Suppose a triangle has two sides of length 42 and 35, and that the angle between these two sides is 120°. Which equation should you solve to find the length of the third side of the triangle?

Answer:

[tex]x1=\sqrt{216} \ and \ y1=\ \sqrt{216}[/tex]

Step-by-step explanation:

Let the first number is x1 and other number is y1 then

[tex]x1 * y1 =216[/tex]

Therefore

[tex]y1=[/tex][tex]\frac{216}{x1}[/tex]

also there sum is

[tex]s1 =x1+y1[/tex]....Eq(1)

Putting the value of y1  in the previous equation

[tex]s1\ =x1 + \frac{216}{x1}[/tex]........Eq(2)

Differentiate the the Eq(2) with respect to x1 we get

[tex]\frac{ds1}{dx1} \ =\ 1+216*\frac{1}{-x1^{2} }[/tex]

[tex]\frac{ds1}{dx1} \ =\ 1-\frac{216}{x1^{2} }\ =\ 0[/tex]

[tex]{x1^{2} }\ =\ 216\\ x1=\sqrt{216}[/tex]

Putting the value of X1 in Eq(1) we get

[tex]y1=\frac{216}{\sqrt{216} } \\y1=\frac{216*\sqrt{216} }{216} \\y1=\ \sqrt{216}[/tex]

So [tex]x1=\sqrt{216} \ and \ y1=\ \sqrt{216}[/tex]

Answer:

1/2

Step-by-step explanation:

The numbers greater than 6 or less than 3 are 7, 8, 2, and 1.

4 numbers out of 8.

4/8 = 1/2

P(greater than 6 or less than 3) = 1/2

Answer:

no supplement

Step-by-step explanation:

Supplementary angles add to 180 degrees,

This angle is larger than 180 degrees by itself, so it has no supplement

Answer:

Step-by-step explanation:

133 is the product of -19 and n

Translate to an equation is:

133 = -19n

then:

n = 133/-19

n = -7

Check:

133 = -19*7

Answer:

41.67%  probability of the sum of the dots indicate a sum less than or equal to 6

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes:

In this problem, we have these possible outcomes:

Format(Dice A, Dice B)

(1,1), (1,2), (1,3), (1,4), (1,5),(1,6)

(2,1), (2,2), (2,3), (2,4), (2,5),(2,6)

(3,1), (3,2), (3,3), (3,4), (3,5),(3,6)

(4,1), (4,2), (4,3), (4,4), (4,5),(4,6)

(5,1), (5,2), (5,3), (5,4), (5,5),(5,6)

(6,1), (6,2), (6,3), (6,4), (6,5),(6,6)

There are 36 possible outcomes.

Desired outcomes:

Sum of 6 or less. They are:

(1,1), (1,2), (1,3), (1,4), (1,5), (2,1), (2,2), (2,3), (2,4), (3,1), (3,2), (3,3), (4,1), (4,2), (5,1)

15 desired outcomes

15/36 = 0.4167

41.67%  probability of the sum of the dots indicate a sum less than or equal to 6

Answer:

Step-by-step explanation:

Given the function f(x) = x⁴-18x²+9 at the interval [-5, 5], the  absolute maximum and minimum values at this end points are as calculated;

at end point x = -5

f(-5) = (-5)⁴-18(-5)²+9

f(-5) = 625-450+9

f(-5) = 184

at end point x = 5

f(5) = (5)⁴-18(5)²+9

f(5) = 625-450+9

f(5) = 184

To get the critical point, this points occurs at the turning point i.e at

dy/dx = 0

if y = x⁴-18x²+9

dy/dx = 4x³-36x = 0

4x³-36x = 0

4x (x²-9) = 0

4x = 0

x = 0

x²-9 = 0

x² = 9

x = ±3

Using the critical points [0, ±3]

when x = 0, f(0) =  0⁴-18(0)+9

f(0) = 9

Similarly when x = 3, f(±3)=  (±3)⁴-18(±3)²+9

f(±3) = 81-162+9

f(±3) = -72

It can be seen that the absolute minimum occurs at x= ±5 and and absolute minimum occurs at x =±3

absolute maximum = 184

absolute minimum = -72

Answer:

Step-by-step explanation:

6 - 3 = 3

The numbers can be simplified to become the number 3.

4p stays the same.

Place the variable and numbers together.

This will result in the equation of 4p + 3.

Answer:

An independent sample.

Step-by-step explanation:

In this scenario, to compare the production techniques used by foreign and local firms in Brazil, a random sample of 80 foreign firms and a random sample of 80 local firms are selected. We can safely conclude that this study uses an independent sample design.

An independent sample design can be defined as a research method that usually involves the use of multiple experimental groups (two or more). The samples or participants are only in one group and as such each group has no relationship with the other. This simply means that, the samples in a particular group is having no relationship with the other samples in another group.

Ultimately this implies, each samples are independent and satisfies only one condition of the independent sample design during the experiment to compare the production technique used by foreign and local firms in Brazil.

Hence, the researcher would use only two variables or conditions: a random sample of 80 foreign firms and a random sample of 80 local firms are selected.

Answer:

Step-by-step explanation:

An isosceles triangle is a triangle in which two of its sides are equal. This also means that in the triangle, two angles are equal. The angles are usually the base angles. Looking at the given triangle ABC, the base angles are angle Angle A and Angle B, thus angle A = ang B

Therefore, the statement that can be used in the proof is

Angle CAB = angle CBA

Answer:

1/9

Step-by-step explanation:

The die has sides 1,2,3,4,5,6

P( less than 5) = 1,2,3,4 / total

                        =4/6 = 2/3

Then rolling again

P(greater than 5) = 6/total = 1/6

P( less than 5,greater than 5) = 2/3* 1/6= 1/9

Answer:

If the radius is really 5.2, then the standard equation of this circle is:

[tex](x-4)^2+(y+2)^2=27.04[/tex]

Now, if there was a typo in your question, and the radius is  "5", then, the equation becomes:

[tex](x-4)^2+(y+2)^2=25[/tex]

Step-by-step explanation:

Recall that the standard equation for a circle of radius R, centered at [tex](x_0,y_0)[/tex], is given by:

[tex](x-x_0)^2+(y-y_0)^2=R^2[/tex]

Therefore in the case of a circle of radius R = 5.2, and centered at (4, -2), we have:

[tex](x-x_0)^2+(y-y_0)^2=R^2\\(x-4)^2+(y-(-2))^2=(5.2)^2\\(x-4)^2+(y+2)^2=27.04[/tex]

Answer:

32 feet

Step-by-step explanation:

area of square is given by side^2

Perimeter of  square is given by 4*side

_______________________________

Given

area of square = 64 sq feet

side^2 = 64

side^2 = 8^2

side = 8

thus side = 8 feet

_______________________________________

The dog pen is fenced with chain, hence chain will be fence at the edge of square and at the perimeter.

Thus, length of chain required will be same as the Perimeter of  square.

Perimeter of given dog pen with side length 8 feet = 4*8 = 32 feet.

Thus, 32 feet of chain fence is required.

Answer:

  (x, y) = (25, 18)

Step-by-step explanation:

Use the angle sum theorem. You can write equations for the right angle and for the linear angle.

  (x +11) +(3y) = 90 . . . . sum of angles making the right angle

  (y +7) +90 +65 = 180 . . . . sum of angles making the linear angle

From the second equation, we have ...

  y = 18 . . . . subtract 162

Substituting into the first equation gives ...

  x + 11 + 3(18) = 90

  x = 25 . . . . subtract 65

The values of x and y are 25 and 18, respectively.

_____

Check

VQ = 18+7 = 25

QR = 25 +11 = 36

RS = 3·18 = 54

ST = 65

The totals are 36 +54 = 90; 25 +36 +54 +65 = 180, as required.

Answer:

same slope and same y intercept

Step-by-step explanation:

y + 11 = -7/9 (x - 18)

y + 11 = -7/9x + 14

y = -7/9x + 3

Answer:

Q = (- 3, 5 )

Step-by-step explanation:

Given the 2 equations

3y - 2x = 21 → (1)

4y + 5x = 5 → (2)

Multiplying (1) by 5 and (2) by 2 and adding will eliminate the x- term.

15y - 10x = 105 → (3)

8y + 10x = 10 → (4)

Add (3) and (4) term by term to eliminate x

23y = 115 ( divide both sides by 23 )

y = 5

Substitute y = 5 into either of the 2 equations and solve for x

Substituting into (2)

4(5) + 5x = 5

20 + 5x = 5 ( subtract 20 from both sides )

5x = - 15 ( divide both sides by 5 )

x = - 3

Solution is (- 3, 5 )

Answer:

5/12

Step-by-step explanation:

The probability of rolling a number greater than 1 is 5/6, because 5 numbers on a 6-sided dice are greater than 1.

The probability of rolling an even number is 3/6, because 3 numbers on a 6-sided dice are even numbers.

[tex]5/6 \times 3/6[/tex]

[tex]=15/36[/tex]

[tex]=5/12[/tex]

Answer:

yes

Step-by-step explanation:

y = 19+ 3x

Let x = 3 and y = 28

28 = 19 + 3*3

28 =19+9

28 = 28

This is true so the point is one the line

Answer:

20% of people jumped the turnstile, 80% of people paid

Step-by-step explanation:

Percentage is a ratio of one part to another part which it is a member of.

In this scenario, we are given that 12 out of 60 people did not pay as they jumped the turnstile; to calculate this as a percentage, we can simply divide 12 by 60 to find the decimal value of 0.2; when 0.2 is converted to a value out of 100, we find that it gives us 20% (0.2/1=x/100, x=0.2*100, x=20)

Assuming everyone else pays, and by taking the complementary members of the total group, we find that 80% of people will have paid.

Answer: 1. sample mean = 97.7; sample standard deviation(s) = 9.9467; standard error (SE) = 2.2241

2. t-critical value = 2.861; margin of error (m) = 97.9 ± 6.363

3. Lower limits = 91.537; upper limit = 104.263

4. d. Sheila is 99% confident that the true population mean is between 91.537 points and 104.263 points.

Step-by-step explanation: Knowing that this sample has 20 individuals, which means n = 20:

1. Sample mean is the average of the data set:

mean = [tex]\frac{81+84+...+115+116}{20}[/tex] = 97.9

Sample standard deviation is the spread of the sample data set from the mean:

s = [tex]\sqrt{\frac{(81-97.9)^{2}+...+(116-97.9)^{2}}{20-1} }[/tex] = 9.9467

Standard Error shows how far the mean of the set is from the true popultaion mean:

SE = [tex]\frac{9.9467}{\sqrt{20} }[/tex] = 2.2241

2. The t-critical value (t) is the value you use to decide if you reject or accept the null hypothesis. It can be calculated by a calculator or found in the t-test table. To use the table:

Degrees of freedom for this set is: n - 1 = 19

Critical value (α) = 0.99. For the t-test: [tex]\frac{1-0.99}{2}[/tex] = 0.005

[tex]t_{19,0.005}[/tex] = 2.861

Margin of error (m) shows, in percentage, how different your results are from the real population value. It is calculated as:

m = 97.9 ± 2.861*2.2241 = 97.9 ± 6.363

3. Lower and Upper limits are the interval the true mean can assume with a determined certainty.

lower limit = 97.9 - 6.363 = 91.537

upper limit = 97.9 + 6.363 = 104.263

4. In this case, the statistics shows that the true population mean is between 91.537 and 104.263, 99% of the time.

Answer:

Find the number of hours by dividing the distance by mph. The number of hours will be to the left of the decimal point:

284 miles / 58 mph

= 4.896551724

= 4 hours

2) Find the number of minutes by multiplying what is remaining from step 1 by 60 minutes. The minutes will be to the left of the decimal point:

0.896551724 x 60

= 53.79310344

= 53 minutes

3) Find the number of seconds by multiplying what is remaining from step 2 by 60 seconds. The seconds will be to the left of the decimal point:

0.79310344 x 60

= 47.5862064

= 47 seconds

The answer is 4 hours 53 minutes and 47 seconds approx

Answer:

891

Step-by-step explanation:

x has to be 1001 and y has to be 11 * 10 = 110 so x - y = 1001 - 110 = 891.

Answer:

891

Step-by-step explanation:

[tex]$1001$ is the smallest integer greater than $1000$. It also happens to be a multiple of $11$, since $1001 = 11 \cdot 91$. So $1001$ is the smallest multiple of $11$ greater than $1000$ and thus $x = 1001$.The greatest multiple of $11$ that is less than $11^2 = 11 \cdot 11$ is$$11 \cdot (11 - 1) = 11 \cdot 10 = 110$$Thus $y = 110$, and we compute$$x - y = 1001 - 110 = \boxed{891}$$[/tex]

Hope this helped! :)

Answer:

Step-by-step explanation:

From the given information:

The study group includes Girls and Boys

So; we can have a table

Groups        Treatment ( Recruiting services)            Points

Girls              likely to be in School  and increase        3-5 %

                    in Body Mass Index, reflecting greater

                    nutrition and/or medical care.                    

                    Net gain in height                                         -

Boys            likely to be in School  and increase        No changes

                    in Body Mass Index, reflecting greater

                    nutrition and/or medical care.                    

                    Net gain in height                                      No changes

Why do you think the author points out the lack of change in the boys?

From the information above; we need to understand that the point the  author is trying to express is that the  Recruiting services Treatment are largely beneficial for the females rather than the males.

Answer:

(a) 2.3

(b) 0.5245

(c) 0.7242

(d) 0.5245

Step-by-step explanation:

The data provided is:

S = {180.5, 181.7, 180.9, 181.6, 182.6, 181.6,  181.3, 182.1, 182.1, 180.3, 181.7, 180.5}

(a)

The formula to compute the sample range is:

[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]

The data set arranged in ascending order is:

S' = {180.3 , 180.5 , 180.5 , 180.9 , 181.3 , 181.6 , 181.6 , 181.7 , 181.7 ,, 182.1 , 182.1 , 182.6}

The minimum value is, 180.3 and the maximum value is, 182.6.

Compute the sample range as follows:

[tex]\text{Sample Range}=\text{max.}_{x}-\text{min.}_{x}[/tex]

                       [tex]=182.6-180.3\\=2.3[/tex]

Thus, the sample range is 2.3.

(b)

Compute the sample variance as follows:

[tex]S^{2}=\frac{1}{n-1}\sum(x_{i}-\bar x)^{2}[/tex]

     [tex]=\frac{1}{12-1}\times [(180.5-181.41)^{2}+(181.7-181.41)^{2}+...+(180.5-181.41)^{2}]\\\\=\frac{1}{11}\times 5.7692\\\\=0.524473\\\\\approx 0.5245[/tex]

Thus, the sample variance is 0.5245.

(c)

Compute the sample standard deviation as follows:

[tex]s=\sqrt{S^{2}}[/tex]

  [tex]=\sqrt{0.5245}\\\\=0.7242[/tex]

Thus, the sample standard deviation is 0.7242.

(d)

Compute the sample variance using the shortcut method as follows:

[tex]S^{2}=\frac{1}{n-1}\cdot [\sum x_{i}^{2}-n(\bar x)^{2}][/tex]

     [tex]=\frac{1}{12-1}\cdot [394913.57-(12\times (181.41)^{2}]\\\\=\frac{1}{11}\times [394913.57-394907.80]\\\\=\frac{5.77}{11}\\\\=0.5245[/tex]

Thus, the sample variance is 0.5245.

Answer:

I guess that the geometric sequence is:

An = 2*5^(n - 2)

we usually have that that a geometric sequence is something like:

A*r^n.

so i will write the first two terms of our sequence separated, and i will calculate the summation of the first seven terms after n = 2.

A0 = 2*5^(-2) = 2/25

A1 = 2*5^-1 = 2/5

Then, the sum for a geometric sequence is:

SN = A(1 - r^N)/(1 - r)

in this case, A = 2 and r = 5, and i will use N = 7 for the sequence 2*5^n

S7 = 2*(1 - 5^7)/(1 - 5) = 39,062.

now we add the first terms that we obtained before and get:

S9 = 2/25 + 2/5 +  39,062 = 39,062.48

Answer:

(x-1)(x+6)

Step-by-step explanation:

=> [tex]x^2+5x-6[/tex]

Using mid-term break formula to find it's factors

=> [tex]x^2+6x-x-6[/tex]

=> x(x+6)-1(x+6)

Taking x+6 common

=> (x-1)(x+6)

Answer:

there is no inequality..

Step-by-step explanation:

Answer:

???

Step-by-step explanation:

Answer:50.18

Step-by-step explanation:

8x+17+9x+11=102

17x+28=102

-28. -28

17x=74

<CAD=9x+11=50.18

x=74/17

Answer:

I saw one person that way

Step-by-step explanation:

she had red hair and green eyes with pale skin