Given that Mike borrowed an amount for 2 years at 2% simple interest, and paid back a total of $3952.
To Determine: The original money he borrowed
Solution:
The formula to find the amount for simple interest is
[tex]A=P(1+rt)[/tex]Where:
A is the Amount paid back
r is the rate
t is the time
Given that
[tex]\begin{gathered} A=3952 \\ r=\frac{2}{100}=0.02 \\ t=2 \end{gathered}[/tex]Substitute the given into the formula
[tex]\begin{gathered} A=P(1+rt) \\ 3952=P(1+0.02\times2) \\ 3952=P(1+0.04) \\ 3952=P(1.04) \\ 3952=1.04P \\ P=\frac{3952}{1.04} \\ P=3,800 \end{gathered}[/tex]Hence, the Mike originally borrow $3,800
Use the model A = Pe^rt to determine the average rate of return under continuous compounding. Round to thenearest tenth of a percent. Avoid rounding in intermediate steps.
Given
[tex]\begin{gathered} P=\$10,000 \\ A=\$14,296.88 \\ t=4 \\ \text{Find }r \end{gathered}[/tex][tex]\begin{gathered} A=Pe^{rt} \\ \text{Solve for }r \\ \frac{A}{P}=\frac{Pe^{rt}}{P} \\ \frac{A}{P}=\frac{\cancel{P}e^{rt}}{\cancel{P}} \\ e^{rt}=\frac{A}{P} \\ \ln e^{rt}=\ln \mleft(\frac{A}{P}\mright) \\ rt=\ln \mleft(\frac{A}{P}\mright) \\ r=\frac{\ln \mleft(\frac{A}{P}\mright)}{t} \\ \\ \text{Substitute the following values} \\ r=\frac{\ln \mleft(\frac{14296.88}{10000}\mright)}{4} \\ r=0.089364\rightarrow8.9364\% \\ \\ \text{Round to tenth of a percent} \\ r=8.9\% \end{gathered}[/tex]Therefore, the average rate of return under continous compounding is approximately 8.9%.
Using the values from the graph, compute the values for the terms given in the problem. Percentage of Market Value of Car (solid line) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 0 Maintenance and Repair Costs as Percentage of Car's Value (dashed line) Ist yr. 2nd yr: 3rd yr. 4th yr. 5th yr. 6th yr. 7th yr. 8th yr. 9th yr. 10th yr. Age of car = 5 years. Original cost = $16,995. The current market value is $ O 13,596.00 0 3,399.00 5,098.50 11,896.50
We can use the graph to find the percentage of the value that correspond to a 5-year-old car in respect to its original value.
For a car that is 5 years old, its value is 20% of the original value.
If the original value is $16,995, we can calculate its actual value multypling its original price by the proportion of value that we have taken from the graph:
[tex]V=0.2\cdot16,995=3,399[/tex]Answer: the current market value is $3,399.
Please help me with this problem I am not able to help my son to understand we keep getting it wrong please help.The function y=−16x^2+v0x models Lindy's height in feet above a trampoline x seconds after she jumps straight up. In the equation of the function, v0 is her initial velocity in feet per second. Lindy lands back on the trampoline 1 second after she jumps. What is the value of v0?Enter your answer in the box.v0= ft/s
EXPLANATION:
We are given the function which models Lindy's height x seconds after she jumps straight up a trampoline. The function is expressed as;
[tex]y=-16x^2+v_0[/tex]Where x is the time in seconds after she jumps, and v_0 is the initial velocity. The result of the function is her height after jumping with the given time x.
If she lands back on the trampoline one second after she jumps, then she is at a height of zero.
The function can now be re-written as follows;
[tex]\begin{gathered} \text{With;} \\ x=1\text{ (time)} \\ y=0\text{ (height)} \end{gathered}[/tex][tex]0=-16(1)^2+v_0[/tex]We can now simplify;
[tex]-16(1)^2+v_0=0[/tex]Add
[tex]-16(1)^2[/tex]to both sides;
[tex]\begin{gathered} v_0=16(1)^2 \\ v_0=16 \end{gathered}[/tex]Therefore;
ANSWER:
The value of v_0( her initial velocity) is;
[tex]v_0=16[/tex]Evaluate your answers as a fraction in simplest form [tex]( \frac{1}{3} ) {4} [/tex]
A fraction in simplest form is 1/81.
[tex]\left(\frac{1}{3}\right)^4[/tex]
Apply exponent rule: [tex]$\left(\frac{a}{b}\right)^c=\frac{a^c}{b^c}$[/tex]
[tex]=\frac{1^4}{3^4}[/tex]
[tex]$$\begin{aligned}&1^4=1 \\&=\frac{1}{3^4}\end{aligned}$$[/tex]
[tex]$$\begin{aligned}&3^4=81 \\&=\frac{1}{81}\end{aligned}$$[/tex]
A fraction is a portion of a larger total. The number is expressed in arithmetic as a quotient, which is the numerator divided by the denominator. Both are integers in a simple fraction. A complicated fraction contains a fraction in either the numerator or the denominator. A suitable fraction has a numerator that is less than the denominator.
In mathematics, a fraction is defined as a portion of the whole. If a pizza is cut into four equal pieces, each slice is represented by 14. Fractions make it easier to distribute and judge numbers and speed up calculations.
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Translate this phrase into an algebraic expression.64 less than twice Greg's heightUse the variable g to represent Greg's height.A+ローロ園×園.x & S?
Answer
64 < 2g
Explanation
Let Greg's height be g
We need to express in equation form,
64 less than twice Greg's height
Greg's height = g
Twice Greg's height = 2g
64 less than twice Greg's height = 64 < 2g
Hope this Helps!!!
Ari took their partner out for dinner and got a check for $60.67. Ari wants to leave a 20% tip. How much is the tip? How much is the total cost for the meal? SHOW ALL OF YOUR WORK.
Given the following question:
Check = $60.67
Ari wants to leave a 20% tip
To find the answer we have to find 20% of $60.67
[tex]\frac{20\times60.67}{100}=20\times60.67=1213.4\div100=12.134[/tex][tex]\begin{gathered} 12.134 \\ 4\text{ < 5} \\ 12.13 \end{gathered}[/tex]The tip is $12.13
The total cost = tip + check
[tex]12.13\text{ + 60.67=}72.8[/tex]The total costs = $72.8
Graph the line. I am only able to use 2 points on this graph.
In order to graph line first we need to calculate the equation of the line
[tex]y-y_1=m(x-x_1)[/tex]where m is the slope and (x1,y1) is a line where the line passing throught
in our case
m=3/4
(x1,y1)=(-4,5)
[tex]y-5=\frac{3}{4}(x+4)[/tex]Then we isolate the y
[tex]y=\frac{3}{4}x+3+5[/tex][tex]y=\frac{3}{4}x+8[/tex]We can calculate another point to obtain the graph in this case the y-intercept (0,8)
The points are
(-4,5) and (0,8)
the graph is
After crossing a bridge, Brian drives at a constant speed. The graph below shows the distance (in miles) versus the time since he crossed the bridge (in FUse the graph to answer the questions.1140100Distance (miles)5020Time (hours)OR(a) How much does the distance increase for each hoursince Brian crossed the bridaeExplanation Check2022 McGraw Hill LLC. All Rights Reserved. Terms of UsePrivacy Cer2Tyne here to search
EXPLANATION
Since Brian drives at a constant speed, in order to get the rate, we need to compute the slope, by applying the slope equation, as shown as follows:
[tex]\text{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]Where (x_1,y_1)=(20,100) (x_2,y_2)= (50,140)
Plugging in the terms into the slope equation:
[tex]\text{Slope}=\frac{140-100}{50-20}=\frac{4}{3}[/tex]In conclusion, the distance will increase by 4 miles per hour.
Find the area of the triangle specified below.
a = 9 meters, b=4 meters, c = 6 meters
A = square meters
(Round to the nearest integer as needed.)
The answer will be 9.562m² using a triangle.
What is are of triangle?
The territory included by a triangle's sides is referred to as its area. Depending on the length of the sides and the internal angles, a triangle's area changes from one triangle to another. Square units like m2, cm2, and in2 are used to express the area of a triangle.
The perimeter will be P = sum of all three side.
s = p/2 = 9.5
Side a = 9 meters, b=4 meters, c = 6 meters
A = [tex]\sqrt{(s)(s-a)(s-b)(s-c)}\\=\sqrt{(9.5)(9.5-9)(9.5-4)(9.5-6)}\\[/tex]
A = 9.562m²
Hence the Area of the triangle is 9.562m².
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The expression 5a + 3c can be used to find the cost of a adults and c children to attend the school play. What is the cost of 4 adults and 9 children to attend the school play?
The expression 5a + 3c can be used to find the cost of a adults and c children to attend the school play, so we have a expression as a function of the number of adults a and the number of children c. Therefore:
[tex]C(a,c)=5a+3c[/tex]What is the cost of 4 adults and 9 children to attend the school play?
[tex]\begin{gathered} a=4 \\ c=9 \\ C(4,9)=5(4)+3(9) \\ C(4,9)=20+27 \\ C(4,9)=47 \end{gathered}[/tex]$47
the table shows the scores of 20 people who took the paramedics licensing test. Find the mean and the standard deviation of the data. the deviation answer needs to be rounded to three decimal places as needed.
a) Mean = 76
b) Standard deviation = 6.728
Explanation:The data set has frequency. So we will apply the formula:
[tex]\text{Mean = }\frac{\sum ^{}_{}fx}{\sum ^{}_{}f}[/tex][tex]\begin{gathered} \text{Mean = }\frac{(69\times7)\text{ + (70}\times1)+(75\times3)\text{ + (81}\times6)\text{ + (82}\times2)+\text{ (92}\times1)}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{483\text{ + 70}+225\text{ + 486 + 164}+\text{ 9}2}{7\text{ + 1 + 3+6+2+1}} \\ \text{Mean = }\frac{1520}{20} \\ \text{Mean = 76} \end{gathered}[/tex]To get the standard deviation, we will apply the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum^{}_{}f(x_i-\mu)^2}{n\text{ - 1}}} \\ \text{where }\sigma\text{ = standard deviation} \\ \mu\text{ = mean, }x_i\text{ = values of x} \\ n\text{ = }\sum ^{}_{}f=20 \end{gathered}[/tex][tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{860}{20-1}} \\ \sigma\text{ = }\sqrt[]{\frac{860}{19}} \\ \sigma\text{ = }\sqrt[]{45.2632} \\ \sigma\text{ = 6.7}28 \\ \\ \text{Standard deviation = 6.7}28 \end{gathered}[/tex]Determine the slope of the line represented by the equation: -5x - 7y = -9DO NOT USE 1 AS THE DENOMINATOR!
ANSWER
[tex]-\frac{5}{7}[/tex]EXPLANATION
We want to find the slope of the given line:
[tex]-5x-7y=-9[/tex]First, put the line in the slope-intercept form:
[tex]y=mx+b[/tex]where m = slope; b = y-intercept
Therefore, we have that:
[tex]\begin{gathered} -7y=5x-9 \\ \Rightarrow y=-\frac{5}{7}x+\frac{9}{7} \end{gathered}[/tex]From the equation above, we see that the slope of the line is:
[tex]-\frac{5}{7}[/tex]Samantha likes to run at least 5 miles each day. She plans a new course: from home to the park is 1 1/3 miles, from the park to the library is 2 2/5 miles, and from the park to home is 2/3 mile. Will Samantha run at least 5 miles on this new course? Use only estimation to decide. Then explain if you are confident in your estimate or if you need to find an actual sum. Show your work.
12 times a number g
12 times a number g means that the coefficient 12 is multiplying the variable g, just as follow:
12g
let f(x)=3x+5 and g(x) =3x^2 -x-10. find (f/g)(x) and state it’s domain
(f/g)(x) = f(x)/f(g)
[tex]\begin{gathered} =\text{ }\frac{3x+5}{3x^2-x-10} \\ =\text{ }\frac{3x+5}{(3x+5)(x-2)} \\ =\frac{1}{(X-2)} \end{gathered}[/tex]Domain: x cannot equal 2
I need help please I'll send the rest after we meet
A line passes through (5,3) with a slope of 3/5,
[tex]y=mx[/tex]where m = slope
[tex]\begin{gathered} y=mx \\ y=\frac{3}{5}x \end{gathered}[/tex]Therefore the points for the graph are:
[tex]\begin{gathered} \lbrack0,0\rbrack \\ \lbrack15,9\rbrack \\ \lbrack10,6\rbrack \\ \lbrack7,4\rbrack \end{gathered}[/tex]1. Write an equation for a polynomial with the following properties: it has even degree, it has at least 2 terms, and, as the inputs getlarger and larger in either the negative or positive directions, the outputs get larger and larger in the negative direction.
the polynomial must be even, so we chose x²
it has at least 2 terms, then we add 1 to the previous item, we get: x² + 1
to get outputs larger and larger in the negative direction, we have to multiply the previous item by -1 to get: -x² - 1
This function has a graph like the next one:
Then, -x² - 1 satisfies all the features needed
how much time has elapse? 3:00 A.M to 7:14 A.M
To know how much time has elapsed from 3:00 A.M. to 7:14 A.M., we subtract the hours with the hours and the minutes with the minutes,
[tex]\begin{gathered} \text{Hours,} \\ 7h-3h=4h \\ \text{ Minutes,} \\ 14\min -0\min =14\min \end{gathered}[/tex]So, the time that has elapsed is 4 hours 14 minutes.
The line with a slope of -1 and that contains the point (1, 3).Find the equation of the line in standard form.
ANSWER
x + y = 4
EXPLANATION
The standard form of a linear equation is given as:
ax + by = c
To do this, we have to find the equation of the line using point-slope method:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through
m = slope
The given slope is -1 ad the point the line passes through is (1, 3).
Therefore, we have:
y - 3 = -1(x - 1)
y - 3 = -x + 1
=> x + y = 1 + 3
x + y = 4
That is the equation of the line in standard form.
For which function is f(-x) = f(x)? (A) f(x) = sqaure root x(B) f(x) = 2x (C) f(x) = x2 (D) f(x) = x2 (E) f(x) = 2^x
Options C and D satisfy the given condition
The function is defined as an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given condition f(-x) = f(x)
Now to find which option satisfies the condition
So we can go through from the options to simply this
If f(x) = root x
= -root x
If f(x) = 2x
= -2x
If f(x) = x2
= x2
If f(x ) = x2
= x2
If f(x ) 2x
= 2-x
Therefore options C and D satisfy the given condition
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Answer:= 2-x
Step-by-step explanation:
A transformation is a nonrigid transformation if it does not preserve what? Can you name anonrigid transformation? What is the rule for the nonrigid transformation?Nonrigid transformationRule (x,y) →
A transformation is nonrigid transformation if it does not preserve the structure of the original object.
An example of a nonrigid transformation is the dilation, and its general rule is:
[tex]D_k(x,y)=(kx,ky)[/tex]where 'k' is the scale factor
A batter averaged 11 hits in 30 times at bat during the first half of the baseball season. He averaged 5 hits in 7 times at bat for the second half of the season. What was his average batting rate for the season?
*Find the answer to the nearest thousandth.
*(Compare total hits to total times at bat; the average of the two halves gives a wrong answer.)
Average batting rate for the season is 0.432.
Given,
Number of hits in first half of the season =11
Number of hits in second half of the season = 5
Number of times at bat during first half of the season = 30
Number of times at bat during second half of the season = 7
then,
Total number of hits in the season = 11+5 = 16
Total number of times at bat during the season = 30+7 =37
To find average batting rate use formula,
[tex]Average batting rate of season =\frac{Total number of hits in season}{Total number of at bat during season} \\\\=\frac{16}{37}\\\\ =0.432[/tex]
Hence, the batter's average batting rate for the season is 0.432.
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Find the midpoint M of the line segment joining the points C=(8,7) and D= (4,-5)
Explanation
We are told to find the midpoint of the line segment. To do so, we will use the formula:
[tex]midpoint=\frac{x_2+x_1}{2},\frac{y_2+y_1}{2}[/tex]In our case
[tex]\begin{gathered} x_1=8,y_1=7 \\ x_2=4,y_2=-5 \end{gathered}[/tex]Substituting the values above
[tex]\begin{gathered} Midpoint=\frac{8+4}{2},\frac{7-5}{2} \\ \\ Midpoint=\frac{12}{2},\frac{2}{2} \\ \\ Midpoint=(6,1) \end{gathered}[/tex]Thus, the midpoint is (6,1)
In the figure, RS is 24 units long. What is the length of WV ?
using,
RS/ST = WV/VT
Where,
RS = 24
ST = 2x + 11
WV
Find the area of this trapezoid. Be sure to include the correct unit in your answer. Continue 13 cm 20 cm 8 cm 5 cm 0 0/0 08 cm cm² X cm³ Ś ? LUULIO AUnicht Decopied Terms of Use | Priva
Given:
• Upper Base of trapezoid = 8 cm
,• Lower base = 20 cm
,• Length of one leg (also height) = 5 cm
,• Length of other leg = 13 cm
Let's find the area of the trapezoid.
To find the area of the trapezoid, apply the formula:
[tex]A=\frac{a+b}{2}*h[/tex]Where:
A is the area
a is the length of upper base = 8 cm
b is the length of the lower base = 20 cm
h is the height = 5 cm
Plug in the values for a, b, and h to find the area, A:
[tex]\begin{gathered} A=\frac{8+20}{2}*5 \\ \\ A=\frac{28}{2}*5 \\ \\ A=14*5 \\ \\ A=70\text{ cm}^2 \end{gathered}[/tex]Therefore, the area of the trapezoid is 70 cm^2
A school band performed a concert on four different days. The band soldtickets and snacks each day of the concert for a fundraiser. The first tableshows the numbers of tickets sold and the amounts of money collected fromticket sales. The second table shows the numbers of snacks sold and theamounts of money collected from snack sales.
Part A:
To determine the price per snack, just multiply any value of the column Amount collected, by its corresponding value in the column of Number of snakcs sold:
53.75/43 = 1.25
Hence, the price per snack is 1.25 dollars
Part B:
The equation is a linear equation. The general formula for a linear equation is:
y - yo = m(x - xo)
where m is the slope and (xo,yo) is a pair of values of the table.
m is calculate as follow:
m = (y2 - y1)/(x2 - x1)
m =
Q1 6.6QUESTION 1IF YOU CANT DO QUESTION 1 DO 2 OR 3THANK YOU
The area is 115
Can some one help me with 7 , 8 and 9 please?
7) The angle asked is ajacent to the leg given and we also have the hypotenuse. So we can use cossine:
[tex]\begin{gathered} \cos x=\frac{8}{18}=\frac{4}{9} \\ x=\arccos (\frac{4}{9})=64\degree \end{gathered}[/tex]8) Here we want the hypotenus given an angle an its opposite leg. So we can use sine:
[tex]\begin{gathered} \sin (65\degree)=\frac{10}{x} \\ x=\frac{10}{\sin (65\degree)}=11.0 \end{gathered}[/tex]9) We want the leg which is opposite of a given angle and we have the hypotenuse. So we can use sine again:
[tex]\begin{gathered} \sin (28\degree)=\frac{x}{15} \\ x=15\cdot\sin (28\degree)=7.0 \end{gathered}[/tex]A carpenter has a plank 8 1/5 feet long. How many feet should be cut off to make a plank 5 7/8 feet long?
Answer:
2 13/40 feet or 2.325 ft
Explanation:
The length of the plank = 8⅕ feet
To determine many feet should be cut off, subtract 5⅞ feet from 8⅕ feet.
[tex]8\frac{1}{5}-5\frac{7}{8}[/tex]Step 1: Convert both fractions to improper fractions.
[tex]=\frac{41}{5}-\frac{47}{8}[/tex]Step 2: Find the lowest common multiple of the denominators 8 and 5.
[tex]\begin{gathered} =\frac{41(8)-47(5)}{40} \\ =\frac{328-235}{40} \\ =\frac{93}{40} \\ =2\frac{13}{40}\text{ feet} \end{gathered}[/tex]2 13/40 feet of the plank should be cut off.
Explain when 'p or q' is true. Select all that apply.A. 'p or q' is true when both p and q are false.B. 'p or q' is true when p is true and q is false.C. 'p or q' is true when p is false and q is true.D. 'p or q' is true when both p and q are true.
SOLUTION
From the truth-table of logic, (p or q) is true either if:
- p is true and q is false
- q is true and p is false
- both p is true and q is true.
Hence these 3 statements must p satisfied for (p or q) to be true.
So, looking at the options, B, C and D are correct
Hence the answer is B, C and D