Show that a discrete metric on a vector space X≠{0} cannot be obtained from a norm (the pair (X,d) is called the discrete metric space if the metric is d(x,x)=0, d(x,y)=1 for x≠y).

Solution:

Note that:

Simplify the LHS, then use cross multiplication to solve for n.

Answer:

n = 15

Step-by-step explanation:

\(\dfrac{1}{5}n=3\)

Multiply both sides by 5:

\(\implies n = 3 \times 5 = 15\)

Answer:

Step-by-step explanation:

U={x|x∈N and x<10}

or U={1,2,3,4,5,6,7,8,9}

B={x|x∈N and x is even and x<10}

or

B={2,4,6,8}

C={x|x∈N and x<10}

or

C={1,2,3,4,5,6,7,8,9}

(B∩C)={2,4,6,8}

(B∩C)'={1,3,5,7,9}

Answer:

it takes the bears 12 days to eat honey together.

Step-by-step explanation:

1/x+9+1/x+16=1/x

(solve this using cross multiplication)

= x^2 = 144

x=12

The number of days that it takes for both of the considered bears to eat a barrel of honey together is 12 days.

More people to do a task means less time it will take.

Less people to do a task means more time it will take.

Thus, they are inversely related.

We can define a constant as "Manpower" needed for doing that specific work.

Each worker has his/her own strength. That strength is applied per unit of time.

Let we define:

Manpower needed for a work = time taken for that work  × strength used for that work per unit of time

(we used multiplication as it represents linear use of strength to finish the task, so using that strength for a finite units of time means you stacked up your strengths that many times to finish that work)

Here, we have:

Assume that:

Then, we get:

Manpower needed for a work = time taken for that work  × strength used for that work per unit of time

\(M = x \times S\\M = y \times T\)

If bear A and bear B both do the work together, then their strenghts will add up.

That means, the combined strength would be S + T per day

The manpower the work needs is still M, therefore, the time needed is:

\(M = \text{Time needed} \times (S + T)\\\\\text{Time needed} = \dfrac{M}{S+T}\)

This is the time needed for both bears to do the work together.

Also, it is given that:

It takes a bear 9 more days to eat a barrel of honey alone than it takes the bear and a second bear to eat the barrel of honey together.

or

Time needed by bear A to do work = 9 + time needed by both bears to do the work

or

\(x = 9 + \dfrac{M}{S + T}\)

Also, it is given that:

It takes the first bear 7 fewer days to eat a barrel of honey alone than it takes the second bear to eat a barrel of honey alone.

or

Time taken by bear A to do the work = Time taken by bear B for that work - 7 days

or

\(x = y - 7\)

Thus, we got these equations:

\(M = S \times x\\M = T \times y\\\\x = \dfrac{M}{S + T} +9\\\\x = y - 7\)

call them first, second, third and fourth equation as per their ordering.

From the first and second equation, we get:

\(S = \dfrac{M}{x}\\\\T = \dfrac{M}{y}\)

Putting these values in the third equation, we get:

\(x = \dfrac{M}{M/x + M/y} + 9\\\\\\x = \dfrac{xy}{x+y} + 9\\\\(x-9)(x+y) = xy\\x^2 -9x -9y + xy = xy\\x^2 -9x = 9y\)

From the fourth equation, we know that:

\(x = y - 7\)

or \(y = x +7\)

Putting this value of y in the  equation \(x^2 -9x = 9y\), we get:
\(x^2 -9x = 9(x+7)\\x^2 -9x = 9x + 63\\x^2 -18x -63 =0\\\\x^2 -21x + 3x -63 = 0\\x(x-21) + 3(x - 21) = 0\\(x+3)(x-21) = 0\\(x+3) = 0, (x-21) = 0\\x = -3, x = 21\)

'x' represents time in number of days. So it cannot be negative.

Thus, the value of x obtained is 21.

Also, we need: Time needed for both the bears to do the work together.

This time is the value of \(\dfrac{M}{S+T}\), which is equal to \(x - 9\) days (from the third equation)

Thus, the time needed  for both the bears to do the work together = \(x-9 = 21-9 = 12 \; \rm days\)

Thus, the number of days that it takes for both of the considered bears to eat a barrel of honey together is 12 days.

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Answer:

n = 4.5

Step-by-step explanation:

10 - 5.5 = n

Answer:

I feel like its 4.5

Step-by-step explanation:

Answer:

Step-by-step explanation: You have to add the number

420

+77

497

6/8 can not be turned into a bigger number unless you are trying to reduce it which would be 3/4

We know that :

The sum of two angles that are complementary = 90°

Smaller angle = x

Larger angle = 2x

We can make the formula as

= 2x + x = 90°

= 3x = 90°

= x = 90 ÷ 3

= x = 30

The smaller angle = x = 30°

The larger angle = 2x = 30 × 2 = 60°

Therefore , the measure of each of the angles are 30° and 60° .

Answer: y = 2x + 7

Step-by-step explanation:

Given line = -1/2

given line = y = -1/2x + 7

Perp line = y = 2x + 7

Answer:

the best way to solve this is to have graph paper, so your numbers and points align. I have a model attached. the first point is hours slept 8. so on your graph go to 8 then across to 83, which is the test score. make a mark to represent this point. do this for all and it will create a line

Answer:

I believe it’s b

Step-by-step explanation:

Answer:

g(x)=(x+2)^2

Step-by-step explanation:

Answer:

approximately 14.2127 but it could also be simplified to the square root of 2 times the square root of 101

Answer:

7

Step-by-step explanation:

$15 to buy salad and $2 for each bag. You need to find how many times 2 goes into 15, and evenly it goes 7 times so, therefore, 7 x 2 = 14 with $1 remainder.

Answer:

6610

Step-by-step explanation:

We have tan(X) = opposite/ adjacent

tan(QBP) = PQ/BQ

tan(35) = PQ/BQ    ---eq(1)

tan(QAP) = PQ/AQ

tan(20) = \(\frac{PQ}{AB +BQ}\)

\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)

230*tan(20) + PQ*tan(20)*tan(35) = PQ

⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)

⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]

\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)

\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)

PQ = 110.4

≈110

Height above sea level = 6500 + PQ

6500 + 110

= 6610

Two linear functions with point (1,4) are given by:

The graph with these two functions is given at the end of the answer.

A linear function, in slope-intercept format, is modeled according to the rule presented below:

y = mx + b

In which the coefficients are described as follows:

A line with slope of 2 is given by:

y = 2x + b.

Supposing that it goes through point (1,4), when x = 1, y = 4, hence we can find the intercept as follows:

4 = 2 + b

b = 2.

Hence the first equation is:

y = 2x + 2.

A line with slope of -2 is given by:

y = -2x + b.

Then the intercept is found as follows, supposing that it also goes through the point (1,4):

4 = -2 + b

b = 6.

Then the equation is:

y = -2x + 6.

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Step-by-step explanation:

-coefficent=1

-collect like terms /variables

-add numbbers (1+2)=3p

Answer:

1

Step-by-step explanation:

(p+q)(p-q)/(p+q)(p-q)=1

[It is an identity : a²-b²= (a+b)(a-b)]

Hope this will help:)

The solution to the inequality 6x - 6 < -30 is x < -4, and it is graphically represented as a closed circle at -4 and shading to the left of -4 on the number line.

To solve the inequality 6x - 6 < -30, we can follow these steps:

Step 1: Add 6 to both sides of the inequality to isolate the variable:

6x - 6 + 6 < -30 + 6

6x < -24

Step 2: Divide both sides of the inequality by 6 to solve for x:

(6x)/6 < (-24)/6

x < -4

The solution to the inequality is x < -4. This means that any value of x less than -4 will satisfy the inequality.

To graph the solution on the number line, we represent -4 as a closed circle (since it is not included in the solution) and shade the region to the left of -4 to indicate all values less than -4.

On the number line, mark a point at -4 with a closed circle:

<--------●-----------------

Then, shade the region to the left of -4:

<--------●================

The shaded region represents the solution to the inequality x < -4.

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Answer:

595.

Step-by-step explanation:

Take $2000 and subtract $810 from it. You now have the total of the two pieces of equipment without the extra pricing. You should get $1,190. Then divide that number by 2. You will get $595.

1st Piece of Equipment = $595

2nd Piece of Equipment = $1,405

2nd Piece is $810 more expensive and the two pieces combined is $2,000.

Answer:

C

Step-by-step explanation:

The following equation defines the population t years after 2010,

P = 45230(1 + 0.02\()^{t}\).

An exponential function's curve is created by a pattern of data called exponential growth, which exhibits higher increases over time.

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and sx is the time period.

Given:

The population in Small town in 2010 was 45,230 people and is growing exponentially at a rate of 2 percent.

The formula;

y = a(1+r)ˣ,

where a is the initial population and r is the rate in decimals and x is the time period.

That means,

P = 45230(1 + 0.02\()^{t}\)

Therefore, the equation is P = 45230(1 + 0.02\()^{t}\)

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Answer:

a)

31.53

31.099

31.009 ⬅ (I'm assuming this one is a decimal too)

b)

0.03

0.009

0.007

Explanation:

Here ya go.

Hope this helps :)

Answer:

no solutions

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer:

a) 4,706 scored between 60 and 80

b) A score of 90.6.

c) 81th percentile.

Step-by-step explanation:

When the distribution is normal, we use the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the zscore of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question, we have that:

\(\mu = 75, \sigma = 15\)

A. About how many scored between 60 and 80?

Proportion:

This is the pvalue of Z when X = 80 subtracted by the pvalue of Z when X = 60. So

X = 80

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{80 - 75}{15}\)

\(Z = 0.33\)

\(Z = 0.33\) has a pvalue of 0.6293

X = 60

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{60 - 75}{15}\)

\(Z = -1\)

\(Z = -1\) has a pvalue of 0.1587

0.6293 - 0.1587 = 0.4706

How many?

0.4706 out of 10,000, so

0.4706*10000 = 4706

4,706 scored between 60 and 80.

B. Approximately what score did only the top 15% exceed?

The 85th percentile, which is X when Z has a pvalue of 0.85. So X when Z = 1.037.

\(Z = \frac{X - \mu}{\sigma}\)

\(1.037 = \frac{X - 75}{15}\)

\(X - 75 = 1.037*15\)

\(X = 90.6\)

A score of 90.6.

C. Find the percentile rank of the person who scored 88.

This is the pvalue of Z when X = 88. So

\(Z = \frac{X - \mu}{\sigma}\)

\(Z = \frac{88 - 75}{15}\)

\(Z = 0.87\)

\(Z = 0.87\) has a pvalue of 0.8078

So, rounding up, the 81th percentile.

Answer:

The Factor is 1.5

Step-by-step explanation:

5.1(which is B'C') divided by 3.4(which is BC) = 1.5

3.6(A'C') divided by divided by 2.4(AC) = 1.5

2.7(A'B') divided by 1.8(AB) = 1.5

Henceforth the factor is 1.5  

|x- 1,200|= 125 is an absolute value equation to represent the boutique owner goal.

Without taking into account direction, absolute value describes how far a number is from zero on the number line. A number's absolute value can never be negative.

The example for absolute value is |-9|=9.

|x- 1,200|= 125 is the correct representation to achieve her goal because it will result in rise of goal. Other options will give negative sign and that is impossible.

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|x- 1,200|= 125 is an absolute value equation to represent the boutique owner goal.

What is meant by absolute value?

Absolute value is a term used in mathematics to refer to the magnitude or distance of a number from zero regardless of its sign. In other words, it is the numerical distance of a number from zero on the number line, regardless of whether it is a positive or negative number. For example, the absolute value of -3 is 3, and the absolute value of 3 is also 3. The symbol for absolute value is two vertical lines surrounding the number or expression, for example |-3| = 3.

Write an example of absolute value.
The example for absolute value is |-9|=9.

|x- 1,200|= 125 is the correct representation to achieve her goal because it will result in rise of goal. Other options will give negative sign and that is imposible.

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The unknown angle measures are d = 76, c = 53, a = 51 and b = 76

From the question, we have the following parameters that can be used in our computation:

The lines

The sum of angles on a line is 180

So, we have

b = 180 - 51 - 53

b = 76

By vertical angle theorems, we have

d = 76

c = 53

a = 51

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Step-by-step explanation:

To solve the inequality |2x + 5| < 2 - x, we need to split it into two cases:

When 2x + 5 > 0:

In this case, the absolute value is positive, so we can simplify the inequality as follows:

2x + 5 < 2 - x

Expanding the left side:

3x + 5 < 2

Subtracting 5 from both sides:

3x < -3

Dividing both sides by 3:

x < -1

So the solution for this case is x < -1.

When 2x + 5 < 0:

In this case, the absolute value is negative, so we can simplify the inequality as follows:

(2x + 5) < 2 - x

Expanding the left side:

-2x - 5 < 2 - x

Adding x to both sides:

-2x - 5 + x < 2

Combining like terms:

-x - 5 < 2

Adding 5 to both sides:

-x < 7

Dividing both sides by -1:

x > -7

So the solution for this case is x > -7.

Taking the union of the two solutions, we get:

-7 < x < -1.

This means that x is between -7 and -1, excluding -7 and -1.

The area of the complex figure is 132 square units

From the information given, we have that the composite shape is a combination of a:

The formula for area of a square is given as:

Area = a ²

Where 'a' is the length of it side

Area = 6²

Area of square = 36 square units

The formula for area of a rectangle is given as:

Area = width × length

Area = 8 × 12

Area of rectangle = 96 square units

Area of the complex figure = Area of square + area of rectangle

= 36 + 96

= 132 square units

Thus, the area of the complex figure is 132 square units

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The solution of the equation  -22 = q + 7(2q - 1) is as follows:

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

Let's solve the equations as follows:

-22 = q + 7(2q - 1)

The variable in the equation is q. A variable is an letter use to represent number in an equation.

-22 = q + 7(2q - 1)

-22 = q + 14q - 7

-22 = 15q - 7

add 7 to both sides of the equation

-22 + 7 = 15q - 7 + 7

-15 = 15q

divide both sides by 15

q = -15 / 15

q = -1

Therefore,

q = -1

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Answer:

-22 = q + 7(2q - 1)

-22 = q + 14q - 7

-22 = 15q - 7

add 7 to both sides of the equation

-22 + 7 = 15q - 7 + 7

-15 = 15q

divide both sides by 15

q = -15 / 15

q = -1

Step-by-step explanation:

1. The percentage of maize flour is given as 16.7 %

2. The common ratio of the GP is r = 1.5.

1. We have to set up equation

60x + 90(1 - x) = 85

60x + 90 - 90x = 85

now we have to solve for the value of x

-30x = -5

x = 5 / 30

x = 0.167

Hence percentage of maize flour is given as 16.7 %

2. a + ar = 20 (1)

ar + ar^2 = 30 (2)

We can rearrange equation (1) to get an expression for a:

a = 20 / (1 + r)

Now, we can substitute a into equation (2) to get an equation only in terms of r:

\(20r / (1 + r) + 20r^2 / (1 + r) = 30\\20r + 20r^2 = 30(1 + r)\\20r + 20r^2 = 30 + 30r\\20r^2 - 10r - 30 = 0\\2r^2 - r - 3 = 0\)

Solving this quadratic equation, we get:

We have two solutions, r = 1.5 and r = -1. But since the GP is increasing, we discard the negative solution. Therefore, the common ratio of the GP is r = 1.5.

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Answer:

5. domain: -1 ≤ x ≤ 1

range: 0 ≤ y ≤ 1

6. domain: x < 1 or -1 < x < 1 or x > 1

range: y ≤ 1 or y > 1

i graphed the functions, hope this helps! <3