Answers
Answer: x = -144
Step-by-step explanation:
x/9 = -16
9*(x/9) = (-16)*9
x = -144
Related Questions
pls help
The distance from the Earth to the Sun is approximately 93,000,000 miles. What is this distance expressed in scientific notation? Answer options with 5 options A. 9.3 times 10 Superscript 6 Baseline miles B. 9.3 times 10 Superscript 7 Baseline miles C. 9.3 times 10 Superscript 8 Baseline miles D. 93 times 10 Superscript 6 Baseline miles E. 93 times 10 Superscript 7 Baseline miles
Answers
Answer:
B. 9.3 x 10^7
Step-by-step explanation:
9.<3<0<0<0<0<0<0.
Move the decimal point until there is only one whole number left.
One sponsor will donate $80 just for entering the race. Another sponsor will donate $12 for each mile she walks. How many miles should she walk if she wants to raise exactly $200 from those two sponsors?
Answers
Answer:
10 miles
Step-by-step explanation:
first you subtract 80 from 200
200-80= 120
then you divide 120 by 12
120/12= 10
she will need to walk 10 miles in order to raise 200 dollars
hope this helped!
a. Show that Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z).
b. Let X1 and X2 be quantitative and verbal scores on one aptitude exam, and let Y1 and Y2 be corresponding scores on another exam. If Cov(X1, Y1) = 5, Cov(X1, Y2) = 1, Cov(X2, Y1) = 2, and Cov(X2, Y2) = 8, what is the covariance between the two total scores X1 = X2 and Y1 +Y2?
Answers
The covariance between the total scores X1 = X2 and Y1 + Y2 is 16.
a. To show that Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z), we need to use the properties of covariance.
The covariance between two random variables X and Y is defined as:
Cov(X, Y) = E[(X - E[X])(Y - E[Y])],
where E[X] represents the expected value of X.
Let's calculate Cov(X, Y + Z) using the definition of covariance:
Cov(X, Y + Z) = E[(X - E[X])(Y + Z - E[Y + Z])].
Expanding the expression:
Cov(X, Y + Z) = E[(X - E[X])(Y + Z - E[Y] - E[Z])].
Distributing the terms:
Cov(X, Y + Z) = E[(X - E[X])(Y - E[Y]) + (X - E[X])(Z - E[Z])].
Now, let's calculate Cov(X, Y) + Cov(X, Z):
Cov(X, Y) + Cov(X, Z) = E[(X - E[X])(Y - E[Y])] + E[(X - E[X])(Z - E[Z])].
Expanding and rearranging the terms:
Cov(X, Y) + Cov(X, Z) = E[(X - E[X])(Y - E[Y]) + (X - E[X])(Z - E[Z])].
As we can see, Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z).
Therefore, we have shown that Cov(X, Y + Z) = Cov(X, Y) + Cov(X, Z).
b. To find the covariance between the total scores X1 = X2 and Y1 + Y2, we can use the properties of covariance and the given covariances:
Cov(X1, Y1 + Y2) = Cov(X1, Y1) + Cov(X1, Y2) + Cov(X1, Y2) + Cov(X1, Y2).
Since Cov(X1, Y2) = Cov(X2, Y1), we can simplify the expression:
Cov(X1, Y1 + Y2) = Cov(X1, Y1) + Cov(X1, Y2) + Cov(X2, Y1) + Cov(X2, Y2).
Plugging in the given covariance values:
Cov(X1, Y1 + Y2) = 5 + 1 + 2 + 8 = 16.
Therefore, the covariance between the total scores X1 = X2 and Y1 + Y2 is 16.
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you have six slices of bread, three tomato slices, and two cheese slices. how many tomato-cheese sandwiches can you make? which ingredient(s) limit the number of sandwiches you can make?
Answers
You can make a maximum of two tomato-cheese sandwiches. because you can only make as many tomato-cheese sandwiches as the number of cheese slices you have
To make a tomato-cheese sandwich, you need one tomato slice and one cheese slice. Since you have three tomato slices and two cheese slices, you are limited by the availability of cheese slices.
Therefore, you can only make as many tomato-cheese sandwiches as the number of cheese slices you have, which in this case is two.
The ingredient that limits the number of sandwiches you can make is the cheese slice. You have more tomato slices than cheese slices, so you cannot make more than two tomato-cheese sandwiches.
Even if you have extra tomato slices, you cannot make additional sandwiches because you do not have enough cheese slices to pair with them.
In summary, the number of tomato-cheese sandwiches you can make is determined by the ingredient with the lowest quantity,
which in this case is the cheese slice. Therefore, you can make a maximum of two tomato-cheese sandwiches.
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The fence around Stan's rectangular backyard is 48 feet. His yard is 3 feet longer than twice its width. What is the length of Stan's yard?
Answers
Answer: Length = 17 ft
Concept:
Here, we need to know how to find the perimeter of a rectangle.
Perimeter (rectangle) = 2 (l + w)
l = length
w = width
If you are still confused, you may refer to the attachment below for a graphical explanation or tell me.
Solve:
**Disclaimer** I assume that the length is [3 feet longer than twice its width] because a [yard] would not use length to measure it. If it was, then you may refer to my answer. If it was not, then you may tell me and I will redo it.
Let x be the width
Let 2x + 3 be the length
Given information
Perimeter = 48 ft
width = x
length = 2x + 3
Given expression deducted from the question
Perimeter = 2 (l + w)
Substitute values into the expression
48 = 2 (2x + 3 + x)
Combine like terms in the parentheses
48 = 2 (2x + x + 3)
48 = 2 (3x + 3)
Expand parentheses and apply the distributive property
48 = 2 · 3x + 2 · 3
48 = 6x + 6
Subtract 6 on both sides
48 - 6 = 6x + 6 - 6
42 = 6x
Divide 6 on both sides
42 / 6 = 6x / 6
x = 7
Find the value of length
Length = 2x + 3 = 2(7) + 3 = 14 + 3 = \(\boxed{17}\)
Hope this helps!! :)
Please let me know if you have any questions
A spinner is divided into five colored sections that are not of equal size: red,
blue, green, yellow, and purple. The spinner is spun several times, and the
results are recorded below:
Spinner Results
Color Frequency
7
16
Red
Blue
Green
Yellow
Purple
19
8
3
Based on these results, express the probability that the next spin will land on
yellow as a percent to the nearest whole number.
Answers
Answer:
15.09%
Step-by-step explanation:
Sum of frequencies = 53
Probability = 8
53
=0.1509
Expressing as a percentage
>> 15.09%
Write an exponential function to model each situation.Find the value of each function after five years.
a. A $12,500 car depreciates 9% each year.
b. A baseball card brought for $50 increases 3% in value each year.
Answers
The exponential functions for the two scenarios given are -
a) \(y = 12500 (0.91)^x\), Price of car after 5 years is $7800.40.
b) \(y = 50 (1.03)^x\), Price of baseball card after 5 years is $57.96.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The exponential function is in the form -
\(y=ab^x\)
Here y is the function, a is the constant base value, b is the rate of growth/depreciation and x is the time in years.
The first statement is -
A $12,500 car depreciates 9% each year.
The value for base is a = $12,500.
The value for rate is 9% = 0.09
Since, the price is depreciating the value for b is b = (1 - 0.09)
The exponential function is -
\(y = 12500 (1 - 0.09)^x\)
\(y = 12500 (0.91)^x\)
The value of car after 5 years can be obtained by substituting x = 5.
\(y = 12500 (0.91)^5\\y = 12500(0.6240)\\y=7800.40\)
Therefore, the equation is \(y = 12500 (0.91)^x\) and the value of car is $7800.40.
The second statement is -
A baseball card brought for $50 increases 3% in value each year.
The value for base is a = $50.
The value for rate is 3% = 0.03
Since, the price is increasing the value for b is b = (1 + 0.03)
The exponential function is -
\(y = 50 (1+0.03)^x\)
\(y = 50 (1.03)^x\)
The value of baseball card after 5 years can be obtained by substituting x = 5.
\(y = 50 (1.03)^5\\y = 50 (1.1592)\\y =57.96\)
Therefore, the equation is \(y = 50 (1.03)^x\)and the value of baseball card is $57.96.
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Miguel wants to bike a total of 100 miles over the course of one week in the summer. He logs how much he bikes each day in the table below.
Miguel’s Biking Log
Day
Miles Completed
Monday
16.3
Tuesday
14 and one-half
Wednesday
18.75
Thursday
12 and one-fourth
Friday
22 and three-fifths
How many total miles does Miguel need to ride on Saturday and Sunday to meet his goal?
15 and three-fifths miles
45 and one-fifth miles
62 and one-half miles
84 and two-fifths miles
Answers
Answer:15 and three-fifths
Step-by-step explanation:
Answer:
15 and three-fifths
Step-by-step explanation:
Find the gradient and intercept on the x and y axes of the straight line with the following equation.
y + 5x = 13
Answers
Answer:
gradient is 5
Step-by-step explanation:
x intercept, replace y with 0
y +5x= 13
0+ 5x =13
0 - 13= -5x
-13= -5x
-13/-5 = -5x/-5
x = 13/5
y intercept, replace x with 0
y+5x=13
y+5(0)=13
y+0=13
y =13
SOMEONE HELP ME!! NO ONE WILL HELP T^T WILL MARK BRAINLIEST
Answers
Answer: nope!
Step-by-step explanation: there are 4 quarts in a gallon and we can see by adding the mango juice, there will be no space!
Water (2 quarts) mango juice (2 quarts) equals a gallon
Ginger ale = one gallon
That’s already 2 gallons and we still have the 2 pints of pineapple juice!
You randomly survey students about whether they like hamburgers or hot dogs. of 129 students who like hamburgers, 46 like hot dogs. of 143 students who dislike hamburgers, 54 like hot dogs. organize the results in a two-way table. include the marginal frequencies.
Answers
Here is the two-way table and the marginal frequencies in bracket:
Like hamburger do not like hamburger Total
Like hot dog 46(0.16) 54 (0.10) 100(0.36)
Do not like hot dog 83(0.30) 95 (0.34) 178(0.64)
Total 129 (0.46) 149 (0.54) 278(1)
What is the two-way table?Number of people who like hamburger but do not like hot dog = 129 - 46 = 83
Number of people who do not like hamburger and do not like hot dog = 149 - 54 = 95
Total number of people who like hot dog = 46 + 54 = 100
Total number of people who do not like hot dog = 83 + 95 = 178
Total = 100 + 178 = 278
The marginal frequency can be determined by dividing each number by the total number of people in the survey.
marginal frequency of people who like hot dog = 100 / 278 = 0.36marginal frequency of people who do not like hot dog = 178 / 278 = 0.64To learn more about two way frequency tables, please check: https://brainly.com/question/27344444
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Please provide explanation.
Answers
Answer:
100 square meters
Step-by-step explanation:
\( {x}^{2} + 6x + 8x = 240\)
\( {x}^{2} + 14x = 240\)
\( {x}^{2} + 14x - 240 = 0\)
\((x - 10)(x + 24) = 0\)
\(x = 10\)
x = -24 will not work (it is extraneous).
\( {x}^{2} = 100\)
So the area of the square region is 100 square meters.
Two taps running at the same rate can fill a tank in 45 mins. How long will it take one tap to fill the same tank?
Answers
Answer:
90 minutes
Step-by-step explanation:
it will take twice as long therefore 90 minutes
Question 10(Multiple Choice Worth 2 points)
(Comparing Data MC)
The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.
A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.
Which drive-thru typically has more wait time, and why?
Burger Quick, because it has a larger median
Burger Quick, because it has a larger mean
Super Fast Food, because it has a larger median
Super Fast Food, because it has a larger mean
Question 11(Multiple Choice Worth 2 points)
(Creating Graphical Representations MC)
The number of carbohydrates from 10 different tortilla sandwich wraps sold in a grocery store was collected.
Which graphical representation would be most appropriate for the data, and why?
Circle chart, because the data is categorical
Line plot, because there is a large set of data
Histogram, because you can see each individual data point
Stem-and-leaf plot, because you can see each individual data point
Question 12(Multiple Choice Worth 2 points)
(Comparing Data MC)
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10, 16, 20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 14, with a median of 14
Bus 18, with a mean of 12
Bus 14, with a mean of 14
Bus 18, with a median of 12
Question 13(Multiple Choice Worth 2 points)
(Appropriate Measures MC)
The line plot displays the number of roses purchased per day at a grocery store.
A horizontal line starting at 1 with tick marks every one unit up to 10. The line is labeled Number of Rose Bouquets, and the graph is titled Roses Purchased Per Day. There is one dot above 1 and 2. There are two dots above 8. There are three dots above 6, 7, and 9.
Which of the following is the best measure of variability for the data, and what is its value?
The range is the best measure of variability, and it equals 8.
The range is the best measure of variability, and it equals 2.5.
The IQR is the best measure of variability, and it equals 8.
The IQR is the best measure of variability, and it equals 2.5.
Question 14(Multiple Choice Worth 2 points)
(Circle Graphs LC)
Chipwich Summer Camp surveyed 100 campers to determine which lake activity was their favorite. The results are given in the table.
Lake Activity Number of Campers
Kayaking 15
Wakeboarding 11
Windsurfing 7
Waterskiing 13
Paddleboarding 54
If a circle graph was constructed from the results, which lake activity has a central angle of 39.6°?
Kayaking
Wakeboarding
Waterskiing
Paddleboarding
Question 15(Multiple Choice Worth 2 points)
(Making Predictions MC)
At a recent baseball game of 5,000 in attendance, 150 people were asked what they prefer on a hot dog. The results are shown.
Ketchup Mustard Chili
63 27 60
Based on the data in this sample, how many of the people in attendance would prefer ketchup on a hot dog?
900
2,000
2,100
4,000
Answers
Q10: The answer is Burger Quick, Q11: The answer is Histogram ,Q12: The answer is Bus 18 ,Q13: The answer is the IQR is the best measure of variability,Q14: The answer is Paddleboarding ,Q15: The answer is 2,100
what is measure of variability ?
In statistics, the measure of variability is a term that refers to how spread out or dispersed a set of data is. In other words, it is a measure of how much the data points in a given set differ from each other.
In the given question,
Question 10: The answer is Burger Quick, because it has a larger median.
Question 11: The answer is Histogram, because it is the best graphical representation for displaying continuous data, like the number of carbohydrates in tortilla sandwich wraps.
Question 12: The answer is Bus 18, with a median of 12, because the median is the best measure of center to use for skewed data, and Bus 18 has a lower median than Bus 14.
Question 13: The answer is the IQR is the best measure of variability, and it equals 2.5, because the IQR is the best measure of variability to use for skewed data, and it is calculated as the difference between the 75th percentile and the 25th percentile, which in this case is 9 - 6.5 = 2.5.
Question 14: The answer is Paddleboarding, because the central angle can be calculated as (54/100) * 360 = 194.4°, and Paddleboarding has the closest central angle to 39.6°.
Question 15: The answer is 2,100, because you can use proportions to estimate that 63/150 of the sample prefers ketchup their hot dog, and then apply that proportion to the total attendance: (63/150) * 5,000 = 2,100.
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Economic growth typically results in rising standards of living and prosperity. However, it also invites negative externalities such as environmental degradation due to over- exploiting of natural resources. As such, the world is confronted with the dilemma of growth versus environmental sustainability. Developing a model explaining the disparity of economic development concentrating on drivers such as tourism sustainability, technological innovation and the quality of leadership would be important not only to facilitate future economic growth in developing countries, but also to the environmental and sociocultural sustainability which ultimately lead to global sustainable development. The present research objective is to develop and test framework of sustainable development by considering the elements of tourism, technological innovation, and national leadership. This further would facilitate growth, environmental and socio-cultural sustainability. Understanding the integration of these dimensions would enable the building of a Sustainable Development Framework (SDF) that would provide better insight in promoting the SDGS agenda. Ultimately, growth and environmental sustainability can be achieved which will benefit the society, the economy, and nations and of course for future sustainable policy recommendation. Based on the issue above, you are required to propose relevant econometric approaches with the aims to test sustainable development by considering the elements of tourism, technological innovation, and national leadership. Question 1 [10 marks] [CLO2] Based on the scenario above, a. Propose an appropriate model specification based on the scenario above. [4 marks] used in the [4 marks] [2 marks] b. Justify the selection of the dependent and independent variables model. c. Justify the selection of the sample period.
Answers
According to the given information, the sample period should be from 2010-2020.
a) Model specification
The model specification based on the scenario above is as follows:
SDF= f(T, TI, NL)
Where: SDF= Sustainable Development Framework
T= Tourism
TI= Technological innovation
NL= National leadership
b) Justification for the selection of the dependent and independent variables model:
Dependent variable: The dependent variable in this model is Sustainable Development Framework (SDF). The model seeks to develop a framework for sustainable development that would facilitate growth, environmental and socio-cultural sustainability.
Independent variables:
The independent variables are tourism sustainability, technological innovation, and quality of leadership. These variables drive economic development. The inclusion of tourism sustainability reflects its importance in the global economy and its potential to drive growth.
The inclusion of technological innovation reflects its potential to enhance productivity and create new industries. The inclusion of national leadership reflects the role of governance in promoting sustainable development and managing negative externalities.
c) Justification for the selection of the sample period:
The sample period should be selected based on the availability of data for the variables of interest. Ideally, the period should be long enough to capture trends and patterns in the data. However, it should not be too long that the data becomes obsolete or no longer relevant.
Additionally, the period should also reflect the context and relevance of the research question. Therefore, the sample period for this study should cover the last decade to capture the trends and patterns in the data and reflect the relevance of the research question.
The sample period should be from 2010-2020.
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PLEASE HELP!! SHOW WORK! WILL AWARD BRAINLIEST TO CORRECT ANSWER!!
Bobby ran and biked for a total of 38 miles in 4 hours. His average running speed was 5 mph and his average biking speed was 11 mph.
Let x = total hours Bobby ran
Let y = total hours Bobby biked
Use substitution to solve for x and y.
a) How many hours did Bobby run?
b) How many hours did he bike? Show your work!
Answers
5x+11y= 38
x+y=4
Use substitution:
x=4-y
5(4-y)+11y=38
6y=18
y=3
x=4-3=1
a) Hours Bobby ran= 1
b) Hours Bobby bike=3
a study is to be conducted to help determine whether a die is fair. how many degrees of freedom are there for a chi-square goodness-of-fit test?
Answers
The degrees of freedom for a chi-square goodness-of-fit test are calculated as the number of categories minus 1.
Suppose we wish to determine if an ordinary-looking six-sided die is fair, or balanced, meaning that each face has a probability of 1/6
of arrival on top when the die is tossed. We could toss the die dozens, maybe hundreds, of times and compare the actual number of times each face arrival on top to the scheduled number, which would be 1/6
of the total number of tosses. We would not expect each number to be exactly 1/6 of the total, but it should be close.
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What is the surface area of the rectangular prism?
Answers
Answer:
Right rectangular prism
A=2(wl+hl+hw)
l Length
w Width
h Height
Can someone help ?????
Answers
Accordingly the answer is Nineteen Fourths.
2. The Access to University course in the college has 252 full-time and 140 part-
time students enrolled this year. What fraction of students are studying part-
time?
Answers
Answer:
\(\frac{5}{14}\)
Step-by-step explanation:
First, find the total number of students:
\(252+140=392\)
Then, divide the number of students at hand by the total number:
\(\frac{140}{392}\)
When possible, reduce the fraction to its simpliest form:
\(\frac{140}{392}\div\frac{28}{28}=\frac{5}{14}\)
prove that the area of triangle is "half of base times height. i.e.(A=1/2×b×h).
please give the explanation and do it ASAP please!
Answers
Answer:
Step-by-step explanation:
any triangle is half of a polygon of 4 sides
the area of a rectangle is height * base or length*width
and since the triangle is half a rectangle then Area=1/2 *b*h
8+3a+7b-5+2a-7b combine like terms means to add the coefficients (numbers) in front of like variables
Answers
3a + 2a = 5a
7b - 7b = 0
8 - 5 = 3
find the missing information to fill in the blanks. diagrams are not drawn to scale. do numbers 6 & 8. don’t take forever when answering both of those questions. all i care about is the steps and the answer.
Answers
6)
\(\begin{gathered} \angle MOL=2\angle MKL\text{ (angle at centre is twice angle at circumference)} \\ 146=2(37x-1) \\ 146=74x-2 \\ 146+2=74x \\ 148=74x \\ x=\frac{148}{74} \\ x=2 \end{gathered}\)\(\begin{gathered} To\text{ get m}\angle MKL,\text{ we have:} \\ \angle MKL=37x-1 \\ \angle MKL=37(2)-1 \\ \angle MKL=74-1 \\ \angle MKL=73^0 \end{gathered}\)Hence, the value of x=2, and the measure of angle MKL is 73 degrees
8)
\(\begin{gathered} m\angle BDC=90^0(angle\text{ in a semi- circle)} \\ m\angle BAC=90^0(angle\text{ in a semi-circle)} \\ 3y+11+y+7+90=180^0(sum\text{ of interior angles in a triangle)} \\ 4y+108=180 \\ 4y=72 \\ y=\frac{72}{4} \\ y=18^0 \end{gathered}\)\(\begin{gathered} 5x+3x+10+90=180^0(sum\text{ of interior angles in a triangle)} \\ 8x+100=180 \\ 8x=180-100 \\ 8x=80 \\ x=\frac{80}{8} \\ x=10^0 \end{gathered}\)Hence,
\(\begin{gathered} i)\text{ m}\angle BDC=90^0 \\ ii)\text{ m}\angle DCB=5x=5\times10=50^0 \\ iii)\text{ m}\angle DBC=3x+10=3(10)+10=30+10=40^0 \\ iv)\text{ m}\angle BCA=3y+11=3(18)+11=54+11=65^0 \end{gathered}\)
What is the difference between axiom and postulate theorem
Answers
Answer:
Axioms or postulates are universal truths. They cannot be proved. Theorem are statements which can be proved.
What is the probability of spinning a number greater than 4?
Answers
Answer:
Please upload the full question.....here the total number of outcomes is not mentioned and hence it can't be solved.
Answer:
Hence, the required probability of getting a number greater than 4, P(E) = 1/3.
Step-by-step explanation:
Is 1.43 grater than, less than, or equal to 1.043?
1.43 1.043?
1.43=1.043?
Please help!
Answers
Answer:
greater than
Step-by-step explanation:
What is the slope of a line perpendicular to the line whose equation is
3x−12y=−108. Fully simplify your answer
Answers
Answer:
Step-by-step explanation:
The given equation is not instandard form. First standard form is neccesary.
Add 108 to both sides.Subtract 12y to both sidesThe result is 3x + 108 = 12y which is equal to 12y = 3x + 108
The slope is represented in this form as m (Y = mx + b)
(with b as the initial value)
Therefore, 3 is the slope.
To find its perpendicular slope.
To find it's perpendicular, know that it is the negative reciprocal.
First negate 3 to become -3 and find it's reciprocalTo find the reciprocal, divide 1 by -3FInally, the slope perpendicular to the line whose equation is 3x - 12y = -108 is \(\frac{1}{-3\\}\)
What is the independent variable in this function?
Answers
Answer:
p.
Step-by-step explanation:
p is the independent variable.
The dependent one is h.
The value of h depends on the value of p.
AM I CORRECT? NEED HELP ASAP!
Answers
Yup! Your answer seems correct to me. .48*4
Imagine a list of all 5-digit numbers that have distinct digits. For example, 70364 and 93145 are two such numbers on the list, while 80628 is not on the list since it repeats the digit 8. 1. How many numbers are listed? 2. How many numbers on the list use the digit 0 at least once?
Answers
Imagine a list of all 5-digit numbers that have distinct digits. For example, 70364 and 93145 are two such numbers on the list, while 80628 is not on the list since it repeats the digit 8. 1. There are 27,216 numbers are listed. 2. There are 15,120 numbers on the list that use the digit 0 at least once.
1. For the first digit, we have 9 choices (1-9), as 0 cannot be the leading digit.
For the second digit, we have 9 choices (0-9, excluding the digit used in the first position).
For the third digit, we have 8 choices (0-9, excluding the digits used in the first and second positions).
For the fourth digit, we have 7 choices (0-9, excluding the digits used in the first, second, and third positions).
For the fifth digit, we have 6 choices (0-9, excluding the digits used in the first, second, third, and fourth positions).
Using the counting principle, the total number of 5-digit numbers with distinct digits is:
9 × 9 × 8 × 7 × 6 = 27,216
Therefore, there are 27,216 numbers listed.
2. To find the number of numbers on the list that use the digit 0 at least once, we can analyse the cases where the digit 0 is present.
Case 1: 0 is in the first position
In this case, we have 1 choice for the first position (0) and then proceed as before, so we have:
1 × 9 × 8 × 7 × 6 = 3,024 possibilities.
Case 2: 0 is in one of the other four positions
In this case, we have 4 choices for the position of 0 (second, third, fourth, or fifth), and the remaining digits can be filled in with the available choices. Therefore, we have:
4 × 9 × 8 × 7 × 6 = 12,096 possibilities.
Adding the possibilities from both cases, we have a total of:
3,024 + 12,096 = 15,120 numbers on the list that use the digit 0 at least once.
Therefore, there are 15,120 numbers on the list that use the digit 0 at least once.
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