MATHEMATICS COLLEGE

Solve this equation
3x+6=-2-2x

Answers

Answer 1

Answer:

Answer:

x = -8/5

x = -1.6

Step-by-step explanation:

3x+6=-2-2x

Add 2x to each side

3x+2x+6=-2-2x+2x

5x+6 = -2x

Subtract 6 from each side

5x+6-6 = -2-6

5x= -8

Divide each side by 5

5x/5 = -8/5

x = -8/5

x = -1.6

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A committee at the College Board has been asked to study the SAT math scores for students in Pennsylvania and Ohio. A sample of 45 students from Pennsylvania had an average score of 580, whereas a sample of 38 students had an average score of 530. The sample standard deviations for Pennsylvania and Ohio are 105 and 114 respectively. Does the study suggest that the SAT math score for students in Pennsylvania and Ohio differ

Answers

Answer:

Step-by-step explanation:

From the given information:

The null hypothesis and the alternative hypothesis can be computed as:

$H_0 :\mu_1 -\mu_2 = 0$ (i.e. there is no difference between the SAT score for students in both locations)

$H_1 :\mu_1 -\mu_2 \geq0$ (i.e. there is a difference between the SAT score for students in both locations)

The test statistics using the students' t-test for the two-samples; we have:

$t = \frac{\overline x_1 -\overline x_2}{\sqrt{(s_1^2)/(n_1)+(s_2^2)/(n_2) } }$

$t = \frac{580 -530}{\sqrt{(105^2)/(45)+(114^2)/(38) } }$

$t = \frac{50}{\sqrt{(11025)/(45)+(12996)/(38) } }$

$t = (50)/(√(245+342 ) )$

$t = (50)/(√(587) )$

$t = (50)/(24.228)$

t = 2.06

degree of freedom = ( $n_1 + n_2$ ) -2

degree of freedom = (45+38) -2

degree of freedom = 81

Using the level of significance of 0.05

Since the test is two-tailed at the degree of freedom 81 and t = 2.06

The p-value = 0.0426

Decision rule: To reject $H_o$ if the p-value is less than the significance level

Conclusion: We reject the $H_o$ , thus, there is no sufficient evidence to conclude that there is a significant difference between the SAT math score for students in Pennsylvania and Ohio.

What is the quotient and remainder of 8 divided 25

Answers

the answer is 3 reminder 1

Find the components of the vertical force Bold Upper FFequals=left angle 0 comma negative 4 right angle0,−4 in the directions parallel to and normal to the plane that makes an angle of StartFraction pi Over 3 EndFraction π 3 with the positive x-axis. Show that the total force is the sum of the two component forces.

Answers

Answer:

$F_p = < - √(3) , -3 >\n\nF_o = < √(3) , -1 >$

Step-by-step explanation:

- A plane is oriented in a Cartesian coordinate system such that it makes an angle of ( π / 3 ) with the positive x - axis.

- A force ( F ) is directed along the y-axis as a vector < 0 , - 4 >

- We are to determine the the components of force ( F ) parallel and normal to the defined plane.

- We will denote two unit vectors: ( $u_p$ ) parallel to plane and ( $u_o$ ) orthogonal to the defined plane. We will define the two unit vectors in ( x - y ) plane as follows:

- The unit vector ( $u_p$ ) parallel to the defined plane makes an angle of ( 30° ) with the positive y-axis and an angle of ( π / 3 = 60° ) with the x-axis. We will find the projection of the vector onto the x and y axes as follows:

$u_o$ = < cos ( 60° ) , cos ( 30° ) >

$u_o = < (1)/(2) , (√(3) )/(2) >$

- Similarly, the unit vector ( $u_o$ ) orthogonal to plane makes an angle of ( π / 3 ) with the positive x - axis and angle of ( π / 6 ) with the y-axis in negative direction. We will find the projection of the vector onto the x and y axes as follows:

$u_p = < cos ( (\pi )/(6) ) , - cos ( (\pi )/(3) ) >\n\nu_p = < (√(3) )/(2) , -(1)/(2) >\n$

- To find the projection of force ( F ) along and normal to the plane we will apply the dot product formulation:

- The Force vector parallel to the plane ( $F_p$ ) would be:

$F_p = u_p(F . u_p)\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ < 0 , - 4 > . < (1)/(2) , (√(3) )/(2) > ]\n\nF_p = < (1)/(2) , (√(3) )/(2) > [ -2√(3) ]\n\nF_p = < -√(3) , -3 >\n$

- Similarly, to find the projection of force ( $F_o$ ) normal to the plane we again employ the dot product formulation with normal unit vector ( $u_o$ ) as follows:

$F_o = u_o ( F . u_o )\n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ < 0 , - 4 > . < (√(3) )/(2) , - (1)/(2) > ] \n\nF_o = < (√(3) )/(2) , - (1)/(2) > [ 2 ] \n\nF_o = < √(3) , - 1 >$

- To prove that the projected forces ( $F_o$ ) and ( $F_p$ ) are correct we will apply the vector summation of the two orthogonal vector which must equal to the original vector < 0 , - 4 >

$F = F_o + F_p\n\n< 0 , - 4 > = < √(3), -1 > + < -√(3), -3 > \n\n< 0 , - 4 > = < √(3) - √(3) , -1 - 3 > \n\n< 0 , - 4 > = < 0 , - 4 >$ .. proven

The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.A 2-column table with 5 rows. Column 1 is labeled x with entries 12 a m, 3 a m, 6 a m, 9 a m, 12 p m. Column 2 is labeled y with entries 6, 10, 6, 2, 6.

Which equation models the data in the table?

y = 6 sine (StartFraction pi Over 6 EndFraction x) + 2
y = 6 sine (StartFraction pi Over 6 EndFraction x) + 4
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 6
y = 4 sine (StartFraction pi Over 6 EndFraction x) + 10

Answers

Modeling the data in the table is done via the equation y = 4 sine (pi/6x) + 6.

What is a cyclic pattern?

Over a period of years, a cyclical pattern recurs with considerable regularity. Cyclical patterns are distinct from seasonal patterns in that they last across a number of years as opposed to only one year for seasonal trends.

Given, The table shows the height of water in feet at different times. The water rises and falls in a cyclical pattern.

Table:

12 AM 6

3 AM 10

6 AM 6

9 AM 2

12 PM 6

from the general formula of wave

y = A sin(bx + c)

Substituting values in the equation from the graph attached below:

6 = A sin(0*b + c)......(1)

10 = A sin3b + c...(2)

6 = A sin6b + c......(3)

2 = A sin9b +c........(4)

Since -c/b is a phase shift of the graph

Thus

-c/b = 6

c = -6b

from equations 2 and 1

2* 6 = Asin(-3b) = -Asin3b

2 * 6 = Asin(-6b) = -Asin6b

2* 6/6 =sin6b/sin3b

1 = Cos3b

Thus b = π/6

from substitution in equations 3

6 = A sin6b + c

=> 6 = Asin 6* pi/6 + c

=> c = 6

$\begin{table}[]\begin{tabular}{ll}12 AM & 6 \n3 AM & 10 \n6 AM & 6 \n9 AM & 2 \n12 PM & 6 \end{tabular}\end{table}$ from substitution in equations 2

10 = A sin3b + c

A = 4

therefore, The equation that models data in the table is y = 4 sine (pi/6x) + 6.

Learn more about cyclic patterns here:

brainly.com/question/15223077

#SPJ3

Answer:

Step-by-step explanation:

The sale price of an item is $330 after a 25% discount. What was the original price of the item?

Answers

Answer:

$440

Step-by-step explanation:

100%-25%=75%

75%=330

1%=330÷75=4.4

100%=100x4.4=440

Hope this helps! Thanks.

Need answer please !!!!!

Answers

Answer: -9

Step-by-step explanation:

f(x)=-5x-4

f(1)=-5(1)-4

=-5-4

f(1) =-9

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Solve this equation 3x+6=-2-2x

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What is a cyclic pattern?

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Solve this equation
3x+6=-2-2x