1) Gathering the data
Time: 10 yrs ago
Interest rate (r) : 9% (0.09)
Future Value: 300
Initial Deposit:?
2) Since the current balance is given, let's call it Future Value because the amount that made that $300 is what we need to find out. Let's go find the Future Value since it's been 10 yrs ago. Plugging into the formula we have:
[tex]\begin{gathered} F=P(1+r/n)^{nt} \\ 300=P(1+\frac{0.09}{1})^{1\cdot10} \\ 300=P(1.09)^{10} \\ 300=2.367363675P \\ P=\frac{300}{2.367363675} \\ P=126.723 \\ P\cong126.72 \end{gathered}[/tex]Notice that, since this investment was compounded yearly, so n=1.
3) So the initial deposit, 10 years ago was approximately $126.72
12–15. Melvin Indecision has difficulty deciding whether to put his savings in Mystic Bank or Four Rivers Bank. Mystic offers 10% interest compounded semiannually. Four Rivers offers 8% interest compounded quarterly. Melvin has $10,000 to invest. He expects to withdraw the money at the end of 4 years. Which bank gives Melvin the better deal?
The better deal between the offer at Mystic Bank and Four Rivers Bank is the deal at Mystic Bank.
What is the better deal?In order to determine which bank has the better offer, the future value of the investment options have to be determined.
The future value of an investment is a function of the amount investment, the number of compounding, the years of the investment and the interest rate.
When an investment is compounded semi-annually, it means that it grows exponentially twice in a year. When an investment is compounded quarterly, it means that is grows exponentially four times in a year.
The formula for calculating future value:
FV = P (1 + r)^nm
Where:
FV = Future value P = Present value R = interest rate m = number of compoundingN = number of yearsInterest rate at Mystic bank = 10% /2 = 5%
Interest rate at Four Rivers Bank = 8% / 4 = 2%
Future value of the investment at Mystic bank :
$10,000 x (1.05)^(2 x 4) = $14,774.55
Future value of the investment at Four Rivers Bank :
$10,000 x (1.02)^(4 x 4) = $13,727.86
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In the game of baseball, home plate is a pentagon.What is the measure of the angle at the bottom of home plate?A. 60°B. 90°C. 120°D. 135°
EXPLANATION
Since the figure is like a pentagon, we need to add the interior angles in order to get the needed angle.
The first part of the figure is composed of a square with two right angles of 90 degrees and two angles of 135, making a total of 90+90+135+135 = 450 degrees.
The left needed angle should add a total of 540 degrees, by the Sum of Interior Angles of a Pentagon Theorem, as follows:
450 + bottom angle = 540
Subtracting -450 to both sides:
bottom angle = 540 - 450
Subtracting angles:
bottom angle = 90 degrees
In conclusion, the value of the bottom angle is 90 degrees.
Multiply 58*7 enter your answers in the boxes to complete the area model
We will get 406 after multiplication .
What does multiply mean?
Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. A multiplication issue has two factors, a product, and two factors. The factors in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the product is the number 54.Calculating the outcome of adding a number several times is known as multiplication in elementary algebra. Each of the numbers and is referred to as a factor of the product, which is the outcome of a multiplication.58 * 7 = 406
We will get 406 after multiplying .
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an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours.Wich has a graph that best represents this rate?
If an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H best represents this rate.
The graphs are attached
Given that the oil-well contractor drills a shaft 7 meters deeper into the ground every 2 hours,
hence the rate at which the shaft drills = 7 meter / 2 hours = 3.5 meters per hour
Since the drill goes into the ground, hence the rate is negative that is -3.5 meters per hour
The slope (rate of change) of a line (m) is given by:
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
a) For graph F, the line passes through the point (0,0) and (10, -20). Hence:
Slope of the line , [tex]m = \frac{-20 - 0}{10 - 0}[/tex]
Slope of the line is - 2 meters per hour
b) For graph G, the line passes through the point (0,0) and (10, -70). Hence:
Slope of the line, [tex]m = \frac{-70 - 0}{10 - 0}[/tex]
Slope of the line is -7 meters per hour
c) For graph H, the line passes through the point (0,0) and (10, -35). Hence:
Slope of the line, [tex]m = \frac{-35 - 0}{10 - 0}[/tex]
Slope of the line is -3.5 meters per hour
d) For graph J, the line passes through the point (0,-3.5) and (10, -3.5). Hence:
Slope of the line, [tex]m = \frac{-3.5 - 3.5}{10 - 0}[/tex]
Slope of the line is 0 meters per hour.
Therefore, if an oil-well contracted drills a shaft 7 meters deeper into the ground every 2 hours, then Graph H best represents this rate.
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FIRST PERSON TO ANSWER THIS GETS BRAINILEST.
Determine if the two expressions in each pair are equivalent.If they are equivalent,select the property that is illustrated.
Answer:
The second one is the Multiplicative Property of Zero.
The fourth one is the Commutative property.
Answer:
The second and third one
Step-by-step explanation:
Paul needs to buy paint to cover all outside surfaces of his shed, depicted below. How much area, in square yards, does he need to cover?
2 sides of shed are rectangles with a base of 12ft and a side of 6 ft.
The other two sides are squares with sides of 6 ft.
The roof consists of four triangles, 2 of the triangles have a base of 6 feet and a height of 6 feet.
The other two triangles have a base of 12 ft and a height of 6 ft
The total surface area Paul is required to paint is 36 yard square.
How to find surface area?He needs to buy paint to cover all outside surfaces of his shed .
2 sides of shed are rectangles with a base of 12ft and a side of 6 ft.
Therefore,
area of a rectangle = lw
where
l = lengthw = widtharea of the rectangle = 12 × 6
area of the rectangle = 72 ft²
The rectangle are two.
Hence, area of the two rectangular faces = 72 + 72 = 144 ft²
The other two sides are squares with sides of 6 ft.
Therefore,
area of the two squares = 6² + 6² = 36 + 36 = 72 ft²
The roof consists of four triangles,
2 of the triangles have a base of 6 feet and a height of 6 feet.
Therefore,
area of the two triangles = 2 (1 / 2 × 6 × 6) = 36 ft²
The other two triangles have a base of 12 ft and a height of 6 ft.
area of the other triangle = 2(1 / 2 × 12 × 6) = 72 ft²
Hence,
total area the paint will cover = 72 + 36 + 72 + 144 = 324 ft² = 36 yard²
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Solve the quadratic equation X^2+5x+6=0 using the completing the square method. Be sure to explain each step.
To complete the perfect trinomial, we add (5/2)² to the given equation and get:
[tex]x^2+5x+(\frac{5}{2})^2+6=(\frac{5}{2})^2.[/tex]Subtracting 6 we get:
[tex]x^2+5x+(\frac{5}{2})^2=\frac{25}{4}-6=\frac{1}{4}.[/tex]Therefore:
[tex](x+\frac{5}{2})^2=\frac{1}{4}.[/tex]Finally, we get:
[tex]\begin{gathered} x+\frac{5}{2}=\pm\sqrt{\frac{1}{4}}, \\ x=\pm\frac{1}{2}-\frac{5}{2}. \end{gathered}[/tex]Answer: [tex]\begin{gathered} x_=-3,\text{ or x=-2.} \\ \end{gathered}[/tex]what happens to a circle's circumference when the radius is doubled
ANSWER
The circumference doubles
EXPLANATION
Let the radius of the circle be r and the circumference be C.
The circumference of a circle is given as:
[tex]C=2\pi r[/tex]If the radius is doubled, the radius becomes:
[tex]2r[/tex]The circumference now becomes:
[tex]\begin{gathered} C^{\prime}=2\pi\cdot(2r) \\ C^{\prime}=2\cdot(2\pi\cdot r) \\ C^{\prime}=2\cdot(2\pi r) \\ C^{\prime}=2C \end{gathered}[/tex]Therefore, the circumference doubles when the radius is doubled.
write the partial fraction decomposition of the rational expression 3x-5/x²-4x-32
Denominator has been factorized on the right.
Now we need to write this fraction as a sum of two fraction.
[tex]\frac{3x-5}{(x+4)(x-8)}=\frac{A}{(x+4)}+\frac{B}{(x-8)}=\frac{A(x+4)+B(x-8)}{(x+4)(x-8)}[/tex][tex]A(x+4)+B(x-8)=3x-5\text{ at this stage we will find A B constants}[/tex]when x = 8 we have following
[tex]A(8+4)+B(8-8)=3\cdot8-5\rightarrow12A+0=19\rightarrow A=\frac{19}{12}\approx1.58[/tex]Similarly when x =-4 A = 17/12 these are the constants
how would I answer and what would be the answer?
Answer: (-1, 0)
The interval of decreasing refers to the interval of x-values where the graph is decreasing or going down.
If we look at the graph:
We can see that the graph starts to decrease or "go down" at values x = -1 and x=0. With this, we can conclude that the interval of decrease for the given graph is (-1, 0)
A straight highway is 100 miles long, and each mile is marked by a milepostnumbered from 0 to 100. A rest area is going to be built along the highwayexactly 6 miles away from milepost 57. If m is the milepost number of therest area, which of the following equations represents the possible locationsfor the rest area?O A. \m-6| = 57OB. 157+ ml = 6O C. Im + 61 = 57OD. 157-ml = 6SUBMIT
Given:
Few data is given
Required:
To calculate which option is correct
Explanation:
157+ ml = 6 means a rest area built along the highway exactly 6 miles away from milepost 57.Therefore this is the correct answer
Required answer:
Option D
Need help with problems
You can write the relation between distance and time, as follow:
y = kx
where y is the distance, x is the time and k is the constant of proportionality.
k can be obtained with the given information, as follow:
k = 90/30 = 3
Then, the equation of the relationship is:
y = 3x,
for a time of 10 seconds, the distance traveled is:
y = 3(10) = 30
Hence, the answer is:
y = 3x , 30 feet
Write a quadratic function in standard form whose graph passes through (-5,0),(0,-8),(4,0)
[tex]y = -1.25 x^{2}+ 5[/tex] is the needed quadratic function in standard form.
What is a quadratic equation?A quadratic equation is one with a single degree 2-variable and has the general form [tex]a x^{2} + bx + c = 0.[/tex] a, b, and c is the constant value, and x consists of a variable.
The quadratic equation's x-intercepts are (-5, 0). That indicated that the quadratic equation's two elements are (x + 5) and (x -0).
f(x) = a (x + 5) (x - 0) (x - 0)
= ax+5a
f(x) = [tex]ax^{2} +5x[/tex]
The quadratic equation's graph goes through (4, 0). Therefore, we must change equation 1 to read x = 4 and f(x) = 0.
0 = a × 4² + (5 × 4)
0 = a × 16 +20
a = [tex]\frac{-20}{16}[/tex]
=-1.25
The quadratic equation is known to have the form ax² + bx + c = 0.
f(x) = -1.25[tex]x^{2}[/tex] + 5x
Consider y= F(x)
∴ The required quadratic equation of function in the standard form is Y = -1.25 x² + 5x.
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Red Lobster charges $30 per person plus a $100 set up fee to cater an event. Olive Garden charges $25 per person plus a $200 set up fee. PART A: How many guests, g, would both restaurants cost the SAME
There would be 20 guests for the restaurants to cost the same
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the number of guests?From the question, we have the following parameters:
Red Lobster
Rate per person = $30
Set up fee = $100
Olive Garden
Rate per person = $25
Set up fee = $200
So, the equations of the restaurants are
Red Lobster = 30g + 100
Olive Garden = 25g + 200
Where the number of guests is g
When the restaurants cost the same amount, we have
Red Lobster = Olive Garden
Substitute the known values in the above equation
So, we have
30g + 100 = 25g +200
Evaluate the like terms
5g = 100
Divide by 5
g = 20
Hence, the number of guests is 20
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continued - calculating gross payRemember, this is money round to the nearest Penny/hundredths place. Take OT rate as 1.5 times the regular pay rate.Take the regular working hours per week as 40 hours.
Given Data:
Total working hours is = 51 hours.
Pay rate=$8.45.
OT rate=1.5 times the regular pay rate.
Regular working hours is 40 hours.
Regular pay can be determined as,
[tex]RP=40\text{ hours}\times8.45\text{ USD=338 USD}[/tex]Thus, the regular pay is $338.
The OT rate can be determined as,
[tex]\begin{gathered} OT=1.5\times8.45\text{ USD} \\ =12.675\text{ USD} \end{gathered}[/tex]Thus, the overtime rate is $ 12.68.
The overtime pay can be determined as,
[tex]\begin{gathered} OT\text{ Pay=(51-40) hours}\times12.675\text{ USD} \\ =139.425\text{ USD} \end{gathered}[/tex]Thus, the overtime pay is $139.43.
The gross pay can be determined as,
[tex]\begin{gathered} GP=RP+OT\text{ Pay} \\ =338\text{ USD+139.425 USD} \\ =447.425\text{ USD} \end{gathered}[/tex]Thus, the gross pay is $ 447.425.
nothing changes with tangent
hello
to solve this question, we have to use trigonometric ratios and in this case, it was specified to use tangent
from the image above, we can see that we have the value of angle and opposite and we need to look for adjacent
trigonometric ratio is given as SOH CAH TOA
[tex]\begin{gathered} \text{soh}=\text{sin}\theta=\frac{opposite}{\text{hypothenus}} \\ \text{cah}=\cos \theta=\frac{adjacent}{hypothenus} \\ \text{toa}=\tan \theta=\frac{opposite}{adjacent} \end{gathered}[/tex]now, let's use the formula of tangent to solve this problem
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \text{opposite}=42 \\ \theta=64^0 \\ \text{adjacent}=x \\ \tan 64=\frac{42}{x} \\ x=\frac{42}{\tan 64} \\ x=20.48 \end{gathered}[/tex]from the calculations above, the value of x is equal to 20.48
Make x the subject of h = 4(x + 3y) + 2
Answer:
x=\frac{1}{4}(h-12y-2)x=4
Step-by-step explanation:x=\frac{1}{4}(h-12y-2)x=
4
1
(h−12y−2)
Step-by-step explanation:
We are given the equation h=4(x+3y)+2h=4(x+3y)+2 .
Simplifying for x, we get,
h=4(x+3y)+2h=4(x+3y)+2
i.e. h=4x+12y+2h=4x+12y+2
i.e. 4x=h-12y-24x=h−12y−2
i.e. x=\frac{1}{4}(h-12y-2)x=
4
1
(h−12y−2)
Thus, the equation for x is x=\frac{1}{4}(h-12y-2)x=
4
1
calculate the perimeter of kite ABCD where AB = 29 cm and CD = 47 cm
Answer:
152 cm
Step-by-step explanation:
Perimeter of kite= 2(a+b)
P= 2(AB+CD) = 2(29+47) = 2 *(76) = 152 cm.
If something remains unclear, be free to ask questions!
Simplify the expression 2^5 +5^4
Therefore
[tex]2^5+5^4=657[/tex]Is the point (-255,76) on the line shown below
Answer:
yes it's is shown in the diagram below and prosperity more than your expectation for me too anymore I just
graph the system below2x-3y=-183x+y=-5
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of equations:
[tex]\begin{gathered} 2x-3y=-18 \\ \\ 3x+y=-5 \end{gathered}[/tex]To graph, we calculate the intercepts in each equation to then draw the straight line corresponding to each equation, like this:
[tex]\begin{gathered} \text{ For }2x-3y=-18 \\ \\ \text{The x-intercept} \\ \\ \:2x-3\cdot 0=-18 \\ \\ x=-9\rightarrow(-9,0) \\ \\ \text{The y -intercept} \\ \\ 2\cdot0-3y=-18 \\ \\ y=6\rightarrow(0,6) \\ \\ \\ \text{For }3x+y=-5 \\ \\ \text{The x-intercept} \\ \\ 3x+0=-5 \\ \\ x=-\frac{5}{3}\rightarrow\left(-\frac{3}{5},0\right) \\ \\ \text{The y- intercept} \\ \\ \:3\cdot 0+y=-5\: \\ \\ y=-5\rightarrow(0,-5) \end{gathered}[/tex]Now we graph:
Rachel wants to buy the same number of gift bags and bows. Gift bags are sold in packs of 6. Bows are sold in packs of 9. What is the least number of gift bags and bows that Racheal can buy?
The question wants the "lowest common multiple" of 6 and 9, so first, lets find some of the miltiples of 6 and 9:
[tex]\text{Multiple}(6)=\mleft\lbrace6,12,18,24,30,36,42,49,\ldots\mright\rbrace[/tex][tex]\text{Multiple}(9)=\mleft\lbrace9,18,27,36,45,54,\ldots\mright\rbrace[/tex]We can see that 18 is a commom multiple of 6 and 9, and is also the smallest, so the lowest common multiple of 6 and 9 is 18. So the least number of gift bags and bows that Rachel can buy is 18.
Let x be a continuous random variable that has a normal distribution with μ = 48 and 6 = 8. Assuming -
≤0.05, find the
probability that the sample mean, x, for a random sample of 16 taken from this population will be between 49.60 and 52.20.
Round your answer to four decimal places.
The probability of the sample mean is 0.2008.
What is probability?
Probability is the quality or state of being probable the extent to which something is likely to happen or be the case.
Sol-Let x be a continuous random variable that has a normal distribution with
μ=48 and σ=8
Thus,
X~N(48,8^2/16)
The standardized value of x is obtained by :
Z= X-48/√8^2/16~N(0,1)
The probability that the sample mean x for a random sample of 16 taken from this population will be between 49.62 and 52.80 can be obtained as:
P(49.62<x<52.80)
P=(49.62-48/√8^2/16<x-48/√8^2/16<52.80-48/√8^2/16)
=P(0.81<Z<2.4)
=P(Z<2.4)-P(Z<0.81)
=0.9918-0.7910
=0.2008
There for the probability is 0.2008.
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18. A rectangular table cloth has a width of 3 yards 1 foot and a length of 4 yards. Part A. Debbie says that the width could also be written as 4 feet. Explain wether you agree or disagree with Debbie. Part B. The cost of the fabric used to make the tablecloth is $0.25 per square foot. Explain how to find the cost of the fabric needed to make the table cloth.
A)
In order to check this sentence, we need to convert the value from foot to yard.
Knowing that 1 yard is equal 3 feet, we have that:
[tex]3\text{ yards 1 foot}=3\cdot3\text{ feet + 1 foot}=9\text{ feet + 1 feet}=10\text{ feet}[/tex]So Debbie's affirmation is incorrect, therefore we disagree.
B)
First we need to calculate the area of the table cloth.
Converting the length to foot, we have:
[tex]4\text{ yards}=4\cdot3\text{ feet}=12\text{ feet}[/tex]Now, calculating the area (which is the product of the length and the width), we have:
[tex]\text{Area}=10\cdot12=120\text{ ft}^2[/tex]If each square foot is $0.25, we just need to multiply the area by the cost of one square foot in order to find the cost of the fabric for the table cloth:
[tex]\text{Cost}=120\cdot0.25=30[/tex]So the cost is $30.
Arrange the quantities in order from smallest to largest.
2.6 km, 109,000 mm, 41.7 hm
The order of the values using the basic unit of meters from smallest to largest. is: 109000 mm < 2.6 km < 41.7 hm
What are the units of measurement of distance or length?
Distance is the gap between any two points under consideration.
The basic unit for measuring distance is the meter.
There are larger as well as smaller units for measuring length or distance which are based on the unit of meter.
The units are as follows:
millimeter, mm = 0.001 m
centimeter, cm = 0.01 m
decimeters, dm = 0.1 m
meter, m = 1 m
kilometer, km = 1000 m
hectometer, hm = 100 m
Now to compare the given quantities making the units same as two quantities can only be compared only when there units are same :
Considering the given values;
2.6 km = 2600 m
109,000 mm = 109 m
41.7 hm = 4170 m
Therefore, after comparison arranging the quantities in order from smallest to largest is 109000 mm < 2.6 km < 41.7 hm
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help ................
Percentage of a number
Find a number which
its a 100% percentage
henW
When 232 is 290%
Then find
X = (100%/290)• 232
Divide 232/29 = 10% = 8 exactly
Now multiply by 10 = 10• 8 = 80
Then 100% = 80
Convert 103 degrees Fahrenheit to degrees Celsius. (Write your answer in fraction format)
to convert Fahrenheit to Celcius we have to apply the next formula:
C°= (F°-32) x 5/9
Replacing:
C = (103-32)x 5/9
C = 71 x 5/9
C = (71 x5)/9 = 355/9
Ms. Banks divides 18 basketballs evenly among 3 bags. For class, she takes 2 basketballs from each bag. How many basketballs are left in one of the bags?
4 basketballs
Explanation
Step 1
Ms. Banks divides 18 basketballs evenly among 3 bag
divide the 18 basketballs by 3 bags
[tex]\frac{18\text{ basketball}}{3\text{ bags}}=6\text{ basketaball per bag}[/tex]Step 2
now, she takes 2 from each bag, so
[tex]\begin{gathered} \text{total basketball per bag=6-2} \\ \text{total basketball per bag =4} \end{gathered}[/tex]Hence, the answer is 4 basketballs.
I hope this helps you
Mr. Lombardo took his two children to a water park. He used the coupon shown below to buy one adult ticket. The price of admission for all three family members was $76. What was the price of each child's ticket? WORLD OF WATER | This coupon is good | for one adult ticket | to World of Water | at a price of $28.00. YOU SAVE $4.00! Use the math you already know to solve the problem. a. What ticket price do you know? How much is that ticket? Explain.
Data Input
1 Adult + 2 children
The price for all three family members
$76
Procedure
Adult ticket = $28
1 Adult + 2 children = $76
2 children = 76 - 1 adult
2 children = 76 - 28
2 children = 48
children = 48/2
children = 24
For each graph below, state whether it represents a function.
I need help with graph 2
Answer: No
Step-by-step explanation:
The graph fails the vertical line test, and thus the graph does not represent a function.