Using compound interest, it is found that he must invest his money at a rate of 8.78% a year.
What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
A(t) is the amount of money after t years. P is the principal(the initial sum of money). r is the interest rate(as a decimal value). n is the number of times that interest is compounded per year.In this problem, the parameters are as follows:
t = 3, A(t) = 60000, P = 46150.3, n = 12.
Hence:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
[tex]60000 = 46150.3\left(1 + \frac{r}{12}\right)^{12 \times 3}[/tex]
[tex]\left(1 + \frac{r}{12}\right)^{36} = 1.3[/tex]
[tex]\sqrt[36]{\left(1 + \frac{r}{12}\right)^{36}} = \sqrt[36]{1.3}[/tex]
[tex]1 + \frac{r}{12} = (1.3)^{\frac{1}{36}}[/tex]
[tex]1 + \frac{r}{12} = 1.00731451758[/tex]
[tex]\frac{r}{12} = 0.00731451758[/tex]
r = 12 x 0.00731451758
r = 0.0878.
He must invest his money at a rate of 8.78% a year.
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Check photo! simple easy 7th grade math.
Answer:
$114.19
Step-by-step explanation:
7.25*15 = 108.75
108.75*1.05 = 114.1875
You can't have less than a cent, so it is $114.19
Answer: $114.19
Step-by-step explanation:
Find the volume of the sphere with r = 9 to the nearest hundredth. Use
3.14 to represent pie.
Answer:
3,052.08
Step-by-step explanation:
Formula for sphere: (4/3)(pi)(r^3)
Filled in: (4/3)(3.14)(729)
Calculated: 3,052.08
please help !! I dont know what the awnser is, i put mean, medium, and mode for the first try adn it gave me partial
Answer:
All of them but the last one
Step-by-step explanation:
3. Choose the graph that shows the solution of the inequality on the number line. n > 4
O
0
2 4 6
8
+444
2
4 6 8
02
4 6 8
0 2 4
6
8
When treasury stock is purchased for $42 per share and subsequently sold for $47 per share, treasury stock is credited for $fill in the blank 1
per share and Paid-in Capital from the Sale of Treasury Stock is
for $fill in the blank 3
per share when the sale is recorded.
2. When treasury stock is purchased for $42 per share and subsequently sold for $40 per share, treasury stock is credited for $fill in the blank 4
per share and Paid-in Capital from the Sale of Treasury Stock is
for $fill in the blank 6
per share when the sale is recorded.
3. When treasury stock is purchased for $38 per share and subsequently sold for $47 per share, treasury stock is credited for $fill in the blank 7
per share and Paid-in Capital from the Sale of Treasury Stock is
for $fill in the blank 9
per share when the sale is recorded.
4. When treasury stock is purchased for $38 per share and subsequently sold for $40 per share, treasury stock is credited for $fill in the blank 10
per share and Paid-in Capital from the Sale of Treasury Stock is
for $fill in the blank 12
per share when the sale is recorded.
Triangle ΔABC has side lengths of a = 18, [tex]b=18\sqrt{3}[/tex] and c = 36 inches.
Part A: Determine the measure of angle A
Part B: Show how to use the unit circle to find tan A
Part C: Calculate the area of ΔABC.
The measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.
What is the law of cosine?When the three sides of a triangle is known, then to find any angle, the law of cosine is used.
It can be given as,
[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle B=\cos^{-1}\left(\dfrac{a^2+c^2-b^2}{2ac}\right) \\\angle C=\cos^{-1}\left(\dfrac{a^2+b^2-c^2}{2ab}\right)[/tex]
Here, a,b and c are the sides of the triangle and A,B and C are the angles of the triangle.
Triangle ΔABC has side lengths of a = 18, b=18√3 and c = 36 inches.
Part A: Determine the measure of angle APut the value, in the cosine law, the measure of angle A.
[tex]\angle A=\cos^{-1}\left(\dfrac{b^2+c^2-a^2}{2bc}\right) \\\angle A=\cos^{-1}\left(\dfrac{(18\sqrt{3})^2+36^2-18^2}{2(18\sqrt{3})(36)}\right) \\\angle A=0.5236\rm\; rad\\\angle A=30^o\rm\; degree\\[/tex]
Part B: Show how to use the unit circle to find tan AUsing the chart of unit circle, the value of tangent A can be found out. The tangent A is,
[tex]\tan A=\tan 30^o\\\tan A=\dfrac{1}{\sqrt{3}}[/tex]
Part C: Calculate the area of ΔABC.Use the following formula to find area of ΔABC.,
[tex]A=\dfrac{ab.\sin C}{2}\\A=\dfrac{18\times18\sqrt{3}.\sin C}{2}\\A=280.6\rm\; in^2[/tex]
Thus, the measure of angle A is 30 degree, the value of tan A is 1/√3 and the area of triangle ABC is 280.6 squared inches.
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One endpoint of a segment is M(0, 8). The midpoint of the segment is
Q(4, 10). What are the coordinates of the other endpoint?
[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ M(\stackrel{x_1}{0}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{x}~,~\stackrel{y_2}{y}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ x + 0}{2}~~~ ,~~~ \cfrac{ y + 8}{2} \right)~~ = ~~\stackrel{\textit{\Large Q}}{(4~~,~~10)}\implies \begin{cases} \cfrac{x+0}{2}=4\\[1em] \boxed{x=8}\\[-0.5em] \hrulefill\\ \cfrac{y+8}{2}=10\\[1em] y+8=20\\ \boxed{y=12} \end{cases}[/tex]
6) Give all asymptotes
A curve asymptote is a line where the distance between the curve and the line approaches 0. The function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
What are asymptotes?A curve asymptote is a line where the distance between the curve and the line approaches 0 when one or both of the x or y coordinates approaches infinity.
The asymptotes are the values for which the function is not defined. The asymptotes of a fractional function are found by equating its denominator's factors against zero. Therefore, the value of the asymptotes is,
[tex](2x-5)=0\\\\2x=5\\\\x=\dfrac52[/tex]
[tex]x-5=0\\\\x=5[/tex]
Now, substitute the value of x as (5/2) and 5, to know if the function is defined or not.
[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(5) = \dfrac{[7(5)-1](5-5)}{[2(5)-5](5-5)}\\\\\\f(5) = \dfrac{(35-1)(0)}{(10-5)(0)} = 0[/tex]
Since for the value of x=5, the function is defined and returns the value as 0. Thus, x=5 is not an asymptote.
[tex]f(x) = \dfrac{(7x-1)(x-5)}{(2x-5)(x-5)}\\\\\\f(\frac52) = \dfrac{[7(\frac52)-1](\frac52-5)}{[2(\frac52)-5](\frac52-5)}\\\\\\f(\frac52) = \dfrac{(16.5)(-2.5)}{(0)(-2.5)} = \dfrac{\infty}{0}[/tex]
Since the function is undefined for the value of x=(5/2). Thus, x=(5/2) is an asymptote.
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help plsssssssssssss
Answer:
m<ABC = 90 degrees m<ABD = 57 degrees
Step-by-step explanation:
OMG this is soooooo easy I love geometry.
Can yall help me with this math
Answer:
2 the change in expected height for every additional centimeter of femur length
Step-by-step explanation:
1 and 4 have 55 is the starting point but is just there to throw you off and 3 has expected femur length, but the graph says expected height
Make a 3-by-6 logic grid on your own paper. Use it to help you solve the logic
puzzle and answer the question given below.
Davis, Roy, and Tom are on the rowing team. Each sits in a different position
(front, middle, and end) and is a different age (18, 19, and 20).
• Tom and the 19-year-old do not sit in the rear.
.
The person who sits in the rear is 20 years old.
Neither Tom nor Roy sits in the front.
Who sits in the middle, and how old is he? Be sure to check both answers.
Answer:
Tom sits in the middle and he is 18
Step-by-step explanation:
On the table you will first mark off Tom from being in the rear, as well as being 19
You will mark off Tom and Roy from the 1st, which places Davis as 1st, you also know that Tom is neither 1st nor last, so he is in the middle.
Now you see that Roy is neither in the 1st nor middle, so he is last.
Last is also the 20 yr old, so Roy is 20yrs and last seat.
Tom is neither 19 or 20.
So Tom is in the middle and 18yrs old
7
Directions: Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Use the picture of the trapezoid below to complete the statements that follow.
10 units
units
14 units
square units, the area of section 2 is
square units, and the area of section 3 is
square
The area of section 1 is
units.
The area of the trapezoid is
square units.
Reset
Submit
Answer:
126 square units
Step-by-step explanation:
Area of section 1 is 8 square units which is triangle and,
Area of triangle is = [tex]\frac{1}{2}\times b\times h[/tex]
b= 2 units and height =8 units
So,
Area of section 1 = [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]
Same Area is of section 2 which is also a triangle and has same base and height.
So,
Area of Section 2 = [tex]\frac{1}{2}\times 2\times 8=8 \quad\text{ square units}[/tex]
Now the Area of section 3 which is square with side of 10 units
So,
Area of section 3 = [tex]a^{2} =10\times10=100\quad \text{square units}[/tex]
Total Area of Trapezoid = [tex]8+8+100=126 \quad \text{square units}[/tex]
For two functions, f(x) and g(x), a statement is made that f(x) = g(x) at x = 5. What is definitely true about x = 5?
A. Both f(x) and g(x) cross the x-axis at 5.
B. Both f(x) and g(x) cross the y-axis at 5.
C. Both f(x) and g(x) have a maximum or minimum value at x = 5.
D. Both f(x) and g(x) have the same output value at x = 5
Answer:
D
Step-by-step explanation:
f(x) = g(x) at x=5
means
f(5) = g(5)
11. Henry had a batting average of
0.340 last season. (Out of 500 at-
bats, he had 170 hits.) If his batting
average stays the same this year,
what is the probability that he'll get
exactly 8 hits in his next 20 at-bats?
Round your answer to the nearest
thousandth.
Answer choices:
6.820
0.788
0.154
0.297
The probability of getting exactly 8 hits in his next 20 at-bats is 0.153 (Round off to the nearest thousandth.).
The correct option is (c)
What is Binomial distribution?Binomial distribution can be thought of as simply the probability of a SUCCESS or FAILURE outcome in an experiment or survey that is repeated multiple times.
Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]
where, n= number of trial,
r= number of success desire,
p= probability of success,
q= probability of Failure
probability of success = 0.34
To find the probability of winning exactly 8 hits in next 20 at-bats we find
dbinom (8, 20, 0.34)
Since p= 0.34
q= 1-p
= 1-0.34
= 0.66
n= 20, r=8
Using Binomial Distribution, we get
Probability= [tex]C^{n}_r\; p^{r} \;q^{(n-r)[/tex]
=[tex]\frac{n!}{r!(n-r)!} p^{r}\; q^{(n-r)}[/tex]
= [tex]\frac{20!}{8!(20-8)!} (0.34)^{8}\; (0.66)^{(20-8)}[/tex]
= 125970 x 0.0001785794 x 0.00683168
= 0.1536830
≈ 0.153 (Round off to the nearest thousandth.)
Hence, the probability of getting exactly 8 hits in his next 20 at-bats is 0.153.
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Consider the graph of the parent exponential function f and transformed function g.
A. shifted up 5 units
B. shifted to the left 1 unit
C. shifted up 3 units
D. shifted to the right 1 unit
Second options in picture.
To produce g, function f was reflected over the x-axis and (blank)
Function g can be defined as (blank)
Answer:
A, g(x) = -f(x)+5
Step-by-step explanation:
For the right triangles below, find the values of the side lengths h and b . Round your answers to the nearest tenth.
Answer:
d
Step-by-step explanation:
There are 2 triangles and 6 circles. What is the simplest ratio of triangles to circles?
Answer:
1: 3
Step-by-step explanation:
2 triangles : 6 circles
Divide each side by 2
2/2 : 6/2
1 :3
1 triangle : 3 circles
1. If you have a 100A as a grade and you get 8 bonus points, what is your grade now?
2. If you have a 90B as a grade and you get 8 bonus points, what is your grade now?
**ANSWER QUICK**
Answer:
1) 108 A+ 2) 98 B+
Step-by-step explanation:
simplify (x^5)(y^7)(x^9)(y^2)
Answer:
x^14 y^9
Step-by-step explanation:
Add the exponent of the x's
(x^5) + (x^9) = x^14
Add the exponent of the y's
(y^7) + (y^2) = y^9
You can't combine different varibles so your answer will be x^14 y^9
16) Find the value of x
Answer:
root 7
Step-by-step explanation:
apply tan60=p/b=root 21/ x
one-half the total of six times a number n and thirty-eight?
3n+19
Explanation:
(1/2)(6n + 38)
What is the distance between (2, 6) and (7, 6)?
8
(2,3)
+17,6)
4
2
What is the best next step in the construction of the perpendicular bisector of AB?
Answer:
B
Step-by-step explanation:
Out of all the answers given as a choice B makes the most sense because the triangle AB and point of intersection of the two circles form an equilateral triangle.
In general to construct a perpendicular bisector after we drew the two circles we have to ...draw a straight line trough the points where the two circles intersect and that is our perpendicular bisector of AB.
Pi/3 is the reference angle for
Answer:
Trigonometry Examples
Since π3 is in the first quadrant, the reference angle is π3 .
Since π3 is in the first quadrant, the reference angle is 60 degrees
Step-by-step explanation:
HOPE THIS WILL HELP YOU
Multiplicaciones que den 35
Answer:
Estos pares de factores son (1, 35) y (5, 7).
espero que esto ayude.
➡ (1,35)
➡ (5,7)
Find the length of the missing side of the right triangle.
Answer:
39 units
Step-by-step explanation:Since two side lengths and a right angle are given, we can use pythogoras theorem to determine the missing side (c) of the triangle. It should be noted that pythgoras theorem can only be used if the triangle is a right triangle.
Pythogoras theorem formula:
[tex](\text{Side}_{1} })^{2} + (\text{Side}_{2} )^{2} = (\text{Hyptenuse})^{2}[/tex]
Substitute the legs of the triangle and the hyptenuse
[tex]\implies (36)^{2} + (15 )^{2} = (c)^{2}[/tex]
Simplify both sides of the equation
[tex]\implies 1296 + 225 = (c)^{2}\\[/tex]
[tex]\implies 1521 = (c)^{2}\\[/tex]
Take square root both sides
[tex]\implies \sqrt[2]{1521 } = \sqrt[2]{c^{2} }[/tex]
Solve for "c" by simplifying the roots
[tex]\implies \sqrt[2]{39 \times 39 } = \sqrt[2]{c \times c }[/tex]
[tex]\implies \boxed{39 = c}[/tex]
Thus, the measure of the missing side length (c) is 39 units.
Rewrite 9 to the 3rd power divided by 9 to the 9th power using a single, positive exponent
Answer:
[tex] \dfrac{1}{9^6} [/tex]
Step-by-step explanation:
[tex] \dfrac{9^3}{9^9} = 9^{3 - 9} = 9^{-6} = \dfrac{1}{9^6} [/tex]
Mrs. Murray wants to hang lights around the edge of the ceiling. The ceiling measures 14.5 feet by 9.6 feet. What is the perimeter, in feet, of Mrs. Murray's ceiling?
What is the perimeter of the ceiling in inches.
Answer:
48.2 feet
or
578.4 inches
Step-by-step explanation:
Perimeter is the distance around the shape or in this case the room. Assuming the room is a rectangle you would have two walls of the same length totaling 4 walls.
To find the perimeter add up 14.5 + 14.5 + 9.6 + 9.6 = 48.2 feet
Since it askes for the answer in inches you have to convert from feet to inches by multiplying your answer by twelve.
Find the time required for an investment of 4,000 dollars to grow to 9,000 dollars at an interest rate
of 5% per year, compounded monthly. Give your answer accurate to 2 decimal places.
years.
Answer:
25 years
Step-by-step explanation:
Find the volume of a cylinder with a radius of 4 meters and a height of 13 meters. Use * 3.14
Find the volume of a cylinder with a radius of 4 meters and a height of 13 meters. Use * 3.14.
Solution:Given,
radius of the cylinder = 4 m
height of the cylinder = 13 m
To find: The volume of the cylinder (where pi = 3.14)
We know that volume of cylinder
[tex] \pi {r}^{2} h[/tex]
Now by using the formula = 3.14 × (4) × (4) × 13
= 3.14 × 208
= 653.12 m³
Hope it helps