How much would the investment be worth?
As the function for interest is already given to us, also,
The principal amount, P = $7,000
The rate of Interest, r = 3%
Time period, t = 5 years
Compounded semiannually, n = 2
Substitute the values,
Hence, the worth of the investment after 5 years at an interest of 3% is $8,123.79.
Answer:
Hello! Let's find the value of Janel's investment after 8 years. In the formula we're using, P will represent the principal amount, r will represent the rate of interest, and t will represent time. Since the interest is compounded semi-annually (twice a year), n = 2. Finally, A represents the value of the investment after t (8 years).
Substitute these values into the formula:
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
[tex]A = 7000(1+\frac{0.03}{2} )^{2*8}[/tex]
Simplify the equation:
[tex]A = 8882.89883357[/tex]
Round this number to the nearest hundredth:
[tex]A = 8882.90[/tex]
The correct answer is B. 8,882.90.
I hope this helps you! Have a great day. :)
Simplify this expression . With each step. please (x2 - x - 2)/(x2 + 5x + 4)
Answer:
I hope dis helps
Step-by-step explanation:
Simplify
x2 + 5x + 4
Trying to factor by splitting the middle term
1.1 Factoring x2 - x - 2
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -2
Step-1 : Multiply the coefficient of the first term by the constant 1 • -2 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -1 .
-2 + 1 = -1 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 1
x2 - 2x + 1x - 2
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-2)
Add up the last 2 terms, pulling out common factors :
1 • (x-2)
Step-5 : Add up the four terms of step 4 :
(x+1) • (x-2)
Which is the desired factorization
Trying to factor by splitting the middle term
1.2 Factoring x2+5x+4
The first term is, x2 its coefficient is 1 .
The middle term is, +5x its coefficient is 5 .
The last term, "the constant", is +4
Step-1 : Multiply the coefficient of the first term by the constant 1 • 4 = 4
Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is 5 .
-4 + -1 = -5
-2 + -2 = -4
-1 + -4 = -5
1 + 4 = 5 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 4
x2 + 1x + 4x + 4
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x+1)
Add up the last 2 terms, pulling out common factors :
4 • (x+1)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x+1)
Which is the desired factorization
Canceling Out :
1.3 Cancel out (x+1) which appears on both sides of the fraction line.
Final result :
x - 2
—————
x + 4
one-half the total of six times a number n and thirty-eight?
3n+19
Explanation:
(1/2)(6n + 38)
16) Find the value of x
Answer:
root 7
Step-by-step explanation:
apply tan60=p/b=root 21/ x
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]
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.
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:
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)
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
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.
find the derivative pls !!
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.
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:
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:
Multiplicaciones que den 35
Answer:
Estos pares de factores son (1, 35) y (5, 7).
espero que esto ayude.
➡ (1,35)
➡ (5,7)
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:
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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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
What is the distance between (2, 6) and (7, 6)?
8
(2,3)
+17,6)
4
2
What is the length of the hypotenuse of the triangle below?
45
h
45°
5√2
90⁰
5√2
Answer:
10
Step-by-step explanation:
find the square root of the sum of the squares
The length of the hypotenuse for the given right angled triangle is 10 units.
What is a Pythagoras theorem?Pythagoras theorem states that the square of the hypotenuse is equivalent to the square of the base and perpendicular.
We can write the formula for Pythagoras theorem as -
(hypotenuse)² = (base)² + (perpendicular)²
Given is to find the length of the hypotenuse in the right angled triangle shown.
Using the Pythagoras theorem, we can write that -
(hypotenuse)² = (base)² + (perpendicular)²
(hypotenuse)² = (5√2)² + (5√2)²
(hypotenuse)² = 2 x (5√2)²
(hypotenuse)² = 2 x 25 x 2
(hypotenuse)² = 100
(hypotenuse) = 10
Therefore, the length of the hypotenuse for the given right angled triangle is 10 units.
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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
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
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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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
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 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
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
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]
Describe a set of transformations that would map Triangle FGH onto Triangle F’G’H’
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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