Annuities
The future value (FV) of an annuity is given by:
[tex]FV=A\cdot\frac{(1+i)^n-1}{i}[/tex]Where:
A is the value of the annuity or the regular payment
i is the interest rate adjusted to the compounding period
n is the number of periods of the investment (or payment)
The given values are:
A = $38,000
n = 7 years
i = 8% = 0.08
Substituting:
[tex]\begin{gathered} FV=\$38,000\cdot\frac{(1+0.08)^7-1}{0.08} \\ FV=\$38,000\cdot\frac{(1.08)^7-1}{0.08} \\ \text{Calculate:} \\ FV=\$38,000\cdot\frac{0.7138243}{0.08} \\ FV=\$38,000\cdot8.9228 \\ FV=\$339,066.53 \end{gathered}[/tex]The future value is $339,066.53
which improper is equal to 4
Looking at the given fractions,
4/4 = 1
12/3 = 4
12/4 = 3
Thus, the improper fraction that is equal to 4 is 12/3
You earn $8.00 for every lawn that you mow. You went out to lunch andspent $25.75. At the end of the day, you had $94.25. Write and solve anequation to figure out howmany lawnsyou mowed.
Let individual move x lawns.
The equation for the number of lawns is,
[tex]8x-25.75=94.25[/tex]Solve the equation to obtai the value of x.
Identify two similar triangles in the figure below, and complete the explanation of why they are similar. Then find AB. B A С C 4 D ZA = (select) and ZABD = (select), so AABD - ACB by the select) Triangle Similarity Theorem. AB=
we know that
If two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
In this problem
A gopher has dug hose and opposite corners of a rectangle yard if the artist 12 m x 16 m how far will the golfer have to run to get from one of its holes to the other
Given:
There are given that a rectangular yard.
Explanation:
To find the distance that one holes to other:
We need to use the Pythagoras theorem.
So,
From the Pythagoras theorem:
[tex]c^2=a^2+b^2[/tex]Where,
[tex]\begin{gathered} a=12 \\ b=16 \end{gathered}[/tex]Then,
Put both values into the above formula
So,
[tex]\begin{gathered} c^2=a^2+b^2 \\ c^2=12^2+16^2 \\ c^2=144+256 \\ c^2=400 \\ c=\sqrt[]{400} \\ c=20 \end{gathered}[/tex]Final answer:
Hence, 20 meters that will the gopher have to run get from one of its holes to the other.
There are given that a rectanglua
For any positive number b not equal to 1 and any number or variable n, evaluate the following expression. logb (b^n) = ?
The logarithm is the inverse function of the exponentiation, and viceversa. The property of the logarithms and exponents tells us:
[tex]\log_b(b^n)=n[/tex] Thus, the correct answer is option A. nSolve sin(x) = 0.23 on 0 ≤ x < 2T.There are two solutions, A and B, with A
Given -
sin(x) = 0.23 on 0 ≤ x < 2π
To Find -
Two solutions, A and B =?
Step-by-Step Explanation -
[tex]0.23\text{ = }\frac{23}{100}[/tex]So, the two solutions will be -
[tex]\begin{gathered} \sin^{-1}(\frac{23}{100})\text{ and }\pi\text{ - }\sin^{-1}(\frac{23}{100}) \\ \\ So,\text{ }\sin^{-1}(\frac{23}{100})\text{ = 0.232} \\ \\ Also,\text{ }\pi\text{ - }\sin^{-1}(\frac{23}{100})\text{ = 3.141 - 0.232 = 2.909} \end{gathered}[/tex]Now, Since A < B
So,
A = 0.232
B = 2.909
Final Answer -
A = 0.232
B = 2.909
s Southern New Ham... t: This question is similar to Example 4 in "1-3 Reading and Participation Ac blications" in Module One. You can check your answers to part c and d to make right track. rectangle has perimeter 86 cm and its length is 1 cm more than twice its width. 1 the dimensions of a rectangle given that its perimeter is 86 cm and its leng e its width. ip your solution using the variables L for the length. W for the width, and P for the perimeter
You have that a rectangle has a perimeter of 86cm and its length is 1cm more than twice its width.
If W is the width and L is the length you can write the previous situation as follow:
part a:
2W + 2L = 86 perimeter of the rectangle
part b:
L = 2W + 1
replace the expression for y into the equation 2x + 2y = 86, just as follow:
2W + 2(2W + 1) = 86 expand the parenthesis
2W + 4W + 2 = 86 subtract 2 both sides and simplify like terms
6W = 86 - 2
6W = 84
W = 84/6
W = 14
L = 2W + 1 = 2(14) + 1 = 28 + 1 = 29
part c:
The length is 29 cm
part d:
The width is 14 cm
If the lines /1 and /2 are parallel, what must be value of y?
ANSWER
y = 130 degrees
STEP-BY-STEP EXPLANATION
Key points to note in the provided figure
Alternate exterior angles are equal
The sum of supplementary angles is 180 degrees
From the figure given, angle y and angle 5x are alternate exterior angles
Since alternate exterior angles are equal. Hence, angle y = angle 5x
y = 5x
Also, angle (2x - 2) and y are supplementary angles
Recall, the sum of supplementary angles is 180 degrees
Hence, we have
y + (2x - 2) = 180
Note, y = 5x
substitute y = 5x into the above equation
5x + (2x - 2) = 180
Open the parenthesis
5x + 2x - 2 = 180
Collect the like terms
5x + 2x - 2 = 180
7x - 2 = 180
Add 2 to both sides of the equation
7x - 2 + 2 = 180 + 2
7x = 182
Divide both sides by 7
7x/7 = 182/7
x = 26 degrees
Since we have gotten the value of x = 26 degrees. Hence, we can now find the value of y
Recall, y = 5x
y = 5(26)
y = 130 degrees
using the values from the graph, compute the values for the terms given in the problem. Choose the correct answer. Age of car = 4 years Original cost = 13,850 The current market value is $ _
Answer:
3462.5$
Step-by-step explanation:
If the percentage after 4 years was 25% then it dropped to 3462.5$.
USE THE NORMAL CURVE TABLE TO DETERMINE THE PERCENT OF DATA SPECIFIED.A) TO THE LEFT OF z = 1.62B) BETWEEN z = -1.53 AND z = -1.82
SOLUTION:
Using a normal distribution table, we find that;
a. The area to the left of z = 1.62 is;
[tex]P(z<1.62)=0.9474[/tex]b. The area between z = -1.53 and z = -1.82, this is;
[tex]P(-1.82From the diagram below, if AC is a tangent line, and if PD = 9 and DC = 32, find the length of BC.
Solution:
Given the circle;
From the circle theorem, triangle PBC is a right triangle.
[tex]\begin{gathered} PB=PD=9 \\ \\ PC=PD+DC=9+32 \\ \\ PC=41 \end{gathered}[/tex]Using the Pythagorean theorem;
[tex]\begin{gathered} BC=\sqrt{PC^2-PB^2} \\ \\ BC=\sqrt{41^2-9^2} \\ \\ BC=\sqrt{1600} \\ \\ BC=40 \end{gathered}[/tex]CORRECT OPTION: C
5(2x-7)+42-3x=2 what is the answer
Problem
5(2x-7)+42-3x=2 what is the answer
Solution
For this case we can distribute the terms on this way:
10x -35 +42 -3x = 2
Now we can aggrupate similar terms and we got:
7x= 2+35-42
7x = -5
And then solving for x we got:
x= -5/7
What are the characteristics of a t-distribution? (Give at least 3characteristics).
Given,
T-distribution.
T-distribution: The T-distribution, also known as the student's t-distribution, is a type of probability distribution that is similar to the normal distribution with its bell shape but has heavier tails.
There are 3 characteristice of the distribution:
shape, central tendency and variability.
Determine the type of triangle that is drawn below. W 5.57 50° X 80° 7.13 5-57 50° V
Given the triangle VWX
AS shown:
[tex]\begin{gathered} m\angle V=m\angle W=50 \\ m\angle X=80 \end{gathered}[/tex]So, the three angles are less than 90, which mean it is an acute triangle
And there are two congruent angles, which mean it is an isosceles triangle
so, the type of the triangle is an acute isosceles triangle
Write an equation of the line in slope intercept form that passes through the given point and is perpendicular to the given line.(-2,4) , y = 2x + 9
We are given the point (-2,4) and the line y=2x+9. We want the equation of the line that passes through the given point and that is perpendicular to the given line.
To do so, we will use the following equation of a line
[tex]y\text{ -a = m\lparen x -b\rparen}[/tex]in this equation, m is the slope of the line and (a,b) is a point in the line. In our case, we are given that (-2,4) is in the line. That is, a=-2 and b=4. So our equation becomes
[tex]y\text{ -4=m\lparen x -\lparen-2\rparen\rparen}[/tex]or equivalently
[tex]y\text{ -4}=m(x\text{ +2\rparen}[/tex]now, we only need to find the value of m. To do so, we use the given line and the fact that the product of the slopes of perpendicular lines is -1.
The given line (2x+9) has a slope of 2. So, we have the following equation
[tex]m\cdot2=\text{ -1}[/tex]so if we divide both sides by 2, we get that
[tex]m=\text{ -}\frac{1}{2}[/tex]So the equation we are looking for becomes
[tex]y\text{ -4 }=\text{ -}\frac{1}{2}(x\text{ +2\rparen}[/tex]We want this equation in the slope intercept form. So we operate to find y in this equation. So first, we distribute on the right hand side. We get
[tex]y\text{ -4}=\text{ -}\frac{1}{2}x\text{ -}\frac{2}{2}=\text{ -}\frac{1}{2}x\text{ -1}[/tex]now we add 4 on both sides, so we get
[tex]y=\text{ -}\frac{1}{2}x\text{ -1+4= -}\frac{1}{2}x+3[/tex]we can check that if x= -2 we get
[tex]y=\text{ -}\frac{1}{2}(\text{ -2\rparen+3=1+3=4}[/tex]which confirms that the point (-2,4) is on the line
Write a numerical expression in the first box that represents the number of points earned or lost each round.then write Andy's final point total at the end of the competition in the second box.
In the first round, Andy has -320 times 1/2, which corresponds to
[tex]-320\times\frac{1}{2}=-\frac{320}{2}=-160[/tex]In the second round, Ansy has
[tex]710\times\frac{1}{4}=\frac{710}{4}=\frac{355}{2}[/tex]which corresponds to 177.5 (in decimals).
Finally, Andy's final point is
[tex]-320\times\frac{1}{2}+710\times\frac{1}{4}-500[/tex]which is equal to
[tex]-160+177.5-500=-482.5[/tex]that is, Andy's final point is - 482.5.
it is due today!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!1
The value of 5/9x - 2/3y + xy when x = 3/5 and y = 1/2 is 3/10
We need to evaluate the expression
5/9x - 2/3y + xy
x = 3/5 and y = 1/2
(5/9)(3/5) - (2/3)(1/2) + (3/5)(1/2)
(15/45) - (2/6) + (3/10)
1/3 - 1/3 + 3/10
= 3/10
Therefore, the value of 5/9x - 2/3y + xy when x = 3/5 and y = 1/2 is 3/10
To learn more about fraction refer here
https://brainly.com/question/78672
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All changes saved1. (07.01 MC)The moon forms a right triangle with the Earth and the Sun during one of its phases, as shown below:EarthSunMoonA scientist measures the angle x and the distance y between the Earth and the moon. Using complete sentences, explain how the scientist can use only thesetwo measurements to calculate the distance between the Earth and the Sun.
Notice that we can use the trigonometric function tangent to find the distance between the Earth and the Sun with the following expression:
[tex]\begin{gathered} \tan x=\frac{y}{ES} \\ \Rightarrow ES=\frac{y}{\tan x} \end{gathered}[/tex]then, if the scientist only have the measure of the distance between the earth and the moon and the angle that forms between the earth and the moon in the sun, we can find out the distance between the Earth and the Sun
Data concerning the time between failures (in hours of operation) for a computer printer have been recorded, and the first quartile equals 36 hours, the second quartile equals 65 hours, and the third quartile equals 74 hours.The value for the lower inner fence equals
1) Let's remind ourselves of what is the Lower Fence.
2) So, let's calculate the Lower Fence given that the Quartiles have been given and the Interquartile Range can be found like this:
[tex]IQR=Q_3-Q_1=74-36=38[/tex]3) So now, we can write down the formula for the Lower Fence as well as plug into that the given data:
[tex]undefined[/tex]A full 275 L tank contains a 20% saline solution. How many litres must be replaced with a 100% saline solution to produce a full tank with a 45% saline solution? Round your final answer to 1 decimal place if necessary.
Let x be the volume of 20% solution in the tank after the given process
Let y be the volume of 100% solution used.
The sum of x and y needs to be equal to the final volume 275L:
[tex]x+y=275[/tex]The amount of substance (salt) in each solution is calculated by multipliying the volume by the concentration (in decimals); then, the amount of salt in 20% solution is 0.2x, in 100% solution is 1y and in the final solution (45%) is 0.45(275).
Sum amount in 20% solution with amount in 100% solution to get the amount in final solution:
[tex]\begin{gathered} 0.2x+y=0.45\left(275\right) \\ 0.2x+y=123.75 \end{gathered}[/tex]Use the next system of equations to answer the question:
[tex]\begin{gathered} x+y=275 \\ 0.2x+y=123.75 \end{gathered}[/tex]1. Solve x in the first equation:
[tex]x=275-y[/tex]2. Use the value of x (step 1) in the second equation:
[tex]0.2\left(275-y\right)+y=123.75[/tex]3. Solve y:
[tex]\begin{gathered} 55-0.2y+y=123.75 \\ 55+0.8y=123.75 \\ 0.8y=123.75-55 \\ 0.8y=68.75 \\ y=\frac{68.75}{0.8} \\ \\ y=85.93 \end{gathered}[/tex]The volume of 100% solution that needs to be used is 85.9 Litres.
Then, the litres that must be replaced with 100% solution to produce a full tank with 45% saline solution is 85.9PLEASE EEEEEEEE this is very important :’)
number attended/ total people
a) 153/225 = 17/25 = 0.68 = 68%
Answer:
A
Step-by-step explanation:
[tex]{ \tt{ = \frac{153 \div 9}{225 \div 9} }} \\ \\ = { \tt{ \frac{17}{25} }} \\ \\ = 0.68 \times 100\% \\ \\ = 68\%[/tex]
Watch help video Find the length of the third side. If necessary, write in simplest radical form. 4V3 8 oc Submit Answer Answer
SOLUTION
Using Pythagoras theorem,
[tex]\begin{gathered} 8^2\text{ = ( 4}\sqrt[]{3})^2+h^2 \\ 64=48+h^2 \\ h^2\text{ = 64 - 48} \\ h^2\text{ = 16} \\ \text{square root both sides , we have :} \\ h\text{ = 4} \end{gathered}[/tex]
Find the conjugate of the following binomial ^15t-^5
The conjugate is formed by changing the sign between the terms of the binomial:
[tex]\begin{gathered} \sqrt{15}t-\sqrt{5} \\ \uparrow\downarrow conjugate \\ \sqrt{15}t+\sqrt{5} \end{gathered}[/tex]In this case, the sign is negative, then the sign of its conjugate is positive.
Answer: [tex]\sqrt{15}t+\sqrt{5}[/tex]1.75,____,6.75,9.25,11.75
Answer:
This looks like an addition (summation is the technical term) series. Here we need to figure out the difference between each number in the series. The difference between 6.75 and 9.25 is 2.5 (You can subtract the larger number from the smaller number to find out). So, 6.75-2.5=4.25.
So the correct answer in the blank is 4.25, and the rule is +2.5.
Step-by-step explanation:
A line shaft rotating at 250 rpm is connected to a grinding wheel by the pulley assembly shown in the diagram. If the grinder shaft must turn at 1200 rpm, what size pulley should be attached to the line shaft?
A line shaft rotating at 250 rpm is connected to a grinding wheel by the pulley assembly shown in the diagram. If the grinder shaft must turn at 1200 rpm, what size pulley should be attached to the line shaft?
grinder shaft
the radius is r=5/2=2.5 in ------> given
Find out the circumference
C=2*pi*r
C=2*pi*2.5 ------> C=5pi in
one revolution is 5pi in
so
1200rpm is
1200*5pi=6,000pi in per minute
step 2
pulley assembly
Diameter x
250 rpm
circumference is equal to -----> C=xpi in
so
xpi*250=6,000pi
simplify
250x=6,000
x=24 in
the diameter of the pulley assembly is 24 inches420, 84, 16.8, 3.36,... What is the explicit rule for this sequence? An =___ *(____)^n-1
Answer:
[tex]a_n=420\ast(0.2)^{n-1}[/tex]Explanation:
The explicit formula for a geometric sequence is always given in the form;
[tex]a_n=a_1\ast(r)^{n-1}[/tex]where an = the nth term of the sequence
a1 = the 1st term of the sequence
r = the common ratio of the sequence
From the given sequence, we can see that the 1st term, a1, is 420.
We can find the common ratio, r, by dividing any number of the sequence with its preceding number;
[tex]\begin{gathered} r=\frac{84}{420}=0.2\text{ or 16.8/84 = 0.2} \\ \therefore r=0.2 \end{gathered}[/tex]Substituting the above values into our formula above, we'll have;
[tex]a_n=420\ast(0.2)^{n-1}[/tex]Solve the following system of equations by using elimination: 3x - y = -1 x + y = 13
Solution
For this case we have the following system of equations:
3x-y =-1 (1)
x +y= 13 (2)
Solving x from the (2) equation we have:
x=13-y (3)
Replacing (3) into (1) we got:
3(13-y) -y= -1
Solving for y we have:
39 -3y -y = -1
4y = 40
y= 10
And solving for x we got:
x= 13-10 = 3
what is the reflexive property of equality?
The reflexive property of equality states that every element is equal to itselft, for example, 3 = 3, or a = a. In algebra is often applied for numbers. In geometry is applied to sides or angles, for example, side A
How much medicine is to be taken in each dose
Problem ID: PRABMVM9 For each of the functions f, g, h, P, and q, the domain is o sxs 100. For which functions is the average rate of change a good measure of how the function changes for this domain? Select all that apply. A. F(x)=x+2 B. g(x)=2* C. h(x)= 111x-23 D. p(x)=50,000 x 3% E. g(x)= 87.5
a) b) c) d)
1) Examining each function, let's test considering that the average rate of change is given by:
[tex]\Delta=\frac{f(b)-f(a)}{b-a}[/tex]2) So let's plug the functions:
[tex]\begin{gathered} a)\text{ }\Delta=\frac{(100)+2\text{ -\lbrack(0)+2\rbrack}}{100-0}=\frac{102-2}{100}=\frac{100}{100}=1 \\ b)\text{ }g(x)=2^x\text{ }\Delta=\frac{2^{100}-2^0}{100-0}=\frac{1.26\times10^{30}}{100}=1.26\times10^{28} \\ c)\text{ }h(x)\text{ = }111x-23\text{ }\Delta=\frac{111(100)-23\text{ -\lbrack{}111(0)-23}}{100}=111 \\ d)\text{ }p(x)\text{ = }50,000\times3^x\Delta=\frac{50,000-3^{100}-\lbrack50,000-3^0}{100}=-5.15\times10^{45} \\ e)q(x)=87.5 \end{gathered}[/tex]3) Since the average rate of change is a "measure of how much a function changes in the given interval" and considering that we have linear and exponential functions and the last one e) is not a function but an equation.
Then we can say that for the functions below the average rate of change is a good measure, not applying for the last one which, indeed is not a function.
a)
b)
c)
d)
Answer:
If you go off of the explanation below... the actual answers are A, C, E...
Step-by-step explanation:
Correct Answer
A)
f(x)=x+2
C)
h(x)=111x−23
E)
q(x)=87.5