Answer: 1344 committees can be formed of four people not from one class
Step-by-step explanation:
We are given:
Members in freshmen = 6
Members in sophomores = 6
Members in juniors = 6
To form a committee of four people not from one class, numerous combinations can occur. They are:
When in a committee, at least one of them are from each classWhen 2 from freshmen, 1 from sophomores, and 1 from junior. The possibility becomes [tex]^6C_2\times ^5C_1\times ^4C_1[/tex]
When 1 from freshmen, 2 from sophomores, and 1 from junior. The possibility becomes [tex]^6C_1\times ^5C_2\times ^4C_1[/tex]
When 1 from freshmen, 1 from sophomores, and 2 from junior. The possibility becomes [tex]^6C_1\times ^5C_1\times ^4C_2[/tex]
Total combinations: [tex](^6C_2\times ^5C_1\times ^4C_1)+(^6C_1\times ^5C_2\times ^4C_1)+(^6C_1\times ^5C_1\times ^4C_2)=(300+240+180)=720[/tex]
If two members come from same classWhen 2 from freshmen, 2 from sophomores, and 0 from junior. The possibility becomes [tex]^6C_2\times ^5C_2\times ^4C_0[/tex]
When 0 from freshmen, 2 from sophomores, and 2 from junior. The possibility becomes [tex]^6C_0\times ^5C_2\times ^4C_2[/tex]
When 2 from freshmen, 0 from sophomores, and 2 from junior. The possibility becomes [tex]^6C_2\times ^5C_0\times ^4C_2[/tex]
Total combinations: [tex](^6C_2\times ^5C_2\times ^4C_0)+(^6C_0\times ^5C_2\times ^4C_2)+(^6C_2\times ^5C_0\times ^4C_2)=(150+60+90)=300[/tex]
If three members come from same classWhen 3 from freshmen, 1 from sophomores, and 0 from junior. The possibility becomes [tex]^6C_3\times ^5C_1\times ^4C_0[/tex]
When 3 from freshmen, 0 from sophomores, and 1 from junior. The possibility becomes [tex]^6C_3\times ^5C_0\times ^4C_1[/tex]
When 0 from freshmen, 3 from sophomores, and 1 from junior. The possibility becomes [tex]^6C_0\times ^5C_3\times ^4C_1[/tex]
When 1 from freshmen, 3 from sophomores, and 0 from junior. The possibility becomes [tex]^6C_1\times ^5C_3\times ^4C_0[/tex]
When 0 from freshmen, 1 from sophomores, and 3 from junior. The possibility becomes [tex]^6C_0\times ^5C_1\times ^4C_3[/tex]
When 1 from freshmen, 0 from sophomores, and 3 from junior. The possibility becomes [tex]^6C_1\times ^5C_0\times ^4C_3[/tex]
Total combinations: [tex][(^6C_3\times ^5C_1\times ^4C_0)+(^6C_3\times ^5C_0\times ^4C_1)+(^6C_0\times ^5C_3\times ^4C_1)+(^6C_1\times ^5C_3\times ^4C_0)+(^6C_0\times ^5C_1\times ^4C_3)+(^6C_1\times ^5C_0\times ^4C_3)]=(100+80+40+60+20+24)=324[/tex]
Total number of committees that can be formed = [720 + 300 + 324] = 1344
Hence, 1344 committees can be formed of four people not from one class
simplify 15 to the power of 18 over 15 to the power of 3
Answer:
15^18/(15^3)=15^15
Step-by-step explanation:
rule for quotients of similar bases with different exponents is:
(a^c)/(a^b)=a^(c-b)
15^18/(15^3)=15^15
A box in the shape of a rectangular prism has the length of 3 5/8 inches, a width of 2 1/2 inches and a height of 4 inches. What is the volume of the box?
Answer:
36 1/4 in^3 : 36.25 in ^3
Step-by-step explanation:
Turn all fractions into decimal form:
3 5/8 in = 3.625
2 1/2 = 2.5
4 = 4
Volume formula = lwh
l = 3.625 in
w = 2.5 in
h = 4 in
V = 3.625 * 2.5 * 4
V = 9.0625 * 4
V = 36.25
What is the first term in the sequence for which d = -2 and a7 = 3?
A. -6
B. 12
C. 15
D. -12
Answer:
First term is 15
Step-by-step explanation:
Given data:
[tex]a_{7} =3\\d=-2[/tex]
Now,
[tex]a+6d=3.....(1)\\a_{n} =a+(n-1)d\\\\\\From equation (1)\\a+6(-2)=3\\a-12=3\\a=12+3\\a=15[/tex]
Therefore first term a =15
Correct option is (c)
What is the range of function g?
g(x) = /x-1+2
A. y > 1
B. y > 2
C. y <2
D. y <1
Answer:
Option B
Step-by-step explanation:
Equation of the function is,
[tex]g(x)=\sqrt{x-1}+2[/tex]
Parent function of the given function 'g' is,
[tex]h(x)=\sqrt{x}[/tex]
By translating the parent function 'h' n=by 1 unit horizontally left and 2 units upwards we get the function 'g'.
That means function 'g' starts from a point (1, 2).
Range of the function 'g' will be all the values of y ≥ 2.
Option B is the answer.
Answer:
Range of the function 'g' will be all the values of y ≥ 2.
Step-by-step explanation:
Please help it’s not hard
Answer:
H
Step-by-step explanation:
y= (1)x-3
Positive gradient, and the y intercept for the graph is -3, F is not the answer, the Y intercept is not -3.
Estimate: 4/5 - 1/2
Answer:
Need help ASAP..
Answer:
3/10
Step-by-step explanation:
Find the LCM of 5 and 2.
LCM = 10
[tex]\frac{4}{5} - \frac{1}{2} = \frac{8 - 5}{10} = \frac{3}{10}[/tex]
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
5 = 5 × 1
2 = 2 × 1
LCM = 2 × 5
10
[tex]\frac{2(4)}{2(5)} -\frac{5(1)}{5(2)}[/tex]
[tex]\frac{8}{10} -\frac{5}{10}[/tex]
[tex]\frac{3}{10}[/tex]
4 times 1
8 over 9 equal
Step-by-step explanation:
4*1 = 4
this indicates multiplication
8/9 = 0.88888888888 which when simplified would go back to 8/9 or .889
8 "over" 9 indicates division!
Help me fast 50 points!!!!!!!!
Answer:
30
Step-by-step explanation:
There are 14 data points on the plot
The median is the middle value, which is between the 7th and 8th data points
Since it is even, we find the average of the 7th and 8th data points
Add the 7th and 8Th data points values and divide by 2
( 30+30)/2 = 60/2 = 30
The median is 30
Answer:
30
Step-by-step explanation:
Middle numbers are 30 and 30 so you add them and then divide by two:
[tex]\frac{30 + 30}{2}[/tex] = [tex]\frac{60}{2}[/tex]= 30
find the coordinate for the mid point of the segment with the points given (-16,0)(0,-16)
(-8,-8)
(8,0)
(8,8)
Answer:
(-8,-8)
Step-by-step explanation:
Coordinates of a midpoint:
The coordinates of the midpoint of a segment is given by the mean of the coordinates of the endpoints.
In this question:
Endpoints (-16,0) and (0,-16).
x-coordinate:
[tex]\frac{-16+0}{2} = -8[/tex]
y-coordinate:
[tex]\frac{0-16}{2} = -8[/tex]
Then:
(-8,-8)
A researcher collects demographic data on the marital status of the study subjects. The variable is measured as the number of years married on a scale of 0-75. What would be the most appropriate measure of central tendency
Answer:
Probably "Median"
The mode doesn't really make sense,
and "mean" would probably be skewed by people who get divorced quickly
I would suggest "Median" the number of years that 1/2 of the couples are above and 1/2 below
Step-by-step explanation:
A car rental costs $32 as a base fee, plus $28 per day. Use the explicit rule f (n )= 28n + 32
Find the charges paid for the first 4 days
Answer:
The charges paid for the first four days are:
$144.Step-by-step explanation:
To obtain the charges paid for the first 4 days, you must use the given explicit rule given:
f (n) = 28n + 32Where:
n = Number of days the person rents the car.As we need to obtain the charges to 4 days, we replace this value in the explicit rule:
f (n) = 28n + 32f (4) = 28(4) + 32f (4) = 112 + 32f (4) = 144With these calculations, you can identify the charges paid for the first 4 days are $144, where $112 is the money by each day of the four days and $32 is the base fee.
Which relation represents a function ?
Answer:
The third choice
Step-by-step explanation:
a relation is a function if an input has at most one output for a given input
Choices 1, 2 and 4 are not functions as they have two different outputs for the same input. (See the red ovals)
Solve the quadratic equation numerically (using tables of x- and y- values).
x2 + 7x+ 12 = 0
x= -1 or x = -1
x= -3 or x = -3
x = -4 or x = -3
x = 2 or x = -1
Answer:
x2 + 7x + 12 = 0
Step-by-step explanation:
(x + 4) (x + 3)
x + 4 = 0 or x + 3 = 0
x = - 4 or x = - 3
What is the solution to this equation?
3x – 5 + 2x = 25
Answer:
[tex]x=6[/tex]
Step-by-step explanation:
We want to find the solution to the equation:
[tex]3x-5+2x=25[/tex]
Rearrange:
[tex](3x+2x)-5=25[/tex]
Combine like terms:
[tex]5x-5=25[/tex]
We can add five to both sides:
[tex]5x=30[/tex]
And divide both sides by five. Therefore:
[tex]x=6[/tex]
Answer:
x = 6
Step-by-step explanation:
First, combine like terms. Like terms are terms that have the same amount of like variables:
3x - 5 + 2x = 25
(3x + 2x) - 5 = 25
5x - 5 = 25
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
First, add 5 to both sides of the equation:
5x - 5 = 25
5x - 5 (+5) = 25 (+5)
5x = 25 + 5
5x = 30
Next, isolate the x by dividing 5 from both sides of the equation:
(5x)/5 = (30)/5
x = 30/5
x = 6
x = 6 is your solution.
~
I am desperate please help.
Answer:
63.69 meters
Step-by-step explanation:
the total perimeter of two identical semi-circular = 100+100 = 200m
d = p/π = 200/3.14 = 63.69
Please help me with my math question?
Answer:
150 mL
Step-by-step explanation:
270 - 120 = 150
Hope this helps!
For Part A, my answer was 435 since I multiplied 5 x 87 = 435.
For Part B, my answer was 540 since I multiplied 22.5 x 24 = 540.
Both of my answers were incorrect. How should I approach this problem?
Answer:
a. 36.25 ft
b. 45 ft
Step-by-step explanation:
GIVE YOUR ANSWER IN FEET !!! as the problem statement says.
not in inches. when you use the scale factor with inches, you get inches as result. then you need to convert them to feet.
how many inches in 1 ft ?
12 !
so, you need to divide your results by 12 to get the feet.
What is the mode of the data set shown below?
{2, 4, 5, 6, 8, 2, 5, 6}
A. 2
B. 5
C. 6
D. 2, 5, and 6
Answer:
D
Step-by-step explanation:
The mode is the value that appears most often in the number set for this set the most common numbers are 2, 5, and 6.
Answer:
d
Step-by-step explanation:
all show up 2 times
Can someone help asap!!?
Answer:
1: B. 2: 6n^6+9n^5+4n^2-4n. 3: D. 4: 6b^2-15b-9. 5: 48x^2-4x-4
Step-by-step explanation:
1.
A trinomial is a polynomial with three terms. The expression 7v^2 +2v +2 has 3 terms.
2.
A polynomial in standard form has its powers listed from highest power to lowest power. The terms are 6n^6, 4n^2, 9n^5, and -4n. Remove the bottom numbers to find 6, 2, 5, and 1. Next, put them in order. 6, 5, 3, 1. Then, re-add the bottom numbers. 6n^6+9n^5+4n^2-4n.
3. A sixth degree polynomial is one with a sixth degree power. So, the answer is either C or D. Next, let's look at the terms. The expression here has 4 terms. So, the answer is D.
4 and 5:
To solve expressions in this form, (a+b)(c+d), turn the expression into an equivalent one, ac+ad+bc+bd. Plug in the numbers (with a negative mark if its -a or a-b) into that expression to get your answer.
4 simplifies out into 6b^2+3b-18b-9, which can be simplified into 6b^2-15b-9
5 simplifies out into 48x^2+12x-16x-4, which can be simplified into 48x^2-4x-4.
the number of grams of is one hundredth of a kilogram is
I don't understand your question. Do you mean "Is the number of grams one hundredth of a kilogram?"
Or did you mean, "The number of grams is one hundredth of a kilogram, what's that in grams?" ?
Edit your question, please.
Which of the following illustrates the truth value of the given conditional statement?
p. 10 > 7
q. 10 > 5
p-~q
Answer:
T T → T
Step-by-step explanation:
Given :
p = 10 > 7
q = 10 > 5
Evaluating if the statements are true :
p = 10 > 7, This is TRUE, Because 10 is truly greater Than 7
q = 10 > 5, This is TRUE, Because 10 is truly greater Than 5
The statements are both True statements :
p = True ; q = True
True and True = True
T & T = T
T T → T
If repetition of digits is allowed, how many different ways 5-digit codes are possible with the condition that the first digit should be a multiple of 3 and the last digit cannot be zero.
a. 17496.
b. 27000.
c. 18000.
d. 30000.
Answer:
b) 27,000
Step-by-step explanation:
3 × 10 × 10 × 10 × 9 = 27000
'3' because the first digit can only be 3,6, or 9
'9' because the last digit cannot be zero, leaving only 9 options
What is g(x)?
A g(x)=-x2
B g(x)=-2x
C g(x)= -x
D g(x)= -|x|
Answer:
Should be A
Hope this helped!
What to numbers multiply to -38 and add to 17
Answer:
-2 and 19
Step-by-step explanation:
Answer:
19 and -2
Step-by-step explanation:
19 * -2 = -38
19 + -2 = 17
Hope this helps
The triangles shown below may not be congruent.
25
56
100
1000
850
O A. True
O B. False
Answer:
B. False
Step-by-step explanation:
The two triangles have the same size and the same shape so they are congruent. The three angles on both the triangles are equal. Just that the triangles are upside down but they are all the same.
The sky ride at an amusement park spans 2,715 feet. Over the course of the day,
Anna rode the sky ride 7 times. How many feet did she ride?
A. 14,025 feet
B. 15,500 feet
C. 19,005 feet
D. 21,000 feet
Whoever answers this then there gonna get Branliest
Answer:
C. 19,005 feet
Step-by-step explanation:
[tex] \begin{array}{ccc} \rm 1 \: time \: ride \implies \: 2175 \: feet\\ \rm 7 \: times \: ride \implies 2175 \times 7 = 19005 \: feet\end{array}[/tex]
hence,
our answer is C)
Answer:
Solution given:
1times ride[tex]\rightarrow: [/tex]2715ft
7 times ride[tex]\rightarrow:[/tex]2715*7=19005ft
Option C 15,500 feet
Which sequence is an example of an arithmetic sequence? A) –8, –4, –2, –1, . . . B) –4, –2, 0, 2, 4, . . . C) –1, –7, –49, –343, . . . D) 2, 4, 8, 16, 32, . . .
i dont have the membership.
Answer:
Answer- D)2,4,8,16,32, . . .
Answer:
b. -4,-2,0,2,4,...
Step-by-step explanation:
ILL GIVE YOU BRAINLIEST IF YOU GET IT RIGHT AND EXPLAIN
A special effects engineer is designing a model of an airplane for some shots in a movie.The wingspan of the model is 8.4 meters wide as shown below. If the scale used to create the model was 1/4 the actual wingspan; what was the true wingspan of the oringal plane?
Answer:
33.6 meters
Step-by-step explanation:
the wingspan is 1/4 of the original size so all you need to do is multiply the scaled down wingspan by 4
Write the equation of the line that passes through the points (-7,8) and (-1,-5).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line.
Answer:
y + 7 = -13/6(x-8)
and
y + 1 = -13/6(x+5)
Step-by-step explanation:
1. Find the slope using [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex].
-5-8/-1+7 = -13/6
2. Plug the slope into the point-slope form, [tex]y-y_{1}=m\left(x-x_{1}\right)[/tex].
y - y1 = -13/6(x-x1)
3. Plug in one of the points to get the answer.
y + 7 = -13/6(x-8)
y + 1 = -13/6(x+5)
simplify 6to the power of-3 over 6 to the power of5
1/1679616 or 5.9537418 times 10 to the power of -7
