Answer:
There are 11550 possible selections
Step-by-step explanation:
Given
[tex]Men = 7[/tex]
[tex]Women = 11[/tex]
Required
How many ways can 4 men and 4 women be selected
The keyword in the question is SELECTION and it means COMBINATION;
So, number of selection is:
[tex]Number = Men * Women[/tex]
[tex]Number = ^7C_4 * ^{11}C_4[/tex]
This gives
[tex]Number = \frac{7!}{(7-4)!4!} * \frac{11!}{(11-4)!4!}[/tex]
[tex]Number = \frac{7!}{3!4!} * \frac{11!}{7!4!}[/tex]
[tex]Number = \frac{7 * 6 * 5 * 4!}{3!4!} * \frac{11 * 10 * 9 * 8 * 7!}{7!4!}[/tex]
[tex]Number = \frac{7 * 6 * 5}{3!} * \frac{11 * 10 * 9 * 8}{4!}[/tex]
[tex]Number = \frac{7 * 6 * 5}{3 * 2 * 1} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = \frac{7 * 6 * 5}{6} * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = 7 * 5 * \frac{11 * 10 * 9 * 8}{4 * 3 * 2 * 1}[/tex]
[tex]Number = 7 * 5 * \frac{7920}{24}[/tex]
[tex]Number = 7 * 5 * 330[/tex]
[tex]Number = 11550[/tex]
Hence;
There are 11550 possible selections
Question 3 (2 points)
Using the statement below, determine the hypothesis and conclusion,
If two integers are even, then their sum is even
Column A
Column B
1.
Hypothesis
a. If two integers are even
2.
Conclusion
b. then their sum is even
c. two integers are even
d. their sum is even
Answer:
Hypothesis
a. If two integers are even
Conclusion
b. then their sum is even
Step-by-step explanation:
We divide the statement into two parts . The first part is true only when the second is also true. The only way we can reject the hypothesis is that the conclusion is false.
In the statement "If two integers are even, then their sum is even" the part "If two integers are even" would be considered true or false on the basis of "then their sum is even" validity. So if the "then their sum is even" (conclusion ) Part is proved then the "If two integers are even" ( hypothesis) is also true.
Hence the hypothesis is
a. If two integers are even
and
Conclusion is
b. then their sum is even
solve for r
8(-3r-5)>104
Answer:
r<-6
Step-by-step explanation:
8(-3r-5)>104
-24r-40>104
-24r>144
r<144÷-24 (the sign switched because we divided by a negative number)
r<-6
A bag contain 6 tiles labeled B,C,D,E,F. And G. One tile will be randomly picked. What is the probability of picking a letter that is a vowel?
N(S)=6
P(vowel letter)= N(vowel letter)÷N(S)
= 1/6
Answer:1/6
Step-by-step explanation:f
Please help. I’ll mark you as brainliest if correct!
One leg of a right triangle has a length of 3 m. The other sides have lengths that are consecutive integers. Find these lengths.
The other leg is ___ m.
Answer:
The other leg is 4 m long, and the hypotenuse is 5 m long
Step-by-step explanation:
Recall that the longest side of a right angle triangle is its hypotenuse, and that the legs and hypotenuse must verify the Pythagorean identity:
[tex]hyp^2=leg_1^2+leg_2^2[/tex]
so, we know that the other two sides have consecutive integers for lengths. That is: if one is "x" in length, the other one must be "x+1"
So we can assume that the largest of this is the hypotenuse: "x+1"
Not, they must verify the Pythagorean identity:
[tex]hyp^2=leg_1^2+leg_2^2\\(x+1)^2=x^2+3^2\\x^2+2\,x+1=x^2+9\\2\,x+1=9\\2\,x=8\\x = 4[/tex]
then, the other side is of length 4 m, and finally the hypotenuse is of length 4+1 = 5 m
12 + 4 - 8 / 2 * 3 workings pls
Answer:
4
Step-by-step explanation:
8/2=4
4*3=12
12+4=16
16-12=4
Solve for x.
5x – 7 = 8x – 4
Answer:
x =-1
Step-by-step explanation:
[tex]5x- 7 = 8x - 4\\\\\mathrm{Add\:}7\mathrm{\:to\:both\:sides}\\5x-7+7=8x-4+7\\\\Simplify\\5x=8x+3\\\\\mathrm{Subtract\:}8x\mathrm{\:from\:both\:sides}\\5x-8x=8x+3-8x\\\\Simplify\\-3x =3\\\\\mathrm{Divide\:both\:sides\:by\:}-3\\\frac{-3x}{-3}=\frac{3}{-3}\\\\Simplify\\x=-1[/tex]
Answer:
x = -1
Step-by-step explanation:
[tex]5x - 7 = 8x - 4\\[/tex]
Collect like terms and simplify
[tex]5x-8x =-4+7\\-3x =3[/tex]
Divide both sides of the equation by -3
[tex]\frac{-3x}{-3} = \frac{3}{-3} \\\\x =-1[/tex]
n engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.4 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 9 engines and the mean pressure was 5.7 pounds/square inch with a variance of 0.81. A level of significance of 0.025 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
Answer:
The calculated t- value = 1.11 > 2.89 at 0.025 level of significance
Null hypothesis is rejected
The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4
Step-by-step explanation:
Step(i):-
Given mean of the Population (μ) = 5.4
Given sample size 'n' = 9
Mean of the sample (x⁻) = 5.7
Standard deviation of the sample (s) = 0.81
Step(ii):-
Null Hypothesis: H₀: The engineer designed the valve such that it would produce a mean pressure of 5.4
H₀: μ = 5.4
Alternative Hypothesis : H₁: μ ≠ 5.4
Level of significance = 0.025
Test statistic
[tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]
[tex]t = \frac{5.7 -5.4}{\frac{0.81}{\sqrt{9} } }[/tex]
t = 1.11
Degrees of freedom
ν = n-1 = 9-1 =8
t₀.₀₁₅ , ₈ = 2.89
The calculated t- value = 1.11 > 2.89 at 0.025 level of significance
Null hypothesis is rejected
The engineer designed the valve such that it would produce a mean pressure is not equal to 5.4
Gutina finds a limited edition shirt from her favorite singer. It was originally $52. Then, she got a discount, 30%. what is the price now?
Answer:
$36.40
Step-by-step explanation:
Purchase Price:
$52
Discount:
(52 x 30)/100 = $15.60
Final Price:
52 - 15.60 = $36.40
$36.40 is the answer. Hope this helps!
Answer:
$36.40
Step-by-step explanation:
Sorry if i'm wrong hope this helps
The Pham family and the Morgan family each used their sprinklers last summer. The water output rate for the Pham family's sprinkler was 25L per hour. The water output rate for the Morgan family's sprinkler was 35L per hour. The families used their sprinklers for a combined 65total of hours, resulting in a total water output of 1975L . How long was each sprinkler used?
Answer:
Pham Family = 30 hours
Morgan Family = 35 hours
Step-by-step explanation:
Step 1 Deriving the equation
Let the duration in hours of Pham Family sprinkler = "x"
Let the duration in hours of Morgan Family = "y"
Total combined duration = 65 hours provided.
That is:
x + y = 65 Equation 1
Pham's sprinkler capacity = 25 litre per hour
Total water through this = 25 litre per hour for "x" hours = 25x
Morgan's sprinkler capacity = 35 litre per hour
Total water through this = 35 litre per hour for "y" hours = 35y
Now, provided
Total water output from both = 1,975 litre
That means
25x + 35y = 1,975 Equation 2
Step 2 Solving the equation
Let us multiply equation 1 with 25
We have
25x + 25y = 65 [tex]\times[/tex] 25
25x + 25y = 1,625 Revised Equation 1
Subtracting revised equation 1 from equation 2 we have:
(25x - 25x) + (35y - 25y) = (1,975 - 1,625)
0 + 10y = 350
y = 350/10 = 35
Since y = 35
Putting value of y in original equation 1 we have
x + 35 = 65
x = 65 - 35 = 30
Thus, Total Sprinkler hours of Pham = 30
Total Sprinkler hours of Morgan = 35
How many 10’s are in 1000
Answer:
Step-by-step explanation:
10x100=1000
Its all about the Zeros
Write the equation of the line that goes through the point
(5,8) and is parallel to the x-axis.
Answer:
Y=8
Step-by-step explanation:
If it's a line that is parallel to the x-axis, and you know the equation of a line is y=mx+b, the slope(m) is 0 because the line is not a positive or negative slope (since it's parallel to the x-axis).
So, we now have y=b, where b is the y-intercept. Now, since we know one of its coordinates are (5,8), we know that this line will always stay on y=8 since 8 is the y coordinate of (5,8)
An easy shortcut is if you see the question say parallel to the x-axis, the equation of the line will be y=___; if it says the line is parallel to the y-axis, the equation will be x=___
the seventh grade winner ran the mile in 5 minutes and 8 seconds. the eight grade winner ran the mile in 4 minutes and 55 seconds. how many more seconds did it take for the seventh grade winner to run a mile?
Answer:
13 seconds more
Step-by-step explanation:
The sum of three consecutive numbers is 600. What is the least of these three numbers?
Answer:
199
Step-by-step explanation:
So we have three consecutive numbers that totals 600 when added.
Let's let the first number be n.
This means that the next number is (n+1), and the subsequent number is (n+2).
This totals 600. In other words:
[tex](n)+(n+1)+(n+2)=600[/tex]
To solve for the integers, solve for n.
Combine like terms:
[tex]3n+3=600[/tex]
Subtract 3 from both sides:
[tex]3n=597[/tex]
Divide both sides by 3:
[tex]n=199[/tex]
So, the first integer is 199.
So our sequence is: 199, 200, 201.
So, the least of the three is 199.
And we're done!
Answer:
199 200 201
Step-by-step explanation:
199+200+201= 600
262 fewer than d is z
write the sentence as a equation
Answer:
Step-by-step explanation:
d - 262 = z
Estimate then find the product of 4x979
Answer:
Around 4000[since 979 close to 1000]
Step-by-step explanation:
4x979
=>3916
John travels in an airplane a distance of 800 km. For half of the distance, the
airplane flies at a speed of 900 km/h and for the rest of the distance, it flies at a
speed of 760 km/h. How long does the trip take?
Answer:
Time for the trip= 0.97 hours
Step-by-step explanation:
Distance covered in total = 800km
First half of the journey
= 800/2= 400km
Speed for first half= 900km/h
Time for the first half= 400/900
Time = 4/9 Hours
Distance covered in total = 800km
Second half of the journey
= 800/2= 400km
Speed for second half= 760km/h
Time for the second half= 400/760
Time = 10/19 Hour
Total time for Trip= 4/9 + 10/19
Time for the trip= 0.97 hours
What is the most appropriate measurement of the amount of liquid in Starpoint's pool?
A. ML.
B. KL.
C. CL.
D. Cg.
Answer: B. KL.
Step-by-step explanation:
A kiloliter (kl) is a unit which is derived from the metric SI (System International). This measurement is used when unit of volume with sides equal to one meter (1m) and as such, is equivalent to one cubic meter. One kiloliter (1kl) is which is same as one thousand liters (1000l). The kiloliter is used when volume of liquid is to be measured. This applies to a pool in the question.
choose all the expression with a difference less than 5
8.3
- 4.07
9.33
-3.99
7.1
- 2.603
12.3
- 7.08
7.005
- 2.005
Answer:
a and c
a and c are the expressions with a difference less than 5
Step-by-step explanation:
a) 8.3-4.07=4.23
b) 9.33-3.99=5.34
c) 7.1-2.603=4.497
d) 12.3-7.08=5.22
e)7.005-2.005=5
Hope this helps ;) ❤❤❤
Proportional ratios are like equivalent fractions, but
Answer:
what is the question?
Step-by-step explanation:
(72- 12 / 3 of 2) + (18 - 6) ÷4
Answer:
I believe the answer is 72.
Is the relationship between the height of a staircase and the number of steps linear?
Answer:A stair rise is the vertical distance from the top of one tread to the top of the next tread. The total run is the overall horizontal distance traveled by the stringer.
Step-by-step explanation:
What is 78 divided by 4.68
Answer:
16.67
Step-by-step explanation:
78 / 4.68
= 7800 / 468
= 16.67
When 78 is divided by 4.68 it gives 16.67 as a result.
DivisionFrom the four basic operations of arithmetic, the division is one. The division is generally done when we want to distribute something in equal portions.
therefore, 78 divided by 4.68 can be solved as,
Given to us78 divided by 4.68
[tex]78\div 4.68\\\\=\dfrac{78}{4.68}\\\\=\dfrac{78}{\dfrac{468}{100}}\\\\\\=\dfrac{78 \times 100}{468}\\\\=\dfrac{7800}{468}\\\\=16.6667 \approx 16.67[/tex]
Hence, when 78 is divided by 4.68 it gives 16.67 as a result.
Learn more about Division:
https://brainly.com/question/369266
A group of 23 friends gets together to play a sport. First, people must be divided into teams. Each teams has to have exaclty 4 players, and no one can be on more than one team. How many teams can they make?
Answer:
5
Step-by-step explanation:
A lamppost casts a shadow of 18 ft when the angle of elevation of the Sun is 33.7 degrees. How high is the lamppost? Round to the nearest foot
Answer:
12 feet or 12 ft
Step-by-step explanation:
We solve for this question using Trigonometric function of Tangent
tan θ = Opposite/ Adjacent
θ = Angle of elevation = 33.7°
Opposite side = Height of the lamp = ??
Adjacent side = Shadow of the lamp = 18 feet
Hence,
tan 33.7° = Opposite/ 18
tan 33.7° × 18 = Opposite
Opposite = 12.004507735 feet
Approximately to the nearest foot = 12.0feet
The height of the lamppost with a shadow of 18 ft. is 12 feet.
Trigonometric ratio
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let h represent the height of the lamppost, hence:
tan(33.7) = h/18
h = 12 feet
The height of the lamppost with a shadow of 18 ft. is 12 feet.
Find out more on Trigonometric ratio at: https://brainly.com/question/1201366
Solve -1 4/5x = 9. 5 1/5 -5 -1/5
Steps to solve:
-1 4/5x = 9
~Simplify
-9/5x = 9
~Multiply 5/-9 to both sides
x = 5
Best of Luck!
Answer:
5
Step-by-step explanation:
a triangle window has area 24 square feet and height six feet. what is its base? define variable, and set up and solve an equation to answer this.
Answer:
6*y/2=24
24*2=48
48/6=8
y=8
Step-by-step explanation:
The equation will be 24 = [tex]\frac{1}{2}[/tex] × b × 6 value of base will be b = 8 ft .
A triangle has area 24 square ft. and height 6 ft.
What will be its base. Find an equation also.
What is the formula of area of triangle ?
Area of triangle is ; Area = [tex]\frac{1}{2}[/tex] × b × h
∵ The equation of area of triangle will be ;
Area = A = [tex]\frac{1}{2}[/tex] × b × h ----- - --- --- --- Equation 1
A = 24 = [tex]\frac{1}{2}[/tex] × b × 6
⇒ b = [tex]\frac{24 * 2}{6}[/tex] = [tex]\frac{48}{6}[/tex] = 8
⇒ b = 8 ft.
Thus , the equation will be 24 = [tex]\frac{1}{2}[/tex] × b × 6 value of base will be b = 8 ft .
To learn more about area of triangle click here ;
https://brainly.com/question/23945265
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Phone numbers in Italy are in the format AB-CDDD-XXXX and have the following conditions · A can be any number 3-9 · B can be any number 4-9 · C can be any number 5-9 · D can be any number 1-7 · X can be any number 0-9 How many total phone numbers can the Italians have? Question 4 options: 720,300,000 phone numbers 823,200,000 phone numbers 102,900,000 phone numbers 16,800,000 phone numbers
Answer:
Hey there!
A: 7
B: 6
C: 5
D: 7
X: 10
7x6x5x7x7x7x10x10x10=720,300,000
Let me know if this helps :)
What are Three ways to name EF
What are the coordinates of B if the midpoint of line segment AB is (2,-5) and the coordinates of point A is (4,4)?
Answer:
i think it will be 20 unit diatance .
The EOQ model
A) determines only how frequently to order.
B) considers total cost.
C) minimizes both ordering and holding costs.
D) all of the alternatives are correct.
Answer:
B) considers total cost.
Step-by-step explanation:
Economic order quantity (EOQ) is the ideal order quantity a company should purchase to minimize inventory costs such as holding costs, shortage costs, and order costs.
The formula for EOQ is:
Q= √2DS/H
Q=EOQ units
D=Demand in units (typically on an annual basis)
S=Order cost (per purchase order)
H=Holding costs (per unit, per year)