Solve for x. please help me its urgent

Answer: [tex]\dfrac{60}{143}[/tex]

Step-by-step explanation:

Given,  A class has five boys and nine girls.

Total students = 5+9=14

Number of ways to choose 6 students out of 14= [tex]^{14}C_6[/tex]  [Using combinations]

Number of ways to choose 4 girls out of 6 (4 girls + 2 boys = 6 ) = [tex]^{9}C_4\times\ ^{5}C_2[/tex]

If the teacher randomly picks six students, then the probability that he will pick exactly four girls:-

[tex]\dfrac{^{9}C_4\times \ ^{5}C_2}{^{14}C_6}[/tex]

[tex]=\dfrac{\dfrac{9!}{4!5!}\times\dfrac{5!}{2!3!}}{\dfrac{14!}{6!8!}}\\\\=\dfrac{1260}{3003}\\\\=\dfrac{60}{143}[/tex]

hence, the required probability = [tex]\dfrac{60}{143}[/tex] .

Answer:

angle C = 38 degrees

Step-by-step explanation:

Refer to attached figure (sorry, forgot to attach earlier)

Given

AIB = 109

Let

CAX = XAB = x

CBY = YBA = y

XIB = YIA = x+y    ........exterior angles

XIB = YIA = 180-109 = 71   ............ sum of angles on a line

=>

x+y = 71

ACB = 180 - 2x -2y  ................. sum of angles of a triangle

= 180 - 2(x+y)

= 180 - 2(71)

= 180 - 142

= 38

Answer:

7/8 = 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8 + 1/8

7/8 = 1/8 + 6/8

7/8 = 4/8 + 3/8

7/8 = 5/8 + 2/8

Step-by-step explanation:

Hope it helps!

The fraction 7/8 can be written as the sum of unit fraction i.e;

1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.

A unit fraction can be defined as a fraction whose numerator is 1.

Given fraction 7/8

can be written as the sum of the unit fraction i.e;

7/8=1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8

Hence,7/8 can be decomposed into sum of unit fraction as

1/8+1/8+1/8+1/8+1/8+1/8+1/8+1/8.

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Answer:

second option

Step-by-step explanation:

Parallel lines have the same slope, and since the slope of the given line is 1/2, we know the slope of the answer will be 1/2, which eliminates the first and last options. We know the slope and a point that belongs to the line, (-2, 1), so we can use point-slope formula to derive the equation of the line.

y - 1 = 1/2(x + 2)

y - 1 = 1/2x + 1

y = 1/2x + 2

Answer:

[tex]Range = 16[/tex]

[tex]Inter\ Quartile\ Range = 6.75[/tex]

[tex]Variance = 20.44[/tex]

[tex]Standard\ Deviation = 4.52[/tex]

Step-by-step explanation:

Given

4, 17, 12, 9, 6, 10, 1, 5, 9, 3

Calculating the range;

[tex]Range = Highest - Lowest[/tex]

From the given data;

Highest = 17 and Lowest = 1

Hence;

[tex]Range = 17 - 1[/tex]

[tex]Range = 16[/tex]

Calculating the Inter-quartile Range

Inter quartile range (IQR) is calculates as thus

[tex]IQR = Q_3 - Q_1[/tex]

Where

Q3 = Upper Quartile and Q1 = Lower Quartile

Start by arranging the data in ascending order

1, 3, 4, 5, 6, 9, 9, 10, 12, 17

N = Number of data; N = 10

---------------------------------------------------------------------------------

Calculating Q3

[tex]Q_3 = \frac{3}{4}(N+1) th\ item[/tex]

Substitute 10 for N

[tex]Q_3 = \frac{3}{4}(10+1) th\ item[/tex]

[tex]Q_3 = \frac{3}{4}(11) th\ item[/tex]

[tex]Q_3 = \frac{33}{4} th\ item[/tex]

[tex]Q_3 = 8.25 th\ item[/tex]

Express 8.25 as 8 + 0.25

[tex]Q_3 = (8 + 0.25) th\ item[/tex]

[tex]Q_3 = 8th\ item + 0.25 th\ item[/tex]

Express 0.25 as fraction

[tex]Q_3 = 8th\ item +\frac{1}{4} th\ item[/tex]

[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]

From the arranged data;

[tex]8th\ item = 10[/tex] and [tex]9th\ item = 12[/tex]

[tex]Q_3 = 8th\ item +\frac{1}{4} (9th\ item - 8th\ item)[/tex]

[tex]Q_3 = 10 +\frac{1}{4} (12 - 10)[/tex]

[tex]Q_3 = 10 +\frac{1}{4} (2)[/tex]

[tex]Q_3 = 10 +0.5[/tex]

[tex]Q_3 = 10.5[/tex]

Calculating Q1

[tex]Q_1 = \frac{1}{4}(N+1) th\ item[/tex]

Substitute 10 for N

[tex]Q_1 = \frac{1}{4}(10+1) th\ item[/tex]

[tex]Q_1 = \frac{1}{4}(11) th\ item[/tex]

[tex]Q_1 = \frac{11}{4} th\ item[/tex]

[tex]Q_1 = 2.75 th\ item[/tex]

Express 2.75 as 2 + 0.75

[tex]Q_1 = (2 + 0.75) th\ item[/tex]

[tex]Q_1 = 2nd\ item + 0.75 th\ item[/tex]

Express 0.75 as fraction

[tex]Q_1 = 2nd\ item +\frac{3}{4} th\ item[/tex]

[tex]Q_1 = 2nd\ item +\frac{3}{4} (3rd\ item - 2nd\ item)[/tex]

From the arranged data;

[tex]2nd\ item = 3[/tex] and [tex]3rd\ item = 4[/tex]

[tex]Q_1 = 3 +\frac{3}{4} (4 - 3)[/tex]

[tex]Q_1 = 3 +\frac{3}{4} (1)[/tex]

[tex]Q_1 = 3 +0.75[/tex]

[tex]Q_1 = 3 .75[/tex]

---------------------------------------------------------------------------------

Recall that

[tex]IQR = Q_3 - Q_1[/tex]

[tex]IQR = 10.5 - 3.75[/tex]

[tex]IQR = 6.75[/tex]

Calculating Variance

Start by calculating the mean

[tex]Mean = \frac{1+3+4+5+6+9+9+10+12+17}{10}[/tex]

[tex]Mean = \frac{76}{10}[/tex]

[tex]Mean = 7.6[/tex]

Subtract the mean from each data, then square the result

[tex](1 - 7.6)^2 = (-6.6)^2 = 43.56[/tex]

[tex](3 - 7.6)^2 = (-4.6)^2 = 21.16[/tex]

[tex](4 - 7.6)^2 = (-3.6)^2 = 12.96[/tex]

[tex](5 - 7.6)^2 = (-2.6)^2 = 6.76[/tex]

[tex](6 - 7.6)^2 = (-1.6)^2 = 2.56[/tex]

[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]

[tex](9 - 7.6)^2 = (1.4)^2 = 1.96[/tex]

[tex](10 - 7.6)^2 = (2.4)^2 = 5.76[/tex]

[tex](12 - 7.6)^2 = (4.4)^2 = 19.36[/tex]

[tex](17 - 7.6)^2 = (9.4)^2 = 88.36[/tex]

Sum the result

[tex]43.56 + 21.16 + 12.96 + 6.76 + 2.56 + 1.96 + 1.96 + 5.76 + 19.36 + 88.36 = 204.4[/tex]

Divide by number of observation;

[tex]Variance = \frac{204.4}{10}[/tex]

[tex]Variance = 20.44[/tex]

Calculating Standard Deviation (SD)

[tex]SD = \sqrt{Variance}[/tex]

[tex]SD = \sqrt{20.44}[/tex]

[tex]SD = 4.52[/tex] (Approximated)

Answer:

A road with a pitch of 1 in 8 is steeper.

Step-by-step explanation:

Let us convert these to the same units so that we can better compare them.

[tex]\frac{1}{8} = 0.125[/tex]

0.125=12.5 %

As 12.5% is greater than 12%, the road with a pitch of 1 in 8 will be steeper.

Answer:

Step-by-step explanation:

-8*3= -24+14=-10

Answer:

-12 and 2.

Step-by-step explanation:

-12*2= -24,

-12+2=-10

Answer:

3906250

Step-by-step explanation:

We can notice that the ratio is 5. 10/2 = 5

Each term gets multiplied by 5 to get the next term.

250 × 5 = 1250 (5th term)

1250 × 5 = 6250 (6th term)

6250 × 5 = 31250 (7th term)

31250 × 5 = 156250 (8th term)

156250 × 5 = 781250 (9th term)

781250 × 5 = 3906250 (10th term)

The 10th term of the geometric sequence is 3906250.

Answer:

Max area is 16

Step-by-step explanation:

If A² + B² = C², then A² + B² = 64. The largest triangle area is when both A² and B² are equal to 32, so 32 + 32 = 64.

So equal side of the triangle is √32 or about 5.6568. The area of the triangle is then 1/2(5.6568 × 5.6568) or 16.

The maximal area of a right triangle is 90.496

Derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus.

Given:

let the perpendicular be 'x'

and base be 'y'

Using Pythagoras theorem

x² + y² = 8²

x² + y² = 64

y²= 64- x²

y = √64-x²

Now, Area of triangle

= 1/2* base* height

=xy/2

=x *√64-x²*1/2

On differentiating both side

A' = 64-2x²/√64-x²*1/2

Setting derivative function equal to zero,

64= 2x²

32=x²

x=5.656

So, Area of triangle = x *√64-x²*1/2

= 90.496

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Answer:

47, 40, 33, 26 are the first four terms of the sequence.

Step-by-step explanation:

Expression representing the sequence is,

[tex]a_n=46-7(n-1)[/tex]

where n = number of term in the sequence

For n = 1,

[tex]a_1=47-7(1-1)[/tex]

    = 47

For n = 2,

[tex]a_2=47-7(2-1)[/tex]

    = 47 - 7

    = 40

For n = 3,

[tex]a_3[/tex] = 47 - 7(3 -1)

   = 47 - 14

   = 33

For n = 4,

[tex]a_4=47-7(4-1)[/tex]

    = 47 - 21

    = 26

Therefore, first four terms of the sequence are 47, 40, 33 and 26.

Answer:

1. = 8

2. =40

3. =37

Step-by-step explanation:

1. x = √(17² - 15²) = 8

2. x =√(9² +41²) = 40

3. x =√(12² + 35²) = 37

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Answer:

here,

A=2×22÷7×17/2×21

A=22×17×3

A=1122 sq.cm

It's adding 3 and subtracting 2 every time.

This means the next two terms would be +3 and -2 since the last one was -2.

The next term = 4+3=7

The next next term = 7-2=5

Answer:

Please see the attached picture.

Hope it helps...

Best regards!!

Answer:

y=2.2

Step-by-step explanation:

1: Distribute all numbers to get rid of all parenthesis

2: Solve

Hope this helped :) LET ME KNOW IF YOU NEED THE ANSWER IN A DIFFERENT FORM I CAN GET IT FOR YOU

Answer:

Step-by-step explanation:

This is a permutation problem. Given the 10 cards with numbers 2, 3, 4,5,5,7,7,7,7,7 on it, if Salvador is going to make a row call, the number of ways he can order a row is as shown below;

Total number of cards = 10!

number of times the digit 5 was repeated = 2times

number of times the digit 7 was repeated = 5times

The number of ways he can make a row call = 10!/2!5!

= 10*9*8*7*6*5!/2*5!

=  10*9*8*7*6/2

=  10*9*8*7*3

= 15,120 different ways

Hence, the number of ways he can order the row is 15,120 number of ways.

Answer:

This is skewed torwards the right. Or in other words positively skewed distribution.

Step-by-step explanation:

All of the values are fairly close together torwards the lower range. While 50.20 is more of an outlier, so this graph would gradualy skew to the right.

Answer:

x = 3

y = -2

Step-by-step explanation:

Given:

8x - 3y = 30 ..................(1)

3x + y = 7 .......................(2)

Eliminate y by adding (1)+3*(2)

8x-3y + 3*( 3x+y) = 30 + 3*7

8x + 9x -3y + 3y = 51

17x = 51

x = 3  .....................(3)

substitute (3) in (2)

3(3) + y = 7

y = 7-9 = -2

y = -2 ....................(4)

Answer:

Step-by-step explanation:

[tex]8x-3y=30\\y=7-3x\\\\8x-3(7-3x)=30\\8x-21+9x=30\\17x=51\\x=3\\\\y=7-3(3)\\y=7-9\\y=-2[/tex]

Answer:

see below

Step-by-step explanation:

Using the Pythagorean Theorem:

a^2+ b^2 = c^2

5^2+ 9^2 = 13^2

25+81 = 169

106 = 169

This is not true so it is not a right triangle

Answer:

[tex]\boxed{\sf Not \ a \ right \ triangle}[/tex]

Step-by-step explanation:

Apply Pythagorean theorem to check if the triangle is a right triangle.

[tex]a^2+ b^2 = c^2[/tex]

[tex]5^2+ 9^2 = 13^2[/tex]

[tex]25+81=169[/tex]

[tex]106=109[/tex]

False statement.

The triangle is not a right triangle.

Answer:

it is the inches milimeters meters

Answer:

Step-by-step explanation:

Given,

Volume of cone ( v ) = 27 π

Radius ( r ) = 3 cm

Height of cone ( h ) = ?

Now, let's find the height of cone:

Volume of cone = [tex] \frac{\pi {r}^{2}h }{3} [/tex]

plug the values

[tex]27\pi = \frac{\pi \: {3}^{2} \: h \: }{3} [/tex]

Evaluate the power

[tex]27\pi = \frac{\pi \times 9 \times h}{3} [/tex]

Divide 9 by 3

[tex]27\pi = 3\pi \: h[/tex]

Divide both sides of the equation by 3π

[tex] \frac{27\pi}{3\pi} = \frac{3\pi \: h}{3\pi} [/tex]

Calculate

[tex]9 = h[/tex]

Swipe the sides of the equation

[tex]h = 9[/tex] cm

Hope this helps..

Best regards!!

Answer:

x=3

Step-by-step explanation:

To solve this problem, we should check the x coordinate of the point where both graphs intersect. Based on both graphs, they intersect at the point (3,-1). So, the input value for which both graphs have the same value is x=3.

Answer:

its x=-2

Step-by-step explanation:

cause i got it wrong and it said the answer was x=-2

Answer:

Yes

Step-by-step explanation:

Let s be the price of snickers, g the price of galaxy and k the price of kitkat.

●For Mariam the equation will be:

8 s + 3 g + 3k = 8

●For Zainab the equation will be:

4 s + 9 g + 4 k = 10.9

Take the first equation and divide both sides by 4 to make it easier.

You get:

● 2s + 0.75 g + 0.75k = 2

Take the second equation and divide both sides by 2 to make easier.

You get:

● 2s + 4.5g + 2k = 5.45

The new system of equation is:

● 2s +0.75g + 0.75k = 2

● 2s + 4.5g + 2k = 5.45

Express s in the first equation using the other variables.

● 2s +0.75g +0.75k = 2

● 2s + 0.75(g+k) = 2

● 2s = 2-0.75(g+k)

● s = 1- 0.325 (g+k)

Replace s by the new expression in the second equation:

●2 [1-0.325(g+k)] +4.5 g +2k = 5.45

●2-0.75(g+k) +4.5g + 2k = 5.45

●2- 0.75g -0.75k +4.5 g +2k = 5.45

●2+ 3.75g + 1.25k = 5.45

● 3.75g +1.25k = 3.45

We have eliminated one variable (s)

We will keep (3.75g+1.25k=3.45) and use it.

Now that we eliminated in the second equation do it again in the first one.

You will get a system of equations with two variables.

Solve it and replace g and k with the solutions.

Finally solve the equation and find s.

The correct answer is 45.5 km

Explanation:

The total distance from the locksmith to the hotel, located in the east of the graph is not directly given; however, this distance can be calculated by considering the partial distances given. This includes the distance from the locksmith to the furniture store (18.3 km), and the distance between the furniture and the hotel (27.2) as the total distance = distance from the locksmith to the furniture store + distance from the furniture store to the hotel. Thus, the total distance is 18.3 km + 27.2 km which is equal to 45.5 km.

Answer:

108, 324, 972

Step-by-step explanation:

This sequence is multiplying by ✖️3.

4✖️3=12✖️3=36✖️3=108✖️3=324✖️3=972

Hope this helps!

Answer:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Step-by-step explanation:

For this problem we have the following function given:

[tex] f(x) = 6x^2 +2 , -6 <x<9[/tex]

[tex] f(x) = 12 , 9 \leq x <13[/tex]

And we want to evaluate f(x=9)

And for this case the answer would be:

[tex] f(9)= 12[/tex]

Best answer:

O 12

Answer:

2 11/12

Step-by-step explanation:

3/4 + 2 1/6

Add the fractions.

35/12

= 2 11/12

Answer:

[tex]2\frac{11}{12}[/tex]

Step-by-step explanation:

[tex]\frac{3}{4}+2\frac{1}{6}=\\\\\frac{18}{24}+2\frac{4}{24}=\\\\2\frac{22}{24}=\\\\2\frac{11}{12}[/tex]

Answer:

The correct answer will be "56".

Step-by-step explanation:

Use a combination of 8 things taken 3 at a time :

⇒  [tex]8_{C_{3}}[/tex]

⇒  [tex]\frac{8!}{(3!(8 - 3)!)}[/tex]

⇒  [tex]\frac{8!}{(3!5!)}[/tex]

⇒  [tex]\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{3\times 2\times 1}[/tex]

⇒  [tex]8\times 7[/tex]

⇒  [tex]56[/tex]

Using the principle of combination, the number of different random samples of size 3 that can be selected is 56.

Using the principle of combination :

Hence, we have ;

8C3 = [8! ÷ (8 - 3)! 3!]

8C3 = [8! ÷ 5!3!]

8C3 = (8 × 7 × 6) ÷ (3 × 2 × 1)

8C3 = 8 × 7

8C3 = 56

Hence, there are 56 different possible samples.

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Answer:  A) N'=(-2, 2) M'=(-1, 0)  L'=(-5, -2)

Step-by-step explanation:

N = (-2, -4)      M = (-3, -2)       L = (1, 0)

Reflection over y = -1

N' = (-2, 2)      M' = (-3, 0)       L' = (1, -2)

Reflection over x = -2

N'' = (-2, 2) M'' = (-1, 0)  L'' = (-5, -2)

Answer:

[tex]\boxed{y\leq 6}[/tex]

Step-by-step explanation:

[tex]y-8 \leq -2[/tex]

Adding 2 to both sides

[tex]y \leq -2+8[/tex]

[tex]y \leq 6[/tex]

You probably want the unsigned area, which means you don't compute the integral

[tex]\displaystyle\int_0^{2\pi}\sin x\,\mathrm dx[/tex]

but rather, the integral of the absolute value,

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx[/tex]

[tex]\sin x[/tex] is positive when [tex]0<x<\pi[/tex] and negative when [tex]\pi<x<2\pi[/tex], so

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\int_0^\pi\sin x\,\mathrm dx-\int_\pi^{2\pi}\sin x\,\mathrm dx[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=(-\cos x)\bigg|_0^\pi-(-\cos x)\bigg|_\pi^{2\pi}[/tex]

[tex]\displaystyle\int_0^{2\pi}|\sin x|\,\mathrm dx=\boxed{4}[/tex]