How many numbers are there between 199sq and 200sq

Answers

Answer 1

Answer: 398

Step-by-step explanation:

200^2 - 199^2 = 399

Answer 2

Answer:

397

Step-by-step explanation:

200^2 - 1 = 40000 - 1 =   39999

199^2 + 1 = 39601+ 1 =    39602

Difference =                         397

A couple of things you should keep in mind.

Between means that the end points are not included. That means you do not subtract 39601 from 40000 to get the answer.The minus 1 from 40000 makes sure that you exclude 40000The plus 1 added to 39601 makes sure that you exclude 49601


Related Questions

find the permutation of these letters (a,b,c) taking a letter at a time​

Answers

Answer:

List the letters in alphabetical order

Step-by-step explanation:

ABC,ACB

BAC,BCA

CAB,CBA

Answer: 6 permutations

Step-by-step explanation: A permutation is an arrangement of objects in which order is important. In this problem, to find the number of permutations of the letters A, B, and C, we find the number of ways we can arrange the order of the letters A, B, and C.

Image provided.

Therefore, there are 6 permutations of the letters A, B, and C.

work out the area of a circle when the radius is 7cm given your answer in terms of pie

Answers

Answer:

49π cm²

Step-by-step explanation:

area = πr²

fill in r=7cm

Find the perimeter of the triangle

Answers

Answer:

=136

Step-by-step explanation:

Lets solve the triangle using the sine formula.

c/sine C=a/sine A

C= 180-(72+16)

=92°

61/Sin 92=a/sin 72

a=(61 sin 72)/sin 92

=58.0

Solving for b:

c/sin C= b/Sin B

61/sin 92= b/Sin 16

b=(61 Sin 16)/Sin 92

=16.82

Perimeter = 61 +58+ 16.82 = 135.82

Answer =136 to the nearest whole number.

The weights of steers in a herd are distributed normally. The standard deviation is
100lbs
100⁢lbs
and the mean steer weight is
1200lbs
1200⁢lbs
. Find the probability that the weight of a randomly selected steer is between
1000
1000
and
1369lbs
1369⁢lbs
. Round your answer to four decimal places.

Answers

Answer:

0.9317

Step-by-step explanation:

Standard deviation of the weights = [tex]\sigma[/tex]=100 lbs

Mean weight = u = 1200 lbs

We need to find the probability that the weight(x) of a randomly selected steer is between 1000 lbs and 1369 lbs i.e. P(1000 < x < 1369)

Since, weights follow the normal distribution we can use the z values to find the required weight. For this we have to convert both the values to z score. The formula for z scores is:

[tex]z=\frac{x-u}{\sigma}[/tex]

1000 converted to z scores is:

[tex]z=\frac{1000-1200}{100}=-2[/tex]

1369 converted to z scores is:

[tex]z=\frac{1369-1200}{100}=1.69[/tex]

So, we have to find the values from z table that lie between -2 to 1.69

P( 1000 < x < 1369 ) = P(-2 < z < 1.69)

P(-2 < z < 1.69) = P(z < 1.69) - P(z < -2)

From the z table:

P(z < 1.69) = 0.9545

P(z < -2) = 0.0228

So,

P(-2 < z < 1.69) = 0.9545 - 0.0228 = 0.9317

Thus,

P( 1000 < x < 1369 ) = 0.9317

From this we can conclude that:

The probability that the weight of a randomly selected steer is between 1000 lbs and 1369 lbs is 0.9317

Final answer:

The probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean of 1200lbs and standard deviation of 100lbs, is approximately 0.9326 or 93.26%.

Explanation:

To find the probability that the weight of a randomly selected steer is between 1000lbs and 1369lbs, given a normal distribution with a mean (μ) of 1200lbs and a standard deviation (σ) of 100lbs, we first convert the weights into z-scores.

The z-score for a value x is given by the formula:

z = (x - μ) / σ

Calculating the z-scores for both weights:

For 1000lbs: z = (1000 - 1200) / 100 = -2

For 1369lbs: z = (1369 - 1200) / 100 = 1.69

We then look up these z-scores in a standard normal distribution table or use a calculator with statistical functions to find the probabilities for each. The probability for a z-score less than -2 is approximately 0.0228, and for a z-score less than 1.69 is approximately 0.9554.

To find the probability that a steer's weight falls between 1000lbs and 1369lbs, we subtract the smaller probability from the larger probability:

Probability = P(z < 1.69) - P(z < -2) = 0.9554 - 0.0228 = 0.9326

Therefore, the probability that a steer weighs between 1000 and 1369lbs is 0.9326, or 93.26% when rounded to four decimal places.

find the slope and the y-intercept of the line 7x-2y=-8​

Answers

Answer:

slope = 7/2

y-int = 4

Step-by-step explanation:

parent formula is y=mx+b ; where m is slope and b is y-int.

begin by rewriting formula to isolate y ; 7x+8=2y ; divide bothe sides by 2 ; so

7/2 x+4=y. slope/m=7/2 and y-int/b=4

Sidney has 46,880 marbles to put into giant jars. She wants to put the same number of marbles in each jar with no extra marbles. How many jars could Sidney use?

Select all possible numbers:

4 , 2 , 10 , 5

Answers

Answer:

4 , 2 , 10 , 5

Step-by-step explanation:

46,880

Since this is an even number, we can divide by 2

46,880/2 =23440

Since this number ends in either a 0 or a 5 we can divide by 5

46880/5 =9376

Since the number is divisible by 2 and 5, we know it is divisible by 10

46880/10 =4688

The only number we need to check is 4

If the last 2 numbers are divisible by 4 then the number is divisible by 4

80/4 = 20  so the number is divisible by 4

46880/4 =11720

46880 is divisible by 4,2,10,5

Answer:

all of the are correct

Two events are disjointed. Find P(A or B), if P(A) = 1/7
and P(B) = 3/7.

1/7
3/7
4/7
2/7

Answers

Answer:

4/7

Step-by-step explanation:

P(A or B) when A and B are disjointed is P(A)+P(B)

P(A or B)=P(A)+P(B)

P(A or B)=1/7 +3/7

P(A or B)=4/7

The value of P(A or B) is 4/7 (3rd option)

What is the formula of P(A or B) of disjoint events ?

Let A and B be two disjoint events.

Then, probability of A is P(A) & probability of B is P(B).

In this case, the probability of A or B is the sum of P(A) & P(B)

∴ P(A or B) = P(A) + P(B)

What is the required probability ?

Given, P(A) = 1/7 & P(B) = 3/7

So, P(A or B) = P(A) + P(B)

                     = 1/7 + 3/7

                     = (1+3)/7

                     = 4/7

Required value of P(A or B) is 4/7

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-42.8451
Round the result to the nearest tenth and then to the nearest hundredth

Answers

Answer:

Tenth:-42.8

Hundredth: -42.85

To explain:

To the right of the decimal point every name of the place ends with -th.

If a number is bigger than 5 you round the number left to it by 1

If it's 4 or smaller you don't do anything.

The diagram shows a scale drawing of a rectangular banner with a scale of 1:30. Calculate
itu,
the actual length, in m, of the banner.
the area, in m', of the banner.​

The diagram showed a banner with the length of 4cm and width of 9cm.
Thank you

Answers

Answer:

Part 1) The actual length of the banner is [tex]1.2\ m[/tex]

Part 2) The area of the banner is [tex]3.24\ m^{2}[/tex]

Step-by-step explanation:

we know that

The scale of the drawing is [tex]\frac{1}{30}[/tex]

That means ----> 1 cm on the drawing represent 30 cm in the actual

Using proportion

Find out the actual dimensions of the banner

Let

L  the actual length of the banner

W the actual width of the banner

For a length of 4 cm in the drawing

[tex]\frac{1}{30}=\frac{4}{L}\\ \\ L=30*4\\ \\L=120\ cm[/tex]

Convert the actual length to meters

[tex]L=120/100=1.2\ m[/tex]

For a width of 9 cm in the drawing

[tex]\frac{1}{30}=\frac{9}{W}\\ \\ W=30*9\\ \\W=270\ cm[/tex]

Convert the actual width to meters

[tex]W=270/100=2.7\ m[/tex]

Find the area of the banner

[tex]A=1.2*2.7=3.24\ m^{2}[/tex]

What is the circumference of the circle shown below, given that the length of
AB (the minor arc) is 4?​

Answers

Answer:

A

Step-by-step explanation:

The following ratio is true for any circle

[tex]\frac{arc}{C}[/tex] = [tex]\frac{centralangle}{360}[/tex] ← C is circumference

[tex]\frac{4}{C}[/tex] = [tex]\frac{30}{360}[/tex] ( cross- multiply )

30C = 1440 ( divide both sides by 30 )

C = 48 → A

Answer:48

Step-by-step explanation:i got it right

factor the GCF: 12a^3b + 8a^2b^2 — 20ab^3

Answers

Answer:

GCF = 4ab

Step-by-step explanation:

We need to factor the GCF of

12a^3b+8a^2b^2-20ab^3

Finding the common term: 4ab

So, GCF = 4ab

Factoring the common term

12a^3b+8a^2b^2-20ab^3= 4ab(3a^2+2ab-5b^2)

The solutions to the inequality y> -3x + 2 are shaded on
the graph. Which point is a solution?
0 (0,2)
O (2,0)
0 (1,-2)
O (-2,1)

Answers

Answer:

(2,0)

Step-by-step explanation:

y> -3x + 2

Substitute the points into the inequality to see if they are a solution

(0,2)

2 > -3(0)+2

2 > 2  False

(2,0)

0> -3(2) + 2

0>-6+2

0> -4   True

(1,-2)

-2> -3(1) + 2

-2 > -3+2

-2 >-1  False

(-2,1)

1> -3(-2) + 2

1 >6+2

1>8  False

Which polynomial function has a leading coefficient of 1, roots –2 and 7 with multiplicity 1, and root 5 with multiplicity 2?

Answers

Answer:

Answer in factored form: [tex]P(x)=(x+2)(x-7)(x-5)^2[/tex]

Answer in standard form: [tex]P(x)=x^4-15x^3+61x^2+15x-350[/tex]

Step-by-step explanation:

I don't see your choices but I can still give you a polynomial fitting your criteria. I will give the answer in both factored form and standard form.

The following results are by factor theorem:

So if x=-2 is a zero then x+2 is a factor.

If x=7 is a zero then x-7 is a factor.

If x=5 is a zero then x-5 is a factor.  It says we have this factor twice.  I know this because it says with multiplicity 2.

So let's put this together.  The factored form of the polynomial is

A(x+2)(x-7)(x-5)(x-5)

or

[tex]A(x+2)(x-7)(x-5)^2[/tex]

Now A can be any number satisfying a polynomial with zeros -2 and 7 with multiplicity 1, and 5 with multiplicity 5.

However, it does say we are looking for a polynomial function with leading coefficient 1 which means A=1.

[tex](x+2)(x-7)(x-5)^2[/tex]

Now the factored form is easy.

The standard form requires more work (multiplying to be exact).

I'm going to multiply (x+2)(x-7) using foil.

First: x(x)=x^2

Outer: x(-7)=-7x

Inner: 2(x)=2x

Last: 2(-7)=-14

--------------------Adding.

[tex]x^2-5x-14[/tex]

I'm going to multiply [tex](x-5)^2[/tex] using formula [tex](u+v)^2=u^2+2uv+v^2[/tex].

[tex](x-5)^2=x^2-10x+25[/tex].

So now we have to multiply these products.

That is we need to do:

[tex](x^2-5x-14)(x^2-10x+25)[/tex]

I'm going to distribute every term in the first ( ) to

every term in the second ( ).

[tex]x^2(x^2-10x+25)[/tex]

[tex]+-5x(x^2-10x+25)[/tex]

[tex]+-14(x^2-10x+25)[/tex]

------------------------------------------ Distributing:

[tex]x^4-10x^3+25x^2[/tex]

[tex]+-5x^3+50x^2-125x[/tex]

[tex]+-14x^2+140x-350[/tex]

-------------------------------------------Adding like terms:

[tex]x^4-15x^3+61x^2+15x-350[/tex]

Answer:

f(x) = (x – 7)(x – 5)(x – 5)(x + 2)

Step-by-step explanation:

What is the factored form of 3x+24y?

Answers

Both 3 and 24 have 3 in common.  This means that you can factor a three out of this equation like so:

3(x + 8y)

If you distribute the three back into the equation then you would then get 3x + 24y (the equation before factoring)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

3 ( x + 8 y )

Step-by-step explanation:

Since 3 is the LCM ( lowest common multiple ) which goes into both numbers, it will go on the outside of the brackets. To get the insides of the brackets you have to divide the original expression by 3

3 ÷ 3 x = x

24 y ÷ 3 = 8 y

And our final factored form is 3 ( x + 8 y )

(4x-4) (3x+17)

The lines. intersect at point C. What is the value of X?

Answers

Answer:

(21, 80)

Step-by-step explanation:

We have the two lines y = 4x -4  and y = 3x + 17. The point 'C' will be given by the interception of them, as follows:

4x -4 = 3x + 17

Solving for 'x':

x = 21

Now, to find 'y' we have:

y = 4(21) -4 = 80

Therefore, they intercept at: (21, 80)

For this case we must find the value of "x":

We have that, by definition:

[tex]4x-4 = 3x + 17[/tex]

Because they are opposite the vertex.

Then, subtracting[tex]3x[/tex] on both sides we have:

[tex]4x-3x-4 = 3x-3x + 17\\x-4 = 17[/tex]

Adding 4 to both sides:

[tex]x = 17 + 4\\x = 21[/tex]

So, the value of x is 21

Answer:

[tex]x = 21[/tex]

. Pots
What is the solution to this equation?
x – 9 = 17
ОА. x= 28
Ов. х = 8
Ос. х = 26
OD. х = 12

Answers

Answer:

с. х = 26

Step-by-step explanation:

x – 9 = 17

Add 9 to each side

x – 9+9 = 17+9

x = 26

What’s x-2 = 3x-84
I just need this answered to be able to answer another equation.
30 points

Answers

Answer: x = 41

Step-by-step explanation: You need to isolate x. First, subtract x from each side. You will get:

-2 = 2x - 84

Next, add 84 to each side.

82 = 2x

Divide by 2 on each side.

X = 41

Answer:41

Step-by-step explanation:x-3x=-84+2

-2x=-82

X=-82/-2

X=41

For the following geometric sequence find the recursive formula: {-1, 3, -9, ...}.

Answers

Based on these first few terms, we can deduce that the next term is computed by switching the sign of the previous one, and multiplying it by 3: we start with -1, we switch the sign (1) and multiply by 3 (3); then again we switch the sign (-3) and multiply by 3 (-9), and so on.

Since switching sign is the same as multiplying by -1, we can compute every next term by multiplying the previous one by -3:

[tex]a_1 = -1\\a_2 = a_1\cdot(-3) = (-1)\cdot(-3)=3\\a_3 =a_2\cdot(-3)=3\cdot(-3)=-9[/tex]

So, the recursive formula is

[tex]a_n = -3a_{n-1}[/tex]

because it states precisely that the next term is -3 times the previous one.

In a population of 1000 individuals, 100 new individuals were born and 200
individuals died over the course of 1 year. Which equation shows how to
calculate the population growth rate of this population?
O
A. 0.10 0.20 = 0.02
O
B. 0.10 - 0.20 = -0.10
O
C. 0.20 +0.10 = 0.30
O
D. 0.20 - 0.10 = 0.10

Answers

Answer:

the answer to this question is b.

Answer:

The correct option is B.

Step-by-step explanation:

It is given that In a population of 1000 individuals, 100 new individuals were born and 200 individuals died over the course of 1 year.

We need to find the population growth rate of this population.

Rate of birth = [tex]\frac{100}{1000}=0.10[/tex]

Rate of death = [tex]\frac{200}{1000}=0.20[/tex]

The formula for rate of change is

Rate of change = Rate of birth - Rate of death

Rate of change = 0.10 - 0.20

Rate of change = -0.10

The required equation is 0.10 - 0.20 = -0.10.

Therefore, the correct option is B.

Factor completely. X^3+6x+x^2+6

Answers

Answer:

(x+1) (x^2+6)

Step-by-step explanation:

x^3+6x+x^2+6

Rearranging the order

x^3+x^2 + 6x+6

We can factor by grouping

Taking an x^2 from the first two terms and a 6 from the last two terms

x^2(x+1) +6(x+1)

Now we can factor out an (x+1)

(x+1) (x^2+6)

Please help me with this question

Answers

Answer:

I

Step-by-step explanation:

At least means greater than or equal to

a ≥ 10

That is a closed circle

We have a closed circle at 10

We have to be at least 10 years old

Closed circle at 10, line going to the right

Find volume of rectangular prism length(4x+3) width (x-6) height (2x-1)

Answers

Answer:

8x^3-46x^2-5x+18

Step-by-step explanation:

The volume of a rectangular prism is L*W*H where

L=length

W=width

H=height.

So we want to probably find the standard form of this multiplication because writing (4x+3)(x-6)(2x-1) is too easy.

Let's multiply (4x+3) and (x-6), then take that result and multiply it to (2x-1).

(4x+3)(x-6)

I'm going to use FOIL here.

First:  4x(x)=4x^2

Outer:  4x(-6)=-24x

Inner:  3(x)=3x

Last:   3(-6)=-18

---------------------------Add.

4x^2-21x-18

So we now have to multiply (4x^2-21x-18) and (2x-1).

We will not be able to use FOIL here because we are not doing a binomial times a binomial.

We can still use distributive property though.

(4x^2-21x-18)(2x-1)

=

4x^2(2x-1)-21x(2x-1)-18(2x-1)

=

8x^3-4x^2-42x^2+21x-36x+18

Now the like terms are actually already paired up we just need to combine them:

8x^3-46x^2-5x+18

Answer:

[tex]\large\boxed{8x^3-46x^2-15x+18}[/tex]

Step-by-step explanation:

The formula of a volume of a rectangular prism:

[tex]V=lwh[/tex]

l - length

w - width

h - height

We have l = 4x + 3, w = x - 6 and h = 2x - 1.

Substitute:

[tex]V=(4x+3)(x-6)(2x-1)[/tex]

use FOIL: (a + b)(c + d)

[tex]V=\bigg[(4x)(x)+(4x)(-6)+(3)(x)+(3)(-6)\bigg](2x-1)\\\\=(4x^2-24x+3x-18)(2x-1)\qquad\text{combine like terms}\\\\=(4x^2-21x-18)(2x-1)[/tex]

use the distributive property: a(b + c) = ab + ac

[tex]V=(4x^2-21x-18)(2x)+(4x^2-21x-18)(-1)\\\\=(4x^2)(2x)+(-21x)(2x)+(-18)(2x)+(4x^2)(-1)+(-21x)(-1)+(-18)(-1)\\\\=8x^3-42x^2-36x-4x^2+21x+18[/tex]

combine like terms

[tex]V=8x^3+(-42x^2-4x^2)+(-36x+21x)+18\\\\=8x^3-46x^2-15x+18[/tex]

use the formula to find the value of $400 invested in 4%

Answers

Answer:

Some part of the question is missing , you are requested to kindly recheck it once. There must be some time provided in the problem

Step-by-step explanation:

find the quotient of 226.84 round your answer to the nearest tenth​

Answers

Answer: 226.8

Step-by-step explanation:  Find the number in the tenth place 8 and look one place to the right for the rounding digit 4 . Round up if this number is greater than or equal to 5 and round down if it is less than 5 .

What is the x intercept of

f(x)=(x-7)^2

Answers

Answer:

The x-intercept is (7,0).

Step-by-step explanation:

See the graph below for explanation

What is the vertex of the graph of the function below?
y= x^2 - 8x+ 12
O A. (2,0)
O B. (4,0)
O C. (2,-4)
O D. (4,-4)​

Answers

Answer:

D. (4, -4)

Step-by-step explanation:

Convert to vertex form by completing the square.

For a polynomial y = x² + bx + c, first add and subtract (b/2)² to the polynomial.  Then factor.

Here, b = -8.  So (b/2)² = (-8/2)² = 16.

y = x² − 8x + 12

y = x²− 8x + 16 − 16 + 12

y = (x − 4)² − 16 + 12

y = (x − 4)² − 4

The vertex is (4, -4).

Final answer:

The vertex of the function y = x2 - 8x + 12 is found by first using the formula -b/2a to find the x-coordinate of the vertex, and then substituting that value into the equation to find the y-coordinate. This results in the vertex being at the point (4,-4).

Explanation:

The vertex of a quadratic function given in the form y = ax2 + bx + c is found using the formula -b/(2a) for the x-coordinate, and substituting that value into the equation to find the y-coordinate. In the given function y = x2 - 8x + 12, a is equal to 1, and b is equal to -8.

Using the vertex form, the x-coordinate of the vertex can be found by using -b/2a, or --8/(2*1), which equals 4. This becomes the x-coordinate of our vertex. Substituting x = 4 into our equation, we find y = (4)2 - 8*4 + 12 = -4. Therefore, the vertex of the given graph is at the point (4,-4), which corresponds to option D.

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If you buy a car for 15500 an average on an average a new car loses 11% of its value the moment that is driven off the lot once you driving the car back to your new car off the lot what is the value be

Answers

Answer:

$13,795

Step-by-step explanation:

15500/x=100/11

(15500/x)*x=(100/11)*x       - we multiply both sides of the equation by x

15500=9.0909090909091*x       - we divide both sides of the equation by (9.0909090909091) to get x

15500/9.0909090909091=x  

1705=x  

x=1705

now we have:  

11% of 15500=1705

what is 10.15384615 as a fraction?

Answers

Answer:

The answer is an attachment I hope it helps!!!

SOS I need help with this question


Equation: 2x^2 + 10x - 3x - 15

Step1: Factor completely (10 points)

step2: after the polynomial is factored, solve the zeroes of the function

step3: describe the end behavior of the graph

step4: will the vertex of the function be minimum or maximum function?

Answers

Answer:

1) (2x - 3)(x + 5)

2) 1.5, -5

3) Open upwards from both ends

4) Minimum

Step-by-step explanation:

Step 1:

The given polynomial is:

[tex]2x^{2}+10x-3x-15[/tex]

Taking out commons, we get:

[tex]2x(x+5)-3(x+5)\\\\ =(2x-3)(x+5)[/tex]

This is the factorized form of the polynomial.

Step 2:

The zeros of the functions occur when the function is equal to zero.

i.e.

[tex](2x-3)(x+5)=0\\\\ \text{According to the zero product property}\\\\ 2x-3=0, x+5=0\\\\ x =\frac{3}{2}=1.5, x = -5[/tex]

This means, the zeros of the polynomial are 1.5 and -5

Step 3:

The end behavior of a graph depends on its degree and the sign of leading coefficient. Since the degree is even and the coefficient is positive the graph of the polynomial will opens upwards from left and right side.

Step 4:

The given polynomial is a quadratic function with positive leading coefficient. Since it open vertically upwards, its vertex will be the lowest most point. So, the vertex will be the minimum of the function.

multiply (2x^2 + 3x - 6)(x - 1)

Answers

Answer:

2x^3 + x^2 - 9x + 6

Step-by-step explanation:

(2x^2 + 3x - 6)(x - 1)

2x^3 + 3x^2 - 6x - 2x^2 - 3x + 6

2x^3 + x^2 - 9x + 6

Other Questions
Before you enter an intersection on a green light, make sure _____. The number of users of the internet in a town increased by a factor of 1.01 every year from 2000 to 2010. The function below shows the number of internet users f(x) after x years from the year 2000:f(x) = 3000(1.01)xWhich of the following is a reasonable domain for the function? Read the excerpt from Raymond's Run.[My father] can beat me to Amsterdam Avenue with me having a two-fire-hydrant head start and him running with his hands in his pockets and whistling.Squeakys description of her father shows readers that sheknows she will never be as fast as her father.admires her fathers natural running ability.wishes her father was a more serious runner.likes that her father can beat her in a race. Every culture has its own views on what is expected in each stage of a persons life. The attitudes a person has as he or she goes through these stages is a result of____? How does the author's use of the term "japanese american" change over the course of the text This is my question hope you could help someone in the future because I dont have time to wait :) How many solutions does the following system of equations have A sample of gas (1.9 mol) is in a flask at 21 C and 697 mm Hg. The flask is opened and more gas is added to the flask. The new pressure is 775 mm Hg and the temperature is now 26 C. There are now ________ mol of gas in the flask. For copper, = 8.93 g/cm3 and M = 63.5 g/mol. Assuming one free electron per copper atom, what is the drift velocity of electrons in a copper wire of radius 0.625 mm carrying a current of 3 A? In January 2014, the polar vortex swept across the eastern US leading some media outlets to claim this was the coldest weather in decades in Baltimore between Jan 6 & Jan 8. It turns out that only 5 years prior, in 2009, Jan 15 Jan 17 were 5 degrees colder in Baltimore than the coldest temperatures in 2014. Why did these media outlets say it was the coldest weather in decades? Many statisticians say that it is a mistake to look at weather temperature records the way that media outlets looked at the Baltimore "record"; why do you think they say this is a "mistake"? The smooth muscle of the digestive viscera is served largely by the ________. (A) pelvic nerves.(B) cephalic plexus.(C) lumbar splanchnic nerves.(D) vagus (X) nerves. The clubhouse has a water tank from which hikers fill their water jugs before walking the trail. The tank is a 5-gallon cylindrical container with a height of 2 feet and a radius of 4 inches. Alex fills his 1-gallon jug from the clubhouse tank before going on a hike. If the 5-gallon tank was full, what was the height of the water in the tank after Alex filled the 1-gallon jug?(A) 1.6 inches(B) 4.8 inches(C) 19.2 inches(D) 964.6 inches A mass oscillates up and down on a vertical spring with an amplitude of 3 cm and a period of 2 s. What total distance does the mass travel in 16 seconds? Boyle's law states that volume is ____________. What is the area of the triangle formed from (0,-1), (0.4), and (4,-1)? Compute the torque about the origin of the gravitational force F--mgj acting on a particle of mass m located at 7-x+ yj and show that this torque is independent of the;y coordinate. A 641-C point charge is at the center of a cube with sides of length 0.47 m. What is the electric flux through one of the six faces of the cube? (Give your answer in scientific notation using N.m2/C as unit) The movement of electrons is what type of energy? A. Kinetic energy B. Magnetic energy C. Charge energy D. Electrical energy Find the general solution for the following homogeneous equations. PLEASE SHOW SOLUTIONS1) (xy+y2)dxx2dy=0 (hint: let u=y/x, so y=ux, dy=xdu+udx))2) 2x2ydx=(3x3+y3)dy. (hint: let v=x/y, so x=vy, dx=vdy+ydv) Lets suppose that a lender has established a 90% loan-to-value ratio cutoff as one of its primary underwriting criteria. If a borrower is willing to make a down payment of $125,000 on a home recently appraised at $550,000, what best describes the lenders decision on whether or not to approve the loan along this dimension?