The formula for finding amount in an investment that involves compound interest is
[tex]A=Pe^{it}[/tex]Where
A is the future value
P is the present value
i is the interest rate
t is the time in years
e is a constant for natural value
From the question, it can be found that
[tex]\begin{gathered} P=\text{ \$3000} \\ i=2\frac{9}{12}years=2\frac{3}{4}years=2.75years \end{gathered}[/tex][tex]\begin{gathered} e=2.7183 \\ i=2.9\text{ \%=}\frac{2.9}{100}=0.029 \end{gathered}[/tex]Let us substitute all the given into the formula as below
[tex]A=3000\times e^{0.29\times2.75}[/tex][tex]\begin{gathered} A=3000\times2.21999586 \\ A=6659.987581 \end{gathered}[/tex]Hence, the amount in the account after 2 years and 9 months is $6659.99
I need help with my pre-calculus homework, the image of the problem is attached. Please show me how to solve this problem, thank you!
Given the following equation:
[tex]\text{ }\frac{\text{ 2}}{5x}\text{ + 4 = }\frac{2}{x}[/tex]Let's find x,
[tex]\text{ }\frac{\text{ 2}}{5x}\text{ + 4 = }\frac{2}{x}[/tex][tex]\text{ 5x( }\frac{\text{ 2}}{5x}\text{ + 4) = (}\frac{2}{x})5x[/tex][tex]\text{ 5x(}\frac{\text{ 2}}{5x})\text{ + 5x(4) = (}\frac{2}{x})5x[/tex][tex]\text{ 2 + 20x = 10}[/tex][tex]\text{ 2 + 20x - 2 = 10 - 2}[/tex][tex]\text{ 20x = 8}[/tex][tex]\text{ }\frac{\text{20x}}{20}\text{ = }\frac{\text{8}}{20}[/tex][tex]\text{ x = }\frac{8}{20}[/tex][tex]\text{ x = }\frac{\frac{8}{4}}{\frac{20}{4}}\text{ = }\frac{2}{5}[/tex]Therefore, the answer is letter A: 2/5
Your friend Pat bought a fish tank that has a volume of 175 liters. The brochure for Pat's tank lists a "fun fact that it would take 7.43 x 1018 tanks of that sizeto fill all the oceans in the world. Pat thinks the both of you can quickly calculate the volume of all the oceans in the world using the fun fact and the size ofher tankPart a.) Given that 1 liter = 1.0 x 10-12 cubic kilometers, rewrite the size of the tank in cubic kilometers using scientific notation.b) Determine the volume of all the oceans in the world in cubic kilometers using the "fun fact"
The tank has a volume of 175 liters
Fun fact: it would take 7.43*10¹⁸ tanks that size to fill all the oceans in the world.
a) Using the convertion 1 liter = 1.0*10⁻¹²km³ you have to rewrite the size of the tank.
For this you have to use cross multiplication:
1 Lts = 1.0*10⁻¹²
175Lts=x
[tex]x=175\cdot1.0\cdot10^{-12}=1.75\cdot10^{-10}[/tex]The volume of the tank is equal to 1.75*10⁻¹⁰ km³
b)
You know that one tank has a volume of 1.75*10⁻¹⁰ km³
To know what volume would 7.43*10¹⁸ tanks of the same size have, multiply the volume of one tank by the number of tanks.
[tex]1.75\cdot10^{-10}\cdot7.43\cdot10^{18}=1300250000\operatorname{km}^3[/tex]Using the fun fact, the determined volume of all oceans in the world is 1300250000km³
A bus travels 8.4 miles eastand then 14.7 miles north.What is the angle of the bus'resultant vector?Hint: Draw a vector diagram.O[?]
A bus travels 8.4 miles east and then 14.7 miles north.
What is the angle of the bus resultant vector?
see the figure below to better understand the problem
The angle of the bus resultant vector R is equal to
tan(x)=14.7/8.4
mm
gB - N³B = d what does B equal?
Answer:
[tex]b \: = \frac{d}{(g - {n}^{3} )} [/tex]
What is the slope of the line that passes through (5,4) and (7,10)a.3b. -3 C. 2D.-2
To find a slope of a line we need two points, so we will do it as follows.
[tex]m=\frac{\Delta y}{\Delta x}=\frac{10-4}{7-5}=\frac{6}{2}=3[/tex]Therefore it is (a) the slope is 3.
Answer:
a.3
Step-by-step explanation:
To find the slope, use the slope formula
m = ( y2-y1)/(x2-x1)
= ( 10-4)/(7-5)
= 6/2
= 3
Can someone give me the answer for my last blank
Answer:
[tex]-\frac{1}{2}[/tex]Step-by-step explanation:
Since we have that:
[tex]p=-0.5[/tex]We'll have that:
[tex]\frac{1}{4p}\rightarrow\frac{1}{4(-0.5)}\rightarrow-\frac{1}{2}[/tex]Therefore, we can conclude that the answer is:
[tex]-\frac{1}{2}[/tex]Find the negative member of the solution set for |2x -4| =6
The negative solution of the absolute value function is x = - 1.
What is the negative solution of an absolute value set?In this problem we need to solve for x in an absolute value function, whose procedure is done by the use of algebra properties:
Step 1 - Initial condition:
|2 · x - 4| = 6
Step 2 - By definition of absolute value:
2 · x - 4 = 6 or - 2 · x + 4 = 6
Step 3 - By compatibility with addition, existence of additive inverse, associative, commutative and modulative properties:
2 · x = 10 or - 2 · x = 2
Step 4 - By compatibility with multiplication, existence of multiplicative inverse, associative, commutative and modulative properties we get this result:
x = 5 or x = - 1
The negative solution of the function is x = - 1.
To learn more on absolute value functions: https://brainly.com/question/14364803
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complete the equation of the line through (-1,6) and (,7-2)
The two points given are
A(-1, 6)
B(7, -2)
We shall start by calculating the slope of the line, since we've been given two points.
[tex]\begin{gathered} \text{The slope which is m, is derived as;} \\ m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{-2-6}{7-\lbrack-1\rbrack} \\ m=\frac{-8}{7+1} \\ m=\frac{-8}{8} \\ m=-1 \end{gathered}[/tex]Next we shall derive the y-intercept, by inserting the known values into the equation in slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ We\text{ shall use the first set of coordinates, that is (-1, 6)} \\ 6=-1(-1)+b \\ 6=1+b \\ 6-1=b \\ b=5 \end{gathered}[/tex]Having calculated the values of m (the slope) and b (the y-intercept), the equation is now;
[tex]\begin{gathered} y=mx+b \\ y=-1x+5 \\ y=-x+5 \end{gathered}[/tex]How many terms are existed in between 10 to 1000 which are divisible by 6?
Answer:166
Step-by-step explanation: There are 166 integers between 1 and 1,000 which are divisible by 6
A bag contains 8 red marbles, 2 blue marbles, 5 white marbles, and 7 black marbles. What is the probability of randomly selecting:A white marble:A red marble:A red marble, white or blue marble: A black marble: A green marble:
A spinner can land on either red or blue You spin seven times and then roll a six sided die. Find the number of possible outcomes in the sample space?
If we spin the spinner once, we can get two possible outcomes (red or blue).
If we spin it twice, the outcomes can be (blue, blue), (blue, red), (red, blue), (red, red); this is, 4 different results.
Then, if we spin the spinner 7 times, there are 2^7=128 possible outcomes.
Finally, we can get any of the 128 possible outcomes from the spinner and rolling a 1; similarly, for rolling a 2, 3,..., 6.
Therefore, the number of possible outcomes of spinning the spinner seven times and rolling a die is
[tex]2^7\cdot6=128\cdot6=768[/tex]There are 768 possible outcomes in the sample space.
If y varies directly with x and y = 90 when 3 = 15, then what is y when = 4?y =+
Recall than a direct variation implies the following type of relationship between y and x:
y = k * x
where k is a constant value
Then you have (by dividing by x, the following:
y / x = k (the constant)
then, we are told that when y = 90 , x = 15, so we have:
90 / 15 = k
6 = k
so,now that we know what the constant k is (6), we can answer the question: What is y when x = 4?
so we write:
y = k * x
y = 6 * 4
y = 24
This is the value of y when x is 4 since the constant k is 6 as we found above.
Another example:
We need to find the variation relationship for a case that when y = 6, x = 12
We think the same way we did before, starting with the fact that a direct variation is of the form:
y = k * x
given the info that when x = 12, y = 6, we can find the constant k:
6 = k * 12
divide by 12 both sides:
6/12 = k
1/2 = k
So k is 1/2 (one half)
Then we can write the variation as:
y = (1/2) x
(the product of 1/2 times x)
Identify the word described by the following statement.The type of rule in which you can find any number of term in the sequence without knowing the first or previous term.
Recursive is the type of rule in which you can find any number of term in the sequence without knowing the first or previous term.
Hence, the answer is Recursive.
In a blood testing procedure, blood samples from 6 people are combined into one mixture. The mixture will only test negative if all the individual samples are negative. If the probability that an individual sample tests positive is 0.11. What is the probability that the mixture will test positive?
From the information available, the mixture will test negative if all 6 samples are negative.
The probability of each is independent of the other for all 6 samples.
The probability of a sample testing positive is 0.11. That means the probability of a sample testing negative would be
[tex]\begin{gathered} P\lbrack neg\rbrack=1-P\lbrack pos\rbrack \\ P\lbrack\text{neg\rbrack}=1-0.11 \\ P\lbrack\text{neg\rbrack}=0.89 \end{gathered}[/tex]However, for all 6 samples, the probability of having a negative result would be a product of probabilities, that is;
[tex]\begin{gathered} P\lbrack tests\text{ negative}\rbrack=0.89\times0.89\times0.89\times0.89\times0.89\times0.89 \\ P\lbrack\text{tests negative}\rbrack=0.89^6 \\ P\lbrack\text{tests negative\rbrack}=0.4969 \end{gathered}[/tex]Therefore if we have the probability of the mixture testing negative as
[tex]P_{\text{neg}}=0.4969[/tex]The probability of the mixture testing positive would be;
[tex]\begin{gathered} P_{\text{pos}}=1-P_{\text{neg}} \\ P_{\text{pos}}=1-0.4969 \\ P_{\text{pos}}=0.5031 \end{gathered}[/tex]ANSWER:
The probability that the mixture will test positive is 0.5031
Rounded to 2 decimal places,
[tex]P_{\text{pos}}=0.50[/tex]Find an equation of the line described below. Write the equation in slope-intercept form (solved for y), when possible Through (15,5) and (5,15)
Given that the required linepasses through the points (15, 5)and (5, 15).
Find the slope of the line using teo-point formula.
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{15-5}{5-15} \\ =\frac{10}{-10} \\ =-1 \end{gathered}[/tex]Substitute the value of m into theslope-intercept form y = mx+c.
[tex]y=-x+c[/tex]Plug in the point (5, 15)to find c, the y-intercept.
[tex]\begin{gathered} 15=-5+c \\ c=20 \end{gathered}[/tex]Thus, y = -x + 20, which is the required equation of line.
Eliza had $14 and Emma had $64 more than Eliza how much did Emma have?
Given
Eliza had $14
Emma had $64 more than Eliza
Find
how much did Emma have
Explanation
as we have given
Eliza has $14
so , Emma = $64 + $14 = $78
Final Answer
Therefore , the Emma had $78
NEED HELP DUE BY WEDNESDAY OR TOMMOROW. Solve each of the equations and select the numbers that represent solutions to more than one of the six equations. Select all that apply. 4x-3=17. 8(x + 1) = 24. 5(x - 2) = 20. 34 - 7x = 20. 31 - x = 29. 3x +6=21. A. x=1. B. x=2. C. x=3. D. x=4.E. x=5. F. X = 6.
We are to solve for x in all the equations and select the ones that occur more than one solution.
Hence,
[tex]\begin{gathered} 4x-3=17 \\ 4x=17+3 \\ 4x=20 \\ x=\frac{20}{4}=5 \\ \therefore x=5 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 5(x-2)=20 \\ x-2=\frac{20}{5} \\ x-2=4 \\ x=4+2=6 \\ \therefore x=6 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 31-x=29 \\ 31-29=x \\ 2=x \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 8(x+1)=24 \\ x+1=\frac{24}{8} \\ x+1=3 \\ x=3-1=2 \\ \therefore x=2 \end{gathered}[/tex]Next,
[tex]\begin{gathered} 34-7x=20 \\ 34-20=7x \\ 14=7x \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \\ \Rightarrow x=2 \end{gathered}[/tex]Lastly,
[tex]\begin{gathered} 3x+6=21 \\ 3x=21-6 \\ 3x=15 \\ x=\frac{15}{3}=5 \\ \therefore x=5 \end{gathered}[/tex]Hence, the numbers that represent solutions to more than one of the six equations are
[tex]\begin{gathered} x=2\text{ \lparen Option 2\rparen} \\ x=5\text{ \lparen Option 5\rparen} \end{gathered}[/tex]based on the data provided what was the rent expenses each month
From the table it can be observed that rate expense for a month is -$1,120.00. The negative value means that amount is reduced.
So rent expense is -$1,120.00, where negative sign is for decrease in amount.
Consider similar figure QRS and TUV below Where QRS is the pre image of TUV.Part A: What is the scale factor ? Part B:Find the the length of RS.
Consider similar figure QRS and TUV below Where QRS is the pre image of TUV.Part A: What is the scale factor ? Part B:Find the the length of RS.
Part A
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional, and this ratio is called the scale factor
so
In this problem
we have that
QS/TV=QR/TU=RS/UV
that means, that the scale factor is
scale factor=TV/QS
substitute the given values
scale factor=2.8/7=0.4
scale factor=0.4Part B
Find the the length of RS
we have that
The length of RS is equal to the length of UV divided by the scale factor
so
RS=5.7/0.4
RS=14.25Part 2
Using the data in this table, what would be the line ofbest fit ( rounded to the nearest tenth)?
Solution
Note: The formula to use is
[tex]y=mx+b[/tex]Where m and b are given by
the b can also be given as
[tex]b=\bar{y}-m\bar{x}[/tex]The table below will be of help
We have the following from the table
[tex]\begin{gathered} \sum_^x=666 \\ \sum_^y=106.5 \\ \operatorname{\sum}_^x^2=39078 \\ \operatorname{\sum}_^xy=6592.5 \\ n=10 \end{gathered}[/tex]Substituting directing into the formula for m to obtain m
[tex]\begin{gathered} m=\frac{10(6592.5)-(666)(106.5)}{10(39078)-(666)^2} \\ m=\frac{-5004}{-52776} \\ m=0.09481582538 \\ m=0.095 \end{gathered}[/tex]to obtain b
[tex]\begin{gathered} \bar{y}=\frac{\operatorname{\sum}_^y}{n} \\ \bar{y}=\frac{106.5}{10} \\ \bar{y}=10.65 \\ and \\ \bar{x}=\frac{\operatorname{\sum}_^x}{n} \\ \bar{x}=\frac{666}{10} \\ \bar{x}=66.6 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} b=\bar{y}- m\bar{x} \\ b=10.65-(0.095)(66.6) \\ b=4.323 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} y=mx+b \\ y=0.095x+4.323 \end{gathered}[/tex]To the nearest tenth
[tex]y=0.1x+4.3[/tex]The least square method didn't give an accurate answer, so we use a graphing tool to estimate instead
Here
m = 0.5 (to the nearest tenth)
b = -23.5 (to the nearest tenth)
The answer is
[tex]\begin{gathered} y=mx+b \\ y=0.5x-23.5 \end{gathered}[/tex]1. Evaluate the following expressions if a = 2. b = 3, x = 4, and y = 5.+3(27-»
When a=2, b=3, x=4, and y=5,
evaluate:
[tex]b^2+3(2x-y)[/tex]Let's replace b, x and y by the appropriate values:
[tex](3)^2+3(2(4)-5)[/tex]now let's solve what is inside the parenthesis:
[tex]9+3(8-5)[/tex]again more solving inside the second parenthesis:
[tex]9+3(3)[/tex]and again, first multiplying what is indicated. Recall that the rule PEMDAS for order of operations indicates that Parenthesis have to be solved first, then exponents, then multiplications and divisions, and the VERY LAST is additions and subtractions:
[tex]9+9=18[/tex]You do the same type of replacement of variables wit numbers, and then use of the rules for order of operations to evaluate the rest.
Like:
[tex]ab+ya^3[/tex]and then evaluate:
[tex]\frac{y+ab}{b+x}[/tex]which of the following is the equation that represents the function given in the table
To determine which of the given equations represents the function given in the table, let us analyze each of them.
The first two equations do bring not integer numbers in such a way that, if we substitute any of the x values given, we will find a y value which is not an integer. This means that both are not the ones we are looking for.
Now, to determine if the third or the fourth is the one, let us substitute one of the x values on it, and if the y value matches, it means that it might be correct.
Checking the fourth, let's use the values:
[tex]\begin{gathered} x=-2 \\ y=16 \end{gathered}[/tex]Substituting the value of x in the equation of the fourth option, we have:
[tex]\begin{gathered} y=6\times(-2)-5 \\ y=-12-5 \\ y=-17 \end{gathered}[/tex]Because the y value found was not the one given, the option is wrong!
Let's check the third option with the same values of x and y:
[tex]\begin{gathered} y=-5\times(-2)+6 \\ y=10+6 \\ y=16 \end{gathered}[/tex]It matches. This substitution alone does not assure this is the right answer, but once it can not be anyone of the other three, and once we expect that one of the four is the function, this match becomes enough for our final answer:
C) y = -5x + 6
hello can you help me with this trigonometry question and in the question I have to answer it in radians hopefully you can help me please
Answer
(34π/7) = (6π/7) in the range of 0 and 2π.
Explanation
We are asked to find an angle between 0 and 2π that are coterminal with (that is, equal to) (34π/7).
34π/7 is 4.857π in decimal form, indicating that it is outside the required range. To find its equivalent in the required range, we keep going a full revolution (2π) till we get there.
(34π/7) - 2π = (20π/7)
This is 2.857π, which is still outside the required range, so, we subtract another revolution from this
(20π/7) - 2π = (6π/7)
This is 0.857π and it is solidly in the required region.
Hope this Helps!!!
Which graphed matches the equation y+6= 3/4 (x+4)?
To start, it is important to find the slope intercept form of the equation
[tex]\begin{gathered} y+6=\frac{3}{4}(x+4) \\ y+6=\frac{3}{4}x+3 \\ y=\frac{3}{4}x+3-6 \\ y=\frac{3}{4}x-3 \end{gathered}[/tex]Once we have the slope intercept form we know that the y intercept is -3 and the slope is positive, it means the line is increasing
The graph will look like this
Property valued at $56,000 is assessed at of itsvalue. If the yearly tax is calculated as $3 per $100 ofassessed value, what is the yearly tax on this property?A. $ 420B. $1.120C. $1,260D. $1,680E $2,240
Since the yearly tax is calculated as $3 per $100 of assessed value, which is 3/4 of $56,000 , the yearly tax on this property can be calculated as: $56,000*3/4*$3/$100 = $ 1260. The answer is option C.
B>DGiven:. E is the midpoint of ADE is the midpoint of BCProve: ΔΑΕΒΑ ΔDECE is the midpoint of ADGiven
We are given a mid-point for segments AD and BC, we have the following:
segments AE and DE are congruent, that is:
[tex]AE\cong DE[/tex]By definition of mid-point.
Segments BE and CE are congruent, that is:
[tex]BE\cong CE[/tex]By definition of mid-point.
We also have that angles AEB and DEC are congruent, that is:
[tex]\angle AEB\cong\angle DEC[/tex]By the vertical angles theorem, which states that when two lines intercept their vertical or opposite angles are equal or congruent.
Now we can conclude that triangles AEB and DEC are congruent, that is:
[tex]\Delta AEB\cong\Delta DEC[/tex]Due to the Side-Angle-Side Theorem, which states that when two triangles have two congruent sides and the angle between the congruent sides also congruent, then the triangles are congruent.
How do you solve the y-intercept of y = 9x + 9 and what is it simplified?
to know y -intercept we only need to replace x by 0. And we get
[tex]y=9\cdot0+9=9[/tex]so the y-intercept is 9
The formula Total cost=C+Shipping cost+Installation is used to find the total cost of a business asset. The formula can be written in symbols as T=C+S+I. Solve the formula for I, the Installation cost of the asset.
Formulas
The formula for the Total Cost is given as:
T = C + S + I
Where C is the shipping cost, I is t
Julie wants to purchase a jacket that costs $125. So far she has saved $42 and plans tosave an additional $25 per week. She gets paid every Friday, so she only gets money toput aside once a week. How many weeks, x, will it take for her to save at least $125?
cost of the jacket = $125
money saved = $42
extra savings = $25/week
Ok
125 = 42 + 25w
w = number of weeks
Solve for w
125 - 42 = 25w
83 = 25w
w = 83/25
w = 3.3
She needs to save at least 3.3 weeks
A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds. How thick will the paper be if you could fold it 10 times?About an inchAbout 2 inchesAbout 3 inchesAbout 4 inches
Given: A piece of paper is folded into half repeatedly. The thickness of the paper in inches is modeled by the function y = 2x/1000, where x is the number of folds.
Required: To determine the thickness of the paper if the paper is folded 10 times.
Explanation: The thickness of the paper is given by the function
[tex]y=\frac{2x}{1000}[/tex]Here, x is the number of folds=10
Hence,
[tex]\begin{gathered} y=\frac{2\times10}{1000} \\ =0.02\text{ inches} \end{gathered}[/tex]Final Answer: After 10 folds, the thickness of the paper is 0.02 inches.