Solve the system by graphing (Simplify your answer completely.)
Will someone please help me with this and give an explanation on how you got it? I don’t understand.

{x+y=8
{x-y=4

Answer:

94 years

Step-by-step explanation:

We can approach the solution using the compound interest equation

[tex]A= P(1+r)^t[/tex]

Given data

P= $40,000

A=  $120,000

r=  1.25%= 1.25/100= 0.0125

substituting and solving for t we have

[tex]120000= 40000(1+0.0125)^t \\\120000= 40000(1.0125)^t[/tex]

dividing both sides by 40,000 we have

[tex](1.0125)^t=\frac{120000}{40000} \\\\(1.0125)^t=3\\\ t Log(1.0125)= log(3)\\\ t*0.005= 0.47[/tex]

dividing both sides by 0.005 we have

[tex]t= 0.47/0.005\\t= 94[/tex]

Answer:

x=4200, y=2700

Step-by-step explanation:

let x be first account

y the second

x+y=6900

0.03x+0.08y=342

solve by addition/elimination)

multiply first equation by 0.03

0.03x+0.03y=207  subtract from second

0.03x+0.03y-0.03x-0.08y=207-342

0.05y=135

y=2700, x=4200

Complete Question:

Find the directional derivative of g(x,y) = [tex]x^2y^5[/tex]at the point (1, 3) in the direction toward the point (3, 1)

Answer:

Directional derivative at point (1,3),  [tex]D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Step-by-step explanation:

Get [tex]g'_x[/tex] and [tex]g'_y[/tex] at the point (1, 3)

g(x,y) = [tex]x^2y^5[/tex]

[tex]g'_x = 2xy^5\\g'_x|(1,3)= 2*1*3^5\\g'_x|(1,3) = 486[/tex]

[tex]g'_y = 5x^2y^4\\g'_y|(1,3)= 5*1^2* 3^4\\g'_y|(1,3)= 405[/tex]

Let P =  (1, 3) and Q = (3, 1)

Find the unit vector of PQ,

[tex]u = \frac{\bar{PQ}}{|\bar{PQ}|} \\\bar{PQ} = (3-1, 1-3) = (2, -2)\\{|\bar{PQ}| = \sqrt{2^2 + (-2)^2}\\[/tex]

[tex]|\bar{PQ}| = \sqrt{8}[/tex]

The unit vector is therefore:

[tex]u = \frac{(2, -2)}{\sqrt{8} } \\u_1 = \frac{2}{\sqrt{8} } \\u_2 = \frac{-2}{\sqrt{8} }[/tex]

The directional derivative of g is given by the equation:

[tex]D_ug(1,3) = g'_x(1,3)u_1 + g'_y(1,3)u_2\\D_ug(1,3) = (486*\frac{2}{\sqrt{8} } ) + (405*\frac{-2}{\sqrt{8} } )\\D_ug(1,3) = (\frac{972}{\sqrt{8} } ) + (\frac{-810}{\sqrt{8} } )\\D_ug(1,3) = \frac{162}{\sqrt{8} }[/tex]

Answer:

a. $21.50

b. $980

c. $25 and $18

Step-by-step explanation:

a. The price that generates the maximum profit is

In this question we use the vertex formula i.e shown below:

[tex](-\frac{b}{2a}, f(-\frac{b}{2a} ))\\\\[/tex]

where a = -80

b = 3440

c = 36000

hence,

P-coordinate is

[tex](-\frac{b}{2a}, (-\frac{3440}{2\times -80} ))\\\\[/tex]

[tex]= \frac{3440}{160}[/tex]

= $21.5

b. Now The maximum profit could be determined by the following equation

[tex]f(p) = 80p^2 + 3440p - 36000\\\\f($21.5) = -80(21.5)^2 + 3440(21.5) - 36000\\\\[/tex]

= $980

c. The price that would enable the company to break even that is

f(p) = 0

[tex]f(p) = -80p^2 + 3440p - 36000\\\\-80p^2 + 3440p - 36000 = 0\\\\p^2 -43p + 450 = 0\\\\p^2 - 25p - 18p + 450p = 0\\\\p(p - 25) - 18(p-25) = 0\\\\(p - 25) (p - 18) = 0[/tex]

By applying the factoring by -50 and then divided it by -80 and after that we split middle value and at last factors could come

(p - 25) = 0 or (p - 18) = 0

so we can write in this form as well which is

p = 25 or p = 18

Therefore the correct answer is $25 and $18

Answer:

1. x/5

2. cubed root of 2x

3.x-10

4.(2x/3)-17

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. Lets find the inverse function for function f(x)=2*x/3-17

To do that first express x through f(x):

2*x/3= f(x)+17

2*x=(f(x)+17)*3

x=(f(x)+17)*3/2   done !!!                        (1)

Next : to get the inverse function from (1) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=(x+17)*3/2 or f'(x)=3*(x+17)/2

This is function is No4 in our list. So f(x)=2*x/3-17 should be moved to the box No4  ( on the bottom) of the list.

2.  Lets find the inverse function for function f(x)=x-10

To do that first express x through f(x):

x= f(x)+10

x=f(x)+10   done !!!                        (2)

Next : to get the inverse function from (2) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=x+10

This is function is No3 in our list. So f(x)=x-10 should be moved to the box No3  ( from the top) of the list.

3.Lets find the inverse function for function f(x)=sqrt 3 (2x)

To do that first express x through f(x):

2*x= f(x)^3

x=f(x)^3/2   done !!!                        (3)

Next : to get the inverse function from (3) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=x^3/2

This is function No2 in our list. So f(x)=sqrt 3 (2x) should be moved to the box No2  ( from the top) of the list.

4.Lets find the inverse function for function f(x)=x/5

To do that first express x through f(x):

x=f(x)*5   done !!!                        (4)

Next : to get the inverse function from (4) substitute x by f'(x)   and f(x) by x.

So the required function is f'(x)=x*5 or f'(x)=5*x

This is function No1 in our list. So f(x)=x/5 should be moved to the box No1  ( on the top) of the list.

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

First let's find how much Susan earns per hour.

She earns $0.004 per word, and she does 90 words per minute, so she will earn per minute:

0.004 * 90 = $0.36

Then, per hour, she will earn:

0.36 * 60 = $21.6

Now, to find how many hours she needs to work to earn $1000, we just need to divide this value by the amount she earns per hour:

1000 / 21.6 = 46.3 hours.

She works 4 hours a day and 3 days a week, so she works 4*3 = 12 hours a week.

If a month has 4 weeks, she will work 12*4 = 48 hours a month, so she will earn:

48 * 21.6 = $1036.8

Answer:

46.3 hours of work to break even.

$1036.8 per month (4 weeks)

Step-by-step explanation:

There are two ways to confirm this is the answer. The first is to note that (3,-2) is on the boundary, so it is part of the solution set. This only works if the boundary line is a solid line (as opposed to a dashed or dotted line).

The second way is to plug (x,y) = (3,-2) into the given inequality to find that

[tex]y \le -x+1\\\\-2 \le -3+1\\\\-2 \le -2[/tex]

which is a true statement. So this confirms that (3,-2) is in the solution set of the inequality.

Answer:

27m

Step-by-step explanation:

It's the Pythagorean Theorem.

20^2+18^2=c^2

400+324=c^2

724=c^2

take the square root of both sides

26.9m=c

to the nearest meter = 27

Answer:

  B

Step-by-step explanation:

You only need to look at the comparison symbol (≤) to determine the correct graph. It tells you the shading is below the boundary line, and the boundary line is included in the solution region (a solid line).

The shading is below the line because y-values are less than (or equal to) values on the line.

Choice B matches the attached graph.

Answer:

it is graph b

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. Given that μ1 and μ2 are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems, the hypothesis are

For null,

H0: μ1 − μ2 = - 10

For alternative,

Ha: μ1 − μ2 < - 10

This is a left tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 115.6

x2 = 129.3

s1 = 5.04

s2 = 5.32

n1 = 8

n2 = 8

t = (115.6 - 129.3)/√(5.04²/8 + 5.32²/8)

t = - 2.041

Test statistic = - 2.04

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [5.04²/8 + 5.32²/8]²/[(1/8 - 1)(5.04²/8)² + (1/8 - 1)(5.32²/8)²] = 45.064369/3.22827484

df = 14

We would determine the probability value from the t test calculator. It becomes

p value = 0.030

Since alpha, 0.01 < the p value, 0.03, then we would fail to reject the null hypothesis.

Answer:

2^52

Step-by-step explanation:

(8^-5/2^-2)^-4 = (2^-15/2^-2)^-4= (2^-13)^-4= 2^((-13*(-4))= 2^52

Answer:

that's cool . . .

\is ok everyone makes mistakes

The Confidence Interval is 0.403 < p < 0.497

The mean of your estimate plus and minus the range of that estimate constitutes a confidence interval. Within a specific level of confidence, this is the range of values you anticipate your estimate to fall within if you repeat the test. In statistics, confidence is another word for probability.

Given:

Sample proportion =  190/425

                                = 0.45

Now, [tex]\mu[/tex] = 1.96 x √[0.45 x 0.55/425]

          [tex]\mu[/tex] = 0.047

So, 95% CI:

0.45-0.047 < p < 0.45+0.047

0.403 < p < 0.497

Learn more about Confidence Interval here:

https://brainly.com/question/24131141

#SPJ5

Answer:

Step-by-step explanation:

c= 2(pi)r

Area = (pi)r^2

28.26 = (pi) r^2

r =[tex]\sqrt{9}[/tex] = 3

circumference = 2 (3.14) (3)

                        = 18.8 in

Answer:  approx 18.8 in

Step-by-step explanation:

The area of the circle is

S=π*R²   (1)   and the circumference of the circle is C= 2*π*R      (2)

So using (1)  R²=S/π=28.26/3.14=9

=> R= sqrt(9)

R=3 in

So using (2) calculate C=2*3.14*3=18.84 in or approx 18.8 in

Answer:

a) Fx=-5N  Fy=-5*sqrt(3) N   b) Fx= 5*sqrt(3) N    Fy=-5N

c) Fx=-5*sqrt(2) N    Fy=-5*sqrt(2)   N

Step-by-step explanation:

The arrow's F ( weight) component on axle x  is Fx= F*sinA  and on axle y is

Fy=F*cosA

a) The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(30)= -5 N      Fy= -10*cos(30)= -10*sqrt(3)/2= -5*sqrt (3) N

b) Now the x component  is co directed to axle x , and y component is opposite directed to axle y.

So x component is positive and y components is negative

So Fx = 10*sin(60)= 5*sqrt(3) N       Fy= -10*cos(60)= -10*1/2= -5 N

c)The x component and y component both are opposite directed to axle x and axle y accordingly.  So both components are negative.

So Fx = - 10*sin(45)= -5*sqrt(2)  N    

 Fy= -10*cos(45)= -10*sqrt(2)/2= -5*sqrt (2) N

Answer:

B) [tex]x^2-3x+15[/tex]

Step-by-step explanation:

[tex]7x^2+6x-9x-6x^2+15=\\7x^2-6x^2+6x-9x+15=\\x^2+6x-9x+15=\\x^2-3x+15[/tex]

A) [tex]x^2+15x+15[/tex]

B) [tex]x^2-3x+15[/tex]

C) [tex]13x^2 + 3x + 15[/tex]

D) [tex]x^4-3x + 15[/tex]

━━━━━━━☆☆━━━━━━━

▹ Answer

B. x² - 3x + 15

▹ Step-by-Step Explanation

7x² + 6x - 9x - 6x² + 15

Collect like terms

x² + 6x - 9x + 15

Subtract

x² - 3x + 15

Final Answer

x² - 3x + 15

Hope this helps!

- CloutAnswers ❁

Brainliest is greatly appreciated!

━━━━━━━☆☆━━━━━━━

Answer:

2-x=-3x-12+6

2-x=-3x-6

8=-3x+x

8=-2x

x=-4

hope it's clear

mark me as brainliest

Answer:

Option B is the correct option.

Step by step explanation

2 - x = -3 ( x + 4) +6

Distribute -3 through the paranthesis

2 - x = - 3x - 12 + 6

Calculate

2 - x = - 3x - 6

Move variable to LHS and change its sign

2 - x + 3x = -6

Move constant to R.H.S and change its sign

- x + 3x = -6 - 2

Collect like terms and simplify

2x = -8

Divide both side by 2

2x/2 = -8/2

Calculate

X = -4

Hope this helps....

Good luck on your assignment..

Answer:

[tex]18x^2+85x+18 = 0[/tex]

Step-by-step explanation:

Given Equation is

=> [tex]2x^2+7x-9=0[/tex]

Comparing it with [tex]ax^2+bx+c = 0[/tex], we get

=> a = 2, b = 7 and c = -9

So,

Sum of roots = α+β = [tex]-\frac{b}{a}[/tex]

α+β = -7/2

Product of roots = αβ = c/a

αβ = -9/2

Now, Finding the equation whose roots are:

α/β ,β/α

Sum of Roots = [tex]\frac{\alpha }{\beta } + \frac{\beta }{\alpha }[/tex]

Sum of Roots = [tex]\frac{\alpha^2+\beta^2 }{\alpha \beta }[/tex]

Sum of Roots = [tex]\frac{(\alpha+\beta )^2-2\alpha\beta }{\alpha\beta }[/tex]

Sum of roots = [tex](\frac{-7}{2} )^2-2(\frac{-9}{2} ) / \frac{-9}{2}[/tex]

Sum of roots = [tex]\frac{49}{4} + 9 /\frac{-9}{2}[/tex]

Sum of Roots = [tex]\frac{49+36}{4} / \frac{-9}{2}[/tex]

Sum of roots = [tex]\frac{85}{4} * \frac{2}{-9}[/tex]

Sum of roots = S = [tex]-\frac{85}{18}[/tex]

Product of Roots = [tex]\frac{\alpha }{\beta } \frac{\beta }{\alpha }[/tex]

Product of Roots = P = 1

The Quadratic Equation is:

=> [tex]x^2-Sx+P = 0[/tex]

=> [tex]x^2 - (-\frac{85}{18} )x+1 = 0[/tex]

=> [tex]x^2 + \frac{85}{18}x + 1 = 0[/tex]

=> [tex]18x^2+85x+18 = 0[/tex]

This is the required quadratic equation.

Answer:

α/β= -2/9      β/α=-4.5

Step-by-step explanation:

So we have quadratic equation  2x^2+7x-9=0

Lets fin the roots  using the equation's  discriminant:

D=b^2-4*a*c

a=2 (coef at x^2)   b=7(coef at x)  c=-9

D= 49+4*2*9=121

sqrt(D)=11

So x1= (-b+sqrt(D))/(2*a)

x1=(-7+11)/4=1   so   α=1

x2=(-7-11)/4=-4.5    so  β=-4.5

=>α/β= -2/9       => β/α=-4.5

Answer:

Sum of 2 digit = 48

Sum of 3 digit = 317

Sum of 4 digit = 3009

Total = 3374

Step-by-step explanation:

Given:

9, 8 and 7

Required

Sum of Multiples

The first step is to list out the multiples of each number

9:- 9,18,....,99,108,117,................,999

,1008

,1017....

8:- 8,16........,96,104,...............,992,1000,1008....

7:- 7,14,........,98,105,.............,994,1001,1008.....

Calculating the sum of smallest 2 digit multiple of 9, 8 and 7

The smallest positive 2 digit multiple of:

- 9 is 18

- 8 is 16

- 7 is 14

Sum = 18 + 16 + 14

Sum = 48

Calculating the sum of smallest 3 digit multiple of 9, 8 and 7

The smallest positive 3 digit multiple of:

- 9 is 108

- 8 is 104

- 7 is 105

Sum = 108 + 104 + 105

Sum = 317

Calculating the sum of smallest 4 digit multiple of 9, 8 and 7

The smallest positive 4 digit multiple of:

- 9 is 1008

- 8 is 1000

- 7 is 1001

Sum = 1008 + 1000 + 1001

Sum = 3009

Sum of All = Sum of 2 digit + Sum of 3 digit + Sum of 4 digit

Sum of All = 48 + 317 + 3009

Sum of All = 3374

Answer:

Since both np > 5 and np(1-p)>5, it is  suitable to use the normal distribution as an approximation.

Step-by-step explanation:

When the normal approximation is suitable?

If np > 5 and np(1-p)>5

In this question:

[tex]n = 24, p = 0.6[/tex]

So

[tex]np = 24*0.6 = 14.4[/tex]

And

[tex]np(1-p) = 24*0.6*0.4 = 5.76[/tex]

Since both np > 5 and np(1-p)>5, it is  suitable to use the normal distribution as an approximation.

Answer:

Step-by-step explanation:

Hello!

You need to test at 1% if the average highway gas mileage is the same for three types of vehicles (midsize cars, SUV's and pickup trucks) to compare the average values of the three groups altogether, you have to apply an ANOVA.

                n  |  Mean |  Std. Dev.

Midsize  | 31 |  25.8   |  2.56

SUV’s     | 31 |  22.68 |  3.67

Pickups  | 14 |  21.29  |  2.76

Be the study variables :

X₁: highway gas mileage of a midsize car

X₂: highway gas mileage of an SUV

X₃: highway gas mileage of a pickup truck.

Assuming these variables have a normal distribution and are independent.

The hypotheses are:

H₀: μ₁ = μ₂ = μ₃

H₁: At least one of the population means is different.

α: 0.01

The statistic for this test is:

[tex]F= \frac{MS_{Treatment}}{MS_{Error}}[/tex]~[tex]F_{k-1;n-k}[/tex]

Attached you'll find an ANOVA table with all its components. As you see, to manually calculate the statistic you have to determine the Sum of Squares and the degrees of freedom for the treatments and the errors, next you calculate the means square for both and finally the test statistic.

For the treatments:

The degrees of freedom between treatments are k-1 (k represents the amount of treatments): [tex]Df_{Tr}= k - 1= 3 - 1 = 2[/tex]

The sum of squares is:

SSTr: ∑ni(Ÿi - Ÿ..)²

Ÿi= sample mean of sample i ∀ i= 1,2,3

Ÿ..= grand mean, is the mean that results of all the groups together.

So the Sum of squares pf treatments SStr is the sum of the square of difference between the sample mean of each group and the grand mean.

To calculate the grand mean you can sum the means of each group and dive it by the number of groups:

Ÿ..= (Ÿ₁ + Ÿ₂ + Ÿ₃)/ 3 = (25.8+22.68+21.29)/3 = 23.256≅ 23.26

[tex]SS_{Tr}[/tex]= (Ÿ₁ - Ÿ..)² + (Ÿ₂ - Ÿ..)² + (Ÿ₃ - Ÿ..)²= (25.8-23.26)² + (22.68-23.26)² + (21.29-23.26)²= 10.6689

[tex]MS_{Tr}= \frac{SS_{Tr}}{Df_{Tr}}= \frac{10.6689}{2}= 5.33[/tex]

For the errors:

The degrees of freedom for the errors are: [tex]Df_{Errors}= N-k= (31+31+14)-3= 76-3= 73[/tex]

The Mean square are equal to the estimation of the variance of errors, you can calculate them using the following formula:

[tex]MS_{Errors}= S^2_e= \frac{(n_1-1)S^2_1+(n_2-1)S^2_2+(n_3-1)S^2_3}{n_1+n_2+n_3-k}= \frac{(30*2.56^2)+(30*3.67^2)+(13*2.76^2)}{31+31+14-3} = \frac{695.3118}{73}= 9.52[/tex]

Now you can calculate the test statistic

[tex]F_{H_0}= \frac{MS_{Tr}}{MS_{Error}} = \frac{5.33}{9.52}= 0.559= 0.56[/tex]

The rejection region for this test is always one-tailed to the right, meaning that you'll reject the null hypothesis to big values of the statistic:

[tex]F_{k-1;N-k;1-\alpha }= F_{2; 73; 0.99}= 4.07[/tex]

If [tex]F_{H_0}[/tex] ≥ 4.07, reject the null hypothesis.

If [tex]F_{H_0}[/tex] < 4.07, do not reject the null hypothesis.

Since the calculated value is less than the critical value, the decision is to not reject the null hypothesis.

Then at a 1% significance level you can conclude that the average highway mileage is the same for the three types of vehicles (mid size, SUV and pickup trucks)

I hope this helps!

Answer:

1. There is no difference in amount of items that people are able to remember before and after being taught the memory device.

2. There is no difference between performance of men and women on memory test.

Step-by-step explanation:

Test 1:

The hypothesis for the two-way ANOVA test can be defined as follows:

H₀: There is no difference in amount of items that people are able to remember before and after being taught the memory device.

Hₐ: There is difference in amount of items that people are able to remember before and after being taught the memory device.

Use MS-Excel to perform the two-way ANOVA text.

Go to > Data > Data Analysis > Anova: Two-way with replication  

A dialog box will open.

Input Range: select all data

Rows per sample= 10

Alpha =0.05

Click OK

The ANOVA output is attaches below.

Consider the Columns data:

The p-value is 0.199.

p-value > 0.05

The null hypothesis will not be rejected.

Conclusion:

There is no difference in amount of items that people are able to remember before and after being taught the memory device.

Test 2:

The hypothesis  to determine whether or not men and women perform differently on the memory test is as follows:

H₀: There is no difference between performance of men and women on memory test.

Hₐ: There is a difference between performance of men and women on memory test.

Consider the Sample data:

The p-value is 0.075.

p-value > 0.05

The null hypothesis will not be rejected.

Conclusion:

There is no difference between performance of men and women on memory test.

Answer:

D. [tex]3^3 - 4^2[/tex]

Step-by-step explanation:

Well if Alia gets 4 squared less than Kelly who get 3 cubed it’s natural the expression is 3^3 - 4 ^2

Answer:

  6/(49π) ≈ 0.03898 m/min

Step-by-step explanation:

  V = πr²h . . . . formula for the volume of a cylinder

  dV/dt = πr²·dh/dt . . . . differentiate to find rate of change

Solving for dh/dt and filling in the numbers, we have ...

  dh/dt = (dV/dt)/(πr²) = (6 m³/min)/(π(7 m)²) = 6/(49π) m/min

  dh/dt ≈ 0.03898 m/min

Answer:

[tex]\boxed{11.78}[/tex]

Step-by-step explanation:

From observations, we can note that BC is the hypotenuse.

As the length of hypotenuse is not given, we can only use tangent as our trig function.

tan(θ) = opposite/adjacent

tan(67) = x/5

5 tan(67) = x

11.77926182 = x

x ≈ 11.78

Answer: Rent = 29%,  Food = 21%,    Fun = 17%

Step-by-step explanation:

Rent =     $433

Food =    $320

Fun =       $260

Other =   $487  

TOTAL = $1500

[tex]\dfrac{Rent}{Total}=\dfrac{433}{1500}\quad =0.2886\quad =\large\boxed{29\%}\\\\\\\dfrac{Food}{Total}=\dfrac{320}{1500}\quad =0.2133\quad =\large\boxed{21\%}\\\\\\\dfrac{Fun}{Total}=\dfrac{260}{1500}\quad =0.1733\quad =\large\boxed{17\%}[/tex]

Answer:

Therefore, the coordinates of point Q is (2,3)

Step-by-step explanation:

Let the coordinates of Q be(a,b)

Let R be the midpoint of PQ

Coordinates of R [tex]=(\frac{4+a}{2}, \frac{3+b}{2})[/tex]

R lies on the line x + y - 6= 0, therefore:

[tex]\implies \dfrac{4+a}{2}+ \dfrac{3+b}{2}-6=0\\\implies 4+a+3+b-12=0\\\implies a+b-5=0\\\implies a+b=5[/tex]

Slope of AR X Slope of PQ = -1

[tex]-1 \times \dfrac{b-3}{a-4}=-1\\b-3=a-4\\a-b=-3+4\\a-b=-1[/tex]

Solving simultaneously

a+b=5

a-b=-1

2a=4

a=2

b=3

Therefore, the coordinates of point Q is (2,3)

Answer:

np = 81  , nQ = 99

Step-by-step explanation:

Given:

X - B ( n = 180 , P = 0.45 )

Find:

Sampling distribution has an approximate normal distribution

Computation:

nP & nQ ≥ 5

np = n × p

np = 180 × 0.45

np = 81

nQ = n × (1-p)

nQ = 180 × ( 1 - 0.45 )

nQ = 99

[tex]Therefore, sampling\ distribution\ has\ an\ approximately\ normal\ distribution.[/tex]

Answer:

Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.

y= -3x+b

Now, we can substitute in the point given to find the intercept.

2= -3(4)+b

2= -12+b

b=14

Finally, put in everything we've found to finish the equation.

y= -3x+14

Answer:

y = -3x + 14

Step-by-step explanation:

First find the reciprocal slope since it is perpendicular.  Slope of the other line is 1/3 so the slope for our new equation is -3.  

Plug information into point-slope equation

(y - y1) = m (x-x1)

y - 2 = -3 (x-4)

Simplify if needed

y - 2 = -3x + 12

y = -3x + 14

Answer:

Option 4

Step-by-step explanation:

=> [tex]-3x^2+2x-4 + 4x^2+5x+9[/tex]

Combining like terms

=> [tex]-3x^2+4x^2+2x+5x-4+9[/tex]

=> [tex]x^2+7x+5[/tex]