What is 6(p+6)- (p-6)

There  are no prime numbers between7,608 and 7,620

A prime number is a whole number greater than 1 whose only factors are 1 and itself

The numbers between 7608 and 7620 are:

7609,7610,7611,7612,7613,7614,7615,7616,7617,7618,7619

Here we have to check these numbers are prime number or not

Prime factorization

7609=7×1087

7610=2×5×761

7611=3×43×59

7612=2×2×11×173

7613=23×331

7614=2×3×3×3×3×47

7615=5×1523

7616=2×2×2×2×2×2×7×17

7617=3×2539

7618=2×13×293

7619=19×401

Hence, proved that there are no prime numbers between7608 and 7620

Answer:

20

Step-by-step explanation:

I did this test is 20

60 percent of 20 is 12 dollars

The original price of a pair of jeans would be; 30 dollar.

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b% Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Given that a pair of jeans is only $12 after a 60% discount.

The original price in percentage terms = 100%

After the first discount, the price is : 100- 60% = 40%

The equation can be used to represent the price;

40% x original price = $12

0.40 x p = 12

where p = original price

Divide both sides of the equation by 0.40;

p= $30

Hence, The original price of a pair of jeans would be; 30 dollar.

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(a) The probability that the next page you read contain zero is 0.8187.

(b) The probability that the next page you read contains  or more typographical errors is 0.0175.

What is probability?

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes

The probability that the next page you read contains zero. The expected number of typographical errors on a page of a certain magazine is  

That is, y = 0.2

Let  is a random variable representing the number of typos per page.

Since, we have a large number of letters per page, and the number of errors in one page will be small, we use Poisson distribution. The probability function of the Poisson distribution is defined as,

\(P(x = i) = e^-^y\frac{y^i}{i!},..... i = 0, 1, 2, ...\)          ...(1)

Here, y is a parameter.

Find the probability that the next page you read contains zero.

That is, find P(y = 0)

plug y = 0 in equation (1), we get

P(x = 0) = 0.8187

The probability that the next page you read contain zero is 0.8187

Given the question that the probability that the next page you read contains  more typographical errors. The expected number of typographical errors on a page of a certain magazine is 0.2

That is y = 0.2

Let is a random variable representing the number of typos per page.

Find the probability that the next page you read contains more typographical errors.

That is find P(x ≥ 2)

P(x ≥ 2) = 1 - P(x ≤ 1)

= 1 - (P(x = 0) + P(x = 1))

= 1 - 0.982477

= 0.0175

The probability that the next page you read contains  or more typographical errors is 0.0175.

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Answer:

h= -28

Step-by-step explanation:

h+14=-14 isolate h by subtracting 14 on both sides

h= -28

Answer:

h=-28

Step-by-step explanation:

k byeeeeeeeeeeeeee:)

The probability that the area covered by a can of spray paint is 0.251

The variable of interest is:

X: are objects that can be painted with a single can of spray paint.

This variable has a normal distribution, with a mean of 25 feet square and a standard deviation of 3 feet square.

Symbolically:

P(X≥27)

To calculate the probability, use the standard normal distribution, so first standardize the value of X using:

Z= (X-μ)/σ

P(X≥27)= P(Z≥(27-25)/3)= P(Z≥0.67)

Now, because the Z-table contains cumulative probability information:

P(Zα≤Z₀)=1-α

you must perform the following conversion to calculate the requested probability:

1 - P(Z<0.67)= 1 - 0.749= 0.251

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Answer:

x^4 + x^3 + 13x + 5

Step-by-step explanation:

Answer:

2nd option

Step-by-step explanation:

Using the rule of radicals

\(\sqrt{a}\) × \(\sqrt{b}\) ⇔ \(\sqrt{ab}\) and \(\sqrt{-1}\) = i

Simplifying the radical

\(\sqrt{-80}\)

= \(\sqrt{16(5)(-1)}\)

= \(\sqrt{16}\) × \(\sqrt{5}\) × \(\sqrt{-1}\)

= 4 × \(\sqrt{5}\) × i

= 4i\(\sqrt{5}\)

Then

6 + \(\sqrt{-80}\)

= 6 + 4i\(\sqrt{5}\)

Answer:

Step-by-step explanation:

6y - y = y(6 - 1) = y * 5

The answer is 5y.

For a real number x, by using mathematical induction it is shown that a\((1 + x)^{2n}\) > 1 + 2nx for every positive integer n.

To prove the inequality a\((1 + x)^{2n}\) > 1 + 2nx  for every positive integer n, we will use mathematical induction.

The inequality holds true for n = 1, and we will assume it is true for some positive integer k.

We will then show that it holds for k + 1, which will complete the proof.

For n = 1, the inequality becomes a\((1 + x)^2\) > 1 + 2x.

This can be expanded as a(1 + 2x + \(x^2\)) > 1 + 2x, which simplifies to a + 2ax + a\(x^2\) > 1 + 2x.

Now, let's assume the inequality holds true for some positive integer k, i.e., a\((1 + x)^{2k}\) > 1 + 2kx.

We need to prove that it holds for k + 1, i.e., a\((1 + x)^{2(k+1)}\) > 1 + 2(k+1)x.

Using the assumption, we have a\((1 + x)^{2k}\) > 1 + 2kx.

Multiplying both sides by \((1 + x)^2\), we get a\((1 + x)^{2k+2}\) > (1 + 2kx)\((1 + x)^2\).

Expanding the right side, we have a\((1 + x)^{2k+2}\) > 1 + 2kx + 2x + 2k\(x^2\) + 2\(x^2\).

Simplifying further, we get a\((1 + x)^{2k+2}\) > 1 + 2(k+1)x + 2k\(x^2\) + 2\(x^2\).

Since k and x are positive, 2k\(x^2\) and 2\(x^2\) are positive as well.

Therefore, we can write a\((1 + x)^{2k+2}\) > 1 + 2(k+1)x + 2k\(x^2\) + 2\(x^2\) > 1 + 2(k+1)x.

This proves that if the inequality holds for some positive integer k, it also holds for k + 1.

Since it holds for n = 1, it holds for all positive integers n by mathematical induction.

Therefore, we have shown that a\((1 + x)^{2n}\) > 1 + 2nx  for every positive integer n.

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Answer:

-27

Step-by-step explanation:

8x - 6 - 7y + 3

X = 3 Y = 6

8(3) - 6 - 7(6) + 3

8 x 3 = 24

7 x 6 = 42

24 - 6 - (42 + 3)

(24 - 6) - 45

18 - 45 = -27

The probability that the triangle is equilateral is `0`.

Let's assume that the two sides of an isosceles triangle are `a`. Then, the perimeter of the triangle is `2a + b = 30`, where `b` represents the base of the triangle.

Substituting the value of `b` in terms of `a` in the above equation, we get:`2a + 2sqrt(a^2 - (30 - 2a)^2/4) = 30`

Simplifying this equation, we get: 4a² - 120a + 675 = 4√(3)a²

Squaring both sides of the equation, we get: 16a⁴ - 960a³ + 40500a² - 243000a + 455625 = 0

The solutions of this equation are: a = 7, 15

The probability of the triangle being equilateral is 0.

An isosceles triangle can be equilateral only if its sides are of equal length. Since there is only one value of `a` such that `2a < 30` and `a` is a whole number, the probability of the triangle being equilateral is 0.

Hence, the probability that the triangle is equilateral is `0`. The given isosceles triangle can have sides of length `7-7-16` or `15-15-0`.

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The answer to the questions are as follows:

(a) A basis for the row space is {(5, -7, 8), (6, 10, 5)}

(b) The rank of the matrix is 2

Step-by-Step Explanation:

To find a basis for the row space and the rank of the matrix, we need to perform row operations on the given matrix until it is in row echelon form. Here are the steps:

Use row operations to swap the first and third rows:

| 1 -3 2 |

| 6 10 5 |

| 5 -7 8 |

Use row operations to subtract 6 times the first row from the second row and 5 times the first row from the third row:

| 1 -3 2 |

| 0 28 -7 |

| 0 -8 2 |

Use row operations to divide the second row by 28 and subtract (-8/28) times the second row from the third row:

| 1 -3 2 |

| 0 1 -1/4 |

| 0 0 3/4 |

The matrix is now in row echelon form. The nonzero rows are the first two rows, which correspond to the first and second rows of the original matrix. Therefore, a basis for the row space is the set of these two rows:

{(5, -7, 8), (6, 10, 5)}

The rank of the matrix is the number of nonzero rows in the row echelon form, which is 2. So, the rank of the matrix is 2.

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Answer:

30 feet

Step-by-step explanation:

For this problem we can use ratios 6:4 and x:20. We can also write these ratios as fractions 6/4 and x/20 or 3/2 and x/20. Set the two fractions equal to each other and solve for x:

3/2 = x/20

1.5 = x/20

30 = x

Answer:

$3867.80

Step-by-step explanation:

f(x)=a(1+r)^{x}

f(x)=exponential growth function

a=initial amount

r=growth rate

{x}=number of time intervals

so let x=years

start amount is 1,500

1,500(1+r)^5=2100

(r+1)^5= 7 /5

((r+1)5) ^1 /5 =( 7 /5 ) ^1 /5

r=0.06961

which is rounded 7 percent growth rate

2024-2010=14 years

1,500(1+0.07)^{14}=

3867.801225

Now round cause it's money

$3867.80

Answer:

24 blue marbles

Step-by-step explanation:

We know

The ratio of red marble to blue marble is 5:6. Meaning for every 11 marbles; there are 5 red and 6 blue.

How many blue marbles are there?

6 x 4 = 24 blue marbles

So, there are 24 blue marbles.

Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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The five values for a data set are: minimum = 0 lower quartile = 2 median = 3. 5 upper quartile = 5 maximum = 10 Bruno created the box plot using the five values. Bruno made error. The left whisker should go from 0 to 2.

Quartiles is a type of quartile that divides data into four parts with approximately the same number. The first quartile or lower quartile (Q1) is the middle value between the smallest value and the median of the data group. The first quartile is a marker that the data in that quartile is 25% below the data group.

The second quartile (Q2) is the median data which marks 50% of the data (dividing the data in half). The third or upper quartile (Q3) is the middle value between the median and the highest value of the data set. The third quartile is a marker that the data in that quartile is 75% below the data group. Quartiles are a form of an ordered statistic because to determine quartiles, data needs to be sorted from smallest to largest value first.

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The correct values for a, b, c, d, and e are a = 16, b = 29, c = 24, d = 22, and e = 30 for group of 75 students on asking whether they like Algebra or Geometry.

For the values of a, b, c, d, and e, we can use the information provided in the table. Let's break it down step-by-step:

We are given that a total of 75 math students were surveyed. Therefore, the total number of students should be equal to the sum of the students who like algebra, the students who like geometry, and the students who do not like either subject.

75 = 45 (Likes Algebra) + 53 (Likes Geometry) + 6 (Does Not Like Either)

Simplifying this equation, we have:

75 = 98 + 6

75 = 104

This equation is incorrect, so we can eliminate options c and d.

Now, let's look at the information given for the students who do not like geometry. We know that a + b = 6, where a represents the number of students who like algebra and do not like geometry, and b represents the number of students who do not like algebra and do not like geometry.

Using the correct values for a and b, we have:

16 + b = 6

b = 6 - 16

b = -10

Since we can't have a negative value for the number of students, option a is also incorrect.

The remaining option is option e, where a = 29, b = 16, c = 24, d = 22, and e = 30. Let's verify if these values satisfy all the given conditions.

Likes Algebra: a + c = 29 + 24 = 53 (Matches the given value)

Does Not Like Algebra: b + d = 16 + 22 = 38 (Matches the given value)

Likes Geometry: c + d = 24 + 22 = 46 (Matches the given value)

Does Not Like Geometry: b + e = 16 + 30 = 46 (Matches the given value)

All the values satisfy the given conditions, confirming that option e (a = 29, b = 16, c = 24, d = 22, and e = 30) is the correct answer.

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The probability of receiving at least two calls between eight and nine in the morning is 0.8009, or 80.09%.

The chance that X represents the number of successes of a random variable in a Poisson distribution is provided by the following formula:

\(P(X=x)=\frac{e^{-u} *u^x}{(x)!}\)

where

The number of successes is x.

The Euler number is e = 2.71828.

μ is the mean in the specified time period

The mean number of calls that an office receives on a Monday between 8:00 AM and 9:00 AM is 8.

It follows that μ = 8

Determine the likelihood of receiving at least two calls between 8:00 and 9:00 in the morning.

You either receive no calls or at least one call. Decimal 1 represents the total of these events' probabilities. Mathematically, it follows that

\(P(X=0)+P(X\geq 1)=1\\\)

We desire \(P(X\geq 1 )\). So

\(P(X\geq 1)=1-P(X=0)\)

where

\(= 1-[P(x=0)+P(x=1)]\\=1-e^{-3} (1+3)\\=1-0.19915\\=0.8009\)

The probability of receiving at least two calls between eight and nine in the morning is 0.8009 or 80.09%.

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Answer: 112.5

Step-by-step explanation: When line AB and CD intersect at point E, angle AEC equals BED so you set them equal to each other and find what x is. 5x -20 = x + 50, solving for x, which gives you 17.5. Finding x will tell you what AEC and BED by plugging it in which is 67.5. Angle BED and BEC are supplementary angles which adds up to 180 degrees. So to find angle CEB, subtract 67.5 from 180 and you get 112.5 degrees.

Answer:

50%

thats the answer

If banks' desired reserve/deposit ratio is 25.0 percent, deposits in macro land are $28800000 and the money supply is $36000000

The deposit ratio is the rate sum of money (stores) that commercial banks must not loan out or invest, the reserve ratio is as a rule fixed by the central banks to control inflation and the volume of cash in circulation inside a given country in a particular time.

Initial bank deposit= 60% of 12000000 = 7200000, The reserve/deposit will calculate as follows (25.0 /100%)=0.25 and If banks desired to keep 25.0  it deposit ratio will be : 1/0.25*7200000= 28800000

So the money supply will be the desired deposited :

=28800000+ 7200000 =36000000

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The perimeter of the triangle is 31 feet when the value if y is 3 feet.

Perimeter of the triangle:

Perimeter of the triangle is obtained by the total distance around the edges of a triangle.

The standard form for the perimeter of the triangle is

P = a + b + c.

where

a, b and c refers the edges of the triangle.

Given,

Here we have the triangle with the side values are (y + 5) feet, (3y + 5) feet, and (4y - 3) feet.

Then we have to find the perimeter of the triangle when the value of y is 3 feet.

We know formula of the perimeter of triangle, so first we have to calculate the side values of it, by apply the value of y as 3,

Apply the value of y as 3 feet then we get the value of the edges are

=> y + 5 => 3 + 5 = 8 feet

=> 3y + 5 => 3(3) + 5 = 14 feet

=> 4y - 3 => 4(3) - 3 = 9 feet.

Therefore, the edges of the triangle are 9ft, 14 ft and 9 ft.

Now, we have to apply the values on the formula of the perimeter of the triangle is, then we get

=> P = 8 + 14 + 9

Then the value of P = 31

Therefore, the value of the perimeter of the triangle is 31 feet.

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Answer:

Step-by-step explanation:

Answer:1 1/12

Step-by-step explanation: 3/4+1/3=13/12=1 1/12

let's keep in mind that a conjugate is no more than the same "pair" but with a different sign between, so the conjugate of meow + quack is simply meow - quack, and so on, let's also recall that i² = -1.

\(\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ -1-\sqrt{5}i\hspace{5em}\stackrel{conjugate}{-1+\sqrt{5}i} \\\\\\ (-1-\sqrt{5}i)(-1+\sqrt{5}i)\implies (-1)^2~~ - ~~(\sqrt{5}i)^2\implies (-1)^2~~ - ~~(\sqrt{5})^2 i^2 \\\\\\ 1~~ - ~~(\sqrt{5^2})i^2\implies 1~~ - ~~(5)(-1)\implies 1-(-5)\implies 1+5\implies \text{\LARGE 6}\)

The rectangular pyramid is cut by a plane containing its altitude and perpendicular to its base and will be divided into two rectangular oblique pyramids.

One of the first areas of mathematics is geometry, along with maths. It is preoccupied with spatial characteristics including the separation, form, size, and relative placement of objects. A geometer is a mathematician who specializes in shape.

A straight plane passes through the apex point of the given pyramid when it is intersected by a plane that is orthogonal to its foundation and contains its altitude. The perpendicular planes are parallel to the base at all times. Therefore, this kind of cross-section is a form of continuous passing through the triangle's vertex point.

The rectangular pyramid is cut by a plane containing its altitude and perpendicular to its base and will be divided into two rectangular oblique pyramids.

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Answer:

45 yards and 176 yards

Step-by-step explanation:

Perimeter of a rectangular playing field = 2(Length + width)

P = 2(L+W)..................... Equation 1

From the question,

Let the width of the rectangular playing field = x yards,

The the Length = 4x-4 yards.

Given: P = 442 yards.

Substitute these values into equation 1

442 = 2(4x-4+x)

442/2 = 5x-4

221 = 5x-4

5x = 221+4

5x = 225

x = 225/5

x = 45 yards.

Width = 45 yards.

Length = (45×4)-4 yards = 176 yards

Hence the dimensions of the playing field are, 45 yards and 176 yards

The mean of the data is 41.7, the median is 41.9 and the mode of the data is 42.9.

Here,

We have,

In mathematics, the three main methods for indicating the average value of a set of integers are mean, median, and mode. Adding the numbers together and dividing the result by the total number of numbers in the list yields the arithmetic mean. An average is most frequently used to refer to this. The middle value in a list that is arranged from smallest to greatest is called the median. The value that appears the most frequently on the list is the mode.

The mean is given as:

mean = summation of the frequency / total frequency

mean = 3708/89 = 41.66

The median of the given data is the central value.

In the given data median is the mean of the ages between 56 and 57.

Median = 45 + (89/2) - 59 / 23  * (5)

Median = 41.9

The mode is given for the data having the highest frquency.

The highest frequency is observed at 40-----44:

Mode = 40 + (28 - 21) / (56 - 21 - 23) (5)

Mode = 42.9

Hence, the mean of the data is 41.7, the median is 41.9 and the mode of the data is 42.9.

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Answer:

1,25:1

Step-by-step explanation:

We just have to divide the number of bats by the number of balls!