The rule of the compounded interest is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]A is the new amount
P is the initial amount
r is the rate in decimal
n is the number of periods per year
t is the time in years
Since the principal is $1000, then
P = 1000
Since the yearly interest rate is 6%, then change it to decimal by dividing it by 100
r = 6/100 = 0.06
Since the interest is compounded yearly, then
n = 1
Since the time is 10 years, then
t = 10
Substitute them in the rule above
[tex]\begin{gathered} A=1000(1+\frac{0.06}{1})^{(1)(10)} \\ A=1000(1.06)^{10} \\ A=1790.847697 \end{gathered}[/tex]The amount of money in the account after 10 years is $1790.847697
3. Mindi forgot to pay her water bill of $79.45, and it is now 28days late. Below is the water department's late fee charges.1-10 Days Late$1.50 per day11-20 Days Late10-Day Late Fee+$2.00 per additional day21-30 Days Late10-Day Late Fee+20-Day Late Fee+$2.50 per additional dayHow much will Mindi owe if she pays her water bill today?
The amount she was supopose to pay = $79.45
It's now 28 days late . The charges will be $2.50 per additional day. Therefore,
[tex]total\text{ additional fe}e=2.50\times28=\text{ \$70}[/tex]The amount she will pay if she pays today will be
[tex]70+79.45=\text{ \$}149.45[/tex]a) graph the following transformation b) draw asymptotec) set domain and range
Given the function :
[tex]f(x)=\log _5x+2[/tex]The graph of the function will be as shown in the following picture
The function will have a vertical asymptote which is the line : x = 0
As shown in the figure :
Domain = ( 0 , ∞ )
Range = ( -∞ , ∞ ) or all real numbers
Express the following expression in the form of a + bi : (16 + 6i) ((12 - 10i) - (2 - 5i))
Given:
There is an expression given as below
[tex]\left(16+6i\right)(\left(12-10i\right)-(2-5i))[/tex]Required:
We need to simplify the given expression and express in form of a+ib
Explanation:
[tex]\begin{gathered} (16+6i)((12-10i)-(2-5i)) \\ =(16+6i)(12-10i-2+5i) \\ =(16+6i)(10-5i) \\ =160-80i+60i+30 \\ =190-20i \end{gathered}[/tex]Final answer:
a + ib = 190 - 20i
7) A spherical balloon is inflated so that its radius increases at a rate of 2 cm/sec. How fastis the volume of the balloon increasing when the radius is 3 cm?4(Use V =for the volume of a sphere)3A) 7270 cm/sec B) 791 cm/sec C) 70 cm/sec D) 8210 cm/sec
The formula for the volume of a sphere is given by:
[tex]V=\frac{4}{3}\pi r^3[/tex]Since we are asked the rate of change of the volume with repect to time, we take the derivative on both sides, taking into account the chain rule:
[tex]\frac{dV}{dt}=\frac{d(\frac{4}{3}\pi r^3)}{dt}[/tex]taking out the constants:
[tex]\frac{dV}{dt}=\frac{4}{3}\pi\frac{d(r^3)}{dx}[/tex]Now we derivate, using the chain rule, that is:
[tex]\frac{df(g(x))}{dx}=f^{\prime}(x)g^{\prime}(x)[/tex]Applying the rule:
[tex]\frac{dV}{dt}=\frac{4}{3}\pi(3r^2)\frac{dr}{dt}[/tex]Simplifying:
[tex]\frac{dV}{dt}=4\pi(r^2)\frac{dr}{dt}[/tex]We have the following known values:
[tex]\begin{gathered} \frac{dr}{dt}=\frac{2\operatorname{cm}}{s} \\ r=3\operatorname{cm} \end{gathered}[/tex]Replacing we get:
[tex]\frac{dV}{dt}=4\pi(3)^2(2)[/tex]Solving we get:
[tex]undefined[/tex]I need to know what a cordanate plain is
A coordinated plane is
For questions 5-6, g(x) is a transformation of f(x) = x2. What is the function g(x) that is represented by the graph? QUESTION 5
The transformation in question 5 shows a shift to the left by 3 units.
A shift to the left by b units has the rule:
[tex]f(x)\to f(x+b)[/tex]Therefore, the shift to the left by 3 units will yield the function:
[tex]x^2\to(x+3)^2[/tex]Hence, the function g(x) will be:
[tex]g(x)=(x+3)^2[/tex]Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total of 18 people took the trip. She was able to purchase coach tickets for $170 and first class tickets for $1010. She used her total budget for airfare for the trip, which was $10620. How many first class tickets did she buy? How many coach tickets did she buy:
Explanation
Let the number of people with coach tickets be x and the number of people with first class tickets be y. Since the trip goers contained a total of 18 people we will have;
[tex]x+y=18[/tex]A coach ticket cost $170 dollars and the first class tickets cost $1010. Also, Sarah spent a total of $10620 to buy the tickets. This would give us;
[tex]170x+1010y=10620[/tex]We will now solve the equation simultaneously.
[tex]\begin{gathered} \begin{bmatrix}x+y=18\\ 170x+1010y=10620\end{bmatrix} \\ isolate\text{ for x in equation 1}\Rightarrow x=18-y \\ \mathrm{Substitute\:}x=18-y\text{ in equation 2} \\ 170\left(18-y\right)+1010y=10620 \\ 3060+840y=10620 \\ 840y=10620-3060 \\ 840y=7560 \\ y=\frac{7560}{840} \\ y=9 \\ \end{gathered}[/tex]We will substiuite y =9 in x=18-y. Therefore;
[tex]\begin{gathered} x=18-9=9 \\ x=9 \end{gathered}[/tex]Answer: From the above, Sarah bought 9 coach tickets and 9 first-class tickets.
-5 > 5 + x/3 I am so confused on these things
Let's solve the inequality:
[tex]\begin{gathered} -5>5+\frac{x}{3} \\ -5-5>\frac{x}{3} \\ -10>\frac{x}{3} \\ -10\cdot3>x \\ -30>x \\ x<-30 \end{gathered}[/tex]Therefore the solution for the inequality is:
[tex]x<-30[/tex]In interval form this solution is written as:
[tex](-\infty,-30)[/tex]This means that x has to be less than -30 for the inequality to be true.
Complete the grouped relative frequency distribution for the data. (Note that we are using a class width of 4.)Write each relative frequency as a decimal rounded to the nearest hundredth, not as a percentage.Relativefrequency Temperature 109 112 110 94 102 106 104 94 108 105 103 107 105 101 93103 99Relative Frequency 93 to 9697 to100101 to 104105 to 108109 to 112
Above you have the given 17 data ordered from least to greatest.
To find the relative frequency:
1. Frequency: Identify the number of data that goes in each temperature range:
93 to 96: 3 data (93,94,94)
97 to 100: 1 data (99)
101 to 104: 5 data (101, 102, 103, 103, 104)
105 to 108: 5 data (105, 105, 106, 107, 108)
109 to 112: 3 data (109, 110, 112)
2. Relative frequency: Find the ratio of the number of data you get in step 1 (Frecuency) to the total number of data (17):
93 to 96:
[tex]\frac{3}{17}\approx0.18[/tex]97 to 100:
[tex]\frac{1}{17}\approx0.06[/tex]101 to 104:
[tex]\frac{5}{17}\approx0.29[/tex]105 to 108
[tex]\frac{5}{17}\approx0.29[/tex]109 to 112
[tex]\frac{3}{17}\approx0.18[/tex]Then, the relative frequencies are:
93 to 96: 0.18
97 to 100: 0.06
101 to 104: 0.29
105 to 108: 0.29
109 to 112: 0.18
Answer: the other person is correct
Step-by-step explanation:
A parabola can be drawn given a focus of (-5, 9) and a directrix of y = 5. Write the equation of the parabola in any form. 12 10 8 6 4 cu 2 -12 -10 -8 -6 -4 -2 2 4 6 8 10 12 -2 directrix 1 -6 -8 F(-5,9) -10 -12
The distance from the directrix to the focus is 4, so p=2. So the vertex of the parabola is (-5,7). Having this we get that
[tex]\begin{gathered} 4p(y-k)=(x-h)^2 \\ 8(y-7)=(x+5)^2 \end{gathered}[/tex]
Help me please just plot the points on the graph
As per given by the question,
There are given that the equation,
[tex]y=4x-2[/tex]Now,
For plot the point on the grpah;
Put the value of x is 0 in the given equation and find the value of y,
So,
[tex]\begin{gathered} y=4x-2 \\ y=4(0)-2 \\ y=-2 \end{gathered}[/tex]And,
Put the value of y is 0 in the given equation to find the value of x,
So;
[tex]\begin{gathered} y=4x-2 \\ 0=4x-2 \\ 4x=2 \\ x=\frac{2}{4} \\ x=0.5 \end{gathered}[/tex]The point on the graph is,
[tex](0,\text{ -2) and (0.5, 0)}[/tex]Hence, the grpah of the given equation is;
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16What exactly are equations?In mathematical formulas, the equals sign is used to indicate that two expressions are equal. A mathematical statement that uses the word "equal to" between two expressions with the same value is called an equation. Like 3x + 5 = 15, for instance. Equations come in a wide variety of forms, including linear, quadratic, cubic, and others. Point-slope, standard, and slope-intercept equations are the three main types of linear equations.So, equations true for x = 2 and x = -2 are:
Roots of x = -2:
x² = 4x² - 4 = 0Roots of x = 2:
x² = 4Now, multiply 4 on both sides as follows:
4x² = 16Therefore, equations that have the roots of x = 2 and x = -2 are:
(A) x² - 4 = 0(D) 4x² = 16Know more about equations here:
https://brainly.com/question/28937794
#SPJ1
Correct question:
Which equations are true for x = –2 and x = 2? Select two options
A. x2 – 4 = 0
B. x2 = –4 3
C. x2 + 12 = 0
D. 4x2 = 16
E. 2(x – 2)2 = 0
1Select the correct answer.Which equation represents a line that is parallel to the x-axis, is perpendicular to the y-axis, and has a slope of 0?A.y=4/5x+5/4B.y=5/4xC.y=4/5D.x=5/4
The slope os the value that accompanies the dependent term.
Therefore, A and B, they are wrong.
If it is parallel to the x-axis and perpendicular to the y-axis, it must have the following form:
[tex]y=c[/tex]Therefore, the answer correct is C. y = 4/5
-3х – 10у = -20 -5x — бу = 20
You can solve a system of equations by graphing
The solution of a system of linear equations is the intersection point both graphs
using a graphing tool
the solution is the point (-10,5)
so
x=-10
y=5
the solution is the intersection point both lines
I will solve the system by substitution
we have
-3х – 10у = -20 --------> equation A
-5x — бу = 20 --------> equation B
isolate the variable y in the equation A
10y=-3x+20
y=-0.3x+2 --------> equation C
substitute equation C in equation B
-5x-6(-0.3x+2)=20
solve for x
-5x+1.8x-12=20
-3.2x=20+12
-3.2x=32
x=-10
substitute the value of x in the equation C
y=-0.3x+2
y=-0.3(-10)+2
y=3+2
y=5
the solution is x=-10 and y=5
how do I solve this linear equations by substitution x=5 x + y = 4
Substitute 5 for x in the equation x+y=4 to obtain the value of y.
[tex]\begin{gathered} 5+y=4 \\ y=4-5 \\ =-1 \end{gathered}[/tex]So solution of the equations is (5,-1).
Try to evaluate 1001/2 without using a calculator. Enter DNE if the number is not real.
Rational exponent rule
[tex]a^{\frac{m}{n}}=\sqrt[n]{a^m}[/tex]Applying this rule to the case given:
[tex]100^{\frac{1}{2}}=\sqrt[]{100^1}=\sqrt[]{100^{}}=10[/tex]Subtract and simplify: (6 + 10i) – (11 + 7i)
Given:
an expression is given as (6 + 10i) - (11 + 7i)
Find:
we have to subtract and simplify the expression.
Explanation:
(6 + 10i) - (11 + 7i) = 6 + 10i - 11 -7i = (6 - 11) + ( 10i - 7i) = -5 + 3i
Therefore, (6 + 10i) - (11 + 7i) = -5 + 3i
Find the equation of the linear function represented by the table below in slope-intercept form.xy1-52-73-94-11
Answer:
[tex]y=-2x-3[/tex]Explanation:
Given the table:
x | 1 2 3 4
y | -5 -7 -9 -11
Find the slope using the two point formula.
Take the points (1, -5) and (2, -7).
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ =\frac{-7-(-5)}{2-1} \\ =\frac{-7+5}{1} \\ =-2 \end{gathered}[/tex]Substitute the value of the slope into the slope-intercept form y = mx+c.
[tex]y=-2x+c[/tex]Plug the point (1, -5) into y = -2x+c to find c.
[tex]\begin{gathered} -5=-2+c \\ c=-5-(-2) \\ =-3 \end{gathered}[/tex]Thus, y = -2x - 3, which is the required equation of the given linear function.
An online store started its business with 15 sales per week. If their sales increased 18% each week, use an exponential model to find the week in which they exceeded 1000 sales per week. Remember, A= P(1+r)^t26 weeks31 weeks38 weeks15 weeks
Given,
The initial sale is 15.
The rate of increase of sale per week is 18 %.
The final sale is 1000.
The week at which the sales exceeds 1000 is:
[tex]\begin{gathered} 1000=15\times(1+\frac{18}{100})^t \\ \frac{1000}{15}=(\frac{118}{100})^t \\ \frac{200}{3}=(1.18)^t \\ log\text{ \lparen}\frac{200}{3})=t\text{ log\lparen1.18\rparen} \\ t=25.37 \end{gathered}[/tex]The sales of the business reach to 1000 in 25th week.
Hence, the sales of the business exceed to 1000 in 26th week.
A person places $531 in an investment account earning an annual rate of 6.1%,compounded continuously. Using the formula V = Pe", where V is the value of theaccount in t years, P is the principal initially invested, e is the base of a naturallogarithm, and ris the rate of interest, determine the amount of money, to thenearest cent, in the account after 16years.
This is the solution, Qxk:
Step 1: Let's review the information provided to us to answer the problem correctly:
Principal = $ 531
Interest rate = 6.1% (0.061) compounded continously
Term = 16 years
Step 2: Let's find the future value of this investment, as follows:
V = Pe^t*r
V
I need a very fast answer to this question please I’m in a hurry
To find f(3 + h) we need to substitute x = 3 + h, into the function, as follows:
[tex]\begin{gathered} f(x)=\frac{1}{(3+h)+2} \\ \text{ Combining similar terms:} \\ f(x)=\frac{1}{h+(3+2)} \\ f(x)=\frac{1}{h+5} \end{gathered}[/tex]
Find the midpoint of the segment with the following endpoints.(4,5) and (9, 2)
Answer: (6.5, 3.5)
Explanation:
The midpoint between two points can be found by taking the mean of the x coordinates, and the mean of the y coordinates.
The points we have are:
(4, 5) where we will call
[tex]x_1=4,y_1=5[/tex]and also the point
(9, 2) where we will call
[tex]x_2=9,y_2=2[/tex]Now, the midpoint will be at
[tex](x_m,y_m)[/tex]Where xm is the mean of the x coordinates, and ym is the mean of the y coordinates:
[tex]x_m=\frac{x_1+x_2}{2}[/tex]subtituting the values:
[tex]x_m=\frac{4+9}{2}=\frac{13}{2}=6.5[/tex]we have xm, now we need ym:
[tex]y_m=\frac{y_1+y_2}{2}[/tex]Substituting the values
[tex]y_m=\frac{5+2}{2}=\frac{7}{2}=3.5[/tex]Thus, the midpoint is at:
[tex](x_m,y_m)=(6.5,3.5)[/tex]What is the equation of the boundary of this inequality?
We have the following:
[tex]y<-3x-5[/tex]The slope of the line -3 and the y-intercept is -5
So the equation of the boundary line is:
[tex]\begin{gathered} y=-3x-5 \\ \end{gathered}[/tex]Tell whether each set of measures for a triangle determines more than one triangle or notriangle.10. 5 cm , 10 cm, 2 cm11. 60°, 60°, 60°12. 7 cm, 7 cm, 15 cm
A triangle is valid if sum of its two sides is greather than the third side. If three sides are a, b and c, then three conditions should be met.
10. 5cm, 10cm, 2cm
[tex]\begin{gathered} 5+10>2 \\ 15>2\text{ -> False} \end{gathered}[/tex]This cannot be a triangle.
11. Since it has all its angles equals, that means it is a equilateral triangle.
12. 7cm, 7cm, and 15cm
[tex]\begin{gathered} 7+7>15 \\ 14>15\text{ -> False} \end{gathered}[/tex]It cannot be a triangle.
The English Channel is the waterway between England and France. It is about 21 kilometers across, and many people have successfully swam across it. In the United States, many pools at gyms are 25 yards long, and 1 lap equals the pool length.Assuming a person swims in a straight line, how can you calculate the number of complete laps a person must swim in a 25-yard pool to equal swimming across the English Channel?A) First, convert the distance across the channel to approximately 13 miles. Next, convert the distance in miles to 22,880 feet. Then, convert the pool length to 75 feet. Finally, multiply the distance by 1 lap 75 ft. to get about 305 laps.B) First, convert the distance across the channel to approximately 34 miles. Next, convert the distance in miles to 179,520 feet. Then, convert the distance in feet to 59,840 yards. Finally, multiply the distance by 1 lap 25 yd. to get about 2,394 laps.C) First, convert the distance across the channel to approximately 34 miles. Next, convert the distance in miles to 59,840 feet. Then, convert the pool length to 75 feet. Finally, multiply the distance by 1 lap 75 ft. to get about 798 lapsD) First, convert the distance across the channel to approximately 13 miles. Next, convert the distance in miles to 68,640 feet. Then, convert the distance in feet to 22,880 yards. Finally, multiply the distance by 1 lap 25 yd. to get about 915 laps.
The first step to find the correct answer indeed is to convert the distance across the channel from kilometers to miles.
Because 1 km is equal to approximately 0.62 miles, 21 kilometers will be just 21 times the 0.62 miles. From this, we are able to calculate the following:
[tex]\begin{gathered} 25\operatorname{km}=25\times0.62mi \\ 25\operatorname{km}\text{ }\cong13mi \end{gathered}[/tex]From this, we are able to say that the correct answer is not B or C.
Now, because 1 mi is equal to 5,280 ft, we can say that 13 mi is equal to 13 times 5,280 ft. From this, we calculate:
[tex]\begin{gathered} 13mi=13\times5,280ft \\ 13mi=68,640ft \end{gathered}[/tex]From this, we are able to say that the correct answer is not A also. To convert it to yards, we need to remember that 1 foot is equal to (1/3) yards, which means that 68,640 ft is equal to 68,640 times (1/3) yards. Calculating, we get the following:
[tex]\begin{gathered} 68,640ft=68,640\times\frac{1}{3}yd \\ 68,640ft=22,880yd \end{gathered}[/tex]Because the lap in the pool is 25 yd, we need to DIVIDE, not to multiply, the distance of the channel in yards we found by the distance of the pool, which is 25 yd.
From this, we get the following answer:
[tex]N_{of\text{ laps}}=\frac{22,880yd}{25\frac{yd}{lap}}=915.2\text{ laps}[/tex]From this, we know that the number of laps a person who wants to swim the same distance of the channel mentioned is equal to approximately 915 laps
And the final answer is D.
MATH HELP WILL MARK BRAINLEST
The objective function ( S for score ) in the given linear programming problem is S = 3x + 5y , the correct option is (a) .
In the question ,
it is given that ,
number of points that a multiple choice question gives = 3 points
number of points that a short answer gives gives = 5 points ,
let the number of multiple choice questions be = x
let the number of short answer questions be = y ,
the final score is denoted by S ,
So , the function , to represent the above situation is ,
S = 3x + 5y
Therefore , The objective function ( S for score ) in the given linear programming problem is S = 3x + 5y , the correct option is (a) .
Learn more about Functions here
https://brainly.com/question/14347935
#SPJ1
complete the Pattern 444 4440 44,400 there are three empty lines I need to finish the pattern
Given:
d. 444 4,440 44,400
e. 9.5 950 9500
The pattern for d as you can see all numbers have 444 but they keep adding extra 0's to each number.
So the next number should have another extra 0 after 44400.
The pattern for all parts a to e seem to be multiplying each number by 10 or dividing by 10 that is why for d. 444 has no 0's but then if you multiply by 10 you get 4440.
If you do 4440*10 you get 44400.
Answer:
The same pattern applies to e.
For the first blank divide 9.5 by 10 so then 9.5 ÷ 10 = 0.95
For the 2nd blank. Multiply by 10 to 95,000 so you get 950,000. Notice how 950,000 has an extra 0.
3rd blank should be 9500000
How much sales tax will Justin pay on a computer priced at $1,723.42 if the sales tax rateis 9.25 percent?
Given : the price of the computer = $1,723.42
The sales tax = 9.25% = 9.25/100 = 0.0925
The sales tax = 9.25% of $1,723.42 = 0.0925 * $1,723.42 = $159.42 (to the nearest cent)
So,
The sales tax = $159.42
Which point on the number line below best represents V30?
We should try different squared numbers that are bigger and smaller than 30 as:
[tex]\begin{gathered} \sqrt{16}=4 \\ \sqrt{25}=5 \\ \sqrt{36}=6 \end{gathered}[/tex]Since 30 is between 25 and 36, the square root of 30 is going to be between 5 and 6. So the point that best represents the square root of 30 is M.
Answer: Point M
fing the probability of .14 .73 .03 is
The probabilities are:
*0.14 -> 14%.
*0.73 -> 73%.
*0.03 -> 3%.