1. Use the data in hprice1.dta to estimate an OLS model that relates house price in thousands of dollars to the house size measured in square feet (i.e., the variable sqrft) and the number of bedrooms in the house (bdrms). Write it the result in equation form.
2. What is the estimated increase in price for a house with one more bedroom, holding square footage constant?
3. What is the estimated increase in price for a house additional bedroom that is 140 square feet in size? Compare this to your answer in question two above.
4. What percentage of the variation in price is explained by square footage and number of bedrooms?
5. The first house in the sample has sqrft=2,438 and bdrms=4. Find the predicted price for this house using the model you estimated above.
6. The actual selling price of the first house in the sample was $300,000 (i.e. price= 300). Find the residual for this house. Does it suggest that the buyer underpaid or overpaid for the house?

For the given functions, f(x)=x²+3x-7, g(x)=3x+5 and h(x)=2x²-4, f(g(x))= 9x² + 30x + 33, h(g(x))= 18x² + 60x + 46, (h-f)(x)= x² - 3x + 3, (f+g)(x)= x² + 6x - 2.

In mathematics, a function is a mathematical object that takes an input (or several inputs) and produces a unique output. It is a relationship between a set of inputs, called the domain, and a set of outputs, called the range.

Formally, a function f is defined by a set of ordered pairs (x, y) where x is an element of the domain, and y is an element of the range, and each element x in the domain is paired with a unique element y in the range. We write this as f(x) = y.

Functions can be represented in various ways, such as algebraic expressions, tables, graphs, or verbal descriptions. They can be linear or nonlinear, continuous or discontinuous, and may have various properties such as symmetry, periodicity, and asymptotic behavior.

To solve these problems, we substitute the function g(x) for x in f(x) and h(x) and simplify the resulting expressions.

f(g(x)):

f(g(x)) = f(3x+5) = (3x+5)² + 3(3x+5) - 7 (using the definition of f(x))

= 9x² + 30x + 33

h(g(x)):

h(g(x)) = h(3x+5) = 2(3x+5)² - 4 (using the definition of h(x))

= 18x² + 60x + 46

(h-f)(x):

(h-f)(x) = h(x) - f(x) = (2x² - 4) - (x² + 3x - 7) (using the definitions of h(x) and f(x))

= x² - 3x + 3

(f+g)(x):

(f+g)(x) = f(x) + g(x) = x² + 3x - 7 + 3x + 5 (using the definitions of f(x) and g(x))

= x² + 6x - 2

When multiplying out a squared term, such as (3x+5)², we can use the FOIL method, which stands for First, Outer, Inner, Last. We multiply the first terms, then the outer terms, then the inner terms, and finally the last terms, and then add up the results. For example:

(3x+5)² = (3x)(3x) + (3x)(5) + (5)(3x) + (5)(5)

= 9x² + 15x + 15x + 25

= 9x² + 30x + 25

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Solving for Cartesian product n(B), we have n(B) = 72 / 24 = 3.

The Cartesian product is a mathematical operation that takes two sets and produces a set of all possible ordered pairs of elements from both sets.

In other words, if A and B are two sets, their Cartesian product (written as A × B) is the set of all possible ordered pairs (a, b) where a is an element of A and b is an element of B.

For example, if A = {1, 2} and B = {3, 4}, then A × B = {(1, 3), (1, 4), (2, 3), (2, 4)}.

By the question.

We know that n (Ax B) represents the number of elements in the set obtained by taking the Cartesian product of sets A and B.

Using the formula for the size of the Cartesian product, we have:

n (Ax B) = n(A) x n(B)

Substituting the given values, we get: 72 = 24 x n(B)

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Check the picture below.

Answer:

x=-3

Step-by-step explanation:

Explanation:

Use the pythagorean trig identity to determine sine based on cos(theta) = 0.6

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\sin^2(\theta)=1-\cos^2(\theta)\\\\\sin(\theta)=\pm\sqrt{1-\cos^2(\theta)}\\\\\sin(\theta)=-\sqrt{1-\cos^2(\theta)} \ \ \text{....sine is negative in quadrant Q4}\\\\\sin(\theta)=-\sqrt{1-(0.6)^2}\\\\\sin(\theta)=-\sqrt{1-0.36}\\\\\sin(\theta)=-\sqrt{0.64}\\\\\sin(\theta)=-0.8\\\\[/tex]

Since [tex]\cos(\theta)=0.6 \text{ and } \sin(\theta)=-0.8[/tex], the location of point P is (0.6, -0.8)

Recall that for any point (x,y) on the unit circle, we have:

[tex]\text{x}=\cos(\theta)\\\\\text{y}=\sin(\theta)[/tex]

meaning cosine is listed first in any (x,y) pairing.

a) The constant k is 5.427 x 10^−12 and its natural logarithm is -26.68.

b) The mean salary of the given model by using the probability density function is approximately $270.86.

a) The cumulative distribution function of the given random variable is provided as follows:

F(x) = {1−kx^−3 if x>44000, and 0 otherwise

The cumulative distribution function is given as

F(x) = 1−kx^−3 if x>44000 and F(x) = 0, if x≤44000i)

We need to check the value of the cumulative distribution function at 44000

We have, F(44000) = 0

0 = 1−k(44000)^−3

⇒ 1 = k(44000)^−3

⇒ k = 1/(44000)^−3

⇒ 5.427 x 10^−12

Taking the natural logarithm of k, we have ln(k) = −28.68 (approx.)

Hence, the constant k is 5.427 x 10^−12 and its natural logarithm to three decimal places is -28.68

b) The probability density function is given as,

f(x) = F'(x) = 3kx^−4, for x>44000 and f(x) = 0, otherwise

The mean or expected value of the random variable is given as

E(X) = ∫[−∞,∞]xf(x)dx

= ∫[44000,∞]x(3kx^−4)dx

= 3k∫[44000,∞]x^−3dx

= 3k[(−1/2)x^−2] [∞,44000]

= (3k/2)(44000)^−2

= 270.86 (approx.)

Therefore, the mean salary given by the model is $270.86 (approx.)

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Answer:

9 words

Step-by-step explanation:

We know

He has 12 words to memorize, and he is 3/4 done.

How many words has Pablo memorized so far​?

We Take

12 x 3/4 = 9 words

So, Pable has memorized 9 words.

Answer:

8×21=168? That would make it 168=168? Or you could multiply even more to make 8×25 or somethin?

Step-by-step explanation: I don't know what answer ur looking for but there's some help

Answer:

x < 21.

Step-by-step explanation:

Given the equation: 8x < 168, solve the inequality.

First, make it as if it was an equality and solve x:

8x = 168  (Divide both sides by 8)

x = 21

That means x < 21.

The expression for the number of non-adult sizes is s - 19.

A value or amount is represented by an expression, which is a collection of numbers, variables, and mathematical operations like addition, subtraction, multiplication, and division. Calculations, complicated mathematical equations, and issues in a variety of disciplines, including science, engineering, economics, and statistics, may all be solved using expressions. Functions that depict a connection between variables, such as sin(x) and log(x), can also be included in expressions. Expressions are frequently employed to simulate real-world circumstances and provide predictions based on mathematical analysis.

Given that the total number od sweatshirts = s.

The number of non-adult sweatshirts can be calculated by:

Number of non-adult sizes = Total number of sweatshirts sold - Number of adult sizes

= s - 19

Hence, the expression for the number of non-adult sizes is s - 19.

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Answer:

-9

Step-by-step explanation:

x = -5

3x + 6

Since x = -5..

Do this

3(-5) + 6

Perform

-15 + 6

Answer: -9

Therefore, when x is equal to -5, the value of 3x + 6 is -9.

An equation is a statement that expresses the equality of two mathematical expressions using mathematical symbols such as variables, numbers, and mathematical operations. The equality is represented by an equal sign "=" between the two expressions. Equations are used to represent mathematical relationships and solve problems in various fields such as physics, chemistry, engineering, and economics.

Given by the question.

3x + 6 = 3(-5) + 6

= -15 + 6

= -9

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The simplified expression is 2cos²(x) + sinx - 1 = 0

The expression we will be simplifying is

=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.

To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:

(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)

Simplifying this expression using the distributive property, we get:

(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)

Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:

1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1

Similarly, for the second fraction, we can use the same identity to obtain:

1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1

Substituting these values back into the original expression, we get:

1 + 1 = 2sinx/(sin⁴x - cos⁴x)

Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:

sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ

Substituting this back into the expression, we get:

2 = 2sinx/(sin²ˣ - cos²ˣ)

Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):

2 = -2sinx/cos(2x)

Multiplying both sides by -cos(2x), we get:

-2cos(2x) = 2sinx

Dividing both sides by 2, we get:

-cos(2x) = sinx

Using the double-angle formula for cosine, we get:

-2cos²(x) + 1 = sinx

Simplifying this expression, we get:

2cos²(x) + sinx - 1 = 0

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Answer:

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Step-by-step explanation:

[tex]735 = 7 \times 105[/tex]

[tex]735 = 7 \times 3 \times 35[/tex]

[tex]735 = 7 \times 3 \times 5 \times 7[/tex]

[tex]735 = 3 \times 5 \times {7}^{2} [/tex]

Answer:

Step-by-step explanation:

C.) P = 3(a+2)-4

The formula which describes the relation between the height of the apple tree and the height of the pine tree p is P=3(a+2)-4, the correct option is C.

A linear equation is an equation that has the variable of the highest power of 1. The standard form of a linear equation is of the form Ax + B = 0.

We are given that;

Growth of apple tree= 2feet

Now,

Let's call the original height of the apple tree "h". According to the problem, if the apple tree grew 2 feet and then tripled its height, it would become 4 feet shorter than the pine tree. So we can write:

3(h+2) - 4 = p

Simplifying, we get:

3h + 2 = p

Now we can see that option (D) P=3a+10 is very similar to our expression, but it has a constant term of 10 instead of 2. This constant term does not match the problem statement, which says that the apple tree would be 4 feet shorter than the pine tree, not taller. Therefore, option (D) is not the correct answer.

Option (A) P-4=3a+2 also does not match the problem statement. If we solve for p, we get:

P = 3a + 6

This means that the apple tree would be 6 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (B) P=2(a+3)+4 also does not match the problem statement. If we solve for p, we get:

P = 2a + 10

This means that the apple tree would be 10 feet shorter than the pine tree, not 4 feet shorter as stated in the problem.

Option (C) P=3(a+2)-4 matches our expression from earlier. If we solve for p, we get:

P = 3a + 2

Therefore, by equation the answer will be P=3(a+2)-4.

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Answer:

Equation: 2(357+30×5) = 580

x=4

Step-by-step explanation:

In one package, there is such a relationship:

357+30X5 = y

(Y is the price of a package)

The price of two parcels is 580:

then. 24=580

y= 290

x=4, so: equation: 2(35x+150) =580

Step-by-step explanation:

A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more for the same amount each book would have cost Rs. 1 less. How many books did he buy?

A

8

B

16

Correct Answer

C

24

D

28

Medium

Open in App

Updated on : 2022-09-05

Solution



Verified by Toppr

Correct option is B)

Let the shopkeeper buy x number of books. 

According to the given condition cost of x books =Rs80

Therefore cost of each book =x80

Again when he had brought 4 more books

Then total books in this case =x+4

So cost of each book in this case =x+480

According to Question, 

x80−x+480=1

x(x+4)80(x+4)−80x=1

x2+20x−16x−320=0

(x−16)(x+20)=0

x=16orx=−20

Hence the shopkeeper brought 16 books

The required ratio of  is (a + c) : c 11:8.

Given that a:b=1:4 and b:c=3:2.

We can simplify the ratio b:c by multiplying both sides by 4 to get b:c=12:8=3:2.

To find the ratio (a+c):c, we need to express a and c in terms of b. From the first ratio, we have [tex]a=\frac14 b$[/tex]. From the second ratio, we have [tex]c=\frac{2}{3}b$[/tex]. Substituting these values into the expression (a+c):c, we get:

[tex]$$(a+c):c = \left(\frac{1}{4}b + \frac{2}{3}b\right):\frac{2}{3}b$$[/tex]

Simplifying the expression inside the parentheses, we get:

[tex]$\frac{1}{4}b + \frac{2}{3}b = \frac{3b}{12} + \frac{8b}{12} = \frac{11b}{12}$$[/tex]

Therefore, the ratio [tex]$(a+c):c$[/tex] is:

[tex]$(a+c):c = \frac{11b}{12}:\frac{2}{3}b = 11:8$$[/tex]

Hence, the required ratio is 11:8$.

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Answer:

The associated growth factor for a 30% increase is 1 + 0.30 = 1.30.

The associated growth factor for a 30% decrease is 1 - 0.30 = 0.70.

The associated growth factor for a 2% increase is 1 + 0.02 = 1.02.

The associated growth factor for a 2% decrease is 1 - 0.02 = 0.98.

The associated growth factor for a 0.04% increase is 1 + 0.0004 = 1.0004.

The associated growth factor for a 0.04% decrease is 1 - 0.0004 = 0.9996.

The associated growth factor for a 100% increase is 1 + 1 = 2.

Step-by-step explanation:

A growth factor is a multiplier that represents the amount by which a quantity changes as a result of a growth rate or percentage change. It is calculated by adding 1 to the decimal form of the growth rate. For example, if the growth rate is 30%, the decimal form is 0.30, and the growth factor is 1 + 0.30 = 1.30.

In case of a decrease, the growth factor is calculated by subtracting the decimal form of the decrease rate from 1. For example, if the decrease rate is 30%, the decimal form is 0.30, and the growth factor is 1 - 0.30 = 0.70.

In cases where the growth rate is a small percentage, it is important to convert it into a decimal by dividing the percentage by 100 before calculating the growth factor.

In the case of a 100% increase, the quantity doubles, so the growth factor is 2 (i.e., 1 + 1).

The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.

The triangle inequality theorem explains the relationship between the three sides of a triangle. This theorem states that for any triangle, the sum of the lengths of the first two sides is always larger than the length of the third side.

Let x be the length of the third side. By the triangle inequality, we have:

3 + 16 > x and 16 + x > 3 and 3 + x > 16

Simplifying, we get:

19 > x and x > 13 and x < 19

The largest possible whole-number length for the third side is 18, which satisfies all three inequalities.

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Answer:Given : number of hours spent studying for a history final exam and the score on that exam.

To Find : Which value is an outlier

(1.5, 65)

(3.5, 71)

(4.5, 98)

(6.5, 88)

Solution:

Number of hours spent studying =x            

Exam score   = y

x         y

1.5       65

2         68

3.5      71

4.5      98

6         82

1.5 -   2   difference = 0.5

2 - 3.5     difference = 1.5

3.5 - 4.5   difference = 1

4.5 - 6       difference = 1.5

No outlier

65  - 68   Difference  3

68 - 71      Difference  3

71 -  98      Difference  27

71 - 82     Difference  11

Hence 98 is outlier

(4.5    ,  98 )  is outlier

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Step-by-step explanation:

Measure of last angle of triangle is 117°

The triangle's characteristics include:

The angle sum property states that the sum of a triangle's three interior angles is always 180 degrees.

Angle of Triangle are

28° and 35°

Let the third angle be x

According to angle sum property

28°+35°+x=180°

x=117°

Measure of last angle of triangle is 117°

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The complete question is;

Find the measure of the last angle of the triangle below.

28⁰

35°

Image is attached below.

Answer:

The sequence is defined as follows:

a1 = 5

an = an-1 - 5, for n > 1

Using this definition, we can find the first four terms of the sequence as follows:

a1 = 5

a2 = a1 - 5 = 5 - 5 = 0

a3 = a2 - 5 = 0 - 5 = -5

a4 = a3 - 5 = -5 - 5 = -10

Therefore, the first four terms of the sequence are: 5, 0, -5, -10.

Approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.

To find the percentage of the area under the normal curve that falls between ±2 standard deviations, we need to follow the following steps:

We need to know the mean (μ) and standard deviation (σ) of the normal distribution in question. If we assume a standard normal distribution (i.e., a normal distribution with mean of 0 and standard deviation of 1), then we can use a z-score table to find the percentage of area under the curve.

The z-score formula is:

z = (x - μ) / σ

For ±2 standard deviations, the values of x are μ ± 2σ. Therefore, the z-scores are:

z = (μ + 2σ - μ) / σ = 2

z = (μ - 2σ - μ) / σ = -2

A z-score table gives the percentage of area under the standard normal curve that falls to the left of a given z-score. Since the normal distribution is symmetric, the percentage of area to the right of a negative z-score is the same as the percentage of area to the left of the corresponding positive z-score.

Using a z-score table, we find that the percentage of area under the standard normal curve that falls to the left of z = 2 is 0.9772, or 97.72%. Therefore, the percentage of area under the curve that falls between ±2 standard deviations is:

97.72% - (100% - 97.72%) = 95.44%

This means that approximately 95.44% of the data falls within ±2 standard deviations of the mean in a normal distribution.

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Answer:

D

Step-by-step explanation:

The square root of 50 is approximately equal to 7.07

-7.1111… can be rounded to -7.11

23/3 is equal to approximately 7.67

-7 1/5 is equal to -7.2

Answer: Xavier will receive $3.21 in change.

Step-by-step explanation:

To find the change Xavier receives, we need to subtract the cost of the dog collar from the amount he paid with his $10 bill:

Change = $10 - $6.79 = $3.21

Therefore, Xavier will receive $3.21 in change.

The smallest number of beads we can take so that the conditions for performing inference are met is 40.

Probability:

The probability of an event is a number that indicates the probability of the event occurring. Expressed as a number between 0 and 1 or as a percent sign between 0% and 100%. The more likely an event is to occur, the greater its probability. The probability of an impossible event is 0; the probability of a certain event occurring is 1. The probability of two complementary events A and B - A occurring or B occurring - adds up to 1.

According to the Question:

Given in the question,

Teacher prepares a large container filled with colored beads. She claims that 1/8 beads are red, 1/4are blue, and the rest are yellow. Your class will test the teacher's claim by randomly drawing a simple sample of beads from the container.

Quadrant                     Frequency

      1                                    18

      2                                   22

      3                                   39

      4                                   21

The proportions are 1/8 , 1/4 and 5/8

Here, the smallest probability is 1/8 , thus it would be used to compute the frequency.

Now,

The expected frequencies are calculated as:

E = np₁ = 15 (1/8) = 1.875

E = np₂ = 16(1/8) = 2

E = np₃ = 30(1/8) = 3.75

E = np₄ = 40(1/8) = 5

E = np₅ = 80(1/8) = 10

Here, conditions are fulfilling for 40 and 90 but the smallest sample size is contained by 40. Thus, the correct option is 40.

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To place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet. Let's discuss it in detail below. Here are the dimensions of the bench press machine, which can help determine the amount of space required to fit two bench press machines in a small area:

The length of the bench press machine is between 48 inches and 54 inches.

The width of the bench press machine is between 28 inches and 32 inches.

The height of the bench press machine is between 48 inches and 56 inches.

Based on the above dimensions of the bench press machine, two machines can be placed in a small area of 10 feet by 10 feet. However, for safe use, the following guidelines should be followed:

There should be at least 6 feet of distance between the two bench press machines. There should be at least 3 feet of clearance in the front of the bench press machine to allow for safe movement during exercises. There should be at least 2 feet of clearance behind the bench press machine to allow for a safe exit in case of an emergency.

Thus, to place two bench press machines in a small area, you will need a space of approximately 10 feet by 10 feet.

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Answer:

Sam's commission for last month can be calculated as follows:

Commission = 3% of sales

Commission = 3/100 * $46,400

Commission = $1,392

Therefore, Sam's total income for last month would be his salary plus commission:

Total income = Salary + Commission

Total income = $1,950 + $1,392

Total income = $3,342

So Sam earned $3,342 in total for last month.

Step-by-step explanation:

The approximate Z-score for this recruit is b. 0.18.

The mean of the head sizes (circumference) of new recruits in the armed forces can be approximated by a normal distribution with a mean 22.8 inches and standard deviation of 1.1 inches. The head size of a recruit was found to be 23 inches.

The approximate Z-score for this recruit. The formula for Z-score is given by:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

where X is the head size of the recruit, μ is the mean head size of recruits, and σ is the standard deviation of head sizes of recruits. Substituting the given values in the above formula, we get,

Z=(23-22.8)(1.1)

Z=0.2/1.1

Z [tex]\approx[/tex] 0.18

Thus, the approximate Z-score for this recruit is b. 0.18.

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The player should be willing to pay up to $1.33 to play this game and not lose money in the long run.

The expected value is the sum of the products of each possible outcome and its probability. Let's calculate the expected value of the game:

E(X) = (1/6) * $4 + (5/6) * (-$2)

E(X) = $0.67

This means that on average, the player can expect to win $0.67 per game. Since it costs $2 to play, the player should not be willing to pay more than $2 - $0.67 = $1.33 to play the game and not lose money in the long run.

Probability theory is based on axioms, which are basic assumptions about the nature of probability. It is used to quantify uncertainty and to make predictions based on the available information. Probability is expressed as a number between 0 and 1, with 0 meaning an event is impossible, and 1 meaning an event is certain.

The concept of probability is used in a variety of fields, including statistics, economics, engineering, and physics. In statistics, probability is used to model random variables, estimate parameters, and test hypotheses. In economics, probability is used to model financial risks and decision-making under uncertainty. In engineering and physics, probability is used to model complex systems and predict the behavior of particles.

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Answer:

Step-by-step explanation:

2(-4) - 3(-2) = -2

 -8 + 6 = -2

   -2 = -2