The simple interest earned on $8,350 principal deposited for 6 years at an interest rate of 2.28% is $ 1, 141. 28
How to determine the simple interestIt is of great importance to know the formula for calculating the simple interest. It is expressed as;
I = PRT/100
Where;
I is the simple interestP is the principal amount or the initial amountR is the interest rateT is the time takenNow, let's substitute the values into the formula, we have;
Simple interest, I = $8,350 × 2. 28 × 6/100
Multiply the denominators
Simple interest, I = 114228/100
Find the quotient
Simple interest, I = 1, 141. 28
Hence, the simple interest is $ 1, 141. 28
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In the diagram, CD 1 AC, BE 1 AC, AE = 17, BE = 8, and CD = 32. Find DE. 32 D В E 8 17 A 45 51 O 68 O 35 Question 3 1 pts a HE
Input data
AE = 17
BE = 8
CD = 32
Procedure
[tex]\begin{gathered} \frac{AD}{AE}=\frac{CD}{BE} \\ \frac{AD}{17}=\frac{32}{8} \\ AD=17\cdot\frac{32}{8} \\ AD=68 \end{gathered}[/tex]
Now for DE
[tex]\begin{gathered} AE+DE=AD \\ DE=AD-AE \\ DE=68-17 \\ DE=51 \end{gathered}[/tex]The answer would be DE=51
Write the ratio as a ratio of whole numbers in lowest terms $2.00 to $0.80
the wholesale cost of shoes is 22.60$ the markup is 45% what is the selling price
Answer:
$32.77
Step-by-step explanation:
Add 45% of the wholesale cost to the entire wholesale cost to get the selling cost:
$22.60 + (45%)($22.60) = $32.77
The selling cost is $32.77.
The business checking account for a pottery store had a balance of $7349.44 before checks for $1349.67 and $344. 12 were written the store manager then made a deposit of $955.30. Findthe current checkbook balance.
Solution
For this case we can solve the problem with the following operation:
7349.44 -1348.67 -344.12 + 955.30 = 6611.95$
Find the missing coordinates to complete the following ordered-pair solutions to the given linear equation.y + 4x = 6(a) (-1, )(b) (4, )....
SOLUTION
Write out the given linear equation
[tex]y+4x=6[/tex]For the first ordered pair,
[tex]\begin{gathered} (-1,\text{?)} \\ x=-1,y=\text{?} \end{gathered}[/tex]Substitute the value of x into the linear equation to find the value of y
[tex]\begin{gathered} y+4x=6 \\ y+4(-1)=6\ldots\text{.}\ldots(\text{expand the paranthesis )} \\ y-4=6\ldots\ldots(\text{add 4 to both sides )} \\ y-4+4=6+4 \\ y=10 \\ \text{The ordered pair is (-1,10)} \end{gathered}[/tex]a). Therefore For the first ordered pair, the missing coordinate y is 10
Similarly, for the second ordered-pair
[tex]\begin{gathered} (4,\text{?)} \\ x=4,y=\text{?} \end{gathered}[/tex]Substitute the value of x into the linear equation to obtain the value of y
[tex]\begin{gathered} y+4x=6 \\ y+4(4)=6 \\ \text{Expand the parenthesis} \\ y+16=6 \\ \text{subtract 16 from both sides } \\ y+16-16=6-16 \\ y=-10 \\ \text{Ordered pair=(4,-10)} \end{gathered}[/tex]b). Therefore for the second ordered pair, the missing coordinates y is -10
convert into paisa RS.35.25
When RS.35.25 is converted into paise it will be :
3525 paise
How Rupee is converted into Paise? Each nation has its own currency. India's currency is the Indian Rupee. We all see and interact with rupees on a daily basis. We see various coins and notes of various denominations.A rupee contains one hundred paise. In addition, we write 1 Rupee = 100 Paise or 100 Paise = 1 Rupee. Let us first define the terms rupees and paise. We will also understand how to convert rupees to paise.Here given , RS.35.25
We know that,
1 rupee equals 100 paise.
When converting rupees to paise, multiply by 100.
For instance,
Rs 35.25 = Rs 35 + 25 paise.
= 35 x 100 paise + 25 paise
= 3500 paisa + 25 paisa
= 3525 paise.
RS.35.25 = 3525 Paise.
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HELP PLEASEEEEEEEEE!!!!!!!! ILL MARK BRAINLIEST
Answer:
(-3)³, (-2)⁴, (-2)³, 3⁰, -3², -2⁴
Find the least common multiple (LCM) of 12 and 18
Answer:
0.0[infinitely reprating] 1 is the smallest
Answer:
36
Step-by-step explanation:
LCM of 12 and 18 is the smallest number among all common multiples of 12 and 18. The first few multiples of 12 and 18 are (12, 24, 36, 48, 60, 72, 84, . . . ) and (18, 36, 54, 72, . . . ) respectively
Find the exact value using a half angle identity: cos 7 pi/8
Answer:
[tex]\cos \frac{7\pi}{8}=-\frac{1}{2}\sqrt[]{2+\sqrt[]{2}}[/tex]Explanation:
Given
[tex]\cos \frac{7\pi}{8}[/tex]Using the identity:
[tex]\begin{gathered} \cos (\frac{7\pi}{2\times4})=\pm\sqrt[]{\frac{1+\cos\frac{7\pi}{4}}{2}} \\ \\ =-\sqrt[]{\frac{1+\frac{1}{\sqrt[]{2}}}{2}} \\ \\ =-\sqrt[]{\frac{2+\sqrt[]{2}}{4}} \\ \\ =-\frac{1}{2}\sqrt[]{2+\sqrt[]{2}} \end{gathered}[/tex]What are the correct answers the drop down both say negative or positive
Given the data set:
(-8,-10) (6, -1), (-5,-7),(3, -2) (10, 0) (4,-3) (-3,-6) , (9, 1)
We will graph the points to find the slope of the line of best fit for the data
The graph will be as shown in the following figure:-
As shown, the given points are the dots of blue color
The line of best fit is the dashed red line
As shown, the line has a positive slope and a negative y-intercept
So, the answer will be:
The line of best fit for the data will have a positive slope and a negative y-intercept value.
Scott is 72 inches tall and Chris is 185 centimeters tall. Who is taller? Show your work. How do we convert this?
SOLUTION:
Step 1:
In this question, we are given the following:
Scott is 72 inches tall and Chris is 185 centimeters tall.
Who is taller? Show your work.
Step 2:
Scott is 72 inches tall
and
Chris is 185 centimeters tall
Converting cm to inches, we have that:
[tex]\begin{gathered} 1\operatorname{cm}\text{ = }0.393701\text{ inch} \\ 185\text{ cm = 185 x 0.393701 = }72.\text{ 834685 }\approx\text{ 72. 8 inch} \end{gathered}[/tex]CONCLUSION:
Since Chris' height = 72.8 inch tall and Scott's height = 72 inch tall
Hence, Chris is taller.
PLS HELP!!! I GIVE BRAINLESS!!!! NOT FOR TEST!!!
Answer:D
Step-by-step explanation:
D (-1,-2)
Select the expressions that are equivalent to - 7(f - 4).
you can multiply each term of the parentheses by -7
[tex]\begin{gathered} -7(f-4) \\ (-7\times f)+(-7\times-4) \\ -7f+28 \end{gathered}[/tex]Solve. ln(–x + 1) – ln(3x + 5) = ln(–6x + 1) –0.67 or 2 option 1 –1.58 or 0.14 option 2–0.14 or 1.58 option 3–2 or 0.67 option 4
SOLUTION
We want to solve
[tex]\ln \mleft(-x+1\mright)-\ln \mleft(3x+5\mright)=\ln \mleft(-6x+1\mright)[/tex]This becomes
[tex]\begin{gathered} \ln (-x+1)-\ln (3x+5)=\ln (-6x+1) \\ \ln (-x+1)-\ln (3x+5)-\ln (-6x+1)=0 \\ \text{From laws of logarithm } \\ \ln \frac{(-x+1)}{(3x+5)}\times\frac{1}{(-6x+1)} \\ \ln \frac{(-x+1)}{(3x+5)(-6x+1)}=0 \end{gathered}[/tex]Since ln 1 = 0, we have
[tex]\begin{gathered} \ln \frac{(-x+1)}{(3x+5)(-6x+1)}=\ln 1 \\ \text{Canceling }\ln ,\text{ we have } \\ \frac{(-x+1)}{(3x+5)(-6x+1)}=1 \\ (-x+1)=(3x+5)(-6x+1) \end{gathered}[/tex]Expanding the equation in the right hand side we have
[tex]\begin{gathered} (-x+1)=(3x+5)(-6x+1) \\ (-x+1)=-18x^2+3x-30x+5 \\ -x+1=-18x^2+3x-30x+5 \\ -18x^2+3x-30x+5=-x+1 \\ -18x^2+3x-30x+x+5-1=0 \\ -18x^2-26x+4=0 \end{gathered}[/tex]Solving the quadratic equation we have
[tex]-18x^2-26x+4=0[/tex]We have
[tex]x=-1.58\text{ or }x=0.14[/tex]Hence, the answer is option 2
Put the number or question when You answer
How many 1/4 pound pork chops can be cut from a 9 1/2 pound boneless pork loin.
For Culinary
Find the volumeof eachfigure, round to th nearest hundredth I'd necessary
Determine the base of right triangle by using pythagoras theorem.
[tex]\begin{gathered} b=\sqrt[]{(15.7)^2-(8.5)^2} \\ =\sqrt[]{174.24} \\ =13.2 \end{gathered}[/tex]Determine the area of base of figure.
[tex]\begin{gathered} A=\frac{1}{2}\cdot13.2\cdot8.5 \\ =56.1 \end{gathered}[/tex]Determine the volume of the figure.
[tex]\begin{gathered} V=A\cdot6.2 \\ =56.1\cdot6.2 \\ =347.82 \end{gathered}[/tex]So volume of the figure is 347.82 yards square.
Hello, I need some assistance with this homework question, please? This is for my precalculus homework. Q8
Part A (Domain and Range)
Domain
The domain is the set of all the values of x for which the function represented by the graph is defined. From the graph:
(A)The domain of the function is:
[tex]\lbrace x|-\inftyRangeThe range is the set of all the values of y for which the function represented by the graph is defined. From the graph:
(A)The range of the function is:
[tex]\lbrace y|-\inftyPart B (Intercepts)(A)The x-intercepts of the function are:
[tex]x=1.4,-1.4[/tex](A)The y-intercept of the function is:
[tex]y=-1[/tex]Part C
The horizontal asymptote is at:
[tex](A)y=-2[/tex]Part D
The vertical asymptotes are at:
[tex](A)x=-2,2[/tex]Part E
The oblique asymptote is usually slant.
From the graph, there are no obliques asymptotes.
Option B is correct here.
positive exponents.2) (22). 2)
To find the result we are going to use the following rule:
[tex](a^m)^n=a^{mn}[/tex]and
[tex]a^m\cdot a^n=a^{m+n}[/tex]Then:
[tex]\begin{gathered} ((2^2)^4\cdot2^3)^4=(2^8\cdot2^3)^4 \\ =(2^{11})^4 \\ =2^{44} \end{gathered}[/tex]Therefore the result is:
[tex]2^{44}[/tex]Find the average rate of change of f(x) = x°-2x² +3+ 3x from x=1 to x=3.Simplify your answer as much as possible.
The average rate of change for a function f(x) from x=a to x=b is:
[tex]\frac{f(b)-f(a)}{b-a}[/tex]For the given function:
[tex]f(x)=x^3-2x^2+3x[/tex]Averate rate of change from x=1 to x=3:
[tex]\begin{gathered} \frac{f(3)-f(1)}{3-1}=\frac{(3^3-2(3)^2+3(3))-(1^3-2(1)^2+3(1))}{3-1} \\ \\ =\frac{(27-2(9)+9)-(1-2+3)}{2} \\ \\ =\frac{(27-18+9)-(2)}{2} \\ \\ =\frac{18-2}{2} \\ \\ =\frac{16}{2} \\ \\ =8 \end{gathered}[/tex]Then, the averate rate of change for the given function from x=1 to x=3 is 8
if log2 5=x and log2 3=y, determine an expression in terms of x ,y, and integers. the first is log 2 20
Answer:
[tex]\log _220\text{ = 2 + x}[/tex]Logarithm base 2 of a number, is the number you have to use as a power of two to get that number, for example, logatithm base 2 of 4 is 2, because 2 to the power of 2 is 4, another example, logarithm base 2 of 8 is 3, because 2 to the power or 3 is 8
[tex]\log _2(4)=2because2^{2\text{ }}=4[/tex][tex]\log _2(8)=3because2^{3\text{ }}=\text{ 8}[/tex]Evaluate. [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) What is the value of the expression? Enter your answer as a simplified fraction in the box.
The value of given expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5
In this question, we have been an expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9)
We need to evaluate given expression.
First we write an improper fraction as proper fraction.
1 1/5 = 6/5
So given expression becomes,
[(1 1/5−2/5)⋅(− 3/4)3]÷(−9)
= [(6/5 − 2/5) × (− 3/4) 3] ÷ (−9)
= [(4/5) × (-9/4)] ÷ (−9)
= (-9/5) ÷ (-9)
= 1/5
Therefore, the value of given expression [(1 1/5−2/5)⋅(− 3/4)3]÷(−9) is 1/5
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If (ax + 3)(bx + 4) = 6x 2+ cx + 12 for all values of x, and a + b = 5, what are the two possible values for c ?
Answers: c = 17 and c = 18
==================================================
Explanation:
Let's expand out the left hand side and rearrange terms like shown in the steps below.
(ax + 3)(bx + 4) = 6x^2 + cx + 12
ax(bx + 4)+3(bx + 4) = 6x^2 + cx + 12
abx^2 + 4ax+3bx + 12 = 6x^2 + cx + 12
abx^2 + (4a+3b)x + 12 = 6x^2 + cx + 12
Then equate the corresponding coefficients
ab = 6 .... x^2 terms4a+3b = c .... x termsWe'll use the fact that a+b = 5. Solving for 'a' gets us a = 5-b
Plug this into the equation dealing with the x^2 coefficients.
ab = 6
(5-b)b = 6
5b-b^2 = 6
0 = b^2-5b+6
b^2-5b+6 = 0
(b-3)(b-2) = 0
b-3 = 0 or b-2 = 0
b = 3 or b = 2
If b = 3, then a = 5-b = 5-3 = 2
If b = 2, then a = 5-b = 5-2 = 3
Therefore, the solutions to this system of equations
[tex]\begin{cases}a+b = 5\\ab = 6\end{cases}[/tex]
are (a,b) = (2,3) and (a,b) = (3,2)
In other words, the answer to the question "what two numbers multiply to 6 and add to 5?" is "2 and 3". The order doesn't matter which is why we can flip the 'a' and b values.
---------------------------------
Go back to 4a+3b = c which was us equating the x coefficients.
This is the same as c = 4a+3b
Plug in a = 2 and b = 3
c = 4a+3b
c = 4*2+3*3
c = 8 + 9
c = 17 is one possible value of c.
Now let's plug in a = 3 and b = 2
c = 4a+3b
c = 4*3+3*2
c = 12 + 6
c = 18 is the other possible value of c.
Select the correct answer.
What is the completely factored form of this polynomial?
x² + 12x²+32
OA.
O B. (x²+4)(x² + 8)
(x + 4)(X + 8)
O C.
O D.
(x²+4)(x + 2)(x + 4)
(x + 2)(x-2)(x² + 8)
G
Reset
Factor form of the polynomial (x+8)(x+4)
What is Polynomial?
A polynomial is an equation made up of coefficients and indeterminates that uses only the addition, subtraction, multiplication, and powers of positive-integer variables. x2 4x + 7 is an illustration of a polynomial with a single indeterminate x.
Given polynomial,
x² + 12x+32
x² + 4x + 8x +32
x(x+4) + 8(x+4)
(x+8)(x+4)
Hence, The completely factored form of this polynomial is (x+8)(x+4)
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help! its due tomorrow
For Question 1,
(a) Teammates eye-level depths in order from lowest to highest:
-3.5 ft < -3 ft < 0 ft < 1.5 ft
(b) Comparison between Teammate B and teammate D depths:
-3.5 ft < -3 ft
so, eye level depth of Teammate B < Teammate D.
For Question 3,
The options given to the designer are:
1 3/4 and 1 5/12
On simplifying these fractions,
1 3/4 = 7/4
1 5/12 = 17/12
On taking the LCM of the denominator of 4 and 12, we get LCM as 12,
So, 7/4 = 21/12
Now, on comparing the two distances,
21/12 > 17/12
(a) So, the distance of 17/12 is closest to the slide.
(b) On comparing the two distances,
we get, 21/12 > 17/12
(c) 17/12 will lie in between 1 and 1 1/2 on the number line whereas 21/12 will lie in between 1 1/2 and 2 on the number line.
What is Number Line?A number line, used to represent the real numbers visually in early mathematics, is a drawing of a graduated straight line. It is presumptively true that each real number and each point on a number line relate to one another. A line with carefully marked equally spaced-out points on it is frequently used to represent integers. Especially when negative numbers are involved, it is frequently used as a teaching tool for basic addition and subtraction. The set R of all real numbers, considered as a geometric space, namely the Euclidean space of dimension one, is the formal definition of the number line, often known as the real line or real number line in advanced mathematics.To learn more about the Number line, refer to:
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Given the sum of the interior angles is 12,600 of a regular polygon, determine the following:
The number of sides =
Each interior angle =
Each exterior angle =
Sum of the exterior angles =
Answer:
72 sidesinterior angle: 175°exterior angle: 5°exterior angle total: 360°Step-by-step explanation:
Given a regular polygon whose interior angles total 12,600 degrees, you want to know the number of sides, the measures of each interior and exterior angle, and the sum of the exterior angles.
Angle sumThe sum of angles of a convex polygon is given by the formula ...
angle sum = 180° × (n -2)
where n is the number of sides.
ApplicationSubstituting the given angle sum, we can solve for n:
12,600 = 180(n -2)
70 = n -2 . . . . . divide by 180
72 = n . . . . . . . add 2
The regular polygon has 72 sides.
Interior angleThe interior angles of a regular polygon are congruent, so each one is ...
12,600°/72 = 175°
Each interior angle = 175°.
Exterior angleThe exterior angle at a vertex is the supplement of the interior angle there:
180° -175° = 5°
Each exterior angle = 5°.
Sum of exterior anglesThe 72 exterior 5° angles have a total of ...
72 × 5° = 360°
Sum of the exterior angles = 360°.
__
Additional comment
The invariant with convex polygons, regular or not, is that the sum of exterior angles is 360°. This fact is what gives rise to the formula for interior angles.
help meeee pleasee!!!
thank youu
Answer:
Domain: A, [1, 7]
Range: [-4, 2]
Step-by-step explanation:
The domain is the set of x-values and the range is the set of y-values.
Question 1-4
Rectangle ABCD is dilated into rectangle AB'C'D', as shown.
B'
B
A
3
6
C
2
D
C'
D'
What is the scale factor of dilation? Enter the answer as a whole number or a simplified fraction in the box. Use "/" for the fraction bar.
The scale factor of the dilation of Rectangle ABCD which generated rectangle AB'C'D is of:
2
What is a dilation?A dilation is when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
If the coordinates are not given, as is the case in this problem, we can observe the scale factor by the ratio of the side lengths of the dilated figure and of the original figure.
In the context of this problem, these lengths are observed as follows:
The original rectangle ABCD has side lengths of 2 and 3.The dilated rectangle AB'C'D' has side lengths of 4 and 6.Hence the scale factor of the dilation is calculated as follows:
Scale factor = 4/2 = 6/3 = 2.
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Sharon makes money by commission rates. She gets 17% of everything she sells. If Sharon sold $37,000 worth of items this month, how much didshe make?O A $629O B. $5,180O C. $6,290O D. $14,800
Answer;
[tex]C;\text{ \$6,290}[/tex]Explanation;
Here, we want to get the amount of commission made by Sharon
Mathematically, we have that she makes 17% of what she sells as commission
We have this as;
[tex]\frac{17}{100}\times37,000\text{ = \$6,290}[/tex]A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s=−16t2+v0t. Find the time(s) that the projectile will (a) reach a height of 400 ft and (b) return to the ground when v0 is 128 feet per second.
At time t = 4 + 3i sec and t = 4 - 3i sec that the projectile will reach a height of 400 ft.
A projectile is launched from ground level with an initial velocity of v₀ feet per second. Neglecting air resistance, its height in feet t seconds after launch is given by s = −16t² + v₀t.
To determine the time that the projectile will reach a height of 400 ft
⇒ s = −16t² + v₀t
Here v₀ = 128 ft/s and s = 400 ft
Substitute the value of v₀ = 128 and s = 400 in the above equation,
400 = -16t² + 128 × t
16t² - 128t + 400 = 0
Which is simplified as :
t² - 8t + 25 =0
Which gives t = 4 + 3i sec and t = 4 - 3i sec
Therefore, time t = 4 + 3i sec and t = 4 - 3i sec that the projectile will reach a height of 400 ft.
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