Jensen and Raju had the same amount of money at first. After Jensen spent
$64 and Raju spent $148, Jensen had 3 times as much money as Raju. How
much money did each boy have at first?

Taking any number x, and adding on its opposite -x, leads to x+(-x) = x-x = 0

This is the inverse property of addition.

A numeric example would be 7 + (-7) = 7-7 = 0

Going back to x-x = 0, we can replace x with any expression (whether simple or complicated) we want.

So in this case, we replace each 'x' with 'x+3' to get (x+3)-(x+3) = 0

The equation (x+3)-(x+3) = 0 has infinitely many solutions. The solution set is the set of all real numbers. We can replace x with any number and the original equation will simplify to a true statement.

Answer:

gross income is $400

The net is $329.40

Deductions are $$70.6

Step-by-step explanation:

Based on the gross amount earned and the various deductions, the net income is $329.40

Net income is the amount that will be earned after all the taxes have been subtracted from the paystub amount.

The net income is therefore:

= 400 - 5.80 - 24.80 - 40

= $329.40

In conclusion, the net income is $329.40.

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Answer:

1) yes ; 2) 1/36 ; 3) 1/36 ; 4) 1/18

Step-by-step explanation:

Given the following :

Two fair dice : 1 green ; 1 red

A) Are the outcomes on the dice independent:

Yes, becomes the outcome of the green dice does not have any effect on the outcome of the red dice.

B) Find P(1 on green die and 5 on red die).

Probability = (number of required outcome) / (total possible outcomes)

Total outcomes of a dice = 6

P(1 on green) = 1 / 6

P(5 on red) = 1/6

P(1 on green die and 5 on red die) :

(1/ 6) × (1/6) = 1/36

C) Find P(5 on green die and 1 on red die)

P(5 on green) = 1/6

P(1 on red) = 1/6

Find P(5 on green die and 1 on red die):

1/6 × 1/6 = 1/36

D) Find P((1 on green die and 5 on red die) or (5 on green die and 1 on red die))

P(5 on green die and 1 on red die) = 1/36

P(1 on green die and 5 on red die) = 1/36

P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) =

P(5 on green die and 1 on red die) + P(1 on green die and 5 on red die)

= (1/36 + 1/36) = 2 /36 = 1/18

Answer:

83, 97, 111 i think that is what you are asking

Answer:

83, 97,111

Step-by-step explanation:

Answer:

341.5 because it makes the most sense

Answer:

340.511

Step-by-step explanation:

The five in the tenths place would make you round up.

Hope this helps! Can I get Brainliest? I’ve never had it before.

Answer:

x=20

Step-by-step explanation:

<2 = <3 when the lines are parallel

3x-10 = x+30

Subtract x from each side

3x-10 -x = x+30-x

2x-10 = 30

Add 10 to each side

2x-10 +10 = 30+10

2x = 40

Divide by 2

2x/2= 40/2

x =20

Answer:

a

mean [tex]\mu = 10[/tex] variance [tex]\sigma^2 = 6[/tex]

b

The binomial random variable x fall into this interval ranges from

     - 5  to  5

c

[tex]P(6 \le x \le 14) = 0.8969[/tex]  

Step-by-step explanation:

From the question we are told that

  The sample size is  [tex]n = 25[/tex]

   The  percentage that look for gas stations and food outlets that are close to or visible from the highway is  [tex]p = 0.40[/tex]

Generally the mean is mathematically represented as

       [tex]\mu = n * p[/tex]

=>     [tex]\mu = 0.40 * 25[/tex]

=>    [tex]\mu = 10[/tex]

The variance is mathematically represented as

      [tex]\sigma^2 = np(1- p )[/tex]

=>   [tex]\sigma^2 = 25 * 0.40(1- 0.40 )[/tex]

=>    [tex]\sigma^2 = 6[/tex]

The  standard deviation is mathematically evaluated as

     [tex]\sigma = \sqrt{\sigma^2}[/tex]

     [tex]\sigma = \sqrt{6}[/tex]

    [tex]\sigma = 2.45[/tex]

The  interval is evaluated as

       [tex]p\pm 2 \sigma[/tex]

=>   [tex]p - 2 \sigma\ \ \ , \ \ \ p + 2\sigma[/tex]

=>   [tex]0.40 - 2 *2.45\ \ \ , \ \ \ 0.40 + 2* 2.45[/tex]

=>   [tex]-4.5\ \ \ , \ \ \ 5.3[/tex]

The binomial random variable x fall into this interval ranges from

     - 5  to  5

Generally

    [tex]P(6 \le x \le 14) = P(\frac{ x - \mu }{\sigma } \le \frac{14 - 10}{{2.45}} ]-P[ \frac{ x - \mu }{\sigma } \le \frac{6 - 10}{2.45 } ][/tex]

     [tex]P(6 \le x \le 14) = P(Z \le 1.63 ]-P[ Z \le -1.63 ][/tex]

     [tex]P(6 \le x \le 14) = [1- P(Z > 1.63 ]] -[1- P[ Z > -1.63 ]][/tex]      

From the z-table  

                 [tex]P(Z > 1.63 ) = 0.051551[/tex]

And

                [tex]P(Z >- 1.63 ) =0.94845[/tex]

=>        [tex]P(6 \le x \le 14) = [1-0.051551] -[1-0.94845][/tex]      

=>        [tex]P(6 \le x \le 14) = 0.8969[/tex]  

The statement which is true about the slope of the given graphed line is that the slope is positive.

Slope is the proportion of decrease or increase in variable y due to increase and decrease in variable x. The formula of calculating slope is as under:

Slope=[tex](y_{2} -y_{1}) /(x_{2} -x_{1})[/tex]

We have to find the slope of the graphed line and for that we have to first take two points which lie on the line whose slope we have to find.

Take the points (0,4) and (-5,2) and calculating slope we get:

slope=(2-4)/(-5-0)

=-2/-5

=2/5

Hence the statement which is true is that the slope is positive.

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#SPJ2

Answer:

$1,540.70

Step-by-step explanation:

1675/335 = 5

3.65 * 335 = 1222.75

Cost of $8.65 per plant, or $2,897.75 for every plant.

12.99 - 8.65 = 4.34

Profit of $4.34 per plant, or $1,540.70 total.

Answer: 7+0.7+0.05

Since 7 is in the ones place it goes in front of the decimal. .7 is in the tenth place because it's behind the decimal. .05 is also behind the decimal so it's in the hundredths place.

Answer:

3 ones

2 tenths

8 hundredths

I'm sorry if I misunderstood.

Good luck though! :)

Please add Brainliest if you'd like, not that it matters.

Answer:8^20

Step-by-step explanation:

I just say 10x2=20 lol

Answer:

[tex]8^{20}[/tex]

Step-by-step explanation:

8^10*2

8^20

Answer:

Difference = 3x² + 3x + 1

See Explanation

Step-by-step explanation:

Required: How changes in sides of a cube affects its volume.

Take for instance the side of the cube is x.

The initial volume would be:

Volume = x * x * x

Volume = x³

When then dimension is increased by 1 unit, the new volume would be

Volume = (x + 1) * (x + 1) * (x + 1)

Expand the brackets

New Volume = (x² + 2x + 1)(x + 1)

New Volume = x³ + 3x² + 3x + 1

[Calculate the difference between both volumes]

Difference = New Volume - Initial Volume

Difference = x³ + 3x² + 3x + 1 - x³

[Collect like terms]

Difference = x³ - x³ + 3x² + 3x + 1

Difference = 3x² + 3x + 1

So, there will be a difference of 3x² + 3x + 1 when the dimension is increased from x to x + 1

Take for instance: a dimension of 2 units is increased to 3 units

Initial Volume = 2³ = 8

New Volume = 3³ = 27

Difference = 27 - 8

Difference = 19

Using the derived formula (x = 2)

Difference = 3x² + 3x + 1

Substitute 2 for x

Difference = 3 * 2² + 3 * 2 + 1

Difference = 3 * 4 + 6 + 1

Difference = 12 + 6 + 1

Difference = 19

Answer:

c)

The distribution is skewed down the middle,

Therefore it is symmetric.

Answer:

12

Step-by-step explanation:

The number of shells collected by Paula is 12 shells

The correct answer is B.

The given expression:

total number of shells collected by the friends, t = 43 shells

number of shells collected by Paula = x

number of shell collected by Bethany = 2x - 3

number of shell collected by Jerrell = [tex]\frac{x}{2} + 2[/tex]

To find:

The number of shells collected by Paula is calculated as follows:

[tex]x + (2x-3 ) + (\frac{x}{2} + 2) = 43\\\\3x + \frac{x}{2} - 1 = 43\\\\\frac{6x + x}{2} = 43 + 1\\\\\frac{7x}{2} = 44\\\\7x = 88\\\\x = \frac{88}{7} \\\\x \approx 12 \ shells[/tex]

Thus, the number of shells collected by Paula is 12 shells

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Answer:

Step-by-step explanation:

step one:

let us re-write the expression in mathematical terms for clarity

we have the expression stated  below

[tex]64a^3-27b^3-144b^2+108ab^2[/tex]    

step two:

We are going to collect like terms before factorization we have

    [tex]64a^3+108ab^2-27b^3-144b^2[/tex]

We can now factorize the expression we have  

[tex]4a(16a^2+27b^2)-3b(9b^2+48b)[/tex]

Answer:

The answer is

Step-by-step explanation:

The distance between two points can be found by using the formula

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(9, -3) and (2, 4)

The distance between them is

We have the final answer as

Hope this helps you

Answer:

the answer would be 9.9

Step-by-step explanation

You must use the distance formula which is [tex]\sqrt{(2-9)^2 +(4-(-3))^2}[/tex]

Simplify - [tex]\sqrt{(-7)^2 +(7)^2}[/tex]

simplify again - [tex]\sqrt{49+49}[/tex]

once more simplify - [tex]\sqrt{98}[/tex]

and you can get your answer by [tex]\sqrt{98\\}[/tex]=9.899 or rounded to the nearest 10th 9.9. I hope this helps!

[tex]\bf \underline{ \underline{Given : }}[/tex]

[tex]\bf \underline{ \underline{To \: be \: calculated : }}[/tex]

Calculate the curved surface area of the cone .

[tex]\bf \underline{ \underline{Formula \: applied : }}[/tex]

Curved surface area of cone = πrl

[tex]\bf \underline{ \underline{Solution : }}[/tex]

First of all,

Radius = Diameter/2

=> Radius,r = 14/2

=> Radius,r = 7 cm

Now,

[tex] \sf{Curved \: surface \: area \: of \: cone =\pi rl}[/tex]

[tex] \sf \: \implies \: \dfrac{22}{ \cancel7} \times \cancel7 \times 8.45[/tex]

[tex] \sf\implies22 \times 8.45[/tex]

[tex] \sf \implies 185.9 \: {cm}^{2} [/tex]

Hence,the Curved surface area of cone is 185.9 cm².

Answer:[tex]S(t)=12-0.75t[/tex]

Step-by-step explanation:

Given: The snow started melting at a rate of 0.75 inches per hour and it is known that 4 hours  after the storm ended, after the storm ended, the depth of snow was down to 9 inches.

Snow melted in 4 hours = [tex]0.75\times4 =3\text{ inches}[/tex]

Initial depth of snow = 9 + 3 inches = 12 inches.

Now, depth of snow on Tristan's lawn = Initial depth -0.75(Number of hours)

Let S(t) be the depth of snow on Tristan's lawn, in inches, t hours after the snow stopped falling.

Then, [tex]S(t)=12-0.75t[/tex]

The linear equation that represents the depth of snow on Tristan's lawn, in inches, t hours  after the snow stopped falling is:

[tex]S(t) = 12 - 0.75t[/tex]

A linear function in the model will have the following format:

[tex]S(t) = S(0) - mt[/tex]

In which:

The snow melts at a rate of 0.75 inches per hour, thus [tex]m = 0.75[/tex] and:

[tex]S(t) = S(0) - 0.75t[/tex]

After 4 hours, there were 9 inches, that is, when [tex]t = 4, S(t) = 9[/tex], and this is used to find S(0).

[tex]S(t) = S(0) - 0.75t[/tex]

[tex]9 = S(0) - 0.75(4)[/tex]

[tex]S(0) = 9 + 0.75(4)[/tex]

[tex]S(0) = 12[/tex]

Hence, the equation is:

[tex]S(t) = 12 - 0.75t[/tex]

A similar problem is given at https://brainly.com/question/16302622

Answer: $160.18

Step-by-step explanation:    

Answer:

$160.18

Step-by-step explanation:

The cabinet's sale price (or in this case, sub-total) is $149. The sales tax is 7.5%, which means you must multiply 149 x 7.5% to get 11.175. After you do this, you must add the 11.175 (which we will round to $11.18 for your tax) to your subtotal ($149). Since $149 + $11.18 = $160.18, you will have to pay a total of $160.18 for the cabinet.

To solve this polynomial equation, we will need to factor the left side.

On the left, we have a a trinomial in a special form that

can be factored as the product of two binomials.

The trinomial on the left can be factored which makes life easier.

This factors as (x + 11)(x - 2) = 0.

This means that either x + 11 = 0 or x - 2 = 0.

Solving each equation from here, we get x = -11 or x = 2.

So the solution is {-11, 2}.

Answer:

2 and -11

Step-by-step explanation:

Step 1: Use the quadratic formula to solve for x

[tex]x=\frac{-b+-\sqrt{b^{2-4ac} } }{2a} \\x=\frac{-9+-\sqrt{9^{2}-4(1) (-22)} }{2(1)} \\x=\frac{-9+-\sqrt{169} }{2(1)}\\x=\frac{-9+-13 }{2}\\x1=\frac{-9+13 }{2}\\x1=\frac{4}{2} \\x1 = 2\\x2 = \frac{-9-13 }{2}\\x2 = \frac{-22 }{2}\\x2 = -11\\[/tex]

Therefore the values of 'x' that make the equation true is 2 and -11

Answer:

x = -9

Step-by-step explanation:

To solve these types of questions,

a). If both the sides of the equation are different,

    2x + 3 = 3x - 6

   There will be exactly one solution.

b). If the coefficient of variable 'x' is same in both the sides of the equation,

    x - 3 = x - 6

    Solution set will be 'none'.

c). If both the sides of the equation are exactly same then equation will have infinite solutions.

   2x + 3 = x + x + 3

In the given equation,

6x - (5x + 5) = -8 - 2(x + 12)

Further simplify the equation,

(6x - 5x) - 5 = - 8 - 2x - 24

x - 5 = -2x - 32

x + 2x = 5 - 32

3x = -27

x = -9

first lets collect the x's so -12x + x is -11x (think about a number line if you are not sure) then we minus 3x so we get  -14x

-9 + 5 is -4 then if we minus 1 we get -5 so

- 14x - 5

Answer: Combine each like term. Any number in this expression with the variable x is a like term. -12x+1x-3x=-14x. The numbers with no variable are like terms. -9+5-1=-5. The simplified expression is -14x-5.

Step-by-step explanation:

Answer/Step-by-step explanation:

∆ABC is similar to ∆CDE. Therefore, the ratio of their corresponding sides are proportional.

This,

[tex] \frac{DE}{AB} = \frac{DC}{AC} [/tex]

[tex] \frac{4}{3} = \frac{x + 3}{x + 1} [/tex]

Solve for x

[tex] 4(x + 1) = 3(x + 3) [/tex]

[tex] 4x + 4 = 3x + 9 [/tex]

[tex] 4x + 4 - 4 = 3x + 9 - 4[/tex]

[tex] 4x = 3x + 5 [/tex]

[tex] 4x - 3x = 3x + 5 - 3x [/tex]

[tex] x = 5 [/tex]

Use the value of x to find AC and DC

[tex] AC = x + 1 = 5 + 1 = 6 [/tex]

[tex] DC = x + 3 = 5 + 3 = 8 [/tex]

Answer:

Step-by-step explanation:

Represent the equation as follows:

[tex]a * b = c[/tex]

Where a,b and c are decimal numbers

To solve further, we make use of trial by error method

Let

[tex]a = 2.52[/tex]

[tex]b = 0.6[/tex]

Such that

[tex]2.5 * 0.6 = c[/tex]

[tex]1.512 = c[/tex]

[tex]c = 1.512[/tex]

This set of digits do not follow the rule in the question

Let

[tex]a = 2.55[/tex]

[tex]b = 1.6[/tex]

[tex]2.55 * 1.6 = c[/tex]

[tex]4.08 = c[/tex]

[tex]c = 4.08[/tex]

The result has only 2 non zeros (4 and 8)

Hence

[tex]2.55 * 1.6 = 4.08[/tex] answers the question.

However, there are other set of numbers that can be used too

One of the equation which illustrates and meets the conditions given is :

First number, x = 1.25

First number, x = 1.25 Second number, y = 0.2

Result = first Number × second number

Result = 1.25 × 0.2

Result = 1.25 × 0.2 Result = 0.25

Evaluating the result : 0.25

Number of digits = 3

Non - zero digits = 2

There are several values of x and y which will satisfy the 3 conditions given.

Therefore, the product of the values 1.25 and 0.2 gives the required output.

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Answer:

[tex]\frac{1}{10}[/tex]

Step-by-step explanation:

cross simplify

[tex]\frac{1}{8}[/tex] • [tex]\frac{4}{5}[/tex] = [tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex]

multiply

[tex]\frac{1}{2}[/tex] • [tex]\frac{1}{5}[/tex] = [tex]\frac{1}{10}[/tex]

Answer:

a) 1/11 (b) 7/22 (c) 5/11 (d) 0 (e) 19/66

Step-by-step explanation:

Given the following :

Number of Blue socks = n(B) = 4

Number of Gray socks = n(G) =5

Number of black socks = n(Bl) = 3

Total number of socks = (4 + 5 + 3) = 12

Probability = ( number of required outcomes / number of total possible outcomes)

Picking 2 socks at random:

A) probability of two blue socks :

Ist pick = p(B) = (4/12) = 1/3

Number of Blue socks left = (4 - 1) =3

Total socks left = 12 - 1 = 11

2nd pick = p(B) = (3/11)

P(2 blue socks) = (1/3 * 3/11) = 3 /33 = 1/11

B) No gray socks :

Number of non - gray socks = (4 + 3) = 7

1st pick = 7/12

After 1st pick non-gray socks left = 6

Total socks left = 11

2nd pick = 6 / 11

P(non-gray) = (7/12 × 6/11) = 42/132 = 7/22

C.) Atleast one black socks = (1 - P(no black))

Number of non-black socks = (4 +5) = 9

1st pick = 9/12 = 3/4

After 1st pick, non-black left = 8, total = 11

2nd pick = 8/11

P(non - black) = (3/4 × 8/11) = 24/44 = 6/11

P(atleast 1 black) = (1 - 6/11) = 5 /11

D.) A green socks

Number of green socks = 0

P(green) = 0

E.) A matching socks :

1) matching black socks :

Ist pick = p(Bl) = (3/12) = 1/4

Number of Black socks left = (3 - 1) =2

Total socks left = 12 - 1 = 11

2nd pick = p(Bl) = (2/11)

P(matching black socks) = (1/4 * 2/11) = 2 /44 = 1/22

11) matching blue socks:

Ist pick = p(B) = (4/12) = 1/3

Number of Blue socks left = (4 - 1) =3

Total socks left = 12 - 1 = 11

2nd pick = p(B) = (3/11)

P(matching blue socks) = (1/3 * 3/11) = 3 /33 = 1/11

111) matching gray socks :

Ist pick = p(B) = (5/12) = 5/12

Number of Blue socks left = (5 - 1) =4

Total socks left = 12 - 1 = 11

2nd pick = p(B) = (4/11)

P(matching gray socks) = (5/12 * 4/11) = 20/132 = 5 /33

Summing the probabilities :

(1/22 + 1/11 + 5/33) = (3 + 6 + 10) / 66 = 19/66

Using the hypergeometric distribution, it is found that there is a:

a) 0.0909 = 9.09% probability that you end up with 2 blue socks.

b) 0.3182 = 31.82% probability that you end up with no gray socks.

c) 0.4545 = 45.45% probability that you end up with at least 1 black sock.

d) 0% probability that you end up with a green sock.

e) 0.2879 = 28.79% probability that you end up with matching socks.

Hypergeometric distribution:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

In this problem:

Item a:

The probability is P(X = 2), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,12,2,4) = \frac{C_{4,2}C_{8,0}}{C_{12,2}} = 0.0909[/tex]

0.0909 = 9.09% probability that you end up with 2 blue socks.

Item b:

The probability is P(X = 0), hence:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,12,2,5) = \frac{C_{5,0}C_{7,2}}{C_{12,2}} = 0.3182[/tex]

0.3182 = 31.82% probability that you end up with no gray socks.

Item c:

The probability is:

[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]

In which

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 0) = h(0,12,2,3) = \frac{C_{3,0}C_{9,2}}{C_{12,2}} = 0.5455[/tex]

[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.5455 = 0.4545[/tex]

0.4545 = 45.45% probability that you end up with at least 1 black sock.

Item d:

There are no green socks, hence 0% probability that you end up with a green sock.

Item e:

Hence, for two gray:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,12,2,5) = \frac{C_{5,2}C_{7,0}}{C_{12,2}} = 0.1515[/tex]

Then, for two black:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,12,2,3) = \frac{C_{3,2}C_{9,0}}{C_{12,2}} = 0.0455[/tex]

Then, the probability of matching socks is:

[tex]p = 0.0909 + 0.1515 + 0.0455 = 0.2879[/tex]

0.2879 = 28.79% probability that you end up with matching socks.

A similar problem is given at https://brainly.com/question/24826394

Answer:

Total Earnings = 18,160

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

2) principal1 + principal2 = 17,000

We'll multiply equation 2) by -1.06

2) -1.06*principal1 -1.06*principal2 = -18,020 then adding equation 1)

1) 1.07 * principal1 *  + 1.06  * principal2= 18,160

.01*principal1 = 140

principal 1 = 14,000

and therefore principal 2 = 3,000

Step-by-step explanation:

Answer:

A length of a ray cannot be measured therefore it's refferd to as infinite. same