Find 2 numbers whose product is 57, and one of the numbers is 5 less than eight times the other number

The farmer requests that the pen's length be 20 feet longer than its breadth. If we use the symbol w to indicate width. The length would then equal w + 20.

You play the part of a middle schooler who is attempting to make your family's farm profitable in Farmer Math.

The challenge first asks us to determine the longest length given that the fencing will not exceed 100 feet.

We are aware that a rectangular area's perimeter is 2l + 2w (where l is the length and w the width)

Therefore, 2l + 2w 100 would be required for the fencing.

In order to solve for w, we will use the values for l and w that we mentioned in the beginning:

2l + 2w ≤ 100

2(w+20) +2w ≤ 100

2w + 40 +2w ≤ 100

4w ≤ 100 - 40

4w ≤60

w ≤ 15

The breadth must therefore be less than or equal to 15.

The longest length is achieved when the width is at its greatest value because the length is 20 feet greater than the width.

This makes the length at w = 15 the longest it can possibly be, at 35.

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The probability of a day in which the company receives 6 or more complaints is 0.3721 likely, or about 37.21%.

A subfield of mathematics called probability is concerned with the investigation of uncertain events. It is the measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1. The higher the probability, the more likely it is that the event will occur.

Given that the number of complaints per day follows a Poisson distribution with a rate parameter λ = 5.

Assume X is a random variable that represents the daily complaint rate.

The probability of receiving 6 or more complaints can be calculated as follows:

we can calculate the probability of X being less than 6 complaints per day as follows:

P(X < 6) = F(5) = e^(-λ) * Σ(λ^k / k!, k=0 to 5)

where e is the base of the natural logarithm, Σ denotes the sum from k=0 to 5, and k! denotes the factorial of k.

Substituting the value of λ = 5, we get:

P(X < 6) = e^(-5) * Σ(5^k / k!, k=0 to 5)

= 0.0337 + 0.1404 + 0.1755 + 0.1463 + 0.0916 + 0.0404

= 0.6279

Therefore, the probability of receiving 6 or more complaints in a day is:

= 1 - 0.6279

= 0.3721

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Answer:  Cars rate in kilometers is 112kmph. I did this by multiplying 70 by 1.6 which got me 112. Then the distance in kilometers traveled after 5 hours is 560 kilometers since 112x5 is 560

Step-by-step explanation:

Answer:

There are 44 jackets and 12 coats.

Step-by-step explanation:

hope this helps

Answer:

458210 in binary

10001111001102

To convert decimal number 4582 to binary, follow these steps:

Divide 4582 by 2 keeping notice of the quotient and the remainder.

Continue dividing the quotient by 2 until you get a quotient of zero.

Then just write out the remainders in the reverse order to get binary equivalent of decimal number 4582.

Using the above steps, here is the work involved in the solution for converting 4582 to binary number:

4582 / 2 = 2291 with remainder 0

2291 / 2 = 1145 with remainder 1

1145 / 2 = 572 with remainder 1

572 / 2 = 286 with remainder 0

286 / 2 = 143 with remainder 0

143 / 2 = 71 with remainder 1

71 / 2 = 35 with remainder 1

35 / 2 = 17 with remainder 1

17 / 2 = 8 with remainder 1

8 / 2 = 4 with remainder 0

4 / 2 = 2 with remainder 0

2 / 2 = 1 with remainder 0

1 / 2 = 0 with remainder 1

Then just write down the remainders in the reverse order to get the answer, The decimal number 4582 converted to binary is therefore equal to : 

1000111100110

Answer:

The answer is in the attachment

Step-by-step explanation:

1 1/4 divided into three parts you mean? You can simply take 1 1/4 or 1.25 and divide that by 3.

By fraction, you would want to convert the mixed number into an improper fraction, that way, it's easier. 1 1/4 to an improper fraction is 5/4.

5/4 divided by 3

Now whenever you're dividing fractions, remember this tip: keep, change, flip. Keep the first fraction, change the division sign to a multiplication sign, and flip the second fraction.

So 3, or 3/1 is now 1/3 and the sign is now multiplication.

5/4 x 1/3 = 5/12

That's your answer!

Hope this helped!

The effect of eliminating a redundant constraint from a linear programming model depends on the specifics of the model and the constraint in question. It is important to analyze the model carefully to determine the effect that eliminating a constraint would have on the optimal solution.

No effect: If the constraint was indeed redundant, meaning that it did not affect the optimal solution, then eliminating it would have no effect on the optimal solution.

Improved solution: If the constraint was affecting the optimal solution, then eliminating it might result in a better solution. For example, if the constraint was limiting the feasible region of the solution, then eliminating it might expand the feasible region and result in a better solution.

Different solution: If the constraint was affecting the optimal solution, then eliminating it might result in a different solution. For example, if the constraint was forcing the optimal solution to go through a particular point, then eliminating it might result in a different solution.

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The expression that will not be equivalent to the number given -(-20) is -20 (option D).

A number is said to be equivalent not only if the number is equal in value, for example, 15 = 10 + 5, but also if the negative or positive sign is equal, for example, 5 is not equal to -5.

The original expression is -(-20), this expression can be simplified as 20 or +20 considering that minus plus minus is equivalent to +. Based on this, the expression that is not equivalent is -20.

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The probability of an event for rolling a die P(E) is 1/2.

What is the probability of an event?

The probability of an event is a number (always positive) that expresses the likelihood that the event will occur. The likelihood that an event will occur falls between zero and one. A certain occurrence has a probability of one while an impossible event has a chance of zero. As implied by its name, probability deals with uncertainty.

Given, E be the event defined as {3,4,6}

So, the total number of an event E, n(E) = 3

For a die, total events are {1,2,3,4,5,6}

So, the total number of rolls of a die event, n(T) = 6

Then,

P(E) = [tex]\frac{n(E)}{n(T)} = \frac{3}{6} = \frac{1}{2}[/tex]

So, the required value of P(E) is 1/2.

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Answer:

The length is 52 meters and the width is 23 meters.

Step-by-step explanation:

Let l stand for length, and w stand for width.

l = 2w + 6

The length is 6 more than twice the width.

2l + 2w = 150

Twice the length plus twice the width is the perimeter of a rectangle.

2(2w + 6) + 2w = 150

4w + 12 + 2w = 150

6w + 12 = 150

6w = 138

w = 23

l = 2(23) + 6

l = 46 + 6

l = 52

The value of the equation is x = 348

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

x ÷ 4 = 87   be equation (1)

On simplifying the equation , we get

x/4 = 87

Multiply by 4 on both sides of the equation , we get

x = 87 ( 4 )

x = 348

Therefore , the value of x is 348

Hence , the equation is x = 348

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The only sort of proof among the following options in the question that is frequently employed in geometry is the 'two-column' proof.

Geometry is the area of mathematics that deals with the characteristics of space and the shapes of particular things as well as the interactions between them in space.

A two-column geometric proof consists of a list of assertions and the justifications for each one's truth.

The statements are listed in a left-hand column, while the justifications for the statements are listed in a right-hand column.

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The formula h = 63.2 + 2.31f ,relates the length of someone's femur (f) to their expected height (h) within a certain population. When f = 39, height(h) is 153.29 cm.

The constant term, 63.2, is the y-intercept of the line that represents the relationship between femur length and height. It represents the expected height of someone with a femur length of 0 cm.

The constant 2.31 represents the slope of the line. It represents the expected change in height for a 1 cm change in femur length. So, for every additional centimeter of femur length, the expected height increases by 2.31 cm.

When f = 39, we can substitute this value into the formula to find the expected height:

h = 63.2 + 2.31 * 39

h = 63.2 + 90.09

h = 153.29 cm

So, when the length of someone's femur is 39 cm, their expected height is 153.29 cm.

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Answer:

x = 115°

y = 50°

Step-by-step explanation:

it is an isosceles triangle, the angles at the base are congruent, x is the opposite angle of 115°, therefore the same value, to find y we subtract the two 65° angles from the sum of the internal angles of the triangle (180°) and we have 50 ° which is the value of Y, look at the figure to understand better

This question finds congruent triangles. A similarity statement relating the 3 triangles is ABC-DAC-DBA.

From the triangle ABC-DAC-DBA, it has conditions that can be said to be congruent, because it has side lengths with patterned comparisons if the magnitudes are not the same.

The conditions for two congruent plane shapes, namely:

The above conditions also apply to congruent triangles.

Two triangles are congruent if they have:

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Answer: B

Step-by-step explanation:

The sine of the complementary angle of 68° is 0.375.

Two angles are called complementary when their measures add to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

The complementary angle of 68° is calculated as;

θ = 90 - 68°

θ = 22°

sin (22° ) = 0.375

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Using the fact that P is the midpoint of the segment AB, we will see that its y-value is -4.

We know that point P partitions directed segment AB in the part to part ratio of 4:4.

Notice that the ratio is equivalent to 1:1

So point P is just the midpoint of the segment, remember that for a segment whose endpoints are (a, b) and (c, d), the midpoint is:

M= ( [a+ c]/2, [b + d]/2)

P is the midpoint of (5,-7) and (1,-1), then the value of the y-coordinate of P is:

y = (-7 + (-1))/2

y = (-7 - 1)/2

y = -4

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Answer:

[tex]{ \sf{ \frac{17}{25} }} \\ [/tex]

Step-by-step explanation:

• For 5/16;

[tex]{ \tt{ \frac{5}{16} = 0.3125 }} \\ \\ { \tt{ |0.5 - 0.3125| = 0.1875 }}[/tex]

• For 17/25;

[tex]{ \tt{ \frac{17}{25} = 0.68 }} \\ \\ |{ \tt{0.5 - 0.68}}| = { \tt{0.18}}[/tex]

By observation, we should get a lesser value of the two values of 0.1875 and 0.18

[tex]{ \tt{0.18 < 0.1872}}[/tex]

Answer:

34.8 pounds

Step-by-step explanation:

The cat weighs 10.4. Which is 24.4 pounds less that the dog. So find the weight of the dog, we need to make an equation. This equation would be:

[tex]dog[/tex][tex]-24.4=10.4[/tex]

Solve:

[tex]dog-24.4=10.4[/tex]

      [tex]+24.4[/tex]     [tex]+24.4[/tex]

[tex]dog=34.8[/tex]

Hope this helped!
Stay safe and have a great day/night! (:

Answer:

5%

Step-by-step explanation:

Decreased amount = 40 - 38

                                 = £ 2

[tex]\sf \boxed{decreased \ percentage = \dfrac{decreased \ amount}{oringinal price}*100 }[/tex]

                                  [tex]= \dfrac{2}{40}*100\\\\= 5 \%[/tex]

The equation for A, in terms of x, represents the amount of money remaining on the card after buying x cups of coffee is $10 - $2x = A.

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. Two expressions are combined in an equation using an equal symbol ("="). The "left-hand side" and "right-hand side" of the equation are the two expressions on either side of the equals sign. Typically, we consider an equation's right side to be zero.

The equation will be written as below,

$10 - $2x = A.

A is the amount of money remaining on the card.

x is cups of coffee.

Therefore, the equation for A, in terms of x, represents the amount of money remaining on the card after buying x cups of coffee is $10 - $2x = A.

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The probability that the mean contents of the bottles in a six-pack is less than 295 ml is approximately 0.1587, or 15.87%.

To solve this, use the standard normal distribution and the cumulative distribution function (CDF) of the normal distribution.

Standardize the value of 295 ml by subtracting the mean of the distribution (298 ml) and dividing by the standard deviation (3 ml):

Z = (295 - 298) / 3 = -1

The CDF of the standard normal distribution gives us the probability that a random variable from a standard normal distribution is less than or equal to a certain value. Using a standard normal table or a calculator with normal distribution functions, we find that the probability that a standard normal random variable is less than or equal to -1 is approximately 0.1587.

Since the contents of the bottles are normally distributed with mean 298 ml and standard deviation 3 ml, we can use the standard normal distribution and the standard score Z to approximate the probability of observing a mean contents of less than 295 ml in a six-pack of bottles. This probability is approximately 0.1587, or 15.87%.

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Answer: $ 0.62

Step-by-step explanation:

First, find out the cost of each bottle:

$4.69/ 36 bottles = $0.1297

                             = $0.13

Therefore, the profit is:

$0.75 - $0.13 =  $ 0.62

The container having same volume and greater surface area than Amanda's container is -

Option 3: Container with dimensions 6 ft × 2 ft × 2 ft.

What is volume?

Each thing in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's borders in three dimensions is referred to as its volume. It is sometimes referred to as the object's capacity.

The measurements of the box filled by Amanada is -

Length = 3 feet, Width = 2 feet and height = 4 feet

The formula for volume of a cuboid is -

Volume = l×w×h

Substitute the values in the equation -

Volume = 3 × 2 × 4

Volume = 24 ft³

The formula for surface area of a cuboid is -

Total Surface Area = 2(lw + wh + lh)

Substitute the values in the equation -

Total Surface Area = 2[(3 × 2) + (2 × 4) + (3 × 4)]

Total Surface Area = 2(6 + 8 + 12)

Total Surface Area = 2(26)

Total Surface Area = 52 ft²

Amanada wants a container with greater surface area and same volume.

The first and fourth containers are cubes and not cuboids so they are not considered.

The second container has same measurements as that Amanda filled, so they will have same volume and surface area.

Consider the third container with measurements -

Length = 6 feet, Width = 2 feet and height = 2 feet

The formula for volume of a cuboid is -

Volume = l×w×h

Substitute the values in the equation -

Volume = 6 × 2 × 2

Volume = 24 ft³

The formula for surface area of a cuboid is -

Total Surface Area = 2(lw + wh + lh)

Substitute the values in the equation -

Total Surface Area = 2[(6 × 2) + (2 × 2) + (6 × 2)]

Total Surface Area = 2(12 + 4 + 12)

Total Surface Area = 2(28)

Total Surface Area = 56 ft²

Therefore, the third container is the right choice.

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the width of the frame is 0.806 inches.

The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.

Given this, Travis decided to make a frame for his birthday. The frame will be cut out of a piece of steel, and the final area of the frame should be 30in².

Since,

Area of frame = total area - cut out area

In our case, it is given that,

Total area = (11+2x)(6+2x)in²

cut out area = 11*6 = 66

So,

30 = (11+2x)(6+2x) - 66  

(11+2x)(6+2x) = 96

66 + 12x +22x +4x² = 96

4x² + 34x -30 = 0

x = 0.806 in

therefore. the width of the frame is 0.806 inches.

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Complete question: