General MathematicsProblem:What sum would have to be invested at 9% conpounded annually to provide an ordinary annuity at ₱8,000 per year for 5 years?
Given that a future value annuity of 8,000 is accrued at 9% compounded annually, the present value of the annuity is evaluated as
[tex]\begin{gathered} PV=P(\frac{1-(1+r)^{-n}}{r})\text{ ----- equation 1} \\ \text{where } \\ PV\text{ }\Rightarrow present\text{ value of the annuity} \\ P\Rightarrow value\text{ of each payment} \\ r\Rightarrow interest\text{ rate} \\ n\Rightarrow period \end{gathered}[/tex]Thus,
[tex]\begin{gathered} P=8,000 \\ r=9\text{\%}=\frac{9}{100}=0.09 \\ n=5 \\ PV\text{ is unknown} \\ \end{gathered}[/tex]Substitute the above value into equation 1, to solve for PV
[tex]\begin{gathered} PV\text{ = 8000(}\frac{1-(1+0.09)^{-5}}{0.09}) \\ \Rightarrow8000\times\frac{1-1.09^{-5}}{0.09} \\ =31117.21 \end{gathered}[/tex]Hence, the sum to be invested is 31117.21
Divide write the answer as a fraction in simplest form 7/8 divided by 6 =
Answer:
[tex]\frac{7}{48}[/tex]Explanation: We have been given a fraction 7/8 and we need to divide it by 6 and write it in simplest terms.
Dividing and simplifying gives us following:
[tex]\frac{7}{8}\text{ Divied 6}\rightarrow\frac{7}{8}\times\frac{1}{6}=\frac{7}{48}=\frac{7}{48}[/tex]What is the length of AC?
Answer:
126 units!
Step-by-step explanation:
I hope this helped!! c:
The sum of an integer and 2 times the next consecutive even integer is -2. Find the value of the lesser integer.
The value of the lesser integer is -2.
According to the question,
We have the following information:
The sum of an integer and 2 times the next consecutive even integer is -2.
Let's take the lesser integer to be x.
Now, the next consecutive integer will be (x+2).
So, we have the following expression:
x + 2(x+2) = -2
x+2x+4 = -2
3x+4 = -2
Moving 4 from the left hand side to the right hand side will result in the change of the sign from plus to minus:
3x = -2-4
3x = -6
x = -6/3
x = -2
Hence, the value of the lesser integer is -2.
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Factor completely.x^2−10x−24 Enter your answer in the box.
Given:
[tex]x^2-10x-24[/tex]To factorize:
It can be written as,
[tex]\begin{gathered} x^2-10x-24=x^2-12x+2x-24 \\ =x(x-12)+2(x-12) \\ =(x-12)(x+2) \end{gathered}[/tex]Therefore, the factorized form is,
[tex](x-12)(x+2)[/tex]which fraction on the number line is equal to 3
Answer:
? can't answer if there's no number line
What is the exponential form of sq.rt (5^x)?
Answer:
Step-by-step explanation:
Comment and Answer
√5^x
The square root is really 0.5 as a decimal or 1/2 as a fraction. Both are powers.
So the square root of 23 can be written as 23^.5
For your question, you divide the power (x) by 2 so it looks like this.
5^(x/2)
2) m angle2=x+88 50° 2 A) -8 C) 8 B) -7 D) 7
A
1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle
2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.
We can finally write
x+88 +50 +50 = 180
x +188 =180 subtract 188 from both sides
x= 180-188
x= -8
3) So x=-8 is the answer.
What is the domain of f(x)?
(-6 , 6)
[-4 , 5]
[-6 , 6]
(-4 , 5)
Answer:
{−6,−4}
Step-by-step explanation:
the domain is all the x- values of the points.
so -6 and -4 are repeated so they are the domain of the points.
Hi thank you so for all your time and help
Hello there. To solve this question, we'll have to remember some properties about trigonometric functions and the right triangle.
We want to find x such that:
[tex]\tan (x)=\sqrt[]{3}[/tex]We'll use the second right triangle to show what we want.
First, given a triangle:
We know that the hypotenuse will be:
[tex]\sqrt[]{x^2+y^2}[/tex]But most importantly, the tangent of the angles α and β can be calculated by only using the legs of the triangle: it is the ratio between the opposite side and the adjacent side to an angle.
[tex]\tan (\alpha)=\frac{y}{x}[/tex]and
[tex]\tan (\beta)=\frac{x}{y}[/tex]Now look at the triangle we have:
We can easily check that:
[tex]\sqrt[]{3}=\frac{\sqrt[]{3}}{1}[/tex]So it would be good to find something that relates the ratio between those two numbers: the tangent of 60º!!
Therefore, we have:
[tex]\tan (60^{\circ})=\frac{\sqrt[]{3}}{1}=\sqrt[]{3}[/tex]And the solution to x is:
[tex]x=60^{\circ}[/tex]This is to hard for me help me out please
Describe in words where cube root of 35 would be plotted on a number line. between 3 and 4, but closer to 3 between 3 and 4, but closer to 4 between 2 and 3, but closer to 2 between 2 and 3, but closer to 3
The ∛35 will be plotted between 3 and 4, but closer to 3 on the number line.
In basic mathematics, real numbers are shown as a fine graphic of a graduated straight line which is called a number line.
Every point on a number line is considered to correspond to a real number, and every real number is assumed to correspond to a point.The integers are typically shown as lines of specially chosen, evenly spaced dots. Even though the image only shows the integers from -3 to 3, as well as values that are in between the integers, the product contains all real numbers, going forever in both directions. When teaching the very foundations , addition and subtraction with negative numbers, it is widely used as a teaching technique.We know that 35 lies between 27 and 64 , and 27 = 3³ and 64 = 4³.
Hence the ∛35 will be plotted between 3 and 4 and since 35 is closer to 27 than 64 , therefore it will be closer to 3.
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all you need is in the photo please answer fastplease
Answer:
The cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]Explanation:
Let x and y represent the cost of a cupcake and cookie respectively.
Given that;
Five cupcakes and two cookies cost $19.75.
[tex]5x+2y=19.75-------1[/tex]Two cupcakes and four cookies cost $17.50.
[tex]2x+4y=17.50-------2[/tex]Let's solve the simultaneous equation by elimination;
multiply equation 1 by 2;
[tex]10x+4y=39.50-------3[/tex]subtract equation 2 from equation 3;
[tex]\begin{gathered} 10x-2x+4y-4y=39.50-17.50 \\ 8x=22 \\ \text{divide both sides by 8;} \\ \frac{8x}{8}=\frac{22}{8} \\ x=2.75 \end{gathered}[/tex]since we have the value of x, let substitute into equation 1 to get y;
[tex]\begin{gathered} 5x+2y=19.75 \\ 5(2.75)+2y=19.75 \\ 13.75+2y=19.75 \\ 2y=19.75-13.75 \\ 2y=6 \\ y=\frac{6}{2} \\ y=3.00 \end{gathered}[/tex]Therefore, the cost of cupcakes and cookies are;
[tex]\begin{gathered} \text{cupcakes = \$2.75} \\ \text{cookies = \$3.00} \end{gathered}[/tex]
a researcher obtains a list of all prisons in the u.s. she draws a random sample of 75 of the prisons on this list. she then obtains a list of all inmates from the warden at each of the 75 prisons and interviews a random sample of 30 inmates at each prison. this is a:
The researcher draws a random sample using a Multistage cluster sample
At each stage, you use smaller and smaller groups (units) to select a sample from a population. National surveys are frequently used to collect data from a large, geographically dispersed group of people. To use as your sample, you randomly select individual units from the cluster.
In multistage cluster sampling, the population is divided into clusters and some clusters are chosen in the first stage. You continue to break up the selected clusters into smaller clusters at each subsequent stage, and you do this until you reach the final step. In the final step, only a few members of each cluster are chosen for your sample.
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Part of the proceeds from a garage sale was 535$ worth of 5$ and 20$ bills. If there were 2 more 5$ bills than 20$ bills, find the number of each denomination
Using concept of Linear equation in two variables, we got 23 is denomination count of 5$ bills and 21 is denomination count of 20$ bills.
Linear equations are used to solve equation in which two variables are connected with each other via some specific methods.
The linear equations in two variables are the equations in which each one of the two variables are of the highest exponent order of the 1 and have one, none, or may be infinitely many solutions. The standard form of a two-variable linear equation is given by ax + by + c = 0 where x and y are the two variables. The solutions can also be written in form of ordered pairs like (x, y).
It is given that 5$ bills are 2 more than 20$ bills,
so let suppose 20$ bills denomination count is x,
then 5$ bills denomination count=x+2;
It is also given that 535$ worth is summation of 5$ bills and 20$ bills
Therefore,[5×(x+2)+(20×x)]=535
On solving for x, we get x=21
Therfore,20$ bills denomination count is 21,and 5$ bills denomination count is 23.
Hence,5$ bills denomination count is 23 and 20$ bills denomination count is 21
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what does x =?
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Find the median and mean of the data set below:
20, 46, 20, 26
3. The diameter of a spherical balloon shrinks to one-half of its original size.How does this affect the volume?Hint: Test two scenarios and compare the volumes! Show your work!!A. The volume is cut in halfB. The volume doublesC. The volume is 1/8 the original volumeD. The volume is 1/4 the original volume
Answer:
C. The volume is 1/8 the original volume
Explanation:
Step 1. To find how the volume changes if the diameter is reduced to one-half of the original size, we will test two scenarios:
• In the first scenario, the diameter will be 2, and in the second scenario, the diameter will be one-half of 2 which is 1.
We will find the volume for these two cases and see how it changes.
Step 2. For a diameter of d=2.
If the diameter is 2, the radius is:
[tex]\begin{gathered} r=d/2 \\ r=2/2 \\ r=1 \end{gathered}[/tex]Using the volume formula for a sphere:
[tex]V=\frac{4\pi}{3}r^3[/tex]In this case:
[tex]V=\frac{4\pi}{3}(1)^3[/tex]We will call this volume, V1:
[tex]V_1=\frac{4\pi}{3}[/tex]Step 3. Now we will find the volume for the second case in which the diameter is d=1.
The radius is:
[tex]\begin{gathered} r=d/2 \\ r=1/2 \\ \end{gathered}[/tex]Using the same formula for the volume:
[tex]V=\frac{4\pi}{3}(\frac{1}{2})^3[/tex]Solving the operations:
[tex]V=\frac{4\pi}{3}(\frac{1}{8})^[/tex]We will call this V2:
[tex]V_2=\frac{4\pi}{3}(\frac{1}{8})^[/tex]Step 4. As you can see, the first part of the previous expression is V1:
[tex]\begin{gathered} V_{1}=\frac{4\pi}{3} \\ V_2=\frac{4\pi}{3}(\frac{1}{8}) \end{gathered}[/tex]Therefore:
[tex]V_2=V_1(\frac{1}{8})[/tex]The second volume is the first volume multiplyed by 1/8 ⇒ it is 1/8 of the original volume.
Answer:
C. The volume is 1/8 the original volume
Nancy spent 2 1/2 hours working on her homework on the weekend. she spent 4/5 of her time working her ela homework. how much time did nancy spend working on her ela homework?
The time Nancy spent working on her ela homework is equal to 2 hours.
The time Nancy spent working on her ela homework can be calculated by multiplication.
We can calculate it by multiplying the fraction of time spent by her on ela homework by the total time she spent on her homework.
As the total time spent by her on homework is 2 1/2 hours we can covert it into decimals as;
2 1/2 = 5/2 = 2.5 hours
Now multiplying it by the fraction of her time spent on ela homework,
Time spent on ela homework = 4/5 × 2.5
Time spent on ela homework = 10/5
Time spent on ela homework = 2 hours.
Hence Nancy spent 2 hours working on her ela homework.
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by what factor does the intensity increase for each whole number increase in the richter scale?
Answer:
By adding the gravity of the earth ang subtracting the number of the enumeration and multiply the square root of need to be the first divorcee you know that I love ckicen nuggets
Step-by-step explanation:
Me to mama o sige na kain na kau
Assume the given function is one to one.Find the indicated values
To solve this question, you have to look for the answers in the table.
Let's analise each part of the question to solve it:
(a) f(1) =
f(1) means the output of the function [f(x)] when x = 1.
Looking for x =1 in the table, you can see that f(x) = 0.
f(1) = 0.
(b) f(x) = 3, x =
Now, you have to find the input (x) when the outpout [f(x)] is 3.
Looking for f(x) = 3, you can see that x = 7.
f(x) = 3, x = 7.
(c) f⁻¹(0) =
Now, you have to evaluate the inverse function.
To look for the values of the inverse function, x will be the output and f⁻¹ will be the input.
To look for f⁻¹(0), look for f(x) = 0 (input) and the output will be 1
f⁻¹(0) = 1.
(d) f⁻¹(x) = 7; x =
Again, you have an inverse function. So, 7 will be the input in the table (x). x is 7 (output).
f⁻¹(x) = 7; x = 3.
Last month, Sally and Roger sold candy to raise money for their debate team. Roger sold 1/3 as much candy as Sally did. If Sally sold 2 9/10 boxes of candy, how many boxes of candy did Roger sell?
The boxes of candy sold by Roger are 29/30.
According to the question,
We have the following information:
Roger sold 1/3 as much candy as Sally sold.
Sally sold [tex]2\frac{9}{10}[/tex] boxes of candy.
Now, first we will convert the boxes of candy sold by Sally from the mixed fraction.
(More to know: there are three kinds of fraction: mixed fraction, proper fraction and improper fraction. We need to change mixed fraction in most of the cases to solve the questions further.)
We have:
29/10
Now, we know that the boxes of candy sold by Roger is 1/3 of 29/10.
So, we have the following expression:
[tex]\frac{1}{3}* \frac{29}{10}[/tex]
29/30
Hence, the boxes of candy sold by Roger is 29/30.
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Choose the correct answer for each row.
Match each equation to the value of x that is the solution. Values of x may be used more than once and some will not be used.
Answer:
Step-by-step explanation:
given that tank=8 and sinx is negative determine sin(2x) cos(2x) and tan(2x)
Answer:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
Explanation:
the tangent of an angle is equal to the opposite side over the adjacent side. So, if the tan(x) = 8, we can represent this as the following diagram:
Therefore, we can calculate the value of the hypotenuse as:
[tex]\text{Hypotenuse = }\sqrt[]{8^2+1^2}=\sqrt[]{64+1}=\sqrt[]{65}[/tex]With the hypotenuse, we can calculate sin(x) and cos(x) as follows:
[tex]\begin{gathered} \sin x=\frac{Opposite}{hypotenuse}=-\frac{8}{\sqrt[]{65}} \\ \cos x=\frac{\text{Adjacent}}{\text{hypotenuse}}=-\frac{1}{\sqrt[]{65}} \end{gathered}[/tex]We type the negative sign because the question says that sin(x) is negative.
Now, we will use the following trigonometric identities to find sin(2x), cos(2x) and tan(2x)
[tex]\begin{gathered} \sin 2x=2\sin x\cos x \\ \cos 2x=1-2\sin ^2x \\ \tan 2x=\frac{2\tan x}{1-\tan ^2x} \end{gathered}[/tex]Therefore, replacing the values, we get:
[tex]\sin 2x=2(\frac{-8}{\sqrt[]{65}})(\frac{-1}{\sqrt[]{65}})=\frac{16}{65}[/tex][tex]\cos 2x=1-2(\frac{-8}{\sqrt[]{65}})^2=1-2(\frac{64}{65})=-\frac{63}{65}[/tex][tex]\tan 2x=\frac{2(8)}{1-8^2}=-\frac{16}{63}[/tex]So, the answers are:
sin2x = 16/65
cos2x = -63/65
tan2x = -16/63
Write an equation of a line that goes through (4, 1) and has a slope of 2.
Five less than a number is at least eight
What.
is it 13?
.......................
5 (u - 5) + 6u = 8 solve for u and simplifly your answer as much as possible
Answer:
u = 3
Step-by-step explanation:
Step 1: Distribute 5 in u - 5
[tex]\displaystyle{5\cdot u - 5\cdot 5 +6u=8}\\\\\displaystyle{5u-25+6u=8}[/tex]
Step 2: Add like terms together (u-term)
[tex]\displaystyle{11u-25=8}[/tex]
Step 3: Add both sides by 25
[tex]\displaystyle{11u-25+25=8+25}\\\\\displaystyle{11u=33}[/tex]
Step 4: Divide both sides by 11
[tex]\displaystyle{\dfrac{11u}{11}=\dfrac{33}{11}}\\\\\displaystyle{u=3}[/tex]
Answer Check
Step 1: Substitute u = 3 in the equation
[tex]\displaystyle{5(3-5)+6(3)=8}[/tex]
Step 2: Evaluate & Simplify
[tex]\displaystyle{5(-2)+18=8}\\\\\displaystyle{-10+18=8}\\\\\displaystyle{8=8}[/tex]
Since the equation is true after substituting u = 3. Therefore, the answer is u = 3.
Please let me know if you have any questions!
determine the equation of line from the graph
Answer:
y = -x
Step-by-step explanation:
Answer: Y=-X
Step-by-step explanation:
Select the correct answer from each drop-down menu.
AABC is translated 6 units up and 3 units left to create AABC
If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at
Reset
V
and vertex B is at
Next
From the translation described, If vertex A is at (-1, 2) and vertex B is at (1, 5), then vertex A' is at (-4, 8). See the justification for the same below.
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect. Angles, polygons, polyhedra, and graphs are the most typical places to find vertices. Nodes are another name for graph vertices.
The explanation of the translation is given as follows:
According to the translation rule for translating a point h units left is given as:- (x, y) → (x-h, k)
The translation rule for translating point k units up is given as:
(x,y) → (x, y+k).
Since ∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5).
Then,
The vertex A' =
A (-1, 2) → (-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at (-4,8).
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From the translation described, the vertex A' is at the point (-4,8).
What is a vertex?A vertex is a specific point of a mathematical object that is often where two or more lines or edges intersect.
Angles, polygons, and graphs are the most typical places to locate the vertices.
The explanation of the translation will be:
Based on the translation rule for translating a point h units left is follows as
(x, y) → (x-h, k)
The translation rule for point k units up is follows as:
(x,y) → (x, y+k).
Since ∆ABC is translated to the 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at; (1, 5).
The vertex A' ;
A (-1, 2)
(-1 -3, 2+6)
= (-4, 8)
Therefore, the vertex A' is at the point (-4,8).
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two angles are a linear pair, and one has twice the measure of the other. Find the smaller angles measure
Answer:
60°Step-by-step explanation:
two angles are a linear pair, and one has twice the measure of the other. Find the smaller angles measure
linear pair = 180°
180 : 3 = 60° (smaller angle)
60° x 2 = 120° (bigger angle)
120 is twice 60 and the sum is 180°
the answer is good
