the famous kate lynn horsefeed is building a box as part of her science project. it is to be built from a rectangular piece of cardboard measuring 25 cm by 40 cm bycutting out a square from each corner and then bending up the sides. find the size of the corner square which will produce a container that will hold the most.

Answer:

-3

Step-by-step explanation:

x² + x = 3

3 - 6 = -3

Answer:

50000

Step-by-step explanation:

To answer this question, we need to first multiply the left side of the given equation and write it as the difference of two squares. This can be done by using the difference of squares formula, which states that the difference of two squares can be written as the product of the square of the sum and the square of the difference.

The left side of the given equation can be written as:

(csc0+ cot 0)(csc0- cot0)

We can then apply the difference of squares formula to this expression to get:

(csc0+ cot 0)(csc0- cot0) = (csc0+ cot 0)(csc0- cot0)

Now, we can see that this expression is equivalent to 1 using the Cancellation Property. This property states that if two numbers or expressions are equal, then their corresponding parts are also equal. In this case, since 1 = (csc0+ cot 0)(csc0- cot0), we can cancel out the corresponding parts on both sides of the equation to get 1 = 1.

Therefore, the correct answer is D. Cancellation Property.

Answer: There are 4.3 hours * 60 minutes per hour = 4.360=258minutes in 4.3 hours.

There are 258 minutes * 60 seconds per minute = 25860=15480 seconds in 258 minutes.

Therefore, the printer at Seneca office can print out 15,480 pages / 5 seconds per page =15480/5=3096 pages in 4.3 hours. Answer: 3096

Step-by-step explanation:

Answer:

22 degrees

Step-by-step explanation:

D=B and C=A

To calculate Keith's equivalent rate with simple compounding, we need to use the following formula:

r = (e^(i/n) - 1) * n

where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.

In this case, we are given that i = 8.27% and we can assume that the number of compounding periods per year is 12, since many loans are compounded monthly. Plugging these values into the formula, we get:

r = (e^(0.0827/12) - 1) * 12

= (1.0082 - 1) * 12

= 0.0082 * 12

= 0.0984 or 9.84%

Therefore, Keith's equivalent rate with simple compounding is [B] 0.0998 or 9.98%.

Answer:

z > 1 1/3

Step-by-step explanation:

See picture

Answer:

9.42cm

Step-by-step explanation:

according to fig :

diameter (d) =3cm so ,

radius (r) = d/2 =3/2 = 1.5cm

solution:

as we know that ,

circumference of a circle = 2πr

=2×3.14×1.5

=9.42 cm

Answer:

21.98 cm

Step-by-step explanation:

The circumference formula is [tex]2\pi r[/tex] which can be expressed as [tex]\pi d[/tex], where r is radius and d is the diameter length.

Since we know the diameter is 3 cm, that means we can plug in that value for d and get [tex]7 \pi[/tex] as the circumference

However, the question tells us to use 3.14 for [tex]\pi[/tex], so we must find the value of [tex]7 * 3.14[/tex]. By doing mental math or by using a calculator we can find this value to be 21.98.

Thus, the circumference of the circle is 21.98 cm

If the degree on x in the denominator is larger than the degree on x a bigger leading exponent than the polynomial in the numerator.

After then the graph to the value found by dividing the leading coefficients of the two polynomials.

To find horizontal asymptotes:

1.  If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).

2.  If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

3. Rational functions (a polynomial divided by a polynomial) and exponential functions have horizontal asymptotes.

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Answer:

25 and 37

Step-by-step explanation:

x+y=62

y-x=12

 +x. +x

y=12+x

x+(12+x)=62

2x+12=62

   -12. -12

2x=50

/2. /2

x=25

25 is one of the numbers

y-25=12

+25 +25

y=37

hopes this helps

The constant rate of change and initial value for the given graph are 40 and 20 respectively. the initial value might represent the fixed cost of the soil.

The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference. The negative slope indicates the rate of decrease while the positive shows the rate of increase.

The given problem can be solved as follows,

(a) The graph given is a straight line that passes through (0, 40) and (10, 240).

The constant rate of change is equivalent to the the slope of the line given as,

⇒ (240 - 40)/(10 - 0) = 20

(b) The initial value of the graph is given as the y-intercept of the line.

Which is given as 40.

It might represent the fixed cost.

Hence, the constant rate of change is given as 40 and the initial value is 20 which might represent the fixed cost.

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The missing graph is attached here.

The equation of line j is x + 3y -13 = 0 which is perpendicular to line k.

How does one point slope?

Line k is perpendicular to line j

m(j) = - m(k)

m(j) = -(1/3)

One slope one point formula:

y - y₁ = m( x - x₁ )

y - 4 = -(1/3)(x - 1)

3y - 12 = -x + 1

x + 3y -13 = 0

Hence, The equation of line j is x + 3y -13 = 0 which is perpendicular to line k.

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The total number of lay-ups in 14 baskets is 10

In fourteen baskets

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

Lay-ups = 5 out of 7 baskets

This means that

Lay-ups = 5/7 baskets

When the number of baskets is 14, we have

Lay-ups = 5/7 * 14

Evaluate

Lay-ups = 10

In one hundred forty baskets

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

Lay-ups = 5 out of 7 baskets

This means that

Lay-ups = 5/7 baskets

When the number of baskets is 140, we have

Lay-ups = 5/7 * 140

Evaluate

Lay-ups = 100

Here, we have

Lay-ups = 20

Recall that

Lay-ups = 5/7 baskets

So, we have

Baskets = 7/5 lay-ups

This gives

Baskets = 7/5 * 20

Evaluate

Baskets = 28

Hence, the number of baskets is 28

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Answer:

86.13

Step-by-step explanation:

area of Triangle: ½ × height × base = ½ ×6×6= 18 cm

area of Rectangle: length × width= 6×9 = 54 cm

area of circle= π × (radius)² then...

area of Half-circle = [π×(radius)²] ÷2 = [3.14×(6/2)²] ÷2 = 14.13 cm

The Area of this figure= 18 + 54 + 14.13 = 86.13 cm

Answer:

[tex]A = 86.13[/tex]

Step-by-step explanation:

In order to find the area of the given figure

We need to divide the figure Into the following shapes

Firstly,

A triangle

Rectangle

Semi Circle

Area of a triangle + Area of a rectangle +  Area of a semi circle = Area of the whole figure

So lets find the area of the figures

Area of Triangle = [tex]\frac{1}{2}[/tex]X[tex]6[/tex]X[tex]6[/tex]

= [tex]18[/tex]

Area of a rectangle = [tex]l[/tex]x[tex]b[/tex]

= [tex]9[/tex]x[tex]6[/tex]=[tex]54[/tex]

Area of a semi circle = [tex]\frac{1}{2}\pi r^{2}[/tex]

= [tex]\frac{1}{2} X \frac{22}{7} X(3)^{2}[/tex]

= [tex]14.13[/tex]

[tex]A = 18 + 54 + 14.13[/tex]

[tex]A = 86.13[/tex]

The total area of the geometry will be 86.13 square units.

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Answer:

2 apples = 0.24 kg

12 apples = 1.44 kg

Step-by-step explanation:

Find the weight of one apple.

If 5 apples weigh 0.60 kg, then 1 apple weighs:

[tex]\implies \sf 1\;apple=\dfrac{0.60}{5}=0.12\; kg[/tex]

Therefore:

To determine if a misspelled name is repeated throughout a dataset, a data analyst can use the COUNT function. This function counts the number of occurrences of a value in a range of cells.

Alternatively, the data analyst could use the COUNTA function, which counts the number of cells in a range that contain data (including text and numbers, but not empty or blank cells). The COUNTA function would also count the number of occurrences of the misspelled name in the dataset.

What is a dataset, using an example?

A collection of numbers or values pertaining to one subject constitutes a data set. An example of a data set might be each student's test scores for a certain class. The amount of fish that each dolphin eats in an aquarium is a data set.

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The rate at which the speed of the wind changes at the 50th mile is 258.114 miles per hour

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

Function: S(d) = 86log d + 112

Express the above function properly

So, we have the following representation

S(d) = 86log(d) + 112

From the question, we have:

Distance = 50th mile.

This means that

d = 50

Substitute the known values in the above equation, so, we have the following representation

S(50) = 86log(50) + 112

Evaluate the logarithm

So, we have the following representation

S(50) = 86 * 1.699 + 112

Evaluate the products

S(50) = 146.114 + 112

Lastly, we have

S(50) = 258.114

Hence, the speed is 258.114 miles per hour

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The change per week in the amount of money in the account is 40

The starting amount of money in the account is 550.

The statement that exemplifies the provided variables is called an equation. In this instance, the scenario is described by taking into account two or more factors. The definition of an equation as a mathematical statement that consists of two expressions joined by an equal sign must be understood.

In this instance, x and y are connected by the formula y=550 + 40x. In light of this, the weekly change in the account's balance is 40 dollars, while the initial balance was 550.

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Answer:

y= 14.875

x= 16.875

Step-by-step explanation:

simultaneous equation

substitution method

Equation of the line is y = -3x + 7.

Two lines in the same plane that are equally spaced apart and never cross each other are said to be parallel lines.

Suppose the line's equation is y=mx + c, where m and c are unknowns.

Since it is parallel to the equation y = -3x + 4 and -3x - y = -4, its slope is now -3. So m = -3.

Additionally, point  (1,4). Therefore, this should be satisfied by our line's equation.

Consequently, 4 = -3(1) + c

therefore c = 7

The line's equation changes to y = -3x + 7.

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The exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].

Let the given equation is [tex]x=e^t-t, y=4 e^{\frac{t}{2}}, 0 \leq t \leq 5[/tex].

Length of Parametric Curve: A parametric curve is a function expressed in components form, such that x=f(t),y=g(t). The length of a parametric curve on the interval a ≤ t ≤ b is given by the definite integral [tex]$L=\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t$[/tex]

Let’s begin by getting the first derivative of the components of the function with respect to the variable t.

[tex]$$\begin{aligned}x & =e^t-t, y=4 e^{\frac{t}{2}} \\\frac{d x}{d t} & =\frac{d}{d t}\left(e^t-t\right)=\frac{d}{d t}\left(e^t\right)-\frac{d}{d t}(t)=e^t-1 \\\frac{d y}{d t} & =\frac{d}{d t}\left(4 e^{\frac{t}{2}}\right)=\left(4 e^{\frac{t}{2}}\right) \frac{d}{d t}\left(\frac{t}{2}\right)=\left(4 e^{\frac{t}{2}}\right)\left(\frac{1}{2}\right)=2 e^{\frac{t}{2}}\end{aligned}$$[/tex]

Substitute the derivatives into the following definite integral which computes the length of the parametric curve on the interval [a,b]=[0,5].

[tex]$$\begin{aligned}L & =\int_a^b \sqrt{\left(\frac{d x}{d t}\right)^2+\left(\frac{d y}{d t}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^t-1\right)^2+\left(2 e^{\frac{t}{2}}\right)^2} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}-2 e^t+1\right)+\left(4 e^t\right)} d t \\& =\int_0^5 \sqrt{\left(e^{2 t}+2 e^t+1\right)} d t \\& =\int_0^5 \sqrt{\left(e^t+1\right)^2} d t \\& =\int_0^5\left(e^t+1\right) d t\end{aligned}$$[/tex]

We need to find the value of the definite integral to get the exact length of the curve.

Take out the limits of integration and evaluate the resulting indefinite integral to solve.

[tex]$$\begin{aligned}L & =\left.\left[\int\left(e^t+1\right) d t\right]\right|_0 ^5 \\& =\left.\left[\int e^t d t+\int 1 d t\right]\right|_0 ^5 \\& =\left.\left[e^t+t\right]\right|_0 ^5\end{aligned}$$[/tex]

Evaluate the solution at the limits of integration to get the length.

[tex]$$\begin{aligned}& L=\left[e^{(5)}+(5)\right]-\left[e^{(0)}+(0)\right] \\& L=\left(e^5+5\right)-\left(e^0+0\right) \\& L=e^5+5-(1+0) \\& L=e^5+5-1 \\& \mathbf{L}=\mathbf{e}^5+\mathbf{4}\end{aligned}$$[/tex]

Therefore, the exact length of the curve is [tex]& \mathbf{L}=\mathbf{e}^5+\mathbf{4}[/tex].

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The bakery sold total 200 cupcake in that day.

The word percent means per hundred and percent value of a quantity refers to the hundred parts of that quantity. Percent value is expressed by sign %.

In order to determine a percent value of a quantity, we divide the quantity by the total quantity and finally the resultant value is multiplied by 100.

In the other hand, when we need to calculate total quantity from a percentage value, we multiply the specific quantity by 100 and finally the resultant is divided by the percentage value.

Given, Number of cupcakes sold at a specific time =26 which was 13 percent of total number of cupcakes sold in that day.

Therefore, number of total cupcakes sold in that day = 26× 100/13 =200

    the total number is 200

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The probability that molly will roll the die less than four times before stopping is 91/216

Probability is the calculation of an outcome or the chance of an event ever happening.

Probability determines the likelihood of an event occurring: P(A) = f / N.

Probability(Event) = Favorable Outcomes/Total Outcomes

She can do this in 1 roll, 2 rolls, or 3 rolls.

Probability of getting 1 in the first roll: 1/6

Probability of getting 1 on the second roll: 5/6∗1/6=5/36

Probability of 1 on the third roll: 5/6∗5/6∗1/6=25/216

As it can happen in 1, 2, or 3 rolls we add the probabilities: 1/6+5/36+2/52

⇒26/216+30/216+25/216

⇒91/216

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The number on the third term and the eleventh term will be 22 and 46, respectively.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

In a game, the number of dominos in different lines structures an A.P. Assuming that the quantity of dominos in the third and eleventh cell together is 68 and the quantity of dominos in the eleventh cell is 24 a bigger number than of the third cell.

Let 'x' be the third number and 'y' be the eleventh number. Then the equations are given below.

x + y = 68          ...1

y = x + 24          ...2

From equations 1 and 2, then we have

x + x + 24 = 68

2x = 44

x = 22

Then the value of the variable 'y' will be given as,

y = 22 + 24

y = 46

The number on the third term and the eleventh term will be 22 and 46, respectively.

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y = e is the equation of the tangent line to the given curve at the specified point , y = [tex]e^{x}[/tex] / x , (1, e)

Through the coordinate geometry formal of point-slope form, the equation of tangent and normal can be calculated.

The tangent has the equation (y - y1) = m(x - x1), and a normal travelling through this point and perpendicular to the tangent has the equation (y - y1) = -1/m (x - x1).

thus , y' =  [tex]\frac{e^{x}-xe^{x} }{x^{2} }[/tex]

y'(1) = 0 = m

Our slope is indicated by the horizontal line.

y−[tex]y_{1}[/tex]=m(x−[tex]x_{1}[/tex])

Our line will simply be our y-coordinate because our slope(m) is 0:

e

Therefore:

The tangent line's equation is y=e.

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The power of the lens is 2.5D

The focal length of 40 cm and a diameter of 5.0 cm.

Optical power (also referred to as dioptric power, refractive power, focusing power, or convergence power) is the degree to which a lens, mirror, or other optical system converges or diverges light. It is equal to the reciprocal of the focal length of the device: P = 1/f.

Power of lens = 1 / focal length (in meters)

For a thin lens in air, the focal length is the distance from the center of the lens to the principal foci (or focal points) of the lens. For a converging lens (for example a convex lens), the focal length is positive and is the distance at which a beam of collimated light will be focused to a single spot.

we have focal length 40cm (.4 m)

so

Converging lenses have positive optical power, while diverging lenses have negative power.

Power of lens = 1/0.4 m

=2.5 D  [The unit of Power of lens is Dioptre]

Therefore, the power of the lens that has a focal length and a diameter of 5.0 cm is 2.5D

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Answer:

....................

Answer:

x = 11

Step-by-step explanation:

the sum of the 3 angles in the triangle = 180°

sum the 3 angles and equate to 180

80 + 60 + 3x + 7 = 180

147 + 3x = 180 ( subtract 147 from both sides )

3x = 33 ( divide both sides by 3 )

x = 11

Answer:

x = 11

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

60 + 80 + 3x+7 = 180

Combine like terms

3x+147=180

Subtract 147 from each side

3x+147-147=180-147

3x = 33

Divide each side by 3

3x/3 = 33/3

x = 11

The correct option is (a) significant.

a(n) significant difference is due to some systematic influence and not due to chance.

Significant: Having or likely to have influence or effect : important. a significant piece of legislation also of a noticeably or measurably large amount. a significant number of layoffs.

Insignificant: small or unimportant

null: Lacking meaning or having no value

serendipitous: come upon or found by accident

As per the question the suitable answer is option (a).

Therefore, the correct answer is Significant

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A(n) significant difference is due to some systematic influence and not due to chance. Choose one answer.

a. significant b. insignificant c. null d. serendipitous