a rectangular poster is to contain 450 square inches of print. the margins at the top and bottom of the poster are to be 2 inches, and the margins on the left and right are to be 1 inch. what should the dimensions of the poster be so that the least amount of poster is used?

Answer:

y=-3x+29

Step-by-step explanation:

y=mx+b or c

m=slope=-3

x=10

y=-1

input the given

-1=-3(10)+b

-1=-30+b

29=b

y=-3x+29

(1.25)t=gallons    so 1.25 times the ammound of hours

Answer:

x=9

Step-by-step explanation:

2x + 10 =28 <---- subtract by 10

2x = 18          < divide by 2

x = 9

The equation 3x = 6.4 can be solved for x by dividing both sides of the equation by 3: 3x/3 = 6.4/3; x = 2.13

So, for 3x and 6.4x to be equal, x must be equal to 2.13. This means that you need to multiply the number 6.4 by 2.13 to equal 3. The equation 3x = 6.4 represents the relationship between two variables, x and 3x. We are trying to find the value of x that would make 3x equal to 6.4. To do this, we divide both sides of the equation by 3. Dividing both sides of an equation by the same number does not change the relationship between the variables; it only scales down the variable's value by the same factor.

So, by dividing both sides of the equation by 3, we get:

3x/3 = 6.4/3

x = 2.13

Finally, to make 6.4x equal to 3, we need to divide 6.4 by 2.13: 6.4 / 2.13 = 3. So, we need to multiply 6.4 by 2.13 to equal 3.

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Answer: the correct answer is A

Step-by-step explanation:

I just took the test

Answer:

O points G and H

The required measure of x would be 9√10 units for the attached figure.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

The right triangle is given in the question, as follows:

We have to determine the measure of x for the attached figure.

According to Euclidian theorem, the required solution would be as:

x² = 27 × (27+3)

x² = 27 × 30

Apply the multiplication operation,

x² = 810

Apply the square root property for both sides

x = 9√10

Therefore, the required measure of x would be 9√10 units.

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The question seems to be incomplete the correct question has been attached below.

If manny paid $114.03 for the items purchased , then he paid the correct amount .

The first step is to determine the total cost of all the items purchased.

Total cost = $32.65 + (3 x $14.89) + $39.99 = $117.02.

Now, determine the cost after the promotional sale: (100 - 10%) x $117.02 = $105.32

The last step is to determine the total cost after tax: (1.08) x 105.32 = $114.03

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Answer:c

Step-by-step explanation:

trust

In the expression given as -5 - (-7) = -5 + x, the value of x is 7.

In Mathematics, expression simply means the mathematical statements which have at least two terms which are then related by an operator. It should be noted that they illustrate the relationship between the data given.

In this situation, it should be noted that the expression is given as:

-5 - (-7) = -5 + x

Collect like terms

-5 + 7 = -5 + x

x = -5 + 5 + 7

x = 7

The value of x is 7.

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Answer:

probability; ( of choosing a yellow marble)

7 yellow marbles + 10 orange marbles = 17 in total

if the no of yellow marbles is 7 therefore = ⁷/10

so that is the probability ⁷/10

Hope this helps

Answer:

a. x < -1/2 (I believe)

Step-by-step explanation:

I know that because the circle is not filled in the symbol is not greater then or equal to. Hence, not c. I think that the graph is saying that x is less then -1/2.

"When graphing a linear inequality on a number line, use an open circle for "less than" or "greater than", and a closed circle for "less than or equal to" or "greater than or equal to"."

Answer:

wheres the grapgh because the drawing you drawed it don't make sense.

Step-by-step explanation:

Answer:

$46,479

Step-by-step explanation:

22% of 49478 is 10885.

You add them.

60363.

Then take 23% of that which is 13883.

Then subtract them.

$46,479

Hope this helps

Answer:

6

Step-by-step explanation:

Answer:

The coefficient would be 6

Step-by-step explanation:

3x2x is just multiplying 3x and 2x (assuming). If that is the case, then when you multiply the two together, your coefficient is 6.

The quantity that gives maximum profit is approximately 111.55 units.

To find the quantity that gives maximum profit, we need to first find the revenue function and then the profit function.

The revenue function is given by:

R(x) = xp = x(120,000 - 150x)

The profit function is given by:

P(x) = R(x) - C(x) = x(120,000 - 150x) - (700/x + 300x + x²)

To find the quantity that gives maximum profit, we need to find the derivative of the profit function and set it equal to zero:

P'(x) = 120,000 - 300x - 700/x² - 2x

Setting P'(x) equal to zero and solving for x, we get:

120,000 - 300x - 700/x² - 2x = 0

Multiplying both sides by x^2, we get:

120,000x² - 300x³ - 700 - 2x³ = 0

Simplifying, we get:

300x³ + 2x³ - 120,000x² - 700 = 0

Dividing both sides by 2, we get:

151x³ - 60,000x² - 350 = 0

Using a graphing calculator or numerical methods, we can find that the real root of this equation is approximately x = 111.55.

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limx → 1 (x2−2x+1)/(x2+2x+1) = 0  Answer: 0.

Given limx → 1(x − 1)/(x2+2x+1)

Apply limit formula we get

limx → 1 x − 1/ x2+2x+1

= [limx → 1 (x − 1)/(x − 1)(x+1)] / [limx → 1 (x+1)/(x+1)]

= limx → 1 1/(x+1)

Now substituting x = 1 in the above expression we get

limx → 1 1/(x+1)= 1/2

Therefore limx → 1 (x − 1)/(x2+2x+1) = 1/2

Answer: 1/2.11. lim x→1
​
Therefore limx → 1 (x2−2x+1)/(x2+2x+1) = 0

Answer: 0.

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Answer:

12

Step-by-step explanation:

Answer:

1) 12 boxes

2) 3, 6, 12

3) 12

4) 110 degrees

Step-by-step explanation:

1) Count the rectangles. Multiply the length of the rectangle in boxes to the width of rectangle in boxes.

Length: 4 boxes

Width: 3 boxes

4 x 3 = 12

12 boxes

2)

10% of 30 is 0.1 times 30.

0.1 x 30 = 30/10 = 3

20% of 30 is 0.2 times 20.

0.2 x 30 = 30/5 = 6

40% of 30 is 0.4 times 20.

0.4 x 30 = 30/2.5 = 12

3) Count the cubes. Reminder there are 2 boxes you cannot see.

Top Layer: 2

Middle Layer: 4

Back Bottom Layer: 4

Front Bottom Layer: 2

2 + 4 + 4 + 2 = 12

4) I cannot see the semicircle clearly, but I do know that a circle is 360 degrees. A semicircle, half of a circle, is 180 degrees.

180/18 (The angle of each section)

10

11 Sections

10 x 11 = 110

Answer:

6 units

Step-by-step explanation:

(-4 , -10) ; (-4 , -4)

Distance = \(\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}\)

               \(= \sqrt{(-4-[-4])^{2}+(-4-[-10])^{2}}\\\\= \sqrt{(-4+4)^{2}+(-4+10)^{2}}\\\\=\sqrt{0+(6)^{2}}\\\\= \sqrt{36}\\\\= 6\)

Answer:

6 units

Step-by-step explanation:

edge2021

Answer:

The total number of people at the stadium was 3200.

Step-by-step explanation:

5% = 160

160 x 20= 3200

Since 20 x 5 is 100, I multiplied 160 by 20 to get 3200.

Answer:

It is C, line KL has a slope of 0 and line MN is undefined and they're perpendicular

Step-by-step explanation:

Answer: I believe the answer is

A. Vertical angles prove Angle1 Is congruent to Angle4.

C. Angle5 and Angle3 are alternate interior angles

E. The triangles are similar because all corresponding angles are congruent.

Answer:

yep

Step-by-step explanation:

The main answer for the first argument is that we cannot prove that the band could play rock music based on the given premises and rules of inference.

1. Let's assign the following propositions:

  - P: The band could play rock music.

  - Q: The refreshments were delivered on time.

  - R: The New Year's party was canceled.

  - S: Alicia was angry.

  - T: Refunds were made.

2. The given premises can be expressed as:

  (¬P ∨ ¬Q) → (R ∧ S)

  R → T

3. To prove that the band could play rock music (P), we need to derive it using valid rules of inference.

4. Using the premises, we can apply the rule of modus tollens to the second premise:

  R → T        (Premise)

  Therefore, ¬R.

5. Next, we can use disjunctive syllogism on the first premise:

  (¬P ∨ ¬Q) → (R ∧ S)     (Premise)

  ¬R                    (From step 4)

  Therefore, ¬(¬P ∨ ¬Q).

6. Applying De Morgan's law to step 5, we get:

  ¬(¬P ∨ ¬Q)  ≡  (P ∧ Q)

7. Therefore, we can conclude that the band could play rock music (P) based on the premises and rules of inference.

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Answer:

KM=60°

Step-by-step explanation:

The average of arc LN and arc KM is equal to 110.

\(\frac{160+KM}{2} =110\)

160+KM=220

KM=60

The required solutions are as follows,
1. Angle e = Angle a
2. Angle f = Angle c
3. Ange a, b, and c add up to 180°.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°

here.
Angle e = Angle and as they are alternate angles,
Angle f = Angle c as they are alternate angles,

Ange a, b, and c add up to 180°. as they lie on a straight line.
Therefore angles e, f, and b also be added to  180°

Thus, the solution of the angles is shown above.

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Answer:

Sorry Bro

Step-by-step explanation:

I don't know the ans plzz donnot mind

\(\large\underline{\sf{Solution-}}\)

Consider LHS

\(\rm :\longmapsto\: \sqrt{\dfrac{secx + 1}{secx - 1} } \)

can be rewritten as

\(\rm \:  =  \: \sqrt{\dfrac{\dfrac{1}{cosx} + 1 }{\dfrac{1}{cosx} - 1} } \)

\(\rm \:  =  \: \sqrt{\dfrac{\dfrac{1 + cosx}{cosx}}{\dfrac{1 - cosx}{cosx}} } \)

\(\rm \:  =  \: \sqrt{\dfrac{1 + cosx}{1 - cosx} } \)

On rationalizing the numerator, we get

\(\rm \:  =  \: \sqrt{\dfrac{1 + cosx}{1 - cosx} \times \dfrac{1 - cosx}{1 - cosx} } \)

\(\rm \:  =  \: \sqrt{\dfrac{1 - {cos}^{2} x}{ {(1 - cosx)}^{2} } } \)

We know,

\(\red{\rm :\longmapsto\:\boxed{\tt{ {sin}^{2}x + {cos}^{2}x = 1}}}\)

So, using this, we get

\(\rm \:  =  \: \dfrac{ \sqrt{ {sin}^{2} x} }{1 - cosx} \)

\(\rm \:  =  \: \dfrac{ sinx }{1 - cosx} \)

\(\rm \:  =  \: \dfrac{1}{ \: \: \: \: \dfrac{1 - cosx}{sinx} \: \: \: \: } \)

\(\rm \:  =  \: \dfrac{1}{ \: \: \: \: \dfrac{1}{sinx} - \dfrac{cosx}{sinx} \: \: \: \: } \)

\(\rm \:  =  \: \dfrac{1}{ \: \: \: \: cosecx - cotx \: \: \: \: } \)

Hence, Proved

\(\rm \implies\:\: \boxed{\tt{ \sqrt{\dfrac{secx + 1}{secx - 1} } = \frac{1}{cosecx - cotx}}}\)

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

Additional Information:-

Relationship between sides and T ratios

sin θ = Opposite Side/Hypotenuse

cos θ = Adjacent Side/Hypotenuse

tan θ = Opposite Side/Adjacent Side

sec θ = Hypotenuse/Adjacent Side

cosec θ = Hypotenuse/Opposite Side

cot θ = Adjacent Side/Opposite Side

Reciprocal Identities

cosec θ = 1/sin θ

sec θ = 1/cos θ

cot θ = 1/tan θ

sin θ = 1/cosec θ

cos θ = 1/sec θ

tan θ = 1/cot θ

Co-function Identities

sin (90°−x) = cos x

cos (90°−x) = sin x

tan (90°−x) = cot x

cot (90°−x) = tan x

sec (90°−x) = cosec x

cosec (90°−x) = sec x

Fundamental Trigonometric Identities

sin²θ + cos²θ = 1

sec²θ - tan²θ = 1

cosec²θ - cot²θ = 1

So on solving the provided question we can say that -  the length is 4.5 times the area Area of rectangle = A = x X 4.5x; x = 5

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. You might also describe it as follows: a quadrilateral that is equiangular, which indicates that all of its angles are equal. The parallelogram might also have a straight angle. Squares are rectangles with four equally sized sides. A quadrilateral of the shape of a rectangle has four 90-degree vertices and equal parallel sides. As a result, it is sometimes referred to as an equirectangular rectangle. Because its opposite sides are equal and parallel, a rectangle is also known as a parallelogram.

here,

the length is 4.5 times the area

let length = x

breadth = 4.5 x

Aare of rectangle = A = x X 4.5x

100 = 4x^2

x = 5

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Answer:

4. 1/3

Step-by-step explanation:

You can use RISE/RUN from the bottom point! You end up with 1/3!

I hope this helps!

Answer:

2!! aka -1/3

Step-by-step explanation:

so you are looking for the slope!! slope equations are always rise over run!! in this you have a negative line because it is going down. you had to rise one to get to the other point and move three points! this would get you -1/3!

Answer:

x = 6

Step-by-step explanation:

• the diagonals of a parallelogram bisect each other , then

5x + 11 = 4x + 17 ( subtract 4x from both sides )

x + 11 = 17 ( subtract 11 from both sides )

x = 6

Since it's divided equally diagonally, 4x+17 and 5x+11 are equal.

Let's set them equal to each other and solve.]

\(4x+17=5x+11\)

Subtract 4x from both sides to combine like terms.

\(17=x+11\)

Now subtract 11 from both sides to isolate the variable and solve for x.

\(6=x\)

Flip the equation to put in standard form and now you have x :)

\(x=6\)

hope this helped!

Salik and Maya are discussing a project that examines the relationship between the number of siblings someone has and their household income. Maya predicts that those with more siblings will have a higher household income. Salik questions whether the number of siblings is a categorical variable since it is a whole number. Our response can be : "In order to conduct this project, we need to choose two quantitative variables, which are variables that can be measured and expressed as numbers. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value."

The number of siblings is a quantitative variable because it can be expressed as a whole number. Household income is also a quantitative variable because it can be measured and expressed as a numerical value. Categorical variables are variables that can be divided into distinct categories or groups, such as gender, race, or occupation. The number of siblings is not a categorical variable because it is a continuous variable that can take on any whole number value.

To examine the relationship between the number of siblings and household income, Maya and Salik could use statistics to analyze their data. They could calculate descriptive statistics such as the mean and standard deviation for each variable, as well as the correlation coefficient to determine the strength and direction of the relationship between the two variables. They could also use probability theory to make predictions about the likelihood of certain outcomes, such as the probability that someone with more siblings will have a higher household income.

The complete question is:

Our classmates, Maya and Salik, are talking about the variables they want to study and how they plan to collect their samples. Here is part of their conversation. Respond in the places that say “your response.”

Double-check that both of their variables are quantitative.

Maya: I want to look at the relationship between the number of siblings someone has and the household income. I predict that those with more siblings have a higher household income.

Salik: We need two quantitative variables for this project. Wouldn’t number of siblings be categorical since it is whole numbers?

Your response:.........

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(a) The presence of a confounding variable Z, such as the severity of the fire, could make the relationship between the number of firefighters (X) and property damage (Y) spurious.

(b) The presence of a confounding variable Z, such as the popularity of the incumbent member or the characteristics of the constituency, could make the relationship between campaign spending (X) and percentage of vote (Y) spurious.

(c) The presence of a confounding variable Z, such as the overall lifestyle or socioeconomic status of the women, could make the relationship between coffee consumption (X) and the risk of depression (Y) spurious.

(d) The presence of a confounding variable Z, such as the overall economic conditions or demand for rum in Havana, could make the relationship between Presbyterian ministers' salaries (X) and the price of rum (Y) spurious.

In each of the given examples, the reported pattern of covariation between X and Y may be influenced by a confounding variable Z. A confounding variable is a variable that is related to both the independent variable (X) and the dependent variable (Y), which can lead to a spurious relationship between X and Y.

The presence of a confounding variable can create the illusion of a direct relationship between X and Y when, in reality, the observed relationship is due to the influence of Z.

For example, in the case of firefighters and property damage, the severity of the fire (Z) could be the underlying factor driving both the number of firefighters and the extent of property damage.

Similarly, in the case of campaign spending and percentage of vote, factors such as the popularity of the incumbent member or the characteristics of the constituency (Z) could be influencing both variables.

In the case of coffee consumption and the risk of depression, other lifestyle or socioeconomic factors (Z) may be responsible for the observed relationship rather than coffee itself. And in the case of Presbyterian ministers' salaries and the price of rum, economic conditions or demand for rum (Z) in Havana could be driving both variables.

Identifying and controlling for confounding variables is crucial in research to ensure accurate interpretations of the relationship between X and Y. It allows researchers to isolate the true causal relationship between the variables of interest.

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