MATH: EXPONENTIAL WORK PROBLEM 1. HELP PLEASE! 13 pts

Answer: 84°

Step-by-step explanation:

On a unit circle, coterminal angles are angles that are in the opposite position of the asked angle. 1524° revolves around 127/15π times across the entire unit circle.

84° is the only positive coterminal angle between 0 and 360 that is in the opposite position of 1524°.

Keep in mind, that there are more coterminal angles, namely 444°, 804°, 1164°, and 1524° itself, but they are outside of the range of 0 and 360 degrees.

It should be noted that the value of 597 subtracted from 884 is 287.

The information is simply that we should subtract 884 and 597 and also illustrate it.

This will be:

884 - 597 = 287.

A word problem illustrating this is that a man had 884 pens and gave 597 pens to his friends. How many pens does he have left?

This will be:

= 884 - 597 = 287

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Answer:

(x-2)/(x-1)

Step-by-step explanation:

(x-2)/(x-1)

Here, we have to perform a sum of vectors and draw the resultant vector and the resultant vector will be <4, 0>.

If we see the image, we can write the vectors as:

w = <3, 3>

u = <-3, -4>

v = <-4, -1>

Now we want to sum:

u - v + w

u - v + w

= <-3, -4> - <-4, -1> + <3, 3>

= <-3 + 4 + 3, -4 + 1 + 3>

= <4, 0>

The graph of the resultant vector can be seen below.

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The average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces

The range is given as:

Sport                   Weight range of ball used

Volleyball            260-280 grams

Basketball           600-650 grams

Water Polo         400-450 grams

Lacrosse            142-149 grams

Football       14-15 ounces

The average of each weight is calculated as:

Average = (Max + Min)/2

So, we have:

Volleyball = (260+280)/2 = 270 grams

Basketball = (600+ 650)/2 = 625 grams

Water Polo = (400+450)/2 = 425 grams

Lacrosse = (142+149)/2 = 145.5 grams

Football = (14+15)/2 = 14.5 ounces

Hence, the average weights of each ball are 270 grams, 625 grams, 425 grams, 145.5 grams and 14.5 ounces

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Missing information in the question

Sport                   Weight range of ball used

Volleyball            260-280 grams

Basketball           600-650 grams

Water Polo         400-450 grams

Lacrosse            142-149 grams

Football       14-15 ounces

The new graphs would make it more difficult to estimate the price of a book.

To do this, we simply combine the frequencies on Felix and Tyler's table.

When this is done, we have the following dataset

3,3,3,3,3,3,3,3,4,4,4,4,5,5,5,5,5,5,5,6,6,6,6,6,6,7,7,7,7, 8,8,8,8,9,9,9,9,9,9,9,9,9,11,11,13,13,13,13,15,15,15,16,16,18,18,18,18,18,19,19,19,19,19,19,29,32,32,36,36,36,38,38,64,64,66,66,66,68,68,69,75,75,76,76,76,76,76,78,78,79,82,82,86,86,86,89,96,96,97,97,99

Next, we create the box & whisker plot and the histogram using the new dataset

(see attachment for the graphs)

The new graphs would make it more difficult to estimate the price of a book.

This is so because the dataset used to create the graphs do not come from the same source

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The values of a and b are 1/4 and 1/5 respectively

The function is given as:

16x^2 - 25y^2 = 1

The above function is a horizontal hyperbola.

A horizontal hyperbola that passes through the origin is represented as:

[tex]\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1[/tex]

Rewrite 16x^2 - 25y^2 = 1 as

[tex]\frac{x^2}{1/16} - \frac{y^2}{1/25} = 1[/tex]

By comparison, we have:

[tex]a^2 = \frac{1}{16}[/tex]

[tex]b^2 = \frac{1}{25}[/tex]

Solve for  a and b

[tex]a = \frac{1}{4}[/tex]

[tex]b = \frac{1}{5}[/tex]

Hence, the values of a and b are 1/4 and 1/5 respectively

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Answer:

x = 3

Explanation:

[tex]\sf Given \ equation: \ log_{10} (1000) = x[/tex]

Solving steps:

[tex]\rightarrow \sf log_{10} (1000) = x[/tex]

apply rule: logₐ(b) = c  then  b = aᶜ

[tex]\rightarrow \sf 1000 = 10^x[/tex]

rewrite following

[tex]\rightarrow \sf 10^3= 10^x[/tex]

cancel out bases

[tex]\rightarrow \sf x = 3[/tex]

Answer:

d.) x = 3

Step-by-step explanation:

you simply need to know 10 to power of how many makes 1000 , In case didn't know you can replace the value of x with the given options and see if it can be solved or not .

Answer: C and B

Step-by-step explanation:

[tex]9x^2 - 6x+1=7\\\\9x^2 - 6x-6=0\\\\x=\frac{-(-6) \pm \sqrt{(-6)^2 - 4(9)(-6)}}{2(9)}\\\\x=\frac{6 \pm \sqrt{252}}{18}\\\\x=\frac{1 \pm \sqrt{7}}{3}[/tex]

The probability of winning the lottery with one ticket is mathematically given as

P(W)=2.99484408*10^{−8}

Generally, the equation for the probability is  mathematically given as

P(1st ball)=1/34

one ball drawn remain

34-1=33

P(2nd ball)=1/33

In conclusion, the probability of winning the lottery with one ticket is

P(W)=1/34*1/33*1/32*1/31*1/30

P(W)=2.99484408*10^{−8}

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The measure of the angles in bold are as follows;

25. 90° and 90°

26. 60° and 60°

When two parallel lines are cut by a transversal , angle relationship are formed. They are alternate angles, corresponding angles etc.

Therefore,

x + 96 + x + 96 = 180

2x  = 180 - 192

2x = -12

x = -6

Hence, the angles are 90 and 90 degrees.

6x = 5x + 10(corresponding angles)

6x - 5x = 10

x = 10

Therefore, the angles are 60 degrees and 60 degrees

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The students in the school would be expected to do household chores for at least two hours every week with 1020 students.

We have given

Time (in hours)                  0–  1    2–3     4–5    6–7

Number of Students         32   64          3        1

A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

The keyword is at least, this means anything under that number will not qualify.

So that leaves 68 out of the 100 sample students.

So if you want to have the same thing but with 1,500 students.

Take off the 2 zeros at the end of 1500 and multiply by 68 to get your answer.

This is because there are 2 zeros in 100, so to cancel out the 2 zeros in 100, take out the 2 zeros in 1500 making it a lot easier.

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Answer: [tex]\frac{25\pi}{4}[/tex]

Step-by-step explanation:

The area of the entire circle is [tex]\pi(5^2)=25\pi[/tex].

The area of a quarter of the circle is thus [tex]\frac{25\pi}{4}[/tex]

The answer is 90% of the crime is between 48.63 and 51.37

The sd = 5 months

n = 36

Mean length = 50

1- 0.90

= 0.1

Critical value = alpha/2 = 1.645

Margin of error

E = 1.645 x 5/√36

= 1.37

50 -  1.37 + 50 + 1.37

= (48.63, 51.37)

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The dimensions of the box of the largest volume that can be constructed are

D=18,9,3

Generally, the equation for the lenght is  mathematically given as

Lenght=(24-2x)

Widht= (15-2x)

Therefore

Volume =L*B*H

V=(24-2x)(15-2x)x

V=(360-48x-30x+4x)x

V=4x^3-78x^2+360x

Differnciating we have

dv/dx=12x^2-156x+360

put dv/dx=0

12(x^2-13x+30)=0

x^2-10x-3x+30=0

(x-10)(x-3)=0

root=10,3

Second diiferciation

d^v/dx^2=24x-156

[tex]lim _{x=3} =-84 < 0[/tex]

In conclusion,

L=24-2x

L=24-2x3

L=18in

w= 15-2x

w=15-2*3

w=9in

h=x

h=2in

Dimension=18,9,3

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A ratio shows us the number of times a number contains another number. The ratio of the volume of the model to the volume of the original is 27/2744.

A ratio shows us the number of times a number contains another number.

Given that the scale factor is 3:14. Therefore, the ratios can be written as,

(a) The ratio of the surface area of the model to the surface area of the original  is,

Surface area Ratio = (3/14)² = 9/196

(b) The ratio of the volume of the model to the volume of the original.

Volume Ratio = (3/14)³ = 27/2744

(c) The ratio of the width of the model to the width of the original.

Width Ratio = 3/14

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Answer: a) 25:16 and b) 125:64

Step-by-step explanation:

For simplicity, assume that two spheres have diameters of 5 and 4.

a) 4pi(5^2) and 4pi(4^2)

   = 100pi:64pi

   = 100:64

   = 25:16

b. 4/3 pi(5^3) and 4/3 pi(4^3)

   = 166.67pi and 85.33pi

   = 500:256

   = 125:64

Answer: [tex]\frac{5x-2y}{3x-2y}[/tex]

Step-by-step explanation:

[tex]\frac{-\frac{2}{x}+\frac{5}{y}}{\frac{3}{y}-\frac{2}{x}}[/tex]
Multiplying the numerator and denominator by xy,

[tex]=\frac{-2y+5x}{3x-2y}\\\\=\frac{5x-2y}{3x-2y}[/tex]

Answer:

1/6

Step-by-step explanation:

Out of 30 tosses, 5 come up heads. So the estimated probability of heads is 5/30, or 1/6.

Answer: 0.17

Step-by-step explanation:

just got it right on quiz

Explanation:

Add up the heights of each bar to get the sample size.

4+4+7+12+11+4+1 = 43

The answers are as follows:

Data is information that has been translated into a form that is efficient for movement or processing.

1. By substituting the values x= 1, 2, 3..

We get the point where f(x)= g(x)

So, f(5)= g(5) =2

Hence, the value of x is 5.

2. As per the given data, during year 14,

revenue from online ads is approximately $4.2 million, whereas revenue from online ads is double than revenue from printed ads.

Also, both line intersect inbetween 7 and 8th year and both online ads and printed ads generated an approximate revenue of $2.2 million.

3. Western Beach erodes from 100 ft to 70 ft.

So, rate of erosion = 30 ft/15 yr = 2 ft/yr.

and,  Dunes Beach builds up from 20 ft to 95 ft.

So,  rate of buildup = 75 ft/15 yr = 5 ft/yr.

Hence,  Dunes beach gets 5 feet every year, and every 5 years the beach loses 25 feet.

b) From the table, beaches will have the same width sometime in year 11 (2006).

c) If the rate remains constant then there is no same width cause of decrease in western beach and increase dunes beach.

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Using the z-distribution, with a critical z-score of z = 1.645, the 90% confidence interval is (-16.4%, -9.66%).

For each sample, the mean and the standard error are given as follows:

Hence, for the distribution of differences, they are given as follows:

The interval is:

[tex]p \pm zs[/tex]

In this problem, we have a 90% confidence level, hence[tex]\alpha = 0.9[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.9}{2} = 0.95[/tex], so the critical value is z = 1.645.

Then the bounds of the interval are:

As a percentage, the 90% confidence interval is (-16.4%, -9.66%).

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Based on the price that Augusta Enterprises issued the bonds, the journal entries would be:

Date                  Account title                              Debit                Credit

July 1, 20x5       Cash                                      $97,000

                         Discount on Bonds payable $3,000

                         Bonds payable                                               $1,000,000

Date                  Account title                              Debit                Credit

July 1, 20x5       Cash                                     $1,020,000

                         Premium on Bonds payable                           $20,000

                         Bonds payable                                              $1,000,000

The cash received from the discounted bond is:

= 1,000,000 x 97%

= $970,000

The cash received from the premium bond is:

= 1,000,000 x 102/100

= $1,020,000

The premium is:

= 1,020,000 - 1,000,000

= $20,000

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On a number line 1.77 would be located between 1 and 2 but it would be closer to 2 than 1.

A number line is used to show the positioning of numbers. 1.77 is between 1 and 2. So, it would be located between 1 and 2 on the number line. Because 1.77 can be rounded off to 2, it would be closer to 2.

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Answer:

The bench costs $325

Step-by-step explanation:

let garden table = x

let bench = y

x = y+64

x+y = 714

y+y+64 = 714 (we know, x = y+64)

2y + 64 = 714

2y = 650

y = 325

Answer:

Bench: $325

Garden Table: $389

Step-by-step explanation:

g + b = 714      Eq. 1

g = b + 64        Eq. 2

g = cost of the garden table

b = cost of the bench

Replacing Eq.2 in Eq.1

(b+64) + b = 714

2b + 64 = 714

2b = 714 - 64

2b = 650

b = 650/2

b = 325

from the Eq. 2

g = b + 64

g = 325 + 64

g = 389

Check:

from the Eq. 1

g + b = 714

389 + 325 = 714

The smallest angle would be 19 degrees. So option D is correct.

The sum of exterior angles of the regular octagon is 360 degrees.

Given;

The angles

x + 13 + 2x - 1 + 2x + 6 + 2x + 12 + 2x - 17 + 3x - 4 + 3x - 10 + 4x = 360

19x - 1 = 360

19x = 359

x = 18.89

The smallest angle would be

2x - 17 = 2(18.89) - 17 = 19

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Answer:

ok so here we know that Baily kicked the target 6 times out of 20 that  is 6/20 and then you just reduce the fraction dividing it by 2 so it will be  3/10

Step-by-step explanation:

hope it helps :)

If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.

A Pareto chart is known to be a form of  a bar graph.

It is made up of different lengths of bars that stands for frequency or cost ( e.g. time or money, and are said to be placed with longest bars on the left and then the shortest are placed to the right.

Since there are 27 light blue cars and this is the first one among the shortest, one can make it to be in the second bar and as such, If I am to to construct a Pareto chart based on the rule of the chart, the second bar color in the graph be labeled light blue.

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The mean is $5.769 million and the standard deviation is $3.905 million.

The mean is the average of a data set.

The standard deviation shows the measure of the dispersion from the mean.

Urban Area         Total Cost       Squared Difference

                        (millions of dollars)    (x - u)²

New York                  16                     104.65  

Los Angeles              13                      52.27

Chicago                      7                          1.51

Washington, D.C.       5                        0.59

Houston                      5                        0.59

Dallas, Fort Worth      4                         3.13

Detroit                        4                          3.13

Miami                         4                          3.13

Phoenix                     4                          3.13

Philadelphia              4                          3.13

San Francisco           3                          7.67

Boston                       3                          7.67

Atlanta                       3                          7.67

13    Total                 75                       198.27

Mean = 5.769 (75/13)                         15.251 (198.27/13)

Standard Deviation = 3.905 (square root of 15.251)

Urban Area         Total Cost

                        (millions of dollars)

New York                  16

Los Angeles              13

Chicago                      7

Washington, D.C.      5

Houston                     5

Dallas, Fort Worth     4

Detroit                       4

Miami                        4

Phoenix                    4

Philadelphia             4

San Francisco          3

Boston                     3

Atlanta                     3

Calculate the mean and standard deviation for this data set (in millions of dollars). (Round your answers to three decimal places.) mean $ million standard deviation $ million

Thus, the mean is $5.769 million and the standard deviation is $3.905 million.

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Answer:

a

Step-by-step explanation:

The vertex is at (4,1).

Also, the graph opens down, so this eliminates e.

So, the answer is a.