The ordered pair (2, 1) is a solution of a direct variation equation. Write the equation and identify the constant of variation.

Answers

Answer 1
A direct variation equation takes the form "b = ka," where the k is the constant of variation. In this case, 1 (b) is one-half as large as 2 (a), so the constant will be 0.5. This would allow the equation to be written as "b = 0.5a," and the constant of variation in this equation is 0.5.

Related Questions

a store buys a baseball cap for $5 and sells it for $20. what is the profit

Answers

the answer is $15
20-5

Please help.. I got stuck on this question please help and explain

Sam earned $150 last week. Jay earned $130 last week. They combined their money and decided to donate ¼ of their total amount to a charity. Then, they spent 40% of the remaining amount at an amusement park. Jay claims that they only have 35% of their original combined total left.

Is jay right or wrong?

Answers

Jay is wrong about his claim
150 + 130 = 280 combined 
they donated 1/4 of the total amount....1/4(280) = 280/4 = 70....so now they have 280 - 70 = 210
then they spent 40%.....210 - 0.4(210) = 210 - 84 = 126..what they have left

35% of 280 = 0.35(280) = 98


Jay is not correct

Marisol is preparing a care package to send to her brother. The package will include a board game that weighs 4 lb and several 14 lb snack packs. The total weight of the care package must be less than 25 lb.

Drag and drop the answer into the box.
Question Answer
Which statement describes the solution to this inequality?


Marisol must send less than 1 snack pack.Marisol must send fewer than 21 snack packs.Marisol must send fewer than 84 snack packs.Marisol must send fewer than 100 snack packs.


Answers

4 + 1/4s < 25
1/4s < 25 - 4
1/4s < 21
s < 21 / (1/4)
s < 21 * 4/1
s < 84

Marisol must send fewer then 84 snack packs <=
So what we gotta do is isolate the variable by
writing it out like this
4 1/4 25 those are the numbers where those go are like this
4x - 1/4 < 25 then move on to the next line on here we write out
4x + 1/4 - 1/4 < 25 + 1/4 (The reason why i put + 1/4 is because you have to isolate the variable by doing addition as well And i always find it easier to convert the fractions to decimals then after you make that line you make the next one like this you have to add 1/4 to 4x then take it away (which is 4x) then put that to the side like this 4x ? ? then we need to find those two ?s by adding 25 and 1/4 (or o.25) which is 25.25 then we need to add that to the second answer 4x ? 25.25 when you have this you need to find out which one is bigger so it is 4x<25.25 (or 25 1/4) then we need to divide 4 and 25.25 to get 6.25 so
the answer is  x < 6.25 so c is your awnser

What is a polynomial with a single root at x = -8 and a double root at x = -2?

Answers

Sent a picture of the solution to the problem (s).

The polynomial equation will be x³ +12x² +36x+32 =0

What are the roots of a polynomial Equation ?

The roots of a polynomial equation is the value at which it will satisfy the quadratic equation , i.e. function (x) = 0 at the root .

It is given that x = -8 is a single root and

x = -2 is double root

x+8 = 0

(x+2 )(x+2)=0   (double root)

The polynomial equation will be

(x+8)(x+2 )(x+2 )=0

(x+8)( x² +4+4x) = 0

x³ +4x+4x²+8x²+32+32x = 0

x³ +12x² +36x+32 =0

Therefore the polynomial equation will be x³ +12x² +36x+32 =0

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Typographic errors in a text are either nonword errors (as when "the" is typed as "teh") or word errors that result in a real but incorrect word. Spell-checking software will catch nonword errors but not word errors. Human proofreaders catch 70% of word errors. You ask a fellow student to proofread an essay in which you have deliberately made 10 word errors. What is the smallest number of misses m with P(X ≥ m) no larger than 0.05? You might consider m or more misses as evidence that a proofreader actually catches fewer than 70% of word errors.

Answers

The probability that a proofreader who catches 70% of the word errors misses exactly 7 out of 10 will be 0.3504.

How to calculate the probability?

It should be noted that this is a binomial distribution.

From the information given, the human proofreaders catch 70% of word errors and a student was asked to proofread an essay in which you have deliberately made 10 word errors.

Here, n = 10

p = 0.3,

q = 1 - 0.3 = 0.7.

The probability will be:

= 1 - (10C0 × 0.3ⁿ × 0.7^10 + 10C1 × 0.3 × 0.7^9 + 10C2 × 0.3² × 0.7^8 + 10C3 × 0.3³ × 0.7^7)

= 1 - 0.6496

= 0.3504

In conclusion, the probability is 0.3504.

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Marina walks from the police station at (-10, -4) to her friend Marissa’s house at (3, -8). She stops half way at a fast food restaurant to buy a soda. What are the coordinates where she stops?

Answers

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -10}}\quad ,&{{ -4}})\quad % (c,d) &({{ 3}}\quad ,&{{ -8}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{3-10}{2}~~,~~\cfrac{-8-4}{2} \right)[/tex]

6578 divided 34

20\5

Answers

You have apparently shared two different problems.  In one case you divide 
6578 by 34, and in the other you divide 6589 by 25.

I arbitrarily choose to focus on the second:

       ______________
25  /        6589

25 goes into 65 twice, with a remainder of 15:

       ______2_____
25  /        6589
               50
          -------------
                 158                25 goes into 158 6 times, with a remainder of 8.

Can you now finish this long division?

You want to place a towel bar that is 10 1⁄4 inches long in the center of a door that is 26 1⁄3 inches wide. How far should you place the bar from each edge of the door?

Answers

bar is 10 1/4" so center would be  10 1/4 / 2 = 5 1/8"

door is 26 1/3" so center would be 26 1/3 / 2 =13 1/6

13 1/6 - 5 1/8 = 8 1/24 inches from the edge

find value of m=30 and n=18. m-n÷3=8

Answers

when m = 30

30 - n/3 = 8

-n/3 = -22
-n = -66
n = 66


when n = 18

m-18/3 = 8
m - 6 = 8
m = 8 + 6
m = 14

hope this helps

How did the forces of liberalism and nationalism affect events in the united states during the 1800s?

Answers

Liberalism lead to the Civil war because liberals believe everyone is born free, and nationalism united the Us make it one nation, indivisible

What is the reflection image of R across the y-axis?

(3, 2)

(–2, 0)

(0, 2)

(–3, –2)


Answers

reflection image of R across the y-axis is (3,2)
answer
(3, 2)

Answer: (3,2)

Step-by-step explanation:

From the given picture , it is given that the point R = (-3,2)

We know that the rule of reflection across y axis is :

[tex](x,y)\rightarrow\ (-x,y)[/tex] i.e.the polarity of x coorinate changes.

Therefore, the reflection image of R across the y-axis will be :-

[tex](-3,2)\rightarrow\ (3,2)[/tex]

Hence, the reflection image of R across the y-axis =(3,2)

How many binary digits does it take to represent the decimal number 2013?

Answers

2^10  = 1024  and 2013 - 1024 = 989

So there will be  10 + 1 = 11 digits Answer

It takes 11 binary digits to represent the decimal number 2013. Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point.

What is meant by decimal number?A decimal is a number with a whole and a fractional part. Decimal numbers are between integers and represent numerical value for whole plus some fraction of a whole. Decimals are numbers that have two parts: a whole number part and a fractional part separated by a decimal point. 12.5 is a decimal number, for example. (12)10 and (300)10 are two examples of decimal numbers. Thus, we can say that the Decimal Number System is the number system that uses the numbers 0 to 9 and has a base of 10, and each digit in this system has a power value of 10.

Therefore, the correct option is C) 11

The complete question is:

How many binary digits does it take to represent the decimal number 2013?

a) 16

b) 8

c) 11

d) 2013

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what is 62 1/2% converted as a fraction

Answers

It is 5/8, 62 1/2% is equivalent to 0.625, which is equivalent to 625/1,000. If you simplify 625/1,000, you get 5/8.
5/8 because you turn it to a decimal which is 0.625 then a fraction and simplify

Evaluate the line integral, where c is the given curve. (x + 9y) dx + x2 dy, c c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0)

Answers

[tex]\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=\int_C\langle x+9y,x^2\rangle\cdot\underbrace{\langle\mathrm dx,\mathrm dy\rangle}_{\mathrm d\mathbf r}[/tex]

The first line segment can be parameterized by [tex]\mathbf r_1(t)=\langle0,0\rangle(1-t)+\langle9,1\rangle t=\langle9t,t\rangle[/tex] with [tex]0\le t\le1[/tex]. Denote this first segment by [tex]C_1[/tex]. Then

[tex]\displaystyle\int_{C_1}\langle x+9y,x^2\rangle\cdot\mathbf dr_1=\int_{t=0}^{t=1}\langle9t+9t,81t^2\rangle\cdot\langle9,1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(162t+81t^2)\,\mathrm dt[/tex]
[tex]=108[/tex]

The second line segment ([tex]C_2[/tex]) can be described by [tex]\mathbf r_2(t)=\langle9,1\rangle(1-t)+\langle10,0\rangle t=\langle9+t,1-t\rangle[/tex], again with [tex]0\le t\le1[/tex]. Then

[tex]\displaystyle\int_{C_2}\langle x+9y,x^2\rangle\cdot\mathrm d\mathbf r_2=\int_{t=0}^{t=1}\langle9+t+9-9t,(9+t)^2\rangle\cdot\langle1,-1\rangle\,\mathrm dt[/tex]
[tex]=\displaystyle\int_0^1(18-8t-(9+t)^2)\,\mathrm dt[/tex]
[tex]=-\dfrac{229}3[/tex]

Finally,

[tex]\displaystyle\int_C(x+9y)\,\mathrm dx+x^2\,\mathrm dy=108-\dfrac{229}3=\dfrac{95}3[/tex]
Final answer:

To evaluate the given line integral, you need to parameterize the curve composed of two segments. Then, you solve the integrals along the two separate segments and take the sum.

Explanation:

To evaluate the line integral where the curve c consists of line segments from (0, 0) to (9, 1) and from (9, 1) to (10, 0) for the function (x + 9y) dx + x² dy, we need to parameterize the curve and solve the integral.

First, we parametrize the line segments. For the segment from (0, 0) to (9, 1), we have x = 9t and y = t for t in [0, 1]. For the segment from (9, 1) to (10, 0) let x = 9 + s and y = 1 - s for s in [0, 1].

Then, we integrate along the first and second segments separately with respect to t. For the first segment, the integral is ∫(9t + 9t) d(9t) + ∫(81t²) dt = ∫18t dt + ∫81t² dt. For the second segment, the integral is ∫(9 + s + 9(1 - s)) ds + ∫(81 + 2 * 9 * s + s²) d(1 - s) = ∫ds + ∫s² ds.

We then evaluate these integrals over the respective bounds, sum them up and that gives the line integral along the path described.

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You received 1⁄3 pound of candy from your grandmother, 1⁄2 pound of candy from your sister, but your best friend ate 1⁄5 pound of candy. How much candy do you have left?

Answers

1/3 + 1/2  = 2/6 + 3/6 = 5/6

5/6 - 1/5 = 25/30 - 6/30 = 19/30 pounds left

HELP ASAP PLEASE!!!!!!!!!!!!!!

Answers

Refer to the image attachment Figure 1 for the letter references. Hopefully the reference image is handy to keep track of all of the empty boxes.
The answers are given in Figure 2 which is also attached.
===================================================================================================================
Focus on the first Magic Square for now (the one in the top row, left side).
The middle row has 9+6+3 = 18 as the magic constant (aka magic sum). Every row, column and diagonal must add to this constant
A = 7 because the first column of values must add to 18
A+9+2 = A+11 = 18 leads to A = 7
----------
C = 10 since that solves 2+6+C = 18 (northeast diagonal)
----------
Solve the equation A+6+E = 18 for E to get E = 5 (plug in A = 7)
As a check, note how C+3+E = 10+3+5 = 18
---------- 
We know that A = 7 and C = 10 so B must be B = 1 since A+B+C = 7+1+10 = 18
----------
Similarly, 2+D+E = 18 and E = 5, so D must be 11. 
As a check, note how B+6+D = 1+6+11 = 18
----------
----------
In summary we have 
A = 7
B = 1
C = 10
D = 11
E = 5
See Figure 2 for the completed magic square
----------
Check:
Row1: 7+1+10 = 18
Row2: 9+6+3 = 18
Row3: 2+11+5 = 18
Column1: 7+9+2 = 18
Column2: 1+6+11 = 18
Column3: 10+3+5 = 18
NorthEast Diagonal: 2+6+10 = 18
NorthWest Diagonal: 7+6+5 = 18
As you can see, we get the same magic constant of 18
===================================================================================================================
Second Magic Square (Top Right)
For this magic square, the magic constant isn't known. So this is mainly a guess and check type of problem. This is what I got
F = 9
G = 6
H = 10
J = 12
K = 5
See Figure 2 for the completed magic square 
----------
Check:
Row 1: 11+4+9 = 24
Row 2: 6+8+10 = 24
Row 3: 7+12+5 = 24
Column 1: 11+6+7 = 24
Column 2: 4+8+12 = 24
Column 3: 9+10+5 = 24
NorthEast Diagonal: 7+8+9 = 24
NorthWest Diagonal: 11+8+5 = 24
===================================================================================================================
Third Magic Square at the very bottom
The magic constant is 12+6+7+9 = 34
----------
Bottom row: 13+3+S+16 = 34 which solves to S = 2
----------
Northeast Diagonal: 13+Q+7+4 = 34 which solves to Q = 10
----------
Second Column: 3+Q+6+M = 34 turns into 3+10+6+M = 34 after substitution and that solves to M = 15
----------
For values R, P, L and N, I couldn't figure out an algebraic way to solve for them. So I had to resort to trial and error (guess and check). This is what I got
R = 11
P = 8
L = 1
N = 14
----------
----------
In summary we have
L = 1
M = 15
N = 14
P = 8
Q = 10
R = 11
S = 2
See Figure 2 for the completed magic square
----------
Check:
Row 1: 1+15+14+4 = 34
Row 2: 12+6+7+9 = 34
Row 3: 8+10+11+5= 34
Row 4: 13+3+2+16 = 34
Column 1: 1+12+8+13 = 34
Column 2: 15+6+10+3 = 34
Column 3: 14+7+11+2 = 34
Column 4: 4+9+5+16 = 34
NorthEast Diagonal: 13+10+7+4 = 34
NorthWest Diagonal: 1+6+11+16 = 34

Of all numbers whose difference is 4​, find the two that have the minimum product.

Answers

Of all numbers whose difference is 4​, find the two that have the minimum product. 2 x2=4


The two numbers whose difference is 4 will be +2 and -2. The two have the minimum product is -4.

What is the number?

A number is a mathematical entity that can be used to count, measure, or name things. For example, 1, 2, 56, etc. are the numbers.

It is given that, there are two numbers whose difference is 4​ and it must have a minimum product.

We have to apply arithmetic operation operations in which we do the addition of numbers, subtraction, multiplication, and division. It has basic four operators that are +, -, ×, and ÷.

Suppose one number is x and the other x−4.

The minimum product is,

=x(x−4)

=x²−4x

Differentiate both sides to obtain minimum value,

=2x-4

2x=4

x=2

The other number is,

=x−4

=2-4

=-2

Thus, the two numbers whose difference is 4 will be +2 and -2. The two have the minimum product is -4.

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Monday’s high temperature was 5 degrees warmer than Sunday high temperature.tuesdays high temperature was eight degrees colder than Monday high temperature. How does Sunday’s high temperature compare to tuesdays

Answers

Sunday's high temp was 3 degrees warmer than Tuesdays

Answer: It means the high temperature of Sunday is 3 degrees warmer than the high temperature of Tuesday.

Step-by-step explanation:

Let the temperature on Sunday be 'x'.

So, Temperature of Monday would be

[tex]x+5[/tex]

Temperature of Tuesday would be

[tex]x+5-8\\=x-3[/tex]

So, Comparing the  Sunday's high temperature to Tuesday's temperature.

[tex]x-3[/tex]

It means the high temperature of Sunday is 3 degrees warmer than the high temperature of Tuesday.

Evaluate 11x -4 when x = -4

Answers

Just replace x=-4 in the equation

11x - 4, x = -4

11(-4) - 4 = -44 - 4 = -48

Hope it helped!
substitute -4 for x
11x-4=-44

If µ = 400 and s = 100 the probability of selecting at random a score less than or equal to 370 equals ____.

Answers

The probability of selecting at random a score less than or equal to 370 is approximately 0.3821.

To find the probability of selecting at random a score less than or equal to 370 from a normal distribution with a mean [tex](\( \mu \))[/tex] of 400 and a standard deviation [tex](\( s \))[/tex] of 100, we can use the z-score formula and the standard normal distribution table.

The z-score formula is given by:

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

Where:

- x is the value of the random variable (370 in this case)

- [tex]\( \mu \)[/tex] is the mean (400)

- s is the standard deviation (100)

Substituting the given values into the formula:

[tex]\[ z = \frac{370 - 400}{100} = -0.3 \][/tex]

Now, we look up the probability corresponding to z = -0.3 in the standard normal distribution table. The probability of selecting a score less than or equal to 370 is the cumulative probability up to z = -0.3.

From the standard normal distribution table, the cumulative probability corresponding to z = -0.3 is approximately 0.3821.

Therefore, the probability of selecting at random a score less than or equal to 370 is approximately 0.3821.

56of the 90pets in the pet show are cats 4/5of the cats are calico cats. What fraction of the pets are calico cats?

Answers

To get the answer, we can divide 56 by 5 to find one fifth of the cats. Then, we can multiply this number to get four fifths of the cats. Then, we put this number over 90 since there is 90 pets in the entire show. Then, this answer ends up being about half all of the pets are calicos.

A theater group made appearances in two cities. The hotel charge before tax in the second city was $500 lower than in the first. The tax in the first city was 3.5% , and the tax in the second city was 7.5% . The total hotel tax paid for the two cities was $347.50 . How much was the hotel charge in each city before tax?

Answers

is pretty much the same as before, so without much fuss

a = charges before tax on first city

b = charges before tax on second city

how much is 3.5% of a?   (3.5/100) * a, 0.035a.

how much is 7.5% of b?  (7.5/100) * b, 0.075b.

the taxes for both cities, summed up to 347.50

so, 0.035a + 0.75b = 347.50

we also know that, whatever "a" may be, the second city charged $500 less, so b = a - 500.

[tex]\bf \begin{cases} \boxed{b}=a-500\\ 0.035a+0.075b=347.5\\ --------------\\ 0.035a+0.075\left( \boxed{a-500} \right)=347.5 \end{cases} \\\\\\ 0.035a+0.075a-37.5=347.5\implies 0.110a=385 \\\\\\ a=\cfrac{385}{0.11}\implies a=3500[/tex]

how much did the second city charge?  well, b = a - 500.

A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge. Each support makes a 65∘ angle with a short vertical support.

Answers

The Answer is x=29.6 feet

How do I find Primefactor of 150

Answers

150

2  75

     3  25 

          5  5  
           
                5  1


2 * 3 * 5* 5
A prime factor is a factor that cannot be factored further.

Starting with 150, determine some of the factors:  150 = 15(10)

Continue:   3     5       2      5      = {2, 3, 5}  None of these can be factored, so the prime factors of 150 are {2, 3, 5}.   Of course, you could include 1 as a prime factor, in which case the prime factor list would be {1, 2, 3, 5}.

What is (f * g * h)(x) Refer the the image below.

Answers

[tex]\bf \begin{cases} f(x)=\sqrt{x+7}\\ g(x)=4x\\ h(x)=x^2\\ (f\circ g\circ h)(x)=f(~~g(~~h(x)~~)~~) \end{cases}\\\\ -------------------------------\\\\ g(~~h(x)~~)=4\boxed{h(x)}\implies g(~~h(x)~~)=4\boxed{x^2} \\\\\\ f(~~g(~~h(x)~~)~~)=\sqrt{\boxed{g(~~h(x)~~)}+7} \\\\\\ f(~~g(~~h(x)~~)~~)=\sqrt{\boxed{4x^2}+7}[/tex]

Find 10-3 write the substraction fact two ways

Answers

10-7
13-7
 the substraction fact two ways.
There is 10 - 3 = 7

And 10 + (-3) = 7

Product of prime factors for 60 = 2x2x3x5
How do i write this in index form?
I have tried by simplifying so it is 2 to the power of 2 x 3 x 5
It stills says it is incorrect, anyone know?

Answers

The prime factors of 60
60 = 2,2,3,5
Index Form =  [tex]2^2 \times 3 \times 5[/tex]
They might want something like below for the index form
[tex]2^2 \times 3^1 \times 5^1[/tex]
Final answer:

The correct index form for the product of prime factors of 60, which is 2x2x3x5, is 2^2 x 3 x 5.

Explanation:

The product of prime factors for 60 is indeed 2x2x3x5. To write this in index form, we group the same numbers together and count how many there are. Then we use the base and exponent form to write it. Here, 2 is repeated twice. So, 2x2 can be written as 2^2. The primes 3 and 5 are each given once, so, we do not write powers for them. Therefore, the correct index form is 2^2 x 3 x 5.

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Which quantity is proportional to 15⁄3?

Answers

Porportional to 15/3 is 5/1 which would then equal 5

The answer is 5 because 15/3=5


HECTOR PLANTED 185 FLOWERS IN 2 DAYS THERE WERE 5 VOLUNTEERS INCLUDING HECTOR WHO EACH PLANTED ABOUT THE SAME NUMBER OF FLOWERS ABOUT HOW MANY FLOWERS DID THEY PLANT

Answers

The answer is very simple each had planted 37 flowers

If you work 37.5 hours per week at $10.65 per hour, how much is your gross pay for a two-week period? (Round off your answer to the nearest cent.)

Answers

it is 798.75 without rounding off the nearest cent.
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