Mathematics College

Chen is checking a division problem by doing the following:

152
× 4
______

+ 2
______

What problem is Chen checking?

Answers

Answer 1
That "+2" is the remainder of a division.  Note that 152 times 4 is 608.
Dividing 608 by 4 results in 152 with no remainder.
Dividing 610 by 4 results in 152 with the remainder 2.
                                                                   ____
Chen is checking the division problem  4 /  610   .

Related Questions

Find the minimum and maximum of f(x,y,z)=x^2+y^2+z^2 subject to two constraints, x+2y+z=4 and x-y=8.

Answers

The Lagrangian for this function and the given constraints is

[tex]L(x,y,z,\lambda_1,\lambda_2)=x^2+y^2+z^2+\lambda_1(x+2y+z-4)+\lambda_2(x-y-8)[/tex]

which has partial derivatives (set equal to 0) satisfying

[tex]\begin{cases}L_x=2x+\lambda_1+\lambda_2=0\\L_y=2y+2\lambda_1-\lambda_2=0\\L_z=2z+\lambda_1=0\\L_{\lambda_1}=x+2y+z-4=0\\L_{\lambda_2}=x-y-8=0\end{cases}[/tex]

This is a fairly standard linear system. Solving yields Lagrange multipliers of [tex]\lambda_1=-\dfrac{32}{11}[/tex] and [tex]\lambda_2=-\dfrac{104}{11}[/tex], and at the same time we find only one critical point at [tex](x,y,z)=\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)[/tex].

Check the Hessian for [tex]f(x,y,z)[/tex], given by

[tex]\mathbf H(x,y,z)=\begin{bmatrix}f_{xx}&f_{xy}&f_{xz}\\f_{yx}&f_{yy}&f_{yz}\\f_{zx}&f_{zy}&f_{zz}\end{bmatrix}=\begin{bmatrix}=\begin{bmatrix}2&0&0\\0&2&0\\0&0&2\end{bmatrix}[/tex]

[tex]\mathbf H[/tex] is positive definite, since [tex]\mathbf v^\top\mathbf{Hv}>0[/tex] for any vector [tex]\mathbf v=\begin{bmatrix}x&y&z\end{bmatrix}^\top[/tex], which means [tex]f(x,y,z)=x^2+y^2+z^2[/tex] attains a minimum value of [tex]\dfrac{480}{11}[/tex] at [tex]\left(\dfrac{68}{11},-\dfrac{20}{11},\dfrac{16}{11}\right)[/tex]. There is no maximum over the given constraints.

A triangle has the side lengths 5, 7, and 11. Which term best describes the triangle? A) acute B) equiangular C) equilateral D) obtuse

Answers

Answer:

D) Obtuse

Step-by-step explanation:

Find the minimum and maximum of f(x, y, z) = y + 4z subject to two constraints, 2x + z = 4 and x2 + y2 = 1. g

Answers

[tex]L(x,y,z,\lambda_1,\lambda_2)=y+4z+\lambda_1(2x+z-4)+\lambda_2(x^2+y^2-1)[/tex]

[tex]L_x=2\lambda_1+2\lambda_2 x=0\implies\lambda_1+\lambda_2x=0[/tex]
[tex]L_y=1+2\lambda_2y=0[/tex]
[tex]L_z=4+\lambda_1=0\implies\lambda_1=-4[/tex]
[tex]L_{\lambda_1}=2x+z-4=0[/tex]
[tex]L_{\lambda_2}=x^2+y^2-1=0[/tex]

[tex]\lambda_1=-4\implies \lambda_2x=4\implies\lambda_2=\dfrac4x[/tex]
[tex]1+2\lambda_2y=0\implies\lambda_2y=-\dfrac12\implies8y=-x[/tex]

[tex]x^2+y^2=1\implies (-8y)^2+y^2=65y^2=1\implies y=\pm\dfrac1{\sqrt{65}}[/tex]
[tex]y=\pm\dfrac1{\sqrt{65}}\implies x=\mp\dfrac8{\sqrt{65}}[/tex]
[tex]2x+z=4\implies z=4\pm\dfrac{16}{\sqrt{65}}[/tex]

We have two critical points to consider: [tex]\left(-\dfrac8{\sqrt{65}},\dfrac1{\sqrt{65}},4+\dfrac{16}{\sqrt{65}}\right)[/tex] and [tex]\left(\dfrac8{\sqrt{65}},-\dfrac1{\sqrt{65}},4-\dfrac{16}{\sqrt{65}}\right)[/tex].

At these points, we respectively have a maximum of [tex]16+\sqrt{65}[/tex] and a minimum of [tex]16-\sqrt{65}[/tex].

Samir works 15 hours for every 19 hours that Mitul works. If x represents the number of hours that Mitul works and y represents the hours that Samir works, which equation correctly models this relationship?

Answers

Samir works 15 out of Mitul's 19...

15/19

y=15/19x

Answer:

[tex]y=\frac{15}{19}x[/tex]

Step-by-step explanation:

Let

x-----> the number of hours that Mitul works

y-----> the hours that Samir works

by proportion

[tex]\frac{x}{y}=\frac{19}{15}\\ \\19y=15x\\ \\y=\frac{15}{19}x[/tex]

The table below shows the results of a survey in which 141141 men and 145145 women workers ages 25 to 64 were asked if they have at least one​ month's income set aside for emergencies. complete parts​ (a) through​ (d). men women total less than one​ month's income 6565 8484 149149 one​ month's income or more 7676 6161 137137 total 141141 145145 286286 ​(a) find the probability that a randomly selected worker has one​ month's income or more set aside for emergencies. the probability is nothing. ​(round to the nearest thousandth as​ needed.) ​(b) given that a randomly selected worker is a​ male, find the probability that the worker has less than one​ month's income. the probability is nothing. ​(round to the nearest thousandth as​ needed.) ​(c) given that a randomly selected worker has one​ month's income or​ more, find the probability that the worker is a female. the probability is nothing. ​(round to the nearest thousandth as​ needed.) ​(d) are the events​ "having less than one​ month's income​ saved" and​ "being male" independent or​ dependent? independent dependent

Answers

Final answer:

The probability that a randomly selected worker has one month's income or more set aside for emergencies is approximately 0.479. Given that a randomly selected worker is a male, the probability that the worker has less than one month's income is approximately 0.460. Given that a randomly selected worker has one month's income or more set aside for emergencies, the probability that the worker is a female is approximately 0.446. The events 'having less than one month's income saved' and 'being male' are independent.

Explanation:

To find the probability that a randomly selected worker has one month's income or more set aside for emergencies, we need to divide the number of workers with one month's income or more by the total number of workers. According to the table, there are 76 men and 61 women with one month's income or more, for a total of 137 workers. The total number of workers is 286. So the probability is 137/286, which is approximately 0.479.

Given that a randomly selected worker is a male, we need to find the probability that the worker has less than one month's income set aside for emergencies. According to the table, there are 65 men with less than one month's income. The total number of men is 141. So the probability is 65/141, which is approximately 0.460.

Given that a randomly selected worker has one month's income or more set aside for emergencies, we need to find the probability that the worker is a female. According to the table, there are 61 women with one month's income or more. The total number of workers with one month's income or more is 137. So the probability is 61/137, which is approximately 0.446.

The events 'having less than one month's income saved' and 'being male' are independent. To confirm independence, we need to check if the probability of both events occurring is equal to the product of their individual probabilities. In this case, the probability of having less than one month's income saved is 65/286 and the probability of being male is 141/286. The probability of both events occurring is (65/286) * (141/286), which is approximately 0.126. This is equal to the product of their individual probabilities, confirming that the events are independent.

what is the prime factorization of 2^3x3x5^2

Answers

2^3x3x5^2
= 8 x 3 x 25
= 600
25 :D hope this helped...!!!

If I didn't try 600 As an answer bro!


bye

Danny charges 35 dollars for 3 hours of swimming lessons. Martin charges 24 dollars for 2 hours of swimming lessons. Who offers a better deals?

Answers

Danny does because 35/3 = 11 and 2/3 an hour. Martin offers 12 an hour because 24/2 =12

Michael started a savings account with $300. After 4 weeks, he had $350 dollars, and after 9 weeks, he had $400. What is the rate of change of money in his savings account per week?

Answers

The rate is not constant be cause 1 is equal to 12.5 and the other is equal to 11.111

True or false. If (7x+4) is a factor of some polynomial function F, then 4/7 is a zero of F. Please help!

Answers

-4/7 is a root of F, if we replace x by -4/7 in F, we will get 0

False, If (7x+4) is a factor of some polynomial function F, then - 4/7 is a zero

What is a factor of a polynomial?

We know that if x = a is one of the roots of a given polynomial x - a = 0 is a factor of the given polynomial.

To confirm if x - a = 0 is a factor of a polynomial we replace f(x) with f(a) and if the remainder is zer then it is confirmed that x - a = 0 is a factor.

Given (7x + 4) is a factor of a polynomial function F.

Then, 7x + 4 = 0.

7x = -4.

x = - 4/7 is a root of the polynomial F or a zero of the polynomial F.

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which of these is the absolute value parent function?

A. f(x) = |x| – 2
B. f(x) = |x|
C. f(x) = |2x|
D. f(x) = |x| + 1

Answers

The answer is B. f(x) = |x|

Answer:

The correct option is B. The absolute value parent function is f(x) = |x|.

Step-by-step explanation:

The absolute parent function is a function where

[tex]f(x)=x[/tex] and [tex]f(-x)=x[/tex]

The graph of absolute function is v-shaped and vertex of the function is (0,0).

According to these conditions the absolute value parent function is

f(x) = |x|

The function f(x) = |x| – 2 shifts 2 units down.

The function f(x) = |2x| stretch by factor 2.

The function f(x) = |x| + 1 shifts 1 units up.

Therefore the correct option is B.

What is the equation of the line that passes through
(10, 4)
and is perpendicular to
5x−y=3

Answers

Solve equation for y.

5x - y = 3

-y = -5x + 3

y = (-5x + 3)/(-1)

y = 5x - 3

The slope for this equation is 5.

The slope of the equation we want is the negative reciprocal of 5.

Let m = slope of equation we want.

m = -1/5

We are given the point (10,4).

Plug both into the point-slope formula.

y - 4 = (-1/5)(x - 10)

y - 4 = (-1/5)x + 2

y = (-1/5)x + 2 + 4

The equation we want is

y = (-1/5)x + 6

Did you follow?

The ruby- throated hummingbird has a wing beat of about 200 beats per second. About how many wings beats would a huming bird have in 3 minutes

Answers

Well 200 beats per second is 12,000 beats a minute times 3 for 3 minutes is 36,000 beats every three minutes

there are 60 seconds in one minute
200 beats per second
200 x 60 = 12000 beats per minute

Then multiply 12000 by 3

36000 wing beats in 3 minutes

hope this helps

Write the expression as the sine, cosine, or tangent of an angle. cos 8x cos 2x - sin 8x sin 2x

Answers

Sum and Difference Formula for Cosine: cos(α±β)= cosαcosβ ∓ sinαsinβ
cos(8x+2x)=cosαcosβ-sinαsinβ
cos(10x)=cosαcosβ-sinαsinβ

Answer:

 cos (A - B) =  cos 6 x

Step-by-step explanation:

given equation,

     = cos 8 x . cos 2 x - sin 8 x . sin 2 x

   using identity

cos (A - B)  = cos (A) . cos(B) -  sin (A) . sin(B)...................(1)

cos 8 x . cos 2 x - sin 8 x . sin 2 x......................................(2)

comparing both the equation (1) and (2)

we get ,

A = 8 x         B = 2 x

hence, from the above identity we can see that

cos (A - B)  = cos (8 x - 2 x)

 cos (A - B) =  cos 6 x

You have 900-grams of an an unknown radioactive substance that has been determined to decay according to D ( t ) = 900 e − 0.002415 ⋅ t D ( t ) = 900 e - 0.002415 ⋅ t where t t is in years. How long before half of the initial amount has decayed?

It will take __ years for half of the initial amount to decay. (Round to 1 decimal place)

Answers

now, the initial amount is 900 grams, so half of that will be 450 grams.

so, how long will it be, for D(t) to turn to 450 grams?

[tex]\bf D(t)=900e^{-0.002415t}\implies 450=900e^{-0.002415t} \\\\\\ \cfrac{450}{900}=e^{-0.002415t}\implies \cfrac{1}{2}=e^{-0.002415t}\\\\ -------------------------------\\\\ \textit{Logarithm Cancellation Rules}\\\\ log_{{ a}}{{ a}}^x\implies x\qquad \qquad {{ a}}^{log_{{ a}}x}=x\\\\ -------------------------------\\\\[/tex]

[tex]\bf log_e\left( \frac{1}{2} \right)=log_e\left( e^{-0.002415t} \right)\implies log_e\left( \frac{1}{2} \right)=-0.002415t \\\\\\ \cfrac{ln\left( \frac{1}{2}\right)}{-0.002415}=t\implies 287.0174661 \approx t[/tex]

Kelly read 30 pages of her 300 page book on 6 hours at this rate how long will it take her to read the entire book

Answers

Take 300 and divide it by the number of pages already read.

300 / 30 = 10

Now multiply this by the number of hours required to read the initial 30 pages.

10 x 6 = 60

So, since it takes Kelly 6 hours to read 30 pages, it should take Kelly 60 hours to read the 300 page book.
It would take Kelly 60 hours to read the whole book

Texasxhic101.
I am adding you to help me

Answers

It would be the number of observations is 15.

The median of the data is not 3. It's four, because both sides are symmetrical and therefore the number in the very center is the median, or 4.

The mean of the data is not 3, as again, it is symmetrical, so therefore the number in the very center is the mean, 4 again.

The range is the max - min, or 4, which is not 5.

If we count the total number of observations, 2 + 3 + 5 + 3 + 2 = 15, then we know the last one is correct.

Find each percentage decrease. round to the nearest percentage from 16 bagels to 0 bagels

Answers

To solve this problem:

The formula would be: New Value – Old Value)/Old Value] x 100 or in the form of variable it would be: [(B-A)/A] x 100 = Answer.

 

So plugging in the information given in our problem it would be:

0 – 16 / 16 x 100 = percent of change

0/16 x 100 = 0%

 

The answer is 0%

Find dy/dx by implicit differentiation. 3x + y = 8 + x2y2

Answers

3 +dy/dx = 0+ 2x²ydy/dx + 2xy²
dy/dx - 2x²ydy/dx = 2xy² -3
(1 - 2x²y) dy/dx = (2xy²-3)/(1-2x²y)
Final answer:

To find dy/dx by implicit differentiation, differentiate both sides of the equation with respect to x, apply the chain rule and product rule, isolate the terms involving dy, and simplify the equation to find dy/dx.

Explanation:

To find dy/dx by implicit differentiation, we need to differentiate both sides of the equation with respect to x. Using the chain rule and product rule, we can simplify the equation and solve for dy/dx. Starting with 3x + y = 8 + x^2y^2:

Step 1: Differentiate each term with respect to x.

Step 2: Apply the chain rule and product rule to simplify the equation.

Step 3: Solve for dy/dx by isolating the terms involving dy.

Step 4: Simplify the equation and rearrange to get dy/dx.

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T Shirt sore keeps 7 white T-Shirts on the shelves for every 3 purple T- Shirts on the shelve how many white T-Shirts on the shelve if 15 purple T-Shirts on the shelve. Show how you get the answer in long form

Answers

I think the answer is 35 because:
[tex]15 \div 3 = 5 \\ 5 \times 7 = 35[/tex]
THE OTHER WAY I DID IT WAS;
[tex]3 + 3 + 3 + 3 + 3 = 15 [/tex]
I ADDED IT 5 TIMES AND GOT 15
[tex]7 + 7 + 7 + 7 + 7 = 35[/tex]
I ADDED IT 5 TIMES AND GOT 35



Simplify.

9y+11z+7y−4z

What is the answer?

A. 23yz
B. 2y + 7z
C. 16y + 7z
D. 16y + 15z

Answers

Answer:

C.  (16y + 7z)

Step-by-step explanation:

9y + 11z + 7y - 4z

1. Simplify the y's: 9y + 7y = 16y

16y + 11z - 4z

2. Simplify the x's: 11z - 4z = 7z

16y + 7z

Answer:

16y+7z

Step-by-step explanation: no thanks im good

a plumber charges a base fee of $55 for a service call plus $35 per hour for each hour worked during the service call the relationship between the total price of the service called and the number of hours worked

Answers

Final answer:

The relationship between the total price and the number of hours worked can be represented by a linear equation. The equation is y = 35x + 55, where y represents the total price and x represents the number of hours worked.

Explanation:

The relationship between the total price of the service call and the number of hours worked can be represented by a linear equation. We can use the formula y = mx + b, where y represents the total price, x represents the number of hours worked, m represents the hourly fee, and b represents the base fee.

In this case, the plumber charges a base fee of $55 and $35 per hour. So the equation that expresses the total price is y = 35x + 55.

The independent variable in this situation is the number of hours worked, which is x. The dependent variable is the total price, which is y. The y-intercept of the equation is 55, which represents the base fee. The slope of the equation is 35, which represents the hourly fee. The y-intercept (b) is the point where the line intersects the y-axis, and the slope (m) determines how steep the line is.

A farmer owns 42 acres of land, of the 42 acres, only 85% can be farmed. How many acres are available for farming?

Answers

Answer: 35.7

How?

Simple. An easy trick I use is by dividing the number by 100, and multiplying by the percent. 

So 42/100 x 85 = 35.7

order the set of numbers from least to greatest
11/20, 1/2, 0.51



a. 0.51, 11/20, 1/2


b. 1/2, 0.51/, 11/20

c. 1/2, 11/20, 0.51

d. 0.51, 1/2, 11/20

Answers

11/20 = 55/100 = 0.55
1/2 = 50/100 = 0.50
0.51 

1/2. 11/20, 0.51  (least to greatest)

C is your answer

hope this helps

Answer:  Option 'b' is correct.

Step-by-step explanation:

Since we have given that

[tex]\frac{11}{20},\frac{1}{2},0.51[/tex]

Now, we have to arrange the set of numbers from least to greatest.

So, for this we have to make the denominator same ,

[tex]\frac{11\times 5}{20\times 5}=\frac{55}{100}[/tex]

Similarly,

[tex]\frac{1\times 50}{2\times 50}=\frac{50}{100}[/tex]

Similarly,

[tex]\frac{51}{100}[/tex]

Numbers In increasing order :

[tex]\frac{50}{100},\frac{51}{100},\frac{55}{100}\\\\\frac{1}{2},0.51,\frac{11}{20}[/tex]

Hence, Option 'b' is correct.

What is the relationship between 0.04 and 0.004?

Answers

0.04 is 10x greater than 0.004

hope this helps
I believe 0.04 is 10x larger than 0.004. I know this because 0.04^-10 = 0.004.

Hope this helped!

Evaluate the expression shown for x=12 -5/6×+7

Answers

Evaluate the expression shown for x=12 -5/6×+7

-5/6(12)+7
-10+7=-3
-3

Answer:

-3

Step-by-step explanation:

The given expression is

[tex]-\frac{5}{6}x+7[/tex]

We need to find the value of given expression for x=12.

Substitute x=12 in the given expression.

[tex]-\frac{5}{6}(12)+7[/tex]

Cancel out the common factors.

[tex]-5\times 2+7[/tex]

After multiplication, we get

[tex]-10+7[/tex]

After subtraction, we get

[tex]-3[/tex]

Therefore, the value of given expression for x=12 is -3.

Let x be a random variable that takes values from 0 to 9 with equal probability 1=10. find the pmf of the random variable y = x mod (3).

Answers

We have [tex]y\in\{0,1,2\}[/tex], and for each possible outcome we can determine the corresponding probability using the fact that [tex]X[/tex] is uniformly distributed among [tex]x\in\{0,1,\ldots,9\}[/tex].

[tex]y=\begin{cases}0&\text{for }x\in\{0,3,6,9\}\\1&\text{for }x\in\{1,4,7\}\\2&\text{for }x\in\{2,5,8\}\end{cases}[/tex]

[tex]\implies\mathbb P(Y=y)=\begin{cases}\dfrac4{10}=\dfrac25&\text{for }y=0\\\\\dfrac3{10}&\text{for }y=1\\\\\dfrac3{10}&\text{for }y=2\end{cases}[/tex]
Final answer:

The pmf of the random variable y = x mod (3) is: P(y=0) = 0.4, P(y=1) = 0.3, and P(y=2) = 0.3.

Explanation:

The random variable y can take on the values 0, 1, and 2, since those are the possible remainder values when x is divided by 3. We need to find the probability mass function (pmf) of y, which represents the probabilities of each possible value of y. The pmf of y can be calculated by finding the probability of each possible value of y based on the probability distribution of x and dividing it by the total number of possible values of x. Since x takes values from 0 to 9 with equal probability, the pmf of y is:

P(y=0) = P(x=0) + P(x=3) + P(x=6) + P(x=9) = 1/10 + 1/10 + 1/10 + 1/10 = 4/10 = 0.4

P(y=1) = P(x=1) + P(x=4) + P(x=7) = 1/10 + 1/10 + 1/10 = 3/10 = 0.3

P(y=2) = P(x=2) + P(x=5) + P(x=8) = 1/10 + 1/10 + 1/10 = 3/10 = 0.3

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G use lagrange multipliers to find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the given plane.x + 9y + 8z = 27

Answers

This basically comes down to maximizing [tex]xyz[/tex] subject to [tex]x+9y+8z=27[/tex] and enforcing [tex]x,y.z>0[/tex]. We have the Lagrangian

[tex]L(x,y,z,\lambda)=xyz+\lambda(x+9y+8z-27)[/tex]

with partial derivatives (set equal to 0 to find critical points)

[tex]\begin{cases}L_x=yz+\lambda=0\\L_y=xz+9\lambda=0\\L_z=xy+8\lambda=0\\L_\lambda=x+9y+8z-27=0\end{cases}[/tex]

Solving the first equation for [tex]\lambda[/tex] gives [tex]\lambda=-yz[/tex]. Substituting this into the next two equations, we have

[tex]xz-9yz=0\implies z(x-9y)=0\implies x=9y[/tex]
[tex]xy-8yz=0\implies y(x-8z)=0\implies x=8z[/tex]

Now

[tex]x+9y+8z=27\implies x+x+x=3x=27\implies x=9[/tex]
[tex]x=9y\implies y=1[/tex]
[tex]x=8z\implies z=\dfrac98[/tex]

So the vertex of the cuboid in the given plane that maximizes the cuboids volume is [tex](x,y,z)=\left(9,1,\dfrac98\right)[/tex], giving a volume of [tex]\dfrac{81}8[/tex].

How much force is required to push a 54-pound sofa across a carpeted floor?

Answers

Sounds like a problem from Physics.  The force required to push a 54 lb sofa across a carpeted floor is most likely LESS than 54 lb.  It depends upon the amount of friction between the bottoms of the sofa legs and the carpet.  In a typical Physics problem, you'd be given the "coefficient of dynamic friction" to assist your determination of how much force is required to push the sofa across the carpet.

3x+y=5
y=2x
Substitution method

Answers

Substitute 2x as y:

3x + y = 5
3x + 2x = 5
5x = 5
x = 1

Now, substitue 1 as x into one of the two equations:

y = 2x
y = 2(1)
y = 2

Hope this helps!

how much should Tabatha budget monthly for insurance that costs $956.89 for the entire year?

Answers

$79.74083  is the answer hope i help you

i divided 956.89 in 12 so that was the answer
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