Answer:
Total interest will $1800 after 5 years.
Step-by-step explanation:
It is given that the principle amount is $6000.
Rate of interest rate is 6% per annum.
Total interest is $1800.
Formula for simple interest is
[tex]I=\frac{P\times r\times t}{100}[/tex]
Where, P is principle, r is rate of interest in percent and t is time in years.
Substitute P=6000, r=6 and I=1800 in the above formula.
[tex]1800=\frac{6000\times 6\times t}{100}[/tex]
[tex]1800=\frac{36000t}{100}[/tex]
[tex]1800=360t[/tex]
Divide both sides by 360.
[tex]\frac{1800}{360}=t[/tex]
[tex]5=t[/tex]
Therefore the total interest will $1800 after 5 years.
Answer:
b. 5 years
Step-by-step explanation:
BRAINLIEST
evaluate the expression
if x=25,y=10,w=14, z=4
(x-y)^2+10wz
Answer:
785
Step-by-step explanation:
(25 - 10)² + 10(14)(4)
= 225 + 560
= 785
Solve for m:
[tex]2=\frac{m}{2} -7[/tex]
Hello! :D
Answer:
[tex]\boxed{m=18}\checkmark[/tex]
*The answer should have a positive sign.*
Step-by-step explanation:
First, you do is switch sides.
[tex]\frac{m}{2}-7=2[/tex]
Then, you add by 7 from both sides.
[tex]\frac{m}{2}-7+7=2+7[/tex]
Add numbers from left to right.
[tex]2+7=9[/tex]
[tex]\frac{m}{2}=9[/tex]
Multiply by 2 from both sides.
[tex]\frac{2m}{2}=9*2[/tex]
Finally, multiply numbers from left to right.
[tex]9*2=18[/tex]
m=18 is the correct answer.
I hope this helps you!
Have a wonderful day! :)
:D
-Charlie
Thanks!
Answer:
m= 18
Step-by-step explanation:
Move all terms not containing "m" to the right side of the equation.
m/2 - 7= 2
Add +7 to each side.
m/2 - 7 = 2
+7 +7
Add 2 and 7.
m/2= 9
Multiply both sides of the equation by 2
m= 9 (2)
Simplify.
m= 18
Bob, driving a new Ford, travels 330 miles in the same amount of time it takes John, driving an old Chevy and traveling 10 miles per hour faster, to travel 390 miles. How fast is Bob driving?
Answer:
55 mph
Step-by-step explanation:
Let x represent Bob's speed. Then John's speed is x+10, and their respective times are found by ...
time = distance/speed
330/x = 390/(x+10) . . . . . . . the times are the same
330(x +10) = 390x . . . . . . . multiply by x(x+10)
3300 = 60x . . . . . . . . . . . . . subtract 330x
55 = x . . . . . . . . . . . . . . . . . . divide by the coefficient of x
Bob is driving at 55 miles per hour.
Bob is driving at a speed of 55 miles per hour.
Let's denote Bob's speed as v miles per hour. Since John is driving 10 miles per hour faster than Bob, John's speed is ( v + 10 ) miles per hour.
The time it takes to travel a certain distance is given by the formula [tex]\( time = \frac{distance}{speed} \)[/tex]
Bob and John travel for the same amount of time, so we can set their times equal to each other:
[tex]\[ \frac{330}{v} = \frac{390}{v + 10} \][/tex]
Cross-multiplying to solve for (v), we get:
[tex]\[ 330(v + 10) = 390v \][/tex]
Expanding the left side:
[tex]\[ 330v + 3300 = 390v \][/tex]
Now, let's move all terms involving (v) to one side:
[tex]\[ 390v - 330v = 3300 \][/tex]
Simplifying, we find:
[tex]\[ 60v = 3300 \][/tex]
Dividing both sides by 60 to solve for v :
[tex]\[ v = \frac{3300}{60} \] \[ v = 55 \][/tex]
A survey is targeted at 12 year old children. Which questions are appropriate for the population? Choose all that apply.
- what year did you graduate high school? NO
- what color was your first car? NO
- where is your favorite vacation spot? MAYBE
- what is the last book you read? YES
- should taxes be increased to find a new park? NO
Answer:
options number four is correct because they are children and they can able to identify the book.
Which equation is represented by the graph below?
A. y= in x-3
B. y= in x-4
C. y=e^x -3
D. y= e^x -4
The answer is:
The equation that is represented by the shown graph is the equation from the option D.
[tex]y=e^{x}-4[/tex]
Why?Since we are given two types of functions, exponential and logarithmic, we need to remember that there is just an option that matches with the graph.
So, from the graph we can see that we are looking for an exponential function which intercepts are located at the point (0,-3) and a point which y-coordinate is equal to 0 and its x-coordinate is located at the x-axis between the number 1 and 2.
From the given options we can see that the only exponential function that intercepts the function at y equal to -3 is the fourth option, so, let's prove that:
Option D,
[tex]y=e^{x}-4[/tex]
Finding the y-intercept, we need to make "x" equal to 0, so:
[tex]y=e^{x}-4[/tex]
[tex]y=e^{0}-4[/tex]
[tex]y=1-4=-3[/tex]
So, we know that the y-intercept point is located at (0,-3)
Finding the x-intercept, we need to make "y" equal to 0, so:
[tex]0=e^{x}-4[/tex]
[tex]e^{x}=4[/tex]
[tex]ln(e^{x})=ln(4)\\x=ln(4)=1.386[/tex]
So, we know that the x-intercept point is located at (1.386,0)
Hence, we have that the axis interception points are (0,-3) and (1.386,0), so, the function that matches with the shown graph is the function from the option D.
[tex]y=e^{x}-4[/tex]
Have a nice day!
Note: I have attached a picture for better understanding.
Answer:
The equation that is represented by the shown graph is the equation from the option D.
Step-by-step explanation:
Determine the number of real solutions for each of the given equations. Equation Number of Solutions y = -3x2 + x + 12 y = 2x2 - 6x + 5 y = x2 + 7x - 11 y = -x2 - 8x - 16 R
Answer:
Step-by-step explanation:
Our equations are
[tex]y = -3x^2 + x + 12\\y = 2x^2 - 6x + 5\\y = x^2 + 7x - 11\\y = -x^2 - 8x - 16\\[/tex]
Let us understand the term Discriminant of a quadratic equation and its properties
Discriminant is denoted by D and its formula is
[tex]D=b^2-4ac\\[/tex]
Where
a= the coefficient of the [tex]x^{2}[/tex]
b= the coefficient of [tex]x[/tex]
c = constant term
Properties of D: If D
i) D=0 , One real root
ii) D>0 , Two real roots
iii) D<0 , no real root
Hence in the given quadratic equations , we will find the values of D Discriminant and evaluate our answer accordingly .
Let us start with
[tex]y = -3x^2 + x + 12\\a=-3 , b =1 , c =12\\D=1^2-4*(-3)*(12)\\D=1+144\\D=145\\D>0 \\[/tex]
Hence we have two real roots for this equation.
[tex]y = 2x^2 - 6x + 5\\[/tex]
[tex]y = 2x^2 - 6x + 5\\a=2,b=-6,c=5\\D=(-6)^2-4*2*5\\D=36-40\\D=-4\\D<0\\[/tex]
Hence we do not have any real root for this quadratic
[tex]y = x^2 + 7x - 11\\a=1,b=7,-11\\D=7^2-4*1*(-11)\\D=49+44\\D=93\\[/tex]
Hence D>0 and thus we have two real roots for this equation.
[tex]y = -x^2 - 8x - 16\\a=-1,b=-8,c=-16\\D=(-8)^2-4*(-1)*(-16)\\D=64-64\\D=0\\[/tex]
Hence we have one real root to this quadratic equation.
Answer:
The first box is "two real solutions," the second box is "no real solution," the third box is "two real solution," and the fourth box is "one real solution".
Step-by-step explanation:
The interior angle of the regular octagon below measures 135º, and the
octagon has rotational symmetry. Which of the following is the measure of an
interior angle after a 90° rotation around the point of symmetry?
Answer:
D
Step-by-step explanation:
Since the shape won't change, it won't deform, nothing will happen to the interior angle.
This figure is symmetric and not deformed, so the measure of the interior angle won't change no matter how many times you rotate it.
So the interior angle would still be 135º.
Correct answer D
Answer:
the answer is D on e2020
Step-by-step explanation:
How can (1/2)x-5=(1/3)x+6 be set up as a system of equations?
Answers:
A) 2y+x=-10
3y+x=18
B) 2y+2x=-10
3y+3x=18
C) 2y-x=-10
3y-x=18
D) 2y-2x=-10
3y-3x=18
Answer:
C)
2y-x=-103y-x=18Step-by-step explanation:
Set each side of the equation equal to y, then rearrange to standard form.
(1/2)x -5 = y . . . left side of the equal sign
x -10 = 2y . . . . multiply by 2
-10 = 2y -x . . . . subtract x
__
(1/3)x +6 = y . . . right side of the equal sign
x +18 = 3y . . . . . multiply by 3
18 = 3y -x . . . . . subtract x
The corresponding system of equations is ...
2y -x = -103y -x = 18The height of a box can be found by dividing its volume by the area of its base,bottom.What is the height of a box that has a volume of 26.35 cubic centimeter and a base area of 4 1/4 square centimeter?
Answer:
6.2 cm
Step-by-step explanation:
[tex]\dfrac{26.35\,\text{cm}^{3}}{4.25\,\text{cm}^{2}}=6.2\,\text{cm}[/tex]
The height of the box is 6.2 cm.
What is the classification for this polynomial?
-2gh
Click on the correct answer.
monomial
binomial
trinomial
Answer:
Monomial
Step-by-step explanation:
Let's look at the edfinitions of all three options.
Monomial: A polynomial with only one term is called a monomial.
Binomial: A polynomial with two terms is called a binomial.
Trinomial: A polynomial with three terms is called a trinomial.
So, according to the definition, the given polynomial is a monomial as it has only one term -2gh ..
Anyone know what the answer can be
The answer would be B (the symbol ~ means similar. In other words, that they are the same shape but not the same size).
It can't be A because the symbol ≈ means "approximately"
It can't be C because the symbol = means equal
It can't be D because the symbol ≅ means congruent
Hope this helped!
~Just a girl in love with Shawn Mendes
help calculus module 5 DBQ
please show work
1. The four subintervals are [0, 2], [2, 5], [5, 6], and [6, 7]. Their respective right endpoints are 2, 5, 6, and 7. If [tex]C(t)[/tex] denotes the change in sea level [tex]t[/tex] years after 2010, then the total sea level rise over the course of 2010 to 2017 is
[tex]\displaystyle\int_0^7C(t)\,\mathrm dt[/tex]
approximated by the Riemann sum,
[tex]C(2)(2-0)+C(5)(5-2)+C(6)(6-5)+C(7)(7-6)\approx\boxed{20\,\mathrm{mm}}[/tex]
2. The sum represents the definite integral
[tex]\boxed{\displaystyle\int_1^4\sqrt x\,\mathrm dx}[/tex]
That is, we partition the interval [1, 4] into [tex]n[/tex] subintervals, each of width [tex]\dfrac{4-1}n=\dfrac3n[/tex]. Then we sample [tex]n[/tex] points in each subinterval, where [tex]1+\dfrac{3k}n[/tex] is the point used in the [tex]k[/tex]th subinterval, then take its square root.
3. The integral is trivial:
[tex]\displaystyle\int_1^4\sqrt x\,\mathrm dx=\frac23x^{3/2}\bigg|_{x=1}^{x=4}=\boxed{\frac{14}3}[/tex]
4. Using the fundamental properties of the definite integral, we have
[tex]\displaystyle\int_1^4f(x)\,\mathrm dx=e^4-e\implies2\int_1^4f(x)\,\mathrm dx=2e^4-2e[/tex]
[tex]\displaystyle\int_1^4(2f(x)-1)\,\mathrm dx=2e^4-2e-\int_1^4\mathrm dx=\boxed{2e^4-2e-3}[/tex]
5. First note that [tex]\sec x[/tex] is undefined at [tex]x=\dfrac\pi2[/tex], so the integral is improper. Recall that [tex](\tan x)'=\sec^2x[/tex]. Then
[tex]\displaystyle\int_0^{\pi/2}\sec^2\frac xk\,\mathrm dx=\lim_{t\to\pi/2^-}\int_0^t\sec^2\frac xk\,\mathrm dx[/tex]
[tex]=\displaystyle\lim_{t\to\pi/2^-}k\tan\frac xk\bigg|_{x=0}^{x=t}[/tex]
[tex]=\displaystyle k\lim_{t\to\pi/2^-}\tan\frac tk[/tex]
[tex]=k\tan\dfrac\pi{2k}[/tex]
Now,
[tex]k\tan\dfrac\pi{2k}=k\implies\tan\dfrac\pi{2k}=1[/tex]
[tex]\implies\dfrac\pi{2k}=\dfrac\pi4+n\pi[/tex]
[tex]\implies k=\dfrac2{1+4n}[/tex]
where [tex]n[/tex] is any integer.
A group of 8 friends (5 girls and 3boys ) plan to watch a movie, but they have only 5 tickets. How many different combinations of 5 friends could possibly receive the tickets ?
You are standing at point B. Point B is 21 feet from the center of the circular water storage tank and 20 feet from point A. \frac{ }{AB} A B is tangent to \odot ⊙ O at A. Find the radius of the tank.
Answer:
r = 6.40 feet
Step-by-step explanation:
Given line AB is tangent to circle O at point A, this means ∡OAB = 90°
Hence this is a right angle triangle and we can use the Pythagorean theorem.
r² + 20² = 21²
r² = 21² - 20²
r² = 441 - 400
r² = 41
r = √41 = 6.40 feet
The radius of the tank is = 6.4ft
Calculating the radius of a tank (circle)The radius of the circle can be calculated using the Pythagorean theorem since a distance in of AB and OB where given.
The formula c²= b²+a²
Where b²= AB = 20ft
a²= AO= r
c² = OB = 21ft
Make a² the subject of formula
a² = c²-b²
= 21² - 20²
= 441-400
= 41
a= √41
a= 6.4ft
Therefore, the radius of the tank is = 6.4ft
Learn more about radius of circle here:
https://brainly.com/question/12908707
Divide 40x/64y by 5x/8y.
Answer:
The correct answer option is C. 1.
Step-by-step explanation:
We are to divide [tex] \frac { 4 0 x } { 6 4 y } [/tex] by [tex] \frac { 5 x } { 8 y } [/tex].
Rewriting them as a fraction in whole:
[tex] \frac { \frac { 4 0 x } { 6 4 y } } {\frac { 5 x } { 8 y } } [/tex]
Changing the division into multiplication by taking the reciprocal of the fraction in the denominator to get:
[tex] \frac { 4 0 x } { 6 4 y } [/tex] × [tex]\frac{8y}{5x}[/tex]
Cancelling out the like terms to get:
1
Caroline drew two triangles and used them to construct a rhombus with two acute angles and two obtuse angles. Which
could be one of the triangles she used?
Answer:
72* 62* & 60* 30* triangles
Step-by-step explanation:
I just remember rhombuses being made with 60 degree triangles from all the examples I did. This may be wrong though. But 90 percent confident lol.
Answer: the triangles marked 75 degrees and 45 degrees
Step-by-step explanation:
A rhombus has equal opposite obtuse angles with equal acute angles.
Evaluate the function g(x) = 2x2 + 3x – 5 for the input values -2, 0, and 3.
g(-2) = -2(-2)2 + 3(-2)-5
g(-2) = -2(4) – 6-5
g(-2) =
g(0) =
-
9(3) =
Evaluate the function
g(x) = 2x2 + 3x – 5 for the input values -2, 0, and 3.
This is tedious math work but necessary to sharpen your skills.
Let x = -2
g(-2) = 2(-2)^2 + 3(-2) – 5
g(-2) = 2(4) - 6 - 5
g(-2) = 8 - 11
g(-2) = -3
Now let x = 0 and repeat the process.
g(0) = 2(0)^2 + 3(0) - 5
g(0) = 0 + 0 - 5
g(0) = -5
Lastly, let x = 3.
g(3) = 2(3)^2 + 3(3) - 5
g(3) = 2(9) + 9 - 5
g(3) = 18 + 9 - 5
g(3) = 27 - 5
g(3) = 22
Did you follow through each step?
Answer:
-19
-5
-14
Step-by-step explanation:
What is the area of the figure below
Answer:
86 m²
Step-by-step explanation:
It can be convenient to think of the figure as an 8×12 rectangle with a 4×5 triangle cut off the corner.
The rectangle area is the product of its length and width:
(12 m)×(8 m) = 96 m²
The triangle area is half the product of its base and height:
(1/2)(4 m)(5 m) = 10 m²
Then the area of the figure is the difference of these:
96 m² -10 m² = 86 m²
Solve by using a matrix. A collection of nickels, dimes and quarters totals $6.00. If there are 52 coins altogether and twice as many dimes as nickels, how many of each kind of coin are there? a. q = 5 d = 60 n = 30 c. q = 15 d = 28 n = 6 b. q = 35 d = 10 n = 5 d. q = 10 d = 28 n = 14 Please select the best answer from the choices provided A B C D
Answer:
The answer is d. q=10 d=28 n=14
Step-by-step explanation:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
-3
-2
-1
0
1
2
Answer:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Select all numbers that are in the domain.
-3
-1
1
Select all numbers that are in the range.
-2
0
2
Have great day :)
Step-by-step explanation:
The -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have domain of a function:
R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
From the above relation, we can see:
-3 is in the domain.
-1 is in the domain.
1 is in the domain.
Thus, the -3, -1, and 1 are in the domain if the domain of the function as follows R = {(-3, -2), (-3, 0), (-1, 2), (1, 2)}
Learn more about the function here:
brainly.com/question/5245372
#SPJ2
Write the quadratic equation in standard form and then choose the value of “b” (2x - 1)(x + 5) =0
We want to write the given function in the form ax^2 + bx + c = 0.
We foil the left side.
(2x - 1)(x + 5) =0
2x^2 + 10x - x - 5 = 0
2x^2 + 9x - 5 = 0
Can you see the value of "b"?
The b-value is the coefficient of x.
So, b = 9.
Done!
your heart beats 240 beats per 4 minutes at this rate how many times will your heartbeat in a hour
don't spam random letters or i'll delete your answer.
Let’s find the amount of heartbeats for 1 minute, so it’s easier to solve.
Since we divide 4 by 4 to get 1, divide 240 by 4 to get the equivalent.
240/4=60.
Your heart beats 60 times per minute.
Since there are 60 minutes in an hour, multiply the amount of heartbeats per minute (60) by 60.
60*60=3,600
Your heart beats 3,600 times per hour.
Hope this helps!
Simplify.
1. 3/10
2. 10/3
3.1/12
Answer:
2. 10/3.
Step-by-step explanation:
The numerator x/2 + x/ 3
= 3x/6 + 2x / 6
= 5x / 6
Now divide this by x/4
5x / 6 / x/4
= 5x/6 * 4/x . The x's cancel so this
= 20/6
= 10/3.
What is the reflection image of P(0, 0) after two reflections, first across x = 4 and then across y = -3?
Answer:
The reflection image of P(0, 0) after two reflections is (8,-6)
Step-by-step explanation:
step 1
Find the coordinates of point P after reflection across x=4
we know that
The distance from point P to the line x=4 is equal to 4 units
so
(0,0) -----> (4+4,0) ----> (8,0)
The reflection image of P is (8,0)
step 2
Find the coordinates of point (8,0) after reflection across y=-3
The distance from point (8,0) to the line y=-3 is equal to 3 units
so
(8,0) -----> (8,-3-3) ----> (8,-6)
What is the solution set?
(0, -2)
(2, 0)
(7, 0)
(5, 3)
Answer:
(5,3)
Step-by-step explanation:
Look for the coordinates of the point of intersection where the 2 graphs cross. This gives the solution.
In this case, they cross at (5,3) and they intersect at only one location (i.e there is only 1 solution)
From the graph, the intersecting point will be (5, 3). Then the correct option is D.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
In a diagram, the two lines are shown.
The lines are intersecting at a point.
From the graph, the intersecting point will be (5, 3).
Then the correct option is D.
The graph is given below.
More about the linear system link is given below.
https://brainly.com/question/20379472
#SPJ2
Find the value of angle L. HELP ASAP!!
Answer:
B) 67
Step-by-step explanation:
Nancy is investing 20,000 in an account paying 7.25% interest compounded weekly. What would Nancy account balance be in 24 years?
[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$20000\\ r=rate\to 7.25\%\to \frac{7.25}{100}\dotfill &0.0725\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{weekly, fifty two times} \end{array}\dotfill &52\\ t=years\dotfill &24 \end{cases}[/tex]
[tex]\bf A=20000\left(1+\frac{0.0725}{52}\right)^{52\cdot 24}\implies A\approx 20000(1.001394)^{1248} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill A\approx 113776.1384~\hfill[/tex]
Please help determine the relationship of the following linear equations
Answer:
Neither
Step-by-step explanation:
step 1
Verify if the lines are parallel
we know that
If two lines are parallel, then their slopes are the same
In this problem the slope of f(x) =2/7 and the slope of g(x)=7/2
Compare
2/7≠7/2
therefore
The lines are not parallel lines
step 2
Verify if the lines are perpendicular
we know that
If two lines are perpendicular, then the product of their slopes is equal to -1
In this problem the slope of f(x) =2/7 and the slope of g(x)=7/2
Multiply
2/7*7/2=1
1≠-1
therefore
The lines are not perpendicular
Hello, I really appreciate your help! Thanks!
Tricia uses the Fermi process to estimate the number of buckets of sand she could store in a warehouse. The buckets are shaped like cylinders. The warehouse is shaped like a rectangular prism.
She estimates the buckets have a height of 15 inches and a diameter of 20 inches.
She estimates the warehouse is 250 feet long, 80 feet wide, and 20 feet high.
Which expression should Tricia use in the process?
A) 7×10^9/5×10^4
B) 5×10^6/5×10^3
C) 7×10^8/5×10^3
D) 5×10^7/5×10^4
Answer:
C) 7×10^8/(5×10^3)
Step-by-step explanation:
In cubic inches, the volume of a bucket of sand is ...
(π/4)(20 in)²(15 in) = 1500π in³ ≈ 5×10^3 in³
__
The volume of the warehouse is
(250 ft)(80 ft)(20 ft) = 400,000 ft³ = 4×10^5 ft³
The conversion to cubic inches is ...
(4×10^5 ft³)(1728 in³/ft³) = 4×1.727×10^8 in³ ≈ 7×10^8 in³
Dividing the warehouse volume by the bucket volume gives the approximate number of buckets that will fit in the warehouse:
(7×10^8)/(5×10^3) . . . . . matches choice C
Beth makes batches of blueberry and banana muffins. Each batch is 6 muffins. She makes 2.5 batches of blueberry muffins. How many batches of banana muffins should beth make if she wants to have a total of 60 muffins?
Answer:
8 batches.
Step-by-step explanation:
Beth made 2.5 batches of blueberry muffins = 15 muffins
Beth needs 60 muffins in total. She already has 15 therefore she only needs 45 more.
45/6 = 7.5
7.5 would not be enough. You need to round up to 8.