The length of a rectangle is six times it’s width. If the area of the rectangle is 486 cm^2, find the perimeter.

Answer:

In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared. The comparison is expressed as a ratio and is a unitless number.

Step-by-step explanation:

I hope it helps

Answer:

The farmer should plant 14 additional trees, for maximum yield.

Step-by-step explanation:

Given

[tex]Trees = 24[/tex]

[tex]Yield = 104[/tex]

[tex]x \to additional\ trees[/tex]

So, we have:

[tex]Trees = 24 + x[/tex]

[tex]Yield = 104 - 2x[/tex]

Required

The additional trees to be planted for maximum yield

The function is:

[tex]f(x) = Trees * Yield[/tex]

[tex]f(x) = (24 + x) * (104 - 2x)[/tex]

Open bracket

[tex]f(x) = 24 * 104 + 104x - 24 * 2x - x * 2x[/tex]

[tex]f(x) = 2796 + 104x - 48x - 2x^2[/tex]

[tex]f(x) = 2796 + 56x - 2x^2[/tex]

Rewrite as:

[tex]f(x) = - 2x^2 + 56x + 2796[/tex]

Differentiate

[tex]f'(x) = -4x + 56[/tex]

Equate [tex]f'(x) = -4x + 56[/tex] to 0 and solve for x to get the maximum of x

[tex]-4x + 56 = 0[/tex]

[tex]-4x =- 56[/tex]

Divide by -4

[tex]x =14[/tex]

The farmer should plant 14 additional trees, for maximum yield.

Answer:

K’(-1,3), L’(-3,0), M’(⅔, -8/3), N’(2, 4/3)

Step-by-step explanation:

Answer:

0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A telephone exchange operator assumes that 9% of the phone calls are wrong numbers.

This means that [tex]p = 0.09[/tex]

Sample of 448

This means that [tex]n = 448[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.09[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.09*0.91}{448}} = 0.0135[/tex]

What is the probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%?

More than 9% + 3% = 12 or less than 9% - 3% = 6%. Since the normal distribution is symmetric, these probabilities are the same, so we find one of them and multiply by 2.

Probability it is less than 6%

P-value of Z when X = 0.06. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.06 - 0.09}{0.0135}[/tex]

[tex]Z = -2.22[/tex]

[tex]Z = -2.22[/tex] has a p-value of 0.0132

2*0.0132 = 0.0264

0.0264 = 2.64% probability that the proportion of wrong numbers in a sample of 448 phone calls would differ from the population proportion by more than 3%

Answer:

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean diameter of 144 millimeters, and a variance of 49.

This means that [tex]\mu = 144, \sigma = \sqrt{49} = 7[/tex]

Sample of 46:

This means that [tex]n = 46, s = \frac{7}{\sqrt{46}}[/tex]

Wat is the probability that the sample mean would differ from the population mean by more than 2 millimeters?

Above 144 + 2 = 146 or below 144 - 2 = 142. Since the normal distribution is symmetric, these probabilities are equal, which means that we find one of them and multiply by two.

Probability the sample mean is below 142:

p-value of Z when X = 142, so:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{142 - 144}{\frac{7}{\sqrt{46}}}[/tex]

[tex]Z = -1.94[/tex]

[tex]Z = -1.94[/tex] has a p-value of 0.0262

2*0.0262 = 0.0524

0.0524 = 5.24% probability that the sample mean would differ from the population mean by more than 2 millimeters.

Answer:

Step-by-step explanation:

the ratio of 24 to 36 is the same as  x to 12

[tex]\frac{24}{36}[/tex] = [tex]\frac{x}{12}[/tex]

then

12*([tex]\frac{24}{36}[/tex])=x

[tex]\frac{24}{3}[/tex] = x

8 = x  

that's it :)

Answer:

3 x² y¹

Step-by-step explanation:

15 x²y³ = 3. 5. x². y³

-18x³yz = -2. 3². x³. y¹. z¹

so, the GCF = 3. x². y¹

Answer:

Solution given:

15x²y³=3*5*x*x*y*y*y

-18x³yz=-3*2*3*x*x*x*y*z

over here common is

3*x*x*y

so

greatest common factor is 3x²y¹

Answer:

F

Step-by-step explanation:

4.85-4.15=0.7 divided by 2 = 0.35+4.15=4.5*25 cause 30-20=10 divided by 2=5+20=25*4.5=112. closest to that is 120

9514 1404 393

Answer:

  h = -4.79(t -0.58)^2 +3.26

Step-by-step explanation:

The coordinates (t1, h1) are the time and height at the maximum. Then 'a' can be found from ...

  h = a(t -t1)^2 +h1

  1.65 = a(0 -0.58)^2 +3.26

  -1.61 = 0.3364a . . . . . subtract 3.26

  -4.786 = a . . . . . . . divide by the coefficient of a

The equation is ...

  h = -4.79(t -0.58)^2 +3.26

Answer:

[tex] - \frac{ \sqrt{3} }{2} [/tex]

Step-by-step explanation:

Unit circle

Answer:

(5,4)

Step-by-step explanation:

The coordinates of a point are the x and y-values of a point. It is organized like (x,y). The x-value is written first and then the y-value. The x-value is the "run" or the horizontal value; so, the value of the axis on the bottom. The y-value is the "rise" or the vertical value. The axes are also labeled. For this graph, the x-value is 5 and the y-value is 4. The final answer is (5,4).

Answer:

The answer is [tex]b=3, a=-2[/tex], and [tex]c=3[/tex].

Step-by-step explanation:

To solve this system of equations, start by solving for (a) in the third equation.

To solve for (a) in the third equation, add [tex]3b[/tex] to both sides of the equation, which will look like [tex]2a=-13+3b\\-a+b-c=2\\2a+3b-4c=-7[/tex]. Next, divide each term in [tex]2a=-13+3b[/tex] by 2 and simplify, which will look like [tex]\frac{2a}{2}=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex]   =  [tex]a=\frac{-13}{2} +\frac{3b}{2} \\-a+b-c=2\\2a+3b-4c=-7[/tex].

Then, replace all variables of (a) with [tex]-\frac{13}{2} +\frac{3b}{2}[/tex] in each equation and simplify, which will look like [tex]-13+6b-4c=-7\\-\frac{2c-13+b}{2}=2\\a=-\frac{13}{2}+\frac{3b}{2}[/tex].

The next step is to reorder [tex]-\frac{13}{2}[/tex] and [tex]\frac{3b}{2}[/tex], which will look like [tex]\frac{3b}{2}-\frac{13}{2}\\-13+6b-4c=-7\\-\frac{2c-13+b}{2} =2[/tex].

Then, solve for (b) in the second equation. To solve for (b) in the second equation start by moving all terms not containing (b) to the right side of the equation, which will look like [tex]6b=6+4c\\a=\frac{3b}{2}-\frac{13}{2} \\-\frac{2c-13+b}{2} =2[/tex]. Next, divide each term in                ([tex]6b=6+4c[/tex]) and simplify, which will look like [tex]b=1+\frac{2c}{3} \\a=\frac{3b}{2} -\frac{13}{2\\}\\-\frac{2c-13+b}{2} =2[/tex].

Then, replace all variables of (b) with [tex]1+\frac{2c}{3}[/tex] in each equation and simplify, which will look like [tex]-\frac{2(2c-9)}{3}=2\\a=c-5\\b=1+\frac{2c}{3}[/tex].

The next step is to solve for (c) in the first equation. To solve for (c) in the first equation start by multiplying both sides of the equation by [tex]-\frac{3}{2}[/tex] and simplify, which will look like [tex]2c-9=-3\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Then, move all terms not containing (c) to the right side of the equation, which will look like [tex]2c=6\\a=c-5\\b=1+\frac{2c}{3}[/tex]. Next, divide each term in [tex]2c=6[/tex] by 2 and simplify, which will look like [tex]c=3\\a=c-5\\b=1+\frac{2c}{3}[/tex].

Then, replace all variables of (c) with 3 in each equation and simplify, which will look like [tex]b=3\\a=-2\\c=3[/tex]. Finally, the list of all the solutions are [tex]b=3,a=-2[/tex], and [tex]c=3[/tex].

Answer:

A - $214.40

Step-by-step explanation:

Since b is the number of boxes of cards and n is the number of ink colors, and we're given the number of boxes of cards, and number of ink colors, we plug in:

4= b

and

3 = n

into the given equation to solve for C.

Using the order of operations we start inside our parentheses and work from there:

C= $25.60*4 + $14.00*4(3 - 1)

C= $25.60*4 + $14.00*4(2)

C= $102.40 + $112

C= $214.40

double occupancy room=x

single occupancy room=y

x + y =   80,    

90x + 80y = 6930

x=53

y=27

Answer:

False

Step-by-step explanation:

The analysis of variance may be described as an hypothesis test which is used to make comparison between variables of two or more independent groups. The null hypothesis is always of the notion that there is no difference in the means. While the alternative hypothesis is the opposite, for two independent groups, the alternative hypothesis is that both means are different, or not equal or not the same. However. When we have more than 2 independent groups, then the alternative hypothesis is stated as : 'the means are not all equal'. This means that the means of each group does not all have to be different, but the mean of one group may be different from that of the other groups or the mean of two groups are different from the other groups and so on.

Answer:

4/3

Step-by-step explanation:

In slope-intercept form [tex]y=mx+b[/tex], [tex]m[/tex] represents the slope of the line.

Let's write [tex]3x+4y=-2[/tex] in slope-intercept form by isolating [tex]y[/tex]:

[tex]3x+4y=-2,\\4y=-3x-2,\\y=-\frac{3}{4}x-\frac{1}{2}[/tex]

Therefore, the slope of this line is [tex]\frac{-3}{4}[/tex]. To find the slope of a line perpendicular to it, multiply the reciprocal of the slope by -1 (take the negative reciprocal).

Therefore, the slope of a line perpendicular to [tex]3x+4y=-2[/tex] is:

[tex]m_{perp}=-(-\frac{4}{3})=\boxed{\frac{4}{3}}[/tex]

Answer:

4/3

Given equation :-

Slope :-

Slope of perpendicular line :-

Answer:

1: $1200

2: Food ($6000)

3: $3000

4: $1800

5: $3000

Step-by-step explanation:

1: 10%*12000 = 1200

2: Food 50%*12000 = 6000

3: 25%*12000 = 3000

4: 15%*12000 = 1800

5: Food - Education = 6000 - 3000 = 3000

Answer:

2.409

Step-by-step explanation:

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\ln 200 = log_{e}200[/tex]

[tex]log_{9}200 = \frac{log_{e}200}{log_{e}9}[/tex]

           = [tex]\frac{5.3}{2.2}[/tex]

           = 2.409

The approximate value of log 200 would be; 2.409

When we raise a number with an exponent, there comes a result.

Let's say you get  a^b = c Then, you can write 'b' in terms of 'a' and 'c' using logarithm as follows [tex]b = \log_a(c)[/tex]'a' is called the base of this log function. We say that 'b' is the logarithm of 'c' to base 'a'

We have given the values in 9 = 2.2 and 200 – 5.3

We need to find the approximate value of log, 200.

Therefore,

㏑ 9 = 2.2

ln 200 = 5.3

[tex]ln 9 = log_{e}9\\\\ln 200 = log_{e}200[/tex]

Using the logarithm property;

[tex]log_{9}200 = \dfrac{log_{e}200}{log_{e}9}\\ = \dfrac{ln 200}{ln 9}\\ = \dfrac{5.3}{2.2}[/tex]

=  2.409

Hence, the approximate value of log, 200 would be; 2.409

Learn more about logarithm here:

https://brainly.com/question/20835449

#SPJ2

Answer:

1.74 or [tex]\frac{103}{59}[/tex]

Step-by-step explanation:

3(x-5) = 8 (11-7x)

3x-15=88-56x

59x=103

x = 1.74

Answer:

1384.5

Step-by-step explanation

Diviseion is just the oppisite of multiplication so you can think to yourself that what times two equals 2769. If you multiply 1384.5 on a calculater you get 2769.

9514 1404 393

Answer:

  you cannot use an equation to pick random numbers

Step-by-step explanation:

"Picked randomly" and "using an equation" are mutually exclusive. A random number cannot be predicted, so an equation cannot be used to generate it.

That being said, many programming languages make use of a "linear congruential generator" for generating random numbers. Such a generator generates a next number (x') from a previous number (x) using the equation ...

  x' = (a·x +c) mod m

Numbers generated in this way are called "pseudo-random numbers." The sequence of generated numbers will repeat at some point, and the statistics of generated numbers may or may not be suitable for any given application. (For example, sequential numbers may tend to be correlated.) The distribution of numbers is inherently uniform, so if you need other distribution, you need to perform some math on what you get from a linear congruential generator. Methods are available for approximating about any kind of distribution you might want.

This is not the only "equation" that can be used, and is certainly not the best.

__

A variety of different values of a, c, m are used in generators of this type. Some are better than others at producing what looks like randomness. Here's a set of numbers you can try: (no claim is made regarding suitability for your purpose)

This will produce numbers in the range 0–16777215. To get numbers in the range of 1-70, you can map these to your range in any suitable fashion. For example, you could add 1 to the integer part of the result from division by 239675.

Below is a graph of the sorted output of 200 values in the range 1–70 from the generator described here. You can see the distribution is approximately linear, and that some values are missing while others show up more often than average. (You expect this with random numbers.) The seed for these numbers (first value of x) is 1337457.

__

There is a web site available that will produce random numbers to your specification, based on the background noise of the universe. They are truly random.

Answer:

Step-by-step explanation:

Even function has following property:

It is easy to show this works with the second choice only. All the others don't work:

This is not correct as x - 1 ≠ -x - 1 so as their squares, so g(x) ≠ g(-x)

The last two choices are not even similarly.

Answer:

B. g(x) = 2x2 + 1

Correct on edge

Answer:

363,000,000

..........

Given: Given that for 16 brownies we need

Butter- [tex]\frac{2}{3}[/tex] cups

unsweetened chocolate-5 ounces

sugar-1-1/2 cup

vanilla-2 teaspoons

eggs-2

flour- 1 cup

To find: The amount of ingredients to make 6 brownies.

Solution: The amount we need to make 6 brownies is,

Butter

[tex](\frac{2}{3}.16)/6\\=0.25125 cups[/tex]

unsweetened chocolate

[tex]\frac{5.6}{16}\\=\frac{30}{16}[/tex]ounces

sugar-0.5625 cup

vanilla-[tex]\frac{12}{16}[/tex]teaspoons

eggs-[tex]\frac{12}{16}[/tex]

flour- [tex]\frac{6}{16}[/tex] cup

Answer:

the answer is 5 and u know the rest

Answer:

x= - 1

Step-by-step explanation:

Answer:

Step-by-step explanation:

As due to congruency,

x + 3 = 3y

[By putting the values of x = 3 and y = 2]

=> 3 + 3 = 3 × 2

=> 6 = 6

and,

x = y + 1

[By putting the values of x = 3 and y = 2]

=> 3 = 2 + 1

=> 3 = 3

Hence, proved

Answer:

[tex]PQ=6\frac{1}{2} =\frac{13}{2}[/tex]

[tex]|Q-P|=\frac{13}{2}[/tex]

[tex]|Q+4|=\frac{13}{2}[/tex]

[tex]Q+4=+-\frac{13}{2}[/tex]

[tex]Q=-4[/tex] ± [tex]\frac{13}{2}[/tex]

[tex]Q=\frac{21}{2} \times2\frac{1}{2}[/tex]

[tex]Answer: C)~2\frac{1}{2}[/tex]

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

Each shirt = $12.25

so, x = shirts = 12.25 x

cost including shipping= 77.49

So,

12.25 x + 3.99=77.49

Answer: D)

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

hope it helps...

have a great day!!

Answer:

$ 1220.00

Step-by-step explanation:

1269.79 = A [tex]e^{.02 * 2}[/tex]

1269.79 /A = [tex]e^{.04}[/tex]

ln(1269.79 /A) = .04 ln(e)

ln(1269.79 /A) = .04

1269.79 /A = [tex]e^{.04}[/tex]

1269.79 /A = 1.0408

A =  1269.79 / 1.0408

$ 1220.00