To calculate the balance on the account after 5 years you have to calculate the simple interest using the formula:
[tex]A=P(1-rt)[/tex]A= total accured amount
P= principal amount
r= interest rate expressed in decimals
t=time
For
P=$5250
r=0.035
t=5years
The balance on the account will be:
[tex]\begin{gathered} A=5250(1+0.035\cdot5) \\ A=6168.75 \end{gathered}[/tex]At the end of the 5 years there will be $6168.75
A police car traveling south toward Sioux Falls, Iowa, at 160km/h pursues a truck east away from Sioux Falls at 140 km/h. At time t=0, the police car is 60km north and the truck is 50km east of Sioux Falls. Calculate the rate at which the distance between the vehicles is changing at t=10 minutes, (Use decimal notation. Give your answer to three decimal places)
The rate of change of the distance between the police car and the truck after 10 minutes is approximately 193.66 m/s
What is a rate of change of a function?The rate of change of a function is the rate at which the output of the function is changing with regards to the input.
The velocity of the police car = 160 km/h south
The velocity of the truck = 140 km/h east
Distance of the police car from Sioux Falls = 60 km north
Distance of the truck from Sioux Falls = 50 km east
Required;
The rate at which the distance between the vehicles is changing at t = 10 minutes
Solution;
Let d represent the distance between the vehicles, we have;
d² = x² + y²
Where;
x = The distance of the truck from Sioux falls
y = The distance of the police car from Sioux Falls
Which gives;
[tex] \displaystyle{ \frac{d}{dt} d^2= \frac{d}{dt}(x^{2}) +\frac{d}{dt} (y^{2}) }[/tex]
Which gives;
[tex] \displaystyle{ 2 \cdot d \cdot \frac{d}{dt} d=2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }[/tex]
After 10 minutes, we have;
y = 60 - (10/60)×160 = 100/3
x = 50 + (10/60)×140 = 220/3
d = √((100/3)² + (220/3)²) = 20•(√146)/3
[tex] \displaystyle{ \frac{d}{dt} d=\frac{2 \cdot x \cdot \frac{dx}{dt} + 2 \cdot y \cdot\frac{dy}{dt} }{2 \cdot d }}[/tex]
Which gives;
[tex] \displaystyle{ \frac{d}{dt} d= \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}}[/tex]
[tex] \displaystyle{ \frac{2 \times \frac{220}{3} \times 140 + 2 \times \frac{100}{3} \times 160}{2 \times \frac{20 \times \sqrt{146}}{3}}\approx 193.66}[/tex]
Therefore;
[tex] \displaystyle{ \frac{d}{dt} d \approx 193.66}[/tex]
The rate of change of the distance between the vehicles with time, [tex] \displaystyle{ \frac{d}{dt} d}[/tex] after 10 minutes is approximately 193.660 m/sLearn more about rate of change of a function here:
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Which of the following identities is used to expand the polynomial (3x - 4y)2?
Recall that to expand a binomial we can use the following formula:
[tex](a+b)^2=a^2+2ab+b^2.[/tex]The above is known as the square of the binomial.
Answer:
Square of binomial.
Is-7+9 = -9 + 7 true, false, or open?
Given g(x) = -2√x², find g(8 + x).
Answer:
g(8 + x) = - 2(8 + x)
Step-by-step explanation:
substitute x = 8 + x into g(x)
g(8 + x) = - 2[tex]\sqrt{(8+x)^2}[/tex] = - 2(8 + x)
Use the appropriate form of the percentages formula. What percent of 10 is 2?
To determine a percentage we can use the following formula:
[tex]\frac{part}{whole}\cdot100\%[/tex]In this case the part is equal to two, the whole is equal to 10, then we have:
[tex]\frac{2}{10}*100\%=20\%[/tex]Therefore, 2 is 20% of 10
evaluate the expression 2(8-4)^2-10÷2
option 1 11
option 2 27
option 3 56
option 4 59
please help quick
I have a time limit
[tex] = 2(4)^{2} - (10 \div 2) \\ = 2(16) - 5 \\ = 32 - 5 \\ = 27[/tex]
THE ANSWER IS OPTION 2. 27
HOPE THIS HELPS
Answer:
Answer is 27
♬
⚫
Domain and range of the quadratic function F(x)=-4(x+6)^2-9
Answer:
Domain: (-∞, ∞)
Range: (-∞, -9]
Step-by-step explanation:
22. After an article is discounted at 25%, it sells for $112.50. The original price of the article was:
A. $28.12
B. $84.37
C. $150.00
D. $152.00
Answer:
the answer is C
Step-by-step explanation:
25% of 150 is 37.5 so 150-37.5 is 112.5
3.50 : 1.50 ratio as a fraction
Answer:
7/3
Step-by-step explanation:
You want the ratio 3.50 : 1.50 written as a fraction.
RatioA ratio can be written 3 ways. Any of them can be reduced to a ratio of mutually prime integers:
3.50 : 1.50 = 3.50/1.50 = 3.50 to 1.50
Here, the fraction can be made to be a ratio of integers by multiplying both numerator and denominator by 2:
3.50/1.50 = (2·3.50)/(2·1.50) = 7/3
The ratio 3.50:1.50 is equivalent to the fraction 7/3.
An initial investment of $200 is appreciated for 20 years in an account that earns 6% interest, compounded continuously. Find the amount of money in the account at the end of the period.
To calculate the final amount of money at the end of the period, considering that the interest is compounded continuously you have to use the following formula:
[tex]A=P\cdot e^{rt}[/tex]Where
A is the accrued amount at the end of the given time
P is the principal amount
r is the annual nomial interes expressed as a decimal value
t is the time period in years
For this investment, the initial value is P= $200
The interest rate is 6%, divide it by 6 to express it as a decimal value
[tex]\begin{gathered} r=\frac{6}{100} \\ r=0.06 \end{gathered}[/tex]The time is t= 20 years
[tex]\begin{gathered} A=200\cdot e^{0.06\cdot20} \\ A=200\cdot e^{\frac{6}{5}} \\ A=664.02 \end{gathered}[/tex]After 20 years, the amount of money in the account will be $664.02
help me with my work please
In the first one, the word increase means you will be add something
+42000
In the second one, the word withdrew means you will subtract something
-40
Aldo will take the 11:49 train to San Diego. The train is estimated to arrive in 4 hours and 32 minutes. What is the estimated arrival time?
Kevonta, this is the solution:
Time of departure : 11:49
Time of travel : 4:32
In consequence, the estimated arrival time if the train departs in the morning is:
11 + 4 = 15 hours
49 + 32 = 81 minutes
81 minutes = 1 hour + 21 minutes
4:21 pm
If the train departs at night, the estimated time of arrival is:
4:21 am
A random number generator is used to select an integer from 1 to 50 (inclusively). What is the probability of selecting the integer 361?
The probability of selecting the integer 361 from the random generator is 0.
What is probability?It should be noted that probability simply has to do with the likelihood that a particular thing will take place.
In this case, a random number generator is used to select an integer from 1 to 50 .
The probability of selecting the integer 361 from the random generator will be 0. This is because the numbers given are from 1 to 50.
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Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a/maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.This task build on important concepts you've learned in this unit and allows you to apply those concepts to a variety ofsituations. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900. Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis,each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with amaximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 persale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weeklysalary is $900.
Given:
Salesman A earn = 65 per sale.
Salesman B earn = 40 per sales and 300weekly salary.
Salesman C earn = 900 weekly salary
Let "x" represent the number of sales each man
Salesman A earn is:
[tex]y=65x[/tex]Salesman B earn is:
[tex]y=40x+300[/tex][tex]\begin{gathered} 65x=40x+300 \\ 65x-40x=300 \\ 25x=300 \\ x=\frac{300}{25} \\ x=12 \end{gathered}[/tex]So total sales is 12 then.
S=0 For Zero week
[tex]\begin{gathered} \text{Salesman A} \\ y=65x \\ y=0 \end{gathered}[/tex][tex]\begin{gathered} \text{Salesman B} \\ y=40x+300 \\ y=40(0)+300 \\ y=300 \end{gathered}[/tex][tex]\begin{gathered} \text{ Salesman C} \\ y=900 \end{gathered}[/tex]For S=1
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(1) \\ y=65 \\ \text{Salesman B}\colon \\ y=40x+300 \\ y=40(1)+300 \\ y=340 \\ \text{Salesman C:} \\ y=900 \end{gathered}[/tex]For s=10
[tex]\begin{gathered} \text{Salesman A:} \\ y=65x \\ y=65(10) \\ y=650 \\ \text{Salesman B:} \\ y=40x+300 \\ y=40(10)+300 \\ y=700 \\ \text{Salesman c:} \\ y=900 \end{gathered}[/tex]how do I find the first five terms of the geometric sequence?
To find the next term of a geometric sequence, the previous term is multiplied by the common ratio r.
[tex]\begin{gathered} r=\frac{1}{2} \\ a_{1=}20 \\ a_2=20\times\frac{1}{2}=10 \\ a_3=10\times\frac{1}{2}=5 \\ a_4=5\times\frac{1}{2}=\frac{5}{2} \\ a_5=\frac{5}{2}\times\frac{1}{2}=\frac{5}{4} \end{gathered}[/tex]Harry HAS 1 1/2 KG whole-wheat flour. He uses 3/4 of the flour to bake bread. How much flour did he use?
Given the following parameter
Mass of flour wheat flour = 1 1/2 kg
If Harry used 3/4 of these flour to bake bread, the amount of flour used is expressed as:
[tex]A=\frac{3}{4}\text{ of 1}\frac{1}{2}[/tex]Convert the mixed fraction into an improper fraction to have:
[tex]\begin{gathered} A=\frac{3}{4}\times\frac{3}{2}kg \\ A=\frac{9}{8}kg \\ A=1\frac{1}{8}kg \end{gathered}[/tex]This shows that Harry used 1 1/8kg of the wheat flour to bake the bread
Find the equation for the line that passes through the point (−2,5), and that is perpendicular to the line with the equation x=−4.
The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y = 5 .
In the question ,
it is given that
the required line is perpendicular to x = -4
the slope of x = -4
x + 4 = 0
0.y = x + 4
slope = 1/0
so the slope of the perpendicular line [tex]=[/tex] 0 .
the equation of the perpendicular line passing through (-2,5) and slope as 0 is
(y - 5) [tex]=[/tex] 0*(x + 2)
y -5 = 0
y = 5
Therefore , The equation of the line perpendicular to x = -4 that passes through the point (-2,5) is y =5 .
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At a sale a sofa is being sold for 67% of the regular price. The sale price is $469. What is the regular price?
We have the following information:
• At a sale, a sofa is being sold for ,67% of the regular price
,• The sale price is $469
And we need to determine the regular price.
To find it, we can proceed as follows:
1. Let x be the regular price. Then we have:
[tex]\begin{gathered} 67\%=\frac{67}{100} \\ \\ 67\%(x)=\frac{67}{100}x \\ \\ \text{ Then we know:} \\ \\ \frac{67}{100}x=\$469 \end{gathered}[/tex]2. Now, we have to solve for x as follows:
[tex]\begin{gathered} \text{ Multiply both sides by }\frac{100}{67}: \\ \\ \frac{67}{100}*\frac{100}{67}x=\frac{100}{67}*\$469 \\ \\ x=\frac{100*\$469}{67}=\$700 \\ \\ x=\$700 \end{gathered}[/tex]Therefore, in summary, the regular price is $700.
Given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 3≤x≤6
STEP - BY - STEP EXPLANATION
What to find?
Rate of change of the given function.
Given:
Step 1
State the formula for rate of change.
[tex]Rate\text{ of change=}\frac{f(b)-f(a)}{b-a}[/tex]Step 2
Choose any two point within the given interval.
(3, 59) and (6, 44)
⇒a=3 f(a) =59
b= 6 f(b)=44
Step 3
Substitute the values into the formula and simplify.
[tex]Rate\text{ of change=}\frac{44-59}{6-3}[/tex][tex]=\frac{-15}{3}[/tex][tex]=-5[/tex]ANSWER
Rate of change = -5
Derive the formular to find the area of the moon and state the assumption taken clearly, physically and mathematically, without defying Keplars laws
Answer:
Area = 4πr²
Step-by-step explanation:
- We know that a moon revolves around its orbit as per Keplar. The moon is not a perfect sphere, so we shall take an assumption;
Assume the moon is a perfect and regular sphere
[tex]{ \tt{volume \: of \: moon = \frac{4}{3} \pi {r}^{3} }} \\ \\ { \boxed{ \tt{ \: v = \frac{4}{3} \pi {r}^{3} }}}[/tex]
- From engineering mathematics (rates of change), we know that volume is first order integral of area and area is the first order derivative of volume;
[tex]{ \tt{area = \frac{d(volume)}{dr} }} \\ \\ { \tt{volume = \int area \: dr}}[/tex]
- So, from our formular;
[tex]{ \tt{area = \frac{dv}{dr} = \frac{4}{3}\pi ( \frac{d ({r}^{3} )}{dr} ) }} \\ \\ { \tt{area = \frac{4}{3}\pi(3 {r}^{2}) }} \\ \\ { \boxed{ \rm{area = 4\pi {r}^{2} }}}[/tex]
r is radius of the moon[tex]{ \boxed{ \mathfrak{DC}}}{ \underline{ \mathfrak{ \: delta \: \delta \: creed}}} \\ [/tex]
how many irrational numbers are there between 1 and 6? is it infinite?
infinite numbers
Explanation
An Irrational Number is a real number that cannot be written as a simple fraction,for example Pi()
[tex]\pi=3.141592654[/tex]Step 1
between 0 an 6 we have 6 integers numbers :(1,2,3,4,5,6)
Step 2
Now check this
a number for example
[tex]\begin{gathered} 3.14 \\ is\text{ different to } \\ 3.145 \\ and\text{ it is diferrent to} \\ 3.1458 \end{gathered}[/tex]so, the answer is infinite numbers
The graph of F(x), shown below, has the same shape as the graph ofG(x) = x - x? Which of the following is the equation of F(x)?F(x) = ?
The graph of G(x) is symmetric with respect to the y-axis. It also passes through the origin.
Since the graph of F(x) moved 4 units upward, we must add 4 to the right of the equation. Thus, the equation of F(x) is as follows.
[tex]F(x)=x^4-x^2+4[/tex]i want to ask a question
We got to use the Secant-Tangent Theorem, here. It says that AC² is equal to the distance BC times the distance from C to the circumference. Let's denote the point in OC where it intercepts the circumference by D, so:
[tex]\begin{gathered} AC^2=CD\cdot BC \\ 20^2=CD\cdot BC \end{gathered}[/tex]Beucase the radius is equal in all points of the circumference, OA=OB=OD, so BC = OA + OC, and CD = OC - OA. So,
[tex]\begin{gathered} 20^2=CD\cdot BC=(OC-OA)\cdot(OA+OC)=OC^2-OA^2=OC^2-8^2 \\ 20^2=OC^2-8^2 \\ OC^2=20^2+8^2=464 \\ OC=\sqrt[]{464}=21.54\approx22\operatorname{cm} \end{gathered}[/tex]Eva counts up. by 3s, while Jin counts up by 5s. What is the least
number that they both say?
Explanation:
This is the LCM (lowest common multiple) of 3 and 5
3*5 = 15
Eva: 3, 6, 9, 12, 15, 18, 21, ...
Jin: 5, 10, 15, 20, 25, ...
9. Rosie's Bakery just purchased an oven for $1,970. The owner expects the oven to last for 10years with a constant depreciation each year. It can then be sold as scrap for an estimatedsalvage value of $270 after 10 years. (20 points)a) Find a linear equation modeling the value of the oven, y, after x years of use.b) Find the value of the oven after 2.5 years.c) Find the y-intercept. Explain the meaning of the y-intercept in the context of this problem.d) Graph the equation of the line. Be sure to label the axes.
a)
The oven devaluated from $1970 to $270 in 10 years.
Since each year it looses the same value, divide the change in the price over the time interval to find the rate of change of the value with respect to time.
To find the change in price, substract the initial price from the final price:
[tex]270-1970=-1700[/tex]The change in price was -$1700.
Divide -1700 over 10 to find the change in the price per year:
[tex]-\frac{1700}{10}=-170[/tex]The initial value of the oven was $1970, and each year it looses a value of $170.
Then, after x years, the value will be equal to 1970-170x.
Then, the linear equation that models the value of the oven, y, after x years of use, is:
[tex]y=-170x+1970[/tex]b)
To find the value of the oven after 2.5 years, substitute x=2.5:
[tex]\begin{gathered} y_{2.5}=-170(2.5)+1970 \\ =-425+1970 \\ =1545 \end{gathered}[/tex]Then, the value of the oven after 2.5 years is $1545.
c)
To find the y-intercept, substitute x=0:
[tex]\begin{gathered} y_0=-170(0)+1970 \\ =1970 \end{gathered}[/tex]The y-intercept is the initial value of the oven when 0 years have passed.
d)
A water tank initially contained 56 liters of water. It is being drained at a constant rate of 2.5 liters per minute. How many liters of water are in the tank after 9 minutes?
−|a+b|/2−c when a=1 2/3 , b=−1 , and c=−3
ENTER YOUR ANSWER AS A SIMPLIFIED FRACTION IN THE BOX.
The value of the expression −|a + b|/2 − c when a =1 2/3 , b=−1 , and c=−3 is 8/3
How to evaluate the expression?From the question, the expression is given as
−|a + b|/2 − c
Also, we have the values of the variables to be
a =1 2/3 , b=−1 , and c=−3
Rewrite a as
a = 5/3
So, we substitute a = 5/3 b=−1 , and c=−3 in −|a + b|/2 − c
This gives
−|a + b|/2 − c = −|5/3 - 1|/2 + 3
Evaluate the difference in the expression
−|a + b|/2 − c = −|2/3|/2 + 3
Divide
−|a + b|/2 − c = −|1/3| + 3
Remove the absolute bracket and solve
−|a + b|/2 − c = 8/3
Hence, the solution is −|a + b|/2 − c = 8/3
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The required simplified value of the given expression is 8/3.
As per the given data, an expression −|a+b|/2−c is given when a=1 2/3, b=−1, and c=−3 the value of the expression is to be determined.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
Here,
Let the solution be x,
x = −|a+b|/2−c
Substitute value in the above equation,
x = - |1 + 2 / 3 - 1|/2 - (-3)
x = -1/3 + 3
x = -1+9 / 3
x = 8/3
Thus, the required simplified value of the given expression is 8/3.
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A solution must be 14% Insecticide. To make 5 gallons of this solution how much insecticide must you use? A) 0.028 gallon B) .36 gallon C) .7 gallon D) 2.8 gallons
Insecticides = 14/100 x 5 = 0.7
Trisha is using the recipe show to make a fruit salad. She wants to use 20 diced strawberries in her fruit salad. How many bananas, apples, and pears show Trisha use in her fruit salad? Fruit Salad Recipe 4 bananas 3 apples 6 pears 10 strawberries bananas apples pears
The original recipe has half of the number of strawberries She wants to use in her salad in this case we will need double the fruits of the recipe given
Bananas
4x2=8 bananas
Apples
3x2=6 apples
Pears
6x2=12 pears
Simplify the expression √112x10y13. Show your work. pls help
Answer: [tex]4x^{5} y^{6} \sqrt{7y}[/tex]
Step-by-step explanation:
1) Separate the radicals
sqrt(112x^10y^13) = sqrt(112)*sqrt(x^10)*sqrt(y^13)
2) For sqrt(112), rewrite it as the product of a perfect square and some other number.
sqrt(112) = sqrt(16) * sqrt(7)
= 4*sqrt(7)
3) For sqrt(x^10), rewrite it in terms of it being raised to a fraction
[tex]\sqrt[n]{x} = x^{\frac{1}{n} }[/tex]
n = 2, so x^(10/2), and when simplified you have x^5
4) For sqrt(y^13), do the same thing.
y^(13/2) = sqrt(y)*(y^6)
5)Combine everything
4x^5y^6sqrt(7y)