Work Shown:
P = 580
r = 0.135
t = 18 months = 18/12 = 1.5 years
A = P*(1+r*t)
A = 580*(1+0.135*1.5)
A = 697.45
Compute the sums below. (Assume that the terms in the first sum are consecutive terms of an arithmetic sequence.) 9 + 4 + (-1) + ... + (-536)
SOLUTION
The terms below make an A.P. Now we are told to find the sum of the AP.
Sum of an AP is given by
[tex]S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack}[/tex]Where S = sum of the AP, a = first term = 9, d = -5, n= ?
So we have to find n first before we can find the sum. The nth term which is the last term = -536. So we will use it to find the number of terms "n"
[tex]\begin{gathered} \text{From T}_{n\text{ }}=\text{ a +(n-1)d where T}_{n\text{ }}=\text{ -536} \\ -536\text{ = 9+(n-1)-5} \\ -536\text{ = 9-5n+5} \\ -536\text{ = 14-5n} \\ -5n\text{ = -536-14} \\ -5n\text{ = -550} \\ n\text{ = 110} \end{gathered}[/tex]Now let's find the sum
[tex]\begin{gathered} S\text{ = }\frac{n}{2}\lbrack2a\text{ + (n-1)d\rbrack} \\ S\text{ = }\frac{110}{2}\lbrack2\times9\text{ + (110-1)-5\rbrack} \\ S\text{ = 55\lbrack{}18+(119)-5\rbrack} \\ S\text{ = 55\lbrack{}18 - 595\rbrack} \\ S\text{ = 55}\times-577 \\ S\text{ = -31735} \end{gathered}[/tex]Therefore, the sum = -31735
When you multiply possible options in each scenario to get the total number of combinations, this is referred to as the fundamental _____ principle.
Fundamental counting principle.
It is also called the counting rule, applying this principle we can know the number of outcomes by multiplying the options of each event together.
Identify the composition that is represented by:r (90, O). T (-2, 4)A translation left 2, up 4 and then a reflection of 90°O A rotation of 90° and then a translation left 2, up 4.A reflection of 90° and then a translation left 2, up 4.O A translation of left 2, up 4 and then a rotation of 90°.
ANSWER:
A rotation of 90° and then a translation left 2, up 4.
STEP-BY-STEP EXPLANATION:
Since r (90, 0) is the first and means a 90 ° rotation and that T (-2, 4) is a translation of 2 units to the left (because it is negative) and 4 units up (because it is positive) , the answer is the option "A rotation of 90° and then a translation left 2, up 4."
Kala the trainer had two solo workout plans that she offers her clients. PlanA and plan B. Each client does either one or the other (not both) on Friday there were 3 clients who did plan A and 5 who did plan B. On Saturday there were 9 clients who did plan A and 7 who did plan B. Kala trained her Friday clients for a total of 6 hours and her Saturday clients for a total of 12 hours. How long does each of the workout plans last?
Answer:
Each of the workouts plans lasts 45 minutes.
Explanation:
Let the duration for Plan A workout = x
Let the duration for Plan B workout = y
Friday
• Plan A --> 3 clients
,• Plan B --> 5 clients
,• Kala trained her Friday clients for a total of 6 hours
[tex]3x+5y=6[/tex]Saturday
• Plan A --> 9 clients
,• Plan B --> 7 clients
,• Kala trained her Saturday clients for a total of 12 hours
[tex]9x+7y=12[/tex]The system of equations is solved simultaneously.
[tex]\begin{gathered} 3x+5y=6\cdots(1) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Multiply equation (1) by 3 in order to eliminate x.
[tex]\begin{gathered} 9x+15y=18\cdots(1a) \\ 9x+7y=12\cdots(2) \end{gathered}[/tex]Subtract.
[tex]\begin{gathered} 8y=6 \\ y=\frac{6}{8}=0.75\text{ hours} \\ 0.75\times60=45\text{ minutes} \end{gathered}[/tex]Substitute y=0.75 into equation (2) to solve for x.
[tex]\begin{gathered} 9x+7y=12 \\ 9x+7(0.75)=12 \\ 9x+5.25=12 \\ 9x=12-5.25=6.75 \\ x=\frac{6.75}{9} \\ x=0.75 \end{gathered}[/tex]x=y=0.75 hours = 45 minutes,
Each of the workouts plans lasts 45 minutes.
A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $540?
Answer
The amount invested at
Step-by-step explanation:
The total amount invested is $5000
Let x be the investment at 5%
Let y be the investment at 15%
Mathematically, this can be expressed as
x + y = 5000 -- equation 1
Since the first part of the investment is invested at 5% and the second part is at 15%
0.05x + 0.15y = 540 --------- equation 2
The systems of equations can be solved simultaneously using the substitution method
x + y =5000 ----- equation 1
0.05x + 0.15y = 540 ------ equation 2
Isolate x in equation 1
x = 5000 - y
Substitute the value of x into equation 2
0.05(5000 - y) + 0.15y = 540
Open the parenthesis
250 - 0.05y + 0.15y = 540
Collect the like terms
-0.05y + 0.15y = 540 - 250
0.1y = 290
Divide both sides by 0.1
0.1y/0.1 =290/0.1
y = $2900
Recall that equation 1 is
x + y = 5000
y = $2900
x = 5000 - y
x = 5000 - 2900
x = $ 2100
Hence, the investment at 5% is $2100 and the investment at 15% is $2900
Linear Programming WorksheetGraph each feasible region. maximize or minimize each objective
Given:
x+2y = 8
x=2, y=0
Substitute x=2 then find value of x as,
2+2y=8
2y=6
y=3
(x,y) = (0,3)
Now, substitute y=0 then find value of y as,
x+2(0)=8
x=8
(x,y) = (8,0)
It is given that P = x+3y
(x,y) = (0,3) then P= 0+3x3
P=9
The maximum valu P=9 and vertiex (0,3)
(x,y) = (8,0) then P=8+0= 8
The mininmum val
Hello. I think I have the right answer. These types of questions have been giving me problems
EXPLANATION
Using a composite figure to approximate the area of the figure will give us the needed surface,
The area of the composite is approximately the area of the squares:
Area of square:
A= base * height = 1.0*1.0 = 1 cm^2
Since we have approximately 22 squares inside the figure, the approximate area will be as follows:
[tex]Area_{composite\text{ figure}}=22*1cm^2=22cm^2[/tex]Therefore, the solution is approximately 22 square units.
A school is organising a fun runThe fun run involves a 4
1
2
mile run around the field, then a 3
2
5
mile run back to the school. Find the total distance of the fun run.Give your answer as a mixed number in its simplest form.
The total distance of the fun run is 7 9/10 miles and it can be written in the simplest fraction form.
Fraction:
The fraction is the part of the whole thing.
For example, a cake is divided into four equal pieces, then each piece is represented by ¼.
Given,
A school is organizing a fun run. The fun run involves a 4 1/2 mile run around the field, then a 3 2/5 mile run back to the school.
Now, we need to find the total distance of the fun run and we have to write it as simplest form.
First we have to convert the given fraction into simplest fraction then we get,
=> 4 1/2 = 9/2
=> 3 2/5 = 17/5
Now , we have to add these to fraction in order to get the total distance,
=> 9/2 + 17/5
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
LCD(9/2, 17/5) = 10
Multiply both the numerator and denominator of each fraction by the number that makes its denominator equal the LCD. This is basically multiplying each fraction by 1.
=> 45/10 + 34/10
=> 79/10
While we convert this into mixed number then we get,
=> 79/10 = 7 9/10
Therefore, the total distance is 7 9/10 miles.
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Which expression uses the commutative property to make it easier to evaluate
Let's begin by listing out the given information:
The commutative property states that for addition, the order in which we add numbers does not change their sum & for multiplication, the order in which we multiply does not change their product.
Mathematically expressed as:
[tex]\begin{gathered} x+y+z=y+z+x \\ x\cdot y\cdot z=y\cdot z\cdot x \end{gathered}[/tex]Therefore, the commutative property of this is:
[tex]\begin{gathered} \frac{4}{3}\cdot\frac{1}{5}\cdot18=\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \Rightarrow\frac{4}{3}\cdot18\cdot\frac{1}{5} \\ \end{gathered}[/tex]Therefore, Option D is the correct answer
I need help answering this if you can show your work to the be good
Let:
x = Number of sodas purchased
y = Number of hamburgers purchased
The food truck charges $3 for sodas, so the total cost for sodas will be:
3*x=3x
also, it charges $8 for each hamburger, hence, the total cost for hamburgers will be:
8*y = 8y
Since Jack wants to spend no more than $30, the total cost must be less or equal than $30:
[tex]\begin{gathered} \text{Total cost }\leq\text{ 30} \\ \text{Total cost = total cost for sodas+total cost for hamburgers} \\ 3x+8y\le30 \end{gathered}[/tex]a bottle of ketchup holds 0.95 liters how maney milliliters does it hold?
Explanation:
The relation between liters and milliliters is:
[tex]1\text{ liter}=1000\text{ milliliters}[/tex]we have to multiply the liters by 1000
Answer:
The answer is 950 milliliters
Equation of line passing thru point -6,-3 and perpindicular to JK -2,7 and 6,5
Equation of the line passing through the point (-6,-3) and perpendicular to the line passing through (-2,7) and (6,5) is y = 4x -19.
First we will find the slope of the line passing through (-2,7) and (6,5).
Slope of the line = (5-7)/(6-(-2)) = -2/8 = -1/4.
We know that,
Product of the slopes of two perpendicular lines = -1.
Let the equation of the line we have to find be y = mx + c.
Slope will be m.
Hence, we can write,
m*(-1/4) = -1
m = -1*(-4/1)
m = 4
Putting (6,5) and m = 4 in y = mx + c , we get
5 = 4*(6) + c
5 = 24 + c
c = 5 - 24 = -19
Hence, the equation of the line is:-
y = 4x -19
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help video S-(x – 6)² +7 for 2 2 +3 x = 3 for Find f(3)
Explanation:
This is a function defined by parts. When x is not 3, the function has the equation on top, but when x is 3, the function has one value: 2.
Answer:
f(3) = 2
Identify the domain and range and tell whether the relation is a function
For a function, every element in the domain must have a unique image in the range.
On checking the domain and range provided in the question, we can see that there are two images for the range when the domain equals -2:
[tex](-2,3)\text{ and (}-2,7)[/tex]Therefore, the given domain and range violate the property of a function.
The relation is NOT a function.
Cut a 10-foot (ft.) long piece of wood into two pieces so that one piece is 2 ft longer than the other. Which of the following equations depicts the given situation?A. x/2 = 10B. x + 2 = 10C. 2x + 2 = 10D. None of the choices
Given:
Cut a 10-foot (ft.) long piece of wood into two pieces so that one piece is 2 ft longer than the other.
Required:
Which of the following equations depicts the given situation?
Explanation:
Let 10 feet long piece of wood cut into two pieces of length x(smaller piece) and
x+2 larger piece.
So, the equation will be
x + x + 2 =10
2x + 2=10
Answer:
Option C is correct.
Three friends rented a kayak. It cost $4 per hour per person to rent the kayak, plus $2 for each life jacket, and $3 to park the car. It cost $57 in all. How many hours did they spend kayaking? Write an equation and solve.
Answer:
13 hours
Step-by-step explanation:
Let y = the total cost
let x = hours
y = 4x + 5 5 = the one time fee of the jacket and the parking
57 = 4x + 5 Subtract 5 from both sides
52 = 4x Divide both sides by 4
13 = x
Which of the equations or inequalities below are true?O A. 7-26O B. 7-224O C. 7-23 5O D. 7 - 2 = -5
Given,
The equation orr inequalities are,
[tex]\begin{gathered} A)7-2\ge6 \\ B)7-2\ne4 \\ C)7-2\leq5 \\ D)7-2=-5 \end{gathered}[/tex]A) In the expression,
7 - 2 = 5
Hence, 7-2 =6 is incorrect.
B) In the expression,
7 - 2 = 5,
Hence,
[tex]7-2\ne4[/tex]Option B is correct.
C) In the expression,
7 - 2 = 5
7 - 2 < 5 is incorrect
Hence, 7 - 2 =< 5 is incorrect.
D)In the expression,
7 - 2 = 5
Hence, 7 - 2 =< -5 is incorrect.
Hence, option B is correct.
Line segment AB is on square ABCD. Segment EF on equilateral triangle EFG is 12 units longer than AB. Square ABCD and triangle EFG have equal perimeters. What is the length of AB?
The length of segment AB as required in the task content is; 36.
What is the length of segment AB?It follows from the task content that the length of the line segment AB which is a side of the square ABCD is to be determined.
Since the perimeters of triangle EFG and square ABCD are equal as given;
Let the length of segment AB = x.
Therefore, EF = x + 12.
Therefore, the perimeter of the equilateral triangle = 3(x +12).
While the perimeter of square ABCD is; 4x.
Therefore, since the perimeters are equal;
3(x + 12) = 4x
3x + 36 = 4x
36 = x.
On this note, thee Length of line segment AB is; 36.
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a coral reef grows 0.15 m every week. how much does it grow in 13 weeks? in centimeters
Given:
A coral reef grows 0.15 m every week.
Coral reefs grow 13 times 0.15m for 13 weeks.
[tex]=13\times0.15m[/tex][tex]=1.95\text{ m}[/tex]We need to convert m into cm.
[tex]1m=100cm[/tex]Multiply 1.95m by 100, we get
[tex]1.95\times100=195cm[/tex]Hence a coral reef grows 195cm in 13 weeks.
Point B is located at -2. Points C and D are each 8 units away from point B. Where are C and D located?
They are located 8 units away, so one has to be away in the left direction and the other one in the right direction
[tex]\begin{gathered} \text{ - 2 - 8 = -10 } \\ \text{ - 2 + 8 = 6} \end{gathered}[/tex]So, C and D are located at -10 and 6
3.
How much greater is the surface area of the rectangular prism than the surface area of the cube?
6 cm
(1 point)
3 cm
2 cm
O 36 cm²
O 33 cm²
O 18 cm²
O 45 cm²
3 cm
The dimensions of the rectangular prism of 6 cm by 3 cm by 2 cm and the dimension of the cube of 3 cm gives the amount the surface area of the prism is greater than the cube as 18 cm²
What is a rectangular prism?A rectangular prism is a six faced solid hexahedron.
The given dimension of the rectangular prism are:
Length = 6 cm
Height = 3 cm
Width = 2 cm
The side length of the cube = 3cm
The surface area of the rectangular prism is therefore:
[tex]A_p[/tex] = 6 × 3 × 2 + 6 × 2 × 2 + 3 × 2 × 2 = 72
The surface area of the rectangular prism is 72 cm²
The surface area of the cube: [tex]A_c[/tex] = 6 × 3² = 54
The surface area of the cube, [tex]A_c[/tex] = 54 cm²
The amount by which area of the rectangular prism is greater than the area of the cube is therefore: [tex]A_p[/tex] - [tex]A_c[/tex] = 72 cm² - 54 cm² = 18 cm²
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Given AFGH ~ ALMN, which must be true? Select all that apply.A.FGLMFHLNB. FH ~ LNC.mZFmZLmZGmZMD. GHMNE. mZH ^mZN
Mrs. Smith has 12 times as many markers as colored pencils. The total number of markers and colored pencils is 78. How many markers does Mrs. Smith have?ok...answers given so far are not helpful in explaining process.
Let:
x = Colored markers
y =
Large Small
3
Blue 17
Red 8 12
Find: P(Red and Small)
Remember to reduce your answer.
Enter
Using mathematical operations, we know that P(Red and Small) is 4/3.
What exactly are mathematical operations?A mathematical function known as an operation converts zero or more input values into a precisely defined output value.The quantity of operands affects the operation's arity.The order of operations refers to the rules that define the sequence in which we should perform the operations necessary to solve an expression.Parentheses, Exponents, Multiplication, Division, and Addition Subtraction are also known as PEMDAS (from left to right).So, simple form of P(Red and Small):
Red balls: 8 (large) + 12 (Small) = 20 red ballsSmall balls: 3 (Blue small balls) + 12 (Red small balls) = 15 small ballsThen, P(Red and Small):
20/154/3Therefore, using mathematical operations, we know that P(Red and Small) is 4/3.
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Find an equation of the tangent line to the graph of y = B(x) at x = 25 if B(25) = −1 and B ′(25) = − 1 5 .
The most appropriate choice for tangent to a curve will be given by-
[tex]3x + 2y = 73[/tex] is the required equation of tangent.
What is tangent to a curve?
Tangent to a curve at a point is the straight line that just touches the curve at that point.
Equation of tangent to a curve at a point [tex](x_1, y_1)[/tex] is given by
[tex]y - y_1 = \frac{dy}{dx}|_{(x_1,y_1)} (x - x_1)[/tex]
Here,
y = B(x), B(25) = -1, B'(25) = -1.5
Equation of tangent =
[tex](y - (-1)) = -1.5(x - 25)[/tex]
[tex]y + 1=-1.5x +37.5\\y + 1 = -\frac{3}{2}x + 37.5\\2y + 2 = -3x + 75\\3x+2y = 75-2\\3x+2y=73[/tex]
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In an office building, 54 office are currently being rented, this represent 30% of the total units. how many offices are in the building
given that,
54 offices are currently rented
and it represent 30% of the total unit
to get the total offices in the building
let the total offices be x
30% of x = 54
30/100 X x = 54
cross multiply
30x = 5400
dividing both sides by 30
30x/30 = 5400/30
x = 5400/30
x = 180
therefore the total offices in the building is 180
The measures of the angles of a triangle are shown in the figure below. Solve for x. (2x+6)° 42°
A triangle is a shape that has a total angle of 180°.
How to solve the triangle?It's important to note that a triangle is a shape that has three sides and the total sum is equal to 180°.
In this case, we have 2x + 6 and 42°. The other angle isn't given and this can't be solved further
The sides will have been illustrated as:
= a + b + c = 180
The expression given will then be allocated for each side to solve it further.
Note that an overview was given as the information is incomplete.
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Jan plans to tell two people each day and will ask that person to tell two other people each day through the day of the opening, and so on. Assume that each new person who hears about the soft opening is also asked to tell two other people each day through the day of the opening and that each one starts the process of telling their friends on the day after he or she first hears. When should Jan begin telling others about the soft opening in order to have at least 700 people know about it by the day it occurs?
Explanation:
From the given question, we can sketch the pattern observed
The figure above helps show how the number of people increases
Initially, Jan tells 2 more people, then the two people tell two more people, then they also tell two more people
Thus
we can see that the model is given by
[tex]\begin{gathered} (2)^n \\ where\text{ n is the number of days} \end{gathered}[/tex]In order to have at least 700 (it also means a minimum of 700), we will have the equation
[tex]2^n\ge700[/tex]We then solve for n
Taking the log of both sides
[tex]n\text{ }log2\ge log700[/tex][tex]n\ge\frac{log700}{log2}[/tex]So that
[tex]\begin{gathered} n\ge\frac{2.845}{0.301} \\ \\ n\ge9.451 \end{gathered}[/tex]So, the number of days will be at least 10 days (Rounded to the nearest whole day )
Issac says that T' will be located at (4,20)Isabella says that T' will be located at (4,12(who is correct and why?
In the given triangle :
The coordinate of T is ( 2, 10 )
Triangle TUV will be dilated by a scale factor of 2
Thus, multiply the coordinates of TUV by 2
T' = 2 x T
T' = 2 x ( 2, 10 )
T' = ( 2x2, 2x10)
T' = ( 4, 20 )
So, T' will be located at ( 4, 20 )
Issac says that T' will be located at (4,20)
Answer : Issac says that T' will be located at (4,20)
Please help me this is so confusing .which of the following, names a ray in the drawing?
From the given figure, let's select the rays given in the option.
A ray can be said to be a straight line which starts from a point and goes to infinity at the other end.
From the given figure, the rays are:
• NK
,• NJ
,• NL
,• NM
Therefore, from the list the, the ray is NK.
ANSWER:
NK