Answer:
The number of ways is 6435
Step-by-step explanation:
Given
[tex]Male = 6[/tex]
[tex]Female = 5[/tex]
[tex]Students = 4[/tex]
Required
Number of ways a group of 8 can be formed
Here, I'll assume each category of people are distinct:
Hence;
[tex]Total = Male + Female + Students[/tex]
[tex]Total = 6 + 5 + 4[/tex]
[tex]Total = 15[/tex]
Number of ways is then calculated as follows:
[tex]^nC_r = \frac{n!}{(n - r)!r!}[/tex]
Where
[tex]n = 15\ and\ r = 8[/tex]
So, we have:
[tex]^{15}C_8 = \frac{15!}{(15 - 8)!8!}[/tex]
[tex]^{15}C_8 = \frac{15!}{7! * 8!}[/tex]
[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9 * 8!}{7!8!}[/tex]
[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7!}[/tex]
[tex]^{15}C_8 = \frac{15 * 14 * 13 * 12 * 11 * 10 * 9}{7 * 6 *5 * 4 * 3 * 2 * 1}[/tex]
[tex]^{15}C_8 = \frac{32432400}{5040}[/tex]
[tex]^{15}C_8 = 6435[/tex]
Hence, the number of ways is 6435
Factor the given polynomial.
9z^2 +15z +4
Select the correct choice below and, if necessary, fill in the answer box within your choice.
A. 9z^2 +15z +4=
B.The polynomial is prime.
Answer:
(3z + 1)(3z + 4)
Step-by-step explanation:
[tex]9 {z}^{2} + 15z + 4 \\ = 9 {z}^{2} + 3z + 12z+ 4 \\ = 3z(3z + 1) + 4(3z + 1) \\ = (3z + 1)(3z + 4)[/tex]
solve system
a = 5 - 2b; a +2b = 6
Answer:
This System has no solutions.
If f(x)=3x+19 find f (-3a-2)
Answer: f(-3a-2)=-9a+13
Step-by-step explanation:
To find f(-3a-2), we plug in -3a-2 into f(x).
f(-3a-2)=3(-3a-2)+19 [distribute]
f(-3a-2)=-9a-6+19 [combine like terms]
f(-3a-2)=-9a+13
Now, we know that f(-3a-2)=-9a+13.
1. What does the slope represent of a graph? (Definition
of Slope)
help!
Answer:
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. ... Slope is calculated by finding the ratio of the "vertical change" to the "horizontal change" between (any) two distinct points on a line.
Step-by-step explanation:
the radius of a circular playground is 77 metre.Calculate the distance covered by a runner in 5 complete rounds around the ground.
Answer:
2419.0265 meters
Step-by-step explanation:
To find the answer you must first find the circumference of the circle. The circumference formula is C = 2 \pi r. So if you plug in 77 you get 483.8053. Then multiply that by 5 and you will have your final answer.
please solve as fast as possible...
No spams please......
Answer:
In ∆ABD and ∆ACD
<BAD =<CAD ( each are half of <A )
<D=<D ( each equal to 90°)
AD = AD ( common)
So ∆ ABD is congruent to ∆ ACD.
Then AB =AC (by C.P.C.T)
Hence,∆ABC is an iso - sceles triangle.
A turtle was swimming 2 feet below the surface of a pond. While looking for food, he went
down 7 more feet
What is the position of the turtle now relative to the surface of the pond?
Answer:
-9 feet
Step-by-step explanation:
The turtle was already at -2 feet below sea level, then the turtle went 7 more feet down. Which means that -2 +7 = -9
please help me guys im lost
Answer:
D. BC ≅ EF
Step-by-step explanation:
ASA means you're trying to show congruence by showing two angles A..A and the segment between them ..S.. are congruent. The figure shows two congruent angles. What remains is to show the segments between are congruent.
__
In ∆ABC, the marked angles are B and C, so the segment between them is BC.
In ∆DEF, the marked angles are E and F, so the segment between them is EF.
These are the segments that need to be shown congruent if you're using ASA.
BC ≅ EF
how to solve |-6y|-9>-1
Answer:
y < -4/3 or y > 4/3
Step-by-step explanation:
|-6y| -9 > -1Since this is an absolute value inequality, we need two equations to set up to solve for y1st equation:-6y - 9 > -12nd equation:6y - 9 > -1Solve both equations:-6y-9>-1-6y > 8y < -4/36y -9 > -16y > 8y > 4/3What is non-collinear?
Answer:
Non-colinear means that three given points do not have a single line connecting all 3 of the points.
Chance left the park traveling 10 mph. Then, 2 hours later, Malik left traveling the same direction at
14 mph. How long until Malik catches up with Chance?
Answer:
8 hours
Step-by-step explanation:
after 8 hours chance will have traveled 100 miles and malik will have traveled 102 miles.
Hotel manager salary and 61,410 which is a 15 increase over the previous year salary what was the previous year salary
537²×15.90²=74²
I know this looks like pythagorean theorem. But how do they teach this to high schooler?
Answer:
It looks like this question is not solvable. So, if this is absolutely correct, write "no solution".
Step-by-step explanation:
Below is the first step to attempt solving the equation.
The little twos at the top of each number are called exponents. This means a number times itself.
So,
537*537=288,369
15.9*15.9=252.81
74*74=5476
Now, take the 288,369*252.81 to get a total of 72,902,566.89 .
Since this answer is (obviously) not equal to the 5476 on the other side, the two are not equal.
Here's how you'd work it out on paper to show it isn't solvable.
(537*537)*(15.9*15.9)= (74*74)
(288,369)*(252.81)= 5476
72,902,566.89 ≠5476
So the answer would be:
Not solvable.
Write in standard form.
2.87 x 104
A.28,700
B. 0.000287
C. 2,870
D. 287,000
The general form of the number is 28,700. The correct option is A.
What is a standard form?Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form.
The given number is 2.87 x 10⁴. The general form of the number can be written as:-
2.87 x 10⁴ = 2.87 x 10000
2.87 x 10⁴ = 28700
Multiply 2.87 by 10000 we will get the general form 28700 for the number.
Therefore, the general form of the number is 28,700. The correct option is A.
To know more about the standard form of the number follow
https://brainly.com/question/17136267
#SPJ5
[tex] \sqrt{2k ^{2} + 17 } - x = 0[/tex]
If k>0 and x=7 in the equation, what is the value of k?
Answer:
[tex]k=4[/tex]
Step-by-step explanation:
So we have the equation:
[tex]\sqrt{2k^2+17}-x=0[/tex]
Where:
[tex]k>0\text{ and } x=7[/tex]
And we want to find k.
Firstly, let's substitute 7 for x. So:
[tex]\sqrt{2k^2+17}-7=0[/tex]
Now, we can solve for k. Add 7 to both sides:
[tex]\sqrt{2k^2+17}=7[/tex]
Square both sides:
[tex]2k^2+17=49[/tex]
Subtract 17 from both sides:
[tex]2k^2=32[/tex]
Divide both sides by 2:
[tex]k^2=16[/tex]
Take the square root of both sides:
[tex]k=\pm\sqrt{16}[/tex]
Evaluate:
[tex]k=\pm 4[/tex]
Remember that we are told k>0. In other words, k must be positive. So, we can ignore the negative answer, giving us:
[tex]k=4[/tex]
So, the value of k is 4.
And we're done!
please help me fast
hope its easy for ya
Answer:
(1) 5x+14
(2)5x+15
(3) x^2 + 7x
(4) 4x+13
(5) x^2 +5x
(6) 6x+16
(7)x^2+4x
Зr + 4 = 12 = Зr
What is the answer
Answer:
r = 8
Step-by-step explanation:
Solve for r:
r + 4 = 12
Subtract 4 from both sides:
r + (4 - 4) = 12 - 4
4 - 4 = 0:
r = 12 - 4
12 - 4 = 8:
Answer: r = 8
Identify each of the following variables as qualitative or quantitative. a. Favorite baby name b. Color of car c. Storage space on a computer drive d. Electrical current a. Is the variable qualitative or quantitative? Why? A. Favorite baby name is a qualitative variable. Its values are numerical. B. Favorite baby name is a quantitative variable. Its values are numerical. C. Favorite baby name is a qualitative variable. Its values are not numerical. D. Favorite baby name is a quantitative variable. Its values are not numerical.
Answer:
C. Favorite baby name is a qualitative variable. Its values are not numerical.
Color of car is a qualitative variable. Its values are not numerical.
Storage space on a computer drive is a quantitative variable. Its values are numerical.
Electrical current is a quantitative variable. Its values are numerical.
Step-by-step explanation:
A qualitative variable is a variable that is categorical and isn't numerical.
For example, your favourite baby names and colours are categorical, they cannot be measured on a numerical scale
Quantitative Variable are variables that can be measured on a numeric scale. Ordinal, interval and ratio scales are quantitative scales.
Storage space can be measured on a numeric scale e.g. the storage space has 400 GB
Electric current can be measured on a numeric scale e.g. eclectic current is 50 volts
explain the process to calculate the distance between A= (9,7), B= (3,2)
Answer:
Step-by-step explanation:
Distance Formula in Pic
You just plug in the numbers for x1,y1 and x2,y2
A is your x1 and y1
B is your x2 and y2
after plugging it you do PEMDAS and solve it
Consider the following exam question and student solution. Determine whether the solution is correct. If it is not correct, write a note to the student explaining why it is wrong and give a correct solution. Exam question: You can buy a 56 pound bag of flour for $9 or you can buy a 1-pound bag for .39 cents. Compare the per pound cost for the large and small bags. Student solution: The large bag price is 56 divided by 9=6.22 per pound, which is much more than the 39 cent per pound price of the small bag.
Answer:
actually a 56 pound bag cost =9
so one pound bag cost =9/56=0.16 cents
Step-by-step explanation:
115% of what number is 138?
Answer:
120
Step-by-step explanation:
120 * 1.15 = 138
Answer:
120
Step-by-step explanation:
115% of the number 120 is 138
Could I get some help on these please? Will give points.
Answer:
X=-4, Y=22, idk about the CBD
Step-by-step explanation:
4y+2=90 degrees
subtract 2 on both sides you would get
4y=88 divide 4 with 88 and get 22
solve both X's so 5x+6=3x-2
i would subtract 3x first so i can get
2x+6=-2
then subtract 6 on both sides so you would have
2x=-8 divide -8 with 2 and get -4
The sum of three consecutive natural numbers is 540, find the numbers.
Answer:
179, 180, 181
Step-by-step explanation:
a +a +1 +a +2 =540
3a +3 =540
3a =540 - 3
3a=537
a=537 :3
a=179 (the first number
b=179 +1 =180 (the second number
c=179 +2 =181 (the third number
Describe the difference between the variance between samples MSB and the variance within samples MSW
Complete Question
The complete question is shown on the first uploaded image
Answer:
The correct option is C
Step-by-step explanation:
Generally
[tex]MS_B[/tex] stand for Mean Square Between which the mean calculated based on the difference between the sample means
While
[tex]MS_W[/tex] stands for Mean Square Within which the mean calculated based on the difference between the elements within the set(group)
Thus
The [tex]MS_B[/tex] measures the differences related to the treatment given to each sample. The [tex]MS_W[/tex] measures the differences related to entries within the same sample.
10 + (-4) Show Example
Answer:
6
Step-by-step explanation:
10
-6
=6
Adding a negative number is simply subtraction.
10-4=6
Martha has 90 red tiles and 72 yellow tiles. She wants to place the tiles in rows using one color for each row without having any tiles left
over. Each row must have the same number of tiles. What is the greatest number of tiles Martha can use for each row?
Answer:
18 tiles
Step-by-step explanation:
If she wants to find the greatest number of tiles for each row, she will want to use up all the tiles. This means we are looking for the highest common factor between the numbers 90 and 72, so all the tiles can be used up in the rows. In order to find the highest common factor we multiply together all the common prime factors between the two:
90 has the prime factors 2x3x3x5
72 has the prime factors 2x2x2x3x3
The prime factors that are common to both are 2, 3 and 3 which multiply together to get:
2x3x3 = 18
The greatest number of tiles Martha can use for each row is 18 and would result in 5 rows of red tiles and 4 rows of yellow tiles.
Hope this helped!
I NEED HELP ASAP!!!!!!!!
Answer:
you can say how u shop a discount stores like shein and shop for clearance. You can also say that u used to spend money to keep up with the trends but u realized u needed the money for other important things, so u stopped
Step-by-step explanation:
Can someone help me with this I will make you brainliset
Answer:
I believe the answer is statements 1, 4, and 6.
Step-by-step explanation:
Answer:
1.4 and 1.7
Step-by-step explanation:
Suppose that the overall probability of living to age 70 is 0.62 and that the overall probability of living to age 80 is 0.23. If a person reaches their 70th birthday, what is the probability that they will live to age 80?
Given :
P( X = 70 ) = 0.62 .
P( X = 80 ) = 0.23 .
To Find :
We need to find If a person reaches their 70th birthday, what is the probability that they will live to age 80 .
Solution :
We need to find :
[tex]P(X=70 | X=80 )[/tex]
We know ,
[tex]P(x,y ) = \dfrac{P(x)}{P(y)}[/tex]
So ,
[tex]P(X=70 | X=80 )=\dfrac{P(X=80)}{P(X=70)}\\\\=\dfrac{0.62}{0.23}=0.371[/tex]
Hence , this is the required solution .
5% of what number is 90?
Hey there!
ANSWER: [tex]4.5 \text { and }1800[/tex]
EXPLANATION:5% of what is 90?
If you want to find 5% of what is 90, you can try doing 90/5%.
[tex]90/5[/tex]%[tex]=1800(ANSWER)[/tex]
To get the decimal form, you can do 90*5%.
[tex]90*5[/tex]%[tex]=4.5(ANSWER)[/tex]
Hope this helps!
[tex]\text {-TestedHyperr}[/tex]