Help me please! can someone summarize it please?





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Delaunay says that the knowledge of how head and neck cancer metastasize could help in devising the means to confine cancerous cells to primary tumors and thus make them more treatable. "Understanding

The percentile rank of score 71 on the test is 26.7 and The score of the 60th percentile on the test is 84.

The figure that a particular percentage falls within is referred to as the percentile. For instance, 80% of the kids in a group of 20 are shorter than you, and Ben is the fourth tallest.

Given:

58, 64, 66, 70, 71, 75, 77, 80, 84, 85, 87, 90, 93, 95, 96

Calculate the percentile of score 71 as shown below,

\(Percentile= n / N \times 100\)

Here, n is the number of scores below 71 and N is the total number of scores,

Percentile = 4 / 15 × 100

Percentile = 0.267 × 100

Percentile = 26.7 percentile

Therefore, the percentile rank of score 71 on the test is 26.7

(B)

Substitute the value in the formula given below,

60 = n / 15 × 100

n / 15 = 60 / 100

n = 0.6 ×  15

n = 9

Thus, the 9th term here is 84,

Therefore, the score of the 60th percentile on the test is 84.

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We have found an x ∈ R such that f(x) = y for any y ∈ R, which means that f is onto.

(a) To prove that f is one-to-one, we need to show that if f(x1) = f(x2), then x1 = x2 for any x1, x2 ∈ R.

So, suppose f(x1) = f(x2). Then, we have:

3x1 - 5 = 3x2 - 5

Simplifying this equation, we get:

3x1 = 3x2

Dividing both sides by 3, we get:

x1 = x2

Thus, we have shown that if f(x1) = f(x2), then x1 = x2, which means that f is one-to-one.

(b) To prove that f is onto, we need to show that for any y ∈ R, there exists an x ∈ R such that f(x) = y.

So, let y ∈ R be arbitrary. We need to find an x ∈ R such that f(x) = y.

We have:

f(x) = 3x - 5

Setting this equal to y, we get:

3x - 5 = y

Adding 5 to both sides and dividing by 3, we get:

x = (y + 5)/3

Thus, we have found an x ∈ R such that f(x) = y for any y ∈ R, which means that f is onto.

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The number of packs of hot dogs bought is 2 packs

The number of packs of hamburgers bought is 4 packs

Let x represent the number of hot dogs bought and y represent the number of hamburgers bought

x + y= 6.........equation 1

2.65x + 6.29y= 30.46.........equation 2

From equation 1

x + y= 6

x= 6 - y

Substitute 6 - y for x in equation 2

2.65(6-y) + 6.29y = 30.46

15.9 - 2.65y  + 6.29y = 30.46

3.64y = 30.46 - 15.9

3.64y= 14.56

y= 14.56/3.64

y= 4

Substitute 4 for y in equation 1

x + y= 6

x + 4= 6

x= 6 - 4

x= 2

Hence 2 packs of hot dogs and 4 packs of hamburgers were bought

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Answer:

The area of the circle is 314 inches

Step-by-step explanation:

Area if a circle = πr²

r = radius

r= d/2

r=20 /2

r=10 inches

Area =3.14×10²

= 3.14×100

=314 inches

Answer:

314 in. cubed

Step-by-step explanation:

The formula to find the area of a circle is:

A= πr²

Pi is 3.14 so substitute that in

A= 3.14(r)²

The radius is 10 because the radius is half of the diameter.  Half of 20 is 10.  So substitute that in the radius symbol.

A= 3.14(10)²

Square 10, which is 10 times 10.  10 times 10 equals 100.

A= 3.14(100)

100 times 3.14 is 314 because 100 has two zeroes which means you move the decimal point in 3.14 two places to the right.  It gets you 314.0 which is just 314.

A= 314

According to the question, the mean, variation, standard deviation, quartiles, median, and percentile for the given data set are:

Mean = 43.33

Variation = 9646.22

Standard Deviation = 98.21

First Quartile (Q1) = 12

Median = 48

Third Quartile (Q3) = 70

65th Percentile = 50

​

To find the mean, variation, standard deviation, quartiles, median, and percentile for the given data set, we can follow these steps:

Step 1: Sort the data in ascending order: 8, 12, 30, 35, 48, 50, 62, 70, 78.

Step 2: Calculate the mean:

\(Mean = \frac{8 + 12 + 30 + 35 + 48 + 50 + 62 + 70 + 78}{9} = 43.33\) (rounded to two decimal places).

Step 3: Calculate the variation:

\(\text{Variation} = \frac{{\sum((x_i - \text{mean})^2)}}{n}\\\\= \frac{{((8 - 43.33)^2 + (12 - 43.33)^2 + \ldots + (78 - 43.33)^2)}}{9}\\\\= 9646.22 \quad\)

Step 4: Calculate the standard deviation:

Standard Deviation = \(\sqrt{(Variation)} = \sqrt{(9646.22)} = 98.21\) (rounded to two decimal places).

Step 5: Calculate the quartiles:

First Quartile (Q1) = 12 (since it is the median of the lower half of the data).

Third Quartile (Q3) = 70 (since it is the median of the upper half of the data).

Step 6: Calculate the median:

The median is the middle value of the sorted data set, which is 48.

Step 7: Calculate the percentile:

To find the 65th percentile, we need to determine the value that separates the lowest 65% of the data from the highest 35%. Since the data set has 9 elements, 65% of 9 is 5.85. Rounding up, we get 6. The 6th element in the sorted data set is 50, which represents the 65th percentile.

Hence, the mean, variation, standard deviation, quartiles, median, and percentile for the given data set can be represented in LaTeX as follows:

\(\text{Mean} &= 43.33 \\\text{Variation} &= 9646.22 \\\text{Standard Deviation} &= 98.21 \\\text{First Quartile (Q1)} &= 12 \\\text{Median} &= 48 \\\text{Third Quartile (Q3)} &= 70 \\\text{65th Percentile} &= 50 \\\)

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Answer:

Step-by-step explanation

what are  the digits

Answer:

10 small bows; 8 large bows

Step-by-step explanation:

Let x = number of small bows.

Let y = number of large bows.

x + y = 18;

3x + 5y = 70

      -3x - 3y = -54

  +   3x + 5y = 70

  -----------------------

               2y = 16

y = 8

x + y = 18

x + 8 = 18

x = 10

Answer: 10 small bows; 8 large bows

The length of line JL which has endpoints J(8,10) and L(20,5) is; JL = 13.

According to the question, we are required to determine the length of line JL.

However, the coordinates of the end points of line JL are given as;

The length of line JL is given by Pythagoras theorem as;

JL = 13.

Therefore, the length of line JL which has endpoints J(8,10) and L(20,5) is; JL = 13.

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Pythagoras theorem is a formula that helps us determine the missing side of a triangle, with the measure of two sides, given.

The Pythagoras theorem formula is expressed as:

\((\small\text{Hypotenuse})^{2} = (\small\text{side}_{1} )^{2} + (\small\text{side}_{2} )^{2}\)

Now, let us take an example to understand the concept better.

A triangle with longest side given as 15 centimeters. The base of the triangle has a length of 9 centimeters. What is the measure of the height?

We are given the following:

When we plug the hypotenuse and the base, in the formula, we get;

Subtract 9² on both sides of the equation to isolate (side₂)².

We can use the rule [a² - b² = (a - b)(a + b)] to simplify the L.H.S

Now, take square root on both sides of the equation to determine the measure of the missing side (height of triangle).

Therefore, the measure of the height is 12 centimeters.

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The whole number for the value (x + 21) is 41.

All integers starting from 0 are called whole numbers. The opposite of their corresponding positive numbers, the negative numbers are additive. The blackboard bold math Z or boldface Z is a common way to represent the set of integers in mathematical terminology.

given,

       x = 20

then by putting the value of x = 20 in

       (x + 21)°      we get,

     = (20 + 21)°

     = 41°

Hence, the whole number of (x + 21) is 41

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The likelihood that the sample mean time required to finish the exam will be less than 47.5 minutes is 0.566.

Given;

The average amount of time needed to finish an exam is 45 minutes, with a standard deviation of 15 minutes. The average amount of time required for 100 randomly chosen pupils is calculated.

Mean (μ) = 45

Standard deviation (σ) = 15

Here, σ/√n = 15/√100

                   = 1.5

To get the probability the sample mean time necessary to complete the examination is less than 47.5 minutes, we need;

P (x < 47.5) = P(z < (x-μ /σ/√n ) )

                  = P(z < 47.5 - 45/1.5)

                  = P(z < 17.5)

                  = 0.566

The probability the sample mean time necessary to complete the examination is less than 47.5 minutes is 0.566

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The angle between the vectors can be found using the dot product. The formula is θ= |A| =√(x12 + y12 + z12) The angle between the vectors -2i + 3j + k and i + 2j - 4k is approximately 137.8 degrees.

v1 • v2 = (-2i + 3j + k) • (i + 2j - 4k)

= -2 - 6 + 1 = -7

|v1| = \(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

=\(\sqrt{(4 + 9 + 1)}\)

=\(\sqrt{14}\)

|v2| = \(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16) }\)

= (\(\sqrt{21}\)

θ= |A| (-7/\(\sqrt{14}\)\(\sqrt{21}\))

=  |A| (-7/21*14)

=  |A|(-7/294)

= 137.8 degrees

The angle between two vectors can be found using the dot product formula. This formula isθ= |A| =√(x12 + y12 + z12). In the case of the vectors -2i + 3j + k and i + 2j - 4k, this formula can be used to find the angle between them. The dot product of the two vectors is -2 - 6 + 1 = -7. The magnitude of the first vector, |v1|, can be found using the Pythagorean theorem, which is

\(\sqrt{((-2)^2 + 3^2 + 1^2)}\)

= \(\sqrt{(4 + 9 + 1)}\)

= \(\sqrt{14}\).

The magnitude of the second vector, |v2|, can be found using the Pythagorean theorem, which is

\(\sqrt{((1)^2 + 2^2 + (-4)^2)}\)

= \(\sqrt{(1 + 4 + 16)}\)

= \(\sqrt{21}\)

Once the dot product and magnitudes are known, the angle between the two vectors can be found using the formula .Therefore, the angle between the two vectors is approximately 137.8 degrees.

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Answer:

35.45

Step-by-step explanation:

Answer:

by using clustering technique answer is 35 or B

Step-by-step explanation:

Edge 2020

The equation that Amy can use to find how many games of Balloon Bouncer, g, she played is; g = (35 - 2a)/3

We are told that Amy used her first 2 tokens at Glimmer Arcade to play a game of Roll-and-Score.

Balloon Bouncer costs 3 tokens per game, and Amy started with a bucket of 35 game tokens.

Thus, the expression for the number of balloon bouncer games played at the arcade is :

2a + 3g = 35

Let :

Glimmer arcade, a = $2 per game

Balloon bouncer, g = $3 per game

Total game tokens = 35

Her spending could be represented using the expression :

2a + 3g = 35  

g = number of balloon bouncer games played

Thus, making g the subject of the formula we have;

g = (35 - 2a)/3

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Answer:

3g + 2 = 35 is the answer.

She played 11 games.

Step-by-step explanation:

The length and the width are 12 yards and 16 yards

The formula for calculating the perimeter of a rectangle is expressed as;

Perimeter =2( l + w)

Given that the parameter are;

Length = 4 + w

Substitute the values into the formula

52 = 2( 4 + w + w)

collect like terms

52 = 2(4 + 2w)

expand the bracket

52 = 8 + 4w

collect like terms

4w = 52 - 8

subtract the values

4w = 48

Make 'x' the subject of formula

w = 12 yards

L = 16 yards

Hence, the values are 12 yards and 16 yards

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The error in the summation notation is that the initial value is n = 1 and n = 1.

The corrected summation of the arithmetic series is \(\sum^8_{n=1}(3+5n)\).

The summation of the arithmetic series is S₈ = 148.

The explicit formula of this arithmetic series is aₙ = 3n + 5.

The recursive formula of this arithmetic series is \(a_n=a_{n+1} +3\).

In Mathematics, the sum of an arithmetic sequence can be calculated by using the following equation:

\(S_n = \frac{n}{2}(2a +(n-1)d)\) or \(\sum^n_{n=1}a_{n}\)

Where:

Based on the arithmetic series 8 + 11 + ...... + 29, we can logically deduce the following parameters;

First term, a₁ = 8

Common difference = a₂ - a₁ = 11 - 8 = 3.

For the nth term (explicit formula) of this arithmetic sequence, we have:

aₙ =  a₁ + (n - 1)d

aₙ =  8 + (n - 1)3

aₙ = 3n + 5

For the number of terms, we have:

29 = 3n + 5

3n = 24

n = 8.

Therefore, the summation notation should be written as;

\(\sum^8_{n=1}(3+5n)\)

Furthermore, the corrected summation is given by;

S₈ = 8/2(2(8) + (8 - 1)3)

S₈ = 4(16 + 21)

S₈ = 148

For the recursive formula, we have:

\(a_n=a_{n+1} +d\)

\(a_n=a_{n+1} +3\)

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Answer:

  The conjecture cannot work for any negative numbers, It works for x > 1.3.

Step-by-step explanation:

An odd power preserves the sign. For |x| > 1, the power increases the magnitude. For x < 0, adding -2 only increases the magnitude more. A negative number of larger magnitude will not be "greater than" the reference. It will be "less than."

It only takes a counterexample to show the conjecture is incorrect.

  x^5 -2 ?? x

  (-2)^5 -2 ?? (-2)

  -32 -2 ?? -2

  -34 < -2 . . . . . . not greater than

Answer:

Step-by-step explanation:

he height of the storage unit is equal to twice its radius (since the diameter is twice the radius), so the height is 2 x 8 = 16 feet.

The storage unit is in the shape of a cylinder, so we can use the formula for the volume of a cylinder, V = πr^2h, where r is the radius and h is the height:

V = π(8^2)(16)

V = π(64)(16)

V = 3,218.69 cubic feet (rounded to two decimal places)

Therefore, the volume of the storage unit is approximately 3,218.69 cubic feet.

we can determine whether x + y = 5 based on the information provided in the two statements.


To solve for x + y, we can use a system of equations.

Statement (1) gives us the equation 4x + y = 17. We can solve for y by subtracting 4x from both sides, giving us y = 17 - 4x.

Statement (2) gives us the equation x + 4y = 8. We can substitute y with 17 - 4x (from statement 1) to get x + 4(17-4x) = 8. Simplifying this equation gives us 15x = 60, or x = 4.

Substituting x = 4 into either statement gives us y = 1.

Therefore, x + y = 4 + 1 = 5.


Based on the information provided in the two statements, we can conclude that x + y does indeed equal 5. Statement (1) and (2) together give us enough information to solve for x and y, which allows us to confirm the main answer.

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About 200 drivers out of a population of 900 prefer a standard transmission over automatic. To answer the question, we need to use proportions. We know that 40 out of 180 drivers prefer a standard transmission.

So, the proportion of drivers who prefer a standard transmission is:

40/180 = 0.2222

To estimate how many drivers out of a population of 900 prefer a standard transmission, we can multiply this proportion by the size of the population:

0.2222 x 900 = 200

Therefore, we can estimate that about 200 drivers out of a population of 900 prefer a standard transmission over automatic. However, it's important to note that this is just an estimate and there could be some variation depending on the characteristics of the population.

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N(t) approaches 550.

The equation N(t) = 550 / (1 + 49e^(-0.7t)) models the number of people in a town who have heard a rumor after t days. The equation describes the growth of the number of people who have heard the rumor over time. The e^(-0.7t) term in the denominator represents the rate of decay or the slowing down of the spread of the rumor as t increases. As t increases without bound, the exponential term approaches 0, so the fraction approaches 550 / (1 + 49 * 0) = 550 / 1 = 550.

This means that as time goes on, the number of people who have heard the rumor will approach 550, the limit or maximum value of N(t). This value is not limited by any of the factors mentioned in the options (b) to (e).

The number of people who started the rumor is not given in the equation and cannot be determined from the information provided.

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Answer:

19/24 pounds

Step-by-step explanation:

To find the total number of pounds, we should add 3/8 and 5/12. They both have different denominators, so we have to find the least common multiple between 12 and 8. The least common multiple between 12 and 8 is 24. 12 should be multiplied by 2 to get 24 (5 too) and 8 should be multiplied by 3 to get 24 (3 too).

\( \frac{3}{8} + \frac{5}{12} \)

\( \frac{3 \times 3}{8 \times 3} + \frac{5 \times 2}{12 \times 2} \)

\( \frac{9}{24} + \frac{10}{24} \)

\( \frac{19}{24} \)

Answer:

c. x <_ -2 or x >_ 4

Step-by-step explanation:

On the number line, the line goes infinity both sides, but stops between x= -2 and x=4

Answer:

460

Step-by-step explanation:

Answer:

460

Step-by-step explanation:

Answer:

3813

Step-by-step explanation:

M.P of water cooler=$4650

Discount% on water cooler=18%

Discount on water cooler=18/100*$4650 i.e.$837

So,selling price=$4650-$837i.e.$3813 Ans.

Answer:

3813

Step-by-step explanation:

the formula will be 18 upon 100 multiply by 4560. the answer is 837. now subtract the original price from the discount. 4560-837 is 3813 which is ur answer.

Answer:

About 54.16 percent

Step-by-step explanation:

To turn a fraction into a percentage you must divide the numerator by the denominator.

Ex: 1/2 the percentage is  0.50 percent so its 50%