Part a: The people can arrive in 5040 ways
Part b: In 120 ways, Jim can arrive first and Kim last
Part c: The probability that Jim will arrive first and Kim last is 1/42
People invited to the party: Jim, Eduardo, Larry, Simone, Ian, Dawn, Tyrone, and Kim
Part a:
Since there are 7 people, the number of ways they can arrive is 7*6*5*4*3*2*1 =.5040 ways
Part b:
For Jim to arrive first and Kim last:
The remaining 5 people can arrive in any order so, the number of ways in which they can arrive is 5*4*3*2*1 = 120 ways
Part c:
The probability that Jim will arrive first and Kim last is given by:
Number of ways Jim can arrive first and Kim last/ Total number of ways in which all the people can arrive at the party
= 120/5040 = 1/42
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The proportion of a population with a characteristic of interest is p = 0.37. What is the standard deviation of the sampling distribution when the sample size is 1,600?
The standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 is equal to 0.0121.
What is a sample proportion?A sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
Mathematically, sample proportion can be calculated by using this formula:
[tex]\hat{p} = \frac{x}{n}[/tex]
Where:
x represent the number of individuals with a specified characteristic.n represent the total number of individuals in a sample.In Mathematics, the standard deviation (SD) of a sample proportion obtained when the sample size is 1,600 can be calculated by using this formula:
Standard deviation (SD) = √(p(1 - p)/n)
Substituting the given parameters into the formula, we have;
Standard deviation (SD) = √(0.37(1 - 0.37)/1,600)
Standard deviation (SD) = √(0.37(0.63)/1,600)
Standard deviation (SD) = √(0.2331)/1,600)
Standard deviation (SD) = √0.0001457
Standard deviation (SD) = 0.0121.
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Tickets of a program at college cost $4 for general admission or $3 with a student ID. If 181 people paid to see a performance and$616 was collected, how many of each type of ticket were sold?In a program at college tickets ?were sold for general admission and?tickets were sold with a student ID.
Tickets were sold for a program at a college .It cost $4 for general admission or $3 with a student ID.
Let
number of people that used student ID = x
number of people that used the general admission cost = y
[tex]x\text{ + y = 181}[/tex][tex]3x\text{ + 4y = 616}[/tex][tex]\begin{gathered} x+y\text{ = 181} \\ 3x+4y=616 \\ x=181-y \\ 3(181-y)+4y\text{ = 616} \\ 543-3y+4y=616 \\ y=616-543 \\ y=73 \\ x+73=181 \\ x=181-73 \\ x=108 \end{gathered}[/tex]108 used the student ID ticket while 73 used the general admission ticket .
Inverse & Composition of Functions
1. Find the inverse of f(x) = x² + 2
Answer: √x−2,−√x−2
Step-by-step explanation:
classify the system as "consistentdependent", "consistent independent", or "inconsistent". choose the best description of its solution. if the system hs exactly one solution give it solution.
The solution of a system is the point where the lines described by the equations of the system intersect, If a system has no solution, it is said to be inconsistent, In this case, both lines have the same slope (-3/2) which means that they are parallel each other, then they will never intersect, and the system has no solution and is inconsistent
State the zero(s) of the function.
f(x) = x³ - 2x² - x + 2
O a
O b
Ос
Od
1 and 2
-1, 1, and 2
-1, 0, and 1
-2, -1, and 1
Answer:
-1, 1, and 2
Step-by-step explanation:
[tex]x^3 - 2x^2 - x+2=0 \\ \\ x^2(x-2)-(x-2)=0 \\ \\ (x^2-1)(x-2)=0 \\ \\ (x-1)(x+1)(x-2)=0 \\ \\ x=-1, 1, 2[/tex]
Caleb is going to see a movie and is taking his 3 kids. Each movie ticket costs $13 and there are an assortment of snacks available to purchase for $3.50 each. How much total money would Caleb have to pay for his family if he were to buy 5 snacks for everybody to share? How much would Caleb have to pay if he bought xx snacks for everybody to share?
The total money would Caleb have to pay for his family if he were to buy 5 snacks for everybody to share is;
How to Solve Algebra Word Problems?
We are told that the cost of each movie ticket is $13. Now, if he buys one movie ticket for his 3 kids, then total he would pay for the 3 kids and himself is;
13 * 4 = $52
Now, an assortment of snacks available to purchase for $3.50 each. Thus, if Caleb buys 5 snacks, then it means that;
Cost of the 5 snacks = 3.5 * 15 = $16.5
Total paid = $52 + $16.5
= $67.5
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following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed
Points which would fall on the line produced by the point-slope form equation y - 3=1/2(x - 7) when graphed are as follow:
c. (1,0)
d. (3, 1)
As given,
Equation of given line
y - 3=1/2(x - 7)
Points which would fall on the line produced by the point-slope form:
a.(0,1)
x=0
y-3=1/2(0-7)
⇒ y=-1/2
b.(1,-1)
x=1
y-3=1/2(1-7)
⇒y=0
c.(1,0)
x=1
y-3=1/2(1-7)
⇒y=0
Required point
d.(3,1)
x=3
y-3=1/2(3-7)
⇒y=1
Required point
Therefore, points which would fall on line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed are as follow:
c. (1,0)
d. (3, 1)
The complete question is :
Which of the following points would fall on the line produced by the point-slope form equation y - 3 = 1/2(x - 7) when graphed?
a. (0,1) b. ( 1,-1) c. (1,0) d. (3,1)
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What are the factors of this expression?
3/4xy
Drag all of the factors of the expression into the box.
The factors of the expression 3xy/4 are 3/4, -1, x and y.
According to the question,
We have the following expression:
3xy/4
Now, we know that when we say factors of an expression then it means that we are talking about numbers or variables which can divide the given expression.
(For example, the factors of 24xy are 24 and the factors of 24 which are 1,2,4,6 including the two variables x and y.)
So, in this case, we will separate each number and variable to find the factors of the given expression:
3/4, x and y and -1
Hence, the factors of the expression 3xy/4 are 3/4, -1, x and y.
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Triangle ABC has vertices A(1,4), B (-3,5) and C(-2, 4) and is rotated 90
degrees clockwise about the origin. What will be the coordinates of C'?
O (2,-4)
O (4,-1)
O(-4,-2)
O (4,2)
Check the picture below.
Which number is equivalent to 3^(4)÷3^(2)
Answer:
9
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
This problem comes straight from a standardized test given in New York in 2014.
Christine gets $71 for working the weekend. She buys $53 in clothes and then
makes another $45 babysitting. How much does she have now?
Answer:
63 i think!
Step-by-step explanation:
71-53 is 18. 18+45 is 63!
Im so so so sorry if im wrong, have a nice day friend!: )
14 pound in 1 stone and 2.2 pound in 1 kilogram. a certain person weight 9 stone.
Given that 1kg=2.2 pound, also there is 14 pounds in 1 stone
There are 9 stones totally,so totally 9 stones will have 405 pounds
To convert into kilogram to should divide pounds by 2.2
[tex]\frac{405}{2}=183.705[/tex]Thus 183.705 is the required answer.
A cylindrical tank with radius 5 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increasing (in m/min)?
The height of the water increasing at a rate of 0.05 m/min
The Volume of a cylinder is
[tex]V = \pi r^{2}h[/tex]
where r is the radius and h is the height of the cylinder.
Given that the radius r of cylinder is 5m and the water is filled at the rate of 4 [tex]m^{3} /min[/tex]
[tex]V = 25\pi h[/tex] ...(1)
Now, differentiating (1) with respect to time t,
[tex]\frac{dV}{dt} = 25\pi \frac{dh}{dt}[/tex]
Substituting the value of [tex]\frac{dV}{dt}[/tex]
4 = [tex]25\pi \frac{dh}{dt}[/tex]
[tex]\frac{dh}{dt}[/tex] = [tex]\frac{4}{25\pi }[/tex]
[tex]\frac{dh}{dt}[/tex] = 0.05 m/min
Hence, the water is increasing at the rate of 0.05 m/min
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The amount of vinegar that melody used for a recipe can be written as a whole number which could be the amount of vinegar that Melody used?A. -3.75 tspB. 1.5 tspC. 2 1/3 tspD. 12/3
Given:
The amount of vinegar that melody used for a recipe can be written as a whole number.
So, we will check the options to find which one represents a whole number
The whole number does not contain numbers after the decimal point and also the denominator will be 1
So, the answer is option D) 12/3 = 4
Find the volume of the cone, use 3 for π
Given:
Cone with diameter of 14 ft, and height of 4 ft.
First, determine the radius of the cone, by dividing the diameter by 2.
[tex]\begin{gathered} r=\frac{d}{2} \\ r=\frac{14\text{ ft}}{2} \\ r=7\text{ ft} \end{gathered}[/tex]Now that we have the radius, substitute π = 3, r = 7 ft, and h = 4 ft to the formula of the volume of the cone.
[tex]\begin{gathered} V=\frac{\pi r^2h}{3} \\ V=\frac{(3)(7\text{ ft})^2(4\text{ ft})}{3} \\ V=\frac{3(49\text{ ft}^2)(4\text{ ft})}{3} \\ V=\frac{588\text{ ft}^3}{3} \\ V=196\text{ ft}^3 \\ \\ \text{Therefore, the volume of the cone is }196\text{ ft}^3. \end{gathered}[/tex]all the odd numbers from 51 to 5001 are written what is the total number of digits used
Answer:
9404 digits
Step-by-step explanation:
The numbers written:
51, 53, 55, 57, 59, . . . 97, 99 [5*5=25 numbers; 50 digits]
101, 103, 105, . . . 997, 999 [9*50=450 numbers; 1350 digits]
1001, 1003, 1005, . . . 4997, 4999, 5001 [40*50+1=2001 numbers; 8004 digits]
Total:
50 + 1350 + 8004 = 9404 digits
Question 22 of 25Which list is ordered from least to greatest?L) 52.932M) 583.31N) 52.930) 8.39P) 89.223A. N, L, M, P, OOB. M, P, L, N, OOC. O, N, L, P, MOD. P. O, L, M, N
Solution
- The ordered list from the least to the greatest is:
[tex]8.39,52.93,52.932,89.223,583.31[/tex]- Thus, using the arrangement of the numbers, we can rearrange using the letters.
O, N, L, P, M
Final Answer
O, N, L, P, M (OPTION C)
Which of the following inequalities would be graphed with an open circle? Select all that apply.
SOLUTION
Note that for an inequality to be graphed with an open circle the inequality sign must be either less than or greater than
Therefore the inequalities are:
[tex]\begin{gathered} 3(x-2)<18 \\ h+6>-3h+12 \end{gathered}[/tex]The table represents an absolute value function f(x). x f(x) −5 1 −4 0 −3 1 −2 2 −1 3 0 4 1 5 2 6 3 7 What are the vertex and range of the function? Vertex (0, 4), Range: {y | 0 ≤ y < ∞} Vertex (0, 4), Range: {y | 4 ≤ y < ∞} Vertex (−4, 0), Range: {y | 0 ≤ y < ∞} Vertex (−4, 0), Range: {y | −4 ≤ y < ∞}
The vertex and range of this absolute value function is: Vertex (0, 4), Range: {y | 0 ≤ y < ∞}.
What is an absolute value function?An absolute value function can be defined as a type of function that consist of an algebraic expression, which is placed within absolute value symbols.
Mathematically, the standard form of the equation for an absolute value function is given by:
y = a|x - h| +k.
Where:
h and k are the vertex of the graph.
Furthermore, an absolute value function is defined by this piecewise rule, especially based on its input:
|x| = -x, x < 0.|x| = x, x ≥ 0.In conclusion, the vertex or turning point of this absolute value function in the table above is at (0, 4).
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Answer:
Vertex (0, 4), Range: {y | 0 ≤ y < ∞}.
Step-by-step explanation:
Find the 9th term of the geometric sequence 4, -16, 64, ...
Answer:
4 to the 9th power :D
Step-by-step explanation:
Please Brainliest
2) A toy store is having a sale on puzzles. For each puzzle, Naomi buys she
gets 75% off of a second puzzle. The original price of each puzzle is
$16.50. Naomi bought 4 puzzles. How much did she spend?
Naomi bought 4 puzzles and she spend total $21.91
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.
Given that : A toy store is having a sale on puzzles. For each puzzle, Naomi buys she gets 75% off of a second puzzle. The original price of each puzzle is $16.50. Naomi bought 4 puzzles
Naomi first puzzle price is $16.50
she get 75% off on as second puzzle
=[tex]16.50(\frac{75}{100} )[/tex]
=12.375
=16.50 - 12.375
= 4.125
So , second puzzle price is 4.124
=[tex]4.125(\frac{75}{100} )[/tex]
=3.09
= 4.125 - 3.09
=1.03
So , third puzzle price is 1.03
=[tex]1.03(\frac{75}{100} )[/tex]
=0.7725
=0.2575
So ,fourth puzzle price is 16.50+4.124+1.03+ 0.2575
=21.91
Total naomi spend 0.2575
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An inground sprinkler nozzle sprays water onto the grass in the shape of a circle, with the nozzle at the center of the circle. On the coordinate plane, the nozzle is located at (20, 0) and the points (35, 0) and (5, 0) lie on the circle. Which equation represents the boundary that the sprinkler covers?
In order to determine which equation represents the boundary, replace the values of the coordinates of the given points, into the choices for the equations, and then verify if the left hand side matches with the right hand side.
For points (35,0) and (5,0) you have:
x = 35
y = 0
x = 5
y = 0
Then, for the first answer choice we have:
[tex]\begin{gathered} (x-20)^2+y^2=225 \\ (35-20)^2+0^2= \\ 15^2=225 \\ (5-20)^2+0^2= \\ 15^2=225 \end{gathered}[/tex]As you can notice, the equation matches for values of x and y.
Then, there is no necessary to verify for the other choices.
Hence, the equation (x - 20)^2 + y^2 = 225 represents the boundary that the sprinkler covers.
find the ratio of the boxes and the circles there are 7 boxes and 10 circles
The ratio of boxes to the circles is 7: 10
It says if Jamal rides his bike to school and back home. It is two miles each way. How many miles does he ride in five days?
Answer:
20 miles
Step-by-step explanation:
If it is two miles each way, then he rides a total of 4 miles every day.
Multiply 4 by 5
4 x 5 = 20
20 miles
Answer:
20 miles
Step-by-step explanation:
he always goes to school and comes back, to that means each day where he goes to school he rides 4 miles each time.
if he does this for 5 days you can write the following:
4*5 = 20 or if you haven't learned multiplication you can think of it like this:
4+4+4+4+4= 20
Plllsss help answer the question in the picture below!!!!!
The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.
What is the difference between standard deviation and histogram?It always displays the median and the middle 50% of the data. For data displayed in histograms, a similar spread measurement is helpful. The term for it is the standard deviation. The standard deviation is an indicator of how much the values in the data set typically deviate from the mean.
The proportion of the generated values that fall inside the range of each histogram bar is used to compute the vertical scale. The sum of the bar heights is therefore one. Only discrete variables (right), where the histogram heights now total to unity, are suitable for relative frequency analysis.
A measurement of how far points deviate from the mean is the standard deviation. The first histogram includes fewer points that are close to the mean and more points that are distant from the mean (scores of 0, 1, 9, and 10). (scores of 4, 5 and 6). As a result, its standard deviation will be higher.
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Pls help me with this ill give brainlist
Carter has 60 balloons , of the balloons are black, and is of the balloons are white. The rest of theballoons are red. How many red balloons Carter has? Show your calculations in the space provided
we have 60 balloons
black balloons are =4/12*60
and that is =20 black balloons
red balloons= 3/12*60=5*3=15
the rest are white
white balloons= 60- 20 black-15 red=25 white balloons
If 3 dogs eat 4 pounds of food per day, how many dogs eat 15 pounds of food?
11 dogs will eat 15 pounds of food.
According to the question,
We have the following information:
3 dogs eat 4 pounds.
We have to find how many dogs will eat 15 pounds.
We have the following expression:
4 pounds = 3 dogs
We can treat dog as a non-living object or a product.
So, we can find the parts devoted to 1 pound:
1 pound = 3/4
Now, we have to find the same for 15 pounds:
15 pounds = (3/4)*15
15 pounds = 11.25
Now, note that the number of dogs can not be in points. So, we will round it off to form a whole number.
So, 15 pounds = 11 dogs
Hence, 15 pounds of food is enough for 11 dogs.
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Find f(4) if f(x) =5x-4
To find f(4) you substitute the x in the given equation for 4:
[tex]\begin{gathered} f(4)=5(4)-4 \\ f(4)=20-4 \\ f(4)=16 \end{gathered}[/tex]Then, f(4) is 16Navy paint is made by mixing 8 cups of blue paint with 2 cups of black paint. If he only has 1 cup of blue pain, how much black paint should he use?
For 1 cup of blue paint, 1/4 cups of black paint is needed
How to determine the amount of black paint?The given parameters are
8 cups of blue paint needed for 2 cups of black paint
This means that
8 cups of blue paint needed = 2 cups of black paint
Divide both sides of the equation by 8
So, we have the following equation
8/8 cups of blue paint needed = 2/8 cups of black paint
Evaluate the quotient
So, we have the following equation
1 cup of blue paint needed = 1/4 cups of black paint
Hence, the amount of black paint is 1/4
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