Need help with this question all parts (Use the image on cypto to help solve the question)

Answers

Answer 1

Answer: Explanation

Part a

We first need to find the encoding and decoding functions used by Boris and Natasha. We know that these two must be linear functions with 1 as the coefficient of x. Then the encoding function must have the form:

$f(x)=x+b$

Where x is the number associated with the letter and b is a constant that we don't know. The decoding function is its inverse:

$f^(-1)(x)=x-b$

Now let's take a look at the table that associates the letters with numbers. The minimum number is 1 associated with A and the maximum is 27 associated with Blank. Now let's write the encoded version of these two:

$\begin{gathered} f(1)=1+b \n f(27)=27+b \end{gathered}$

And let's find the difference between their encoded values:

$f(27)-f(1)=(27+b)-(1+b)=27-1+b-b=27-1=26$

So the difference between their encoded values is the same as the difference between their decoded values. Since 1 and 27 are the minimum and maximum decoded values their difference is the greatest of all the difference between two decoded values. Then there's no other pair of decoded values with a difference equal to 26 and since the difference between two encoded values is the same as the difference between two decoded values we can assure that 26 is the maximum difference between two encoded values and it corresponds to the pair A - Blank.

This implies that if the difference between the minimum and maximum value in the message sent by Boris and Natasha is 26 we can assure that this pair of values is the one corresponding to A and Blank.

Part b

The minimum and maximum values in the message are 15 and 41 and their difference is 41 - 15 = 26. This means that 15 is the encoded value of A and 41 is that of Blank. Then we can construct two equations using the encoding function:

$\begin{gathered} f(1)=1+b=15 \n f(27)=27+b=41 \end{gathered}$

By substracting 1 from both sides of the first equation and 27 from both sides of the second equation we obtain b:

$\begin{gathered} 1+b-1=15-1\Rightarrow b=14 \n 27+b-27=41-27\Rightarrow b=14 \end{gathered}$

So b=14 and the encoding function is f(x)=x+14.

Then the decoding function is f⁻¹(x) = x - 14.

Part c

Now we need to decode the message. We simply need to evaluate the decoding function at all the numbers in the encoded message:

$\begin{gathered} f^(-1)(25)=25-14=11 \n f^(-1)\left(19\right)=19-14=5 \n f^(-1)(30)=30-14=16 \n f^(-1)(41)=41-14=27 \n f^(-1)(17)=17-14=3 \n f^(-1)(15)=15-14=1 \n f^(-1)(26)=26-14=12 \n f^(-1)(27)=27-14=13 \n f^(-1)(28)=28-14=14 \n f^(-1)(18)=18-14=4 \n f^(-1)(29)=29-14=15 \n f^(-1)(34)=34-14=20 \n f^(-1)(22)=22-14=8 \end{gathered}$

Then we replace each encoded value by its respective decoded value so the message in numbers is:

11 5 5 16 27 3 1 12 13 27 1 14 4 27 4 15 27 20 8 5 27 13 1 20 8

Using the table associating numbers and letters we obtain the final message:

KEEP CALM AND DO THE MATH

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For what values of a does the equation ax^2+x+4=0 have only one real solution?

Answers

Answer:

1/16

Step-by-step explanation:

To have one real solution, the discriminant must be 0.

b² − 4ac = 0

1² − 4a(4) = 0

1 − 16a = 0

a = 1/16

The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches. Men the same age have mean height 69.3 inches with standard deviation 2.8 inches. What are the z-scores for a woman 6 feet tall and a man 5'10" tall? (You may round your answers to two decimal places) z-scores for a woman 6 feet tall: z-scores for a man 5'10" tall:

Answers

Answer: The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

Step-by-step explanation:

Let x and y area the random variable that represents the heights of women and men.

Given : The heights of women aged 20 to 29 are approximately Normal with mean 64 inches and standard deviation 2.7 inches.

i.e. $\mu_1 = 64$ $\sigma_1=2.7$

Since , $z=(x-\mu)/(\sigma)$

Then, z-score corresponds to a woman 6 feet tall (i.e. x=72 inches).

[∵ 1 foot = 12 inches , 6 feet = 6(12)=72 inches]

$z=(72-64)/(2.7)=2.96296296\approx2.96$

Men the same age have mean height 69.3 inches with standard deviation 2.8 inches.

i.e. $\mu_2 = 69.3$ $\sigma_2=2.8$

Then, z-score corresponds to a man 5'10" tall (i.e. y =70 inches).

[∵ 1 foot = 12 inches , 5 feet 10 inches= 5(12)+10=70 inches]

$z=(70-69.3)/(2.8)=0.25$

∴ The z-scores for a woman 6 feet tall is 2.96 and the z-scores for a a man 5'10" tall is 0.25.

(10 points) Starting salaries of 64 college graduates who have taken a statistics course have a mean of $42,500 with a standard deviation of $6,800. Find an 90% confidence interval for ????. (NOTE: Do not use commas or dollar signs in your answers. Round each bound to three decimal places.) Lower-bound: 41101.87 Upper-bound: 43898.13

Answers

Answer:

41101.750 to 43898.250

Step-by-step explanation:

Using this formula X ± Z (s/√n)

Where

X = 42500 --------------------------Mean

S = 6800----------------------------- Standard Deviation

n = 64 ----------------------------------Number of observation

Z = 1.645 ------------------------------The chosen Z-value from the confidence table below

Confidence Interval Z

80%. 1.282

85% 1.440

90%. 1.645

95%. 1.960

99%. 2.576

99.5%. 2.807

99.9%. 3.291

Substituting these values in the formula

Confidence Interval (CI) = 42500 ± 1.645(6800/√64)

CI = 42500 ± 1.645(6800/8)

CI = 42500 ± 1.645(850)

CI = 42500 ± 1398.25

CI = 42500+1398.25 ~. 42500-1398.25

CI = 43898.25 ~ 41101.75

In other words the confidence interval is from 41101.750 to 43898.250

Final answer:

To find a 90% confidence interval for the mean starting salary, use the formula CI = sample mean ± (Z * sample standard deviation / √n).

Explanation:

To find a 90% confidence interval for the mean starting salary, we will use the formula:

CI = sample mean ± (Z * sample standard deviation / √n)

Given that the sample mean is $42,500, the sample standard deviation is $6,800, and the number of college graduates is 64, we can substitute these values into the formula to calculate the confidence interval. The lower-bound is $41,101.87 and the upper-bound is $43,898.13.

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Work out

1/3 + 2/9

Give your answer in its simplest form

Answers

Step-by-step explanation:

1/3 + 2/9 = 3/9 + 2/9 = 5/9

Topic: Fractions

If you like to venture further, feel free to check out my insta (learntionary). I'll be constantly posting math tips and notes! Thanks!

Answer:

5/9

Step-by-step explanation:

In how many ways can 4 light bulbs be selected from a batch of 43 lights bulbs to be tested for defects? Assume no light bulb will be tested more than once.

Answers

Answer:

There are 123,410 ways

Step-by-step explanation:

The number of ways or combinations in which we can select k elements from a group of n elements is given by:

$(n!)/(k!(n-k)!)$

In this case, we can replace n by 43 and k by 4, because we are going to select 4 light bulbs from a batch of 43 light bulbs.

So, the number of combinations is calculated as:

$(43!)/(4!(43-4)!)=123,140$

It means that there 123,410 ways to select 4 light bulbs from a batch of 43 lights bulbs to be tested for defects

Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate? Equation = (use h as variable)
Weekly Rate = $

Answers

Answer:

$837.96

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Step-by-step explanation:

Final answer:

By setting up an equation based on her hourly work and pay, we find that Linda's hourly rate of pay is $8.5 per hour.

Explanation:

To answer this question, we need to set up an equation based on the information provided. We know that Linda earns a normal hourly rate for her first 40 hours and twice that for the hours she works over 40. The total money she made is $544.

If we define h as her hourly rate, then for the first 40 hours, she earns 40h dollars. For the extra hours (in this case 12), she earns double her normal rate, meaning she earns an additional 2h*12 dollars. Setting up the equation gives us:

40h+2h*12 = 544

Solving this equation will give us the value of h, which is her hourly rate. 40h+24h=544, simplifying this will result in 64h=544. So her hourly rate is 544/64 = $8.5.

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