On a recent survey, 60% of those surveyed indicated that they preferred taking a trip to the beach over a trip to the mountains. If 810 people preferred a trip to the mountains, how many people were surveyed?

1) 486


2) 870


3) 1,350


4) 2,025

Answer:

The factors of given polynomial    x =-1 , -2 and x =3

Step-by-step explanation:

Step(i):-

Given the polynomial  

                    f(x) =  x³ - 7x -6

 put x =-1

               f(-1) = (-1 )³- 7(-1) - 6 = -1+7-6=0

(x+1) is a one factor

By using synthetic division

                   x³    x²      x      constant

     x=-1  ↓   1      0      -7        -6

             ↓   0     -1      1          6

                  1       -1      -6       0    

The polynomial    x² - x - 6

Step(ii):-

The factors ( x+1)(x² - x - 6 ) = 0

     x = -1 and x² - x - 6 =0

    x =-1    and  x² - 3x + 2 x - 6 =0

   x =-1     and  x (x -3) + 2( x-3) =0

   x =-1     and  (x+2)(x-3) =0

Final answer:-

The factors of given polynomial    x =-1 , -2 and x =3

Answer:

For figure 1:

Area of rectangle = 7x + 21

For figure 2:

Area of rectangle = [tex]\mathbf{p^2-9p }[/tex]

Step-by-step explanation:

We need to find area of rectangle

The formula used is: [tex]Area\:of\:rectangle=Length\times Width[/tex]

For figure 1:

Length = 7

Width = x+3

Putting values in formula and finding area of rectangle

[tex]Area\:of\:rectangle=Length\times Width\\Area\:of\:rectangle=7\times (x+3)\\Now,\: multiply\:7\:with\:terms\;inside\:the\:bracket\\Area\:of\:rectangle=7(x)+7(3)\\Area\:of\:rectangle=7x+21\\[/tex]

So, area of rectangle = 7x + 21

For figure 2:

Length = p

Width = p-9

Putting values in formula and finding area of rectangle

[tex]Area\:of\:rectangle=Length\times Width\\Area\:of\:rectangle=p\times (p-9)\\Now,\: multiply\:p\:with\:terms\;inside\:the\:bracket\\Area\:of\:rectangle=p(p)-p(9)\\Area\:of\:rectangle=p^2-9p\\[/tex]

So, area of rectangle = [tex]\mathbf{p^2-9p }[/tex]

Answer:

B) 267.5

Step-by-step explanation:

162.5+105=267.5

The requried, we cannot conclude that the mean cyclic time is greater than 3.5 hours for the new process of producing a type of novolac resin based on the given data.

To determine if we can conclude that the mean cyclic time is greater than 3.5 hours for the new process of producing a type of novolac resin, we need to perform a hypothesis test.

We can use a one-sample t-test to test the null hypothesis that the mean cyclic time is equal to 3.5 hours against the alternative hypothesis that the mean cyclic time is greater than 3.5 hours.

Using the given data, we can calculate the sample mean and sample standard deviation of the cyclic times for the six batches produced. The sample mean is:

x = (3.45 + 3.47 + 3.57 + 3.52 + 3.40 + 3.63) / 6
  = 3.50 hours

The sample standard deviation is:

[tex]s = \sqrt ((3.45 - 3.50)^2 + (3.47 - 3.50)^2 + (3.57 - 3.50)^2 + (3.52 - 3.50)^2 + (3.40 - 3.50)^2 + (3.63 - 3.50)^2) / (6 - 1)) }[/tex]
 = 0.086 hours

The test statistic for the one-sample t-test is:
[tex]t = ( \bar x-\mu) / (s / \sqrt(n))[/tex]

where μ is the hypothesized mean cyclic time, n is the sample size, and s is the sample standard deviation.

Substituting the given values, we get:

[tex]t = (3.50 - 3.5) / (0.086 / \sqrt(6))[/tex]
= 0

The degree of freedom for the t-test is n - 1 = 5.

Using a t-table or a calculator, we can find the critical value of t for a one-tailed test with α = 0.05 and 5 degrees of freedom to be 1.833.

Since the calculated t-value of 0 is less than the critical value of 1.833, we fail to reject the null hypothesis. Therefore, we cannot conclude that the mean cyclic time is greater than 3.5 hours based on the given data.

Therefore, we cannot conclude that the mean cyclic time is greater than 3.5 hours for the new process of producing a type of novolac resin based on the given data.

Learn more about the hypothesis here:

https://brainly.com/question/32606843

#SPJ12

Answer:

0,2 0r 2/2

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, you put it into slope intercept form

y = mx + b

m is the slope

b is the y intercept

y = 2/3 + 4

Answer:

x = 4.99°

Step-by-step explanation:

Reference angle = x

Opposite side to x = 20 cm

Hypotenuse = 230 cm

Applying trigonometric ratio formula, we would have the following equation:

[tex] sin(x) = \frac{Opp}{Hyp} [/tex]

Plug in the values

[tex] sin(x) = \frac{20}{230} [/tex]

[tex] x = sin^{-1}(\frac{20}{230}) [/tex]

x = 4.99° (approximated to nearest hundredth)

Answer:

(x, y)  -->   (x + 14, y + 8)

Step-by-step explanation:

Look at 1 original point and its corresponding translated point.

Let's look at F and F'.

To go from F to F', you need to go right in x 14 units.

Then you need to go up in y 8 units.

The translation rule is to add 14 to x and 8 to y.

(x, y)  -->   (x + 14, y + 8)

Answer:

fhddffhfdjdfgjmtgfjn

Step-by-step explanation:

fgngng ndgngfnngfngfn

Answer:

Whats your question?

Step-by-step explanation:

Answer:

1.2 years

Step-by-step explanation:

The value of a certain account after t years is given by :

B = 600 × 1.2t dollars ....(1)

We need to find how long will it take for the value of the account to increase to $900 i.e. we need to find the value of t.

Put B = $900 in equation (1).

[tex]900=600\times 1.2t\\\\t=\dfrac{900}{600\times 1.2}\\\\t=1.2\ \text{years }[/tex]

So, it will take 1.2 years of the account to increase to $900.

Answer:

for every 3 trombone players in the band there will be 5 trumpet players in the band

Step-by-step explanation:

example 6 trombone = 10 trumpet

Answer:

HI sorry for the late answer:>

Step-by-step explanation:

Answer:

it is indeed HI

Step-by-step explanation:

Answer:

3 plus 3

Step-by-step explanation: its in the parenthesis

Answer:

You have to add 3 and 3 first. That has to be done first.

Answer:

[tex]x<12[/tex] or [tex]x > 27[/tex]

Step-by-step explanation:

Given

[tex]Lower\ Bound = 20[/tex]

[tex]Upper\ Bound = 35[/tex]

[tex]Height = 8[/tex]

Required

Represent as a compound inequality

Let the pole height be x:

So, the combine height of the pole and the sign is [tex]x + 8[/tex]

The height must be less than 20ft.

So, we have:

[tex]x + 8 < 20[/tex]

Subtract 8 from both sides

[tex]x + 8 - 8 < 20 - 8[/tex]

[tex]x < 20 - 8[/tex]

[tex]x<12[/tex]

or The height must be less than35ft

So, we have:

[tex]x + 8 > 35[/tex]

Subtract 8 from both sides

[tex]x + 8 - 8 > 35 - 8[/tex]

[tex]x > 35 - 8[/tex]

[tex]x > 27[/tex]

So, the compound inequality is:

[tex]x<12[/tex] or [tex]x > 27[/tex]

Answer:

Slope= -2

Step-by-step explanation:

Answer:

40 for $3

Step-by-step explanation:

you get an extra 18 for $1:00 here if you got 2 of each 22+22 is 44 for $4 40+40 is 80 for $6

hope this helps

The answer is C hope it helps

Answer:

Step-by-step explanation:

so these two lines cross at some point.. and they want to know the y point at which they cross... sooo..

solve them as a system to find the points that are common to both

Eq. 1)  5x -2y = 16

Eq. 2) -4x+6y=-15

i'll use the elimination method as these equations "lend" themselves to that way.. they are easy to solve that way .. in other words..

multiply Eq. 1 by 3  the add Eq. 2 .. to it... add the terms as columns....

    15x-6y = 48

+ ( -4x+6y=-15)

=    11x+ 0y =33

x=3    

nice, now plug 3 in for x in one of the Eq.   try Eq. 1

5(3)-2y=16

15-2y=16

-2y =1

y = [tex]-\frac{1}{2}[/tex]

since we're looking for the y coordinate...  that's your answer [tex]-\frac{1}{2}[/tex]

Answer:

$5.8

Step-by-step explanation:

0.3 + 0.5 + 5 = 5.8

Answer:

24 divided by 6= 4

Step-by-step explanation:

U

Answer:

C

Step-by-step explanation:

Answer: You can multiply both the numerator and the denominator by the same root, that will get rid of the root in the denominator.

Hoped this was helpful!

Answer:

The middle one

Step-by-step explanation:

3/4=75%

Answer:

Muhammed

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

Using PEMDAS, we do what inside the parentheses first.

Multiplication before subtraction:

9-6 = 3.

Finally, 3^2 = 9

Answer : The average rate of change between 1 year and 4 years  of age is 7.33 lbs per year.

Step-by-step explanation :

As we know that the average rate of change between two input values is the total change of the output values divided by the change in the input values.

From the table, we conclude that:

The weight of 1 year of age = 20 lbs

The weight of 4 years of age = 42 lbs

Now we have to determine the average rate of change between 1 year and 4 years  of age.

The input (years) has changed by = 4 years - 1 year = 3 years

The output has changed by = 42 lbs - 20 lbs = 22 lbs

Average rate of change = Output ÷ Input

Average rate of change = [tex]\frac{22\text{ lbs}}{3\text{ years}}[/tex]

Average rate of change = 7.33 lbs per year

Therefore, the average rate of change between 1 year and 4 years  of age is 7.33 lbs per year.

Answer: 9.4

Step-by-step explanation:

if you see on the screenshot if you draw a line between the 2 it mesures 9.4

Answer:

9.4

Step-by-step explanation:

Did the diagnosic

Answer:

103 ft.

Step-by-step explanation:

Answer:

TrIaNgLe

Step-by-step explanation: