The repeating decimal z=0.142857142857142857 as fraction

The probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328

The given parameters are:

Start by calculating the mean:

[tex]\mu = np[/tex]

[tex]\mu = 100 * 82\%[/tex]

[tex]\mu = 82[/tex]

Calculate the standard deviation:

[tex]\sigma = \sqrt{\mu(1 - p)[/tex]

[tex]\sigma = \sqrt{82 * (1 - 82\%)[/tex]

[tex]\sigma = 3.84[/tex]

Within ± 0.02 of the population proportion are:

[tex]x_{min} = 82 * (1 - 0.02) = 80.38[/tex]

[tex]x_{max} = 82 * (1 + 0.02) = 83.64[/tex]

Calculate the z-scores at these points using:

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

So, we have:

[tex]z_1 = \frac{80.36 - 82}{3.84} = -0.43[/tex]

[tex]z_2 = \frac{83.64 - 82}{3.84} = 0.43[/tex]

The probability is then represented as:

P(x ± 0.02) = P(-0.43 < z < 0.43)

Using the z table of probabilities, we have:

P(x ± 0.02) = 0.3328

Hence, the probability that the sample proportion is within ± 0.02 of the population proportion is 0.3328

Read more about probability at:

https://brainly.com/question/25870256

#SPJ1

Answer:One of the factors of the given expression is (2h + 1).

Step-by-step explanation:

ed

Answer:

C on edge 23

Step-by-step explanation:

because i said so

The value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

The square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.

We have (−5, 3) be a point on the terminal side of θ.

Perpendicular = -5

Base = 3

From Pythagoras' theorem:

Hypotenuse² =  (3)² + (-5)²

Hypotenuse = √34

cosθ = 3/√34

cscθ = -√34/5

tanθ = -5/3

Thus, the value of cosθ = 3/√34, cscθ = -√34/5, and tanθ = -5/3 if the (−5, 3) be a point on the terminal side of θ.

Learn more about Pythagoras' theorem here:

https://brainly.com/question/21511305

#SPJ1

The value of x and y from the given figure are 3 and 36

From the given similar triangles, the following expression is true

4/6 = x/54

Cross multiply

6x = 4 *54

x = 4 * 9

x = 36

Similarly

y/6 = 27/54
y/6 = 1/2

x =3

Hence the value of x and y from the given figure are 3 and 36

Learn more on similar triangle here; https://brainly.com/question/14285697

#SPJ1

The sum of the function will be (r – s)(x) = –2x² + x – 3, The difference of the function will be (r – s)(x) = –2x² + x – 3, and The product of the function will be (r × s)(x) = 2x³ – 6x².

The complete question is attached below.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The functions are given below.

r(x) = x – 3

s(x) = 2x²

The sum of the function will be

(r + s)(x) = x – 3 + 2x²

(r + s)(x) = 2x² + x – 3

The difference of the function will be

(r – s)(x) = (x – 3) – 2x²

(r – s)(x) = –2x² + x – 3

The product of the function will be

(r × s)(x) = (x – 3) (2x²)

(r × s)(x) = 2x³ – 6x²

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ1

Answer:

It's 3

Step-by-step explanation:

if you go to desmos graphing calculator it'll help you get the solutions for these if you type it in every number and letter and for exponents type ^ its shift then type 6.

The probability is 0.2153.

It is a branch of mathematics that deals with the occurrence of a random event.

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]^{n}C_x* P^{x}* (1-p)^{n-x}[/tex]

n=18, p=0.8

So,

[tex]^{18}C_{14}* 0.8^{14}* (1-0.8)^{18-14}[/tex]

=0.2153

Hence, the probability is 0.2153.

Learn more about probability here:

https://brainly.com/question/13708171

#SPJ1

Of the food donated, 1 lb 6 oz of vegetables, 2 lb 3 oz of meat, and 8 oz of condiments were weighed, the total weight of food donated is 65 ounces.

Units are used to measure and express quantities. In the context of the given problem, units are used to indicate the weight of the donated food items.

Pounds (lb) and ounces (oz) are units of weight commonly used in the United States. One pound is equal to 16 ounces.

To add these weights together, we need to make sure they are all in the same units. Let's convert everything to ounces:

- 1 lb 6 oz = 22 oz (since 1 lb = 16 oz, and 6 oz + 16 oz = 22 oz)

- 2 lb 3 oz = 35 oz (since 2 lb = 32 oz, and 3 oz + 32 oz = 35 oz)

- 8 oz = 8 oz

Now we can add the weights:

22 oz + 35 oz + 8 oz = 65 oz

Therefore, the total weight of food donated is 65 ounces.

For more details regarding unit system, visit:

https://brainly.com/question/28579178

#SPJ2

Step-by-step explanation:

Answer:

898

Step-by-step explanation:

898999

Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.

To determine whether Mr. Tan bases his decision on instinct, mean, median, or mode, we need to consider the given information that Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts.

Instinct refers to a natural or intuitive decision-making process that is not based on specific calculations or statistical measures. While Mr. Tan's decision-making process could involve some level of instinct, it is unlikely to be the primary basis for his decision.

The mean is the average value calculated by summing up all the values and dividing by the total number of values. However, the mean does not provide any information about the distribution of the sizes or the fact that Mr. Tan produces more medium-sized shirts.

The median is the middle value when the data is arranged in ascending or descending order. However, we do not have any information about specific values or the distribution of sizes, so we cannot determine the median.

The mode refers to the value or values that appear most frequently in a set of data. Since Mr. Tan produces more medium-sized shirts than either large-sized or small-sized T-shirts, it implies that medium-sized shirts are the mode in his production. This suggests that Mr. Tan's decision is based on the mode, as he produces more shirts of this size than any other size.

Therefore, based on the given information, it can be inferred that Mr. Tan bases his decision on the mode, which indicates that he produces more medium-sized shirts than either large-sized or small-sized T-shirts. The correct answer is option D: Mode.

for such more question on Mode

https://brainly.com/question/14532771

#SPJ8

The trip to the lake took  4 hours.

The first step is to determine the distance of the trip.

Distance = average speed x time

24 km/h x 5 = 120 km

Time = distance / average speed

120 / 30 = 4 hours

To learn more about average speed, please check: https://brainly.com/question/21734785

#SPJ1

Answer:

y=3x-21

Step-by-step explanation:

Given points A(2,5) and B(8,3), line AB must contain them.

To calculate the slope, [tex]m_{\text{AB}}[/tex], of line AB, use the slope formula:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m_{\text{AB}}=\dfrac{(3)-(5)}{(8)-(2)}[/tex]

[tex]m_{\text{AB}}=\dfrac{-2}{6}[/tex]

[tex]m_{\text{AB}}=-\frac{1}{3}[/tex]

Since the slope isn't undefined, line AB must cross the y-axis somewhere.  To find the y-intercept, build and equation in slope-intercept form:

[tex]y=m_{\text{AB}}x+b_{\text{AB}}[/tex]

[tex]y=\left(-\frac{1}{3} \right) x+b_{\text{AB}}[/tex]

Substituting values for a known point (point A) on line AB...

[tex](5)=\left(-\frac{1}{3} \right) (2)+b_{\text{AB}}[/tex]

[tex]5=-\frac{2}{3} +b_{\text{AB}}[/tex]

[tex](5)+\frac{2}{3} =(-\frac{2}{3} +b_{\text{AB}})+\frac{2}{3}[/tex]

Finding a common denominator...

[tex]\frac{3}{3}*5+\frac{2}{3} =b_{\text{AB}}[/tex]

[tex]\frac{15}{3}+\frac{2}{3} =b_{\text{AB}}[/tex]

[tex]\frac{17}{3}=b_{\text{AB}}[/tex]

So, the equation for line AB is  [tex]y=-\frac{1}{3} x +\frac{17}{3}[/tex]

Since line AB and line BC form a right angle, they are perpendicular.  Perpendicular lines have slopes that are opposite (opposite sign) reciprocals (fraction flipped upside-down) of each other.  Stated another way, the slopes multiply to make negative 1.

[tex]m_{\text{AB}}*m_{\text{BC}}=-1[/tex]

[tex]\left( -\frac{1}{3} \right) *m_{\text{BC}}=-1[/tex]

[tex]-3*\left( -\frac{1}{3} *m_{\text{BC}} \right) =-3*(-1)[/tex]

[tex]m_{\text{BC}} =3[/tex]

Since the slope isn't undefined, line BC must also cross the y-axis somewhere.  To find the y-intercept, build and equation in slope-intercept form:

[tex]y=m_{\text{BC}}x+b_{\text{BC}}[/tex]

[tex]y=(3) x+b_{\text{BC}}[/tex]

Substituting values for a known point (point B) on line BC...

[tex](3)=3 * (8)+b_{\text{BC}}[/tex]

[tex]3=24+b_{\text{BC}}[/tex]

[tex](3)-24=(24+b_{\text{BC}})-24[/tex]

[tex]-21=b_{\text{BC}}[/tex]

So, the equation for line BC is  [tex]y=3 x -21[/tex]

Answer:

80

Step-by-step explanation:

when you do the math you get two answers, -90 and 80

we dont use -90 because -90 units cannot be manufactured

Answer:

c. x/7

Step-by-step explanation:

seven is dividing something, and X is the placeholder in this equation.

So, since x is being divided by seven, that rules out B., because that's backwards.

A. and D. don't involve division, so they're both incorrect as well.

Thus we are left with C. x/7

Answer:

x= 0, y= -1

Step-by-step explanation:

To obtain the values of x and y from a system of equations, start by labelling the given equations.

8x +5y= -5 -----(1)

7x -3y= 3 -----(2)

Let's solve by elimination.

Here, I will be working to eliminate the y term. This is done by ensuring both equations have the same numerical value in the coefficient of y.

(1) ×3:

24x +15y= -15 -----(3)

(2) ×5:

35x -15y= 15 -----(4)

Add the two equations together since the coefficient of y has opposite signs.

(3) +(4):

24x +15y +35x -15y= -15 +15

59x= 0

Divide both sides by 59:

x= 0

Now, substitute the value of x into any equations to find the value of y.

Substitute x= 0 into (1):

8(0) +5y= -5

5y= -5

Divide both sides by 5:

y= -5 ÷5

y= -1

Additional:

For similar questions on system of equations, do check out the following!

Answer:

Even though only 6% of students scored higher than Karl, we cannot know his personal score based on his percentile. He could have gotten a 62, as long as everyone else [94% of the class] got an even lower score.

So, we cannot know Karl's mark, we are only able to understand Karl's score in relation to the rest of the students in his law course.

Step-by-step explanation:

first function, f(x) = 5x-3 goes with option B

2nd function, 4- 4x goes with option A

3rd function goes with option D

4th goes with option C

In scientific Notation , After 10 years he will have in total 2 x 10 ³ pounds.

Scientific Notation is a way of writing very large or small quantities.

It is written in the form of  x 10ˣ

It is given that

The colony of bees has a single queen, hundreds of male drones and roughly 60,000 female worker bees.

The quantity of honey produced is 200 pounds.

After 10 years he will have in total

200 * 10 = 2000 pounds

In scientific Notation it will be written as

2 x 10 ³ pounds.

To know more about Scientific Notation

https://brainly.com/question/18073768

#SPJ1

Answer:

b

Step-by-step explanation:

[tex] \sqrt{72} + \sqrt{162} \\ \\ \sqrt{2 \times 2 \times 2 \times 3 \times 3} + \sqrt{2 \times 3 \times 3 \times 3 \times 3} \\ \\ 2 \times 3 \sqrt{2} + 3 \times 3 \sqrt{2} \\ \\ 6 \sqrt{2} + 9 \sqrt{2} \\ \\ (6 + 9) \sqrt{2} \\ \\ 15\times1.4 \\ \\ 21[/tex]

[tex] \sqrt{50} - \sqrt{8} \\ \\ \sqrt{2 \times 5 \times 5} - \sqrt{2 \times 2 \times 2} \\ \\ 5 \sqrt{2} - 2\sqrt{2} \\ \\ (5 - 2) \sqrt{2} \\ \\ 3 \sqrt{2} \\ \\ 1.7 \times 2 \\ \\ 3.4[/tex]

[tex]2 \sqrt{28} + \sqrt{28} \\ \\ 2 \sqrt{2 \times 7 \times 7} + \sqrt{2 \times 7 \times 7} \\ \\ 2 \times 7 \sqrt{2} + 7 \sqrt{2} \\ \\ 14 \sqrt{2} + 7 \sqrt{2} \\ \\ (14 + 7) \sqrt{2} \\ \\ 21 \times 1.4 \\ \\ 29.4[/tex]

Answer:

13, 19, 25.

Step-by-step explanation:

y=3x+10

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

x=1, y=3(1)+10=3+10=13

x=3, y=3(3)+10=9+10=19

x=5, y=3(5)+10=15+10=25

Answer:

a computer is an electronic device,which input data/instruction,store and processes it and produces output in the desired from

The coordinates of point F are 4 and negative 2.5. Option C is correct.

A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.

It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.

The location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.

'c' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x.

The coordinates of point F are 4 and negative 2.5.

Hence, the Option C is correct.

To learn more about the Cartesian plane refer;

https://brainly.com/question/27538987

#SPJ1

Answer: 20

Step-by-step explanation:

f(-4) = -4² - (-4)

f(-4) = 16 + 4

f(-4) = 20

using elimination method

2x + 3y = 6 -----(1)

-

x + 3y = 12-------(2)

———————

x = 12

substitute x as 12 into equation (1) or (2), let's choose equation (1)

2(12) + 3y = 6

24 + 3y = 6

collect like terms

3y = 6 - 24

3y = 18

divide both sides by 3 ( to make y the subject of formula )

3y = 18

— —

3 3

y = 6

therefore X = 12 and y = 6

Hope this helps eh

Good luck ✅.

Answer:

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

Step-by-step explanation:

given f(x) with zeros x = a and x = b then the corresponding factors are

(x - a) and (x - b)

f(x) is then the product of these factors

Given zeros are x = 4, x = 0, x = - 3 then the factors are

(x - 4) , (x - 0), (x - (- 3)) , that is

(x - 4) , x , (x + 3)

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

Answer:

the second option listed

(A = 53 degrees)

(a = 13.3)

(c = 16.6)

Step-by-step explanation:

SOH CAH TOA

(sin = opposite / hypotenuse)

(cos = adjacent / hypotenuse)

(tan = opposite / adjacent)

For this question, you are provided an angle (37), and its opposite (10)

so, we can solve for either sin or tan first.

tan = opposite / adjacent

tan 37 = 0.7535540501

0.7535540501 = 10/a  [multiply by a]

0.7535540501a = 10 [divide by [0.7535540501]

a = 13.2704482163

rounded to the nearest tenth, a = 13.3

we know that the three angles shown here must add up to 180

so,

90 + 37 + A = 180

127 + A = 180

- 127           - 127

A = 53

--this is enough information to answer, but I will also solve side c to prove my answer

c = hypotenuse

a²+ b²=c²

[13.3]² + [10]² = c²

176.89 + 100 = c²

276.89 = c²

√276.89 = √c²

16.6400120192 = c

c = 16.6 (rounded to the nearest tenth)

**I am assuming this is a right triangle, otherwise there wouldn't be a matching answer

Answer:

The relationship between the scale factor and perimeter of an image and its pre-image is a, b = perimeter = 2a + 2b. the relationship between the scale factor and area of an image and its pre-image is k∧2 (ab).

Step-by-step explanation:

Relationship between the scale factor and perimeter of an image and its pre-image.

Scale factor = k

Pre-image lengths: a, b = perimeter = 2a + 2b

Image lengths: ka, kb = perimeter = 2ka + 2 kb = k (2a + 2b) = 2 * preimage perimeter.

She has to say that the perimeter of the image is the perimeter of the preimage times the same scale factor.

What should she say about the relationship between the scale factor and area of an image and its pre-image?

area of the pre-image = ab

are of the image = (ka)(kb) = k^2 (ab)

The area of the image is the area of the preimage times the square of the scale factor.

Support her statements using scale factors of 5 and 6.

Scale factor 5

length of the pre-image = 3 x 4 = perimeter = 2 (3 + 4) = 2(7) = 14

length of the image = 3*5 x 4*5 = 15 x 20 = perimeter = 2 (15 + 20) = 2 (35) = 70

14 * 5 = 70 which shows the prediction

area of the pre-image = 3 * 4 = 12

area of the image = 15 * 20 = 300

12 * (5^2) = 12*25 = 300 which is the value predicted.

Now you can do the same using scale factor 6.

For more explanation, refer the following link:

https://brainly.com/question/4528070

#SPJ10