how many rectangles of different sizes can be formed from 36 identical rectangles

Answers

Answer 1

Answer:

i think answer is 5

Step-by-step explanation:

since you could think what are factors of 36
1x36
2x18
3x12
4x9 and
6x6


Related Questions

the square root of 7956​

Answers

The square of 7956 is 89.196

Answer:

89.19

Step-by-step explanation:

           8 9  .  1     9

         79,56 . 00, 00

8    |  64

      |  1556

169 |  1521

      |      3500

1781 |      1781

              1719

17829|        6200

       

               

         

     

Question
In the xy-plane, what is the y-intercept of the graph of the equation y = 6 (x − 1/2) (x+3)?
-9
-1/2
-1/2
3
9

Answers

Answer:

-9

Step-by-step explanation:

To find the y intercept, substitute 0 in for x.

So, the equation looks like this:

[tex]y=6(0-\frac{1}{2} )(0+3)[/tex]

Now, just solve for y and you will get y = -9

The y-intercept of the graph of the equation is y = -9 which is the correct answer that would be an option (A).

What is the equation of a line?

The general equation of a line is y = mx + c

where m is the slope of the line and c is the intercept.

A linear equation is defined as an equation in which the highest power of the variable is always one.

Given equation as:

y = 6 (x - 1/2)(x+3)

To determine the y-intercept of the graph of the equation

Substitute the value x = 0 in the equation,

y = 6 (0 - 1/2)(0+3)

Apply the arithmetic operation and solve for y

y = -9

Hence, the y-intercept of the graph of the equation is y = -9.

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B
23. Find the EXACT circumference of the circle
if AB = 2in and BC = 11in.
A
C
a. √117 in
b.
5√5π in
c.
35.1 in
d. 5√5 in

Answers

Answer:

C. 35.1

Step-by-step explanation:

First get the length of AC by using the Pythagorean Theorem, that ends up being about 11.18. Then you need to get the radius of the circle so you divide 11.18 by 2 and get 5.59. Then plug 5.59 for r into 2(pi)(r). 2(pi)(5.59) = 5.123

Answer:

Answer B is correct

Step-by-step explanation:

First, let us find the diameter (AC) of the circle using the Phythogerem theorem.

AC² = AB² + BC²

AC² = 2² + 11²

AC² = 4 + 121

AC² = 125

AC = √ 125

AC = 5√5

And now let us find the circumference of the circle.

C = π × d

C = π × 5√5

C = 5√5π in

he table shows the mean number of basketball goals made by four random samples of players from the school team during this year’s season. Sample # Sample Mean Number of Goals 1 7 2 4 3 5 4 8 Is a valid prediction for the mean of the population possible using these samples? No, there are not enough samples. Yes, the sample means are all less than 10. Yes, the variation of the sample means is small. No, the variation of the sample means is too great.

Answers

The valid prediction for the mean of the population possible using these samples is C. Yes, the variation of the sample means is small

What is a sample mean?

It should be noted that a sample mean is an average of a set of data . Also, the sample mean can be used to calculate the standard deviation, central tendency, and the variance of a data set.

The sample mean can be applied to a variety of uses, including calculating population averages.

Here, the sample variance is a measure of the degree to which the numbers in a list are spread out. Here, the numbers given are close to each other.

If the numbers in a list are all close to the expected values, the variance will be small and if they are far away, the variance will be large.

Therefore, the correct option is C.

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Answer:

C: Yes, the variation of the sample means is small.

Step-by-step explanation:

Correct answer on edge

AB passes through A(-3,0) and B(-6,5). what is the equation of the line that passes through the origin and is parallel to AB?

Answers

Answer:

  y = -5/3x   or   5x +3y = 0

Step-by-step explanation:

To write the equation of a line through the origin, we need only find its slope. It is parallel to the line through the given points, so will have the same slope.

Slope

The slope of a line through points (x1, y1) and (x2, y2) is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

For the given points, the slope is ...

  m = (5 -0)/(-6 -(-3)) = 5/(-3) = -5/3

Equation

The line trough the origin has a y-intercept of zero, so its equation will be ...

  y = mx

For the slope we found, the desired equation is ...

  y = -5/3x

Standard form

If we multiply by 3 and add 5x, we have ...

  3y = -5x

  5x +3y = 0 . . . . . . standard form equation of the line

identify the TRUE statement relating to a property of the function y = sin x

A. one cycle of the function is 180 degrees
B. The maximum and minimum values of the function are 1 and -1 respectively
C. The amplitude of the function is 2 units
D. The equation of the baseline is y = -1

Answers

The true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B

Properties of the function

The following are the properties of the sin trigonometric ratio of the function;

The sine graph rises till +1 and then falls back till -1 from where it rises again.The function y = sin x is an odd functionThe domain of y = sin x is the set of all real numbersThe range of sine function is the closed interval [-1, 1]The amplitude of the function is half its range valueOne cycle of the function is 6. 28

From the above listed deductions, we can see that the true statement about the function y = sin x is that the range which is always known as the maximum and minimum values of the function are 1 and - 1 respectively.

Thus, the true statement relating to a property of the function y =sin x is that the maximum and minimum values of the function are 1 and -1 respectively. Option B

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Dexter has plotted the line shown in red.
What is the slope of the line?
-8-6-4-2
CA

10
O

Answers

Answer:

-1/3

Step-by-step explanation:

1:make y the subject.

2:slope of line is the coefficient of x

Vectors u and v are shown in the graph. What is -3(u•v)?

Answers

[tex]\mathbf{u} =\langle -6, -10 \rangle \\ \\ \mathbf{v}=\langle 7,8 \rangle \\ \\ \mathbf{u} \cdot \mathbf{v}=(-6)(7)+(-10)(8)=-122 \\ \\ \therefore -3(\mathbf{u} \cdot \mathbf{v})=-3(-122)=\boxed{366}[/tex]

The value of -3(u•v) is 366 when vector u= -6i - 10j and vector v=-6i - 10j is given.

What is dot product ?

The dot product of two vectors is the sum of the products of their corresponding components.

Here, u= -6i - 10j, from the figure as u goes 6 coordinate left to the y axis and and 10 coordinates below the x axis.

v= 7i + 8j, from the figure as v corrdinates right to the y axis and 8 coordinats upwards to the x axis.

Therefore u.v= (-6i - 10j).(7i + 8j)

                      = -42 - 80

                      = -122

So, -3(u.v)= (-3)×(-122)

                =366

Hence, the value of -3(u•v) is 366

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Cory saw 27 animals in the woods. two-thirds of them were insects. one-third of the insects were ants. the rest of the insects were flies. cory saw two times as many squirrels as rabbits. cory also saw a family of deer: a buck, a fawn, and a doe. how many of each animal did cory see?

Answers

Number of ants = 6

Number of flies = 12

Number of buck = 1

Number of fawn = 1

Number of doe = 1

Number of squirrels = 3

Number of rabbit = 6

What is the number system?

A system of writing numbers is known as a number system. It is the mathematical notation for consistently employing digits or other symbols to represent the numbers in a particular set. It represents the arithmetic and algebraic structure of the numbers and gives each number a distinct representation.

A system for representing numbers is called a number system. It also defines a set of numbers to represent a quantity and is referred to as the system of numeration.

Given,

Total number of animals Cory saw = 27

Number of insects = [tex]27 \times \frac{2}{3}[/tex]

                               [tex]= 18[/tex]

Remaining number of animals = [tex]27-18[/tex]

                                                   = [tex]9[/tex]

From the insects-

Number of ants = [tex]18 \times \frac{1}{3}[/tex]

                          [tex]=6[/tex]

Number of flies = [tex]18-6[/tex]

                          = [tex]12[/tex]

Number of buck  = 1

Number of fawn = 1

Number of doe = 1

Let the number of squirrels be [tex]x[/tex]

Then, the number of rabbits = [tex]2x[/tex]

Remaining animals = [tex]2x+x[/tex]

⇒ [tex]9=3x[/tex]

⇒ [tex]x= 3[/tex]

Therefore,

Number of squirrels = 3

Number of rabbits = [tex]2x[/tex]

                               = 6

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If segment fd = 45 units and segment de = 60 units, what is the value of a? round the solution to the nearest hundredth.

Answers

The value of 'a' closest to hundredths is 41.41

What is Triangle and its segment?

A triangle could also be  a polygon with three sides and three angles. The three sides for a triangle DEF shown above, written symbolically as △DEF, are line segments DE, EF, and DF

If three sides of a triangle are adequate to three sides of another triangle, then the triangles are congruent. (2) If three angles of a triangle are respectively  adequate to three angles of another triangle, then the 2 triangles are congruent.

According to the given data:

Since this is often a right triangle, we'll  use trig functions:

cos theta = adjacent / hypotenuse;

cos a=FD/DE;

cos a=45/60.

Taking the inverse of each side:

cos-1(cos a) =cos-1(3/4);

a=41.40962211.

After Rounding to the closest hundredth:

The value of a is 41.41.

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What is the volume of the pyramid

Answers

Answer:

Option A - 32 cm³

Step-by-step explanation:

Volume of a pyramid is given by the formula :

V = [tex]\frac{lwh}{3}[/tex]

Substituting values given gives us :

V = (4)(4)(6)/3

V = (16)(6)/3

V = 96/3

V = 32

Units will be cm³ as this is volume

Hope this helped and have a good day

Answer:

A. 32 cm³

Step-by-step explanation:

V = (1/3)(area of base)(height)

The base is a square of side 4 cm.

area of base = side × side

V = (1/3)(4 cm × 4 cm)(6 cm)

V = 32 cm³

Express each fraction as a decimal:

- 2 4/100

Answers

-0.24

this is because whenever it’s /100, the decimal at the back moves 2 twice

meaning it starts from -24. to -2.4 and lastly -0.24

whenever the dot ends at .24, a zero must be added

The sector area of a region of a circle is 23 mi². The central angle, 0 (theta), is 25°. What is the radius?

Answers

The radius of the sector is 10.27 miles

How to find the radius of a sector?

The area of a sector can be represented as follows;

area of a sector = ∅ / 360 × πr²

where

r = radius∅ = central angle

Therefore,

∅= 25 degrees

area of the sector  = 23 miles²

area of a sector = ∅ / 360 × πr²

23 = 25 / 360 × πr²

cross multiply

23 × 360  = 25πr²

8280 = 25πr²

divide both sides by 25

πr² =  8280 / 25

πr² =  331.2

r² =  331.2 / 3.14

r² = 105.477707006

r = √105.477707006

r = 10.2702336877 miles

Therefore, the radius of the sector is 10.27 miles

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PLEASE HELP IM STUCK

Answers

Answer:

23

Step-by-step explanation:

The question gives the first equation:

0.05N + 0.10D = 2.20

It can be rewritten as:

0.05$ times the number of nickels plus 0.10$ times the number of dimes is equivalent to $2.20.

Notice that 0.05$ or 5 cents is equivalent to one nickel and 0.10$ or 10 cents is equivalent to one dime.

The question asks for N+D. We know that N stands for the number of nickels Daniel has and D stands for the number of dimes Daniel has. We also know that Daniel only has dimes and nickels in his pocket. Therefore N+D most be equivalent to the total number of coins, which is given in the question to be equal to 23 coins.

Therefore...

N+D = 23

help help help help help help pleaseeeeee

Answers

The maximum height is; 180 ft and the Total time in the air is 12 seconds

How to solve projectiles?

We are given the equation that represents the height of the rocket as;

d = 60t - 5t²

Taking the derivative of the formula gives us;

d' = 60 - 10t.  

-10t represents the acceleration.  The 60 represents the initial velocity.

Set 60 - 10t = 0 and solve for t to get;

t = 60/10 = 6seconds.  

That's when the maximum height occurs. Plug that value of t into the original quadratic equation to get the maximum height.

d(6) = 60t - 5t²

d(6) = 60(6) - 5(6²)

d(6) = 180

So,  maximum height is about 180 ft.  

Thus, total time in air = 2 * 6 = 12 seconds

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A building has 63 apartments and 70 bathrooms. What is the ratio of apartments to bathrooms in the building?

Answers

Answer:

63:70

Step-by-step explanation:

The ratio of apartments to bathrooms in the building is 9:10.

Given that, a building has 63 apartments and 70 bathrooms.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The ratio of apartments to bathrooms is 63:70

= 9:10

Therefore, the ratio of apartments to bathrooms in the building is 9:10.

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ff is a trigonometric function of the form f(x)=a\sin(bx+c)+df(x)=asin(bx+c)+df, left parenthesis, x, right parenthesis, equals, a, sine, left parenthesis, b, x, plus, c, right parenthesis, plus, d.
Below is the graph f(x)f(x)f, left parenthesis, x, right parenthesis. The function intersects its midline at (3,-6.5)(3,−6.5)left parenthesis, 3, comma, minus, 6, point, 5, right parenthesis and has a maximum point at (4,-2)(4,−2)left parenthesis, 4, comma, minus, 2, right parenthesis.
Find a formula for f(x)f(x)f, left parenthesis, x, right parenthesis. Give an exact expression.
\qquad f(x)=f(x)=f, left parenthesis, x, right parenthesis, equals
\qquad

Answers

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

How to derive a sinusoidal expression

In this problem we need to find a sinusoidal expression that models the curve seen in the picture. The most typical sinusoidal model is described below:

f(x) = a · sin (b · x + c) + d    (1)

Where:

a - Amplitudeb - Angular frequencyc - Angular phased - Vertical midpoint

Now we proceed to find the value of each variable:

Amplitude

a = - 2 - (-6.5)

a = 4.5

Angular frequency

b = 2π / T, where T is the period.

0.25 · T = 4 - 3

T = 4

b = 2π / 4

b = π / 2

Midpoint

d = - 6.5

Angular phase

- 2 = 4.5 · sin (π · 4/2 + c) - 6.5

4.5 = 4.5 · sin (π · 4/2 + c)

1 = sin (2π + c)

π = 2π + c

c = - π

The trigonometric function that represents the curve seen in the picture is f(x) = 4.5 · sin (π · x / 2 - π) - 6.5.

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If two marbles are selected at random with replacing between draws, what is the probability that the outcome is red then yellow? (round your answer to four decimal places. )

Answers

The probability that the outcome is red then yellow is 0.036.

Given that in a jar there are 8 red marbles, 1 yellow marble and 6 green marbles.

We are required to find the probability of obtaining a red then yelow marble if two marbles are drawn and replacement is used.

Probability is the calculation of finding the chance of happening a event among all the events possible. It lies between 0 and 1.

Probability=Number of items/ Total items.

Number of red marbles=8

Number of yellow marble=1

Number of green marbles=6

Total marbles=15

Probability of obtaining red marble=8/15

Probability of obtaining yellow marble=1/15 (Because replacing is there so the number of total marbles do not decrease)

Required probability=8/15*1/15

=8/225

=0.035555

After rounding off we will get 0.036.

Hence the probability that the outcome is red then yellow is 0.036.

Question is incomplete. The following line should be included in question:

A jar contains 8 red marbles , a yellow marble and 6 green marbles.

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Logistic regression analyses require that your single dependent variable is a ratio variable.

a. true
b. false

Answers

Answer: false
although this analysis does not require the dependent and independent variables to be related linearly, it requires that the independent variables are linearly related to the log odds.

_______ 14. What is the value of x?
A. 11°
B. 22°
C. 32°
D. 43°
E. 86°

Answers

Answer: Choice D

Reason:

Add up the arc measures, then divide by 2

x = (32 + 54)/2

x = 86/2

x= 43 degrees

can you guys help me please or you can just explain how to solve it thanks

Answers

The composition of transformation that maps ABCD to EHGF is "(x, y) → (x', -y') → (x' + 6, y' + 3)".

What are the transformation rules?

The basic transformation rules are:

Translation: (x, y) → (x + a, y + b);Reflection: (x, y) → (x, -y) over x-axis; (x, y) → (-x, y) over y-axis;Dilation: (x, y) → (kx, ky)Rotation 90° counter-clockwise: (x, y) → (-y, x)Rotation 180°: (x, y) → (-x, -y)

Calculation:

The given quadrilateral ABCD has vertices,

A(-5, 2), B(-3, 4), C(-2, 4), and D(-1, 2)

The transformed quadrilateral EHGF has vertices,

E(1, 1), H(3, -1), G(4, -1), and F(5, 1)

In the map ABCD to EHGF, the transformations that took place are:

1) Reflection over x-axis

2) Translation by (x + a, y + b)

Step 1: Reflection over x-axis; (x, y) → (x, -y)

A(-5, 2) → A'(-5, (-2)) = A'(-5, -2)

B(-3, 4) → B'(-3, (-4)) = B'(-3, -4)

C(-2, 4) → C'(-2, (-4)) = C'(-2, -4)

D(-1, 2) → D'(-1, (-2)) = D'(-1, -2)

So, the reflected quadrilateral is A'B'C'D'

Step 2: Translation by (x, y) → (x + a, y + b);

The reflected quadrilateral A'B'C'D' is now translated by

A'B'C'D' → EHGF

So, (for A'(-5, -2) and E(1, 1))

x + a = 1

⇒ -5 + a = 1

⇒ a = 1 + 5

a = 6

and

y + b = 1

⇒ -2 + b = 1

⇒ b = 1 + 2

b = 3

Thus, the translation is (x + 6, y + 3).

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Given that x=2y and 3y=5z. Find the ratio x:y:z hence or otherwise find the amount of money Ali got if Ali, Ben and Chris shared Kshs. 36000 in the ratio x:y:z respectively

Answers

Answers

The ratio x:y:z is 10:5:3  

Ali got 20,000

===================================================

Explanation:

Let

x = amount Ali goty = amount Ben gotz = amount Chris got

Those amounts add to 36,000

x+y+z = 36,000

We're told that x = 2y, so let's replace x with 2y in the equation above to get these steps

x+y+z = 36,000

2y+y+z = 36,000

3y+z = 36,000

We're also told that 3y = 5z, so we can replace that previously mentioned 3y with 5z to end up with one variable, in which we can solve for like shown below.

3y+z = 36,000

5z+z = 36,000

6z = 36,000

z = (36,000)/6

z = 6,000

This tells us that Chris got 6,000

Use this to find y

3y = 5z

3y = 5*6,000

3y = 30,000

y = (30,000)/3

y = 10,000

Ben received 10,000

Lastly, determine x.

x = 2y

x = 2*10,000

x = 20,000 which is the amount Ali got.

The ratio x:y:z turns into 20,000:10,000:6,000 which fully simplifies to 10:5:3 after dividing all three parts by the GCF 2000. It might be tempting to try to reduce the 10:5 portion into 2:1, but we cannot divide by 5 since it's not a factor of that 3 at the end.

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

Check:

Ali + Ben + Chris = 20,000 + 10,000 + 6,000 = 36,000

which helps confirm the answer.

Why is proficiency in statistics an important skill for a data analyst?

Answers

Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

What is Data analysis?

Data analysis can be regarded as the  process of collecting as well as modeling, and analyzing data so as to be able to extract insights that support decision-making.

Some Types of Data Analysis are:

Descriptive Analysis.Exploratory Analysis.Inferential Analysis.Predictive Analysis.Causal Analysis.Mechanistic Analysis.

It should be noted that Proficiency in statistics is an important skill for a data analyst because it is needed in  identifying patterns and correlations in data.

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Marcia made 10 bracelets for 5 friends. Jen made 12 bracelets for 4 friends. Are these ratios/rates equivalent?

Answers

Answer:

These ratios are not equivalent as Marcia is 2 per friend while Jen is 3 per friend

Step-by-step explanation:

Marcia made 10 bracelets for 5 friends where each friend will be getting 2 bracelets with a 1:2 ratio

Jen made 12 bracelets for 4 friends where each friend will be getting 3 bracelets with a 1:3 ratio

Based on our Starbucks analysis report, 4 out of every 20 drinks are returned because of a customer complaint and 16/20 are not returned. Starbucks makes $4 on a typical drink not returned (probability of 16/20 ), but loses -$6 (probability of 4/20) when a drink is returned because the employee has to re-make it. What is the Expected Value of this problem and are they going to make a profit ?

Answers

Answer:

Step-by-step explanation:

the expected profit should be 2 dollars a drink

The answer to this problem is $2 for each drink

What is the slope of the line shown in the graph? Express your answer as an improper fraction or as an integer as appropriate. Show your work

Answers

Slope can be found between two points using the formula [tex]\frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].

If we substitute in your points (which is x and which is y does not matter as long as it is consistent), we will get

[tex]\frac{(4-1)}{(2-0)}[/tex].

Simplifying this further, your slope will be

[tex]\frac{3}{2}[/tex].

hope this helps!

Using the image, find the midpoint of the line segment. Reduce all fractions and enter using a forward slash (i.e. "/").

Answers

Midpoint formula x1+x2/2, y1+y2/2
=5+5/2, 2+-5/2
=5, -1.5

HELPPP SIMPLE QUESTION‼️‼️‼️‼️‼️

Four less than a number x is twice another number y.

write in an equation

Answers

Answer:

x - 4 = 2y

Step-by-step explanation:

"four less than a number x" therefore; x - 4

"is twice another number y" therefore; 2y

a writer wrote 10,010 words for his book on the first day of writing. he wrote 9,760 words on the second day, 9,510 words on the third day, and continued this way in an arithmetic sequence. write an explicit rule showing the equation for the number of words the writer would write on the 14th day, and solve.

Answers

Answer:

rule: an = 10010 -250(n -1)day 14: 6760 words

Step-by-step explanation:

The first three terms of the arithmetic sequence for the number of words written are 10010, 9760, 9510. These have a common difference of 9760-10010 = -250. The first term and common difference can be used to make the explicit equation for the words written on the n-th day.

Formula for Arithmetic Sequence

The explicit formula for the n-th term of an arithmetic sequence with first term a₁ and common difference d is ...

  [tex]a_n=a_1+d(n-1)[/tex]

Application

For first term a₁ = 10010 and common difference d = -250, the explicit rule is ...

  [tex]a_n=10010-250(n-1)[/tex]

On day 14, n=14, and the number of words written is ...

  [tex]a_{14}=10010-250(14-1)\\\\a_{14}=10010-250(13)=10010-3250\\\\a_{14}=6760[/tex]

The writer would write 6760 words on the 14th day.

The black graph is the graph of y =f(x). Choose the equation for the red graph. A. y - 1 = f() B. y + 1 = f() C. = f(x - 1) D. f(x)​

Answers

Answer: C

Step-by-step explanation:

The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.

Other Questions
More volatility in returns produces ______ difference between the arithmetic and geometric averages. a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times. How long is the vine? The ________ is managements minimum desired rate of return on a capital investment. What are the indications for a pelvic examination during adolescence? (select all that apply.) If the aircraft turns to the heading indicated by the heading marker, it will? What type of diet do the authors suggest that boisei possessed? what kind of analysis did they perform to arrive at that conclusion? The wizard of oz is at its core the story of a journey, over the course of which the character of dorothy evolves and changes. what principle is at play here? Find center,foci and vertices of ellipse for 4x2+y2+2x-10y=6 Oxidation of ______ contributes to plaque formation in the development of atherosclerosis. If the angular speed of a 1. 1-m baseball bat is 2. 0 rad/s, what is the tangential speed of the tip of the bat?. name 5 water functions What is the ph of a 2. 3 m solution of the weak acid h2s, with a ka of 1. 19107? the equilibrium expression is: h2s(aq) h2o(l)h3o (aq) hs(aq) 3. In AABC, a = 35, c = 25, and mcan be drawn given these measurements? You go for a run and breathe heavily for an extended amount of time. How is this affecting your pH levels?A. Decreasing the pH, making it more acidic.B. Increasing the pH, making it less acidic.C. Increasing the pH, making it more acidic.D. Decreasing the pH, making it less acidic. -20, 10, -5,I need the next sequence Louise Tammy Dolores and Cheryl score 78 points in the tennis matches they play. A score consecutive number of points from smallest to greatest in respect to the order of the name is mentioned. How many points does Lewis score? Options:A. 19 pB. 20 pC. 21 pD. 18 p Titan Mining Corporation has 6.3 million shares of common stock outstanding, 220,000 shares of 3.6 percent preferred stock outstanding, and 105,000 bonds with a semiannual coupon rate of 5.3 percent outstanding, par value of $1,000 each. The common stock currently sells for $73 per share and has a beta of 1.15, the preferred stock has a par value of $100 and currently sells for $83 per share, and the bonds have 17 years to maturity and sell for 107 percent of par. The market risk premium is 7.1 percent, T-bills are yielding 3.1 percent, and the companys tax rate is 23 percent.a. What is the firms market value capital structure? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .1616.)b. If the company is evaluating a new investment project that has the same risk as the firms typical project, what rate should the firm use to discount the projects cash flows? (Do not round intermediate calculations enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) A standard deck of cards contains 52 cards. There are four suits (spades, clubs, hearts, and diamonds) and thirteen of each suit (2-10, jack, queen, king, ace). One card is selected at random from the deck. What is the probability the card selected is an Ace or a heart? Calculate the pressure (in atm) exerted by 1.82 moles of a gas in a steel vessel of volume 5.43 l at 69.50 c. The u. S. Supreme court has ruled that ________ must decide the facts that lead to a death sentence.