Which of the following statements are true?
A. The equation Ax = b is referred to as a vector equation.
B. A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax = b has at least one solution.
C. The first entry in the product Ax is a sum of products.
D. The equation Ax = b is consistent if the augmented matrix [Ab] has a pivot position in every row.
E. If the columns of an m \times n matrix A span {\mathbb R}^m, then the equation Ax = b is consistent for each b in {\mathbb R}^m.
F. If A is an m \times n matrix whose columns do not span {\mathbb R}^m, then the equation Ax = b is inconsistent for some b in {\mathbb R}^m.

Answer:

a) We can not estimate the probability.

b) Zero probability.

c) There is a probability between 95% and 99% that they have between 475 and 525 customers on a given day.

Step-by-step explanation:

a) We can not said nothing because we only know the average of customers per day. We need to know the probability distribution of the amount of customers per day to answer this question.

b) Now that we know that the variance is 100, although we do not know the exact distribution of the values, we can use the empirical rules to estimate the probability of having at least 700 customers on a given day.

If the variance is 100, the standard deviation is √100=10.

Applying the empirical rule (68-95-99.7 rule), we know that there is probability 0.15% of having at least 500+3*10=530 customers per day (more than 3 deviations from the mean).

Then, we can conclude that the probability of having at least 700 customers per day is zero.

c) To estimate this probability, we have to calculate how many deviations from the mean this values represent:

[tex]\Delta_1=475-500=-25=2.5\sigma\\\\\Delta_2=525-500=25=2.5\sigma[/tex]

We have an interval that have a width of ±2.5 deviations from the mean.

For 2 deviations from the mean, it is expected to have 95% of the data.

For 3 deviations from the mean, it is expected to have 99.7% of the data.

Then, for the interval 475 to 525, we can estimate a probability between 95% and 99%.

Answer:

the dimension of the poster = 90 cm length and 60 cm  width i.e 90 cm by 60 cm.

Step-by-step explanation:

From the given question.

Let p be the length of the of the printed material

Let q be the width of the of the printed material

Therefore pq = 2400 cm ²

q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]

To find the dimensions of the poster; we have:

the length of the poster to be p+30 and the width to be [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex]

The area of the printed material can now be:  [tex]A = (p+30)(\dfrac{2400 }{p} + 20)[/tex]

=[tex]2400 +20 p +\dfrac{72000}{p}+600[/tex]

Let differentiate with respect to p; we have

[tex]\dfrac{dA}{dp}= 20 - \dfrac{72000}{p^3}[/tex]

Also;

[tex]\dfrac{d^2A}{dp^2}= \dfrac{144000}{p^3}[/tex]

For the smallest area [tex]\dfrac{dA}{dp }=0[/tex]

[tex]20 - \dfrac{72000}{p^2}=0[/tex]

[tex]p^2 = \dfrac{72000}{20}[/tex]

p² = 3600

p =√3600

p = 60

Since p = 60 ; replace p = 60 in the expression  q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]   to solve for q;

q = [tex]\dfrac{2400 \ cm^2}{p}[/tex]

q = [tex]\dfrac{2400 \ cm^2}{60}[/tex]

q = 40

Thus; the printed material has the length of 60 cm and the width of 40cm

the length of the poster = p+30 = 60 +30 = 90 cm

the width of the poster = [tex]\dfrac{2400 \ cm^2}{p} + 20[/tex] = [tex]\dfrac{2400 \ cm^2}{60} + 20[/tex]  = 40 + 20 = 60

Hence; the dimension of the poster = 90 cm length and 60 cm  width i.e 90 cm by 60 cm.

Answer:

[tex]\frac{9}{8}[/tex]

Step-by-step explanation:

27 ÷ 9 = 3

3 * 3 = 9

9 ÷ 8 = [tex]\frac{9}{8}[/tex]

Answer:

10 players

Step-by-step explanation:

If you count the x’s, there are 10.

Why ask this question? You could have just counted

Answer:

22 players

Step-by-step explanation:

It specifically says 'at least 3 runs' so you would have to count all the x's in the columns 3, 4, and 5.

There are 10 x's in the 3 column

There are 3 x's in the 4 column

There are 9 x's in the 5 column

Hope this helps!

Answer:

To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _zeros_ polynomial. Then we find the intervals determined by the real _zeros and use test points in each interval to find the_ sign of the polynomial on that interval.

If P(x) = x(x+2)(x-1)

And P(x) ≥ 0

We see that P(x) ≥ 0 on the intervals (-2, 0) and (1, ∞).

Step-by-step explanation:

The complete question is attached to this solution

To solve inequality of a polynomial, we first obtain the solutions of the polynomial. The solutions of the polynomial are called the zeros of the polynomial.

If P(x) = x(x+2)(x-1)

The solutions of this polynomial, that is the zeros of this polynomial are 0, -2 and 1.

To now solve the inequality that arises when

P(x) ≥ 0

We redraw the table and examine the intervals

The intervals to be examined as obtained from the zeros include (-∞, -2), (-2, 0), (0, 1) and (1, ∞)

Sign of | x<-2 | -2<x<0 | 0<x<1 | x>1

x               | -ve | -ve | +ve | +ve

(x + 2)       | -ve | +ve | +ve | +ve

(x - 1)         | -ve | -ve | -ve | +ve

x(x+2)(x-1) | -ve | +ve | -ve | +ve

The intervals that satisfy the polynomial inequality P(x) = x(x+2)(x-1) ≥ 0 include

(-2, 0) and (1, ∞)

Hope this Helps!!!

Answer:

4

Step-by-step explanation:

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

m=(6-(-2))/(3-1)

m=8/2

m=4

Answer:

c

Step-by-step explanation:

when the absolute value of slope gets smaller, the graph of line gets less steeper.

Answer:  [tex]\bold{\dfrac{8}{17}=47.1\%}[/tex]

Step-by-step explanation:

[tex]\dfrac{\text{painter or sculptor}}{\text{total artists}}=\dfrac{6+2}{6+2+9}=\dfrac{8}{17}[/tex]

Answer:

Length = 550 m

Width = 275 m

Area = 151,250 m2

Step-by-step explanation:

One side of the farmland is bounded by the river, so the perimeter we will need to enclose is:

[tex]Perimeter = Length + 2*Width = 1100\ m[/tex]

And the area of the farmland is given by:

[tex]Area = Length * Width[/tex]

From the Perimeter equation, we have that:

[tex]Length = 1100 - 2*Width[/tex]

Using this in the area equation, we have:

[tex]Area = (1100 - 2*Width) * Width[/tex]

[tex]Area = 1100*Width - 2*Width^2[/tex]

Now, to find the largest area, we need to find the vertex of this quadratic equation, and we can do that using the formula:

[tex]Width = -b/2a[/tex]

[tex]Width = -1100/(-4)[/tex]

[tex]Width = 275\ m[/tex]

This width will give the maximum area of the farmland. Now, finding the length and the maximum area:

[tex]Length = 1100 - 2*Width = 1100 - 550 = 550\ m[/tex]

[tex]Area = Length * Width = 550 * 275 = 151250\ m2[/tex]

Answer:

24.99

Step-by-step explanation:

If the area of the quarter circle is 38.465, then the equation to find this would be

3.14*r^2 / 4 = 38.465. we solve for r, the radius, and get two solutions. 7 and -7. Obviously the length of the radius can't be -7, so we know the radius is 7.

Now we must solve for the perimeter. The perimeter is equal to 2r + (2*3.14*r)/4

Plugging 7 in as the radius, r, we get 24.99 as our final answer.

Answer:

what is this boiii?

Answer:

A= 1/2bh

Step-by-step explanation:

(how its supposed to be said: Area= one half base times height)

:)

Answer:

(1) As a simple definition, a triangle is a two-dimensional figure that has 3 sides (and 3 angles as well).

(2) A triangle as shown in attached picture has the area that is typical calculated by the multiplication of half of base and height.

A = (1/2) x Base x Height

Base can be a particular side of triangle

Height is the perpendicular line segment between the opposite vertex of selected base and that base.

Hope this helps!

:)

Answer:

Step-by-step explanation:

We have to find the reported happiness of person of family income of $25,000, $35,000 and $45,000

Given that the formula for finding relation between a people happiness and his income is

y = 0.065x - 0.613

a) find the happiness of person of family income os $25,000

we put x = 25 as in the equation above

[tex]y=0.065(25)-0.613\\\\=1.625-0.613\\\\=1.02 \approx 1[/tex]

Hence, person happiness with with family income of $25,000 on a scale of 3 is y = 1

That means they come under catergory "not to happy"

b) Find the happiness of person of family income os $35,000

we put x = 35 as in the equation above

[tex]y=0.065(35)-0.613\\\\=1.667-0.613\\\\=1.667 \approx 1.7[/tex]

Hence, person happiness with with family income of $35,000 on a scale of 3 is y = 1.7

That means they come under catergory "not to happy" and "fairly happy"

c) Find the happiness of person of family income os $45,000

we put x = 45 as in the equation above

[tex]y=0.065(45)-0.613\\\\=2.925-0.613\\\\=2.312 \approx 2.3[/tex]

Hence, person happiness with with family income of $45,000 on a scale of 3 is y = 2.3

That means they come under catergory  "fairly happy"

The scale would show the data as follows:

Happiness Scale at Income 25, 35, 45 &amp; 55 thousand :

1.012 (Not too happy), 1.662 (Fairly Happy), 2.315 (Fairly Happy) , 2.965 (Very Happy)

Important Information :

Relationship between happiness scale 'y' and income in 1000s 'x' :y = 0.065x − 0.613, for people in income group between [tex]25000 & 55000[/tex]

Happiness scale : At level of income, between 25 and 55 thousands.

Putting value of income 'x' to find scale of happiness i.e. 'y'

For income 'x' = 25 thousand : [tex]y = 0.065 (25) - 0.613 = 1.625 - 0.613 = 1.012[/tex] For income 'x' = 35 thousand : [tex]y = 0.065 (35) - 0.613 = 2.275 - 0.613 = 1.662[/tex]For income 'x' = 45 thousand : [tex]y = 0.065 (45) - 0.613 = 2.925 - 0.61 = 2.315[/tex] For income 'x' = 55 thousand :[tex]y = 0.065 (55) - 0.613 = 3.575 - 0.61 = 2.965[/tex]

Learn more about "Happiness Scale" here:

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Answer:

0.96 radians

Step-by-step explanation:

Formula

1° = [tex]\frac{\pi }{180}[/tex] radians

Multiplying both sides by 55, It becomes

55° = [tex](\frac{\pi }{180} )*55[/tex]

55° = [tex]\frac{55\pi }{180}[/tex]

= 172.8/180

= 0.96 radians

Answer:

work is shown and pictured

Answer: x<3

Step-by-step explanation:

Answer:

It will take 800seconds to you to run 5000m

Step-by-step explanation:

Let time taken to run 5000m is x

Using ratio and proportion

200:32=5000:x

200/32=5000/x

200*x=5000*32

200x=160000

x=800seconds

Answer:

8400

Step-by-step explanation:

Its too long and I answered it before

Answer:

The value 155 is zero standard deviations from the [population] mean, because [tex] \\ x = \mu[/tex], and therefore [tex] \\ z = 0[/tex].

Step-by-step explanation:

The key concept we need to manage here is the z-scores (or standardized values), and we can obtain a z-score using the next formula:

[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]

Where

Carefully looking at [1], we can interpret it as the distance from the mean of a raw value in standard deviations units. When the z-score is negative indicates that the raw score, x, is below the population mean, [tex] \\ \mu[/tex]. Conversely, a positive z-score is telling us that x is above the population mean. A z-score is also fundamental when determining probabilities using the standard normal distribution.

For example, think about a z-score = 1. In this case, the raw score is, after being standardized using [1], one standard deviation above from the population mean. A z-score = -1 is also one standard deviation from the mean but below it.

These standardized values have always the same probability in the standard normal distribution, and this is the advantage of using it for calculating probabilities for normally distributed data.

A subject earns a score of 155. How many standard deviations from the mean is the value 155?

From the question, we know that:

Having into account all the previous information, we can say that the raw score, x = 155, is zero standard deviations units from the mean. The subject   earned a score that equals the population mean. Then, using [1]:

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

[tex] \\ z = \frac{155 - 155}{50}[/tex]

[tex] \\ z = \frac{0}{50}[/tex]

[tex] \\ z = 0[/tex]

As we say before, the z-score "tells us" the distance from the population mean, and in this case this value equals zero:  

[tex] \\ x = \mu[/tex]

Therefore

[tex] \\ z = 0[/tex]

So, the value 155 is zero standard deviations from the [population] mean.

Measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.

The terminal side of an angle is the rotated side of the initial side around a point to form an angle. This rotation can be clockwise or counter clock wise.

The terminal side of an angle in standard position rotated one-sixth of a revolution counterclockwise from the positive x-axis.

The total degree in a complete rotation of a side is 360 degrees. The side is rotated 1/6. Thus the angle is rotated is,

[tex]\theta=\dfrac{1}{6}\times360\\\theta=60^o[/tex]

Multiply it with π/180 to find the measure of the angle in radian.

[tex]\theta=60\dfrac{\pi}{180}\\\theta=\dfrac{\pi}{3}\\[/tex]

Hence, the measure of the angle which is made by rotating a side as terminal side by one-sixth of a revolution counterclockwise is 60 degree and π/3 radian.

Learn more about the terminal side of an angle here

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Answer:

4

Step-by-step explanation:

A=P0(1+rt).

We know that A=$3,500,P0=$2,800 and r=7.5%=0.075, so we can rearrange the formula for A to get an explicit expression for t:

A=P0(1+rt)⟹t=A−P0P0r,

and substituting the known quantities gives

r=$3,500−$2,800$2,800×0.075=3.33,

which means, since the interest is paid annually, that she must wait four years for the total investment to exceed $3,500.

Answer:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Step-by-step explanation:

Let X the random variable of interest that a woman must wait for a cab"the amount of time in minutes " and we know that the distribution for this random variable is given by:

[tex] X \sim Unif (a=0, b =12)[/tex]

And we want to find the following probability:

[tex] P(X<11)[/tex]

And for this case we can use the cumulative distribution function given by:

[tex] P(X\leq x) =\frac{x-a}{b-a}, a \leq x \leq b[/tex]

And using this formula we have this:

[tex] P(X<11) = \frac{11-0}{12-0}= 0.917[/tex]

Then we can conclude that the probability that that a person waits fewer than 11 minutes is approximately 0.917

Answer:

12

Step-by-step explanation:

f(-4) = -8-5(-4) = -8+20 = 12

Answer:

f(-4) = 12

Step-by-step explanation:

f(-4) = -8 - 5(-4)

= -8 + 20

= 12

Step-by-step explanation:

-8x + 4 > 5 - 3x

-8x + 3x > 5 - 4

-5x > 1

x > 1 / - 5

Answer:

Intervals = (1,064) , (1,036)

Step-by-step explanation:

Given:

Use 95% method

Mean = 1,050

Standard deviation = 7

Find:

Intervals.

Computation:

95% method.

⇒ Intervals = Mean ± 2(Standard deviation)

⇒ Intervals = 1,050 ± 2(7)

⇒Intervals = 1,050 ± 14

⇒ Intervals = (1,050 + 14) , (1,050 - 14)

⇒ Intervals = (1,064) , (1,036)

The Intervals = (1,064) , (1,036)

Given that:

Based on the above information, the calculation is as follows:

Intervals = Mean ± 2(Standard deviation)

Intervals = 1,050 ± 2(7)

Intervals = 1,050 ± 14

Intervals = (1,050 + 14) , (1,050 - 14)

Intervals = (1,064) , (1,036)

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[tex]answer \\ = 2 , 4 , 5 \\ additional \: information \\ let \: r \: be \: a \: relation \: a \: to \: b. \: then \: the \: set \\ of \: first \: components \: or \: the \: set \: of \: \\ elements \: of \: a \: are \: called \: domain \\ and \: the \: set \: of \: second \: components \\ or \: the \: set \: of \: elements \: of \: b \: are \: called \: the \: range. \\ hope \: it \: helps[/tex]

Answer:

x ≤ -4

Step-by-step explanation:

2(3 - x) ≥ 14

Divide by 2

2/2(3 - x) ≥ 14/2

(3 - x) ≥ 7

Subtract 3 from each side

3-x-3  ≥ 7-3

- x ≥ 4

Divide each side by -1, remembering to flip the inequality

x ≤ -4

Answer:

-4

Step-by-step explanation:

6-2x≥14 (/expand )

-2x≥14-6=-2x≥8

x≤8/-2=-4

Answer:

  C

Step-by-step explanation:

The function of table A can be written as ...

  y = 100x -92

__

The function of table B can be written as ...

  y = 10x +446

__

The function of table C can be written as ...

  y = (5/3)·3^x

__

The function of table D can be written as ...

  y = 2x +413

__

The exponential function of Table C will have the largest y-values for any value of x greater than 6.

_____

Comment on the functions

When trying to determine the nature of the function, it is often useful to look at the differences of the y-values for consecutive x-values. Here, the first-differences are constant for all tables except C. That means functions A, B, D are linear functions.

If the first differences are not constant, one can look at second differences and at ratios. For table C, we notice that each y-value is 3 times the previous one. That constant ratio means the function is exponential, hence will grow faster than any linear function.

Answer:

yes, what the other user  is correct i just took the quiz

Step-by-step explanation:

Answer:

We know that:

The original price was $515

and

It was $125 off

so we need to find the price of the sofa after the discount.

$515 - $125 = $390

The sale price of the sofa after the discount was $390

hope This helps and pls mark me brainliest if it did :)

Answer:

D

Step-by-step explanation:

Length × Width = Area

So we'll substitute the Area of the circle having formula, πr²