The number N (in thousands) of existing condominiums and cooperative homes sold each year from 2000 through 2008 in the United States is approximated by the model N=0.4825t4−11.293t3+65.26t2−48.8t+578 0≤t≤8 where t represents the year, with t=0 corresponding to

Answer:

2 cm²

Step-by-step explanation:

Perimeter of a rectangle = perimeter of a square + perimeter of a square

2 congruent squares, side by side

The perimeter of the two squares = 6*sidelength.

Perimeter of a rectangle = 6 cm

The perimeter of the two squares = 6 * length

= 6l

Perimeter of a rectangle = The perimeter of the two squares

6 = 6l

l = 6/6

l = 1

Length = 1 cm

What is the total area of the squares.

Area of a square = lenght²

Area of two squares = 2(length ²)

= 2(1²)

= 2(1)

= 2 cm²

Answer:

\(\frac{1}{3}\)

Step-by-step explanation:

The correct options are:

x= 30° + 360° k * = 60° +180° k = 60° + 120°k (where k is an integer)

The given equation is 2 sin(3x) - √3 = 0.

We have to find all real number solutions in degrees.

General solution of the equation:

2 sin(3x)

= √3sin(3x)

= √3 / 2

By using the formula for sin 60°, we have:

sin 60° = √3 / 2

Therefore, we get:

3x = 60° + 360°k or 3x

= 120° + 360°k (where k is an integer)

Thus, we get:

x = 20° + 120°k or x

= 40° + 120°k (where k is an integer)

Hence, the correct options are:

x= 30° + 360° k *

= 60° +180° k

= 60° + 120°k

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Answer:

A. \( x \leq -16\)  

B. b > 11

C. \( c \leq -13 \)

D. \( x \geq -9\)

Step-by-step explanation:

Given the following algebraic expression;

A. \( \frac {3x}{4} \leq 12 \)

We would simplify the equation by multiplying all through by 4;

\( 4 * \frac {-3x}{4} \leq 12 * 4\)

\( -3x \leq 48\)

Divide both sides by -3;

\( x \leq -16\)

B. 5b - 28 > 27

Rearranging the equation, we have;

5b > 27 + 28

5b > 55

Divide both sides by 5

b > 11

C. \( 13c \leq -169\)

Divide both sides by 13

\( c \leq -13 \)

D. \( 3x - 7 \geq 4x + 2\)

Collecting like terms, we have;

\( 3x - 4x \geq 2 + 7\)

\( -x \geq 9\)

Divide both sides by -1

\( x \geq -9\)

Answer:

29.645

As a decimal

Step-by-step explanation:

To match decimal values with their corresponding hexadecimal values, we need to convert the decimal numbers into their hexadecimal equivalents using division and remainders.

To match each decimal value on the left with the corresponding hexadecimal value, we need to convert the decimal numbers into their hexadecimal equivalents.

Here are a few examples:

1. Decimal 10 = Hexadecimal A

To convert 10 to hexadecimal, we divide it by 16. The remainder is A, which represents 10 in hexadecimal.

2. Decimal 25 = Hexadecimal 19

To convert 25 to hexadecimal, we divide it by 16. The remainder is 9, which represents 9 in hexadecimal. The quotient is 1, which represents 1 in hexadecimal. Therefore, 25 in decimal is 19 in hexadecimal.

3. Decimal 128 = Hexadecimal 80

To convert 128 to hexadecimal, we divide it by 16. The remainder is 0, which represents 0 in hexadecimal. The quotient is 8, which represents 8 in hexadecimal. Therefore, 128 in decimal is 80 in hexadecimal.

Remember, the hexadecimal system uses base 16, so the digits range from 0 to 9, and then from A to F. When the decimal value is larger than 9, we use letters to represent the values from 10 to 15.In conclusion, to match decimal values with their corresponding hexadecimal values, we need to convert the decimal numbers into their hexadecimal equivalents using division and remainders.

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We can use the binomial distribution to model the number of burned-out fluorescent tubes in this classroom, with the number of trials (n) equal to 12 and the probability of success (p) equal to the constant probability of a burned-out tube.

the most appropriate    probability   model to describe the number of burned-out fluorescent tubes in a classroom with 12 fluorescent tubes, assuming a constant probability of a burned-out tube, is the binomial distribution.

the binomial distribution is used when we have a fixed number of independent trials (in this case, the number of fluorescent tubes), each with a constant probability of success (in this case, the probability of a burned-out tube), and we are interested in the number of successful trials (burned-out tubes) out of the total number of trials.

the assumptions of independence and constant probability of a burned-out tube are satisfied in this scenario, since each fluorescent tube operates independently of the others and the probability of a burned-out tube is assumed to be constant.

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The uniform model assumes equal probabilities for all values within a given range when there is no reason to believe that any X-values are more likely than others.

In statistics, the uniform model assumes that all values within a given range have an equal probability of occurring. This means that there is no preference or bias towards any specific value within the range. The uniform distribution is often represented by a rectangular shape, where the probability of any particular value occurring is constant.

The uniform model is typically used when there is no reason to believe that any X-values are more likely than others. This means that there is no prior information or evidence indicating that certain values are more probable or occur more frequently than others. In other words, there is no specific distribution or pattern in the data that suggests any particular value is more likely to occur.

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Answer:

f(-2)=2

Step-by-step explanation:

Replace all x’s with -2’s.

f(-2)=4(-2)+10

f(-2)=-8+10

f(-2)=2

The answer is 2

Answer:

22,5 ft

Step-by-step explanation:

36÷2,4×1,5=22,5

The sum of the volume of the square prism and the square pyramid is 672 cubic inches.

What is prism ?

A prism is a three-dimensional geometric shape that has two identical, parallel polygonal bases and rectangular sides that connect the bases. The sides are perpendicular to the bases and their shape depends on the shape of the base. For example, if the base is a square, the prism is called a square prism. If the base is a rectangle, the prism is called a rectangular prism. The height of the prism is the perpendicular distance between the bases.

According to the question:
First, let's calculate the volume of the square prism:

The formula for the volume of a square prism is V = lwh, where l is the length, w is the width, and h is the height.

In this case, the length (l) and width (w) of the prism are both equal to a, which is 10 inches, and the height (h) is 6 inches. So, we have:

V_prism = lwh = 10 x 10 x 6 = 600 cubic inches

Next, let's calculate the volume of the square pyramid:

The formula for the volume of a square pyramid is V = (1/3)Bh, where B is the area of the base and h is the height.

In this case, the base of the pyramid is a square with side length b, which is 6 inches, so the area of the base is:

\(B = b^2 = 6^2 = 36 square inches\)

The height of the pyramid is also 6 inches, so we have:

V_pyramid = (1/3)Bh = (1/3) x 36 x 6 = 72 cubic inches

Finally, the total volume is the sum of the volumes of the prism and pyramid:

V_total = V_prism + V_pyramid = 600 + 72 = 672 cubic inches

Therefore, the sum of the volume of the square prism and the square pyramid is 672 cubic inches.

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9514 1404 393

Answer:

  $98.15

Step-by-step explanation:

2005 is 15 years after 1990. Using the formula we find ...

  c(15) = 63·1.03^15 ≈ 63·1.55797

  c(15) ≈ 98.152

An ounce of the chemical costs about $98.15 in 2005.

Answer: Statistical

Step-by-step explanation:

I think its statistical because its quantitative data, meaning you can count it.

Answer:

I think the answer you're looking for is 86400

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

First, knowing that two angles on a horizontal line split by a vertical line at any angle is equal to 180 degrees, I try to find which of the combinations of angle x and z equal 180.

A. x = 63, and z = 104 and together they equal 170, so not A

B. x = 76 and z = 63 and together they equal 139 so not B

C. x = 76 and z = 104 and together they equal 180 so it could be C, but we must check D to make sure.

D. x = 63 and z = 76 and together they equal 139 so not D.

From all of this it must be option C

Answer:

-3x^2-3x+2

Step-by-step explanation:

3x^2+3x-1+(-3x^2-3x+2)=1

3x^2+3x-1-3x^2+3x+2=1

Answer:

132 m

Step-by-step explanation:

Refer to attachment for figure.

In smaller triangle with angle theta , we have ,

⇒ tanθ = p/b

⇒ tanθ = h/121m

⇒ tanθ = h/121 m

In triangle with angle 90-∅

⇒ tan(90-θ) = p/b

⇒ cot θ = h/144 m

Multiplying these two ,

=> tanθ . cotθ = h/121 m × h/144m

=> 1 = h²/ (121 m × 144m )

=> h² = 121m × 144m

=> h= √ ( 121m × 144m)

=> h = 11m × 12m

=> h = 132 m

The form of the partial fraction decomposition of the given function is:

\(\frac{A}{x+5}+\frac{B}{x-4}\)

To find the form of the partial fraction:

The rational expression given is: \(\frac{x-20}{x^2+x-20}\)

Factor the provided rational expression's denominator:

\(\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{x^2+5 x-4 x-20} \\&=\frac{x-20}{x(x+5)-4(x+5)} \\&=\frac{x-20}{(x+5)(x-4)}\end{aligned}\)

Apply the partial fraction decomposition method now:

\(\begin{aligned}\frac{x-20}{x^2+x-20} &=\frac{x-20}{(x+5)(x-4)} \\&=\frac{A}{x+5}+\frac{B}{x-4}\end{aligned}\)

Therefore, the form of the partial fraction decomposition of the given function is:

\(\frac{A}{x+5}+\frac{B}{x-4}\)

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The correct question is given below:
Write out the form of the partial fraction decomposition of the function. Do not determine the numerical values of the coefficients.

\(\frac{x-20}{x^2+x-20}\)

By using implicit differentiation, the values of ∂z/∂x and ∂z/∂y are:

∂z/∂x = \(\frac{yz}{6e^{6z}-xy }\), ∂z/∂y = \(\frac{xz}{6e^{6z}-xy }\).

What does implicit differentiation mean?

Representing the derivative of a dependent variable as a symbol, solving the resulting expression for the symbol, and determining the derivative of a dependent variable in an implicit function by differentiating each term independently.

The given equation is \(e^{2z}=xyz\).

To find ∂z/∂x we have to consider z as a function of x and we have to consider y as a constant.

Now, differentiating with respect to x we will get:

e2z × 6 × ∂z/∂x = z × y + xy × 1 × ∂z/∂x

We will use the Chain rule of LHS and the Product rule on RHS.

⇒∂z/∂x [2e2z - xy] = yz

⇒∂z/∂x = yz / [2e2z - xy]

Therefore ∂z/∂x = \(\frac{yz}{6e^{6z}-xy }\).

To find ∂z/∂y we have to consider z as a function of y and we have to consider x as a constant.

Now, differentiating with respect to y we will get:

e2z × 2 × ∂z/∂y = z × x + xy × 1 × ∂z/∂y

⇒∂z/∂y [2e2z - xy] = xz

⇒∂z/∂y = xz / [2e2z - xy]

Therefore ∂z/∂y = \(\frac{xz}{6e^{6z}-xy }\).

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Answer:

See below for proof.

\(S_{500}=125250\)

Step-by-step explanation:

Given arithmetic series:

Therefore:

\(S_n=1+2+3+...+(n-2)+(n-1)+n\)

\(S_n=1+(1+1)+(1+2)+...+(1+n-3)+(1+n-2)+(1+n-1)\)

\(S_n=1+(1+1)+(1+2(1))+...+(1+(n-3)(1))+(1+(n-2)(1))+(1+(n-1)(1))\)

Let:

Therefore:

\(S_n=a+(a+d)+(a+2d)+...+(a+(n-3)d)+(a+(n-2)d)+(a+(n-1)d)\)

Reverse the order:

\(S_n=(a+(n-1)d)+(a+(n-2)d)+(a+(n-3)d)+...+(a+2d)+(a+d)+a\)

Add the two expressions for Sₙ:

\(2S_n=(2a+(n-1)d)+(2a+(n-1)d)+(2a+(n-1)d)+...+(2a+(n-1)d)\)

Therefore, the term (2a + (n – 1)d) has been repeated n times:

\(2S_n=n(2a+(n-1)d)\)

Divide both sides by 2:

\(S_n=\dfrac{1}{2}n(2a+(n-1)d)\)

\(S_n=\dfrac{1}{2}n(a+a+(n-1)d)\)

Replace  a with  a₁  (first term) and a + (n – 1)d  with  aₙ (last term):

\(S_n=\dfrac{1}{2}n(a_1+a_n)\)

To find the sum of the series 1 + 2 + 3 + ... + 500, substitute the following values into the formula:

Therefore:

\(\implies S_{500}=\dfrac{1}{2}(500)(1+500)\)

\(\implies S_{500}=250(501)\)

\(\implies S_{500}=125250\)

Answer:

Step-by-step explanation:

|14-(6-x)| = |14-6+x| = |8+x|

|8+x| = 8+x if x > -8

|8+x| = -x-8 if x < -8

|8+x| = 0 if x= -8

Answer:

2.Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Step-by-step explanation:

The object of "Euclidean geometry" (more commonly called "plane geometry") is, in principle, the study of the shapes and properties of natural bodies. However, geometry is not an experimental science since its object is not to study certain aspects of nature but a necessarily arbitrary reproduction of it.

After the definitions, Euclid then poses his famous postulates (his requests), the fifth of which has remained Euclid's postulate, often called axiom (or postulate) of parallels and which was the subject of much research and controversy as to its necessity:

From the above explanation, we could deduce that the correct option is Option 2.

Answer:

The answer is B, Through a given point not on a line, there exists exactly one line parallel to the given line through the given point.

Step-by-step explanation:

a) To find the value of k, we use the given information that there are 5.5 pounds of salt in the barrel after 10 minutes.

By substituting these values into the equation Q(t) = 15(1 - e^(-kt)), we can solve for k. The rounded value of k is provided as the answer.

b) As t approaches infinity, the amount of salt in the barrel will reach a maximum value and stabilize. This is because the exponential function e^(-kt) approaches zero as t increases without bound. Therefore, the amount of salt in the barrel will approach a constant value over time.

a) We are given the equation Q(t) = 15(1 - e^(-kt)) to represent the amount of salt in the barrel at time t. By substituting t = 10 and Q(t) = 5.5 into the equation, we get 5.5 = 15(1 - e^(-10k)). Solving this equation for k will give us the desired value. The calculation for k will result in a decimal value, which should be rounded to four decimal places.

b) As t approaches infinity, the term e^(-kt) approaches zero. This means that the exponential function becomes negligible compared to the constant term 15. Therefore, the equation Q(t) ≈ 15 holds as t approaches infinity, indicating that the amount of salt in the barrel will stabilize at 15 pounds. In other words, the concentration of salt in the barrel will reach a constant value, and no further change will occur.

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Answer:

=24m/12m

=2m

Step-by-step explanation:

24m /12m

=2m

a) approximately 0.1706. b) approximately 0.9877 c) approximately 0.0123. d) approximately 0.004, or 0.4%., The answer is (B) No, because the probability of more than one case is very small.

To solve this problem, we will use the concept of the Poisson distribution. The Poisson distribution is often used to model rare events occurring in a fixed interval or population, where the average rate of occurrence is known.

a. The mean number of cases in groups of 15,509 children can be calculated using the formula for the Poisson distribution, which is the product of the average rate and the size of the group:

Mean number of cases = (average rate) * (group size)

Given that the average rate is 0.000011 (11 cases per million children) and the group size is 15,509, we can calculate the mean:

Mean number of cases = 0.000011 * 15,509 ≈ 0.1706

b. To find the probability that the number of tumor cases in a group of 15,509 children is 0 or 1, we can use the Poisson distribution. The probability mass function for the Poisson distribution is given by:

P(X = k) = (e^(-λ) * λ^k) / k!

where X is the random variable representing the number of cases, λ is the average rate, and k is the number of cases.

Using the mean from part (a), which is 0.1706, we can calculate the probability of 0 or 1 cases:

P(X = 0) = (e^(-0.1706) * 0.1706^0) / 0! ≈ 0.8439

P(X = 1) = (e^(-0.1706) * 0.1706^1) / 1! ≈ 0.1438

To find the probability of 0 or 1 cases, we sum these probabilities:

P(X = 0 or 1) = P(X = 0) + P(X = 1) ≈ 0.8439 + 0.1438 ≈ 0.9877

c. To find the probability of more than one case, we can subtract the probability of 0 or 1 case from 1:

P(X > 1) = 1 - P(X = 0 or 1) = 1 - 0.9877 ≈ 0.0123

d. To determine whether the cluster of four cases appears to be attributable to random chance, we compare the observed number of cases to what we would expect based on random chance. In this case, we would expect the number of cases to follow a Poisson distribution with a mean of 0.1706.

If the observed number of cases falls within the range of values that can be reasonably expected based on the Poisson distribution, then the cluster of four cases can be attributed to random chance. However, if the observed number of cases is unusually high or low compared to what we would expect, it suggests that there may be other factors at play.

Based on the given information, we can calculate the probability of observing four or more cases using the Poisson distribution with a mean of 0.1706:

P(X ≥ 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)

Using the Poisson probability mass

function as before, we can calculate each term and then subtract from 1:

P(X ≥ 4) ≈ 1 - 0.8439 - 0.1438 - 0.0245 - 0.0042 ≈ 0.004

Since the probability is very small (less than 0.05), the cluster of four cases appears to be statistically significant and unlikely to occur by random chance alone. Therefore, we would conclude that the cluster of four cases is not attributable to random chance alone.

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Answer:

Option C

Step-by-step explanation:

By applying tan rule in the given triangle ABC,

tan(a) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)

         = \(\frac{BC}{AC}\)

         = \(\frac{21}{20}\)

Therefore, Option C is the correct option.