1. What happened when you had a negative plus a negative, (-a) + (-b)?
I
2. What happened when you had a positive plus a negative, a + (-b)?
***Is this the same as a positive minus a positive, a - b?
3. What happened when you had a positive minus a negative, a - (-b)?
4. What happened when you had a negative minus a negative, (-a) - (-b)?​

Answers

Answer 1

Answer:

See Explanation

Step-by-step explanation:

1.

What happens when negative adds to negative; e.g (-a) + (-b)

First, we need to simplify the expression

[tex](-a) + (-b)[/tex]

Open the brackets

[tex]-a - b[/tex]

Factorize

[tex]-(a+b)[/tex]

So, what happens is that: the two numbers are added together and the result is negated;

E.g.

[tex](-5) + (-3) = -(5 + 3) = -8[/tex]

2.

What happens when positive is added to negative; e.g. a + (-b)

First, we need to simplify the expression

[tex]a + (-b)[/tex]

Open the brackets

[tex]a - b[/tex]

So, what happens is that: the negative number is subtracted from the positive number

And Yes; [tex]a + (-b)[/tex] is the same as [tex]a - b[/tex] (As shown above)

E.g.

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

3.

What happens when to positive minus a negative; e.g. a - (-b)

First, we need to simplify the expression

[tex]a - (-b)[/tex]

Open the brackets

[tex]a + b[/tex]

So, what happens is that; the two numbers are added together.

E.g.

[tex]5 - (-3) = 5 + 3 = 8[/tex]

4.

What happens when negative minus a negative; e.g. (-a) - (-b)

First, we need to simplify the expression

[tex](-a) - (-b)[/tex]

Open the brackets

[tex]-a + b[/tex]

Reorder

[tex]b - a[/tex]

So, what happens is that; the first number is subtracted from the second.

E.g.

[tex](-5) - (-3) = 3-5 = -2[/tex]


Related Questions

Write 4–6 sentences explaining why it is important to have precise definitions in mathematics.

Answers

Mathematics can be tricky so precise definitions are important. Without them there can be confusion which more often then not will generate a wrong answer. With clear precise definitions it is easier to understand the topic. Therefore, it is easier to get the correct answer.

A leaf blower was marked up 100% from an original cost of $152. If Eva bought the leaf blower and paid 7% sales tax, how much in total did she pay?

Answers

Answer:

$325.28

Step-by-step explanation:

152+152=304

304x1.07=325.28

Answer:

325.28

Step-by-step explanation:

increase the price by 100 %

152* 100%

152

Add this to the original price

152+152 = 304

Now find the sales tax

304 * 7%

304 * .07

21.28

Add this to the amount of the purchase price

304+21.28

325.28

The equation of a circle centered at the origin with a radius of unit length is x2 + y2 = 1. This equation changes if the center of the circle is not located at the origin or the radius is not of unit length.

Answers

Answer:

The equation for a unit radius circle, centered at the origin is:

x^2 + y^2 = 1

Now, if we want to move it horizontally, you can recall to the horizontal translations:

f(x) -----> f(x - a)

Moves the graph to the right by "a" units.

A vertical translation is similar.

Then, if we want a circle centered in the point (a, b) we have:

(x - a)^2  + (y - b)^2 = 1.

Now, if you want to change the radius, we can actually write the unit circle as:

x^2 + y^2 = 1^2

Where if we set x = 0, 1 = y, this is our radius

So if we have:

x^2 + y^2 = R^2

And we set the value of x = 0, then R = y.

So our radius is R.

Then:

"A circle of radius R, centered in the point (a, b) is written as:

(x - a)^2 + (y - b)^2 = R^2

a function includes the points (4, -3) and (-9,4). what fraction in lowest terms represents the output value of this function for an input of zero

Answers

Answer:

  -11/13

Step-by-step explanation:

The equation of the line through these points can be written using the 2-point form of the equation of a line:

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (4 -(-3))/(-9-4)/(x -4) -3

  y = (-7/13)x +28/13 -3

For x=0, the value of y is ...

  y = 28/13 -39/13 = -11/13

The output for an input of 0 is -11/13.

Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video
Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the
END OF THE IPOD ERA
players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007
through 2011 (in millions) were
approximately
N(0= -165t2 + 13.13t+ 39.9 (0 < t< 4)
in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

Answers

Answer:

a. t = 2.48 will be a period within 2009.

b. 56.16 million

Step-by-step explanation:

Here is the complete question

Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the early years but began to grow rapidly after 2005. But the iPod era is coming to a close. Smartphones with music and video

Apple introduced the first iPod in October 2001. Sales of the portable music player grew slowly in the

END OF THE IPOD ERA

players are replacing the iPod, along with the category of device it helped to create. Sales of the iPod worldwide from 2007

through 2011 (in millions) were

approximately

N(0= -2.65t2 + 13.13t+ 39.9 (0 < t< 4)

in year t, where t= 0 corresponds to 2007. Show that the worldwide sales of the iPod peaked sometime in 2009. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

a. Show that the worldwide sales of the iPod peaked sometime in 2009

N(t) = -2.65t² + 13.13t + 39.9

To find the maximum value of N(t), we find dN(t)/dt and equate it to zero

dN(t)/dt = d[-2.65t² + 13.13t + 39.9]/dt

dN(t)/dt = -5.3t + 13.13 = 0

-5.3t = - 13.13

t = -13.13/(-5.3)

t = 2.477

t ≅ 2.48

d²N(t)/dt² =d[-5.3t + 13.13]/dt = -5.3 < 0. So, t = 2.48 is a maximum point

Since t = 2 is 2009 and t = 3 is 2010, t = 2.48 will be a period within 2009.

b. What was the approximate largest number of iPods sold worldwide from 2007 through 2011?

The approximate largest number of ipods sold is when t = 2.48

N(2.48) = -2.65(2.48)² + 13.13(2.48) + 39.9

N(2.48) = -16.29856 + 32.5624 + 39.9

N(2.48) = 56.16384

N(2.48) ≅ 56.16 million

Avi's pet hamster Chubby loves to run in his hamster wheel. During one "race", Avi counts 100100100 rotations of the wheel. She wants to know how far Chubby ran, so she measures the diameter of the wheel and finds that it is 20 \text{ cm}20 cm20, start text, space, c, m, end text. How far did Chubby run? Round your answer to the nearest \text{cm}cmstart text, c, m, end text.

Answers

Answer:

63 cm

Step-by-step explanation:

If Chubby ran his wheel, which has a diameter of 20cm, we want to find its circumference - this will tell us how far Chubby has ran one one full rotation of the wheel.

The formula for the circumference of a circle is [tex]2\pi r[/tex], where r is the radius. We know the diameter is 20, which is double the radius, so the radius is [tex]20\div2=10[/tex] cm.

We can know substitute inside the formula:

[tex]2\cdot \pi \cdot10\\\\2\cdot 3.14 \cdot10\\\\ 6.28\cdot10\\\\62.8[/tex]

62.8 rounded to the nearest cm is 63.

Hope this helped!

Answer:

6280

Step-by-step explanation:

If Q(x)=x2−6x−2, find Q(−4).

Answers

Answer:

Q(-4) = 38

Step-by-step explanation:

Q(x)=x² − 6x − 2

To find Q(−4) substitute the value of x which is - 4 into Q(x)

That's

Q(-4) = (-4)² - 6(-4) - 2

Q(-4) = 16 + 24 - 2

We have the final answer as

Q(-4) = 38

Hope this helps you

Make Q the subject of the formula A = Q2 - 2a.

Answers

Answer:

[tex]\huge\boxed{Q = \sqrt{A+2a}}[/tex]

Step-by-step explanation:

[tex]A = Q^2 -2a[/tex]

Adding 2a to both sides

[tex]Q^2 = A+2a[/tex]

Taking sqrt on both sides

[tex]Q = \sqrt{A+2a}[/tex]

A random sample of 1003 adult Americans was asked, "Do you pretty much think televisions are a necessity or a luxury you could do without?" Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without.

Requried:
a. Obtain a point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without.
b. Verify that the requirements for constructing a confidence interval about p are satisfied.
c. Construct and interpret a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a luxury they could do without.
d. Is it possible that a supermajority (more than 60%) of adult Americans believe that television is a luxury they could do without ? Is it likely?
e. Use the results of part (c) to construct a 95% confidence interval for the population proportion of adult Americans who believe that televisions are a necessity.

Answers

Answer:

a)0.519

b)requirements for constructing a confidence interval about p are satisfied.

c)0.488, and 0.550

d)yes this is because there is no possibility

that the true proportion is not captured in the confidence interval.

e)

0.450, 0.512

Step-by-step explanation:

a)The point estimate for the population proportion of adult Americans who believe that televisions are a luxury they could do without can be calculated as

521 of that adult that indicated that televisions are a luxury they could do without/1003 adults surveyed,

p = 521/1003

= 0.519.

b)

np(1-p)=1003×(0.519)×(1-0.519)

=250.39≥10 and the sample size is less than 5% of the population

therefore, requirements for constructing a confidence interval about p are satisfied.

c) we were given 95% confidence,

Then α=(1-0.95)

= 0.05

From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96

confidence interval can the be calculated using the formula below

- p ± Z*√ p (1 – p)/n

=0.519 ± 1.96√0.519×(1 – 0.519)/(1003)

= 0.519 ± 1.96×0.0158

0.519 ± 0.031

= 0.488, and 0.550

d) yes this is because there is no possibility

that the true proportion is not captured in the confidence interval.

e)the sample size can be calculated as

P=x/n

=(1003-521)/1003

=0.481

But we're given 95% confidence interval

Then

α=(1-0.95)=

0.05

From the Z-tables,we can get the critical value is Z , which is (0.05/2) = Z (0.025) = 1.96

Then convidence interval=

- p ± Z*√ p (1 – p)/n

=0.481 ± 1.96√0.481×(1 – 0.481)/(1003)

0.450, 0.512

State the correct polar coordinate for the graph shown:

Answers

Answer:

Solution : ( - 5, 5π / 4 )

Step-by-step explanation:

There are four cases to consider here, the first two with respect to r > 0, the second two with respect to r < 0. r is the directed distance from the pole, and theta is the directed angle from the positive x - axis. Let's start by listing coordinates when r is positive. r here is 5 units from the positive x - axis.

( 5, θ ) theta here is between 30 and 60 degrees, so we can say it's about 45 degrees.

( 5, θ ) theta here is the remaining negative side of 360 - 45 = 315. That would make it - 315.

And when r is negative ( r < 0 ),

( - 5, θ ) now the point is going to lie on the ray pointing in the opposite direction of the terminal side of theta. This will be 45 degrees more than 180, or 180 + 45 = 225 degrees.

Right away we know that ( - 5, 225° ) is our solution, we don't have to consider the second case. Converting 225 to radians in terms of π will be 5π / 4 radians, giving us a solution of ( - 5, 5π / 4 ) or option b.


A box of chocolates contains five milk chocolates, three dark chocolates, and four white chocolates. You randomly select and eat three chocolates. The first piece is milk
chocolate, the second is white chocolate, and the third is milk chocolate. Find the probability of this occuring.

Answers

Answer:

60/220

Step-by-step explanation:

we use combination,

[tex] (\frac{5}{1} ) \times ( \frac{4}{1} ) \times ( \frac{3}{1} )[/tex]

[tex]5 \times 4 \times 3 = 60[/tex]

then, all divided by,

[tex] (\frac{12}{3}) = 220 [/tex]

[tex]60 \div 220[/tex]

The probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

What is Probability?

The probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

The sample contains five milk chocolates, three dark chocolates, and four white chocolates. Therefore, the probability that the first piece is milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{5}{12}[/tex]

Now, since the chocolate is been eaten the sample size will reduce from 12 chocolates in total to 11 chocolates in total (four milk chocolates, three dark chocolates, and four white chocolates). Therefore, the probability of the second piece being white chocolate is

[tex]\rm Probability=\dfrac{\text{Number of White choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{11}[/tex]

Now, as the chocolate is been eaten the sample size will reduce from 11 chocolates in total to 10 chocolates in total (four milk chocolates, three dark chocolates, and three white chocolates). Therefore, the probability of the third piece being milk chocolate is

[tex]\rm Probability=\dfrac{\text{Number of Milk choclates}}{\text{Total number of choclates}}[/tex]

[tex]\rm Probability=\dfrac{4}{10}[/tex]

Thus, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is

[tex]\rm Probability=\dfrac{5}{12}\times \dfrac{4}{11} \times \dfrac{4}{10} = \dfrac{80}{1320} = 0.06[/tex]

Hence, the probability of the first piece being milk chocolate, the second being white chocolate, and the third being milk chocolate is 0.06.

Learn more about Probability:

https://brainly.com/question/795909

Find the sum of the first 12 terms of the sequence 512, 256, 128, …

Answers

Answer: 1023.75 (a)

Step-by-step explanation:

The sequence is a Geometric progression with the common ratio of ¹/₂ and first term of 512.

a = 512, r = ¹/₂. To determine the ratio, just divide the second term by the first term.

Now to calculate the sum, we consider two formula here and select the one that is most appropriate,

(1)  a( rⁿ - 1 )/r - 1, when r is greater than 1

(2) a( 1 - rⁿ )/1 - rⁿ, when r is less than 1.

In this question, formula 2 shall be appropriate because r is less than 1.

so,

S₁₂      =  512( 1 - 0.5¹² )/1 - 0.5

             512( 1 - 2.44 ₓ 10⁻⁴ )/0.5

          = 512( 0,9998 )/0.5

          = 511.875/0.5

          = 1023.75

The answer is a

32. Identify all real and non-real zeros of the function f(x) = x^3 + 5x^2 + 3x + 15.
options:

A. x = 0, −5, 1.7i, −1.7i

B. x = 0,−5, 1.7i

C. x = −5, 1.7i, −1.7i

D. x = 0,−3, −5

Answers

Answer:

x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Step-by-step explanation:

Solve for x:

x^3 + 5 x^2 + 3 x + 15 = 0

The left hand side factors into a product with two terms:

(x + 5) (x^2 + 3) = 0

Split into two equations:

x + 5 = 0 or x^2 + 3 = 0

Subtract 5 from both sides:

x = -5 or x^2 + 3 = 0

x = (0 ± sqrt(0^2 - 4×3))/2 = ( ± sqrt(-12))/2:

x = -5 or x = sqrt(-12)/2 or x = (-sqrt(-12))/2

sqrt(-12) = sqrt(-1) sqrt(12) = i sqrt(12):

x = -5 or x = (i sqrt(12))/2 or x = (-i sqrt(12))/2

sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):

x = -5 or x = (i×2 sqrt(3))/2 or x = (-i×2 sqrt(3))/2

(2 i sqrt(3))/2 = i sqrt(3):

x = -5 or x = i sqrt(3) or x = (-2 i sqrt(3))/2

(2 (-i sqrt(3)))/2 = -i sqrt(3):

Answer: x = -5 or x = i sqrt(3) or x = -i sqrt(3)

Answer:

C. x = −5, 1.7i, −1.7i

Step-by-step explanation:

Quick answer:

C. x = −5, 1.7i, −1.7i

explanation:

C. is the only answer option that does NOT have 0 as a root, which is impossible, because there is a constant term, which means that all roots are non-zero. In other words, we cannot extract x as a factor.

Complete answer:

All odd degree polynomials have at least one real root.

By the real roots theorem, we know that

if there is a real root, it must be of the form [tex]\pm[/tex]p/q where q is any of the factors of the leading coefficient (1 in this case) and p is any factor of the constant term d (15 in this case).

Values of [tex]\pm[/tex]p/q are

On trial and error, using the factor theorem, we see that

f(-5) = 0, therefore -5 is a real root.  By long division, we have a quotient of x^2+3 = 0, which gives readily the remaining (complex) roots of +/- sqrt(5) i

The answer is {-5, +/- sqrt(5) i}, or again,

C. x = −5, 1.7i, −1.7i

please answer! I need these points for grade!

Answers

Answer:

∡NMO = 59°

Step-by-step explanation:

if MO bisect =>

=> ∡LMN = 2∡LMO =>

=> 5x - 22 = 2(x + 31)

5x - 22 = 2x + 62

5x - 2x = 62 + 22

3x = 84

x = 28°

∡LMO = ∡NMO => ∡NMO = x + 31

=> ∡NMO = 28 + 31 = 59°

Find the value of x , 5x =625 , also find 3x and 2x-1

Answers

Answer:

That's your answer

x= 125

3x= 375

2x-1= 249

You are to manufacture a rectangular box with 3 dimensions x, y and z, and volume v=8000. Find the dimensions which minimize the surface area of this box.

Answers

Answer:

20 by 20 by 20

Step-by-step explanation:

Let the total surface of the rectangular box be expressed as S = 2xy + 2yz + 2xz

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz ... 1

Given the volume V = xyz = 8000 ... 2

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20 by 20 by 20.

The dimensions which minimize the surface area of this box is 20 *20* 20. This can be calculated by using surface area and volumes.

The calculation for total surface area:

Let the total surface of the rectangular box be expressed as:

S = 2xy + 2yz + 2xz

where,

x is the length of the box

y is the width and

z is the height of the box.

S = 2xy + 2yz + 2xz .................(1)

Given:

Volume V = xyz = 8000 .............(2)

From equation 2;

z = 8000/xy

Substituting into equation 1;

S = 2xy + 2y(8000/xy)+ 2x(8000/xy)

S = 2xy+16000/x+16000/y

Differentiating the resulting equation with respect to x and y will give;

dS/dx = 2y + (-16000x⁻²)

dS/dx = 2y - 16000/x²

Similarly,

dS/dy = 2x  + (-160000y⁻²)

dS/dy = 2x - 16000/y²

Note that at the turning point, ds/dx = 0 and ds/dy = 0, hence;

2y - 16000/x² = 0 and 2x - 16000/y² = 0

2y = 16000/x² and 2x = 16000/y²

2y = 16000/(8000/y²)²

2y = 16000×y⁴/64,000,000

2y = y⁴/4000

y³ = 8000

y =³√8000

y = 20

Given 2x = 16000/y²

2x = 16000/20²

2x = 16000/400

2x = 40

x = 20

Since, Volume of the box is V = xyz

8000 = 20(20)z

8000 = 400z

z = 8000/400

z = 20

Hence, the dimensions which minimize the surface area of this box is 20*20*20.

Find more information about Surface area here:

brainly.com/question/1090412

what is 76.32 divided by 24.98 using compatible numbers to estimate each quotient?

Answers

Answer:

Approximately 3.05

Step-by-step explanation:

Using "compatible numbers" we can simply round these numbers to integer values.  Let's make 76.32 => 76 and 24.98 => 25

So from here let's do 76/25 to get 3 R 1/25

1/25 as a decimal is .04

So far, we have 3.04.  Going back to Look at our decimals, .32 and .98, there is a larger difference in our down rounding with the .32 than the up rounding from our .98.  So we should consider an extra value in our decimal.

Considering our whole number of 3.0, we can assume that our rounding will have an increase of about .01 or .015 in error.

Thus our number will be 3.04 + .01.

Making our quotient approximately 3.05.

Cheers.

A hunter shot 7 ducks. The hunter's dog recovered 5/7 of the ducks. How many ducks were recover

Answers

Answer:

5

Step-by-step explanation:

Just multiply 5/7 by 7 since his dog retrieved 5/7 out of the 7 ducks he shot.

Answer:

5

Step-by-step explanation:

7*5/7

7 represents the # of ducks

5/7 represents the # of ducks that were recovered

The question asks the number of ducks that were recovered so you should multiply the total # of ducks there are by the fraction that were recovered.

Suppose we want to test the color distribution claim on the M&M’s website that a bag of plain M&M’s is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown. We select a sample of 400 plain M&M’s and found the following: Color Blue Orange Green Red Yellow Brown Frequency 30 48 55 66 70 131
Is there evidence to doubt the color distribution claimed by the website? Use =0.05

Answers

Answer:

Calculated χ² = 13.425

χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24

The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.

Step-by-step explanation:

Color             Blue      Orange     Green    Red   Yellow    Brown

Frequency     30         48              55        66         70         131

Expected      40           40              40        80          80        120

H0:  The bag of plain M&Ms is made up of 10% blue, 10% orange, 10% green, 20% red, 20% yellow, and 30% brown

Ha: The color distribution is not equal to  the distribution stated in the null hypothesis.

Calculate chi square

χ² = (30-40)² /40 + (48-40)²/40 + (55-40)²/40 + (66-80)²/80 + (70-80)²/80 + (131-120)²/120

χ² = 2.5 + 1.6 + 5.625 + 2.45 + 1.25= 13.425

The critical region for χ²  for 5 degrees of freedom with ∝= 0.05 is

χ² (5,0.025) >14.45 and χ²(5,0.975) <1.24

The given data does not fall in the critical region so we accept H0 and conclude there is no evidence to doubt the color distribution claimed by the website.

Assume that a random sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level.

Answers

Answer:

Margin of Error = z∝/2 * Standard Error

Step-by-step explanation:

The formula for standard error is given by

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

Where p is the probability or proportion of success q=1-p and n is the number of trials or samples.

Now Margin of Error is given by

ME = z∝/2 * Standard Error

The confidence level is used to estimate the value of alpha.

For example 90% confidence means alpha= 1-0.9= 0.1 and alpha by 2 would be 0.05 . So the value for alpha by 2 would be 1.96

wo independent samples have been selected, 100 observations from population 1 and 76 observations from population 2. The sample means have been calculated to be x⎯⎯⎯1=11.9 and x⎯⎯⎯2=12.9. From previous experience with these populations, it is known that the variances are σ21=27 and σ22=23. (a) Determine the rejection region for the test of

Answers

Answer:

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

Step-by-step explanation:

A test for the difference between two population means is to be performed.

As the population variances are known, the z-test will be used.

The hypothesis can be defined as follows:

H₀: μ₁ = μ₂ vs. Hₐ: μ₁ ≠ μ

Assume that the significance level of the test is, α = 0.05.

The critical region can be defined as follows:

The critical value of z for α = 0.05 is:

[tex]z_{\alpha/2}=z_{0.05/2}=z_{0.025} =-1.96\\\\z_{1-\alpha/2}=z_{1-0.05/2}=z_{0.975} =1.96[/tex]

Use a z-table.

[tex]\text{Critical Region} = z<-1.96\ \text{or}\ z>1.96[/tex]

x + y + z = -6 -2x – 2y – 2z = 12 5x + 5y + 5z = -30 find x y and z please

Answers

Answer:

  x = s, y = t, z = -6 -s -t

Step-by-step explanation:

These are dependent equations. For some values s and t, the solution is ...

  x = s, y = t, z = -6 -s -t

Y varies inversely with x. If Y=17 and k(The constant of variation) =76, what is x? Round to the nearest tenth if necessary.

Answers

Answer:

x ≈ 4.5

Step-by-step explanation:

Given y varies inversely with x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

Here k = 76 and y = 17 , thus

17 = [tex]\frac{76}{x}[/tex] ( multiply both sides by x )

17x = 76 ( divide both sides by 17 )

x ≈ 4.5 ( to the nearest tenth )

Answer the questions attached about the given sequence: -33, -27, -21, -15, ...

Answers

Answer:

see below

Step-by-step explanation:

-33, -27, -21, -15,....

-33 +6 = -27  

-27+6 = -21

-21+6 = -15

This is an arithmetic sequence

The common difference is +6

explicit formula

an=a1+(n-1)d  where n is the term number and d is the common difference

an = -33 + ( n-1) 6

an = -33 +6n -6

an = -39+6n

recursive formula

an+1 = an +6

10th term

n =10

a10  = -39+6*10

      = -39+60

      =21

sum formula

see image

The sum will diverge since we are adding infinite numbers

Use the gradient to find the directional derivative of the function at P in the direction of Q. g(x, y, z) = xye^z, P(2, 4, 0), Q(0, 0, 0)

Answers

Answer: Find answer in the attached files

Step-by-step explanation:

Which of the following points IS a solution to the system: y > - 3x + 4 / y > 2x / - y < 7 Selected answer is not correct.

Answers

Answer:

Solution : Third Option

Step-by-step explanation:

The first step here is to make all the signs uniform. As you can see the third inequality has a less than sign, which we can change to a greater than sign by dividing negative one on either side, making the inequality y > - 7.

[tex]\begin{bmatrix}y>-3x+4\\ y>2x\\ y>-7\end{bmatrix}[/tex]

Now take a look at the third option. Of course the y - coordinate, 3, is greater than - 7, so it meets the third requirement ( y > - 7 ). At the same time 3 > 1( 2 ) > 2, and hence it meets the second requirement as well. 3 > - 3( 1 ) + 4 > - 3 + 4 > 1, meeting the first requirement.

Therefore, the third option is a solution to the system.

|5x|=3 please help me

Answers

Answer: see below

Explanation:

|5x| = 3

5x = 3
x = 3/5

5x = -3
x = -3/5

Find the sum of all solutions to this equation : ((2x-4)/x+1)) * ((2x+8)/2) * ((2x-70)/(x+2)) =0

Answers

Answer:

x=0 or x=2 or x=−4 or x= (7)(2)

Step-by-step explanation:

Jay is copying an angle. His work so far is shown below. Explain the importance of his next step, which is placing the point of the compass on L, opening the compass to N, and drawing an arc.


A. This ensures that when he draws another arc for angle Y, that it will be the right distance from point Z. <-- MY ANSWER


B. This arc is to make sure that both L and N are equidistant from M.


C. This arc makes sure that the distance from L to N is the same as the distance from Y to Z.


D. This way there will be two arcs drawn on both angles when he is done.

Answers

Answer:

  your answer is correct.

Step-by-step explanation:

For the purpose here, we'll call the missing point on the arc through Z point X.

Essentially, you want to make ΔXYZ ≅ ΔLMN by SSS. The construction so far ensures LM ≅ MN ≅ XY ≅ YZ. By copying the length LN to XZ, you ensure the congruence of the remaining sides of the triangles.

Then ∠XYZ ≅ ∠LMN because corresponding parts of congruent triangles are congruent.

In short, XZ needs to be the same distance as LN.

Which of the following best defines the midpoint of a segment? A. The point that splits a line segment into two equal parts. B. Any point on a line segment in between the two endpoints. C. When a line segment is split into equal thirds, a midpoint is any point in the middle third. D. Any point that is closer to one endpoint of the segment than the other.

Answers

Answer:

A. The point that splits a line segment into two equal parts.

Step-by-step explanation:

A. The point that splits a line segment into two equal parts.

Midpoint, as the word suggests, means the point which lies in the middle of something. The correct option is A.

What does a midpoint mean?

Midpoint, as the word suggests, means the point which lies in the middle of something. The midpoint of a line segment means a point which lies in the mid of the given line segment.

The statement that best describes the midpoint of a segment is the point that splits a line segment into two equal parts.

Learn more about Midpoint:

https://brainly.com/question/5127660

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