Find the range of the following data set.
11,5, 1, 11, 12
01
1.
017

Answer:

[tex]y-x = 16[/tex]

Step-by-step explanation:

Given

Set 1: (9,5,y,2,x)

Set 2: (8,x,4,1,3)

Required

(y - x)

First the mean values of set 1 and set 2 has to be calculated

For set 1

[tex]Mean _1 = \frac{(9+5+y+2+x)}{5}[/tex]

Collect like terms

[tex]Mean _1 = \frac{9+5+2+y+x}{5}[/tex]

[tex]Mean _1 = \frac{16+ y+x}{5}[/tex]

For set 2

[tex]Mean _2 = \frac{(8+x+4+1+3)}{5}[/tex]

Collect like terms

[tex]Mean _2 = \frac{8+4+1+3+x}{5}[/tex]

[tex]Mean _2= \frac{16+ x}{5}[/tex]

Given that the mean of set 1 is twice the mean of set 2;

[tex]Mean_1 = 2Mean_2[/tex]

[tex]\frac{16+ y+x}{5} =2 * \frac{16+x}{5}[/tex]

Multiply both sided by 5

[tex]5 * \frac{16+ y+x}{5} = 5 * 2 * \frac{16+x}{5}[/tex]

[tex]16+ y+x = 2 * (16+x)[/tex]

Open bracket

[tex]16+ y+x = 32 + 2x[/tex]

Subtract 16 from both sides

[tex]16+ y+x- 16 = 32 + 2x - 16[/tex]

[tex]16 - 16 + y+x = 32 - 16 + 2x[/tex]

[tex]y+x = 16 + 2x[/tex]

Subtract 2x from both sides

[tex]y+x-2x = 16 + 2x-2x[/tex]

[tex]y-x = 16[/tex]

Answer: D. 5

Step-by-step explanation:

Typically when you have exponents in a form like this, you would multiply 1/3 with 3 to get 1/3 * 3/1. The threes cancel out and you're left with an exponent of 1. And 5 to the 1 power is 5.

Answer:

So if you multiply you get 3*2 square rooted of 2-2*3*7 =

6 square rooted of -40

That is the most simplified I hope

A) $400

B) $800

C) 400*X

D) revenue=400x

Answer: 525

Step-by-step explanation:

3 km =30 hm

35hm*15=525

Answer:

$70,000

Step-by-step explanation:

Profit = Revenue - Costs

x = 120,000 - 50,000

x = 70,000

Answer:

x=2           x =8

Step-by-step explanation:

(x-2)(x-8)=0

Using the zero product property

x-2 = 0    x-8 = 0

x=2           x =8

Answer:x = 2 and x = 8

Step-by-step explanation:

( 2 - 2)( 8 - 8)

(0)(0)

=0

Answer: D  180 degrees rotation about the origin.then a dilation by a scale factor of one-third.

Step-by-step explanation:

A( -9,3)    B(-9,6)  C (0,3)  

After a rotation of 180 degrees you will have the new points as

A (9,-3)   B( 9,-6)  C (0, -3)

The you after dilating it by a scale factor of 1/3

you will get the coordinates

A ( 3,-1)  B( 3,-2)   C(0,-1)  

which match is what was given in the question.

Answer:

a 180° rotation about the origin, then a dilation by a scale factor of One-third

Step-by-step explanation:

took the test

Answer:

Answere is X= 8

Step-by-step explanation:

Use sine law

Sin(angle) = Opposite/ Hypotenuse

Sin (30) = 4 /X

X = 4 / sin (30)

X = 8

Answer:

Step-by-step explanation:

Answer:

B) (0,2)

Step-by-step explanation:

2 ≥ 2(0)-1

2 ≥ 0-1

2 ≥ -1

Answer:

2 2/5

Step-by-step explanation:

12/5

5 goes into 12 2 times

12 - 5*2

12-10 =2

There is 2 left over.  This goes over the denominator

2 2/5

Answer: ( 77.27 , 83.93)

Therefore at 95% confidence/prediction interval is

= ( 77.27 , 83.93)

Step-by-step explanation:

Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.

The confidence interval of a statistical data can be written as.

x+/-zr/√n

Given that;

Mean x = 80.6 words per minute

Standard deviation r = 7.2

Number of samples n = 18

Confidence interval = 95%

z(at 95% confidence) = 1.96

Substituting the values we have;

80.6+/-1.96(7.2/√18)

80.6+/-1.96(1.697056274847)

80.6 +/- 3.33

= ( 77.27 , 83.93)

Therefore at 95% confidence/prediction interval is

= ( 77.27 , 83.93)

Answer:

The interest earned is $421.2.

Step-by-step explanation:

This is a simple interest problem.

The simple interest formula is given by:

[tex]E = P*I*t[/tex]

In which E is the amount of interest earned, P is the principal(the initial amount of money), I is the interest rate(yearly, as a decimal) and t is the time.

In this question:

[tex]P = 2880, I = 0.045, t = 3 + \frac{1}{4} = 3.25[/tex]

So

[tex]E = P*I*t[/tex]

[tex]E = 2880*0.045*3.25[/tex]

[tex]E = 421.2[/tex]

The interest earned is $421.2.

Answer:

a) the graph has a minimum

b) (3, 0)

c) x=3

d) N/A

c) (0, 9)

*forgot how to solve for roots

Step-by-step explanation:

Desmos

Answer:

line s and t would not meet even if you extend them and also they have the same slope and gradient

Answer:

4/25

Step-by-step explanation:

The probability the first spin lands on gray is 8/10 = 4/5.

The probability the second spin lands on blue is 2/10 = 1/5.

The probability of both events is 4/5 × 1/5 = 4/25.

Answer:

Step-by-step explanation:

A=πr^2

But A=88/63

88/63=πr^2

88/63π=r^2

√88/63π=r

Answer:

160 units and $6400

Step-by-step explanation:

We have that the cost per x unit is: 20 * x + 0.25 * x ^ 2

the price per unit is 100, therefore revenue for each unit would be 100 * x

However:

profit = revenue - cost

p (x) = 100 * x - 20 * x - 0.25 * x ^ 2

for the maximum value profit we must derive and equal 0:

p '(x) = 100 - 20 - 0.5 * x

0 = 80 - 0.5 * x

0.5 * x = 80

x = 80 / 0.5

x = 160

Therefore, the maximum profit occurs when there are 160 units, replacing we have:

p (x) = 100 * 160 - 20 * 160 - 0.25 * 160 ^ 2

p (x) = 6400

that is to say that the $ 6400 is the maximum profit.

Answer:

9

Step-by-step explanation:

Just dont even try with these use a calculator every time. even if you're confident

Answer:

9

Step-by-step explanation:

1+2 is the first equation to do, which equals 3. Then from the beginning we have 6 ÷2 and as there is no sign from this to the brackets it will be multiply. 6÷2 is 3. multiply it by 3 (what the brackets equal) and the answer is 9

Answer:

The coefficients for the quadratic regression curve are

a = (-2/3) = -0.6667

b = (11/3) = 3.6667

c = 1 = 1.0000

y(x) = -0.6667x² + 3.6667x + 1.0000

Step-by-step explanation:

Quadratic regression curve gives a general expression of

y = ax² + bx + c

And the points on the curve include

(1, 4), (3, 6), (4, 5), (5, 2)

Taking the points one at a time and substituting them into general quadratic curve expression

(1, 4), x = 1, y = 4

y = ax² + bx + c

4 = a + b + c (eqn 1)

(3, 6), x = 3, y = 6

6 = a(3²) + b(3) + c

6 = 9a + 3b + c (eqn 2)

(4, 5), x = 4, y = 5

5 = a(4²) + b(4) + c

5 = 16a + 4b + c (eqn 3)

Combining the 3 equations and solving simultaneously

4 = a + b + c

6 = 9a + 3b + c

5 = 16a + 4b + c

From eqn 1, c = 4 - a - b

Substituting this into eqn 2 and 3, we have

6 = 9a + 3b + 4 - a - b

2 = 8a + 2b (*)

5 = 16a + 4b + 4 - a - b

1 = 15a + 3b (**)

8a + 2b = 2

15a + 3b = 1

a = (-2/3), b = (11/3)

c = 4 - a - b

c = 4 - (-2/3) - (11/3)

c = 1

Hence, the coefficients for the quadratic regression curve are

a = (-2/3) = -0.6667

b = (11/3) = 3.6667

c = 1 = 1.0000

y(x) = -0.6667x² + 3.6667x + 1.0000

Hope this Helps!!!

Answer:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13        for the function.

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4         for the inverse.

Step-by-step explanation:

we know that if we have the function f(x) = y, then the inverse of f(x) (let's call it g(x)) is such that:

g(y) = x.

now we have

y=4x-3

y=(1/4)x+3/4

The only table that works for our first function is:

x: -5,  -3,   0,  1,  4

y:-23, -15, -3, 1, 13

You can see this by replacing the values of x and see if the value of y also coincides.

Then, using the fact that the other table must be for the inverse, we should se a table with the same values, but where the values of x and y are interchanged.

The second table is that one:

x:-23, -15, -3, 1, 13

y: -5,   -3,  0,  1,  4

Answer: B and D

x:-23, -15, -3, 1, 13

y:-5, -3, 0, 1, 4

x:-5, -3, 0, 1, 4

y:-23, -15, -3, 1, 13

Step-by-step explanation:

Answer:

9.52% probability of getting both candies green

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

The order in which the candies are selected is not important. They are also selected without replacement. So we use the combinations formula to solve this question.

Combinations formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

Find the probability of getting both candies green

Desired outcomes:

2 green, from a set of 5. So

[tex]D = C_{5,2} = \frac{5!}{2!3!} = 10[/tex]

Total outcomes:

2 from a set of 4+5+6 = 15. So

[tex]T = C_{15,2} = \frac{15!}{2!13!} = 105[/tex]

Probability:

[tex]p = \frac{D}{T} = \frac{10}{105} = 0.0952[/tex]

9.52% probability of getting both candies green

Answer:

30 years old

Step-by-step explanation:

Joe's age can be set to x. Since Billy is twice as old as Joe, his age can be set to 2x. They add up to 45. You can set up an equation, 2x+x=45.

Simplify the equation.

3x=45, x=15

Joe is 15. Billy is 2(15)=30.

Answer:

The total repair cost was around $300 .

Step-by-step explanation:

I wasn't sure when you were saying to round, so here are two options.

(For rounding at the end) :

82+157+58 = 297

Rounds to 300.

(For rounding as he's adding everything up) :

80+160+60= 300.

So either way it's 300!

Hope this helped!

Answer:

A is correct Please brainliest me

Thus, also saying that it is equivalent.

Step-by-step explanation:

The expression stated- (3m+1-m)

It also states to give a equal amount

What is equalevent expression?- Equivalent expression are those expression  that looks different but are same.

For example, 2+2 is 4 and 1 plus 3 is 4

it is different expression but the same answer.

The Expression- 3m+1-m

Simplify. How?- By adding LIKE terms.

Here- 3m+ 1 - m = (3-1) m + 1

see the same.

To conclude, 3-1) m + 1  = 2m + 1

If you’d wanna write in another way, it would be 2m + 1 can be written as m + m + 2 - 1

so a is correct

Answer:

[tex]5[/tex]

Step-by-step explanation:

Let [tex]x[/tex] be the number of tuba players.

We are given that the number of saxophone players is one less than twice the number of tuba players.

There are 9 saxophone players.

[tex]9 = 2 x-1[/tex]

[tex]9+1=2x[/tex]

[tex]10=2x[/tex]

[tex]10 \div 2=x[/tex]

[tex]5=x[/tex]

Answer:

Yes, we have reason to believe that fewer than one-fifth are heated by oil.

Step-by-step explanation:

A one-sample proportion test is to be performed to determine whether fewer than one-fifth of the homes in a certain city are heated by oil.

The hypothesis can be defined as follows:

H₀: The proportion of homes in a certain city that are heated by oil is not less than one-fifth, i.e. p ≥ 0.20.  

Hₐ: The proportion of homes in a certain city that are heated by oil is less than one-fifth, i.e. p < 0.20.

The information provided is:

n = 1000

x = 136

α = 0.05

Compute the sample proportion as follows:

[tex]\hat p=\frac{x}{n}=\frac{136}{1000}=0.136[/tex]

Compute the test statistic as follows:

[tex]z=\frac{\hat p-p}{\sqrt{\frac{p(1-p)}{n}}}[/tex]

  [tex]=\frac{0.136-0.20}{\sqrt{\frac{0.136(1-0.136)}{1000}}}\\\\=-5.9041\\\\\approx -5.90[/tex]

The test statistic value is, -5.90.

Decision rule:

Reject the null hypothesis if the p-value of the test is less than the significance level.

Compute the p-value as follows:

[tex]p-value=P(Z<-5.90)\\\\=1-P(Z<5.90)\\\\=1-(\approx 1)\\\\=0[/tex]

The p-value of the test is, 0.

p-value = 0 < α = 0.05

The null hypothesis will be rejected at 5% level of significance.

Conclusion:

The proportion of homes in a certain city that are heated by oil is less than one-fifth.

Answer:

y^6/x^2

Step-by-step explanation:

(y^3/2x^-1/2)^4= y^(4*3/2)x^(-1/2*4)=y^6x^-2= y^6/x^2