Answer:
$15,539.67
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P\left(1+\frac{r}{n}\right)^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = $11,000r = 5.8% = 0.058n = 4 (quarterly)t = 6 yearsSubstitute the given values into the formula and solve for A:
[tex]\implies \sf A=11000\left(1+\frac{0.058}{4}\right)^{(4 \times 6)}[/tex]
[tex]\implies \sf A=11000(1.0145)^{24}[/tex]
[tex]\implies \sf A=15539.67451...[/tex]
Therefore, the value of the investment after 6 years will be $15,539.67 to the nearest cent.
Approximate the area under the curve y = x^2 from x = 0 to x = 3 using a Right Endpoint approximation with 6 subdivisions.
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Subdivide the interval [0, 3] into 6 subintervals of equal length, ∆x = (3 - 0)/6 = 1/2. Then the partition is
[tex]\left[0,\dfrac12\right] \cup \left[\dfrac12,1\right] \cup \left[1,\dfrac32\right] \cup \cdots \cup \left[\dfrac52,3\right][/tex]
The right endpoint of the [tex]i[/tex]-th subinterval is
[tex]r_i = \dfrac12 + (i-1)\times\dfrac12 = \dfrac i2[/tex]
with [tex]i\in\{1,2,3,\ldots,6\}[/tex].
Then the area under the [tex]y=x^2[/tex] on the interval [0, 3] is approximately
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \sum_{i=1}^6 (r_i)^2 \Delta x = \frac18 \sum_{i=1}^6 i^2[/tex]
Recall that
[tex]\displaystyle \sum_{n=1}^N n^2 = \frac{N(N+1)(2N+1)}6[/tex]
Then the approximate value of the area is
[tex]\displaystyle \int_0^3 x^2 \, dx \approx \frac{6\times7\times13}{48} = \boxed{\frac{91}8}[/tex]
The actual value of the area is 9, so this approximation is an overestimation, as is always the case when using a right endpoint sum for an increasing function.
At a pizza restaurant it costs $4 to make a small pizza that sells for $12, and it costs $6 to make a large pizza that
sells for $15. In one week, the restaurant spent a total of $1100 to make pizzas and sold all of them for $2910. How
many small pizzas were sold?
small pizzas were sold?
someone help me with rest please asap!!
Answer:
3. Definition of Midpoint
4. VAT, Vertical Angles Theorem
5. ASA, Angle-Side-Angle Theorem
Hi 4 questions, about inequality’s and y intercepts and slope. Only 4 questions :)
The slope and y-intercept will be the negative 5/2 and 4.
The complete question is attached below.
What is the equation of line?The equation of line is given as
y = mx + c
Where m is the slope and c is the y-intercept.
The equation is given below.
y > -(5/2)x + 4
The slope and y-intercept will be the negative 5/2 and 4.
The graph is also attached below.
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Just a question about the problem, dont need the answer if you dont want to solve it, but would 15 be negative? Thats all, Thanks!
[tex]f(x)=x^{2} +15x+3[/tex]
Answer:
[tex]x = -\frac{15}{2}[/tex]
Step-by-step explanation:
Hello!
The formula for the AOS is given to you, and you simply have to plug in the information given by the equation.
Equation of a Parabola (Standard): [tex]y = ax^2 + bx + c[/tex]
Comparing it to our equation:
a = 1b = 15c = 3Plug it in to the AOS formula:
[tex]x = \frac{-b}{2a}[/tex][tex]x = \frac{-15}{2(1)}[/tex][tex]x = -\frac{15}{2}[/tex]You only have to input 15 in to the correct box since the negative sign is already placed for you.
HELP THIS IS URGENT I NEED IT SOON! PLEASE
If f(x) = x2 − 6x − 4 and g(x) = 5x + 3, what is (f + g)(−3)?
41
35
11
−35
Answer:
11
Step-by-step explanation:
(f + g)(x)
= f(x) + g(x)
= x² - 6x - 4 +5x + 3 ← collect like terms
= x² - x - 1
then
(f + g)(- 3) = (- 3)² - (- 3) - 1 = 9 + 3 - 1 = 11
Answer:
11
Step-by-step explanation:
F(–3)=(–3)²–6(–3)–4===> 9+18–4=23
g(–3)=5(–3)+3=‐15+3=–12
23–12=11
(basic algebra) please help me with question:
Please help i dont get this at all so please i will highly appreciate it .Thank youuu!!!
Answer:
2nd box, 4th box and 5th box
Step-by-step explanation:
An oatmeal container has a volume of 269 cubic inches. If the radius of the container is 3 cm, which statement below describes how to calculate the height?
The height of the volume of the container is 93.898cm.
We have given that,
An oatmeal container has a volume of 269 cubic inches.
Volume=269 cubic inches.
Radius=3cm
What is the formula for volume?
[tex]V=\pi r^2h[/tex]
[tex]269=\pi (3)^2h\\\269=9\pi h\\\h=\frac{269\pi }{9}\h=93.89871[/tex]
The height of the volume of the container is 93.898cm.
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It takes 405 bricks to build 1 wall of a room. If there are 5 rooms (with 4 walls each), how many bricks will be needed to build all the walls?
Answer:
Bricks for 1 wall= 405
If there are 5 rooms with 4 walls,
Walls= 5 x 4= 20
Bricks= 405 x 20
= 8100
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Which equation best describes this line?
Find the range of the given function y = 3x + 2 for the domain 4 and -4.
Answer:
Range: (-10 , 14)
Step-by-step explanation:
Given information:
Equation: y = 3x +2Domain: (-4 , 4)Range: (x , y)?
Plug in domain of x = -4 and x = 4 into equation to find range.
f(-4) = 3 * -4 + 2 = -10
f(4) = 12 + 2 = 14
Range: (-10 , 14)
!!!! PLEASE HELP !!!!
The senior classes at High School A and High School B planned separate trips to
New York City. The senior class at High School A rented and filled 4 vans and 3
buses with 133 students. High School B rented and filled 9 vans and 1 bus with 167
students. Each van and each bus carried the same number of students. How
many students can a van carry? How many students can a bus carry
A) Van: 23, Bus: 16
C) Van: 6, Bus: 34
B) Van: 25, Bus: 36
D) Van: 16, Bus: 23
Which expression is equivalent to |8|+|-7|
Answer:
8 + 7.
Step-by-step explanation: It is absolute value.
m∠a=(48−x)°m∠b=(9x−38)°m∠c=90°
Answer:
Option C:
m∠a = 38°m∠b = 52°m∠c = 90°Step-by-step explanation:
Hello!
The sum of all angles in a triangle is 180°.
Add up all the angles and solve for x by setting the equation to 180°.
Solve for x∠a + ∠b + ∠c = 180°(48 - x)° + (9x - 38)° + 90° = 180°10° + 8x + 90° = 180°8x = 180° - 90° - 10°8x = 80°x = 10°Now that we solved for x, we can plug it back into each equation to solve for each angle.
Angle A48° - x48° - 10°38°Angle B9x - 38°9(10°) - 38°90° - 38°52°Angle C90°The answer is Option C:
m∠a = 38°m∠b = 52°m∠c = 90°Please help!!!!! ASAP, If you can, i would love the steps on how to do it!! Thanks
Answer:
(5,18) & (-5 , 38)
Step-by-step explanation:
Solutions of linear and quadratic system of equations:A linear equation represented by a line in a graph intersect the quadratic equation represented by a parabola zero, one or two times.
f(x) = x² - 2x + 3 -------------------(I)
f(x) = -2x + 28 ---------------------(II)
x² - 2x + 3 = -2x + 28
x² - 2x + 2x + 3 - 28 = 0
x² - 25 = 0
x² = 25
x = √25 = √5*5
x = ± 5
Plugin x = 5 in equation (II),
f(5) = -2*5 + 28
= -10 + 28
= 18
(5 , 18)
Plugin x = -5 in equation (II),
f(-5) = -2*(-5) + 28
= 10 + 28
= 38
(-5, 38)
Answer:
(5, 18) and (-5, 38)
Step-by-step explanation:
Given system of equations:
1) f(x) = x² - 2x + 3 ⇒ y = x² - 2x + 3
2) f(x) = -2x + 28 ⇒ y = -2x + 28
Solve using the Substitution Method:
Step 1: Substitute the the first equation into the second equation.
⇒ x² - 2x + 3 = -2x + 28
Step 2: Solve for x.
x² - 2x + 3 = -2x + 28 [ Add 2x to both sides. ]
x² - 2x + 2x + 3 = -2x + 2x + 28
⇒ x² + 3 = 28 [ Subtract 28 from both sides. ]
x² + 3 - 28 = 28 - 28
⇒ x² - 25 = 0 [ Factor using the following rule: a² - b² = (a - b)(a + b). ]
(x - 5)(x + 5) = 0
⇒ x - 5 = 0, x + 5 = 0 [ Solve for the values of x. ]
x - 5 + 5 = 0 + 5, x + 5 - 5 = 0 - 5
⇒ x = 5, x = -5
Step 3: Solve for y.
Substitute the found x-values into one of the given equations.
y = x² - 2x + 3 ⇒ y = (5)² - 2(5) + 3 ⇒ y = 25 - 10 + 3 ⇒ y = 18
y = x² - 2x + 3 ⇒ y = (-5)² - 2(-5) + 3 ⇒ y = 25 + 10 + 3 ⇒ y = 38
The solutions to the system of equations are:
⟹ x₁ = 5, y₁ = 18 ⇒ (5, 18)
⟹ x₂ = -5, y₂ = 38 ⇒ (-5, 38)
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If L (-5,4),M(2,2), N(0,-3), S(-7,-1), what is the length of diagonal LN
The length of the diagonal LN would be 8.60 units.
To find the distance between the two coordinates, We use distance formula ;
[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2-y_1)^2}[/tex]
Lets put the values of L and N,
d= [tex]\sqrt{(0 - -5)^2 + (-3-4)^2}[/tex]
d =[tex]\sqrt{25+49}[/tex]
d= [tex]\sqrt{74}[/tex]
d= 8.60 units
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x varies directly as y. Find x when y=12 and k=6
72
x varies directly as y
hence x=k y
k=6
y=12
x=6×12
x=72
The sum of the series: -2+(-8) + (-32)++ (-2048) equals
I really neeed help!!! Please I’m begging you!!!!!!
Answer:
-2090
Step-by-step explanation:
1) Remove parentheses.
-2 -8 -32 -2048
2) Simplify - 2 - 8 to -10.
-10 - 32 - 2048
3) Simplify -10-32 to -42.
-42 - 2048
4) Simplify.
-2090
Please help answer this question asap 2/11
The correct answer is option A which is the value a₃₂ = 7.
What is the matrix?A matrix is a specific arrangement of items, particularly numbers. A matrix is a row-and-column mathematical structure. The a_{ij} element in a matrix, such as M, refers to the i-th row and j-th column element.
In the given matrix the value of a₃₂ means that the element of the third row and the second column.
So the value of a₃₂ will be 7. which is present in the third row and the second column.
Therefore the correct answer is option A which is the value a₃₂ = 7.
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If the proportion of the total disposable income spent on consumer goods and services is 93 percent and if
consumers spend 85 percent of each additional dollar, what is
a. the apc?
b. the aps?
c. the mpc?
d. the mps?
Answer:
what?????????????????
What is the degree of polynomial: 2x- root 5
Answer: 1
Step-by-step explanation:
[tex]2x-\sqrt{5}=2x^{1}-\sqrt{5}[/tex], and thus the highest exponent of x is 1
Which linear function has the steepest slope?
Answer:
[tex]y=-8x+5[/tex]
Slope-intercept form:
[tex]\implies y=mx+b[/tex] [tex](\text{m=slope};\text{b=y-intercept})[/tex]
Using the slope-intercept form, let's identify the other slopes:
Option A:
[tex]y=-8x+5[/tex]
[tex]\text{slope}=-8[/tex]
Option B:
[tex]y-9=-2(x+1)[/tex] (This equation is in point-slope form, the slope it too the left, making it -9)
[tex]\text{slope}=-9[/tex]
Option C:
[tex]y=7x-3[/tex]
[tex]\text{slope}=7[/tex]
Option D:
[tex]y+2=6(x+10)[/tex]
[tex]\text{slope}=2[/tex] (Using point-slope terms, we can find the slope.)
⇒ A 'steep'est slope is closest to almost having a vertical slope or pitch, or relatively high gradient, as a hill, an ascent, stairs, etc.
[tex]\text{This could be a line }[/tex] ⇒ ([tex]\text{positive or negative}[/tex])
Hence, the linear function with the steepest slope is Option A: [tex]y=-8x+5[/tex].
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8+6=?
what is the answer to the question
Answer: 14
Step-by-step explanation:
because 8 +4 is 14
y = 7x (6/7,-1/4) ….
Answer:
This point is not on the line, NOT TRUE
Step-by-step explanation:
The equation of the line is written in the slope-intercept form,
y = mx + b
where m represents the slope
b represents the y-intercept
where the format of a point is (x, y)
Given: y = 7x (6/7, -1/4)
we can plug in the point (6/7, -1/4)
-1/4 = 7(6/7)
-1/4 = 6
-1/4 does not equal 6 so this point is not on the line
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A website sells a dress at £20 and shoes at £25. The website has an offer: Buy a dress and shoes together and get 1 3 off the price. There is also a shipping and handling charge of £4 added at the end, after any discount. If Ruth buys both a dress and shoes, how much will she actually pay?
£36
20+25=45 Take away 13 and it's 32. 32+4 (the shipping charge) is 36. So Ruth pays 36 pounds.
please solve and tell me all that apply
Answer:
-x+4, 4+-x
Step-by-step explanation:
Obtain these answers by moving the X and 4 around and multiplying the equation by -1
dentify the method that will be used in solving for x.
5 + x = three-fourths
distributive property
multiplication property of equality
division property of equality
subtraction property of equality
Answer:
I believe you're trying to say 5+x= 3/4
please help me please
Answer:
b I think.
Step-by-step explanation:
sorry if im wrong
several people are sitting evenly spaced around a circular table and the positions are labelled 1, 2 ,3 and so on .The people at positions 3 and 15 are directly opposite each other how many people are sitting at the table
12 will be opposite to 24. Then the number of the people are sitting at the table will be 24.
What is Algebra?The analysis of mathematical representations is algebra, and the handling of those symbols is logic.
The several people are sitting evenly spaced around a circular table and the positions are labelled 1, 2, 3 and so on.
The people at positions 3 and 15 are directly opposite each other.
Then the number of the people are sitting at the table will be
1 is opposite to 13
2 is opposite to 14
3 is opposite to 15
Similarly, 12 will be opposite to 24.
Then the number of the people are sitting at the table will be 24.
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