an experimenter flips a coin 100 times and gets 42 heads. find the 90% confidence interval for the probability of flipping a head with this coin. a) [0.239, 0.451] b) [0.339, 0.501] c) [0.259, 0.501] d) [0.339, 0.301]

trigonometry, the branch of mathematics concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names and abbreviations are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc)

Even though the first student scored 150, the expected average IQ score for the remaining four students is still 100.

Explain average

The average is a statistical measure that represents the central tendency of a set of values. It is calculated by adding up all the values and dividing them by the total number of values. The average provides a single value that represents the typical value in the set and is often used to compare different sets of data or to summarize large amounts of data.

According to the given information

Let X be the random variable representing the IQ score of an individual student. Then, the sample mean of the five students, denoted by Y, can be expressed as:

Y = (X1 + X2 + X3 + X4 + X5) / 5

Given that the first student scored 150, the expected value of the sample mean of the remaining four students, denoted by E(Y|X1=150), can be calculated as follows:

E(Y|X1=150) = E((X2 + X3 + X4 + X5) / 4 | X1 = 150)

Since X1 = 150 is an observed value, we can treat it as a constant and apply the linearity of expectation:

E((X2 + X3 + X4 + X5) / 4 | X1 = 150) = (E(X2 | X1 = 150) + E(X3 | X1 = 150) + E(X4 | X1 = 150) + E(X5 | X1 = 150)) / 4

Now, since the sample is random, the remaining four IQ scores are also independent and identically distributed as X, with the same mean of 100. Therefore, we have:

E(X2 | X1 = 150) = E(X3 | X1 = 150) = E(X4 | X1 = 150) = E(X5 | X1 = 150) = E(X)

Thus, we can simplify the expression as:

E(Y|X1=150) = (4E(X) / 4) = E(X) = 100

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Answer:

The Correct answer is sinA/3.2=sin110°/4.6

The maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.

To maximize the profit function P(t) = 60t^2 + 420t - 440, we need to find the value of t that will give us the maximum profit.

One way to do this is to use calculus. We can take the derivative of P(t) with respect to t and set it equal to zero to find the critical points:

P'(t) = 120t + 420

Set P'(t) = 0 and solve for t:

120t + 420 = 0

t = -3.5

This gives us one critical point at t = -3.5. However, this value of t doesn't make sense in the context of the problem - we can't sell tickets at a negative price!

So we need to check the endpoints of the domain of the function, which is given by the constraint that t is greater than or equal to zero (we can't charge a negative price for tickets either).

When t = 0, P(0) = -440.

When t is very large, say t = 100, P(100) = 600000 - 44000 - 440 = 555120.

Therefore, the maximum profit occurs at the endpoint t = 100, where the profit is $5551.20.

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The correct statement about scale factor is the radius of the larger can will be 8 inches. (option c).

Let's first consider the dimensions of the small can of tomato paste. We are given that it has a radius of 2 inches and a height of 4 inches. Therefore, its volume can be calculated using the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Substituting the given values, we get:

V_small = π(2²)(4) = 16π cubic inches

Using these dimensions, we can calculate the volume of the larger can using the same formula:

V_large = π(6²)(12) = 432π cubic inches

Now, let's compare the volumes of the small and large cans. We have:

V_large = 432π cubic inches > 16π cubic inches = V_small

Therefore, we can conclude that the volume of the larger can is greater than the volume of the smaller can. But is it three times greater? Let's compare:

V_large = 432π cubic inches 3

V_small = 3(16π) cubic inches = 48π cubic inches

We see that 432π cubic inches is not equal to 48π cubic inches, so option b) is not correct.

Finally, let's consider the radius of the larger can. We found earlier that it is 6 inches, which is greater than the radius of the smaller can, but it is not 8 inches. Therefore, option c) is correct.

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Complete Question:

A small can of tomato paste has a radius of 2 inches and a height of 4 inches. Suppose the larger, commercial-size can has dimensions that are related by a scale factor of 3. Which of these true?

a) The radius of the larger can will be 5 inches.

b) The volume of the larger can will be 3 times the volume of the smaller can

c) The radius of the larger can will be 8 inches.

d) The volume of the larger can is 3 times the volume of smaller can

The total amount of money received by each child after splitting $9 among 15 children is equal to $0.60.

Total number of children is equal to 15

Total amount of money distributed among 15 children = $9

To find out how much each child receives,

We can divide the total amount of money by the number of children.

In this case, there are 15 children and $9 to split.

So, the amount of money each child receives is equal to,

(Total amount of money )/ ( total number of children )

= $9 ÷ 15

= $0.60

Therefore, amount of money received by each child in the group of 15 children is equal to $0.60.

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(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°

(4) m∠1=88°m∠2=42° m∠3=113°

An angle is a geometric figure formed by two rays that share a common endpoint, called the vertex. The measure of an angle is typically expressed in degrees or radians, and it describes the amount of rotation needed to bring one of the rays into coincidence with the other.

A triangle is a closed two-dimensional shape with three straight sides and three angles.

(1) m∠1=45°(sum of 3 angles of a triangle is always 180°)

(2) m∠1=180°-129°=51°(sum of two interior angles on the same side is equal to the exterior angle)

(3) m∠1= 152°-115°=37°(sum of two interior angles on the same side is equal to the exterior angle)

(4) m∠1=88°(sum of 3 angles of a triangle is always 180°),m∠2=42°(vertically opposite angle theorem), m∠3=113°(sum of 3 angles of a triangle is always 180°)

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The two column proof is written as follows

Statement                                                           Reason

MA = XR                                           given (opposite sides of rectangle)

MK = AR                                           given (opposite sides of rectangle)

arc MA = arc RK                               Equal chords have equal arcs

arc MK = arc AK                               Equal chords have equal arcs

An arc is a portion of the circumference of a circle, and a chord is a line segment that connects two points on the circumference.

If two chords in a circle are equal in length, then they will cut off equal arcs on the circumference. This is because the arcs that the chords cut off are subtended by the same central angle.

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The company should use the adjusted R² approach to select variables for their recommendation system, as it will better account for the influence of multiple variables and help create a more accurate model for predicting subscriber's movie ratings.

To build a successful movie recommendation system for the online media streaming company, it's important to consider the appropriate statistical approach for selecting variables.

In this case, the company should use the adjusted R² approach instead of the p-value approach.

The adjusted R² approach is more suitable for this scenario because it measures the proportion of variance in the dependent variable (subscriber's ratings) that is predictable from the independent variables (movie and subscriber data).

Adjusted R² takes into account the number of variables and adjusts for overfitting, which is important when dealing with a large dataset, like the one the streaming company has.

It helps in identifying the most influential factors and creating a model that better predicts movie ratings.
On the other hand, the p-value approach focuses on the statistical significance of individual variables, which might lead to including variables that are significant but not necessarily the best predictors for movie ratings.

This could result in a less accurate recommendation system.

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The point of intersection in the first quadrant is (3, 4) from the equation of circle.

We can start by substituting the equation of the line into the equation of the circle and solving for z and y.

The equation for the circle is:

(x - h)^2 + (y - k)^2 = r^2

Substituting h = 0, k = 3, and r = 3, we get:

x^2 + (y - 3)^2 = 9

Now, we substitute y = 2z + 3 into the equation:

x^2 + (2z + 3 - 3)^2 = 9

Simplifying, we get:

x^2 + 4z^2 = 9

Since we are looking for a point in the first quadrant, both x and z must be positive. We can solve for z in terms of x:

4z^2 = 9 - x^2

z^2 = (9 - x^2)/4

z = sqrt[(9 - x^2)/4]

Substituting this into the equation y = 2z + 3, we get:

y = 2sqrt[(9 - x^2)/4] + 3

To find the point of intersection in the first quadrant, we need to find a value of x that satisfies both this equation and the equation of the circle. We can substitute the equation for y into the equation for the circle:

x^2 + [2sqrt((9 - x^2)/4)]^2 = 9

Simplifying, we get:

x^2 + (9 - x^2)/2 = 9

Multiplying both sides by 2:

2x^2 + 9 - x^2 = 18

Solving for x:

x^2 = 9

x = 3

Substituting x = 3 into the equation for y, we get:

y = 2sqrt[(9 - 3^2)/4] + 3 = 4

Therefore, the point of intersection in the first quadrant is (3, 4).

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Answer:

48 ounces

Step-by-step explanation:

12*4= 48

From the given information, you can deduce that triangle QTR is equilateral and equiangular (all angles are 60 degrees)

b, c, d, and f are true

The opposite angles of a parallelogram are congruent (b)

If 2 parallel lines are cut by a transversal, then the corresponding angles are congruent (d)

Angle RQT is congruent to angle QRT, and angle QRT is congruent to angle S. By the transitive property, angle RQT is congruent to angle S (c)

Transitive property, like c (f)

The product of two terms gives the walkway's area around the garden: 15x+13.5.

A rectangle is a four-sided polygon with two pairs of parallel and congruent sides, and four right angles. The opposite sides of a rectangle are equal in length and parallel to each other, while the adjacent sides are perpendicular to each other.

Area of garden = 4(4.5x + 3.5) = 18x+14

The combined area of the garden and the walkway = 5.5​(6x+5​) =33x+27.5

The area of the walkway (Aw) around the garden is the result of subtracting the total area minus the inner area:

Aw=combined area -Area of garden

=33x+27.5-18x-14

=15x+13.5

Thus, we can say that the area of the walkway around the garden is the sum of two terms: 15x+13.5.

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The longest segment that would fit inside the cylinder is approximately 9.06 centimeters.

The longest segment that would fit inside the cylinder would be the diagonal of the cylinder's base, which is equal to the diameter of the base. The diameter of the base is equal to twice the radius, so it is 6 cm. Using the Pythagorean theorem, we can find the length of the diagonal:

[tex]diagonal^2 = radius^2 + height^2 \\diagonal^2 = 3^2 + 8^2 \\diagonal^2 = 9 + 64 \\diagonal^2 = 73 \\diagonal = sqrt(73)[/tex]

Therefore, the longest segment that would fit inside the cylinder is approximately 8.54 cm (rounded to the nearest hundredth).
To find the longest segment that would fit inside the cylinder, we need to calculate the length of the space diagonal of the cylinder. This is the distance between two opposite corners of the cylinder, passing through the center. We can use the Pythagorean theorem in 3D for this calculation.

The terms we'll use are:
- Radius (r): 3 cm
- Height (h): 8 cm

To find the space diagonal (d), we can use the following formula:

[tex]d = \sqrt{r^2 + r^2 + h^2}[/tex]
Plug in the values:

[tex]d = \sqrt{((3 cm)^2 + (3 cm)^2 + (8 cm)^2)} d = \sqrt{(9 cm^2 + 9 cm^2 + 64 cm^2)} d = \sqrt{(82 cm^2)}[/tex]
d ≈ 9.06 cm

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The longest segment that can fit inside the cylinder is. [tex]$\sqrt{73}$ cm[/tex].

The longest segment that can fit inside a cylinder is a diagonal that connects two opposite vertices of the cylinder.

The length of this diagonal by using the Pythagorean theorem.

Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares on the other two sides.

This theorem can be written as an equation relating the lengths of the sides a, b and the hypotenuse c, often called the Pythagorean equation:[1]

[tex]{\displaystyle a^{2}+b^{2}=c^{2}.}[/tex]

The theorem is named for the Greek philosopher Pythagoras, born around 570 BC.

The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.

The proofs are diverse, including both geometric proofs and algebraic proofs, with some dating back thousands of years.

Consider a right triangle with legs equal to the radius.

[tex]$r$[/tex] and the height [tex]$h$[/tex] of the cylinder, and with the diagonal as the hypotenuse.

Then, by the Pythagorean theorem, the length of the diagonal is:

[tex]$\sqrt{r^2 + h^2} = \sqrt{3^2 + 8^2} = \sqrt{73}$[/tex]

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Similarly, if the spread of the training group's distribution is smaller than the spread of the no training group's distribution.

The training group ran faster on average, than the no training group.

To determine which pair of dot plots provides the strongest statistical evidence that the training group ran faster.

Compare the center and spread of the two groups.

The center of the training group's distribution is consistently to the left (i.e., lower times) of the center of the no training group's distribution.

Overlap between the two distributions, then we can conclude that the training group ran faster on average, than the no training group.

100 by adding data.

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We need to examine the dotplots and summary statistics of the two groups to determine which pair of dotplots provides the strongest statistical evidence that the training group ran faster, on average, than the no training group.

To determine which pair of dotplots provides the strongest statistical evidence that the training group ran faster, we need to compare the centers and spreads of the two groups. If the center of the training group is shifted to the left (smaller times) compared to the center of the no training group, and if the spread of the training group is smaller than the spread of the no training group, then we have stronger evidence that the training group ran faster, on average, than the no training group.

Without seeing the actual dotplots, we cannot make a definitive determination. However, we can describe what to look for in the dotplots. Specifically, we want to see a clear separation between the centers of the two groups, and we want to see less overlap between the dots in the training group than in the no training group.

In addition, we can calculate summary statistics for the two groups, such as the mean and standard deviation, to help us compare the centers and spreads of the two groups. If the mean of the training group is significantly smaller than the mean of the no training group, and if the standard deviation of the training group is significantly smaller than the standard deviation of the no training group, then we have stronger evidence that the training group ran faster, on average, than the no training group.

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Answer:

2.07 cm

Step-by-step explanation:

Hypotenuse = 2 cm

Adjacent side = a

Formula

cos θ = Hypotenuse/Adjacent side

cos 15 = 2/a

Note

The value of cos 15 is approximately 0.965.

0.965 = 2/a

a = 2/0.965

a = 2.07 cm ( approximately )

The inequality represented by the given number line is: -60 ≥ m.

We can see the values that an inequality represents by placing it on a number line.

On a number line, inequalities are represented by drawing a straight line and designating the end points as an open or closed circle.

On a number line, inequality is represented as follows:

For the given number line,

-6 is shown with the closed circle, with lines extending towards +∞

Thus, the inequality represented by the given number line is: -60 ≥ m.

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Answer:

The formula for the area of a trapezoid is:

Area = (b1 + b2) / 2 x h

where b1 and b2 are the lengths of the two parallel bases, and h is the height.

We are given that the area of the trapezoid is 96 ft, the height is 8 ft, and one of the bases (b1) is 11 ft. We can use this information to find the length of the other base (b2).

Substituting the given values into the formula for the area of a trapezoid, we get:

96 = (11 + b2) / 2 x 8

Multiplying both sides by 2 and dividing by 8, we get:

24 = 11 + b2

Subtracting 11 from both sides, we get:

b2 = 13

Therefore, the length of the other base is 13 ft.

Answer:

135.07 mm2

Step-by-step explanation:

height = 10.39 mm

area = 135.07 mm2

The current in the circuit when the resistance is 12 ohms is 40 amps.

What is fraction?

A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.

We can use the inverse proportionality formula to solve this problem, which states that:

current (in amps) x resistance (in ohms) = constant

Let's call this constant "k". We can use the information given in the problem to find k:

24 amps x 20 ohms = k

k = 480

Now we can use this constant to find the current when the resistance is 12 ohms:

current x 12 ohms = 480

current = 480 / 12

current = 40 amps

Therefore, the current in the circuit when the resistance is 12 ohms is 40 amps.

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The z- score that has 20.9 of the distribution's area to its right is roughly 0.84.

To find the z- score that has 20.9 of the distribution's area to its right, we can use a standard normal distribution table or a calculator with a normal distribution function.

Using a standard normal distribution table, we can look for the area to the left of the z- score with an area of 1-0.209 = 0.791. The closest value we can find in the table is 0.7901, which corresponds to a z- score of 0.84.

Alternatively, we can use a calculator with a normal distribution function.However, 0, 1) = 0, If we use the formula" normalcdf(z. 209" to find the z- score, we get z = 0.84.

therefore, the z- score that has 20.9 of the distribution's area to its right is roughly 0.84.

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The coordinates of the reflected polygon F'G'H'I' are as follows:

F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).

What is the reflection?

In mathematics, reflection is defined as the mirror image of a figure crossing a line (drawn or imagined), known as the line of reflection.

The vertices of the polygon FGHI are as follows:

F(2, -1)

G(5, 2)

H(8, 3)

I(6, 0)

To reflect the polygon FGHI across the line y = -1, we need to flip the points over the line.

Now we can reflect each of the points of the polygon across the line y = -1 to get the image:

F(2, -1) stays in the same place because it lies on the line of reflection.

G(5, 2) is reflected to G'(5, -4) by flipping it vertically across the line y = -1.

H(8, 3) is reflected to H'(8, -5), and

I(6, 0) is reflected to I'(6, -2).

Hence, The coordinates of the reflected polygon F'G'H'I' are as:

F'(-2, -1), G'(5, -4), H'(8, -5), and I'(6, -2).

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Complete question:

The complete question is attached in the image.

The psychologist finds that the estimated Cohen's d is  0.32, the t statistic is 2. 83, and r² is 0.073.  Using r² and the extension of Cohen's guidelines for interpreting the effect size using r², there is a small treatment effect.   job seeker finds that the estimated Cohen's d is 0.88, the t statistic is 7. 78, and r² is 0.479.Using r² and the extension of Cohen's guidelines for interpreting the effect size with r², there is a large treatment effect

To calculate the estimated Cohen's d, we use the formula

d = (M - M0) / SD

where M is the mean of the treatment group (job seekers who received training on using the Internet to find job listings), M0 is the mean of the control group (typical job seeker), and SD is the pooled standard deviation of the two groups. Using the given values, we have

M = 8.7 months

M0 = 7.4 months

SD = 4.1 months

So, d = (8.7 - 7.4) / 4.1 = 0.32

Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.32, there is a small treatment effect.

To calculate r², we use the formula

r² = t² / (t² + df)

where t is the t statistic, df is the degrees of freedom (n-2 for a two-group design), and n is the sample size. Using the given values for the Internet training group, we have

t = 2.83

n = 81

df = 79

So, r² = 2.83² / (2.83² + 79) = 0.073

Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an r² of 0.073, there is a small treatment effect.

For the job seekers who received training on interview skills, we can calculate Cohen's d and r² in a similar way

d = (M - M0) / SD = (8.1 - 7.4) / 0.8 = 0.88

t = 7.78

n = 81

df = 79

r² = 7.78² / (7.78² + 79) = 0.479

Using Cohen's guidelines for interpreting effect size with Cohen's d, a value of 0.2 is considered a small effect, 0.5 a medium effect, and 0.8 a large effect. Therefore, with an estimated Cohen's d of 0.88, there is a large treatment effect.

Using the extension of Cohen's guidelines for interpreting effect size with r², a value of 0.01 is considered a small effect, 0.09 a medium effect, and 0.25 a large effect. Therefore, with an  r² of 0.479, there is a medium to large treatment effect.

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Answer:.317

.091

Small to med

Med

.875

.431

Large

Large

Step-by-step explanation:

Therefore , the solution of the given problem of unitary method comes out to be during the 4-second period, the tram's elevation changed by 3 metres every second.

To complete the assignment, use the iii . -and-true basic technique, the real variables, and any pertinent details gathered from basic and specialised questions. In response, customers might be given another opportunity to sample expression the products. If these changes don't take place, we will miss out on important gains in our knowledge of programmes.

Here,

By dividing the overall elevation change (12 metres) by the total time required (4 seconds),

it is possible to determine the change in the tram's elevation every second. We would then have the average rate of elevation change per second.

=> Elevation change equals 12 metres

=> Total duration: 4 seconds

=>  12 meters / 4 seconds

=> 3 meters/second

As a result, during the 4-second period, the tram's elevation changed by 3 metres every second.

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Answer:

1

Step-by-step explanation:

First of all we use the "law of sines"

to get the measure/length we need the opposing angle of it of the side, now in this case the missing side is x

and its opposing angle is missing so using common sense, the sum of angles in the triangle is 180°

180°=70°+51°+ x

x = 180°-121°

=59°

Using law of sines:

(sides are represented by small letters/capital letters are the angles)

a/sinA= b/sinB= c/sinC

We have one given side which is "9"

so,

9/sin70= x/sin59

doing the criss-cross method,

9×sin59=sin70×x

9×sin59/sin70=x

x=8.2 (answer 1)

I hope this was helpful <3

The action that would reduce the amount the person paid in taxes to 1,000 is option (D) Receiving a $49,000 tax credit

In this scenario, the person has $50,000 in taxable income and pays a 10% income tax rate, which amounts to $5,000 in taxes. To reduce the tax liability to $1,000, the person needs to receive a tax credit of $49,000. Tax credits directly reduce the amount of tax owed, whereas tax deductions reduce taxable income.

A tax deduction of $4,000 would lower the taxable income to $46,000, resulting in a lower tax liability of $4,600, which is not low enough to reach $1,000. Therefore, a tax credit of $49,000 is needed to reduce the tax liability to $1,000.

Therefore, the correct option is (D) Receiving a $49,000 tax credit

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The given question is incomplete, the complete question is:

A person has $50,000 in taxable income for a year and pays a 10 percent income tax rate, equal to $5,000. Which action would reduce the amount the person paid in taxes to $1,000?

A.Receiving a $4,000 tax deduction

B.Receiving a $4,000 tax credit

C. Receiving a $49,000 tax deduction

D. Receiving a $49,000 tax credit

The shortest driving distance between the stadium and the animal shelter is given as follows:

10 blocks.

Suppose that we have two points of the coordinate plane, and the ordered pairs have coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex].

The shortest distance between them is given by the equation presented as follows, derived from the Pythagorean Theorem:

[tex]D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

The coordinates are given as follows:

Since the spaces are filled by houses, we cannot apply the formula, hence the shortest distance is:

6 - (-3) + 3 - 2 = 9 + 1 = 10 blocks.

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Answer:

To write the equation of the line that passes through the points (2, 7) and (0, -5), we can use the slope-intercept form of a linear equation, which is:

y = mx + b

Where m is the slope of the line, and b is the y-intercept.

First, we can find the slope of the line by using the formula:

m = (y2 - y1) / (x2 - x1)

Where (x1, y1) = (2, 7) and (x2, y2) = (0, -5)

m = (-5 - 7) / (0 - 2)

m = -12 / -2

m = 6

So the slope of the line is 6.

Next, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Where (x1, y1) = (2, 7)

y - 7 = 6(x - 2)

Simplifying this equation, we get:

y - 7 = 6x - 12

y = 6x - 5

So the equation of the line that passes through the points (2, 7) and (0, -5) is y = 6x - 5.