Multiply the price of popcorn by the number of bags so 6b.
Multiply the price of candy by the number bought, so 3.25c
Add those together to get total :
6b + 3.25c
Now the most she can spend is 50 so set the equation to less than it equal to what she can spend:
6b + 3.25c <= 50
Final answer:
The inequality representing Samantha's budget for purchasing popcorn and candies is 6b + 3.25c ≤ 50.
Explanation:
To formulate the inequality representing the possible values for the number of bags of popcorn (b) and the number of candies (c) Samantha can purchase without exceeding her $50 budget, we can set up an expression based on the given prices for each item.
The cost of the popcorn bags is $6, and the cost of each candy is $3.25.
The inequality that represents this scenario would be:
6b + 3.25c ≤ 50
This inequality denotes that the total cost of b popcorn bags and c candies, which is the sum of $6 times the number of popcorn bags plus $3.25 times the number of candies, should be less than or equal to $50.
Samantha must choose combinations of b and c that satisfy this inequality to stay within her budget.
Parker was able to pay 44% of his college tuition with his scholarship.The remaining $10,054.52 he paid for with a student loan.What was the cost of Parker's tuition?
Answer: the cost of Parker's tuition is $17955
Step-by-step explanation:
Let x represent the cost of Parker's tuition.
Parker was able to pay 44% of his college tuition with his scholarship. This means that the amount that he was able to pay with his scholarship would be
44/100 × x = 0.44 × x = 0.44x
The amount that is remaining for him to pay would be
x - 0.44x = 0.56x
If he paid the remaining $10,054.52 with a student loan, it means that
0.56x = 10054.52
x = 10054.52/0.56
x = 17954.5
Rounding up to the nearest whole number, it becomes
x = $17955
PLEASSEEEEEEEE HELP!!!
Answer:
Step-by-step explanation:
Triangle DEF is a right angle triangle.
From the given right angle triangle
DF represents the hypotenuse of the right angle triangle.
With m∠D as the reference angle,
DE represents the adjacent side of the right angle triangle.
EF represents the opposite side of the right angle triangle.
To determine EF, we would apply the Sine trigonometric ratio
Sin θ = opposite side/hypotenuse. Therefore,
Sin 26 = EF/4.5
0.44 = EF/4.5
EF = 4.5 × 0.44 = 1.98 yo 2 decimal places
The person is a member for super for a female boss over in the and loss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss.
Answer:
1998
y=6x+1944
Step-by-step explanation:
The percentage of Male workers who prefer a female boss over a male boss increased approximately linearly from 5% in 1974 to 9% in 1998. Predict when 9% of male workers will prefer a female boss
it is explicit from the question that 9% of male workers prefer female boss in 1998. but we can predict a model for this by getting the slope of the graph
y=the year
x=the percentage of men who prefer a female boss
s=y2-y1/(x2-x1)
s=1998-1974/(9-5)
s=24/4
s=6
therefore we have
y=mx+c
y=6x+c........1
when y=1998,x=9
1998=6(9)+c
c=1944
from equation 1
y=6x+1944
if you in invested $500 at 5% simple interest for 2 years, how much interest do you earn? show work and answer in complete sentances to earn full credit. if you invest $500 at 3% compound monthly for 2 years, how much interest do you earn? show work and answer in complete sentances to earn full credit which would you rather do?
Answer:
Step-by-step explanation:
1) The formula for simple interest is expressed as
I = PRT/100
Where
P represents the principal
R represents interest rate
T represents time in years
I = interest after t years
From the information given
T = 2 years
P = $500
R = 5%
Therefore
I = (500 × 5 × 2)/100
I = $50
2) Principal, P = $500
It was compounded monthly. This means that it was compounded 12 times in a year. So
n = 12
The rate at which the principal was compounded is 3%. So
r = 3/100 = 0.03
It was compounded for just 2 years. So
t = 2
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. Therefore
A = 500 (1+0.03/12)^12 × 2
A = 500 (1.0025)^24
A = $530.88
The interest is
530.88 - 500 = $30.88
Please look at the questions again! Some of the answers are incorrect. Here is a hint: For question 1, you should not spend more than one-third of $2,000? Calculate: $2,000 / 3. For question 2, how much is the rent and housing expenses? Calculate: $650 + $60 + $10 + $20 + $20. How much can you afford? You should not spend more than one-third of $2,100. Looks like the rent and expenses are too high for your budget, right?
Answer:question 1)$6.66.67
Question2) Rent and expenses =$760
Rent and expenses are too high for the budget
Step-by-step explanation:
1)$2000×(1/3)= $666.67
2)Rent and expenses =$(650+60+10+20+20)= $760
$2100×(1/3)= $700
Rent and expenses should not exceed one third of $2100, which is $700 but it exceeded by$60. Therefore budget is too high.
Final answer:
These Mathematics questions involve calculating budgets to manage income and expenses. For budgeting housing costs, the recommendation is not to exceed one-third of income. A budget table is used to track all monthly expenses against income to determine savings potential and necessary adjustments.
Explanation:
The subject of these questions is Mathematics, specifically focusing on budgeting and personal finance. In these scenarios, students are learning to apply mathematical operations to real-life situations involving income, expenses, and budget planning.
For question 1, you would calculate the maximum amount you should spend on housing from a $2,000 monthly budget by dividing $2,000 by 3, which gives you $666.67. This is because it's recommended to spend no more than one-third of your income on housing.
For question 2, adding together the rent and housing expenses ($650 + $60 + $10 + $20 + $20), you get a total of $760. If you have an income of $2,100, you should not spend more than $700 on housing (which is one-third of your income), so $760 is indeed too high for the budget.
Creating a budget table is an essential skill for financial literacy. When constructing one, you list your monthly income and subtract all your expenses, including housing, utilities, groceries, and any other costs, to see what is left for savings and discretionary spending. For example, with an after-tax monthly income of $2,589.10, if you spend $790 on rent, $75 on a cell phone, and have other listed expenses, you'd subtract all these from your income to see if you can save the desired 10%.
Maria went to the restaurant and waited 90 seconds to place her order. Use the trend line equation to predict how many employees were working. Round to the nearest whole number if necessary.
Answer:
3 employees
Step-by-step explanation:
The complete question is
The manager of a fast food restaurant collected data to study the relationship between the number of employees working registers and the amount of time customers waited in line to order. He made a scatter plot of the data and created a trend line with the equation y = -70x + 300, where y is the total amount of time waited in seconds and x is the number of employees working registers. Maria went to the restaurant and waited 90 seconds to place her order. Use the trendline equation to predict how many employees were working. Round to the nearest whole number if necessary.
Let
x ---> is the number of employees working registers
y ---> is the total amount of time waited in seconds
we have
[tex]y=-70x+300[/tex]
This is the equation of a line in slope intercept form
where
The slope is equal to
[tex]m=-70\ \frac{seconds}{employee}[/tex] ---> is negative because is a decreasing function
The y-intercept is equal to
[tex]b=300\ sec[/tex]
For y=90 seconds
substitute in the linear equation and solve for x
[tex]90=-70x+300[/tex]
[tex]70x=300-90\\70x=210\\x=3\ employees[/tex]
To predict the number of employees based on a 90-second wait time, substitute 90 into the given trend line equation and solve for y. For example, using y = -0.1x + 10, we get approximately 1 employee. Ensure you use the specific trend line equation provided for accurate results.
To predict how many employees were working based on Maria's wait time of 90 seconds, we need the trend line equation that describes the relationship between waiting time and the number of employees.
Assuming we have a trend line equation of the form y = mx + b,
where y represents the number of employees, x the waiting time in seconds, and m and b are constants,you can substitute 90 for x and solve for y.
For example, if the trend line equation is y = -0.1x + 10, substituting 90 for x:
y = -0.1(90) + 10
y = -9 + 10
y = 1
Therefore, according to this trend line, approximately 1 employee would be working. Always remember to check your specific trend line equation and solve accordingly.
Y=2x-7, 3x-2=9 solving systems
Johns bank account increased in value from last year to this year by 8% to $250 if the the account increases by the same percentage over the next year what will be the value next year
A.$258
B.$260
C.$264
D.$268
E.$270
Answer:
$ 270
Step-by-step explanation:
Do 250 X 1.08 to get the answer
Using the percentage increase formula, John's bank account value of $250 will increase by 8% to $270 after one year.
To find the future value of John's bank account, we will use the percentage increase formula. If his account increased by 8% this year to $250, we can calculate next year's balance by multiplying $250 by 1.08 (which represents a 100% principal plus an 8% increase).
Step-by-step calculation:
Convert the percentage increase to a decimal: 8% becomes 0.08.Add 1 to the decimal equivalent of the percentage increase to find the growth factor: 1 + 0.08 = 1.08.Multiply the current year's value by the growth factor: $250 times 1.08.Calculate the result: $250 times 1.08 = $270.Therefore, the value of John's bank account if it increases by the same percentage over the next year will be $270.
Rebeca spent $32.55 for a photo album and three identical candles. The photo album cost $17.50 and the sales tax was $1.55. How much did each candle cost
Answer: $4.50 per candle
Step-by-step explanation:
$32.55 - $17.50 - $1.55 = $13.50 for all the candles
To find the price of a single candle we divide our answer by 3
13.50/3 = $4.50
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment? Group of answer choices $104.54 $378.21 $450.71 $1225.56
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$450.71
____________________________
*100% CORRECT ANSWERS
Question 1
A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the monthly payment?
$1082.84
Question 2
A family is purchasing a house and needs to finance a 195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the total amount the family will pay back to the bank (to the nearest dollar)?
$389,822
Question 3
Mr. Winking is purchasing a car and needs to finance $24,000 from the bank with an annual percentage rate (APR) of 4.8%. He is financing it over 5 years and making monthly payments. What is the monthly payment?
$450.71
Multiples of 3 and 5 Problem 1 If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.
Answer: 233,168
Step-by-step explanation:
Formula: 1 + 2 + 3 + ... + n = n(n+1)/2
Sum of all the numbers below 1000 that is divisible by 3:
3 + 6 + 9 + ... + 999 = 3 (1 + 2 + 3 + ... + 333) = 3 x 333 x 334 / 2 = 166,833
Sum of all the numbers below 1000 that is divisible by 5:
5 + 10 + 15 + ... + 995 = 5 (1 + 2 + 3 + ... + 199) = 5 x 199 x 200 / 2 = 99,500
As we add up 166,833 and 99,500, the numbers that are divisible by 3*5 = 15 would be counted double. Therefore, subtract the result for numbers divisible by 15 just once:
Sum of all numbers below 1000 that is divisible by 15:
15 + 30 + 45 + ... + 990 = 15 (1 + 2 + 3 + ... + 66) = 15 x 66 x 67 / 2 = 33165
Therefore, [ 166,833 + 99,500 ] - 33,165 = 233,168
To find the sum of all the multiples of 3 or 5 below 1000, you need to find the sum of the multiples of 3 and 5 separately and then subtract the sum of the multiples of 15. The sum is 233,003.
Explanation:To find the sum of all the multiples of 3 or 5 below 1000, we can use the concept of arithmetic series. First, we need to find the sum of the multiples of 3 and the sum of the multiples of 5 below 1000. Then, we need to subtract the sum of the multiples of 15 (since numbers that are multiples of both 3 and 5 have been counted twice).
Using the formula for the sum of an arithmetic series, the sum of the multiples of 3 below 1000 is given by:
3 + 6 + 9 + ... + 999 = (1/2)(3 + 999)(333) = 166,833
Similarly, the sum of the multiples of 5 below 1000 is:
5 + 10 + 15 + ... + 995 = (1/2)(5 +995)(199) = 99,500
Finally, the sum of the multiples of 15 below 1000 is:
15 + 30 + 45 + ... + 990 = (1/2)(15 + 990)(66) = 33,330
Now, we can calculate the sum of all the multiples of 3 or 5 by adding the sum of the multiples of 3 to the sum of the multiples of 5 and then subtracting the sum of the multiples of 15:
166,833 + 99,500 - 33,330 = 233,003
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A mathematically proficient students would approach a challenging problem solving task with a certain disposition. Describe at least two examples of what that disposition would look and sound like in a classroom.
Answer:
g6h12
Step-by-step explanation:
Answer: mmmmm.
Step-by-step explanation:
A function f(x) is said to have a removable discontinuity at x=a if: 1. f is either not defined or not continuous at x=a . 2. f(a) could either be defined or redefined so that the new function IS continuous at x=a. Let f(x) = {((6)/(x)+(-5 x+18)/(x(x-3)), "if", x doesnt = 0 "and" x doesnt =3),( 3, "if", x=0) :} Show that f(x) has a removable discontinuity at x=0 and determine what value for f(0) would make f(x) continuous at x=0 . Must redefine f(0)= ?
The function f(x) has a removable discontinuity at x=0. To make f(x) continuous at x=0, we must redefine f(0) as -1/3.
To determine if f(x) has a removable discontinuity at x=0, we need to check if f(x) is either not defined or not continuous at x=0.
Looking at the definition of f(x), we see that f(0) is defined as 3. Therefore, f(x) is defined at x=0.
Next, let's examine the continuity of f(x) at x=0. We need to evaluate the limit of f(x) as x approaches 0.
Using the given definition of f(x), we have:
lim(x->0) (6/x) + (-5x + 18)/(x(x-3))
To evaluate this limit, we can simplify the expression by finding a common denominator. The common denominator is x(x-3):
lim(x->0) [6(x-3) + (-5x + 18)] / [x(x-3)]
Simplifying the numerator:
lim(x->0) (6x - 18 - 5x + 18) / [x(x-3)]
= lim(x->0) (x) / [x(x-3)]
Now, we can cancel out the x term:
lim(x->0) 1 / (x-3)
As x approaches 0, the denominator (x-3) approaches -3. Therefore, the limit is:
lim(x->0) 1 / (x-3) = 1 / (-3) = -1/3
Since the limit of f(x) as x approaches 0 exists and is equal to -1/3, we can redefine f(0) to be -1/3 to make f(x) continuous at x=0.
Thus, f(x) has a removable discontinuity at x=0, and we must redefine f(0)=-1/3 to make f(x) continuous at x=0.
Guided Practice
Which of the following is a Pythagorean triple?
A. 15, 20, and 25
B. 15, 16, and 24
O
c. 15, 21, and 28
Answer:
A. 15, 20, and 25
Step-by-step explanation:
Note that 3-4-5 is a pythagorean triple via following:
[tex]\sqrt{ (3^2 + 4^2 )} = 5^2[/tex]
Dividing 15, 20, and 25 by 5 nets you the pythagorean triple 3-4-5.
Amy has a collection of marbles in three sizes, small, medium, and large. She has five times as many small marbles as medium marbles. The number of large marbles is two more than three times the number of medium marbles. a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has. b.Write an algebraic expression to represent the number of large marbles she has. c.If Amy has a total of 560 marbles, how many of each size does she have? Show your work. (please i need help im really stuck)
Answer: she has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
Let w represent the number of small marbles Amy has.
Let x represent the number of medium marbles Amy has.
Let y represent the number of large marbles Amy has.
a) She has five times as many small marbles as medium marbles. This means that
w = 5x
b) The number of large marbles is two more than three times the number of medium marbles. This means that
y = 3x + 2
c) If Amy has a total of 560 marbles, it means that
5x + x + 3x + 2 = 560
9x = 560 - 2
9x = 558
x = 558/9 = 62
w = 5x = 62 × 5
w = 310
y = 3x + 2 = 3 × 62 + 2
y = 188
Answer:
A. s = 5x
B. y = 3x + 2
C y=166
Step-by-step explanation:
Anything will help! Thank you.
Step-by-step explanation:
(a) If g is the number of gallons left in the tank, and t is the time in hours since 8AM:
g = 8 gal − (1 gal / 24 mi) (60 mi / 1 hr) (t hr)
g = 8 − 2.5t
(b) If d is the distance traveled:
d = 60 mi/hr × t hr
d = 60t
(c) When George runs out of gas, g = 0.
0 = 8 − 2.5t
t = 3.2
The distance he travels is:
d = 60(3.2)
d = 192
George travels 192 miles.
3.2 hours after 8AM, the time is 11:12AM.
I needz duh help pwease and tank chu?
Answer:
Step-by-step explanation:
Let h represent the number of hours that Jamarcus can rent the truck.
To rent a truck, the charge is $16 per hour and also a fueling fee of $25
The total cost of renting the truck for x hours would be
16h + 25
Since Jamarcus wants to rent the truck and can spend no more than $125, the inequality representing the situation would be
16h + 25 ≤ 125
16h ≤ 125 - 25
16h ≤ 100
h ≤ 6.25
2) 3x - 5 ≥ - 11
3x ≥ - 11 + 5
3x ≥ - 6
x ≥ - 6/3
x ≥ - 2
The correct graph is option A
Answer:
a
Step-by-step explanation:
When large bags of candies are packaged, the number of candies in each bag must be within 4 of 120 pieces. Write an absolute value equation to represent p
Answer:
Step-by-step explanation:
p = 120 ± 4
suppose sin(a)=3/4
use the trig identity sin^2(a)+cos^2(a)=1
and the trig identity tan(a)=sin(a)/cos(a)
to find tan (a) in quad II.
Round to the nearest hundredth.
well, we know the sine, and we also know that we're on the II Quadrant, let's recall that on the II Quadrant sine is positive whilst cosine is negative.
[tex]\bf sin^2(\theta)+cos^2(\theta)=1~\hspace{10em} tan(\theta )=\cfrac{sin(\theta )}{cos(\theta )} \\\\[-0.35em] ~\dotfill\\\\ sin^2(a)+cos^2(a)=1\implies cos^2(a) = 1-sin^2(a) \\\\\\ cos^2(a) = 1-[sin(a)]^2\implies cos^2(a) = 1-\left( \cfrac{3}{4} \right)^2\implies cos^2(a) = 1-\cfrac{3^2}{4^2} \\\\\\ cos^2(a) = 1-\cfrac{9}{16}\implies cos^2(a) = \cfrac{7}{16}\implies cos(a)=\pm\sqrt{\cfrac{7}{16}}[/tex]
[tex]\bf cos(a)=\pm\cfrac{\sqrt{7}}{\sqrt{16}}\implies cos(a)=\pm\cfrac{\sqrt{7}}{4}\implies \stackrel{\textit{on the II Quadrant}}{cos(a)=-\cfrac{\sqrt{7}}{4}}\\\\[-0.35em]~\dotfill\\\\tan(a)=\cfrac{sin(a)}{cos(a)}\implies tan(a)=\cfrac{~~\frac{3}{4}~~}{-\frac{\sqrt{7}}{4}}\implies tan(a)=\cfrac{3}{4}\cdot \cfrac{4}{-\sqrt{7}}\\\\\\tan(a)=-\cfrac{3}{\sqrt{7}}\implies \stackrel{\textit{rounded up}}{tan(a) = -1.13}[/tex]
Write a formula that describes the value of an initial investment of $300 growing at an interest rate of 6% compounded continuously.
The correct answer would be B.
The lower e is used for continuous compounding and it is raised by the interest rate times the amount of time
Formula that describes the value of an initial investment of [tex]\$300[/tex] growing at an interest rate of [tex]6\%[/tex] compounded continuously is equals to [tex]A(t) = 300e^{.06t}[/tex].
What is compounded continuously?" Compounded continuously is defined as the interest calculation and reinvestment of the amount over infinite period."
Formula used
[tex]A(t) = P e^{rt}[/tex]
[tex]A(t) =[/tex] Final amount
[tex]P =[/tex] Principal amount
[tex]t =[/tex] time period interest is applied
[tex]r=[/tex] rate of interest
According to the question,
Given,
Principal amount [tex]= \$300[/tex]
Rate of interest [tex]= 6\%[/tex]
As per the given condition interest compounded continuously,
Substitute the value in the formula of interest compounded continuously we get,
[tex]A(t) = 300 e^{\frac{6}{100} t}\\\\\implies A(t) = 300 e^{.06 t}[/tex]
Hence, Option (B) is the correct answer.
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Geoff wants to purchase a circular area rug for his room, but he can't decide between the small size and the large size. A small rug covers an area of approximately 67 square feet. If a large size rug has twice the dimensions of a small rug, how many times larger is the large rug?
Answer: The larger rug is 4 times larger
Step-by-step explanation:
The formula for determining the area of a circle is expressed as
Area = πr²
Where
r represents the radius of the circle.
π is a constant whose value is 3.14
The small circular rug covers an area of approximately 67 square feet. This means that
67 = πr²
r² = 67/π = 67/3.14 = 21.34
r = √21.34 = 4.62
If a large size rug has twice the dimensions of a small rug, it means that the radius of the larger rug would be
2 × 4.62 = 9.24
The area of the larger rug would be
3.14 × 9.24² = 268.06ft²
Therefore
268.06/67 = 4
The larger rug is 4 times larger
An array with m rows and n columns is not: A: An m-by-n array. B: An n-by-m array. C: A two-dimensional array. D: An n times m dimensional array.
Answer:
B, An n-by-m array.
Step-by-step explanation:
when working with 2D arrays, rows come first and then columns. so all options here are correct except option B
Bill buys a stock that decreases by 20% on the first day, and then on the second day the stock increases by 30% of its value at the end of the first day. What was the overall percent increase in Bill's stock over the two days?
Answer:
4%
Step-by-step explanation:
Let the stock be $10
A 20% decline = 80/100 * 10
= 8
A 30% increase = 30/100 * 8
= 2.4 + 8 = 10.4.
Overall increase = 10.4 - 10 = 0.4
Percentage overall increase = 0.4/10 * 100
= 4%
Can someone please help me?!?
Write an equation for the sine wave. What is the amplitude and period?
Now, you are going to determine the frequency of the tone you created.
Frequency=1/period
Part2
Finally, do some research on different frequencies. Pick 3 different sounds and determine their frequency. Compare and contrast those sounds to the frequency of your tone. What conclusions can you make about frequency?
Answer:
See the explanation.Step-by-step explanation:
Part 1:
An equation of sine wave can be written as y = 5 Sin(2x + 3).
The amplitude of the above equation is 5.
The period of the function is [tex]\frac{2\pi }{2} = \pi[/tex].
The frequency of the function is [tex]\frac{1}{\pi }[/tex].
Part 2:
[tex]y = 2 Sin(3x + 5) + 9.......(1)\\y = 5 Sin(4x + 8) + 12.....(2)\\y = 3 Sin(x + 6) + 2......(3)[/tex]
The above given equations numbered 1, 2 and 3 represents three different sound waves.
For (1), the frequency is [tex]\frac{1}{\frac{2\pi }{3} } = \frac{3}{2\pi }[/tex].
For (2), the frequency is [tex]\frac{4}{2\pi } = \frac{2}{\pi }[/tex].
For (3), the frequency is [tex]\frac{1}{2\pi }[/tex].
Frequency of sounds refers the speed of vibration.
The taken three siounds has different frequencies.
How do you do this problem?
Answer:
C) ¼ ∫ u⁵ du, where u = sin(4x)
Step-by-step explanation:
∫ cos(4x) sin⁵(4x) dx
Using u substitution:
u = sin(4x)
du = 4 cos(4x) dx
¼ du = cos(4x) dx
¼ ∫ u⁵ du
An initial investment of $1000 is appreciated for 4 years in an account that earns 4% interest, compounded annually. Find the amount of money in the account at the end of the period.
Answer: $116.99
Step-by-step explanation:
By using compound interest formula which said:
A = P ( 1 + r/n )^(n×t)
P=Principal= 1000
r=rate=4/100
n=1
t= 4
Apply the above formula
A = P ( 1 + r/n )^(n×t)
A = 1000(1 + 0.04/1)^(1 × 4)
A= 100(1.04)^4
A= 100 × 1.17
A = 116.99
Use the following recursive formula to answer the question.
a1=−3/2
an=an−1+1/2
What is a9?
Answer:
2 1/2
Step-by-step explanation:
Each term is 1/2 added to the previous term. The first term is -3/2, so the first 9 terms of the sequence are ...
-3/2, -1, -1/2, 0, 1/2, 1, 1 1/2, 2, 2 1/2
a9 is 2 1/2.
I'm pretty sure the answer to
a1=−32
an=an−1+12
is 5/2
A piece of wire 40 cm long is cut into two piece, each to be bent to make a square.The length of a side of one square is to be 4 longer than length of a side of the other. How should the wire be cut
Answer: the wire should be cut into 12 cm and 28 cm
Step-by-step explanation:
All sides of a square is equal.
The perimeter of a square is the distance around the square.
Let L represent the length each side of one of the squares. Then the perimeter of this square is 4L.
The length of a side of one square is to be 4 longer than length of a side of the other. This means that the length of each side of the other square is L + 4
The perimeter of the other square would be 4(L + 4) = 4L + 16
Since the piece of wire is 40 cm long, then
4L + 4L + 16 = 40
8L = 40 - 16 = 24
L = 24/8 = 3
The perimeter of the first square is
4L = 4 × 3 = 12
The perimeter of the second square is
4L + 16 = 4 × 3 + 16= 28
Final answer:
To make two squares with one side being 4 cm longer than the other, a 40 cm wire should be cut into pieces of 12 cm and 28 cm.
Explanation:
The question concerns cutting a 40 cm long piece of wire into two pieces to form two squares, where the length of a side of one square is 4 cm longer than the length of a side of the other square. Let's denote the length of the side of the smaller square as x cm. Thus, the side of the larger square will be x + 4 cm. Since the perimeter of a square is four times its side length, the total length of wire used for the smaller square will be 4x cm, and for the larger square will be 4(x + 4) cm.
Combining the total length of both squares, we have:
4x + 4(x + 4) = 40
This simplifies to:
8x + 16 = 40
Subtracting 16 from both sides, we get:
8x = 24
Dividing both sides by 8, we find:
x = 3
Therefore, the side of the smaller square is 3 cm, and the side of the larger square is 7 cm. To find out how long each piece of wire must be cut, we calculate the perimeters:
Smaller square wire length: 4(3) = 12 cm
Larger square wire length: 4(7) = 28 cm
So the wire should be cut into one 12 cm piece and one 28 cm piece.
A golden rectangle has side lengths in the ratio of about 1 to 1.62. To the nearest tenth, what is length of the shorter side of a golden rectangle with a longer side length of 40 inches?
Answer: The length of the shorter side of a golden rectangle is about 24.7 inches.
Step-by-step explanation:
Given : A golden rectangle has side lengths in the ratio of about 1 to 1.62.
Since 1.62 > 1 , so
[tex]\dfrac{\text{Length of shorter side}}{\text{Length of longer side}}=\dfrac{1}{1.62}[/tex]
If the length of the longer side is 40 inches , then we have
[tex]\dfrac{\text{Length of shorter side}}{\text{40 inches}}=\dfrac{1}{1.62}\\\\ \Rightarrow\ \text{Length of shorter side}=\dfrac{1}{1.62}\times \text{40 inches}\\\\ \Rightarrow\ \text{Length of shorter side}=24.6913580247\approx24.7\text{ inches}[/tex]
Hence, the length of the shorter side of a golden rectangle is about 24.7 inches.
To find the length of the shorter side of a golden rectangle with a longer side of 40 inches, divide 40 by the golden ratio (1.62), yielding approximately 24.7 inches as the length of the shorter side, rounded to the nearest tenth.
Explanation:To calculate the length of the shorter side of a golden rectangle with a longer side length of 40 inches, we use the ratio of the sides of a golden rectangle. Given that this ratio is about 1 to 1.62, we divide the length of the longer side by the golden ratio (approximately 1.62) to find the length of the shorter side.
Using this method:
Length of longer side = 40 inchesLength of shorter side = 40 inches / 1.62Let's do the calculation:
Length of shorter side ≈ 24.7 inches (rounded to the nearest tenth)
Find the area of the shape (1,3) (5,3) (7,-1) (1,-1)
Step-by-step explanation:
The given four sides of quadrilateral = (1,3), (5,3), (7,-1) and (1,-1)
To find, the area of the shape (quadrilateral) = ?
We know that,
The area of quadrilateral = [tex]\dfrac{1}{2} [x_{1}( y_{2}-y_{3})+x_{2}( y_{3}-y_{4})+x_{3}( y_{4}-y_{1})+x_{4}( y_{1}-y_{2})][/tex]
= [tex]\dfrac{1}{2} [1( 3+1)+5( -1+1)+7( -1-3)+1}( 3-3)][/tex]
= [tex]\dfrac{1}{2} [1(4)+5( 0)+7( -4)+1}( 0)][/tex]
= [tex]\dfrac{1}{2} [4+0-28+0][/tex]
= [tex]\dfrac{1}{2} [32][/tex]
= 16 square units.
Thus, the area of the shape (quadrilateral) is 16 square units.