If the subspace of all solutions of Ax 0 has a basis consisting of vectors and if A is a ​matrix, what is the rank of​ A

The value of x is  = -5, -3

Answer:

12,464 ft

Step-by-step explanation:

I assume that the elevation of the lake is the altitude at the surface of the water.

The surface of the lake is 922 ft above the deepest point of the lake.

11,542 ft + 922 ft = 12,464 ft

Answer:

x=3 15/16 hours together

Step-by-step explanation:

the painter paints 1/7 of the house in 1 hour

the assistant paints 1/9 of the house in 1 hour

x=# of hours it takes them together to paint the house

(1/7)x+(1/9)x=1 (job finished)

multiply both sides by the LCM which is 63

63(1/7)x+63(1/9)x=63(1)

9x+7x=63

16x=63

x=63/16

x=3 15/16 hours together

Answer: Kim took 50 minutes to read the third book.

Step-by-step explanation: If you substract 120 - 15 = 105. Then divide 105 / 3 = 35. And finally add 35 + 15 = 50.

Answer:

see explanation

Step-by-step explanation:

Given the 2 equations

2x + 3y = 10 → (1)

x + y = 7 → (2)

Multiplying (2) by - 3 and adding to (1) will eliminate y

- 3x - 3y = - 21 → (3)

Add (1) and (3) term by term to eliminate y, that is

- x = - 11 ( multiply both sides by - 1 )

x = 11

Substitute x = 11 into either of the 2 equations and evaluate for y

Substituting into (2)

11 + y = 7 ( subtract 11 from both sides )

y = - 4

Solution is (11, - 4 )

Answer:

It will take 11/30(cistern/hour) for the tank to be full

Answer:

36

Step-by-step explanation:

To find the average of a series of numbers, add them together and then divide by the count of numbers, i.e., 4.

(35 + 27 + 54 + 28) / 4 = 36

Answer:

answer is 36

Step-by-step explanation:

for finding average we have to add all the numbers and by dividing that by the total number present we can get the average

so there are 4 numbers

average= 35+27+54+28/ 4

or 144/4= 36 (ans)

thank uu

Answer:

Read Exp:

Step-by-step explanation:

1.) 4 is the Base and 8 is the Exponent.

2.) 9^4 = 9 x 9 x 9 x 9 = 6561.

3.) (-5)^2 = -5 x -5 = 25.

4.) 3^3 = 3 x 3 x 3 = 27.

5.) (1/2)^5 = 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 0.03125

Have to change it to a simplified fraction:

* 1/32

Answer:

160 balloons

Step-by-step explanation:

Step 1: State what is known

She blew up 24 balloons

She only inflated 15%

We want to find the total amount of balloons

Let the total balloons equal "x"

Step 2: Write you equation

[tex]0.15x=24\\\frac{0.15x}{0.15} =\frac{24}{0.15} \\x = 160[/tex]

Therefore there are 160 balloons in total

Answer:

[tex]\sqrt{\frac{9}{4}}[/tex]       [tex]\frac{5}{3}[/tex]         [tex]\sqrt{5}[/tex]       [tex]2.5[/tex]

Step-by-step explanation:

Given

[tex]\sqrt{\frac{9}{4}}[/tex]

[tex]\sqrt{5}[/tex]

2.5

[tex]\frac{5}{3}[/tex]

Required

Order from least to greatest

Start by simplifying each expression

[tex]\sqrt{\frac{9}{4}}[/tex]

Split square root

[tex]\frac{\sqrt{9}}{\sqrt{4}}[/tex]

Take square root of numerator and denominator

[tex]\frac{3}{2}[/tex]

[tex]1.5[/tex]

Hence

[tex]\sqrt{\frac{9}{4}} = 1.5[/tex]

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

[tex]\sqrt{5}[/tex]

[tex]\sqrt{5} = 2.2361[/tex] (Approximated)

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

[tex]2.5[/tex]

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

[tex]\frac{5}{3}[/tex]

[tex]\frac{5}{3} = 1.6667[/tex]

Considering the simplified expression; the number from least to greatest is:

[tex]\sqrt{\frac{9}{4}}[/tex]       [tex]\frac{5}{3}[/tex]         [tex]\sqrt{5}[/tex]       [tex]2.5[/tex]

Answer:

(a) the time for the event of the highest 5% is 15.29 minutes.

(b) the time for the event of the lowest 50% is 12 minutes.

(c) the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.

(d) the time for the event of the lowest 80% is 13.68 minutes.

Step-by-step explanation:

We are given that the time required to cook a pizza at a neighborhood pizza joint is normally distributed with a mean of 12 minutes and a standard deviation of 2 minutes.

Let X = the time required to cook a pizza at a neighborhood pizza joint.

The z-score probability distribution for the normal distribution is given by;

                              Z  =  [tex]\frac{X-\mu}{\sigma}[/tex]  ~ N(0,1)

where, [tex]\mu[/tex] = mean time = 12 minutes

           [tex]\sigma[/tex] = standard deviation = 2 minutes

(a) We have to find the time for the event of the highest 5%, that means;

           P(X > x) = 0.05     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] > [tex]\frac{x-12}{2}[/tex] ) = 0.05

           P(Z > [tex]\frac{x-12}{2}[/tex] ) = 0.05

Now, in the z table, the critical value of x that represents the top 5% of the area is given as 1.645, i.e;

                      [tex]\frac{x-12}{2}=1.645[/tex]

                      [tex]{x-12}=1.645\times 2[/tex]

                      x = 12 + 3.29 = 15.29 minutes.

Hence, the time for the event of the highest 5% is 15.29 minutes.

(b) We have to find the time for the event of the lowest 50%, that means;

           P(X < x) = 0.50     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.50

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.50

Now, in the z table, the critical value of x that represents the lowest 50% of the area is given as 0, i.e;

                      [tex]\frac{x-12}{2}=0[/tex]

                      [tex]{x-12}=0[/tex]

                      x = 12 + 0 = 12 minutes.

Hence, the time for the event of the lowest 50% is 12 minutes.

(c) We have to find the time for the event of the middle 95%, that means we have to find the time for the event of 2.5% and above 97.5%;

Firstly, the time for the event of the lowest 2.5%, i.e;

           P(X < x) = 0.025     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.025

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.025

Now, in the z table, the critical value of x that represents the lowest 2.5% of the area is given as -1.96, i.e;

                      [tex]\frac{x-12}{2}=-1.96[/tex]

                      [tex]{x-12}=-1.96 \times 2[/tex]

                      x = 12 - 3.92 = 8.08 minutes.

Firstly, the time for the event of the below 97.5%, i.e;

           P(X < x) = 0.975     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.975

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.975

Now, in the z table, the critical value of x that represents the top 2.5% of the area is given as 1.96, i.e;

                      [tex]\frac{x-12}{2}=1.96[/tex]

                      [tex]{x-12}=1.96 \times 2[/tex]

                      x = 12 + 3.92 = 15.92 minutes.

Hence, the time for the event of the middle 95% is 8.08 minutes and 15.92 minutes.

(d) We have to find the time for the event of the lowest 80%, that means;

           P(X < x) = 0.80     {where x is the required time}

           P( [tex]\frac{X-\mu}{\sigma}[/tex] < [tex]\frac{x-12}{2}[/tex] ) = 0.80

           P(Z < [tex]\frac{x-12}{2}[/tex] ) = 0.80

Now, in the z table, the critical value of x that represents the lowest 80% of the area is given as 0.8416, i.e;

                      [tex]\frac{x-12}{2}=0.8416[/tex]

                      [tex]{x-12}=0.8416 \times 2[/tex]

                      x = 12 + 1.68 = 13.68 minutes.

Hence, the time for the event of the lowest 80% is 13.68 minutes.

Answer:

Wednesday: 45 - 18

Thursday: 55 - 22

Step-by-step explanation:

18*2.5=45

55/5=11

11*2=22

Answer:

Trees Planted Unknown Value = 45

Trees Harvested Unknown Value = 22

Step-by-step explanation:

Plants : Harvest

= 5 : 2

= x : 18

= 5 * x : 2 * x

= 5 * x : 18 / 2

= 5 * x : 9

= 5 * x : x

= 5 * x : 2 * x

= 5 * 9 : 2 * 9

= 45 : 18

Trees planted value  = 45

Plants : Harvest

= 5 : 2

= 55 : y

= 5 * y : 2 * y

= 55 / 5 : 2 * y

= 11 : 2 * y

= y :  2 * y

= 5 * y : 2 * y

= 5 * 11 : 2 * 11

= 55 : 22

Trees harvested value  = 22

I really hope this helps! Tell me if I am incorrect!

Answer:

Step-by-step explanation:

8/2

Numerator is bigger than denominator. So it is improper fraction and rational number

Rational numbers are any number that can be written in p/q form

Answer:

it should be improper fraction

Step-by-step explanation:

because the numerator is greater than the denominator.

Hope it helps :)

Answer:

3.935 x 10^5.

Step-by-step explanation:

There are five digits after the first 3 so  it will be 10^5.

The answer is 3.935 x 10^5.

393500 equals 3.935×10⁵

If we write xⁿ then we mean to say that x is multiplied n times.

The exponent of a number says how many times the number is multiplied by itself.

393500=3.935×100,000=3.935×10⁵

Hence, 393500=3.935×10⁵

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Answer:

A - x (x+3) = Area of the rectangle

B- 28 inches squared

Step-by-step explanation:

B- using the formula from A

x = 4

x + 3 = 4 +3 = 7

4 times 7 is 28

Answer: 28ins²

Step-by-step explanation:

From the question, let the width of the rectangle = xins.

Therefore, the breadth                                            = ( x + 3 )ins.

(A) The area of the rectangle which is L x B          = x( x+ 3 )

                                                                              = (x² + 3x)ins² . In polynomial.

(B) The area of the rectangle if the width is 4ins, that is if x = 4ins.To find the area, we substitute for x in the area above

                                                                             = 4² + 3 x 4

                                                                             = 16 + 12

                                                                             = 28ins²

Answer:

B. 0.36

Step-by-step explanation:

Given:

Right ∆ABC,

AB = 5

BC = 13.93

CA = 13

Required:

Value of sin C

SOLUTION:

[tex] sin(C) = \frac{opposite}{hypotenuse} [/tex]

Opposite = 5

Hypotenuse = 13.93

[tex] sin(C) = \frac{5}{13.93} [/tex]

[tex] sin(C) = 0.3589 [/tex]

[tex] sin(C) = 0.36 [/tex]

the answer would be B, 0.36

Answer:

yes

Step-by-step explanation:

take for example

in the expression: 3x²+5x+2=0,

the coefficients here are +3 and +5 while +2 is a constant. +3 and +5 are coefficients of the variables x² and x respectively

Answer:

[tex](x-3-2i)(x-3+2i)[/tex]

Steps:

[tex]8x^2-48x=-104[/tex]

[tex]8x^2-48x+104=0[/tex]

Divide both sides by 8

[tex]x^2-6x+13=0[/tex]

But we can't factor it.

Using the Quadratic Formula to calculate the roots:

[tex]$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$[/tex]

[tex]$x=\frac{-(-48)\pm \sqrt{(-48)^2-4\cdot 8\cdot 104}}{2\cdot 8}$[/tex]

[tex]$x=\frac{48\pm32i}{16}$[/tex]

[tex]x_1=3+2i\\x_2=3-2i[/tex]

The answer might be

[tex](x-(3+2i))(x-(3-2i))[/tex]

[tex](x-3-2i)(x-3+2i)[/tex]

Answer:

Pritam gets $22.50

Step-by-step explanation:

Ratios

Pritam =3

Sarah=6

Emily=4

The ratio between Sarah and Emily = 6:4

=3:2

If Sarah gets $15 more than Emily

Then,

Sarah gets $45

Emily gets $30.

The ratio between Pritam and Sarah = 3:6

= 1:2

Since Sarah gets $45,

Pritam gets half as much= $45 / 2

=$22.50

Answer: No

Step-by-step explanation: no because one is negative 1 3/4 and the other one isint in the negatives

The sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 by cumulative property.

A summation, also abbreviated as a sum, is the outcome of adding two or more numbers or quantities. Here are always an integer number of terms in a summation. There are summations with an infinite set of parameters.

The summation is to add or subtract any two or more terms by doing that operation we will get a new result which could be big or small depending upon the number.

Cumulative property is the property summation states;

x + y will be equal to y + x ⇒ x +y = y + x

Now given,

The sum of  -1 3/4 and 2 1/2 ⇒  -1 3/4 + 2 1/2  

By cumulative property,

-1 3/4 + 2 1/2   = 2 1/2 + -1 3/4

The difference between 2 1/2 and 1 3/4 ⇒  2 1/2 -  1 3/4

Hence "The sum of -1 3/4 and 2 1/2 is the same as the difference between 2 1/2 and 1 3/4 by cumulative property".

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Answer:

b. The paint will not fill the tray by 5.22 in3.

Step-by-step explanation:

The computation is shown below:

First we have to determine the volume of tray by using the following equation

[tex]V = L \times W \times H[/tex]

Now transform this from dimensions to inches

Now  putting the values,

[tex]V = 10\times12\times (5\times(\frac{1}{2.54})) \\\\As\ 5 cm = 5 \times (\frac{1}{2.54})[/tex]

the volume would be equivalent to the

236.22 inches^3

Now 1 gallon is 231 inches^3

So, the remaining would be

= 236.22 - 231

= 5.22^3

Therefore the correct option is b.

Hence, all the other options are wrong

Answer:

[0,6] means that its the numbers from 0 through 6 containing 0 and 6

[0,6) means that it contains the numbers from 0 through 6 containing 0 but not 6

(0,6) means that it contains the numbers from 0 through 6 containing not 0 or 6.

Step-by-step explanation:

Answer:

6½ gallons

Step-by-step explanation:

Givem the cost of 1gallon of gas = $2.78. . If Cory buys $18 of gas, we are to find the number of gallons did he buy. To do that we will use the equality method as shown;

$2.78 ,= 1gallon

$18 = x gallon

Cross multiply

2.78 × x = 1×18

2.78x = 18

Divide through by 2.78

2.78x/2.78 = 18/2.78

.x = 6.5

Hence Cory buys about 6½ gallons of gas for $18

Answer:

316,912,650,057,057,350,374,175,801,344

Step-by-step explanation:

You can see that this sequence is geometric so you need to know the geometric sequence which is [tex]x_{n} =r^{n-1}[/tex] and if you plug in every thing you get [tex]x_{n}[/tex]=[tex]2^{99-1}[/tex] which would be [tex]2^{98}[/tex] which is 316,912,650,057,057,350,374,175,801,344

Answer:

1/4

Step-by-step explanation:

3 red + 6 green = 9 total

P( red) = red/total = 3/9 = 1/3

Now we don't put it back

2 red + 6 green = 8 total

P( green) = green/total = 6/8 = 3/4

P (red, keep,green) = 1/3 * 3/4 = 1/4

Answer:

[tex]\Large \boxed{{\frac{1}{4} }}[/tex]

Step-by-step explanation:

There are 3 red clips and 6 green clips.

Total clips = 3 + 6 = 9

The probability of picking a red clip is 3/9 = 1/3.

You don’t put the red clip back.

Now there are 2 red clips and 6 green clips.

Total clips = 2 + 6 = 8

The probability of picking a green clip is 6/8 = 3/4

P(pulling out a red clip and then a green clip) = 1/3 × 3/4 = 3/12 = 1/4

Answer:

1

Step-by-step explanation:

[tex](-140 ^0) ^ -2\\1^-2\\1\\[/tex] (Any number whose exponent in 0, becomes 1)

Answer:

Approximately

W=132.29

Step-by-step explanation:

W=k(TA√F)/R

T=78°F

R=5.6 inches

F=4

A=1000 square feet

W=$72

Solve for k

W=k(TA√F)/R

72=k(78*1000*√4)/5.6

72=k(78,000*2) / 5.6

72=k(156,000) / 5.6

72*5.6 =156,000k

403.2=156,000k

k=403.2/156,000

=0.002585

Solve for w when F=6, A=1500, T= 78, R=5.6 inches

W=k(TA√F)/R

W=0.002585(78*1500*√6) / 5.6

=0.002585(78*1500*2.4495) / 5.6

=0.002585(286,591.5) /5.6

=740.8390 / 5.6

=132.2927

W=132.2927

Approximately 132.29

Answer:

Neptune is 2.86 times further away from Saturn.

Step-by-step explanation:

Distance from Neptune to Earth is [tex]4.3\times 10^9\ km[/tex]

Distance from Saturn to Earth is [tex]1.5\times 10^9\ km[/tex]

We need to find how many times Neptune is further away from Saturn. It can be calculated by dividing distance from Neptune to Earth to the distance from Saturn to Earth as follows :

[tex]\dfrac{d_N}{d_S}=\dfrac{4.3\times 10^9}{1.5\times 10^9}\\\\\dfrac{d_N}{d_S}=2.86\\\\d_N=2.86\times d_S[/tex]

It would mean that Neptune is 2.86 times further away from Saturn.

Answer:

B

Step-by-step explanation:

To achieve an average of 95% on 4 tests, the sum of the scores Olivia gets must be 95 * 4 = 380. Right now, the sum of her scores is 89 + 98 + 96 = 283 so she must get at least a 380 - 283 = 97% on her last test.