ANSWER
The interest rate is 150%
EXPLANATION:
Given that;
The initial amount is $5000
The total amount $20, 000 after 2 years
Total period of the investment is 2 years
To find the interest rate, follow the steps below
1. Find the interest on the investment after two years
In the given data,
The initial amount (principal) is $5000
The total amount after 2 years is $20, 000
Recall that,
Total amount = Interest + principal
20, 000 = interest + 5000
subtract 5000 from both sides of the equation
20, 000 - 5,000 = interest + 5000 - 5000
15,000 = interest
Therefore, the interest on the investment after 2 years is $15, 000
Step 2; Find the interest rate using the simple interest formula
[tex]\text{ I }=\text{ }\frac{P\times R\times T}{100}[/tex]Where
I is the interest
P is the principal
R is the interest rate
T is the time of the investment
[tex]\begin{gathered} \text{ 15, 000 }=\text{ }\frac{5000\times\text{ r}\times\text{ 2}}{100} \\ \text{ } \\ \text{ 15000 }=\text{ }\frac{10,000r}{100} \\ \text{ 15, 000 }=\text{ 100r} \\ \text{ Divide both sides by 100} \\ \frac{15,000}{100}\text{ }=\text{ }\frac{100r}{100} \\ \text{ r }=\text{ 150\%} \end{gathered}[/tex]Therefore, the interest rate is 150%
According to the United States Treasury Department, the U.S national debt was 1.815 x 10 to the 13th power dollars on September 30, 2015 . On September 29, 2005 , the national debt was 4.974 x 10 to the power of 12 dollars . Find the amount of Increase in the national debt from September of 2005 to september of 2015? Write a sentence describing the increase in the national debt from 2005 to 2015 using scientific notation and using standard form.
The U.S national debt on 2015 was 1.815 * 10^13
The U.S national debt on 2005 was 4.974 * 10^12
So, the amount of increase =
1.815 * 10^13 - 4.974 * 10^12 =
18.15 * 10^12 - 4.974 * 10^12 =
(18.15 - 4.974) * 10^12 = 13.176 * 10^12
= 1.3176 * 10 * 10^12 = 1.3176 * 10^13
These dot plots show the ages (in years) for a sample of sea turtles and a sample of sharks. Sea Turtles 00 000 to 0000 000 : 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Sharks 000000 : OO 00000 0000 000 OO o 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 Age (in years) What are the differences between the centers and spreads of these distributions? Select two choices: one for the centers and one for the spreads. O A. Centers: The sea turtles have a lower median age than the sharks. B. Spreads: The ages of the sea turtles are more spread out. O C. Centers: The sea turtles have a greater median age than the sharks. O D. Spreads: The ages of the sharks are more spread out
Options C and D.
The median age of the Sea turtles is 55 while the median age of the sharks is 30, thus validating OPTION C
We can get the ranges of the two distributions to be:
Sea Turtles: 65 - 45 = 20
Sharks: 55 - 10 = 45
Sharks have a larger range, validating OPTION D
In the parallelogram ABCD, MLA = 2x + 50 and m C = 3x + 40. The measure of LA is
The measure of angle m∠A will be 70°,for the parallelogram ABCD
Parallelogram and its Properties:
Parallelogram is a special kind of quadrilateral, in which opposite sides are equal and parallel to each other.
Properties:
1. Opposite sides are parallel to each other.
2. Length of opposite sides are equal.
3.Diagonally opposite angles are equal.
4. Diagonals bisects each other.
5. Sum of any two adjacent angle is 180°
From figure,
ABCD is a parallelogram
m∠A = 2x + 50
m∠ C = 3x + 40
In a parallelogram ABCD we know opposite angles are equal to each other,
m∠A = m∠C
2x + 50 = 3x + 40
3x - 2x = 50 - 40
x = 10
Hence,
m∠A = 2x + 50
put the value of x we get,
m∠A = 2 * 10 + 50
= 20 + 50
= 70°
m∠A = 70°
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1. What is the solution of the matrix equation?L-02(-2, 1)(10, 6)(-4, 3)O(-3, 4)
Solving Matrix Equation.
[tex]\begin{gathered} \begin{bmatrix}{8} & {5} & {} \\ {\square} & {\square} & {} \\ {5} & {4} & {}\end{bmatrix}\begin{bmatrix}{x} & {} & {} \\ {\square} & {} & {} \\ {y} & {} & {}\end{bmatrix}=\text{ }\begin{bmatrix}{2} & {} & {} \\ {} & {} & {} \\ {1} & {} & {}\end{bmatrix} \\ \end{gathered}[/tex]Thus, the correct answer is;
x = 3/7 and y = -2/7
Below is a pattern that can be used to cut out and fold to make a cube. If each edge is 5 inches, what will be the surface area of the cube? A 30 in? B 120 in С 150 in? D 3,125 in
In words, the surface area of a cube is the area of the six squares that cover it. The area of one of them is a*a, or a^2
[tex]A=6a^2[/tex]Here, a = 5 inches
[tex]\begin{gathered} A=6\cdot(5^2) \\ A=6\cdot25 \\ A=150 \end{gathered}[/tex]The answer would be 150 in^2
Simplify the following expression. Leave your answer in the form a^b.3^19/3^13= ___
Given the expression:
[tex]\frac{3^{19}}{3^{13}}[/tex]To simplify the expression, we will use the following rule of the exponents:
[tex]\frac{a^m}{a^n}=a^{m-n}[/tex]The answer will be:
[tex]\begin{gathered} \frac{3^{19}}{3^{13}}=3^{19-13}^{} \\ \\ =3^6 \end{gathered}[/tex]you will write the answer as 3^6
Write the STANDARD FORM of the equation through the point (4,-4) witha slope of -2.
The general equation of line with the slope "m" and passing points (a,b) is :
y - b = m (x -a)
In the given question:
Slope m = -2, passing points (a,b) = (4,-4)
Substitute the value of a = 4, b = -4 in the general equation of line
[tex]\begin{gathered} y-b=m(x-a) \\ y-(-4)=(-2)(x-4) \\ y+4=-2(x-4) \\ y+4=-2x+8 \\ y+2x=8-4 \\ 2x+y=4 \end{gathered}[/tex]The equation with the slope -2 and passing points (4,-4) is 2x + y = 4
Answer : 2x + y = 4
find a slope of the line that passes through (6,8) and (95,86)
find a slope of the line that passes through (6,8) and (95,86)
Applying the formula to calculate the slope
we ahve
m=(86-8)/(95-6)
m=78/89
therefore
the slope is 78/89A standard die is rolled. Find the probability that the number rolled is less than 3. Express your answer as a fraction
Once a die has the numbers 1,2,3,4,5 and 6, it means the numbers that are less than 3 are just the numbers 1 and 2. Now the probability can be built as follows:
As we can see above, once there are just two possibilities of numbers that are less than 3, the probability that the number rolled is less than 3 is equal to 2/6.
How would I solve this and what would be the answer?
Solution
(1). Domain
Since the graph is a polynomial, thus
The domain is all the elements of the set of Real Number
[tex]DOMAIN=(-\infty,\infty)[/tex](2) . Range
Notice that the graph is on the x - axis and above the x - axis throughout
The range will be
[tex]Range=\lbrack0,\infty)[/tex](3). x - intercept
We check where the graph touch the x - axis ( we have two)
That is at
[tex]\begin{gathered} x=-1 \\ \text{and} \\ x=2 \end{gathered}[/tex](4). y - intercept
We also check where the graph touch the y - axis
That is at
[tex]y=4[/tex](5). End Behaviour
First from the graph
[tex]x\rightarrow\infty,f(x)\rightarrow\infty[/tex]Second from the graph
[tex]x\rightarrow-\infty,f(x)\rightarrow\infty[/tex]Which best describes what happens when the number of trials increases significantly
Solution:
Given:
[tex]\begin{gathered} Head,H=4 \\ Total=12 \\ P(H)=\frac{4}{12} \\ P(H)=\frac{1}{3} \end{gathered}[/tex]From the probability, it can be deduced that as the number of trials increases, the observed frequency will get closer to the expected frequency.
Therefore, if the number of trials increases significantly, then the observed frequency of landing heads up gets closer to the expected frequency based on the probability of the coin landing heads up.
Hi, i need help with question 1 of my Precalculus homework.
The interval notation uses the form (x1,x2) and it depends on whether the interval includes or does not includes the limits. if the interval includes the limit then we use the notation [x1,x2].
a. Since neither of the endpoints is included in the inequality the interval notation should be
[tex]-1b. The inequality includes all numbers greater or equal to 5, the interval notation should be [tex]x\ge5=\lbrack5,\infty)[/tex]c. The inequality includes all numbers that are less to 4 but does not include number -4, the interval notation should be
[tex]-4>x=(-\infty,-4)[/tex]d. The solution for the inequality includes two solutions, then we write both separately and unite them together. The interval notation should be
[tex]-4\le x<-1or0e. The interval notation should be between numbers 5 and 100 [tex]\lbrack5,100\rbrack[/tex]f. The numbers should be all less than pi, but it does not include pi
[tex](-\infty,\pi)[/tex]g. all numbers greater or equal to 3
[tex]\lbrack3,\infty)[/tex]h. All numbers less or equal to -2
[tex](-\infty,-2\rbrack[/tex]i. All numbers greater than 0, but it does not include 0
[tex](0,\infty)[/tex]j. all numbers less than e but it does not include e
[tex](-\infty,e)[/tex]Pls helpppp I don't know what 2×2 IS plsss
we have
2*2=2+2=4
5*5=5+5+5+5+.5=25
5 times 5
example
2*3
its 2 times 3
3+3=6
4*3
4 times 3
3+3+3+3=12
Answer:
2 x 2 = 4.
two multiplied by two equals four.
A chemistry student needs 80.0 mL of ethanolamine for an experiment. By consulting the CRC Handbook of Chemistry and Physics, the student discovers thatthe density of ethanolamine is 1.02 g.cm. Calculate the mass of ethanolamine the student should welgh out.Be sure your answer has the correct number of significant digits.
STEP 1: Identify and Set Up
We are given a question that requires us to find mass when given volume and density.
It is common knowledge that these parameters are related by the formulae:
[tex]\begin{gathered} \text{density = }\frac{\text{mass}}{\text{volume}} \\ \text{This gives mass = volume }\times\text{ density} \end{gathered}[/tex]We use this relation to find mass
STEP 2: Execute
Density = 1.02 g/cc
Volume = 80ml = 80 cc
Mass is therefore:
[tex]\text{mass = 1.02}\times80=81.6g[/tex]Mass = 81.6g
What is 10 meters long by 7 meters wide in square meters?
1) Assuming this is a quadrilateral, then the area is width times length
So
A =10 x 7
A= 70 m²
It's an area of 70 m²
in 2 years steve wants to buy a bicycle that 800.00. if he opens a savings account that earns 3 % interest compounded monthly how much will he have to despoit as principal to have enough money in 2 years to buy the bike
Answer
393.55
Explanation
The amount that results after an amount P is invested at compound interest at rate r% and time period t is given as
A = P (1 + r)ᵗ
For this question,
A = 800
r = 3% = 0.03
t = 2 (12) = 24 (Since the interest is compounded monthly, over 2 years)
P = ?
800 = P (1 + 0.03)²⁴
800 = P (1.03)²⁴
800 = P (2.0328)
2.0328P = 800
Divide both sides by 2.0328
(2.0328P/2.0328) = (800/2.0328)
P = 393.55
Hope this Helps!!!
Luke opened a savings account 3 years ago. the account earns 6%interest compounded quarterly if the current balance is 300.00 how much did he deposit initially
Answer
This is similar to the first one too.
A = P (1 + r)ᵗ
For this question,
A = 300
r = 6% = 0.06
t = 3 (4) = 12 (Since the interest is compounded quarterly, over 3 years; there are 4 quarters per year)
300 = P (1 + 0.06)¹²
300 = P (1.06)¹²
300 = P (2.0122)
2.0122P = 300
Divide both sides by 2.0122
(2.0122P/2.0122) = (300/2.0122)
P = 149.09
Hope this Helps!!!
Find the equation of the line with Slope = 5 and passing through (-7,-34). Write your equation in the form y=mx+b .
[tex](\stackrel{x_1}{-7}~,~\stackrel{y_1}{-34})\hspace{10em} \stackrel{slope}{m} ~=~ 5 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-34)}=\stackrel{m}{ 5}(x-\stackrel{x_1}{(-7)}) \implies y +34= 5 (x +7) \\\\\\ y+34=5x+35\implies {\Large \begin{array}{llll} y=5x+1 \end{array}}[/tex]
solve each inequality graph and check the solution (JUST NUMBER 8)
ANSWER
p ≤ -3
EXPLANATION
To solve this inequality first we have to subtract 5 from both sides:
[tex]\begin{gathered} 2-5\ge5-5+p \\ -3\ge p \end{gathered}[/tex]That's the solution, but we can flip it to see it more clearly:
[tex]p\le-3[/tex]To graph this, we have to draw a line from -3 to the left. Usually we have to draw a filled circle on -3, to indicate that that value is included in the solution.
I need help with the hidden message. Help me please. Thank You I really appreciate it if you have helped me.
We have symbols that represent a letter and a number.
With the equations or relations in the left we have to find the numeric value for each picture, and then use the letter to complete the hidden message.
First equation is:
[tex]\begin{gathered} \text{spyder web + spyder web =16} \\ 2\cdot\text{spyder web = 16} \\ \text{spyder web = }\frac{16}{2}=8 \end{gathered}[/tex]So, the value of a spyder web is 8 and the letter for that is i.
The second equation is:
[tex]\begin{gathered} \text{candy - spyder web = 9} \\ \text{candy - 8 =9} \\ candy\text{ = 9+8=17} \end{gathered}[/tex]The value of candy is 17 and the letter is T.
The Third equation is:
[tex]\begin{gathered} \text{spyder web }\cdot\text{ cat - candy = 7} \\ 8\cdot\text{cat - 17 =7} \\ 8\cdot\text{cat=7+17=24} \\ \text{cat}=\frac{24}{8}=3 \end{gathered}[/tex]The value of cat is 3 and the letter is S.
The fourth equation is:
[tex]\begin{gathered} ballons\text{ / cat =11} \\ \text{ballons /3 =11} \\ \text{ballons}=11\cdot3=33 \end{gathered}[/tex]The value of ballons is 33 and the letter is E.
The fifth equation is:
[tex]\begin{gathered} \text{bat + (ballons - candy) = 23} \\ \text{bat + (33-17) = 23} \\ bat+16=23 \\ \text{bat = 23 - 16 = 7} \end{gathered}[/tex]The value of bat is 7, but there is some mistake, it must be 6 and the letter C.
The sixth equation is:
[tex]\begin{gathered} \text{bat}+\text{cat}\cdot pumpkin\text{ = 27} \\ 6+3\cdot\text{pumpkin}=27 \\ 3\cdot\text{ pumpkin = 27-6=21} \\ \text{pumpkin =}\frac{21}{3}=7 \end{gathered}[/tex]The value of pumpkin is 7 and the letter is O.
The seventh equation is:
[tex]\begin{gathered} \text{spyder / spyder web }\cdot\text{ pumpkin = 21} \\ \frac{spyder}{8}\text{ }\cdot7=21 \\ \text{spyder = 21}\cdot\frac{8}{7}=3\cdot8=24 \end{gathered}[/tex]The value of spyder is 24 and the letter is B.
The last equation is:
[tex]\begin{gathered} tree\text{ +ghost}=0 \\ tree\text{ + 0=0} \\ \text{tre}e\text{ = 0} \end{gathered}[/tex]The only value for ghost is zero and the letter L and the value of tree is zero too and the letter is O.
The hidden message is:
BOIL IS IOOOCEOT
A restaurant sells tea for $1.50 plus $0.50 per refill. the restaurant brews enough tea for 4 refills per customer. The linear function that represents the total cost of, r , tea refill is C(r)=0.5r+1.5.
C(r)=0.5r+1.5.
The domain of a function is the set of all input variables of the function. In this case "r"
The domain r is the number of tea refills.
I need help simplifying this question (last answer that is cropped is 1 over 9 with exponent of 5
To simplify this expression we need to follow this procedure:
It means that the correct answer is:
[tex]\frac{1}{9^5}[/tex]Determine the Coordinate represented in the Table of Values. ch on at 2 7 9 6 3 5 una) f(9) = 5b) f(5) = 9c) f(5, 9) = 14d) f(9, 5) = 14
Given the table:
x f(x)
2 6
7 3
9 5
To determine the coordinate given in the table, we have the following:
f(2) = 6
f(7) = 3
f(9) = 5
From the answer choices, the only coordinate given is:
f(5) = 9
ANSWER:
f(9) = 5
10.2 x 3.80
I am still confused on this question
Answer: 38.76
Step-by-step explanation:
All you have to do is move both decimals to the right and multiply, example, 10.2 = 102. & 3.80 = 380., then you multiply both numbers. In this case, 102 x 380 is 38760. After you multiply both numbers, you move the decimal to the left, so 38760. = 38.760 or 38.76.
Enter the value of the expression using the Order of Operations. (4 x 3) + 23 x 4-3
Starting with the expression:
[tex](4\times3)+23\times4-3[/tex]Solve parenthesis first. Since 4 times 3 equals 12, then the expression is equal to:
[tex]12+23\times4-3[/tex]Next, solve for multiplications. In this case, solve 23 times 4:
[tex]12+92-3[/tex]Finally, solve additions and substractions from left to right:
[tex]\begin{gathered} 12+92-3=104-3 \\ =101 \end{gathered}[/tex]Therefore:
[tex](4\times3)+23\times4-3=101[/tex]List the sale price of the item. Round to two decimal places when necessary. Original price: $25; Markdown: 12%.
Answer
Sale Price = $22
Explanation
Mark down percentage is given as
[tex]\text{Markdown percentage = }\frac{(Original\text{ Price) - (Sale Price)}}{(Original\text{ }Price)}\times100[/tex]For this question,
Markdown percentage = 12%
Original Price = $25
Sale Price = ?
[tex]\begin{gathered} \text{Markdown percentage = }\frac{(Original\text{ Price) - (Sale Price)}}{(Original\text{ }Price)}\times100 \\ 12=\frac{25-(\text{Sale Price)}}{25}\times100 \\ \text{Divide both sides by 100} \\ 0.12=\frac{25-(\text{Sale Price)}}{25} \\ \text{Cross multiply} \\ 25-(\text{Sale Price) = (0.12 }\times25) \end{gathered}[/tex]25 - (Sale Price) = 3
Sale Price = 25 - 3
Sale Price = $22
Hope this Helps!!!
Sam used his calculator to multiply two large numbers. His calculator gave the result 6E7. Which numbers are equal to the result his calculatorshowed? Select all that apply.0.00000066x 1076 x 1076,000,00060,000,000
The expression: 6E7, is a way of writing a number in scientific notation and it is equivalent to:
[tex]6\cdot10^7[/tex]Since 10^7=10,000,000, then:
[tex]6\cdot10^7=60,000,000[/tex]Determine The Domain for the relation below
Answer:
The domain would be all real numbers.
Step-by-step explanation:
For Interval notation, it would be written as (-∝, ∝)
(I don't know what signs those are, but they are supposed to be infinity signs)
Domain is what x can or can't be. In the function that is in the image, the function is y=a constant. So, no matter what x is, y will always be the constant. So, x can be all real numbers.
Hope this helps!
I was on vacation for this unit and having a hard time
1.a
We can rewrite the given information in an algebraic expression as follows:
[tex]\frac{3}{8}x=6[/tex]where x represents the number of 3/8-inch thick books. Solving for x:
[tex]x=\frac{6}{\frac{3}{8}}[/tex]We can rearrange the operation:
[tex]x=\frac{6}{3}\cdot8[/tex][tex]x=\frac{48}{3}[/tex][tex]x=16[/tex]Then, we need 16 3/8-inch books to make a stack 6 inches tall.
1.b
To solve this exercise, we can use the same procedure as in 1.a.
0. Writing the information in an algebraic expression.
[tex]\frac{1}{2}x=2\cdot\frac{3}{4}[/tex]where x represents the groups of 1/2 pound.
We can convert the mixed number into an improper fraction:
[tex]2\cdot\frac{3}{4}=\frac{2\cdot4+3}{4}=\frac{8+3}{4}=\frac{11}{4}[/tex]2. Rewriting the operation:
[tex]\frac{1}{2}x=\frac{11}{4}[/tex][tex]x=\frac{\frac{11}{4}}{\frac{1}{2}}[/tex][tex]x=\frac{11\cdot2}{4\cdot1}[/tex][tex]x=\frac{22}{4}[/tex][tex]x=5.5[/tex]We have 5.5 groups of 1/2 pounds in 2 (3/4) pounds.
Answer:
• 1.a 16
,• 2.b 5.5
Hi tutor,What is the connection between the slope of a tangent of a function at a given point, and it’s derivative evaluated at that point? If possible, can you please use a diagram and derivation steps to help explain?
Given:
Derivative and sope of tangent
Required:
We want to define relation
Explanation:
The derivative of a function gives us the slope of the line tangent to the function at any point on the graph. This can be used to find the equation of that tangent line for example
and the slope of that tangent is the derivative of function at point P
Now to find equation of a tangent line
1) Find the first derivative of f(x).
2) Plug x value of the indicated point into f '(x) to find the slope at x.
3) Plug x value into f(x) to find the y coordinate of the tangent point.
4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line.
In parallelogram ABCD, which angle is congruent to
In parallelogram ABCD, which angle is congruent to ?
Let us draw the parallelogram to better understand the problem.
As you can see from the above figure,
∠ABC and ∠CDA are congruent. (drawn in black color)
Also, ∠BCD and ∠DAB are congurent. (drawn in red color)
This means that the opposite angles are congruent in a parallelogram.
Therefore, the correct answer is option C
∠ABC and ∠CDA are congruent.