16.7.1
One-fifth of the length of a foot-race is 7 miles. Find the length of the race.

Answer:

[tex]2(-36 - 3i) +(5 +2i)(12 - 2i) \\ \implies - 72 - 6i + 60 - 10i + 24i + 4\\ \implies \: - 8 + 8i[/tex]

Answer: Definition: Ratio of the size of the map to its subject: Scale ... so scale = 1 cm / 100,000 cm = 1/100,000. - Scale ... STEP 1: - 2 cm represents 5 km

Step-by-step explanation:

STEP 1: - 2 cm represents 5 km - (write in full)

- STEP 2: - 1 cm represents 2.5 km - (divide so left side = 1)

- STEP 3: - 1 cm represents 250,000 cm - (convert to same units)

- STEP 4: - scale is 1 : 250,000 - (express as a representative fraction)

9514 1404 393

Answer:

Step-by-step explanation:

Let 'a' represent the number of pounds of Arabian Mocha in the mix. Then the number of pounds of Costa Rican blend is (100-a). The cost of the mix will be ...

  9.10(100 -a) +13.10(a) = 11.58(100)

  4a = 248 . . . . . . . . . . . . . collect terms, subtract 910

  a = 62 . . . . . . . . . . . . divide by 4

62 pounds of Arabian Mocha and 38 pounds of Costa Rican blend should be mixed.

Answer:

108801

Step-by-step explanation:

Well, you should first add 99 to 99999 which is 10098. And since it's not a palindrome you need to keep adding 99 to the sum until you reach one.

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This is with a calculator

Btw, I used calculator soup.com for it.

100089, 100188, 100287, 100386, 100485, 100584, 100683, 100782, 100881, 100980, 101079, 101178, 101277, 101376, 101475, 101574, 101673, 101772, 101871, 101970, 102069, 102168, 102267, 102366, 102465, 102564, 102663, 102762, 102861, 102960, 103059, 103158, 103257, 103356, 103455, 103554, 103653, 103752, 103851, 103950, 104049, 104148, 104247, 104346, 104445, 104544, 104643, 104742, 104841, 104940, 105039, 105138, 105237, 105336, 105435, 105534, 105633, 105732, 105831, 105930, 106029, 106128, 106227, 106326, 106425, 106524, 106623, 106722, 106821, 106920, 107019, 107118, 107217, 107316, 107415, 107514, 107613, 107712, 107811, 107910, 108009, 108108, 108207, 108306, 108405, 108504, 108603, 108702, 108801, 108900, 108999, 109098, 109197, 109296, 109395, 109494, 109593, 109692, 109791, 109890

Answer:

[tex]Sales = 86.749[/tex]

Step-by-step explanation:

Given

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

[tex]Competitors = 4[/tex]

[tex]Population = 12000[/tex]

See comment for complete question

Required

The sales

We have:

[tex]Sales = 0.845*(competitors) + 5.79*(population) + 13.889[/tex]

Substitute values for competitors and population

[tex]Sales = 0.845*4 + 5.79*12 + 13.889[/tex]

[tex]Sales = 3.38 + 69.48 + 13.889[/tex]

[tex]Sales = 86.749[/tex]

Step-by-step explanation:

Given

f(x) = 2x + 9

f^-1 (x) = ?

Let

y = f(x)

y = 2x + 9

Interchanging the roles of x and y we get

x = 2y + 9

2y = x - 9

y = ( x - 9) / 2

Therefore

⏩f^-1(x) = (x-9)/2

Hope it will help :)

This is the answer.

Hope it helps!!

Answer:

[tex]120.\sqrt{2}.\sqrt[3]{3}[/tex]

Step-by-step explanation:

[tex]\sqrt{32} = \sqrt{16.2} =\sqrt{4^{2}.2} = 4\sqrt{2}[/tex]

[tex]\sqrt[3]{81} =\sqrt[3]{27.3} =\sqrt[3]{3^{3}.3 }=3\sqrt[3]{3}[/tex]

∴[tex]5\sqrt{32}.2\sqrt[3]{81} =5. [4\sqrt{2}].2.[3\sqrt[3]{3} ][/tex]

                   [tex]=120.\sqrt{2}.\sqrt[3]{3}[/tex]

Angle QNM is =x by alternate angle reason (QU is parallel to MP)

X = 69

Answer

$0.1346

Explanation:

Find probability of each card and the value of each card and then add them together.

Probability of getting a heart = 13/52

Price of one heart =$0.30

Pay for one heart = 13/52×0.30=$0.075

Probability of getting a queen =4/52

Price of one queen =$0.55

Pay for one queen =4/52×$0.55=$0.0423

Probability of getting a queen of hearts =1/52

Price of one queen =$0.90

Pay for one queen =1/52×$0.90=$0.0173

Therefore the pay for one draw= $0.075+$0.0423+$0.0173=$0.1346

Answer:

eh width = 103.5 inches

Step-by-step explanation:

x = width

Length = (x/2 - 5 )*6

so 384=x+3x-30

414=4x

x=414/4=103.5 inches

Answer:

y = -4/3x -46/3

Step-by-step explanation:

The question tells us to write an equation that is:

- parallel to the given line

- goes through the point (-7, -6)

Parallel lines will have the same slope, because if the slope was different, they would eventually intersect and not be parallel lines anymore.

We are going to use the point-slope form to find the other line.

Point-slope form uses a point that the graph will cross through and the slope of the graph to find the graph in y = mx + b form (also called slope-intercept form).

(I attached the point-slope form as an image below)

m = slope

x1 = x coordinate of the point

y1 = y coordinate of the point

We are going to substitute our slope into the form first:

y - y1 = (-4/3)(x - x1)

Next let's put in our point (-7, -6):

(Remember! -7 is our x coordinate & -6 is our y coordinate :-) )

y - (-6) = -4/3(x - (-7))

(cancel out the negatives to make them positive)

y + 6 = -4/3 (x +7)

Now solve for x using basic algebra:

y + 6 = -4/3 (x +7)

(distribue the -4/3)

y + 6 = -4/3x - 28/3

(subtract 6 from both sides)

y = -4/3x -46/3

That's your answer!

Hope it helps (●'◡'●)

Answer:

Step-by-step explanation:

y + 6 = -4/3(x + 7)

y + 6 = -4/3x - 28/3

y + 18/3 = -4/3x - 28/3

y = -4/3x - 46/3

Answer: 21

Step-by-step explanation:

My teacher just did it

Answer:

The first term is 6; the common difference in 0.8.

Step-by-step explanation:

The nth term is:

[tex] a_n = a_1 + (n - 1)d [/tex]

The sum of the first n terms is:

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] a_{n} = a_1 + (n - 1)d [/tex]

[tex] a_{11} = a_1 + (11-1)d [/tex]

[tex] a_1 + 10d = 14 [/tex]        Equation 1

[tex] S_n = \dfrac{n(a_1 + a_n)}{2} [/tex]

[tex] S_{26} = \dfrac{26(a_1 + a_{26})}{2} [/tex]

[tex] \dfrac{26(a_1 + a_1 + 25d}{2} = 416 [/tex]

[tex] \dfrac{52a_1 + 650d)}{2} = 416 [/tex]

[tex] 26a_1 + 325d = 416 [/tex]        Equation 2

Equation 1 and Equation 2 form a system of equations in 2 unknowns.

To eliminate a_1, subtract 26 times Eq. 1 from Eq. 2.

[tex] 65d = 52 [/tex]

[tex] d = \dfrac{52}{65} [/tex]

[tex] d = \dfrac{4}{5} = 0.8 [/tex]

[tex] a_1 + 10d = 14 [/tex]

[tex] a_1 + 10 \times 0.8 = 14 [/tex]

[tex] a_1 + 8 = 14 [/tex]

[tex] a_1 = 6 [/tex]

Answer:

The first term is 6; the common difference in 0.8.

Answer:

B. -3

Step-by-step explanation:

Answer:

[tex]x^{2} -16[/tex]

a = 1

b=0

c= -16

i assume the next question is to factor that...

(x-4)(x+4)

Step-by-step explanation:

Answer:

8/22: this fraction will NOT terminate

189/270: this fraction WILL terminate

Step-by-step explanation:

I saw in the question that it says to solve the question by demonstrating the method discussed in class. I don't know what's the method you were taught, but I'll explain how I solved it.

When a fraction is in its simplest form, write out the prime factors of the denominator. If the denominator has 2s and/or 5s, the fraction WILL terminate in their decimal form.

8/22 in its simplest form is 4/11:

The only prime factors of the denominator, 11, are 1 and 11. There are no 2s and/or 5s present, so this fraction will NOT terminate.

189/270 in its simplest form is 7/10.

The prime factors of 10 are 2 and 5, meaning that this fraction WILL terminate.

Hope it helps (●'◡'●)

Explanation:

It's most effective to use a contingency table because we have two variables here: 1) the responses, and 2) the party affiliation.

We can have the responses along the rows and the party affiliation along the columns, or vice versa.

See the example below. The values are completely random simply for the purpose of the example (and not drawn from any real life data source).

As per the given options, the appropriate for the displaying these data will be contingency table. Hence, option D is correct.

A pie chart is a visual depiction of information in the shape of a pie, where the pieces of the pie represent the magnitude of the data. To depict data as a pie chart, you need a list of quantitative variables as well as categorical variables.

As per the given information in the question,

A contingency table in statistics is a particular kind of matrix-style table that shows the frequency of the variables. They are extensively utilized in scientific, engineering, business intelligence, and survey research.

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Answer:

Independent

Step-by-step explanation:

From the word independent, which means being able ot stand alone, that is the absence or presence of one has no impact on the outcome of each phenomenon. Two events A and B are said to be independent, if the occurence of one has no bearing on the probability or chance that B will occur. This means that each event occurs without reliance on the occurence of the other. This is different from mutually exclusive event whereby event A has direct bearing in the probability of the occurence of event B.

Answer:

The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.

The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 25 - 1 = 24

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.0639

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.0639\frac{6}{\sqrt{25}} = 2.5[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 22 - 2.5 = 19.5 minutes

The upper end of the interval is the sample mean added to M. So it is 22 + 2.5 = 24.5 minutes

The 95% confidence interval for the population mean of such waiting times is between 19.5 and 24.5 minutes. This means that we are 95% sure that the true mean waiting time of all calls for this company is between 19.5 and 24.5 minutes.

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 24 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.99}{2} = 0.995[/tex]. So we have T = 2.797

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.797\frac{6}{\sqrt{25}} = 3.4[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 22 - 3.4 = 18.6 minutes

The upper end of the interval is the sample mean added to M. So it is 22 + 3.4 = 25.4 minutes

The 99% confidence interval for the population mean of such waiting times is between 18.6 and 25.4 minutes. This means that we are 99% sure that the true mean waiting time of all calls for this company is between 18.6 and 25.4 minutes.

Answer:

2/1000 broken down to 1/500

Step-by-step explanation:

convert 100cm to mm

10mm-1cm

x-100

x=1000mm

since the question says as a fraction

2mm/1000mm

1mm/500mm

The ratio [tex]2mm:100cm[/tex] expressed as a fraction in its lowest term is [tex]\frac{1 mm}{500mm}[/tex].

To express the ratio 2mm:100cm as a fraction in its lowest term, we need to convert both measurements to the same unit.

Since 1cm is equal to 10mm, we can convert the ratio as follows:

[tex]2mm:100cm[/tex]

[tex]= 2mm : (100cm \times 10mm/cm)[/tex]

[tex]= 2mm : 1000mm[/tex]

Now, we can write the ratio as a fraction: [tex]\frac{2mm}{1000mm}[/tex]

To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

[tex]\frac{2mm}{1000mm}[/tex]

= [tex]\frac{1 mm}{500mm}[/tex]

Therefore, the ratio [tex]2mm:100cm[/tex] expressed as a fraction in its lowest term is [tex]\frac{1 mm}{500mm}[/tex].

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Answer:

Part 1)

10,000 different numbers.

Part 2)

A) 1 in 10,000.

Step-by-step explanation:

Part 1)

Since there are four digits and there are ten choices for each digit (0 - 9) and digits can be repeated, then we will have:

[tex]T=\underbrace{10}_{\text{Choices For First Digit}}\times\underbrace{10}_{\text{Second Digit}}\times\underbrace{10}_{\text{Third Digit}}\times \underbrace{10}_{\text{Fourth Digit}} = 10^4=10000[/tex]

Thus, 10,000 different numbers are possible.

Part 2)

Since there 10,000 different tickets possible, the chance of one being the correct combination will be 1 in 10,000.

This is equivalent to 0.0001 or a 0.01% chance of winning.

Answer:

0.0002

Step-by-step explanation:

4 decimal places means tenths, hundredths, thousandths, and ten thousandths places. If we count 4 decimal places, we come to 0.0002. The number next to it, 3, rounds down, so the answer should be 0.0002.

The answer is D

Hope that was fast enough

This is one single number that's slightly smaller than 400 thousand.

======================================================

Explanation:

There are 26 letters in the english alphabet. We don't use letters i or o, so we have 26-2 = 24 choices for that first slot.

Then we have 10 choices for the second slot because there are 10 single digits 0 (zero) through 9.

After making the selection for the second slot, we have 10-1 = 9 choices left for the third slot. The fourth slot has 10-2 = 8 digits to pick from. The subtraction occurs because we cannot reuse the digits.

Finally, the last slot will be a letter. We have 24-1 = 23 letters left to pick from.

Overall, we have 24*10*9*8*23 = 397,440 different license plates possible.

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Extra info (optional section)

You may be wondering "why do we multiply those values?". Well consider a simple example of having only 2 slots instead of 5.

Let's say the first slot is a letter A to Z, excluding letters i and o. The second slot will be the digit from 0 through 9.

If you make a table with 24 rows and 10 columns, then you'll have 24*10 = 240 cells overall. Notice the multiplication here. The 24 rows represent each letter, and the 10 columns are the digit numeric digits.

Each inner cell is a different two character license plate. For example A5 is one such plate. This idea can be extended to have 5 characters.

Answer:

The answer is 10, hope this helps!

Step-by-step explanation:

Answer:

We can use three solution and they are

(1)completing the square

(2)quadratic formula

(3) factorisation method

The quadratic equation 2x^2 - 4x = -2 has  two values .

   (1)completing the square

   (2)quadratic formula

   (3) factorization method

Given,

           quadratic equation 2x^2 - 4x = -2

                   2x² - 4x + 2 =0

Now solve this equation by factor,

                    2x² - 4x + 2 = 0

                    2x² - ( 2+2)x +2 = 0

                    2x² - 2x -2x + 2 = 0

                    2x(x- 1 ) -2 ( x -1) = 0

                    (2x - 2) ( x- 1) =0

                  2x - 2 = 0   or  x - 1 = 0

                   x = 1 or x = 1

So, this equation has 2 value of x.

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Answer:

20

Step-by-step explanation: