Answers
We want to create a real-life reasonable problem in which we can apply the laws of exponents.
Using a compound interest example;
Word Problem:
Calculate the final value of a $2,000 investment in an account with a 5% interest compounded Quarterly for 5 years.
Solving the word problem;
We have the following parameters;
[tex]\begin{gathered} \text{ Principal P = \$2,000} \\ \text{Rate r = 5\%} \\ \text{Time t = 5 years} \\ \text{ Number of times compounded n = 4} \end{gathered}[/tex]Recall that the formula for compound interest is;
[tex]F=P(1+\frac{r}{n})^{nt}[/tex]Substituting the given values;
[tex]\begin{gathered} F=2000(1+\frac{0.05}{4})^{4(5)} \\ F=2000(1+0.0125)^{20} \\ F=2000(1.0125)^{20} \\ F=2000\times(1.0125)^{20} \\ F=\text{ \$2,564.07} \end{gathered}[/tex]Therefore, the solution to the problem is;
The final
Related Questions
if a baker has 7/3 cups of chocolate, the baker can make a maximum of .... cakes.
Answers
She calls for 4/5 cup of chocolate
She had 7/3 cups of chocolate.
[tex]\begin{gathered} \text{The bake can make a ma}\xi mum\text{ of = }\frac{7}{3}\text{ }\frac{.}{.}\text{ }\frac{4}{5} \\ \text{ = }\frac{7}{3}\text{ x }\frac{5}{4} \\ \text{ = }\frac{35}{12} \\ \text{ = 2}\frac{11}{12} \\ \end{gathered}[/tex]Maximum number of cakes a baker can make = 2
The average height of a barometer during one week was 30.84 inches. for six week days of the same week the average height was 30.18 inches. what was the height on sunday?
Answers
The height of the barometer on Sunday = 34.8 inches
How is the barometer height on Sunday calculated?
Consider the barometer height for one week,
The average height of a barometer during one week = 30.84 inches
The total height of a barometer during one week = 30.84 * 7
= 215.88
Consider the barometer height for 6 weekdays,
The average height of a barometer for 6 weekdays of the same week= 30.18 inches
The total height of a barometer for 6 weekdays = 30.18 *6
=181.08
The barometer height on Sunday = One week height- 6 days height
=215.88 - 181.08
=34.8 inches
What is a height?
Height is the distance vertically between an object or figure's top and bottom. Height is also referred to as altitude . Average height is the sum of all the heights divided by the number of the given heights.To learn more about height, refer:
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Write the coordinates of the vertices after a reflection over the y-axis
Answers
The most appropriate choice for reflection will be given by-
After reflection over y-axis, coordinate of K will become K' (6, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
After reflection over y-axis, coordinate of M will become M' (0, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
What is reflection?
Reflection of a figure about a line is a transformation in which a mirror image of the figure can be obtained over the line.
The line is called the line of reflection.
Here,
After reflection over the y - axis, sign of x coordinate will be same.
Coordinate of K = (-6, -1)
After reflection over y-axis, coordinate of K will become K' (6, -1)
Coordinate of L = (0, -1)
After reflection over y-axis, coordinate of L will become L' (0, -1)
Coordinate of M = (0, -2)
After reflection over y-axis, coordinate of M will become M' (0, -2)
Coordinate of J = (-6, -2)
After reflection over y-axis, coordinate of J will become J' (6, -2)
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how would we name the polyonomial below?think about the degree and number term
Answers
We have the expression:
[tex](x+4)+(2x-7)[/tex]Adding the parts with x and the parts without x we have:
[tex](x+2x)+(4-7)_{}[/tex]Wich gives us:
[tex]3x\text{ - 3}[/tex]Wich is a polinomial of first degree.
the equation 2x-20/3=2x models temperature change, where x represents the difference in degrees in the last 24 hours. solve for x
a. x = -5
b. x = -2
c. x = 2
d. x= 13
Answers
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.
The answer is x = -5 for the following equation (2x - 20) /3 = 2x.A formula for the question at hand is 2x minus 20 divided by 3 Equals 2x, or (2x - 20) /3 = 2x.
The difference in degrees over the last 24 hours is represented by x in this equation, which predicts temperature change.
We must find x in the given equation.
(2x - 20) /3 = 2x \s (2x - 20) = 3(2x) (2x) ...........(Multiply by 3 on both sides)
2x - 20 + 20 = 6x + 20 ...........(Add 20 to both sides)
2x - 6x = 6x + 20 - 6x ..........(Subtract 6x from both sides) (
-4x = 20 \s x = -5 ..........(Divide by - 4 on both sides)
As a result, x = -5 for the given equation (2x - 20) /3 = 2x.
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Simplify the following radical
√175x^5
Answers
Simplified version of the given radical expression would be...
[tex]5x^2\sqrt{7x}[/tex]
Hope this helps!
What is the slope of the line? ASAP.
Answers
Answer:
The slope would be 25/1 or 25.
Step-by-step explanation:
Use the formula y2-y1 over x2-x1. Or use rise over run.
ross is camping 4 miles west and 11 miles north (-4,11)
Answers
Using the equation for the distance between two points, the distance between Ross and Rachel is given by the following option:
D. 19 miles.
What is the distance between two points?Suppose that we have two points with coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]. The shortest distance between them is given by the equation presented as follows:
[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
This formula is derived from the Pythagorean Theorem, as the points form a right triangle in the xy-plane, and the hypotenuse represents the distance between them.
Their coordinates in this problem are as follows:
Ross: (-4, 11).Rachel: (8, -4).Each unit on the plane represents a mile, hence their distance is given as follows:
[tex]D = \sqrt{(8 - (-4))^2+(-4 - 11)^2}[/tex]
D = 19.2 miles.
Rounded to 19 miles, hence option D is correct.
Missing informationThe complete problem is given by the image at the end of the answer.
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suppose that you were trying to predict house price based on square footage, distance from the beach, and lot size for miami, florida. run a multiple regression predicting price based on square footage, and lot size. assume you are trying to determine if the slope of lot size is different than 0, and you find a p value 0.5677. what conclusion can you make?
Answers
The slope for lot size is not different from 0.
We will let the slope of the size be β
So the hypothesis can be: β = 0 (Null Hypothesis) , β≠ 0 (Alternate Hypothesis)
If we consider a confidence level (the probability for which we can be confident that the null hypothesis is true) to be 95% (Probability = 0.95) then the level for which we are not confident that the null hypothesis is true will be (100 - 95)% = 5% (Probability = 0.05)
Thus, for this coefficient the P value is 0.5782.
As the p-value is more than the Probability for which we are not confident (0.05), so in this regard we can state then there is no such significance difference seen in this regard. Thus, we accept the null hypothesis here. This means that we can take the coefficient to be 0.
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How do I get the other number and it’s bye using writing perfect-square trinomials
Answers
25
1) We must start by reminding the binomials. Since this question refers to a perfect square trinomial then we can write:
[tex](a-b)^2=a^2-2ab+b^2[/tex]2) Now we can look at the expression. Let's start by dividing that 10 by 2, since we have to write that -10x as 2 times the product of x and the other term:
[tex]\begin{gathered} -\frac{10}{2}=5 \\ (x-5)^2=x^2-2(5)(x)+5^2=x^2-10x+25 \end{gathered}[/tex]Note that the second term is 5²= 25
3) Hence, the answer is 25
3^8 x 3^4 divide 3^2 x 3^8
Answers
⇒I will be using the laws of exponents. As indicated below :
⇒[tex]x^{n} *x^{m} \\=x^{n+m}[/tex]
This just simply means that if you are multiplying powers of the same base you keep one base as a result and add the exponents.
⇒ The other law of exponents is indicated below:
⇒[tex]x^{n} /x^{m} \\=x^{n-m}[/tex]
This means that if you are dividing powers of the same base you keep one base and subtract the exponents.
N.B : BODMAS RULES ALSO APPLY
[tex]\frac{(3^{8} *3^{4} )}{(3^{2}*3^{8} ) } \\=\frac{3^{8+4} }{3^{2+8} } \\=\frac{3^{12} }{3^{10} } \\=3^{12-10} \\=3^{2} \\=9[/tex]
Attached is your solution. Goodluck!!
Use the information given to enter an equation in standard form.Slope is -9, and (3,2) is on the line.
Answers
Firts get the equation
Second, write the equation in form of Ax +
Which brand of granola typically weighs more?
Brand A bags typically weigh more because the median of brand A is higher than that of brand B.
Brand B bags typically weigh more than brand A bags because there is a high outlier at 52.5.
Brand A bags typically weigh more than brand B bags because there are no outliers in the distribution.
Brand B bags typically weigh more because the range of weights is higher than that of brand A.
Answers
Brand A bags typically weigh more because the median of brand A is higher than that of brand B and is denoted as option A.
What is Median?This is referred to as the middle value which separates the higher half from the lower half of a data or distribution. This is calculated by first ordering the numbers which could be from the lowest to highest or vice versa.
A data sample which has a higher figure as the median means that it has higher values present in the data distribution. This term provides an insight on certain properties of the values of the data which are given.
In this scenario, the median of brand A is higher than that of brand B which means that it has more weight and is therefore the reason why option A was chosen as the correct choice.
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Eli dug a trench
18
20
of a meter long. The next day he dug another 17
20
B
of a meter. What is a reasonable estimate of the total length of the trench?
Answers
The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters so option (C) is correct.
What is summation?A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities.
There could be only two terms, but there could be one hundred, a thousand, or a million.
Here are always an integer number of terms in a summation.
As per the given,
Length of the trench on the first day = 18/20 meters
Length of the trench on the second day = 9/20
Total length of the trench = 18/20 + 9/20
Take LCM as 20
⇒ (18 + 9)/20 = 27/20
⇒ 1.35 which is closest among the given option by 1 1/2 meters.
Hence "The summation is the adding two quantities thus the reasonable estimate of the total length of the trench is 1 1/2 meters".
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The length of a rectangle is 5 feet more than the width. The perimeter of the rectangle is 58 feet. Find the length & width of the rectangle.
Answers
Answer:
Length: 17 ft. Width: 12 ft.
Step-by-step explanation:
x + 5 + x +5 + x + x = 58
4x + 10 = 58
4x = 48
x = 12
12 + 5 = 17
Please help
3. In the formula A = lw, find A when I is
5 inches and w is 25 inches.
Answers
The question is Basically asking what is 5 times 25. When two letters are next to each other, and have no sign, it means to multiply them. So 2b would be 2 times b. Or xy would be x times y. 5 times 25 is 125
Answer:
125 inches squared
Step-by-step explanation:
A=lw
A=(5)(25)
A=125
HELP ME PLSS OMLLL IMA CRY
Answers
Answer:
Remember, ratios are just fractions, and fractions are just division problems.
Step-by-step explanation:
Step-by-step explanation:
25%of 20 is 5
subtract from the total of the whole candy.
What does do the congruence criterion mean.
Please explain what AAS, SSS, ASA, and HL mean.
Answers
AAS = Angle , angle and one side of 2 congruent triangles
SSS = All 3 sides are measure same of the 2 triangles.
ASA = 2 angles and the side between them are same
HL = A right triangle is congruent if its hypotenuse and one of its legs are congruent with the hypotenuse and one of its other legs.
What is meant by congruency?The dimensions of the triangles' sides and angles determine whether two or more triangles are congruent. A triangle's size is determined by its three sides, and its shape by its three angles. Pairs of corresponding sides and corresponding angles in two triangles are said to be equal if they are congruent. They share a similar size and shape. In triangles, there are numerous congruence conditions. For the two triangles to be congruent, they must be the same size and shape. It should be possible to superimpose the two triangles under examination. A triangle's position or appearance appears to change when we rotate, reflect, and/or translate it. In that situation, we must recognize the six components of a triangle.
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triangle ABC has coordinates A(1,4) B(3.-2) and C(4,2) . Find the coordinates of the image ABC after a reflection over the x axis.
Answers
The given vertices are A(1,4), B(3,-2), and C(4,2).
The reflection over the x-axis is expressed as
[tex](x,y)\rightarrow(x,-y)[/tex]This means we have to multiple each y-coordinate with -1. Let's do it!
[tex]\begin{gathered} A(1,4)\rightarrow A^{\prime}(1,-4) \\ B(3,-2)\rightarrow B^{\prime}(3,2) \\ C(4,2)\rightarrow C^{\prime}(4,-2) \end{gathered}[/tex]Therefore, the vertices of the new triangle are A'(1,-4), B'(3,2), and C'(4,-2)help quick 30 points
Answers
Answer:
y = -5x + 6
Step-by-step explanation:
Looking at the graph it looks that the slope of the line is -5
and the y intercept is (0, 6)
So the slope intercept form is y = -5x + 6
this should be correct hope this helps
Does anyone have an answer or explanation? I kind of need it before 12pm (CDT)
A museum charges $10 for general admission and $2 for each special exhibit you attend.
What does f(0) = 10 represent in the context of this problem?
Answers
Answer:
i d k 20???????????
Step-by-step explanation:
Answer:
The visitor attended no special exhibits and so paid a total of $10 just to get in.
An equation to represent the cost of admission could look like this:
f(x) is the total cost.
x is the number of special exhibits attended.
f(x) = 2x + 10
If I see no special exhibits on my visit,
x = 0, then
f(0) = 2•0 + 10
f(0) = 10
I only pay $10.
Find the exact solution to the equation 42 equals 3 x squared, leaving your answer in square root form. Show your work.
State if your solution is rational or irrational. Explain.
Find the closest integer approximation to your solution and explain how you found it.
Answers
The solution is x = √ 14, it is irrational
The closest integer approximation to the solution is 4
How to determine the valueFrom the information given, we have that;
42 equals 3 x squared
This is represented as;
3x² = 42
Let's take the following steps to determine the value of x
Divide both sides by the coefficient of x²
x² = 42/3
x² = 14
Take the square root of both sides, we have;
x = √ 14
The solution is an irrational number
What is an irrational number?An irrational number is described as a number that cannot be expressed in a fractional form.
They are real numbers that expressed as quotients
Examples of irrational numbers are;
√5, √7, √11, √13
Now, let's find the square root, we have
= 3. 74
Take '7' as 1 and add to the whole number 3, we get;
= 4 ; to the closest integer
Hence, the value is 4
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Forty years ago, uncle Luke was 5 times
as old as his
nephew. Today, Uncle Luke is 16 yeas older than his nephew. How
old is uncle Luke now?
Answers
Answer: Uncle Luke is at 50 years old
Step-by-step explanation: I went through trial and error first with simple t-charts. In the first one, I simply implemented the piece of info that Luke was 5 times older than the nephew. But then, I realized that Luke would always be 5 years older than his nephew. Here was the info for that t-chart:
[tex]\left \{ {{N=1} \atop {L=5}} \right. \left \{ {{N=2} \atop {L=6}} \right. \left \{ {{N=3} \atop {L=7}} \right.[/tex]
Next, I tried a chart starting with the nephew at 2 years of age, and got an age gap of 8. This helped me realize that I would have to start at 4 years of age in order to have an age gap of 16
[tex]\left \{ {{N=2} \atop {L=10}} \right.[/tex] | [tex]\left \{ {{N=4} \atop {L=20}} \right. \left \{ {{N=5} \atop {L=21}} \right.[/tex] (remember there are 1 increments)
Next, I realized that N=4, L=20 was 40 years ago, so if now the nephew was 44, we can increment 16 to get 50
44+16=50
the measure of the angle of a triangle are shown in the figure below. solve for x
x°
44°
61°
Answers
Answer: x=75°
Step-by-step explanation:
x+44+61=180 ==> three angles in a triangle add up to 180 degrees
x+105=180
x+105-105=180-105
x=75°
if charlene brewster has times of 8.4, 8.6, 8.3, 8.5, 8.7, and 8.5 and a performance rating of 110%, what is the normal time for this operation? is she faster or slower than normal? [px]
Answers
Normal time taken for operation = 7.7
Charlene's work performance is faster than normal time.
Need to define Charlene's average time:
8.4 + 8.6 + 8.3 + 8.5 + 8.7 + 8.5)/6
Avg time taken= 8.5.
Performance rating = 110/100 = 1.1
normal time taken: 8.5/1.1
normal time taken= 7.7
hence, 8.5 [tex]\geq[/tex] 7.7
Charlene is faster than normal time.
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Prove that (X+2)^2+(X-2)^2=2(x^2+4) for all values of x
Answers
Answer:
see explanation
Step-by-step explanation:
consider the left side
(x + 2)² + (x - 2)² ← expand factors using FOIL
= x² + 4x + 4 + x² - 4x + 4 ← collect like terms
= 2x² + 8 ← factor out 2 from each term
= 2(x² + 4)
= right side , thus proven
Simplify the following expression
Answers
Answer:
y
-------------
x²¹ z⁵
Step-by-step explanation:
(x⁻⁹ y³ z⁻²)²
-------------------
x³ y⁵ z
x⁻¹⁸ y⁶ z⁻⁴
-------------------
x³ y⁵ z
y⁶
-------------------
x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴
y
-------------------
x²¹ z⁵
I hope this helps!
After simplification by rule of exponent solution is,
⇒ y / x²¹ z⁵
We have to given that;
The expression is,
⇒ (x⁻⁹ y³ z⁻²)² / x³ y⁵ z
Now, We can simplify by rule of exponent as;
⇒ (x⁻⁹ y³ z⁻²)² / x³ y⁵ z
⇒ x⁻¹⁸ y⁶ z⁻⁴ / x³ y⁵ z
⇒ y⁶ / x³ ⁺ ¹⁸ y⁵ z¹ ⁺ ⁴
⇒ y / x²¹ z⁵
Thus, After simplification by rule of exponent solution is,
⇒ y / x²¹ z⁵
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Write a simplified expression for the right half of the equation that can be used to find the nth term in the sequence6,7,8 9,10
Answers
Renna pushes the elevator button, but the elevator does not move. The mass limit for the elevator is 450450450 kilograms (\text{kg}kgstart text, k, g, end text), but Renna and her load of identical packages mass a total of 620\,\text{kg}620kg620, start text, k, g, end text. Each package has a mass of 37.4\,\text{kg}37.4kg37, point, 4, start text, k, g, end text.
Write an inequality to determine the number of packages, ppp, Renna could remove from the elevator to meet the mass requirement.
pls help
Answers
The inequality to determine the number of packages Renna could remove from the elevator to meet the mass requirement is 620 - 37.4g = 450.
What is an inequality?An inequality is simply used to show the relationship between the expressions that are not equal.
The mass limit is given as 450 grams. Renna has a package that has a weight of 620g.
Each package has 37.4g.
Let the number of packages to remove be p.
The expression will be:
= 620 - (37.4 × p) = 450
620 - 37.4g = 450.
This illustrates the concept of inequality.
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Write a paragraph that explains how the Sumerians were different from other people of their time.
Your paragraph must include a topic sentence, at least two support sentences, and a conclusion
sentence that restates but does not repeat the topic sentence.
Answers
The Sumerians were different from other people of their time as they wee more advanced.
Who were the Sumerians?The Sumerians were a southern Mesopotamian people whose civilisation flourished between approximately 4100 and 1750 BCE. Sumer was an ancient civilization that flourished in the Fertile Crescent region of Mesopotamia, between the Tigris and Euphrates rivers. Sumerians are regarded as the creators of civilisation as we know it today, according to their advancements in language, governance, building, and other fields.
They were able to take technologies produced elsewhere and use them on a far larger scale. This allowed them to mass-produce commodities such as textiles and pottery, which they could subsequently trade with others.
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