If the unicorn seat on a merry–go–round is 5 feet from the center, and the merry–go–round completes a full rotation in 6 seconds, how many feet does the unicorn travel in one second

Answer:

(x - 2) and (x + 3) is a factor of: 2x² + 2x - 12

Step-by-step explanation:

2x² + 2x - 12 given equation

Now divide it by 2 we get,

x² + x - 6

then

x² + x - 6

x² + 3x - 2x - 6

x(x + 3) - 2(x + 3)

(x - 2) (x + 3)

Answer:

2 ( x+3)(x-2)

Step-by-step explanation:

2x^2+2x−12

Factor out 2

2 ( x^2 +x-6)

Factor inside the parentheses

What 2 numbers multiply to -6 and add to 1

3*-2 = -6

3+-2 =1

2 ( x+3)(x-2)

Answer:

If you were doing... 25(13x-15 8)-13(12-23x), the answer would be...

624x-3156

If you were doing... 25(13x-158)-13(12-23x), the answer would be...

624x-4106.

Step-by-step explanation: Simplify the expression.

I hope this helps you out! ☺

The simplification of algebraic expression 25(13x - 158) - 13(12 - 23x) is 624x - 4106.

An algebraic expression is an expression built up from constant, variables, and algebraic operations : addition, subtraction, multiplication, division and exponentiation.

To simplify an algebraic expression, we can only add or subtract the like terms. Like terms are variables with same exponent.

Given in the question,

algebraic expression = 25(13x - 158) - 13(12 - 23x)

Simplifying the expression,

[tex]= 25(13x - 158) - 13(12 - 23x)\\\\= 325 x - 3950 - 156 + 299x\\\\=325x + 299x - 3950 - 156\\\\= 624x - 4106[/tex]

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Answer:

£120

Step-by-step explanation:

Given that

The price after reduction = £78

So, 65% = £78.

We have to calculate 100 %

To do so, find 5% and multiply that by 20

65% = £78

5% = 78/13 = £6

So, 100% = 6 x 20 = £120

Hope this helps.

Good Luck

Please mark brainiest

Answer:

77

Step-by-step explanation:

The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.

(The sum of the measures of the intercepted arcs)/2

(76+78)/2

154/2

77

The option that correctly describes the graph below is A. Piecewise function.

A piecewise function is a function that reacts in different ways based on the input received at every point in time. This function has different intervals and funtions that apply to the respective domains.

Sometimes, these graphsa re recognized by the three main parts that they have. So, the function that is represented by the graph is the piecewise function.

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Answer:

b. 3p-2q

Step-by-step explanation:

Let the position vector of P=p

Let the position vector of Q=q

Point R divides segment PQ in ratio 3:2 externally.

[tex]\text{Position Vector of R }=\dfrac{\text{(Position Vector of P)m }-\text{(Position Vector of Q) n}}{m-n}[/tex]

m:n = 3:2

Therefore:

[tex]\text{Position Vector of R }=\dfrac{3p -2q}{3-2}\\=3p-2q[/tex]

Answer:

-12m-6n

Step-by-step explanation:

Let's break this down systematically

Start:

8m + 2n - 4(5m - 2n)

Use the distributive property

8m + 2n - 4(5m - 2n)

8m + 2n - 20m - 8n

Match like terms m and n

8m - 20m = -12m

2n - 8n = -6n

-12m-6n

Answer:

A.) 25.2

Step-by-step explanation:

Given the following :

Times in first four races :

26.3, 28.4, 25.6 and 29.1

The range of a list of values is the difference between the maximum and minimum value of the list or data.

In her first four races :

Range = 29.1 - 25.6 = 3.5

Value of range in her first four races = 3.5

In other to make the range larger:

Either she has a value less than the least time in her previous four races or she has a value greater than the maximum value of her previous race in her next race.

With a time of 25.2 in her next race : least value in the data will be 25.2

Range = 29.1 - 25.2 = 3.9

With a time of 26.1 in her next race :

Range = 29.1 - 25.6 = 3.5

With a time of 28.0 in her next race :

Range = 29.1 - 25.6 = 3.5

With a time of 29.1 in her next race :

Range = 29.1 - 25.6 = 3.5

Answer:

25.2

Step-by-step explanation:

Your friend swims on the school team.

In her first four races, her times are 26.3, 28.4, 25.6, and 29.1 seconds.

Which time listed for her next race would make the range larger?

Answer:

B is correct

Step-by-step explanation:

What is need to be done here is to set up an exponential equation for both scenario.

The exponential equation to set up is as follows;

V = P(1 + r)^t

It looks exactly like an equation used to get the amount on a compound interest after a stipulated number of years.

We have the following definitions;

V is the future value.

P is the present value

r is the rate in percentage

t is the time in years

So, for A, we have;

Kindly note that 4% = 4/100 = 0.04

110,000(1+0.04)^t = 110,000(1.04)^t

For B, we have;

6/100 = 0.06

100,000(1+0.06)^t = 100,000(1.06)^t

Now expected value of B is twice that of A.

The equation that defines this would look like;

100,000(1.06)^t = 2(110,000(1.04)^t)

Answer:

7/12 ≈ 0.583

Step-by-step explanation:

See picture below. There are 21 totals higher than 6 out of 36 possible outcomes. The probability is therefore 21/36 = 7/12.

Answer: 21/36 or 7/12. = 58.33%

Step-by-step explanation: 36 possible outcomes

Of those, combinations resulting in numbers greater than 6 are:

# | combinations

7 | 6

8 | 5

9 | 4

10 | 3

11 | 2

12 | 1

The sum of those combinations is 21.

So 21/36 = 0.5833

or 7/12 = 58.33%

Answer:

(7/2, -5/2)

Step-by-step explanation:

We can solve this multiple ways: Algebraically (Substitution or Elimination) or Graphically

Step 1: Write 1st equation in terms of y

y = 8 - 3x

Step 2: Substitute y of 2nd equation

x - 3(8 - 3x) = 11

Step 3: Solve for x

x - 24 + 9x = 11

10x - 24 = 11

10x = 35

x = 7/2

Step 4: Plug x to find y

3(7/2) + y = 8

21/2 + y = 8

y = -5/2

Answer:

Step-by-step explanation:

let's organize our information :

The trick here is to multiply x-3y=11 by -3 then add it to 3x+y=8 to get rid of x and get a normal equation

we get : -3x+9y= (-33)

then after the addition : 3x+y-3x+9y=8-33⇔ 10y=(-25)

   so y=(-25)/10= -5/2

so y= (-5/2) and x= 21/6

Answer:

1. A pentagonal Pyramid

2. Super Easy, tell me to draw one if you need but i am not gonna give in that much effort right now

Answer:

The mean, median, and standard deviation of the University of Oregon are $451.33, $467.5, and $113.61 respectively.

The mean, median, and standard deviation of the University of Washington are $396.67, $380, and $56.27 respectively.

Step-by-step explanation:

We are given that a sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Oregon is: $295, $475, $345, $595, $538, $460.

A second sample of the amount of rent paid for one-bedroom apartments of similar size near the University of Washington is: $495, $422, $370, $333, $370, $390.

Firstly, we will calculate the mean, median, and standard deviation for the data of the University of Oregon.

Arranging the data in ascending order we get;

X = $295, $345, $460, $475, $538, $595.

The mean of the above data is given by the following formula;

                  Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                                   =  [tex]\frac{\$295+ \$345+ \$460+\$475+ \$538+\$595}{6}[/tex]

                                   =  [tex]\frac{\$2708}{6}[/tex]  = $451.33

So, the mean price of rent near the University of Oregon is $451.33.

For calculating the median, we first have to observe that the number of observations (n) in the data is even or odd.

                    Median  =  [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]

                    Median  =  [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]

Here, the number of observations is even, i.e. n = 6.

So,  Median  =  [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]

                     =  [tex]\frac{(\frac{6}{2} )^{th} \text{ obs. } + (\frac{6}{2}+1 )^{th} \text{ obs.}}{2}[/tex]

                     =  [tex]\frac{(3 )^{rd} \text{ obs. } + (4 )^{th} \text{ obs.}}{2}[/tex]

                     =  [tex]\frac{\$460 +\$475}{2}[/tex]  = $467.5

Hence, the median price of rent for the University of Oregon is $467.5.

Now, the standard deviation is calculated by using the following formula;

         Standard deviation, S.D.  =  [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]

                     =  [tex]\sqrt{\frac{ (\$295 - \$451.33)^{2} +(\$345 - \$451.33)^{2} +......+(\$595 - \$451.33)^{2} }{6-1} }[/tex]

                     =  $113.61

So, the standard deviation for the University of Oregon is $113.61.

Now, we will calculate the mean, median, and standard deviation for the data of the University of Washington.

Arranging the data in ascending order we get;

X = $333, $370, $370, $390, $422, $495.

The mean of the above data is given by the following formula;

                  Mean, [tex]\bar X[/tex]  =  [tex]\frac{\sum X}{n}[/tex]

                                   =  [tex]\frac{\$333+ \$370+ \$370+\$390+ \$422+\$495}{6}[/tex]

                                   =  [tex]\frac{\$2380}{6}[/tex]  = $396.67

So, the mean price of rent near the University of Washington is $396.67.

For calculating the median, we first have to observe that the number of observations (n) in the data is even or odd.

                    Median  =  [tex](\frac{n+1}{2} )^{th} \text{ obs.}[/tex]

                    Median  =  [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]

Here, the number of observations is even, i.e. n = 6.

So,  Median  =  [tex]\frac{(\frac{n}{2} )^{th} \text{ obs. } + (\frac{n}{2}+1 )^{th} \text{ obs.}}{2}[/tex]

                     =  [tex]\frac{(\frac{6}{2} )^{th} \text{ obs. } + (\frac{6}{2}+1 )^{th} \text{ obs.}}{2}[/tex]

                     =  [tex]\frac{(3 )^{rd} \text{ obs. } + (4 )^{th} \text{ obs.}}{2}[/tex]

                     =  [tex]\frac{\$370 +\$390}{2}[/tex]  = $380

Hence, the median price of rent for the University of Washington is $380.

Now, the standard deviation is calculated by using the following formula;

         Standard deviation, S.D.  =  [tex]\sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }[/tex]

                     =  [tex]\sqrt{\frac{ (\$333 - \$396.67)^{2} +(\$370 - \$396.67)^{2} +......+(\$495 - \$396.67)^{2} }{6-1} }[/tex]

                     =  $56.27

So, the standard deviation for the University of Washington is $56.27.

Answer:

-17

Step-by-step explanation:

4.5*6=27

so -44++27

Answer:

Wrong values are plotted in the question statement graph.

Please find correct graph.

Step-by-step explanation:

Given that:

[tex]y =x+3[/tex] and [tex]-1<x<5[/tex]

i.e. we can put a value of x in the equation which is greater than -1 and lesser than 5.

OR

we can say, the points where x = -1 and x = 5 will not be included in the graph (they will be shown as hollow circle).

Now, let us put the values one by one:

x = -1, y = -1 + 3 =2

x = 0, y = 0 + 3 = 3

x = 1, y = 1 + 3 = 4

x = 2, y = 2 + 3 = 5

x = 3, y = 3 + 3 = 6

x = 4, y = 4 + 3 = 7

x = 5, y = 5 + 3 = 8

Therefore, the table of values become:

[tex]\begin{center}\begin{tabular}{ c c } x & y\\ -1 & 2\\ 0 & 3 \\ 1 & 4 \\ 2 & 5 \\ 3 & 6 \\ 4 & 7 \\5 & 8\\\end{tabular}\end{center}[/tex]

Points (-1, 2) and (5, 8) will not be included in the graph.

Please find attached corrected graph.

Answer:

D

Step-by-step explanation:

So that you can have an equation equal to zero to solve for x

Answer:

Percentage error is 39.39%

Step-by-step explanation:

It is given that,

The calculated value that Erika spend on school supplies this year is $115.

Actual value that she spent is $82.50.

We need to find Erika's percent of error. Percentage error is given by the formula as follows :

[tex]\%=\dfrac{\text{calculated value}-\text{actual value}}{\text{actual value}}\times 100\\\\\%=\dfrac{115-82.5}{82.5}\times 100\\\\\%=39.39\%[/tex]

So, Erika's percent of error is 39.39%.

Answer:

reflexive property of simliarity

Step-by-step explanation:

Answer: A) 1, 2, 4

Step-by-step explanation:

The range of a function is every y value.

Answer:

A. {1, 2, 4}

Step-by-step explanation:

Well let’s take a step back,

What is range?

Range is the amount of y-value son a graph or table.

So the range is (1, 4, 2)

Answer:

Step-by-step explanation:

This is exponential, of the form

[tex]y=a(b)^x[/tex] where a is the initial amount and b is the growth/decay rate. If Ginny begins the study with 1200 frogs in the population, our a value is 1200.

If the population is decreasing 3% per year, it is decreasing 100% - 3% = 97% which, as a decimal, is .97. Our exponential function, then, is

[tex]y=1200(.97)^x[/tex]

Answer:

[tex]h(t) = 0.75t^2 + 4t + 12[/tex]

Step-by-step explanation:

The equation given calculates the derivative of the height in relation to the time, that is, the rate of change of the height. To find the equation for the height, we need to integrate this equation:

[tex]dh/dt = 1.5t + 4[/tex]

Multiplying both sides by 'dt', we have:

[tex]dh = (1.5t + 4)dt[/tex]

Using the integral in both sides:

[tex]\int dh = \int (1.5t + 4) dt[/tex]

[tex]h = 0.75t^2 + 4t + h(0)[/tex]

[tex]h = 0.75t^2 + 4t + 12[/tex]

So the height after t years is represented by this equation:

[tex]h(t) = 0.75t^2 + 4t + 12[/tex]

Answer:

y=-5x-4

Step-by-step explanation:

y=mx+b

-5=-5m+b

-5=-1+b

b=-4

y=-5x-4

:D

Answer:

We accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.

Step-by-step explanation:

We have,

x = 1334

n = 1334 + 5663 = 6997

we have to:

p = x / n = 1334/6997 = 0.1907

The hypothesis is:

H0: P = 0.20

H1: P <0.20

P = 0.2 and Q = 1 - P = 0.8

the test statistic is:

Z = (p - P) / [(P * Q / n) ^ (1/2)]

replacing:

Z = (0.1907 - 0.20) / [(0.2 * 0.8 / 6997) ^ (1/2)]

Z = -1.96

now, the p-value is

P = 0.0250, from normal table, attached

Here p-value> 0.01, so we accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.

Answer:

4.2 kanban containers required

Step-by-step explanation:

Given the following information :

Waiting time = 0.25 days

Average peocessing time = 0.15 days / container

Daily usage (Demand rate) = 2000 per day

Container capacity = 200 wheels

Policy variable ( Alpha) = 5% = 0.05

Therefore, number of kanban containers needed for the wheels can be calculated using:

(Number of containers(x) * container size) = (Demand rate (waiting time + processing time)*(1 + alpha))

x * 200 = 2000(0.25 + 0.15)*(1 + 0.05)

200x = 2000(0.40)*(1.05)

200x = 840

x = 840 / 200

x = 4.2

4.2 kanban containers required

Answer:

4y+6

Step-by-step explanation:

Perimeter is adding up the outside

so.. there are y+y = 2y

y+3 + y+3 = 2y+6

2y+6 + 2y = 4y+6

Hope this helps :)

Answer:

Step-by-step explanation:

Answer: (2, 3) and (4,2) are not equal.

Step-by-step explanation:

An ordered pair is something like (x, y)

and two pairs (x1, y1) and (x2, y2) are only equal if x1 = x2 and y1 = y2

in this case, we have (2, 3) and (4, 2)

you can see that in the pairs the value of x is different, and the value of y is also different. Then we have that the pairs can not be equal.

Answer: 1 * 10^9

Step-by-step explanation:

1*10^9 = 1,000,000,000, which is the closest you can get.

Hope it helps <3

Answer:

6

Step-by-step explanation:

3(4 - 2)

Expand brackets.

3(4) + 3(-2)

12 + - 6

= 6

━━━━━━━☆☆━━━━━━━

▹ Answer

6

▹ Step-by-Step Explanation

Follow PEMDAS:

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

3(4 - 2)

3(2)

= 6

Hope this helps!

CloutAnswers ❁

Brainliest is greatly appreciated!

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Answer:

AC = 4 units

Step-by-step explanation:

[tex] OB = OC = 3 (Radii \:of \:same \:circle) \\

OA = OB + AB = 3 + 2 = 5\\

OA \perp AC.. (tangent\: \perp radius) \\

\therefore m\angle OCA = 90\degree \\[/tex]

By Pythagorean theorem:

[tex] AC^2 = OA^2 - OC^2 \\

= 5^2 - 3^2 \\

= 25-9\\

= 16\\

AC =\pm \sqrt{16}\\

AC = \pm 4[/tex]

Since, side of a triangle can't be negative.

Therefore, AC = 4 units