Answer:
The only possible groups that could be made if each group have the same number of people is 2 groups of 14 or 4 groups of 7. Since each group cannot have more than 10 people, the only group left is 4 groups of 7.
Help me out .... Solve for x and y.
ANSWER
x=24 , y=8√3
EXPLANATION
The given triangle is a right triangle
To find x, we use the cosine ratio, given by:
[tex] \cos(30 \degree) = \frac{adjacent}{hypotenuse} [/tex]
[tex]\cos(30 \degree) = \frac{x}{16 \sqrt{3} } [/tex]
[tex] \frac{ \sqrt{3} }{2} = \frac{x}{16 \sqrt{3} } [/tex]
Solve for x,
[tex]x = \frac{ \sqrt{3} }{2} \times 16 \sqrt{3} [/tex]
[tex]x = 8 \times 3 = 24[/tex]
To find the value of x, we use the sine ratio:
[tex] \sin(30 \degree) = \frac{opposite}{hypotenuse} [/tex]
[tex]\sin(30 \degree) = \frac{y}{16 \sqrt{3} } [/tex]
[tex] \frac{1}{2} = \frac{y}{16 \sqrt{3} } [/tex]
Solve for y to get,
[tex]y = \frac{1}{2} \times 16 \sqrt{3} [/tex]
[tex]y = 8 \sqrt{3} [/tex]
Solve the system of equations using the addition method 2a+3b=-1 ; 3a+5b=-2
Answer:
Then, a=-1 and b=-1
Step-by-step explanation:
We need to solve the following system of equations using the adition method:
2a+3b=-1 (i)
3a+5b=-2 (ii)
First, we multiply the equation (i) by -3 and the equation (ii) by 2, so we get:
-6a-9b=3
6a+10b=-4
Adding the two equations we have:
-6a-9b=3
6a+10b=-4
--------------------------
0 + b = -1
Then b=-1. Now, let's substitute the value of b into equation (i):
2a+3b=-1
2a + 3(-1) = -1
2a -3 = -1
2a = 2
a = 1
Then, a=-1 and b=-1
Answer:
a = 1 and b= -1
Step-by-step explanation:
It is given two equations,
2a + 3b = -1 and
3a + 5b = -2
To find the solution of given equations
Let, 2a + 3b = -1 ----(1)
3a + 5b = -2 ------(2)
(1) * -3 ⇒
-6a - 9b = 3 ----(3)
(2) * 2 ⇒
6a + 10b = -4 -----(4)
(3) + (4 )⇒
-6a - 9b = 3 ----(3)
6a + 10b = -4 -----(4)
0 + b = -1
(1) ⇒ 2a + 3b = -1
2a + (3 * -1) = -1
2a = -1 + 3 = 2
a = 2/2 =1
Therefore, a = 1 and b = -1
a right triangle has one side that measures 4 in. the angle opposite that side measures 80° what is the length og the hypotenuse if the triangle? round to the nearest tenth.
Answer:
The length of the hypotenuse is 4.1 in
Step-by-step explanation:
we know that
In the right triangle of the problem
The function sine of angle of 80 degrees is equal to divide the opposite side to the angle of 80 degrees (4 in) by the hypotenuse
Let
x ----> the hypotenuse
so
sin(80°)=4/x
isolate the variable x
x=4/sin(80°)
x=4.1 in
Answer:
B: 4.1 in.
Step-by-Step Explanation:
on edge! hope this helps!!~ （=´∇｀=）
What is the probability of drawing any face card from a standard deck of 52 playing cards?
Answer:
Counting aces: 30%.
Not counting aces: 23%
Step-by-step explanation:
If you're counting aces, it's 30%. But if you're only counting Queens, Kings and Jokers then it's about 23%.
I hope this helps
The following graph shows the preimage, P(x)=x−−√, and the image after a vertical dilation of I(x)=k⋅P(x).
What is the value of k in this transformation?
Answer:
k = 3
Step-by-step explanation:
The graph P(x) is a square root function. It has a vertex of (0,0) and has the following points:
x f(x)
0 0
1 1
2 √2
3 √3
4 2
P(x) appears to be the function √x.
The image of l(x) changes the points of the function to
x f(x)
0 0
1 3
2 3√2
3 3√3
4 6
You can divide the function values of l(x) by P(x).
3/1 = 3
6/2 = 3
The scale factor for the dilation is 3. k= 3.
In the triangle below what ratio is cot G
Answer:
h/g
Step-by-step explanation:
we know that
The cotangent of angle G is equal to divide the adjacent side angle G to the opposite side angle G
so
cot(G)=h/g
How is the product of 3 and 2 shown on a number line?
Answer:
A
Step-by-step explanation:
Answer:
The answer is A
Step-by-step explanation:
Did the Quiz on Edge
A homeowner has 5 zucchini plants in her garden. Over the course of the season, the yields (number of zucchinis per plant) are: Plant 1 2 3 4 5 Yield 15 12 17 14 22 Using the information in the table provided, to the nearest tenth, calculate the average yield per plant and the standard deviation. A. average yield per plant: a0 B. standard deviation: a1
Answer:
Average = 16, standard deviation =
Step-by-step explanation:
15+12=27
27+(17+14)+22=27+31+22=80
80/5=16
Distance from 22 to 16=6, from 12 to 16=4, so deviation = 5
Answer:
Average yield per plant is 16 and standard deviation is 3.4058.
Step-by-step explanation:
Given : A homeowner has 5 zucchini plants in her garden.
Plant 1 2 3 4 5
Yield 15 12 17 14 22
Average : [tex]\frac{\text {Sum of all yields}}{\text{Total no. of plants}}[/tex]
Average : [tex]\frac{15+12+17+14+22}{5}[/tex]
Average : [tex]16[/tex]
Standard deviation =[tex]\sqrt{\frac{\sum(x_i-\bar{x})^2}{n}[/tex]
=[tex]\sqrt{\frac{(15-16)^2+(12-16)^2+(17-16)^2+(14-16)^2+(22-16)^2}{5}[/tex]
=[tex]3.4058[/tex]
Hence average yield per plant is 16 and standard deviation is 3.4058.
a party rental company has chairs and tables for rent. the total cost to rent 12 chairs and 2 tables is $47. the total cost to rent 3 chairs and 5 tables is $50. what is the cost to rent each chair and each table.
cost to rent each chair: $ ?
cost to rent each table: $ ?
Answer:
t= $ 6.75 cost for table
c= $ 1.50 chair cost
Step-by-step explanation:
Answer:
chair 2.50
table 8.50
Step-by-step explanation:
help please thanks a lot
Answer:
7 x
------ = -----------
20 400
Step-by-step explanation:
We want a ratio of bass over the total in the pond
Adding the samples
(8+6) 14 7
-------- = ------------ = ---------
(20+20) 40 20
Set this equal to a ratio of 400 total fish
Bass on top, total fish on bottom
7 x
------ = -----------
20 400
A new firehouse is being built equidistant from three other fire stations. Positioned on a grid, the current fire stations would be located at (3, 7), (−1, −1), and (−4, 8). What are the coordinates of the location where the new firehouse should be built?
Answer:
answer is C
Step-by-step explanation:
What are the r- values of the following data to three decimal places?
A. 0.811
B. 0.901
C. -0.811
D. -0.901
Answer:
Option D. -0.901
Step-by-step explanation:
we know that
The correlation coefficient r measures the strength and direction of a linear relationship between two variables. The value of r is always between +1 and –1
Using a Excel tool (Correl function)
The value of coefficient r is -0.9006876
Round to three decimal places
r=-0.901
see the table attached
for each ordered pair, determine whether it is a solution to the system of equations.
7x - 4y = 8
y = -9x - 2
(0,-2) is it a solution ?
(5,3) is it a solution ?
(-2,16) is it a solution ?
(-4,-9) is it a solution ?
Answer:
If the question is asking for a solution for both, then only point (0,2)
Point (0,2) is a solution to both equations
Point (5,3) is a solution to neither (meaning not any of the equations)
Point (-2, 16) is not a solution to the first equation, but is to the second
Point (-4, -9) is a solution to the first, but not to the second.
Step-by-step explanation:
Using the Property of substitution. 7x-4y=8
(0,-2)
7(0)-4(-2)=8
7(0)=0
-4(-2)=8
0+8=8
This solution is true.
(5,3)
7(5)-4(3)=8
7(5)=35
-4(3)=-12
35-12=23 (not 8)
This solution is not true.
(-2,16)
7(-2)-4(16)=8
-14-64=-78 (not 8)
This solution is not true.
(-4,-9)
7(-4)-4(-9)=8
-28+36=8
This solution is true
__________________________________________________________
Y=-9x-2
(0,-2)
-2=-9(0)-2
-9(0)=0-2=-2
-2=-2
This solution is true
(5,3)
3=-9(5)-2
-45-2=-47
3=-47
This solution is not true
(-2,16)
16=-9(-2)-2
16=18-2
16=16
This solution is true.
(-4,-9)
-9=-9(-4)-2
-9=36-2
-9=34
This solution is not true.
Final answer:
By substituting the x and y values from each ordered pair into the two given equations, we can determine whether the ordered pairs (0,-2), (5,3), (-2,16), and (-4,-9) are solutions. An ordered pair is a solution if it satisfies both equations of the system.
Explanation:
To determine whether each ordered pair is a solution to the system of equations:
7x - 4y = 8
y = -9x - 2
We will substitute the x and y values from each ordered pair into both equations.
For the ordered pair (0,-2), substitute x = 0 and y = -2:
7(0) - 4(-2) = 8 satisfies the first equation, and -2 = -9(0) - 2 satisfies the second equation, so (0,-2) is a solution.
Repeating this process for the other ordered pairs, (5,3), (-2,16), and (-4,-9), will reveal whether they satisfy both equations.
If both equations are satisfied by a particular ordered pair, then that ordered pair is a solution to the system of equations.
Which expression can be used to determine the length of segment ZY? See image.
Answer:
[tex]\sqrt{8^{2} + 3^{2} }[/tex]
Step-by-step explanation:
We see that this is a rectangle triangle, and that the ZY side is the hypotenuse.
It's length is then square root of the sum of the squares of the other sides:
[tex]hyp = \sqrt{a^{2} + b^{2} }[/tex]
So, in this case:
[tex]ZY = \sqrt{8^{2} + 3^{2} }[/tex]
The 8 and 3 numbers are easy to get from the graphic... and the order doesn't matter (8² + 3² = 3² + 8²).
That's an easy rule to remember.
I hope it helps.
Answer:
[tex]|ZY|=\sqrt{8^2+3^2}[/tex]
Step-by-step explanation:
ZY is the hypotenuse of triangle XZY.
The two shorter legs are;
YX=3 units
and
XZ=8 units.
According to the Pythagoras Theorem;
[tex]|ZY|^2=|XZ|^2+|YX|^2[/tex]
This implies that;
[tex]|ZY|^2=8^2+3^2[/tex]
We take the positive square root to obtain;
[tex]|ZY|=\sqrt{8^2+3^2}[/tex]
The second choice is correct
Determine the factors of 5x2 + 6x − 8. (5x − 1)(x + 8) (5x − 8)(x + 1) (5x − 4)(x + 2) (5x − 2)(x + 4)
Answer:
(5x − 4)(x + 2)
Step-by-step explanation:
For the purpose, it is sufficient to make sure the middle terms match.
The middle term in the product of each of the answer choices is ...
-1+40 ≠ 6
-8+5 ≠ 6
-4+10 = 6 . . . . . the third selection is the one you want
-2+20 ≠ 6
Answer: The correct option is (C) (5x − 4)(x + 2).
Step-by-step explanation: We are given to determine the factors of the following quadratic expression :
[tex]E=5x^2+6x-8.[/tex]
To factorize the given expression, we need to find two integers whose sum is 6 and whose product is -40.
The factorization is as follows :
[tex]E\\\\=5x^2+6x-8\\\\=5x^2+10x-4x-8\\\\=5x(x+2)-4(x+2)\\\\=(5x-4)(x+2).[/tex]
Thus, the factors of the given expression are (5x - 4) and (x + 2). That is,
[tex]5x^2+6x-8=(5x-4)(x+2).[/tex]
Option (C) is CORRECT.
Please help me.... (:
Answer:
x = 5
Step-by-step explanation:
The line segment divides the sides in proportion, that is
[tex]\frac{14}{10}[/tex] = [tex]\frac{2x-3}{x}[/tex] ( cross- multiply )
10(2x - 3) = 14x ← distribute left side
20x - 30 = 14x ( subtract 14x from both sides )
6x - 30 = 0 ( add 30 to both sides )
6x = 30 ( divide both sides by 6 )
x = 5
A photo booth charges a $500 fee for two hours at a party, plus $50 per additional hour. Cindy doesn't want to spend more than $700 on the photo booth rental. What is the maximum number of additional hours (beyond the first two) that Cindy can rent the photo booth for her party?
Answer:
YOU CAN HAVE 4 MORE HOURS WITH THE PHOTO BOOTH
Step-by-step explanation:
500 IS FOR 2 HOURS SHE DONT WANT TO WASTE MORE THAN 700 SO ITS 50 DOLLARS FOR ANOTHER HOUR
500 + 50 IS 550 THATS ONE HOUR ADDED 550+50 = 600 THATS 2 HOURS 600 + 50=650 THATS 3 HOURS 650+50= 700 SHE GOT IT FOR 4 HOURS IN TOTAL SHE HAD IT FOR 6 HOURS COUNTING THE 2 HOURS FOR IT AT THE PARTY . PERIODDT.....
Cindy can rent the photo booth for a maximum of 4 additional hours beyond the first two hours included in the base fee, given her budget of $700.
The student is asking how many additional hours Cindy can rent a photo booth for her party, given her budget constraints. Initially, there is a $500 fee for two hours, and each additional hour costs $50. Cindy has a budget of $700 in total, which means she can spend $200 on additional hours beyond the first two hours included in the base fee. To calculate the maximum number of additional hours, we divide the additional budget ($200) by the cost per additional hour ($50).
So, the calculation is
$200 / $50 = 4 additional hours.
Cindy can thus rent the photo booth for a maximum of 4 additional hours without exceeding her budget of $700.
In 2010, the estimated population of Los Angeles was 3.79 × 106 people. The population of California that same year was about 9.84 times this number. Which expression shows the approximate population of the state of California in 2010?
Answer:
The approximate population of the state of California in 2010 was [tex]37,293,600\ people[/tex]
Step-by-step explanation:
Let
x----->the estimated population of Los Angeles in 2010
y----->the estimated population of the state of California in 2010
we know that
[tex]y=9.84x[/tex] ------> equation A
we have
[tex]x=3.79*10^{6}\ people[/tex]
Substitute the value of x in the equation A and solve for y
[tex]y=9.84(3.79*10^{6})=37.2936*10^{6}\ people[/tex]
[tex]37.2936*10^{6}=37,293,600\ people[/tex]
Answer:
3.73 × 10^7 people
Step-by-step explanation:
The original equation 3.79 × 10^6 = 3790000. 3790000× 9.84=37293600. 37293600 estimated is about 37300000. That would make 3.73 × 10^7 the expression that represents the amount of people in California.
If KLMN is a square, then ___________________.
A. it must be a rhombus
B. it might be a rhombus
C. it cannot be a rhombus
-Hello There-
A square is always a rhombus because it satisfies all the properties of rhombus but every rhombus cannot a square.
Therefore, If KLMN is a square, then it must be a rhombus.
Have A Fantastic Day
Be Safe,
TheBlueFox
Answer:
It must be a rhombus
Step-by-step explanation:
A roulette wheel has 38 slots around the rim. the first 36 slots are numbers from 1 to 36. half of these 36 slots are red, and the other half are black. the remaining 2 slots are numbered 0 and 00 and are green. if the roulette wheel is spun 152 times predict about how many times the ball will land on 17 or 20
Answer:
15 or 16 times
Step-by-step explanation:
The ball will land on 6 or 29 about 14 times.
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
Given:
There are 2 slots that have a "6" or a "29" on them. The other 36 slots have different numbers.
The probability of landing on "6" or "29"
= 2/38
= 1/19
Now, Multiply this probability by the number of trials to get
= 266 x (1/19)
= 14
Hence, we expect the ball will land on 6 or 29 about 14 times.
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A and b are two similar 2D shapes. The area of shape awhich is 12cm is 200cm squared. Calculate the area of shape b which is 15cm
Answer: Area of shape which is 15 cm is 312.5 square cm.
Step-by-step explanation:
Since we have given that
Area of shape of 12 cm = 200 sq. cm
We need to find the area of shape of 15 cm.
As we know the "Area similarity theorem" which states that ratio of areas of two similar shapes is equal to the square of ratio of corresponding sides.
So, it becomes,
[tex]\dfrac{12^2}{15^2}=\dfrac{200}{x}\\\\\dfrac{144}{225}=\dfrac{200}{x}\\\\144x=200\times 225\\\\144x=45000\\\\x=\dfrac{45000}{144}\\\\x=312.5\ cm^2[/tex]
So, Area of shape which is 15 cm is 312.5 square cm.
The area of shape B which is of 15 [tex]\text{cm}[/tex], is 312.5 [tex]\text{cm}^2[/tex].
Given information:
The two shapes A and B are given
The dimensions of shape A is 12 [tex]\text{cm}[/tex]
The area of the shape A is 200 [tex]\text{cm}^2[/tex]
Now, we need to calculate the area of the shape of 15 [tex]\text{cm}[/tex]
As we know that area will be square of the given values in the question.
So, according to the question:
[tex]\frac{A^2}{B^2} =\frac{200}{x}[/tex]
[tex]\frac{12^2}{15^2} =\frac{200}{x}\\\\\frac{144}{225}=\frac{200}{x} \\\\x=(200\times 225)/144\\\\x=312.5 \text{cm}^2[/tex]
Hence, the area of shape B which is of 15 cm, is 312.5 [tex]\text{cm}^2[/tex].
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(Two questions)The temperature in an office is controlled... PLEASE
Answer:
a) the temperature is y = 16° C at 9 AM.
b) The probability of selecting 2 vowels at the same time is 2.8%
Step-by-step explanation:
a)
Temperature = y=?
Time = x = 9 A.M
The given equation is:
[tex]y = 19 + 6 sin (\frac{\pi }{12}(x-11))[/tex]
Putting x = 9 and solving
[tex]y = 19 + 6 sin (\frac{\pi }{12}(9-11))\\y = 19 + 6 sin (\frac{\pi }{12}(-2))\\y = 19 + 6 sin (\frac{-\pi }{6})\\y = 19 + 6(-0.5)\\y = 19 - 3\\y = 16[/tex]
So, the temperature is y = 16° C at 9 AM.
b)
WORD CLEMSON
Total Words = 7
Vowels = e, o = 2
Probability of selecting 2 vowels at the same time = P(2 Vowels) =?
We will use the formula of combinations nCr = n! / r! (n-r)!
As we are selecting three letter out of 7, the sample space will be 7C3
And
As there are only two vowels in the given word, and we have to find the probability of selecting two vowels so our event space will be 2C2.
P(2 Vowels) = 2C2 / 7C3
= 1/35
= 0.028 = 2.8%
So, The probability of selecting 2 vowels at the same time is 2.8%
24) The student body of 10 students wants to
elect four representatives.
A) Combination: 210
(B) Combination: 270
C) Permutation: 420
D) Combination: 630
Answer:
210
Step-by-step explanation:
There are calculators online that can help you with questions like this, and give you a step by step explaination to show the work
The Combination to elect four representatives out of 10 students is 210.
The correct option is (A).
What is permutation and combination?permutations and combinations, the various ways in which objects from a set may be selected, generally without replacement, to form subsets. This selection of subsets is called a permutation when the order of selection is a factor, a combination when order is not a factor.
Firstly, n=10 and r=4
Combination: C(n,r)=C(10,4)
= [tex]\frac{10!}{4!(10-4)!}[/tex]
= [tex]\frac{10!}{4!* 6!}[/tex]
= [tex]\frac{10*9*8*7}{4*3*2*1}[/tex]
= 210
and permutation: P(n,r)=P(10,4)
= [tex]\frac{10!}{(10-4)!}[/tex]
= 10*9*8*7
= 5040
Hence, the combination of data is 210 and permutation is 5040.
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A geometric sequence {an} is defined by the function
f(1) = a1 = 6 and f(n) = an = (1.2)*f(n - 1) for n ≥ 2.
Find f(38).
A)273.6
B)326.26
C)5103.3735
D)6124.0482
ANSWER
C)5103.3735
EXPLANATION
The recursive definition of the given sequence is;
[tex]f(1) = a_1 = 6[/tex]
and
[tex]f(n) = a_n = (1.2) \times f(n - 1)[/tex]
The explicit definition is
[tex]f(n) = a_n =6 (1.2)^{n - 1} [/tex]
We substitute n=38 to obtain:
[tex]f(38) = a_ {38}= 6(1.2)^{37} [/tex]
[tex]f(38) = 5103.3735[/tex]
The correct choice is C.
(2X-3)(3X+4)
I NEED HELP ON THIS ANSWER PLEASEE
Answer:
6X^2 -X -12
Step-by-step explanation:
(2X-3)(3X+4)
FOIL
first 2X*3X = 6X^2
outer 2X *4 = 8X
inner -3 *3X = -9x
last = -3 *4 =-12
Add them together = 6X^2 +8X -9X -12
= 6X^2 -X -12
Answer:
6x^2 - x - 12
Step-by-step explanation:
2x(3x + 4) = 6x^2 + 8x
-3(3x + 4) = -9x - 12
6x^2 + 8x - 9x - 12
6x^2 - x - 12
HELPPPP 15 POINTS!!! I need an answer fast
Answer:The answer is B
Step-by-step explanation:Because the exponent is 6 for Silver Town and 8 for Lake City
Answer:
Step-by-step explanation:
10^6=1000000
1000000x8.2
silver town 8200000
lake city 164000000
John got 20% discount at a sale .He got a new shirt for $12 .What is the original price of the shirt ?
The original price of the shirt must be $15 if a 20% discount resulted in the final price becoming $12
The original price of the shirt is $15.
What is Discount?Discount refers to the condition of the price of a bond that is lower than the face value. The discount equals the difference between the price paid for and it’s par value.
Discount is a kind of reduction or deduction in the cost price of a product. It is mostly used in consumer transactions, where people are provided with discounts on various products. The discount rate is given in percentage.
Discount = Original price - Buying Price
Given,
Buying price of the shirt john bought = $12
Discount on shirt John bought = 20% of the original price
Let, the original price be x
then,
discount = 20% of x = 20x/100
Discount = Original price - Buying Price
20x/100 = x - $12
x = $12 + 20x/100
x = ($1200 + 20x)/100
100x = $1200 + 20x
80x =$1200
x = $1200/80
x = $15
Hence, the shirt cost $15 originally.
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Find the level of a two-sided confidence interval for t = 2.776 with sample size 5. express the answer as a percent.
Using a t-distribution calculator, it is found that the confidence level is of 95%.
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm t\frac{s}{\sqrt{n}}[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.t is the critical value.n is the sample size.s is the standard deviation for the sample.In this problem, we have that t = 2.776, df = 5 - 1 = 4 for a two-tailed interval, hence looking at the t-table it is found that the confidence level is of 95%.
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Lorena is driving a truck that is painting the lines on a new road. The lines she paints are 0.152 meters wide, and she will paint a total length of 5.45 × 105 meters of lines. The shape created by the lines will be a rectangle, and the area will be the product of the length and width.
Approximately what area of the road will Lorena be painting?
5.602 × 10 (5) m2
8.284 × 10 (4) m2
8.698 × 10 (1) m2
8.284 × 10 (5) m2
5.602 × 10 (4) m2
Answer:
8.284 × 10^4 m^2
Step-by-step explanation:
The area is the product of length and width:
(5.45·10^5 m)·(0.152 m) = 0.8284·10^5 m^2 = 8.284·10^4 m^2
The probability of a student getting an A....
Answer:
[tex]P (M\ and\ C) = \frac{1}{4}=25\%[/tex]
Step-by-step explanation:
We call M the event in which a student gets an A in math and we call C the event in which a student gets an A in chemistry. As the events are not mutually exclusive, then.
[tex]P (M\ or\ C) = P (M) + P (C) - P (M\ and\ C)[/tex]
In this case we know that:
[tex]P (M\ or\ C) = \frac{7}{10}[/tex]
[tex]P (M) =\frac{17}{20}[/tex]
[tex]P (C) =\frac{1}{10}[/tex]
So
[tex]P (M\ and\ C) = P (M) + P (C) - P (M\ or\ C)[/tex]
[tex]P (M\ and\ C) = \frac{17}{20} + \frac{1}{10} -\frac{7}{10}[/tex]
[tex]P (M\ and\ C) = \frac{1}{4}[/tex]