What are the equivalent fraction and decimal for 33-%?31and 0.3331and 333103- and 0.3331and 0.333
Answers
The qustion asks to express 33% in its equivalent fraction and decimal.
33% can be expressed directly as 33/100
This is the equivalent fraction
We can now proceed from here to get the decimal that is equivalent to this
Mathematically, that will be 33/100 = 0.33
33% in its equivalent fraction and decimal is 33/100 and 0.33 respectively
Related Questions
Your daughter found three pieces of ribbon in all different colors. Their lengths were 2 meters and 1 decimeter; 3 meters and 9 decimeters; and 6 meters and 4 decimeters. What was the length of the ribbons in all? Give a decimal answer in meters.
Answers
Answer:
convert the lengths to meters
10dm=1m
1dm=0.1m
hence, firs ribbon
2m+0.1m=2.1m
Second Ribbon
3m and 9dm
convert 9dm into Metres we get 0.9m
hence, 3m+0.9m=3.9m
Third Ribbon
6m+0.4m=6.4m
Choose all the answers that apply. Which of the following is an example of an ion? Ar Na+ F+ Cl-
Answers
Answer:
Na+ and Cl- should be examples of an ion.
<Hope I answered your question>
Answer:
Na+ and Cl- should be examples of an ion.
Step-by-step explanation:
what is the mode median mean and range of 4,5,0,2,3,1
Answers
Answer:
Mode = none, Median = 2.5, Mean= 2.5
Step-by-step explanation:
Hope this helps! :)
Step-by-step explanation:
the mode is the data item that occurres the most often.
but in 4, 5, 0, 2, 3, 1 every number appears only once. so, the mode is 0, 1, 2, 3, 4, 5 (as special case this average number can have more than one value - like in our case here).
the median is the value in the data set that lies directly in the middle between the other values (half of them are higher, the other half is lower).
if our data set has an even number of data points, or there is no unique middle value for other reasons, then the median is the mean value of the 2 middle values.
in our case 2 and 3 are the 2 middle values, so the median is (2+3)/2 = 2.5
the mean value is directly the average value across the whole data set : the sum of all values divided by the number of values.
(0+1+2+3+4+5)/6 = 15/6 = 2.5
the range is the difference between the highest and the lowest value in the data set : 5 - 0 = 0
As a bowling instructor, you calculate your students' averages during tournaments. In 5 games, one bowler had the following scores: 143, 156, 172, 133, and 167. What was that bowler's average?
Answers
Answer:
154.2
Step-by-step explanation:
143 plus
156 plus
172 plus
133 plus
167 = 771
divide by 5 equals 154.2
A person is studying the relationship between temperature and mental ability. So,
she devised a test in which a group of 10 mice are timed as they run through a maze
which leads to food and water. The researcher repeats the test 3 times with each
group to see how much they improve and she uses three groups.
• Group 'A', does the test under normal room temperature of 76°F.
• Group 'B', does the test in the cold at a temperature of 45°F.
• Group 'C' does the test under a hot temperature of 105°F.
How would you most correctly describe Group 'C' in a statistical study?
Answers
Answer:
control
Step-by-step explanation:
You need to borrow $2550 to help contribute to an upcoming family reunion. You can borrow the money from two different banks.
Bank A will lend you $2550 for six months at an interest rate of 11.5%
How much money will you owe at the end of each period of time? Which bank offer will you choose and why?
Bank B will lend you $2550 for twelve months at an interest rate of 7.5%
Answers
Amount to be repaid for Bank A is $2,696.625 and Amount to be repaid for Bank B is $2,741.25. However, I will choose Bank B because it offers a lower interest rate.
How to calculate the simple interest?The formula to calculate the simple interest is;
I = PRT
Where;
P is principal
R is rate
T is time
Now, we are given that;
Bank A;
Principal amount; P = $2550
Interest rate; R = 11.5% = 0.115
Time; t = 6 months = 0.5 years
Thus;
I = (2550 * 0.115 * 0.5)
I = $146.625
Amount to be repaid = 2550 + 146.625
Amount to be repaid = $2,696.625
Bank B;
Principal amount; P = $2550
Interest rate; R = 7.5% = 0.075
Time; t = 12 months = 1 year
Thus;
I = (2550 * 0.075 * 1)
I = $191.25
Amount to be repaid = 2550 + 191.25 = $2,741.25
Thus, bank B offers a more favorable interest rate and as such would be the preferred bank.
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*Today's Assignment*
Design a salary slip for the month of March 2023 with information given below.
Fixed vs variable ratio- 70:30
Ctc - 18L
Basic- 50%
Hra- 20%
Da - 12%
Insurance - 2500
Incentive- 75% target completion
Pf 12%
Earned leaves - 2
LOP - 4
Calculate net pay
Answers
A salary slip for the month of March 2023 with information given below.
Salary Slip - March 2023
Employee Details:
Name: [Employee Name]
Employee ID: [Employee ID]
Designation: [Employee Designation]
Earnings:
Basic Salary: [Basic Salary]
House Rent Allowance (HRA): [HRA]
Dearness Allowance (DA): [DA]
Incentive: [Incentive]
Total Earnings: [Total Earnings]
Deductions:
Provident Fund (PF): [PF]
Insurance: [Insurance]
Loss of Pay (LOP): [LOP]
Total Deductions: [Total Deductions]
Net Pay: [Net Pay]
Breakdown:
Basic Salary: 50% of CTC (18L) = [Basic Salary]
HRA: 20% of Basic Salary = [HRA]
DA: 12% of Basic Salary = [DA]
Incentive: 75% of target completion = [Incentive]
Total Earnings = Basic Salary + HRA + DA + Incentive = [Total Earnings]
PF: 12% of Basic Salary = [PF]
Insurance: Rs. 2500 = [Insurance]
LOP: [LOP]
Total Deductions = PF + Insurance + LOP = [Total Deductions]
Net Pay = Total Earnings - Total Deductions = [Net Pay]
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please help with this question
Answers
The probability of the sample mean being less than 25.3 is given as follows:
0.9713 = 97.13%.
The sample mean would not be considered unusual, as it has a probability that is greater than 5%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a normally distributed variable that has mean represented by \(\mu\) and standard deviation represented by \(\sigma\) is obtained by the equation presented as follows:
\(Z = \frac{X - \mu}{\sigma}\)
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution of the data-set, depending if the obtained z-score is positive(above the mean) or negative(below the mean).The z-score table is used to obtain the p-value of the z-score, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation given by the equation presented as follows: \(s = \frac{\sigma}{\sqrt{n}}\).The parameters for this problem are given as follows:
\(\mu = 25, \sigma = 1.3, n = 68, s = \frac{1.3}{\sqrt{68}} = 0.1576\)
The probability of a score less than 25.3 is the p-value of Z when X = 25.3, hence:
Z = (25.3 - 25)/0.1576
Z = 1.9
Z = 1.9 has a p-value of 0.9713.
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In a swimming competition, Peter swam 600m and Gabriel swam 2km .What is the ratio of Peter’s distance to Gabriel’s? Give your answer in its simplest form.
b. Express the ratio 20cm to 15m in the form 1: n
c. Express the ratio 60 cm to 20 m in the form 1 : n
Answers
Answer:
Yes, because Gabriel is the swimming. He was in 2nd or maybe 10th.
Answer:
Step-by-step explanation:
6TH GRADE MATH SOMEONE PLEASE GIVE ANSWER TYSM
Answers
The surface area of the vase is 168.4 square inches.
What is a cylinder?
A cylinder is a three-dimensional geometric shape that has two congruent circular bases connected by a curved surface.
The surface area of the cylindrical vase can be found using the formula SA = B + Ph, where B is the area of the base, P is the perimeter of the base, and h is the height of the vase. Since the vase has a circular base, the area of the base can be found using the formula for the area of a circle: B = πr², where r is the radius of the base.
The diameter of the vase is 4.3 inches, so the radius is half of that, or 2.15 inches. The area of the base is therefore:
B = πr² = 3.14 * (2.15)² ≈ 14.46 square inches.
The perimeter of the base is the circumference of the circle, which can be found using the formula C = 2πr:
P = 2πr = 2 * 3.14 * 2.15 ≈ 13.53 inches.
Now we can use the formula SA = B + Ph to find the surface area of the vase:
SA = B + Ph = 14.46 + 13.53 * 11 ≈ 168.39 square inches.
Rounding to the nearest tenth of a square inch, the surface area of the vase is approximately 168.4 square inches.
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Determine by inspection whether the vectors are linearly independent. Justify your answer. [ 8 [ 12 -6 -9 4] 6]A. The set of vectors is linearly independent because nothing times the first vector is equal to the second vector. (Type an integer or a simplified fraction.) B. The set of vectors is linearly dependent because nothing times the first vector is equal to the third vector. (Type an integer or a simplified fraction.) C. The set of vectors is linearly dependent because one of the vectors is the zero vector. D. The set of vectors is linearly independent because none of the vectors are multiples of the other vectors.
Answers
✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅✅
Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.
What is Matrix?A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.
To determine if the set of vectors is linearly independent, we need to check if any of the vectors can be expressed as a linear combination of the others.
Let's consider the first vector [8 -6 4].
If we try to express this vector as a linear combination of the other vectors, we get:
[8 -6 4] = a[12 -9 6] + b[0 0 0]
where a and b are constants.
We can immediately see that this equation has infinite solutions, because the third component of the second vector is zero, which means we can choose any value for b and still satisfy the equation.
Therefore, the set of vectors is linearly dependent.
Hence, Option C is correct, the set of vectors is linearly dependent because one of the vectors is the zero vector.
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Determine by inspection whether the vectors are linearly independent. Justify your answer.
[8 -6 4][12 -9 6]
A. The set of vectors is linearly independent because nothing times the first vector is equal to the second vector. (Type an integer or a simplified fraction.)
B. The set of vectors is linearly dependent because nothing times the first vector is equal to the third vector. (Type an integer or a simplified fraction.)
C. The set of vectors is linearly dependent because one of the vectors is the zero vector.
D. The set of vectors is linearly independent because none of the vectors are multiples of the other vectors.
Before beginning voice lessons, Chad already knew how to sing 805 pieces, and he expects
to leam 2 new pieces during each week of lessons. How many weeks of lessons will Chad
need before he will be able to sing a total of 937 pieces?
Answers
Let's create an equation to find the # of weeks until Chad learns 937 pieces.
x = # of weeks
937 = 2x + 805
Subtract 805 from both sides.
132 = 2x
Divide both sides by 2
66 = x
Chad will need 66 weeks of lessons to learn 937 pieces.
Pls answer this quickly. I need at atleast 70%
Answers
The equation of the line with yellow point in slope intercept form is y = 7 / 6 x + 2.
How to find the equation of a line?The equation of a straight line can be represented in different form such as slope intercept form, point slope form, etc.
Therefore, let's represent the line with yellow point in slope intercept form.
Hence,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (0, 2) and (6, 9).
m = 9 - 2 / 6 - 0
m = 7 / 6
Hence, let's find the y-intercept
y = 7 / 6 x + b
2 = 7 / 6(0) + b
b = 2
Therefore,
y = 7 / 6 x + 2.
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QUICK! 40 points. Consider this cone with the diameter measure of 17 inches.
A cone with diameter 17 inches and slant height of 22 inches.
What is the surface area of the cone?
SA = Pir2 + Pirl
A. 204Pi in.2
B. 259.25Pi in.2
C. 446.25Pi in.2
D. 663Pi in.2
Answers
259.25π in² is the surface area of the cone
The surface area of a cone can be calculated using the formula SA = πr² + πrl
where r is the radius and l is the slant height.
Given that the diameter is 17 inches, the radius (r) is half of the diameter, which is 17/2 = 8.5 inches.
The slant height (l) is given as 22 inches.
Substituting these values into the formula:
Surface Area = π(8.5)² + π(8.5)(22)
= 72.25π + 187π
= 259.25π
Therefore, the surface area of the cone is 259.25π in²
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The following questions pertain to the properties of the STANDARD NORMAL distribution. (a) True or False: The distribution is bell-shaped and symmetric. True False (b) True or False: The mean of the distribution is 0. True False (c) True or False The probability to the left of the mean is 0. True False (d) True or False The standard deviation of the distribution is 1. True False
Answers
Answer:
a. The distribution is bell-shaped and symmetric: True.
b. The distribution is bell-shaped and symmetric: True.
c. The probability to the left of the mean is 0: False.
d. The standard deviation of the distribution is 1: True.
Step-by-step explanation:
The Standard Normal distribution is a normal distribution with mean, \( \\ \mu = 0\), and standard deviation, \( \\ \sigma = 1\).
It is important to recall that the parameters of the Normal distributions, namely, \( \\ \mu\) and \( \\ \sigma\) characterized them.
We can use the Standard Normal distribution to find probabilities for any normally distributed data. All we have to do is normalized them through z-scores:
\( \\ z = \frac{x - \mu}{\sigma}\) [1]
Where \( \\ x\) is the raw score that we want to standardize.
Therefore, taking into account all this information, we can answer the following questions about the Standard Normal distribution:
(a) True or False: The distribution is bell-shaped and symmetric
Answer: True. As the normal distribution, the standard normal distribution is also bell-shape and it is symmetrical around the mean. The standardized values or z-scores, which represent the distance from the mean in standard deviations units, are the same but when it is above the mean, the z-score is positive, and negative when it is below the mean. This result is a consequence of the symmetry of this distribution respect to the mean of the distribution.
(b) True or False: The mean of the distribution is 0.
Answer: True. Since the Standard Normal uses standardized values, if we use [1], we have:
\( \\ z = \frac{x - \mu}{\sigma}\)
If \( \\ x = \mu\)
\( \\ z = \frac{\mu - \mu}{\sigma}\)
\( \\ z = \frac{0}{\sigma}\)
\( \\ z = 0\)
Then, the value for the mean is where z = 0. A z-score is a linear transformation of the original data. For this reason, the transformed mean is equivalent to 0 in the standard normal distribution. We only need to find distances from this zero in standard normal deviations or z-scores to find probabilities.
(c) True or False: The probability to the left of the mean is 0.
Answer: False. The probability to the left of the mean is not 0. The cumulative probability from \( \\ -\infty\) until the mean is 0.5000 or \( \\ P(-\infty < z < 0) = 0.5\).
(d) True or False: The standard deviation of the distribution is 1.
Answer: True. The standard normal distribution is a convenient way of calculate probabilities for any normal distribution. The standardized variable, represented by [1], permits us to use one table (the standard normal table) for all normal distributions.
In this distribution, the z-score is always divided by the standard deviation of the population. Then, the standard deviation for the standard normal distribution are times or fractions of the standard deviation of the population, since we divide the distance of a raw score from the mean of the population, \( \\ x - \mu\), by it. As a result, the standard deviation for the standard normal distribution will be times (1, 2, 3, 0.96, -1, -2, etc) the standard deviation of any normal distribution, \( \\ \sigma\).
In this case, the linear transformation of the original data for one standard deviation from the mean is z = 1. Therefore, the standard deviation for the standard normal distribution is the unit.
Answer:
A: true
B: true
C: false
D: true
When running an Ostrich can cover a distance of 22 miles per 1/2 hour. Convert the Ostrich's running speed to miles per hour. i really need help
Answers
answer:
im pretty sure you would divide 22 by .5 or 1/2 and you get 12 by rounding up the decimal
What is 35 degrees Celsius in Fahrenheit equal
Answers
Answer:
95°Fahrenheit
hipe this helps you
kerry is going to use these instructions to make a fizzy drink
mix 7 parts apple juice with 3 parts lemonade
kerry thinks that she has 280ml of applejuice and 180 ml lemonade.
if kerry is correct what is the greatest amount of fizzy drink she can make?
second part:
kerry has 280 ml of applejuice but only has 160 ml of lemonade.
Does this affect the greatest amount of fizzy drink she can make?
Give a reason for your answer.
Answers
a) She can make 400 milliliters of the fizzy drink.
b) The change does not affect the greatest amount of drink.
If kerry is correct what is the greatest amount of fizzy drink she can make?We know that the fizzy drink is 7 parts apple juice and 3 parts lemonade. And Kerry thinks that she has 280ml of apple juice and 180 ml lemonade.
If we divide the total amount of apple juice in 7 parts, then each part has:
280ml/7 = 40ml
Then we need 3 parts of 40ml of the lemonade, this is:
3*40ml = 120ml
Then the total amounf of drink fizz that she can make is:
280ml + 120ml = 400ml.
b) Now she has 160 ml of lemonade, but she needs 120 ml of it, so this change does not affect the greatest amount of fizzy drink she can make.
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Elyas is on holiday in Greece.
He wants to buy a pair of sunglasses for €90
The exchange rate is €1 = £0.875
Elyas says, "The sunglasses cost less than £70"
Using a suitable approximation, show that Elyas is wrong.
Answers
Answer:
To convert euros to pounds, we have to multiply the amount in euros by the exchange rate. So, the sunglasses cost 90 * 0.875 = 78.75 pounds.
To use a suitable approximation, we can round the exchange rate to the nearest hundredth, which is 0.88. This makes the calculation easier and gives a close estimate of the actual value.
Using the rounded exchange rate, the sunglasses cost 90 * 0.88 = 79.2 pounds.
We can see that both the exact and the approximate values are greater than 70 pounds, so Elyas is wrong. The sunglasses cost more than 70 pounds
Step-by-step explanation:
Joyce saved $220 on an item that was 75% off what was the original price
Answers
Answer:
$880
Step-by-step explanation:
Use the equation:
\(P=(1-d)x\) with d being the discount in a decimal form, and P being the price that was bought at.
220=(1-0.75)x
simplify parenthesis terms
220=0.25x
divide both sides by 0.25
880=x
So, the original price was $880.
Hope this helps! :)
Jsjsjs I hate this school app
Answers
I HOPE IT'S HELP PLZ FOLLOWING ME
what is the quotient of -0.75 0.4 please help
Answers
The quotient of -0.75 /0.4 is approximately -1.88.
What is the quotient?
This refers to the value you get after division operation has been carried out.
given in the question:
-0.75/0.4 = -1.875
≈ -1.88
Recall, according to the sign rule in mathematics:
Any negative number divided by a positive number gives a negative value.
hence the quotient of -0.75/0.4= -1.875
≈ -1.88
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B. Analyze the problem below and answer the questions that follow. a monthly salary of Php 18.500 Complete the table below which shows the deductions on Bianca has her payslip Name Bianca Ramos Assistant For the month of September 2020 Basic Salary 18,500 00 Position Financial Allowances Total Earnings 18.500 00 DEDUCTIONS Description SOCIAL SECURITY SYSTEM MEDICARE (PHILHEALTH) PAGIBIG (FUND) BIR (WITHHOLDING TAX) Amount of Deduction (11) (12) (13) (14). Total Deductions (15) NET PAY (16)
Answers
The completed table showing Bianca Ramos's tax deduction and NET PAY
is presented as follows;
SOCIAL SECURITY SYSTEM = Php 1,147
MEDICARE (PHILHEALTH) = Php 268.25
PAGIBIG (FUND) = Php 370
BIR (WITHHOLDING TAX) = Php 5,509.19
Total deductions = Php 7,294.44
NET PAY = Php 11,205.56
Reasons:
Based on online search, the tax rate for the items on the table are as follows;
SOCIAL SECURITY SYSTEM = 6.20% of earnings
MEDICARE (PHILHEALTH) = 1.45% of earnings
PAGIBID (FUND) = 2% of salary
BIR (WITHOLDING TAX) = P1,342.47 + 32% over P5,479
Bianca Ramos's basic salary = 18,500.00
Which gives the deduction amount as follows;
SOCIAL SECURITY SYSTEM = 0.062 × 18,500.00 = 1,147
MEDICARE (PHILHEALTH) = 0.0145 × 18,500.00 = 268.25
PAGIBIG (FUND) = 0.02 × 18,500.00 = 370
BIR (WITHHOLDING TAX) = 1,342.47 + 0.32×(18,500 - 5,479) = 5,509.19
Total deductions = 1,147 + 268.25 + 370 + 5,509.19 = 7,294.44
NET PAY = 18,500 - 7,294.44 = 11,205.56
Her net pay = Php 11,205.56
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d) Suppose you begin making a monthly payment of $75.00. Fill in the table.
Month Current balance
1
2
3
4
5
6
7
8
9
10
11
12
WYPIE
$2750.00
Interest
$45.38
Payment
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
$75.00
Amount applied to principal
$29.62
Answers
Answer:
Step-by-step explanation:
Answer:
For month 1, the current balance is $2750.00, the interest is $45.38, and the payment is $75.00. The amount applied to principal is $29.62.
For the remaining months, the interest and payment amount will stay the same, but the current balance and amount applied to principal will change based on the previous month's numbers.
Point of view:
Here's your answer but I prefer you to focus and study hard because school isn't that easy. But i'm glad I could help you!
:)
Kate did a survey to find the average hand span of the students in her class. She asked the following question:
What is the hand span of each student in the class?
Is Kate's question a statistical question, and why or why not?
Yes, because it asks a question that can be answered correctly
Yes, because it anticipates variability in students' hand spans
No, because it does not ask a question that can be answered correctly
No, because it does not anticipate variability in students' hand spans
Answers
Hey! I am here with some geometry questions today!
Please only answer if you know the answer and can support it by showing you work. If you have a comment or do not know the answer, tell me that in the comment section, do not answer the question. Don't take my points and I want take yours!
Anyways, please show all of you work and explain your thinking! Good luck!
Answers
Answer:
ParallelogramStep-by-step explanation:
ED = FG = 4, easy to calculateED ║ FG, both are vertical line segmentsEF = DG = √5²+1²= √26EF ║ DG as the slopes are samem(EF) = (7-6)/(6-1) = 1/5m(DG) = (3-2)/(6-1) = 1/5As we see the opposite sides are parallel and congruent. This is the property of a parallelogram
You start driving west for 3 miles, turn right, and drive north for
another 13 miles. At the end of driving, what is your straight line
distance from your starting point? Round to the nearest tenth of a
mile.
Answers
Answer:
13.3 miles
Step-by-step explanation:
Picture a right triangle with legs of 3 and 13. The hypotenuse is the straight line distance back to the starting point. Use the Pythagorean theorem to find the hypotenuse (c):
c² = 13² + 3² = 178
c = √178 = 13.3 miles
determine the surface area and volume
Answers
The surface area of a cylinder is 284m² and it's volume is 366.9m³
What is the surface area and volume of a cylinder?To find the surface area and volume of a cylinder, we need to know the radius (r) and height (h) of the cylinder. The formulas for the surface area (A) and volume (V) of a cylinder are as follows:
Surface Area (A) = 2πr² + 2πrhVolume (V) = πr²hFrom the given question, the data are;
radius = 4mheight = 7.3ma. The surface area of the cylinder is;
SA = 2π(4)² + 2π(4)(7.3)
SA = 283.999≈284m²
b. The volume of the cylinder is
v = πr²h
v = π(4)²(7.3)
v = 366.9m³
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Write a formula that describes the value of an initial investment of $4000 that loses value at a rate of 10% per year, compounded six times per year.
Answers
since the investment is losing 10%, let's plug that in the compound interest equation but with a negative rate of 10%.
\(~~~~~~ \underset{\textit{with a negatie rate}}{\textit{Compound Interest Earned Amount}} \\\\ A=P\left(1~~ - ~~\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$4000\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{six times} \end{array}\dotfill &6\\ t=years\dotfill &t \end{cases}\)
\(A=4000\left(1~~ - ~~\frac{0.10}{6}\right)^{6\cdot t}\implies A=4000\left( \frac{59}{60} \right)^{6t}\)
b) How many times would you expect the
spinner to land on a shaded section if it were
spun 40 times?
Answers
The number of times the spinner lands on a shaded section are 8 times.
What is the probability?
Probability is the branch of mathematics concerned with numerical descriptions of the likelihood of an event occurring or of a proposition being true.
We have,
2 Shaded sections are on a spinner,
8 unshaded sections are on a spinner,
10 total sections are on a spinner,
Therefore,
The probability of the spinner to land on a shaded section:
P = 2 ÷ 10 = 1 ÷ 5
consider x, the number of times the spinner lands on a shaded section.
If the spinner were spun 40 times:
so, \(\frac{x}{40} = \frac{1}{5}\)
By cross multiplying we get,
5x = 40
x = 8
Hence, the number of times the spinner lands on a shaded section are 8 times.
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