+
Simplify the following expressions by combining the like terms!
3) 4x-7-y+6-2y
4) 6y + 2(y + 1) - 5
5) 3(2+3x) + 4(y + 2x) - 6

Answers

Answer 1

Answer:

5) 3(2+3x)+4(y+2x)-6

Step-by-step explanation: its gone be -6 either way

Answer 2
3) given equation,4x-7-y+6-2y
=4x-3y-1

4) given equation,6y+2(y+1)-5
=6y+2y+2-5
=8y-3

5) given equation,3(2+3x)+4(y+2x)-6
=6+9x+4y+8x-6
=17x+4y

Related Questions

im having trouble with this question! pls help

Answers

Using a proportional relationship, it is found that the unit rate of change is of 9.

The relation d = 9t is graphed at the end of the answer.

What is a proportional relationship?

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

In this problem, we have d as a function of t, hence the relationship is:

d = kt.

When t increases by 0.2, d increases by 1.8, hence the constant is given as follows:

k = d/t = 1.8/0.2 = 9

The relation d = 9t is graphed at the end of the answer.

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Select the equation of a straight line that is perpendicular to the line y = 3x - 2.
A y = 3x - 5
B 3y=x+2. C y=- -3x-2 D y= -x/3+2 E y=1\3x-2

Answers

[tex]y = mx + b \\ y = nx + c \\ for \: the \: two \: lines \: to \: be \: perpendicular \\ m.n = - 1[/tex]

[tex]m = 3 \\ \\ 3n = - 1 \\ n = \frac{ - 1}{3} [/tex]

Answer: D

[tex]y = \frac{ - x}{3} + 2[/tex]

Carly takes three steps to walk the same distance as jim walks in four steps. each of carly’s steps covers 0. 5 metres. how many metres does jim travel in 24 steps?

Answers

The distance travelled by Jim in 24 step is 9 miles by unitary method.

According to the given question.

The number of steps travelled by Jim = 24

Also, it is given that "Carly takes three steps to walk the same distance as Jim walks in four steps".

Therefore, by unitary mehod we can say that

The number of steps walked by Carly = 3 × (24/4) = 3 × 6  = 18

So, the distance travelled by Carly in 18 steps

= 18 × 0.5miles

= 9 miles

Since, the Carly's 18 steps is equals to Jim's 24 steps.

Therefore, the distance travelled by Jim in 24 step is 9 miles.

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A certain type of thread is manufactured with a mean tensile strength of kilograms and a standard deviation of kilograms. How is the variance of the sample mean changed when the sample size is

Answers

In the case above:

(a) If there is an increased from 64 to 196, then the variance decreases.

(b) If there is a decreased from 784 to 49, then the variance increases.

What occurs if the variance increases?

Standard Error is known to be the square root of the variance. if a given variance increases, so its standard error also.

Since the standard error takes place in the denominator, hence, if the standard error increases, the variance goes up.

Therefore, In the case above:

(a) If there is an increased from 64 to 196, then the variance decreases.

(b) If there is a decreased from 784 to 49, then the variance increases.

See full question below

A certain type of thread is manufactured with a mean tensile strength of 78.3 kilograms and a standard deviation of 5.6 kilograms. How is the variance of the sample mean changed when the sample size is (a) increased from 64 to 196? (b) decreased from 784 to 49?

What is the variance about?

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Determine what type of model best fits the given situation: A. none of these B. exponential C. linear D. quadratic

Answers

The option c is correct. Linear model suits best to this graphical representation out of the exponential and quadratic model.

According to the statement

We have given that a model in the graphical representation and we have to tell that which type of model used in this representation.

So,

According to this representation,

A linear representation is a representation on a category of vector spaces or similar.

The other meaning is that when the growth increases linearly or at the constant speed.

In this graphical representation, linear representation is used because it increases or decreases linearly not suddenly.

linear representation explain this graph perfectly.

So, Linear model suits best to this graphical representation.

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Mia, Keela And Michelle are selling girl scout cookies.In all they have sold $800 worth of cookies. Mia sold 57 boxes, Keela sold 28 boxes and Michelle sold 15 boxes. How should the girls split the money so that they earn the same fraction as the boxes of cookies that they sold? Should Mia and Michelle get the same amount of money? Why Or Why not?

Answers

Answer:

the money should be split as per each girl sold. total boxes sold is 100.

Step-by-step explanation:

total boxes sold is 100. Mia sold 57/100 keela 28/100 and Michelle 15/100.

mia=456$

keela=224$

michelle=120$

calculated as boxes sold/100 x 800$

You are given an expression for the volume of the rectangular prism. determine an expression for the missing dimension. v=4x^3 5x^2-32x-33 and the dimensions are (x 1)and (x 3)

Answers

V = 4x^3 + 5x^2 - 32x - 33

4x^3 + 5x^2 - 32x - 33 / x + 1
4x^2 + x - 33

4x^2 + x - 33 / x + 3
4x - 11

please help I'm so tired and I need to turn this in tomorrow

Answers

Considering the given box plots, it is found that:

a) They had the same IQR.

b) Athlete A went on the shortest training ride.

c) Athlete B went on more rides longer than 35 miles.

d) Athlete B had a greater median distance.

What is a box plot?

It is a plot that focuses the interquartile range of the population, which is the difference between the third and the first quartile, but gives a five number summary of the population, composed by these following measures.

The smallest value.The first quartile.The median.The third quartile.The highest value.

Hence, for Athlete A, we have that:

The smallest value is 12.The first quartile is 27.The median is of 29.The third quartile is 34.The highest value is of 45.IQR: 34 - 27 = 7.

For Athlete B, we have that:

The smallest value is 18.The first quartile is 32.The median is of 37.The third quartile is 39.The highest value is of 41.IQR: 39 - 32 = 7.

Hence:

a) They had the same IQR.

b) Athlete A went on the shortest training ride.

c) Athlete B went on more rides longer than 35 miles(as it is less than his median).

d) Athlete B had a greater median distance.

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Gilbert plans to invest $14 000 into two types of bonds. one bond yields 8% interest each year and the other bond yields 12% interest each year. he needs to earn $1400 each year to consider the investment successful. how much should he invest in each bond?

Answers

invest in each bond = $7000

What is Profit and Loss?

An income statement, also known as a profit and loss account, is one of a company's financial statements and displays the company's receipts and outlays for a specific time period. It explains how revenues are converted into net income or net profit.

According to the given data:

Let n be the amount invested at 8%

the amount invested at 12% would be : 14000-n

so,

8n+12(14000-n) = 1400

8n + 168000 - 12n = 1400 * 100

4n + 168000 = 140000

n = 28000/4

   =  7000

Therefore,

At 12% amount invested

= 14000 - 7000

= $7000

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Suppose that 4 ≤ f '(x) ≤ 5 for all values of x. what are the minimum and maximum possible values of f(8) − f(3)?

Answers

The minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

In the question, we are given that, 4 ≤ f'(x) ≤ 5 for all values of x.

Taking the given inequality as (i).

We are asked to find the minimum and maximum possible values of f(8) - f(3).

We multiply (i) by dx throughout, to get:

4dx ≤ f'(x)dx ≤ 5dx.

To find this, we integrate (i) in the definite interval [8, 3] with respect to dx, to get:

[tex]\int_{3}^{8}4dx \leq \int_{3}^{8}f'(x)dx \leq \int_{3}^{8}5dx\\\Rightarrow [4x]_{3}^{8} \leq [f(x)]_{3}^{8} \leq [5x]_{3}^{8}\\\Rightarrow 4*8 - 4*3 \leq f(8)-f(3) \leq 5*8 - 5*3\\\Rightarrow 20 \leq f(8) -f(3) \leq 25[/tex]

Thus, the minimum value of f(8) - f(3) is 20.

The maximum value of f(8) - f(3) is 25.

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How many solutions does the equation −3y 3y 4 = 4 have? none infinitely many one four

Answers

A given linear equation has infinitely many solutions.

What is a linear equation?There are only one or two variables in a linear equation. No variable can be multiplied by a number larger than one or used as the denominator of a fraction in a linear equation. All of the points fall on the same line when you identify the values that make a linear equation true and plot those values on a coordinate grid.As much as possible, reduce the equation to y = mx + b. Verify the exponents in your equation. It is nonlinear if it has exponents. Your equation is linear if there are no exponents in it.The definition of a linear equation is an equation with a maximum degree of one.

Given: −3y 3y 4 = 4

            3y+4=3y+4

The given linear equation satisfies any value of 'y'.

So, A given linear equation has infinitely many solutions.

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Mrs. Wood is a librarian at Westside Library. In examining a random sample of the library's book collection, she found the following. 716 books had no damage, 68 books had minor damage, and 43 books had major damage. Based on this sample, how many of the 36,500 books in the collection should Mrs. Wood expect to have major damage? Round your answer to the nearest whole number. Do not round any intermediate calculations.

Answers

Using proportions, it is found that Mrs. Wood should expect 1,898 books out of the 36,500 to have major damage.

What is a proportion?

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

For this problem, the proportion of books with major damage is:

43/(716 + 68 + 43) = 0.051995.

Hence, out of 36,500 books, the expected amount of books with major damage is:

0.051995 x 36,500 = 1898.

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Consider two forces of 17 and 42 pounds both acting in the horizontal direction on a single object. find the resultant force acting on the object. magnitude = direction angle =

Answers

The forces have a magnitude of 59 pounds, and their direction angles are zero.

What is the magnitude of force?The total amount of forces exerted on an object is referred to as the magnitude of force. The strength of the force increases when all the forces are pulling in the same direction. The force's strength reduces when forces are exerted on an item from different angles.When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out. When two forces operating on a body in opposite directions along the same line of action are equal in magnitude, they cancel one another out.According to this formula, the amount of net force acting on an item is equal to the mass times the acceleration of the object.Magnitude is a term that refers to size or importance. The depth of the Grand Canyon serves as an illustration of magnitude. The scope of the hunger crisis in the world serves as an illustration of magnitude. A measurement of the energy released by an earthquake, as shown on the Richter scale (geology).

Two forces of 17 and 42 pounds act horizontally on an object.

i.e

F1 = 17 pounds

F2 = 42 pounds

As the magnitude of the force represents the sum of all the forces

The direction is the same

Magnitude : 17 + 42 = 59 pounds

The Direction angles : 0

As they have the same direction so angle will be 0.

The forces have a magnitude of 59 pounds, and their direction angles are zero.

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Answer:59 and 0

Step-by-step explanation:

EDGE

Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.

Answers

The rate of change in the plant's height in terms of inches per week will be 1 2/3 inches.

How to calculate the rate?

Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable.

The calculation for the rate of change is simple in that it takes the current value of a stock or index and divides it by the value from an earlier period.

The change in y (y being the height of the plant) over 4 weeks was 6 2/3 inches and there are four weeks. Therefore, the average height will be:

= 6 2/3 ÷ 4

= 1 2/3 inches

The average rate of change of the plant growth per week was 1 2/3 inches.  

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Complete question:

Alan's bamboo plant adds some flair to his apartment. In four weeks, Alan has trimmed a total of 6 2/3 inches off the top of the plant. What is the rate of change in the plant's height in terms of inches per week? Ignore the growth rate of the plant.

a.+1 2/3B)-1 2/3C)+3/5D)-5/2

Which of the following ordered pairs lies on the graph of h(x) = -2x squared?

(1, 4)
(1, -4)
(1, -2)

Answers

By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

What ordered pair lies on the curve generated by a given function?

In this problem we have three ordered pairs to be checked on a given function by direct evaluation, a ordered pair lines on the curve of function if and only if the x-value of the ordered pair leads to the y-value by evaluating in the function. Now we proceed to evaluate each of the three points at the function presented in the statement:

(x, y) = (1, 4)

h(1) = - 2 · 1²

h(1) = - 2

By direct evaluation we conclude that the point (x, y) = (1, - 2) lies on the graph of the quadratic equation h(x) = - 2 · x². (Correct choice: C)

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Find the sum of 10 x 2 + 7 x + 6 10x 2 +7x+6 and 6 x + 5 6x+5.

Answers

The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Sum of expressions

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

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True or false: f(x) is a function

Answers

Answer Section 1. <3
Heyy, I'm sunny and I'm here to help you :)
(P.S: answer in explanation)

----------------------------------------------------------------------------------------------------------
Explanation Section:

It is
false

If f(x) is a function , then for each value of x there should be  a single y values

For input 0 there is a output 0

for input 10, the output is 2

for input 15, output is 3

For input 5, we have two output 1 and 3

for single input 5, the function cannot have two outputs 1  and 3

So this f(x) is not a function

Bye! - SunnyBunny <3

Which expression is equivalent to the given expression?

Assume the denominator does not equal zero.

a^3b^5 / a^4b

A. b^4 / a

B. a / b^4

C. 1 / ab^4

D. ab^4

Answers

The expression which is equivalent to the given expression by means of evaluation using the laws of indices is; Choice A; b⁴/a.

Which of the answer choice represents an expression which is equivalent to the given expression?

The given expression according to the task content is; a³b⁵/a⁴b.

It therefore follows from the laws of indices that each variable can be evaluated by means of their exponents as follows;

a^(3-4)b^(5-1)

Consequently we have;

b⁴/a.

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Bentley's family took a road trip to the Grand Canyon. Bentley fell asleep 59% of the way through the trip. If the total length of the trip was 300 miles, how many miles had they travelled when Bentley fell asleep?​

Answers

Answer:177

Step-by-step explanation:so for short, you need to multiply the 300 miles with the 59 precent we have and divide it to 100 this provides us the answer of miles he slept through the road trip

The number of miles they had travelled when Bentley fell asleep is 177 miles.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Bentley fell asleep 59% of the way through the trip.

The total length of the trip was 300 miles.

The number of miles

= 59% of 300

= 59/100 ×300

= 59×3

= 177 miles

Therefore, the number of miles they had travelled when Bentley fell asleep is 177 miles.

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Evaluate f(-3) for f(x) = 2^x
a. 1/8
b. -8
c. 8
d. -6

Answers

Answer:

A

Step-by-step explanation:

f(-3) = 2^-3

to get rid of a negative in an exponent, move the whole thing to the denominator.

1/(2^3)

2^3 = 2×2×2

1/(2×2×2)

1/8

what is the parent function of g(x) = 3cos (x + 180°) + 1

Answers

The parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

What are parent functions?

Parent functions are the basic function that represents the entire family of that function family

How to determine the parent function?

The function is given as;

g(x) = 3cos (x + 180°) + 1

As a general rule, the parent function of any function is the basic equation of the function family

The basic equation of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

Hence, the parent function of the function g(x) = 3cos (x + 180°) + 1 is f(x) = cos(x)

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Type the missing number in this sequence: 4, , 144, 864, 5,184, 31,104

Answers

The missing number in the given series is 24.

What is missing number in the given sequence?

Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places.

Given the series,

4, ?, 144, 864, 5184, 31104

Multiplying with 6 in each term in the given sequence.

4×6 = 24

24×6 = 144

144×6 = 864

864×6 = 5184

5184×6 = 31104

Following the above sequence, we get the 2nd term is 24.

Hence the missing number is 24.

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Which of the following shapes could be formed by taking a longitudinal section perpendicular to the base of a rectangular prism?

Answers

The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.

What is a three dimensional shape?

A three dimensional shape is a shape that has length, width and height. Examples of three dimensional shapes are cone, cylinder, prism and pyramid.

A two dimensional shape is a shape that have both length and width. Examples of two dimensional shape are circle, rectangle, square.

A rectangular prism is a three-dimensional shape, having six faces, where all the faces are rectangles.

The longitudinal section perpendicular to the base of a rectangular prism is a rectangle.

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A basketball is shot into the air. its height is represented by the polynomial equation h(t) = –16t2 35t 5, where h is the height of the basketball at t seconds. what is the height of the basketball at 0.5 seconds?

Answers

The height of the basketball at 0.5 seconds will be = 26.5

What is a polynomial equation?

A polynomial equation is an equation where a polynomial is set equal to zero. i.e., it is an equation formed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It has different exponents. The highest one gives the degree of the equation.

Example of a polynomial equation is: 2x2 + 3x + 1 = 0, where 2x2 + 3x + 1 is basically a polynomial expression which has been set equal to zero, to form a polynomial equation.

According to the given equation if we put value in it we will follow the following steps -

[tex]h(t) = - 16t^{2} + 35t+ 5\\ h(0.5) = -16(0.5)^{2} + 35(0.5) + 5\\h(0.5) = -16(0.25) + 17.5 + 5\\h(0.5) = 4 + 17.5 + 5\\h(0.5) = 26.5\\[/tex]

Therefore, the height of the basketball at 0.5 s will be 26.5

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Answer:

Is the question supposed to be (1.5), if so then the answer would be 21.5

Step-by-step explanation:

ht=-16t^2+35t+5

h(1.5)=-16(1.5)^2+35(1.5)+5

=21.5

Please helppppp!!
Question #1 (Question un ) : What is the smallest positive integer k such that k/660 can be expressed as a terminating decimal?

Give BRAINLIST IF ANSWER!!!!!

Answers

Answer:

k = 33

Step-by-step explanation:

Terminating decimal numbers:  Decimals that have a finite number of decimal places.

For a decimal to be terminating, the factors of the denominator must only contain 2 and/or 5.  As 2 and 5 are prime numbers, use prime factorization to rewrite the denominator.

Prime factorization of 660:

⇒ 660 = 2 × 2 × 3 × 5 × 11

⇒ 660 = 2² × 3 × 5 × 11

Therefore:

[tex]\implies \sf \dfrac{k}{660}=\dfrac{k}{2^2 \cdot 3 \cdot 5 \cdot 11}[/tex]

The fraction will only be a terminating decimal if both 3 and 11 in the denominator are canceled out.  To do this, their lowest common multiple must be the numerator:

⇒ LCM of 3 and 11 = 3 × 11 = 33

[tex]\implies \sf \dfrac{33}{660}[/tex]

[tex]\implies \sf k=33[/tex]

Therefore, the smallest positive integer k such that k/660 can be expressed as a terminating decimal is 33.

Answer:

33

Step-by-step explanation:

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

Answers

The number of rectangles of different sizes can be formed from 36 identical rectangles is 5

Number of rectangles

From the question, we have proofs of;

Total number of identical squares = 36

Now, let the measurement of the side of each square be 1 unit

We have that the formula for area of a square is;

Area of a square = Side × Side square units

We have the area of the square to be;

Area of each square = 1×1 = 1 square units

This is so because the rectangles are identical both in length and width

Let's find the area of the identical squares

Area of total 36 identical squares

=  36×1 square units

=  36 square units

So Area of the rectangle = length × breadth square units

if the rectangles are formed from 36 identical squares then their areas are the same

Total area of required rectangles = 36 square units

It can be written as;

36 = length × breadth

36 = 1×36 36 = 2×1836 = 3×1236 = 4×936 = 6×6

(1,36) , (2,18),(3,12),(4,9),(6,6) are the different rectangles formed from 36 identical squares

Total rectangles = 5

Thus, the number of rectangles of different sizes can be formed from 36 identical rectangles is 5

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find the size of each of the angles marked with letter​​

Answers

Answer:

angle l = 115

angle k = 115

angle j = 114

angle i = 66

Step-by-step explanation:

angle l = it is opposite to 115 so its the same

angle k = opposite opposing angles with angle l

angle j = 180-66=114 (between 2 parallel lines the sum of 2 angles is 180)

andle i = 180-114=66 (straight line = 180 degrees so subtract angle j to get i)

PLEASE I REALLY NEED HELP ON THIS QUESTION QUICKLY

Answers

Answer:

4/7

Step-by-step explanation:

[tex]\frac{6}{7} times \frac{2}{3}[/tex] 6x2=12

7x3=21

[tex]\frac{12}{21} = \frac{4}{7}[/tex]

PLEASE HELP IM STUCK PLS

Answers

Answer:

The slope is -3.

Step-by-step explanation:

The slope is the Rise/Run between the two points.  The change in y for every change in x.  Take the two points and calculate the:

RISE = (-6 - 3) = -9

RUN = (8 - 5) = 3

Rise/Run, or slope, is = -9/3 or -3

I graphed a line with slope of -3 and then added 18 to force the line to intersect the two given points.

if x : y = 0.75 : 0.90 and y : z = 1/3 : 1/4
(A) simplify the ratio x : y and y : z

(B) find x : y : z

Answers

Step-by-step explanation:

x:y=0.75:0.90

Here,

Dividing by the value of y=0.90,

x:y=0.75/0.90:0.90/0.90

=5/6:1

Similarly,

y:z=1/3:1/4

Dividing by 1/3,we get,

y:z=1:3/4

Now,

X:y:z=5/6:1:3/4

Multiplying by both value of y,0.90×1/3=3/10

x:y:z=5/6×3/10:1×3/10:3/4×3/10

By solving this,

x:y:z=1/4:3/10:9/40
Other Questions
Emily has been asked to find out howTemperature affects photosynthesis in waterweed. She has been given the equation:light energyglucose + oxygenCarbondioxide+ waterWhat should she investigate? A 1. 3106mol sample of sr(oh)2 is dissolved in water to make up 25. 0 ml of solution. what is the ph of the solution at 25. 0c? In Biology, a binomial name is:A. A two syllable name used to identify the species of an organism.B. A name given to an organism that has Bilateral symmetry.C. A first name and last name, commonly used in the United States and other westernized cultures.D. A two part naming system that consists of the Genus name and the Species name. what is the area of the figure bellow? mention some of the bad habits people follow in your society or community PLEASE NEED ASAP!!!Read the following excerpt from The Cask of Amontillado and answer the question.At the most remote end of the crypt there appeared another less spacious. Its walls had been lined with human remains, piled to the vault overhead, in the fashion of the great catacombs of Paris. Three sides of this interior crypt were still ornamented in this manner. From the fourth side the bones had been thrown down, and lay promiscuously upon the earth, forming at one point a mound of some size.The passage above provides a description of which story element?CharacterSettingRising actionClimax In ________________ people learn through rewards and punishments to respond behaviorally in certain ways. What is the period of y = 2cos(3x - 2)? Question 8What is wrong with the following equation: 8 + (6/2) = 17-5The loft Find the slope of the line. On a coordinate plane, a line goes through (0, negative 6) and (2, 0). a. Negative one-third c. 3 b. One-third d. Negative 3 Please select the best answer from the choices provided A B C D Who provides implementation guidance for the information security program within the dod?. 4. Hieroglyphics originated in: A Iraq B Iran C Mesopotamia D Egypt In june 1948, when the united states, britain, and france introduced a separate currency in their zones of control in the city of berlin, the soviet union responded with. Which of these lines from the play indicates that brutus fears caesar will become a corrupt ruler? "it must be by his death, and for my part/i know no personal cause to spurn at him" "and, to speak truth of caesar/i have not known when his affections swayed/more than his reason." "but tis a common proof/that lowliness is young ambitions ladder," "crown him that,/and then i grant we put a sting in him/that at his will he may do danger with." Will has twice as many stamps in his collection as Carlton and Ashley do in their collections combined. If Ashley has 30 stamps and she has a third as many as Carlton has, how many stamps are in Wills collection? A zookeeper is monitoring the population of penguins. the group needs to have exactly two times more males than females for the population to thrive. the zoo only has room for a maximum of 10 female penguins. let x represent the number of female penguins and y represent the number of male penguins. write the constraints that represent the possible number of male and female penguins that can live in a thriving population at the zoo. 0 < x 10 and 0 < y 20 x > 0 and y > 0 0 < x 10 and y > 20 x > 0 and y < 10 root word, suffix, prefix for Hemoglobinopathy. Valleys carved by glaciers tend to be cross sectional shapes like the letter ______, while valleys carved by water tend to have cross sectional shapes like the letter ______. Should there be a change to the status of your RBT certification status, this change must be communicated with your supervisor in a timely manner and within 24 hours. A. true B. false For plato and his doctrine of forms, a person can determine whether an act is courageous if he or she can __________