6). positive integer n is the product of the odd numbers from 99 to 199, inclusive. if n is divisible by 5k , what is the greatest possible value of k?

Answers

Answer 1

The greatest possible value of k such that n is divisible by 5k is 39.

What is odd number?

Any number that cannot be divided by two is considered an odd number. For instance, 25 is strange because it cannot be split by 2. A integer is considered to be divisible by two if its last digit is any of the following: 0, 2, 4, 6, or 8.

To find the greatest possible value of k such that n is divisible by 5k, we need to determine the highest power of 5 that divides n.

The product of the odd numbers from 99 to 199, inclusive, can be expressed as:

n = 99 * 101 * 103 * ... * 197 * 199

To find the power of 5 that divides n, we need to determine the number of factors of 5 in the product.

A factor of 5 is introduced for every multiple of 5 in the product. We need to count the multiples of 5 in the range from 99 to 199.

The largest multiple of 5 in that range is 195, which is 39 * 5.

Therefore, there are 39 multiples of 5 in the product.

To find the highest power of 5 that divides n, we divide 39 by k and find the largest possible integer value for k.

The largest possible value of k is the largest factor of 39.

The factors of 39 are 1, 3, 13, and 39.

Since we are looking for the greatest possible value of k, the answer is 39.

Therefore, the greatest possible value of k such that n is divisible by 5k is 39.

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Related Questions

Line $m$ is parallel to line $n$ and the measure of $\angle 1$ is $\frac 18$ the measure of $\angle 2$. What is the degree measure of $\angle 5$?

Answers

The angle of m∠5 is 116 degrees.

How to find angles when parallel lines are cut by a transversal?

When parallel lines are cut by a transversal, angle relationships are formed. This include corresponding angles, alternate angles , vertical angles etc.

Therefore, line m and n are parallel lines cut by the a transversal.

Hence,

m∠2 = 64 degrees

Therefore,

m∠5 = m∠4 (alternate angles)

Therefore,

m∠5  + m∠2 = 180

m∠5  = 180 - 64

m∠5  = 116 degrees.

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The degree measure of the angle labelled 5; m<5 = 116°.

What is the measure of the angle labelled 5 in the task content?

The angle measure of the angle labelled 5 as in the complete task content in the attached image can be determined as follows;

It follows from the complete task content that; that the measure of angle 2 is; 64°.

On this note, it follows from the sum of angle measures on a straight line theorem that; m<4 = 180° - 64° = 116°.

Additionally, it follows from the congruence of alternate angles theorem that <4 and <5 are congruent and hence, their measures are equal.

Therefore, m<5 = 116°.

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Determine the intercepts of the line. Do not round your answers. 7x-5=4y-6
x intercept: (_),(_)
y intercept: (_),(_)
Please help!

Answers

The intercepts are x intercept: (-1/7,0) and y intercept: (0,1/4)

How to determine the intercepts?

The function is given as:

7x-5=4y-6

Set y = 0 to determine the x-intercept

7x - 5 = -6

Add 5 to both sides

7x = -1

Divide by 7

x = -1/7

Set x = 0 to determine the y-intercept

- 5 = 4y - 6

Add 6 to both sides

4y = 1

Divide by 4

y = 1/4

Hence, the intercepts are x intercept: (-1/7,0) and y intercept: (0,1/4)

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Read the excerpt from Chapter 3 of Wheels of Change . In 1881, as women in the United States continued to struggle with hoops and corsets and other fashion architecture, their counterparts in England formed the Rational Dress Society. This society called for more reasonable clothing solutions, including limiting the weight of a woman's undergarments to seven pounds. Why was the Rational Dress Society formed? to advocate for more functional cycling and athletic gear for women to push for more beautiful, intricate styles of clothing for women to encourage English women to dress differently than American women to promote safer, more comfortable styles of dress for women

Answers

Step-by-step explanation:

Chapter 3 of Wheels of Change .

But the bicycle craze had a more lasting impact on women’s clothing than just the use of bloomers. Thanks in large part to cycling, the innovation of rational dress reformers were starting to take effect by the end of the 1890s. Corsets were on their way out, dresses were getting shorter, and women no longer wore the heavy, bulky undergarments that gave them round, unnatural shapes. These changes went a long way toward unburdening women and setting the stage for them to be healthier and more active in the coming century.

Based on the excerpt, women in the 1890s became more independent and their lives improved as a result of

a rise in the popularity of bicycles.

a rise in the popularity of corsets.

cycling becoming less socially acceptable.

clothing becoming more restrictive.

Answer:

to promote safer, more comfortable styles of dress for women

Step-by-step explanation:

to promote safer, more comfortable styles of dress for women

Is the point (−2, 10) on the circle with radius 5 and center (2, 13)?

Answers

Answer:

  yes

Step-by-step explanation:

The point can be demonstrated to lie on the circle by plotting both on a graph. It can also be shown to lie on the circle by showing the distance from center is equal to the radius.

Graph

The attachment shows a graph of the circle. Its equation is ...

  (x -h)² +(y -k)² = r² . . . . . . for center (h, k) and radius r

We have (h, k) = (2, 13) and r = 5, so the equation is ...

  (x -2)² +(y -13)² = 25 . . . . graphed equation

The point in question is also graphed, and is shown to lie on the circle.

Distance

If the given point satisfies the circle's equation, it lies on the circle.

For (x, y) = (-2, 10), we find ...

  (-2 -2)² +(10 -13)² = (-4)² +(-3)² = 16 +9 = 25 . . . . . the equation is satisfied

11y^2-xy dxUse the method for solving homogeneous equations to solve the following differential equation.

Answers

The solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].

A homogeneous differential equation has a homogeneous function as one of its components, if f(λx, λy) = λⁿf(x, y), for any non-zero constant λ, the function is said to be homogenous. The homogeneous differential equation's generic form is of the type f(x, y).dy + g(x, y).dx = 0. The degree of the homogeneous differential equation is the same for the equation's variables x and y.

In the question, we are asked to solve the homogeneous differential equation, (11y² - xy)dx + x²dy = 0.

The given equation can be solved as follows:

Grouping by differentials, gives us: x²dy = (xy - 11y²)dx.We now substitute, u = yx, making y = ux, or, dy = u.dx + x.du.Making the substitutions, we get: x²(u.dx + x.du) = (u - 11u²)x²dx.Expanding the parentheses, we get: ux².dx + x³.du = ux².dx - 11u²x².dx.Reducing ux².dx, we get: x³.du = -11u²x².dx.Dividing by x³ and u², we get du/u² = -11/x.Now, we integrate both sides of the equation: [tex]\int \frac{1}{u^2}du = \int -\frac{11}{x}dx[/tex]Calculating the resulting integrals, we get: -1/u = C - 11 ln(x).Undoing the substitution, u = y/x, we get: -x/y = C - 11 ln(x)The final solution is: [tex]y = \frac{x}{11 ln (x) + C}[/tex]

Thus, the solution to the homogenous differential equation, (11y² - xy)dx + x²dy = 0, is [tex]y = \frac{x}{11 ln (x) + C}[/tex].

The provided question is incomplete. The complete question is:

"Use the method for solving homogenous equations to solve the following differential equation.

(11y² - xy)dx + x²dy = 0".

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A boat traveled north for 28 miles, then turned x° southwest and traveled for 25 miles before stopping. When it stopped, the boat was 18 miles from its starting point.

A triangle shows the course of a boat. Starting at the dock, it travels 18 miles to the left, then 25 miles up and to the right, and then 28 miles down and back to the dock. The angle between 25 miles and 28 miles is x degrees.

Law of cosines:

By how many degrees did the direction of the boat change when it made its first turn? Round to the nearest degree.
30 degrees
39 degrees
46 degrees

Answers

The number of degrees that the direction of the boat change when it made its first turn is 39°.

How to calculate the value?

From the information given, we would use the cosine function to solve the information.

This will be:

18² = 28² + 25² - 2(28)(25)(cos x)

324 = 784 + 625 - 1400cosx

x = 39.19

Therefore, the value is 39°.

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This system of equations has been placed in a matrix:

y = 700x + 200
y = 5,000 − 75x

Complete the matrix by filling in the missing numbers.

Answers

Answer:

Hello,

Step-by-step explanation:

here is the answer in a picture.


What is the distance between the points (4,3) and (1,-1) on the coordinate
plane?
A. 10 units
B. 50 units
C. 5 units
D. 25 units

Answers

Answer:

The distance between the points (4,3) and (1,-1) is C. 5 units.

Step-by-step explanation:

Answer
C.
(5 Units)

Explanation
Distance formula: square root of (x2-x1)^2+ (y2-y1)^2
(4-1)^2+ (3--1)^2
3^2 + 4^2
9 + 16
25
square root of 25 is 5

Explain how to solve 4^(x + 3) = 7 (x+3 being an exponent) using the change of base formula. Include the solution for x in your answer—round your answer to the nearest thousandth.

Answers

Using natural logarithms properties, we will see that:

x = -1.596

How to solve the equation?

Here we can use the property:

[tex]ln(a^b) = b*ln(a)[/tex]

Now we have the equation:

[tex]4^{x + 3 }= 7[/tex]

If we apply the natural logarithm in both sides, we get:

[tex]ln(4^{x + 3 })= ln(7)\\\\(x + 3)*ln(4) = ln(7)\\\\x + 3 = ln(7)/ln(4)\\\\x = ln(7)/ln(4) - 3 = log_4(7) - 3 = -1.596[/tex]

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please put it in expanded form and solve it

Answers

Answer:

1/xyz^3

Step-by-step explanation:

exponents are subtracted when divided

x^0 is 1

negative exponents are positive in the denominator

(4x^0y^-2z^-3) / (4xy-1)

(4xy^-2z^-3) / (4xy^-1)

x-1y^-1z^-3

1/xyz^3

Find the area of the shaded regions.​

Answers

The area of the shaded circle is given as follows: 84.82 cm².

What is the area of a circle?

The area of a circle of radius r is given by pi multiplied by the radius squared, as given by the formula presented next:

[tex]A = \pi r^2[/tex]

In this problem, we have that the important data is given in the bullet-points as follows:

The radius is of r = 6 cm.The shaded area is 75% of the circle.

Hence the shaded area in cm² can be found a applying the formula given at the beginning of this problem, as is presented below:

[tex]A = 0.75\pi \times 6^2 = 84.82[/tex]

The multiplication by 0.75 happened because as stated in the bullet point, the shaded area corresponds to only 75% of the entire circle.

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Suppose that you are interested in determining the average height of a person in a large city. You begin by collecting the heights of a random sample of 256 people from the city. The average height of your sample is 64 inches, while the standard deviation of the heights in your sample is 4 inches.The standard error of your estimate of the average height in the city is .

Answers

The standard error of the estimate of average height in the city is 0.25.

Given average height 64 inches, sample mean and sample standard deviation of 4 inches.

We have to determine the standard error of the estimate of the average height in the city.

Standard error is the error which is predicted before research to happen in research. It is calculated by dividing the standard deviation of the sample by the square root of the sample size.

n=256

μ=mean

s = sample standard deviation

Standard error=s/[tex]\sqrt{n}[/tex]

=4/[tex]\sqrt{256}[/tex]

=4/16

=0.25

Hence the standard error of the estimate of the average height is 0.25.

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The formula d=1/2n+26 relates the nozzles pressure n (in pounds per square inch) of a free hose and the maximum horizontal distance the water reaches d (in feet). How much pressure is needed to reach a fire 50 feet away?

Answers

The pounds of pressure needed to reach a fire 50 feet away is 48 pounds

Formula

d = 1/2n + 26

where

n = nozzle pressure in pounds per square feetd = distance the water reaches

If d = 50 feet

d = 1/2n + 26

50 = 1/2n + 26

50 - 26 = 1/2n

24 = 1/2n

n = 24 ÷ 1/2

n = 48 pounds

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Write two expressions to show the total area of advertisement space on one page.

Answers

The area covered by the advertisement on the page is [tex]ab \ unit^2[/tex].

What is the definition of area of a rectangle?

The area of a rectangle covers is the space it takes up inside the boundaries of its four sides. The dimensions of a rectangle determine its area. In general, the area of a rectangle is equal to the product of its length and breadth of the rectangle.

The formula of area of rectangle is [tex]length \times breadth[/tex] [tex]unit^2[/tex]

let the given page represents a rectangle.

We take the length of the advertisement is [tex]a[/tex] unit and breadth of the advertisement is [tex]b[/tex] unit.

The area of the advertisement [tex]=a \times b \ unit^2[/tex]

                                                   [tex]=ab \ unit^2[/tex]

Therefore, the area covered by the advertisement on the page is [tex]ab \ unit^2[/tex]

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Can someone please help me on this

Answers

Answer:

? = 38°

Step-by-step explanation:

We can use the property of sine to find the missing angle value.

sin (angle) = opposite / hypotenuse

sin (?) = 16 / 26                                  <----- Insert values

? = sin⁻¹(16 / 26)                                 <----- Rearrange

? = 37.97...                                         <----- Solve

? = 38°                                               <----- Round

The duration of shoppers' time in BrowseWorld's new retail outlets is normally distributed with a mean of 41.8 minutes and a standard deviation of 17.3 minutes. How long must a visit be to put a shopper in the longest 20 percent

Answers

A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula. In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

How long must a visit be to put a shopper in the longest 20 percent?

Here [tex]\mu=41.8 , \sigma=17.3[/tex]

The 100-20=80th percentile, which is X when Z has p-value of 0.8, so Z=0.84

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

[tex]0.84=\frac{X-41.8}{17.3}[/tex]

14.532=X-41.8

X=14.532+41.8

X=56.33

A visit must be of at least 56.33 minutes to put a shopper in the longest 20 percent.

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Does anyone know how to do this

Answers

Considering the area of the rectangle, we have that the length is of 8 units and the width is of 10 units.

What is the area of a rectangle?

The area of a rectangle of length l and width w is given as follows:

A = lw.

In this problem, the area is of 80 square units, while the length and the width are consecutive even integers, hence:

A = 80.w = l + 2.

Then:

l(l + 2) = 80

l² + 2l - 80 = 0

(l + 10)(l - 8) = 0.

We need the positive measure, hence:

l -  8= 0 -> l = 8 units.

w = l + 2 = 10 units.

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If I start with the number 7 and count by 4s, the following sequence is obtained: 7, 11, 15, 19, 23, and so forth. A new sequence is formed when I start with a different number and count by a different number. Suppose the 2nd number of the new sequence is 8 and the 5th number is 17. What is the 10th number of the new sequence

Answers

Answer:

a₁₀ = 32

Step-by-step explanation:

the sequence is arithmetic since there is a count on , a common difference

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₂ = 8 and a₅ = 17 , then

a₁ + d = 8 → (1)

a₁ + 4d = 17 → (2)

subtract (1) from (2) term by term to eliminate a₁

3d = 9 ( divide both sides by 3 )

d = 3

substitute d = 3 into (1)

a₁ + 3 = 8 ( subtract 3 from both sides )

a₁ = 5

Then

a₁₀ = 5 + (9 × 3) = 5 + 27 = 32

What is 125x + 64y¹2 written as a sum of cubes?
O (25x3)3 + (44)3
O (5x³)3 + (164)³
O (25x³)3 + (8y4)3
(5x3)3 + (4y4)3

Answers

quick answer: (5x3)3 + (4y4)3

please hit the like button if it is correct :D

Identify the factors of 6ab − 8a 21b − 28. (2a 4)(3b − 7) (2a − 4)(3b 7) (2a 7)(3b − 4) (2a − 7)(3b 4)

Answers

Answer: ) (2a+7)(3b- 4)

Step-by-step explanation:

Can 1775 dollars buy 2 large balloons and 16 small balloons 1 large balloon = 300 cubic feet 1 small balloon - 40 cubic feet helium costs $1.60 per cubic foot

Answers

No, 1775 dollars cannot buy 2 large balloons and 16 small balloons if helium costs $1.60 per cubic foot.

Calculating the Costs of Balloons

It is given that,

Helium costs $1.60 per cubic foot.

Volume of one large balloon = 300 cubic feet

Thus, the price of one large balloon = $1.60 × 300

= $480

Volume of one small balloon = 40 cubic feet

Thus, the price of one small balloon = $1.60 × 40

= $64

How much buying 2 large and 16 small balloons costs?

So, as calculated above,

One large balloon costs $480, and one small balloon costs $64

Therefore, the cost of two large balloons = $480 × 2

= $960

Cost of 16 small balloons = $64 × 16

= $1024

Total cost of balloons = $960 + $ 1024

= $1984

Since, $1984>$1775,

Therefore, $1775 cannot buy all those balloons if helium costs $1.60 per cubic foot.

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Can anyone solve this?

Answers

Answer:

BT = 18, DA = 6

Step-by-step explanation:

- EBT and SDA are similar triangles

- EBT has a perimeter of 63

- SDA has a perimeter of 21

- BT = 6x

- DA = x+3

We know that EBT has side lengths that are three times bigger than the side lengths of SDA since 63 = 21 x 3.

so

6x is equal to 3(x+3).

6x = 3x + 9

3x = 9

x = 3

Now we know that:

BT = 18

and

DA = 6

Emily can read 30 pages in 45 minutes. At this rate, how many pages
will she read in 3 hours?

Answers

She can read 120 pages
60x3=180(Number of minutes in 3 hours)
180/45=4
4x30=120

Complete the recursive formula of the geometric sequence -0.25\,,-2\,,-16\,,-128,...−0.25,−2,−16,−128,...minus, 0, point, 25, comma, minus, 2, comma, minus, 16, comma, minus, 128, comma, point, point, point.
b(1)=b(1)=b, left parenthesis, 1, right parenthesis, equals
b(n)=b(n-1)\cdotb(n)=b(n−1)⋅b, left parenthesis, n, right parenthesis, equals, b, left parenthesis, n, minus, 1, right parenthesis, dot

Answers

The recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]

How to determine the recursive formula?

The sequence is given as:

[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]

The first term of the above sequence is

[tex]b(1) = -0.25[/tex]

Calculate the common ratio using

r = b(2)/b(1)

So, we have:

r = -2/-0.25

Evaluate

r = 8

So, we have:

[tex]b(n) = b(n-1)\cdot 8[/tex]

Hence, the recursive formula of the geometric sequence is [tex]b(1) = -0.25[/tex], [tex]b(n) = b(n-1)\cdot 8[/tex]

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Complete question

Complete the recursive formula of the geometric sequence

[tex]-0.25\,,-2\,,-16\,,-128,..[/tex]

[tex]b(1) =[/tex]

[tex]b(n) = b(n-1)\cdot[/tex]

Which of the following is a geometric sequence?

Answers

Answer:

A

Step-by-step explanation:

Geometric sequence is when, during each successive number, a constant is being multiplied. In answer choice A, each number is getting multiplied by 3, so it is a geometric sequence.

Given that a function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25 and that h(8) = 19 and h(-2) = 2, select the statement that could be true for h.

Answers

The true statement for h regarding the function is  that C. h(2) = 16.

How to illustrate the function?

From the information given, the function, h, has a domain of -3 ≤ x ≤ 11 and a range of 1 ≤ h(x) ≤ 25.

This illustrates that the range or h has to be less than or equal to 25.

The option that correctly fits this is C.

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Find the probability of winning a lottery by selecting the correct six integers, where the order in which these inte

Answers

The probability of winning a lottery by selecting the correct six integers, are

[tex]\begin{aligned}&(a) 1.68 \times 10^{-6} \\&(b) 5.13 \times 10^{-7} \\& (c) 1.91 \times 10^{-7} \\&(d)8.15 \times 10^{-8}\end{aligned}[/tex]

What is binomial distribution?

The binomial distribution is a type of probability distribution that expresses the probability that, given a certain set of characteristics or assumptions, a value would take one of two distinct values.

Part (a); positive integers not exceeding 30.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other twenty-four.

[tex]\frac{\left(\begin{array}{c}6 \\6\end{array}\right)\left(\begin{array}{c}24 \\0\end{array}\right)}{\left(\begin{array}{c}30 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}30 \\6\end{array}\right)}=1.68 \times 10^{-6}[/tex]

Part (b); positive integers not exceeding 36.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the other thirty.

[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}30 \\0\end{array}\right)}{\left(\begin{array}{c}36 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}36 \\6\end{array}\right)}=5.13 \times 10^{-7}[/tex]

Part (c); positive integers not exceeding 42.

To calculate the probability, use binomial coefficients. Pick six of the six accurate integers and none of the 36 other integers.

[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}36 \\0\end{array}\right)}{\left(\begin{array}{c}42 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}42 \\6\end{array}\right)}=1.91 \times 10^{-7}[/tex]

Part (d); positive integers not exceeding 48.

To calculate the probability, use binomial coefficients. Choose six of the six accurate integers and none of the other 42.

[tex]\frac{\left(\begin{array}{l}6 \\6\end{array}\right)\left(\begin{array}{c}42 \\0\end{array}\right)}{\left(\begin{array}{c}48 \\6\end{array}\right)}=\frac{1}{\left(\begin{array}{c}48 \\6\end{array}\right)}=8.15 \times 10^{-8}[/tex]

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The complete question is-

Find the probability of winning a lottery by selecting the correct six integers, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 30. b) 36. c) 42. d) 48.

What is the approximate side length of the square? 3.0 units 3.5 units 4.2 units 4.9 units

Answers

Answer:

(っ◔◡◔)っ ♥ the answer is C ♥

Step-by-step explanation:

Determine if y varies directly with x. Give the constant of variation, when appropriate. (picture below)

A) Does y vary directly with x?

B) What is the constant of variation?

Answers

Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.

Variation

y = k × x

where,

k = constant of proportionality

y = -40

x = -5

y = k × x

-40 = k × -5

-40 = -5k

k = -40/-5

k = 8

when,

y = 8 and x = 2.5

y = k × x

8 = k × 2.5

8 = 2.5k

k = 8/2.5

k = 3.2

when,

y = 5 and x = 4

y = k × x

5 = k × 4

5 = 4k

k = 5/4

k = 1.25

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0 divided by 0 is? 45 points for who answer its correct not for a homework

Answers

Answer:

Undefined

Step-by-step explanation:

No multiplicative inverse exists for 0

Answer:

undefined

Step-by-step explanation:

a single value can't be assigned to a fraction where the denominator is 0 so the value remains undefined.

Other Questions
Which of the following occurs when mountain belts are eroded?a.erosion is accompanied by isostatic reboundb. the continental crust becomes thinnerc. deep metamorphic and plutonic rocks can be uplifted to the surface the ten days when jews concentrate on prayer, contemplation, and self-searching is called International loans extended at favorable repayment terms have temporarily raised the living standard in some developing countries but O a. have never become a source of discretionary funding that benefits unintended beneficiaries. O b. have never insulated public officials from their own incompetence. O c. have not necessarily increased their ability to become self-supporting at that higher standard of living. O d. have also dislodged corrupt governments from power. O e. have also helped most countries achieve industrial status. A recently launched supplemental typing keypad gained significant popularity on Amazon Shopping due to its flexibility. This keypad can be connected to any electronic device and has 9 buttons, where each button can have up to 3 lowercase English letters. The buyer has the freedom to choose which letters to place on a button while ensuring that the arrangement is valid. A keypad design is said to be validif: . All 26 letters of the English alphabet exist on the keypad. Each letter is mappedto exactly one button. mappect to A button has at most 3 letters mapped to it! . . Examples of some valid keypad designs are: 1 abc 2 def 3 ghi 4 jkl 5 mno 6 par 7 stu 8 VWX 9 yz 1 ajs 2 bot 3 cpu Bo N 4 dkv 5 hmz 6 gl 7 enw 8 fax 9 iry jkl mno 8 9 17 stu WWX Z 2 ajs boti cou 4 dk 6 6 a | hmz 8 tax 9 Iry enw In the left keypad, Thello" can be typed using the following button presses: 31 twice (prints 'h'), [2] twice (prints e), [4] thrice (prints ), 14) thrice (prints 1). [5] thrice (prints o"). Thus, total number of button presses - 2 + 2 +13+3+3 = 13. In the right keypad, Ithello can be typed using the following button presses: [5] once (prints h'), [71 once (prints 'e'), [6] twice (prints 1). [6] twice (prints ''), [2twice (prints "o"). Thus, total number of button presses = 1 + 1 + 2 + 2 + 2 = 8. The keypad click count is defined as the number of button presses required to print a given string. In order to send messages faster, customers tend to set the keypad design in such a way that the keypad click count is minimized while maintaining its validity. Given a string text consisting of lowercase English letters only, find the minimum keypad click count, Graph the quadratic function f(x) = (x + 3)2 - 1. Give the (a) vertex, (b) axis, (c) domain, and (d) range. Then determine (e) the largest open interval of the domain over which the function is increasing and (f) the largest open interval over which the function is decreasing. 15Select the correct answer.How does the President develop the idea that Sonia Sotomayor's appointment to the Supreme Court is especiallyimportant?O A.Cm B.O C.O D.He focuses on the sacrifices that Sotomayor's family made in order to support her dreams.He addresses how visionary the founders were by including timeless concepts in the ConstitutionHe explains how Sotomayor's struggles and achievements can serve as a model for what others canaccomplish.He emphasizes the challenges she faced and continues to face in her professional journey.ResetNextbill4012:45 AM5/2/22023 find the 4th partial sum, s4, of the series [infinity] n2 n=9 s4 = A staff nurse delegates a task to a nursing assistive personnel (NAP), knowing that the NAP has never performed the task before. As a result, the patient is injured, and the nurse defensively states that the NAP should have known how to perform such a simple task. Which element of the decision-making process is the nurse lacking?a.Authorityb.Autonomyc.Responsibilityd.Accountability if mitochondria originated as prokaryotic symbionts, which characteristics might they share with prokaryotes? click all that apply. true or false the activities of homeodomain transcription factors in controlling development are based on rearrangement of nuceosomes Identify the C4H9Cl isomer given the following proton NMR data: doublet ? 1.04 (6H) multiplet ? 1.95 (1H) doublet ? 3.35 (2H) A) (CH3)3CCl B) CH3CH2CH2CH2Cl C) CH3CH2CHClCH3 D) (CH3)2CHCH2Cl the strategic alternatives of a company are influenced by a number of factors. the factors that a marketing manager must consider are three types: external, financial, and internal. what is a ligamentwhat are tendonswhy is the skeletal system important to uswhat is the main function of the skeletal system This expression estimates the gain-bandwidth product of an op-amp Clue: The GBW depends on the transconductance of the input stage and the value of the compensation capacitor. GBW [Hz] = To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?X 0 1 2 3 4P(X) 0.051 0.225 0.317 0.19 0.217Expected value = 2.297A previous analysis of historical records found that the mean value of orders for promotional goods is 20 dollars, with the company earning a gross profit of 29% on each order. Calculate the expected value of the profit contribution next year.Expected value = 13.3226The fixed cost of conducting the four promotions is estimated to be 12000 dollars with a variable cost of 4.25 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer to the next highest integer.)Breakeven point = ???Help, please applying each format separately, such as font size and then bold, is called ________ formatting. The cut off between visible and infrared light is usually said to be somewhere between 700 and 800nm.why is silicon transparent to most infrared light but opaque to visible lighta.Visible photons have greater energy than the gap, so they can be absorbed whereas infrared photons pass throughb.Visible photons have greater energy than the gap, so they cant interact with the silicon as the infrared photon canc.Infrared photon have less energy than the gap, and so, unlike visible photon, they can be absorbed and reemitted from the materiald.Infrared photon have less energy than the gap, and so they are only partially absorbed whereas visible photons are fully absorbed _____ are more concerned with the end results, whereas _____ are concerned with the means to get those results.options: 1) Humanists; capitalists 2) Utilitarians; deontologists 3) Deontologists; utilitarians 4) Capitalists; utilitarians The three methods used to classify costs into their fixed and variable components includesleast-squares regressionscatter diagramshigh-low method plot the point whose spherical coordinates are given. then find the rectangular coordinates of the point. (a) (6, /3, /6)