3. Michel invests $850 at 7%/a simple interest. How long will he
have to leave his investment in the bank before earning $200 in interest
Answers
\(~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\dotfill&\$200\\ P=\textit{original amount deposited}\dotfill & \$850\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ t=years \end{cases} \\\\\\ 200=850(0.07)t\implies \cfrac{200}{850(0.07)}=t\implies \stackrel{\textit{about 3 years, 4 months and 10 days}}{3.36\approx t}\)
Related Questions
Find cos θ for θ = 45°
Answers
Answer:
\( \cos( \theta) \\ \cos(45) = \cos( \frac{\pi}{4} ) \\ = \frac{1}{ \sqrt{2} } \\ or \\ = \frac{ \sqrt{2} }{2} \)
= 20 = 135°
= θ - 65.5°
A dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length. How many 12-inch pieces can the dressmaker cut from 10 of these rolls of ribbon?
Before you try that problem, answer the question below.
How many inches of ribbon does the dressmaker have, in total?
Answers
The 12-inch pieces the dressmaker can cut from 10 of these rolls of ribbon will be 30 strips.
What is the unitary method?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Given a dressmaker has a ribbon of 3 feet in length,
and he has a total of 10 rolls,
total length of ribbon = 10*3 = 30 feet
and 1 feet = 12 inches
30 feet = 12*30 inches
30 feet = 360 inches
the dressmaker has 360 inches of ribbon.
The dressmaker needs to cut 12-inch pieces of ribbon from rolls of ribbon that are 3 feet in length.
The number of rolls she has = 10 rolls
so,
12 inches strips from 360 inches of ribbon
= 360/12 = 30 strips.
Hence the dressmaker can make 30 strips of 12 inches from 360 inches of total ribbon.
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Pete grabbed 18 mixed nuts, StartFraction 2 Over 9 EndFraction of which were almonds. Which equation shows how to determine the number of almonds Pete grabbed?
18 divided by StartFraction 2 Over 9 EndFraction = 81
18 times StartFraction 2 Over 9 EndFraction = 4
StartFraction 2 Over 9 EndFraction divided by 18 = StartFraction 1 Over 81 EndFraction
StartFraction 9 Over 2 EndFraction divided by 18 = one-fourth
Answers
Answer:
18 times StartFraction 2 Over 9 EndFraction = 4
Amount of almonds = 18 × [2/9]
Amount of almonds = 4 almonds
Step-by-step explanation:
Given:
Number of mixed nuts = 18
Probability of almonds = 2/9
Find:
Amount of almonds
Computation:
Amount of almonds = Number of mixed nuts × Probability of almonds
Amount of almonds = 18 × [2/9]
Amount of almonds = 36 / 4
Amount of almonds = 4 almonds
Answer:
IT'S B I CAN CONFIRM BC I JUST FINISHED THE TEST
Step-by-step explanation:
4.
Consider the following amount of energy
used for three different activities:
. 1 minute of walking uses
25 kilojoules of energy
A (4
• 1 minute of jogging uses 84 kilojoules
of energy
1 minute of swimming uses
50 kilojoules of energy
a) How many more kilojoules of energy
would you use in an hour of jogging
than an hour of swimming?
b) To the nearest tenth, how many
minutes of walking would you have to
do to burn up the 1,130 kilojoules in a candy bar
Answers
In given word problem ,
a) 2040 more kilojoules of energy would you use in an hour of jogging than an hour of swimming .
b) 45 minutes 2 seconds of walking would you have to do to burn up the 1,130 kilojoules in a candy bar.
What is word problem ?
Our extensive collection of math word problems ranges from addition, subtraction, multiplication, and division to more specialised operations. Mathematical questions that are written as one or more sentences and ask students to use their mathematical understanding to solve problems from "real-life" situations are known as word problems. As a result, for kids to understand the word problem, they need to be familiar with the terminology that goes along with the mathematical symbols that they are already used to.
Here the given ,
=> 1 minute walking = 25 kilojoules
=> 1 minute jogging = 84 kilojoules
=> 1 minute swimming = 50 kilojoules.
a) 1 hour = 60 minutes.
1 hour jogging = 60*84 = 5040 kilojoules.
1 hour swimming = 60*50 = 3000
Then , => 5040-3000=2040 kilojoules.
Therefore 2040 more kilojoules of energy would you use in an hour of jogging than an hour of swimming .
b) x minute of walking = 1130 kilojoules.
=> 25*x=1130
=> x = 1130/25 = 45minutes 2 seconds.
Therefore 45 minutes 2 seconds of walking would you have to
do to burn up the 1,130 kilojoules in a candy bar.
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Use the matrix tool to solve the system of equations choose the correct ordered pair -5x+6y=-3 6x-6y=12
Answers
Answer:
Hello,
x=9
y=7
Step-by-step explanation:
\(A*U=B\\\\\begin{bmatrix}-5&6\\6&6\\\end{bmatrix}*\begin{bmatrix}x\\y\end{bmatrix}=\begin{bmatrix}-3\\12 \end{bmatrix}\\\\\\A^{-1}=\begin{bmatrix}1&1\\1&\dfrac{5}{6}\\\end{bmatrix}\\\\\\A^{-1}*A*U=A^{-1}*B\\\\U=\begin{bmatrix}9\\7 \end{bmatrix}\\\)
3. Graph each line y, y1, y2, y3, and y4 and record the data in the table below.
(Graph all five lines together so that you can compare them)
It’s question 3
Answers
A right triangular prism has a height of 26 cm and base edges of 10 cm, 24 cm, and 26 cm. What is the lateral area of the prism?
Answers
Answer:
1,560 cm²
Step-by-step explanation:
LA = (10+24+26) × 26
= 60×26
= 1,560
Please check pictureQuestionWhich of the following is a power function? Select all correct answers.Select all that apply:f(x)=6⋅16xf(x)=4x−−√9f(x)=10⋅3xf(x)=5⋅15x f(x)=−18x−−√3
Answers
Answer:
The correct options are:
\(\begin{gathered} f(x)=4\sqrt[9]{x} \\ . \\ f(x)=-18\sqrt[3]{x} \end{gathered}\)Explanation:
A power function is a function that has the variable to the power of some fixed real number. A power function can't have the variable (x, in this problem) in the exponent.
Then, the only two option that follow this are:
\(\begin{gathered} f(x)=4\sqrt[9]{x} \\ . \\ f(x)=-18\sqrt[3]{x} \end{gathered}\)Because we can rewrite the exponent as:
\(\begin{gathered} f(x)=4\sqrt[9]{x}=4x^{\frac{1}{9}} \\ . \\ f(x)=-18\sqrt[3]{x}=-18x^{\frac{1}{3}} \end{gathered}\)Which is clearly, the variable to the power of a real number.
If the following data were transformed and points with the coordinates
(x, log(y)) were plotted, what points would be plotted? Round log(y) to three
decimal places.
X
1
2
3
y
12
83
580
Answers
If the data were transformed and points with the coordinates
(x, log(y)) were plotted then the points (1, 1.079), (2, 1.919), (3, 2.763) were plotted.
To plot the points with the coordinates (x, log(y)), we need to take the logarithm of the y-values.
Let's calculate the logarithms for the given data:
x y log(y)
1 12 log(12) = 1.079
2 83 log(83) = 1.919
3 580 log(580) = 2.763
Therefore, the points that would be plotted are (1, 1.079), (2, 1.919), (3, 2.763)
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Multiply me by 4. Then subtract 29 and you get 23. What is my number?
Answers
Answer:
13 is your number
Step-by-step explanation:
23 = -29 x 4x
add 29 to both sides
52 = 4x
divide both sides by 4
13 = x
Answer:
13
Step-by-step explanation:
13 x 4 = 52 - 29 = 23
determine if the square root of 43 is rational or irrational and give a reason for your answer
Answers
After answering the presented question, we can conclude that As a result, 43 squared is an irrational number.
what is rational numbers?A rational number is one that can be stated as a ratio (or fraction) of two integers. A rational number is a nonzero denominator fraction. Rational numbers include 1/2, 1/5, and 3/4. A rational number, "0" can also be stated in a variety of ways, such as 0/1, 0/2, and 0/3. Nevertheless, 1/0, 2/0, 3/0, and so on. The number seven makes sense. A rational number is the product of dividing two integers. To get the rational number 7, divide the whole number 7 by the whole number 1. A rational number is one that can be divided by two integers to get 7.
43's square root is an irrational number.
Assume the square root of 43 is rational to show why. So we can write it as a fraction in its most basic form, as follows:
√43 = a/b
where a and b are integers with no factors in common.
When we square both sides of this equation, we get:
\(43 = a^2 / b^2\)
When we multiply both sides by b2, we get:
\(43b^2 = a^2\)
As a result, 43 squared is an irrational number.
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In ΔHIJ, j = 33 cm, ∠H=148° and ∠I=21°. Find the length of i, to the nearest centimeter.
Answers
Answer:
The length of i to the nearest centimeter is 62 cm
Step-by-step explanation:
Please find the image uploaded for diagram and solution.
If a is -3 then what is a squared
Answers
Answer:
a = -3
(-3)² = -9
Answer: -9
Step-by-step explanation:
-3 x -3 = -9
(I think)
find the perimeter of a triangle where one side is 2 inches, one side is 6 inches and another side is 10 inches.
(a) 2in.
(b) 9in.
(c) 36in.
(d) 18in.
Answers
Answer:
(d) 18 in.
Step-by-step explanation:
When we're given the three sides of a triangle, one formula we can use for perimeter of a triangle is:
P = s1 + s2 + s3, where
P is the perimeter,and s1, s2, and s3 are the three sides:P = 2 + 6 + 10
P = 8 + 10
P = 18
Thus, the perimeter of the triangle is 18 in.
15 POINTS
Using Pythagoras' theorem, calculate the length
of XY.
Give your answer in centimetres (cm) to 1 d.p.
Answers
Answer:
13.27 cm
Step-by-step explanation:
I am using (xy) to mean the length of the side xy
7^2 + (xy)^2 = 15^2
49 + (xy)^2 = 225
(xy)^2 = 225-49
(xy)^2 = 176
Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm
13.3cm
Step-by-step explanation:
The Pythagorean theorem is a^2+ b^2 = c^2
Plug the values into the equation.
7^2+ b^2 = 15^2
Simplify.
49 ÷ b^2 = 225
Subtract 49 from both sides.
b^2 = 176
Take the square root of both sides.
vb^2 = v176
b=13.266
b=13.3cm
What is the y-intercept of the graph that is shown below?
Answers
Your answer is (0 , 2)
Apologies if this is wrong
The Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile. Find a linear function which models the taxi fare F as a function of the number of miles driven, m
Answers
The equation that models the taxi fare F as a function of the number of miles driven is F = 2.40 + 0.40m
What is an equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, the Topology Taxi Company charges 2.40 for the first fifth of a mile and 0.40 for each additional fifth of a mile.
The function will be:
F = 2.40 + (0.40 × m)
F = 2.40 + 0.40m
where m = number of miles
F = taxi fare.
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Write y = 5(x - 8)^2 + 4 in standard form
Answers
Answer:
\(y=5x^2-80x+324\)
Step-by-step explanation:
Which expression is equivalent to −13(12+3)?
Answers
The expression which is equivalent to - 13 (12 + 3) is - 195.
We are given the expression:
- 13 (12 + 3)
We need to solve the expression to find the value of it.
We will first solve the brackets:
So, adding 12 and 3, we get that:
= - 13 ( 15 )
Now, we will multiply 13 and 15 and also note that it will have a minus sign as - × + = -
So, we get that:
= - 195
Therefore, the expression which is equivalent to - 13 (12 + 3) is - 195.
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The graph shows the function f(x).
On a coordinate plane, a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
Which equation represents f(x)?
f(x) = Negative RootIndex 3 StartRoot x EndRoot
f(x) = Negative RootIndex 3 StartRoot x minus 1 EndRoot
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot minus 1
f(x) = Negative RootIndex 3 StartRoot negative x EndRoot
Answers
The equation that represents the given data is \(\RM \\f(x) = -\sqrt[3]{-x} ,\) Option D is the correct answer.
What is a Function ?It is a statement where two variables , one dependent and one independent are related.
It is given that
a cube root function goes through (8, 2), has an inflection point at (0, negative 1), and goes through (8, negative 3).
The equation given in the options are
\(\rm f(x) = -\sqrt[3]{x} \\f(x) = -\sqrt[3]{x-1} \\f(x ) =-\sqrt[3]{-x} -1 \\f(x) = -\sqrt[3]{-x}\)
The function goes through (8,2)
Substituting the values
f(x) = -2
f(x) = \(\sqrt[3]{7}\)
f(x) = -3
f(x) = 2
The equation that represents the given data is
\(\RM \\f(x) = -\sqrt[3]{-x} ,\) Option D is the correct answer.
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Answer:
D
Step-by-step explanation:
if you take away 25 from a number you will be left with two and halftimes 30. what is the number?
Answers
If you take away 25 from (100) you get 75.
70 also equals 2.5*30
o III. Read each passage and make a conclusion about it (5 POINTS EACH) 1. Video gaming is one of the largest industries in America. Each day more and more children are getting addicted to video games. There have many video game opponents accusing the industry of becoming too violent. It is not uncommon to play a shoot em up game where ten people are getting killed every minute. Yet, despite societal pressure to eliminate violent video games, as each day passes, more games are getting hooked. 2. He had always wanted to serve the country, but this seemed like madness. He was supposed to fight in a war in a foreign land, helping to protect people whom he did'nt know. Angelo had a strong sense of patriotism, but he was worried about the bombs, death and carnage that could await him in Iraq. He pondered whether he would ever see his family again.
Answers
Answer:
come india
Step-by-step explanation:
ok
Please help me with this system of equations problem
Answers
Answer:
5x-2y=3
-3x+4y=1
5x-2y=-3x+4y+2
+2y
5x=-3x+6y+2
+3x
8x=6y+2
divide by 2
4x=3y+1
-3y+4x=1
wait so that means that -3x+4y=-3y+4x so that means that both x and y are equal so lets just say their the same
-3x+4x=1
x=1
y=1
Hope This Helps!!!
deigo has $500 dolars in his saving account each month he takes out $20 to pay for karate class. let m be the number of months write an expression yo show the total amount ain deigos saving account after m months
Answers
The expression shows the total amount in Diego's savings account after m months is 500 - 20m.
What is the total amount?
Two numbers are added together to form the sum. It is simple to figure out the sum of small integers. You can add two numbers using your fingertips. When two or more numbers are added together, a mathematical sum or maths sum is the outcome. It is the sum of the numbers when they are added up.
Here, we have
Given: Deigo has $500 in his saving account each month he takes out $20 to pay for karate class.
Let m be the number of months. Write an expression to show the total amount in Diego's savings account after m months.
The expression:
= 500 - 20m
Here m is the number of months
Hence, the expression shows the total amount in Diego's savings account after m months is 500 - 20m.
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how to solve this question?
Answers
The revised Doubtful Debts Provision should be, $4,555.
Now, Using a net debtors value of $91,100 and a provision rate of 5%, use the calculation to get the adjusted Provision for Doubtful Debts (PDD):
Net Debts x Provision Rate equals Adjusted PDD.
The computation would then be:
= $91,100 x 0.05
= $4,555 is the adjusted PDD.
Because of the additional $550 in bad debt and the revised net debtors value of $91,100, the Provision for Doubtful Debts must be raised by ,
= $4,555 - $3,500
= $1,055
Hence, The revised Doubtful Debts Provision should be $4,555.
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In Exercises 1-3, decide whether enough information is given to prove that the triangles are congruent using either the SSS Congruence Theorem (Theorem 5.8) or the HL Congruence Theorem (Theorem 5.9). Explain.
Answers
The congruency proofs that can be used for each of the triangles are;
1) SSS Congruency
2) None
3) HL Congruence
How to prove the triangle congruency postulate?
1) The SSS congruency postulate states that If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.
Now, we see that we are shown 2 corresponding sides that are congruent. However, the third side is automatically congruent using the reflexive property of congruence.
Thus, we conclude that the congruency can be proved using SSS Congruency postulate.
2) In this one, we are given 2 congruent sides and the included angle and so it is SAS Congruency and neither SSS nor HL congruency can be used.
3) The HL congruence Postulate states that if the hypotenuse and leg of one right triangle are congruent to the hypotenuse and leg of another right triangle, then the two triangles are congruent.
In this case, we see that the hypotenuse is congruent to itself by reflexive property of congruence while the one leg is also congruent and so we can use HL Congruence Theorem
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7. The Taylor Rule states that the central bank should set the short-term nominal interest rate (i)
based on the inflation gap [the difference between inflation (3.14) and desired inflation (3.14*)] and the
output gap (the percentage difference between real GDP (Y) and potential GDP (Y*) An
example of a Taylor Rule would be the formula
i - 3.14 = 1.5 +0.5(3.14-3.14*) +0.5 (Y-Y*/Y*)
The term on the left-hand side is the real interest rate. Consider the following table
Inflation rate (3.14), %
Target inflation rate (3.14*), %
Output gap, %
Real interest rate
Nominal interest rate
Base Scenario Scenario B Scenario C
4.0
20
2.0
20
0.0
20
20
20
00
a. Fill in the real and nominal interest rates chosen by the policy maker in the base scenano
b. How does scenario B differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move the inflation rate toward its target?
c. How does scenario C differ from the base scenario in terms of the inflation and output gaps?
Calculate the real interest rate. Has the real interest rate moved in the direction that would
move output toward the potential level?
d. Suppose a new chair of the central bank is appointed and she switches to a new policy rule of
the form given in the next equation. Recalculate the real and nominal interest rates for the
three scenarios. What has been the effect of the change in weights?
i-3.14=1.5 +0.75(3.14-3.14*) +0.25(Y-Y*/Y*)
Answers
The weight on the inflation gap has increased from 0.5 to 0.75. The real interest rate is 16.86% and Nominal interest rate is 20%
a. In the base scenario, the real interest rate will be 20%, and the nominal interest rate will be 20%.
b. In scenario B, inflation rate will be higher (4%) compared to the base scenario (3.14%).
Output gap is 0% in both the scenarios, however, in the base scenario inflation gap is 0% (3.14 - 3.14) and in scenario B, inflation gap is 0.86% (4 - 3.14).
Now, let's calculate the real interest rate.
Real interest rate in base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario B = 20% - 3.14% + 1.5 + 0.5 (4-3.14) + 0.5 (0-0/0)
= 19.22%.
The real interest rate has moved in the direction to move inflation rate towards its target.
c. In scenario C, the output gap will be 20% compared to 0% in the base scenario.
Inflation gap is 0% in both the scenarios
Inflation rate is 3.14% and in scenario C, inflation rate is 2%.
Let's calculate the real interest rate. Real interest rate in the base scenario = 20% - 3.14%
= 16.86%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.5 (3.14 - 3.14) + 0.5 (20-0/20)
= 20.15%.
Real interest rate in scenario C = 20% - 2% + 1.5 + 0.75 (3.14-3.14) + 0.25 (20-0/20) = 18.78%.
The new policy rule has changed the weight of the output gap in the Taylor Rule from 0.5 to 0.25.
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PLEASE HELP !! ILL GIVE BRAINLIEST !!
Answers
Answer:
its d
Step-by-step explanation:
trust me
Answer:
MNP and ONK
Step-by-step explanation:
Vertical angles are angles which are vertical to each other and are parallel to each other.
7) Find the approximate sum (24,687 +38,403 +53,628) to the nearest thousand:
Answers
The approximate sum of the values to the nearest thousand is 117000
Sum of numbers and rounding upAny number of digits after that number becomes zero and this is known as rounding down. If the digit in the smallest place is greater than or equal to 5, then the digit is added with +1.
Given the expression below;
24,687 +38,403 +53,628 = 116718
Hence the approximate sum of the values to the nearest thousand is 117000
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This is a regular octagon.
What is the measure of x?
IX
x = [? ]°
Enter
![This is a regular octagon.What is the measure of x?IXx = [? ]Enter](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/IgeiXoMEXHBunBi1GUJK7WQLIpxWMx8W.png)
Answers
Answer:
x=360/8
=45 degrees,,,,
The measure of x = 45°.
What is exterior angles of a regular polygon?Exterior angles of a polygon are formed when by one of its side and extending the other side. The sum of all the exterior angles in a polygon is equal to 360 degrees. You are already aware of the term polygon. A polygon is a flat figure that is made up of three or more line segments and is enclosed. The line segments are called the sides and the point where two sides meet is called the vertex of the polygon.
According to question,
There is a regular octagon.
Number of sides in regular octagon, n = 8
Since, measure of each exterior angle = 360°÷8
= 45°
Hence, the measure of each exterior angle of a regular octagon is 45°
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