A random sample of 100 chemistry students were asked how many lab classes he or she was enrolled in september 2000. the results showed a mean of 1.65 lab classes with a standard deviation of 1.39. ten years later, a similar survey was conducted to determine if the distribution changed. the 2010 sample mean was 1.82 with a standard deviation of 1.51. do the data provide statistical evidence that the mean number of lab classes taken in the first survey is different from the survey taken 10 years later? perform the appropriate test using a = 0.02​

Answers

Answer 1

Using the t-distribution, as we have the standard deviation for the samples, it is found that the data does not provide statistical evidence that there is a difference.

What are the hypotheses tested?

At the null hypotheses, it is tested if there is no difference in the means, that is, the subtraction is of 0, hence:

[tex]H_0: \mu_1 - \mu_2 = 0[/tex]

At the alternative hypotheses, it is tested if there is a difference, hence:

[tex]H_1: \mu_1 - \mu_2 \neq 0[/tex]

What are the mean and the standard error of the distribution of differences?

For each sample, they are given by:

[tex]\mu_1 = 1.82, s_1 = \frac{1.51}{\sqrt{100}} = 0.151[/tex]

[tex]\mu_2 = 1.65, s_2 = \frac{1.39}{\sqrt{100}} = 0.139[/tex]

Hence, for the distribution of differences, they are given by:

[tex]\overline{x} = \mu_1 - \mu_2 = 1.82 - 1.65 = 0.17[/tex]

[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.151^2 + 0.139^2} = 0.205[/tex]

What is the test statistic?

The test statistic is given by:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

In which [tex]\mu = 0[/tex] is the value tested at the null hypothesis.

Then:

[tex]t = \frac{\overline{x} - \mu}{s}[/tex]

[tex]t = \frac{0.17 - 0}{0.205}[/tex]

[tex]t = 0.83[/tex]

What is the decision?

Considering that it is a two-tailed test, as we are testing if the mean is different of a value, with 100 + 100 - 2 = 198 df and a significance level of 0.02, the critical value is of [tex]|t^{\ast}| = 2.3453[/tex].

Since the absolute value of the test statistic is less than the critical value, we do not reject the null hypothesis, which means that the data does not provide statistical evidence that there is a difference.

More can be learned about the t-distribution at https://brainly.com/question/13873630


Related Questions

help one of these qtns pls

Answers

Answer:

(a) 3x + 4 = 2x + 1

3x - 2x = 1 - 4

x = -3

Step-by-step explanation:

To solve for 'X', you must move all 'x' to the left-hand side, as seen through the working out. To balance it, you move all the lone numbers without (constants) to the right. Remember: when you move values across the 'equals' sign, the sign of the value you are moving becomes switched. For example, if you're moving 3x + 1 = 0 and you wish to move 1 to the other side, it becomes 3x = 0 ( - 1).

what are three expressions that are equivalent to 15+45

Answers

Answer:

40+20, 50+10, 46+14

Step-by-step explanation:

15+45=60 =   50+10=60 46+14=60

25= 5(3X-4)^1/3
PLEASE HELP AND SHOW WORK!
THANKS SM

Answers

Answer:

[tex]x=43[/tex]

Step-by-step explanation:

Given equation:

[tex]25=5(3x-4)^{\frac13}[/tex]

Divide both sides by 5:

[tex]\implies 5=(3x-4)^{\frac13}[/tex]

Cube both sides:

[tex]\implies 5^3=((3x-4)^{\frac13})^3[/tex]

[tex]\implies 125=(3x-4)^{\frac33}[/tex]

[tex]\implies 125=(3x-4)^1[/tex]

[tex]\implies 125=3x-4[/tex]

Add 4 to both sides:

[tex]\implies 129=3x[/tex]

Divide both sides by 3:

[tex]\implies x=43[/tex]

Answer:

x = 43

Step-by-step explanation:

25 = 5∛(3x - 4)On cubing the entire expression :15625 = 125(3x - 4)3x - 4 = 1253x = 129x = 43

I don't know how to solve this

Answers

Answer:

7

Step-by-step explanation:

List out possible numbers that would add to the answer choices and see which has most possibilities

7

3 + 4

5 + 2

1 + 6

10

5 + 5

4 + 6

11

5 + 6

12

6 + 6

I think the answer is 7. If it’s not, the answer is 10. Sorry if I’m wrong!

Which term describes a line segment that connects a vertex of a triangle to a point on the line containing the opposite side, so that the line segment is perpendicular to that line?

Answers

Answer: C

Step-by-step explanation:


HELP PLEASE I REALLY SUCK AT MATH

Answers

Answer:

D is the answer because 4 goes into all of them.

Using your answer from #7, find the perimeter of the triangle.
Answer From #7: 9

Answers

Answer:

58

Step-by-step explanation:

x=9

3(9) + 1 + 4(9) -8 + (9) - 7 = 58

Find the geometric mean of 24 and 32

Answers

Answer:27.712812921102

Step-by-step explanation:

24*32=x*x

√768=√x²

27.712812921102=x

Geometric mean formula

GM=√ab

a=24

b=32

Find GM

√(24)(32)√76827.7128

On rounding

GM=27.7

-x= x – 10

How many solutions does this equation have?

A.Infinitely many solutions

B.No solutions

C.Two solutions

D. One solution

Answers

Answer:

D

Step-by-step explanation:

Answer: One if any.

-x = x - 10                  Add x to both sides

-x+x = x + x - 10          Combine

0 = 2x - 10                   Add 10 to both sides

10 = 2x - 10+10            Combine

10 = 2x                         Divide by 2

10/2=2x/2

x = 5

Definite Answer: One Solution

In ΔNOP,the measure of ∠P=90°, NP = 16, ON = 65, and PO = 63. What ratio represents the cosecant of ∠N?

Answers

Answer: 65/63

Step-by-step explanation:

The cosecant of angle N is the reciprocal of the sine of angle N.

Using SOHCAHTOA, the sine of angle N is 63/65.

This means that the cosecant of angle N is 65/63.

Factorize x2(2x + 3y) + 3x (2x + 3y) +2 (2x + 3y)

Answers

Answer:

(2x+3y)(x2+3x+2). it may helps you

Answer:

[tex]\tt 2x^3+3x^2y+6x^2+9xy+4x+6y[/tex]

Step-by-step explanation:

[tex]\tt x^2(2x + 3y) + 3x (2x + 3y) +2 (2x + 3y)[/tex]

Expand by distributing terms:-

[tex]\tt 2x^3+3x^2y+3x(2x+3y)+2(2x+3y)[/tex]

Expand by distributing terms:-

[tex]\tt 2x^3+3x^2y+6x^2+9xy+4x+6y[/tex]

~

Please Help! Will Give Brainlest! Locks In an Hour!

Answers

Answer:

B. - 0.383

Step-by-step explanation:

Since cotangent of angle is:

cot λ = cos λ / sin γ

And

cos λ = x/1, sin λ = y / 1

The value of cot λ is:

cot λ = x/y = - 0.358/0.934 = - 0.383 (rounded)

Correct choice is B

Help on this pleasse.

Answers

Answer: 40 degrees

Step-by-step explanation:

Find the average squared distance between the points of r{(x,y): 0x, 0y} and the point (,)

Answers

The average squared distance between the points is their variance

The average squared distance is 8/3

How to determine the average squared distance?

The given parameters are:

R={(x,y): 0<=x<=2, 0<=y<=2}

The point = (2,2).

f(x,y) = (x-2)² + (y-2)²

The squared distance is calculated as:

D² = f(x,y) = (x-2)² + (y-2)²

Where the area (A) is:

A = xy

Substitute the maximum values of x and y in A = xy

A = 2 * 2

A = 4

The minimum values of x and y are 0.

So, the limits for the integrals are 0 to 2

The integral becomes

[tex]D\² = \int \int (x-2)\² + (y-2)\² dx dy[/tex]

Expand

[tex]D\² = \int \int x\² -4x + 4 + (y-2)\² dx dy[/tex]

Evaluate the inner integral with respect to x from 0 to 2

[tex]D\² = \int \frac 13x^3 -2x^2 + 4x + x(y-2)\² |\limits^2_0 dy[/tex]

Expand

[tex]D\² = \int [\frac 13(2)^3 -2(2)^2 + 4(2) + (2)(y-2)\²] dy[/tex]

Simplify

[tex]D\² = \int \frac 83 + (2)(y-2)\² dy[/tex]

Expand

[tex]D\² = \int \frac 83 + 2y^2-8y + 8 \ dy[/tex]

Evaluate the integral with respect to y from 0 to 2

[tex]D\² = [\frac 83y + \frac 23y^3- 4y^2 + 8y ]|\limits^2_0[/tex]

Expand

[tex]D\² = \frac 83*2 + \frac 23*2^3- 4*2^2 + 8*2[/tex]

D² = 32/3

The average squared distance (AD²) is calculated as:

AD² = D²/A

So, we have:

AD² = 32/3 [tex]\div[/tex] 4

Evaluate the quotient

AD² = 32/12

Simplify

AD² = 8/3

Hence, the average squared distance is 8/3

Read more about average distance or variance at:

https://brainly.com/question/15858152

The average squared distance between the points of R = {(x,y): 0<=x<= h, 0<=y<=k } is 8/3.

How do determine the average squared distance?

From the given parameters R = {(x,y): 0<=x<= h, 0<=y<=k }

The squared distance from point (h, k) is calculated as

D² = f(x,y) = (x-2)² + (y-2)²

Where the area (A) will be

A = xy

Substitute the maximum values of x and y

A = 2 × 2 = 4

The minimum values of x and y are 0.

So, The integral becomes

[tex]D^{2} = \int \int(x-2)^2 +(y-2)^2 dx dy\\\\D^{2} = \int \int\limits^2_0 (x)^2 -4x + 4+(y-2)^2 dx dy\\\\D^{2} = \int1/3(x)^3-2x^{2} +4x + 4+x(y-2)^2 dy\\\\D^{2} = \int8/3+2y^{2} -8y +8 dy[/tex]

[tex]D^2 = {8/3y +2/3y^2 -4y^2+8y[/tex]

By expanding we get,

D^2 = 32/3

The average squared distance (AD²) is calculated as:

AD² = D²/A

AD² = 32/3  4

AD² = 32/12

AD² = 8/3

Hence, the average squared distance is 8/3

Read more about average distance;

brainly.com/question/15858152

#SPJ4

Two basketballs fell, without bouncing, from a net and a chair at the same time. The ball which fell from the net rolled 30 feet. Note: Figure is not drawn to scale The horizontal and vertical distances traveled by the balls formed similar triangles. How far did the second ball roll from the chair? A. 6 feet B. 22 feet C. 4 feet D. 3 feet

Answers

Answer:

c

Step-by-step explanation:

100pts Help rounding!

Answers

Answer:

5

Step-by-step explanation:

5 158/559

= 5 + 158/559

= 5 + 0.28264758

= 5.28264758

= 5 (rounded to nearest whole number)

Answer:

5

Explanation:

[tex]\rightarrow \sf 5\dfrac{158}{559}[/tex]

[tex]\rightarrow \sf 5.282647585[/tex]

The whole number is the quotient in any fraction.

Brainliest available

Find "X"

Answers

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

[tex]\qquad \sf  \dashrightarrow \: ({4}^{2}) \star ( {2}^{9} ) = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: ({ {2}^{2}) }^{2} \star ( {2}^{9} ) = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \: ({ {2}^{}) }^{4} \star ( {2}^{9} ) = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \:2 {}^{4 + 9} = {2}^{x} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 4 + 9[/tex]

[tex]\qquad \sf  \dashrightarrow \:x = 13[/tex]

hence, value of x is 13

[tex]➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖➖[/tex]

Answer:

x = 13

Step-by-step explanation:

[tex]\left(4^2\right)\left(2^9\right)=2^x[/tex]

[tex]\mathrm{multiply}[/tex]

[tex]4^2=16[/tex]

[tex]2^9=512[/tex]

[tex]16*512=8192[/tex]

[tex]8192=2^x[/tex]

[tex]\mathrm{Flip \;the \;equation}[/tex]

[tex]2x=8192[/tex]

[tex]log(2x)=log(8192)(Take \;log \;of\; both \;sides)[/tex]

[tex]x*(log(2))=log(8192)[/tex]

[tex]x=\frac{log(8192)}{log(2)}[/tex]

[tex]x=13[/tex]

[RevyBreeze]

Scientists put marks on 72 moose as part of an effort to estimate the local moose population. Later, the scientists flew over the area and counted a total of 430 moose, of which 43 were marked. To the nearest whole number, what is the best estimate for the moose population?

Answers

Answer:

72x430/43

Step-by-step explanation:

What are the solution(s) for the quadratic equation?

Y=5x^2-9x+4

Show work

Answers

Let's see

[tex]\\ \rm\rightarrowtail 5x^2-9x+4=0[/tex]

[tex]\\ \rm\rightarrowtail 5x^2-5x-4x+4=0[/tex]

[tex]\\ \rm\rightarrowtail 5x(x-1)-4(x-1)=0[/tex]

[tex]\\ \rm\rightarrowtail (5x-4)(x-1)=0[/tex]

[tex]\\ \rm\rightarrowtail x=4/5,1[/tex]

help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Answers

Answer:

The top-left one.

Step-by-step explanation:

The bottom pictures show that Chef B chopped more carrots than Chef A.

So those pictures are incorrect.

The top-right picture shows that Chef A chopped twice as many carrots as Chef B. So, that isn't correct either.

Finally, we get to the top-left picture.

Chef A chopped 3 times as many carrots as Chef B.

Thus the correct answer is the top-left picture.

Also, I would appreciate it if you marked me as brainliest.

The top left I took the test

3) 18 mm
4mm

4) 11 in
19 in

5) 5 mi
11 m

Answers

Answer:

3= perimeter=44 area=73

4= perimeter=60 area=209

5= perimeter=32 area=55

Step-by-step explanation:

18x4=72

18+18+4+4=44

11+11+19+19=60

11x19=209

5x11=55

5+5+11+11=32

what is the measure of the angle shown?

Answers

Answer:

35 degrees

Step-by-step explanation:

Answer:

The measure of the angle is 35 degrees

Step-by-step explanation:

There are two measurements on the protractor.

If the angle is acute you will use the smaller measurenment of the two, and if the angle is obtuse, you will use the larger of the two.

In this case the angle is acute, so the measure is 35 degrees.

Hope that helps!

find the direct variation of y-x=4 (PLEASE TRY TO EXPLAIN THE ANSWER)​

Answers

Answer:  x = -4 + y

Step-by-step explanation:

Subtract y from both sides y- x - y = 4 - y

Simplify -x = 4 - y

Divide by -1

-x ÷ -1,

4 ÷ -1,

y ÷ -1,

Simplify x = -4 + y

HELLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLO

Answers

Answer:

hi

Step-by-step explanation:

Need done ASAP

If f(x)=2x+7 and g(x)=5x-3, which expression represents (f-g)(x) ?
Please show work

Answers

Solution SOLUTION
(
f
+
g
)
(
x
)
=
(
2
x
+
7
)
+
(
5
x

2
)
=
7
x
+
5
(f+g)(x)=(2x+7)+(5x−2)=7x+5
(
f

g
)
(
x
)
=
(
2
x
+
7
)

(
5
x

2
)
=
9

3
x
(f−g)(x)=(2x+7)−(5x−2)=9−3x
(
f

g
)
(
x
)
=
(
2
x
+
7
)

(
5
x

2
)
=
(
2
x
+
7
)
(
5
x

2
)
(f⋅g)(x)=(2x+7)⋅(5x−2)=(2x+7)(5x−2)
(
f
g
)
(
x
)
=
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2
x
+
7
)
(
5
x

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=
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+
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5
x

2
(
g
f

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(5x−2)
(2x+7)

=
5x−2
2x+
Answer

5
(f+g)(x)=7x+5
(
f

g
)
(
x
)
=
9

3
x
(f−g)(x)=9−3x
(
f

g
)
(
x
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=
(
2
x
+
7
)
(
5
x

2
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(f⋅g)(x)=(2x+7)(5x−2)
(
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)(x)=

A robot vacuum cleans a dirty floor using multiple passes. During each pass, 24% of the dirt is removed. If the floor initially has 550 ml of dirt, write a function to find out how much dirt will remail after 10 passes?

please include function and value.​

Answers

The function is given by y = 550(0.76)ˣ, after 10 passes, the number of dirts is about 35.36 ml

How to solve an exponential function?

Let y represent the amount of dirt on the floor after x passes.

The floor initially has 550 ml of dirt, hence a = 550.

During each pass, 24% of the dirt is removed. Hence b = 100% - 24% = 76% = 0.76

The equation is given by:

y = 550(0.76)ˣ

After 10 passes:

y = 550(0.76)¹⁰ = 35.36 ml

The function is given by y = 550(0.76)ˣ, after 10 passes, the number of dirts is about 35.36 ml

Find out more on exponential function at: https://brainly.com/question/12940982

(b) A line has the equation y = 6x + 11
Does the point (-3,15) lie on the line? Explain you answer as fully as possible

Answers

Hi, to begin, the ordered pair value (-3, 15) has an x-value of -3. So, to see if it lies on the line of your equation y = 6x + 11, plug -3 in for x. This gives you y = 6(-3) + 11 = -7 So the ordered pair answer for this would be (-3, -7) and not (-3, 15). So the answer is no.

Hey there!

-----------------------_----------_---------

PLS HELP ME

Use the box-and-whisker plot to complete each of the following statements.

A)The median of Set A is approximately ___ the median of Set B.
Answers I can pick from: Half of, the same, twice

B) The range of Set B is approximately ___ the range of Set A.
Answers I can pick from: Half of, the same, twice

C) The interquartile range of Set A is ____ the interquartile range of Set B.
Answers I can pick from: Less then, greater then, the same

D. There is ____ overlap between the two data sets.
Answers I can pick from: some, much, little, like, no

Answers

To find the range, interquartile range, and median of the box plot, see the image attached below to use as a guide.

What is a Box Plot?

A box plot consists of a rectangular box, a vertical line that divides the box, and two whiskers extending from the box.

The box plots being referred to in the question are missing, however, the diagram attached shows how to determine the values you will need in solving the question.

The median is represented by the vertical line that divides the rectangular box.

The range = max value - min value.

The interquartile range = the range of the rectangular box = Q3 - Q1.

In summary, to find the range, interquartile range, and median of the box plot, see the image attached below to use as a guide.

Learn more about box plot on:

https://brainly.com/question/14277132

Solve for x: √(32^0 + 2/3)=(0.6)^2-3x​

Answers

Step-by-step explanation:

Given: √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

Asked: Find the value of x = ?

Solution: Given that √{32⁰ + (2/3)} = (0.6)²⁻³ˣ

⇛√{1 + (2/3)} = (0.6)²⁻³ˣ

⇛√{(1/1) + (2/3) = (0.6)²⁻³ˣ

⇛√{(1*3 + 2*1)/3} = (0.6)²⁻³ˣ

⇛√{(3 + 2)/3} = (0.6)²⁻³ˣ

⇛√(5/3) = (0.6)²⁻³ˣ

Squaring on both sides then

⇛{√(5/3)}² = {(0.6)²⁻³ˣ}²

⇛√(5²/3²) = {0.6}(²⁻³ˣ)²

⇛√{(5*5)/(3*3)} = {0.6}(²⁻³ˣ)²

⇛5/3 = {0.6}(²⁻³ˣ)²

[[tex]\mathsf{\because}[/tex] (aᵐ)ⁿ = aᵐⁿ]

⇛5/3 = (0.6)²*²⁻³ˣ*²

⇛5/3 = (0.6)⁴⁻⁶ˣ

⇛5/3 = (6/10)⁴⁻⁶ˣ

⇛5/3 = {(6÷2)/(10÷2)})⁴⁻⁶ˣ

⇛5/3 = (3/5)⁴⁻⁶ˣ

⇛(3/5))⁻¹ = (3/5)⁴⁻⁶ˣ

[[tex]\mathsf{\because}[/tex] a⁻ⁿ = 1/aⁿ]

Base are the same, so the exponents must be equal.

[tex]\mathsf{\therefore}[/tex] -1 = 4 - 6x

Shift the number 4 from RHS to LHS, changing it's sign.

⇛-1 - 4 = -6x

⇛-5 = -6x

⇛x = {(-5)/(-6)}

[tex]\mathsf{\therefore}[/tex] x = 5/6

Answer: Hence, the value of x for the given problem is 5/6.

also read similar questions: (1/3)^-2 + (1/4)^-2 = (125)^x Find the value of x? https://brainly.com/question/25746379?referrer

(3^-2 × 4^-2)^-3 = 12^x In the given expression find the value of x. https://brainly.com/question/25746273?referrer

Which effect did World War II have on the United States?

a) The United States became the richest, most powerful nation in the world.


b) The war caused the United States to enter another severe depression.


c) The war had little effect on the United States.


d) The United States became second in power only to England.

Answers

Answer:

the anwer is A cause jobs and industials had 96 percent and corperate profits after taxes doubled

Answer:

a

Step-by-step explanation:

world War 2 did in fact cause the United States to become the richest and most powerful

Other Questions
11. Which of the following gives the correct relation between the acceleration due to gravity and period of a pendulum?g = 2LT2g = 42LT2g = 2LTg = 22LTPlease show all of your algebra. What type of job can i get with a finance and marketing double major Review the amendments in the Bill of rights C. Choose three rights to focus on the rights you believe are the mostimportant ones in the document. Take notes in the table provided below about each right. Include the amendmentnumber and the name of the right, identify a current real-world scenario that illustrates conflict around that right, anddescribe the reasons explaining the different sides of the conflict. WHo is friends with Dixie Damileo Hurry one main difference between the United States constitucion and state constitution is that state constitutions...A. cant be amended. B. state specific services to provideC. provide supremacy over the federal governmentD. don't include how to set up local governments Question 16 of 20What is true of the federal level of government and the state and local level inthe creation of public policy?A. Both set policy related to public education.B. Both set policy related to family law.C. Both set policy related to the economy.D. Both set policy related to foreign countries.SUBMIT Complete the paragraph regarding the effects of the September 11 attacks.On May 1, 2011, US forces killed al Qaeda leader_____In Pakistan after a ten-year search for the leader of the 9/11attacks. In 2011, President Obama announced a plan to withdraw troops from Afghanistan by_____ PLEASE VERY SIMPLE QUESTION: The graph above shows the effect of sew biological oxygen demand (BOD) and dissolved oxygen (DO) in a flowing stream. The smallest fish populations will most likely be found at point... what is 60 divided by 4? A microwave has a period 0.000015 s has a wavelenth of ?(Round your answer to the nearest hundreth. Add a zero to the begining of the number if necessary.) What is the first step when creating a charcoal drawing?A. Draw a surface lineB. Add a cast shadowC. Draw a dark outlineD. Select a viewpoint or photo to draw from Find the larger solution of the exponentialequation2^x^2= 4^3x Complete the sentence with the correct pronoun.Mary told her friend, Janice, "________________________ can come to our house.""Thanks for the invitation," said Janice.A.) YouB.) IC.) WeD.) she The airplane flew 4,848 miles in 8 hours. How many miles per hour did it fly? Which point on the number line is at 58/100 The diameter of a circular placemat is 42 centimeters. What is the approximate area of the circular placemat A person bloody type is inherited true or false (PLS HELP QUICK POINTS)A soda can holds 235.5 in^3 of liquid. If the cab is 5 inches tall, what is the distance across the top of the soda can. Canned foods must be purchased from an approved source to make sure they A. will be delivered during off-peak hours.B. have a shelf life of two years or more.C. can be safely stored on the floor in dry storage areas. D. have been processed to destroy disease-causing microorganisms PLS HELP ASAPAuthors can draw on and use elements from other works. This element is an object or event that represents a larger idea. This element adds additional meaning and understanding to stories. What element is it? 1. symbol2. allusion3. allegory