The average daily balance and the finance charge will be $958.33 and $9.58 respectively.
How to compute the finance?Average Daily Balance will be calculated thus:
7 * $800 = $5,600
3 * $700 = $2,100
9 * $1,000 = $9,000
3 * $950 = $2,850
8 * $1,150 = $9,200
Total = $28,750
Average Daily Balance = Total amount / Number of period
= $28,750/30
= $958.33
Finance Charge:
= $958.33 * 0.01
= $9.58
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How can each type of sequence be helpful in everyday situations? Provide an example and the corresponding equation for each type.
Answer:
The two types of the sequence include
1) Arithmetic sequence
2) Geometric sequence
An arithmetic sequence is an ordered set of numbers that have a common difference between each consecutive term. For example in the arithmetic sequence 3, 9, 15, 21, 27, the common difference is 6. An arithmetic sequence can be known as an arithmetic progression.
The Nth term of an arithmetic sequence is given below as
[tex]\begin{gathered} T_n=a+(n-1)d \\ \text{Where,} \\ a=\text{first term} \\ n=Num\text{mber of terms} \\ d=\text{common difference}=T_2-T_1=T_3-T_2 \end{gathered}[/tex]A geometric progression, also known as a geometric sequence, is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
The Nth term of a geometric sequence is given below as
[tex]\begin{gathered} U_n=ar^{n-1} \\ \text{Where,} \\ a=\text{first term} \\ r=\text{common ratio=}\frac{t_2}{t_1}=\frac{t_3}{t_2} \end{gathered}[/tex]Real life illustrations of the types of sequence
Sequences are useful in our daily lives as well as in higher mathematics. For example, the interest portion of monthly payments made to pay off an automobile or home loan, and the list of maximum daily temperatures in one area for a month are sequences.
Example: arithmetic sequence
A boy building a tower with blocks uses 15 for the bottom row. Each row has 2 fewer blocks than the previous row. Suppose that there are 6 rows in the tower. Find a for n = 6
The number of blocks in each row forms an arithmetic sequence with a₁ = 15 and d= −2. The formula to be used is an = a₁ + (n − 1)d.
[tex]\begin{gathered} t_n=a+(n-1)d \\ T_6=15+(6-1)(-2) \\ T_6=15+5(-2) \\ T_6=15-10 \\ T_6=5 \end{gathered}[/tex]Hence,
On the sixth row, he will have 5 blocks left
Example: geometric sequence
A country's population is growing in such a way that each new generation is 1.5 times as large as the previous generation. Suppose there are 100 insects in the first generation. How many will there be in the fifth generation?
Here,the common ratio r=1.5
[tex]U_n=a(1.5)^{n-1}[/tex]Triangle RST has vertices R(1, 2), S(4, -2), and T(2, -5). The triangle is rotated 90° counterclockwise about the origin. Which are the coordinates of the image of vertex T?
Answer:
(5, 2)
Explanation:
If point P with coordinates (x, y) is rotated 90 degrees counterclockwise about the origin, the image will have (-y, x) as coordinates of the image, P'.
So if triangle RST was rotated 90 degrees counterclockwise about the origin, we'll have the below as coordinates of the image of vertex T;
[tex]T(2,-5)\rightarrow T^{\prime}\lbrack(-(-5),2)\rbrack\rightarrow T^{\prime}(5,2)[/tex]4 divided by 48.03 Long Division
Answer: 12.00705
Step-by-step explanation:
I need help defining variables and changing them into an inequality.
Enrollment in finite mathematics plus enrollment in calculus is less than 300.
The first step in solving a word problem is identifying the variables. The variables in any algebraic expression is the unknown value, and to solve it we usually assign a letter to represent it (x and y being the most commonly used).
In the question above, we already know that the number of student enrollees is less than 300 and not equal to 300 (might as well be just 20, we do not know) but we do know that it is NOT EQUAL TO 300, but less than.
Also we do not know the number of those enrolled for finite mathematics, so we shall call that f. Those that enrolled for calculus we shall call c. Since both categories are less than 300, the two variables f and c can now be written as an inequality which reads,
f plus c is less than 300
That is;
f + c ⊂ 300
PLEASE HELP!! Fill in the gaps to factorise the expression below
simplifying with like terms; 3x^2 + 5x - 2x^2
Simplifying,
[tex]\begin{gathered} 3x^2+5x-2x^2 \\ \rightarrow3x^2-2x^2+5x \\ \rightarrow x^2+5x \end{gathered}[/tex]Please helpppppppppp
,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,
Abel owns a dog walking business. He walks12 dogs every day of the week. If Abel walks2.6 miles each day, how many miles does hewalk in one week?
Abel walks 2.6 miles each day of the week.
The week has 7 days.
So, to calculate how many miles he walks in one week we simply have to multiply the number of miles that he walks per day (2.6) by the number of days in a week (7).
2.6 miles per day x 7 days = 2.6 x 7 = 18.2 miles a week.
3) Rotate counterclockwise around the origin180°180°Ay41NН.2.4xK44What is the rule? (x,y) - (___)H(__)l'(_,J'(___)K'(__)
We have the next points
H(-4,1)
I(-2,2)
J(-1,-2)
K(-4,-4)
The rule to rotate 180° counterclockwise
[tex](x,y)\rightarrow(-x,-y)[/tex]with rule, we can find the points
H'=(-(-4),-1)=(4,-1)
I'=(-(-2),-2)=(2,-2)
J'=(-(-1),-(-2))=(1,2)
K'=(-(-4),-(-4))=(4,4)
so the answer is
H'=(4,-1)
I'=(2,-2)
J'=(1,2)
K'=(4,4)
we can graph them they are the points in red
The answer is 3(sign)2 I need help with the work
First, notice that the two sides of the right triangle are equal, then, using the pythagorean theorem,we get:
[tex]\begin{gathered} 6=\sqrt[]{x^2+x^2}=\sqrt[]{2x^2} \\ \Rightarrow\sqrt[]{2}x=6 \\ \Rightarrow x=\frac{6}{\sqrt[]{2}}\cdot(\frac{\sqrt[]{2}}{\sqrt[]{2}})=\frac{6\sqrt[]{2}}{2}=3\sqrt[]{2}_{} \\ x=3\sqrt[]{2} \end{gathered}[/tex]therefore, x = 3*sqrt(2)
Which of the following is an example of a theorem? A. the areas of two congruent figures are equal. B. the area of a square is the square of the length of its side. C. the area of a rectangle is the product of its base and height. D. the area of a rectangle is the sum of all its non-overlapping parts
Theorem is a statement that can be proved or that is proven to be true.
Option A is a theorem because it is proven that the area of two congruent figures are equal.
Option B is a theorem because the area of a square is the square of the length of its side.
[tex]\begin{gathered} A_{square}=l\times l \\ A_{square}=l^2 \end{gathered}[/tex]Option C is a theorem because the area of a rectangle is the product of its base and height.
[tex]\begin{gathered} A_{rec\tan gle}=b\times h \\ A_{rec\tan gle}=bh \end{gathered}[/tex]Thus, A, B and C are CORRECT
Juan is designing an exercise room in his house. How many square feet of rubber flooring will he need to cover the floor? The product is sold in whole square yards. How many square yards should he buy? Explain. 10 ft 3 ft 9 ft 13 ft The total area of the exercise room is 103 ft. This is also the total amount of rubber flooring that Juan must have. (Type a whole number.) The number of square yards equivalent to this total area is 11.4 square yards. (Round to the nearest tenth as needed.) Since rubber flooring is sold in whole sq. yards, Juan must purchase exactly square yards.
The amount of rubber flooring will be the area of the floor.
We can calculate the area as the sum of two rectangles:
Then, the area is:
[tex]A=10\cdot4+9\cdot7=40+63=103ft^2[/tex]We can convert this area into square yards as:
[tex]A=103ft^2\cdot(\frac{1\text{ yd}}{3\text{ ft}})^2=103\cdot\frac{1}{9}\text{ yd}^2\approx11.44\text{ yd}^2[/tex]As we have to purchase a whole number of square yards, we will buy the next integer greater than 11.44, that is 12 sq yd.
Answer:
The floor area is 103 square feet.
This is equivalent to 11.44 square yards.
He has to purchase 12 square yards of rubber floor.
Solve x^2-6+58=0 please fast I need help
Answer:
No real solutions.
Step-by-step explanation:
When solving this equation, you have to figure out if the two sides of an equation equal each other.
Solve.
x^2-6+58 = 0
Answer: No real solutions.
This is due to the fact that x^2-6+58 does not equal 0.
Hope this helps!
Btw, if this is correct, could I have Brainliest? Thanks!
PLEASE HELP ME I WAS SICK AND I DONT UNDERSTAND.DUE IN 1 HOUR!!!!
Answer:
x=11
Step-by-step explanation:
The inside(interior) angles of a triangle must add up to 180 degrees. A line is 180 degrees, so the angle GFH (the measure of the acute angle at point F) would be 180-(11x+1)
Now we have information on all 3 angles of the triangle; they must sum up to 180, so add all of these equations together
180-(11x+1) = 179-11x
Add this to 3x+19 and 70 gives 268-8x=180
Solving this equation for x we get -8x=180-268
-8x=-88
x=11
Hoped this helped and I hope you feel better!
Answer:
11°
Step-by-step explanation:
Here,
∠FGH=3x+19
∠GHF=70°
∠QFG=11x+1
Now,
11x+1+∠GFH=180[Sum of a straight line is 180°]
∴∠GFH=179-11x
Again,
∠GFH+∠GHF+∠FGH=180[Sum of all angles of a triangle is 180]
179-11x+70+3x+19=180
-11x+3x=180-179-70-19
-8x=-88
∴x=11°
How many presents would Dracula wrap in 8 hours if he wrapped 3 presents every 20 minutes?
First, you can know how many minutes are 8 hours using the rule of three like this
[tex]\begin{gathered} 1\text{ hour}\rightarrow60\text{ minutes} \\ 8\text{ hours }\rightarrow\text{ x minutes} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{8\text{ hours }\ast\text{ 60 minutes}}{1\text{ hour}} \\ x=480\text{ minutes} \end{gathered}[/tex]Now, using the rule of three again, you can find out how many gifts Dracula would wrap in 8 hours if she wrapped 3 gifts every 20 minutes
[tex]\begin{gathered} 20\text{ minutes}\rightarrow3\text{ presents} \\ 480\text{ minutes}\rightarrow x\text{presents} \end{gathered}[/tex][tex]\begin{gathered} x=\frac{480\text{ minutes}\ast3\text{ presents}}{20\text{ minutes}} \\ x=\frac{1440}{20}\text{ presents} \\ x=72\text{ presents} \end{gathered}[/tex]Therefore, Dracula would wrap 72 gifts in 8 hours if he wrapped 3 gifts in 20 minutes
what is the value of K in the equation
Simplify the equation to obtain the value of k.
[tex]\begin{gathered} 5k-2k=12 \\ 3k=12 \\ k=\frac{12}{3} \\ =4 \end{gathered}[/tex]So value of k is 4.
A law firm is going to designate associates and partners to a big new case. The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1300. The law firm assigned a total of 19 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services. Write a system of equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case. Define the variables that you use to write the system.
The number of associates is 9 and the number of partners is 10.
Given, The daily rate charged to the client for each associate is $700 and the daily rate for each partner is $1300.
The law firm assigned a total of 19 lawyers to the case and was able to charge the client $19300 per day for these lawyers' services.
we need to determine the number of associates assigned to the case and the number of partners assigned to the case.
Suppose the number of associates is x and the number of partners be y.
Then the required equations are formed:
x+y=19 ..eq(1)
700x+1300y=19300 ...eq(2)
from eq(1) we get:
y=19-x .. eq(3)
Plug eq(3) into eq(2)
700x+1300(19-x)=19300
700x+24700-1300x=19300
700x-1300x=19300-24700
-600x=-5400
x=9
Thus, y=19-9
y=10
Thus the number of associates are 9 and the number of partners are 10.
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suppose that you have a 10,000 in a rather risky investment recommend by your financial advisor during the first year your investment decreases by 50% of its original value during the second year your investment at the end of year 1 increases by 60%. Weiser tells you that there must have there must have been a 10% overall increase of your original $10,000 investment. Is your financial advisor using percentages Properly? If Not, what is your actual gain or loss of your original $10,000 investment?
The financial advisor is NOT using percentages properly, because the 60% increase would multiply the new value after one year, and not the initial value.
So first let's find the investment after one year:
[tex]\begin{gathered} 10000-50\text{\% of 10000} \\ =10000-0.5\cdot10000=10000-5000=5000 \end{gathered}[/tex]Then, we have an increase of 60%, so:
[tex]\begin{gathered} 5000+60\text{\% of 5000} \\ =5000+0.6\cdot5000=5000+3000=8000 \end{gathered}[/tex]The final value is 8000, which is lesser than the original value, so we have a loss.
The percentual loss is:
[tex]\frac{10000-8000}{10000}=\frac{2000}{10000}=0.2=20\text{\%}[/tex]Graph the line that passes through the point: (1,-1) and is parallel to another line whose slope is 1.
The line that passes through the point (1,-1) and is parallel to another line whose slope is 1 will be y = x-2.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that line that passes through the point (1,-1) and is parallel to another line whose slope is 1.
The standard from the equation is,
y = mx + c
The equation with slope 1 is,
y = x +c
For the y-intercept, the value of y is -1.
-1 = 1(1) + c
-1 = 1+c
c = -2
Substitute the value of the slope, m as -1 and c as -2 we get,
y = 1x-2
y = x-2
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A car's rear windshield wiper rotates 130°. the total length of the wiper mechanism is 21 inches and the length of the wiper blade is 14 inches. find the area wiped by the wiper blade. (round your answer to one decimal place.)
We have that the formula for the area of the sector of a circle is:
[tex]A=\frac{\pi\cdot r^2\cdot\alpha}{360}[/tex]In this case, we have to find the area of the sector of a circle with radius r= 21 and then the area in the case of the r=21-14=7, and then find the difference.
Given the information, we have the following:
[tex]\begin{gathered} \alpha=130 \\ r_1=21 \\ r_2=7 \\ \Rightarrow A_1=\frac{(3.1416)(21)^2(130)}{360}=500.3 \\ \Rightarrow A_2=\frac{(3.1416)(7)^2(130)}{360}=55.6_{} \\ \Rightarrow A=A_1-A_2=500.3-55.6=444.7_{} \\ A=444.7 \end{gathered}[/tex]therefore, the area wiped by the wiper blade is 444.7in²In AWXY, WY is extended through point Y to point Z, YWX = (3x + 17), XYZ = (10x – 5), and WXY = (3x - 2). Find WXY.
Let's draw the figure to better understand the scenario:
To be able to get the measure of ∠WXY, we will be using the relationship of the interior angles of a triangle.
The sum of all interior angles of a triangle is 180°. Therefore we can say,
[tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + }\angle XYW=180^{\circ}[/tex]The formula or measure of ∠XYW isn't given. However, we observed that ∠XYW and ∠XYZ are pairs of Supplementary Angles. This means that the sum of two angles is equal to 180°.
We get,
[tex]\text{ }\angle XYW\text{ + }\angle XYZ=180^{\circ}[/tex]Therefore,
[tex]\text{ }\angle XYW\text{ }=180^{\circ}\text{ - }\angle XYZ[/tex]We will use this to complete the formula of the sum interior angles, substituting ∠XYW = 180° - ∠XYZ.
[tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + }\angle XYW=180^{\circ}[/tex][tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + (}180^{\circ}-\angle XYZ)=180^{\circ}[/tex]Substituting the given formulas of each angle, let's find x.
[tex]\text{ }\angle YWX\text{ + }\angle WXY\text{ + (}180-\angle XYZ)=180^{\circ}[/tex][tex](3x+17)+(3x-2)+(180-(10x-5)^{})=180^{\circ}[/tex][tex]\text{-4x + 200 = 180}[/tex][tex]\text{-4x = 180 - 200 = -20}[/tex][tex]\frac{\text{-4x}}{-4}\text{ = }\frac{\text{-20}}{-4}[/tex][tex]\text{ x = 5}[/tex]Let's substitute x = 5 to ∠WXY = 3x - 2 to find its measure.
[tex]\angle WXY=3x-2=\text{ 3(5) - 2}[/tex][tex]\text{ = 15 - 2}[/tex][tex]\angle WXY=13^{\circ}[/tex]Therefore, the measure of ∠WXY = 13°.
Sort the cards so that each group adds up to 100%
Answer:
Add the 20%, 0.40 and the 40/100 chart
Add the 1/10, the 0.10, and the 80/100 chart
And finally, add the 6%, the 4/100 chart, and the 90/100
Classify the triangle as acute, right , or obscure and classify it as equilateral , isosceles , or scalene
Step 1:
What is an isosceles triangle?
What is Isosceles Triangle? A triangle with two sides of equal length is an isosceles triangle.
Step 2: What is an acute angle?
An acute angle is an angle that measures between 90° and 0°.
Step 3:
The figure is an acute isosceles.
Final answer
Acute Isosceles
given (10,5) and (x,-10), find all x such that the distance between these two points is 17. separate multiple answers with a comma.
x = (2, 18)
Explanation:Given the points (10, 5) and (x, -10)
The distance between these points is:
[tex]\begin{gathered} D=\sqrt[]{(x-10)^2+(-10-5)^2} \\ \\ =\sqrt[]{(x-10)^2+(-15)^2} \\ \\ =\sqrt[]{(x-10)^2+225} \end{gathered}[/tex]The distance is given to be 17, so
[tex]\begin{gathered} \sqrt[]{(x-10)^2+225}=17 \\ \\ (x-10)^2+225=17^2 \\ (x-10)^2=17^2-225 \\ (x-10)^2=289-225 \\ (x-10)^2=64 \\ x-10=\pm\sqrt[]{64}=8 \\ x=\pm8+10 \\ x=8+10=18 \\ OR \\ x=-8+10=2 \end{gathered}[/tex]x = 2 or x = 18
2x+y=-11 rewrite in slope intercept form
Answer:
In slope-intercept form:
[tex]y = - 2x - 11[/tex]
Which is the correct simplified version ofthe expression -7(2x - 3)?a. - 14x + 21b. - 14x - 21c. -5x – 10d. -14% - 10
The given expression is - 7(2x - 3)
The first step is to open the bracket by multiplying each term inside the bracket by the term outside. Then we would add or subtract where necessary.
It becomes
- 7 * 2x + - 7 * - 3
Recall, - * - = +
The simplified expression would be
- 14x + 21
The correct option is A
A farmers land is separated in sections of size 2 1/7 acres. Suppose there are 4 3/8 such sections. How many acres of land does the farmer own? Write your answer as a mixed number in simplest form.
We were told that the farmer's land is separated in sections of size 2 1/7 acres. Converting 2 1/7 to improper fraction, we multiply 2 by 7 and add 1. The denominator remains 7. it becomes 15/2
There are 4 3/8 such sections. Converting 4 3/8 to improper fraction, it becomes 35/8
Therefore, the number of acres of land that the farmer owns is
15/2 * 35/8 = 525/16
Converting to improper fraction, it becomes
32 13/16 acres
Answer:
32 13/16 acres
Step-by-step explanation:
Please help!! College Algebra. Need answer fast!!
One is traveling at a constant pace of 30 mph and is 5 miles south of the intersection. The distance d between the cars changes with time t as [tex]\sqrt{26-320t+1000t ^{2}}[/tex].
Given that,
An intersection is being approached by two cars. One is traveling at a constant pace of 30 mph and is 5 miles south of the intersection. At the same time, the second vehicle is traveling at a constant speed of 10 mph and is located one mile to the east of the intersection.
We have to describe how the distance d between the cars changes with time t.
The distance is d=[tex]\sqrt{(t_{1}) ^{2} +(t_{2}) ^{2}}[/tex]
t₁=1-10t
t₂=5-30t
d=[tex]\sqrt{(1-10t) ^{2} +(5-30t) ^{2}}[/tex]
d=[tex]\sqrt{1-20t+100t^{2}+25-300t+900t ^{2}}[/tex]
d=[tex]\sqrt{26-320t+1000t ^{2}}[/tex]
Therefore, We got the distance d between the cars changes with time t as [tex]\sqrt{26-320t+1000t ^{2}}[/tex].
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zachs orange paint is made by mixing 3 cups of red for every 5 cups of yellow. we know that Zach brought 24 cups of red paint. how many cups of yellow paint must he get to make his orange paint mixture?
For the information given in the statement you have
[tex]\frac{\text{number of cups of red paint}}{\text{ number of cups of yellow paint}}=\frac{3}{5}[/tex]Then
[tex]\frac{3}{5}=\frac{24\text{ cups of red paint}}{\text{ x cups of yellow paint}}[/tex]Solving for x
[tex]\begin{gathered} \frac{3}{5}=\frac{24}{x} \\ \text{Apply cross multiplication} \\ 3\cdot x=24\cdot5 \\ 3x=120 \\ \text{ Divide by 3 into both sides of the equation} \\ \frac{3x}{3}=\frac{120}{3} \\ x=40 \end{gathered}[/tex]Therefore, he must get 40 cups of yellow paint to make his orange paint mixture.
6) Rotate clockwise around the origin 270°270°AYRSх6-2TQ QWhat is the rule? (x,y) → (Q' (_)R' (_)S'(__)T'(___)
we know that
The rule for a rotation by 270° about the origin is (x,y)→(y,−x)
so
we have
R(-5,0) -------> R'(0,5)
S(-3,0) ------> S'(0,3)
T(-1,-3) ------> T'(-3,1)
Q(-6,-3) ----> Q'(-3,6)
step 2
Graph the image
Plot the ponts of the image
using a graphing tool
please wait a minute to draw the figure
