There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
To determine the total number of color-wheel size combinations for the kickboard scooter, we need to multiply the number of color options by the number of wheel size options.
Given that there are 4 color options (silver, red, blue, and purple) and 2 wheel size options (125mm and 180mm), we can use the multiplication principle to find the total number of combinations:
Total combinations = Number of color options × Number of wheel size options
Total combinations = 4 colors × 2 wheel sizes
Total combinations = 8
There are a total of 8 color-wheel size combinations for the kickboard scooter. This means that customers have 8 different options to choose from when selecting the color and wheel size for their scooter.
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Cliff takes out a $5,000 personal loan with 7
fixed annual interest compounded monthly to pay for his wedding. He repays the loan in 2 year.s
How much total interest does Cliff pay on his loan?
Cliff pays a total interest of approximately $679.90 on his $5,000 loan.
To calculate the total interest paid on the loan, we need to use the formula for compound interest:
[tex]A = P(1 + r/n)^{(nt)}[/tex]
Where:
A is the final amount (loan amount + interest)
P is the principal (loan amount)
r is the annual interest rate (in decimal form)
n is the number of times interest is compounded per year
t is the number of years
Given that Cliff takes out a $5,000 loan with a fixed annual interest rate of 7% compounded monthly, we can substitute the values into the formula:
P = $5,000
r = 7% = 0.07
n = 12 (monthly compounding)
t = 2 years
[tex]A = 5000(1 + 0.07/12)^{(12 \times 2)[/tex]
Calculating this expression:
A ≈ 5000[tex](1.00583)^{(24)[/tex]
A ≈ 5000(1.13598)
A ≈ 5679.90
The final amount (A) is the loan amount plus the total interest paid. Therefore, to find the total interest paid, we subtract the principal (P) from the final amount (A):
Total Interest = A - P
Total Interest = 5679.90 - 5000
Total Interest ≈ $679.90
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The heights of american adult men are normally distributed with a mean of 69.7 inches and a standard deviation of 2.7 inches what is the standard score for a height of 6 foot 2 inches
Answer:
1.5926
Step-by-step explanation:
-We need to first convert the height in feet to inches: Since there are 12 inches in a foot, that means there are 74 inches in a height of 6 foot 2 inches.
-Since the observed height is 74 inches and the mean height is 69.7 inches, we can find the z score by using the following formula:
z = (x-mean) / standard deviation
-We would fill this out like this:
z = (74-69.7) / 2.7
-This equals = 1.592592593
-Rounded to 4 decimal places, this equals 1.5926
Find the value of y.
Answer:
y = [tex]\sqrt{55}[/tex]
Step-by-step explanation:
using the Altitude- on- Hypotenuse theorem
(altitude)² = product of parts of hypotenuse
then
y² = 11 × 5 = 55 ( take square root of both sides )
y = [tex]\sqrt{55}[/tex]
Solve the linear inequality. Express the solution using interval notation.
13 ≤ 4x − 3 ≤ 29
[tex]13 \leqslant 4x - 3 \leqslant 29 \\ 13 + 3 \leqslant 4x \leqslant 29 + 3 \\ 16 \leqslant 4x \leqslant 32 \\ 16 \div 4 \leqslant x \leqslant 32 \div 4 \\ 4 \leqslant x \leqslant 8[/tex]
Write an equation for the function graphed below
The rational function graphed in this problem is defined as follows:
y = -2(x - 1)/(x² - x - 2).
How to define the rational function?The vertical asymptotes of the rational function for this problem are given as follows:
x = -1 and x = 2.
Hence the denominator of the function is given as follows:
(x + 1)(x - 2) = x² - x - 2.
The intercept of the function is given as follows:
x = 1.
Hence the numerator of the function is given as follows:
a(x - 1)
In which a is the leading coefficient.
Hence:
y = a(x - 1)/(x² - x - 2).
When x = 0, y = -1, hence the leading coefficient a is obtained as follows:
-1 = a/2
a = -2.
Thus the function is given as follows:
y = -2(x - 1)/(x² - x - 2).
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)The mean voltage of a battery is 15 and S.D 0.2.Find the probability that four such batteries connected in series will have combined voltage of 60.8 or more volts
The probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
To find the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts, we need to use the concept of the Central Limit Theorem.
In this case, we know that the mean voltage of a single battery is 15 volts and the standard deviation is 0.2 volts. When batteries are connected in series, their voltages add up.
The combined voltage of four batteries connected in series is the sum of their individual voltages. The mean of the combined voltage will be 4 times the mean of a single battery, which is 4 * 15 = 60 volts.
The standard deviation of the combined voltage will be the square root of the sum of the variances of the individual batteries. Since the batteries are connected in series, the variance of the combined voltage will be 4 times the variance of a single battery, which is 4 * (0.2)^2 = 0.16.
Now, we need to calculate the probability that the combined voltage of four batteries is 60.8 or more volts. We can use a standard normal distribution to calculate this probability.
First, we need to standardize the value of 60.8 using the formula:
Z = (X - μ) / σ
Where X is the value we want to standardize, μ is the mean, and σ is the standard deviation.
In this case, the standardized value is:
Z = (60.8 - 60) / sqrt(0.16)
Z = 0.8 / 0.4
Z = 2
Next, we can use a standard normal distribution table or calculator to find the probability associated with a Z-score of 2. The probability of obtaining a Z-score of 2 or more is approximately 0.0228.
Therefore, the probability that four batteries connected in series will have a combined voltage of 60.8 or more volts is approximately 0.0228 or 2.28%.
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The area of a square is 36 sq.cm, then its perimeter is a) 24 cm b) 6 cm c) 144 cm d) 36 cm
Answer:
Step-by-step explanation:
3.6*
It is very easy to find the perimeter of a square when its area is given in the question. For that, you only ned to know one fomula. That formula is: Area = side^2
For this particular question, the given value for the area of the square is 36 sq.cm. So, we can solve for the side(s) by substituting the given value in the above mentioned formula.
We get
36 = s^2
Now, we need to get the square root of both sides, which gives us
s = √36 s = 6 cm
Since all the sides of a square are equal in length, the side length is 6 cm. Now to determine the perimeter, we must multiply the side length by 4 (because there are 4 equal sides in a square). That gives us Perimeter = 4 x side length Perimeter = 4 x 6 cm.
Therefore, the perimeter of the square is 24 cm.
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Alexei finances her purchase of a $900 television. Her one-year loan has a fixed annual interest rate of 2.5%.
What is Alexei's monthly payment?
Alexei's monthly payment is approximately $18.56.
Alexei finances her purchase of a $900 television with a one-year loan that has a fixed annual interest rate of 2.5%. To find Alexei's monthly payment, we can use the formula for calculating monthly loan payments.
The formula for calculating monthly loan payments is:
M = (P * r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = monthly payment
P = principal loan amount
r = monthly interest rate (annual interest rate divided by 12)
n =number of monthly payments
In this case, the principal loan amount (P) is $900, the annual interest rate (r) is 2.5% (or 0.025 when expressed as a decimal), and the number of monthly payments (n) is 12 (since it is a one-year loan).
First, we need to calculate the monthly interest rate (r) by dividing the annual interest rate by 12: r = 0.025 / 12 = 0.002083.
Next, we can substitute the values into the formula:
M = (900 * 0.002083 * (1 + 0.002083)^12) / ((1 + 0.002083)^12 - 1)
Simplifying the formula gives us:
M = (900 * 0.002083 * 1.002083^12) / (1.002083^12 - 1)
Calculating the values inside the formula gives us:
M = (900 * 0.002083 * 1.026260) / (1.026260 - 1)
Further simplifying the formula gives us:
M = (900 * 0.002083 * 1.026260) / 0.026260
Finally, calculating the expression gives us:
M ≈ 18.56
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Sets Sets M and Fare defined as follows: M = {a,b,c,d} F = {c, d, e, f} Find the intersection of M and F.
The intersection of sets M and F contains the elements "c" and "d".
To find the intersection of sets M and F, we need to identify the elements that are common to both sets.
M = {a, b, c, d}
F = {c, d, e, f}
The intersection of M
and F is denoted by M ∩ F, which represents the set containing elements that are present in both M and F.
Looking at the elements in M and F, we can see that the common elements between the two sets are "c" and "d".
Therefore, the intersection of M and F can be expressed as:
M ∩ F = {c, d}
So, the intersection of sets M and F contains the elements "c" and "d".
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Type the correct answer in each box.
Day Amount
1
$26
2
$23
3
$31
4
$26
5
534
The table shows the amount Bill spent on 5 days last week.
The mean of the amount he spent is $
The mean absolute deviation is $
Reset
Next
The mean absolute deviation is $106.6.
Given the table shows the amount Bill spent on 5 days last week.
DayAmount12622313126534To find the mean of the amount he spent: The formula for calculating the mean of a given set of values is mean=∑x/n where x represents the values, n represents the number of values, and ∑x represents the sum of the values.
Mean=total sum of values/total number of values Mean=(26+23+31+26+534)/5Mean=640/5Mean=128So,
the mean of the amount he spent is $128.To find the mean absolute deviation: The mean absolute deviation (MAD) is the average distance between each data value and the mean. MAD shows how much the data set deviates from the mean. The formula for calculating the MAD is MAD=∑|xi−m|/n where xi represents the values, m represents the mean, and n represents the number of values. So, the calculation for each day is:
Day Amount Absolute deviation from mean1 26 |128-26|=102 23 |128-23|=105 31 |128-31|=974 26 |128-26|=102 534 |128-534|=406
The sum of all absolute deviations is:
10+10+97+10+406=533The mean absolute deviation (MAD) is: MAD=533/5=106.6So.
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Can someone help me please? ASAP
Answer:
triangle XYZ is similar to triangle RPQ
scale factor = 2/5
Step-by-step explanation:
Angles X and R are given as congruent.
Angles Z and Q are right angles, so they are congruent.
Then, angles Y and P must be congruent.
The similarity statement is
triangle XYZ is similar to triangle RPQ
To find the scale factor, divide the length of a side of the image by the length of the corresponding side in the original.
10/25 = 2/5
The scale factor is 2/5.
21x² - 2x + 1/2 =0
find the following quadratic equation by factorization method
PLESE SOMEONE HELP
Step-by-step explanation:
21x²-2x +1/2 = 0
x² - 2x ×21 + 1/2× 21 = 0
factor and solve if necessary
y-5y-36
Answer:
Step-by-step explanation:
-4(y+9)
Sandro would like to retire at age 60 with an income of $1500 per month from his
retirement savings. If he is to receive these payments until he is 90 years old, what
amount would he need in his retirement savings account at age 60, if the account
earns 4.5% compounded monthly?
The amount (present value at age 60) that Sandro would neet in his retirement savings account in order to have a monthly income of $1,500 until he is 90 years old, compounded at 4.5% monthly is $296,041.74.
How the present value is computed:The present value is computed using an online fiance calculator that discounts the future withdrawals (monthly income) for a 360-months period.
End of withdrawal period = 90 years old
Beginning of withdrawal period = 60 years old
The number of years between 60 and 90 = 30 years
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 4.5%
PMT (Periodic Payment) = $-1,500
FV (Future Value) = $0
Results:
Present Value (PV) = $296,041.74
Sum of all periodic payments = $540,000 ($1,500 x 360 months)
Total Interest = $243,958.26
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