Find the arc length and area of a sector with radius R =60 inches and central angle equals 30° round your answer to the nearest hundredth

Answer:

Answers are below.

Step-by-step explanation:

x2 - 2 x = 4 x + 12

x2+ 12 x = 0

x2 + 8 = 0

9x2 + 6 x - 3 = 0

These are all quadratic equations because they have x2 in all of them.

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Answer:

x^2 - 2x = 4x + 1

2x^2 + 12x = 0

9x^2 + 6x - 3 = 0.

Step-by-step explanation:

A quadratic equation will contain a term with an exponent of 2 as the highest exponent.

Answer:x=17 y=10

Step-by-step explanation:

Answer:

Central graph

Step-by-step explanation:

When a function has a negative rate of change, it means that as the x value increases, the y value decreases. The only graph that does this continuously is the central one. Hope this helps!

The calculated product of the numbers is 1000

The graph with a negative rate to be (c)

From the question, we have the following parameters that can be used in our computation:

100 times 10

When represented as an equation, we have

100 times 10 = 100 * 10

Evaluate the products

So, we have the following result

100 times 10 = 1000

Next, we interpret the graph

From the graphs, we have the graph with a negative rate to be (c)

Using the above as a guide, we have the following:

the result is 19/125

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Answer:

you need to include a picture of all the graphs

Answer:

24x - 17y + 8z

Step-by-step explanation:

Answer:

An angle with a positive measure will have rotated counterclockwise, or doesn't cross over itself at the start of the rotation. As you can see, the only graph that initially turns counterclockwise is the first graph.

Step-by-step explanation:

Answer:

x=8

Step-by-step explanation:

[tex]square \: both \: side \\ \sqrt{ {x}^{2} } = \sqrt{64 } \: \: \: \\ \\x = 8[/tex]

Question:

Which represents [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction?

[tex]2+ \frac{3}{6}[/tex]

[tex]3 + \frac{3}{6}[/tex]

[tex]3+ \frac{5}{6}[/tex]

[tex]4+ \frac{1}{6}[/tex]

Answer:

[tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]

Step-by-step explanation:

Given

Mixed Fraction:  [tex]2 \frac{3}{6}[/tex]

Required

Express as the sum of a whole number and fraction.

Given that [tex]2 \frac{3}{6}[/tex]  is a mixed fraction; it can be converted to the sum of a whole number and a fraction by following the steps below.

1. Convert the mixed fraction to improper fraction

[tex]2 \frac{3}{6} = \frac{(6 * 2 + 3)}{6}[/tex]

2. Split the numerator

[tex]2 \frac{3}{6} = \frac{((6 * 2) + (3))}{6}[/tex]

3. Split fraction to 2

[tex]2 \frac{3}{6} = \frac{(6 * 2)}{6} +\frac{(3)}{6}[/tex]

Simplify

[tex]2 \frac{3}{6} = \frac{(12)}{6} +\frac{(3)}{6}[/tex]

[tex]2 \frac{3}{6} = 2 + \frac{3}{6}[/tex]

Hence, [tex]2 \frac{3}{6}[/tex] as the sum of a whole number and a fraction is equivalent to [tex]2+ \frac{3}{6}[/tex]

Answer:

90 copies

Step-by-step explanation:

24*3= 72

1/2*24= 12 for 30 seconds

1/2*6= 6 for 15 seconds

45/15=3

72+18= 90

Answer:

  m = 1 + 2log(x)/log(y)

Step-by-step explanation:

Taking logarithms, you have ...

  log(x) +m·log(y) = log(y) +3log(x)

  m·log(y) = log(y) +2·log(x) . . . . subtract log(x)

  m = (log(y) +2·log(x))/log(y) . . . divide by the coefficient of m

  m = 1 +2·log(x)/log(y) . . . . . . . simplify a bit*

_____

* The "simplified" form will depend on your preference. Here, I like the integer 1 brought out because most logs are irrational. The result may be very slightly more accurate if we add 1, rather than log(y)/log(y)--depending on your calculator.

Answer:

D=A^-1

Step-by-step explanation:

Given that A is invertible and matrix D satisfies AD=I

Where I is an identity matrix

D is the inverse of A

Multiply both sides of AD=I by A^-1

A^-1(.AD) =A^-1 I

A^-1 .A=I

Therefore D=A^-1

Answer:

21 days.

Step-by-step explanation:

You just divide the total number of miles by miles traveled a day.

8925÷425=21

It will takes 21 days.

Answer:21 days

Step-by-step explanation:

Answer: 1,694

Step-by-step explanation: 11(11d + 3z + 8) d = 10 and z = 12

                                             121d + 33z + 88

                                             121(10) + 33(12) + 88

                                             1210 + 396 + 88

                                             1,694

Answer:

The probability of winning a jackpot is [tex]P = 0.000003[/tex]

The probability of winning the pick 5 game  is  [tex]P_a = 0.00001[/tex]

The earning of the lottery organisation if the game were to be runed for no profit is  [tex]x =[/tex]$10 000

Step-by-step explanation:

From the question

    The sample size is  n= 37

    The number of selection is  [tex]r = 5[/tex]

Now the number of way by which these five selection can be made is mathematically represented as

         [tex]\left n} \atop {}} \right.C_r = \frac{n!}{(n-r)!r! }[/tex]

Now  substituting values

         [tex]\left n} \atop {}} \right.C_r = \frac{37!}{(37-5)!5! }[/tex]

          [tex]\left n} \atop {}} \right.C_r = 333333.3[/tex]

Now the probability of winning  a jackpot from any of the way of selecting 5 whole number from 37 is mathematically evaluated as

         [tex]P = \frac{1}{333333.3}[/tex]

        [tex]P = 0.000003[/tex]

Now the number of ways of selecting 5 whole number from 0 to 9 with repetition is mathematically evaluated as

        [tex]k = 10^5[/tex]

Now the probability of winning the game is

      [tex]P_a = \frac{1}{10^5}[/tex]

      [tex]P_a = 0.00001[/tex]

We are told that for a $1 ticket that the pick 5 game returns $50 , 000

  Generally the expected value is mathematically represented as

           [tex]E(X) = x * P(X =x )[/tex]

In this question the expected value is  $1

So

          [tex]1 = x * 0.00001[/tex]

So      [tex]x = \frac{1}{0.00001}[/tex]

        [tex]x =[/tex]$10 000

Answer:

20

Step-by-step explanation:

The current area is 120(80)=9600 and he want to expand it by 4400 so that the new area will be 9600+4400=14000 

14000=(120+x)(80+x) 

14000=9600+200x+x^2 

x^2+200x-4400=0 

x^2-20x+220x-4400=0 

x(x-20)+220(x-20)=0 

(x+220)(x-20)=0, since x is an increase it must be greater than zero so 

x=20ft 

(120+20)(80+20)=14000ft^2

Answer:

There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.

Test statistic t=-1.8974

P-value = 0.0326

Step-by-step explanation:

The question is incomplete:

"In Hamilton County, Ohio the mean number of days needed to sell a home is 86 days (Cincinnati Multiple Listing Service, April, 2012). Data for the sale of 40 homes in a nearby county showed a sample mean of 80 days with a sample standard deviation of 20 days. Conduct a hypothesis test to determine whether the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county. Round your answer to four decimal places."

This is a hypothesis test for the population mean.

The claim is that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.

Then, the null and alternative hypothesis are:

[tex]H_0: \mu=86\\\\H_a:\mu< 86[/tex]

The significance level is 0.05.

The sample has a size n=40.

The sample mean is M=80.

As the standard deviation of the population is not known, we estimate it with the sample standard deviation, that has a value of s=20.

The estimated standard error of the mean is computed using the formula:

[tex]s_M=\dfrac{s}{\sqrt{n}}=\dfrac{20}{\sqrt{40}}=3.1623[/tex]

Then, we can calculate the t-statistic as:

[tex]t=\dfrac{M-\mu}{s/\sqrt{n}}=\dfrac{80-86}{3.1623}=\dfrac{-6}{3.1623}=-1.8974[/tex]

The degrees of freedom for this sample size are:

[tex]df=n-1=40-1=39[/tex]

This test is a left-tailed test, with 39 degrees of freedom and t=-1.8974, so the P-value for this test is calculated as (using a t-table):

[tex]\text{P-value}=P(t<-1.8974)=0.0326[/tex]

As the P-value (0.0326) is smaller than the significance level (0.05), the effect is  significant.

The null hypothesis is rejected.

There is enough evidence to support the claim that the mean number of days until a home is sold is different than the Hamilton county mean of 86 days in the nearby county.

Answer:

54000-65000

Step-by-step explanation:

round the numbers first down to 1200 and 45, and multiply, then round up for the larger, like 1300 and 50 to get your answer.

Answer:

(a) 9.18% of people have an intraocular pressure lower than 12 mm Hg.

(b) 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Step-by-step explanation:

We are given that the distribution of intraocular pressure in the general population is approximately normal with mean 16 mm Hg and standard deviation 3 mm Hg.

Let X = intraocular pressure in the general population

So, X ~ Normal([tex]\mu=16,\sigma^{2} = 3^{2}[/tex])

The z score probability distribution for normal distribution is given by;

                             Z  =  [tex]\frac{ X-\mu}{\sigma } }[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = population mean = 16 mm Hg

           [tex]\sigma[/tex] = standard deviation = 3 mm Hg

(a) Percentage of people have an intraocular pressure lower than 12 mm Hg is given by = P(X < 12 mm Hg)

       P(X < 12) = P( [tex]\frac{ X-\mu}{\sigma } }[/tex] < [tex]\frac{ 12-16}{3 } }[/tex] ) = P(Z < -1.33) = 1 - P(Z [tex]\leq[/tex] 1.33)

                                                   = 1 - 0.9082 = 0.0918 or 9.18%

The above probability is calculated by looking at the value of x = 1.33 in the z table which has an area of 0.9082.

(b) We have to find that 80% of adults in the general population have an intraocular pressure that is greater than how many mm Hg, that means;

        P(X > x) = 0.80      {where x is the required intraocular pressure}

        P( [tex]\frac{ X-\mu}{\sigma } }[/tex] > [tex]\frac{ x-16}{3 } }[/tex] ) = 0.80

        P(Z > [tex]\frac{ x-16}{3 } }[/tex] ) = 0.80

Now, in the z table the critical value of z which represents the top 80% of the area is given as -0.842, that is;

                           [tex]\frac{ x-16}{3 } } = -0.842[/tex]

                           [tex]x -16 = -0.842 \times 3[/tex]

                           x = 16 - 2.53 = 13.47 mm Hg

Therefore, 80% of adults in the general population have an intraocular pressure that is greater than 13.47 mm Hg.

Answer:

i and iii) In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4

ii) [tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]

And using the normal standard table or excel we got:

[tex]P(z<-2.25)=0.0122[/tex]

iv) [tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]

And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:

[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]

Step-by-step explanation:

Let X the random variable that represent amount of time people spend exercising in a given week, and for this case we know the distribution for X is given by:

[tex]X \sim N(3.8,0.8)[/tex]  

Where [tex]\mu=3.8[/tex] and [tex]\sigma=0.8[/tex]

Part i and iii

In the figure attached part a we have the illustration for the area required for the probability of less than 2 hours and in b the illustration for the probability that X would be between 2 and 4

Part ii

We are interested on this probability:

[tex]P(X<2)[/tex]

We can use the z score formula given by:

[tex]z=\frac{x-\mu}{\sigma}[/tex]

Using this formula we have:

[tex]P(X<2)=P(\frac{X-\mu}{\sigma}<\frac{2-\mu}{\sigma})=P(Z<\frac{2-3.8}{0.8})=P(z<-2.25)[/tex]

And using the normal standard table or excel we got:

[tex]P(z<-2.25)=0.0122[/tex]

Part iv

We want this probability:

[tex]P(2<X<4)[/tex]

Using the z score formula we got:

[tex]P(2<X<4)=P(\frac{2-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{4-\mu}{\sigma})=P(\frac{2-3.8}{0.8}<Z<\frac{4-3.8}{0.8})=P(-2.25<z<0.25)[/tex]

And we can find the probability with the following difference and usint the normal standard distirbution or excel and we got:

[tex]P(-2.25<z<0.25)=P(z<0.25)-P(z<-2.25)= 0.5987-0.0122= 0.5865[/tex]

Answer:

the savings is 6000

Step-by-step explanation:

We are told that the ratio of savings to expenditure is 2: 8, that is, that person saves 2 when he spends 8.

They tell us to find the savings when the cost is 24,000, so we are left with:

24000 * 2/8 = 6000

which means that when 24000 are spent the savings is 6000

Answer:

23 years.

Step-by-step explanation:

It is given that the initial price of painting is $150 and its values increasing by 3% annually.

We need to find how many years will it take until it is doubled in value.

The value of painting after t years is given by

[tex]y=150(1+0.03)^t[/tex]

[tex]y=150(1.03)^t[/tex]

The value of painting after double is 300. Substitute y=300.

[tex]300=150(1.03)^t[/tex]

Divide both sides by 150.

[tex]2=(1.03)^t[/tex]

Taking log both sides.

[tex]\log 2=\log (1.03)^t[/tex]

[tex]\log 2=t\log (1.03)[/tex]

[tex]t=\dfrac{\log 2}{\log (1.03)}[/tex]

[tex]t=23.44977[/tex]

[tex]t\approx 23[/tex]

Therefore, the required number of years is 23.

ANSWER: It is false that All equations are identities, but not all identities are equations, as all identities are equations, but only some equations are identities.

HOPE THIS HELP

Isolate the variable by dividing each side by factors that don't contain the variable.

Exact Form:

x=5 (over)/6

Decimal Form:

x=0.8¯3

(Hopefully this helped you solve the problem.)

Answer:

5

Step-by-step explanation:

47-5=42

42/6=7

5/6 is the number we have to  subtract from 47/6 to make 7

Two or more expressions with an Equal sign is called as Equation.

We have to find the number when we need to subtract from 47/6 to make 7.

Let the unknown number be x

47/6-x=7

Add x-7 on both the sides

47/6-7=x

Take LCM as 6

(47-42)/6=x

When 42 is subtracted from 47 we get 5.

5/6=x

Hence, 5/6 we have to  subtract from 47/6 to make 7

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Answer:

36 degrees

Step-by-step explanation:

This problem can be solved with the help  concept of sum of angles of any triangle.

sum of angles of any triangle is 180.

Given angular value of triangle ABC is A=2x B=6x C=2x

Thus sum of A, B , C is 180

A+B+C = 180 plug in th evalue of angle A, B and C

=>2x+6x+2x = 180

=> 10x=180

=> x = 180/10 = 18

Value of angle C in terms of x is 2x

Thus angular value of angle c = 2*18 = 36 degrees.

Answer:

Equation : y = -0.9x − 1.5

Step-by-step explanation:

Slope is rise over run, 7 over 8

-7/8 = -0.875, round to nearest tenth

-0.875 = -0.9

y- intercept is the point that crosses the y-axis,

the line crosses the y-axis at -1.5

Answer:

15

Step-by-step explanation:

1/6 of 90 is 15

The number of times 3 should be selected is 45/2.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We know that;

Number of spins= 90

Number of selected= 3

Now,

If the spinner has 4 equal sections and one of them has a 3, then the probability of landing on 3 is 1/4.

To find the expected number of times that the spinner lands on 3 in 90 spins, we need to multiply 1/4 by 90.

=1/4 * 90

=45/2

Therefore, by algebra the answer will be 45/2.

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Answer: 78

Step-by-step explanation: Remember every triangle ads up to a total of 180 degrees. You just have to make sure that it adds up to 180