Linda built a games board in industrial arts class. The top was a rectangle of 60cm by 48cm. What was the largest size of identical felt squares she could use to cover the top exactly?

Answer:

Please check the explanation.

Step-by-step explanation:

Given the table

Time, x(hours)             Number of Cells, y

0                                   100

1                                     200

2                                    400

h                                     6400

We know that the exponential function is of the form

A(b)ˣ = y

substituting x = 0 and y  = 100

A(b)⁰ = 100

A×1 = 100           ∵ (b)⁰ = 1

substituting x = 1 and y = 200

A(b)¹ = 200

Ab = 200

plug in A = 100

100×b = 200

b = 200/100

b = 2

So, the values of A and b are:

Thus, the equation of the exponential function becomes:

A(b)ˣ = y

substituting A = 100 and b = 2

100(2)ˣ = y

Thus, the equation of the exponential function becomes:

Given that we have to determine the value of 'h' hours at y = 6400

so substituting y = 6400

100(2)ˣ = y

100(2)ˣ = 6400

divide both sides by 100

\(\frac{100\cdot \:2^x}{100}=\frac{6400}{100}\)

Simplify

\(2^x=64\)

\(\:2^x=2^6\)              ∵ 2⁶ = 64

\(x=6\)

Therefore, in 6 hours i.e. x = 6 h, the number of cells present will be 6400.

Answer:

7^18

Step-by-step explanation:

When you have an exponent to another exponent, you can multiply the exponents.

(7^3)^6

3*6 = 18

7^18

Answer:

Step-by-step explanation:

2

Answer:

x = 2

Step-by-step explanation:

0.3(12x-16)= 0.4(12-3x) take the x's and put them into.

Answer:

14m^2

Step-by-step explanation:

area of triangle = 1/2bh

= 1/2(3)(4) = 6

area of rectangle = bw

=(4)(2) = 8

6+8 = 14

Answer:

14m²

Step-by-step explanation:

rectangle area= 4*2=8

triangle area= 1/2*3*4=6

total area=14

Answer:

B.

Step-by-step explanation:

you know that (a+b+c)/d is the same as a/d + b/d + c/d.

and (a×b)/(c×d) is the same as (a/c)×(b/d).

and the powers of variables subtract when the variables are divided, and the powers add when the variables are multiplied.

14a⁸y³ / 7a⁴y

14/7 = 2

a⁸/a⁴ = a⁴

y³/y = y²

=> 2a⁴y² is the first part. that eliminates already all other answer options. only B can be right.

but let's practice and look at the second part :

-7a⁴y⁵ / 7a⁴y

-7/7 = -1

a⁴/a⁴ = 1

y⁵/y = y⁴

=> -y⁴ is the second part. B is still confirmed.

the third part :

28a¹²y² / 7a⁴y

28/7 = 4

a¹²/a⁴ = a⁸

y²/y = y

=> + 4a⁸y is the third part. B confirmed.

Answer: it will move down.

Step-by-step explanation:

because of gravity.

The integers in the grid are 1, 2, 6, 45, 53, 11, 109, 169, 322, 600, 14, and 1042.

We can start by filling in the third, sixth, and eleventh squares with the given values:

_   _   6   _   _   11  _   _   _   _   14  _

Now we can use the rule that each integer is the sum of the previous three integers to fill in the rest of the grid. We can work from left to right, filling in one square at a time.

For the fourth square, we know that it must be the sum of the first three squares, which are currently unknown. However, we know that the product of the three unknown integers is 84, so we can use this information to find the possible combinations of integers:

1 × 2 × 42

1 × 3 × 28

1 × 4 × 21

1 × 6 × 14

2 × 3 × 14

2 × 4 × 7

3 × 4 × 7

Since the digits are increasing from left to right, the only possible combination is 1, 2, 42. Therefore, the fourth square is 45.

Continuing in this way, we can fill in the rest of the squares:

1   2   6   45  53  11  109 169  322 600  14  1042

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Step-by-step explanation:

(a) What is the area of the base of the box? Use appropriate units.

A=lw

A=8(4)

A=32 inches

(b) What is the volume of the box? Use appropriate units. How can

you use your answer to part (a) to determine the volume?

V=lwh

V=8(4)(5)

V=160 inches

To find the expected value of X, we need to first determine the probability of having a pair of consecutive zeroes in a given bit string of length n. Let P be the probability of having a pair of consecutive zeroes in any given position of the bit string.

We can calculate P by considering the possible pairs of consecutive zeroes that can occur in a bit string of length n. There are n-1 pairs of adjacent bits in the bit string, so the probability of a given pair being two zeroes is 1/4 (since there are four possible pairs: 00, 01, 10, 11). However, if the first bit is 0 or the last bit is 0, then there are only n-2 pairs, and the probability of a given pair being two zeroes is 1/2. Therefore, the probability of having a pair of consecutive zeroes in a bit string of length n is:

P = [(n-2)/n * 1/4] + [1/n * 1/2] + [1/n * 1/2] + [(n-2)/n * 1/4]
 = (n-3)/2n + 1/n

Now, let Xi be the random variable that counts the number of pairs of consecutive zeroes that start at position i in the bit string (where 1 <= i <= n-1). Then X = X1 + X2 + ... + Xn-1 is the total number of pairs of consecutive zeroes in the bit string.

To find the expected value of X, we use linearity of expectation:

E[X] = E[X1] + E[X2] + ... + E[Xn-1]

We can calculate E[Xi] for any i by considering the probability of having a pair of consecutive zeroes starting at position i. If the i-th and (i+1)-th bits are both 0, then there is one pair of consecutive zeroes starting at position i. The probability of this occurring is P. If the i-th bit is 0 and the (i+1)-th bit is 1, then there are no pairs of consecutive zeroes starting at position i. The probability of this occurring is 1-P. Therefore, we have:

E[Xi] = P * 1 + (1-P) * 0
      = P

Finally, we substitute our expression for P into the formula for E[X] to get:

E[X] = (n-3)/2n + 1/n * (n-1)
    = (n-3)/2n + 1

So the expected value of X for a random bit string of length n is (n-3)/2n + 1.
To find the expected value of a random function X that counts the number of pairs of consecutive zeroes in a random bit string of length n, we can follow these steps:

1. Calculate the total number of possible bit strings of length n. There are 2^n possible bit strings since each position can be either a 0 or a 1.

2. Find the probability of each pair of consecutive zeroes occurring in the bit string. Since there are 2 possible values for each bit (0 or 1), the probability of a specific pair of consecutive zeroes is 1/4 (0.25).

3. Determine the maximum number of pairs of consecutive zeroes in a bit string of length n. The maximum number is n - 1 since the first n - 1 bits can form pairs with the bits that follow them.

4. Calculate the expected value by multiplying the probability of each pair of consecutive zeroes by the number of pairs that can occur, and sum the results. The expected value E(X) can be calculated using the formula:

E(X) = Sum(P(i) * i) for i from 0 to n - 1, where P(i) is the probability of i pairs of consecutive zeroes occurring.

To simplify the calculation, consider that each position has a 1/4 chance of forming a consecutive zero pair with the following position, and there are n - 1 such positions:

E(X) = (1/4) * (n - 1)

So, the expected value of a random function X that counts the number of pairs of consecutive zeroes in a random bit string of length n is (1/4) * (n - 1).

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Answer: (1,10)

Step-by-step explanation:

Assuming these are the correctly written equations:

-x + 5y = 49, and

x - 4y = -39

I'll rewrite them:

5y = x + 49

y = (1/5)x + (49/5)

-4y = -x -39

y = (1/4)x + (39/4)

=====

I'll assume the question is to find the point these two lines intersect (?).

See the attached graph.  They intersect at (1,10).

Answer:

\( \sqrt{45 {x}^{2} } + \sqrt{5 {x}^{2} } + 4x \sqrt{5} \\ = 3 \sqrt{5} x + \sqrt{5} x + 4x \sqrt{5} \\ = 8x \sqrt{5} \\ thank \: you\)

The least appropriate measure of central tendency for a data set that contains outliers is the mean. This is because the mean is calculated by taking the sum of all the values in the data set and dividing it by the number of values. This means that the mean is heavily influenced by outliers, as they are included in the calculation.

The median, 2nd quartile, and 50th percentile are all more appropriate measures of central tendency for a data set that contains outliers, as they are not affected by the presence of outliers. The median is calculated by taking the middle value of the data set, the 2nd quartile is calculated by taking the median of the upper half of the data set, and the 50th percentile is calculated by taking the value at the 50th percentile of the data set.

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The absolute minimum and maximum values of the function f(x,y) = 1+xy – x – y on the region D, bounded by the parabola y = x^2 and the line y = 4, we can follow these steps:

Find the critical points of f(x,y) by setting the partial derivatives of f equal to zero:

fx = y - 1 = 0

fy = x - 1 = 0

Solving these equations simultaneously gives the critical point (1,1).

Check the boundary of region D, which is composed of two curves: y = x^2 and y = 4.

2.1. Along the curve y = x^2:

Substituting y = x^2 into f(x,y), we obtain a function of one variable:

g(x) = f(x, x^2) = 1 + x^3 - 2x^2

Taking the derivative of g(x) and setting it equal to zero to find its critical points:

g'(x) = 3x^2 - 4x = 0

x(3x - 4) = 0

Solving for x, we get x = 0 and x = 4/3. Plugging these values into g(x), we find that g(0) = 1 and g(4/3) = -1/27.

Therefore, the minimum value of f(x,y) along the curve y = x^2 is g(4/3) = -1/27, and the maximum value is g(0) = 1.

2.2. Along the line y = 4:

Substituting y = 4 into f(x,y), we obtain a function of one variable:

h(x) = f(x, 4) = 1 + 4x - x - 4

Simplifying, we get h(x) = 3x - 3.

Taking the derivative of h(x) and setting it equal to zero to find its critical point:

h'(x) = 3 = 0

Since h'(x) is never zero, there are no critical points along the line y = 4. We only need to check the endpoints of the line segment that lies within D.

At the endpoint (4/2, 4), we have f(2, 4) = -2, and at the endpoint (-2, 4), we have f(-2, 4) = 9.

Therefore, the minimum value of f(x,y) along the line y = 4 is f(2,4) = -2, and the maximum value is f(-2,4) = 9.

Compare the values obtained in steps 1 and 2 to find the absolute minimum and maximum values of f(x,y) on D.

The values of f at the critical point (1,1), along the curve y = x^2, and along the line y = 4 are:

f(1,1) = -1

g(4/3) = -1/27

g(0) = 1

f(2,4) = -2

f(-2,4) = 9

Therefore, the absolute minimum value of f(x,y) on D is f(-2,4) = 9, and the absolute maximum value is f(0) = 1.

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Answer:

It will cover 4.5 miles in 30 seconds.

Step-by-step explanation:

An airplane is flying from nyc to la.

The distance it travels in miles,d, is related to the to the time in seconds, t, by the equation :

d=0.15t ...(1)

Let us assume we need to find the distance at t = 30 s.

Put t = 30 s in equation (1).

d=0.15 × 30

d = 4.5 miles

Hence, it will cover 4.5 miles in 30 seconds.

The solution to the equation is p = -72.

The equation, we need to isolate the variable 'p' on one side of the equation. Let's go through the steps:

-p/12 = 6

To get rid of the fraction, we can multiply both sides of the equation by 12:

12 * (-p/12) = 12 * 6

This simplifies to:

-p = 72

To isolate 'p,' we can multiply both sides of the equation by -1:

(-1) * (-p) = (-1) * 72

This gives us:

p = -72

Therefore, the solution to the equation is p = -72.

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Answer:

Yes

Step-by-step explanation:

As the number of rows increases the number of chairs also increases according to the graph

Answer:

3/8

Step-by-step explanation:

convert 1/4 to 2/8 and then subtract and that would equal the distance. distance of 3/8 hope this helps

The distance in units between 5/8 and 1/4 on a number line is 3/8.

Here,

We have to find,

The distance in units between 5/8 and 1/4 on a number line.

What is Number line?

Number line is a line in which all types off numbers are show like the negative number the positive numbers and fraction.

Now,

Distance between the 5/8 and 1/4 is find as,

\(\frac{5}{8} - \frac{1}{4} = \frac{5}{8} - \frac{2}{8} = \frac{3}{8}\)

Hence, The distance in units between 5/8 and 1/4 on a number line is 3/8.

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The equation given, 5x + 10y, does not represent the total amount of fiber in a package containing x apples and y oranges.

To calculate the total amount of fiber in a package containing x apples and y oranges, you would need to know the amount of fiber in each apple and orange and the number of apples and oranges in the package.

For example, if each apple contains 3 grams of fiber and each orange contains 2 grams of fiber, and there are x apples and y oranges in the package, the total amount of fiber in the package would be:

Total fiber = (3 grams of fiber per apple)(x apples) + (2 grams of fiber per orange)(y oranges)

Total fiber = 3x + 2y grams

what is number?

A number is a mathematical concept used to represent quantity or magnitude. Numbers can be used to count objects, measure distances or sizes, perform calculations, and describe various other mathematical concepts. The most basic types of numbers are the natural numbers, which include all positive integers (1, 2, 3, ...), and sometimes zero (0) as well. Other types of numbers include fractions, decimals, negative numbers, complex numbers, irrational numbers, and more. Numbers are a fundamental concept in mathematics and are used extensively in many fields, including science, engineering, economics, and finance.

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Answer:

14 and 1/4

Step-by-step explanation:

So the equation would be-

6 x 2 and 3/8

I would break this up, so

6 x 2 = 12

6 x 3/8 = 18/8

Simplify

18/8 = 9/4 = 2 and 1/4

12 + 2 and 1/4 = 14 and 1/4

Answer:

14 and 1/4

Step-by-step explanation:

Answer:

tape

Step-by-step explanation:

tape is tape

Answer:

Step-by-step explanation:

5x + 15 = 2x + 3

5x + 15 - 15 = 2x + 3 - 15

5x = 2x + 3 - 15

5x - 2x = 2x - 2x + 3 - 15

5x - 2x = 3 - 15

3x = 3 - 15

3x = -12  ( divide both sides by 3)

x= -4

Answer:so for i the answer is f(t) = 6t/3 +3t - 43t/2

Step-by-step explanation:

Ok this is for i 6t/3 + 3t -43t/2

Answer:

(2, 12)

Step-by-step explanation:

x + 10 = 4x + 4

   - 4           - 4

x + 6 =  4x

- x         - x

6 = 3x

divide 3 on each side

2 = x

then plug 2 in either equation

ei) y = 2 + 10

    y = 12

Answer:

Step-by-step explanation:

x =(-7+√-7)/-2=(7-i√ 7 )/2= 3.5000+1.3229i

 or:

x =(-7-√-7)/-2=(7+i√ 7 )/2= 3.5000-1.3229i

Case 1 :

Radius, r = 5 feet.

Area,

\(A=\pi r^2\\\\A = 3.14\times 5^2\ feet^2\\\\A = 78.5\ feet^2\)

Case 2 :

Diameter, d = 56 mm.

So, radius, r = d/2 = 28 mm.

Area,

\(A = 3.14\times 28^2\ mm^2\\\\A = 2461.76\ mm^2\)

Hence, this is the required solution.

Answer:

\( 48\pi \:m/min\)

Step-by-step explanation:

Diameter = 48 m

Therefore radius r = 48/2 = 24 m

\(Area \: of \: circular \: oil \: slick \\ A = \pi {r}^{2} \\ differentiating \: w \: r \: to \: t \: on \: \\ both \: sides \\ \\ \frac{dA}{dt} = \frac{d}{dt} (\pi {r}^{2} )\\ \\ \frac{dA}{dt} =\pi \frac{d}{dt} {r}^{2} \\ \\ \frac{dA}{dt} =\pi \times 2{r}\\ \\ \frac{dA}{dt} =2\pi {r} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =2\pi \times {24} \\ \\ \bigg(\frac{dA}{dt} \bigg)_{r=24} =48\pi \: m \: per \: min\)

Given the information:

Overall average (μ) = 55.0 units

Process population standard deviation (σ) = 1.84

Sample size (n) = 16

To determine the 3-sigma UCL (Upper Control Limit) and LCL (Lower Control Limit) for a 2-sigma X chart, we can use the following formulas:

UCL = μ + 3 * (σ / √n)

LCL = μ - 3 * (σ / √n)

Plugging in the values:

UCL = 55.0 + 3 * (1.84 / √16)

LCL = 55.0 - 3 * (1.84 / √16)

Calculating the values:

UCL = 55.0 + 3 * (1.84 / 4)

LCL = 55.0 - 3 * (1.84 / 4)

UCL = 55.46

LCL = 54.54

Therefore, the 3-sigma UCL for the 2-sigma X chart is 55.46 units, and the LCL is 54.54 units.

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This is the required solution that satisfies the given differential equation and initial condition.

The given differential equation is f '(x) = 6x², where the initial condition is given as f(0) = −9.

We can start with integration and find the particular solution: ∫f '(x) dx = ∫6x² dx ⟹ f(x) = 2x³ + C, where C is the constant of integration.

To find the constant C, we will use the initial condition given as

f(0) = −9f(0) = 2(0)³ + C = C = -9

Therefore, the particular solution is:f(x) = 2x³ - 9

Hence, this is the required solution that satisfies the given differential equation and initial condition.

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The value of k could be 48, 49, 50, 51, or 52, as these all result in the fractions being in lowest terms.

To further explain, let's look at each of the possible values of k and see how they result in the fractions being in lowest terms:

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The distance of the electricity pole from T is 53 km

Given that;

The ST is 54 kilometer long

(180 - 28) + (180 - 70) = 262 degree is the angle PST,

which is the product of the angles at S and T.

S has a 62 degree angle.

The law of sines can be written as:

sin(62)/SP = sin(262/ST)

To find SP, we can rearrange this equation as follows:

SP = sin(62)/sin(262)x(ST)

When we enter the values we are aware of, we obtain:

SP = sin(62)/sin(262)*54 km

We can evaluate this expression to determine that:

SP ≈ 53.5 km Consequently, 53.5 kilometer or so separate T from the electricity pole.

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