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The solution that makes both expressions true is x = 8.55556 and y = 10.31746.

To solve for x and y, we need to use a system of equations involves finding the values of x and y that satisfy both equations simultaneously.

We can start by using the first equation to solve for x:

2x + 7x = 77

Combining like terms:

9x = 77

Dividing both sides by 9:

x = 8.55556 (rounded to six decimal places)

Now that we know the value of x we can use either equation to solve for y. Let's use the second equation:

5x + 7y = 115

Substituting x = 8.55556:

5(8.55556) + 7y = 115

Simplifying:

42.7778 + 7y = 115

Subtracting 42.7778 from both sides:

7y = 72.2222

Dividing both sides by 7:

y = 10.31746 (rounded to six decimal places)

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Out of a population of 100,000, the number of people who read at least two newspapers is = 33,000.

Let's approach this problem using the inclusion-exclusion principle.

First, we can add up the proportions of people who read each paper to get:

P(I) + P(II) + P(III) = 10% + 30% + 5% = 45%

However, this includes the people who read two or more papers multiple times, so we need to subtract those out. We can calculate these as follows:

P(I&II) + P(I&III) + P(II&III) = 8% + 2% + 4% = 14%

2P(I&II&III) = 2%

Using the inclusion-exclusion principle, we can now find the proportion of people who read at least two papers:

P(at least 2 papers) = P(I) + P(II) + P(III) - (P(I&II) + P(I&III) + P(II&III)) + 2P(I&II&III)

Plugging in the values, we get:

P(at least 2 papers) = 45% - 14% + 2% = 33%

So, the number of people who read at least two newspapers is:

0.33 * 100,000 = 33,000

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Complete question is:

A certain town of population size 100,000 has three newspapers: I , II and III the proportions of townspeople that read these papers are:  

I= 10 percent

II= 30% percent

II=5 percent

I&II=8 percent

I&III=2 percent

II&III=4 percent

I&II&III=1 percent

How many people read at least two newspapers?

Answer:

92, Hope this helps

Step-by-step explanation:

10000-5200= 4800/52 = 92.307 rounded up = 92

The ways to pack are

This is further explained below.

Generally, The science, art, and technology of packaging involves confining or safeguarding goods for distribution, storage, sale, and usage. The process of creating, analyzing, and designing packages is sometimes referred to as packaging.

In conclusion,

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Answer:

1/100.

Step-by-step explanation:

So, we can make the following deductions from the information given in the question or problem above.

[1]. "You and your neighbor attempt to use your cordless phones at the same time."

DEDUCTION: Two people are involved, that is you and your neighbor are both involved.

[2]. "Your phones independently select one of ten channels at random to connect to the base unit. "

DEDUCTION: Both cordless phones can choose one channels each which is random. The number of channels available is ten.

Therefore, the probability that both your phone and your neighbor phone pick the same channel can be calculated or determined as follows:

The probability that both your phone and your neighbor phone pick the same channel = probability that both your phone will pick one channel out of the ten channels ×  the probability that your neighbor phone pick one channel out of the ten channels.

The probability that both your phone and your neighbor phone pick the same channel = 1/10 × 1/10 = 1/100.

Therefore, The probability that both your phone and your neighbor phone pick the same channel = 1/100.

Answer:

x=-5

Step-by-step explanation:

First, subtract 6

6-6-3x=21-6

-3x=15

Then, divide by -3

-3x/-3=15/-3

x=-5

Answer:

2 workers = 6 days

4 workers = 3 days

Step-by-step explanation:

If it takes 2 workers 6 days, if you seep up the process with 4 workers, you would divide the days by 2 because you multilpied the workers by 2. So, it would take 3 days with 4 workers. I hope that makes sence.

Answer:

The factors of the expression are 18x and 4-y

Given the expression 72x - 18xy

Find the factor of each term:

72x = 18 * 4 * x

18xy = 18 * x * y

Since 18x is common to both terms, hence the factored form is expressed as:

72x - 18xy = 18x (4 - y)

Step-by-step explanation: Hope this helps!! Mark me brainliest!!

Answer:

18x(4−y)

Step-by-step explanation:

72x−18xy

Factor out 18.

18(4x−xy)

Consider 4x−xy. Factor out x.

x(4−y)

Rewrite the complete factored expression.

18x(−y+4)

Evaluate

18x(4−y)

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Answer: 6.5

Step-by-step explanation:

\(|-6.5| = 6.5\)

_________

There are a total of 3 forwards on the team.

A fraction represents a part of the whole or group of objects.In a fraction, numerator and denominator are separated by a horizontal bar known as the fractional bar

Given:

2/8 of the players are forwards.

Total number of players on the team = 12

We will determine the total number of forwards on the team by multiplying the total number of players by the fraction representing the forwards.

Fraction representing the forwards:

= 2/8

= 1/4

Total forwards on the team:

= 12 * (1/4)

= 3.

Translated question:

Of the 12 players on the team, 2/8 are forwards. What are the total forward in the team?

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Answer:

\(\dfrac{\sqrt{2}-\sqrt{6} }{4} }\)

Step-by-step explanation:

Find the exact value of cos(105°).

The method I am about to show you will allow you to complete this problem without a calculator. Although, memorizing the trigonometric identities and the unit circle is required.    

We have,

\(\cos(105\°)\)

Using the angle sum identity for cosine.

\(\boxed{\left\begin{array}{ccc}\text{\underline{Angle Sum Identity for Cosine}}\\\\\cos(A+B)=\cos(A)\cos(B)-\sin(A)\sin(B)\end{array}\right}\)

Split the given angle, in degrees, into two angles. Preferably two angles we can recognize on the unit circle.

\(105\textdegree=45\textdegree+60\textdegree\\\\\\\therefore \cos(105\textdegree)=\cos(45\textdegree+60\textdegree)\)

Now applying the identity.

\(\cos(45\textdegree+60\textdegree)\\\\\\\Longrightarrow \cos(45\textdegree+60\textdegree)=\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\)

Now utilizing the unit circle.

\(\boxed{\left\begin{array}{ccc}\text{\underline{From the Unit Circle:}}\\\\\cos(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\cos(60\textdegree)=\dfrac{1}{2}\\\\\sin(45\textdegree)=\dfrac{\sqrt{2} }{2}\\\\\sin(60\textdegree)=\dfrac{\sqrt{3} }{2} \end{array}\right}\)

\(\cos(45\textdegree)\cos(60\textdegree)-\sin(45\textdegree)\sin(60\textdegree)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\)

Now simplifying...

\(\Big(\dfrac{\sqrt{2} }{2}\Big)\Big(\dfrac{1 }{2}\Big)-\Big(\dfrac{\sqrt{2} }{2}\Big)(\dfrac{\sqrt{3} }{2}\Big)\\\\\\\Longrightarrow \Big(\dfrac{\sqrt{2} }{4} \Big)-\Big(\dfrac{\sqrt{6} }{4} \Big)\\\\\\\therefore \cos(105\textdegree)= \boxed{\boxed{\frac{\sqrt{2}-\sqrt{6} }{4} }}\)

Answer:

-19

Step-by-step explanation:

f(x)=5x+1

F(-4) - substitute -4 as the x

F(-4)=5(-4)+1

F(-4) = -20 + 1

f(-4) = -19

Answer: 4



Step-by-step explanation:

Answer:

Hellooooo! Whats up?

Step-by-step explanation:

Answer: (2 - 8x2 - 15) = -29/1 = -29

              (2 + 12x - 3x) = 0

(2 + 12•x - 3•x) = 0

9x = -2

x = -2/

9

≈ -0.222222

Step-by-step explanation:

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I am new here

Answer:

2 pounds

Step-by-step explanation:

$6= 12 pounds

$1= 12÷6=2

Hope this helps! Thanks.

Answer:

A and D are correct. This is a parallelogram, which is a quadrilateral. B is not correct because not all the sides are congruent. C is not correct. E and F are not correct because this parallelogram does not have any right angles.

Given:

Let's factor using synthetic division.

Equate the divisor to zero:

x - 5 = 0

x = 5

List all terms of the polynomial: 1, -7, 2, 40

Palce the numbers representing the divisor and dividend into a long division-like configuration

To factor using synthetic division, we have:

Therefore, the factored expression is:

The zeros are also the roots of the polynomial.

The zeros of a polynomial are all the x-values that makes the polynomial equal to zero,

To find the zeros, equate each afctor to zero:

(x - 4) = 0

x = 4

(x + 2) = 0

x = -2

Thus, the zeros are:

x = 4, -2

ANSWER:

Answer:

9/1 x 3/1

Step-by-step explanation:

Answer:

0.15

Step-by-step explanation:

\(\frac{3}{20}=\frac{15}{100}\)

0.15

Answer:

0.15

Step-by-step explanation:

Convert 3/20 to a decimal by applying long division

3 ÷ 20 = 0.15

Answer:

Hi,

In a square, all sides are equal.

The area is obtained by multiplying one side by another side.

So, A = L^2

A = Area

L = length of a side

24ft^2 = L^2

L = square root(24) = 4.9

L = 4.9

We can say x^2 = 24

And the length of one side is therefore 4.9

Answer:

(x + 4)^2 + (y + 7)^2 = 36

Step-by-step explanation:

The given information describes a circle with its center at (-4, -7) and tangent to the vertical line x = 2. To determine the radius of the circle, we need to find the distance between the center and the tangent line.

The distance between a point (x1, y1) and a line Ax + By + C = 0 is given by:

d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

In this case, the equation of the line is x = 2, which can be written as 1x + 0y - 2 = 0. Therefore, A = 1, B = 0, and C = -2. The center of the circle is (-4, -7), so x1 = -4 and y1 = -7. Substituting these values into the formula, we get:

d = |1*(-4) + 0*(-7) - 2| / sqrt(1^2 + 0^2)

d = |-6| / sqrt(1)

d = 6

Therefore, the radius of the circle is 6 units. The equation of a circle with center (h,k) and radius r is given by:

(x - h)^2 + (y - k)^2 = r^2

Substituting the values we have found, we get:

(x + 4)^2 + (y + 7)^2 = 36

This is the equation of the circle that satisfies the given conditions.

The constant that will be used in Digby's linear inequality will be 8.

What are linear inequalities, exactly?

Inequality is a mathematical statement that states that neither side is equal. When a link causes a non-equal comparison between two expressions, an inequality develops. The inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters '<' and '>' denote severe inequalities, whereas " ≤ and ≥ " denote slack inequalities.

Now,

Given that The temperature during a winter day was less than 8 degrees Fahrenheit.

let x be the temperature in degree Fahrenheit

then the linear inequality to show the statement will be

x<8 where 8 is a constant

Hence,

          The constant that will be used in Digby's linear inequality will be 8.

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Answer:

The awnser is 8.

Step-by-step explanation:

i just know<33

Answer:

33

Step-by-step explanation:

Answer:

The system that can be used is:

\(10x + 2y = 56\)

\(9x + 3y = 60\)

Step-by-step explanation:

We have that:

x is the price of a package of sugar cookies, y is the price of a package of oatmeal cookies.

Shaikha sold 10 packages of sugar cookies and 2 packages of oatmeal cookies for $56.

This means that:

\(10x + 2y = 56\)

Khalid sold 9 packages of sugar cookies and 3 packages of oatmeal cookies for $60.

This means that \(9x + 3y = 60\)

System that can be used:

The system that can be used is:

\(10x + 2y = 56\)

\(9x + 3y = 60\)

Answer:

Minimum=60

First Quartile(Q1)=79

Median=86

Third Quartile (Q3)=89

Interquartile range (IQR)=10