We want to calculate the amount needed as an initial investment to have 120000 after 30 years.
Recall that the formula of annual compounding is given by the formula
[tex]S\text{ =}P\text{ \lparen1+r\rparen}^t[/tex]where P is the principal, r is the interest rate and t is the time in years. When compounded continously the formula is
[tex]S=Pe^{rt}[/tex]where the variables have the same meaning. In both cases we want to find P sucht that
[tex]S=120000[/tex]when t=30 and r is the interest rate that we are given.
So we have the following equation in the first case
[tex]120000=P\text{ \lparen1+}\frac{6}{100})^{30}[/tex]so if we divide both sides by (1+6/100)^30 we get
[tex]P=\frac{120000}{(1+\frac{6}{100})^{30}}\approx20893.22[/tex]so for Plan A 20893.22 is needed to have 120000 after 30 years.
now, we want to do the same with the second plan. We have
[tex]120000=Pe^{\frac{5.8}{100}30}[/tex]so we divide both sides by exp(5.8*30/100). So we get
[tex]P=\frac{120000}{e^{\frac{5.8}{100}\cdot30}}\approx21062.45[/tex]so for Plan B 21062.45 is needed to have 120000 after 30 years
What is the missing length?Area of shaded region = 184 mm^2.p = ___ milimeters.
The formula to calculate the area of a triangle is
[tex]A=\frac{p\cdot b}{2}[/tex]in our case we have p is the height of the triangle, and b is the base of the triangle
A=184 mm^2
b=16mm
we substitute the data given
[tex]184=\frac{p\cdot16}{2}[/tex]then we isolate the p
[tex]p=\frac{184\cdot2}{16}[/tex][tex]p=23[/tex]Which list shows the numbers below in order from least to greatest?5.78, -5.9, 58%, 23-5.9, 23. 5.78, 58%2.-5.9, 58%, 5.78-5.9, 23. 58%, 5.7858%, 23. 5.78, -5,9o
The numbers in the alternatives are the same, so we have to see which is the lowest to start with.
There are two negative ones: -5.9 and -23/4. Dividing the second one we have:
[tex]-\frac{23}{4}=-5.75[/tex]We can see that -5.9 is lower than -5.75. So we have only two alternatives left.
58% is equivalent of 58/100, so:
[tex]\frac{58}{100}=0.58[/tex]So 58% = 0.58, which is lower than 5.78.
So we have the order, from least to greatest:
-5.9, -23/4, 58%, 5.78.
This corresponds to the third alternative.
The profit in dollars of running an assembly line that produces custom uniforms each day is given by P(t)=−40t2+960t−4,000
where t represents the number of hours the line is in operation. Determine the number of hours the assembly line should run in order to make a profit of $1,760 per day.
Answer:
12
Step-by-step explanation:
[tex]-40t^2+960t-4000=1760 \\ \\ -t^2+24t-100=44 \\ \\ t^2-24t+144=0 \\ \\ (t-12)^2=0 \\ \\ t=12[/tex]
Directions - Find the x and y-intercepts for each Standard Form equation. Write your answer as an ordered pair.2x + 4y = 8x - intercept =y - intercept =
We have the following:
[tex]2x+4y=8[/tex]solving for y:
[tex]\begin{gathered} \frac{2}{4}x+\frac{4}{4}y=\frac{8}{4} \\ \frac{1}{2}x+y=2 \\ y=-\frac{1}{2}x+2 \end{gathered}[/tex]now, x- intercept is when y is equal to 0, therefore
[tex]\begin{gathered} 0=-\frac{1}{2}x+2 \\ \frac{1}{2}x=2 \\ x=2\cdot2 \\ x=4 \end{gathered}[/tex]y-intercept is when x is equal to 0, therefore
[tex]\begin{gathered} y=-\frac{1}{2}\cdot0+2 \\ y=2 \end{gathered}[/tex]The answer is:
x - intercept = (4, 0)
y - intercept = (0, 2)
The number of bacteria in a culture is given by the function n(t)=920e^.2twhere t is measured in hours.(a) What is the relative rate of growth of this bacterium population?(b) What is the initial population of the culture (at t=0)?(c) How many bacteria will the culture contain at time t=5?
Answer:
a. Relative rate of growth = 0.2
b. Initial population: 920
c. 2501
Explanation:
If we have an exponential function of the form
[tex]y=A_0e^{kt}[/tex]Then
A0 = inital amount
k = relative rate of growth
t = time
Now in our case we have
[tex]n(t)=920e^{0.2t}[/tex]Therefore,
Inital population = 920
Relative rate of growth = 0.2
Now at t = 5, the above formula gives
[tex]n(5)=920e^{0.2*5}[/tex]
which evaluates to give
[tex]n(5)=2500.8[/tex]which rounded to the nearest whole number is
[tex]\boxed{n(5)=2501.}[/tex]√2 + √5 + √5 =A. √2 + 3√5 or B. √2 + 2√5Which one?
You have the following expression:
√2 + √5 + √5
In order to simplify the given expressions, you consider the terms with square roots as factor that you can simplify in the same way of the simplification in algebra. That is, if you have √5 + √5, you can sum the coefficients of these terms. Thus, what you have is √5 + √5 = 2√5.
Then, for the given expression you obtain:
√2 + √5 + √5 = √2 + 2√5
Three friends go on a road trip from Phoenix, AZ toLas Vegas, NV, a distance of 286 miles. The car theyare driving gets 33 miles per gallon. If the price ofgasoline averages $3.86/gallon, how much willeach student have to pay for the trip
First, let's find how many gallons are needed:
[tex]\begin{gathered} \frac{286miles}{33\text{ }\frac{miles}{gallon}} \\ 8.7gallons \end{gathered}[/tex]If the price of one gallon is $3.86, then they will have to pay:
[tex]\begin{gathered} 3.86*8.7 \\ 33.58 \end{gathered}[/tex]The price they will have to pay is $33.58.
Dividing the price by 3 (each student):
[tex]\begin{gathered} \frac{33.58}{3} \\ 11.2 \end{gathered}[/tex]Answer: Each student will have to pay $11.20.
can someone help with the first problem and show me on a graph
Solution:
The parent graph given was transformed by first shifting it by 3 units to the right, and then shifting 2 units up.
This is shown below:
Therefore, the transformation is a translation of 3 units right and then 2 units up.
answer the question below show work write the x and y intercepts
ANSWER:
STEP-BY-STEP EXPLANATION:
We have the following system of inequalities:
[tex]\begin{gathered} f(x)>|x| \\ \: g(x)<-\frac{1}{2}x+1 \end{gathered}[/tex]This system can only be solved graphically, therefore
for f(x):
The x and y intercept is (0, 0)
for g(x)
The x-intercept is (2, 0) and y-intercept is (0, 1)
The solution to the system will be the area where the shadows of each inequality overlap
Just like that:
how do you do 0.52 divided by 2?
Given the Division:
[tex]0.52\div2[/tex]You can identify that, in this case, the Dividend is:
[tex]0.52[/tex]And the Divisor is:
[tex]2[/tex]Then, you can rewrite it in this form:
Notice that the Dividend is a Decimal Number. Then, you can follow these steps to solve the Division:
1. Take the first digit of the Dividend. Since it is 0, any number multiplied by zero is zero, you can place 0 at the top. Place 0 under the first digit of the Dividend too.
2. Subtract the numbers:
3. Bring down the next digit. Since it is the first digit after the Decimal Point, you need to write a Decimal Point at the top:
4. Divide the new number by the Divisor.
5. Find a number whose multiplication with the Divisor 2 gives you 5 as the result or a number closer to 5. These would be 2.
6. Place the number 2 at the top and multiply the divisor by it.
7. Place the result below the number 5 and subtract them.
8. Apply the same procedures with the other digits.
Then:
Hence, the answer is:
[tex]=0.26[/tex]You use a garden hose to fill a wading pool. If the water level rises 11 centimeters every 3 minutes and you record the data point of (9,y), what is the value of y? Use slope to justify your answer.
The value of y is 33 cm.
Given:
You use a garden hose to fill a wading pool. If the water level rises 11 centimeters every 3 minutes and you record the data point of (9,y).
points are (3, 11) and (9, y)
3 minutes = 11 cm
divide by 3
1 minute = 11/3 cm
In 9 minutes, the rise will be ,
= 9 * 11/3
= 3*11
y = 33 cm
slope between (3,11) and (9,33)
m = 33 - 11 / 9 - 3
= 22/6
m = 11/3(this is justification).
Therefore the value of y is 33 cm.
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A bank loaned out $7,500, part of it at the rate of 11% annual interest, and the rest at 14% annual
interest. The total interest earned for both loans was $1,020.00. How much was loaned at each rate?
The 11% annual rate amount is $1000 and 14% annual rate amount is $6500 for total interest $1020.
What is interest?
The financial fee for borrowing money is called interest, and it is typically stated as a percentage, such as an annual percentage rate (APR). For the use of their money, lenders may earn interest, and borrowers may pay interest. For borrowing money or other assets, interest is a cost that must be paid. Principal is the amount borrowed, and interest is calculated as a percentage of principal over a specified period of time.
Here the principal P = $7500
Let us take 11% annual rate part amount as x.
Then remaining is 7500-x.
Now the interest I = PNR/100
=>1020= (x×11×1)/100+((7500-x)×14×1)/100
=> 1020×100=11x+105000-14x
=>102000=105000-3x
=>3x=105000-102000
=>3x=3000
=>x=1000
Now 7500-1000=6500.
Hence $1000 for 11% annual rate and $6500 for 14% annual rate.
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The worktop is to be covered with square tiles each measuring 4cm by 4cm. How many tiles are needed to cover the worktop.
Answer now.
Answer:
The numbers of tiles is 1900.
Step-by-step explanation:
Firstly, the worktop is 3.04 m^2 or if using conversion that 1m is 100cm, it is 304 cm^2.
Secondly, the surface are of worktop = number of tiles*(side^2).
304 cm^2 = tiles*(3.04cm^2)
Thirdly, solving how many tiles there are, 304 cm^2 / 3.02cm^2
Mortgages (47-49)Eli is buying a townhouse that costs $276,650. He has $28,000 in savings and earns $4,475 a month. Eli would liketo spend no more than 30% of his income on his mortgage payment. Which loan option would give Eli the lowestmonthly payment? Show your work.A. 30 year FHA, 3.5% down and a fixed rate of 6.5%B. 30 year fixed, 5% down at a fixed rate of 6.25%C. 30 year fixed, 6.5% down and a fixed rate of 5.75%D. 30 year fixed, 10% down at a fixed rate of 5%
Cost C = $276,650
Initial quote = $28000
If Eli spends 30% of 4,475 = $1342.5 monthly
Then now calculate
3.5% down of $276,650 = $9682.75
Substract $28000- $9682.75 = 18317.25
Now find ,fixed rates
For 6.5% , interest is.
She have to pay a quote of (276,650- 9682.75)/12•30
. = $741.57
For 5% down of $276,650 = 13832.5
Eli have now $28000- $13832.5 = 14167.5
She have to pay a quote of (276,650- 13832)/30•12 = $262818/360
. = $730
Interest fixed rate 6.25%
Then find 730• ( 1+ 6.25/100)^ 30 = 4500 in 30 years
Now option C)
6.5% down = $276,650x 6.5/100 = $17982.25
Eli have now $28000 - 17982.25 = 10017.75
She have to pay a quote of (276,650 - 17982)/30•12
. = $718.52
Then find 718.52•( 1+ 5.75/100)^30 = 3844.6. in 30 years
Option D)
10% down = $276,650x10/100 = $27,665
Eli have now $28000- 27,665 = $335
She have to pay a quote of (276,650 - 27665)/30•12 =
. = $691.625
Then find now 691.625•(1+ 5/100)^30 = $2989.16 in 30 years
So ,in conclusion we have to choose the minor value of quote. In this case is
ANSWER IS
OPTION D) $2989,16
what is (15+ -7) (-4)
Answer:
-32
Explanation:
Given the expression:
[tex]\mleft(15+-7\mright)(-4)[/tex]We can rewrite this as:
[tex]\begin{gathered} (15-7)(-4) \\ =8\times-4 \\ =-32 \end{gathered}[/tex]The property taxes on a house were $1140. What was the tax rate if the house was valued at $190,000? Follow the problem-solvingprocess and round your answer to the nearest hundredth of a percent, if necessary.
Okay, here we have this:
Considering the provided information we obtain that:
$1140 is x%
$190,000 is 100%
So, here we have the following proportion:
[tex]\frac{190000}{1140}=\frac{100}{x}[/tex]Now, let's solve for x:
[tex]\begin{gathered} x=\frac{1140\cdot100}{190000} \\ x=\frac{114000}{190000} \\ x=\frac{3}{5} \\ x=0.6 \end{gathered}[/tex]Finally we obtain that the tax rate was 0.6%.
(-3,-5) (-6,10)Find the slope
Weare asked to find the slope of the segment that joins the points (-3, -5) and (-6, 10) on the plane.
We used the formula for the slope:
slope = (y2 - y1) / (x2 - x1)
which in our case gives:
slope = (10 - -5) / (-6 - -3) = 15 / -3 = -5
The slope is -5.
which relation is a function A.(2,3),(1,5),(2,7)B.(-1,5),(-2,6),(-3,7)C.(11,9),(11,5),(9,3)D.(3,8),(0,8),(3,-2)
A function can only have one out put value (y) for every input value (x).
A. (2,3) (2,7)
input value 2 has 2 different output values (3 and 7)
It's not a function.
Same case for C and D.
Correct option . B-
Determine whethersecx cotx-cosxsin(-x) cot²xand cotx are equivalent. Justify your answer.
we have the expression
[tex]\frac{secxcot^2x-cosx}{sin(-x)cot^2x}[/tex]Rewrite the given expression
Remember that
sin(-x)=-sin(x)
[tex]\frac{\frac{1}{cosx}\frac{cos^2x}{sin^2x}-cosx}{-sinx\frac{cos^{2}x}{s\imaginaryI n^{2}x}}[/tex]Simplify the expression
[tex]\begin{gathered} \frac{\frac{cosx}{s\imaginaryI n^2x}-cosx}{-\frac{cos^2x}{s\imaginaryI nx}} \\ \\ \frac{\frac{cosx-sin^2xcosx}{sin^2x}}{-\frac{cos^2x}{sinx}} \\ \\ \frac{cosx-s\imaginaryI n^{2}xcosx}{s\imaginaryI n^{2}x}\colon-\frac{cos^{2}x}{s\imaginaryI nx} \\ \\ \frac{sinx(cosx-sin^2xcosx)}{sin^2x(cos^2x)} \\ \\ \frac{(cosx-sin^2xcosx)}{sin^x(cos^2x)} \\ \\ \frac{cosx(1-s\imaginaryI n^2)}{s\imaginaryI nx(cos^2x)} \\ \\ \frac{(1-s\imaginaryI n^2)}{s\imaginaryI nx(cosx)} \\ \\ \frac{cos^2x}{s\imaginaryI nx(cosx)} \\ \\ \frac{cosx}{sinx} \\ \\ cotx \end{gathered}[/tex]therefore
The answer is
yes, the expression is equivalent to cot(x)Find three consecutive odd Integers such that the sum of the largest and twice the smallest is 25.x represents the smallest integer, then which equation could be used to solve the problem?
ANSWER
7, 9, 11
EXPLANATION
We want to find three consecutive odd numbers.
Let the smallest number be x.
Then, the next odd number is (x + 2).
The last odd number is (x + 4).
The sum of the largest odd number and twice the smallest number is 25:
(x + 4) + 2x = 25
=> x + 4 + 2x = 25
3x + 4 = 25
3x = 25 - 4
3x = 21
x = 21 / 3
x = 7
Therefore, the three consecutive numbers are:
7
(7 + 2) = 9
(7 + 4) = 11
They are 7, 9, 11
10. Use the Distributive Property to solve the equation 3(x - 6) + 6= 5x - 6.
3(x-6)+6 = 5x-6
Apply distributive property:
3x-18+6= 5x-6
Combine like terms
3x-12 = 5x-6
Move x terms to the right:
3x-5x = -6+12
-2x = 6
divide both sides by -2
x=-3
Assignment: 5.4 Bellwork Wednesday 2/03 Problem iD: PRABRBYC Rose wants to construct a fence around her garden. The garden is circular in shape with a diameter of 9 ft. What is the length of fencing material she will need to fence around the outside her garden?
The garden is described as having a circular shape. The diameter is 9 feet. The length of fencing material needed to fence around the outside of her garden refers to the perimeter or the circumference of the circular garden.
The circumference of a circle is given as;
[tex]\begin{gathered} \text{Cir}=2\pi r \\ r=\frac{\text{diameter}}{2} \\ r=4.5 \\ \text{Cir}=2\times3.14\times4.5 \\ \text{Cir}=28.26 \end{gathered}[/tex]Therefore, Rose would need 28.26 feet of fencing material
Hello! Need a little help on part B. Thank you!
we have the system of equations
[tex]\begin{gathered} f(x)=\log_2x+2 \\ g(x)=\log_2x^3-6 \end{gathered}[/tex]Equate the functions f(x) and g(x)
[tex]\log_2x+2=\log_2x^3-6[/tex]Apply property of logarithms
[tex]\begin{gathered} \operatorname{\log}_2x+2=3\operatorname{\log}_2x-6 \\ 3\operatorname{\log}_2x-\operatorname{\log}_2x=2+6 \\ 2\operatorname{\log}_2x=8 \\ \operatorname{\log}_2x=4 \end{gathered}[/tex]Apply the definition of logarithm
[tex]\begin{gathered} 2^4=x \\ x=16 \end{gathered}[/tex]John has 4 different flags that he wants to hang on the wall. How many different wayscan the flags be arranged in a row?
It is given that,
John has 4 different flags that he wants to hang on the wall.
To find the number of different ways can the flags be arranged in a row:
There are 4! ways can the flags be arranged in a row.
That is,
[tex]\begin{gathered} 4!=4\times3\times2\times1 \\ =24 \end{gathered}[/tex]Hence, the answer is 24 different ways.
Can you help me on what 6x equals? (Grade 10, angles)
First we need to find the value of x, we can use the fact that the sum of the interior angles of a quadrilateral is 360°
[tex]6x+6x+9x+9x=360[/tex][tex]\begin{gathered} 30x=360 \\ \end{gathered}[/tex]then we isolate the x
[tex]x=\frac{360}{30}[/tex][tex]x=12[/tex]then for 9x and 6x, we substitute the value of x=12
[tex]6(12)=72[/tex][tex]9(12)=108^{}[/tex]if x =12, therefore, the angle 6x=72° and the 9x=108°
Calculate the given percent of each value.of 2 = 1.84
we have that
2 represents the 100%
Applying proportion, find out how much percentage represents 1.84
100/2=x/1.84
solve for x
x=100*1.84/2
x=92%
the answer is 92%A realtor wanted to determine if there was a relationship between the size (in 100 square feet) of a new custom-built home and the price (in thousands of dollars) of the home.
Size, x Price, y
26 235
27 273
41 387
29 253
33 295
34 335
36 395
45 475
22 203
a) Determine the Person Correlation Coefficient.
b) Test whether there is a relation between size and price.
c) Draw the scatter diagram
d) Determine the Least Square line.
e) If a new custom-built home is of a size 3700 square feet what would be its price.
¬¬
The graphs , solutions and table are attached below and check out the calculation part just by scrolling down.
What is statistics ?In the field of applied mathematics known as statistics, gathering, describing, analyzing, and drawing conclusions from numerical data are important tasks. Probability theory, linear algebra, and differential and integral calculus are the main mathematical foundations of statistics.
Calculationsee the graphs and table attached below
a ) The cluster (points) shows upward direction and nearly to linear form. So it is positive Correlation.)
b ) calculation part for this part has been attached in pictures below since it was not possible to write here .
the regression line of y on x is =
Y = 11.5355X - 58.7667
c ) r^2 = 58313.22 / 62507.5556 = 0.9328
It is high correlation, So the regression equation is good fit to the given data. 93% of the total variation in y occurs because of the variation in their x.
d ) H0: Slope of Regression Coefficient is Zero
H1: Slope of Regression coefficient is not Zero.
calculation part in pictures attached .
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I need help with this Question 5 and Question 6
5) The rate of change from 2000 to 2012 is 0.80
6) The rate of change from 2012 to 2015 is 0.32
From the question, we have
5) Rate of change from 2000 to 2012 = (3.64-2.02)/2.02
=1.62/2.02
=0.80
6) Rate of change from 2012 to 2015 = (3.64-2.45)/3.64
=1.19/3.64
=0.32
Subtraction:
Subtraction represents the operation of removing objects from a collection. The minus sign signifies subtraction −. For example, there are nine oranges arranged as a stack (as shown in the above figure), out of which four oranges are transferred to a basket, then there will be 9 – 4 oranges left in the stack, i.e. five oranges. Therefore, the difference between 9 and 4 is 5, i.e., 9 − 4 = 5. Subtraction is not only applied to natural numbers but also can be incorporated for different types of numbers.
The letter "-" stands for subtraction. Minuend, subtrahend, and difference are the three numerical components that make up the subtraction operation. A minuend is the first number in a subtraction process and is the number from which we subtract another integer in a subtraction phrase.
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Consider the following table with information about a sample of students from Phoenix HighSchool and where they live. If a person is randomly selected determine the following probability:P(Female or Suwanee).SnellvilleSuwaneeTotalFemaleValeTotal102030StoneMountain121426S16243050803023B.c.D. TOA.8040
The total number of students are T = 80.
Determine the number of students who are Female od Suwanee.
[tex]10+12+8+16=46[/tex]The probability for slected person is Student or Suwanee is,
[tex]\begin{gathered} P\text{ (Female or Suwanee)=}\frac{46}{80} \\ =\frac{23\cdot2}{40\cdot2} \\ =\frac{23}{40} \end{gathered}[/tex]So answer is 23/40.
Option A is correct.
on a family trip mr perers travels 130 miles in two hours at this rate how many miles will he travel in 30 minutes?
Answer:
32.5
Step-by-step explanation:
130 miles divided by 120 minutes (2 hours) then take that number and multiply by 30 minutes