The total of all the present values of the payments is $2,973,483.
What is the present value?The present value is the future cash flows discounted to the present day's values.
The present value can be determined using an online finance calculator that inputs the future cash flows, the interest rate, and the period.
How is the total present value determined?The total present value is a function of the summation of the four present values.
Since the present values are given, computing the total involves the mathematical operation of addition.
Present Values:1st payment $320,640
2nd payment $787,116
3rd payment $878,611
4th payment $987,116
Total PV $2,973,483
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Answer:
The correct answer is $878,611 for plato users
Step-by-step explanation:
prove the formula sin 3 A + sin A = 4 sin A cos2A
We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.
In the given question,
We have to prove the formula sin 3A+sin A = 4sinAcos^2A
The given expression is sin 3A+sin A = 4sinAcos^2A
To prove the formula we take the left side terms to the right side terms
The left side is sin 3A+sin A.
As we know that sin 3A = 3sinA − 4sin^3A
To solve the left side we put the value of sin 3A in sin 3A+sin A.
=sin 3A+sin A
=3sinA − 4sin^3A+sin A
Simplifying
= (3sinA+sin A) − 4sin^3A
= 4sinA − 4sin^3A
Taking 4sinA common from both terms
= 4sinA(1 − sin^2A)
As we know that cos^2A=1 − sin^2A. So
= 4sinAcos^2A
We proved the right hand side.
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1. Juan bought fruit from the grocery store. The variables below define his purchase. Juan's bananas cost half as much as apples. Which equations can be used to model his purchase? Select each correct equation.* a = the number of apples he bought b = the number of bananas he bought x= the cost of an apple in dollars y= the cost of a banana in dollars A- a= 1/2 bb- y=1/2 xc- a=2bd- x=2ye- y=2af- b=1/2 x
Juan's bananas cost half ( 1/2) as much as apples.
x= the cost of an apple in dollars
y= the cost of a banana in dollars
Multiply the cost of an apple by 1/2 (half). that expression must be equal to the cost of a banana.
y = 1/2 x (option b)
Find a unit vector u in the direction of v. Verify that ||0|| = 1.v = (4, -3)U =
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
Answer
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Explanation
The unit vector in the direction of any vector is that vector divided by the magnitude of the vector.
u = Unit vector in the direction of v = (vector v)/(magnitude of vector v)
v = <4, -3> = 4i - 3j
Magnitude of v = |v| = √[4² + (-3)²] = √(16 + 9) = √25 = 5
u = (4i - 3j)/5 = (4i/5) - (3j/5)
u = <(4/5), (-3/5)>
Magnitude of u = ||u|| = √[(4/5)² + (-3/5)²] = √[(16/25) + (9/25)] = √(25/25) = √(1) = 1
Hope this Helps!!!
What is a feature of function g if g(x) = log (x-4) -8
The domain and range of the logarithmic function are
[tex]\begin{gathered} \text{domain}(\log x)=(0,\infty) \\ \text{range}(\log x)=(-\infty,\infty) \end{gathered}[/tex]Therefore, if
[tex]g(x)=\log (x-4)-8[/tex]We require that
[tex]\begin{gathered} x-4>0 \\ \Rightarrow x>4 \end{gathered}[/tex]Notice that the -8 term does not affect the range of function g(x); thus,
[tex]\begin{gathered} \text{domain}(g(x))=(4,\infty) \\ \text{range}(g(x))=(-\infty,\infty) \end{gathered}[/tex]Set g(x)=-8; then,
[tex]\begin{gathered} \Rightarrow\log (x-4)-8=-8 \\ \Rightarrow\log (x-4)=0 \\ \Rightarrow x=5 \end{gathered}[/tex]Therefore, y=-8 is not an asymptote of g(x), and, as shown above, the domain and range of g(x) are x>4, y->all real numbers.
Calculate the limit when x->4 as shown below,
[tex]\lim _{x\to4}g(x)=(\lim _{x\to4}\log (x-4))-8=(-\infty)-8=-\infty[/tex]Therefore, there is a vertical asymptote at x=4
Answer:
Hope this helps ;)
Step-by-step explanation:
Drag each number to the correct location on the table
Step-by-step explanation:
There is no table attached, please recheck and resend.
If joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters. How far was joey from home?
The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters.
What is subtraction?To subtract in mathematics is to take something away from a group or a number of objects.
The group's total number of items decreases or becomes lower when we subtract from it.
It is known that East and West are the opposite of each other.
So, 15 2/3 towards the east let's take it positively.
And 21 3/4 towards left let's consider it negative.
So, the distance from the home
⇒ | ( 15 + 2/3) - (21 +3/4) |
⇒ | 15 -21 + 2/3 - 3/4 |
⇒ | -6 + (8 - 9)/12 |
⇒ | -6 - 1/12 |
⇒ | -(6 +1/12) |
⇒ 6 1/12
Hence "The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters".
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Fill in the missing number to complete the linear equation that gives the rule for this tablex: 4, 5, 6, 7y: 32, 40, 48, 56y = ?x
according to the equation and information given we can see that the equation is in the form
[tex]y=kx[/tex]in which k is the constant of proportionality
use one of the points to find the constant
[tex]\begin{gathered} 32=k(4) \\ k=\frac{32}{8} \\ k=8 \end{gathered}[/tex]replace withone of the points to see if its true in all the points
[tex]\begin{gathered} 40=8\cdot5 \\ 40=40 \end{gathered}[/tex]according to this the equation for the table will be
[tex]y=8x[/tex]Find the surface area of the triangular prism. 13 in. 5 in. 4 in. 12 in.
The first face is a triangle with height 5in and base 12in
Traingular face area = 1/2 x bh
=1/2 x 12 x 5
= 30 in^2
The area of the other triangular base = 30 in^2
Area of left side face = Length x breadth
= 5 x 4 = 20in^2
Area of the slant face = Length x breadth
= 13 x 4 = 52in^2
Area of the bottom face = Length x breadth
= 12 x 4 = 48in^2
Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2
=180in^2
Amplitude, period, and phase shift of sine and cosine functions
We are given that
[tex]y=-2+2\cos (2x-\frac{\pi}{3})[/tex]Note: Given the cosine function
[tex]y=a\cos (bx-c)+d[/tex]then
[tex]\begin{gathered} Amplitude=a \\ Period=\frac{2\pi}{b} \\ PhaseShift=\frac{c}{b} \\ VerticalShift=d \end{gathered}[/tex]Comparing the question with what is written in the note
We have
[tex]\begin{gathered} a=2 \\ b=2 \\ c=\frac{\pi}{3} \\ d=-2 \end{gathered}[/tex]We want to find
(a). Amplitude
From the given question, the amplitude (a) is
[tex]\begin{gathered} a=2 \\ Amplitude=2 \end{gathered}[/tex](b).Period
From the given question, the period is
[tex]\begin{gathered} Period=\frac{2\pi}{b} \\ Period=\frac{2\pi}{2} \\ Period=\pi \end{gathered}[/tex](c). Phase Shift
From the given question, the phase shift is
[tex]\begin{gathered} PhaseShift=\frac{c}{b} \\ PhaseShift=\frac{\pi}{3}\times\frac{1}{2} \\ PhaseShift=\frac{\pi}{6} \end{gathered}[/tex]Simplify the expression by combing like terms.21v + 8 - 12v - 7 + 3t - t
We need to simplify the like terms.
"The like terms are whose with the same variable and exponent"
Therefore, the like terms are:
21v - 12v = 9v
8 - 7 = 1
3t - t = 2t
Now, the result is :
9v + 2t + 1
Hence, the correct answer is option D.
Draw a line connecting each sphere to its volume in terms of π and round it to the nearest tenth. (Not all of the values will be used.)
Remember that
The volume of a sphere is equal to
[tex]V=\frac{4}{3}\pi r^3[/tex]N 1
we have
D=9 units
r=9/2=4.5 units
substitute
[tex]\begin{gathered} V=\frac{4}{3}\pi(4.5)^3 \\ V=121.5\pi\text{ unit3} \\ V=381.5\text{ unit3} \end{gathered}[/tex]N 2
we have
r=2 units
[tex]\begin{gathered} V=\frac{4}{3}\pi2^3 \\ V=10.6\pi\text{ unit3} \\ V=33.5\text{ unit3} \end{gathered}[/tex]N 3
we have
D=14 units
r=14/2=7 units
[tex]\begin{gathered} V=\frac{4}{3}\pi7^3 \\ V=457.3\pi\text{ unit3} \\ V=1,436\text{ unit3} \end{gathered}[/tex]N 4
we have
r=9 units
[tex]\begin{gathered} V=\frac{4}{3}\pi9^3 \\ V=972\pi\text{ unit3} \\ V=3,052.1\text{ unit3} \end{gathered}[/tex]helpppppppppppppppppppppppppppppp
Answer:
[tex]f^{-1}[/tex](x) = x/2 - 3/2
Step-by-step explanation:
Swap x and y and solve for y.
Original equation:
y = 2x + 3
Swapped equation:
x = 2y + 3
Now, solve for y:
x -3 = 2y
y = (x-3)/2
If it's wrong, it might just be the way you format your answer, since Pearson (what I assume you're using) is specific about that.
Maybe, [tex]f^{-1}[/tex](x) = x/2 - 3/2 or [tex]f^{-1}[/tex](x) = (x-3)/2
A student at a junior college conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week. X, and grade-point average, y. Shefound that a linear relation exists between the two variables. The least-squares regression line that describes this relation is ý = -0.0579x + 2.9408(Round to the nearest hundredth as needed.)(Part b) Interpret the slope.For each additional hour that a student spends playing video games in a week, the grade-point average will decrease by 0.0579 points, on average.(Part c) if appropriate, interpret the y-intercept.A. The grade-point average of a student who does not play video games is 2.9408.B. The average number of video games played in a week by students is 2.9408.C. It cannot be interpreted without more information.
exactly For sentence A "The grade-point average of a student who does not play video games is 2.9408" we can verify as follows:
That means this sentence "The grade-point average of a student who does not play video games is 2.9408" is true.
For sentence B "The average number of video games played in a week by students is 2.9408" is not exactelly correct because the average number of hours of video game played is not specified.
For sentence C "It cannot be interpreted without more information" let's look over an illustration.
We can see, we can interpret the y-intercept as the moment where x = 0 which means when the student does not play a video game. So this sentence is false.
I mean the correct sentence is sentence A.
102,410,000,000,000,000,000,000,000 in scientific notation round to two digits after the decimal
We have a big integer and want to write in scientific notation.
To do this we need to count how many places we need to move the decimal point.
In this case we need to move the decimal point to left so the exponent of 10 will be positive.
So,
[tex]\begin{gathered} 102,410,000,000,000,000,000,000,000=1.0241\cdot10^{29} \\ \text{Round to two digits after the decimal:} \\ 1.02\cdot10^{29} \end{gathered}[/tex]We move the decimal point 29 places to left so the exponent of 10 is 29.
I need to write this equation that has a infinite number of solutions
2 (8x+4) -x =
Simplify the equation:
2(8x)+2(4) -x
16x +8 -x
15x +8
If both sides of the equation are equal o equivalent, there is an infinite number of solutions.
2 (8x+4) -x = 15x + 8
Question 8 > Find the area of the trapezoid shown below 9 19 18 21 23 I Question Help ve
288 u²
1) Let's calculate the area of that trapezoid by plugging into the formula below the measures of the altitude, larger base, smaller one:
[tex]\begin{gathered} S=\frac{(B+b)h}{2} \\ S=\frac{(23+9)18}{2} \\ S=288 \end{gathered}[/tex]2) So that trapezoid has an area of 288 u²
2. State two (2) values of θ (theta) to the nearest degree forsin θ = − 0. 966
To find a value of θ theta given a value of sin(θ) we must use the arcsin function, it receives a value of an sin as argument and returns the value of the angle θ. Then we must use a calculator and input
[tex]\begin{gathered} \theta=\arcsin\left(x\right) \\ \\ \theta=\arcsin(-0.966) \\ \\ \theta=−75 \end{gathered}[/tex]The result is already rounded to the nearest degree. Therefore, one value of θ that satisfies sin θ = −0.966 is θ= -75°
Now to find the other value we will look at the symmetry in the trigonometric circle:
Then, the other value of theta will be
[tex]\begin{gathered} \theta_2=-75°-30° \\ \\ \theta_2=105° \end{gathered}[/tex]Final answer:
[tex]\begin{gathered} \theta=-75° \\ \theta_2=-105° \end{gathered}[/tex]The graph shows a dilation of trapezoid TRAP with respect to the origin which statements are true about the figures select three
A dilation means an elongation of the sides of a figure
So in a dilation the sides are bigger than at the original figure
A key formula for found dilation is Pithagoras theorem
For calculate T'R'
T'R' is the exact diagonal of OT' and OR', that means
OT' + OR' = T'R' in vectorial sum
OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum
So then T'R'^2 = 5^2 + 5^2 = 50.
and T'R'= √50
Now find TR to find the factor of dilation that is
T'R'/TR
suppose s is between r and t use the segment addition postulate to solve for each variable RS equals 2z plus 6 St equals 4z - 3 RT = 5z + 12
If s is between r and t, then:
RS + ST = RT
Where RS = 2z + 6
ST = 4z - 3
RT = 5z + 12
So, we get:
(2z + 6) + (4z - 3) = 5z + 12
Solving for z, we get:
2z + 6 + 4z - 3 = 5z + 12
6z + 3 = 5z + 12
6z + 3 - 5z = 12
z + 3 = 12
z = 12 - 3
z = 9
Answer: z = 9
A parallelogram has an area of 364.5 cm2. If the base is 27 cm, What is the height?
Answer:
Height = 13.5cm
Explanation:
The area of a parallelogram is obtained using the formula below:
[tex]\text{Area}=\text{Base}\times Height[/tex]Substituting the given values:
[tex]\begin{gathered} 364.5=27\times\text{Height} \\ \text{Height=}\frac{364.5}{27} \\ H\text{eight}=13.5\operatorname{cm} \end{gathered}[/tex]how do i expand -4(-x-8)
Answer:
4x+32
Step-by-step explanation:
mutiply the -4 to both numbers inside parentheses. negative * negative= positive. -4*-x=4x, -4*-8=32
Classify the triangle with side lengths 8,13,20. a) Acute b) Right c) Obtuse
for right angles triangle,
hyposenuse square should be equal to sum of square of other two sides
it fails that law so its not right angled triangle
Convert to fractional Notation 4 19/100
to solve this we need to convert the number 4 to a fraction with denominator 100 and add both fractions
to do that we can multiply 4 and 1 by 100, like this:
[tex]\frac{4\cdot100}{1\cdot100}=\frac{400}{100}[/tex]now we can add the fractions
[tex]\frac{400}{100}+\frac{19}{100}=\frac{419}{100}[/tex]So the answer is: 419/100
Need help with my math yall please??
The value of the expression after simplification is found as -3.
What is termed as simplification?Simplify simply way of making something easier to understand. Simply or simplification in mathematics refers to reducing an expression/fraction/problem to a simpler form. It simplifies the problem by calculating and solving it. We can —Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This helps make the expression simple to understand and solve.For the given expression;
5x + 8 = 2x - 1
Subtract 8 from both side.
5x + 8 - 8 = 2x - 1 - 8
Simplify
5x = 2x - 9
Subtract both side by 2x.
5x - 2x = 2x - 9 - 2x
3x = -9
Divide both side by 3.
3x/3 = -9/3
x = -3
Thus, the value of the expression is found as -3.
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Which graph represents the solution of −2x≤4(x−6)?
Answer:
See attachments.
Step-by-step explanation:
Given inequality:
[tex]-2x\leq 4(x-6)[/tex]
Solve the inequality by first expanding the brackets:
[tex]\implies -2x\leq 4x-24[/tex]
Subtract 4x from both sides:
[tex]\implies -2x-4x\leq 4x-24-4x[/tex]
[tex]\implies -6x\leq -24[/tex]
Divide both sides by -6 (remembering to reverse the inequality sign as we are dividing by a negative number).
[tex]\implies \dfrac{-6x}{-6}\leq \dfrac{-24}{-6}[/tex]
[tex]\implies x\geq 4[/tex]
When graphing inequalities on a coordinate plane:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.Therefore, to graph the given inequality on a coordinate plane:
Draw a solid line at x = 4.Shade above the line (i.e. shade to the right of the line).(See attachment 1).
When graphing inequalities on a number line:
< or > : open circle.≤ or ≥ : closed circle.< or ≤ : shade to the left of the circle.> or ≥ : shade to the right of the circle..Therefore, to graph the given inequality on a number line:
Place a closed circle at 4.Shade to the right of the circle.(See attachment 2).
how many shirts can Jeanette sew at most of and still have 1. spool of thread left
Answer:
The number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]Explanation:
Given a graph that relates the number of spools of thread left to the number of shirts sewn.
We want to find the number of shirts sewn at most, when there is just 1 spool of thread left.
To get that, let us draw a straight horizontal line from y=1 (spools of thread remaining =1) to join the line of the graph and also trace it down.
Tracing the line down we can observe that it is at shirt sewn equals 5.
So, the number of shirts sewn at most, when there is just 1 spool of thread left is;
[tex]5\text{ shirts}[/tex]Jim baked 48 cookies with 4 scoops of flour. How many scoops of flour does Jim need in orderto bake 96 cookies? Assume the relationship is directly proportional.
Given:
Jim baked 48 cookies with 4 scoops of flour.
So, the unit rate will be = 48/4 = 12 cookies/scoop of flour
So, for 96 cookies, the number of scoops of flour will be =
96/12 = 8
So, the answer will be 8 scoops of flour
Finding Slope
HELP ME PLS
The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
The first point = (-5,6)
The second point = (-9,-6)
The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.
The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Where m is the slope of the line
[tex](x_1,y_1)[/tex] is the coordinates of the first point
[tex](x_2,y_2)[/tex] is the coordinates of the second point
Substitute the values in the equation
The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]
= -12/-4
= 3
Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3
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complete the table to show the total change in the average mean daily in the price of for stocks over a five-day.
Answer: -$0.26, -$0.7, $0.65, and -$1.6
The number of days = 5
Average price = Total change in price / the number of days
For Stock A
Total change in price = -$1.30
Average price = - 1.30 / 5
Average price = -$0.26
STOCK B
Average change in price = -$0.14
From, Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.14 x 5
Total price = - $0.7
For stock C
Average price = 3.25 / 5
Average price = $0.65
Stock D
Average price = Total price / number of days
Total price = Average price x number of days
Total price = -0.32 x 5
Total price = - $1.6
The answer are -$0.26, -$0.7, $0.65, and -$1.6
Alyssa will correctly label the numbers 48.4, 48482, 48.09, and 48on the number line below.
The numbers under consideration are:
[tex]48.4,\text{ 48}\frac{1}{2},\text{ 48.09, 48}\frac{3}{5}[/tex]Converting all the numbers to decimal:
[tex]\begin{gathered} 48\frac{1}{2}=\text{ 48+0.5 = 48.5} \\ 48\frac{3}{5}=\text{ 48 + }0.6\text{ = 48.6} \end{gathered}[/tex]Therefore, the numbers can be written as:
48.4, 48.5, 48.09, and 48.6
Out of these numbers, only 48.6 is closest to 49
[tex]48\frac{3}{5}\text{ is closest to 49}[/tex]