MATHEMATICS COLLEGE

A number, n, is multiplied by -3/8. The product is -0.5 What is the value of n?

Answers

Answer 1

Answer:

Answer:

n=4/3

Step-by-step explanation:

n*(-3/8)=-0.5

n=0.5/3/8

n=1/2 / 3/8

n=4/3

Check:

4/3*-3/8=-0.5

4/3*-3/8=-1/2

-1/2=-0/5

CORRECT!

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The quality control manager at a light bulb manufacturing company needs to estimate the mean life of the light bulbs produced at the factory. The life of the bulbs is known to be normally distributed with a standard deviation (sigma) of 80 hours. A random sample of 16 light bulbs indicated a sample mean life of 1000 hours. What is a 95% confidence interval estimate (CIE) of the true mean life (m) of light bulbs produced in this factory

A missile uses an internal computer clock to measure time in tenths of a second. The missile guidance system needs the time from launch, in seconds, in order to calculate its distance from the launch site. It obtains this by multiplying the computer clock time by 0.1. So, for example, a reading of 50 tenths of a second is 5 seconds. For one particular missile system, the conversion factor of 0.1 is stored in 8 bits as the binary number 0.000110012.The missile’s internal computer clock shows 200 tenths of a second. Convert this to seconds using your result from Part (i) of this question. Do not round your answer. The missile guidance system now records that it has travelled for this number of seconds.

Answers

Using proportions, it is found that the missile's internal computer clock is of 20 seconds.

According to the information given, this question can be solved by proportions, using a rule of three.

50 tenths of a second is equivalent to 5 seconds, and we want to find the equivalent to 200 tenths of a second, thus, the rule of three is:

50 tenths - 5 seconds

200 tenths - x seconds

Applying cross multiplication:

$50x = 5(200)$

$50x = 1000$

$x = (1000)/(50)$

$x = 20$

The missile's internal computer clock is of 20 seconds.

A similar problem is given at brainly.com/question/24372153

A garden shop determines the demand function q = D(x) = 5x + 200 / 30x + 11 during early summer for tomato plants where q is the number of plants sold per day when the price is x dollars per plant.(a) Find the elasticity.
(b) Find the elasticity when x = 2.
(c) At $2 per plant, will a small increase in price cause the total revenue to increase or decrease?

Answers

Answer: a) $E(x)=(-5945)/((30x+11)(5x+200))$ , b) 0.7975, demand is inelastic, c) increase.

Step-by-step explanation:

Since we have given that

$D(x)=(5x+200)/(30+11)$

So, derivative w.r.t x would be

$D'(x)=(5(30x+11)-30(5x+200))/((30x+11)^2)\n\nD'(x)=(150x+55-150x-6000)/((30x+11)^2)\n\nD'(x)=(5945)/((30x+11)^2)$

As we know that

$E(x)=(-xD'(x))/(D(x))\n\n\nE(x)=((-(-)5945x)/((30x+11)^2))/((5x+200)/(30x+11))\n\n\nE(x)=(5945x)/((30x+11)(5x+200))$

(b) Find the elasticity when x = 2.

So, we put x = 2, we get that

$E(2)=(5945* 2)/((30(2)+11)((5(2)+200)))\n\nE(2)=(11890)/((60+11)(10+200))\n\nE(2)=(11890)/(71* 210)\n\nE(2)=(11890)/(14910)\n\nE(2)=0.7975$

Since, 0.7975 < 1, so the demand is inelastic.

The total revenue will also increase with increase in price.

As total revenue = $price* quantity$

Hence, a) $E(x)=(-5945)/((30x+11)(5x+200))$ , b) 0.7975, demand is inelastic, c) increase.

Final answer:

This problem involves the calculation of the elasticity of a demand function using the derivative of the function. The elasticity is then used to analyze the effect on the total revenue when the price changes. The elasticity at a specific point is calculated and used for further analysis.

Explanation:

For part (a), to find the elasticity of the demand function, we need to use the formula for the price elasticity of demand, which is E = (dQ/dX) * (X/Q). Here, dQ/dX is the derivative of the demand function concerning X. This needs to be calculated first. The value of E provides us with the measure of elasticity.

For part (b), when x = 2 we substitute this value into the formula for E to get the elasticity at x = 2.

For part (c), based on the concept of elasticity, if E > 1, the demand is said to be elastic and a price decrease will result in an increase in total revenue, and vice versa. If E < 1, the demand is said to be inelastic and a price decrease will result in a decrease in total revenue, and vice versa. So, after calculating E at x = 2, we can use it to determine the effect on total revenue.

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Solve F(x) for the given domain.F(x)= x2 + 3x-2
F(-1) =
Jutaານເພະາ
a. -4
b. -6
C. 2.

Answers

Answer:

A. -4

Step-by-step explanation:

F(-1) means we must plug the number "-1" in for each x.

F(x) = x^2 + 3x - 2

F(-1) = (-1)^2 + 3(-1) - 2

= 1 - 3 - 2

= -4

candy box is made from a piece of cardboard that measures 45 by 24 inches. Squares of equal size will be cut out of each comer. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume? inches should be cut away from each corner to obtain the maximum volume. A square with a side of length (Round to the nearest hundredth as needed.)

Answers

Answer:

Each square should have 5 inches of side and area = 25 square inches.

Step-by-step explanation:

Candy box is made that measures 45 by 24 inches.

Let the squares of equal size x inches has been cut out of each corner.

The sides will then be folded up to form a rectangular box.

Now we have to find the size of square that should be cut from each corner to obtain maximum volume of the box.

Now the box is with length = (45 - 2x) inches

and width = (24 - 2x) inches

and height = x inches

Volume of the candy box = Length × width × height

V = (45 - 2x)(24 - 2x)(x)

V = x(1080 - 48x -90x + 4x²)

= x(1080 - 138x + 4x²)

= 4x³ - 138x² + 1080x

Now we will find the derivative of volume and equate it to zero.

$(dV)/(dx)=12x^(2)-276x+1080=0$

12(x² - 23x + 90) = 0

x² - 23x + 90 = 0

x² - 18x - 5x + 90 = 0

x(x - 18) - 5(x - 18) = 0

(x - 5)(x - 18)=0

x = 5, 18

Now for x = 18 Width of the box will be = (24 - 2×18) = 24 - 36 = -12

Which is not possible.

Therefore, x = 5 will be the possible value.

Therefore, square having area 25 square inches should be cut out from each corner to get the maximum volume of candy box.

Final answer:

The size of the square that should be cut away from each corner to obtain the maximum volume for a box made from a cardboard measuring 45 by 24 inches is 3 inches.

Explanation:

To find the size of the square that should be cut from each corner to obtain the maximum volume, we should first make an equation for the volume of the box. If x is the length of the side of the square, then the dimensions of the box are (45-2x) by (24-2x) by x, thus the volume of the box V is (45-2x)(24-2x)x.

By using calculus, we can find the derivative of this function, set it to zero and solve, this will give the critical points where the maximum and minimum volumes will be.

The derivative is found to be -4x^2 + 138x - 1080. Setting this to zero and solving, we find that x = 3 and x = 90 are the critical points for the maximum and minimum volumes. Since we cannot cut corners more than 24 inches (this would make the width negative), x = 3 inches is the only feasible solution.

So, 3 inches should be cut away from each corner to obtain the maximum volume.

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What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. in² The figure contains a triangle. One side is 11.1 inches. A second side is 7 inches. The angle between the given sides is 84 degrees.

Answers

The area of a triangle with sides 11.1 inches, 7 inches and 84 degree angle between the given sides is 38.6 in²

What is an equation?

An equation is an expression that shows the relationship between two or more variables and numbers.

The area of the triangle is given as:

Area of triangle = (ab * sin∝)/2

where a,b are the sides and ∝ is the angle between the sides, hence:

Area of triangle = (11.1 * 7 * sin84)/2 = 38.6 in²

The area of a triangle with sides 11.1 inches, 7 inches and 84 degree angle between the given sides is 38.6 in²

Find out more on equation at: brainly.com/question/2972832

Answer:

38.6

Step-by-step explanation:

A consumer advocate wants to collect a sample of jelly jars and measure the actual weight of the product in the container. He needs to collect enough data to construct a confidence interval with a margin of error of no more than 3 grams with 95% confidence. The standard deviation of these jars is usually 3 grams. Estimate the minimum sample size required.