a. If a family has 5 children, in how many ways could the parents have 2 boys and 3 girls as children?

Answer:

y-1/y^2 +4y

Step-by-step explanation:

2y - 1/y x (y + 4) - y-2/y^2 +4y - 2y -8

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

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

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

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

y-1/y^2 +4y

Answer:

[tex]\dfrac{y-1}{y(y+4)}[/tex]

Step-by-step explanation:

Given expression:

[tex]\implies \dfrac{2y-1}{y^2+4y}-\dfrac{y-2}{y^2+2y-8}[/tex]

Factor the denominators of both fractions:

[tex]\implies \dfrac{2y-1}{y(y+4)}-\dfrac{y-2}{y^2+4y-2y-8}[/tex]

[tex]\implies \dfrac{2y-1}{y(y+4)}-\dfrac{y-2}{y(y+4)-2(y+4)}[/tex]

[tex]\implies \dfrac{2y-1}{y(y+4)}-\dfrac{y-2}{(y-2)(y+4)}[/tex]

Cancel the common factor (y - 2) of the right fraction:

[tex]\implies \dfrac{2y-1}{y(y+4)}-\dfrac{1}{(y+4)}[/tex]

Adjust the fractions based on the LCM of y(y + 4):

[tex]\implies \dfrac{2y-1}{y(y+4)}-\dfrac{y}{y(y+4)}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

[tex]\implies \dfrac{2y-1-y}{y(y+4)}[/tex]

Simplify:

[tex]\implies \dfrac{y-1}{y(y+4)}[/tex]

Answer:

185,104 is between 100,000 and 200,000.

Hope this helps :)

Step-by-step explanation:

100,000 comes before 185,104 and 200,000 comes after 185,104.

Answer: [tex]-\frac{15}{2}[/tex] or -7.5

Step-by-step explanation:

[tex]\frac{1}{5} x + \frac{1}{4} = \frac{1}{2} (x+5)[/tex]

[tex]\frac{1}{5} x + \frac{1}{4} = \frac{1}{2}x + \frac{5}{2}[/tex]

[tex]\frac{1}{5} x + \frac{1}{4} - \frac{5}{2}= \frac{1}{2}x[/tex]

[tex]\frac{1}{4} - \frac{5}{2}= \frac{1}{2}x - \frac{1}{5} x[/tex]

[tex]-\frac{9}{4} = \frac{3}{10} x[/tex]

[tex]-\frac{9}{4} divide \frac{3}{10}= x[/tex]

[tex]x = -\frac{15}{2}[/tex]

By removing the taxes from the gross pay, we can see that Carlos' net pay is 1,320.30 dollars.

To get Carlos' net pay, we need to take his gross pay, which is $1,800.00 and subtract all the taxes shown here.

The taxes (in percentage) are:

The total percentage in these taxes is 19% + 6.2% = 25.2%

Then a 25.2% of the gross pay will be gone in taxes, then we need to subtract:

0.252* $1,800.00 = $453.60

We also need to subtract the $26.10 for Medicare, then we will get that Carlos' net pay is given by the expression:

$1,800.00 - $26.10 - $453.60 = $1,320.30

We conclude that, after taxes and that, Carlos' net pay is 1,320.30 dollars.

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Value of the manuscript is as follows

A. The value of the manuscript 5 years ago is $250.

B. The value of the manuscript now is $10,000.

Appreciation is an increase in the value of an asset over time. This is unlike depreciation, which lowers an asset's value over its useful life. The appreciation rate is the rate at which an asset grows in value.

% increase=(new price - original price) / original price

8.0= 2000/original price

8*original price = 2000

original price = $250

So the value of the manuscript 5 years ago is $250.

Increase is 2000 , 5 times that.

new price is $10,000

The value of the manuscript now is $10,000.

Hence , the manuscript has the following value:

A. The manuscript was worth $250 five years ago.

B. The manuscript is currently worth $10,000.

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The equation of the plane contains the curve with the vector (6 sint, cost, -cost) is [tex]F(t)=(6sint\ , \ cost , \ -cost)[/tex]

It is given that a plane contains the curve with the vector (6 sint, cost, -cost) which can be written as  [tex]x(t)=6sint ,\ y(t)=cost , \ z(t)=-cost[/tex]

Putting above values in equation (1) , we get

[tex]F(t)=(6sint\ , \ cost , \ -cost)[/tex]

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Based on the distance of her friend's house, the rate at which Daisy walked to the house was 140 m/s and the rate at which she walked home was 70 m/ s.

The rate that Daisy walked to her friend's house can be found by the formula:
= Distance to friend's house / Number of minutes it took

= 700 / 5

= 140 m/ s

When Daisy was walking home, her rate was:

= Distance to home / Number of minutes it took

= 700 / 10

= 70 m/ s

Rest of the question:
What was Daisy's walking speed going to her friend's house and coming back?

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7.25 is the right response as a change figure.

According to the query, Joyce purchased 2.2 pounds of apples for a total of $1.25 per apple.

As a result, Joyce has paid a total of 2.2 x 1.25 = 2.75.

She then paid the $10 bill:

Amount left over: 10 - 2.75 = 7.25

Therefore, 7.25 is the right response as the remaining sum.

Cost price is the sum of money that is paid to the maker or the buyer for the good. They'll alter the sum and set a selling price later.

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The values of the two unknowns x and y are 8 and 32 respectively.

Here, we are given the following set of ratios-

21x, 1/4, y/8

These ratios are all equivalent, this implies-

2/x = 1/4 = y/8

Let us take the first two ratios-

2/x = 1/4

cross multiplying the two we get

2 x 4 = x

8 = x

x = 8

We've found the value of x

Now, let us take the other two ratios-

1/4 = y/8

again, cross multiplying the two we get

y = 4 x 8 y = 32

Thus, the values of the two unknowns x and y are 8 and 32 respectively.

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Your question was incomplete. Check for full content below-

21x, 1/4, 7/8

If the given set of ratios is equivalent, find the unknowns.

Answer:

Option 3

Step-by-step explanation:

See attached image.

Answer:

25:15

Hope this helps :)

Step-by-step explanation:

5:3 so since there is 25 dogs we had to multiply 5 to the 5 in 5:3. We will have to multiply 5 to the 3 in 5:3 to get number of cats.

5:3 = 25:15

Answer:

[tex] = 15[/tex]

Step-by-step explanation:

Taking that the ratio of dogs to cats is 5:3, then:

The number of dogs = 25, so:

[tex]5 = 25 \\ 3 = x \\ x= 25 \times 3 \div 5 \\ x = 15[/tex]

Answer:

C(x) = 20x + 120

Step-by-step explanation:

(a). If x=5 (you replace x with 5)

C(5) = 20(5) + 120

= 100+120=$220

Cost of producing five items is $220

(b). if x=16

C(16) = 20(16) + 120

= 320 + 120 = $440

Cost of producing sixteen items is $440

(c). C(35) = 820

This means that the cost of producing 35 items is $820

Hope this helps :⁠-⁠) xoxo

Answer:

Hope this helps :)

412 × 77 = 31,724

Which is estimated about 30,000 something.

The possible cubes of an integer whose square is 100 can be 1000 and (-1000).

If the square of an integer is 100, then to find the value of integer we need to know the square root of 100

There exist two square roots of any number  one with negative sign and another with positive sign

The square roots of the given integer  that is 100  are 10 and -10

Now, we need to find out the value of [tex]10^{3}[/tex] and [tex]-10^{3}[/tex]

First cube  [tex]10^{3}[/tex] which can also be written as 10×10×10 = 1000

Second cube [tex]-10^{3}[/tex] which can also be written as( -10)×(-10)×(-10) = (-1000)

So, the possible cubes of an integer whose square is 100 can be 1000 and (-1000).

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Answer:

     the value of h(4) is 36 from given equation.

Step-by-step explanation:

Given that

        h(x) = x³ - 2x² + x

To find

So, according the question

We have,

        h(x) = x³ - 2x² + x

For finding the value of h(4) from the given polynomial equation, we have to replace x from 4 or in other word we have to put x = 4 in given polynomial equation.

So, let's put x = 4 in that equation.

We get,

        h(4) = (4)³ - 2(4)² + 4

               = 64 - 2×16 + 4

               = 68 - 32

        h(4) = 36  

Answer: Hance the value of h(4) is 36 from given equation.

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Answer:

the father is 45 and the son is 15

Answer/Step-by-step explanation:

5k + 3 ≤ -32 or -4k + 7 < -29

     -3      -3              -7      -7

5k ≤ -35               -4k < -36

÷5     ÷5               ÷-4    ÷-4

k ≤ -7                       k > 9

<----                     ------------>

<----|----------------O----------->

     -7                 9

(-∞, -7], (9, ∞)

I hope this helps!

Answer:

1000

Step-by-step explanation:

The equation is,

→ 34.624 × x = 34624

Solving for the value of x,

→ 34.624 × x = 34624

→ x = 34624/34.624

→ [ x = 1000 ]

Thus, value of x is 1000.

The variable terms of the expression 5 - 8n - 3n² are: n, n²

(5 - 8n - 3n²)

In this question, we have been given an expression 5-8n-3n^2

We need to name the variable terms of the expression.

Also, we need to underline the variable part of each term.

We know that,  variable is a term which represents an unknown value or quantity.

We have been given an quadratic expression.

5 - 8n - 3n²

We can observe that, 5, -8, -3 are fixed numbers i.e., constants.

And the alphabet n can take any real value.

Consider the first term,

5 => it is a constant

Consider the second term,

- 8n => here, the variable is n

Consider the third term,

- 3n² =>  here, the variable is n²

Now, we underline the variable part of each term.

5 - 8n - 3n²

Therefore, the variable terms of the expression 5 - 8n - 3n² are: n, n²

(5 - 8n - 3n²)

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Part 1

[tex](f+g)(x)=f(x)+g(x) \\ \\ =(6x+3)+(x^2 +10x-7) \\ \\ =\boxed{x^2 + 16x-4}[/tex]

Part 2

[tex](f-g)(x)=f(x)-g(x) \\ \\ =(6x+3)-(x^2 +10x-7) \\ \\ =6x+3-x^2-10x+7 \\ \\ =\boxed{-x^2 - 4x+10}[/tex]

Part 3

[tex](f\cdot g)(x)=f(x) \cdot g(x) \\ \\ =(6x+3)(x^2 +10x-7) \\ \\ =6x^3 + 60x^2 - 42x+3x^2 + 30x-21 \\ \\ =\boxed{6x^3 + 63x^2 - 12x-21}[/tex]

Part 4

[tex]\left(\frac{f(x)}{g(x)} \right)=\frac{f(x)}{g(x)} \\ \\ =\boxed{\frac{x^2 + 10x-7}{6x+3}}[/tex]

Answer:

Above sea level (positive)

Below sea level (negative)

Temperature (can be both)

Money loans (can be both)

science (protons have both negative and positive charge)

Step-by-step explanation:

I suppose you mean

[tex]f(x) f(y) = f(x + y) + f(x - y)[/tex]

Let [tex]x=1[/tex] and [tex]y=0[/tex]. Then

[tex]f(1) f(0) = f(1 + 0) + f(1 - 0) \implies f(1) f(0) = 2 f(1) \implies f(0) = 2[/tex]

Now if we fix [tex]y=1[/tex], the functional equation reduces to the recurrence relation

[tex]f(x) f(1) = f(x + 1) + f(x - 1) \implies f(x+1) - 3f(x) + f(x-1) = 0[/tex]

and we can find [tex]f(7)[/tex] with a few rounds of substitution.

[tex]x=1 \implies f(2) - 3f(1) + f(0) = 0 \implies f(2) = 3f(1) - f(0) = 7[/tex]

[tex]x=2 \implies f(3) - 3f(2) + f(1) = 0 \implies f(3) = 3f(2) - f(1) = 18[/tex]

[tex]x=3 \implies f(4) - 3f(3) + f(2) = 0 \implies f(4) = 3f(3) - f(2) = 47[/tex]

[tex]x=4 \implies f(5) - 3f(4) + f(3) = 0 \implies f(5) = 3f(4) - f(3) = 123[/tex]

[tex]x=5 \implies f(6) - 3f(5) + f(4) = 0 \implies f(6) = 3f(5) - f(4) = 322[/tex]

[tex]x=6 \implies f(7) - 3f(6) + f(5) = 0 \implies f(7) = 3f(6) - f(5) = \boxed{843}[/tex]

[tex] \tt{ \\ - 24 - ( - 19) \\ \\ \green \rightarrow - 24 + 19 = - 5}[/tex]

The derivative of the given equation is x = −3√2 ≈−1.259921049894873.

In mathematics, the derivative is the rate of variation of a function given respect to a variable. Derivatives are essential for solving calculus related differential equation issues.

The derivative is defined as the slope of a straight line that is tangent towards the curve at a certain location. An additional derivative definition is the limit of the function's instantaneous rate of evolution as the time between observations approaches zero. activity, such as currency and interest rate risk, for a set length of time.

It is significant because many physical phenomena, such as velocity, acceleration, and force, are defined with an instantaneous rate of change of some other quantity.

Given :

9x^2(1+2x^-3).

= [tex]9\left(\frac{2}{x^3}+1\right) x^2[/tex]

= [tex]\frac{\mathrm{d}}{\mathrm{d} x}\left[9\left(\frac{2}{x^3}+1\right) x^2\right][/tex]

= [tex]=9\left(\frac{\mathrm{d}}{\mathrm{d} x}\left[\frac{2}{x^3}+1\right] \cdot x^2+\left(\frac{2}{x^3}+1\right) \cdot \frac{\mathrm{d}}{\mathrm{d} x}\left[x^2\right]\right)[/tex]

=  [tex]=9\left(\left(2 \cdot \frac{\mathrm{d}}{\mathrm{d} x}\left[\frac{1}{x^3}\right]+\frac{\mathrm{d}}{\mathrm{d} x}[1]\right) x^2+\left(\frac{2}{x^3}+1\right) \cdot 2 x\right)[/tex]

= [tex]=9\left(\left(2(-3) x^{-4}+0\right) x^2+\left(\frac{2}{x^3}+1\right) \cdot 2 x\right)[/tex]

= [tex]=9\left(2\left(\frac{2}{x^3}+1\right) x-\frac{6}{x^2}\right)[/tex]

= [tex]=18\left(\frac{2}{x^3}+1\right) x-\frac{54}{x^2}[/tex]

= [tex]\frac{18 x^3-18}{x^2}[/tex]

x = −3√2 ≈−1.259921049894873.

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Answer:

100 is your answer

Step-by-step explanation:

I simply switched around the equation the answered it that way

Example: n×50=5,000

5000/50=n

500/50=100

Answer:

nine, you could find the answer from the instruction

Answer:

I genuinely believe the answer is five

Step-by-step explanation:

==================================================

Explanation:

The first digit must be even, so we have this subset {2,4} to pick from for that first digit. There are 2 choices here.

Whatever is picked for the first digit cannot be re-selected. So we have 5-1 = 4 choices left for the second digit, and then 4-1 = 3 choices for the third digit.

Overall we have 2*4*3 = 24 different passcodes.

The linear equation that passes through (10, 6) and (30, 12) is:

y = (3/10)*x + 3

Remember that the general line equation (in the slope-intercept form) is:

y = a*x + b

Where a is the slope and b is the y-axis intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), the slope will be:

a = (y₂ - y₁)/(x₂ - x₁)

Then in this case the slope is:

a  = (12 - 6)/(30 - 10) = 6/20 = 3/10

Replacing that in our line we get:

y = (3/10)*x + b

To find the value of b we replace the values of one of the points, i will use (10, 6), it gives:

6 = (3/10)*10 + b

6 = 3 + b

6 - 3 = b = 3

Then we conclude that the linear equation is:

y = (3/10)*x + 3

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Based on the population of Brazil in 1855 and 1860, the estimated population in 1870 is C. 19.15 million

The increase in the population between 1855 and 1860 was:

= 12.51 - 10.112

= 2.398 million

The increase is:

= 2.398/10.112

= 24%

With an increase of 24% every 5 years, the population in 1870 is:

= 10.112 x (1 + 24%)³

= 19.27 million

In conclusion, we can estimate that the population of Brazil in 1870 was 19.15 million.

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