Mathematics College

## Answers

**Answer 1**

From the table, to transform points in rectangle ABCD into A'B'C'D', we have to apply the next rule: (x, y) → (x+1, y-3). That is,

A(2, 4) → (2+1, 4-3) → A'(3, 1)

C(2, -1) → (2+1, -1-3) → C'(3, -4)

D(-6, -1) → (-6+1, -1-3) → D'(-5, -4)

Then, if we want to transform a point in A'B'C'D', the rule is: (x,y) → (x-1, y+3). Applying this rule to point B', we get:

B'(-5, 1) → (-5-1, 1+3) → **B(-6, 4)**

## Related Questions

Sketch vector v. Be sure to number your axes. Then find the magnitude of vector v. Show all work.

### Answers

**Step 1**

Sketch the vector V.

[tex]v=-2i\text{ +5j}[/tex]

**Step 2**

Find the magnitude of the vector. The magnitude of a vector is given as;

[tex]\begin{gathered} |v|=\sqrt{(i)^2+(j)^2} \\ i=-2 \\ j=5 \\ \left|a+bi\right|\:=\sqrt{\left(a+bi\right)\left(a-bi\right)}=\sqrt{a^2+b^2} \end{gathered}[/tex][tex]\begin{gathered} |v|=\sqrt{(-2)^2+(5)^2} \\ |v|=\sqrt{4+25} \\ |v|=\sqrt{29} \end{gathered}[/tex]

Therefore, the magnitude is given as;

[tex]|v|=\sqrt{29}[/tex]

The distance from Boston, Massachusetts to Little Rock, Arkansas is 1,452.8 miles. How many ft/min would you have to drive to get there in 20 hours and 45 minutes?

### Answers

First we find the speed in mi/h.

We know that 20 h 45 min is equal to 20.75 hours, then the speed is

[tex]\frac{1452.8\text{ mi}}{20.75\text{ h}}=70.01\text{ mi/h}[/tex]

Now we convert the speed to ft/min:

[tex]70.01\text{ mi/h}\cdot\frac{1\text{ h}}{60\text{ min}}\cdot\frac{5280\text{ ft}}{1\text{ mi}}=6161.27\text{ ft/min}[/tex]

**Therefore you would have to drive at a speed of 6161.27 ft/min**

4^3/(-12+ 2^2)

(2x2)^2 + (-5 x 2 x 3 ) + 2

[tex] \frac{4^3/(-12 +2^2)}{(2x3)^2 +(-5 x2 x 3)+2} [/tex]

i need help!!

### Answers

**Answer:**

-1

**Step-by-step explanation:**

[tex]\frac{\frac{64}{-12+4}}{(6)^2+(-30)+2} \\ \\ =\frac{\frac{64}{-8}}{36-30+2} \\ \\ =\frac{-8}{8} \\ \\ =-1[/tex]

Which statement regarding the association shown could explain the relationship?A. class size appears to have little effect on test scores.B. schools is more affluent areas have larger class sizes, which is associated with higher test scores.C. schools in more affluent areas have smaller class sizes, which is associated with higher test scores. D. schools in less affluent areas have smaller class sizes, which is associated with lower test scores.

### Answers

[tex]\begin{gathered} \text{From the scatterplot, we can s}ee, \\ \text{The size of the class is depent on the test score.} \\ \text{Higher the test score obtain in the smaller classes.} \\ Thus,\text{the answer C is correct.} \end{gathered}[/tex]

Net Worth Statement Assets House (current value) Checking account Automobile Investments Total Assets Value $85,000 $2,500 $18,500 $7,000 $113,000 Llabilities Mortgage Credit card debt Total Liabilities $62,000 $9,500 $71,500 Based on the information in the statement, what is Phillip's net worth? A $184,500B $41,500 C $71,500D $41,500

### Answers

Value of total assests is ;

$85,000 +$2,500 +$18,500 +$7000=$113,000

Value of total liabilities = $62,000 + $9,500 = $71,000

Net worth = $ 113,000-$71,500 =**$41,500**

Generate ordered pairs for y = x^2 - 9 using x = -4,-2,0,2 and 4. Identify the corresponding graph.

### Answers

Given,

The equation is y=x^2-9.

The values of x are -4, -2, 0, 2, 4.

The odered pair are,

At x= - 4,

The value of y is,

[tex]y=(-4)^2-9=7[/tex]

The ordered pair is (-4, 7).

At x= - 2,

The value of y is,

[tex]y=(-2)^2-9=-5[/tex]

The ordered pair is (-2, -5).

At x= 0,

The value of y is,

[tex]y=(0)^2-9=-9[/tex]

The ordered pair is (0, -9).

At x= 2,

The value of y is,

[tex]y=(2)^2-9=-5[/tex]

The ordered pair is (2, -5).

At x= 4,

The value of y is,

[tex]y=(4)^2-9=7[/tex]

The ordered pair is (4, 7).

The corresponding graph is,

Out of 50 students, 17 want pepperoni pizza, 19 want sausage pizza and the rest want a supreme pizza. What percent of the students want a supreme pizza?

### Answers

First, lets find how many students want the supreme pizza. Let 'x' be the number of those students. Then, given the information, we have:

[tex]x+17+19=50[/tex]

solving for 'x', we get:

[tex]\begin{gathered} x+17+19=50 \\ \Rightarrow x+36=50 \\ \Rightarrow x=50-36=14 \\ x=14 \end{gathered}[/tex]

we have that x = 14 students want a supreme pizza.

Now, if we suppose that the 50 students are the 100%, then, using a rule of three, we get:

[tex]\begin{gathered} 50\rightarrow100\% \\ 14\rightarrow y\% \\ \Rightarrow y=\frac{14\cdot100}{50}=\frac{1400}{50}=28 \\ y=28\% \end{gathered}[/tex]

**therefore, 28% of the students want a supreme pizza**

Question 9 Which equation would generate the arithmetic sequence: -5,- 14,- 23,-32,-41, A an = -5+9(n-1) B an = -5-9(n-1) C None of the other answers are correct D an = 9+5(n-1) E a = 9-5(n-1)

### Answers

**B**

**1)** Examining the Arithmetic Sequence:

(-5,-14, -23,-32,-41,..)

We have the following information:

a_1 = -5

Common ratio:-9

**2**) From these data, we have the Explicit formula:

[tex]a_n=-5_{}-9(n-1)[/tex]

**3) **Looking at the options we have some formulas, so we can state that the equation that would generate the Arithmetic Sequence is described in option **B**

Find the equation of the circle having the given properties:

### Answers

The equation of a circle is given by:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

3.

Using the points (4, 0), (0, 2) and (0, 0), we have:

[tex]\begin{gathered} (0,0)\colon \\ h^2+k^2=r^2 \\ (0,2)\colon \\ h^2+(2-k)^2=r^2 \\ h^2+4-2k+k^2=r^2 \\ \text{Comparing both equations:} \\ h^2+k^2=h^2+4-2k+k^2 \\ 4-2k=0 \\ k=2 \\ (4,0)\colon \\ (4-h)^2+k^2=r^2 \\ 16-8h+h^2+4=r^2 \\ \text{Comparing this last equation with the first one:} \\ 16-8h+h^2+4=h^2+4 \\ 16-8h=0 \\ h=2 \\ \\ h^2+k^2=r^2 \\ r^2=4+4=8 \end{gathered}[/tex]

So the equation of this circle is:

[tex](x-2)^2+(y-2)^2=8[/tex]

4. Principal Sanders wants to know if wearing school uniforms will help students improve theirmath test scores. She decides to conduct an experiment to find out She chooses two groups ofstudents to test One group will wear uniforms, the other will not.Part A. Define the variables and treatment for the experiment. (3 points)I1 What is the control variable? Why?

### Answers

**Note that:**

The control variable is the variable that does not change (that is, constant ) in an experiment. It does not take part in the experiment

The response variable is the dependent variable that determines the outcome of the experiment.

The treatment of an experiment is the independent variable, and it determines the outcome of the experiment.

**From the illustration given in this exercise, the control variable, the response variable, and the treatments are identified below with reasons.**

**1) The control variable = The mathematical abilities of the students**

**Reason:** The students chosen for the experiment must have the same mathematical abilities to prevent bias in the results of the experiment.

**2) The response variable = Math test scores**

**Reason:** The maths test scores of the two groups of students are the outcomes of the experiment, hence the response variable.

**3) The treatment for the experiment = Wearing of school uniforms**

**Reason:** Wearing of school uniforms is the treatment that the two groups of students were subjected to in order to confirm if their will be any effects on their Maths test scores.

(3x-3)

[6(x - 10)] What is the value of x?

### Answers

(3x - 3)

3(x - 1)

[6(x - 10)]

6x + 6 times -10

simplify 6 times -10 to -60

6x - 60

I don't know how to shade for the 2nd one please help

### Answers

**Answer:** Your result (without simplifying) is actually 2/36, so you would **shade two boxes out of the 36 shown**.

**NOTE: **For problem #19, you have 6 boxes for shading, so each box represents 3 increments (3x6=18 boxes). For your result of 5/18, you should only shade the **first box and 2/3 of the next box** (the other four boxes should be unshaded).

Hope this helps!

**Step-by-step explanation:**

6x - 5y = - 4Direct variationХ5?k=Not direct variation2y = 14xDirect variationk ==Not direct variation

### Answers

**Direct Variation** is of the form (directly proportional);

[tex]\begin{gathered} y\propto x \\ y=kx \end{gathered}[/tex]

While **indirect variation** (inversely proportional) is of the form;

[tex]\begin{gathered} y\propto\frac{1}{x} \\ y=\frac{k}{x} \end{gathered}[/tex]

So, for each of the given question we want to determine if they are direct or indirect variation;

1.

[tex]\begin{gathered} 6x-5y=-4 \\ -5y=-4-6x \\ -5y=-6x-4 \\ y=\frac{-6x-4}{-5} \\ y=\frac{6}{5}x+\frac{4}{5} \end{gathered}[/tex]

Therefore, this is a **Direct variation **with proportionality constant;

[tex]k=\frac{6}{5}[/tex]

2.

[tex]\begin{gathered} 2y=14x \\ y=\frac{14x}{2} \\ y=7x \end{gathered}[/tex]

Therefore, this is a **Direct variation **with proportionality constant;

[tex]k=7[/tex]

Give the domain of the following rational function using (a) set-builder notation and (b) interval notation.f(y) = y —— y-1 ——————————————————(a) Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A. The domain of the given function is {yly is a real number, y # ____}(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)B. The domain of the given function is {yly is a real number).

### Answers

**ANSWER:**

**(a)**

**A. The domain of the given function is {yly is a real number, y ≠ 1}**

**(b)**

[tex]\begin{equation*} D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right) \end{equation*}[/tex]

**STEP-BY-STEP EXPLANATION:**

We have the following function:

[tex]f(y)=\frac{y}{y-1}[/tex]

The domain of a function, are the input values of the function, in this case, it corresponds to the values that y can take.

Since it is a rational function and it cannot take values that make the denominator zero, so we set the denominator equal to zero, like this:

[tex]\begin{gathered} y-1=0 \\ \\ y\ne1 \end{gathered}[/tex]

(a)

That means that y can take the value of all reals except 1.

So the correct answer is:

**A. The domain of the given function is {yly is a real number, y ≠ 1}**

(b)

In its interval form it would be:

[tex]D=\left(-\infty\:,\:1\right)\cup\left(1,\:\infty\:\right)[/tex]

Which graph shows a function with a range of all real numbers greater than or equal to -1?55444-3+3+3+2-2-2+14 4-5-4-3-2-1₁ 1 2 3 4 5 x-5-4-3-111 2 3 4 5 x--5--3-2-11 1 2 3 4 5 x-2+-24-3+-3-3--4<-4O-5-4-3-2-1₁. 12-2-11-4 5 X543214+3YO

### Answers

**Answer:**

**The graph that has a range of all real numbers greater than or equal to -1 is the graph below (top middle graph).**

**Explanation:**

Since the range or the y-values of the graph must be greater than or equal to -1, then the graph must be increasing starting from y = -1.

Out of the 4 graphs, only the two graphs in the middle shows a graph that is increasing.

The graph at the top part is increasing starting from y = -1 while the graph at the bottom part is increasing starting from y = 1 hence**, the answer is the graph at the top middle part.**

15x²y/(x+1)^3* (x+1)/24x^5y

### Answers

The simplified value of the given **expression **in the form of a **fraction **is [tex]\frac{5}{8\cdot(x+1)^2\cdot x^3}[/tex] .

The given expression is: [tex]\frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

we will use the properties of **exponents **to simplify the expression.

Taking the **powers **of the like terms and combining we get :

[tex]\implies \frac{15x^2y}{(x+1)^3}\cdot\frac{(x+1)}{24x^5y}[/tex]

[tex]\implies \frac{15}{24} \times \frac{x^{2-5}y^{(1-1)}}{(x+1)^{3-2}}[/tex]

[tex]\implies \frac{5}{8\cdot(x+1)^2\cdot x^3}\\[/tex]

Therefore we get the simplified equation for the expression.

Expressions are mathematical statements that comprise either numbers, variables, or both and at least two terms associated by an **operator**. Mathematical operations include addition, subtraction, multiplication, and division.

In mathematics, there are two different types of expressions: algebraic expressions, which also include variables, and numerical expressions, which solely comprise numbers. A set sum of money appears to be a constant.

A **variable **is a symbol that has no predetermined value. A term may consist of one constant, one variable, or a combination of variables and constants multiplied or divided. A number that is additionally multiplied by a variable is referred to as the coefficient in an expression.

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1. Given: f(x)=x²-5x +1

A) Which is larger f(2) or f(-2)?

B) Which is smaller f(0) or f(4)?

### Answers

A. The **function **f(-2) is larger than f(2)

B. The function f(4) is smaller than f(0)

Given,

The function; f(x) = x²- 5x + 1

We have to find;

A. The** larger** is f(2) or f(-2)

Here,

f(2) = 2²- 5 x 2 + 1 = 4 - 10 + 1 = - 6 + 1 = -5

f(-2) = -2²- 5 x -2 + 1 = 4 + 10 + 1 = 15

That is,

The function f(-2) is larger than** f(2)**

B. The smaller is f(0) or f(4)

Here,

f(0) = 0²- 5 x 0 + 1 = 0 - 0 + 1 = 1

f(4) = 4²- 5 x 4 + 1 = 16 - 20 + 1 = - 4 + 1 = -3

That is,

The function f(4) is **smaller** than f(0)

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What is an equation of the line that passes through the point (6,-2) and is parallel to the line y=2/3x+4?

### Answers

point = (6,-2)

Parallel to y= 2/3x+4

If 2 lines are parallel, both have the same slope

Slope intercept form:

y= mx +b

where:

m= slope

b= y intercept

so, for y= 2/3x+4

slope = 2/3

So far we have

y= 2/3x +b

Replace x,y by the coordinate point given (6,-2) and solve for b:

-2 = 2/3 (6) + b

-2 = 4 + b

-2-4 = b

-6 = b

Final equation:

**y= 2/3x - 6**

Question 7. Y=(5/2)^xSketch the graph of each of the exponential functions and label three points on each graph.

### Answers

Given:

[tex]y=\mleft(\frac{5}{2}\mright)^x[/tex]

To sketch the graph:

First find the three points.

Put x=-1 we get,

[tex]\begin{gathered} y=(\frac{5}{2})^{-1} \\ =\frac{2}{5} \\ =0.4 \end{gathered}[/tex]

Put x=0 we get,

[tex]\begin{gathered} y=(\frac{5}{2})^0 \\ =1 \end{gathered}[/tex]

Put x=1 we get,

[tex]\begin{gathered} y=(\frac{5}{2})^1 \\ =2.5 \end{gathered}[/tex]

Therefore, the three points are, (-1, 0.4), (0, 1), and (1, 2.5).

The graph is,

I need help with this practice problem Having trouble solving it If you can use Desmos to graph it

### Answers

The graph of the function:

[tex]f(x)=\cot (x+\frac{\pi}{6})[/tex]

is shown below:

By graphing at least one full period of the function, we would take the limit of the function as:

[tex]-\pi\le x\le\pi[/tex]

**Hence, the graph of at least one full period is:**

How to evaluate:16% of 575102% of 75080 is 25% of what number?

### Answers

you can evaluate a percentage like follow.

the 16% of 575 is 0.16(575)=345

the 102% of 250 will be 750

Enter the value of the expression using the Order of Operations. (4 x 3) + 23 x 4-3

### Answers

Starting with the expression:

[tex](4\times3)+23\times4-3[/tex]

Solve parenthesis first. Since 4 times 3 equals 12, then the expression is equal to:

[tex]12+23\times4-3[/tex]

Next, solve for multiplications. In this case, solve 23 times 4:

[tex]12+92-3[/tex]

Finally, solve additions and substractions from left to right:

[tex]\begin{gathered} 12+92-3=104-3 \\ =101 \end{gathered}[/tex]

Therefore:

[tex](4\times3)+23\times4-3=101[/tex]

Barney and Robin went shopping at H&M. The store was having a sale on all shirts and pants. Barney spent $70 on 3 shirts and 2 pairs of pants and Robin bought 1 shirt and 4 pairs of pants for $90. d) Use a graphing calculator, to graph your equations in parts a and b. What is the coordinate point where these two lines intersect? How does this compare to your response in part c?

### Answers

Barney spent $70 on 3 shirts and 2 pairs of pants

Robin bought 1 shirt and 4 pairs of pants for $90

Let x be the cost for each shirt

Let y be the cost for each pair of pants

3x+2y=70 **(1)**

x+4y=90** (2)**

Having this system of equations, we can graph on the graph calculator:

The solution of two linear equations corresponds to the intersection of the two lines because the coordinate pair naming every point on a graph is a solution to its corresponding equation:

In this case the solution is: (10, 20) and corresponds to the cost of the shirt and pant.

Shirt: $10

Pant:$20

Which of the following represents the factorization of the trinomial below?x2 – X-20A. (x-4)(x-5)B. (X + 4)(x-5)oC. (x-2)(x-10)0D. (x+2)(x-10)

### Answers

**Answer:**

(x+4)(x-5)

**Step-by-step explanation:**

**Second order polynomial in the following format:**

ax² + bx + c = 0

Has roots x¹ and x².

Can be factored as:

(x - x¹)(x - x²)

So, we have to find the roots.

**Finding the roots:**

Bhaskara formula, which is:

[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

In the polynomial given in this question:

a = 1, b = -1, c = -20

So

[tex]x=\frac{-(-1)\pm\sqrt{(-1)^2-4\ast1\ast(-20)}}{2}=\frac{1\pm\sqrt{81}}{2}[/tex]

The roots are:

[tex]x^1=\frac{1+9}{2}=5,x^2=\frac{1-9}{2}=-4[/tex]

The factored form is:

(x - x¹)(x - x²) = (x - (-4))(x - 5) = (x+4)(x-5)

Which graph represents the function f(x) = -x + 31?

### Answers

**Answer:**

**Step-by-step explanation:**

I hope this helps! :) If it does could you please mark me brainliest?

**Answer:**

Slope : -1

y = intercept : (0,31)

**Step-by-step explanation:**

A boat is heading towards a lighthouse, whose beacon-light is 135 feet above the water. The boat's crew measures the angle of elevation to the beacon, 4 deg What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary .

### Answers

The ship's **horizontal distance **from the lighthouse is: 1930.59 feet.

**What is tangent or tan in trigonometry?**

The ratio of the side opposite the angle we know or want to know over the side next to that angle is known as the **tangent**, which is sometimes abbreviated as** T-A-N**. The side touching the angle that is NOT the **hypotenuse**, or the side opposite the right angle, is the neighboring side.

Given in the question,

Height of lighthouse = 135 feet,

angle of elevation = 4 degree,

We know that, **tan **Θ = perpendicular/ base

Here, height is perpendicular and **distance **is base,

Putting the values,

**tan4**° = 135/B

B = 1930.59 feet

Therefore, **distance **is 1930.59 feet.

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**Answer:The answer is 1930.59**

**Step-by-step explanation:**

5 markers cost $6.55.Which equation would help determine the cost of 4 markers?

### Answers

5 markers -------> $6.55

4 markers -------> x

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Knowledge check that with the kids on the other hand ✋ the

### Answers

**. The function h measures the height.**

**. The units on h meters.**

**. h'(t) measures the velocity**

**. The units on h'(t) are meters per second**

**. The units on t are seconds**

7. Tres hermanos tienen una bolsa de golosinas. Quieren regalarle a su padre un trozo de twizzler cada uno. Si cada trozo de twizzler que regalan tienen 100 mm, ¿cuántos centímetros de twizzler tendrá en total el padre?

### Answers

Como cada uno de los hermanos le regalará un trozo de twizzler a su padre, ékl tendra tres twizzlers. En milímetros eso es

[tex](3)(100)=300\text{ mm}[/tex]

Ahora tenemos que convertir los milimetros a centímetros. Recordemos que un centímetro tiene 10 milímetros. Entonces, tenemos que dividir la cantidad total de milímetros entre 10.

[tex]\frac{300}{10}=30[/tex]

**Por lo tanto el padre tendrá 30 cm de twizzler en total.**

Suppose some government bonds are paying 5.8% simple interest. How much should you invest in the bonds if you want them to be worth $5,000 in 9 years? Round your final answer to two decimal places.

### Answers

The simple interest formula is given by:

[tex]FV=PV(1+in)[/tex]

FV: future value

PV: present value

i: interest rate

n: interest periods

We have from the question:

FV: $5000

PV: ?

i: 5.8%

n: 9.

Then:

[tex]5000=PV(1+(0.058\cdot9))[/tex]

Thus

[tex]PV=\frac{5000}{1.522}\Rightarrow PV=3285.15[/tex]

Then, **we should invest in $3285.15 to have $5000 in 9 years.**

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what is the line segment addition to fall the distance of the given line segment if I was mayor of a city, I would put all of my effort to enhance the educational experience for students.ADD A BODY AND A CONCLUSION(this must have 200 words) 1. How have your beliefs about learning shaped your education and career choices?2. How did the Modes of Learning Assessment challenge you? How did it surprise you? Factor the expression using the GCF.1812 I'm using goformative to do my work, I have number 13 answer right but the rest show my answers incorrect, I will appreciate if you can help me with my question I will paste the image of the question I have. dont need an explanation just the answer. Community takes too long lol Solve for x -34>5x-4 or 5x-4 -9Need this asap please Grade 1:What is present simple? 3. Jose began the day with eight Magikarps. After spending the day at the lake, he ended up with sixteen Magikarps. mini lesson[tex]y = - 3x - 10[/tex]math what recent series of discoveries have made astronomers more optimistic about our prospects of finding life out there? Alexander is a stockbroker. He earns 13% commission each week. Last week, he sold $7,500 worth of stocks. How much did he make last week in commission? If he averages that same amount each week, how much did he make in commission in 2011? Last week, he made $ in commission. what is 10+5 rounded to the nearest thousand PO Triangle ABC is similar to triangular DEF. What is the value of x? the first drop down answers are 18,10,7,14the second drop down box options are 16.5,30.5,44.5the third options are 2.5, 1.5, 1,3 the fourth options are 14n, 18n, 7n, 10nthe fifth options are each movie tickets cost the same amount, there is a service fee for buying tickets online, the cost increase as tge number of tickets increase, the leaste amount of tickets you cab buy is 1 Which choice is equivalent to the quotient shown here when x > 0?A.2xB.2x2C.D. while free diving in the ocean, Tanya streeter once said a record by diving 525 ft and 3 and 1/2 minutes. how many feet per minute did she dive? x Michael uses synthetic division to divide f(x) by g(x), his last line of work 0/3is shown. How would he write his answer of f(x) divided by g(x). *7 0 24 0 07x^2+24 An unknown gas is found to consist of 10.48 g of nitrogen and 11.96 g if oxygen. What is the percentage composition of this gas? * A. 53.3% N, 46.7% O B. 74.5% N, 25.5% O C. 28.6% N, 71.4 % O D. 46.7%N, 53.3%O If someone says that taking vitamin C is correlated with fewer cold symptorns, you shouldSelect one:a. remember that correlation is not causation and look for more evidence regarding vitamin C and coldsb. assume that vitamin C is the cause of the lack of cold symptomsC.assume that colds are caused by not taking vitamin CD all of these