You took a test last week and the average grade was a 73. The standard deviation was
4.9 points. List the values at one, two, and three standard deviations from the mean
and-one, -two, -3 deviations from the mean.
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Answers
Values at one, two and three standard deviations are 77.9, 82.8 and 87.7 respectively. Values at -1, -2 and -3 standard deviations are 68.1, 63.2 and 58.3 respectively.
The average grade given = 73
So, the mean, μ = 73
The standard deviation, σ = 4.9
We need to find the 1,2 and 3 standard deviations and -1, -2 and -3 deviations from the mean.
We use the formula z = μ + nσ to find the values at nth deviations.
When n = 1
z = 73 + 1 x 4.9 = 77.9
When n = 2
z = 73 + 2 x 4.9 = 82.8
When n = 3
z = 73 + 3 x 4.9 = 87.7
When n = -1
z = 73 -1 x 4.9 = 68.1
When n = -2
z = 73 - 2 x 4.9 = 63.2
When n = -3
z = 73 - 3 x 4.9 = 58.3
Hence, these are the required values.
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Related Questions
Find the product of 32 and 46. Now reverse the digits and find the product of 23 and 64. The products are the same!
Does this happen with any pair of two-digit numbers? Find two other pairs of two-digit numbers that have this property.
Is there a way to tell (without doing the arithmetic) if a given pair of two-digit numbers will have this property?
Answers
Let's calculate the products and check if they indeed have the same value:
Product of 32 and 46:
32 * 46 = 1,472
Reverse the digits of 23 and 64:
23 * 64 = 1,472
As you mentioned, the products are the same. This phenomenon is not unique to this particular pair of numbers. In fact, it occurs with any pair of two-digit numbers whose digits, when reversed, are the same as the product of the original numbers.
To find two other pairs of two-digit numbers that have this property, we can explore a few examples:
Product of 13 and 62:
13 * 62 = 806
Reversed digits: 31 * 26 = 806
Product of 17 and 83:
17 * 83 = 1,411
Reversed digits: 71 * 38 = 1,411
As for determining if a given pair of two-digit numbers will have this property without actually performing the multiplication, there is a simple rule. For any pair of two-digit numbers (AB and CD), if the sum of A and D equals the sum of B and C, then the products of the original and reversed digits will be the same.
For example, let's consider the pair 25 and 79:
A = 2, B = 5, C = 7, D = 9
The sum of A and D is 2 + 9 = 11, and the sum of B and C is 5 + 7 = 12. Since the sums are not equal (11 ≠ 12), we can determine that the products of the original and reversed digits will not be the same for this pair.
Therefore, by checking the sums of the digits in the two-digit numbers, we can determine whether they will have the property of the products being the same when digits are reversed.
1. A ride in a cab costs $0.60 plus $0.14 per mile.
a. Write an equation for traveling x miles in the cab.
b. The cab charges $0.88 for a ride of how many miles?
c. How much does the cab charge for a trip of 8 miles?
Answers
The equation for traveling x miles in the cab can be written as:
Cost = $0.60 + $0.14 * x. The cab charges $0.88 for a ride of 2 miles. And the cab charges $1.72 for a trip of 8 miles.
a. The equation for traveling x miles in the cab can be written as:
Cost = $0.60 + $0.14 * x
b. To find the number of miles for a cab ride that costs $0.88, we can set up the equation:
$0.88 = $0.60 + $0.14 * x
Subtracting $0.60 from both sides, we get:
$0.88 - $0.60 = $0.14 * x
$0.28 = $0.14 * x
Dividing both sides by $0.14, we find:
x = $0.28 / $0.14
x = 2 miles
Therefore, the cab charges $0.88 for a ride of 2 miles.
c. To calculate the cost of a trip of 8 miles, we can substitute x = 8 into the equation:
Cost = $0.60 + $0.14 * 8
Cost = $0.60 + $1.12
Cost = $1.72
Therefore, the cab charges $1.72 for a trip of 8 miles.
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Hunter and his children went into a movie theater and will buy bags of popcorn and drinks. Each bag of popcorn costs $5.50 and each drink costs $6. Hunter has a total of $80 to spend on bags of popcorn and drinks. Write an inequality that would represent the possible values for the number of bags of popcorn purchased, bb, and the number of drinks purchased, d.d.
Answers
Answer:
......
Step-by-step explanation:
.......
Answer:
5.50b+6d≤80
Step-by-step explanation:
One bag of popcorn costs $5.50, so bb bags of popcorn cost 5.50b.5.50b. One drink costs $6, so dd drinks cost 6d.6d. The total 5.50b+6d5.50b+6d must be less than or equal to \$80:$80
Ashley works at Macy’s selling perfume. She earns a salary of $1,500 a month plus 15% of her total sales on perfume. What does she earn, in total, at the end of the month if she sells 1 bottle of Marc Jacobs’ “Daisy”, worth $96?
Answers
Answer:
1,514.40
Step-by-step explanation:
15% of 96 is 14.40$. if she only sold one bottle its 1514.40.
AREA OF CIRCLES HELP PLS
Answers
Answer:
a=π9² is the formula with the radius plugged in
radius is half
Answer:
243in^2
Step-by-step explanation:
18/2=9
3 x 9 x 9=243
what is the difference in area between a circle with a diameter of 3 meters and a square with a side length of 3 meters? Write Your Answer In Terms Of pi.
Answers
Given the word problem, we can deduce the following information:
1. The diameter of the circle is 3 meters.
2. The side length of the square is 3 meters.
To determine the difference in area between a circle and a square, we note first the formulas of a circle with a diameter d and the area of a square with side length d:
\(A_{circle}=\frac{\pi d^2}{4}\)where:
d=diameter
\(\text{A}_{square}=d^2\)where:
d=side length
The figures are shown below:
Based on this, the difference of areas would be:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ \end{gathered}\)Next, we plug in d=3:
\(\begin{gathered} A_{square}-A_{circle}=d^2-\frac{\pi d^2}{4} \\ =(3)^2-\frac{\pi(3)^2}{4} \\ =9-\frac{9\pi}{4} \end{gathered}\)Therefore, the difference in areas is:
\(9-\frac{9\pi}{4}\)
2. Next she needs to find her maximum heart rate m by subtracting her age a from 220. Write an
equation she can use.
Answers
Answer:
220 - a = m
Step-by-step explanation:
a is her age
1. How many more monthly payments are made for a five-year loan than for a three-year loan?
Answers
Answer: There are 24 more payments made.
Step-by-step explanation:
In a 5 year loan there is 60 months
In a 3 year loan there is 36 months.
the standard normal curve shown below models the population distribution of a random variable. what proportion of the values in the population does not lie between the two z-scores indicated on the diagram?
Answers
Answer:
The answer is B. 0.1131 because the molecule has been observed and the hill is upwards so there you have
What must you do when you divide and multiply by a negative number?
Answers
Answer:
When you multiply both sides by a negative value you make the side that is greater have a "bigger" negative number, which actually means it is now less than the other side! This is why you must flip the sign whenever you multiply by a negative number.
Step-by-step explanation:
HELP FOUR MORE MINUTES LEFT ON MY TEST!
Answers
Find (f/g)(5) for the functions
f(x) and g(x) given below.
f(x) = x2 +1 and g(x) = x - 4
=
=
(f/g)(5) = [?]
=
Answers
Answer:
11
Step-by-step explanation:
(f/g)(5)=
f(5)=(5)2+1÷g(5)=5-4
10+1/1
11/1
(f/g)=11
The required simplified value of the given function as (f/g)(5) is 26.
What is simplification?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,
f(x) = x² +1
f(5) = 5² + 1
f(5) = 26
g(x) = x - 4
g(5) = 5 - 4 = 1
f/g(5) = f(5) / g(5)
= 26 / 1 = 26
Thus, the required simplified value of the given expression (f/g)(5) is 26.
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An object is moving at a speed of 6 inches every 4 to 5 days. express the speed in yards per year. round your answer to the nearest 10th
Answers
Answer:
The speed in yards per year is 60.8.
Step-by-step explanation:
To convert the speed from inches per day to yards per year, we need to first convert the speed to inches per year and then convert the units to yards per year.
First, we can convert the speed to inches per year by multiplying the speed by the number of days in a year:
Speed (inches/day) * Days per year = Speed (inches/year)
6 inches/day * 365 days/year = 2190 inches/year
Next, we can convert the units to yards per year by dividing the speed in inches per year by the number of inches per yard:
Speed (inches/year) / Inches per yard = Speed (yards/year)
2190 inches/year / 36 inches/yard = 60.8 yards/year
Rounding to the nearest 10th, we have:
60.8 yards/year ≈ 60.8 yards/year
Therefore, the speed in yards per year is 60.8.
I DONT KNOW WHAT 1+1 IS HELP MEEEEEEEE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
2
..................................
Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage. Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In last five years, the market value of the house has increased by 4.8% per year 6. If she wants to sell the house today, the total transaction cost will be 5% of selling price Given the above information, please calculate the internal rate of return (IRR) of this investment in house
Can you show the math as far as formulas go?
Answers
Given the following information: Five years ago, someone used her $40,000 saving to make a down payment for a townhouse in RTP. The house is a three-bedroom townhouse and sold for $200,000 when she bought it. After paying down payment, she financed the house by borrowing a 30-year mortgage.
Mortgage interest rate is 4.25%. Right after closing, she rent out the house for $1,800 per month. In addition to mortgage payment and rent revenue, she listed the following information so as to figure out investment return: 1. HOA fee is $75 per month and due at end of each year 2. Property tax and insurance together are 3% of house value 3. She has to pay 10% of rent revenue for an agent who manages her renting regularly 4. Her personal income tax rate is 20%. While rent revenue is taxable, the mortgage interest is tax deductible. She has to make the mortgage amortization table to figure out how much interest she paid each year 5. In the last five years, the market value of the house has increased by 4.8% per year 6.
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can someone please help me with 13? there’s only two options you can see them in the picture
Answers
Answer:
The value of x is 5.8
Step-by-step explanation:
Here. we want to find the value of x
To do this, we need the appropriate trigonometric identity
As we can see 10 is the opposite as it faces the side given
x is the adjacent
The trigonometric identity relating opposite and adjacent is tan . Tan is the ratio of the opposite to the adjacent
Thus, mathematically;
Tan 60 = 10/x
x = 10/tan 60
x = 5.8
WILL GIVE BRAINLIEST!!
A line has a slope of 1/3 and passes through the point (–9, –3). What is its equation in slope-intercept form?
Answers
Answer:
y = \(\frac{1}{3}\) x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here slope m = \(\frac{1}{3}\) , then
y = \(\frac{1}{3}\) x + c ← is the partial equation
to find c substitute (- 9, - 3) , that is x = - 9, y = - 3 into the partial equation
- 3 = \(\frac{1}{3}\) (- 9) + c = - 3 + c ( add 3 to both sides )
0 = c
y = \(\frac{1}{3}\) x + 0 , that is
y = \(\frac{1}{3}\) x
What is the number of the parking space covered by the car?
Answers
Answer:
87
Step-by-step explanation:
Look at it upside down!
A group of adult males has foot lengths with a mean of 26.84 cm and a standard deviation of 1.29 cm. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. Is the adult male foot length of 23.8 cm significantly low or significantly high?
Significantly low values are ___ cm or lower.
Significantly high values are ___ cm or higher.
Select the correct choice below and fill in the answer box(es) to complete your choice.
A) The adult male foot length of 23.8 cm is not significant because it is between __ cm and __ cm
B) The adult male foot length of 23.8 cm is significantly low because it is less than __ cm
C) The adult male foot length of 23.8 cm is significantly high because it is greater than __ cm
Answers
The option B, "The adult male foot length of 23.8 cm is significantly low because it is less than 24.26 cm" is correct.
In the given question, a group of adult males has foot lengths with a mean of 26.84 cm and a standard deviation of 1.29 cm.
We have to find the adult male foot length of 23.8 cm significantly low or significantly high.
According to thumb rule, a value is significantly low if it is 2 standard deviations below mean and significantly high if it is 2 standard deviations above mean
Mean = 26.84 cm
Standard deviation = 1.29 cm
Significantly low value = 26.84 - 2*1.29 = 24.26 cm
Significantly high value = 26.84 + 2*1.29 = 29.42 cm
Significantly low values are 24.26 cm or lower.
Significantly high values are 29.42 cm or higher.
The adult male foot length of 23.8 is lower than the significant low value of 24.26.
So the option B, "The adult male foot length of 23.8 cm is significantly low because it is less than 24.26 cm" is correct.
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Yo I need help with this
Answers
Answer:
1) n + 12
2) n + 7
3) 15x
4) 2y - 20
5) \( \dfrac{x}{-2} + 7 \)
6) 2n - 3
7) 3(12 + x)
Jake is riding a skateboard down a ramp that is In the shape of a right
triangle. The
ramp has a height of 5 feet and a base of 12 feet. What is the
length of the ramp?
Ramp
O A. 11 ft
0 B. 119 ft
C. 13 ft
® D. 169 ft
Answers
Answer: 13
Step-by-step explanation:
a^2 + b^2 = c^2
12^2 + 5^2 = 169
root169 = 13
A 12-sided solid has faces numbered 1 to 12. The table shows the results of rolling the solid 200 times. Find the experimental probability of rolling a number less than 3
Answers
The experimental probability of rolling a number less than 3 is 0.11 or 11% when rolling a 12-sided solid numbered from 1 to 12, based on the provided data.
The number of faces that are numbered less than 3 on a 12-sided solid is 2, i.e., 1 and 2. Therefore, the probability of rolling a number less than 3 can be calculated by adding the frequencies of rolls that resulted in 1 and 2, and then dividing the sum by the total number of rolls.
From the table, we can see that the frequency of rolling a 1 is 10 and the frequency of rolling a 2 is 12. Therefore, the total frequency of rolling a number less than 3 is 10 + 12 = 22.
The total number of rolls is 200.
The experimental probability of rolling a number less than 3 is the frequency of rolling a number less than 3 divided by the total number of rolls:
Experimental probability = Frequency of rolling a number less than 3 / Total number of rolls
Experimental probability = 22 / 200
Experimental probability = 0.11
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Jill babysat for 7 1/2 hours and earned $63.75. How much money does she earn per hour?
Answers
Answer:
$8.50 per hour
Step-by-step explanation:
63.75 / 7.5 = 8.5
in its standardized form, the normal distribution has a mean of 0 and a standard deviation of 1 has a mean of 1 and a standard deviation of 1 has an area equal to .5 cannot be used to approximate discrete probability distributions
Answers
Option-A is correct that is has a mean of 0 and standard deviation of 1 is the standardized form of the normal distribution.
Given that,
We have to find what is the standardized form of the normal distribution.
We know that,
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
Therefore, Option-A is correct that is has a mean of 0 and standard deviation of 1 is the standardized form of the normal distribution.
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3x+5<6x+8
4x+3 is <7x+5
Answers
The solution to the inequalities 3x + 5 < 6x + 8 and 4x + 3 < 7x + 5 is x > -1 and x > -2/3 respectively
InequalityInequality signs are;
Greater than >Less than <Equal to =Less than equal to ≤Greater than equal to ≥3x + 5 < 6x + 8
collect like terms3x - 6x < 8 - 5
-3x < 3
divide both sides by -3x > 3/-3
The inequality sign is flipped from < to greater than because of the division with negative value.
x > -1
2. 4x + 3 < 7x + 5
collect like terms4x - 7x < 5 - 3
-3x < 2
divide both sides by -3The inequality sign is flipped from < to greater than because of the division with negative value.
x > -2/3
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Suppose that $50,000 from a retirement account is invested in a large-cap stock fund. After 20 yr, the value is $175,222.57. Use the model A=Pe^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps. The average rate is approximately __%
Answers
Answer:
6%
Step-by-step explanation:
The average rate is approximately 2%
The formula for calculating the average rate of return under continuous compounding is expressed as \(A=Pe^{rt\)
Given the following parameters
\(P = \$50,000\)
A = $175,222.57
t = 20 years
Substitute the given parameters into the formula to get the rat\(175,222.57 = 5000e^{20r}\\e^{20r}=\frac{175,222.57.}{5000}\\e^{20r}= 35.155514\\lne^{2r}=ln 35.155514\\2r = 3.5597\\r = 3.5597/2\\r =1.779 \%\)
Hence the average rate is approximately 2%
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Which of the following is NOT considered to be a Time-Series method of forecasting?
Simple Linear Regression
Moving Average
Exponential Smoothing
Seasonality Analysis
Multiplicative/Additive Decomposition
Answers
The correct option is Simple Linear Regression. Simple Linear Regression is NOT considered to be a Time-Series method of forecasting. The other methods are Time-Series method.
Time-Series analysis is a technique for forecasting future values based on previous observations. It includes various methods such as Moving Average, Exponential Smoothing, Seasonality Analysis, and Multiplicative/Additive Decomposition. Simple Linear Regression, on the other hand, is a method of predicting the relationship between two variables through a straight-line equation. Therefore, it is not considered to be a Time-Series method of forecasting.
A moving average is a common Time-Series method that calculates the average of a specific number of past observations to forecast future values. Exponential smoothing, another popular Time-Series method, assigns more weight to recent observations than to older ones. Seasonality analysis and multiplicative/additive decomposition are also Time-Series methods that are used to analyze trends and patterns in data over time.
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Which statement is correct?
Answers
The following statements are correct in the inscribed quadrilateral in a circle:
x° + y° = 180°
z = 87°
x = 82°
How to determine which statement is correct in the inscribed quadrilateral in a circle?An inscribed quadrilateral is a quadrilateral whose four vertices lie on a circle. Here are some properties of an inscribed quadrilateral in a circle
Since the opposite angles of an inscribed quadrilateral in a circle are supplementary i.e. the sum of the opposite angles is 180 degrees. We can write the following statements:
x° + y° = 180°
z° + 93° = 180°
z = 180 - 93 = 87°
Since x is an inscribed angle that intercepts the arc 58 + 106° = 164°. Thus, by the Inscribed Angle Theorem:
x = 164/2 = 82°
y = 180 - 82 = 98°
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Tommy's age is 5 years younger than Jack's age. The sum of their ages is 33. How old is Tommy?
Answers
Answer:
Tommy is 14 years old.
Step-by-step explanation:
14+5=19
Jack is 19 years old.
14+19=33
Hope this helps!
\(\huge\mathcal {♨Answer♥}\)
\(\large\texttt{Let's get Jack's age as x}\)
\(\large\texttt{So Tommy's age is x-5}\)
( x - 5 ) + x = 33
2x - 5 = 33
2x = 33 + 5
2x ÷ 2 = 38 ÷ 2
x = 19
So Jack's age is 19
Then,
Tommy's age is = x - 5
= 19 - 5
= 14
☆...hope this helps...☆
_♡_mashi_♡_
What is 0.82 as a fraction in simplest form?
(I also need the work if not its ok!)
Answers
Answer:
f 41/50
Step-by-step explanation: