45% of the population of a city are men
and 15% are children. If the number of
women is 64,400, find the number of
children.

No, the rank of the product of two n by n square matrices A and B, denoted as AB, cannot be less than n-1 if both A and B have ranks of n-1.

According to the Rank-Nullity theorem, for any matrix M, the sum of its rank and nullity is equal to the number of columns in M. In this case, the number of columns in AB is n, so the sum of the rank and nullity of AB must be n.

If rank(A) = rank(B) = n-1, it means that both A and B have nullity 1. The nullity of a matrix is the dimension of its null space, which consists of all vectors that get mapped to the zero vector when multiplied by the matrix. Since both A and B have rank n-1, their null spaces consist only of the zero vector.

Now, considering AB, if the rank of AB were less than n-1, it would mean that the nullity of AB is greater than 1.

However, this would violate the Rank-Nullity theorem since the sum of the rank and nullity of AB must be n, which is the number of columns.

Therefore,  if rank(A) = rank(B) = n-1, the rank of AB cannot be less than n-1.

For more such questions on rank

https://brainly.com/question/28839672

#SPJ8

Answer:

x = 1.71

Step-by-step explanation:

\(x^3-20=-15\\x^3=-15+20\\x^3=5\\\sqrt[3]{x^3} =\sqrt[3]{5} \\x=1.71\)

Answer:

1 2/3

Step-by-step explanation:

3x-20= -15

   +20   +20

3x = 5

= 1 2/3

Hope This Helps!

Answer: time=distance/speed

if speed is given in ml per hour then:

time=410/120=3.417 hours=3 hours 25 min

plus half an hour totally for stops.

total time will be 3 hours 55 min.

if speed is given in km per hour you have to convert to ml per hour 1st:

1 km = 0.62 ml

120 km/hr = 120*0.62 ml/hr.

Step-by-step explanation:

Answer:

maybe put the answer choices ....

Step-by-step explanation:

Answer:

1661 was each sold

Step-by-step explanation:

I hope

Answer:

416 adult tickets were sold and 765 student tickets were sold

Step-by-step explanation:

We would first define our variables,

a=amount of adult tickets sold   s=amount of student tickets sold

Now we will create our equations,

5a+1s=2845

(adult price times amount of adult tickets sold + children price times amount of children tickets sold=amount that type of ticket made)

a+s=1181

(amount of adult tickets sold+ amount of child tickets sold=total tickets sold)

We'll use the substitution method to find the answer,

a=1181-s

5(1181-s)+s=2845

5905-5s+s=2845

5905-4s=2845

-4s=-3060

4s=3060

s=765

a+765=1181

a=1181-765

a=416

The circumference of the circle is 25. 12cm

The formula for calculating the circumference of a circle is expressed as;

C = 2πr

Given that;

The formula for radius is expressed as;

Radius = diameter/2

Radius = 8/2

Radius = 4cm

Substitute the values

Circumference, C = 2× 3.14 × 4

Multiply through

Circumference = 25. 12cm

Hence, the value is 25. 12cm

Learn more abut circumference here:

https://brainly.com/question/14283575

#SPJ1

Answer:

$0.64 per cup

Step-by-step explanation:

There are 16 cups in 1 gallon, so the number of cups in 2 gallons is:

1 gallon: 16 cups

2 gallon = 2 x 1 gallon = 2 x 16 cups = 32 cups

So we need to find the price of each cup:

1 cup = ($20.48 / 32 cups) = $0.64 per cup.

The proof for  AB ≅ CD is:

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

Consider triangle ABC and triangle ADC.

Here, side BC is parallel to side AD.

From the attached figure we can observe that AC is a transversal.

so, ∠BCA and ∠CAD would be alternate angles formed by two parallel lines and transversal.

By property of  Alternate Interior angles,

∠BCA ≅ ∠CAD

Also, we can observe that side AC is common side to ΔABC and ΔADC.

We rewrite this proof as,

Step                 Statement                                Reason

 1              ∠B ≅ ∠D, BC || AD                          Given

 2               ∠BCA ≅ ∠CAD                Alternate Interior angles

 3                      AC ≅ AC                             common side

 4                 ΔABC ≅ ΔADC         Angle-Angle-Side rule of congruency

 5                   AB ≅ CD            Corresponding sides of congruent triangle

This is the required proof.

Learn more about congruent triangles here:

https://brainly.com/question/29789245

#SPJ1

Answer:

17y+24

Step-by-step explanation:

simplify so the first step would be to multiply whats in the parentheses by the number outside in this case its 6 youd get:

12y+24+5y

then you simplify farther by adding like terms

17y+24

Answer:

43.6 has 3 significant figures.

Answer:

$14.4

Step-by-step explanation:

First set a porpotion of 20/100 = x/18

Then do 20x18=360

360 Divided by 100=3.6

So 18-3.6=14.4

Answer:

$14.40

Step-by-step explanation:

Answer:

a table of products of two factors especially the integers 1 to 12 have a nice day

Step-by-step explanation:

:)

Step-by-step explanation:

The formula to find the interior angle of a polygon is 180(n - 2) over n.

So, we know that the interior angle of the polygon which is 120, therefore we can produce this equation, 180(n - 2) over 2 n, equals to 120.

Now we use algebric method to solve for n.

180n − 360 = 120n

60n = 360

n = 6

The equation will be  \(y=40000+16000*x\)

Solve one of the equations for a particular variable. After that, insert that into the other equation and find the variable there. To find the value for the other variable, enter that value into either equation.

Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true. Two expressions joined by the equals symbol ("=") form an equation.

To know more about identities visit:-

brainly.com/question/14681705

#SPJ1

Answer:

x = 2

Step-by-step explanation:

P = \(\frac{x-2}{x+1}\)

P will equal zero when the numerator is equal to zero , that is

x - 2 = 0 ( add 2 to both sides )

x = 2

P = 0 when x = 2

Answer:

whaaaaaattttt                        

Step-by-step explanation:

.................................... i think c or f

Answer:

P(A)=0.25

P(B)=0.077

P(AB)=0.192

P(BA)=0.083

Check below for the full numbers, I rounded it for you.

Step-by-step explanation:

What is P(A), the probability that the card is a club?

So whenever you get a deck of cards you'll have 52 which have 4 suits, think of it like UNO, and club is one of the suit's name! This mean all this question is asking you is the probability of getting a club out of the 52 cards which is

52/4=13

So we know that there is 13 club cards.

Meaning the probability is a 25% since you can only get it 1/4 of the time.

P(A)=0.25

What is P(B), the probability that the card is a 5?

Same as what I stated earlier but this time you only have 4 cards that can be a "5" out of the 52 cards.

4/52=0.076923

P(B)=0.077

What is P(A and B), the probability that the card is a club and a 5?

Keep a eye on the working "and" this means it's referring to the possibility of getting a club and a 5 and since this can only happen once the chances are extremely slim.

1/52=0.1923076

P(AB)=0.192

What is P(BA), the conditional probability that the card is a 5 given that it is a club?

This assumes that you're only drawing from a deck of ONLY clubs so the chances of getting a 5 in that stack.

1/12=0.08333 (3 keeps going)

P(BA)=0.083

(This one might be wrong since I haven't done conditional probability in a long time but I feel somewhat confident, I do feel confident about the rest so no worries.)

Is P(BA) = P(B)? Are the events A and B independent?

No, P(BA) = P(B) is not true since A and B do influence one another since what if I get a 5 without replacement this results in change of chances of A.

Answer:

1.1/4

2.1/13

3.1/52

4.1/13

5. Yes p(B/A)=P(B) and Yes, events A and B are independent events.

Step-by-step explanation:

khan academy walk through

Since the optimal production level is within the company's maximum capacity of 150 items, the company should produce and sell 75 items to maximize profit.

A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.

To find the optimal production level a that maximizes profit, we need to determine the point at which marginal revenue equals marginal cost.

The marginal cost function is the derivative of the cost function, which is C'(a) = 50.

The marginal revenue function is the derivative of the revenue function, which is R'(a) = -0.5(3/8 - 110).

Setting these two equal and solving for a gives:

50 = -0.5(3/8 - 110)

a = 75

Since the optimal production level is within the company's maximum capacity of 150 items, the company should produce and sell 75 items to maximize profit.

To know more about Function visit:

brainly.com/question/12431044

#SPJ1

The simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

Given information:

f(x) = (log₂(x) + 2) and g(x) = (log₂(x³) - 6)

h(x) = f(x) + g(x) = (log₂(x) + 2) + (log₂(x³) - 6)

Using the rules of logarithms, we can simplify g(x) as follows:

g(x) = log₂(x³) - 6

= 3 log₂(x) - 6.

Now we can substitute this into the expression for h(x):

h(x) = (log₂(x) + 2) + 3 log₂(x) - 6

= 4 log₂(x) - 4

Therefore, the simplified expression for h(x) is h(x) =  4 log₂(x) - 4.

To learn more about the expression;

brainly.com/question/24242989  

#SPJ1

Answer:

D. is correct.

\(2 * 1 = 2\)

\(4 * 1=4\)

\(4 + 2 = 6\)

________________________________________________________

The product of answer choice D.(6) is not equal to the product of \(\frac{2}{3}\) × 4, because \(\frac{2}{3}\) × 4 is actually \(2\frac{2}{3}\)

________________________________________________________

We learned how to find whole numbers through an expression with fractions.

Questions related to the topic? Ask me in the comments box.

The sequence, \(a_n =e ^{\frac{{-8}}{\sqrt{n}}}\), is convergent sequence because the limit of an exists, that is as n approaches infinity, so the sequence an approaches 1 ( finite value).

The sequence can be convergent if the limit is zero, or if the limit is finite. The divergent sequence is one whose limit is not finite. The limit can be found suing the limit properties or by simplification method, as applicable. We have, an sequence, \(a_n =e ^{\frac{{-8}}{\sqrt{n}}}\). We have to check whether the sequence converges or diverges. Using limits, \(lim_ {n->\infty } a_n = lim_{n-> oo} e^{\frac{-8}{\sqrt{n}}} \)

n approaches infinity, so square root of n approaches infinity,

= e⁻⁰

= 1/e⁰ = 1 ( finite )

Therefore, it is a convergent sequence.

For more information about convergence of sequence, visit :

https://brainly.com/question/30646523

#SPJ4

The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.

Given that;

1) 2/3 + 6/3

We combine the numerators over the common denominators

= ( 2 + 6 ) / 3

= 8/3

2) 4/6 + 9/6

We combine the numerators over the common denominators

= ( 4 + 9 ) / 6

= 13/6

3) 6/6 + 6/6

We combine the numerators over the common denominators

= ( 6 + 6 ) / 6
= 12/6

= 2

The values of (2/3 + 6/3), ( 4/6 + 9/6 ) and ( 6/6 + 6/6 ) are 8/3, 13/6 and 2 respectively.

Learn more about fractions here: https://brainly.com/question/10354322

#SPJ1

Answer:

x=30

Step-by-step explanation:

Find the value of x that will make A and B parallel

For A & B to be parallel, the interior angles must be supplementary, i.e.

4x+2x = 180

6x=180

x=30

When x=30, the interior angles are 120 and 60 which are supplementary.

Answer:

∠ R = 90°

Step-by-step explanation:

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

∠ R + ∠ S + ∠ T = 180° , substitute values

∠ R + 29° + 61° = 180°

∠ R + 90° = 180° ( subtract 90° from both sides )

∠ R = 90°

4.2 x 10^8 is  2*10^6  times the value of 2.1 x 10^2 when division is performed.

The concept that will be used to solve the question is division operation.

We were given 4.2 x 10^8 which is greater than  2.1 x 10^2

The operation can be expressed as :

4.2 x 10^8 =( n *2.1 x 10^2)

where n = the number of times that 4.2 x 10^8  is greater than 2.1 x 10^2

Then make n the subject of the formular which is

n = 4.2 x 10^8/2.1 x 10^2

n = 2*10^6

Therefore, the values of 4.2 x 10^8 is greater than 2.1 x 10^2 in 2*10^6 times.

Read more about division at:

brainly.com/question/11421834

#SPJ1

The values of the angles are:  (a) 154⁰( b) 26⁰ (c) 154⁰  (d) 154⁰  (e) 90⁰  (f) 116⁰  (g) 64⁰  (h) 154⁰  (j) 154⁰

We should use the types of angles to determine the sizes of the angles each.

a) To find the value of a, we have 180-26 = 154⁰ The reason is the angle on a straight line

(b) The value of b is 26⁰ (vertically opposite angles)

(c) The value of c is : c=j=54⁰  (vertically opposite angles)

(d) The angle b is : 180-26 = 154 ( angles on a straight line)

(e) The angle e is : 90⁰

(f) The value of angle f is 180-64 =116⁰⁰  ( angles on a straight line)

(g) Angle g is given as: 64⁰  (vertically opposite angles)

(h) The value of angle: g=h=64⁰ ( Alternate angles are equal)

(j) Angle j is: c=j=154⁰  (vertically opposite angles)

In conclusion, he values of the angles are:  (a) 154⁰( b) 26⁰ (c) 154⁰  (d) 154⁰  (e) 90⁰  (f) 116⁰  (g) 64⁰  (h) 154⁰  (j) 154⁰

Learn more about value of angles on https://brainly.com/question/29098736

#SPJ1

The constant of variation of the given problem is calculated as; 240 miles

A constant of variation (k) is defined as a ratio that represents the relationship between the independent variable (x) and the dependent variable (y).

Now, we are told that average speed, s, in miles per hour is inversely proportional to the time, t, the trip takes in hours. Thus;

s ∝ 1/t

Thus;

s = k(1/t)

where k is the constant of proportionality

we are told that If the train takes 2 hours, and the average speed is 120 mph. Thus;

120 = k(1/2)

Multiply both sides by 2 to get;

240 miles = k

Read more about Constant of Variation at; https://brainly.com/question/25215474

#SPJ1

Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

The probability of the complement of the event is 0.05.

The complement of an event is the probability of that event not occurring. The relationship between the probability of an event and its complement is that they always add up to 1.

Therefore, if the probability of an event occurring is p, then the probability of its complement not occurring is 1-p.

In the case where the probability of an event is 0.95, the probability of its complement not occurring would be 1-0.95 = 0.05. This means that the probability of the complement of the event is 0.05.

This concept is important in probability theory and is used to calculate the probabilities of events and their complements. It allows us to consider all possible outcomes of a given situation and calculate the likelihood of each of them.

for such more question on probability

https://brainly.com/question/13604758

#SPJ11

The percentage of people under 18 in the sample of 250 people from Ohio is higher than the percentage of people under 18 in the United States.

This can be demonstrated mathematically using the following formula: (28/250)*100 = 11.2%. This is higher than the US percentage of 23.5%, which indicates that the sample of 250 people from Ohio had a higher proportion of people under 18 than the US population as a whole. To calculate this, we can use the formula to find the difference between the two percentages: (28% - 23.5%) = 4.5%. This means that the small town in Ohio has a higher percentage of people under 18 than the national average. Therefore, it is true that the percentage of people under 18 in the small town in Ohio is higher than the national average.

Learn more about percentages here:

https://brainly.com/question/16797504

#SPJ4

Given info:-

Evaluate the expression 8-5xy^3 for x=3 and y = -2.

8 - 5xy^3

⇛8 - 5(3)(-2)^3

⇛8 - 15(-2*-2*-2)

⇛8 - 15(-8)

⇛8 - (-120)

⇛8 + 120

⇛128 Ans.