help please ill give brainlest !!

Help Please Ill Give Brainlest !!

Answers

Answer 1

Answer:

-31, 9, 1, 5, 37

Step-by-step explanation:

f(x) = -2(-2)^2 + 1

f(x) = 4^2 + 1

f(x) = 8+1

f(x) = 9

f(x) = -2(0)^2 +1

f(x) = 0^2 + 1

f(x) = 0 + 1

f(x) = 1

f(x) = -2(1)^2 + 1

f(x) = -2^2 + 1

f(x) = 4+1

f(x) = 5

f(x) = -2(3)^2 + 1

f(x) = -6^2 + 1

f(x) = 36+1

f(x) = 37


Related Questions

can anyone help on this
-3+(-17)

Answers

-3-7
The answer is -20

What is the answer to the following calculation, rounded to the correct number of significant figures?100.000 g+ 75.0 g

Answers

Answer:

175g

Step-by-step explanation:

100.000g+75.0g= 175g

ps. pls give brainliest answer :)

The sum of the numbers 100.000g and 75.0g in expression is 175g.

What are mathematical operations?

Calculate the answer using a math operator is referred to as a mathematical operation.

Basic mathematical operations are addition, multiplication, subtraction and division.

The given numbers are,

100.000g and 75.0g

The zeros can be neglected after decimal points,

So the numbers can be written as,

100g and 75g.

To find the required expression, add 100g and 75g.

100g + 75g = 175g.

The required sum of the numbers is 175g.

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9x+3y=-6 rewrite this equation in slope intercept form (y=Mx+b)

Answers

y=-3x-2
subtract 9x from 9x
divide each term in 3y=-6-9x by 3 and simplify

provide an appropriate response. the owner of a computer repair shop has determined that their daily revenue has mean $7200 and standard deviation $1200. the daily revenue totals for the next 30 days will be monitored. what is the probability that the mean daily revenue for the next 30 days will be less than $7000?

Answers

The probability that the mean daily revenue for the next 30 days will be less than $7000 IS 0.7333

Standard deviation of the sample is equal to the population's Standard Deviation divided by the square root of the sample's item count.

Standard Deviation of the sample = [tex]1200/\sqrt{30} = 219.09[/tex]

SD of the sample is equal to the population's Standard Deviation divided by the square root of the sample's item count.

To reach a result of 300, divide 7500 by the mean of 7200. 300 divided by the sample's SD (219.09) yields a result of 1.37. A z-table search for +1.37 returns a result of 0.9147. Accordingly, there is a 0.9147 percent chance that the average daily revenue over the following 30 days will be less than $7500.

To get a result of -200, divide 7000 by the mean of 7200. Divide -200 by the sample's standard deviation (219.09), and you'll get -0.91. search for -0.91 in a z-table receive a score of 0.1814. The likelihood that the mean daily revenue for the following 30 days would be less than $7000 is therefore 0.1814.

Simply subtract the likelihood that the mean daily revenue is less than $7000 (0.1814) from the likelihood that the mean daily revenue is less than $7500 (0.9147) to arrive at the probability that the mean daily revenue for the upcoming 30 days will be between $7000 and $7500. This yields a result of 0.7333.

There is a 73.33% chance that the average daily income over the following 30 days will be less than $7000.

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Given f(x) = -x - 2, find f(-6).

Answers

Answer:

f( -6) = 4

Step-by-step explanation:

f(x) = -x -2  You will replace x with -6

f(-6) - -(-6) -2

f(-6) = 6 - 2

f(-6) = 4

Hello I just need help with A and B on my homework I was able to complete C

Answers

ANSWERS

a) 58

b) 62.2

EXPLANATION

a) The median is the middle value. It separates the data set in two. To find the median we have to put the data in order, from least to greatest:

[tex]44,49,53,54,58,74,74,74,80[/tex]

The number of data is odd, this means that the median will be one of the values of the data set and not a mean between two of them. If there are 9 values, the median is the 5th value - so we have 4 values to the left and 4 values to the right.

The first 4 values are 44,49,53,54, so the median is 58.

b) The mean is the sum of all values of the data set divided by the amount of data:

[tex]\bar{x}=\frac{44+49+53+54+58+74+74+74+80}{9}=\frac{560}{9}=62.2222\ldots[/tex]

Rounded to one decimal place, the mean is 62.2


14. In exercise 13, suppose grapes cost
$2.35 per pound, oranges cost $0.99 per
pound, and apples cost $1.65 per pound.
Estimate how much Adrian paid for all
the fruit.

Answers

Assume grapes cost $2.35 per pound, oranges cost $0.99 per pound, and apples cost $1.65 per pound in exercise 13. Adrian paid a total of $5 for the fruits.

What is Estimation?Calculations are made easier and more realistically when a number is estimated, which is a plausible estimation of its true value.To estimate something is to approximate it as accurately as possible.To acquire a quick and approximate response, this is obtained by rounding off the values used in the calculation. Rounding integers to the closest whole number is the simplest method for estimating. Rounding off makes getting a rough answer quicker. Koel, for instance, makes a 3950 monthly deposit toward the cost of her new home. This value can be rounded out to 4000 to make the calculation easier. To round a number, determine its nearest required digit. To avoid working with fractions or decimals, numbers are frequently rounded to the next whole number.

Therefore,

The cost of Grapes = $2.35 per pound

The cost of Oranges = $0.99 per pound

The cost of Apples = $1.65 per pound

If Adrian purchased one pound of each fruit,

He paid:

$2.35 + $0.99 + $1.65 = $4.99 = $5 (Approx.)

So, Adrian paid $5 in total for the fruits.


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Write the factored form of the polynomial function with real coefficients, a lead coefficient of 1, and zeros of − 2 , − 4 , 3 , and 3 .

Answers

The equation of the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

How to determine the polynomial equation?

The given parameters are

Leading coefficient = 1

Zeros =  − 2 , − 4 , 3 , and 3 .

Polynomial equations have their multiplicities to add up to their degree.

This means that the multiplicity of the zeros is 1

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

So, we have

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

From the question, the polynomial is to be factored

This means that we represent it as

P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

Hence, the polynomial equation is P(x) = (x + 2)(x + 4)(x - 3)(x + 3)

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Polynomial is an expression consisting of indeterminates and coefficients the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3)

What is Polynomial?

Polynomial is an expression consisting of indeterminates and coefficients, which involves  the operations like addition, subtraction, multiplication, and positive-integer powers of variables

Factors are the numbers which divide the expression or number with a remainder zero.

We need to write the factored form of the polynomial functions with real; coefficients and zeros minus two comma  minus four comma three and 3.

The leading coefficient of the polynomial is 1. Leading coefficient means coefficient of leading term.

Zeros =  − 2 , − 4 , 3 , and 3 .

Let the polynomial is of variable x.

The equation of the polynomial is then calculated as

P(x) = (x - zero)^ multiplicity

(x-(-2))=x+2

(x-(-4))=x+4

(x-3)=x-3

So the factored form is (x+2)(x+4)(x-3)(x-3)

the polynomial is P(x)=(x+2)(x+4)(x-3)(x-3)

Hence the factored form of polynomial function is (x+2)(x+4)(x-3)(x-3).

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Monica deposits $200 into a savings account that pays a simple interest rate of 4.4%. Paul deposits $300 into a savings account that pays a simple interest rate of 3.3%. Monica says that she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your response.

Answers

Formula of simple interest rate:

[tex]S\mathrm{}I=\frac{P\times R\times T}{100}[/tex]

Where,

[tex]\begin{gathered} P=\text{ Principal} \\ R=\text{ Rate} \\ T=\text{ Time} \end{gathered}[/tex]

For Monica interest rate is:

[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{200\times4.4\times1}{100} \\ =8.8 \end{gathered}[/tex]

For Paul interest rate is:

[tex]\begin{gathered} S\mathrm{}I\mathrm{}=\frac{300\times3.3\times1}{100} \\ =3\times3.3 \\ =9.9 \end{gathered}[/tex]

No, Paul interest rate higher then Monic.

1) If a horizontal asymptote exists for this function, identify its location.4x + 6x3x3 - 2x + 1AyoB3B) y =4OyD Does Not Exist

Answers

For this problem, we are given the following rational function:

[tex]f(x)=\frac{4x^3+6x}{3x^3-2x+1}[/tex]

We need to determine the horizontal asymptote for this function. In order to determine this, we need to calculate the limit of the function when x approaches infinity. We have:

[tex]\lim_{x\rightarrow\infty}\frac{4(\infty)^3+6\cdot\infty}{3(\infty)^3-2\cdot\infty+1}=\frac{4}{3}[/tex]

The horizontal asymptote exists at y= 4/3. The correct option is C.

A shipping box has a volume of 1,000 cubic inches. What is the length of one side of the box?

Answers

The length of one side of the box is 10 inches.

How to find the volume of a cube?

Suppose that: The side length of the considered cube is L units.

Then, we get the Volume of that cube = L³ cubic units.

The volume of a cube is of the form V =  L³, where L is the side length.

Given that the shipping box has a volume of 1,000 cubic inches.

Here, we know the volume V, but not the measure of length. So, we can plug in the value 1000 for V and solve for L:

1000 =  L³

Cube root both sides:

L = [tex]\sqrt[3]{1000}[/tex]

Therefore, each side is 10 inches.

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Emily estimated that there were
315 students at a soccer game.
The actual number of students at
the game was 350. What was the
percent error of her estimate?


I thought it was 8%. Please show your work, and maybe tell me why I was right or wrong? Thank you!

Answers

The percentage error in the measurement of the number of student at the soccer game. given that 315 student was estimated and 350 student were actually at the game is 10%

What is a percentage error?

The percentage error is the measure of the difference between an actual value and a estimate given as a percentage.

The percentage error of her estimate is found from the percentage error formula, as follows;

[tex]\delta = \dfrac{v_A - v_E}{v_E} \times 100\%[/tex]

Where:

δv=The percentage error

[tex]v_A[/tex] = The approximate value or estimated value = 315

[tex]v_E[/tex] = The exact or correct value = 350

Therefore; [tex]\delta = \dfrac{|315 - 350|}{350} \times 100\%= 10\%[/tex]

The percentage error of her estimate is 10%

The method and information used in calculating the percentage error determines the value of the error in percentage, however, based on the values of estimated value of 315, and the actual value of 350, the percentage error is 10%

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2/3 is what percent of 1/4? of 1/6

Answers

Let's first calculate the percentage for 1/4

[tex]\begin{gathered} P=\frac{2/3}{1/4} \\ P=\frac{8}{3} \\ P=2.666 \\ P=267\text{ \%} \end{gathered}[/tex]

Let's first calculate the percentage for 1/6

[tex]\begin{gathered} P=\frac{2/3}{1/6} \\ P=\frac{12}{3} \\ P=4 \\ P=400\text{ \%} \end{gathered}[/tex]

s\\line t find the measure of each angle HELP ME NOWWW

Answers

The values of the angles for the two parallel lines will be ∠1 = 115°, ∠2=115°, ∠3=148°, and ∠4 = 148°.

What are lines and angles?

Straight lines with little depth or width are present. You will learn about a number of lines, including transversal, intersecting, and perpendicular lines. A figure called an angle is one in which two rays originate from the same point.

Given that the lines s and t are parallel to each other. The values of the different angles will be:-

∠1  = 115° Exterior angle property

∠2 = 115° Vertically opposite angle

The value of angle ∠3 will be calculated by the supplementary angle property.

∠3 = 148°

The value of angle ∠4 is 148 by vertically opposite angle property.

∠4 = 148°

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sarah has 85 and 89 on her first two math 23 tests. what must she get on the third test to have at least 90% test average?Assume three tests and represent the problem with an inequality

Answers

The value that Sarah must she get on the third test to have at least 90% test average is represented by the inequality x ≥ 96.

What is an inequality?

Inequalities are created through the connection of two expressions. It should be noted that two expressions in an inequality aren't always equal. They are denoted by the symbols ≥ < > ≤.

In this case, Sarah has 85 and 89 on her first two math 23 tests.

Let the third test be represented as x. This will be illustrated as:

(85 + 89 + x) / 3 ≥ 90

Cross multiply

85 + 89 + x ≥ 90 × 3

174 + x ≥ 270

Collect like terms

x ≥ 270 - 174

x ≥ 96

The value is x ≥ 96.

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Which angle pair is NOT an example of Corresponding Angles?

angle 2 and angle 10

angle 1 and angle 11

angle 13 and angle 15

angle 8 and angle 16​

Answers

Answer:

Step-by-step explanation:  

So briefly corresponding angles are angles that have the same position as another angle on the same figure. In your example there a multiple figures. The only pair that is NOT a corresponding angle is 1 and 11 because they have no lines in common they are not on the same figure! Hope this helps!

six distinct positive integers are randomly chosen between and , inclusive. what is the probability that some pair of these integers has a difference that is a multiple of ?

Answers

Answer:

So the probability of this happening is exactly 1 - it must be true

Step-by-step explanation:

If we calculate modulo(5) for each of the six numbers (the integer remainder after dividing by 5), we will get six values from 0 to 4.

By the pigeonhole principle, since there are 6 numbers and only 5 possible values, at least two must share the same value modulo 5. Pick two of those, say x and y, in which case x mod 5 = y mod 5, therefore (x - y) mod 5 = 0. In other words, their difference is a multiple of 5.

So the probability of this happening is exactly 1 - it must be true

Angle P in Triangle PQR has the same measure as Angle S in Triangle STU. Which other condition is necessary to prove that these triangles are similar?

Answers

△PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

What is the congruency of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved. Therefore, if all three sides of two triangles are the same, then the triangles are said to be congruent. If we have a side, an angle between the sides, and then another side that is congruent, we know they are congruent. In other words, side, angle, side.

So, to prove that △PQR ≅ △STU:

∠P = ∠S (Given)PQ = ST (Option B)∠Q = ∠T (Option D)

So, with these three conditions, △PQR ≅ △STU is under ASA condition.

Therefore, △PQR is congruent to △STU (△PQR ≅ △STU) under ASA condition using options (B) and (D).

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PLEASE HELP! due soon

Answers

Answer:

Your answer is 103.2413793103448

Step-by-step explanation:

[tex]29.94[/tex] ÷ [tex]29[/tex] [tex]= 1.032413793103448[/tex]

[tex]1.032413793103448[/tex] × [tex]100 = 103.2413793103448[/tex]

24.94 is 29% of 86
86 is your answer

At a local print shop, 10 copies can be made for $4. At this rate, how much would it cost to make 75 copies?​

Answers

Answer:

$30

Step-by-step explanation:

10 x 7 = 70

7 x 4 = 28

Since it's $4 to make 10 copies, it'll be $2 to make 5

28 + 2 = 30

$30 for 75 copies (a bad deal honestly)

Please mark Brainliest!!

Answer:

$30 dollars for 75 copies

Step-by-step explanation:

What we know:

$4 for every 10 copies.

How to figure out:

Divide 4/10 = .4    .4 is the cost per copy.

We do this because if it is 4 dollars per 10 copies, then we have to figure out the cost per copy. So we have to do how many dollars goes into each copy.

Now we know the cost of one copy we can multiply the amount of copies we need by the price of one.

75 x 0.4 = 30     30 is the price of 75 copies.

pls explain with working out

Answers

Answer: 26m

Step-by-step explanation:

The area is 36m^2, the possible measurement that could've worked is 4m for width and 9m for length (4x9=36). Now just do 4+4+9+9 = 26m.

Hope this helped

(7g - 6) - (-3n - 4) find the difference and show your work. Please this is due tomorrow

Answers

Answer:

7g + 3n - 2

Step-by-step explanation:

(7g - 6) - (-3n - 4)

7g - 6 + 3n + 4

7g + 3n - 2

I hope this helps!

Please Help me graph the linear equation!! 70 Points

Answers

Answer:

Step-by-step explanation:

We will follow the same steps as in the previous question. First, we can start by leaving the variable [tex]y[/tex] alone.

[tex]2y=5x+11[/tex][tex]y=\frac{5x+11}{2}[/tex]

In this step, let's be careful to give the variable [tex]x[/tex] odd numbers. The rational expression will then be an integer.

For [tex]x=1,y=8[/tex]For [tex]x=-1, y=3[/tex]For [tex]x=-3, y=-2[/tex]

Finally, connect these three points. You can see the connected version in the photo. Good luck!

20 = 4 (y + 8) - 8y solve for y and simplify your answer as much as possible

Answers

Answer:

y = 3

Step-by-step explanation:

20 = 4 (y + 8) - 8y

20 = 4y + 32 - 8y

20 - 32 = 4y - 8y

-12 = -4y

-4y = -12

-4y/-4 = -12/-4

y = 3

To check

20 = 4 (y + 8) - 8y

20 = 4 (3 + 8) - 8(3)

20 = 12 + 32 - 24

20 = 44 - 24

20 = 20

Correct~

Answer: y = 3

Step-by-step explanation:

1. Distribute the 4 to the terms in the parenthesis.

20 = 4y + 32 - 8y

2. Combine like terms (those containing y).

20 = -4y + 32

3. Isolate terms with y by subtracting 32 from both sides.

-12 = -4y

4. Divide both sides by -4.

3 = y

Area of circle when r is 14

Answers

Answer:

The area is 196π, or 615.752160 when evaluated to 6 decimal places.

Step-by-step explanation:

There is an equation for the area of a circle:

A=π[tex]r^{2}[/tex], Where A is the area and r is the radius. π is π, it is its own number. Plugging in the radius stated we can evaluate:

A=π([tex]14^{2}[/tex])

A=196π

If we write out π and evaluate with an (un)reasonable amount of decimal places:

π≅3.1415926536

A=196×(3.1415926536)

A≅615.752160

Answer:

A = [tex]\pi ^{2}[/tex]

Step-by-step explanation:

A≈615.75

Elijah put 2x+3
2
x
+
3
dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?

Answers

Elijah put $53 in the Bank in the first week .

In the question ,

it is given that Elijah put (2x+3) in the first week .

In the second week Elijah put double the first week savings

that means second week deposit = 2*(2x+3) = 4x+6

in the third week he doubled the amount that was in the bank ,

which means third week deposit = 2*(first week + second week deposit)

= 2*(2x+3+4x+6)

Also given that total amount in the bank = $477

total amount = first week + second week + third week deposit

substituting the values we get

477 = (2x+3) + (4x+6) + 2*(2x+3+4x+6)

477 = 2x+3+4x+6+4x+6+8x+12

477 = 18x + 27

18x = 477-27

18x = 450

x = 450/18

x = 25

the amount deposited in the first week = 2x+3

                                                                  = 2(25)+3

                                                                  = 50+3 = $53

Therefore , Elijah put $53 in the Bank in the first week .

The given question is incomplete , the complete question is

Elijah put 2x+3 dollars in the bank the first week. The following week he doubled the first week’s savings and put that amount in the bank. The next week, he doubled what was in the bank and put that amount in the bank. He now has $477 in the bank. How much money did he put in the bank the first week?

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PLSSSSS
WILL MARK BRAINLIEST!!!
SIMPLEEE
(Yr7)

Answers

Answer:

Step-by-step explanation:

the answer I have given below

kind regards

Which operation comes first in the problem below? 4(3.7 +1.23) -12 A. Addition B. Subtraction C. Multiplication D. Division

Answers

A. Addition

Explanation

PEMDAS is an acronym for the words parenthesis, exponents, multiplication, division, addition, subtraction. Given two or more operations in a single expression, the order of the letters in PEMDAS tells you what to calculate first, second, third and so on, until the calculation is complete

Step 1

so, firts calculate the parenthesis

[tex]\begin{gathered} 4(3.7+1.23)-12 \\ 4(4.93)-12 \end{gathered}[/tex]

the operation in parenthesis is an addition

i hope this helps you

Find the equation to the line below.y =[?-x ++ [ ]

Answers

Note that a line whose equation is in the form :

[tex]y=mx+b[/tex]

has a slope of m

and a y-intercept of b

Slope is also equal to rise/run :

[tex]m=\frac{\text{rise}}{\text{run}}[/tex]

where rise is the number of vertical units between two points and run is the number of horizontal units between two points.

Note also that upward and right movement is positive, downward and left movement is negative.

From the figure, the vertical units between two given points is 3 units upward, so this is positive.

The horizontal units between them is 2 units to the right which is also positive.

The slope will be :

[tex]m=\frac{\text{rise}}{\text{run}}=\frac{3}{2}[/tex]

Next is to solve for b (y intercept).

y-intercept is the point where the line intersects the y-axis.

From the graph, the lines intersects at point (0, 2) on the y-axis

Therefore, the value of b is 2

Rewriting the equation, the answer is :

[tex]\begin{gathered} y=mx+b \\ y=\frac{3}{2}x+2 \end{gathered}[/tex]

72.1232 rounded to the nearest thousandth

Answers

72.1232 rounded to the nearest thousandth is 72.123.

What does it mean to round to the nearest thousandth?

The term "rounding to the nearest thousandth" refers to the practice of rounding any decimal number to the next thousandth value. Thousandth in the decimal system signifies (1/1000) or 0.001. 3.125, for example, is the number 3.1249 rounded to the closest thousandth.

To round it to the closest thousandth, we must focus on the number following this spot - tens of thousandths. This figure will determine whether we round up or round down. "Five and above go up like a bird," as the phrase goes. Therefore, this will give a value of 72.123.

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Consider the function f(x) =cotx. Which of the following are true? 2 answers [tex]\sqrt{x} ^2+2x-3[/tex] the equation 5x+7=4x+8+x-1 is true for all real numbers substitute a few real numbers for x to see that this is so and then try solving the equation A coordinate grid is shown from negative 6 to 6 on both axes at increments of 1. Figure ABCD has A at ordered pair negative 4, 4, B at negative 2, 2, C at negative 2, negative 1, D at negative 4, 1. Figure A prime B prime C prime D prime has A prime at ordered pair 4, 0, B prime at 2, negative 2, C prime at 2, negative 5, D prime at 4, negative 3.Part B: Are the two figures congruent? Explain your answer. victoria would like to segment website sessions by what media the sessions came from to help her manager show the influence of media on website sessions. what dimension should she use? how did gaius marius transform the roman military? group of answer choices by permitting landless men to serve in the army, he tapped a large reservoir of idle manpower. he developed a professional corps of engineers assigned to each legion to provide onsite advice and solutions to situations that arose. by permitting slaves to serve in the army with possibilities of freedom for service, he expanded the size of military forces dramatically. he established uniform military laws to which both officers and common soldiers were subject, which also gave them significant privileges for their service. james, age 8, understands that a dollar changed into 4 quarters is still a dollar. this means that james has achieved the cognitive milestone of . Give a number in scientific notation that isbetween the two numbers on a number line.71 X 103 and 71,000,000 change this standard form equation into slope intercept form. 4x-5y= -17 which approach takes a look at the external environment outside the bounderies of the organization? group of answer choices contemporary approach quantitative approach behavioral approach classical approach What is the difference between chromosomes, sister chromatids, non-sister chromatids, separated chromatids? The ratio of the volume of two spheres is 8:27. What is the ratio of their radii? What qualities might a general have that would be helpful as president? study was made of seat belt use among children who were involved in car crashes that caused them to be hospitalized. it was found that children not wearing any restraints had hospital stays with a mean of 7.37 days and a standard deviation of 3 days with an approximately normal distribution. (a) find the probability that their hospital stay is from 5 to 6 days, rounded to five decimal places. (b) find the probability that their hospital stay is greater than 6 days, rounded to five decimal places. The sum of a number and -4 is greater than 15. Find the number A one-on-one marketing appointment, whether that roller coaster travels far too fast for my comfort, and I will never ride it againL 5 adverbs PLEASE HELP 20(2)(7)+(9)(3) Suppose that 27 percent of American households still have a traditional phone landline. In a sample of thirteen households, find the probability that: (a)No families have a phone landline. (Round your answer to 4 decimal places.) (b)At least one family has a phone landline. (Round your answer to 4 decimal places.) (c)At least eight families have a phone landline. what are the coordinates of a?