0.065x+1500\ge3350[/tex]We will then solve for x
[tex]\begin{gathered} 0.065x\ge3350-1500 \\ 0.065x\ge1850 \\ x\ge\frac{1850}{0.065} \\ x\ge28461.5385 \end{gathered}[/tex]Answer: $28461.5385
please help I feel like I get it buy I don't know the answer
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To find the area of the figure you can find the area of the figures that make it up and then add these areas, in other words
[tex]A_f=A_r+A_R[/tex]Where
The formula to find the area of a rectangle is
[tex]\begin{gathered} A=l\cdot w \\ \text{ Where A is the area,} \\ \text{l is the length and} \\ w\text{ is the width of the rectangle } \end{gathered}[/tex]So, you have
[tex]\begin{gathered} l_r=3\text{ mm} \\ w_r=1\text{ mm} \\ A_r=l_r\cdot w_r \\ A_r=3\operatorname{mm}\cdot1\operatorname{mm} \\ A_r=3\operatorname{mm}^2 \end{gathered}[/tex][tex]\begin{gathered} l_R=6\text{ mm} \\ w_R=2\text{ mm} \\ A_R=l_R\cdot w_R \\ A_R=6\operatorname{mm}\cdot2\operatorname{mm} \\ A_R=12\operatorname{mm}^2 \end{gathered}[/tex]Finally, adding the areas you have
[tex]\begin{gathered} A_f=A_r+A_R \\ A_f=3\operatorname{mm}^2+12\operatorname{mm}^2 \\ A_f=15\operatorname{mm}^2 \end{gathered}[/tex]Therefore, the area of the figure is 15 square milimeters.
Please help. Calculus
Answers
Answer:
0.339 m/min
Step-by-step explanation:
You want to know the rate of change of the third side in a triangle with sides 10 m and 14 m and an angle between them of 60°. The angle is increasing at 2°/min.
Law of CosinesThe law of cosines tells you the third side (c) satisfies the relation ...
c² = a² +b² -2ab·cos(C)
Filling in the given values, we have ...
c² = 10² +14² -2(10)(14)cos(C) = 296 -280cos(C)
Rate of changeTaking the square root and differentiating with respect to time, we have ...
c = √(296 -280cos(C))
c' = 280sin(C)·C'/(2√(296 -280cos(C)))
We want the value of this when C=60°, and C' = 2°/min = π/90 rad/min.
c' = 280(sin(60°))·(π/90)/(2√(296 -280cos(60°))) = (14π√3/9)/(2√156)
c' ≈ 0.339 . . . . m/min
The third side is increasing at a rate of about 0.339 meters per minute.
A bakery can make 33 cheesecakes for every 3 blocks of cream cheese. Which table
represents the relationship between the number of cheesecakes the bakery makes and
the number of blocks of cream cheese the bakery uses?
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Answer:
it would be A.
Step-by-step explanation:
Why? well, if you divide 33/the total number of cream cheese blocks (3) you get 11. so for every 11 cheesecakes made, one cream cheese block is used. :)
Find x and y . Approximate your answer to one decimal place. I used comma for decimal separation. A random variable X has as a range of values the values 1, 2 and 3 with probabilities P (X = 1) = 0.2, P (X = 2) = x, and P (X = 3) = y. If Var (X) = 0.29, then x = and y =
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We have a random discrete variable X, that takes values 1, 2 and 3.
As the probabilities of all the sample space is equal to 1.
So then we can define x in function of y:
[tex]\begin{gathered} P(x=1)+P(x=2)+P(x=3)=1 \\ 0.2+x+y=1 \\ y=1-0.2-x \\ y=0.8-x \end{gathered}[/tex]We can start by calculating the mean of X as:
[tex]\begin{gathered} \mu=\sum ^3_{i\mathop=1}p_i\cdot x_i \\ \mu=0.2\cdot1+x\cdot2+y\cdot3 \\ \mu=0.2+2x+3(0.8-x) \\ \mu=0.2+2x+2.4-3x \\ \mu=2.6-x \end{gathered}[/tex]We can write the variance of X as:
[tex]\begin{gathered} \sigma^2=\sum ^3_{i\mathop=1}p_i\cdot(x_i-\mu)^2 \\ \sigma^2=0.2\cdot(1-(2.6-x))^2+x\cdot(2-(2.6-x))^2+(0.8-x)\cdot(3-(2.6-x))^2 \\ \sigma^2=0.2\cdot(x-1.6)^2+x\cdot(x-0.6)^2+(0.8-x)\cdot(x+0.4)^2 \\ \sigma^2=0.2\cdot(x^2-3.2x+2.56)+x\cdot(x^2-1.2x+0.36)+(0.8-x)(x^2+0.8x+0.16) \\ \sigma^2=0.2x^2-0.64x+0.512+x^3-1.2x^2+0.36x+0.8x^2+0.64x+0.128-x^3-0.8x^2-0.16x \\ \sigma^2=(1-1)x^3+(0.2-1.2+0.8-0.8)x^2+(-0.64+0.36+0.64-0.16)x+(0.512+0.128) \\ \sigma^2=-x^2+0.2x+0.64 \end{gathered}[/tex]As the variance, σ², is equal to 0.29, then we can find the possible values for x as:
[tex]\begin{gathered} \sigma^2=0.29 \\ -x^2+0.2x+0.64=0.29 \\ -x^2+0.2x+0.64-0.29=0 \\ -x^2+0.2x+0.35=0 \\ x^2-0.2x-0.35=0 \end{gathered}[/tex]We can find the roots of this equation as:
[tex]\begin{gathered} x=\frac{-(-0.2)\pm\sqrt[]{(-0.2)^2-4\cdot1\cdot(-0.35)}}{2\cdot1} \\ x=\frac{0.2\pm\sqrt[]{0.04+1.4}}{2} \\ x=\frac{0.2\pm\sqrt[]{1.44}}{2} \\ x=\frac{0.2\pm1.2}{2} \\ x_1=\frac{0.2-1.2}{2}=-\frac{1}{2}=-0.5 \\ x_2=\frac{0.2+1.2}{2}=\frac{1.4}{2}=0.7 \end{gathered}[/tex]The value of x = -0.5, as it is a probability, has to have a value of between 0 and 1, is not valid.
Then, the only valid value for x is x = 0.7.
We then can calculate y as:
[tex]y=0.8-x=0.8-0.7=0.1[/tex]Answer: x = 0.7 and y = 0.1
When graphing a sine curve model using the equation y = sine b x, the period (or wavelength) will be represented by StartFraction 2 pi Over b EndFraction, so b = StartFraction 2 pi Over period EndFraction.
Determine the equation for the sine curve that models the E wave if the
wavelength of E = 1.042 meters.
a.
y = sine (6.03 x)
b.
y = sine (1.042 x)
c.
y = sine (5.68 x)
d.
y = sine (7.59 x)
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3. David’s watch broke. He decides to get it fixed instead of replacing it. Since David is a loyal customer, he received a coupon in the mail for a discount. The total cost to repair the watch can be represented by 0.07r + (r – 20), where r represents the original cost of the repair. Explain what each part of the expression represents in the context of the problem.
Show your work please :)
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What each part of the expression represents in the context of the problem include the following:
r is the original cost of the repair.0.07r is the tax.(r – 20) represents the discount.What is an algebraic expression?In Mathematics, an algebraic expression simply refers to a mathematical equation that can be used in showing the relationship that typically exist between two or more numerical quantities, variables, as well as in conjunction with different mathematical operations.
In this exercise, we are provided with the following algebraic expression:
0.07r + (r – 20)
In the context of fixing David’s broken watch, the expression 0.07r most likely represents the amount of money charged as tax while the variable r represents the original cost of the repair. Additionally, the expression (r – 20) is the discount David received to fix his broken watch.
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A restaurant sells pizzas according to the formula y=8.50+0.45(x-3), where x represents the total number of toppings. You can spend no more than $10 on a pizza. What is the range of the this situation?
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the formula is
[tex]y=8.50+0.45\left(x-3\right)[/tex]For $10,
[tex]\begin{gathered} 10=8.5+0.45(x-3) \\ 10-8.5=0.45x-1.35 \\ 1.5+1.35=.45x \\ \frac{2.85}{0.45}=x \\ x=6.3 \end{gathered}[/tex]So when, x=6.3, y=$10,
A cubic meter of water weighs 1 000 kg. What is
the weight of 2 meters by 3 meters by 20
centimetre of water?
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Answer:
1200
Step-by-step explanation:
First , we need to calculate the new volume using the dimensions given.
V=L×W×H
L=3meters
W=2meters
H=20Centimeters
H=(20/100)meters=0.2 meters
V=3×2×0.2=1.2m³
using simple proportions
if 1m³=1000kg
then. 1.2m³=Y
Y=(1.2m³×1000kg)/1m3
Y=1200kg
1. question ❓given A(-3,4) B(0,1) and C(4,2), reflect as follow. Ry-axis (ABC). what is a B?2
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The reflection across the y axis the x value changes sign but the y value remain the same.
The answer is C
How is 3:1 interpreted?
A. 3 in 1
B. 3 out of 1
C. 3 to 1
D. 3 vs 1
E. None of these
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Answer:
3 to 1.
Step-by-step explanation:
3:1 is a ratio, which is comparing 2 different things.
tony wants to write large numbers as the product of as many whole numbers greater than 1 as possible. he writes 144 as 2 x 72 but he sees he can go further and writes it as 2 x 2 x 36. can he go further still? explain your reasoning.
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Tony can still go further go and write 144 as the product of whole numbers greater than one in the following way -
2 x 2 x 2 x 2 x 3 x 3
What are whole numbers?Whole numbers include all natural numbers and 0. They are real numbers that do not include fractions, decimals, and negative integers.
Given is tony, who wants to write large numbers as the product of as many whole numbers greater than 1 as possible. So, he writes 144 as
2 x 72 but he sees he can go further and writes it as 2 x 2 x 36.
Yes we can still go further and write 144 as the product of whole numbers greater than 1. We have -
144 = 2 x 72 = 2 x 2 x 36 = 2 x 2 x 2 x 18 = 2 x 2 x 2 x 2 x 9 =
2 x 2 x 2 x 2 x 3 x 3
Now, he cannot go on further to express 144 as the product of whole number greater than 1. The last digit 3 is a prime number and is divided by either 1 or itself. So, if the last digit in the product expansion is a prime number, than we cannot break it further into smaller whole numbers.
Therefore, tony can still go further go and write 144 as the product of whole numbers greater than one in the following way -
2 x 2 x 2 x 2 x 3 x 3
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class A: 1,2,3,3,4,4,4,4,5,3find the interqwarta le range
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Class: 1,2,3,3,4,4,4,4,5,3
First, order from lowest to highest
1,2,3,3,3,4,4,4,4,5
Median = (1,2,3,3) 3, 4,(,4,4,4,5) = (3+4)/2 = 3.5
Find the median of the first and last half:
Q1 = 1,2,3,3,3.5 = 3
Q3 = 3.5,4,4,4,5 = 4
Then for the interquartile: Q3- Q1 = 4 -3 = 1
4. Mrs. Santiago asked her fifth-grade students to fill out a survey at the end of the school year. 4/5 of the class filled out a survey, and 11/12 of them rated Mrs. Santiago as an excellent teacher. What Fraction of the class rated Mrs. Santiago an excellent teacher?
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We just need to multiply the fractions
[tex]\frac{4}{5}\times\frac{11}{12}=\frac{4\times11}{4\times3\times5}=\frac{11}{15}[/tex]Then, 11/15 of the class rated Mrs. Santiago as an excellent teacher
Evaluate both the upper and lower limit of f(x) = 2x over [0,2] for n = 10,100,1000
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We can solve both limits by using Riemann sums, which is represented by the following:
[tex]\lim _{n\to a}\sum ^n_{i=1}f(x_{i-1})\Delta x,\text{ where }\Delta x=\frac{b-a}{n}[/tex]Then, for our function:
[tex]undefined[/tex]Select all the equations that represent a line perpendicular to the line 3x - 2y = 10
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All the equations of the family:
y = (-2/3)*x + c
Where c is a real number, are perpendicular to the linear equation 3x - 2y = 10
How we can find the perpendicular equations?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Now, two linear equations are only perpendicular if the slope of one is equal to the inverse of the opposite of the other line's slope.
So, a line perpendicular to y = m*x + b is of the form:
y = (-1/m)*x + c
In this case, the given line is:
3x - 2y = 10
Writing this in slope-intercept form we get:
-2y = 10 - 3x
y = (10 - 3x)/-2
y = (3/2)*x - 5
So the slope of a perpendicular line will be: (-2/3)
Then any line of the form:
y = (-2/3)*x + c
Is perpendicular to the given line.
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Help mee pleasee!!
thank you <3
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The linear equation y = -500x + 5000 that models the price-sales.
What is an equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
Two points for $6, 2000 sales/day and $8, 1000 sales/day which is given in the question.
The slope varies in y as x changes.
m = (2000-1000 )/(6-8) = -500
The equation of a line with slope m is:
⇒ y = -500x+ b
Solve for b using one of the points (y-intercept)
2000 = -500(6)+b
5000 = b
The other point will provide the same result. To find b, you simply need one point (either one).
The linear relationship is:
y = -500x + 5000
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The length and width of a rectangle are consecutive odd integers. The perimeter of the rectangle is 120 meters. Find the length and width of the rectangle.
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The value of the length and the width of the rectangle are 29.5 and 30.5 meters respectively
How to determine the dimension of the rectangle?From the question, the statement is given as
Length and width are consecutive odd integers
Where perimeter = 120 meters
Represent the dimensions with x and y
Where Length = x and Width = y
And also, we have
y = x + 1
The perimeter of a rectangle is
Perimeter = 2 x (Length + Width)
Mathematically, this can be represented as
Perimeter = 2 x (x + y)
So, we have
2 x (x + y) = 120
Substitute y = x + 1 in 2 x (x + y) = 120
2 x (x + x + 1) = 120
This gives
2 x (2x + 1) = 120
Divide by 2
2x + 1 = 60
So, we have
2x = 59
Divide by 2
x = 29.5
Substitute x = 29.5 in y = x + 1
So, we have
y = 29.5 + 1
Evaluate
y = 30.5
Hence, the length and the width are 29.5 and 30.5
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1. Noah placed an empty bowl on a scale. He added different amounts of a liquid to the
bowl, recording the amount of liquid added, in tablespoons, and the total weight of
the bowl and liquid, in grams, each time on a scatter plot. He fit the line
y = 14.75x+861.82 to the data in his scatter plot, where x represents the amount
of the liquid, in tablespoons, and y represents the total weight of the bowl and the
liquid, in grams.
a. Interpret the slope of the line based on the context.
b. Interpret the y-intercept of the line based on the context.
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a) slope of the line based on the context is 14.75
b) y-intercept of the line based on the context is 861.82
what is slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
m = Δy/Δx
where, m is the slope
Given equation:
y = 14.75x+861.82
Now, using the general form
y= mx+ c
Now, comparing it with the given equation
m=14.75
and c= 861.82
a) slope of the line based on the context is 14.75
b) y-intercept of the line based on the context is 861.82
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percents build on another in strange ways.it would seem that if you increased a number by 5% and then increased its result by 5%more , the overall increase would be 10% (a) increase 100 by 5%(b)increase your result form (a)by 5%(c)what was the overall percent increase of the number 100? why is not 10%
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Answer:
Explanation:
a) increase 100 by 5%
[tex]\begin{gathered} 105\text{\% of 100 = 1.05}\times100 \\ =105 \end{gathered}[/tex]b) increase your result form (a)by 5%
[tex]\begin{gathered} 105\text{\% of 105 = 1.05}\times105 \\ =110.25 \end{gathered}[/tex]c) The overall percent increase of the number 100;
[tex]\begin{gathered} \text{ \%P = }\frac{110.25-100}{100}\times100\text{\%} \\ \text{ \%P= 10.25\%} \end{gathered}[/tex]It is not 10% because the second 5% increase was not on the initial number 100.
increasing 105 by 5% is more than increasing 100 by 5%.
Therefore, increasing 100 by 5% followed by increasing the result by 5% is greater than increasing 100 by 10%.
2. Complete the table below by stating the number of solutions and explaining orsolving to show your reasoning.a) x2 - 25 = 0b) (x - 2)2 = 0c) (x - 3) ? = 81Number of solutions: Number of solutions: Number of solutions:0101201N2Type Here:Type Here:Type Here:Explain or show yourreasoning on how yousolved the aboveproblem.Explain or show yourreasoning on how yousolved the aboveproblem.Explain or show yourreasoning on how yousolved the aboveproblem.Type Here:Type Here:Type Here:I
Answers
For the first equation:
x^2 - 25 = 0...... x^2 = 25..... x = sqrt(25)..... x = 5 and x = -5.... so it has two solutions: 5 and -5
For the second euation:
(x - 2)^2 = 0.... the solution is x = 2 because when x = 2, (2 - 2)^2 = 0 ^ 2 = 0
So it only has one solution: 2
For the third equation:
(x - 3)^2 = 81.... x - 3 = sqrt(81) = -9 and +9
x - 3 = -9... x = -6
x - 3 = 9... x = 12
so it has two solutions: -6 and 12
A sandbox is 4 ft long, 2 ft wide, and 1 ft deep.
How many bags of sand are needed to fill the sandbox if each bag is 0.4 cubic feet?
Answers
Answer:
20
Step-by-step explanation:
4 x 2 x 1 = 8
8 divide by 0.4 = 20
A CD has a diameter of 12 cm. The hole in the middle of the CD has a diameter of 1.5 cm. Find the area of one side of the CD to the nearest tenth. Use 3.14 for π .
Answers
A CD has a diameter of 12 cm and the diameter of the hole in the middle is 1.5 cm. So the area of the CD excluding the area of the hole will be 111.27 cm².
What is the area?The area is a mathematical concept that expresses the size of a region on a planar or curved surface. The area of an open surface or the boundary of a three-dimensional object is referred to as the surface area, while the area of a plane region or plane area is the area of a form or planar lamina.
According to the question, the given values are :
Diameter of CD = 12 cm.
Radius of CD, r₁= D/2 = 6 cm
Diameter of hole = 1.5 cm.
Radius of hole, r₂ = D/2 = 0.75 cm.
Area of one side of CD, A = Area of CD - Area of hole
Area of circle = πr²
A = π(6)² - π(0.75)²
A = 36π - 0.5625π
A = 35.437π cm².
The area of CD will be, A = 35.437 × 3.14 = 111.27 cm².
Hence, the area of one side of the CD will be 111.27 cm².
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what is the Value of x if -3 + 7x = x - 17a). -7/3b). -3/7c). 3/7d). 7/3
Answers
Solve x
[tex]\begin{gathered} -3+7x=x-17 \\ 7x-x=-17+3 \\ 6x=-14 \\ x=\frac{-14}{6}=\frac{-7}{3} \\ \end{gathered}[/tex]The value of x is -7/3
2.1.9 An initial investment amount P, an annual interest rate r, and a time t are given. Find the future value of the monthly, (c) daily, and (d) continuously. Then find (e) the doubling time I for the given interest rate. P = $2500, r=3.95%, t = 8 yr a) The future value of the investment when interest is compounded annually is $ 3408.29 (Type an integer or a decimal. Round to the nearest cent as needed.) b) The future value of the investment when interest is compounded monthly is $ (Type an integer or a decimal. Round to the nearest cent as needed.)
Answers
When the interest is compounded monthly, we have to do two things:
- Calculate the number of periods: in this case we have 8*12=96 months.
[tex]8\text{years}\cdot12\text{ months/year}=96\text{ months}[/tex]- The monthly interest rate: we have to divide the annual nominal rate by 12 (the number of periods in the year).
[tex]\begin{gathered} r=3.95\text{ \%} \\ r_m=\frac{3.95}{12}=0.32917\text{ \%} \end{gathered}[/tex]Then, we can calculate the future value as:
[tex]\begin{gathered} FV=C(1+r_m)^m \\ FV=2,500\cdot(1+0.0032917)^{96}=2,500\cdot1.37091864=3,427.30 \end{gathered}[/tex]The future value when compounded monthly is $3,427.30.
General formula:
[tex]FV=PV\cdot(1+\frac{r}{m})^{m\cdot n}[/tex]m: number of subperiods (monthly --> m=12)
