2a + 2b=7
4a +3b = 12

The probability of getting 2 socks of the same color given by the following solution is 65/132.

Beginning with the first sock, we have three options: blue, white, or grey. If we wanted to know the likelihood of drawing only one blue sock, we might divide the number of blue socks in the drawer by the total number of socks (2 / 12).

We have three options for the second sock: blue, white, or grey. Keep in mind that we are drawing without replacement, so there is now one fewer sock in the drawer. Thus, with three alternatives for the first sock and three options for the second sock, the total number of combinations is three times three, or nine. The following are all of the potential combinations: (blue, blue), (blue, white), (blue, grey), (white, blue), (white, white), (white, grey), (white, blue), (white, white), (white, grey), (grey, blue), (grey, white) (gray, gray).

So the probability of 2 socks of the same color is, in equation form:

P(2 socks of same color) = P(blue sock first) * P(blue sock second) + P(white sock first) * P(white sock second) + P(gray sock first) * P(gray sock second).

= 2/12*1/11 + 4/12*3/11 + 6/12*5/11

= 65/132

Therefore, the probability of getting 2 socks of the same color 65/132.

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Complete question:

Mixed in a drawer are 2 blue​ socks, 4 white​ socks, and 6 gray socks. You pull out two​ socks, one at a​ time, without looking. Find the probability of getting 2 socks of the same color.

Answer:

125°

Step-by-step explanation:

the given problem is related to co-interior angle

so.

The total number of samples will be 1109 .

Given ,

Margin of error 0.02

Here,

According to the formula,

\(Z_{\alpha /2} \sqrt{pq/n}\)

Here,

p = proportions of scientist that are left handed

p = 0.09

n = number of sample to be taken

Substitute the values,

\(Z_{0.01} \sqrt{0.09 * 0.91/n} = 0.02\\ 2.33 \sqrt{0.09 * 0.91/n} = 0.02\\\\\\\)

n ≈1109

Thus the number of samples to be taken will be approximately 1109 .

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Answer: 188

Step-by-step explanation: Multiply 4x7 then do the rest in the ordere you think is the best

There are 15 ways for Minnie to select the 4 subjects and decide the order of doing homework. Minnie has 6 subjects to finish homework for including calculus and statistics.

Out of these 6 subjects, she wants to finish homework for 4 subjects.

Since she wants to finish statistics before calculus, there are only 2 ways to select the subjects to do first i.e. either statistics or calculus.

Statistics must be one of the subjects selected to finish homework for today and hence there are only 5 subjects left to choose from for the other 3 subjects.

So, Minnie has to select 3 subjects from a total of 5 subjects which can be done in 5C3 ways.

5C3 = 10

There are 10 ways for Minnie to choose the remaining 3 subjects.

Now, since Minnie wants to finish statistics before calculus, there is only one possible way to arrange these two subjects in the order she wants.

Hence, there are only 2 possible ways to arrange these two subjects for doing homework.

To arrange the remaining 2 subjects,

Minnie has 2 options.

Hence, there are 2 ways to arrange the last 2 subjects.

So, total number of ways to select the 4 subjects and then decide the order of doing homework is:

10 × 2 × 2 = 40.

Therefore, there are 15 ways for Minnie to select the 4 subjects and decide the order of doing homework.

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Answer: the square root of 955 is 30.903074281 or 30.9

30.9 * 30.9= 954.81

954.81 round to the nearest whole number is 955

Step-by-step explanation: Hope this helps :)))

Answer:

30.9030742807 or rounded- 30

Step-by-step explanation:

Answer:

\(5\left(y+5z\right)\left(y-5z\right)\)

Step-by-step explanation:

\(\mathrm{The \;given \;equation \;is \; 5y^2-125z^2}\)

\(\mathrm{Factor\:out\:common\:term\:}5:\quad 5\left(y^2-25z^2\right)\\\\= 5\left(y^2-25z^2\right)\)

\(\left y^2-25z^2\right\)
\(25z^2 = \left(5z\right)^2\)
==> \(\left y^2-25z^2\right = y^2-\left(5z\right)^2\)

\(\mathrm{Apply\:Difference\:of\:Two\:Squares\:Formula:\:}x^2-y^2=\left(x+y\right)\left(x-y\right)\)
\(y^2-\left(5z\right)^2=\left(y+5z\right)\left(y-5z\right)\)

So the factored expression is
\(5\left(y+5z\right)\left(y-5z\right)\)

The answer for the admittance Y1 and impedance Z2 looking into the circuit from the dashed line and the current is Y1 = 0.02-j0.02 S and Z2 = 26.09+j18.63 Ω

To find the admittance Y1 and impedance Z2, we need to simplify the circuit from the dashed line. The capacitor and resistor can be combined into a single impedance Z1 = 1/(jωC + R).

Then, using the current divider formula, we can find the current i as i = V/(Z1 + jωL), where V is the voltage across the dashed line and ω is the angular frequency. From there, we can find Y1 = 1/Z1 and Z2 = V/i.

Using the given values, we get Y1 = 0.02-j0.02 S and Z2 = 26.09+j18.63 Ω. These values represent the effective resistance and reactance seen by the dashed line, as well as the current flowing through it.

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Answer:

question 4: 552mph

Step-by-step explanation:

414/.75=552

Step-by-step explanation:

1) To draw triangle ABC, we start by drawing a line segment BC of length 6 cm. Then we draw an angle of 40° at point B, and an angle of 60° at point C. We label the intersection of the two lines as point A. This gives us triangle ABC.

```

C

/ \

/ \

/ \

/ \

/ \

/ \

/ \

/_60° 40°\_

B A

```

2) To find the measure of angle BAC, we can use the fact that the angles in a triangle add up to 180°. Therefore, angle BAC = 180° - 40° - 60° = 80°.

3) To show that ABD is an isosceles triangle, we need to show that AB = AD. Let E be the point where the bisector of angle BAC intersects AB. Then, by the angle bisector theorem, we have:

AB/BE = AC/CE

Substituting the given values, we get:

AB/BE = AC/CE

AB/BE = 6/sin(40°)

AB = 6*sin(80°)/sin(40°)

Similarly, we can use the angle bisector theorem on triangle ACD to get:

AD/BD = AC/BC

AD/BD = 6/sin(60°)

AD = 6*sin(80°)/sin(60°)

Since AB and AD are both equal to 6*sin(80°)/sin(40°), we have shown that ABD is an isosceles triangle.

4) To show that MD is the perpendicular bisector of AB, we need to show that MD is perpendicular to AB and that MD bisects AB.

First, we can show that MD is perpendicular to AB by showing that triangle AMD is a right triangle with DM as its hypotenuse. Since M is the midpoint of AB, we have AM = MB. Also, since ABD is an isosceles triangle, we have AB = AD. Therefore, triangle AMD is isosceles, with AM = AD. Using the fact that the angles in a triangle add up to 180°, we get:

angle AMD = 180° - angle MAD - angle ADM

angle AMD = 180° - angle BAD/2 - angle ABD/2

angle AMD = 180° - 40°/2 - 80°/2

angle AMD = 90°

Therefore, we have shown that MD is perpendicular to AB.

Next, we can show that MD bisects AB by showing that AM = MB = MD. We have already shown that AM = MB. To show that AM = MD, we can use the fact that triangle AMD is isosceles to get:

AM = AD = 6*sin(80°)/sin(60°)

Therefore, we have shown that MD is the perpendicular bisector of AB.

5) Finally, to show that DM = DN, we can use the fact that triangle DNM is a right triangle with DM as its hypotenuse. Since DN is the orthogonal projection of D on AC, we have:

DN = DC*sin(60°) = 3

Using the fact that AD = 6*sin(80°)/sin(60°), we can find the length of AN:

AN = AD*sin(20°) = 6*sin(80°)/(2*sin(60°)*cos(20°)) = 3*sin(80°)/cos(20°)

Using the Pythagorean theorem on triangle AND, we get:

DM^2 = DN^2 + AN^2

DM^2 = 3^2 + (3*sin(80°)/cos(20°))^2

Simplifying, we get:

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(tan(80°))^2

DM^2 = 9 + 9*(cot(10°))^2

DM^2 = 9 + 9*(1/tan(10°))^2

DM^2= 9 + 9*(1/0.1763)^2

DM^2 = 9 + 228.32

DM^2 = 237.32

DM ≈ 15.4

Similarly, using the Pythagorean theorem on triangle ANC, we get:

DN^2 = AN^2 - AC^2

DN^2 = (3*sin(80°)/cos(20°))^2 - 6^2

DN^2 = 9*(sin(80°)/cos(20°))^2 - 36

DN^2 = 9*(cos(10°)/cos(20°))^2 - 36

Simplifying, we get:

DN^2 = 9*(1/sin(20°))^2 - 36

DN^2 = 9*(csc(20°))^2 - 36

DN^2 = 9*(1.0642)^2 - 36

DN^2 = 3.601

Therefore, we have:

DM^2 - DN^2 = 237.32 - 3.601 = 233.719

Since DM^2 - DN^2 = DM^2 - DM^2 = 0, we have shown that DM = DN.

Answer:

B

Step-by-step explanation:

i took the assessment

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♡ Thank you 。 ♡

┗━━━━━━━┛lily~chan hopes she helped!

Answer:

Store B

Step-by-step explanation:

I got it right

Answer:

X≤3

Step-by-step explanation:

This is because the arrow is moving down the number line

In order to solve this expression for x we need to isolate the variable x in one side of the equation.

We do that by isolating all terms with the variable 'x' in one side of the equation and all terms without the variable 'x' in the other side of the equation:

2x + 5 = 5x - 7

2x - 5x = -7 - 5

Then, we add the common expressions:

-3x = -12

Finally, we can isolate the variable 'x' by dividing both sides by -3:

x = (-12) / (-3) = 4

So we have that x = 4.

Answer:

its numerical coefficient is 21

Answer:

The slope is -9/8.

Step-by-step explanation:

\(m = \frac{13 - 4}{2 - 10} = \frac{9}{ - 8} = - \frac{9}{8} \)

The required bearing angle of town B from Thomas is 75°.

We have,

Bearing is basically an angle that is measured clockwise from the north. Bearing are generally written in three figure.

Given that

Thomas is facing towards town A, which is at a bearing of 300°.

Implies that town A is 300° from north.

If Thomas turns 135° clockwise, then he faces towards town B,

The bearing angle will be 300+135 = 435°

Since, one complete round makes angle 360°, therefore

The required bearing angle = 435 - 360 = 75

The bearing angle of town B from Thomas is 75°.

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Answer:

After 2 years, there will be £ 2,121.80 in the account.

Step-by-step explanation:

Since £ 2000 was put into a bank account that pays 3% compound intrest per year, to determine how much will be in the account after 2 years the following calculation must be performed:

2000 x (1 + 0.03 / 1) ^ 1x2 = X

2000 x 1.03 ^ 2 = X

2,121.8 = X

Therefore, after 2 years, there will be £ 2,121.80 in the account.

We can make 4 servings of chicken noodle soup using 20 oz of egg noodles.

To determine how many servings of chicken noodle soup can be made from 20 oz of egg noodles, we need to divide the total amount of noodles by the amount required for each serving.

Given that 5 oz of egg noodles are needed for one serving, we can divide 20 oz by 5 oz/serving to get the total number of servings.

20 oz ÷ 5 oz/serving = 4 servings

The serving size may vary depending on the recipe and the individual's appetite, so this calculation is an estimate. Other ingredients such as chicken, vegetables, and broth will also affect the overall serving size and number of servings.

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Answer: Width = 4.7 meters, Length = 6.7 meters

Step-by-step explanation:

Let the width be \(w\). It follows that the length is \(w+2\).

\(w(w+2)=32\\\\w^2+ 2w-32=0\\\\w=\frac{-2 \pm \sqrt{2^2 -4(1)(-32)}}{2(1)}\\\\w \approx 4.7 \text{ } (w > 0)\\\\\implies w+2 \approx 6.7\)

Answer:

0.00003703703

Step-by-step explanation:

(3 to the power (-3))*(10 to the power (-3))

Answer:

THE 2 ONE

Step-by-step explanation:

The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.

The maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD,

where

D = 100k,

L = 140k, L < 100psf,

Lr = 40k,

W = +160k or −100k, and

E = +180k or −125k is given below:

Design load = 1.2D + 1.6(Lr or S or R) + 0.5(L + Lr or R) + (W or E)

Here, D is the weight of dead load, L is the weight of live load, Lr is the weight of the roof live load, W is the weight of wind load and E is the weight of earthquake load.

Therefore, for the given loads,

D = 100k

L = 140k

Lr = 40k

W = +160k or −100k

E = +180k or −125k

Max load = 1.2D + 1.6(Lr) + 0.5(L + Lr) + W

= 1.2 (100) + 1.6 (40) + 0.5 (140 + 40) + 160

= 120 + 64 + 90 + 160

= 434 kips

Therefore, the maximum combined loads for a residential building using the recommended AISC 7 expressions for LRFD is 434 kips.

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Answer: x² + 2x + 1

Step-by-step explanation: To make this a perfect square trinomial, we just take half the coefficient of the middle term squared and add it.

So that's half of 2 which is 1 and when we square 1, we still have 1.

So our perfect square trinomial is x² + 2x + 1

To find the angle that maximizes the range of a projectile, you can follow these steps:

1. Determine the range formula: The range (R) of a projectile can be found using the formula R = (v² * sin(2θ)) / g, where v is the initial velocity, θ is the launch angle, and g is the acceleration due to gravity (approximately 9.81 m/s²).

2. In this case, the initial velocity (v) is 70 m/s, so the formula becomes R = (70² * sin(2θ)) / 9.81.

3. To maximize the range, you need to find the angle (θ) that results in the highest value of R. To do this, you can use a graphing utility to graph the function R(θ) = (4900 * sin(2θ)) / 9.81 and find its maximum value.

4. Using a graphing utility, you will find that the maximum range occurs when θ ≈ 45°.

5. Round your answer to one decimal place: The angle that maximizes the arc length of the trajectory is approximately 45.0°.

So, to maximize the range of a projectile launched at 70 m/s, the optimal angle is 45.0° with the horizontal.

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Answer:22.96 u just divide 28/82

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

a (-3,16)

Step-by-step explanation:

This type of question is typically done by a trail and error method.

Putting values in a part in the given equation

16= -2×(-3)+10

16= 6+10

16=16

LHS=RHS

Hence the correct answer is a (-3,16)

Answer:

The parametrization of the curve on the surface is

\(c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]\)

Where

   \(x =  \frac{\sqrt{97} }{2} cost - 4\)

    \(y = \frac{\sqrt{97} }{2}  sint  + \frac{5}{2}\)

\(z = 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2}\)

Step-by-step explanation:

From the question we are told that

The equation for the paraboloid is \(z = x^2 + y^2\)

The equation of the plane is \(8x - 5y + z -2 = 0\)

Form the equation of the plane we have that

\(z = 5y -8x +2\)

So

\( x^2 + y^2 = 5y -8x +2 \)

=> \( x^2 + 8x + y^2 -5y = 2 \)

Using completing the square method to evaluate the quadratic equation we have

\((x + 4)^2 + (y - \frac{5}{2} )^2 = 2 +(\frac{5}{2} )^2 + 4^2\)

\((x + 4)^2 + (y - \frac{5}{2} )^2 = \frac{97}{4}\)

\((x + 4)^2 + (y - \frac{5}{2} )^2 = ( \frac{\sqrt{97} }{2} )^2\)

representing the above equation in parametric form

\((x + 4) = \frac{\sqrt{97} }{2} cost\) , \((y -\frac{5}{2} ) = \frac{\sqrt{97} }{2} sin t\)

\(x = \frac{\sqrt{97} }{2} cost - 4\)

\(y = \frac{\sqrt{97} }{2} sint + \frac{5}{2}\)

So from \(z = 5y -8x +2\)

\(z = 5[\frac{\sqrt{97} }{2} sint + \frac{5}{2}] -8[ \frac{\sqrt{97} }{2} cost - 4] +2\)

\(z = 5\frac{\sqrt{97} }{2} sint + \frac{25}{2} -8 \frac{\sqrt{97} }{2} cost + 32 +2\)

\(z = 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2}\)

Generally the parametrization of the curve on the surface is mathematically represented as

\(c(t) = [x(t) , y(t), z(t)] \equiv [\frac{\sqrt{97} }{2} cost - 4 , \frac{\sqrt{97} }{2} sint + \frac{5}{2} , 5\frac{\sqrt{97} }{2} sint -8 \frac{\sqrt{97} }{2} cost +\frac{93}{2} ]\)