Find the distance between the points (2, 8) and (-1, 9).
1.√10
2. √2
3.2√3

Answer:

a. 94.444 m/s

b. 0.001 s

Step-by-step explanation:

#a

#b

The solution to the given quadratic expression using the completing the square is  x = ±√10 +8

This is a method of factoring quadratic expression. Given the quadratic function.

x^2 − 16x + 54 = 0

Subtract 54 from both sides

x^2 − 16x = -54

Complete the square

x^2 -16x +8^2 = -54 + 64

(x-8)² = 10
x - 8 = ±√10
x = ±√10 +8

Hence the solution to the given quadratic expression using the completing the square is  x = ±√10 +8

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The majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.

The dot plot is the way of representation of the data. This data is plotted in the form of points or dots over an x-y axis. The dot plot is also known as the strip plot.

The data given in the table is-

3.01, 3.26, 3.26, 3.79, 4.26, 4.34, 5.17, 5.94, 5.94, 5.94, 5.94, 7.14, 7.54, 7.90, 8.03, 9.15, 10.25, 11.98, 12.84, 19.86

The majority of data is between 3.01 to 7.90. The percentage of these data values to total data is 70%.

When data is represented in dot plot, then the distribution is a normal distribution. The data set has the value of median and mode equal to 5.94.

Median=5.94

Mode=5.94

Thus, the majority of data is between 3.01 to 7.90, when data is represented in dot plot, then the distribution is normal distribution and data set has 5.94 median.

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The given expression [tex]3 \dfrac{6}{5}[/tex]  can be written as [tex]\sqrt[5]{3^6}[/tex].

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication and division.

The given value can be written as:-

[tex]3\dfrac{6}{5} = \sqrt[5]{3^6}[/tex]

Therefore the given expression [tex]3 \dfrac{6}{5}[/tex]  can be written as [tex]\sqrt[5]{3^6}[/tex].

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Taking into account the definition of a system of linear equations, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.

A system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.

Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. That is to say, the values ​​of the unknowns must be sought, with which when replacing, they must give the solution proposed in both equations.

In this case, a system of linear equations must be proposed taking into account that:

The tickets to gone with the wind, at the classic movie house, cost $4.50 for adults and $2 for children.

45 people attended the Saturday matinee showing and the Classic movie House sold $162.50 worth of tickets.

So, the system of equations to be solved is

[tex]\left \{ {{x+y=45} \atop {4.50x+2y=162.5}} \right.[/tex]

There are several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "x" from the first equation you get:

x=45 - y

Then, substituting the expression in the second equation you get:

4.50×(45 - y) +2y=162.5

Solving:

4.50×45 - 4.50y +2y=162.5

4.50×45 - 4.50y +2y=162.5

202.5 -2.5y= 162.5

-2.5y= 162.5 -202.5

-2.5y= -40

y= (-40)÷ (-2.5)

y=16

Now, replacing in the expression x=45 - y you get:

x=45 -y

x= 45-16

x= 29

Finally, the number of adults attended the Saturday matinee showing is 29 and the number of children attended the Saturday matinee showing is 16.

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Answer:

D) 8

Step-by-step explanation:

Use the Intersecting Chords Theorem to find the value of x:

[tex]x*x=16*4\\\\x^2=64\\\\x=8[/tex]

Answer:

Step-by-step explanation:

A set of random numbers can be used for simulating a situation by defining how the numbers will be used to represent the possible outcomes. Trials are repeated using newly-generated random numbers until there are a sufficient number of trials to give a reasonable prediction of the probability of interest.

__

We can simulate the situation as follows:

Here are our trials and results.

48 09 52 47 65 05 60 44 64 97 -- 3 of 10

11 96 69 33 54 86 43 13 47 31 -- 5 of 10

56 52 16 97 22 26 29 57 94 23 -- 5 of 10

42 66 97 09 62 17 35 52 98 26 -- 5 of 10

53 44 26 82 41 88 38 32 64 31 -- 6 of 10

73 43 45 30 41 29 59 15 81 66 -- 5 of 10

23 54 46 11 32 12 95 52 28 34 -- 6 of 10

41 59 26 41 19 53 14 73 32 05 -- 7 of 10

82 87 37 09 67 70 03 44 78 21 -- 5 of 10

11 15 30 29 89 37 97 79 34 25 -- 7 of 10

__

Of these 10 trials, 4 showed the result that at least 6 of the next 10 students will choose a computer course. That is, the probability is estimated to be about 4/10 = 40%.

_____

Additional comment

Here, we can only predict the probability of interest as some multiple of 10%, since we have numbers sufficient for only 10 trials.

We could arrange the random numbers a different way and reuse them, but we choose not to for the purpose of this answer. For that to make sense, we need to have assurance that these numbers are truly random.

The number of repeated values among these 100 pairs of digits suggests that this is a poor set of numbers to be using. 26 and 41 each show up 4 times, for example. The probability of that happening by chance in a truly random set of numbers is about 0.03%. A chance event is considered to be unlikely if its probability is less than 1%.

Answer:50%

Step-by-step explanation:believe me it is 50%. 40% isn’t even a option. 50% is the correct answer.

Answer:

[tex]x=e^5\approx148.413[/tex]

Step-by-step explanation:

[tex]4\ln x-8=12\\\\4\ln x=20\\\\\ln x = 5\\\\x=e^5[/tex]

Answer:

y=−1 or y=−9

Step-by-step explanation:

y2+10y=−9

Step 1: Subtract -9 from both sides.

y2+10y−(−9)=−9−(−9)

y2+10y+9=0

Step 2: Factor left side of equation.

(y+1)(y+9)=0

Step 3: Set factors equal to 0.

y+1=0 or y+9=0

y=−1 or y=−9

Answer:

y=−1 or y=−9

Answer:

Here is the ans ..hope it helps:)

Answer:

60.

Step-by-step explanation:

P = 2( 17 + 13)

= 2 * 30

= 60

Answer:

Mean: 95, Median: 50 Mode: 25

Step-by-step explanation:

1.Mean: add all the numbers then divide by the number of numbers there

25+25+25+25+50+50+125+125+125+375= 950

950 divided by 10 = 95

2.Median :is the number in the middle of all the numbers in this case we have 2 so we will ad those two then divide them by two

50+50=100 100/2 = 50.

3. Mode : this is the most recurring number there and in this case it's 25

Answer: the correct answer is.....101 ft sq.

Step-by-step explanation:

There are 142506 different selections of twenty-five pastries

The given parameters are:

The number of different selections is calculated using:

[tex]C(n + r - 1,r) = \frac{(n + r - 1)!}{r!(n - 1)!}[/tex]

The above formula is used because repetitions are allowed.

So, we have:

[tex]C(6 + 25 - 1,25) = \frac{(6 + 25 - 1)!}{25!(6 - 1)!}[/tex]

Evaluate the sum and difference

[tex]C(30,25) = \frac{30!}{25!5!}[/tex]

Evaluate the expression

C(30,25) = 142506

Hence, there are 142506 different selections of twenty-five pastries

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Answer:

[tex]\cos^{-1}( \cos 43^{\circ}) = 43^{\circ}[/tex]

Step-by-step explanation:

The correct answer of the given function [tex]cos^{-1}[/tex] (cos 43°) will be 43°.

The fundamental 6 functions of trigonometry have a range of numbers as their result and a domain input value that is the angle of a right triangle.

It will be possible to comprehend the graphs, domains, differentiation, and integration of the four quadrants' trigonometric functions.

The trigonometric function is only valid for the right angle triangle and it is 6 functions which are given as sin cos tan cosec sec cot.

We know that the inverse trigonometric function of any function will vanish.

[tex]cos^{-1}[/tex]  (cos 43°)  = 43° cos inverse has vanished with cos and thus 43° is coming out to be the answer.

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Answer:

ai = 190.0

Step-by-step explanation:

I'll presume the sequence is arithmetic, simply because assuming the series is mathematical, there is more than one solution.

Assuming the series is comprised of numbers in an arithmetic progression, you will have...  (see attachment for better explanation and step by step.)

Answer:

1,514,919

Step-by-step explanation:

I just used a calculator cuz in 6th you can use one but here's the answer

Answer:

If the couple purchases a house and they made all their payments, their total cost of the house would be $1,541,919.

Explanation:

$256,000
$443,504
$513,765
$328,650 +
------------------

$1,541,919

The standard deviation of the amount paid for monthly water usage is $35.25

From the summary statistics, we have:

Standard deviation, σ = 2350

Rate = $0.015

The standard deviation of the amount is calculated using:

σ = Standard deviation * rate

This gives

σ = 2350 * $0.015

Evaluate

σ = $35.25

Hence, the standard deviation of the amount paid for monthly water usage is $35.25

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Answer:

Step-by-step explanation:

The brick layer builds ( 1 wall ) / ( 6 hrs )

That's the same as ( 1/6 wall ) / ( 1 hour )

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

The apprentice builds ( 1 wall ) / ( 16 hrs )

That's the same as ( 1/16 wall ) / ( 1 hour )

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

Let t = the time that the brick layer works

t + 5 = the timer the apprentice works

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

( brick layer's rate ) x ( brick layer's time ) +

( apprentice's rate ) x ( apprentice's time ) = 1

( 1 is the whole job )

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

(1/6) · t + (1/16) · (t + 5) = 1

Multiply both sides by 48

8t + 3t + 15 = 48

11t = 33

t = 3

t + 5 = 8

the brick layer works 3 hrs

The apprentice works 8 hrs

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

Check:

(1/6) · t + (1/16) · (t + 5) = 1

(1/6) · 3 + (1/16) · (3 + 5) = 1

1/2 + 1/2 = 1

There are 16 oz in a pound so it would be cheaper to purchase 1 pound for $3.75

Answer:

3/16 of the class share guitars today.

Step-by-step explanation:

1/4 x 3/4 = 3/16! :)

The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units

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

Let p and q represent the length of the diagonals.

Hence:

[tex]p=\sqrt{9^2+6^2+2(9)(6)cos(34)}=14.371\ units\\\\q=\sqrt{9^2+6^2-2(9)(6)cos(34)}=5.241\ units[/tex]

The length of the shorter diagonal is 5.241 units and the length of the longer diagonal is 14.371 units

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Answer:

18 quarters = $4.50

8.00-4.50=3.50

10 dimes+10 quarters=$3.50

Answer= you have 10 dimes and 28 quarters

Step-by-step explanation:

Answer:

You would have 18 quarters and 35 dimes

Step-by-step explanation:

Answer:

it's not reasonable because the t-shirts alone cost 30 and the shoes cost 20 so it would cost 50 altogether.

Answer:

The answer to this question is -2.

Step-by-step explanation:

First, multiply one of the equations by something that can cancel out the other variable.

3x+2y=20

3(x+4y=0)

3x+2y=20

3x+12y=0

Now, subtract both equations.

-10y=20

Now, divide both sides by -10.

y=-2

Hope this helps!

Julia paid $124 to social security as a payroll tax, $29 in Medicare as a payroll tax, 13% of her income to the federal government as an income tax, and 6% of her income to state government as an income tax.

It is defined as the tax rate applied on the solely earned money by a single entity.

Julia paid to social security as a payroll tax = 6.2% of 2000

= (6.2×2000)/100

= $124

Julia paid to Medicare as a payroll tax = 1.45% of 2000

= (1.45×2000)/100

= $29

Julia paid a percent of her income to the federal government as an income tax:

= (260/2000)×100

= 13%

Julia paid a percent of her income to state government as an income tax:

= (120/2000)×100

= 6%

Thus, Julia paid $124 to social security as a payroll tax, $29 in Medicare as a payroll tax, 13% of her income to the federal government as an income tax, and 6% of her income to state government as an income tax.

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Answer:

Learning Objective: Use the mean and range to compare the spread and averages.

a) Sarah Mean = 70.9, Katie Mean = 78.9

b) Sarah Range = 15, Katie Range = 25

c) Sentences

- The mean shows, on average, Sarah was 8 seconds quicker than Katie.

- The range shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.

Step-by-step explanation:

Given:

Sarah's Data Set:

Katie's Data Set:

To Find:

Work:

The mean of a data set is commonly known as the average. You find the mean by taking the sum of all the data values and dividing that sum by the total number of data values. The formula for the mean of a population is [tex]\mu = \frac{{\sum}x}{N}[/tex].

The formula for the mean of a sample is [tex]\bar{x} = \frac{{\sum}x}{n}[/tex].

Both of these formulas use the same mathematical process: find the sum of the data values and divide by the total. For the data values given above, the solution is: [tex]\frac{709}{10} = 70.9[/tex]

Therefore, the mean of Sarah's data set is 70.9.

For Katie's Data Set, [tex]\frac{789}{10} = 78.9[/tex].

Therefore, the mean of Katie's data set is 78.9.

To fill in the summary, we have to use the data we just calculated.

That summary can be found in the answer section.

Answer:

Sarah's mean = 70.9

Katie's mean = 78.9

Sarah's range = 15

Katie's range = 25

The mean shows that on average Sarah was 8 seconds faster than Katie. The range shows that Sarah was more consistent with her times. Katie had a larger spread of times which shows she was less consistent.

Step-by-step explanation:

Identifying the mean time for Katie and Sarah

The mean ( average ) is equal to the sum of the numbers in the data set ( the sum of the swimming times ) divided by the number of values in the data set ( which is given as 10 )

Mean for Sarah : Sum of her swimming times : 79 + 70 + 68 + 75 + 69 + 64 + 69 + 75 + 64 + 76 = 709

Number of values = 10

So mean = 709 / 10 = 70.9 seconds.

Mean for Katie : Sum of her swimming times : 79 + 79 + 76 + 81 + 89 + 76 + 64 + 85 + 82 + 78 = 789

number of values = 10

so mean = 789 / 10 = 78.9

Using this information we can identify what the first to blanks are. The mean shows that on average Sarah was ___ seconds ____ than Katie.

The mean time for Sarah was 70.9 seconds and the mean time for Katie was 78.9 seconds. So on average Sarah was faster and by 8 seconds ( which can be found by subtracting Sarah's mean from Katie's )

Identifying the range

The range is equal to the largest value ( longest swim time ) subtracted by the smallest value ( or quickest swim time )

Range for Sarah : Sarah's highest swim time is 79 seconds and her lowest is 64 seconds.

So her range = 79 - 64 = 15 seconds

Range for Katie : Katie's highest swim time is 89 seconds and her lowest time is 64 seconds

So her range = 89 - 64 = 25

Using this information we can fill out the remaining blanks.

The range shows that ____ was more consistent with her times. ___ had a larger spread of times which shows she was ____ consistent.

The higher the range the less consistent you are vise versa. Katie had a larger range hence, Sarah was more consistent and Katie was less consistent.