Find the area of a circle with a diameter of 8yards. Use 3.14. The area of the circle is approximate

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:

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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:    x1=1   x2=-2  and x3=2

Step-by-step explanation:

1st   x1=1 is 1 of the roots , so

F(1)=1-1-4+4=0 - true

So lets divide x^3-x^2-4x+4 by (x-x1), i.e  (x^3-x^2-4x+4) /(x-1)=(x^2-4)

x^2-4 can be factorized as (x-2)*(x+2)

So x^3-x^2-4x+4=(x-1)*(x^2-4)=(x-1)(x-2)*(x+2)

So there are 3 dofferent roots:

x1=1   x2=-2  and x3=2

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:

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:

For this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:

[tex] z_{\alpha}= 1.64[/tex]

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:  

[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]  

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

Step-by-step explanation:

We have the following dataset given:

[tex] X= 43[/tex] represent the households consisted of one person

[tex]n= 125[/tex] represent the sample size

[tex] \hat p= \frac{43}{125}= 0.344[/tex] estimated proportion of  households consisted of one person

We want to test the following hypothesis:

Null hypothesis: [tex]p \leq 0.27[/tex]

Alternative hypothesis: [tex]p>0.27[/tex]

And for this case we can find the critical value with the significance level [tex]\alpha=0.05[/tex] and if we find in the right tail of the z distribution we got:

[tex] z_{\alpha}= 1.64[/tex]

The statistic is given by:

[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)  

Replacing we got:  

[tex]z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86[/tex]  

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

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:

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

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:

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:

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:

Lateral Surface Area = 15.072 [tex]mm^2[/tex]

Step-by-step explanation:

Given that:

Base of Cylinder has radius, r = 1.2 mm

Height, h = 2 mm

To find:

Lateral Surface area of cylinder = ?

Solution:

We know that total surface area of a cylinder is given by:

[tex]TSA = 2\pi r^2+2\pi rh[/tex]

Here [tex]2\pi r^2[/tex] is the area of two circular bases of the cylinder and

[tex]2\pi rh[/tex] is the lateral surface area.

Please refer to the attached image for a better understanding of the Lateral and Total Surface Area.

So, LSA = [tex]2\pi rh[/tex]

[tex]\Rightarrow LSA = 2 \times 3.14 \times 1.2 \times 2\\\Rightarrow LSA = 6.28 \times 2.4\\\Rightarrow LSA = 15.072\ mm^2[/tex]

So, the answer is:

Lateral Surface Area of given cylinder = 15.072 [tex]mm^2[/tex]

Answer:

LSA  =   24.1

Step-by-step explanation:

I just did this, I dont know how to upload my work, but It marked it as right and gave me the green check mark. The answer is 24.1

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:

the answer is C. y=[x-4]-2

Answer:

Step-by-step explanation:

Y=(x+4)-2

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:

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:

  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:

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:

that's cool . . .

\is ok everyone makes mistakes

Answer:

6

Step-by-step explanation:

We want to find the units digit of [tex]2^{4000}[/tex]. Let's first look for a pattern:

[tex]2^{1}=2[/tex]

[tex]2^{2}=4[/tex]

[tex]2^{3}=8[/tex]

[tex]2^{4}=16[/tex]

[tex]2^{5}=32[/tex]

[tex]2^{6}=64[/tex]

[tex]2^{7}=128[/tex]

[tex]2^{8}=256[/tex]

...and so on

Notice the units digits: 2, 4, 8, 6, 2, 4, 8, 6, ... It repeats every four!

This means that for every exponent of 2 that is a multiple of 4 (like 4000 in the problem), the units digit will always be the fourth number in the repeating pattern: 6.

The answer is thus 6.

~ an aesthetics lover

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:

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:

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:

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:

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:

Approximately standard deviation= 108

Step-by-step explanation:

Let's calculate the mean of the data first.

Mean =( 330+ 274+ 492 +371 +160+ 283+ 164)/7

Mean= 2074/7

Mean= 296.3

Calculating the variance.

Variance = ((330-296.3)²+( 274-296.3)²+ (492-296.3)²+( 371-296.3)²+ (160-296.3)² (283-296.3)²+(164-296.3)²)/7

Variance= (1135.69+497.29+38298.49+5580.09+18577.69+176.89+17503.29)/7

Variance= 81769.43/7

Variance= 11681.347

Standard deviation= √variance

Standard deviation= √11681.347

Standard deviation= 108.080

Approximately 108

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]

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:

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]

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▹ 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!

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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.