From the statement of the problem we know that:
• the principal amount of money invested is P = $85000,
,• the rate per year is 7.5%, in decimals r = 0.075,
,• the time is t = 5 years.
The interest earnt I is equal to the difference between the total accrued amount A and the principal amount P:
[tex]I=A-P=P(1+r\cdot t)-P=P\cdot r\cdot t.[/tex]Replacing by the data of the problem we find that the simple interest is:
[tex]I=85000\cdot0.075\cdot5=31875.[/tex]Answer
The simple interest is $31875.
Solve for y.
|6y + 12| = -18
Answer: y=-5
Step-by-step explanation:
12-12=0
-18-12=-30
6y=-30
y=-5
The expression x^(3) gives the volume of a cube, where x is the length of one side of the cube. Find the volume of a cube with a side length of 2 meters.
Answer:
8 cubic meters
Explanation:
The length of one side of the cube = x
For any cube of side length, x:
[tex]\text{Volume}=x^3[/tex]Therefore, the volume of the cube with a side length of 2 meters is:
[tex]\begin{gathered} V=2^3 \\ =8\; m^3 \end{gathered}[/tex]Graph two or more functions in the same family for which the parameter being changed is the slope, m. and is less than 0.Refer to the graph of f(x) = x + 2
We have the expression:
[tex]f(x)=x+2[/tex]If the slope is changing being less than 0, that is:
You buy items costing $3000 and finance the cost with a simple interest fixed installment loan at 5% simple interest per year. The finance charge is $600.a) How many years will you be paying?b) What is your monthly payment?
Given:
The principal amount is P = $3000.
The rate of interest is r = 5% = 0.05.
The interest rate is A = $600.
The objective is,
a) To find the number of years.
b) To find the monthly payment.
Explanation:
a)
The general formula for simple interest is,
[tex]A=P\times n\times r\text{ . . . . . .(1)}[/tex]To find n:
On plugging the given values in equation (1),
[tex]\begin{gathered} 600=3000\times n\times0.05 \\ n=\frac{600}{3000\times0.05} \\ n=4 \end{gathered}[/tex]b)
Since, the total amount of the item can be calculated as,
[tex]T=A+P\text{ .. . . . (2)}[/tex]On plugging the obtained values in equation (2),
[tex]\begin{gathered} T=600+3000 \\ T=3600 \end{gathered}[/tex]To find monthly payment:
Now, the monthly payment can be calculated as,
[tex]m=\frac{T}{n\times12}\text{ . . . . .(3)}[/tex]Here, m represents the monthly payment, the product of 12 is used to convert the number of years into the number of months.
On plugging the obtained values in equation (3),
[tex]\begin{gathered} m=\frac{3600}{4\times12} \\ m=75 \end{gathered}[/tex]Hence,
a) The number of years is 4 years.
b) The monthly payment is $75.
Samantha started with $25 in her account. she saves $7 per week. Australia has no money in his account, but adds $15 per week. for how many weeks will Australia have more money in his account than Samantha
In this problem we can made a function to calculate the total amount for Samantha (S) and total amound of Australia (A) fon any time:
[tex]\begin{gathered} S=25+7t \\ A=0+15t \end{gathered}[/tex]when t is the number of weeks. if we made equal the ecuation we will have the time when they would have the same amound:
[tex]\begin{gathered} S=A \\ 25+7t=15t \end{gathered}[/tex]and we solve for t
[tex]\begin{gathered} 25=15t-7t \\ 25=8t \\ \frac{25}{8}=t \\ 3.125=t \end{gathered}[/tex]This means that in the next full number Australia will have more money than Samantha, so in 4 weeks this is going to happen.
Sketch the graph and circle the points that are solutions. (0-0)(2,5)(-3,-5)(-3,2)
(-3,-5)
1) Let's plot both inequalities to solve that geometrically at first.
y ≤ -1/3x -2
y< 2/3x +1
2) Since the possible solutions to that Linear system of Inequalities are within the darker and common region, after examining those options we can write:
The only (-3,-5) of those is a possible solution to that System.
3) Hence the only possible solution between them is (-3,-5).
One group (A) contains 75 people. Two fifths of the people in group A will be selected to win $20 fuel cards. There is another group (B) in a nearby town that will receive the same number of fuel cards, but there are 154 people in that group. What will be the ratio of no winners in group A to nonwinners in group B after the selections are made? Express your ratio as a fraction or with a colon.
group A contains 75 people
Two-fifths of the people in group A (75*2/5=30) win $20 fuel cards.
so there are 30 fuel cards and 75-30=45 non-winners in group A
group B are 154 people and the same number of fuel cards, so 30
the number of non-winners in group B is 154-30=124
So the ratio of no winners in group A to nonwinners in group B is:
45/124
Calculate the answers. 13. An orbiting satellite is positioned 3,105 mi above the earth (rearth = 3,959 mi) and orbits the earth once every 201.3 min. Assuming its orbit is a circle, find the distance traveled in 50.0 min.
first you will calculate the speed of the orbiting satelite
[tex]\text{speed = }\frac{dis\tan ce}{time}[/tex]distance = circumference of the of the orbit
[tex]\begin{gathered} \text{circumference = 2}\times\pi\times\text{ r} \\ r\text{ = radius of the earth + the height of the satelite above the earth} \\ r\text{ = 3105+3959 =7064mi} \end{gathered}[/tex][tex]\text{circ of the orbit = }2\text{ }\times3.142\times7064=\text{ 44390.176}[/tex][tex]\text{speed = }\frac{44390.176}{201.3}\text{ = 220.52mi/min}[/tex]distance covered in 50.0 min
distance = speed X time
[tex]\text{distance = 220.52}\times50=11026mi[/tex]the distance traveled is 11026 mi
Write the equation in standard form for the hyperbola with vertices (-9,0) and (9,0) and a conjugate axis of length 16
The given vertices are (-9,0) and (9,0).
Notice that they lie on the x-axis since they have 0 as their y-coordinate.
Hence, the hyperbola is a horizontal hyperbola.
Recall that the equation of a horizontal hyperbola is given as:
[tex]\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1[/tex]Where (h,k) is the center and a>b.
As both vertices are equidistant from the origin, the center of the hyperbola is (0,0), and the equation becomes:
[tex]\frac{x^2}{a^2}-\frac{y^2}{b^2}=1[/tex]Note that the vertices are at (-a,0) and (a,0).
Compare with the given vertices (-9,0) and (9,0). It follows that a=9.
Substitute this into the equation:
[tex]\frac{x^2}{9^2}-\frac{y^2}{b^2}=1[/tex]Recall that the length of the conjugate axis is given as 2b, it follows that:
[tex]\begin{gathered} 2b=16 \\ \Rightarrow b=\frac{16}{2}=8 \end{gathered}[/tex]Substitute b=8 into the equation:
[tex]\begin{gathered} \frac{x^2}{9^2}-\frac{y^2}{8^2}=1 \\ \Rightarrow\frac{x^2}{81}-\frac{y^2}{64}=1 \end{gathered}[/tex]The required equation in standard form is:
[tex]\frac{x^2}{81}-\frac{y^2}{64}=1[/tex]Simplify the expression.9n+ 18(2n-6)
The given expression is,
[tex]\begin{gathered} 9n+18(2n-6) \\ 9n+36n-108 \\ \\ 45n=108 \end{gathered}[/tex]A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that no two of the civil engineers will sit together? [ 9! × 10!/4!)]
The software engineers can be seated on a round table with no two civil engineers sitting together is 9!×10!/4!
Given, a company has 10 software engineers and 6 civil engineers.
we need to determine in how many ways can they be seated around a round table so that no two civil engineers will sit together.
10 software engineers can be arranged around a round table in :
=(10-1)!
= 9! ways .... eq(A)
Now, we must arrange the civil engineers so that no two can sit next to one another. In other words, we can place 6 civil engineers in any of the 10 *-designated roles listed below.
This can be done in ¹⁰P₆ ways ...(B)
From A and B,
required number of ways = 9!×¹⁰P₆
= 9! × 10!/4!
Hence the number of ways the engineers can be seated is 9! × 10!/4!.
Learn more about Permutations and combinations here:
brainly.com/question/4658834
#SPJ1
if you can tee the picture well please tell me
Since they give us the equation they have gotten for the line of best fit, we use it to estimate what thye answer is when x = 25:
Use:
y = 1.708 x - 4.011
then when x = 25:
y = 1.708 (25) - 4.011
y = 38.689
I don't read if the want you to round the answer to a given number of decimals, but if you try exactly the number we got (with the three decimals) that would be the most exact.
If f(x) = 2x+3, what is f(-2)
Answer: f(-2) = -1
Step-by-step explanation:
2x + 3
2(-2) +3
-4 + 3
-1
Answer:
Step-by-step explanation:
you plug in the -2 to the equation for x
f(-2)= 2(-2)+3
f(-2)=-1
Simplify the following: (4x + 3) -2(4x - 7) - 3(x +7)
Simplify: (4x + 3) -2(4x - 7) - 3(x +7)
Explanation:
[tex]\begin{gathered} (4x+3)-2(4x-7)-3(x+7) \\ =4x+3-8x+14-3x-21 \\ =4x-11x+17-21 \\ =-7x-4 \end{gathered}[/tex]Final answer: -7x-4 is required simplify form .
x – a is the factor of a polynomial P(x) if P(a) is equal to
we know that
If (x-a) is a factor of P(x)
then
For x=a
the value of P(a)=0
therefore
the answer is option DFind the area of the prism in the figure shown.
TherWe are asked to determine the area of the triangular prism. To do that we will add the area of the surfaces of the prism and add them together.
we have that the front and back areas are the areas of a triangle which is given by the following formula:
[tex]A_t=\frac{bh}{2}[/tex]Where:
[tex]\begin{gathered} b=\text{ length of the base} \\ h=\text{ height of the triangle} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} b=3 \\ h=4 \end{gathered}[/tex]Substituting the values we get:
[tex]A_t=\frac{\left(3\right)\lparen4)}{2}[/tex]Solving the operations:
[tex]A_t=6[/tex]Since the front and back faces are the same triangle we can multiply the result by 2:
[tex]A_t=2\times6=12[/tex]Therefore, the areas of the front and back faces add up to 12.
Now, we determine the area of the right side. This is the area of a rectangle and is given by the following formula:
[tex]A_r=lh[/tex]Where:
[tex]\begin{gathered} l=\text{ length of the rectangle} \\ h=\text{ height of the rectangle} \end{gathered}[/tex]In this case, we have:
[tex]\begin{gathered} l=5 \\ h=4 \end{gathered}[/tex]Substituting the values we get:
[tex]A_r=\left(5\right)\left(4\right)[/tex]Solving the operation:
[tex]A_r=20[/tex]Now, we determine the area of the left face which is also a rectangle with the following dimensions:
[tex]\begin{gathered} h=5 \\ l=5 \end{gathered}[/tex]Substituting we get:
[tex]A_l=\left(5\right)\left(5\right)=25[/tex]Therefore, the area of the left side is 25.
The area of the bottom face is also a rectangle with the following dimensions:
[tex]\begin{gathered} h=5 \\ l=3 \end{gathered}[/tex]Substituting we get:
[tex]A_b=\left(5\right)\left(3\right)=15[/tex]Now, the total surface area is the sum of the areas of each of the faces:
[tex]A=A_t+A_r+A_l+A_b[/tex]Substituting the values we get:
[tex]A=12+20+25+15[/tex]Solving the operations:
[tex]A=72[/tex]Therefore, the surface area is 72.
I need help with my algebra
We have the next equation line:
[tex]3x-y\text{ = 5}[/tex]We need to solve the equation for y to get the equation form
[tex]-y\text{ =5-3x}[/tex]Multiply the equation by -1
[tex](-1)-y\text{ =(-1)(5-3x)}[/tex][tex]y\text{ = -5+3x}[/tex]Where the y-intercept is -5 and the slope is 3x.
To find the line parallel we need to know that the parallel lines have the same slope.
The parallel line also intercepts y at point (0,-7).
[tex]y=mx+b[/tex]Replace the slope=m = 3
and the y-intercept is -7.
So the parallel line is:
[tex]y=3x-7[/tex]Fart A Now that you have converted a terminating decimal number Into a fractlon, try converting a repeating decimal number Into a fraction. Repeating decimal numbers are more difficult to convert Into fractions. The first step is to assign the given decimal number to be equal to a varlable, x. For the decimal number 0.3, that means X = 0.3. if x = 0.3, what does 10x equal? Font Sizes
Given x = 0.3, we're asked to find 10x. All we need to do is multiply 10 by 0.3(which is the value of x);
[tex]10\text{ }\ast\text{ 0.3 = 3}[/tex]Therefore, 10x is equal to 3.
On the desmos app can you have more standard forms or only one?
Answer: I am pretty sure you can only have one.
Step-by-step explanation:
The illustration below shows the graph of y as afunction of xComplete the following sentences based on thegraph of the function.(Enter the x-intercepts from least to greatest.)* This is the graph of a (nonlinear, linear orconstant) function.* The y-intercept of the graph is the function value y = ___.The x-intercepts of the graph (in order from leastto greatest) are located at x = ___ and x = ___.* The greatest value of y is y = ___ and it occurswhen x = ___.* For x between x = 2 and x = 6, the function value y (<, 2, or =) 0.
* This is the graph of a (nonlinear, linear or constant) function.
Answer:
This is the graph of a nonlinear function (In this case it is a quadratic function).
--------------------------------------------------------------------------------------
The y-intercept of the graph is the function value y =
Answer:
From the graph we can conclude that, the y-intercept is:
[tex]y=-6[/tex]----------------------------------------------------------------------------
The x-intercepts of the graph (in order from least to greatest) are located at x = ___ and x = ___.
Answer:
From the graph, we can conclude that the x-intercepts are located at:
[tex]\begin{gathered} x=2 \\ and \\ x=6 \end{gathered}[/tex]----------------------------------------------------------------------
The greatest value of y is y = ___ and it occurs
Answer:
From the graph, we can see that the vertex of the function is:
[tex]\begin{gathered} y=2 \\ when \\ x=4 \end{gathered}[/tex]----------------------------------------------------------------
For x between x = 2 and x = 6, the function value y is.
Answer:
For those values, y is always greater than or equal to 0, so:
[tex]2\le x\le6\to y\ge0[/tex]Use complete sentences to explain the process you would use to find the volume of the shipping box.(Trying to help my son with this)
Part A)
The given shipping box is a cuboid.
Recall that the longest length of the cuboid is diagonal.
The length of the longest item that fits inside the shipping box is the measure of the diagonal of the given box.
Given that measure breadth=16 inches and measure height = 12 inches.
Recall the formula for the diagonal d of the cuboid is
[tex]d=\sqrt[]{l^2+b^2+h^2}[/tex]We need to find the measure of the length of the cuboid.
Consider the base of the cuboid which is in rectangle shape.
Here breadth of the rectangle is 16 inches and diagonal of the rectangle is 24 inches.
Recall the formula for the diagonal of the rectangle is
[tex]diagonal_{}=\sqrt[]{l^2+b^2}[/tex]Substitute diagonal =24 inches and breath =16 inches, we get
[tex]24_{}=\sqrt[]{l^2+16^2}[/tex][tex]24_{}=\sqrt[]{l^2+256}[/tex]Taking square on both sides, we get
[tex]24^2_{}=l^2+256[/tex][tex]576-256=l^2[/tex][tex]320=l^2[/tex]Taking square root on both sides, we get
[tex]\sqrt[]{320}=l[/tex][tex]l=17.89\text{ inches}[/tex]Now, substitute l=17.89, b=16, and h=12 in the diagonal of the cuboid equation to find the diagonal of the cuboid.
[tex]d^{}=\sqrt[]{17.89^2+16^2+12^2}[/tex][tex]d^{}=\sqrt[]{320+256+144}=\sqrt[]{720}=26.83\text{ inches}[/tex]Hence the length of the longest item that fits inside the shipping box is 26.8 inches.
Part B)
Consider the length l=17.89 inches, b=16 inches, and height h=12 inches.
Recall the formula for the volume of the cuboid is
[tex]V=l\times w\times h[/tex]Substitute the length l=17.89 inches, b=16 inches, and height h=12 inches, we get
[tex]V=17.89\times16\times12[/tex][tex]V=3434.88inches^3[/tex]Hence the volume of the given shipping box is 3434.88 cubic inches.
Write a rule for the nth term of the geometric sequence given a_2 = 64, r = 1/4
The n-th term of a geometric sequence is given by the formula:
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ r=\text{ common ration} \\ a_1=\text{ first term} \end{gathered}[/tex]Given that:
[tex]\begin{gathered} a_2=64 \\ r=\frac{1}{4} \\ n=2 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} a_2=a_1(\frac{1}{4})^{2-1}=64 \\ a_1(\frac{1}{4})=64 \\ a_1=64\times4 \\ =256 \end{gathered}[/tex]Therefore, the rule for the nth term of the sequence is
[tex]\begin{gathered} U_n=a_1r^{n-1} \\ U_n=256_{}(\frac{1}{4})^{n-1} \end{gathered}[/tex]13. A 640 kg of a radioactive substance decays to 544 kg in 13 hours. A. Find the half-life of the substance. Be sure to show your work including the formulas you used. Round to the nearest tenth of an hour. Only solutions using formulas from the 4.6 lecture notes will receive credit.B. How much of the substance is present after 3 days? Be sure to show the model you used.C. How long does it take the substance to reach 185 kg? Be sure to show your work.
EXPLANATION
The equation for half-life is given by the following formula:
[tex]H=\frac{t\cdot\ln(2)}{\ln(\frac{A_0}{A_t})}[/tex]Replacing terms:
[tex]H=\frac{t\cdot\ln(2)}{\ln(\frac{A_0}{A_t})}=\frac{13\cdot\ln(2)}{\ln(\frac{640}{544})}=\frac{9.0109}{0.1625}=55.45[/tex]The half-life time is H =55.4 hours.
B) After three days, that is, 72 hours, the amount of substance will be given by the following relationship:
[tex]A=A_o\cdot e^{-(\frac{\ln2}{H})t}=640\cdot e^{-(\frac{\ln2}{55.4})\cdot72}=640\cdot e^{-0.90084}[/tex]Multiplying terms:
[tex]A=640\cdot0.4062=259.96\text{ Kg}[/tex]There will be 259.96 Kg after 3 days.
C) In order to compute the number of days that will take to the substance to reach a concentration equal to 185 Kg, we need to apply the following formula:
[tex]t=\frac{\ln (\frac{A}{A_o})}{-\frac{\ln (2)}{t\frac{1}{2}}}[/tex]Replacing terms:
[tex]t=\frac{\ln (\frac{185}{544})}{-\frac{\ln (2)}{55.45}}=\frac{-1.0785}{-0.0125}=\frac{1.0785}{0.0125}=86.28\text{ hours}[/tex]It will take 86.28 hours to the substance to reach 185 Kg.
what is the slope for (0,-3),(-3,2)
Given the general rule for the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]We have the following in this case:
[tex]\begin{gathered} (x_1,y_1)=(0,-3) \\ (x_2,y_2)=(-3,2) \\ \Rightarrow m=\frac{2-(-3)}{-3-0}=\frac{2+3}{-3}=-\frac{5}{3} \\ m=-\frac{5}{3} \end{gathered}[/tex]therefore, the slope is m=-5/3
can someone please show me if im correct because i got 12
Given the expression:
-3 + 15
Let's evaluate the expression.
Here, we have an addition operation.
To perform the operation, add -3 and 15.
Hence, we have:
-3 + 15 = 12
Therefore, the answer to the operation is 12.
ANSWER:
12
Chain rule in calculus
In the given example:
[tex]\begin{gathered} u=4x^3-5 \\ f(u)=u^4 \\ \text{If we do a function composition then they will be the same} \\ f(x)=\big(4x^3-5\big)^4\rightarrow f(u)=u^4,\text{ note that }u=4x^3-5 \end{gathered}[/tex]Solve for each derivative of dy/du and du/dx
[tex]\begin{gathered} \frac{du}{dx}=3\cdot4x^{3-1}-0 \\ \frac{du}{dx}=12x^2 \\ \\ \frac{dy}{du}=4\cdot u^{4-1} \\ \frac{dy}{du}=4u^3,\text{ then substitute }u \\ \frac{dy}{du}=4(4x^3-5)^3 \\ \\ \text{Complete the chain rule} \\ \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx} \\ \frac{dy}{dx}=\big(4(4x^3-5)^3\big)\big(12x^2\big)\text{ or }\frac{dy}{dx}=48x^2(4x^3-5)^3 \\ \end{gathered}[/tex]Consider the following graph. Determine the domain and range of the graph? Is the domain and range all real numbers?
ANSWER
Domain = [-10, 10]
Range = [4]
EXPLANATION
Domain of a graph is the set of all input values on x-axis; while
Range is the set of all possible output values on y-axis.
Determining the Domain from the given graph,
The set of all INPUT values on x-axis are -10, -9, -8,....0......5,6,7,8,9,10.
So the Domain = [-10, 10].
Determining the Range from the given graph,
For the set of all possible OUTPUT values on y-axis, we only have 4,
So the Range = [4]
Hence, Domain = [-10, 10] and Range = [4]
Laying down my n buffer is concerned after receiving her weekly paycheck she believes that her deductions for social security,Medicare,and federal income ta withholding (fit) may be incorrect Larsen is paid a salary of 4330 she is married filling jointly and prior to this payroll check has total earnings of 140,460 what are the correct deductions for social security Medicare and fit assume a rate of 6.3% on 142,809 for social security and 1.45% for Medicare
Correct deduction for social security Medicare and fit at 6.3% = 8,996.967
Correct deduction for Medicare at rate of 1.45% = 2,070.731
What is Medicare?Medicare is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.
After deductions the total earning = 140,460
The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;
= 6.3/100 × 142,809
= 899696.7/100
= 8,996.967
The correct deduction for Medicare at the rate of 1.45%;
= 1.45/100 × 142,809
= 207,073.05/100
= 2,070.731.
Learn more about Medicare here:
https://brainly.com/question/24304697
#SPJ1
In 3 plays the southside football team drove 10 1/2 yards . How many yards did they average in each day?
If in three plays southside football team drove [tex]10\frac{1}{2}[/tex] yards, then the number of yard they drove average in each day is [tex]3\frac{1}{2}[/tex] yards
Number matches played by southside football team = 3
Total distance they drove = [tex]10\frac{1}{2}[/tex] yards
Convert the mixed fraction to the simple fraction
[tex]10\frac{1}{2}[/tex] yards = 21/2
Number of yards they drove average in each day = Total distance they drove ÷ Number matches played by southside football team
Substitute the values in the equation
= 21/2 ÷ 3
= 21/2 × (1/3)
= 7/2 yards
Convert the simple fraction to the mixed fraction
7/2 yards = [tex]3\frac{1}{2}[/tex] yards
Hence, if in three plays southside football team drove [tex]10\frac{1}{2}[/tex] yards, then the number of yard they drove average in each day is [tex]3\frac{1}{2}[/tex] yards
Learn more about average here
brainly.com/question/3841552
#SPJ1
Which of the following could be the product of two consecutive prime numbers?
Answer:
There is no question
Step-by-step explanation:
Have a nice day