The list shows the ages of animals at a zoo. Plot the numbers in the list to create a histogram by dragging the top of each bar to the top of each bar to the correct height in the chart area

Answers

Answer 1

Based on the data given, the histogram is attached

A histogram is a graphical representation of data points organized into user-specified ranges.

Similar in appearance to a bar graph, the histogram condenses a data series into an easily interpreted visual by taking many data points and grouping them into logical ranges or bins.

From the information, the range of the dataset will be:

= 68 - 32

= 36

The number of classes will be:

= 36 / 10

= 3.6

= 4 approximately.

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The List Shows The Ages Of Animals At A Zoo. Plot The Numbers In The List To Create A Histogram By Dragging
The List Shows The Ages Of Animals At A Zoo. Plot The Numbers In The List To Create A Histogram By Dragging

Related Questions

I can find the perimeter and area of the rectangle

Answers

Answer:

A = 72, P = 38

Step-by-step explanation:

Area can be found by getting the area of the overall figure, and then subtracting the blank space in the corner

12 * 7 = 84

3 * 4 = 12(invisible rectangle in top right)

84 - 12 = 72

Perimeter can be found by adding all of the sides

12 + 7 + (12-4) + 3 + 4 + (7-4)

The numbers in brackets are the unlabeled sides on the top and left.

Answer:

[tex]P=38\\ A=72[/tex]

Step-by-step explanation:

To find the perimeter (P), add up all of the side lengths of the figure:

(numbers in parenthesis are the unlabeled values in the figure).

[tex]12+7+(8)+3+4+(4)=38[/tex]

To find the area of the figure (A), multiply the length and width of the original rectangle [tex](12*7=84)[/tex]. Then, subtract this amount (84) minus the area of the missing rectangle in the top left corner [tex](4*3=12)[/tex].

Subtract the required values: [tex]84-12=72[/tex].

Therefore, the perimeter of the figure is 38 units, and the area of the figure is 72 units.

Choose the function that shows the correct transformation of the quadratic function shifted eight units to the left and one unit down.

ƒ( x) = ( x + 8) 2 + 1
ƒ( x) = ( x - 8) 2 + 1
ƒ( x) = ( x + 8) 2 - 1
ƒ( x) = ( x - 8) 2 - 1

Answers

we conclude that the correct option or the translated function is the last one.

f(x) = (x - 8)² - 1

Which is the correct equation for the transformed function?

The parent quadratic function is:

y = g(x) =  x²

If we translate this function 8 units to the left, then we will have the new function:

f(x) = g(x - 8)

And if now we translate this function one unit downwards, we will get:

f(x) = g(x - 8) - 1

Now we can replace g(x) by the parent quadratic function we willl get:

f(x) = (x - 8)² - 1

From this, we conclude that the correct option is the last one.

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A classroom fish tank contains x goldfish the tank contains four times as many cups as goldfish enter an equation that represents the total number of guppies y in the fishtank

Answers

i’m confused on the question…please retype it and i’ll be able to answer

Consider the series one-fourth, startfraction 1 over 16 endfraction startfraction 1 over 64 endfraction startfraction 1 over 256 endfraction ellipsis which expression defines sn? limit of (one-fourth) superscript n baseline as n approaches infinity limit of (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (1 minus (one-fourth) superscript n baseline) as n approaches infinity limit of one-third (one-fourth) superscript n baseline as n approaches infinity

Answers

The sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)

How to evaluate the sum of the series?

The complete question is added as an attachment

The given series is a geometric series. So, we first calculate the common ratio (r) using:

r = T2/T1

From the series, we have:

T1 = 1/4 and T2 = 1/16

Substitute the known values in the above equation

r = (1/16)/(1/4)

So, the equation becomes

T = 1/16 / 1/4

Rewrite as product

T = 1/16 * 4

Evaluate the product

r = 1/4

The formula to calculate the sum of a geometric series of is:

Sn = a(1 - r^n)/(1 - r)

Where

a = 1/4 -- the first term

r = 1/4 --- the common ratio

Substitute the known values in the above equation

Sn = 1/4 * (1 - (1/4)^n)/(1 - 1/4)

Simplify the denominator

Sn = 1/4 * (1 - (1/4)^n)/(3/4)

Divide 1/4 by 3/4

Sn = 1/3 * (1 - (1/4)^n)

Take the limit to infinity of the series

Sn = lim n⇒∝ 1/3(1 - (1/4)^n)

We can conclude that, the sum of the series is: (c) lim n⇒∝ 1/3(1 - (1/4)^n)

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Answer:

Step-by-step explanation:

B

Rational functions v and w both have a point of discontinuity at x = 7. which equation could represent function w?

Answers

The correct option is C.

The formula that could be used to represent a  function w is

= w(x)=v(x-7)+7

What is Rational function?

A polynomial divided by another polynomial can be used to represent a rational function. Since polynomials are defined everywhere, the set of all numbers excluding the zeros in the denominator constitutes the domain of a rational function.

Example 1. x = f(x) (x - 3). The denominator, x = 3, only contains one zero. When the denominator is zero, rational functions are no longer defined.

According to the given Information:

Rational functions whose point of discontinuity is at x=7.

When a point of discontinuity exists for a rational function,

It occurs when:

q(x) = r(x-a),  x=a

In this instance, we are required to notice the following relationship, which is a union of a parent rational function and a vertical translation:[tex]w(x)=v(x-a)+k\\ \forall k \in \mathbb{R}[/tex], (2)

If we are aware of a=7 and k=7 .

The equation that could be used to represent a  function w is. w(x)=v(x-7)+7

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I understand that the question you are looking for is:

Rational functions v and w both have a point of discontinuity at x = 7. Which equation could represent function w?

A. w(x)=v(x-7)

B. w(x)=v(x+7)

C. w(x)=v(x-7)+7

D. w(x)=v(x)+7

A soccer game lasts 90 minutes without running into overtime. The coach
plans to switch players out every 12 1/2 minutes. Approximately how many
switches will the coach make in one game?

Answers

Answer: 7 Switches will be made.

Step-by-step explanation:

[tex]\frac{90}{12.5}=[/tex] number of switches

[tex]7.2=[/tex] number of switches

however you cannot have a fraction of a switch so you must round it to a whole number, which in this case is 7.


Please help me

Given the quadratic function, describe in words the transformations and then
provide a sketch of the graph.
y = − 1/²(x+4)² - 7

Answers

It is upside down and has been shifted 4 to the left and 7 units dow

Find the distance between the pair of points: (3,1) and (4,-5).

Answers

Answer:

9.2195445 (9.22 rounded)

Step-by-step explanation:

#1: Use the distance formula to determine the distance between the two points:

Distance = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]

#2: Substitute the actual values of the points into the distance formula:

[tex]\sqrt{((-4)-3)^{2}+(5-(-1))^{2}}[/tex]

#3: Simplify:

- Subtract 3 from -4: [tex]\sqrt{(-7)^{2}+(5-(-1))^{2}}[/tex]

- Raise -7 to the power of 2: [tex]\sqrt{49+(5-(-1))^{2}}[/tex]

- Multiply -1 by -1: [tex]\sqrt{49+(5+1)^{2}}[/tex]

- Add 5 and 1: [tex]\sqrt{49+6^{2}}[/tex]

- Raise 6 to the power of 2: [tex]\sqrt{49+36}[/tex]

- Add 49 and 36: [tex]\sqrt{85}[/tex] (Decimal form: 9.2195445 (9.22 rounded))

The distance between the two points (3,1) and (4,-5) is 9.22.

When reuben had 3 years left in college, he took out a student loan for $16,902. the loan has an annual interest rate of 4.5%. reuben graduated 3 years after acquiring the loan and began repaying the loan immediately upon graduation.

Answers

Answer:

Reuben will have to pay $19,183.77 when he starts to pay the loan off after 3 years.

Step-by-step explanation:

There are 3 important parts to this equation:

1) 16,902

2) 4.5%

3) 3 years

First, let's find the interest rate in decimal form. This is easy enough to do.

take the interest rate (4.5%) and divide by 100. You can do this in your head by moving the decimal point but I will just write it out for the example:

4.5/100 = 0.045

Now that we have that number. we want to get the dollar amount for the interest. this is done by taking the loan amount and multiplying it by the decimal form of the percentage:

16,902 * 0.045 = 760.59

Since the interest rate is NOT compounding the rest is simple.

760.59 * 3 = 2,281.77

2,281.77 + 16902 = 19,183.77

Hope this helps.

What is the domain and range of each function?
FIRST PERSON TO ANSWER GETS BRAINLIEST OR 5 STARS :D

A) f(x) = −2x
Domain:
Range:

g(x) = ½x2 + 5
Domain:
Range:

Answers

For f(x) we have:

domain: set of all real numbers.range: set of all real numbers.

And for g(x):

domain: set of all real numbersrange: set of all real numbers such that y ≥ 5.

How to get the domain and range of each function?

The domain of a function is the set of inputs that we can use on the function, and the range is the set of outputs.

a) f(x) = -2x

This is just a linear equation, as you can see, for no value of x we have a problem, then the domain is the set of all real numbers.

Similar for the range, it covers the set of all real numbers, then:

domain: set of all real numbers.range: set of all real numbers.

b) g(x) = 0.5*x² + 5

This is a quadratic function, so the domain is the set of all real numbers again.

Now the range will have a minimum, which is at the vertex of the parabola.

For the parabola the vertex is at x = 0:

g(0) = 0.5*0² + 5 = 5

Then the range is the set of all real numbers equal to or larger than 5.

domain: set of all real numbersrange: set of all real numbers such that y ≥ 5.

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Consider the sequence Three-fourths, four-fifths, StartFraction 5 Over 6 EndFraction, StartFraction 6 Over 7 EndFraction, ellipsis



Which statement describes the sequence? 3/4, 4/5, 5/6, 6/7,...

The sequence diverges.
The sequence converges to 1.
The sequence converges to ∞.
The sequence converges to –∞.

Answers

Using limits, it is found that the correct statement defining the sequence is:

The sequence converges to 1.

What is the rule that defines this sequence?

The numerator starts at 3 and increases by 1, while the denominator starts at 4 and increases by 1, hence the rule is:

[tex]\sum_{n = 0}^{\infty} \frac{3 + n}{4 + n}[/tex]

To verify if it converges, we find the limit as n goes to infinity, hence:

[tex]\lim_{n \rightarrow \infty} \frac{3 + n}{4 + n} = \lim_{n \rightarrow \infty} \frac{n}{n} = \lim_{n \rightarrow \infty} 1 = 1[/tex]

Hence the sequence converges to 1.

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Answer:

B i took quiz

Step-by-step explanation:

Harmony earns a $42,000 salary in the first year of her career. Each year, she gets a 4%, percent raise.
Which expression gives the total amount Harmony has earned in her first n years of her career?

Answers

Answer:

42000*1.04^(n-1)

Step-by-step explanation:

4% is equal to 0.04, a raise is 1+0.04=1.04

1.04 is now the number we are multiplying by to get a new yearly salary for Harmony.

42000*1.04^(n-1) since n is how many years after she has the job you have to raise it to the power and subtract one.

Don't get this question

Answers

Answer:

17 and 18

Step-by-step explanation:

Writing every 2 digit number gives us :

10-99 including 10 and 99

For the first one we are looking for numbers where the number 3 appears only once so 33 would be invalid.

13,23,30,31,32,34,35,36,37,38,39,43,53,63,73,83,93

There are 17 2-digit numbers that have 3 exactly once

For the second one we are looking for number where the number 3 appears a minimum of once so 33 would be valid :

13,23,30,31,32,33,34,35,36,37,38,39,43,53,63,73,83,93

There are 18 2-digit numbers that have 3 at least once

Hope this helped and have a good day

Which of the following could be appropriate values for an equation to be in Standard Form (Ax + By = C)?
A=-6, B = 8 and C = 3
A=4, B = 0 and C = 9
A=1/6, B = 2/9 and C=0
A=4, B = 1/4 and C=0

Answers

Answer:

  (2)  A=4, B=0, C=9 . . . (4x = 9)

Step-by-step explanation:

A linear equation in standard form has mutually prime integer coefficients with a positive leading coefficient.

Choices:The leading coefficient is negative. Not appropriateCoefficients meet the criteria. Appropriate valuesCoefficients are not integers. Not appropriateCoefficients are not integers. Not appropriate

The values that would be the appropriate values for an equation to be in standard form (Ax + By = C) is A = 4, B = 0 and C = 9.

Linear equation in standard form:

The linear equation is the equation which has the coefficient as the mutual prime numbers and the coefficient must be the positive leading coefficient.

From the choices,

A = -6, B = 8 and C = 3. In this case, the coefficient of x (A = -6) is negative, which doesn't leads to positive leading coefficient.A = 4, B = 0 and C = 9. In this case, the coefficient also leads to positive leading coefficient and also lead to mutual prime.A = 1/6, B = 2/9 and C = 0. In this case, the coefficient of x and y which are A = 1/6 and B = 2/9 are integers, which doesn't leads to mutual prime.A = 4, B = 1/4 and C = 0. In this case, the coefficient of y which is B = 1/4 is integers, which doesn't leads to mutual prime.

Therefore, the values that would be the appropriate values for an equation to be in standard form as it lead to positive leading coefficient and mutual prime is A = 4, B = 0 and C = 9.

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Work out the area of the triangle.
?m2

Answers

The area of the triangle is 557. 7cm²

Area of a triangle

In order to determine the area of a triangle, we have to know the size of the base and the size of the height

The formula for finding the area of a triangle is given as = half the base multiplied by the height

In mathematical form, it is written as;

Area = 1/ 2 × base × height

From the figure given, we have their lengths to be'

base = 57. 2 m

height = 19. 5 m

Let's substitute the values

Area = 1/ 2 × 57. 2 × 19. 5

Area = 1/ 2 × 1115. 4

Find the ratio

Area = 557. 7 m²

The area of the triangle is 557. 7cm²

Hence, the area of the triangle is 557. 7cm²

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Solve the inequality. Enter the answer as an inequality that shows the value of the variable; for example f > 7, or 6 < w. Where necessary, use <= to write and use >= to write . 15 > y + 10
pls help

Answers

The solution to the given inequality is y < 5

Solving inequality expressions

Inequality are equations  not separated by an equal sign. Given the following parameters

15 > y + 10

Subtract 10 from both sides

15 - 10 > y + 10 - 10

5 > y

Swap

y < 5

Hence the solution to the given inequality is y < 5

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In fig. 6.39, side QP and RQ of ΔPQR are produced to points S and T respectively, if ∠SPR = 135° and ∠PQT = 110°, find ∠PRQ.

Answers

Answer:

PRQ = 65 degrees

Step-by-step explanation:

Angles SPR and QPR and angles TQP and RQP form linear pairs, so they are supplementary (angle measures add up to 180 degrees).

SPR + QPR = 180

135 + QPR = 180

QPR = 45

TQP + RQP = 180

110 + RQP = 180

RQP = 70

Since interior angles of a triangle add up to 180 ...

QPR + RQP + PRQ = 180

45 + 70 + PRQ = 180

PRQ = 65

Can someone help me with these problems please having trouble and show work!

Answers

Answer:

solution will be

1. 4x²-6x-4

2. 8x³+4x²-8x-4

3. x-x+3x³+x²+12

Step-by-step explanation:

1. (4x+2)(x-2)

apply foil method (a+b)(c+d)=ac+ad+bc+bd

(4x+2)(x-2)=4x.x + 4x(-2) + 2x + 2(-2)

4x²-8x+2x-44x²-6x-4

2. (4x²-4) (2x+1)

apply the same method as question no.1

(4x²-4) (2x+1)=4x².2x + 4x².1 + -4.2x-4.1

8x³+4x²-8x-4

3. (x²+3) (x³-x²+4)

Distributive parentheses

(x²+3) (x³-x²+4)= x².x³ + x²(-x²) + x².4+ 3x³+3(-x²) +3.4

x-x+3x³+x²+12

Identify the domain of the function shown in the graph

Answers

Using it's concept, the domain of the function shown in the graph is:

B. [tex]-6 \leq x \leq 6[/tex].

What is the domain of a function?

The domain of a function is the set that contains all possible input values for the function. In a graph, the domain is the set that contains all values of x.

From this graph, the function is defined for values of x between -6 and 6, hence the domain is given by:

B. [tex]-6 \leq x \leq 6[/tex].

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im being timed so please be quick thank you !!

Answers

Answer:

#3

Step-by-step explanation:

The y-intercept (the point where the line intersects with the y-axis) is -2, and the slope is 2/3 (two units up every three units to the right).

Answer:

C.

Step-by-step explanation:

First, look for the graph that shows a line with a y-intercept of -2. There is only one graph that shows a line with a y-intercept of -2. The graph will be the third graph. Please see attachment for the equation in a graphing calculator.

Hope this helps!

Need help please someone answer quick

Answers

Answer:

2x/19

Quotient = division

Product = multiplication

Difference = subtraction

Sum = addition

how do u solve this? what’s the answer?

Answers

The functions that have the properties are (d) I and II only

How to determine the functions?

The function property is given as:

[tex]a(x) = a^{-1}(x)[/tex]

The above implies that the inverse function and the original function are equal.

From the list of options, we have:

(a) y = x

Make x the subject

x = y --- the same as the  original function

(b) y = 1/x

Make x the subject

x = 1/y --- the same as the  original function

Hence, the functions that have the properties are (d) I and II only

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What must be true for lines a and b to be parallel lines? Select two options.

Lines a and b are crossed by transversals c and d. The angles formed by lines a, c, and d, clockwise from top left, are (3 x minus 1) degrees, 2, blank, blank, blank, 1. The angles formed by lines b and c are blank, (4 x minus 10) degrees, blank, blank. The angles formed by lines b and d are 58 degrees, blank, blank, blank.
mAngle1 = (4 x minus 10) degrees
mAngle2 = 58Degrees
x = 20
(3 x minus 1) degrees equals = (4 x minus 10) degrees
Angle1 = 58

Answers

The expression that must be true for a to be parallel to b are mAngle2 = 58Degrees and <1 = 4x - 10

Lines and angles

A line is the shortest distance between two points and the point where two lines meet is known as an angle

From the figure shown

m<2 = 58 degrees (alternate exterior angle)

Since the sum of angles on a straight line is 180 degrees, hence;

3x-1+<2 + 4x - 10= 180

3x-1 + 58 + 4x - 10 =180

7x + 47 = 180

7x = 180- 47

7x = 133

x = 19

Hence the expression that must be true for a to be parallel to b are mAngle2 = 58Degrees and <1 = 4x - 10

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Answer:

angle 2=58 degrees

angle 1=4x-10 degrees

Step-by-step explanation:

PLEASE HELP AND SHOW ALL STEPS

Answers

Combining the like terms, the simplified polynomials are given as follows:

a) 4x² - 14x + 17

b) -5x² - 20x + 8

How are polynomials simplified?

Polynomials are simplified combining the like terms, that is, adding these numbers with the same variable.

Item a:

4(x - 2)(x + 1) - 5(2x - 5)

Applying the distributive property:

4(x² - x - 2) - 10x + 25

4x² - 4x - 8 - 10x + 25

Combining the like terms:

4x² - 4x - 10x - 8 + 25

4x² - 14x + 17

Item b:

-5(x + 2)² + 28

-5(x² + 4x + 4) + 28

-5x² - 20x - 20 + 28

-5x² - 20x + 8

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Find the perimeter of each of these rectangles

Answers

Answer:

a) 10√3 + 5√3 + 10√3 + 5√3 = 30√3 cm

b) (√10 + √2) + (√10 - √2) + (√10 + √2) + (√10 - √2)

= 4√10 cm

c) Simplifying √72: √36 x √2 = 6√2

   Simplifying √18: √9 x √2 = 3√2

   Finding the perimeter: 6√2 + 3√2 + 6√2 + 3√2 = 18√2 cm

Write the equation of the line through the points (1,3) & (-2,5)in slope-intercept form

Answers

Answer:

y = -⅔x + 11/3

Step-by-step explanation:

The slope is

[tex] \frac{5 - 3}{ - 2 - 1} = - \frac{2}{3} [/tex]

Substituting into point-slope form,

y - 3 = -⅔(x - 1)

y - 3 = -⅔x + ⅔

y = -⅔x + 11/3

Volume=
Help me please thanks so much

Answers

Answer:

30.7

Step-by-step explanation:

It's 30.7 because 707/23

Answer:

16261 u3

Step-by-step explanation:

V = (base area)(height)=(707)(23)= 16261 u3

Hope this helps

For questions 4-5, determine which function is graphed.

Answers

Question 4: y=(x-1)(x-6)
Question 5: y=(x+3)(x+1)

Check all the true statements.

Answers

We can conclude that the true statement from the given expressions are DE || AC and 2DE = AC

Similar triangles

Triangles are similar if the measure of the similar sides are all equal to a constant.

From the given diagram, you can see that the measure of BA is congruent to BC. This shows that the line DE is parallel to AC that is DE || AC.

Also twice the measure of the sides DE will be equivalent to AC that is 2DE = AC.

Hence we can conclude that the true statement from the given expressions are DE || AC and 2DE = AC

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In AON networks, a(n) __________ is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.

Answers

In AON networks, "node" is a point where one or more lines (arrows) begin or terminate, commonly used for depicting an event or activity.

What is Activity-on-Node (AON) diagram?

Scheduling logic diagrams of the most fundamental kind. Any activity on the schedule that has no float; Total Float = 0; is considered a critical activity.

Between the project's start and finish, there are vital activity(s) that must be completed continuously. This is known as the critical path.

The importance of AON diagram are-

Because it helps identify the essential path, the arrow diagram is crucial for the project timeline. The critical route is used to determine the most effective schedule while still achieving the objectives required for a project to be successful. The critical path indicates the longest time of every dependent task.It is possible to organize tasks and determine not only when they must be finished but also which ones must be performed and which ones can be skipped while still reaching the project's goals and objectives by creating a schedule. An arrow diagram is essential because of this. It results in the project's ideal schedule.

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3x-4y=11 3x+2y=2please help, I need to find what the answer is for x and y Sarah is conducting a science experiment where she initially has a population of 4 fruit flies. Every week the population triples. She writes the function f(x)=4(3)x to predict the population growth. Which rule can also model the function? Help meh ill mark you all 4 plz if you can . It took 500 newtons of force to push a car 4 meters. How much work was done? b. What devices can now be used to create Digital Art? Do Ilboe.org bookmarksLesson 2 Review...< ExitTopic 5 AssessmentIMPLAYERDrag each expression to its equivalent expression. Each expression may be used only once.+ 141X ++13ExpressionEquivalent Expression-3414+3+34See pls help this is due soon check 2 that apply Which of the following scenarios illustrates the law of demand? A. A research company finds that the more expensive a particular brand of a designer handbag, the more that consumers are willing to purchase the brand. B. Kathleen eats more steak when the price is low, and less when the price is high. C. Francis does not care about the price of coffee at the coffee shop he must buy two cappuccinos every day, regardless of the price. D. John likes to drink spring water. At $2 he buys four bottles of water, and at $1.50 he still buys four bottles of water. A flat screen tv uses 120 watts. How much energy is used up if it is left on for 15 min?A.) 4jB.) 15jC.) 0.67jD.) 108,000j The purpose of mitosis is to produce A. Sex cellsB. Body cells C. DNA If a cross section of a rectangular prism is cut perpendicular to the base, what would be the shape of the resulting cross section Which statement describes the movement of the medium by a transverse wave? A. at an obtuse angle to the wave B. parallel to the wave C. at a right angle to the wave D. at an acute angle to the wave COULD I GET GET SOME HELP PLZ? REWARD BRAINLIEST Which operation should you perform first when evaluating the expression:3 to the power of 2+2 A crate rests on a flatbed truck which is initially traveling at 13.6 m/s on a level road. The driver applies the brakes and the truck is brought to a halt in a distance of 38.1 m. If the deceleration of the truck is constant, what is the minimum coefficient of friction between the crate and the truck that is required to keep the crate from sliding If you were to go north from the Sahel, you'd find __________. If you'd go south from the Sahel, you'd find __________.Sahara; Niletropical grasslands; SaharaSahara; tropical grasslandsNile; Sahara Help Plzzz!!!!!!!! 15+PTS and brainliest!!!!!!!!!!!!!!!Why was it important to surround Frances borders with powerful countries? Explain the strategy behind doing this. Write or Discuss how the quantity of modern news presents an advantage for those who wish to be informed citizens. Pls help!!You are a Jewish member of the United Nations, and you consider yourself an Orthodox Jew. Considering Orthodox Jews strictly follow the Torah and its teachings, killing is not permitted. What options can you come up with as punishment for those who commit hate crimes against various groups other than the death penalty? Can you come up with three different alternatives? Solve the quadratic equation x^2- 11x = 12 using any method. Describe the method you chose and why you chose it.