Two men and 7 women can together do a piece of work in 4 days. It is done by 4 men and 4 women in 3 days. How long would it take for one man or one woman to do the work

[tex]\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &499\\ r=rate\to 10\%\to \frac{10}{100}\dotfill &0.10\\ t=\textit{elapsed time}\dotfill &3\\ \end{cases} \\\\\\ A=499(1-0.10)^3\implies A=499(0.9)^3\implies A=363.771 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{\textit{total depreciation 499 - 363.771}}{135.229}~\hfill[/tex]

54=3x/4

18=x/4

18*4=x

72=x

In the number 526, the underlined digit '5' represents the 100's place, so its value is not simply 5, but 500. A helpful tool to work with such problems is the place value chart.

In the number 526, the emphasized or underlined digit represents the 100's place. So, the value of this specific digit, which happens to be 5, isn't simply 5 but 500 in the context of this particular group of digits. You can easily understand this by breaking down the number: 526 equals 500 (5 hundreds) plus 20 (2 tens) plus 6 (6 ones).

Another easy method to identify the value of an underlined or specific digit in a number is by knowing the place value chart, which runs from right to left as: Ones, Tens, Hundreds, Thousands, and so on. The third digit from right is the Hundreds place, and since in 526, 5 is in this position, its value becomes 500.

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The expression (1/7x + 11/7) can be factored as (x + 11) after dividing each term by 1/7. The factored form simplifies the original expression and represents the common factor, 1/7, that was pulled out.

To factor out 1/7 from the expression (1/7x + 11/7), you can simply divide each term in the expression by 1/7. This is equivalent to multiplying each term by the reciprocal of 1/7, which is 7/1.

Starting with the expression (1/7x + 11/7):

(1/7x) ÷ (1/7) = x

(11/7) ÷ (1/7) = 11

So, factoring out 1/7, the expression becomes x + 11.

Therefore, the factored form of (1/7x + 11/7) is (x + 11).

Answer:

x = 2.5

------------------

Equation:

3 + 5 = 8

Starting:

8x = 20

Conclusion:

x = 2.5

Check:

2.5 * 8 = 20

The slope-point form of line:

[tex]y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (-9, 7) and (6, 2). Substitute:

[tex]m=\dfrac{2-7}{6-(-9)}=\dfrac{-5}{6+9}=-\dfrac{5}{15}=-\dfrac{1}{3}\\\\y-7=-\dfrac{1}{3}(x-(-9))\\\\\boxed{y-7=-\dfrac{1}{3}(x+9)}[/tex]

The slope-intercept form of line:

[tex]y=mx+b[/tex].

We have the slope m:

[tex]y=-\dfrac{1}{3}x+b[/tex]

Pu the coordinates of the point (6, 2) to the equation:

[tex]2=-\dfrac{1}{3}(6)+b[/tex]

[tex]2=-2+b[/tex]             add 2 to both sides

[tex]4=b\to b=4[/tex]

[tex]\boxed{y=-\dfrac{1}{3}x+4}[/tex]

Answer: He bought two notebooks- 0.99*2=1.98.

He bought three pens - 0.95*3= 2.85

1.98+2.85=4.83

Answer:

30 students

Step-by-step explanation:

Yesterday: 1/3 of the 75 students (75 / 3) = 25 students

There are now 50 students remaining to give their speeches.

Today: 2/5 of the 50 students (50 / 5 = 10 x 2 ) = 20 students

50 - 20 = 30 students remaining to give their speeches.

Therefore, 30 students still haven't given their speeches.

To find out how many students still haven't given their speeches, we first need to calculate the number of students who gave their speeches yesterday and today. Since there were 75 students in total and 1/3 of them gave their speeches yesterday, we multiply 75 by 1/3:

75 * 1/3 = 25 students

This means that 25 students gave their speeches yesterday. To find out how many students were left for today, we subtract the number of students who gave speeches yesterday from the total number:

75 - 25 = 50 students remained

Today, 2/5 of the remaining students gave their speeches. We calculate this by multiplying the number of remaining students by 2/5:

50 * 2/5 = 20 students

Therefore, 20 students gave their speeches today. Now, we subtract the number of students who have given their speeches today from the remaining number of students to find out how many have not given their speeches yet:

50 - 20 = 30 students

Thus, 30 students still haven't given their speeches.

Answer:

The congruent side length is 6. The third side length is 3.

Step-by-step explanation:

Answer:

47

Step-by-step explanation:

13. The points that shows f(x) = g(x) are (0, 3) and (4, -5)

14a, h(45) = 7 means that after 45 days of planting the height will be 7 cm

14b. h(65) = 11

15a. g(t) = 1

15b. f(x) = 11

16. t = 8

How to find the solution of the graph

13. The solution of the graph is the point of intersection of the line and the curve

14. For the function, the value after the equality sign shows the value h while the value in the parenthesis shows the value for t

15. g(t) = 4t - 7

g(2) = 4(2) - 7 = 1

f(-3) = (-3)² + 2 = 11

f(t) = 14 - 3t

-10 = 14 - 3t

-24 = -3t

-24/-3 = t

t =8

Final answer:

The y-intercept of function f(x) can be found by using the given points to determine the slope and then plugging in the slope and a point into the point-slope equation. The y-intercept of function g(x) is given by the table. The positive difference in the y-intercept values of f(x) and g(x) is -0.5.

Explanation:

The y-intercept of a linear function represents the value of the function when x is equal to 0. To find the y-intercept of function f(x), we can use the given points (0,1) and (2,7) to determine the slope of the line. The slope is calculated by taking the difference in the y-coordinates and dividing it by the difference in the x-coordinates:

slope = (7 - 1) / (2 - 0) = 3.

Now that we have the slope, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.

Using the point (0,1) and the slope 3, we get:

y - 1 = 3(x - 0).

Simplifying the equation gives us:

y = 3x + 1.

The y-intercept of function g(x) is given by the table as the value of g(x) when x = -1, which is 1.5.

The positive difference in the y-intercept values of f(x) and g(x) is given by:

1 - 1.5 = -0.5.

Answer:

Step-by-step explanation:

Lets try to simplify each to check which one is incorrect so it will be NOT true

first one is :

distribute the exponent so :

[tex](3x^2y^5)^3 =3^3x^{2*3}y^{5*3}[/tex]

[tex]27x^6y^{15}[/tex] CORRECT

Second one is :

[tex](1000x^{12}y^{20}z^{-30})^{0} =1[/tex]

CORRECT because anything raised to exponent 0 is 1 .

Last one is :

[tex]4^2 *4^3 = 4^{2+3}\\=4^{6}\\=(4)^{2*3}\\=16^{3}[/tex]

so Last is INCORRECT

Answer:

8

Step-by-step explanation:

1.25x8+2.75x4

That relationship can be expressed by either of ...

For this case we have to find an equation according to 15 chairs distributed in three rows of 5 chairs each.

If in each row there are 5 chairs, and we have a total of three rows, then, the total of chairs will be given by the multiplication of the rows by the number of chairs in each row, then we have the following equation:

[tex]15 = 3 * 5[/tex]

Answer:

[tex]15 = 3 * 5[/tex]

Step-by-step explanation:

Note that:

length of foot = y

length of forearm = x = 17

Equation: y = 0.860x + 3.302

Plug in 17 for x in the equation, and simplify. Remember to follow PEMDAS, first multiply, then combine like terms:

y = (0.860)(17) + 3.302

y = 14.62 + 3.302

y = 17.922

length of foot = y = 17.922 inches long

~

Answer:

17.922 inches long

Step-by-step explanation:

y=0.860x + 3.302

y= 0.860(17) + 3.302

y= 14.62 + 3.302

y=  17.922

Hope it helps!!

Answer:

70.653333

Step-by-step explanation:

Go to the website, cymath.com

Search up your question.

Helps a lot for me

See ya! ;-)

Answer:

Check attached graph of the line in picture

Step-by-step explanation:

Step-by-step explanation:

We have been given an equation y+6=45(x+3) in point slope form.

It says to use the point and slope from given equation to create the graph.

So compare equation y+6=45(x+3) with point slope formula

y-y1=m(x-x1)

we see that m=45, x1=-3 and y1=-6

Hence first point is at (-3,-6)

slope m=45 is positive so to find another point, previous point will move 45 units up then 1 unit right and reach at the location (-2,39).

Now we just graph both points (-3,-6) and  (-2,39) and join them by a straight line. Final graph will look like the line in attached graph.

Answer:

$1062.5

Step-by-step explanation:

Since it is given that Money is increased by 25% from July to December.

Also, Mike deposit $850 in a bank account

Thus, He get money at the end of December = $850 × (100 + 25)%

⇒ Total Money = $850 × 125%

⇒ Total Money = $850 × 1.25

⇒ Total Money = $1062.5

Answer:

512 baseball cards

Step-by-step explanation:

At 13, Stephanie had 137 baseball cards.

There are 28-13 = 15 years between 13 and 28

For those 15 years, she got 25 cards a year.

15 * 25 = 375

In those 15 years, she got 375 cards.

She started with 137, and she gained 375.

137+375 = 512

She now has   512 cards.

Answers:

Problem 1) ASA

Problem 2) ASA

Problem 3) AAS

Problem 4) Neither

Problem 5) AAS

Problem 6) Neither

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

Explanation:

Any time we have ASA is when we can match up two pairs of angles and a pair of sides between the two pairs of angles. With problems 1 and 2, this happens. The corresponding angles that are congruent are the ones that have the same angle markers.

AAS is slightly different from ASA in that the side is not between the angles. This happens with problem 3 and problem 5. For problem 3, for instance, the second pair of angles are the two vertical angles. These angles are not marked, but they are congruent due to the vertical angle theorem. The same thing can be said about problem 5 as well.

With problem 4 and problem 6, we don't have any information about any pairs of angles, so we can't use AAS or ASA at all. We don't know if the triangles are congruent or not. They might be, but we simply don't have enough info to say either way.

Answer:

10+55x

Step-by-step explanation:

this is your answer because we don't know how man hour he drove after reaching the high but we know how many mile he dove to the high way.

hope this helps

The expression for total distance from the airport hours after reaching the highway is 10 + 55h

Given:

let h hours be the time taken.

Reggie drives 10 miles from the airport to the highway.

and, the speed= 55 Km/h

So, Distance = 55 x h = 55h

Then, the expression for total distance from the airport hours after reaching the highway

= 10 + 55h

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Answer:

the first one is -1 15/18 the next one is -1 14/18

Step-by-step explanation:

The mixed numbers that are equivalent to −1 5/6 ​ and​ −1 7/9 are −1 15/18 and −1 14/18, respectively.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

The LCD is the lowest common denominator for any two or more fractions. Now, for the given mixed numbers the two fractions given are 5/6 and 7/9, therefore, their LCD is the LCM of the denominator, in this case, the denominators are 6 and 9, therefore, the LCM of these two is 18.

Further to get the mixed number, the fraction is needed to be multiplied such that their denominator becomes 18.

Multiply both the numerator and the denominator by 3, therefore,

(5/6) × (3/3) = 15/18

Multiply both the numerator and the denominator by 2, therefore,

(5/6) × (2/2) = 14/18

Thus, the mixed fractions can be written as,

hence, the mixed numbers that are equivalent to −1 5/6 ​ and​ −1 7/9 are −1 15/18 and −1 14/18, respectively.

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Calculate the difference between purchase and sales costs:

$52,000 - $42,000 = $10,000

Calculate what fraction of $52,000 is $10,000:

[tex]\dfrac{\$10,000}{\$52,000}=\dfrac{10}{52}=\dfrac{5}{26}[/tex]

Transform it to the percent:

[tex]\dfrac{5}{26}=\dfrac{5}{26}\cdot100\%=\dfrac{500}{26}\%\approx19\%[/tex]

Answer:

the answer is $9.45.

Step-by-step explanation:

5*6=30,30/6=5,1.89*5=9.45.

Answer:

y  <  −  2 x /3 − 3

Hope This Helps!

Answer:

216

Step-by-step explanation:

Multiply 6 by 6 and then multiply it again by 6.

Hope this helps

Answer:

216

hope this helps....

Answer:

the answer is

B if im not mistaken

let me know if im wrong

Step-by-step explanation:

The equivalent expression of the expression 1.18 x 0.6 will be;

⇒ (118 x 1/100) x (6 x 1/10)

Option B is true.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ 1.18 x 0.6

Now,

Solve the expression as;

The expression is,

⇒ 1.18 x 0.6

Since, 1.18 = 118 x 1/100

And, 0.6 = 6 x 1/10

Thus, The equivalent expression is,

⇒ 1.18 x 0.6 = (118 x 1/100) x (6 x 1/10)

Therefore, The equivalent expression of the expression 1.18 x 0.6 will be;

⇒ (118 x 1/100) x (6 x 1/10)

Option B is true.

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Answer:

Area of rectangle is equal to multiply the length by width

i.e [tex]A = l\times w[/tex]           .....[1]

where

A is the area of rectangle ,

l is the length and

w is the width of the rectangle respectively.

Given : Area of rectangular do pen(A) = [tex]8\frac{1}{2} = \frac{17}{2}[/tex] square feet and width(w) = [tex]3\frac{2}{5} = \frac{17}{5}[/tex] feet.

To calculate the length in feet.

Substitute the given values in [1],  we get

[tex]\frac{17}{2}= l\times \frac{17}{5}[/tex]

Multiply both sides by [tex]\frac{5}{17}[/tex] we get;

[tex]l = \frac{17}{2} \times \frac{5}{17} =\frac{5}{2} = 2\frac{1}{2}[/tex] feet.

Therefore, the length in feet is, [tex]2\frac{1}{2}[/tex]

Answer:

Q. 1

Note that x = 9. Plug in 9 for x.

√(x + 7) = √(9 + 7)

Simplify. Add, then root

√(9 + 7) = √16 = √(4 * 4) = 4

4, or (B) is your answer

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Q. 2

Note that x = 16. Plug in 16 for x

√(x + 20) = √(16 + 20)

Simplify. Add, then root.

√(16 + 20) = √36 = √(6 * 6) = 6

6, or (D) is your answer

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Q. 3

Note that x = 9. Plug in 9 for x.

3 + √(9 + 7) - √(3(9))

Simplify. Combine the terms. Remember to follow PEMDAS.

3 + √(16) - √(27)

3 + 4 - 3√3

Simplify to get the final answer. Note that you can only combine terms with the same amount for roots

(3 + 4) - 3√3

7 - 3√3, or (C) is your answer

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Q. 4

Note that x = 6. Plug in 6 for x.

√(24 - (6))

Simplify. First solve the parenthesis

√(24 - 6) = √(18)

Simplify. Change the root to a decimal.

√18 = √( 3 * 3 * 2) = ~4.24

4.24, or (A) is your answer

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Q. 5

Note that x = 2. Plug in 2 for x in the expression.

6 + √(14 + x) - √(9x)

6 + √(14 + 2) - √(9(2)

Simplify. Follow PEMDAS. First, simplify the parenthesis

6 + √(16) - √18

Next, simplify the roots

6 + 4 - 3√2

Simplify. Combine like terms

(6 + 4) - 3√2

10 - 3√2

Change to decimal

- 3√2 ≈ -4.24

Subtract

10 - 4.24 = 5.76

5.76 or (C) is your answer

~

Put the values of x to the expreesions.

[tex]\sqrt{a}=b\iff b^2=a[/tex]

[tex]Q1.\\x=9\\\\\sqrt{x+7}=\sqrt{9+7}=\sqrt{16}=\boxed{4}\ \text{because}\ 4^2=16\\\\Q2.\\x=16\\\\\sqrt{x+20}=\sqrt{16+20}=\sqrt{36}=\boxed{6}\ \text{because}\ 6^2=36\\\\Q3.\\x=9\\\\\sqrt{x+7}=\sqrt{7+9}=\sqrt{16}=4\ \text{because}\ 4^2=16\\\sqrt{3x}=\sqrt{3\cdot9}=\sqrt9\cdot\sqrt3=3\sqrt3;\ \sqrt9=3\ \text{because}\ 3^2=9\\\\3+\sqrt{x+7}-\sqrt{3x}=3+4-3\sqrt3=\boxed{7-3\sqrt3}\\\\Q4.\\x=6\\\\\sqrt{24-x}=\sqrt{24-6}=\sqrt{18}=\sqrt{9\cdot2}=\sqrt9\cdot\sqrt2=\boxed{3\sqrt2}\approx\boxed{4.24}[/tex]

[tex]Q5.\\x=2\\\\\sqrt{14+x}=\sqrt{14+2}=\sqrt{16}=4\\\sqrt{9x}=\sqrt{9\cdot2}=\sqrt9\cdot\sqrt2=3\sqrt2\\\\6+\sqrt{14+x}-\sqrt{9x}=6+4-3\sqrt2=\boxed{10-3\sqrt2}\approx\boxed{5.76}[/tex]