What value of x is I the solution set of 3(x-4)>5x+2

Answer:

a)The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

b) The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Step-by-step explanation:

Step(i):-

Sample size 'n' =75

Mean of the sample x⁻ = 17.8

standard deviation of the sample (S) = 5.9

Mean of the Population = 15

Null hypothesis:H₀:μ = 15 years

Alternative Hypothesis :H₁:μ≠15 years

Step(ii):-

Test statistic

                         [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }[/tex]

                        [tex]t = \frac{x^{-} -mean}{\frac{S}{\sqrt{n} } }=\frac{17.8-15}{\frac{5.9}{\sqrt{75} } }[/tex]

                    t = 4.111

Degrees of freedom

ν = n-1 = 75-1=74

t₀.₀₂₅ = 1.9925

The calculated value t = 4.111 > 1.9925 at 5 % level of significance

Null hypothesis is rejected

The claim that the average time on death row is not 15 years

P-value:-

The p-value is 0.000101<0.05

we reject Null hypothesis

The claim that the average time on death row is not 15 years

Answer:

Length of Shortest Side = 12 inches

Step-by-step explanation:

Length of Shortest Side = L = 3x

Length of Longest Side = W = 5x-4

Condition:

2L+2W = Perimeter

2(3x)+2(5x-4) = 56

6x+10x-8 = 56

16x-8 = 56

Adding 8 to both sides

16x = 56+8

16x = 64

Dividing both sides by 14

=> x = 4

Now,

Length of the Shortest Side = L = 3(4) = 12 inches

Length of the Longest Side = W = 5(4)-4 = 16 inches

Answer:

12 inches

Step-by-step explanation:

The length is the longest side.

The width is the shortest side.

Length : [tex]l=5x-4[/tex]

Width : [tex]w=3x[/tex]

Apply formula for the perimeter of a rectangle.

[tex]P=2l+2w[/tex]

[tex]P=perimeter\\l=length\\w=width[/tex]

Plug in the values.

[tex]56=2(5x-4)+2(3x)[/tex]

[tex]56=10x-8+6x[/tex]

[tex]56=16x-8[/tex]

[tex]64=16x[/tex]

[tex]4=x[/tex]

The shortest side is the width.

[tex]w=3x[/tex]

Plug in the value for x.

[tex]w=3(4)[/tex]

[tex]w=12[/tex]

Hi there! :)

Answer:

Given the information, we can write an equation in slope-intercept form

(y = mx + b) to graph the line:

Plug in the slope for 'm', the y-coordinate of the point given for 'y', and the

x-coordinate given for 'x':

-4 = -2/3(-7) + b

-4 = 14/3 + b

Solve for b:

-12/3 = 14/3 + b

-12/3 - 14/3 = b

-26/3 = b

Therefore, the equation of the line is y = -2/3x - 26/3 (Graphed below)

Some points on the line include:

(-7, -4)

(-4, -6)

(0, -26/3)

(2, -10)

(5, -12)

Answer:

[tex]\boxed{9}[/tex]

Step-by-step explanation:

The two angles are complementary to each other.

That means they add up to 90 degrees.

[tex]5x+15+30=90[/tex]

[tex]5x+45=90[/tex]

[tex]5x=45[/tex]

[tex]x=9[/tex]

Answer:

x = 9

Step-by-step explanation:

So you know that the total is 90 degrees.

What you need to do is create an equation.

5x + 15 + 30 = 90

Then, solve the equation like this.

5x + 15 + 30 = 90

5x + 45 = 90

5x = 90 - 45

5x = 45

x = 45 ÷ 5

x = 9

Hope this helps! :)

Answer:

x should equal 1

Step-by-step explanation:

(1*129)-3=126

129-3=126

126=126

Answer:

x=1

Step-by-step explanation:

We can start by adding 3 to both sides to get rid of the -3

That leaves us with 129x=129

It ends up working out really evenly because by dividing both sides by 129, we are left with x=1

Answer:

192

Step-by-step explanation:

There are a total of 15 marbles . When the lavender is left out 14 remain.

Using combinations we find that each of the four color marbles can be chosen in the following way.

2C1*4C1*4C1*6C1= 2*4*4*6=  192

We select  one of the two red marbles , one of the four green marbles, one of the four yellow marbles, one of the 6 orange marbles leaving the lavender out.. We apply combinations and then multiply to get the answer.

Answer:

Inventory turnover ratio is 3.74

explanation:

Inventory turnover is a ratio of the number of times a company's inventory is sold and replaced in a given period.

Inventory turn over ratio is calculated as ; Cost of goods sold ÷ Average stock of goods sold

= $35,500 / $9500

= 3.74

Answer:

RA

Step-by-step explanation:

Answer:  ($143.69, $156.31)

Step-by-step explanation:

Confidence interval to estimate  population mean :

[tex]\overline{x}\ \pm z\dfrac{\sigma}{\sqrt{n}}[/tex]

, where [tex]\sigma[/tex] = population standard deviation

n= sample size

[tex]\overline{x}=[/tex] Sample mean

z= critical value.

As per given,

n= 40

[tex]\sigma[/tex] = $15.50

[tex]\overline{x}=[/tex] $150

Critical value for 99% confidence level = 2.576

Then, 99% confidence interval for the population mean:

[tex]150\pm(2.576)\dfrac{15.50}{\sqrt{40}}\\\\\Rightarrow\ 150\pm6.31 \ \ (approx)\\\\\Rightarrow(150-6.31,150+6.31)=(143.69,156.31)[/tex]

Hence, the required confidence interval : ($143.69, $156.31)

Answer:

z(max) = 650 $

x₁ = 10 units

x₂ = 15 units

Step-by-step explanation:

That is a linear programming problem, we will use a simplex method to solve it

Formulation:

Let´s call  x₁  number of chairs   and x₂ number of tables then :

Item              (in hours)     cutting       assembly      finishing        Profit ($)

Chairs (x₁)                              1                   2                     1                      20

Tables (x₂)                              2                   1                      1                      30

Availability                           40                 42                   25

Objective Function

z  =  20*x₁   +  30x₂   ( to maximize) subject to:

x₁  +  2x₂   ≤  40

2x₁  + x₂    ≤  42

x₁ + x₂     ≤    25

x₁  ,   x₂  >= 0

Using excel or any other software we find:

z(max) = 650

x₁ = 10

x₂ = 15

The chairs and tables manufactured by the factory is an illustration of linear programming, where the maximum revenue is 674

Let x represent chairs, and y represent tables

So, the given parameters are:

Cutting:

So, the constraint is:

[tex]\mathbf{x + 2y \le 40}[/tex]

Assembly:

So, the constraint is:

[tex]\mathbf{2x + y \le 42}[/tex]

Finishing:

So, the constraint is:

[tex]\mathbf{x + y \le 25}[/tex]

The unit profit on the items are:

So, the objective function to maximize is:

[tex]\mathbf{Max\ z = 20x + 30y}[/tex]

And the constraints are:

[tex]\mathbf{x + 2y \le 40}[/tex]

[tex]\mathbf{2x + y \le 42}[/tex]

[tex]\mathbf{x + y \le 25}[/tex]

[tex]\mathbf{x,y \ge 0}[/tex]

Using graphical method (see attachment for graph), we have the following feasible points:

[tex]\mathbf{(x,y) = \{(10,15),\ (17,8),\ (14.67, 12.67)\}}[/tex]

Calculate the objective function using the feasible points.

[tex]\mathbf{z = 20 \times 10 + 30 \times 15}[/tex]

[tex]\mathbf{z = 650}[/tex]

[tex]\mathbf{z = 20 \times 17 + 30 \times 8}[/tex]

[tex]\mathbf{z = 580}[/tex]

[tex]\mathbf{z = 20 \times 14.67+ 30 \times 12.67}[/tex]

[tex]\mathbf{z = 673.5}[/tex]

Approximate

[tex]\mathbf{z = 674}[/tex]

Hence, the maximum revenue is 674

Read more about linear programming at:

https://brainly.com/question/14225202

Answer:

[tex]AG=22[/tex]

Step-by-step explanation:

Follow the next steps:

[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F} =\frac{C-D}{F-G} =\frac{A-C}{A-F} =\frac{B-D}{E-G} =\frac{A-D}{A-G}[/tex]

Let:

[tex]\frac{A-B}{A-E} =\frac{B-C}{E-F}\\ \\\frac{4}{A-E} =\frac{5}{10x}\\ \\Solving\hspace{3}for\hspace{3}A-E\\\\A-E=8x[/tex]

Now:

[tex]\frac{C-D}{F-G} =\frac{A-C}{A-F} \\\\\frac{2}{F-G} =\frac{9}{18x} \\\\Solving\hspace{3}for\hspace{3}F-G\\\\F-G=4x[/tex]

Hence:

[tex]A-G=(A-E)+(E-F)+(F-G)=22x[/tex]

Finally:

[tex]\frac{B-D}{E-G} =\frac{A-D}{A-G}\\\\\frac{A-D}{B-D} =\frac{A-G}{E-G}\\[/tex]

[tex]\frac{11}{7} =\frac{22x}{14x} \\\\\frac{11x^{2} }{7} -\frac{11}{7} =0\\\\[/tex]

Hence:

[tex]x=1\\x=-1[/tex]

Since it would be absurd for [tex]x=-1[/tex], the real solution is [tex]x=1[/tex]

Therefore:

[tex]AG=22[/tex]

The answer is 47 pounds

Explanation:

1. First, let's calculate the amount of money that was spent on chicken

$5 per pound of chicken x 25 pounds = $125

2. Calculate the amount of money left to buy beef by subtracting the total spend on chicken to the total of the budget.

$454 (total) - $125 (chicken)  =  $329

3. Calculate how many pounds of beef you can buy with the money left by dividing the money into the price for one pound.

$329 / $7 = 47 pounds

Answer:

Step-by-step explanation:

Let

T = number of trees

A = number of acorns

Given:

A =  18T + 4 ...........................(1)

A = 20T -4 .........................(2)

Equate A from (1) and (2)

20T-4 = 18T+4

simplify and solve for T

20T - 18T = 4+4

2T = 8

T = 4 trees

A = 18T + 4 = 72+4 = 76 acorns, or

A = 20T - 4 = 80 - 4 = 76 acorns.

Answer:

25

Step-by-step explanation:

We can use the Pythagorean theorem to solve

a^2 + b^2 = c^2

We know the two legs and want to find the hypotenuse

15^2+ 20 ^2 = c^2

225 + 400 = c^2

625 = c^2

Taking the square root of each side

sqrt(625) = c^2

25 = c

Answer:

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Step-by-step explanation:

The amount of Carbon-14 after t years is given by the following equation:

[tex]A(t) = A(0)e^{-rt}[/tex]

In which A(0) is the initial amount and r is the decay rate, as a decimal.

Carbon–14 is a radioactive isotope that decays exponentially at a rate of 0.0124 percent a year.

This means that [tex]r = \frac{0.0124}{100} = 0.000124[/tex]

How many years will it take for carbon–14 to decay to 10 percent of its original amount?

This is t for which:

[tex]A(t) = 0.1A(0)[/tex]

So

[tex]A(t) = A(0)e^{-rt}[/tex]

[tex]0.1A(0) = A(0)e^{-0.000124t}[/tex]

[tex]e^{-0.000124t} = 0.1[/tex]

[tex]\ln{e^{-0.000124t}} = \ln{0.1}[/tex]

[tex]-0.000124t = \ln{0.1}[/tex]

[tex]t = -\frac{\ln{0.1}}{0.000124}[/tex]

[tex]t = 18569.2[/tex]

It will take 18,569.2 years for carbon–14 to decay to 10 percent of its original amount

Answer:

33333 x 166667 = 5555511111

I think that is the answer you wanted

Step-by-step explanation:

      166667

     x 33333

5555511111

Answer:

Step-by-step explanation:

[tex]2 \frac{3}{7} \times 5\frac{5}{6} \div 11 \frac{1}{3} [/tex]

Convert the mixed number to an improper fraction

[tex] \frac{17}{7} \times \frac{35}{6} \div \frac{34}{3} [/tex]

To divide by a fraction, multiply the reciprocal of that fraction

[tex] \frac{17}{7} \times \frac{35}{6} \times \frac{3}{34} [/tex]

Reduce the number with the G.C.F 7

[tex]17 \times \frac{5}{6} \times \frac{3}{34} [/tex]

Reduce the numbers with the G.C.F 17

[tex] \frac{5}{6} \times \frac{3}{2} [/tex]

Reduce the numbers with the G.C.F 3

[tex] \frac{5}{2} \times \frac{1}{2} [/tex]

Multiply the fraction

[tex] \frac{5}{4} [/tex]

In mixed fraction:

[tex]1 \frac{1}{4} [/tex]

Hope this helps..

Good luck on your assignment...

Answer:

[tex]\large \boxed{\text{Eight days}}[/tex]

Step-by-step explanation:

1. Calculate the hours

[tex]\text{Hours} = \text{1800 flags} \times \dfrac{\text{1 h}}{\text{45 flags}} = \textbf{40 h}[/tex]

2. Calculate the days

[tex]\text{Days} = \text{40 h} \times \dfrac{\text{1 da}}{\text{5 h}} = \text{8 da}\\\\\text{It will take $\large \boxed{\textbf{eight days}}$ to make 4500 flags.}[/tex]

Answer:

angle JKL =  120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are 90 degrees.

Consider quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL + angle KLM + angle LMJ + angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

angle JKL = 360 - 90 - 60 -90 = 120 degrees

Answer:

120 degrees

Step-by-step explanation:

Since arc JL is 60 degrees, the central angle is also 60 degrees.

Point K is the intersection of tanges at J and L, therefore KJM and KLM are complementary or equal 90 degrees.

look at quadrilateral JKLM whose sum of internal angles = 360.

Therefore

angle JKL plus angle KLM plus angle LMJ plus angle MJK = 360 degrees

angle JKL + 90 + 60 + 90 = 360

Answer:

1 + 1 = 2

Step-by-step explanation:

^

Answer:

no , it's happening to everyone , even I can't see it .

Answer:

A=82°

a= 67.4

c = 60.1

Step-by-step explanation:

For A

A+B+C =180°

A= 180-(B+C)

A= 180-(36+62)

A= 189-(98)

A= 82°

For a

a/sinA= b/sinB

a/sin82= 40/sin36

a= (40*sin82)/sin36

a=( 40*0.9903)/0.5878

a=67.39

Approximately = 67.4

For c

c/sinC= b/sinB

c= (sinC*b)/sinB

c= (sin62*40)/sin36

c =(0.8829*40)/0.5878

c = 60.08

Approximately = 60.1

Answer:

B. 5

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

You know that the empty barrel is 1/4 of the full barrel. Find 1/4 of 20 to get 0.25 x 20 = 5

Answer:

C. 0.0009

Step-by-step explanation:

0.09/100

= 0.0009

Answer:A

Step-by-step explanation:0.09=0.9

Answer:

x = 8.9 units

Step-by-step explanation:

We will use the theorem of intersecting tangent and secant segments.

"If secant and tangent are drawn to a circle from an external point, the product of lengths of the secant and its external segment will equal the square of the length of tangent."

8(8 + 2) = x²

x² = 80

x = √80

x = 8.944

x ≈ 8.9 units

Therefore, length of the tangent = 8.9 units

Answer:

Reject H0

Age and pressure are related

Step-by-step explanation:

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 10% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value. In the given scenario we reject the null hypothesis because job pressure and age are related to each other.

Answer:

14π or 43.96

Step-by-step explanation:

C = 2πr and we know that r = 7 so C = 14π or 43.96.

Answer:

Angle 2= 45

Angle 3= 45

Angle 4= 135

Angle 5= 135

Angle 6= 45

Angle 7= 45

Angle 8= 135

Answer: 6 with milk, 9 without

Step-by-step explanation:

2/5 of the cookies he eats are dunked.  Thus, simply do 2/5, or .4*15 to get that 6 cookies are dunked, and 15-6 to get that 9 cookies are not dunked.

Hope it helps <3

Answer:

63

Step-by-step explanation:

Given that;

The bag has two red marbles,  n(red) =2

three green ones marbles,  n(green) = 3

one lavender one marbles,  n(lavender) = 1

two yellows marbles,            n(yellow ) = 2

two orange marbles.              n(orange) = 2

number of non green marbles = 2+1+2+2 = 7

The objective is to find out how many sets of four marbles include exactly two green marbles

Since sets of four marbles contain exactly two green marbles, then N(select 2 from 3 marbles and 2 from 7 marbles)

= [tex]^3C_2 \times ^{7}C _2[/tex]

= [tex]\dfrac{3!}{2!(3-2)!} \times \dfrac{7!}{2!(7-2)!}[/tex]

= [tex]\dfrac{3*2!}{2!} \times \dfrac{7*6*5!}{2!(5)!}[/tex]

=  [tex]3 \times 7\times 3[/tex]

= 63