A normally distributed population has a mean of 500 and a standard deviation of 60. Determine the probability that a random sample of size 16 selected from this population will have a sample mean less than 475. A. 0.3251 B. 0.0712 C. 0.7124 D. 0.0475

Answer:

All real numbers are solutions.

0=0

Step-by-step explanation:

Let's solve your equation step-by-step.

x+2x−1=−8+3x+7

Step 1: Simplify both sides of the equation.

x+2x−1=−8+3x+7

x+2x+−1=−8+3x+7

(x+2x)+(−1)=(3x)+(−8+7)(Combine Like Terms)

3x+−1=3x+−1

3x−1=3x−1

Step 2: Subtract 3x from both sides.

3x−1−3x=3x−1−3x

−1=−1

Step 3: Add 1 to both sides.

−1+1=−1+1

0=0

Answer:

All real numbers are solutions.

Answer:

2ay

Step-by-step explanation:

To simplify first we expand the brackets.

ax+ay- (ax-ay)

Now collect like-terms

ax-ax= 0

ay- (-ay) = 2ay

Therefore The simplified version would be 2ay

Answer:

y =-3/2x+4

Step-by-step explanation:

simple

Answer:

Vectors [tex]p_{1} = 2+5\cdot x + 3\cdot x^{2}[/tex], [tex]p_{2} = 4+11\cdot x +6\cdot x^{2}[/tex] and [tex]p_{3} = 1+2\cdot x +x^{2}[/tex] are linearly independent.

Step-by-step explanation:

From Linear Algebra, we must remember that a set of vectors is linearly independent if and only if coefficients of its linear combinations are all zeroes. That is:

[tex]\Sigma\limits_{i=1}^{n} \alpha_{i}\cdot p_{i}= 0[/tex], where [tex]\alpha_{i} = 0[/tex]. (Eq. 1)

Where:

[tex]p_{i}[/tex] - i-th Polynomial of the set of vectors, dimensionless.

[tex]\alpha_{i}[/tex] - i-th coefficient associated with the i-ith polynomial of the set of vectors, dimensionless.

Let [tex]p_{1} = 2+5\cdot x + 3\cdot x^{2}[/tex], [tex]p_{2} = 4+11\cdot x +6\cdot x^{2}[/tex] and [tex]p_{3} = 1+2\cdot x +x^{2}[/tex] elements of the set of vectors, whose linear combination is:

[tex]\alpha_{1}\cdot p_{1}+\alpha_{2}\cdot p_{2}+\alpha_{3}\cdot p_{3}= 0[/tex]

[tex]\alpha_{1}\cdot (2+5\cdot x+3\cdot x^{2})+\alpha_{2}\cdot (4+11\cdot x +6\cdot x^{2})+\alpha_{3}\cdot (1+2\cdot x+x^{2}) = 0[/tex]

[tex](2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3})+(5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3})\cdot x+(3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3})\cdot x^{2} = 0[/tex]

Values of coefficient are contained in the following homogeneous system of linear equations:

[tex]2\cdot \alpha_{1}+4\cdot \alpha_{2}+\alpha_{3} = 0[/tex] (Eq. 2)

[tex]5\cdot \alpha_{1}+11\cdot \alpha_{2}+2\cdot \alpha_{3} = 0[/tex] (Eq. 3)

[tex]3\cdot \alpha_{1}+6\cdot \alpha_{2}+\alpha_{3} = 0[/tex] (Eq. 4)

The solution of this system is:

[tex]\alpha_{1} = 0[/tex], [tex]\alpha_{2} = 0[/tex], [tex]\alpha_{3} = 0[/tex]

Which means that given set of vectors are linearly independent.

Let us first change these fractions into each other's equivalent fractions , so that we can order them from the smallest to the largest .

[tex] (i) \: \frac{1}{2} = \frac{(1 \times 3)}{6} [/tex]

[tex]\implies \color{olive} \frac{1}{2} = \color{hotpink} \frac{3}{6}[/tex]

[tex](ii) \: \frac{1}{3} = \frac{(1 \times 2)}{6} [/tex]

[tex]\implies\color{olive} \frac{1}{3} = \color{hotpink} \frac{2}{6} [/tex]

[tex](iii) \: \frac{5}{6} = \frac{(5 \times 1)}{6} [/tex]

[tex]\implies\color{olive} \frac{5}{6} = \color{hotpink} \frac{5}{6} [/tex]

Therefore, the fractions arranged in order from the least to the greatest :-

[tex] \bold\color{hotpink} { \color{olive} = \color{hotpink} \frac{1}{3}

,

\color{olive} \frac{1}{2}

,

\color{hotpink} \frac{5}{6} }[/tex]

Answer:

t=3

Step-by-step explanation:

5t-4=|11

+4 |+4

5t= | 15

÷5 | ÷5

t = 3

Answer:

91.44

Step-by-step explanation:

Answer:

x = 48, y = 70

Step-by-step explanation:

Since 2 sides are congruent, then the triangle is isosceles and the base angles are congruent, thus

x + 7 = 55 ( subtract 7 from both sides )

x = 48

The sum of the 3 angles in a triangle = 180°

Subtract the sum of the 2 angles from 180 for y, that is

y = 180 - (55 + 55) = 180 - 110 = 70

Answer:

add them all up and subtract 420 from 15+20+12!

Step-by-step explanation:

hope this helps

Answer and Step-by-step explanation:

Solution:

The equation is given by:

z – z0 = a(x – x0) + b(y – y0).

The point (1, 2, 3) is given , substitute them for x0, y0 and z0:

Z – 3 = a (x – 1) + b(y-2)

Both a and b should be negative, because normal vector to point in the negative x and y direction so that plane will enclose a tetrahedron with finite area in the first octant.

This will only happen if z becomes smaller as we move towards the positive x and y directions.

To find expressions for V, firstly find expression for x, y and z intercepts.

X – Intercepts (y and z = 0) : 2b +a -3 / a

y- Intercepts (x, z = 0): 2b + a- 3 / b

z – Intercepts( x, y = 0): 3 – a – 2b

The base is = (2b+a-3)2/ 2ab

Volume is 1/3 base x height, so

V (a, b) = - (2b+a-3)3 / 6ab

The gradient vector:

ΔV (a, b) = |- (3(2b+a-3)2 ab-b (2b+a-3)3)/6a2b2, (6(2b+a-3)2 ab-a(2b+a-3)3)/6a2b2| = 0

b (2b+a-3)2 [ (2b+a-3) -3a] = 0

a (ab + a-3)2 [(2b +a -3) – 6b] = 0

Where a, b not equal to 0.

We cannot solve for 2b +a-3 = 0 because, that will lead to V = 0, which is impossible.

Therefore, we only solve for second halves equations, which are system of linear equations:

-2a + 2b = 3 and a – 4b = 3

Which gives a = -3 and b = -3/2

Put in equation:

Z – 3 = -3 (x-1) – 3/2 (y-2)

3x +3/2 y +z = 9

Multiplying by 2:

6x + 3y + 2z = 18.

Answer:

Option (b)

Step-by-step explanation:

From the graph attached in the figure,

Graph (a) is a scatter plot of a data set.

Data in this graph is not connected. In other words, a scatter plot represents a discrete function.

Similarly, in the graph (b) there is a straight line.

All points lying on this straight line are connected and follow the same rule.

Therefore, graph (b) represents a continuous function.

Therefore, Option (b) is the correct option.

Answer:

(5, -3)

Step-by-step explanation:

translation rule: (x+5, y+2)

(0+5, -5+2)

(5, -3)

Answer:

The first picture is a function. The second picture is not a function.

Step-by-step explanation:

The first one is a function because no x-values repeat. Different x-values can be paired with the same y-function.

The second one is not a function because it fails the horizontal line test. The line would touch in two spots, therefore failing the line test.

The volume of the sphere and the volume of the cylinder can be

expressed in terms of their radius.

Correct response:

The given parameters are;

Radius of the sphere = Radius of the cylinder

Height of the cylinder = Diameter of the sphere

Required:

The ratio of the volume of a sphere to the volume of a cylinder.

Solution:

Let r represent the radius of the sphere, we have;

The diameter of the sphere, D = 2·r

Therefore, the height of the cylinder, h = D = 2·r

The volume of the cylinder is; [tex]V_{cylinder}[/tex] = π·r²·h

[tex]\mathrm{The \ volume \ of \ a \ sphere\ is} \ V_{sphere} = \mathbf{ \dfrac{4}{3} \cdot \pi \cdot r^3}[/tex]

Therefore;

[tex]\mathbf{\dfrac{V_{sphere}}{V_{cylinder}}} = \dfrac{\dfrac{4}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 \cdot h} = \dfrac{\dfrac{4}{3} \cdot \pi \cdot r^3 }{\pi \cdot r^2 \times 2 \cdot r} = \dfrac{\dfrac{4}{3} }{2} =\dfrac{4}{6} = \dfrac{2}{3}[/tex]

[tex]\dfrac{2}{3} \ expressed as \ a \ ratio \ is \ 2:3[/tex]

Learn more about the volumes of solids here:

https://brainly.com/question/3376338

Answer:

95 degrees

Step-by-step explanation:

The was it has been rotated

Answer:

The range of the following set of points is {4, -2, -8}

Step-by-step explanation:

∵ The set of points is {(3, 4), (7, -2), (11, -8)}

∵ The range is the y-coordinates of these points

∵ The y-coordinates of the points are 4, -2, -8

∴ The range is {4, -2, -8}

∴ The range of the following set of points is {4, -2, -8}

Answer:

the correct answer is 180.8. i saw that other ppl had this answer on brianly but had 0 star ratings even though they were correct.

Step-by-step explanation: i just took this test and trusted the person who ansered and got it wrong.

Answer:

12 days

Step-by-step explanation:

95÷4=23.75

285÷23.75=12

Answer:

12 days

Step-by-step explanation:

multiply by 3 to get the answer

(1.) 20.4

(2.) 150

(3) 8

(4.) 15

Answer:

18 students for each teacher and 10 for each tutor, and if the academy had 80 students it would have 8 tutors

Step-by-step explanation:

Complete Question

Problem 9-8 (modified). The height of adult males in a particular city is normally distributed, with mean 69.5 in. and standard deviation 2.65 in.

When a random sample is taken of size  20, find (1) the standard error of Xbar

(2) the probability that Xbar falls within .5 in. of the true mean

Probability=

Answer:

1

[tex]\sigma_{\= x} = 0.5926[/tex]

2

[tex]P( 69 < \= X < 70) = 0.60134[/tex]

Step-by-step explanation:

From the question we are told that

  The true  mean is  [tex]\mu = 69.5 \ in[/tex]

  The standard deviation is  [tex]\sigma = 2.65 \ in[/tex]

    The sample size is n =  20

Generally the standard error of Xbar[tex](\= x)[/tex] is mathematically represented as

     [tex]\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }[/tex]

=>  [tex]\sigma_{\= x} = \frac{ 2.65 }{\sqrt{ 20 } }[/tex]

=>  [tex]\sigma_{\= x} = 0.5926[/tex]

Generally for  [tex]\= x[/tex] to fall within 0.5 of the true mean the [tex]\= x[/tex] must be within

     [tex]a = \mu + 0.5[/tex]

=>   [tex]a = 69.5 + 0.5[/tex]

=>   [tex]a = 70[/tex]

or  [tex]b = \mu -0.5[/tex]

=>    [tex]b = 69.5 -0.5[/tex]

=>    [tex]b = 69[/tex]

Generally the probability that  [tex]\= x[/tex] fall with 0.5  of the true mean is mathematically represented as

     [tex]P( 69 < \= X < 70) = P(\frac{69 - 69.5 }{ 0.5926} < \frac{\= X - \mu }{ \sigma_{\= x} } <\frac{70- 69.5 }{ 0.5926})[/tex]

=>  [tex]P( 69 < \= X < 70) = P(-0.844 < Z < 0.844)[/tex]

=>  [tex]P( 69 < \= X < 70) = P( Z < 0.844) - P( < -0.844)[/tex]

From the z table the probability of  (  Z    < 0.844)  and   (  Z    < -0.844)  is  

     [tex]P( Z < 0.844) = 0.80067[/tex]

and

    [tex]P( Z < - 0.844) = 0.19933[/tex]

So

   [tex]P( 69 < \= X < 70) = 0.80067 - 0.19933[/tex]

=>  [tex]P( 69 < \= X < 70) = 0.60134[/tex]

The standard error of the given data comes to be 0.593.

It is given that

mean [tex]\mu[/tex] = 69.5 inch

Standard deviation [tex]\sigma[/tex] = 2.65 inch

Sample size n =20

The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation.

The standard error is given by:

[tex]SE =\frac{\sigma}{\sqrt{n} }[/tex]

[tex]SE =\frac{2.65}{\sqrt{20} }[/tex]

[tex]SE=0.593[/tex]

Hence, the standard error of the given data comes to be 0.593.

To get more about standard errors visit:

https://brainly.com/question/1191244

Answer: Start with the parent function y=1/x^2

Add 3 to x in the denominator, because the graph is shifted left 3.

Add 1 to the fraction, because the graph is shifted up 1 unit

Step-by-step explanation:

Answer:

Find the equation using slope-intercept form.

y=−3(0,−5)/4 x+y

Answer:

x + x - 272 = 600

Step-by-step explanation:

Let the amount raised by Kate by x and let the amount raised by Isabelle be y.

Now, we are told that Kate raised $272 more than Isabelle.

Thus, since amount raised by Kate is x, then amount raised by Isabelle is x - 272. We are told that together they raised $600.

Thus;

x + x - 272 = 600

Thus;

equation to represent the total amount of money the girls raised is;

x + x - 272 = 600

Answer:

The first one

Step-by-step explanation:

Complete question :

An electronics store receives a shipment of 35 graphing calculators, including 7 that are defective. 8 of these calculators are selected for a local high school. (A) How many selections can be made? (B) How many of these selections will contain no defective calculators?

Answer:

23535820 ways

3108105 ways

Step-by-step explanation:

A.) How many selections can be made:

Number of ways of selecting 8 calculators from 35

35C8 :

Combination formula :

nCr = n! /(n-r)! r!

35C8 = 35! / (35-8)!8!

35C8 = 35! / 27! 8!

35C8 = (35*34*33*32*31*30*29*28) / (8*7*6*5*4*3*2*1)

35C8 = 948964262400 / 40320

= 23535820 ways

B.) number of non-defective calculators :

35 - 7 = 28

28C8 = n! /(n-r)! r!

28C8 = 28! / (28-8)!8!

28C8 = 28! / 20! 8!

28C8 = (28*27*26*25*24*23*22*21) / (8*7*6*5*4*3*2*1)

28C8 = 2506375872000 / 40320

= 3108105 ways

Answer:

288

Step-by-step explanation:

The ratio of gas to miles is 3:72. That is a proportion. 3:72 is the same as 12:288. (multiply both by 4)

Answer:

The y-intercept is 0

Step-by-step explanation:

Answer:

-6, -3, 0, 3

Step-by-step explanation: