A polling company is trying to estimate the percentage of adults that consider themselves happy. A confidence interval based on a sample size of 360 has a larger than desired margin of error. The company wants to conduct another poll and obtain another confidence interval of the same level but reduce the error to one-third the size of the original sample. How many adults should they now interview

1)

y = x + 4

5x + 3y = -4

5x + 3(x + 4) = -4

5x + 3x + 12 = -4

8x + 12 = -4

8x = -4 -12

8x = -16

x = -2

substitute x into the equation

y = -2 + 4

y = 2

Answers : x = -2 , y = 2

Answer:

1) [tex]{y,x}={2,-2}[/tex]

2) [tex]{y,x} = {-4,-2}[/tex]

Step-by-step explanation:

1) [tex]y=x+4 \\ 5x+3y=-4[/tex] <---------- given linear equations

Equations Simplified or Rearranged :

[tex]y - x = 4 \\3y + 5x = -4[/tex]

Graphic Representation of the Equations : PICTURE #1

[tex]x + y = 4 \\5x + 3y = -4[/tex]

Solve by Substitution :

// Solve equation [1] for the variable  y

[tex][1] y = x + 4[/tex]

// Plug this in for variable  y  in equation [2]

[tex]3*(x +4) + 5x = -4 \\ [2] 8x = -16[/tex]

// Solve equation [2] for the variable  x

[tex]8x = - 16 x = - 2[/tex]

// By now we know this much :

[tex]y = x+4\\ x = -2[/tex]

// Use the  x  value to solve for  y

[tex]y = (-2)+4 = 2[/tex]

Solution :

[tex]{y,x} = {2,-2}[/tex]

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

2) [tex]y=2x \\-8x-2y=24[/tex] <----- linear equations given

Equations Simplified or Rearranged :

[tex]y - 2x = 0 \\ -2y - 8x = 24[/tex]

Graphic Representation of the Equations : PICTURE #2

[tex]-2x + y = 0 \\\\-8x - 2y = 24[/tex]

Solve by Substitution :

// Solve equation [1] for the variable  y

[tex][1] y = 2x[/tex]

// Plug this in for variable  y  in equation [2]

[tex][2] -2*(2x) - 8x = 24\\ [2] - 12x = 24[/tex]

// Solve equation [2] for the variable  x

[tex][2] 12x = - 24 [2] x = - 2[/tex]

// By now we know this much :

[tex]y = 2x \\ x = -2[/tex]

// Use the  x  value to solve for  y

[tex]y = 2(-2) = -4[/tex]

Solution :

[tex]{y,x} = {-4,-2}[/tex]

The order of the steps to solve the provided logarithmic equation is arranged as,

[tex](x^2 - 15) =(2x)[/tex]

[tex]x^2 +2x-15=0[/tex]

[tex](x-5)(x+3)=0[/tex]

[tex]x-5=0,x+3=0[/tex]

Potential solution are -3 and 5.

The exponent of the log rule says that the raising a logarithm with a number to its base is equal to the number.

When the base is common ion equality equation, then the two log values can be compares using exponent rule of logarithm.

The given logarithmic equation in the problem is,

[tex]\log(x^2 - 15) = \log(2x)[/tex]

The order of solution of the above expression,

As the base is common, then the two log values can be compares using  exponent rule of logarithm.

[tex](x^2 - 15) =(2x)[/tex]

Bring all the terms, one side of the expression as,

[tex]x^2 +2x-15=0[/tex]

Find the factors of the above quadratic equation using the split the middle term method as,

[tex]x^2 -5x+3x-15=0\\x(x-5)+3(x-5)=0\\(x-5)(x+3)=0[/tex]

Equate the factors to the zero to find out the values of x,

[tex]x-5=0,x+3=0[/tex]

The potential solution are,

[tex]x=5,-3[/tex]

Thus, the order of the steps to solve the provided logarithmic equation is arranged as,

[tex](x^2 - 15) =(2x)[/tex]

[tex]x^2 +2x-15=0[/tex]

[tex](x-5)(x+3)=0[/tex]

[tex]x-5=0,x+3=0[/tex]

Potential solution are -3 and 5.

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Answer:

11. It will take about 26 minutes to install a singular tile.

12. It will take about 10 more minutes to install a light than it does to install a cable.

Step-by-step explanation:

11. Since installing 15 new tiles took a total of 390 minutes and each tile took the same amount of time, you can divide the total amount of time by the number of tiles.

390/15= 26 minutes

It will take about 26 minutes to install a single tile.

12. By looking at the chart it can be assumed that installing a light takes about 22 minutes since it is in the middle of 20 and 24 minutes. Installing a cable only takes 12 minutes.

22-12= 10 minutes

It takes about 10 minutes longer to install a light than it does a cable.

It took about 26 minutes to install a single tile and 10 minutes longer to install a light than it does a cable.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given,

Installing 15 new tiles took a total of 390 minutes and each tile took the same amount of time,

We have to divide the total amount of time by the number of tiles.

390/15= 26 minutes

It will take about 26 minutes to install a single tile.

By observing the chart, it can be assumed that installing a light takes about 22 minutes since it is in the middle of 20 and 24 minutes. Installing a cable only takes 12 minutes.

22-12= 10 minutes

It takes about 10 minutes longer to install a light than it does a cable.

Hence, it took about 26 minutes to install a single tile and 10 minutes longer to install a light than it does a cable.

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#SPJ2

Answer:the answer is d

Step-by-step explanation:

d is correct

Answer: is b

Step-by-step explanation:

Answer:

Step-by-step explanation:

To convert this mixed numbers;  mixed numbers are converted by multiplying the denominator with the whole number and add answer gotten to the numerator.  you then place final answer over the denominator.

1.  21 /3  x  9 2/3  = 21/3 x 29/ 3

7 x 9.67  = 67.66

2.  5 3/7 x 2 2/5  =  38 / 3   x   12 /5  =

                             12.67   x  2.4 =  30.43

3.  2 6/13  x  2 1/4  =  32 / 14   x  9 /4

                                     2.28  x  2.25  = 9.13

4.  2 11/12 x 3 7/9   =  35 / 12  x  34 /9

                                  2.916  x 3.77   =  11.016

5.  5 3/5 x 5 1/7  =  28/5  x 31 / 7

                              5.6   x 4.428  = 24.8

6.   2 2/3 x 2 11/14   =  8/3  x  39/14

                                    2.66      x  2.78 =  7.413

7.   7 1/4  x 2 1/2  = 29/4   x  5 /2

                              7.25   x 2.5   = 18.125

8.  1 12/3  x 2 2/3 =  15 /3   x  8/3

                               5  x 2.66   =  13.33

9. 2 3/4  x 1 1/6 =   11/4  x 7/6

                                2.75 x  1.166  = 3.20

10.  10 1/3  x 2 1/5 =  31/3 x 11/5

                                  10.33  x  2.2  =  22.726

Answer/Step-by-step explanation:

[1] [tex]3rs = 3 * r *s[/tex]

[2] [tex]12xy = 2*2*3*x*y[/tex]

[3] [tex]5x^2=5*x*x[/tex]              

[4] [tex]36x^2=2*2*3*3*x*x[/tex]

[5] [tex]25^2=5*5*x*x[/tex]

[6] [tex]30x^2=2*3*5*x*x[/tex]

[7] [tex]5x^3=5*x*x*x[/tex]

[8] [tex]24y^3=2*2*2*3*y*y*y[/tex]

[9] [tex]9xy=3*3*x*y[/tex]

[10] [tex]12x^4=2*2*3*x*x*x*x[/tex]

Factoring means to factor a number means to break it up into numbers that can be multiplied together to get the original number.

[tex][RevyBreeze][/tex]

Answer:

[1] 3*r*s

[2] 12ry=2*2*x*y

[3]  5x2=5*x*x            

[4] 36x2=2*2*3*3*x*x

(5] 252=5*5*x*x

[6] 30x2=2*3*5*x*x

[7] 5x3=5*x*x*x

[8] 24y3=2*2*2*3*y*y*y

[9]9xy=3*3*x*y

[10] 12x4= 2*2*3*x*x*x*x

Step-by-step explanation:

The horizontal velocity of the cannonball is released at an angle of 20˚ at a velocity of 12m/s is 11.276 m/s.

Velocity is the rate of change of position with respect to time. It is a scalar quantity.

We know that the velocity is a scalar quantity therefore, it can be divided into two components such that the first component is the vertical component which is equal to the (V sinθ), while the other component is the horizontal component(V cosθ), where V is the velocity and θ is the angle of the velocity from the positive x-axis.

Now, in order to calculate the horizontal velocity of the cannonball we can write,

[tex]\rm V_x = V\ Cos\theta[/tex]

[tex]V_x = 12 (Cos\ 20^o)\\\\V_x = 11.276\rm\ m/s[/tex]

Hence, the horizontal velocity of the cannonball is released at an angle of 20˚ at a velocity of 12m/s is 11.276 m/s.

Learn more about Velocity:

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Answer:

x=13.243568

Step-by-step explanation:

1000=58.3x+227.9

Step 1: Flip the equation.

58.3x+227.9=1000

Step 2: Subtract 227.9 from both sides.

58.3x+227.9=1000

         −227.9   −227.9

58.3x=772.1

Step 3: Divide both sides by 58.3

58.3x/58.3 = 772.1/58.3

x=13.243568

Answer:

(i just use app sorry if I'm wrong)

10.....

thats all you can simplify out of it

Answer: In terms, it would be false when solved it 248 = 10

Step-by-step explanation:

When you multiply 62 and 4 you will get 248

When you add 3 and 7 you will get 10

Obviously [tex]248\neq 10[/tex] so this equation can't be simplified and it's false

Answer:

60 ounces

Step-by-step explanation:

there are 16 ounces in a pound plus the extra 4 ounces times 3 is 60 ounces in total

Step-by-step explanation:

5(y+52) = -13

5y + 260 = -13

5y = -13 -260

y = -273 ÷ 5

y = -54.6

Answer:

Step-by-step explanation:

The constant is 6

Hope this helps!

Answer:

654 girls

Step-by-step explanation:

sum the parts of the ratio , 4 + 3 = 7 parts

divide total by 7 to find the value of one part of the ratio

1526 ÷ 7 = 218 ← value of 1 part of the ratio , then

number of girls = 3 × 218 = 654

Solution:

Note that:

Find the speed of her bike of both the days and compare.

This means that:

Hence, the day after Monday is the day, she rode her bike faster than on Monday.

Answer:

The next day

Step-by-step explanation:

she covered 8 miles in 1 hour on Monday but on tuesday she covered 9 miles in 1 hour so she biked faster the next day.

Answer:

-0.06

Step-by-step explanation:

Answer:

Ms. Red can do 25 more push ups than Ms. Lopez.

Step-by-step explanation:

25 x 2 = 50.

50 is how many Ms. Red can do.

50-25= 25.

Answer:

*

Step-by-step explanation:

Pattern A: is adding 2 dots each time

Pattern B: is going up 1,2,3,4 (adding that amount each time)

Pattern C: Times by 3 each time

The expected number of female children in a family with three children is 1.5.

The correct option is B.

We have to determine

What is the expected number of female children in a family with three children?

Probability is defined as the sum of all observations and the number of observations.

The expected value of female children= Probability of female children x Total number of children.

A child can be male or female, so there are 2 combinations, the favorable outcome is female.

The probability of female children = 1/2.

Therefore,

The expected number of female children in a family with three children is;

[tex]= \dfrac{1}{2}\times 3\\\\=1.5[/tex]

Hence, The expected number of female children in a family with three children is 1.5.

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Answer:

4x+2

and 22

Step-by-step explanation:

2x-5+6+2x-5+6=4x+2

if x=5, so perimeter 4(5)+2=20+2=22

Answer:

$31950

Step-by-step explanation:

We multiply 30,000 by .065 to get 1950. We ad them together to get $31,950. :)

Answer:

$31,950 dollars

Step-by-step explanation:

Given the following question:
Initial price of the car is $30,000...
The car has an increase tax of 6.5% (which means 6.5% of the initial price of the car is the sales tax.)

In order to find the total cost of the car, we need to find 6.5% of $30,000 and then add that number to the initial price to have the answer.

[tex]\frac{6.5\times30000}{100} =6.5\times30000=19500\div100=1950[/tex]
[tex]30000+1950=31950[/tex]
[tex]t=31950[/tex]

Therefore, the car has the total cost (including tax) of "$31,950 dollars."

Hope this helps.

This is wrong because the difference of x and 4.5 that is (x- 4.5) is negative two times that is -2(x -4.5). Then the correct option is C.

BODMAS rule means for the Bracket, Order, Division, Multiplication, Addition, and Subtraction.

Emma read the statement "the quotient of six and a number, x, is the same as negative two times the difference of x and 4. 5. " She translated it as shown below.

[tex]\rm 6 x = -2 x - 4. 5[/tex]

This is wrong because the difference of x and 4.5 that is (x- 4.5) is negative two times that is -2(x -4.5).

Thus, She should have used parentheses to show that Negative 2 is multiplied by (x minus 4. 5). Then the correct option is C.

More about the BODMAS rule link is given below.

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Answer:

D: PQ is congruent to QR

Step-by-step explanation:

In a rectangle, there are a few statements that are always true. Opposite sides are congruent and parallel and all angles meet at 90 degrees. However, adjacent sides (sides that are touching/share a vertex) are not necessarily congruent. They can be; if they are then that rectangle is a square. Nevertheless, if adjacent sides are not congruent, then it is still a rectangle, so long as they meet at a right angle.

Answer: D

Step-by-step explanation:

Answer: a minute and a half

Step-by-step explanation:

3/4 +3/4 is 6/4 which is 1 1/2 or 1 2/4

Total pounds=1lbs

Total mins:-

Answer:

4d+3

Step-by-step explanation:

Combine the like terms 3d + d which is 4d and 5 - 2 is 3, keep the addition symbol, and you will get 4d+3

The answer is 4d+3

(3d+5)(d-2)

you add 3d+1d=4d

You now subtract 5-2=3 (since the higher absolute value is +5, your answer will be +3, not -3)

=4d+3 :)

Answer:

A,B,D

Step-by-step explanation:

case A) If the price is marked down by  percent, the new price will be

we know that

If the price is marked down by 10  percent

then the new price will be

10%= 10/100=0.10

(1 - 0.10) *$28= 0.90 * $28

=$25.20

therefore The statement case A) is True

case B) If the price is marked down by 25 percent, the new price will be $21

we know that

If the price is marked down by 25 percent

then the new price will be

25%=25/100=0.25

(1-0.25)* $28=0.75*$28

=$21

therefore The statement case B) is True

case C) If the price is marked down by 50 percent, the new price will be $19 we know that

If the price is marked down by 50 percent

then the new price will be

50%=50/100=0.50

(1-0.50)*$28= 0.50*$28

=14

therefore The statement case C) is False

case D) If the price is marked down by  35 percent, the new price will be $18.20

we know that

If the price is marked down by 35 percent

then the new price will be

35%= 35/100=0.35

(1-0.35)* $28=0.65*$28

=18.20

therefore The statement case D) is True

case E) If the price is marked down by 40 percent, the new price will be $29.80 we know that

If the price is marked down by 40 percent

then the new price will be

40%=40/100=0.40

(1-0.40)*$28= 0.60*$28

=$16.80

therefore The statement case E) is False

Answer:x=125

Step-by-step explanation:

180-55=125

Answer:

Step-by-step explanation:

x+55=180[Sum of linear pair]

x=180-55

x=125