The order of the outcomes is irrelevant when calculating the total outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations.
15 different 2-member committees are possible.
What is a permutation vs combination?Subsets of a set can be created in two different ways: combination and permutation. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a particular order.The various ways in which items from a set may be chosen, usually without replacement, to form subsets, are called permutations and combinations. When the order of the selection is a factor, this selection of subsets is referred to as a permutation; when it is not, it is referred to as a combination.The order of the outcomes is irrelevant when calculating the total outcomes of an event using combinations. We will use the formula nCr = n! / r! * (n - r)! to calculate combinations.C(6,2) = 6!/(4!2!) = 15.
15 different 2-member committees are possible.
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arrange the numbers in increasing order a. 8.08 8.081 8.09 8.008b. 14.204. 14.200. 14.240 14.210
Given:
a)
[tex]8.08,8.081,8.09,8.008[/tex]b)
[tex]14.204,14.200,14.240,14.210[/tex]Required:
To arrange in the increasing order.
Explanation:
a)
Here, the first two places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 8.008.
The second lowest number is 8.08.
The third lowest number is 8.081
The fourth lowest number is 8.09.
So, the numbers are in ascending order is,
[tex]8.008,8.08,8.081,8.09[/tex]b) Here, the first t places' numbers are the same.
Let us check the hundredth decimal place.
The lowest number is 14.200.
The second lowest number is 14.204.
The third lowest number is 14.210.
The fourth lowest number is 14.240.
So, the numbers ar
A store sells 3 T-shirts for 28.14
Answer:
Step-by-step explanation:
1 T shirt = 28.14
There are 2 methods this can be done.
Method `1
Adding 3 times
28.14 + 28.14 + 28.14 = $84.42
Method 2
Multiplying 28.14 by 3
28.14 times 3 = $84.42
Therefore answer is 84.42
If Santa drives at an average speed of 60 miles per hour for a distance of 1,260 miles, how long will Santa's trip take?
Step 1: Speed is defined as the rate of covering a distance, mathematically it is given by
[tex]\begin{gathered} S\text{peed}=\frac{\text{distance}}{\text{time}} \\ S=\frac{d}{t} \end{gathered}[/tex]Step 2: Make the time (t) of the subject in the above speed formula
[tex]t=\frac{d}{S}[/tex]Step 3: Given the distance covered and the average speed used during the trip as
[tex]\begin{gathered} S=60\text{miles per hour} \\ d=1260\text{ miles} \end{gathered}[/tex]Step 4: Substitute the values for distance and speed in the time formula in step 2
[tex]\begin{gathered} t=\frac{d}{S} \\ t=\frac{1260}{60} \\ t=21\text{ hours} \end{gathered}[/tex]Hence, Santa's trip will take up to 21 hours
Answer:
To find out the time required to travel the distance of 1260 miles we need to divide the total distance travelled by the distance travelled in one hour.
[tex]1260/60=21[/tex]
So, it tool 21 hours for Santa to complete the trip
Reuben drove 243 miles using 12 gallons of gas. At this rate, how many miles would he drive using 16 gallons of gas?
Answer:
324 miles
Step-by-step explanation:
Set up a proportion
243
12
=
x
16
Cross multiply
12
x
=
3888
x=324 miles
You rent an apartment that costs \$1000$1000 per month during the first year, but the rent is set to go up 8% per year. What would be the rent of the apartment during the 5th year of living in the apartment? Round to the nearest tenth (if necessary).
If you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount of the apartment during the 5th year of living in the apartment is $1469.32
The initial rent amount = $1000
The percent of rent increase each year = 8%
Time period = 5 years
Here we can use the compound interest equation
A = [tex]P(1+\frac{r}{100})^t[/tex]
Substitute the values in the equation
The rent amount of the apartment during the 5th year of living in the apartment = [tex]1000(1+\frac{8}{100})^5[/tex]
= $1469.32
Hence, if you rent an apartment that cost $1000 per month during the first year, but the rent is set to go up 8% per year, the the rent amount of the apartment during the 5th year of living in the apartment is $1469.32
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David will rent a car foe a day. The rental company offers two pricing options: Option A and Option B. For each pricing option, cost (in dollars) depends on miles driven, as shown below.
Let
y ----> total cost in dollars
x -----> number of miles
we have that
Option B
y=50
Option A
Find out the slope
take two points from the graph
(0,20) and (150,50)
m=(50-20)/(150-0)
m=30/150
m=1/5=$0.20 per mile
therefore
y=0.20x+20
Part A
For x=75 miles
Option A -----> y=0.20(75)+20=$35
Option B ------> y=$50
therefore
Option A costs less
Find out the difference
$50-$35=$15
Cost $15 less than the other option
Part B
Looking at the graph
For x=150 miles
Both options cost the same
If David drives more than this amount option B costs less
note: this is a multi-part question. once an answer is submitted, you will be unable to return to this part. 7 women and 7 men are on the faculty in the mathematics department at a school. how many ways are there to select a committee of five members of the department if at least one woman must be on the committee?
No. of ways of selecting the 5 member committee by combination= 1981
What are the number of ways of selecting the 5 member committee ?
No. of women faculty in the mathematics department = 7
No. of men faculty in the mathematics department = 7
Total number of faculty members = 14
Condition - at least one woman must be on the committee
No. of ways of selection = C (14, 5) - C (7, 5)
We know that combination C(n , r) = [tex]\frac{n!}{(n-r)!r!}[/tex]
Consider the total combination C (14, 5),
[tex]C (14, 5)=\frac{14!}{9!5!} \\\\=\frac{14 *13* 12 *11 *10 *9!}{9!* 5!} \\\\=\frac{14 *13* 12 *11 *10}{120} \\\\= \frac{240240}{120} \\\\= 2002[/tex]
Consider the combination of men C (7, 5) ,
[tex]C (7, 5)=\frac{7!}{2!5!} \\\\=\frac{7*6*5!}{2!* 5!} \\\\=\frac{7*6}{2} \\\\= 7*3\\\\=21[/tex]
No. of ways of selection = C (14, 5) - C (7, 5)
= 2002 - 21
=1981
No. of ways of selecting the 5 member committee of the department with least one woman by combination= 1981
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awnser for this question
The equation of the line that is parallel to k and passes through (-1, 3) is
- x + 2y = 7
How to find the equation of a line?The equation of a line can be represented in different form such as point slope form, slope intercept form and standard form.
Therefore, the equation of the line is parallel to k.
Parallel line shave the same slope.
Therefore, let's find the slope of k to find the slope of the equation of the line.
Hence, using (7, 2)(1, -1)
m = -1 - 2 / 1 - 7
m = - 3 / -6
m = 1/ 2
Therefore, the slope of the line is 1 / 2. Let's find the y-intercept using the point (-1, 3)
3 = 1 / 2(-1) + b
3 = - 1 / 2 + b
b = 3 + 1 / 2
b = 7 / 2
Hence, the equation is as follows;
y = 1 /2x + 7 / 2
2y = x + 7
2y - x = 7
- x + 2y = 7
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The side lengths of a rectangle have a ratio of 7 to 5. If the perimeter is 300 meters, find the length and width of the rectangle.
The length is 25 cm and width is 35 cm. A rectangle is a closed two-dimensional shape with four sides, four corners, and four right angles (90°). A rectangle's opposite sides are equal and parallel.
What is perimeter?A perimeter is a closed path that encompasses, surrounds, or outlines a two-dimensional shape or length. The circumference of a circle or an ellipse is its perimeter. There stood several practical applications for calculating the perimeter. Perimeter is the length of the shape's boundary. It is given by the sum of the shape's sides. It has one dimension and is measured in linear units. Area, on the other hand, quantifies the amount of space occupied by the shape. It has two dimensions and is measured in square units. The perimeter of an object is the distance around it.Therefore,
The sides of the rectangle are in the ratio of 7: 5
Let the length 1=5x
and the breadth b=7 x
Now, perimeter =2(1+b)=300cm
2(5 x+7 x)=300
2(35 x)=300
70 x=300
x=4.28
Therefore, Length 1=5x =25 cm
and the breadth b=7x= 35 cm
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help please do in few mins
The length of the red line segment on this number line is: C. 2 1/2.
What is a number line?A number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line can be used to compare or determine the difference (distance) between two numbers plotted on it. Additionally, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Note: Each interval on this number line represents 1/4 and the total intervals between the red dots is 10.
From the number line shown above, we have:
Distance = 10 × (1/4)
Distance = 10/4
Distance = 5/2
Distance = 2 1/2.
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How many positive factors of 96 are also multiples of 12?
The number of positive factors of 96 which are also multiples of 12 are 4 which are 12,24,48, and 96.
Positive factors of 96 = 1,2,3,4,6,8,12,16,24,32,48 and, 96
Multiples of 12 upto 96 = 12,24,36,48,60,72, 84 and 96
Common numbers between the two are 12,24,48 and 96.
Hence, there are only 4 positive factors of 96 which are also the multiples of 12
Factors
Factors are the numbers that can divide a number exactly. Hence, after division, there is no remainder left.
Multiples
A multiple is a result obtained by multiplying a number by an integer(it shouldn’t be a fraction). The multiples of the whole number are obtained by taking out the product of the counting numbers and that of whole numbers.
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a random sample of 80 observations results in 50 successes. a. construct the 95% confidence interval for the population proportion of successes. b. construct the 95% confidence interval for the population proportion of failures
In 95% confidence interval for the population proportion of successes
exists CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80).
In 95% confidence interval for the population proportion of failures
exists CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80).
What is meant by confidence interval?The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.
You have a 5% probability of being incorrect with a 95% confidence interval. You have a 10% probability of being incorrect with a 90% confidence interval. A 95% confidence interval is narrower than a 99% confidence interval (for example, plus or minus 4.5 percent instead of 3.5 percent).
a) Sample proportion of successes (phat) = 50/80 = 0.625
z-critical for 95% CI is 1.96
CI = 0.625 +/- 1.96 × sqrt(0.625 × 0.375/80)
b) sample proportion of failures (phat) = 30/80 = 0.375
CI = 0.375 +- 1.96 × sqrt(0.375 × 0.625/80)
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Select all of the following equation(s) that are quadratic in form.
A C E
Those are the answers
Answer:
A- x4 – 6x2 – 27 = 0D- 6(2x + 4)2 = (2x + 4) + 2E- 6x4 = -x2 + 5Step-by-step explanation:
NEED HELP PLEASE!!!!!
Answer: [tex]x=-\frac{1}{2}, y=\frac{9}{2}[/tex]
Step-by-step explanation:
[tex]5x+7=7x+8\\\\2x=-1\\\\x=-\frac{1}{2}\\\\\implies y=5\left(-\frac{1}{2} \right)+7=\frac{9}{2}[/tex]
NEED HELP ASAP THIS IS OVERDUE !!!
Answer:
A
Step-by-step explanation:
The slope goes up by 11 and over by 1.
Answer: D
Step-by-step explanation:
y= [tex]\frac{1}{55}[/tex]×
What is the y-intercept in the equation y = 45x + 65?
Answer:
The y intercept is : 65
Step-by-step explanation:
The y intercept is 65 as it is in the form of y=mx+c.
The c is the y intercept, being 65
Find the equivalent ratio to the ratio 9 to 27 by simplifying the ratio. 3 to 1 , 1 to 3, 1 to 27 ,9 to 3
Given data:
The given ratio is 9:27.
The given ratio can be written as,
[tex]\begin{gathered} 9\colon27=\frac{9}{27} \\ =\frac{1}{3} \\ =1\colon3 \end{gathered}[/tex]Thus, the given ratio can be written as 1:3 so, second option is correct.
A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
A segment MN has endpoints M(-7.-6) and N(7,7). Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
___________________________
Find the coordinates of partition point P that divides the segment into a 5:2 ratio.
5:2 means that it is divided into 7, and we do not move two positions from (7,7)
X axis
7- (-7) = 14
14/7 = 2
7-2*2 = 3
Y axis
7-(-6)= 13
13/7 =
7 - 2* (13/7) = 49/7 - 26/ 7 = 23/7 = 3 2/7
______________________________
Answer
(3, 3 2/7)
Two numbers have a sum of 35 and a product of 250. what is the number
Sandi randomly selects a single bill from an envelope containing 8 ones, 5 fives, 4 tens, and 3 twenties. Whatis the expected value of the money she selects?expected value =
the formula to get the expected value is
[tex]E(x)=\sum ^n_{i\mathop=1}x_if(x_i)[/tex]So, first we calculate teh probabilities. We have 20 bills in total. so we divide the quantity of bills of each value by the total:
we have 8 ones: 8/20= 2/5
5 fives: 5/20=1/4
4 tens: 4/20= 1/5
3 twenties = 3/20
now, we multiply each value with te probabilitiy of picking it and add all
[tex]E=\text{ 1}\cdot\frac{2}{5}+5\cdot\frac{1}{4}+10\cdot\frac{1}{5}+3\cdot\frac{3}{20}=\text{ 4.1}[/tex]the expected value is 4.1
Which number is greatest?
-1
-4
-6
Answer:
Step-by-step explanation:
-1>-4>-6
-1 is the greatest number.
Ms.walker bought a computer for 15% off from the list price of p dollars. if the sales tax was 8%, how much did she pay for the computer including sales tax?
Ms. Walker paid $0.918*p for the computer including sales tax .
In the question ,
it is given that
discount on list price for the computer is 15%
sales tax = 8%
let the list price for the computer be $p .
So, sales price is = p - 0.15*p = 0.85*p
tax on sale price is = 8% of 0.85*p = 0.08*0.85*p = 0.068*p
Total Price = sale price + tax on sale price
Substituting the values of tax and sale price ,
we get
total price = 0.85*p + 0.068*p
= 0.918*p
Therefore , she paid $0.918*p for the computer including the sales tax .
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A car's velocity is modeled by v(t) = 0.5t^2 -14t+ 80 for 0 less than or equal to t less than or equal 14, where the velocity is in feet per second and time is in seconds. Where does the car come to a complete stop?
The car stops after moving for 20 seconds
How to determine when the car comes to a stop?From the question, the function is given as
v(t) = 0.5t^2 - 14t + 80
When the car comes to a stop, the vehicle is 0
This is represented as
v(t) = 0
So, we have
0.5t^2 - 14t + 80 = 0
Expand the equation
0.5t^2 - 10t - 4t + 80 = 0
Factorize the equation
0.5t(t - 20) - 4(t - 20) = 0
So, we have
(0.5t - 4)(t - 20) = 0
Solve for t
t = 8 and t = 20
20 is greater than 8
Hence, the car comes to a stop at 20 seconds
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with grade > * 0.2 Add, subtract, multiply, and divide whole numbers: word problem
A group of tourists needs rental cars to get around the city. There are 3,376 tourists in
the group. If each rental car holds 8 people, how many cars will the group need?
Using division, we know that the number of cars needed by 3,376 tourists is 422.
What is division?The division is splitting into equal parts or groups.The division allows us to divide or 'share' numbers to find an answer.Division sign (÷) is a symbol consisting of a short horizontal line with a dot above and another dot below, used to indicate mathematical division.The division of any number by zero is undefined. In this case, the result can be written as infinity. For example, 15/0 = ∞, i.e. undefined.We can represent the division with ÷, slash (/), or a horizontal line ( _ ). We can use these symbols at our convenience when dealing with different types of computations or division questions.So, the total number of groups of tourists = 3376
One car holds 8 people.To find the number of cars needed. Hence,
The number of cars needed = 3376/8= 422Therefore, using division we know that the number of cars needed by 3,376 tourists is 422.
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Of the ice cream cones sold yesterday at Zeke's Ice Cream Shop, 3/10 were chocolate and another 3/10 were vanilla. What fraction of the ice cream cones sold were either chocolate or vanilla?
The fraction of ice cream cones sold that are either chocolate or vanilla is 3/5.
What is the fraction?A fraction is a non-integer that is made up of a numerator and a denominator. An example of a fraction is 3/5. 3 is the numerator and 5 is the denominator.
In order to determine the fraction of ice cream cones sold that are either chocolate or vanilla, add the fraction of chocolate cones sold and vanilla cones sold together. Addition is the process of determining the sum of two or more numbers.
Fraction of ice cream cones sold that are either chocolate or vanilla = 3/10 + 3/10 = 6/10 = 3/5.
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Kayla gave 13 of a pan of brownies to Ella and 16 of the pan to Eli. Which choice is the MOST reasonable for the part of the pan of brownies Kayla gave away?
The reasonable fraction for the part of the pan of brownies Kayla gave away is 1/2.
How to illustrate the information?Kayla gave 1/3 of a pan of brownies to Ella and 1/6 of the pan to Eli.
Therefore, the part given away will be the addition of the fractions. This will be:
= 1/3 + 1/6
= 2/6 + 1/6
= 3/6
= 1/2
Therefore, 1/2 of the brownies were given away.
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professor smith loves dark chocolate, and she would like to find out the proportion of the population that shares her preference. she randomly sampled 150 people, and 120 people choose dark chocolate. to construct a 95% confidence interval, she should use:
Use 1-Prop Z Int to create a 95% confidence interval.
Z test should be employed because there is only one set of samples collected and the sample size is huge.
An observed percentage is compared to a theoretical one using a one proportion z-test. The test statistic is determined as follows:
z = (p-p0) / √(p0(1-p0)/n)
where:
p = observed sample proportion
p0 = hypothesized population proportion
n = sample size
You can reject the null hypothesis if the p-value associated with the test statistic z is less than your selected level of significance (popular choices are 0.10, 0.05, and 0.01).
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Which of the following values are solutions to the inequality 9 ≤ -7+ 4x?
I. - 4
II. O
III. 4
Answer: Inequality Form: x ≥ 4
lll. 4
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer:
Your answer is x ≥ 4
Step-by-step explanation:
a) Simplify both sides of the inequality.
9 ≤ 4x − 7
b) Flip the equation.
4x − 7 ≥ 9
c) Add 7 to both sides.
4x − 7 + 7 ≥ 9 + 7
4x ≥ 16
d) Divide both sides by 4.
4x/4 ≥ 14/4
x ≥ 4
Determine whether the two triangles are similar. If they
are similar, write the
similarity statement.
Answer:
not similar
Step-by-step explanation:
You want to know if two isosceles triangles are similar, given that one has a base angle of 78°, and the other has an a.pex angle of 16°.
Base angleThe base angles of the triangle with a.pex angle 16° will be ...
(180° -16°)/2 = 82° . . . . . . not 78°
SimilarityTwo isosceles triangles will be similar if they have congruent base angles. These triangles do not, so they are not similar.
Practice Problems
1. Mai and Priya were on scooters. Mai traveled 15 meters in 6 seconds. Priya travels
22 meters in 10 seconds. Who was moving faster? Explain your reasoning
2. Here are the prices for cans of juice that are the same brand and the same size at
different stores. Which store offers the best deal? Explain your reasoning
Store X: 4 cans for $2.48
per can
Store Y: 5 cans for $3.00
Store Z: 59 cents
Topic B
3. Costs of homes can be very different in different parts of the United States.
1. A450-square-foot apartment in New York City costs $540,000. What is the
price per square foot? Explain or show your reasoning
2. A 2,100-square-foot home in Cheyenne, Wyoming, costs $110 per square
foot. How much does this home cost? Explain or show your reasoning
4. There are 33.8 fuld ounces in a liter. There are 128 fuid ounces in a galon. About
how many liters are in a gation?
A 2
B. 3
C. 4
D. 5
Is your estimate larger or smaller than the actual number of liters in a gallon? Explain
how you know.
-
Answer:
1. Mai was moving faster as she covered a greater distance in the same amount of time.
Speed = Distance
-----------
Time
2. The best deal is Store Z. We must divide to determine the price each business is charging for a single can in order to particularly choose the greatest deal.
For Store X, each can is $0.62
For Store Y, each can is $0.60
Store Z is the best deal due to how cheap each can of juice costs.
3 (Part 1) It costs $1,200 for each square foot. The cost of the apartment is $540,000 & the area of the apartment is 450 feet. You can divide 540,000 by 450 and you should get 1,200.
3 (Part 2) The home costs $231,000. You can use the two numbers in the question "2,100" and "110". You should get $231,000 after adding those two numbers.
4. Approximately 3.8 liters are in a gallon. 3.8 is closest to 4 so you can round it up to 4 liters.
Step-by-step explanation: