Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant. So, what is the highest possible number of inhabitants in that little town?

By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

The given options, the only value greater than 1 is 1.003. Therefore 0.886, which is less than 1 and makes the inequality true.

The given number sentence is 5.3 × > 5.3, where we need to find the scaling factor that makes the inequality true. To do this, we can divide both sides of the inequality by 5.3. This gives us:

5.3 × x > 5.3 ÷ 5.3 × k

We need to find the value of k that makes the inequality true. Simplifying the right-hand side of the equation, we get:

5.3 ÷ 5.3 × k = k × 1 = k

Substituting this into our equation, we get:

5.3 × x > k

We know that 5.3 × 1 = 5.3, which means that k must be greater than 1 to satisfy the inequality. Among the given options, the only value greater than 1 is 1.003. However, this value would make the inequality too large, so it is not the correct answer.

The correct answer is therefore 0.886, which is less than 1 and makes the inequality true.

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Answer:

18 tiles

Step-by-step explanation:

If she wants to find the greatest number of tiles for each row, she will want to use up all the tiles. This means we are looking for the highest common factor between the numbers 90 and 72, so all the tiles can be used up in the rows. In order to find the highest common factor we multiply together all the common prime factors between the two:

90 has the prime factors 2x3x3x5

72 has the prime factors 2x2x2x3x3

The prime factors that are common to both are 2, 3 and 3 which multiply together to get:

2x3x3 = 18

The greatest number of tiles Martha can use for each row is 18 and would result in 5 rows of red tiles and 4 rows of yellow tiles.

Hope this helped!

Given:

f(x) = 2x - 5

g(x) = 4x + 3

(f + g)(x) can be found as,

Therefore, (f + g)(x)=6x-2.

It would take 21 weeks for the population to surpass 16,000.

The insect population P in a certain area fluctuates with the seasons and is estimated by the function P = 15,000 + 2500 sin(πt/52), where t is given in weeks.

For the population to surpass 16,000, we can set up the following equation:

15,000 + 2500 sin(πt/52) = 16,000

Subtracting 15,000 from both sides, we get:

2500 sin(πt/52) = 1000

Dividing both sides by 2500, we get:

sin(πt/52) = 0.4

We know that sin(πt/52) is positive when t is between 0 and 52 and between 104 and 156 since sine is positive in the first and second quadrants. Therefore, we can write:

πt/52 = sin⁻¹(0.4)

Multiplying both sides by 52/π, we get:

t = (52/π) sin⁻¹(0.4)

Using a calculator, we can evaluate sin⁻¹(0.4) to be approximately 0.4115 radians.

t = (52/π) (0.4115)

t = 21.02

Therefore, it would take 21 weeks for the population to surpass 16,000.

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The probability of drawing a king from a standard deck of 52 cards is 1/13.

In a standard deck of 52 playing cards, there are four kings: the king of hearts, the king of diamonds, the king of clubs, and the king of spades.

To find the probability of drawing a king, we need to determine the ratio of favorable outcomes (drawing a king) to the total number of possible outcomes (drawing any card from the deck).

The total number of possible outcomes is 52 because there are 52 cards in the deck.

The favorable outcomes, in this case, are the four kings.

Therefore, the probability of drawing a king is given by:

Probability = (Number of favorable outcomes) / (Number of possible outcomes)

= 4 / 52

= 1 / 13

Thus, the probability of drawing a king from a standard deck of 52 cards is 1/13.

This means that out of every 13 cards drawn, on average, one of them will be a king.

It is important to note that the probability of drawing a king remains the same regardless of any previous cards that have been drawn or any other factors.

Each draw is independent, and the probability of drawing a king is constant.

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Answer:

Step-by-step explanation: 1,872

Answer: 1,872

Step-by-step explanation:

Answer:

√130 is the distance between (9,-3) (0,-10)

The length of line x in the figure of the cube given is 19.

Calculate the length of the base of the cube, which is the diagonal of the lower sides :

base length = √10² + 6²

base length = √136

The length of x is the diagonal of the cube

x = √(√136)² + 15²

x = √136 + 225

x = √361

x = 19

Therefore, the length of line x in the figure given is 19.

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Answer:

a) reflection across the x-axis

b) f(x) =( x-3)²

c) f(x) = x² + 6 is a vertical taranslation up by '6' units

Step-by-step explanation:

Explanation

Given that the parent function

              f(x) = x²

a) f(x) = x² is rotation across the x-axis then the new function

 f(x) = - x²

b) ) f(x) = x² is a horizontal translation right by '3' units then the function is changes to f(x) = (x-3)²

c)  

f(x) = x² is a vertical translation up '6' units then the function is changes to f(x) = x² +6  

Answer:

$20

Step-by-step explanation:

First you have to find how much for the least amount of money. So divide to get 9 and $4, which is the least. Now we multiply them by 5 to get 45 cards and $20. So the answer is $20

The graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

The functions for this problem are defined as follows:

When a function is multiplied by 2, we have that it is vertically stretched by a factor of 2.

Hence the graph of the function y = 2|x| is a vertical stretch by a factor of 2 of the parent function y = |x|.

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Answer:

1538.60 ft³  and   6.50 cm

Step-by-step explanation:

Volume of a cylinder = area of a circle x height

                                   = \(\pi \)r²×\(h\)

1)  Volume =  \(\pi \)r² x \(h\)

                 = 3.14 x 7² x 10

                 = 1538.60 ft³ (to the nearest hundredth)

2)  Volume =  \(\pi \)r² x \(h\)

   58.9849 = 3.14 x 1.7² x \(h\)

   58.9849 = 9.0746 x \(h\)

                \(h\) = 58.9849 ÷ 9.0746

                   = 6.50 cm (to the nearest hundredth)

Answer:

0

Step-by-step explanation:

for y= -2*(3^x), as x is greater, the slope is steeper, and since the two graphs don't intercept in the picture we can see, they won't ever intercept because the slop of y=-2x+3 stays the same. as x becomes greater the distance between the two graphs is larger

Step-by-step explanation:

We can simplify the given expression using the rules of absolute values:

l-80-20l – 100 + l-100l

= -(20l + 80) - 100 + 100 (since |x| = -x when x is negative)

= -20l - 80

= -20(l + 4)

Therefore, the simplified expression is -20(l + 4).

Answer:

100

Step-by-step explanation:

\( | - 80 - 20| - 100 + | - 100| \\ = | - 100| - 100 + | - 100| \\ = 100 - 100 + | - 100| \\ = | - 100| \\ = \boxed{100}\)

____________

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The probability that the student is absent is 3/20

A probability is a number that reflects the chance or likelihood that a particular event will occur. Probabilities can be expressed as proportions that range from 0 to 1, and they can also be expressed as percentages ranging from 0% to 100%.

The probability that the student will be absent and it will be on Monday is 3 /100.

The probability that it will be Monday is 1/5

Therefore the probability that the student will be absent any day is 3/100÷1/5 = 3/20

Since it is certain that it is Monday , the probability that it is Monday is 1.

Therefore, the probability that the student is absent on that Monday is 1 × 3/20 = 3/20

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Solution

A Square-based pyramid has 5 faces

A Triangular-based pyramid has 4 faces.

The value of angle RPQ in the circle is 115 degrees.

The intersecting chords theorem, also known as the chord theorem, is an elementary geometry statement that describes a relationship between the four line segments formed by two intersecting chords within a circle.

If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175 degrees

arc angle SA = 55 degrees

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

The angle is 115°.

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Answer:

y=3x-7

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=3(x-2)

y+1=3(x-2)

y+1=3x-6

y=3x-6-1

y=3x-7

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Answer:

you have to divide 105 by 3

Step-by-step explanation:

Answer:

35 words a minute

Step-by-step explanation:

105/3=35

Answer:

x = 16

Step-by-step explanation:

\(-5+\frac{x}{-16} =-6\)

\(-5+\frac{16}{-16} =-6\)

\(-5-1=-6\)

\(-6=-6\)

Answer:

101

Step-by-step explanation:

-5 + ×/-16=-6

-5+x=96

x= 101

Answer:

the answer is 'B'

Step-by-step explanation:

8x+5-5x+8+2x+7

5x+20

Expression A decays at a rate of 5% every three months, while Expression B grows at a rate of 12% every four months  and  Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.

It is a mathematical statement tat consists of variables , constants and mathematical operators.

It is given that

The company's records show the sales of short boards decrease every three months as represented by expression A, where t is the number of years that the boards have been for sale.

The company's records show that the sales of long boards increase every four months as represented by expression B, where t is the number of years that the boards have been for sale.

\(\rm Expression\; A = 624(0.95)^{4t}\\\\Expression \; B = 725(1.12)^{3t}\)

From observing both the expression the initial value is when t = 0

when t = 0,

A = 624

B = 725

and so Expression A decays at a rate of 5% every three months, while expression B grows at a rate of 12% every four months  and  Expression A has an initial value of 624, while expression B has an initial value of 725 , Option B and E are the correct statements.

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The set of numbers best describes the possible values of x in the equation is option c. only negative values of x.

Since the equation is

x - 1 = x

So, here the x should be canceled out

So, it should be like

0 = -1

Hence, we can say that

The option c is correct,

And, the rest of the options are incorrect.

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Answer:

A rough calculation or guess is approximately correct, but not exact. roughly adverb.

Step-by-step explanation: