Answer:
Lucy needs to invest $55,194.16
Step-by-step explanation:
The given information are;
The interest rate of the account = 7% compounded daily
The amount at the end of 6 years = $84,000
The time duration = 6 years
The amount Lucy
The formula for compound interest is
[tex]A(t) = P \times \left ( 1 + \dfrac{r}{n} \right )^{n \times t}[/tex]
Where;
r = The interest rate = 7% = 0.07
n = The number of times a year = 365
t = The number years = 6 years
A(t) = The amount after 6 years = $84,000
P = The initial amount invested
Therefore, we have;
[tex]\$ 84,000 = P \times \left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}[/tex]
[tex]P = \dfrac{\$84,000}{\left ( 1 + \dfrac{0.07}{365} \right )^{365 \times 6}} =\dfrac{\$84,000}{1.522} = \$55,194.16[/tex]
Therefore, Lucy needs to invest $55,194.16.
In a particular year, a total 44,064 of students studied in two of the most popular host countries when traveling abroad. If 8382 more students studied in the most popular host country than in the second most popular host country, find how many students studied abroad in each country. There were ____ students who studied abroad in the most popular host country.
Step-by-step explanation:
Total=44,064
Host countries= 2
2nd most popular country= x
Popular country=x+8382
x+x+8,382=44,064
2x=44,064-8,382=35,682
2x=35,682
x=17,842
2nd most popular=17,842
Popular=17,842+8,382=26,224
Answer=26,224
There were students who studied abroad in the most popular host country by forming the equation is 26,224
How equations are formed?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions printed on the left and right sides. We have LHS = RHS (left-hand side = right-hand side) in every mathematical equation. To determine the value of an unknown variable that represents an unknown quantity, equations can be solved. A statement is not an equation if it has no "equal to" sign. It will be regarded as a phrase.
Here, It is given:
Total number of students = 44,064
Number of Host countries= 2
Let the 2nd most popular country= x
So, the Popular country becomes x+8382
Now, According to the question:
⇒x+x+8,382=44,064
⇒2x=44,064-8,382=35,682
⇒2x=35,682
⇒x=17,842
Hence, The number of students in 2nd most popular country=17,842
And, The number of students in a popular country
= 17,842+8,382=26,224
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Which algebraic expression represents the phrase below?
five times the sum of a number and eleven, divided by three times the sum of the number and eight
5(x + 11) + 3(x + 8)
5x+11
3X+8
5(X+11)
3(x+8)
5x + 11 + 3x + 8
Answer:
[tex] \frac{5x + 11}{3(x + 8)} [/tex]
Step-by-step explanation:
[tex] \frac{5x + 11}{3(x + 8)} [/tex]
Five times the sum of a number and eleven, divided by three times the sum of the number and eight
Five times the sum= 5(_+_)
a number and eleven= x+11
divided= ÷ or /
3 times the sum of= 3(_+_)
the number and eight.
Together it will be
[tex]the \: \: one \: written \: in \: the \: answering \: section[/tex]
Hope this helps ;) ❤❤❤
Which table of values will generate this graph? On a coordinate plane, points are at (negative 2, 0), (0, 1), (0, negative 4), and (3, 0). A 2-column table with 2 rows. Column 1 is labeled x with entries negative 4, 1. Column 2 is labeled y with entries negative 2, 3. A 2-column table with 2 rows. Column 1 is labeled x with entries negative 2, 3. Column 2 is labeled y with entries negative 4, 1. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 4, 0, 0, 1. Column 2 is labeled y with entries 0, negative 2, 3, 0. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 0, 3. Column 2 is labeled y with entries 0, negative 4, 1, 0.
Answer:
Option D.
Step-by-step explanation:
The given points are (-2,0), (0,1), (0,-4) and (3,0).
In each ordered pair first element is x-coordinate and second is y-coordinate.
For 4 points, the table must have 2 columns and 4 rows.
So, the required table of values is
x y
-2 0
0 -4
0 1
3 0
Therefore, the correct option is D.
The function f(t) = -6r+ 11 has the range {- 37. - 25. - 13, -1). Select the domain values from the list
1. 2. 3. 4. 5. 6. 7. 8. Justify your choices by explaining how you determined the domain values.
answer
-6r+-11=-37
-6r=-37+11
-6r=-48
r=8
Help!!!!! Thank you!!!!
Answer:
97
Step-by-step explanation:
5 * 85 - 4* 82 = 97
the sum of x and y is twice x. y=
Answer:
y is x because if x+y is 2x then y must equal x
The sum of x and y is twice x. Then the value of y will be equal to x.
What is an expression?Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.
It is given that sum of x and y is twice x. Then the value of y will be calculated as below:-
x + y = 2x
y = 2x - x
y = x
Therefore, the sum of x and y is twice x. Then the value of y will be equal to x.
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Help please thanks don’t know how to do this
Answer:
a = 11.71 ; b = 15.56
Step-by-step explanation:
For this problem, we need two things. The law of sines, and the sum of the interior angles of a triangle.
The law of sines is simply:
sin(A)/a = sin(B)/b = sin(C)/c
And the sum of interior angles of a triangle is 180.
45 + 110 + <C = 180
<C = 25
We can find the sides by simply applying the law of sines.
length b
7/sin(25) = b/sin(110)
b = 7sin(110)/sin(25)
b = 15.56
length a
7/sin(25) = a/sin(45)
a = 7sin(45)/sin(25)
a = 11.71
values of r and h, what do you notice about the proportions of the cylinders?
Answer:
Below
Step-by-step explanation:
r us the radius of the base and h is the heigth of the cylinder.
The volume of a cylinder is given by the formula:
V = Pi*r^2*h
V/Pi*r^2 = h
We can write a function that relates h and r
Answer:
One of the cylinders is short and wide, while the other is tall and thin.
Step-by-step explanation:
sample answer given on edmentum
the constant proportionality of y=5x
Answer:
k = 5
Step-by-step explanation:
The equation of proportionality is
y = kx ← k is the constant of proportionality
Given
y = 5x , then k = 5
Hassan built a fence around a square yard. It took 48 m^2 of lumber to build the fence. The fence is 1.5 meters tall.
Answer:
Step-by-step explanation:
Please check ones more because this might be incorrect.
The area is in square meters...Let's change it
Square 48= 48*48 =2304
2304 divided by 4( 4 since the formula for the area of a sqaure is s*s and square has 4 sides)
2304 divided by 4 = 576
The formula for area of a square is S*S(side times side)
Let's apply the formula here.
so, 576 times 576
331776 square meters
Hope this is right and helps! :)
( This just my point of view. Please check this onces again)
Answer:
the answer is 64
Step-by-step explanation:
khan
PLZ HELP WILL GIVE BRAINLIEST
Answer:
Hey there!
We have the slope is equal to -2.5, and the y intercept is 3.
Thus, the equation is y=-2.5x+3
Hope this helps :)
PLZ HELP ME NEED THIS FAST WILL GIVE BRAINLIEST
Answer: l = 60 ft and w = 30 ft
P = 2(l + w)
180 = 2(l + w)
Let x = width of his yard
Let 2x = length of his yard
[tex]180=2(2x+x)[/tex]
[tex]\frac{180}{2}=\frac{2(2x+x)}{2}[/tex]
[tex]90=3x[/tex]
[tex]\frac{90}{3} =\frac{3x}{3}[/tex]
[tex]x=30ft[/tex]
l = 2x = 30(2) = 60 ft
Check:
180 = 2(l + w)
180 = 2(60 + 30)
180 = 2(90)
180 = 180
LS = RS
m
A. not enough information
B. 70
C. 42
D. 38.5
Answer:
C
Step-by-step explanation:
Using Parts Whole Postulate we can write:
∠LQP = ∠LQR + ∠PQR
We know that ∠LQP = 77° and ∠LQR = 35° so we can write:
77° = 35° + ∠PQR
Therefore the answer is 77 - 35 = 42°.
There were 35 students in a class. They were given math books (each priced at $0.55) and other books the total value of which was n dollars. How much money was spent to provide the students with all these books.
Answer:
$19.25
Step-by-step explanation:
Answer:
19.25+n or n+19.25 you have to add it not multiply
Step-by-step explanation:
Andrew drives through 5 intersections with stoplights on his way to work. He records that he is stopped by a red light in 2 of the 5 intersections. If he uses this as his general probability of getting stopped at a red light on his way to or from work, how many times can he expect to be stopped at a red light over the next 40 times he drives through an intersection on his route? Andrew should expect to be stopped times.
Answer:
He should expect to be stopped a total of 16 times
Step-by-step explanation:
What the question is saying is that out of every 5 intersections, he would be stopped at 2.
Now, for forty times in which he passes through an intersection , we want to know the number of times in which he would be stopped
In this case we only need to multiply the probability by the number of times in which he passes an intersection and that would be 2/5 * 40 = 16 times
Answer:
16
Step-by-step explanation:
2. Global Cable paid dividends of $0.28 and $0.16 per share last year. Given yesterday's closing price was $11.27, determine the current yield on the stock? Round to the nearest tenth.
Answer:
3.90%
Step-by-step explanation:
Relevant Data provided as per the question below:
Annual dividend = $0.28 and $0.16
Current per share = $11.27
According to the given situation, the calculation of the current yield of the stock is shown below:-
Current yield is
[tex]= \frac{Annual\ dividend}{Current\ share\ price} \times 100\\\\ = \frac{0.28 + 0.16}{11.27} \times 100[/tex]
[tex]= \frac{0.44}{11.27} \times 100[/tex]
= 3.90%
Therefore for computing the current yield of the stock we simply applied the above formula.
A school has 400 students. They all come to school by bus, and each bus carries the same number of students. How many students might there be on each bus?
Answer:
100 students on each bus
Step-by-step explanation:
100*4 is 400 so there might be just 4
Answer:
Hey there!
It's possible that there are 200 busses, and each bus carries only 2 people, there are 10 busses and each bus carries 40 people, or there are 5 busses and each bus carries 80 people.
Hope this helps :)
PLEASE HELP ME ASPA What is the equation of the line that has a slope of -4 and passes through the point (2, 3)? y = -4x + 5 y = -4x – 5 y = -4x + 11 None of these choices are correct.
Answer:
Third option is the right choice.
Step-by-step explanation:
y = -4x + 11 (Slope = m = -4)
3 = -4(2) + 11
3 = -8 + 11
3 = 3
True.
Explain how to get the volume of this figure
Answer:
350 meters cubed.
Step-by-step explanation:
If you visualize it, there are two rectangular prisms: one flat one on the top, and one large one on the bottom.
The width of the top one is 5 meters. The length is 7 meters. The height is 8 - 5 = 3 meters. So, one prism has a volume of 5m x 7m x 3m.
The width of the bottom one is 7 meters. The length is 7 meters. The height is 5 meters. So, the bottom prism has a volume of 7m x 7m x 5m.
(5 * 7 * 3) + (7 * 7 * 5)
= (35 * 3) + (49 * 5)
= 105 + 245
= 350
So, the volume of the figure is 350 meters cubed.
Hope this helps!
5.
Which of the following equations has the sum of its roots as 3?
(A) 2x² – 3x + 6 = 0
(B) - x²+ 3x - 3 = 0
(C)√2x²-3/√2x+1
(D) 3x² – 3x + 3 = 0
Answer:
B
Step-by-step explanation:
Given a quadratic equation in standard form, ax² + bx + c = 0 ( a ≠ 0 )
Then the sum of the roots = - [tex]\frac{b}{a}[/tex]
A 2x² - 3x + 6 = 0
with a = 2 and b = - 3
sum of roots = - [tex]\frac{-3}{2}[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3
B - x² + 3x - 3 = 0
with a = - 1 and b = 3
sum of roots = - [tex]\frac{3}{-1}[/tex] = 3 ← True
C [tex]\sqrt{2}[/tex] x² - [tex]\frac{3}{\sqrt{2} }[/tex] x + 1
with a = [tex]\sqrt{2}[/tex] and b = - [tex]\frac{3}{\sqrt{2} }[/tex]
sum of roots = - [tex]\frac{-\frac{3}{\sqrt{2} } }{\sqrt{2} }[/tex] = [tex]\frac{3}{2}[/tex] ≠ 3
D 3x² - 3x + 3 = 0
with a = 3 and b = - 3
sum of roots = - [tex]\frac{3}{-3}[/tex] = 1 ≠ 3
Thus the equation with sum of roots as 3 is B
The first three steps in determining the solution set of the system of equations algebraically are shown.
y = x2 − x − 3
y = −3x + 5
What are the solutions of this system of equations?
(−2, −1) and (4, 17)
(−2, 11) and (4, −7)
(2, −1) and (−4, 17)
(2, 11) and (−4, −7)
Answer:
(2, −1) and (−4, 17)
Step-by-step explanation:
I used a graphing tool to graph the systems of equations. The parabola and line pass at points (2, -1) and (-4, 17).
Answer:(2, −1) and (−4, 17) Its C on Edge 2023
Step-by-step explanation: Its (C) after an extensive research
Please answer this question now
Answer:
d = 8.5
Step-by-step explanation:
The following data were obtained from the question:
Angle D = 100°
Opposite D = d
Opposite E = e = 6
Opposite F = f = 5
Thus, we can obtain the value of d by using the cosine rule as shown below:
d² = e² + f² – 2ef Cos D
d² = 6² + 5² – 2 × 6 × 5 × Cos 100°
d² = 36 + 25 – 60 × Cos 100°
d² = 61 – – 10.419
d² = 61 + 10.419
d² = 71.419
Take the square root of both side.
d = √71.419
d = 8.5
Therefore, the value of d is 8.5
Circle O below has radius 1. Eight segment lengths are labeled with lowercase letters. Six of these equal a trigonometric function of theta. Your answer to this problem should be a six letter sequence whose letters represent the segment lengths that equal the following functions (in the correct order):
sin(theta),
cos(theta),
tan(theta),
csc(theta),
sec(theta),
cot(theta).
So, for example, you would answer a,k,h,c,b,d if you thought
sin(theta) = a,
cos(theta) = k,
tan(theta) = h,
csc(theta) = c,
sec(theta) = b,
cot(theta) = d.
I was able to come up with:
sin(theta) = d,
cos(theta) = a,
tan(theta) = h,
csc(theta) = f,
sec(theta) = g,
cot(theta) = h.
Answer:
32
Step-by-step explanation:
49 students choose to attend one of three after school activities: football, tennis or running.
There are 18 boys.
11 students choose football, of which 1 are girls.
29 students choose tennis.
7 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
The probability that student chose running is 9/49 .
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
Consider the information as that 49 students choose to attend one of three after-school activities: football, tennis, or running.
11 students choose football, 29 students choose tennis.
The students choose running = 49 - 11 - 29 = 9.
The students choose running = 0
This means out of 49 students 9 choose running.
P(E) = 9/49
Hence, the probability that student chose running is 9/49 .
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Fill in blanks to write the particular equation of this
transformed cosine graph
Answer:
f ( x ) = -3*cos ( x ) -2
Step-by-step explanation:
Solution:-
The standard generalized cosine function is given in the form:
f ( x ) = a* cos ( w*x - k ) + b
Where,
a: The magnitude of the waveform
w: the frequency of the waveform
k: The phase difference of the waveform
b: The vertical offset of central axis from the origin
To determine the amplitude ( a ) of the waveform. We will first determine the central axis of the waveform. This can be determined by averaging the maximum and minimum values attained. So from graph:
Maximum: 1
Minimum: -5
The average would be:
Central axis ( y ) = [ 1 - 5 ] / 2
= -4 / 2
y = -2
The amplitude ( a ) is the difference between either the maximum value and the central axis or minimum value and the central axis. Hence,
a = Maximum - Central value
a = 1 - (-2)
a = 3
The waveform is inverted for all values of ( x ). That means the direction of amplitude is governed to the mirror image about x-axis. Hence, a = -3 not +3.
The offset of central axis from the x - axis ( y = 0 ) is denoted by the value of ( b ).
b = ( y = -2 ) - ( y = 0 )
b = -2 ... Answer
The frequency of the waveform ( w ) is given as the number of cycles completed by the waveform. The peak-peak distance over the domain of [ 0, 2π ]. We see from the graph is that two consecutive peaks are 2π distance apart. This means the number of cycles in the domain [ 0, 2π ] are w = 1.
The phase difference ( k ) is determined by the amount of "lag" or "lead" in the waveform. This can be determined from the x-distance between x point value of peak and the origin value ( x = 0 ). The peak and the origin coincides with one another. Hence, there is no lag of lead in the waveform. Hence, k = 0.
The waveform can be written as:
f ( x ) = -3*cos ( x ) -2
PLSSSS HELP The area of a cylinder varies jointly with the radius and the height. When the radius is 3 and the height is 6 the area is 36π. Find the are when the radius is 4 and the height is 5
Answer:
167.55
Step-by-step explanation:
so it varies jointly so
A-area if cylinder
so
[tex]a \: \alpha \: \pi \: r \: ^{2} h[/tex]
so
[tex]a = k\pi \: r^{2}h[/tex]
where k is the constant
so apply the first set of values to get k=2/3
then substitute the k with the second set of values
How many solutions does this system have? x minus y = negative 4. 3 x + y = 8. one two an infinite number no solution
Answer:
One solution
Step-by-step explanation:
Answer:
The correct answer is A.) one
Step-by-step explanation:
I just did the test on edge 2021 and got it right!
Which could be used to solve this equation? 3 and one-fifth + n = 9 Subtract 3 and one-fifth from both sides of the equation. 3 and one-fifth minus 3 and one-fifth + n = 9 + 3 and one-fifth Add 3 and one-fifth to both sides of the equation. 9 + 3 and one-fifth = 12 and one-fifth
Answer:
Subtract [tex]3\frac{1}{5}[/tex] from both sides.
Step-by-step explanation:
We want to isolate the variable [tex]n[/tex]. To do this, we have to get rid of [tex]3\frac{1}{5}[/tex], which we can do by subtracting itself, since it equals 0.
[tex]3\frac{1}{5} + n =9[/tex]
[tex]n = 5\frac{4}{5}[/tex]
Answer:
ITS A
Step-by-step explanation:
Simplify: 14 - 2+ 8 = 2 *3
helppp meeee
Answer:
20=6?
Step-by-step explanation:
14-2+8=2*3
14-2+8=6
12+8=6
20=6?
Answer:
These to equations aren't equivalent.
Step-by-step explanation:
14-2+8=2*3
12+8=6
20=6
Hope this helps ;) ❤❤❤
Solve and CHECK the following: 2(a−3)/3=4
Answer:
2(a - 3). = 4
_______
3
Cross multiply.
2(a- 3) = 12
2a - 6 = 12
2a = 12 + 6
2a = 18
a = 18 ÷ 2
a = 9
Answer:
a = 9
Step-by-step explanation:
Given
[tex]\frac{2(a-3)}{3}[/tex] = 4 ( multiply both sides by 3 to clear the fraction
2(a - 3) = 12 ( divide both sides by 2 )
a - 3 = 6 ( add 3 to both sides )
a = 9
As a check substitute a = 9 into the left side of the equation and if equal to the right side then it is the solution.
[tex]\frac{2(9-3)}{3}[/tex] = [tex]\frac{2(6)}{3}[/tex] = [tex]\frac{12}{3}[/tex] = 4 = right side
Thus solution is a = 9