2. Find the approximate volume of the cone. Use alt+227 or pi for pi as needed.

SHOW YOUR WORK

The correct answer is:
a. V1, V2 form the basis; V3 = 4V1 + V2, V4 = -4V1 + V2

To find a subset of the vectors that forms a basis for the space spanned by the vectors and express each vector that is not in the basis as a linear combination of the basis vectors, follow these steps:

1. Write the given vectors as rows of a matrix:
  A = | 1   0  1  1 |
      |-7   7 -4  1 |
      |-3   7  0  5 |
      |-11  7 -8 -3 |

2. Perform Gaussian elimination to find the row-reduced echelon form (RREF) of the matrix A.

3. The RREF of matrix A is:
  RREF(A) = | 1  0  1  1 |
            | 0  1 -2  3 |
            | 0  0  0  0 |
            | 0  0  0  0 |

4. Identify the pivot columns in the RREF matrix. In this case, the first and second columns have pivots.

5. The pivot columns correspond to the original vectors that form a basis. In this case, V1 and V2 form the basis.

6. Express each vector that is not in the basis as a linear combination of the basis vectors. For V3 and V4, we can see that:
  V3 = 4V1 + V2
  V4 = -4V1 + V2

So, the correct answer is:
a. V1, V2 form the basis; V3 = 4V1 + V2, V4 = -4V1 + V2

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Answer:

2y92+83(n83-5)+12

Step-by-step explanation:

well if you carry the 4 and move the decimal over 3 places and divide by a hamsterball & justin biebers nipple, you get the answer

The measure of the other acute angle to the nearest degree is 34°, since the trigonometric tangent ratio of one acute angle is 3/2.

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

we shall call the acute angles X and Y such that;

tan X = 3/2 {opposite/adjacent}

X = tan⁻¹(3/2) {cross multiplication}

X = 56° approximately to the nearest degree

Y = 180° - (56 + 90)° {sum of interior angles of a triangle}

Y = 180° - 146°

Y = 34°

Therefore, the measure of the other acute angle to the nearest degree is 34°, since the trigonometric tangent ratio of one acute angle is 3/2.

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The equation of line g is y = (3/10)x + 1.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line f is y - 7 = (3/10)(x - 4).

Since line g is parallel to line f, it will have the same slope as line f, which is 3/10.

Hence, the equation of line g can be written in the form:

y - y1 = m(x - x1)

Where (x1, y1) is the given point (10, 4) and m is the slope of line f, which is 3/10.

Substituting the values, we get:

y - y1 = m(x - x1)

y - 4 = (3/10)(x - 10)

y - 4 = (3/10)x - 3

y = (3/10)x + 1

Therefore, y = (3/10)x + 1 is the equation of line g.

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The MLE of λ = 1/p is:

â = 1/0.6364 = 1.5714 (rounded to four decimal places).

Let Y be the number of components that survive 24 hours. Then Y ~ Bin(22, p), where p is the probability that a component survives 24 hours. The maximum likelihood estimator (MLE) of p is the sample proportion of components that survive 24 hours, which is y/n = 14/22 = 0.6364.

Now, let X be the lifetime of a component, which is exponentially distributed with parameter λ = 1. Then the probability that a component survives 24 hours is P(X > 24) = e^(-24λ). Substituting λ = 1, we get p = e^(-24).

The likelihood function L(p) is then given by:

L(p) = (22 choose 14) * p^14 * (1-p)^8

Taking the natural logarithm of L(p), we get:

ln L(p) = ln(22 choose 14) + 14 ln p + 8 ln(1-p)

To find the MLE of p, we differentiate ln L(p) with respect to p and set the result to zero:

d/dp ln L(p) = 14/p - 8/(1-p) = 0

Solving for p, we get:

p = 14/22 = 0.6364

This is the same as the MLE of p we obtained earlier, which makes sense since p = e^(-24) is a function of the MLE of p.

Therefore, the MLE of λ = 1/p is:

â = 1/0.6364 = 1.5714 (rounded to four decimal places).

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We cannot conclude that the new beta-blocker medicine is effective at treating high blood pressure at a significance level of αα = 0.01.  

We can perform a chi-squared test to determine if there is a significant difference between the number of subjects in the treatment group who had their high blood pressure successfully treated and the number of subjects in the control group who had their high blood pressure successfully treated.

First, we need to calculate the expected counts for each group. Since we know that the treatment group had 114 successful outcomes, and the control group had 100 successful outcomes, we can calculate the expected counts as follows:

Expected counts for treatment group: (114 * 180) / 210 = 146.7

Expected counts for control group: (100 * 180) / 210 = 187.3

Next, we can calculate the chi-squared value using the formula:

chi-squared = sum(([tex]observed - expected)^2[/tex]/ expected)

where observed and expected are the actual counts and expected counts, respectively.

For the treatment group, the observed count is 114, and the expected count is 146.7. Therefore, we calculate the chi-squared value as:

chi-squared = [tex](114 - 146.7)^2[/tex] / 146.7 = 12.2

For the control group, the observed count is 187.3, and the expected count is 187.3. Therefore, we calculate the chi-squared value as:

chi-squared = (187.3 - [tex]187.3)^2[/tex] / 187.3 = 0

We can then calculate the p-value using the formula:

p-value = 2 * (chi-squared / degrees of freedom)

where degrees of freedom is the number of categories minus 1 for each cell. In this case, we have two cells, one for the treatment group and one for the control group, so the degrees of freedom is 2 - 1 = 1.

Substituting the values into the formula, we get:

p-value = 2 * (12.2 / 1) = 2.44

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We can conclude that for all integers a and b, if a|b, then a ≤ b.

To prove that for all m and n, if m ≠ n, then m+n ≠ Q, we will use proof by contradiction.

Assume that for some m and n, m ≠ n, and m+n = Q, where Q is a rational number. By the definition of a rational number, Q can be expressed as the ratio of two integers, p and q, where q ≠ 0.

Thus, we have:

m + n = p/q

Multiplying both sides by q, we get:

mq + nq = p

Rearranging, we get:

mq = p - nq

Since p, n, and q are integers, p - nq is also an integer. Therefore, mq is an integer.

But we know that m and n are integers and m ≠ n, which implies that m and n have different prime factorizations. Therefore, mq cannot be an integer, as it would require m and q to have a common factor, which is not possible.

This contradicts our assumption that m+n = Q, and hence, we can conclude that for all m and n, if m ≠ n, then m+n ≠ Q.

To prove that for all integers a and b, if a|b, then a ≤ b, we will use direct proof.

Assume that a and b are integers such that a|b, i.e., there exists an integer k such that b = ak.

To prove that a ≤ b, we need to show that a is less than or equal to k times a, i.e., a ≤ ka.

Dividing both sides of the equation b = ak by a (which is possible as a ≠ 0 since it is a divisor of b), we get:

b/a = k

Since k is an integer, we know that b/a is also an integer. Therefore, a must be less than or equal to b/a.

Multiplying both sides of the inequality a ≤ b/a by a (which is a positive number since a > 0), we get:

[tex]a^2 ≤ ab[/tex]

Since a and b are both positive integers, we know that [tex]a^2 ≤[/tex] ab implies that [tex]a ≤ b[/tex].

Therefore, we can conclude that for all integers a and b, if a|b, then a ≤ b.

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If Sheila’s test had a z-score of 2.2 then her test score was 89.6%.

We can use the formula for calculating the z-score of a value,

z = (x - μ) / σ, value we want to convert to a z-score is x, mean of the distribution is μ,  standard deviation of the distribution is σ and z score is z. In this case, we know that the average mark on the test was 72%, which means μ = 72. We also know that the standard deviation was 8%, which means σ = 8. We know that Sheila's z-score was 2.2,

We can rearrange the formula to solve for x,

x = μ + zσ

Substituting in the values we know,

x = 72 + 2.2 * 8

x = 72 + 17.6

x = 89.6

Therefore, Sheila's test score was 89.6%.

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|| (3,3) - (1,1) || < 2 + r

Simplifying this inequality, we get:

2√2 < 2 + r

r > 2√2 - 2

So, any value of r such that r > 2√2 - 2 will satisfy the condition B2(1,1)∩Br(3,3)≠0.

For the first question, we need to find an r such that the open ball centered at (0,0) with radius 1 (denoted as Br(0,1)) intersects with the open ball centered at (2,0) with radius t (denoted as Bt(2,1)). Since the usual norm is the Euclidean norm, the distance between (0,0) and (2,0) is 2. Thus, we have the inequality:

|| (2,0) - (0,0) || < 1 + t

Simplifying this inequality, we get:

2 < 1 + t

t > 1

So, any value of r such that 1 < r < 3 will satisfy the condition Br(0,1) ∩ Bt(2,1)≠0.

For the second question, we need to find an r such that the open ball centered at (1,1) with radius 2 (denoted as B2(1,1)) intersects with the open ball centered at (3,3) with radius r (denoted as Br(3,3)). Using the Euclidean norm, we have:

|| (3,3) - (1,1) || < 2 + r

Simplifying this inequality, we get:

2√2 < 2 + r

r > 2√2 - 2

So, any value of r such that r > 2√2 - 2 will satisfy the condition B2(1,1)∩Br(3,3)≠0.

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The A 5 gallons of water will pour through the hose in 8 minutes.

The formula to be used for calculation of amount of water pouring through hose :

Total amount of water = amount of water pouring per minute × amount of time (in minutes)

Keep the values in formula to find the total amount of water

Total amount of water = 2.5 × 8

Performing multiplication on Right Hand Side of the equation

Total amount of water = 20 quarts

Now performing unit conversion

Amount of water in gallon = amount of water in quarts × 0.25

Amount of water in gallon = 20 × 0.25

Amount of water = 5 gallon

Hence, the correct answer is A 5.

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The randomly select 500 students and observe that 85 of them smoke. Estimate the probability that a randomly selected student smokes , the correct answer is 27.
To estimate the probability that a randomly selected student smokes, we use the proportion of students who smoke in our sample of 500. We observed that 85 out of 500 students smoke, so the proportion is: 85/500 = 0.17
To convert this proportion to a probability, we simply round to two decimal places: 0.17 ≈ 0.27
Therefore, the estimated probability that a randomly selected student smokes is approximately 0.27, which is answer choice a.

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Answer:Domain is all real numbers

Step-by-step explanation:

f(x)=x^2

it is a parabola and all parabola’s domains are all real numbers

The given set of ordered pairs represents a function because each output has exactly one corresponding input. So, the correct answer is A) Yes, because for each output there is exactly one input.

A relation between two variables is a set of ordered pairs, where the first element in each pair corresponds to the input or independent variable (usually denoted by x), and the second element corresponds to the output or dependent variable (usually denoted by y).

In the given set of ordered pairs, each output has exactly one corresponding input, and therefore the relation satisfies the definition of a function. For example, the input of 3/4 is associated with only one output of -2, and the output of -7 is associated with only one input of -2. Hence, the relation represents a function.

So, the correct answer is A).

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the answer is  -2 (6 x + 7)

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2.

b = 1, ≥

From the diagram, the solution to the inequality is x ≥ 1 and x ≤ -3

Hence:

|x + b| ≥ 2

x + b ≥ 2 or -(x + b) ≥ 2

x ≥ 2 - b or x ≤ -2 - b

2 - b = 1 and -2 - b = -3

b = 1

Hence |x + 1| ≥ 2

The inequality solved to give a solution of x ≥ 1 and x ≤ -3 is |x + 1| ≥ 2. b = 1, ≥

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Answer:

Step-by-step explanation:

300

in sequare

Answer: 3060 in³

Step-by-step explanation:

Volume is how much a shape can hold.  It's a 3 dimensional measurement so you need to multiply 3 dimensions

V= length x width x height

Sometimes students get confused with which is which side but it really doesn't matter because multiplication is commutative meaning you can switch it and it doesn't matter.  Like  5x2 is the same thing as 2x5  both will still be 10

length=15

width=12

height= 17

If Volume = length x width x height

=15 x 12 x 17 =  =3060

Because it's 3 dimensional, units are are cubed as well. but questions says no units

The sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is 37 for k= 18.

The cubic equation is given as,

p(x) = x³ - x² - 18x +k

To find the real roots of the cubic equation p(x) we can equate p(x) =0 , we get,

x³ - x² - 18x +k = 0

⇒ x² (x -1) - 18(x - k/18) = 0

For factoring the equation we can equate  (x -1) = (x - k/18) by comparing it with solving of general equations.

That is by arranging the cubic equation after equating (x -1) = (x - k/18)  we will get,

(x-1)(x² -18) =0

Thus we get,

(x -1) = (x - k/18)

⇒ k/18 =1

⇒ k =18

The cubic equation which will give us real roots will become,

p(x) = x³ - x² - 18x +18

By factoring we can find the real roots as,

x³ - x² - 18x +18 =0

⇒ (x² -18)(x -1) =0

⇒x= 1 , x = 3√2 and x= -3√2

Let us say, a = 1 , b = 3√2 and c = -3√2 are the required real roots.

The square of real roots are as follows,

a² = 1

b² = 18

c² = 18

Thus, the sum of squares of the real roots of p(x) = x³ - x² - 18x +18 is

= a² + b²+ c²

= 1 + 18 + 18

= 37

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Therefore, the length of a side of the square is x/4 inches by the equation.

In this context, we have a wire that we need to bend into a square. A square has four equal sides, so if we let s be the length of one side of the square, then the total length of the wire must be 4s.

The equation 4s = x represents this relationship, where x is the total length of the wire.

To solve for s, we can isolate s on one side of the equation by dividing both sides by 4. This gives us:

4s / 4 = x / 4

Simplifying, we get:

s = x / 4

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There are indeed 48 triangles that can be chosen from the rectangular array shown .

To find the 48 triangles, you should use the Combination formula which will show you the number of ways to pick 3 points when given 8 points.

C ( n, k ) = n! / ( k ! x ( n - k ) ! )

C ( 8 , 3 ) = 8 ! / (3 ! x ( 8 - 3 ) ! )

C ( 8, 3 ) = 336 / 6

C ( 8, 3) = 56

Now, there are technically 56 ways to pick the points but some of these ways are collinear and these cannot form triangles. Each row will have 4 such points so the number of ways to pick triangles is:

= 56 - ( 4 x 2 )

= 48 triangles

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The area of the parallelogram formed by the given vertices A(1, 0, -1), B(1, 7, 2), C(2, 4, -1), and D(0, 3, 2) is 2√21 square units.

To calculate the area of a parallelogram, we can use the cross product of two vectors formed by the sides of the parallelogram. The vectors AB and AD can be calculated by subtracting the coordinates of the initial and final points.

The cross product of these vectors gives us a vector representing the area of the parallelogram. Taking the magnitude of this vector gives us the area of the parallelogram. The magnitude of the cross product of AB and AD is 24, so the area of the parallelogram is 24 square units.

In this case, the vector AB is (-3, 7, 3), and the vector AD is (-1, 3, 3). Taking the cross product of these vectors gives us the vector (-12, 6, 24). The magnitude of this vector is √(12² + 6² + 24²) = √756 = 2√21. Therefore, the area of the parallelogram is 2√21 square units.

Complete Question:

Find the area of the parallelogram whose vertices are A(1, 0, −1), B(1, 7, 2), C(2, 4, −1), D(0, 3, 2).

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1. The modal number of pairs of shoes owned by the children will be; 3.

2. The median number of pairs of shoes owned by the children  will be;3.

3. The Mean is 3.

1. The modal number of pairs of shoes owned by the children would be 3.

2. The median number of pairs of shoes owned by the children are;

= 14/2 th term

= 7 th term

= 3

3. The Mean would be

= (1 x 2+ 2 x 3+ 3 x 5+ 4 x 2 + 5 x 1+ 6x 1)/ (2 +3 +5 +2 + 1 +1)

= 42/14

= 3

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The center of mass of the thin parabola plate is located at the point (1/2, 3/10).

The center of mass of a two-dimensional object is the point (X', Y') where the object would balance if it were suspended from that point. The coordinates X' and Y' are given by the formulas:

X' = Mx / M

Y' = My / M

where M is the total mass of the object, Mx is the moment of the object with respect to the x-axis, and My is the moment of the object with respect to the y-axis. The moments are defined as integrals of the density over the region:

Mx = ∫∫ xρ(x,y) dA

My = ∫∫ yρ(x,y) dA

where ρ(x,y) is the density of the object at the point (x,y) and dA is an element of area.

In this case, the density of the thin plate is constant, so we can take it out of the integrals:

Mx = ∫∫ x dA = ∫∫ x dx dy

My = ∫∫ y dA = ∫∫ y dx dy

The region bounded by the parabola y = x² and the line y = 0 can be described as the set of points (x,y) such that 0 ≤ y ≤ x². Therefore, we can set up the integrals as follows:

Mx = ∫∫ x dx dy = ∫0^1 ∫0ˣ x dx dy = ∫0^1 (1/2)x² dy = 1/6

My = ∫∫ y dx dy = ∫0^1 ∫0ˣ y dx dy = ∫0^1 (1/2)x⁴ dy = 1/10

where we have used the fact that the total mass of the plate is equal to the area of the region, which is 1/3.

Finally, we can use these values to compute the coordinates of the center of mass:

X' = Mx / M = (1/6) / (1/3) = 1/2

Y' = My / M = (1/10) / (1/3) = 3/10

Therefore, the center of mass of the thin plate is located at the point (1/2, 3/10).

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The price should you sell the bracelets at is given by the term of the amount is $64.

The increase in income that comes from selling one more unit of output is known as marginal revenue. Although marginal revenue can remain constant above a certain level of output, it will eventually start to decline as the output level rises due to the law of diminishing returns. According to economic theory, companies that are completely competitive keep on producing goods until marginal revenue and marginal cost are equal.

Price, the sum of money required to purchase a specific good. Price is also a measure of value insofar as it reflects what consumers are willing to pay for a product's worth.

Overall marginal cost (MC) = Explicit (stated) marginal cost + Profit per unit given up = $2 + $6 = $8

Profit is maximized when Marginal revenue (MR) equals Overall MC.

P = 120 - 2Q

Total revenue (TR) = P x Q = 120Q - 2Q2

MR = dTR/dQ = 120 - 4Q

Equating with Overall MC,

120 - 4Q = 8

4Q = 112

Q = 28

P = 120 - (2 x 28) = 120 - 56 = $64.

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The price should you sell the bracelets at is given by the term of the amount is $64.

The term "marginal revenue" refers to the additional income generated by selling one additional unit of output. Although marginal income can remain constant above a particular output level, it will ultimately start to decrease as the output level increases owing to the law of diminishing returns.

Companies that are entirely competitive continue to produce items until marginal income and marginal cost are equal, according to economic theory. A certain good's price is the amount of money needed to buy it. Insofar as it represents what customers are prepared to pay for a product's worth, price is likewise a measure of value.

Overall marginal cost (MC) = Explicit (stated) marginal cost + Profit per unit given up = $2 + $6 = $8

Profit is maximized when Marginal revenue (MR) equals Overall MC.

P = 120 - 2Q

Total revenue (TR) = P x Q = 120Q - 2Q2

MR = dTR/dQ = 120 - 4Q

Equating with Overall MC,

120 - 4Q = 8

4Q = 112

Q = 28

P = 120 - (2 x 28)

= 120 - 56

= $64.

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Substituting n = -1 in the given expression, we get:

n² + n² + n² for n = -1

= (-1)² + (-1)² + (-1)²

= 1 + 1 + 1

= 3

Therefore, n² + n² + n² for n = -1 is equal to 3.

Answer:

-1

Step-by-step explanation:

4x + 13 = 9

4x + 13 - 13 = 9 -13

4x = -4

-4/4 = -1

X = -1

Answer:

-1.

Step-by-step explanation:

4x + 13 = 9

4x =  9 -13

4x = -4

x = -4/4

X = -1

y(x) = a_0 (1 - x^2/3 + 2x^4/45 - 8x^6/315 + ...)

that the solution is only valid for |x| < 1, since the differential equation is singular at x = ±1.

We can solve the given differential equation using the Frobenius method, by assuming that the solution can be represented as a power series:

y(x) = ∑(n=0)^(∞) a_n x^n

Differentiating the series twice, we get:

y'(x) = ∑(n=1)^(∞) n a_n x^(n-1)

y''(x) = ∑(n=2)^(∞) n(n-1) a_n x^(n-2)

Substituting these into the differential equation, we get:

(1-x^2) ∑(n=2)^(∞) n(n-1) a_n x^(n-2) - 2x ∑(n=1)^(∞) n a_n x^(n-1) + 2 ∑(n=0)^(∞) a_n x^n = 0

Simplifying and shifting the indices, we get:

∑(n=0)^(∞) [(n+2)(n+1) a_{n+2} - 2n a_n + 2a_n] x^n = 0

This gives us the following recurrence relation for the coefficients:

(n+2)(n+1) a_{n+2} = 2n a_n - 2a_n

Simplifying further, we get:

a_{n+2} = - (2n/(n+2)(n+1)) a_n

Starting with n = 0, we can compute the coefficients a_n in terms of a_0:

a_2 = - 2/3 a_0

a_4 = 2/15 a_2 = - 4/45 a_0

a_6 = - 2/21 a_4 = 8/315 a_0

a_8 = 2/99 a_6 = - 16/3465 a_0

...

The general form of the solution is then:

y(x) = a_0 (1 - x^2/3 + 2x^4/45 - 8x^6/315 + ...)

that the solution is only valid for |x| < 1, since the differential equation is singular at x = ±1.

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a) The equilibrium point is x = 2 or x = 8

b) The consumer surplus equilibrium point is $6,062.67

c) The producer surplus equilibrium point is $13,208.67

a) To find the equilibrium point, we need to set the demand function equal to the supply function and solve for x:

D(x) = S(x)

[tex](x - 5)^2 = x^2 + x + 3[/tex]

Expanding the left side and simplifying, we get:

[tex]x^2 - 10x + 22 = 0[/tex]

Using the quadratic formula, we get:

[tex]x = (10[/tex] ± [tex]\sqrt{36})/ 2[/tex]

[tex]x = 5[/tex] ± [tex]3[/tex]

[tex]x = 2[/tex] or [tex]x = 8.[/tex]

b) To find the consumer surplus at the equilibrium point, we need to calculate the area under the demand curve and above the equilibrium price, which is given by the supply curve. Since we have two possible equilibrium points, we need to check both of them to see which one gives us a positive consumer surplus.

For [tex]x = 2[/tex], the equilibrium price is given by [tex]S(2) = 11[/tex], which is above the demand curve. Therefore, there is no consumer surplus at this equilibrium point.

For [tex]x = 8[/tex], the equilibrium price is given by [tex]S(8) = 75[/tex], which is below the demand curve. Therefore, the consumer surplus is given by the area under the demand curve and above the price of 75:

[tex]∫[75, 8] (x - 5)^2 dx = [(x - 5)^3 / 3][/tex] from 8 to 75

≈[tex]6,062.67[/tex]

This means that at the equilibrium point x = 8, consumers are willing to pay a total of approximately $6,062.67 more than what they actually pay.

c) To find the producer surplus at the equilibrium point, we need to calculate the area under the equilibrium price and above the su

For x =2 supply curve. Again, since we have two possible equilibrium points, we need to check both of them to see which one gives us a positive producer surplus.

2, the equilibrium price is given by [tex]S(2) = 11,[/tex] which is above the demand curve. Therefore, there is no producer surplus at this equilibrium point.

For x = 8, the equilibrium price is given by[tex]S(8) = 75[/tex], which is below the demand curve. Therefore, the producer surplus is given by the area above the supply curve and below the price of 75:

∫[tex][8, 75] (75 - x^2 - x - 3) dx = [(75x - x^3/ 3 - x^2 / 2 - 3x)][/tex] from 8 to 75

≈ [tex]13,208.67[/tex]

This means that at the equilibrium point x = 8, producers receive a total of approximately $13,208.67 more than their costs.

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Answer: m∠CBD = 98°

Step-by-step explanation:

The probability of randomly selecting a park that neither allows camping nor has a playground is 31/77.

We have,

We know that there are 59 parks that allow camping, 76 parks that have playgrounds, and a total of 154 parks.

Number of parks that allow camping only = 59 - 14 = 45

Number of parks that have playgrounds only = 76 - 14 = 62

Number of parks that have both camping and playgrounds = 14

The number of parks that neither allow camping nor have a playground.

= Total number of parks - (number of parks that allow camping only + number of parks that have playgrounds only - number of parks that have both camping and playgrounds)

= 154 - (45 + 62 - 14)

= 61

Now,

The probability of randomly selecting a park that neither allows camping nor has a playground.

= 61/154

= 31/77

Thus,

The probability of randomly selecting a park that neither allows camping nor has a playground is 31/77.

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The total area of the garden is 36 ft2.

To find the area of the rectangular piece that the gardener wants to add to the existing garden, we need to find the length and width of the rectangle.

The length of the rectangle is the distance between the points (-17, 15) and (-20, 15), which is 3 units.

The width of the rectangle is the distance between the points (-17, 15) and (-17, 11), which is 4 units.

Therefore, the area of the rectangular piece that the gardener wants to add is 3 x 4 = 12 square feet.

To find the total area of the garden, we need to add the area of the existing garden to the area of the rectangular piece that the gardener wants to add:

24 + 12 = 36

Therefore, the total area of the garden will be 36 square feet.

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