Am I correct for the following questions? because I'm not sure if I am.

If not what are the correct choices?

Which of the lines are parallel?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D


Which of the lines are perpendicular?
(1) a and b
(2) a and c
(3) a and D
(4) b and c
(5) b and D
(6) c and D


Please show all the work on how you got your answers

A system of equations can have no solution, one unique solution, or infinitely many solutions. A single solution indicates that the equations intersect at a point, no solution suggests parallel lines, and infinitely many solutions mean the equations are the same line expressed differently.

When discussing a system of equations, the possible solutions include having no solution, one unique solution, or infinitely many solutions. If a system has no solution, this typically means the equations represent parallel lines that never intersect. In contrast, if there is one solution, the equations represent two lines that intersect at a single point, such as the given solution (8, 2). The presence of infinitely many solutions indicates that the equations are the same line, represented in different forms, and thus they intersect at every point along the line.

To determine which of these scenarios applies to a particular system of equations, one should begin by determining the number of unknowns and the number of equations given. A single linear equation in two variables, such as those given in Practice Test 4 Solutions 12.1 Linear Equations, represents a line. A system composed of two linear equations can be solved using algebraic methods such as substitution or elimination.

If the system consists of the same equation expressed differently, such as y = 2x + 3 and 2y = 4x + 6, then they are essentially the same line, and the system would have infinitely many solutions.

[tex]\bf ~\hspace{5em} \textit{ratio relations of two similar shapes} \\\\ \begin{array}{ccccllll} &\stackrel{\stackrel{ratio}{of~the}}{Sides}&\stackrel{\stackrel{ratio}{of~the}}{Areas}&\stackrel{\stackrel{ratio}{of~the}}{Volumes}\\ \cline{2-4}&\\ \cfrac{\stackrel{similar}{shape}}{\stackrel{similar}{shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array}~\hspace{6em} \cfrac{s}{s}=\cfrac{\sqrt{Area}}{\sqrt{Area}}=\cfrac{\sqrt[3]{Volume}}{\sqrt[3]{Volume}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \cfrac{small}{large}\qquad \qquad \stackrel{sides}{\cfrac{3}{7}} ~~ = ~~ \stackrel{areas}{\sqrt{\cfrac{A_1}{98}}}\implies \left( \cfrac{3}{7} \right)^2 = \cfrac{A_1}{98}\implies \cfrac{3^2}{7^2}= \cfrac{A_1}{98} \\\\\\ \cfrac{9}{49}= \cfrac{A_1}{98}\implies 882 = 49A_1\implies \cfrac{882}{49}=A_1\implies 18=A_1[/tex]

Answer:

The answer to your question is 18 in²

Step-by-step explanation:

Data

Big rectangle                  Small rectangle

Area = 98 in²                   Area = ?

Height = 7 in                    Height = 3 in

Process

1.- Calculate the base of the big rectangle

         Area = base x height

solve for base

         base = Area / height

substitution

          base = 98 / 7

          base = 14 ni

2.- Use proportions to find the base of the small rectangle

           x / 3 = 14 / 7

Simplify

          x = (14)(3) / 7

result

          x = 6 in                    

3.- Calculate the area of the small rectangle

          Area = 6  x 3

                   = 18 in²

Answer:

The vertex is the point (6,-31)

Step-by-step explanation:

we have

[tex]f(x)=x^2-12x+5[/tex]

This is a vertical parabola open upward

The vertex represent a minimum

Convert to vertex form

Complete the square

[tex]f(x)=(x^2-12x+6^2)+5-6^2[/tex]

[tex]f(x)=(x^2-12x+36)-31[/tex]

Rewrite as perfect squares

[tex]f(x)=(x-6)^2-31[/tex] -----> equation in vertex form

therefore

The vertex is the point (6,-31)

Answer:

[tex] Y(t)= 475 (1.076)^t [/tex]

Where Y(t) represent the average annual per capita health care costs

475 represent the initial amount for the average annual per capita health care costs

t represent the number of years since 1970

And 1.076 represent the growth factor given by:

[tex] 1+r = 1.076[/tex]

And solving for r we got:

[tex] r = 1.076-1 =0.076[/tex]

So for this case we can say that the value 1.076 represent the growth factor.

Step-by-step explanation:

For this case we have the following model given:

[tex] Y(t)= 475 (1.076)^t [/tex]

Where Y(t) represent the average annual per capita health care costs

475 represent the initial amount for the average annual per capita health care costs

t represent the number of years since 1970

And 1.076 represent the growth factor given by:

[tex] 1+r = 1.076[/tex]

And solving for r we got:

[tex] r = 1.076-1 =0.076[/tex]

So for this case we can say that the value 1.076 represent the growth factor.

Final answer:

In the provided expression, 1.076 represents the annual growth factor of US health care costs, indicating an annual increase of 7.6% since 1970.

Explanation:

The expression 475 * 1.076 ^ t represents the average annual per capita health care costs in the US as a function of the number of years since 1970. Here, 1.076 signifies the annual growth factor of the costs, which means health care costs have been increasing by 7.6% each year since 1970. This exponential function captures the trend of increasing health care expenditure, which plays a significant role in the nation's economy, consuming a larger share of the Gross Domestic Product (GDP) over time.

Answer:

7

Step-by-step explanation:

24/1/3 -8/5/6- 8/1/2 (accorin to fractions la)

improper fraction make it into proper fraction

73/3- 53/6- 17/2 (change the base of 3 and 2 into 6)

146/6-53/6-51/6= (146-53-51)/6

= 7

Answer:

Step-by-step explanation:

you got to try your hardest

Answer:

I do not know sorry

Step-by-step explanation:

Answer: her sales for the month of May is $55000

Step-by-step explanation:

Let x represent her total sales for the month of May.

Each month she receives a 5% commission on all her sales of medical supplies up to $20,000. This means that for her first sales worth $20000, she earns a commission of

5/100 × 20000 = 1000

She also earns 8.5% on her total sales over $20,000. This means that for sales over $20000, she earns

8.5/100(x - 20000) = 0.085x - 1700

Her total commission for May was $3,975. The expression becomes

1000 + 0.085x - 1700 = 3975

0.085x = 3975 + 1700 - 1000

0.085x = 4675

x = 4675/0.085

x = 55000

Kim's total sales for the month of May were $55,000. The first $1,000 of her commission came from the 5% commission on her first $20,000 in sales. The remaining $2,975 of her commission came from the 8.5% commission on her additional $35,000 in sales.

To find out Kim's sales for the month of May, let's first understand her commission structure. She earns a 5% commission on all her sales of medical supplies up to $20,000, and 8.5% on any of her total sales over $20,000. Her total commission for the month of May is given as $3,975.

If her sales were $20,000 or below, her commission would be 5% of that, which would be $1,000 at most. Her commision is definitely more than that, we can infer that her sales were more than $20,000.

To figure out her actual sales, we need to subtract $1,000 from her total commission of $3,975, which gives us $2,975. This amount is the commission she earned at the rate of 8.5% for sales over $20,000. To find out the sales corresponding to this commission, we should divide $2,975 by 8.5% (or 0.085). That gives us the sales amount over $20,000 as $35000.

Therefore, Kim's total sales for the month are the $20,000 she sold to make the first $1,000 of her commission, plus the additional $35,000. So Kim's total sales for the month of May were $55,000.

https://brainly.com/question/6615293

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Answer:

  see below

Step-by-step explanation:

When a line goes through the origin, it expresses a proportional relationship such that for every point on the line ...

  y/x = constant

The graph shows points (-5, 4) and (5, -4) as being on the line. So, we can determine the constant to be ...

  constant = (y-value)/(x-value) = -4/5 . . . . . using point K

Then the proportion can be written as ...

  y/x = -4/5

Multiplying both sides of this equation by -1 lets us also write the same relation as ...

  -y/x = 4/5 . . . . matches the 2nd answer choice

Answer:

a) Independent

b) Quantitative  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 517

Sample:

Married lawyers and their spouses.

Response variable:

Comparison of academic aptitudes of married lawyers and their spouses.

a) The given sampling is an example of independent sampling.

This is an independent sample because an individual of sample does not effect any other individual of the sample.

b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.

It is a quantitative measure because the scores can be expressed in numerical.

Answer:

The sampling is independent and the response variable is quantitative.

Explanation:

Given a random sample of [tex]517[/tex] couples

Learn more about Random sample, refer:

Answer:

P[X=3,Y=3] = 0.0416

Step-by-step explanation:

Solution:

- X is the RV denoting the no. of customers in line.

- Y is the sum of Customers C.

- Where no. of Customers C's to be summed is equal to the X value.

- Since both events are independent we have:

                         P[X=3,Y=3] = P[X=3]*P[Y=3/X=3]

              P[X=3].P[Y=3/X=3] = P[X=3]*P[C1+C2+C3=3/X=3]

        P[X=3]*P[C1+C2+C3=3/X=3] = P[X=3]*P[C1=1,C2=1,C3=1]        

              P[X=3]*P[C1=1,C2=1,C3=1]  = P[X=3]*(P[C=1]^3)

- Thus, we have:

                        P[X=3,Y=3] = P[X=3]*(P[C=1]^3) = 0.25*(0.55)^3

                        P[X=3,Y=3] = 0.0416

Answer: 60°

Step-by-step explanation:

When a figure has a rotational symmetry, it maps onto itself under rotation about a point at the centre.

When an hexagon rotate onto itself,

the vertices must cover to vertices and from sides to sides. There are six angles in a hexagon and the sum of the angles is 360°. Therefore, each angle has a measure of 360°/6 is equal to 60°.

Rotating subsequently by 60 degree will rotate a hexagon onto itself. A hexagon has 6 rotations, that is, a hexagon has a rotational symmetry of 6 and at angle 60°, the hexagon will rotate onto itself.

Answer:

Vol=[tex]450,000m^3[/tex]

Step-by-step explanation:

Volume of rectangular prism is obtained using the formula:

[tex]V=whl\\w-width\\h-height\\l-length[/tex]

Dimensions of shipping containers is given as:

[tex]w=2.5m\\h=2.5m\\l=6m\\[/tex]

To obtain the volume of the cargo ship, we need to calculate the volume of 1 unit of a shipping container then multiply it by the number of containers the ship can carry.

let n be the number of containers ship can carry.

[tex]V_c=whl\\V_c=2.5m\times2.5m\times6m\\V_c=37.5m^3\\[/tex]

Volume of ship,[tex]V_s[/tex]

[tex]V_s=nV_c[/tex]

But n=12000

[tex]V_s=12000\times37.5m^3\\=450,000m^3[/tex]

Answer: the area of the shaded region is 72.96 ft²

Step-by-step explanation:

The formula for determining the area of a circle is expressed as

Area = πr²

Where

r represents the radius of the circle.

π is a constant whose value is 3.14

From the information given,

Diameter of circle = 16 feet

Radius = diameter/2 = 16/2 = 8 feet

Area of circle = 3.14 × 8² = 200.96ft²

The sides of the square are equal. To determine the length of each side of the square, L, we would apply Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side²

Therefore,

16² = L² + L²

256 = 2L²

L² = 256/2 = 128

L = √128 ft

Area of the square is

L² = (√128)²

Area = 128 ft²

Area of shaded region is

200.96 - 128 = 72.96 ft²

Answer:

a= 0.0897

b= 0.71186

Power of the test for detecting a true mean output voltage of 5.1 volts is 0.28814.

Step-by-step explanation:

See attached pictures.

The value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.

It is the ratio of favorable events to the total events.

Given

Standard deviation ([tex]\sigma[/tex]) = 0.25

[tex]\mu[/tex] = 5

n = 8

The acceptance region as

4.85 ≤ [tex]\rm \bar{x}[/tex] ≤5.15

a.  Then type I error of probability,

[tex]\alpha = P(4.85> \bar{x}\ when\ \mu =5) + P(\bar{x}\ > 5.15\ when\ \mu =5)\\\alpha = P(\dfrac{4.85-5}{0.25\sqrt{8} } > \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } ) + (\dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} } > \dfrac{4.85-5}{0.25\sqrt{8} })\\\alpha = 2P ( z <-1.697)= 0.0897[/tex]

Where, [tex]z = \dfrac{\bar{x} - \mu}{\sigma / \sqrt{n} }[/tex]

b.  type II error

[tex]\beta = P(4.85 \leq \bar{x} \leq 5.15\ when\ \mu = 5.1)\\\beta = (\dfrac{4.85 - \mu}{0.25/\sqrt{8} }\leq \dfrac{\bar{x} - \mu}{0.25/\sqrt{8} }\leq \dfrac{5.15 - \mu}{0.25/\sqrt{8} }\ when\ \mu=5.1 )\\\beta = P(-2.8284\leq z\leq 0.5657)\\\beta = P(z\leq 0.5657)- P(z\leq -2.8284)\\[/tex]

therefore, the power of the test for detecting a true mean output voltage of 5.1 volt is

[tex]\begin{aligned} 1 - \beta &= 0.28281 \\\beta &= 0.71186\\\end{aligned}[/tex]

Thus, the value of [tex]\alpha[/tex] and [tex]\beta[/tex] are 0.0897 and 0.71186 respectively.

More about the probability link is given below.

https://brainly.com/question/795909

Answer:

A. small changes have been made within exact quotations.

Step-by-step explanation:

Brackets are pair of marks which enclose words or figures in order to separate them from the context. Thus, the use of brackets indicate that the quotation's exact punctuation has been adapted to the punctuation or grammar structure of the essay.

Answer:

The answer is b and d.

Step-by-step explanation:

Answer:24

Step-by-step explanation:

By setting up an equation c + 2c = 72, where 'c' represents cheese slices and '2c' represents pepperoni slices, and solving for 'c', we find there were 24 slices of pizza with just cheese.

To solve the problem about the number of pizza slices with different toppings, we can set up an equation based on the information given.

If 'c' represents the number of slices with just cheese, then 2c would represent the number of slices with pepperoni, because there are twice as many pepperoni slices as there are cheese slices. Since the total number of slices is 72, we can form the following equation:

c + 2c = 72

Combining like terms (c + 2c), we get 3c = 72. To find the value of 'c', we divide both sides of the equation by 3:

3c / 3 = 72 / 3

c = 24

Therefore, there were 24 slices of pizza with just cheese.

Answer:

[tex]a_1 = 5,\\a_n =4 a_{n-1}[/tex]

Step-by-step explanation:

The first term of the geometric sequence is

[tex]a_1 =5[/tex].

The common ratio between the consecutive terms is

[tex]\dfrac{20}{5} = 4,[/tex]

[tex]\dfrac{80}{20} = 4;[/tex]

therefore, we see that the nth term is found by

[tex]a_n =4 a_{n-1}[/tex]

Thus, the recursive formula for the geometric sequence is

[tex]a_1 = 5,\\a_n =4 a_{n-1}.[/tex]

The recursive formula for finding the nth term of a geometric sequence is a_n = a_1 * r^(n-1), where a_n represents the nth term, a_1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80. The recursive formula for this sequence is a_1 = 5 and a_n = 4 * a_(n-1).

The recursive formula for finding the nth term of a geometric sequence is given by: an = a1 * r(n-1) where an represents the nth term, a1 is the first term, and r is the common ratio. In this case, the given sequence is 5, 20, 80, ...

Since the first term is 5, and the common ratio between terms is 4, the recursive formula for this sequence is: a1 = 5 and an = 4 * an-1.

Answer:

Step-by-step explanation:

Answer:

x = 8, y = 4√3, z = 8√3

Step-by-step explanation:

Assuming that y is the altitude of the triangle (perpendicular to the hypotenuse), the triangles are similar.  So we can write proportions:

x / 4 = 16 / x

x² = 64

x = 8

4 / y = y / 12

y² = 48

y = 4√3

z / 12 = 16 / z

z² = 192

z = 8√3

Note: after finding one side, you can also use Pythagorean theorem to find the other two sides.

Answer:

[tex]y=\frac{24}{x}[/tex]

Step-by-step explanation:

We have been given that a certain function is an inverse proportion. We are asked to find the formula for the function if it is known that the function is equal to 12 when the independent variable is equal to 2.  

We know that two inversely proportional quantities are in form [tex]y=\frac{k}{x}[/tex], where y is inversely proportional to x and k is constant of variation.

Upon substituting [tex]y=12[/tex] and [tex]x=2[/tex] in above equation, we will get:

[tex]12=\frac{k}{2}[/tex]

Let us solve for constant of variation.

[tex]12\cdot 2=\frac{k}{2}\cdot 2[/tex]

[tex]24=k[/tex]

Now, we will substitute [tex]k=12[/tex] in inversely proportion equation as:

[tex]y=\frac{24}{x}[/tex]

Therefore, the formula for the given scenario would be [tex]y=\frac{24}{x}[/tex].

Answer:

360 mg.

Step-by-step explanation:

The medicine has a decay rate of 40% in 25 hours, which means after 24 hours its amount will be 100% - 40% = 60% it's original value.

Let us call [tex]t[/tex] the number of hours passed and [tex]d[/tex] the number of 24-hours passed, then we know that

[tex]t = 24d[/tex].

Now, the amount [tex]c[/tex] of medicine left after time [tex]d[/tex] (dth 24-hour) will be

[tex]c = 1000(0.6)^d[/tex]

and since [tex]t =24d[/tex], we have

[tex]$\boxed{c = 1000(0.6)^{\frac{t}{24} }}$[/tex]

We now use this equation to find the final amount after [tex]t =48 hours[/tex]:

[tex]c = 1000(0.6)^{\frac{48}{24} }[/tex]

[tex]c = 1000(0.6)^2 }[/tex]

[tex]\boxed{c =360mg}[/tex]

Answer: Xavier bought 2 apples and 9 bananas.

Step-by-step explanation:

Let x represent the number of apples that Javier bought.

Let y represent the number of bananas that Javier bought.

At the store, he bought $6 worth of apples and bananas. Each apple costs $0.75 and each banana costs $0.50. This is expressed as

0.75x + 0.5y = 6 - - - - - - - - - - - - 1

He bought a total of 11 apples and bananas altogether. This means that

x + y = 11

Substituting x = 11 - y into equation 1, it becomes

0.75(11 - y) + 0.5y = 6

8.25 - 0.75y + 0.5y = 6

- 0.75y + 0.5y = 6 - 8.25

- 0.25y = - 2.25

y = - 2.25/ - 0.25

y = 9

x = 11 - y = 11 - 9

x = 2

Answer:

The probability that the customer must open 3 or more bottles before finding a prize is 0.64

Step-by-step explanation:

In order for a customer to have to open at least 3 bottles before winning a prize, then the first two bottles shouldnt have a price. The probability that a bottle doesnt have a price is 1-0.2 = 0.8. Since the bottles are independent from each other, then the probability that 2 bottles dont have a prize is 0.8² = 0.64. Therefore, the probability that the customer must open 3 or more bottles before finding a prize is 0.64

Answer:

We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.

Step-by-step explanation:

We know that the probability that each bottle cap reveals a prize is 0.2 and winning is independent from one bottle to the next.

Therefore, we get p=0.2 and q=1-p=1-0.2=0.8.

So we will calculate the probability that the buyer will not win the prize in the first and second bottles. We get:

[tex]P=0.8\cdot0.8=0.64[/tex]

We conclude that the probability that a customer must open three or more bottles before winning a prize is P=0.64.

The system has infinitely many solutions because both equations represent the same line in the coordinate plane. So C. Infinity many solutions will be the answer.

To determine the number of solutions for this system of equations, let's analyze it:

[tex]\[\left\{\begin{array}{l}x + y = 3 \\5x + 5y = 15\end{array}\right.\][/tex]

We can simplify the second equation by dividing both sides by 5:

[tex]\[x + y = 3\][/tex]

This equation is identical to the first equation in the system. So, the two equations represent the same line in the coordinate plane.

When two equations represent the same line, they have infinitely many solutions, because every point on the line satisfies both equations.

Therefore, the correct answer is:

(C) Infinitely many solutions

Complete Question:

Answer:

The probability associated with the range lethal morphine blood levels is 0.9902.

Step-by-step explanation:

Let X = lethal blood concentration of morphine.

The random variable X is normally distributed with parameter μ = 2.5 μg/ mL and σ = 0.95 μg/ mL.

Compute the probability of X within the range 0.05 to 4.95 μg/ mL as follows:

[tex]P(0.05<X<4.95)=P(\frac{0.05-2.5}{0.95}<\frac{X-\mu}{\sigma}<\frac{4.95-2.5}{0.95})\\=P(-2.58<Z<2.58)\\=P(Z<2.58)-P(Z<-2.58)\\=P(Z<2.58)-[1-P(Z<2.58)]\\=2P(Z<2.58)-1\\=(2\times0.9951)-1\\=0.9902[/tex]

*Use a z-table for the probability.

Thus, the probability associated with the range lethal morphine blood levels is 0.9902.

Using the properties of the normal distribution, we calculate the probability associated with the lethal morphine blood levels range of 0.05 to 4.95 µg/mL is essentially 1.0 (100%), meaning a lethal concentration is almost certain to fall within this range.

To calculate the probability associated with the range of lethal morphine blood levels, we need to use the properties of the normal distribution. The mean (μ) lethal concentration is 2.5 µg/mL and the standard deviation (σ) is 0.95 µg/mL. We are examining the range 0.05 to 4.95 µg/mL.

First, we calculate the z-scores for both the lower limit (0.05 µg/mL) and the upper limit (4.95 µg/mL) of the range using the formula:

Z = (X - μ) / σ

For the lower limit:

Zlower = (0.05 - 2.5) / 0.95 ≈ -2.58

For the upper limit:

Zupper = (4.95 - 2.5) / 0.95 ≈ 2.58

Using a standard normal distribution table, we find the corresponding probabilities for both z-scores. Since the z-scores are symmetrical about the mean, the probability for both is the same. Thus, the probability up to Zlower is about 0.495 (adjusted from table values), and the probability up to Zupper is also about 0.495.

To find the probability within the range, we subtract the probability of the lower limit from the upper limit:

P(0.05 µg/mL < X < 4.95 µg/mL) = P(Zupper) - P(Zlower)

P(0.05 µg/mL < X < 4.95 µg/mL) ≈ 0.495 - (1 - 0.495) = 0.495 - 0.505 = -0.01

The negligible negative value suggests an error, likely due to rounding issues when looking up z-scores in the standard normal distribution table. Correctly, the total area under the curve, which corresponds to the probability of the range, should be virtually 1.0 (or 100%) since both z-scores are quite extreme (far in the tails of the distribution).

Therefore, practically, the probability associated with the given range of lethal morphine blood levels is essentially 1.0 (or 100%), meaning it is almost certain that a lethal concentration falls within this range.

The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.

To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.

Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:

P(20, 7) = 20! / (20 - 7)!

where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.

The number of different possibilities for how the people could get off the elevator can be calculated using the concept of permutations.

To calculate the number of different possibilities for how the people could get off the elevator, we can use the concept of permutations.

Since each person can choose one of the seven floors to get off at, and there are twenty people, we need to find the number of permutations of 20 people taken 7 at a time. This can be calculated using the formula:

P(20, 7) = 20! / (20 - 7)!

where the exclamation mark (!) denotes factorial. Evaluating this expression gives us the total number of different possibilities for how the people could get off the elevator.

Answer:

Length=96 feet

Width=70 feet

Step-by-step explanation:

Let the length = l

The width 26 feet less than its length=l-26

Perimeter of the giant rectangular movie screen= 332 feet

Perimeter of a rectangle = 2(L+W)

332=2(l+l-26)

332=2(2l-26)

Expanding the brackets

332=4l-52

4l=332+52

4l=384

l=384/4=96

The Length of the giant rectangular movie screen is 96 feet.

The Width, W=l-26=96-26=70 feet

The dimensions of the screen are: [tex]Length: 96\ feet[/tex] and [tex]Width: 70\ feet[/tex]

To find the dimensions of the IMAX screen, we need to set up a system of equations based on the given information. Let's denote the length of the screen by [tex]\( L \)[/tex] and the width by [tex]\( W \)[/tex].

Given:

1. The width is [tex]26 \ feet[/tex] less than the length: [tex]\( W = L - 26 \)[/tex]

2. The perimeter of the rectangle is [tex]332\ feet: \( 2L + 2W = 332 \)[/tex]

First, we can simplify the perimeter equation:

[tex]\[2L + 2W = 332\][/tex]

Divide both sides by [tex]2[/tex]

[tex]\[L + W = 166\][/tex]

Now, substitute the expression for [tex]\( W \)[/tex] from the first equation into the simplified perimeter equation:

[tex]\[L + (L - 26) = 166\][/tex]

Combine like terms:

[tex]\[2L - 26 = 166\][/tex]

Add 26 to both sides:

[tex]\[2L = 192\][/tex]

Divide both sides by [tex]2[/tex]

[tex]\[L = 96\][/tex]

Now that we have the length, we can find the width using the equation [tex]W = L - 26 \)[/tex]

[tex]\[W = 96 - 26 = 70\][/tex]

Answer:

3/35

Step-by-step explanation:

(15/50)×(14/49)

= 3/35 or 0.0857

Answer:

3/35.

Step-by-step explanation:

Probability (the first one selected has the decoder ring) = 15/50 = 3/10.

Probability (the second one selected has the decoder ring) = 14/49 = 2/7.

Therefore the probability that both have the ring =

3/10 * 2/7

= 6/70

= 3/35.

Note: The probabilities are multiplied because the 2 events are independent.