The Department of Transportation (DOT) monitors sealed bids for new road construction. For new access roads in a certain state, let low bid (thousands of dollars) and let estimate of fair cost of building the road (thousands of dollars). The joint probability density of X and Y is f(x,y)= e^-y/10/10y 0< y

Answer:

6 bags

Step-by-step explanation:

3/4 = .75

4.5/.75 = 6 =

6 BAGS

Answer:

The car travels 83 1/3 meters in 3 seconds.

Step-by-step explanation:

Speed of car  = 100 KM/ hour

1 km= 1000m

1 hour = 3600 seconds

Lets find speed of car in Meters/second

speed of car in m/sec = 100*1000 m/3600 second

here we have taken 1000 for km and 3600 for hour

speed of car in m/sec = 100*1000 m/3600 second = 500/18 m/second

speed of car in m/sec = 250/9  m per sec

We know that

distance = speed*time

speed = 250/9  m per sec

time =3 second

distance = 250/9 * 3 meters = 250/3 meters = 83 1/3 meters.

Thus, car travels 83 1/3 meters in 3 seconds.

Answer:

1/2

Step-by-step explanation:

The numbers 3 or odd are 1, 3, 5, and 7.

4 numbers out of 8.

4/8 = 1/2

P(3 or odd) = 1/2

Answer:

[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]

[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]

Step-by-step explanation:

For this case we have the following info given:

[tex]n_1 = 41 , \bar X_1 =42700 , s_1 = 2030[/tex]

[tex]n_2 = 41 , \bar X_2 =36375 , s_2 = 1360[/tex]

And for this case we want a 98% confidence interval. The significance would be:

[tex] \alpha= 1-0.98=0.02[/tex]

The degrees of freedom are:

[tex] df = n_1 +n_2 -2= 41+41 -2= 80[/tex]

And the critical value for this case is:

[tex] t_{\alpha/2}= 2.374[/tex]

And the confidence interval would be given by:

[tex](\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1}+\frac{s^2_2}{n_2}}[/tex]

And replacing we got:

[tex] (42700- 36275) -2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}= 5519.071[/tex]

[tex] (42700- 36275) +2.374 \sqrt{\frac{2030^2}{41} +\frac{1360^2}{41}}=7330.929[/tex]

The answer is 41 because all of the them are in the 7 times table .so I deducted 2 from each one of them and 41 was not part

Answer:

b

Step-by-step explanation:

The slope is 3/4 and the y-intercept is y(0,2)

The slope is what we multiply by the variable ( here t) and the y-intercept is the number we add

Answer:

C

Step-by-step explanation:

(f-g)(x)=(3x-5)-(x+3) = 3x-5-x-3 = 2x-8

Answer:

2x -8

Step-by-step explanation:

f (x) = 3x - 5

g(x) = x + 3,

(f - g)(x) = 3x - 5 - ( x+3)

Distribute the minus sign

            = 3x-5 -x-3

Combine like terms

           = 2x -8

Complete question:

Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder auto-mobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. There is no production on weekends, so on Friday the line is diassembled and cleaned. On Monday, the line must be set up to run whichever product will be produced that week. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Letx4 5 the number of 4-cylinder connecting rods produced next week x6 5 the number of 6-cylinder connecting rods produced next week s4 5 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise s6 5 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

a) Using the decision variables x4 and s4, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units

b) Using the decision variables x6 and s6, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units

c) Write a constraint that requires that production be setup for exactly one of the two rods

d) Write the cost function to be minimized

Answer:

a) x₄ ≤ 8000s₄

b) x₆ ≤ 8000s₆

c) s₄ + s₆ = 1

d) MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆

Explanation:

a) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 8000 units, is written as:

x₄ ≤ 8000s₄

b) The constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 to 6000 units is written as:

x₆ ≤ 8000s₆

c) The constraint that requires that production be setup for exactly one of the two rods:

Since we have:

x₄ ≤ 8000s₄ ; x₆ ≤ 8000s₆

The constraint that requires that production be setup for exactly one of the two rods will be:

s₄ + s₆ = 1

d) Write the cost function to be minimized:

Since we are to find the cost function to be minimized, we take the function below:

MIN 15x₄ + 18x₆ + 2000s₄ + 3500s₆

Answer:

15

Step-by-step explanation:

Answer: 15

Step-by-step explanation: (9-6) + 12

                                              (3) + 12

                                              15

Answer:

Step-by-step explanation:

hello,

I assume that you want to develop the expression

[tex](7x-3)(4x^2-3x-6)=7x(4x^2-3x-6)-3(4x^2-3x-6)\\= 28x^3-21x^2-42x-12x^2+9x+18\\\\=28x^3-33x^2-33x+18[/tex]

hope this helps

Answer:

5676039

Step-by-step explanation:

-14² + 5675843

Solve for exponent.

196 + 56758

Add the numbers.

= 5676039

Answer:

All angles in any quadrilateral adds up to 360°

Step-by-step explanation:

We can prove this by using 180(n - 2)

n = 4 for a quadrilateral

180(4 - 2)

180(2)

360°

So, 360 - (125 + 67 + 80) = 88°

Answer:

See below

Step-by-step explanation:

The interior angles of a quadrilateral (having 4 sides) add up to 360 degrees.

=> So, to find x, we'll simply subtract the rest if the angles from 360

So,

=> x = 360-125-67-80

=> x = 88 degrees

Answer: 53.333333, 53 1/3

Step-by-step explanation:

The unit rate in this question means how many calories for one ounce.  Thus, you can simply divide 480 by 9 to get 53.3333333

Answer:

Step-by-step explanation:

Calories in a low calorie dinner = 480 calories

Serving at one time = 9 ounce

then,

Unit rate = Amount of calories in one serving

So,

Amount of calorie in 9 serving = 480

Amount of calorie in 1 serving = 480/9

In simple form : 160/3

= 53.33 calories

Hope this helps...

Good luck on your assignment..

Answer:

B.90°counterclockwise

Answer: B

Step-by-step explanation:

A. If you rotate a figure in the first quadrant 180 degrees clockwise it will end up in the third quadrant so the answer can't be A.

B. If you rotate a figure in the first quadrant 90 degrees counterclockwise it will end up in the second quadrant because you will rotate it backwards and as you could see A prime is in the second quadrant.

C.If you rotate a figure in the first quadrant 180 counterclockwise it will end up in the third quadrant. SO the answer can't be it C.

D.If your rotate a figure in the first quadrant 270 counterclockwise it will end up in the fourth quadrant. So the answer can't be D.

Answer:

The number of people who voted in this election was 1.24 times the number who voted in the last election

Step-by-step explanation:

The multiplier for a increase of a% is 1 + a/100.

The multiplier for a decrease of b% is 1 - b/100.

In this question:

Up by about 24%, so we want the multiplier for a increase of 24%.

So

1 + (24/100) = 1 + 0.24 = 1.24

The number of people who voted in this election was 1.24 times the number who voted in the last election

Answer:

12%.

Step-by-step explanation:

It is given that, after adding up all your expenses for the month you spent $465.36. your total budget for the month is $529.

Total budget = $529

Total expenditure = $465.36

Under budget = $529 - $465.36 = $63.64

We need to find the percentage of under budget.

[tex]\%=\dfrac{\text{Under budget}}{\text{Total budget}}\times 100[/tex]

[tex]\%=\dfrac{63.64}{529}\times 100[/tex]

[tex]\%=0.12030\times 100[/tex]

[tex]\%=12.030\%[/tex]

[tex]\%\approx 12\%[/tex]

Therefore, the required percentage is 12%.

[tex]3x^2-15x= 15\\\\x^2 -5x = 5\\\\x^2-5x-5=0\\\\\Delta = 25+20\\\\\Delta = 45\\\\\\x = \dfrac{5\pm \sqrt{\Delta}}{2}\\\\\\x = \dfrac{5\pm \sqrt{45}}{2}\\\\\\x = \dfrac{5\pm 3\sqrt{5}}{2}\\\\\\[/tex]

This is because we have two pairs of congruent sides (AB = CD and AC = CA) with a pair of congruent angles between them. Those angles are the alternate interior angles BAC and DCA

------------------

Similar to reason 2, but the converse means we go in reverse more or less. The original theorem states that if we have parallel lines, then the alternate interior angles are congruent. This time we know the alternate interior angles are congruent, so we conclude the lines are parallel.

Answer:

see below

Step-by-step explanation:

Reason 4 is SAS  AB = CD, BAC = DCA  and AC = CA so we have Two sides and the included angle

Reason 6 is if two lines are cut by a transversal and the alternate interior angles are congruent, then the lines are parallel.

Answer: x=48°

Step-by-step explanation:

The 3 angles of the triangle add up to 180°. We can set the angles to 180 and solve.

47+85+x=180               [combine like terms]

132+x=180                    [subtract both sides by 132]

x=48

Answer:

x=48

Step-by-step explanation:

Total sum of angles in a triangle =180

47+85+x=180

132+x=180

x=180-132

x=48

Answer:

Step-by-step explanation:

Plug in 2 for x.

f(2) = -3(2)² - 7

f(2) = -3(4) - 7

f(2) = -12 - 7

f(2) = -19

Answer:  A) 0.5

Step-by-step explanation:

The denominator should be in the form 1 + e sin θ

Currently the denominator is: 2 + 1 sin θ

Divide the denominator by 2 to get:  1 + 0.5 sin θ

Thus, e = 0.5

Answer:

Domain stays the same while the range changes

Step-by-step explanation:

While reflecting cross x-axis, the x coordinates remains the same while the y-coordinate changes to its opposite.

=> x- coordinate = Domain

=> y-coordinate = Range

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Domain is the set of values for which the given function is defined.Range is the set of all values which the given function can output.

When reflecting across the x-axis, the x coordinates remain constant, but the y coordinate changes to its inverse.

The Domain represent as x-coordinate and the range as y-coordinate

The domain stays the same, but the range changes. is true about the domain and range of each function. Option C is correct.

Hence, option C is correct.

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Answer: 6p^3+29p^2+22p-21

Answer:

5

Step-by-step explanation:

[tex]\frac{6}{7}=0.857142857142857142857142...[/tex]

Or 0.857142 with "857142" recurring.

The hundredths place is the second decimal place of a number. In this case, it would be 5.

Answer:

B

Step-by-step explanation:

the hotpotuse is always the biggest

the rest is pretty easy to determine

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

A triangle is a polygon that has three sides and three vertices. It is one of the basic figures in geometry. A right-angled triangle is a triangle having one of its angles with a measure of 90°. The slanted side of that triangle is called Hypotenuse and it is the longest side in that triangle.

If one of the angle is of 90°  then the triangle is right angled triangle.

We can see that the Hypotenuse is always the biggest side among all the sides.

Then the perpendicular side BC is the second biggest and then the base of the triangle.

Therefore, the order must be AB > BC > AC.

The orders that the sides of the triangle ABC from longest to shortest length will be AB, BC, and AC.

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Take a look at the attachment below. It proves that the inverse of matrix P does exists, as option c,

Hope that helps!

Answer:  C

Step-by-step explanation:

Given    a    b

             c    d

Multiply the reciprocal of the determinant by    d   -b

                                                                             -c     a

Determinant = ad - bc = 2(-3) - 4(1)

                                    = -6    -    4

                                    =      -10

[tex]-\dfrac{1}{10}\left[\begin{array}{cc}-3&-4\\-1&2\end{array}\right] \\\\\\\\=\left[\begin{array}{cc}\dfrac{-3}{-10}&\dfrac{-4}{-10}\\\\\dfrac{-1}{-10}&\dfrac{2}{-10}\end{array}\right]\\\\\\\\=\left[\begin{array}{cc}\dfrac{3}{10}&\dfrac{2}{5}\\\\\dfrac{1}{10}&-\dfrac{1}{5}\end{array}\right][/tex]  

Answer:

Colin can do this is 272 ways.

Step-by-step explanation:

The first counter goes to Obi and the second to Zeema, so the order is important. This means that we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this question:

Two counters from a set of 17. So

[tex]P_{(17,2)} = \frac{17!}{(17-2)!} = 272[/tex]

Colin can do this is 272 ways.

Answer:

may 5 the is squareroot day and it is when the day and the month has the first two digits in the date are the square root of the last two digits. examples 2nd February,2004 3rd March 2009 and the last time we had one was April 4th 2016. The next square root day is May 5th 2025

Answer:

The answer is "2nπ".

Step-by-step explanation:

Given:

[tex]4 \cos x= -\sin^2x+4.......(1)[/tex]

We know:

[tex]\Rightarrow \sin^2 x+\cos^2 x=1\\\\\Rightarrow \sin^2 x= 1 -\cos^2 x\\[/tex]

put the value of [tex]\sin^2 x[/tex] value in the above equation:

[tex]\Rightarrow 4 \cos x= - (1-\cos^2 x)+4\\\\\Rightarrow 4 \cos x= - 1+\cos^2 x+4\\\\\Rightarrow 4 \cos x= \cos^2 x+3\\\\\Rightarrow \cos^2 x-4 \cos x+3=0\\\\[/tex]

Let [tex]\cos x= A[/tex]

[tex]\Rightarrow A^2-4A+3=0 \\ \Rightarrow A^2-(3A+A)+3=0 \\\Rightarrow A^2-3A-A+3=0\\\Rightarrow A(A-3)-1(A-3)=0\\\Rightarrow (A-3)(A-1)=0 \\[/tex]

[tex]\Rightarrow A- 3=0 \ \ \ \ \ \ \ \ \ \ \ \Rightarrow A -1 =0 \\\\[/tex]

[tex]\Rightarrow A= 3\ \ \ \ \ \ \ \ \ \ \ \Rightarrow A =1 \\\\\Rightarrow \cos x = 3\ \ \ \ \ \ \ \Rightarrow \cos x =1\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow \cos x =\cos 0\\\\\Rightarrow x = \cos^{-1} 3\ \ \ \ \ \ \ \Rightarrow x = 0\\\\[/tex]

The value of x is [tex]2n\pi\ \ \ _{where} \ \ \ \ \ \ \ n=1, 2, 3......[/tex]

[tex]\boxed{\bold{x=2 n \pi}}[/tex]

Answer:

2.5

Step-by-step explanation:

the other persons answer is wrong

The number after rounding to the one significant figure is 4000.

The term significant figures refers to the number of important single digits (0 through 9 inclusive) in the coefficient of an expression in scientific notation

Rounding off means a number is made simpler by keeping its value intact but closer to the next number

According to the given question we have an expression.

[tex]\frac{798}{8} (41)[/tex]

When we evaluate this expression we get

[tex]\frac{798}{8} (41)[/tex]

[tex]=99.75(41)[/tex]

[tex]= 4089.75[/tex]

Here, the first significant figure is 4 and the second one is 0 which is less than 5.

Hence, the number after rounding to the one significant figure is 4000.

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