A trucker had a load of grain containing 2 tons. She unloaded 1 ton 1,200 pounds at the warehouse. How much grain does she still have left on the truck?

Answer:

The answer is b. [tex]4x^2+3y^2-24y-144=0[/tex]

Step-by-step explanation:

The equation is:

[tex]r=\frac{-72}{12+6\sin(\theta)}[/tex]

Cross multiply;:

[tex]r(12+6\sin(\theta)=-72[/tex]

Expand;:

[tex]12r+6r\sin(\theta)=-72[/tex]

Divide through by 6;:

[tex]2r+r\sin(\theta)=-12[/tex]

[tex]2r=-12-r\sin(\theta)[/tex]

Substitute;:

[tex]y=r\sin(\theta), r=\sqrt{x^2+y^2}[/tex]

[tex]2\sqrt{x^2+y^2}=-12-y[/tex]

Square both sides;:

[tex](2\sqrt{x^2+y^2})^2=(-12-y)^2[/tex]

[tex]4(x^2+y^2)=144+24y+y^2[/tex]

[tex]4x^2+4y^2=144+24y+y^2[/tex]

Simplify;:

[tex]4x^2+3y^2-24y-144=0[/tex]

Answer:

1 : 25

Step-by-step explanation:

Mix 20 ml per 500 ml. of water the ratio is = 20 : 500

Or [tex]\frac{20}{500}[/tex] = [tex]\frac{1}{25}[/tex] = 1 : 25

1 ml insecticide per 25 ml of water.

The ratio of the amount of insecticide to the amount of water is 1 : 25

Fractions are written as the ratio of two integers. The ratio of the amount of insecticide to the amount of water is 1:25

Fractions are written as the ratio of two integers

From the given question, we have the following measurement:

20ml per 500 ml of water

Required

The ratio of the amount of insecticide to the amount of water

Ratio  = 20ml/500ml
Ratio = 1/25 = 1:25

Hence the ratio of the amount of insecticide to the amount of water is 1:25

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Answer:

Option C

Step-by-step explanation:

We have to find the pair of terms composed of like terms.

(A) 2a, 2b  Unlike terms

(B) -3x, +3y Unlike terms

(C) abc, cab

    As we know cumulative property of multiplication shows a×(b×c) = (a×b)c

    Therefore, both the terms abc and cab are similar.

(D) 4mn, 3my Unlike terms

Option C is the answer.

Since we know the population standard deviation and the sample size is above 30, then we use the z statistic. The formula for z score is:

z = (x – u) / s

where,

x = the sample mean or sample value = 8.6 hours

u = the population mean = 8.4 hours

s = the standard deviation = 1.8 hours

Substituting into the given equation:

z = (8.6 – 8.4) / 1.8

z = 1.11

Using the standard probability distribution tables for z, a value of z = 1.11 has a probability of:

p = 0.8665

However this is still not the correct answer since this refers to the left of z. What we are trying to find is to the right of z since problem ask for exceeds 8.6 hours, therefore the correct answer is:

P (x>8.6 hours) = 1 – 0.8665

P (x>8.6 hours) = 0.1335

Therefore there is a 13.35% chance that the mean rebuild time is greater than 8.6 hours.

Final answer:

The probability that the product operates is 0.6706 or 67.06%.

Explanation:

To find the probability that the product operates, we need to find the probability that all 40 integrated circuits are not defective. Since the probability of any integrated circuit being defective is 0.01, the probability that a circuit is not defective is 1 - 0.01 = 0.99. Since the integrated circuits are independent, we can multiply the probabilities together:

P(product operates) = (0.99)⁴⁰ = 0.6706

Therefore, the probability that the product operates is 0.6706 or 67.06%.

2 inches = 0.1666 feet

15 x 24 x 0.1666 = 59.98 cubic feet

 1 cubic yard = 27 cubic feet

59.98 is greater than 27 so 1 cubic yard of topsoil will not be enough

Final answer:

The probability that you win if you go first is calculated as a sum of an infinite geometric series considering the odds of drawing the red chip in the first or subsequent rounds and is found to be 1/2.

Explanation:

The probability that you win the game if you go first can be found by considering the possibilities of either drawing the red chip on your first turn or on subsequent turns after both you and your friend did not draw the red chip in the previous rounds. In the first round, you have a 1/6 chance of picking the red chip and winning immediately. If you don't draw the red chip, then your friend has a 1/5 chance of drawing it on their first turn, assuming you drew a blue chip.

If both of you fail to draw the red chip on the first turn, the situation repeats with you having another chance to win with the same odds as your first turn. Since this can go on indefinitely, the probability of you winning can be expressed as a geometric series:

P(you win) = 1/6 + (5/6)(4/5)(1/6) + (5/6)^2(4/5)^2(1/6) + ...

This series can be summed up using the formula for the sum of an infinite geometric series a/(1-r), where a is the first term of the series (1/6 in this case), and r is the common ratio ((5/6)(4/5)). The common ratio can be simplified to (4/6) or (2/3), and the sum of the series gives us the final probability. Therefore, the probability that you win the game if you go first is:

P(you win) = 1/6 / (1 - (2/3)) = 1/6 / (1/3) = 1/2.

The difference between the squares of two numbers is 7. Four times the square of the first number increased by the square of the second number is 73. By formulating this information into equations, the numbers, thus, obtained are 3 and 4 or -3 and -4.

An equation is a combination of numbers, variables, functions, mathematical operations, etc. in a meaningful way. The equation comprises two or more expressions separated by the equality sign(=), indicating the equivalency.

Let the numbers be x and y, then according to the question,

[tex]x^2 - y^2 = 7[/tex] ...(i)

[tex]4x^2 + y^2 = 73[/tex] ...(ii)

Add both equations,

[tex](x^2 - y^2) + (4x^2 + y^2) = 7 + 73\\(x^2 + 4x^2) + (-y^2 +y^2) = 80\\5x^2 = 80\\x^2 = 16\\x = \pm4[/tex]

Put x = 4 in equation (i),

[tex]4^2 - y^2 = 7\\16 - y^2 = 7\\y^2 = 16-7\\y^2 = 9\\y = \pm3[/tex]

So, the numbers are 3 and 4 or -3 and -4.

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it  to calculate the cost of $100 for every 50lbs, you would use 100x

 then you need to add that to the 1200

 so the equation would be y = 1200+100x

B is the correct answer

it is simply y=-2

hoped I helped :)

volume of square middle = 12 x 12 x 7 = 1008

 if you put the 2 ends together it would be a cylinder so volume for that is:

3.14 x 6^2 x 7 = 791.28

1008 + 791.28 = 1799.28  round it off to 1800 mm^3

So D is the correct answer

Answer:

4th option is correct.

Step-by-step explanation:

Here in the given image, we can see that there can be 2 figures if separated. A cuboid with dimensions 12*12*7 and a cylinder with radius as 6 mm and height as 7 mm.

We will first find the volume of cuboid.

V = [tex]12\times12\times7[/tex] = 1008 cubic mm

Now, volume of cylinder is given as : [tex]\pi r^{2} h[/tex]

[tex]3.14\times6^{2}\times7[/tex] = 791.28 cubic mm

Now adding both the volumes to get the volume of complete figure:

V = [tex]1008+791.28=1799.28[/tex] cubic mm

Now this value is closest to option 4th : 1800 cubic mm.

Therefore, last option is true.

Answer:

  C.)  (-1, 2)

Step-by-step explanation:

You can plot the points on a graph, or you can just find the midpoint:

  midpoint = (O + N)/2 = ((-1, 9) +(-1, -5))/2 = (-1-1, 9-5)/2 = (-2, 4)/2

  midpoint = (-1, 2)

The total cost of the least is $19,920.

Here,

lease a car at $415 per month for 4 years.

We have to find the total cost of the least.

What is Multiplication?

Multiplication is the process of calculating the total of one number multiplied by another.

Now,

lease a car at $415 per month for 4 years.

1 years = 12 month

4 years = 4 x 12 = 48 months.

Hence, total cost of the least = $415 x 48

                                            = $19,920

So, The total cost of the least is $19,920.

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Answer:

Step-by-step explanation:

Arc STR measures twice the measure of angle R, and arc WRS measures twice the measure of angle T.

STR = 2  x ∠R and WRS = 2  x ∠T   --- This is because of the Inscribed Angle Theorem

If the measure of arcs STR and WRS are added together, the total would be 360° since a full circle is made up of 360°.

So mSTR + mWRS = 360°

Substituting the angle measures of R and T in for the arcs, the equation becomes:

2 • ∠R + 2 • ∠T = 360°

Simplifying further:

2 • [∠R + ∠T] = 360°   

∠R + ∠T = 360° / 2

∠R + ∠T = 180°   - This proves that opposite angles of a quadrilateral inscribed in a circle are supplementary.

Answer:

C.) 23/21

Step-by-step explanation:

just took the test on edge

Answer:

A. It is the same as the gross pay.

Explanation:

To get the amount of income tax withheld, we use the table attached.

We are given that:

1- This biweekly gross salary is $780, therefore, we will go to the row having a minimum payment of $780 (red border)

2- The number of claimed allowances is 6, therefore, we will go to the column with 6 claimed allowances (blue border)

We now find the intersection between the row and the column. As we can see in the table, it is zero.

This means that the deducted taxes based on the givens is zero which means that the net pay is the same as the gross pay.

Hope this helps :)

Final answer:

To calculate the net pay, deduct the taxes and other deductions from the gross salary. Since the deductions will be greater than zero, the net pay will be $11 less than the gross pay.

Explanation:

To calculate the net pay, we need to deduct the taxes and other deductions from the gross salary. The main deductions to consider are Social Security, Medicare, and federal and state taxes. Let's break it down.

Subtract the total deductions from the gross salary to find the net pay.

Since the deductions will be greater than zero, the net pay will be $11 less than the gross pay. Therefore, the correct answer is option c. $11 less than the gross pay.