The formula that calculates the compound rate from the given values is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
How to determine the compound interest rate?The compound interest formula is:
[tex]I = P(1 + \frac rn)^{nt} - P[/tex]
Where:
P represents the principal amountr represents the compound interest raten represents the number of times the interest is compoundedt represents the time in yearsI represents the interestWe start by adding P to both sides
[tex]P + I = P(1 + \frac rn)^{nt}[/tex]
Divide through by P
[tex]\frac{P + I}{P} = (1 + \frac rn)^{nt}[/tex]
Take the nt-th root of both sides
[tex]\sqrt[nt]{\frac{P + I}{P}} = 1 + \frac rn[/tex]
Subtract 1 from both sides
[tex]-1 + \sqrt[nt]{\frac{P + I}{P}} = \frac rn[/tex]
Multiply through by n
[tex]r = n(-1 + \sqrt[nt]{\frac{P + I}{P}})[/tex]
In this case, t = 10
So, we have:
[tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
Hence, the formula that calculates the compound rate is [tex]r = n(-1 + \sqrt[10n]{\frac{P + I}{P}})[/tex]
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If cos(x)=-4/5 in quadrant II then determine the following sin(x/2),cos(x/2),tan(x/2)
Answer:
[tex]sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]
Step-by-step explanation:
angles in II quadrant are found by solvig 180- ∅ where ∅ is the acute angle
Let us then find the acute angle: in[tex]cos^{-} (\frac{4}{5}) = 36.86^{0} \\\\so \ x \ the \ angle \ in \ the \ second \ quadrant \ is \ 180-36.86=143.13^{0} \\\\sin(\frac{143.13}{2} )=0.9487\\\\cos(\frac{143.13}{2} )=0.3162\\\\tan(\frac{143.13}{2} )=2.9999=3\\[/tex]
9. If f(x)=x². g(x)=2x-1. and h(x) =find the following.
Answer:
Please see the attached picture ! :D
-------- HappY LearninG <3 ----------
this is my last question i swear pls help
Answer:
To find a
sin 30=a/6in
1/2=a/6in
2a=6in
a=6in/2
a=3in
To find b
cos 30=b/6in
/3/2=b/6in
2b=/3*6in
b=2/3(two radical three)
I don't get the radical sign so I use / sign on the last 3 steps on the second
The area of the top of a square table
is 269 in2. What are the dimensions
of the top?
Answer:
[tex]\sqrt{269}[/tex] is ≈ 14.01
Step-by-step explanation:
If the table top is a square, to find the area, you would multiply one side times itself.
If you are given the area, and need to find the sides, you will take the square root of the area to find the side length.
Your question doesn't say to round, but 269 is not a perfect square.
[tex]\sqrt{269}[/tex] is ≈ 14.01
If the area of the base was 169, that is a perfect square. [tex]\sqrt{169}[/tex] = 13
Drag the tiles to the correct boxes to complete the pairs.
Sam works as a baggage carrier at an airport facility. He owes a certain amount of money, in dollars, to his friend Daniel. The function y = 12x − 40 represents the amount of money that Sam has after paying Daniel back in terms of the number of hours he works at the airport.
Match the values and variables to the aspects of the situation they represent.
x-variable
y-variable
12
40
the amount in dollars that Sam owes Daniel
arrowRight
the number of hours Sam works at the airport
arrowRight
the amount in dollars that Sam has after paying back Daniel
arrowRight
the amount in dollars that Sam earns per hour
arrowRight
The values have being matched to the variables that they represent here:
x-variable: the number of hours Sam works at the airporty variable: the amount in dollars that Sam has after paying back Daniel12: amount in dollars that Sam earns per hour.40: the amount in dollars Sam owes DanielHow to solve for the equation.The equation of this form y = 12x-40
The variable y has been said to be the amount sam has after Daniel has been paid.
X is the amount that has to be multiplied by what he earns in dollars by the hour.
40 dollars is the amount that he owes which is going to be subtracted from what he earns by the hour.
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The length of a rectangle is 3 meters and the width is 14 meters. What is the perimeter of the rectangle? Do not include units in your answer.
Which numbers should replace the question marks?
The first missing number in the sequence is 35, and the last missing number is 77.
Next number of the given sequenceThe two missing numbers in the given sequence is calculated as follows;
= ? 49 63 ?
The given sequence is factor 7 which increases by 2
= 7 x 5 7 x 7 7 x 9 7 x 11
= 35 49 63 77
Thus, the first missing number in the sequence is 35, and the last missing number is 77.
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The sequence's initial missing number is 35, and its last missing number is 77.
The following number in the list is
The two missing numbers are determined as follows for the given sequence:
= ? 49 63 ?
The sequence is factor 7, which rises by 2 in the specified order.
= 7 x 5 7 x 7 7 x 9 7 x 11
= 35 49 63 77
Thus, the first missing number in the sequence is 35, and the last missing number is 77.
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How many Squares are there ?
Answer:
6
Step-by-step explanation:
most of them are rectangles
Simplify using trigonometric identities
2sinθ - sin2θ cosθ
Double angle identity for sine:
[tex]\sin(2x) = 2 \sin(x) \cos(x)[/tex]
[tex]\implies 2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta)[/tex]
Factorize the left side.
[tex]2 \sin(\theta) - 2 \sin(\theta) \cos^2(\theta) = 2 \sin(\theta) \left(1 - \cos^2(\theta)\right)[/tex]
Pythagorean identity:
[tex]\cos^2(x) + \sin^2(x) = 1[/tex]
[tex]\implies 2 \sin(\theta) \left(1 - \cos^2(\theta)\right) = 2 \sin^3(\theta)[/tex]
so that
[tex]\boxed{2 \sin(\theta) - \sin(2\theta) \cos(\theta) = 2 \sin^3(\theta)}[/tex]
The arithmetic-geometric mean (AM-GM) inequality: if a,b ≥ 0, then [tex]\frac{a+b}{2} \geq \sqrt{ab}[/tex]. (1)
(a) Let a, b, c, d ≥ 0 and consider the positive real numbers [tex]\sqrt{ab} [/tex] and [tex]\sqrt{cd} [/tex]. Use (1) to prove the four-variable AM-GM inequality:
[tex]\frac{a+b+c+d}{4} \geq \sqrt[4]{abcd}[/tex]. (2)
(b) Let a, b, c ≥ 0 and define [tex]m= \frac{a+b+c}{3}[/tex].
(i) Show that [tex]m=\frac{a+b+c+m}{4}[/tex].
(ii) Hence use (2) to prove the three-variable AM-GM inequality:
[tex]\frac{a+b+c}{3} \geq \sqrt[3]{abc}[/tex].
(a) The inequality follows from the binomial theorem.
[tex](a - b)^2 = a^2 - 2ab + b^2 \ge 0 \implies a^2 + 2ab + b^2 = (a+b)^2 \ge 4ab \\\\ \implies \dfrac{(a+b)^2}4 \ge ab \\\\ \implies \dfrac{a+b}2 \ge \sqrt{ab} ~~~~~~~~ (1)[/tex]
By the same reasoning,
[tex]\dfrac{c+d}2 \ge \sqrt{cd}[/tex]
Adding these results together, we have
[tex]\dfrac{a+b}2 + \dfrac{c+d}2 = \dfrac{a+b+c+d}2 \ge \sqrt{ab} + \sqrt{cd}[/tex]
and since [tex]\sqrt{ab}[/tex] and [tex]\sqrt{cd}[/tex] are both positive, they also satisfy the AM-GM inequality,
[tex]\dfrac{\sqrt{ab} + \sqrt{cd}}2 \ge \sqrt{\sqrt{ab}\times\sqrt{cd}} = \sqrt[4]{abcd}[/tex]
and the 4-variable result follows,
[tex]\dfrac{a+b+c+d}2 \ge 2\times\dfrac{\sqrt{ab}+\sqrt{cd}}2 \ge 2 \sqrt[4]{abcd} \\\\ \implies \dfrac{a+b+c+d}4 \ge \sqrt[4]{abcd} ~~~~~~~~ (2)[/tex]
(b.i) With [tex]m=\frac{a+b+c}3[/tex], we have
[tex]\dfrac{3m}4 = \dfrac{a+b+c}4 \implies m - \dfrac m4 = \dfrac{a+b+c}4 \\\\ \implies m = \dfrac{a+b+c+m}4[/tex]
(b.ii) From (2) it follows that
[tex]\dfrac{a+b+c+m}4 \ge \sqrt[4]{abcm} = \sqrt[4]{abc\times\dfrac{a+b+c+m}4}[/tex]
Using the result from (b.i), this is equivalent to
[tex]\dfrac{a+b+c}3 \ge \sqrt[4]{abc\times\dfrac{a+b+c}3}[/tex]
Take 4th powers on both sides.
[tex]\left(\dfrac{a+b+c}3\right)^4 \ge abc \times \dfrac{a+b+c}3[/tex]
Divide both sides by [tex]\frac{a+b+c}3[/tex].
[tex]\left(\dfrac{a+b+c}3\right)^3 \ge abc[/tex]
Finally, take the cube root of both sides.
[tex]\dfrac{a+b+c}3 \ge \sqrt[3]{abc}[/tex]
as required.
I need help with question 30 please! :)
Answer:
B ∩ (¬A ∩ ¬C)
Step-by-step explanation:
You want to exclude the section C shares with A, the one C shares with B and the one it shares with both. Intersecting ¬A (not A) with ¬C (not C) you obtain the entire area except A and C, which then can be intersected with B to obtain the highlighted area.
Explain how to solve a system of equations using the addition method. Use 3x - 4y=12 and 2x+y=8 to illustrate.
The solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
We have two equations:
3x - 4y=12 and
2x+y=8
Multiplu by 4 on both side in equation 2x+y=8
8x + 4y = 32
Add the equaton 8x + 4y = 32 and 3x - 4y=12
3x - 4y=12
8x + 4y = 32
11x = 44
x = 4
Similarly, we can find the value of y:
y = 0
Thus, the solution to the equations 3x - 4y=12 and 2x+y=8 are x = 4 and y = 0
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find x and y !!!!!!! pls help 50 points !!
Answer:
x = 15
y = 60
Step-by-step explanation:
Angles (x + 50) and (3x + 20) follows corresponding angle theorem.
corresponding angles are equal to each other.-----
⇒ x + 50 = 3x + 20
⇒ x - 3x = 20 - 50
⇒ -2x = -30
⇒ x = 15
The angles (x + 50) and (2y - 5) lies on a straight line which sum ups to 180°
⇒ (x + 50) + (2y - 5) = 180
⇒ 2y + x + 45 = 180
⇒ 2y + 15 + 45 = 180
⇒ 2y + 60 = 180
⇒ 2y = 120
⇒ y = 60
HELP ASAP the proportion a is to b as w is to x can correctly be expressed as
Answer:
a is to b,
a : b
w is to x,
w : x
a is to b as w is to x,
a : b : : w : x
In fraction form,
a/b = w/x
When half of 3,926 is added to a quarter of 1,924
Answer:
2444
Step-by-step explanation:
A half of 3916 is 1963.
A quarter of 1924 is 481.
Therefore, 1963 + 481 = 2444.
Jesse wants to gift wrap a cylindrical pencil case that has a radius of 1.5 inches and a height of 8 inches. What is the area of the paper she will need to cover the entire surface?
Answer:
Jesse will need about 89.5 square inches of gift wrap.
Step-by-step explanation:
We need to find the amount of wrapping paper that will cover the entire outside surface of the cylindrical gift. This means that we need to find its surface area, which is the total area an object's surface occupies.
The formula for cylinder surface area is as follows:
[tex]A=2\pi rh+2\pi r^{2}[/tex] (where r = radius and h = height)
In this case, the radius, or r, is 1.5 in, and the height, or h, is 8 in. Plugging these values into our formula, we get a total surface area of:
[tex]A=2\pi rh+2\pi r^{2}\\= 2\pi *1.5*8+2\pi * 1.5^{2} \\= 24\pi +4.5\pi \\=28.5\pi \\ \approx \text{\bf 89.5 \bf $in^{2}$ }[/tex]
Hope this helps!
Answer:
28.5 pi square inches
Step-by-step explanation:
The surface area of a cylinder is the lateral area plus two times the area of the base circle. The lateral area is the perimeter of the base circle times the height, and the perimeter of a circle is 2*pi*r.
Therefore the lateral area is:
LA = Perimeter*Height
= 2*pi*r*h
= 2*pi*1.5*8
= 24pi
The base area would be A = pi*r*r since the bases of cylinders are circles.
BA = pi*r*r
= pi*1.5*1.5
= 2.25 pi
Since there are two circles (top AND bottom) in a cylinder, the final surface area of the cylinder would be:
SA = LA + 2BA
= 24pi + 2*2.25pi
= 24pi + 4.5pi
= 28.5 pi
f= 2/T + 5 solve for t
Answer: [tex]T=\frac{2}{F-5}[/tex]
Step-by-step explanation:
[tex]F=\frac{2}{T}+5\\\\F-5=\frac{2}{T}\\\\\frac{1}{F-5}=\frac{T}{2}\\\\T=\frac{2}{F-5}[/tex]
What linear function represents the sequence 8,3,-2,-7
• What sorts of follow up questions about the statistics might you ask that person in order to obtain the
data needed to make a decision about the validity of that statement? Be sure to use concepts and
vocabulary from this week to guide your response.
The type of follow-up questions that can be asked to obtain the data needed to make a decision about the validity of that statement are:
How was the data obtained?Was the experiment controlled?How large were the control group and the placebo group?Was it a blind/double-blind test?Were extreme outliers removed from the data before running the experiment?What are Follow-Up Questions?This refers to the type of questions that are asked to a person in order to get extra information about a topic.
Hence, we can see that from the complete question, there is the need to perform tests to get results which would involve the procurement of data, controlled experiments, etc, and the follow-up questions that can be used are given above.
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The circle below is centered at the point (-3, 4) and has a radius of length 3.
What is its equation?
A. (x- 4)2 + (y + 3)2 =
32
0
B. (x + 4)2 + (y- 3)2 =
32
T c. (x- 3)2 + (y + 4)2 = 9
O D. (x+ 3)2 + (y- 4)2 = 9
Answer: [tex](x+3)^2 + (y-4)^2 = 9[/tex]
Step-by-step explanation:
See attached image, this is straight formula substitution.
the entire school went 250 students went to the soap box derby the math club went in 2 busses each holding 6 students
The number of students from the math club that went to the soap box derby.
How to solve algebra word problems?From the question, we see that there are two vans and 6 students in each van.
Thus, to get the number of students from the math club that went to the soap box derby, we will solve as follows;
Number of students that went to derby = 2 × 6 = 12
Complete question is;
The entire school 250 students went to the soap box derby. The math club went in 2 vans and each van held 6 students how many students from the math club went to the soap box derby
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2. The graph shows the vertical displacement y, in centimeters, that a weight bouncing from a spring would achieve if there were no friction, for a given number of seconds, x
(a) What is the weight’s maximum displacement?
(b) From its resting position, how long does it take the weight to bounce one direction, then the other, and then return to its resting position?
(c) What is the graph’s frequency and what does it indicate in this situation?
(d) How is the weight moving during the time period x = 6 to x = 7.5?
(a) The maximum displacement of the wave is 14 cm.
(b) The time for the wave to bounce opposite directions before coming to rest is 3.0 s.
(c) The period of the wave is 3.0 s and the amplitude is 14 cm.
(d) The graph’s frequency is 0.33 Hz
(e) The wave attained maximum displacement at time 6 s and 7.5 s.
How to Interpret period of a wave?A) The maximum displacement of the wave is the point of maximum rise of the curve = 14 cm
B) Time of motion of the wave; This is the time for the wave to bounce opposite directions before coming to rest makes a complete cycle
It takes the wave 0.75s to bounce up and the 2.25 s to bounce down, and finally it came to rest at 3.0 s.
C) The period of the wave is the time taken for the wave to make a complete cycle = 3 s
Frequency of the wave
f = 1/T
f = 1/3 = 0.33 Hz
The frequency indicates the number of cycles in a second.
D) Position of the wave at time 6 s and 7.5 s
The wave attained maximum displacement at time 6 s and 7.5 s.
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Given a normally distributed data set with the mean = 88 and the standard deviation = 6, according to the empirical rule, what percent of the data points are below 100?
According to the empirical rule, the percent of the data points that are below 100 is; 95.44%
How to use Empirical Rule in Statistics?We are given;
Mean; μ = 88
Standard deviation; σ = 6
Sample mean; x' = 100
Formula for z-score is;
z = (x' - μ)/σ
z = (100 - 88)/6
z = 2
Now, from the empirical rule of normal distribution graph attached, we see that at z = 2, the percentage is 95.44%. However, we want to find the percentage that lie below 100. Thus, this is 95.44%
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(f) 3x+0.25x+0.10(2x)+0.05 (x+3)=24.65
Answer:
x=7
Step-by-step explanation:
3x + 0,25x + 0,10 (2x) +0,05 (x + 3) = 24,65
<=> 3x+0,25x+0,2x+0,05x+0,15=24,65
<=> 3,5x=24,5
<=> x=7
2. Anthropological perspectives on racial types and human physical variation. Besides, discuss the history of racial types and Anthropologists conclusion about human race.
In ancient civilization, the individuals with varying physical appearance were fill member of the society by adopting the cultural norms.
What is physical variation?It should be noted that the physical variation means the range of values for the mental and physical characteristics of human beings.
Classical variations invested the most importance in tribal affiliation rather than the physical appearance.
Also, societies still equate physical characteristics like eye and hair color.
Anthropologists conclusion about human race is that there are no human biological races.
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What is the product of the polynomials below?
(5x²-x-3)(2x+6)
OA. 10x² +28x² +12x+3
OB. 10x³ +28x2² -12x-18
OC. 10x²+28x²-12x-3
OD. 10x² +28x² + 12x+18
Answer: B
Step-by-step explanation:
[tex](5x^2 -x-3)(2x+6)\\\\=2x(5x^2 - x-3)+6(5x^2 - x-3)\\\\=10x^3 - 2x^2 - 6x+30x^2 - 6x-18\\\\=\boxed{10x^3 +28x^2 - 12x-18}[/tex]
i’m confused on whether its 12 or 18, pls help
Answer:
Notice that the triangles ABC and AMN are similar.
Thus:
[tex]\frac{AC}{MN} = \frac{AB}{MB}\\\\\frac{AC}{6} = \frac{8}{4} = 2\\\\ AC = 12\,\,ft.[/tex]
Leigh earned the following score from the judges for her balance bean routine. 9.20 9.30 9.20 9.30 9.20 9.00. Q2 cross off the lower score and the highest score
Answer: I am not so sure but I think it’s asking for the median so that would be ANSWER 9.2
Step-by-step explanation:
What is the equation of the graph that represents the parent function f(x)= x^4 stretched vertically by a factor of 2, then shifted down 3 spaces
The equation of the function is f"(x) = 2x^2 - 3
How to determine the equation?The parent function is given as:
f(x) = x^4
When it is stretched vertically by a factor of 2, the rule is
f'(x) = 2f(x)
So, we have
f'(x) = 2x^2
When shifted down 3 spaces, the rule is
f"(x) = f'(x) - 3
So, we have:
f"(x) = 2x^2 - 3
Hence, the equation of the function is f"(x) = 2x^2 - 3
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Linear model function
Using equations of linear model function, the number of hours Jeremy wants to skate is calculated as 3.
How to Write the Equation of a Linear Model Function?The equation that can represent a linear model function is, y = mx + b, where m is the unit rate and b is the initial value.
Equation for Rink A:
Unit rate (m) = (35 - 19)/(5 - 1) = 16/4 = 4
Substitute (x, y) = (1, 19) and m = 4 into y = mx + b to find b:
19 = 4(1) + b
19 - 4 = b
b = 15
Substitute m = 4 and b = 15 into y = mx + b:
y = 4x + 15 [equation for Rink A]
Equation for Rink B:
Unit rate (m) = (39 - 15)/(5 - 1) = 24/4 = 6
Substitute (x, y) = (1, 15) and m = 6 into y = mx + b to find b:
15 = 6(1) + b
15 - 6 = b
b = 9
Substitute m = 6 and b = 9 into y = mx + b:
y = 6x + 9 [equation for Rink B]
To find how many hours (x) both would cost the same (y), make both equation equal to each other
4x + 15 = 6x + 9
4x - 6x = -15 + 9
-2x = -6
x = 3
The hours Jeremy wants to skate is 3.
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