For fixed population standard deviation and level of significance, the minimum sample size needed to guarantee a given margin of error ......... as the margin of error increases.
a. stays the same
b. increases
c. decreases

The linear equation of the following graph in slope-intercept form will be; y=1/2x

The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.

The slope of the line is calculated as follows:

m = Δy/Δx

To find the linear equation of the following graph in slope-intercept form.

Therefore, the slope of the line is;

m = Δy/Δx

m = 1/2

When we simplify it, then we get the equation as;

y=1/2x

Hence, The linear equation of the following graph in slope-intercept form will be; y=1/2x

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The probability that the next report will weigh less than 45 grams = 0.106

In this question, we have been given the weight of written reports produced in a certain department has a normal distribution with mean 60 grams and standard deviation 12 grams.

We need to find the probability that the next report will weigh less than 45 grams.

We have mean= 60 grams

Standard Deviation = 12 grams

First we convert 45 to z score.

45 converted to z score for given mean and standard deviation will be:

z = (45 - 60)/12

z = -1.25

So, from standard normal table a P-value:

P(x<45) = 0.10565

Therefore, the probability would be 0.10565

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Answer:

36

Step-by-step explanation:

4/9 x = 16

9/4 * 4/9 x = 16 * 9/4

x = 36

Answer:

Step-by-step explanation:

perimeter = hypotenuse + side a + side b

sin = opposite / hypotenuse

tan = opposite/adjacent

find the hypotenuse

let x = hypotenuse

sin(55 deg) = 56 / x

x * sin(55 deg) = 56

x = 56 / sin(55 deg) use a calculator

x ~ 68.36

find the side adjacent to 55 degrees

let x = adjacent leg

tan(55 deg) = 56 / x

x * tan(55 deg) = 56

x = 56 / tan(55 deg) use a calculator

x ~ 39.21

add them together

perimeter = 56 + 68.36 + 39.21

perimeter ~ 163.57 or 164

Answer:

PLEASE ADD A DANG PICTURE

Step-by-step explanation:

The outlier of 2 decreases the mean page count.

What is mean and median?

The mean is that the variety you get by dividing the total of a collection of values by the quantity of values within the set.

In distinction, the median is that the middle variety in an exceedingly set of values once those values square measure organized from smallest to largest.

Main Body:

From the picture we can  know that outlier of 2 does not effect the median page count.

But outlier of 2 decreases the mean page count.

it can be found out by taking mean

(1+2+3+2+1+2+2+1)/8= 1.75

and if we remove outlier of 2 ,then

(1+3+2+1+2+2+1)/7 = 1.86

Hence ,the outlier of 2 decreases the mean page count.

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Answer:

the answer is d

Step-by-step explanation:

Answer:     0.26666667 (0.3)

Answer:

2/12 of the pizza is left.

Step-by-step explanation:

7/12 plus 3/12 is 10/12, then minus that from 12/12 and you get 2/12.

The earnings for both Cynthia and Javier are same for x hours.

What is commission?

When an employee completes a task, typically selling a certain volume of goods or services, they are compensated financially. Sales commissions are occasionally used by employers as incentives to boost employee productivity. It is possible to receive a commission in place of or in addition to a salary.

Given:

Cynthia earns $680 in commissions and is paid $10.25 per hour.

Javier earns $410 in commissions and is paid $12.50 per hour.

So, the equation is

10.25x + 680 = 12.5x + 410

To simplify this equation for x.

10.25x+ 680 =12.5x +410

    680 ‐ 410 = 12.5x ‐ 10.25x

             270 = 2.25x

                  x = 270/2.25

                  x = 120

If we plug x = 120 in both the values 10.25x + 680 and 12.5x + 410 then we will get the same values.

Hence, the earnings for both Cynthia and Javier are same for x hours.

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Answer:

should be the first one, x > 360

Step-by-step explanation:

im sorry if its wrong :*(

Question 1

[tex](f \circ g)(-2)=f(-2) \cdot g(-2)=10 \cdot 3=\boxed{30}[/tex]

Question 2

[tex](g \circ h)(1)=g(1) \cdot h(1)=2(1^2 -9)=\boxed{-16}[/tex]

Question 3

[tex](g/f)(0)=\frac{g(0)}{f(0)}=\frac{0^2 -9}{6}=\boxed{-3/2}[/tex]

Question 4

[tex](h/f)(-3)=\frac{h(-3)}{f(-3)}=\frac{3^2 -9}{12}=\boxed{0}[/tex]

Answer:

Using substitution method for to solve, X = -4 and Y = 6

Step-by-step explanation:

1)  x+2y = 8

2) x+y = 2

solve 2)

x = 2-y

Then replaced it in 1)

(2-y) + 2y = 8

2 + y = 8

y = 6

then

x = 2 - 6

X = -4

Richard is 23years old and Thiago is 5years old

A word problem is a mathematical exercise where significant background information on the problem is presented in ordinary language rather than in mathematical notation.

From the question,

Let R stands for Richard

     T stands for Teo

we were told that the combined age of Richard and Teo is 28

i.e

R + T = 28 ......eqn (i)

we were also told that  Richard is 13 years older than twice Teo’s age

i.e

R = 2T + 13 .....eqn(ii)

substituting 2T + 13 for R in eqn (i)

(2T+13)+T = 28

expanding the bracket

3T + 13 = 28

collecting like terms

3T = 28 - 13

3T = 15

T = 15/3

T = 5

Teo age is 5years

From eqn (i)

R + T = 28

R + 5 = 28

R = 28 - 5

R = 23

Hence, Richard age is 23years

From eqn (ii)

R = 2T + 13

substituting for R in the eqn

23=2T+13

collecting like terms

23-13=2T

10=2T

T=10/2

T=5

Hence. Thiago age is 5years

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Answer:

x = 12.5

Step-by-step explanation:

The inside angles of a triangle should sum 180°

then

2x + (7x+5) + (180 - (11x-25)) = 180

2x + 7x + 5 + 180 - 11x -25 = 180

-2x - 25 = 0

2x = -25

x -25/2

x = 12.5

Answer: 2 2/3 or 8/3

Step-by-step explanation:

3 5/6 = 23/6

-1 1/6 = -7/6

23/6-7/6

16/6

simplify

8/3

Answer:

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

Step-by-step explanation:

3 [tex]\frac{5}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{6}{6}[/tex] + [tex]\frac{5}{6}[/tex]  = [tex]\frac{23}{6}[/tex]   ( [tex]\frac{6}{6}[/tex] is the same one)

1 [tex]\frac{1}{6}[/tex] can be written [tex]\frac{6}{6}[/tex] + [tex]\frac{1}{6}[/tex] = [tex]\frac{7}{6}[/tex]

Adding a negative number is like subtracting a positive number.

[tex]\frac{23}{6}[/tex] -  [tex]\frac{7 }{6}[/tex]  =   [tex]\frac{16}{6}[/tex]  6 goes into 16 2 times with 4 left over

2 [tex]\frac{4}{6}[/tex]  Divide the top and bottom by 2 to get

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

The situation could be modeled by a linear function is

(2) A gym charges a $50 initial fee and then $30 monthly.

A linear function in mathematics is one that has either one or two variables and no exponents.

2) Let y be the total amount charged by the gym to a person for x months.

as the initial amount for every person is $30.

The gym charges [tex]50+30x[/tex] $ after x months.

Hence this is a linear equation.

The remaining situations cannot be expressed as a linear equation because they include percentages in them.

Every situation that has a percentage is an exponential function.

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Answer:

Yes, they are parallel.

Step-by-step explanation:

61 + 119 = 180

One line is 180 degrees.

Answer:

2 1/4

Step-by-step explanation:

Subtract the whole numbers first:

8 - 6 = 2

To subtract the fractions, change 1/2 to 2/4 since they equal the same thing and 2/4 has the same denominator as 1/4:

2/4 - 1/4 = 1/4 <--- all we needed to do was subtract the numerators

Your final answer is 2 1/4.

Answer:

x = 3

y = 195

Step-by-step explanation:

y = 60x + 15

y = 65x

65x = 60x + 15

5x = 15

x = 3

y = 65(3)

y = 195

Hope it helps!

Answer: 6 divided by 2/3

Step-by-step explanation:

The division equation which represents the situation is 6 ÷ 2/3 = 9.

Division is one of the operation in mathematics where number is divided  into equal parts as that of a definite number.

Division equation is the equation involving the operation of division.

The model shows there are 9 pieces that are each 2/3 feet long.

We can calculate the total length of the pieces using the multiplication equation.

9 × 2/3 = 6

Total length = 6 feet

Length of each piece = 2/3 feet

Number of pieces can be found using the division equation,

6 ÷ 2/3 = 9

Hence the division equation for the given situation is 6 ÷ 2/3 = 9.

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Answer: y = 0x + 8

Step-by-step explanation:

The slope-intercept form is y=mx + b

The slope is 0, and y-intercept is at (0,8)

So our equation is

y = 0x + 8

A line 'a' and line 'b' are perpendicular to each other.

We know that the formula for the slope of line passing through two points (x1, y1) and (x2, y2) is,

m = (y2 - y1)/(x2 - x1)

A line 'a' passes through points (-3,5) and (0,0)

Let m1 be the slope of line 'a'

m1 = (0 - 5)/(0 - (-3))

m1 = -5/3

A line 'b' passes through points (3,5) and (0,0).

Let m2 be the slope of line 'b'

m2 = (0 - 5)/(0 - 3)

m2 = (-5)/(-3)

m2 = 5/3

We can observe that, m1 * m2 = -1

Since the product of slopes of the lines is -1, the lines a and b are perpendicular.

Therefore, the lines are perpendicular.

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For the given statement about hundredth digit of the given decimal z the following statement is true:

Option E. statement (1) and (2) together are not sufficient.

As given in the question,

Let us consider decimal z is represented by k.lmn

Here hundredth digit of z is equal to m

Now,

(1) The tenths digit of 100z is 2.

100z

= 100(k.lmn)

=klm.n

This implies n = 2

(2) The units digit of 1,000z is 2.

1,000z

= 1,000(k.lmn)

= klmn

This implies n =2

From both the statements we are getting the value of n which is not sufficient to get the value of required 'm'.

Therefore, Option E is the correct answer which shows both the statements are not sufficient to get the value required hundredth digit of decimal z.

The complete question is:

What is the hundredths digit of the decimal z ? (1) the tenths digit of 100z is 2. (2) the units digit of 1,000z is 2.

A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

C. Both statements together are sufficient, but neither statement alone is sufficient.

D. Each statement alone is sufficient.

E. Statements (1) and (2) together are not sufficient.

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Answer:

2/9 = approximately 0.22.

Step-by-step explanation:

There are a total of 12 possible outcomes when the spinner is spun once, so the probability of getting a result that is not green is 8/12, or 2/3. Similarly, the probability of getting green on the second spin is 4/12, or 1/3.

To find the probability of getting a result that is not green on the first spin and green on the second spin, you can multiply the probabilities of each individual event. Therefore, the probability of getting not green then green is (2/3) * (1/3) = 2/9 = approximately 0.22.

Alternatively, you could also use the principle of complementary probabilities to calculate the probability of getting not green on the first spin and green on the second spin. The probability of getting not green on the first spin is 1 - (4/12) = 8/12 = 2/3, and the probability of getting green on the second spin is still 4/12 = 1/3. Multiplying these probabilities gives a result of (2/3) * (1/3) = 2/9 = approximately 0.22.

Answer:

h(6) = 180

Step-by-step explanation:

h(a)=5a²

for a=6

h(6) = 5(6)²

h(6) = 5*36

h(6) = 180

Answer:

B) 10

Step-by-step explanation:

The triangles are congruent by HL. Thus, by CPCTC, [tex]x=10[/tex].