A hardware store carries 42 types of boxed nails and 36 types of boxed screws. the store manager wants to build a rack so that he can display the hardware in rows. he wants to put the same number of boxes in each row, but he wants no row to contain both nails and screws. what is the greatest number of boxes that he can display in one row? how many rows will there be if the manager puts the greatest number of boxes in each row?

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(x-3y=9\implies -3y=-x+9\implies y=\cfrac{-x+9}{-3} \\\\\\ y=\cfrac{-x}{-3}+\cfrac{9}{-3}\implies y=\cfrac{1}{3}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a likne whose slope is 1/3 and it passes through (-10 , 9)

\((\stackrel{x_1}{-10}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-10)}) \implies y -9= \cfrac{1}{3} (x +10) \\\\\\ y-9=\cfrac{1}{3}x+\cfrac{10}{3}\implies y=\cfrac{1}{3}x+\cfrac{10}{3}+9\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{37}{3} \end{array}}\)

The data is usually anonymized before it is sold, meaning that individual patient identities are protected.

Hospitals collect a wide variety of data on patient health and medical procedures, including demographic information, diagnoses, procedures, and treatments.

This data can be very valuable to public health organizations like the CDC, which use it to better understand patterns and trends in disease and illness.

For example, the CDC might use hospital data to track the spread of a particular disease or to identify areas where certain types of illnesses are more common.

Hence, The data is usually anonymized before it is sold, meaning that individual patient identities are protected.

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The factor form of the quadratic equations are listed below:

Case 13: (b - 4) · (b - 2)

Case 14: (n + 4) · (n + 2)

Case 15: 2 · (n + 9) · (n - 6)

Case 16: 5 · (n + 2)²

Case 17: 2 · (k + 5) · (k + 6)

Case 18: (a - 10) · (a + 9)

Case 19: (p + 10) · (p + 1)

Case 20: 5 · (v - 2) · (v - 4)

Case 21: 2 · (p + 2) · (p - 1)

Case 22: 4 · (v - 2) · (v + 1)

Case 23: (x - 10) · (x - 15)

Case 24: (v - 5) · (v - 2)

Case 25: (p + 6) · (p - 3)

Case 26: 6 · (v + 10) · (v + 1)

In this problem we find quadratic equations of the form a · x² + b · x + c, whose factor form is introduced below:

a · x² + b · x + c = a · x² + a · (- r₁ - r₂) · x + a · r₁ · r₂ = a · (x - r₁) · (x - r₂)

Where r₁, r₂ are real roots.

Now we proceed to present the factor form of each quadratic equation:

Case 13

b² - 6 · b + 8 = (b - 4) · (b - 2)

Case 14

n² + 6 · n + 8 = (n + 4) · (n + 2)

Case 15

2 · n² + 6 · n - 108 = 2 · (n² + 3 · n - 54) = 2 · (n + 9) · (n - 6)

Case 16

5 · n² + 10 · n + 20 = 5 · (n² + 2 · n + 4) = 5 · (n + 2)²

Case 17

2 · k² + 22 · k + 60 = 2 · (k² + 11 · k + 30) = 2 · (k + 5) · (k + 6)

Case 18

a² - a - 90 = (a - 10) · (a + 9)

Case 19

p² + 11 · p + 10 = (p + 10) · (p + 1)

Case 20

5 · v² - 30 · v + 40 = 5 · (v² - 6 · v + 8) = 5 · (v - 2) · (v - 4)

Case 21

2 · p² + 2 · p - 4 = 2 · (p² + p - 2) = 2 · (p + 2) · (p - 1)

Case 22

4 · v² - 4 · v - 8 = 4 · (v² - v - 2) = 4 · (v - 2) · (v + 1)

Case 23

x² - 15 · x + 50 = (x - 10) · (x - 15)

Case 24

v² - 7 · v + 10 = (v - 5) · (v - 2)

Case 25

p² + 3 · p - 18 = (p + 6) · (p - 3)

Case 26

6 · v² + 66 · v + 60 = 6 · (v² + 11 · v + 10) = 6 · (v + 10) · (v + 1)

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Answer:

40 m²

Step-by-step explanation:

First, find the perimeter. Using the perimeter formula, p = 2l + 2w, solve for the side lengths of the length and width.

Let w represent the width. The length can be represented by w + 3, since the length is 3 m longer than the width.

Plug in 26 as the perimeter, and plug in w and w + 3 for the width and length:

p = 2l + 2w

26 = 2(w + 3) + 2w

Simplify and solve for w:

26 = 2w + 6 + 2w

26 = 4w + 6

20 = 4w

5 = w

Find the length by adding 3 to this:

5 + 3

= 8

Now, find the area using the area formula, A = lw

Plug in the length and width:

A = lw

A = 8(5)

A = 40

So, the area of the rectangle is 40 m²

Answer:

\(x=\sqrt{p-m}\)

Step-by-step explanation:

if you divide a square, that makes it a square root

and then you just subtract the m

Answer:

\(x = 1.2, y = -1.1\)

Step-by-step explanation:

One methodology to solve a system of equations is to get the coefficients of one of the variables equal so that it can be eliminated by either addition or subtraction of the transformed equations

Looking at the two equations:

\(7x-4y=12.8 \dots[1]\)

\(4x-7y=12.5\dots[2]\)

we can make the coefficients of y the same by multiplying [1] by 7 and [2] by 4

Multiplying [1] by 7 :

\(7(7x - 4y) = 7 (12.8)\\49x - 28y = 89.6\dots[3]\)

Multiplying [2] by 4:

\(4(4x-7y) = 4(12.5)\\\\16x - 28y = 50\dots[4]\\\)

Since the y coefficients are the same, we can eliminate the y term by subtracting equation [2] from equation [1]

[1] - [2]:

\(49x - 28y - (16x - 28y) = 89.6 - 50\)

\(49x - 16x - 28y + 28y = 39.6\)

\(33x = 39.6\)

\(x = \dfrac{39.6}{33}\)

\(x = 1.2\)

Substitute for x in Equation [1]
\(7x - 4y = 12.8\\\\7(1.2) - 4y = 12.8\\\\8.4 - 4y = 12.8\\\\\)

Subtract 8.4 from both sides:
\(8.4 - 8.4 - 4y = 12.8 - 8.4\\\\-4y = 4.4\\\\\)

Divide both sides by -4:
\(\dfrac{-4y}{-4} = \dfrac{4.4}{-4}\\\\y = - 1.1\)

Solution:

\(\boxed{x=1.2, y = -1.1}\)

D since the line is going to the right.

d

good luck  

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A tessellation is a pattern formed by arranging shapes to fill a plane without any gaps or overlaps. Among the characteristics listed, the one that is NOT necessary for a tessellation is "using shapes with straight sides."

Tessellations can be created with a variety of shapes, including those with curved sides. For example, tessellations can be formed using semi-regular shapes, such as a combination of hexagons and equilateral triangles, or using irregular shapes that fit together in a repeating pattern. Tessellations can also be made with curved shapes like circles, which can form a pattern known as "circle packing."

However, the other characteristics mentioned are essential for a tessellation. A repeating pattern is necessary because it ensures that the shapes can be arranged indefinitely across the plane. Congruent shapes are also essential, as they ensure a uniform pattern and that all shapes fit together perfectly. Lastly, no gaps or overlaps are a fundamental requirement for tessellations, as the purpose is to cover the entire plane seamlessly.

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In light of our responses to the presented questions, using equations, we can deduce that the person's estimated height is 0.0225 meters, or 2.25 centimeters.

A mathematical equation is a sentence that suggests that other equations are equivalent. The two sides of an equation are separated by the algebraic symbol (F).

For example, the statement "\(2x+3=9\)" states that the value "9" in the total is indicated by the combination "\(2x + 3\)". The goal of equation solving is to determine the value or values of the fact(s) that will allow an equation to be true.

Equations can be simple or complicated, linear or nonlinear, and they can involve one or more variables. For example, in the equation "\(2x^2+2x-3-0,\) *the variable x is raised to the power of 2 for the solution. Lines are frequently used in geometry, algebra, and equations.

We may determine the person's height in meters using the scale diagram. Assume the individual's height is "h" metres.

As a result, the ratio of the length of the lorry to the height of the person in the diagram is:

\(900cm : 4.5cm\)

When we simplify this ratio, we get:

\(20 : 01\)

As a result, the individual's height in metres is:

\((4.5cm) \times (1metre/100cm) \times (1/200)=0.0225m\)

As a result, the person's estimated height is 0.0225 metres or 2.25 Centimetres.

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Answer:

Second option 168= 18.X + 12.2X

Step-by-step explanation:

Area of the shape is in two parts,

Are of the larger rectangle is Lenght x width

Lenght is 12cm and width is x +2x

Area = 12 x 3x = 36x cm²

Area of the smaller rectangle = 6 x X = 6xcm²

Total area 36x + 6x = 168cm²

Another method

Find the area of the big rectangle including the cut off area

Lenght x width = 18 x (2x + X)

Area =18 x 3x or 18.3x

Calculate the white area

Length x width = 6 x 2x = 12x

Deduct the white area from the larger area

168= 18.3x - 12x

Third method

Divide the rectangle from top down

First rectangle length x width = 18x X or 18x

Second rectangle length x width = 12 x 2x

168= 18. x + 12 . 2x

The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The figure shown has a total area of 168 cm².

Now, We can find as;

Area of rectangle = Length x width

Hence, We can formulate;

⇒ 18 × x + 12 × 2x = 168

Thus, The correct equation which can be used to find the value of x is,

⇒ 168 = 18 × x + 12 × 2x

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Answer:

x=6, y=-3

Step-by-step explanation:

Elimination is literally the process of eliminating one of the variables through the process of making them the same.

\(\left \{ {{-8x-9y=-21} \atop {-2x-4y=0}} \right.\)

After looking at this equation, it is evident that x can be eliminated easier than y. Therefore, we will multiply the bottom line by four to make the top and bottom x the same.

\(\left \{ {{-8x-9y=-21} \atop {-8x-16y=0}} \right.\)

Then, we can eliminate x by subtracting the top equation from the bottom equation.

\(-8x-9y-(-8x-16y)=7y\\-21-0=-21\\7y=-21\)

Thus, y=-3.

If we insert that back into an equation,

\(-2x-4(-3)=0\\-2x+12=0\\-2x=-12\\x=6\)

We get x=6.

By calculating distance of fourth and fifth fall we found out that total distance covered by bungee jumper is 253.2 feet

In mathematics, a sequence is an enumerated collection of objects in with a pattern.

Here first we will find a pattern in jumper

97.2,64.8,43.2.....

Here we can see that difference between first two fall is = 97.2-64.8=32.4

and difference between second and third fall is 64.8-43.2=21.6 which  is 2/3 of 32.4

so by following same pattern

difference between third and fourth fall is

\(\frac{2}{3}\times21.6=14.4\)

And difference between fourth and fifth fall is

\(\frac{2}{3}\times14.4=9.6\)

Hence fourth fall is 43.2-14.4=28.8

and fifth fall is 28.8- 9.6=19.2

Hence total distance = 97.2+64.8+43.2+28.8+19.2=253.2 feet

By calculating distance of fourth and fifth fall we found out that total distance covered by bungee jumper is 253.2 feet .

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The probability of selecting 2 lemon jawbreakers in succession is  0.1512

From the question, we have the following parameters that can be used in our computation:

So, we have

Total = 7 + 3 + 8

Total = 18

This also means that

P(lemon) = 7/18

Simplify

P(lemon) = 7/18

Using the above as a guide, we have the following:

P(Lemon, Lemon) = 7/18 * 7/18

Evaluate the products

So, we have

P(Lemon, Lemon) = 0.1512

Hence, the probability of selecting 2 lemon jawbreakers in succession is  0.1512

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Answer:

Smaller angle = 53.2

Larger angle = 126.8

Step-by-step explanation:

Lets say x is the measure of the supplement. Since we know they're supplementary, we know their angle measure sum will equal 180. We can set up our equation like this \(x + (x-73.6) = 180\). Note: (x - 73.6) is the measure of the smaller angle. By solving, we get 126.8 degrees for the measure of the supplement. If we plug in the value of x into (x-73.6), we get 53.2 degrees as the angle measure of the smaller angle.

In 10 days, you would drive a total distance of 110 miles to and from school.

To calculate the total number of miles you drive to and from school in 10 days, we need to multiply the round-trip distance by the number of days. The round-trip distance to school is 11 half miles, which can also be expressed as 11/2 miles or 5.5 miles.

To find the total distance traveled in 10 days, we multiply the round-trip distance by the number of days:

Total distance = Round-trip distance * Number of days

Total distance = 5.5 miles * 10 days

Total distance = 55 miles

Therefore, in 10 days, you would drive a total of 55 miles to and from school.

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Answer:

Surface Area  = 4928 ft^2

Step-by-step explanation:

Easy way -

First find the area of each face i.e.

56 * 20 =  1120

65 * 20 = 1300

33 * 20 = 660

2 * (1/2 * 56 * 33) = 1848

Total = 4928 ft^2

The table that shows only viable solutions for the total number of pages Selma has read after x minutes have elapsed is:

A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.

A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.

This table corresponds to Selma reading at a pace of 2 pages per minute, and the total pages read after x minutes align with the given entries in the table.

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Answer:

(-3x -3 - 24x/(x²-5))

Step-by-step explanation:

(x - 3x³ - 3x² - 10x + 15) / p = x² - 5

(-3x³ - 3x² - 9x + 15) / p = x² - 5

p = (-3x³ - 3x² - 9x + 15)/(x² - 5) = -3x - 3 - 24x/(x² - 5)

- -3x³ + 15x

---------------------------------

0 - 3x² - 24x + 15

- - 3x² + 15

‐-----------------------------------

0 - 24x + 0

Answer and Step-by-step explanation:

The Domain of the function is: [-infinity, +infinity]

The Range of the function is: [-1, + Infinity]

X - intercepts - (0,0), (I think it is 5,0)

Y - Intercept - (0,0)

Answer and Step-by-step explanation:

The y-intercept is (0, 3)

The value 3 is in the y place.

#teamtrees #WAP (Water And Plant)

Answer:

(7, 4)

Step-by-step explanation:

In this case, where we reflect W(7, -4) over the x-axis, the x-coordinate of the reflection is the same:  7.  But the -4 becomes +4 through this reflection.

Reflected point is (7, 4)

Answer:

5

(40+24)=64

64÷8=8

(2^2-1)=3

8-3=5

The height of the cylinder is 4 feet.

The volume of a cylinder can be found as follows;

volume of a cylinder = base area × height

Therefore,

base area = πr²

volume of the cylinder = 48π ft³

base area = 12π ft²

Therefore, let's find the height of the cylinder as follows:

48π = 12π × h

divide both sides of the equation by 12π

h = 48π / 12π

h = 4 ft

Therefore,

height of the cylinder  = 4 feet

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Answer:

Step-by-step explanation:

None of them are correct. The closest is D.

The domain is all real x or (-∞, ∞)

The range is [0, ∞).

Post-tests are generally not necessary. Since you've rejected the null hypothesis and there are only two treatments, it's already evident that there is a significant difference between them, and no further comparisons are needed.

a) Under what circumstances are post-tests necessary when you fail to reject the null hypothesis with k=2 treatments?

In this case, post-tests are typically not necessary. Since you failed to reject the null hypothesis and there are only two treatments, there is no need for further comparisons or tests.

b) Even if you fail to reject the null hypothesis, post-tests (such as pairwise comparisons) may still be necessary when there are more than two treatments. These tests can help you identify if there are any significant differences between specific pairs of treatments, which might not have been evident when looking at the overall test.

c) When you reject the null hypothesis with more than two treatments, post-tests are almost always necessary. These tests, such as Tukey's HSD or Bonferroni correction, help you determine which specific treatments are significantly different from each other, providing more detail about the differences among treatments.

d) In this case, post-tests are generally not necessary. Since you've rejected the null hypothesis and there are only two treatments, it's already evident that there is a significant difference between them, and no further comparisons are needed.

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Answer:

True?

Step-by-step explanation:

There not really an equation here.

But that is correct.

-47 is less than -20

Answer:

i. 2x²+5x-3

ii. x=-27/2

iii. length of rectangle= 2x-11= 2*11-1=21cm

Step-by-step explanation:

i. ax²=bx=c

(2x-1) (x=3)

2x²=6x-x-3

=2x²=5x-3