Find the ordered pair $(x,y)$ if

\begin{align*}
x+y&=(3-x)+(3-y),\\
x-y &=(x-2)+(y-2).
\end{align*}
Thanks

The probability a selected person is both tall and fat is 0.341

From the question, the given parameters are

People = 100

Fat = 55

Tall = 62

So, the individual probabilities are

P(Fat) = 55/100

P(Tall) = 62/100

Evaluate

P(Fat) = 0.55

P(Tall) = 0.62

The probability a person is both tall and fat is

P(Fat and Tall) = P(Fat) * P(Tall)

So, we have

P(Fat and Tall) = 0.55 *  0.62

Evaluate

P(Fat and Tall) = 0.341

Hence, the probability is 0.341

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Answer:

y = - [tex]\frac{3}{2}[/tex] x - 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here m = - [tex]\frac{3}{2}[/tex] , then

y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation

to find c substitute (- 6, 5 ) into the partial equation

5 = 9 + c ⇒ c = 5 - 9 = - 4

y = - [tex]\frac{3}{2}[/tex] x - 4 ← equation of line

Answer:

625 pages

Step-by-step explanation:

Rate x time of the one printer + the rate x time of the second printer = 1000 pages

t= time

([tex]\frac{300}{10}[/tex] )t +( [tex]\frac{400}{8}[/tex]) t = 1000

30t + 50t = 1000

t(30 + 50) = 1000

80t = 1000   Divide both sides by 80

t = 12.5

It took 12.5 minutes to get this job done with both printers.

Look at printer b

[tex]\frac{400}{8}[/tex] (12.5) = pages

50 x 12.5 = 625 pages

4x² - 18x - 5 cannot be factored by grouping.

Factoring a polynomial involves writing it as a product of two or more polynomials.

In other words, it is a process of finding the factor.

Therefore, let's factor the quadratic equation as follows:

4x² - 18x - 5

Factorization by grouping means that we need to group the terms with common factors before factoring.

The grouping method can be used to factor polynomials whenever a common factor exists between the groupings.

Hence,

4x² - 18x - 5 cannot be factorise by grouping because it has no common factor.

in other word, we cannot, however, use the grouping method to factor 4x² - 18x - 5 because factoring out the GCF from both groupings does not yield a common factor.

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When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.

The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I

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Answer:

See below.  I added words tro the first question "Is a" so that I could answer it.

Step-by-step explanation:

f(x) = -3x³ + 9x² - 5x + 15

f(x) = -(x-3)(3x² + 5)

x((9-3x)x-5)+15

-3(x-1)[tex]x^{3}[/tex] + 4(x-1) + 16

=======

a) Is a [ghost happy]?

O Yes  Yes, as long as it can haunt.

O No

b) Is x + 1 a factor of f(x)?

O Yes  Yes

No

1 a factor of f(x)?  

Always

c) Is a 3 a factor of f(x)?

O Yes

O No    No, as far as I can see.

Answer:

$302.69

Step-by-step explanation:

399 x 30% = 119.7 # finding how much you save

399 - 119.7 = 279.3 # how much the item costs with the sale

279.3 x 8.375 = 23.39 # the sales tax for the discounted item

297.3 + 23.39 = 302.69 # adding sales tax to the discounted item

I think this is right. I was never that great at sales tax and discount.

The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true.

As given in the question,

If one amount is proportional to another, the two amounts increase and decrease at the same rate so there is always the same relationship between them

a:b = c:d

a ÷b = c ÷d

ad = bc

let Sal earns $480 per week and he works 40hours per week

  480÷40 = 12

Lidia earn $300 per week and she works 25 hours per week

   300÷25 = 12

Cross product of their salaries is  

480×25=1200

300×40=1200

The ratio of their salaries and their product are equal.

Hence, The given statement "Sal earns $480 per week. Lidia earns $300 per week. Are their salaries proportional if Sal works 40 hours per week and Lidia works 25 hours per week" is true

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Answer:

Your answer would be

(a) FPUGT.

Answer: 5 3/5

Step-by-step explanation:

3 + 2 = 5

2/5 + 1/5 = 3/5

5 + 3/5 = 5 3/5

Hope this helps!

Answer:

[tex]5 \times 107 = 535[/tex]

This is equivailent to the following

The conservationist expects to be in the lake would be; 142 trouts.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given, that determine the number of trout in a lake, a conservationist catches 200 trout, tags them, and throws them back into the lake.  

We have to find conservationists who expect to be in the lake.

Now, initially, trout count = 200

Then, again 56 trouts caught then, trout count = 200 + 56

But 14 of them are tagged that means; they are part of 200 trouts so we should not count again in 56 trouts.

So, trout count = 200 + 56 – 14  = 142.

Hence, the conservationist expects would be; 142 trouts.

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Given the right triangle:

The Pythagorean theorem states that:

From the problem, we identify:

And a is our missing value. Using the Pythagorean theorem:

An inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.

Given that, You have a goal to practice the piano for an average of at least 45 minutes per day for one week.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

Let m be the number of minutes you need to practice on the seventh day

The inequality for the given situation is

245+m≤315

⇒ m≤315-245

⇒ m≤70

Therefore, an inequality that represents the number of minutes m you need to practice on the seventh day is m≤70.

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"Your question is incomplete, probably the complete question/missing part is:"

You have a goal to practice the piano for an average of at least 45 minutes per day for one week. The first six days you practice a total of 245 minutes.

Write and solve an inequality that represents the number of minutes m you need to practice on the seventh day.

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

If we start with 180 g of the isotope, after one half-life the quantity will diminish to  180 g/2 = 90 g which exists half the original quantity.

This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]

After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]

After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]

But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.

The original quantity can then be rapidly computed for six half-lives using the formula below:

[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

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1) The x-intercept lies at (1, 14), and the y-intercept lies at (3, 42).

2) This means that after 3 cuts, the length of the string is 33 inches.

3) Therefore, the 42-inch string can be cut into 14 pieces of 3 inches each.

The x-intercept is the point on the graph where a line crosses the x-axis.

The y-intercept is the point on the graph where a line crosses the y-axis.

The x- and y-intercepts are the coordinate points for graphing data.

Thus, the x- and y-intercepts are coordinate points where the graph of a function or an equation touches the two axes.

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The height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

It is defined as the law to prove that two triangles have the same shape, but it is not compulsory to have the same size. The ratio of the corresponding sides is in the same proportions and the corresponding angles are congruent.

It is given that:

Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

D = 39.75 m

d = 34.9 m

H:h = D:d

H/1.85 = 39.75/34.9

H = 2.11 m

Thus, the height of the tree is approximately 2.11 meters if Kayla is 1.85 meters tall. At 12 noon, she measures the length of a tree's shadow to be 28.15 meters.

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Answer:

Find the total number of oranges.

Total oranges = 90 × 5

= 450

Since 1/5 were rotten oranges,

Fraction of oranges that were not rotten

= Fraction of total oranges - Fraction of rotten oranges

= 5/5 - 1/5

= 4/5

Number of oranges not rotten = 4/5 × 450

= 360

Answer: slope is -3

Step-by-step explanation: (-5,6) and (-9,-6)

Take your Y values and subtract them -6-6=-12

Take your X values and subtract them -9-(-5) or -9+5= -4

Then your -12 will be your numerator and your -4 will be your denominator

Then Divide

-12/-4= -3

I hope this helps!  

the reflection over the line y=x tells us to swap the points.

Therefore the point (0,-8) becomes (-8,0)

The probability that a randomly selected band member is a senior given that he or she plays the trumpet is 34.78%.

Probability is defined as the likeliness of an event to happen. It can be calculated by dividing the total desired outcomes by the total outcomes.

P = desired outcomes / total outcomes

Of the 108 band members, if 23 play the trumpet, and 8 are seniors who play the trumpet, then the probability that a randomly selected band member is a senior given that he or she plays the trumpet is 8 divided by 23.

P = 8/23 x 100

P = 34.78%

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Simplify the expression and express in standard form.

So answer is,

The answer is the stratified sample assures that the opinions of employees from both locations will be represented..

The survey results will accurately reflect the opinions of both urban and rural employees if you choose this option. By soliciting feedback from employees in both regions, it will be possible to ensure that any policy based on the results of this survey not only represents the interests of urban employees, who make up the bulk of the workforce, but also those of rural employees.

Option B is untrue since a stratified sample will cost more to implement than a straightforward random sample and won't always result in financial savings.

Option C does not applicable because it is just a supposition without any supporting data.

Choice D is False, since a stratified sample in this situation produces results that are more typical of the store's employees from both locations than a random sample.

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Hello!

First, let's write the possible options:

Dice: 6 different results.

• 1, 2, , 4, 5, 6.

Spinner: 4 different results.

• A, B, C, D.

Knowing it, let's solve each alternative of your exercise:

In the dic, we have 6 possible results and we want a specific number. SOo, we can write it as 1/6.

In the spinner, we have 4 possible results and we want a specific one too. So, we have 1/4.

Now, remember he r"and" rule: when we consider two events happening simultaneously, we must multiply their probabilities.

Solving:

We'll solve it in a similar way.

We have three possible odd numbers (1, 3, 5) in a total of 6 options. So, 3/6 = 1/2.

For the spinner, the reasoning will be the same: 1/.

Let's calculate:

In a dice, we have four numbers less than 5: 1, 2, 3,4.

In the spinner, there are 3 consonants (B, C, D).

Let's calculate:

Step 1:

Draw the table for the input x and output y.

Step 2:

From the table, we can see that the function is an exponential function.

Step 2:

Find the inverse of the function.

Step 3:

The two graphs below, show the graph of the inverse for both negative and positive square roots of x.

Final answer

The blue graph is the inverse of the red graph.

The new point is (-2, -9).

What happens when a point is reflected about an axis?
The x-coordinate remains constant when a point is reflected across the x-axis, but the y-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the x-axis as (x, -y).
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).

Given, the point to be reflected is : A : (2, -9)
Also, the axis through which the point is to be reflected is y-axis.
Following the statement established in the literature, we have:
The point (2, -9) when reflected over the y-axis,  the x-coordinate is assumed to be the additive inverse, thus the new co-ordinate is (-2, -9).
The new point is (-2, -9).

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Given:

It can be written as follows.

Dividing 5.44 by 6.8, we get

Hence the quotient is