Noah has 5 m of rope how many pieces of rope of length 1/2 meter can he cut from it

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: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!

Answer:

#\(\beta=0.5492\)

#This Value of \(\beta\) goes to indicate that there is greater \(50\%\) probability that \(\mu<8\) will not be acknowledged at \(\mu =5\)

Step-by-step explanation:

From the question we are told that:

Amount of sleep for adults \(X=P(< 6)\)

Hypothesis test has power \(p=0.4272\)

Mean \(\=x =4hours\)

Generally the equation for \(\beta\) is mathematically given by

\(\beta=1-P\)

\(\beta=1-0.4508\)

\(\beta=0.5492\)

Therefore

This Value of \(\beta\) goes to indicate that there is greater \(50\%\) probability that \(\mu<8\) will not be acknowledged at \(\mu =5\)

A total of 8 workers are required for a building time of 15 days.

In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:

n ∝ 1 / t

n = k / t

Where k is the proportionality ratio, which can be eliminated by building the following formula:

n₁ · t₁ = n₂ · t₂

If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:

n₂ = n₁ · (t₁ / t₂)

n₂ = 10 · (12 / 15)

n₂ = 10 · (4 / 5)

n₂ = 8

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Answer:

option C

Step-by-step explanation:

Group common terms

8u³+7u³+7u²-6u+6+6

15u³+7u²-6u+12

Answer:

25

Step-by-step explanation:

The increase in certain individuals leads to:

An increase in certain individuals within a bacterial population can lead to:

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Answer:

vertical 5

Step-by-step explanation:

0.1000 but yeah because that is the only way to meausre so yeah hope i help lol

If each term in the sum a1+a2+a3...+an is  7 and the sum equals 350, C: 40 would be equal to n.

In equation form, it is:  

                  7s +  77t = 350

In this equation,

          s represents the number of 7's

          t represents the number of 77's

          thus, the number of terms i.e n = s + t =?

now solving the equation,

        7 (s + 11t) = 350

        7 (s + 11t) = 350

            s + 11t = 50

            s + 11t = 50

now, if  

       s=39     &      t =1  

then

         s + 11t = 50 -> 39 + 11 (1)  = 50

Since the number of terms n = s + t

        n = s + t

        n = 39 + 1

        n = 40

Hence, the if each term in the given sum is 7 which gives a total sum as 350, then number of terms in the given series is 40.

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Answer:

9x ≥ 81

Step-by-step explanation:

Given

Total = $81 (atleast)

Required

Represent as an inequality

Let the number of weeks he x

If he saves $9 in a week, then he will save $9x in weeks

From the question we understand that he needs at least $81

At least, in inequality means ≥

So, the inequality is:.

9x ≥ 81

Answer:

B

Step-by-step explanation:

2/3, 1/6, and 1/5​ fractions have an LCD of 30 which is correct option(D).

The lowest common denominator is defined as the set of fraction denominators with the lowest common multiple. The lowest positive integer with more than one denominator in the set is LCD.

LCD by division of prime numbers

(D) 2/3, 1/6, 1/5​

The factors of the denominators 3, 6, 5

3 = 3 x 1

6 = 3 x 2 x 1

5 = 5 x 1

The LCD = 3 x 2 x 5 = 30

Hence, 2/3, 1/6, and 1/5​ fractions have an LCD of 30.

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Answer:

a) Population of adults who watch local news

b) Population of adults who use cell phones or tablets.

c) They conducted a sample survey

d) I will find the results interesting.

I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.

Step-by-step explanation:

a) This finding is applicable to the population of adults who watch local news.

This is because the sample will be collected from the population of adults who watch local news to see the percentage that actually get those local news from their cell phones or tablet computers.

b) This finding is applicable to the population of adults who use cell phones or tablets.

The sample will be collected from the population of adults who use cell phones or tablets. A survey can now be carried out to find out what they use their phones or tablets for, whether to search for restaurants or get weather reports.

c) The Pew Researchers conducted a sample survey because a census data cannot contain the information about weather reports, local restaurants or news channel. Precise information can only be gotten from a sample survey.

d) Yes, I will. Having an idea of how large the population of those that search for local restaurants on phones and tablets will enable me to channel my publicity towards this media. I as a restaurant owner will also enable a Search Engine Optimization for my website to place my restaurant on the top when local restaurants are searched.

Answer:

C.) The relationship is proportional

Step-by-step explanation:

If D is true, then it is not proportional, constants of proportionality must not include multuplting or subtracting from anything.

Also quick way to tell— the line doesn’t start from 0,0

Examining the figure, the correct options are

Two angles are said to be congruent when they are equal to each. The symbol to represent congruency is ≅

The following angles are congruent in the figure

Corresponding angles refers to angles that are in a position that are in matching position to another angle.

Corresponding angles are said to be equal when there are parallel lines intersected across by a line called transversal line.

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Answer:

112.5

Step-by-step explanation:

450(45/220) = 450/4 = 112.5

Using the shell method, the volume of the solid generated when R is revolved about the y-axis is V= 324π cubic units.

The shell method refers to a method of finding volumes of the solid by decomposing a solid of revolution into cylindrical shells. It is one of the methods to find the volume of the solid. This solid is generated when region R is rotated about an axis or the y-axis. In case it is y-axis then the following formula is used:

V= ∫_a^b▒〖2πx [f(x)-g(x)]dx〗

Where y = f(x), y = g(x), and the interval is considered as [a,b].

The given curves are: y = 11 − x, y = 0, x = 3, x = 9

V= ∫_3^9▒〖2πx [11-x-0]dx〗

V= 2π∫_3^9▒〖(11x-x^2)dx〗

V= 2π[11/2 x^2-  1/3 x^3]

V= 2π[11/2 9^2-  1/3 9^3-  11/2 3^2+  1/3 3^3]

V= 2π[891/2-  729/3-  99/2+  27/3]

V= 2π[729/2-  702/3]

V= 2π[396-234]

V= 2π[162]

V= 324π cubic units

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Answer:

-9

Step-by-step explanation:

According to the the video, the Golden Ratio is a figure in mathematics theorized by mathematicians as a value that indicates natures beauty symmetry

\(\mathbf{The \ value\ of \ the \ Golden \ ratio \ is \ \phi} = \mathbf{\dfrac{1 + \sqrt{5} }{2} }\)

Good examples of the Golden Ratio in art and architecture is the Great Pyramid of Giza, constructed in 2570 B.C. and the temple of Parthenon for which construction began in 447 BC and the decoration completed in 432 BC

The reason the temple of Parthenon is so interesting is that the temple just like the pyramid were meant to last indefinitely, such that they can only be made to last so long by the deities, as such by building using the Golden Ratio found in nature including the spiral galaxies, is in recognition of nature's beauty which is aesthetically pleasing to the eyes, harmonious, and maybe preservative

2. The common presence of the Golden Ratio in the universe can be seen as both a grand design and a coincidence, however, due to the higher prevalence than random occurrence, it can be taken as a design that can be observed in nature

3. The topic helps reinforce the belief in the application of math to daily life, because it is a good portrayal of how math can contribute to all aspect of human life

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Answer:

Step-by-step explanation:

for additional examples of the Golden Ratio. Select your favorite example from the video (or your own research) and explain

why this specific example is so interesting to you. (Possible keywords: the golden ratio + in nature, + in art, + in the human body, + in geometry).

Answer:

D 35

Step-by-step explanation:

2/5 = 14/x

solve for x by cross multiplying

5x=70

150 degrees is the measure of the angle x from the figure

The given diagram is a circle and the angle x and 30 degrees can be seen to be on a straight line.

The sum of the measure of angle on a straight line is 180 degrees, hence:

x + 130 = 180

Subtract 130 degrees from both sides to have:

x + 30 - 30 = 180 - 30
x = 180 - 30
x = 150 degrees

Hence the measure of the angle x from the given equation is 150 degrees

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a) The 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.

b) The 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.18, 0.40) cm.

(a) To find a 95% confidence interval for the mean length of the skulls of this species of bird, we can use the following formula:

mean ± (t-score * standard deviation / square root of sample size)

Where mean is the sample mean (5.68 cm), standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).

To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 1.833.

Plugging in the values, we get:

5.68 ± (1.833 * 0.29 / √(10))

= 5.68 ± 0.33

So the 95% confidence interval for the mean length of the skulls of this species of bird is (5.35, 6.01) cm.

(b) To find a 95% confidence interval for the true standard deviation of the skull length of the given species of bird, we can use the following formula:

standard deviation / √(sample size) * t-score

Where standard deviation is the sample standard deviation (0.29 cm), and sample size is the number of skeletons (10).

To find the t-score, we can use the t-distribution table for 9 degrees of freedom (sample size - 1). For a 95% confidence interval, the t-score with 9 degrees of freedom is 2.306.

Plugging in the values, we get:

0.29 / √(10) * 2.306

= 0.11

So the 95% confidence interval for the true standard deviation of the skull length of the given species of bird is (0.29 - 0.11, 0.29 + 0.11) = (0.18, 0.40) cm.

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Answer:

Area = 3097.96\(m^{2}\)

Perimeter = 270.96m

Step-by-step explanation:

Step 1: State the shapes making up the indoor sports exhibiti\(\pi\)on

2 rectangles

1 semi circle

Step 2: Find the area and perimeter of the shapes

ARectangle1 = lw = (10)(40) = 400m^2

PRectangel1 = 2l + w = 2(10) + 40 = 60m

ARectangle2 = lw = (33)(68) = 2244m^2

PRectangel2 = l + w = 33 + 68 = 101m

ASemiCicle = \(\frac{\pi r^{2}}{2} =\frac{\pi 17^{2} }{2} =\frac{289\pi }{2}=144.5\pi=453.96m^{2}\)

PSemiCircle = \(2\pi r=2\pi(17)=35\pi =109.96m\)

Step 3: Add up the areas and perimeters

Area = 400 + 2244 + 453.96

Area = 3097.96\(m^{2}\)

Perimeter = 60 + 101 + 109.96

Perimeter = 270.96m

Therefore the area of the indoor sports exhibition is 3097.96\(m^{2}\) and the perimeter is 270.96 m

Step-by-step explanation:

Kindly find attached the rough sketch of the triangular pyramid and the rough sketch of it cross section.

Basically a triangular pyramid has a triangular base. when a fictitious line is made to pass through perpendicularly to the base, the cross section that will result will still have a triangular orientation but this time a smaller one compared to the original triangular orientation or sides of the pyramid  

The value of x is 33.2

Similar triangles are triangles that have the same shape, but their sizes may vary. The corresponding angles of similar triangles are congruent or equal.

Also the ratio of corresponding sides of similar triangles are equal.

Therefore;

Triangle EHG and EFG are similar

39/36 = 36/x

36 × 36 = 39x

39x = 1296

divide both sides by 39

x = 1296/39

x = 33.2

Therefore the value of x is 33.2

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The minimum value of \($\|\mathbf{v}\|$\) is zero.

The minimum value of \($\|\mathbf{v}\|$\) is zero, as it is the distance between the origin and a point on the line. To solve this problem, the formula \($\|\mathbf{v}\| = \sqrt{x^2 + y^2}$\) can be used, where x and y are the coordinates of the point on the line. Since the equation of the line is \($\dbinom{10}{3} \dbinom{-2}{1}t$\), the coordinates of the point on the line can be found by substituting \($t = 0$: $x = 10 \cdot 0 - 2 \cdot 0 = 0$, and $y = 3 \cdot 0 + 1 \cdot 0 = 0$\) . Substituting these values into the formula for \($\|\mathbf{v}\|$ gives $\|\mathbf{v}\| = \sqrt{0^2 + 0^2} = 0$\). Therefore, the minimum value of \($\|\mathbf{v}\|$\) is zero.

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Important information

12 lawns can be mowed in 3 hours

We need to know how many they can mow in 18 hours

Solving the question

Knowing that 12 lawns can be mowed in 3 hours we will take that and find the unit rate, we do this by dividing the numbers by each other.

lawns÷hours= how many hours per lawn

12÷3 = 4  ← Meaning they can mow 1 lawn in 4 hours

Finding the unit rate is helpful because if you want from here you can just add it 18 times.

Now we are going to multiply 18 by our unit rate of 4 to find our answer

18×4 = 72

Meaning in 18 hours they can mow 72 lawns

Statement

Therefore in 18 hours they are able to mow 72 lawns

Answer: 72 lawns

Step-by-step explanation:

I did the test (K12)