Find the values of x and y. The diagram is not to scale

If the surface area of the rectangular box is 4 m² then the dimensions that maximize its volume is  (2/√3 , 2/√3 , 1/√3)  .

In the question ,

let length of rectangular box be = l

let width of rectangular box be = b and

let height of rectangular box be = h .

Since the box has no top ,

So , the surface area is = lb + 2bh + 2hl = 4

we get h = (4-lb)/(2l + 2b) .

The volume of the box is given as  V = l×b×h .

Substituting the value of h from above in the volume formula , we get ,

V = lb(4-lb)/(2l + 2b)

differentiating it with respect to l ,

we get ,

dV/dl = [((2l+2b)(4b-2lb²)-lb(4-lb).2)/(2l+2b)²] = 0

Simplifying further ,

we get ,

2l² + 4lb - 8 = 0       ....equation(1)

Differentiating volume with respect to "b" .

dV/db = [((2l+2b)(4l-2l²b)-lb(4-lb).2)/(2l+2b)²] = 0

simplifying further ,

we get ,

2b² + 4lb - 8 = 0        ...equation(2) .

Simplifying equation(1) and (2) , we get

l = b  ,

Substituting l = b in equation(1) ,

we get ,

2l² + 4l² = 8

l = 2/√

and b = 2/√3 .

Substituting the values in h ,

we get ,

h = (4-lb)/(2l + 2b)

h = 1/√3 .

Therefore , the dimensions of the box is (2/√3 , 2/√3 , 1/√3) .

The given question is incomplete , the complete question is

A rectangular box with no top is to have a surface area of 4 m². find the dimensions (in m) that maximize its volume.

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(-∞, ∞) is the domain of y=-0.25x² and (−∞,0] is range.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

The given function is y=-0.25x²

y equal to minus zero point two five times of x square.

We need to find the domain and range of the function.

Let us find few points of x and y.

x    0    1            2           3              4

y    0    -0.25    -1        -0.5625     -4

In the given attachment the graph is given.

The domain is:

{x∣x is R} or (-∞, ∞)

The range is {x∣x≤0} or (−∞,0]

Hence, the domain of y=-0.25x² is (-∞, ∞) and range is (−∞,0].

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The required linear function y = -x + 2.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

The equation for the slope, m, of a line is:

m = y₁- y₀ / x₁ - x₀                         {equation 1}

The equation f(0) = 2 tells us that x₀ = 2and y₀ = 0,

substitute this into equation [1].

m = y₁- (0) / x₁ - 2                         {equation 2}

The equation f(3) = -1 tells us that x₁ = -1 and y₁= 3,

substitute this into equation [2].

m = 3/-3

m = -1

Substitute m to the equation y = mx + b,

y = -x + b

Now, substitute the value of x = 2 and y = 0

b = 2.

Now the linear function,

y = -x + 2

Therefore the linear function y = -x + 2.

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The correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."

The relationship between two terms on either side of an equal sign is easily demonstrated using a simple equation.

Additionally, one or more of the four arithmetic operations that simple equations do include addition, fundamental arithmetic, multiplication, and division.

The three possible forms of the equation system are point-slope form, standard form, and slope-intercept form.

So, given equations:

y = 1/2 * x - 3

y = - 1/2 * x - 3

As we are aware, a line's slope-intercept form is:

y = m x + c  

Therefore, it is clear from equations 1 and 2 that:

m1 = 1/2 and c1 = -3

m2 = -1/2 and c2 = -3

Therefore, the correct statement according to the given equation is statement (D)"They have a single solution since they have various y-intercepts but the same slopes."

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Complete question:
A system of equations is given below. y=1/2x-3 and -1/2x-3. Which of the following statements best describes the two lines?

a. They have the same slope but different y-intercepts, so they have no solution.

b/. They have the same slope but different y-intercepts, so they have one solution.

c. They have different slopes but the same y-intercept, so they have no solution.

d. They have different slopes but the same y-intercept, so they have one solution.

Answer:

73u/ - 11

Step-by-step explanation:

Answer:

-5.05. U -6

Step-by-step explanation:

Distribute the Negative Sign:=3.65u−11+−1(−5+8.7u)=3.65u+−11+(−1)(−5)+−1(8.7u)=3.65u+−11+5+−8.7uCombine Like Terms:=3.65u+−11+5+−8.7u=(3.65u+−8.7u)+(−11+5)=−5.05u+−6

The transition to -24 degrees will take three hours .The balance between energy coming into and going out of the planet's system determines its temperature.

Explanation:

-8% / -24 = 3.

The transition to -24 degrees will take three hours.

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the probability that a person picked at random from the group is a male or female is fit to climb Mount Shasta is  0.472 (or in percent near 47.2%).

The probability is computed by dividing the total number of possible outcomes by the number of possible ways the event might occur. Probability and odds are two distinct ideas. Odds are calculated by dividing the likelihood of an event by the likelihood that it won't.

Classical: (equally probable outcomes) (equally probable outcomes) Let S be the sample space (the collection of all unique outcomes that might occur).

Subjective Probability. Definition of Relative Frequency.

1. Determine the number of male climbers:

200 men - 100%

x men - 12 %

. Of the 60 people in California who are physically capable of climbing Mount Shasta, 24 are men, leaving 36 women.

 The likelihood that a guy will be selected at random from the group is

 The likelihood that a random member of the group is physically capable of climbing Mount Shasta is: 0.472

 0.472 (or, in percentage terms, close to 47.2%).

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Answer:

m∠5 + m∠6 =180°

m∠2 + m∠3 = m∠6

m∠2 + m∠3 + m∠5 = 180°

Step-by-step explanation:

m∠5 + m∠6 are linear pairs, so their sum has to be 180°.

m∠2 + m∠3 = m∠6 because of the exterior angle theorem, which states that the measure of an exterior angle is equal to the sum of the two opposite interior angles. (using this logic, m∠1 equals the sum of m∠5 and m∠3, and m∠4 equals the sum of m∠2 and m∠2).

m∠2 + m∠3 + m∠5 = 180° because the triangle sum property says that the sum of a triangle's interior angles will equal 180°.

Possible distinction between  the center of the sphere and  surface of the sphere is

The sphere is one of the most significant mathematical figures. Spheres and nearly-spherical objects can be seen in both nature and industry.

Soap bubbles and other bubbles have a spherical shape when they are in an equilibrium state. The celestial sphere is a fundamental concept in astronomy, and the Earth is usually represented as spherical in geography.

The majority of pressure vessels, curved mirrors and lenses, and other manufactured items are based on spheres. Because spheres roll effortlessly in all directions, the majority of balls used in sports and toys are spherical, just like ball bearings.

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Answer:

Step-by-step explanation:

3,808

Answer: 3808

Step-by-step explanation:

2 times 34 = 68

68 times 56 = 3808

Answer is 3808

Answer:

12 and 24 gcf = 4

so the only choice left is

(H) 4x²y

(I) 4xy

12x²y³ + 20x³y = lowest of x is x² and y is y

then its

(H) 4x²y

Answer: 9:50 AM/PM

Step-by-step explanation: Since the shorthand (hour) is on the 9, the hour is 9:00. The long hand (minutes) is on the 10, so it is 50. So, therefore we have 9:50. We don't know if it's am or pm, so we don't know if it's in the morning or the afternoon.

by using log notation, the value of x =㏒₃500 or x = 5.657

Log notation is a mathematical expression used to represent any exponential relationship in its inverse form.

we use log notation to solve an equation in where an unknown variable is in index form. By applying logarithm laws, we write an exponential equation in the inverse form and finally we get the unknown values.

in the above equation 3ˣ = 500

using log notation, we get ㏒₃500 = x

                                    x= 5.657

hence, the solution is x = 5.657

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Answer:

(1, - 1 )

Step-by-step explanation:

x + y = 0 → (1)

5x + y = 4 ( subtract 5x from both sides )

y = 4 - 5x → (2)

substitute y = 4 - 5x into (1)

x + 4 - 5x = 0

4 - 4x = 0 ( subtract 4 from both sides )

- 4x = - 4 ( divide both sides by - 4 )

x = 1

substitute x = 1 into (1) and solve for y

1 + y = 0 ( subtract 1 from both sides )

y = - 1

solution is (1, - 1 )

The term that describes measures that would be taken to decrease the size of a professional sports is contraction.

Contraction is the act of decreasing or drawing collectively to make smaller; the alternative of expansion. In this case, the proprietors need to lessen the wide variety of groups with the aid of using removing franchises which are dropping the maximum money. Players who're on Minor League or break up contracts aren't completely assured their salaries. A participant on a break up or Minor League settlement will earn the prorated part of his Major League earnings for time spent at the Major League roster.

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Answer:   (4b, -3a)

Reason:

When reflecting over the line y = x, we swap the positions of the x and y coordinates.

The reflection rule is [tex](\text{x},\text{y}) \to (\text{y},\text{x})[/tex]

As an example: [tex](2,3) \to (3,2)[/tex]

Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

The area of a shape is the space enclosed within the perimeter or the boundary of the given shape.

Here, μ = 100, σ = 15 and x = 125. We need to compute P(X >= 125). The corresponding z-value is calculated using Central Limit Theorem.

z = (x - μ)/σ

z = (125 - 100)/15 = 1.67

z = 1.67

Therefore,

P(X >= 125) = P(z <= (125 - 100)/15)

= P(z >= 1.67)

= 1 - 0.9525

= 0.0475

Area to the right of 125 is 0.0475 and area to the left of 125 is 0.9525 .

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Following equation represents the parabola in the graph:

x=1/12(y+4)^2-2

From the graph, we see that;

Focus = (-4, -2)

We use the equation x=h−p  to find the directrix.

General form of equation of a parabola is;

(y - k)² = 4p(x - h)

where;

focus is (h + p, k)

directrix is x = h - p

If we are talking about the function y = ax² + bx + c, then since it is a continuous function on the whole real line, it must cross the y–axis at (0 , c).

However x = y² + 1 is a parabola(not a function) that does not cross the y–axis.

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Answer:

The answer should be A.

Step-by-step explanation:

Congruent triangle: The values of x, y, and z are x = 23; y = 7 and z = 11.

What is a congruent triangle?

If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent.

Given: ΔPRS ≅ ΔCFH

Since both triangles are congruent, m<R = m<F

m<F is a right angle = 90°.

Thus, 13y - 1 = 90

13y = 90 + 1

13y = 91

y = [tex]\frac{91}{13}[/tex]

y = 7

Also, by inspection

PS = CH

⇒ 2x - 7 = 39

⇒ 2x = 39 + 7

⇒ 2x = 46 ⇒ x = [tex]\frac{46}{2}[/tex]

x = 23

Since m<R is 90°, then

m<S = 180 - (90 + 28)

m<S = 62°

By inspection,

m<S = m<H

Thus,

⇒ 6z - 4 = 62

⇒ 6z = 66

z = [tex]\frac{66}{6}[/tex]

z = 11

Hence, x = 23, y = 7 and z = 11.

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

in our case the desired cases are all students with financial aid : 6101

and the totally possible cases are 10730.

so, the probability to pick a student at random, who receives financial aid is

6101 / 10730 = 0.568592731... = 56.8592731...% ≈

≈ 57%

The solution of the inequality 9x + 6  ≥  132 and -7x + 19 < -128 is x ≥ 14 and x > 21.

Compound inequalities are a type of inequality that has two or more parts.

In other words, a compound inequality is an inequality that combines two simple inequalities.

Therefore, let's solve the compound inequality as follows:

9x + 6 ≥ 132 and -7x + 19 < -128

Let's solve them independently.

9x + 6 ≥ 132

subtract 6 from both sides of the inequality

9x + 6 ≥ 132

9x + 6 - 6 ≥ 132 - 6

9x ≥ 126

divide both sides by 9

x ≥ 126 / 9

x ≥ 14

-7x + 19 < -128

subtract 19 from both sides of the inequality

-7x + 19 - 19 < - 128 - 19

-7x < - 147

divide both sides by - 7

x > - 147 / -7

x > 21

Therefore, the solution is  x > 21 and x ≥ 14

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The probability that the flight is less than 71 minutes is 0.1471

Let the distribution of the time to fly between New York City and Chicago be X

X~U(66,100)

where,

66 = minimum

100 = maximum

We need to find P(X<71)

We know that in the case of uniform distribution,

P(X<x) = (x - a) / b -a

where,

a = min value

b = max value.

Hence P(X<71)

= (71 - 66) / (100 - 66)

= 5/34

= 0.1471

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a) California has the lowest premium and Pennsylvania has the highest premium.

b) Pennsylvania has the highest median premium.

c) Texas has the smallest range of premium. California has the smallest interquartile range.

Insurance Premium:

A premium is the amount an individual or business pays for an insurance policy. Premiums are paid for policies that cover health insurance, auto insurance, home insurance, and life insurance. When the premium is paid, it becomes income for the insurance company. It also constitutes liability, as the insurer must pay for claims arising from the policy. Failure to pay individual or corporate premiums may result in the cancellation of the policy.

The insurance company actuary is responsible for determining premium payments using statistics and calculations. Determine the likelihood of encountering an event or accident requiring insurance coverage. We will also be charged for any costs associated with the coverage.

Using the above factors to determine the premium, the actuary determines the price charged by the insurance company so that the amount the actuary receives is greater than the amount the company has to pay for the claim. increase.

Information gathered by actuaries is entered into tables called actuarial tables and passed on to insurance companies who set premium prices.

From the above discussion, we get:

a) California has the lowest premium and Pennsylvania has the highest premium.

b) Pennsylvania has the highest median premium.

c) Texas has the smallest range of premium. California has the smallest interquartile range.

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The upper bound of the length of the line is 12.34 cm

From the question, we have the following parameters that can be used in our computation:

Length of the line = 12.3 cm

From the question, we understand that

Time = rounded to the nearest one decimal place

The highest number that can be rounded to 12.3 to the nearest one decimal place is 12.34

This means that

Upper bound = 12.34

Hence, the upper bound is 12.34 cm

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The function that have a zero at x = 4  are

The first function is

f(x) = -2x^2 - 18x - 40

Substitute the value of x = 4

f(4) = -2(4)^2 - 18(4) - 40

= -2(16) - 72 - 40

= -32 - 72 - 40

= -144

The result is not zero

The second function is

f(x) = 2x^2 - 11x + 12

f(4) = 2(4)^2 - 11(4) +12

= 32 - 44 + 12

= 0

The result is zero

The third function is

f(x) = 3x^3 + x^2 - 48x - 16

f(4) = 3(4)^3 + 4^2 - 48(4) - 16

= 192 + 16 - 192 - 16

= 0

The result is zero

The fourth function is

f(x) = x^2 - 3x - 28

f(4) = 4^2 - 3(4) - 28

= 16 - 12 - 28

= -24

The fifth function is

f(x) = x^3 - 4x^2 - x + 4

f(4) = 4^3 - 4(4)^2 - 4 + 4

= 64 - 64 - 4 + 4

= 0

Therefore, the function f(x) = 2x^2 - 11x + 12, f(x) = 3x^3 + x^2 - 48x - 16 and  f(x) = x^3 - 4x^2 - x + 4 have zero at x equals 4

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The probability that a randomly selected american enjoys both activities is 23 % .

Given :

14 % of americans like to only cook and 48 % of americans like to only shop, while 85 % enjoy either cooking or shopping .

14 % = 0.14

48 % = 0.48

overlapping is 85 % = 0.85

P ( A ) = 0.14

P ( B ) = 0.48

P ( A and B ) = 0.85

we know that,

P ( A or B ) = P ( A ) + P ( B ) - P ( A and B )

= 0.14 + 0.48 - 0.85

= 0.62 - 0.85

= -0.23

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The probability that the ladybug will be at position 1 at time t+1 is ((1/2)*(12/50) + (1/2)*(16/50)) = 14/50 = 0.28.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures and the risk of health impacts are related.

The probability is computed by dividing the total number of outcomes by the number of possible ways the event could occur. Probability and odds are two separate ideas. Odds are calculated by dividing the likelihood that something will occur by the likelihood that it won't.

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Answer:

7/5

Step-by-step explanation:

Go up from the lower left point along the orange line 7 units.

7 units up = a rise of 7

Now go right on the orange line 5 units.

5 units right = a run of 5

slope = rise/run = 7/5

Answer: 7/5

The amount for handle soend on Christmas present will be 240.

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;

Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.

Now,

Since, Hadlee spent 1/4 of her money on Christmas presents she had 180 remaining.

Let the amount for handle soend on Christmas present = x

Hence, The amount for handle soend on Christmas present will be;

⇒ x - 1/4x = 180

⇒ 3/4x = 180

⇒ 3x = 180 × 4

⇒ 3x = 720

⇒ x = 240

Thus, The amount for handle soend on Christmas present will be 240.

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