A simple random sample of 100 men is chosen form a population with mean height 71 in and standard deviation 2.5 in. What is the probability that the average height of the men in the sample is less than 70.5in?

Answer:

0.963

Step-by-step explanation:

It’s correct

Answer:

1/3

Step-by-step explanation:

thats the slope so im assuming :/

the answer is k=4.6. hope this helps

Answer:

Yes please i really need it

Step-by-step explanation:

Answer:

[tex]Average = 10[/tex]

Step-by-step explanation:

Given

[tex]First\ Three = 14[/tex] --- Average

[tex]Next\ Seven= 4[/tex] --- Average

Required

Determine the overall average

Represent the sum of the first three with x.

So:

[tex]\frac{x}{3} = 14[/tex]

Solve for x

[tex]x = 14 * 3[/tex]

[tex]x = 42[/tex]

Represent the sum of the next seven with y.

So:

[tex]\frac{y}{7} = 4[/tex]

Solve for y

[tex]y = 4 * 7[/tex]

[tex]y = 28[/tex]

The overall average is calculated as thus:

[tex]Average = \frac{x + y}{7}[/tex]

[tex]Average = \frac{42 + 28}{7}[/tex]

[tex]Average = \frac{70}{7}[/tex]

[tex]Average = 10[/tex]

Answer:r/8>16

Step-by-step explanation:

r/8-16

It says 16 less, so we have to subtract 16 from r divided by 8.

That would be r/8-16.

Answer: 5x-30-9

-159

Step-by-step explanation:

-159 is the answer

Answer:

greater than

Step-by-step explanation:

1.994 is closer to 2 than 1.493 so it is greater!

Answer:The mixed number 2 3/7 can be converted to the improper fraction 17/7. The easiest way to do this is to multiply the denominator of the fraction (7 in...

Step-by-step explanation:

Answer:

29

Step-by-step explanation:

Given the expression [tex]75_8 = 23_x[/tex] where x is the unknown base:

[tex]75_8 = 23_x\\7\times8^1 +5\times8^0 = 2\times x^1+3 \times x^0\\56+5 = 2x+3\\61 = 2x+3\\2x = 61-3\\2x = 58\\x = 58/2\\x = 29[/tex]

Hence the missing base is 29

Answer:

A) s = $40 (in thousands of dollars)

B) point of diminishing returns is at;

(20, 2000) in thousands of dollars

Step-by-step explanation:

We are given the profit function as;

P = −0.1s³ + 6s² + 400

A) To maximize the profit, we need to find the first derivative and equate it to zero.

Thus;

dP/ds = -0.3s² + 12s

At dP/ds = 0, we have;

-0.3s² + 12s = 0

0.3s² = 12s

0.3s = 12

s = 12/0.3

s = $40 (in thousands of dollars)

B) To find the point of diminishing returns, we need to find the 2nd derivative of the given profit function and equate to zero.

Thus;

d²P/ds² = -0.6s + 12

At d²P/ds² = 0, we have;

-0.6s + 12 = 0

0.6s = 12

s = 12/0.6

s = 20

At s = 20,

P = −0.1(20)³ + 6(20)² + 400

P = -800 + 2400 + 400

P = 2000

Thus; point of diminishing returns is at;

(20, 2000) in thousands of dollars

Answer:

[tex]a = 1[/tex]

Step-by-step explanation:

Given

[tex]4x - 3(x + a) = 2[/tex]

[tex]x = 5[/tex]

Required

Determine the value of a

[tex]4x - 3(x + a) = 2[/tex]

Substitute 5 for x

[tex]4(5) - 3(5 + a) = 2[/tex]

Open all brackets

[tex]20 - 15 - 3a = 2[/tex]

[tex]5 - 3a = 2[/tex]

Collect Like Terms

[tex]-3a = 2 - 5[/tex]

[tex]-3a = -3[/tex]

Solve for a

[tex]a = -3/-3[/tex]

[tex]a = 1[/tex]

Answer:

Step-by-step explanation:

Given

RS=9y+2, ST=2y+6, and RT= 52

The addition postulate is true for the number line.

RS+ST = RT

Substitute

9y+2+(2y+6) = 52

9y+2y+8 = 52

11y = 52-8

11y = 44

y = 44/11

y = 4

Find RS

RS = 9y+2

RS = 9(4)+2

RS = 36+2

RS = 38

Find ST:

ST = 2y+6

ST = 2(4)+6

ST = 8+6

ST = 14

Hence y = 4, RS = 38 and ST = 14

Answer:

30°

Step-by-step explanation:

<4=<2=30

(vertical opposite angles are equal)

Answer:

30 degrees

Step-by-step explanation:

Since 4 is equal on the other side of 2, it would be congruent, which is the same as 2. So, 30 degrees.

Answer:

h(4) = -28

General Formulas and Concepts:

Order of Operations: BPEMDAS

Step-by-step explanation:

Step 1: Define

h(n) = -2n² + 4

h(4) is n = 4

Step 2: Solve

Answer:

4

Step-by-step explanation:

Since the entire length is 11, and one segment is 7, you'll subtract and end up with the answer 4.

The length of AB if Point B is on the line segment AC, BC = 7 and AC = 11, is 4.

A line segment is a measurable route between two points. Line segments can make up any polygon's sides because they have a set length.

Given:

Point B is on the line segment AC, BC = 7 and AC = 11,

Write the expression for the above phrase as shown below,

The length of the AC = The length of AB + the length of BC

11 = 7 + The length of AB

The length of AB = 11 - 7

The length of AB = 4

Thus, The length of AB is 4.

To know more about line segments:

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#SPJ5

True.

When you break it down, it's 0.45 compared to 0.50, so 0.5 is greater than 0.45 by 0.05. Also, 0.5 is closer to 0.

Complete Question

Because of the relatively high interest rates, most consumers attempt to pay off their credit card bills promptly. However, this is not always possible. An analysis of the amount of interest paid monthly by a bank's Visa cardholders reveals that the amount is normally distributed with a mean of 25 dollars and a standard deviation of 8 dollars. (Round all decimals to at least 3 places.) (a) What proportion of the bank's Visa cardholders pay more than 28 dollars in interest

Answer:

0.354

Step-by-step explanation:

We solve for z score in this question.

The formula is given as:

z = (x-μ)/σ, where

x is the raw score = $28

μ is the population mean = $25

σ is the population standard deviation = $8

z= 28 - 25/8

z = 0.375

P-value from Z-Table:

P(x<28) = 0.64617

P(x>28) = 1 - P(x<28)

= 1 - 0.64617

= 0.35383

Approximately to 3 decimal places = 0.354

The proportion of the bank's Visa cardholders pay more than 28 dollars in interest is 0.354.

Answer:

The coordinates of endpoint S are [tex]S(x,y) = (8,-18)[/tex].

Step-by-step explanation:

Let [tex]T(x, y) = (0, 6)[/tex] and [tex]M(x,y) = (4,-6)[/tex], which is the midpoint of line segment ST. From Linear Algebra we get that midpoint is the following vector sum of endpoints S and T. That is:

[tex]M(x,y) = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot T(x,y)[/tex] (Eq. 1)

Now clear S in the previous expression:

[tex]S(x,y) = 2\cdot M(x,y) - T(x,y)[/tex] (Eq. 1b)

Then, the coordinates of point S are:

[tex]S(x,y) = 2\cdot (4,-6) - (0,6)[/tex]

[tex]S(x,y) = (8, -18)[/tex]

The coordinates of endpoint S are [tex]S(x,y) = (8,-18)[/tex].

Answer:

 [tex]\mu_{x} = 0.8[/tex]

   [tex]\sigma  =  0.095  [/tex]  

  The shape of this sampling distribution is approximately normal

Step-by-step explanation:

From the question we are told that

  The population proportion is [tex]p = 0.8[/tex]

  The sample size is  n = 100

Generally the expected value of this sampling distribution is mathematically represented as

          [tex]\mu_{x} = p = 0.8[/tex]

Generally the standard deviation of this sampling distribution is mathematically represented as

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

=>  [tex]\sigma  =  \sqrt{ \frac{0.8 (1- 0.8 )}{100 } } [/tex]    

=>  [tex]\sigma  =  0.095  [/tex]      

Generally given that the sample is  large (i.e  n  >  30 ) and the standard deviation is finite then the shape of this sampling distribution is approximately normal

Answer:

0

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

If 5 friends are sharing the berries, how many pounds of berries does each friend receive? Is the answer to 3/4 divided by 2/5 greater than or less than 1.

Answer:

Crest = Highest point of the wave.

Trough = Lowest point of the wave.

Wavelength = Distance from one crest/trough to the next (m)

Wave Height = Height from trough to crest (m)

Wave steepness = ratio of wave height to wavelength.

Amplitude = distance from the centre of wave to the bottom of the trough (m)

Step-by-step explanation:

Answer:

The least common denominator is 77 so the fractions would become 63/77 and 66/77.

Answer:

12.54

Step-by-step explanation:

Answer:

0.8152 ≤ p ≤ 0.8608

579

Step-by-step explanation:

Given the following :

Samples size n = 1000

Deaths within 10 years, p = 838

α = 95%

Construction a two way confidence interval:

p ± Zα/2 * √p(1-p) / n

point estimate p = 838/n = 838/1000 = 0.838

Z0.05/2 = Z0.025 = 1.96

0.838 - 1.96√0.838(1-0.838) / 1000

0.838 - 1.96*0.0116514 = 0.8152

0.838 + 1.96√0.838(1-0.838) / 1000

0.838 + 1.96*0.0116514 = 0.8608

0.8152 ≤ p ≤ 0.8608

b) Using the point estimate of p obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of p is less than 0.03

Error (E) = 0.03

To find the samome size, use the relation:

n = (Zα/2 / E)² * p(1-p)

n = (1.96/0.03)² * 0.838(1-0.838)

n = (1.96/0.03)² * 0.838 * 0.162

n = 4268.4444 * 0.838 * 0.162

n = 579.46

n = 579

Answer:

x = 2/3

Step-by-step explanation:

To find x-intercept/zero, subtract y = 0

0 = 3x + 2

Move variable to the left-hand side and change its sign

-3 = 2

Divide both ides of the equation by - 3

x = - 2/3

Solution

x = - 2/3

Alternate form

x = - 0.6

2 sin²(x) + 3 sin(x) + 1 = 0

(2 sin(x) + 1) (sin(x) + 1) = 0

2 sin(x) + 1 = 0   OR   sin(x) + 1 = 0

sin(x) = -1/2   OR   sin(x) = -1

The first equation gives two solution sets,

x = sin⁻¹(-1/2) + 2nπ = -π/6 + 2nπ

x = π - sin⁻¹(-1/2) + 2nπ = 5π/6 + 2nπ

(where n is any integer), while the second equation gives

x = sin⁻¹(-1) + 2nπ = -π/2 + 2nπ

2 cot(x) sec(x) + 2 sec(x) + cot(x) + 1 = 0

2 sec(x) (cot(x) + 1) + cot(x) + 1 = 0

(2 sec(x) + 1) (cot(x) + 1) = 0

2 sec(x) + 1 = 0   OR   cot(x) + 1 = 0

sec(x) = -1/2   OR   cot(x) = -1

cos(x) = -2   OR   tan(x) = -1

The first equation has no (real) solutions, since -1 ≤ cos(x) ≤ 1 for all (real) x. The second equation gives

x = tan⁻¹(-1) + nπ = -π/4 + nπ

sin(x) cos²(x) = sin(x)

sin(x) cos²(x) - sin(x) = 0

sin(x) (cos²(x) - 1) = 0

sin(x) (-sin²(x)) = 0

sin³(x) = 0

sin(x) = 0

x = sin⁻¹(0) + 2nπ = 2nπ

2 cos²(x) + 2 sin(x) - 12 = 0

2 (1 - sin²(x)) + 2 sin(x) - 12 = 0

-2 sin²(x) + 2 sin(x) - 10 = 0

sin²(x) - sin(x) + 5 = 0

Using the quadratic formula, we get

sin(x) = (1 ± √(1 - 20)) / 2 = (1 ± √(-19)) / 2

but the square root contains a negative number, which means there is no real solution.

2 csc²(x) + cot²(x) - 3 = 0

2 (cot²(x) + 1) + cot²(x) - 3 = 0

3 cot²(x) - 1 = 0

cot²(x) = 1/3

tan²(x) = 3

tan(x) = ± √3

x = tan⁻¹(√3) + nπ  OR   x = tan⁻¹(-√3) + nπ

x = π/3 + nπ   OR   x = -π/3 + nπ

Answer:

put one point at (0,3)

put another point at (1,-3)

draw a line between them

Step-by-step explanation:

could u vote me brainliest plz? thx :)

The standard formula for calculating the equation of a line is expressed as

y = mx + b

m is the slope of the line

b is the y-intercept of the line

Given the equation to graph expressed as g(x) = 3 - 6x

First, we need to get the x and y-intercept of the line expressed as:

For the x-intercept, y = 0

0 = 3 - 6x

6x = 3

x = 0.5

The x-intercept is at (0.5, 0)

For the y-intercept, x = 0

y = 3 - 6(0)

y = 3

The y-intercept is at (0, 3)

Plot the graph of a line passing through the coordinate points (0.5, 0) and (0, 3) as shown below;

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