What is an equation of the line that passes through the points (4, -7) and (-4,5)? Put your answer in fully reduced form.​

Answer:

-33

Step-by-step explanation:

Answer:

-33

Step-by-step explanation:

−5^2 + (−2)^3 =

= -25 + (-8)

= -33

Answer:

x =19.20

Step-by-step explanation:

We can use ratios to solve

14 wings      12 wings

------------- = ---------------

22.40          x

Using cross products

14x = 22.40 * 12

14x =268.8

Divide each side by 14

14x/14 = 268.8/14

x =19.20

The symmetric closure of relation r is:

{(1, 1), (1, 2), (1, 3), (2, 1), (2, 3), (3, 1), (3, 2)}

To find the symmetric closure of a relation, we need to add pairs that ensure symmetry in the relation. If (a, b) is in the relation, then (b, a) should also be included.

Given the relation r = {(1, 1), (1, 2), (1, 3), (3, 1), (2, 3)}, let's identify the pairs that need to be added for symmetry:

(1, 2) is in the relation, so we add (2, 1)

(1, 3) is in the relation, so we add (3, 1)

(3, 1) is in the relation, so we add (1, 3)

The updated relation with the added pairs for symmetry is:

r = {(1, 1), (1, 2), (1, 3), (3, 1), (2, 3), (2, 1), (3, 1), (3, 2)}

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Answer:

Original angle = 122*

Supplementary angle = 58*

Step-by-step explanation:

A supplementary angle is one of two angles that make up 180*

If one angle is 30*, its supplementary angle is 150*. 30 + 150 = 180.

So in this case we have two angles, the original and the supplementary angle. The original angle is 64* more than the supplementary angle. The key word is MORE.

The formula to figure it out would look like this:  x + (x + 64) = 180

x is the supplementary angle

x + 64 is the original angle (64 MORE than its supplementary angle)

180 is the total measure of the two angles because they are supplementary and we know that supplementary angles always equals 180* when added together.

Take the formula and do a little algebra.

x + (x + 64) = 180

Subtract 64 from both sides

x + x = 116

Combine the x's

2x = 116

Divide both side by 2

x = 58

Remeber we know that the original angle is 64 more than the supplementary angle, so we'll add the 64 to the value of x and we get 122.

x + 64 = 122

Check our work:

x + (x + 64) = 180

58 + 58 + 64 = 180

Given :

⠀

To Find :

⠀

Solution :

Now,

⠀

According to the Question :

⠀

\(\longrightarrow\qquad \sf{{x + (x + 64) {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{x + x + 64 {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{2x + 64 {}^{ \circ} = {180}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{2x = {180}^{ \circ} - 64 {}^{ \circ}}}\)

⠀

\(\longrightarrow\qquad \sf{{2x = {116}^{ \circ} }}\)

⠀

\(\longrightarrow\qquad \sf{{x = \dfrac{{116}^{ \circ}}{2} }}\)

⠀

\(\longrightarrow\qquad \mathfrak{\pmb{{x = {58}^{ \circ} }}}\)

⠀

Therefore,

⠀

Henceforth ,

Answer:

If I say to you that we are travelling along at a "constant" speed of 25 m/s... a. ... So every seem 28 mis covend. b. What does the "m/s" after the number 25 mean? ... The object's motion will change - au acceleration will occur. 9. A car is moving ... c. What do you think a graph of velocity versus time would look like? Sketch it.

Step-by-step explanation:

The division of 36 acorns among the squirrels would be as follows:
- The black squirrel carries 35 acorns in 7 trips.
- The gray squirrel carries 1 acorn in 1 trip

1. Determine the number of times each squirrel can carry acorns:
  - The brown squirrel can carry 2 acorns at a time, so it will need to make 36 / 2 = 18 trips.
  - The gray squirrel can carry 3 acorns at a time, so it will need to make 36 / 3 = 12 trips.
  - The black squirrel can carry 5 acorns at a time, so it will need to make 36 / 5 = 7 trips.

2. Allocate the acorns to each squirrel:
  - Start by giving the black squirrel 7 trips worth of acorns, which is 7 x 5 = 35 acorns.
  - Since there are only 36 acorns in total, the black squirrel can take all of them.
  - This leaves 36 - 35 = 1 acorn remaining.

3. Distribute the remaining acorn(s) to the other squirrels:
  - If there is only 1 acorn left, it can be given to either the brown or gray squirrel.
  - Since the gray squirrel can carry more acorns per trip, it makes sense to give the remaining acorn to the gray squirrel.

So, the division of 36 acorns among the squirrels would be as follows:
- The black squirrel carries 35 acorns in 7 trips.
- The gray squirrel carries 1 acorn in 1 trip.

This is just one possible way to divide the acorns, considering the carrying capacities of the squirrels. The actual division may vary depending on the specific situation and requirements.

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(a) There are 36 possible outcomes.

(b) There are 9 outcomes possible with odd numbers appearing on each die.

(c) The probability that both dice will show an odd number is 0.25

To determine the number of possible outcomes, we multiply the number of possible outcomes for each die, which is 6. Therefore, the total number of possible outcomes is

6 x 6 = 36

To count the number of outcomes with odd numbers on each die, we need to count the number of ways we can get an odd number on one die and an odd number on the other die. Since there are three odd numbers on each die (1, 3, 5), there are three ways to get an odd number on each die. Therefore, the total number of outcomes with odd numbers on each die is

3 x 3 = 9

To calculate the probability of both dice showing an odd number, we need to divide the number of outcomes with odd numbers on each die (which is 9, as calculated in part (b)) by the total number of possible outcomes (which is 36, as calculated in part (a)). Therefore, the probability of both dice showing an odd number is

9/36

which simplifies to 1/4 or 0.25 when rounded to two decimal places.

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Convenience purchase: Coca-Cola. Shopping purchase: Apple iPhone. Specialty purchase: Rolex. These brand name products correspond to their respective purchase types based on convenience, shopping involvement, and specialty appeal in the consumer marketplace.

Convenience purchases refer to low-involvement purchases made by consumers for everyday items that are readily available and require minimal effort to obtain. These purchases are typically driven by convenience and habit rather than extensive consideration or brand loyalty.

Shopping purchases involve higher involvement and more deliberate decision-making. Consumers invest time and effort in comparing options, seeking the best value or quality, and may consider multiple brands before making a purchase. These purchases often involve durable goods or products that require more consideration.

Specialty purchases are distinct and unique purchases that cater to specific interests, preferences, or hobbies. These purchases are driven by passion, expertise, and a desire for premium or specialized products. Consumers are often willing to invest more in these purchases due to their unique features, quality, or exclusivity.

Three specific brand name products in the consumer marketplace that correspond to these types of purchases are

Convenience Purchase: Coca-Cola (Soft Drink)

Coca-Cola is a widely recognized brand in the beverage industry. It is readily available in various sizes and formats, making it a convenient choice for consumers seeking a refreshing drink on the go.

With its widespread availability and strong brand presence, consumers often make convenience purchases of Coca-Cola without much thought or consideration.

Shopping Purchase: Apple iPhone (Smartphone)

The Apple iPhone is a popular choice for consumers when it comes to shopping purchases. People invest time researching and comparing features, pricing, and user reviews before making a decision.

The shopping process involves considering various smartphone brands and models to ensure they select a product that meets their specific needs and preferences.

Specialty Purchase: Rolex (Luxury Watches)

Rolex is a well-known brand in the luxury watch industry and represents specialty purchases. These watches are associated with high-quality craftsmanship, precision, and exclusivity.

Consumers who are passionate about luxury watches and seek a premium product often consider Rolex due to its reputation, heritage, and unique features. The decision to purchase a Rolex involves a significant investment and is driven by the desire for a prestigious timepiece.

These examples illustrate how different types of purchases align with specific brand name products in the consumer marketplace, ranging from convenience-driven choices to more involved shopping decisions and specialty purchases driven by passion and exclusivity.

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Therefore, the farmer should produce 2 bushels of wheat to maximize profits at a price of $15 per bushel.

To determine the number of bushels of wheat that this farmer should produce to maximize profits, we need to consider the relationship between the quantity of wheat produced and the total revenue and total cost associated with each quantity.

The total revenue (TR) is calculated as the price per bushel multiplied by the quantity of wheat produced (Q), which can be expressed as TR = P  Q. In this case, the price of wheat is given as $15.

The total cost (TC) is the sum of all costs associated with producing each bushel of wheat. It includes both variable costs (VC), which depend on the quantity produced, and fixed costs (FC), which are independent of the quantity produced. Mathematically, TC = VC  Q + FC.

The profit () is the difference between the total revenue and the total cost, which can be written as  = TR + TC. To maximize profits, the farmer needs to produce the quantity of wheat that results in the highest profit.

To find this quantity, we can use the concepts of marginal cost and marginal revenue. The marginal cost (MC) is the additional cost of producing one more bushel of wheat, which can be calculated as the change in total cost divided by the change in quantity, or MC = TC/Q. The marginal revenue (MR) is the additional revenue earned by selling one more bushel of wheat, which is equal to the price per bushel, or MR = P.

At the profit-maximizing quantity, the marginal revenue equals the marginal cost, or MR = MC. This is because if MR is greater than MC, the farmer can increase profits by producing more wheat until MR equals MC. Conversely, if MR is less than MC, the farmer can increase profits by producing less wheat until MR equals MC.

To solve for the profit-maximizing quantity, we can set MR = MC and solve for Q. Since MR = P in this case, we have:
P = MC
$15 = ΔTC/ΔQ

To calculate the marginal cost, we need to know the variable cost per bushel of wheat. Let's assume that this cost is constant and equal to $5 per bushel. Then we can write:
MC = ΔTC/ΔQ
MC = (VC × Q + FC) - (VC × (Q - 1) + FC)
MC = VC
MC = $5

Substituting into the equation P = MC, we get:

$15 = $5
ΔTC/ΔQ

Solving for Q, we get:

ΔTC/ΔQ = $15 - $5
ΔTC/ΔQ = $10
Q = TC/VC
Q = FC/VC + ΔTC/ΔQ
Q = 0 + $10/$5
Q = 2

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To find the length of the other leg of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have the hypotenuse as 39 and one leg as 15. Let's denote the length of the other leg as "x". Applying the Pythagorean theorem, we have:

15^2 + x^2 = 39^2

225 + x^2 = 1521

x^2 = 1521 - 225

x^2 = 1296

Taking the square root of both sides, we get:

x = √1296

x ≈ 36

Therefore, the length of the other leg of the right triangle is approximately 36 when rounded to the nearest tenth.

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Measures of variability describe diversity in a distribution.

Measures of variability describe the spread or dispersion of values in a distribution. They provide information about how spread out or clustered the data points are. Common measures of variability include the range, variance, and standard deviation.

Measures of central tendency, on the other hand, describe the center or average of a distribution. They provide information about the typical or central value around which the data points are located. Common measures of central tendency include the mean, median, and mode.

Standard deviation is a specific measure of variability that quantifies the average amount by which data points in a distribution deviate from the mean. Association refers to the relationship or connection between two or more variables in a dataset, often analyzed using correlation or regression analysis. It is not a measure of diversity in a distribution.

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Answer:

The equation for the total cost of the gym membership over t months is CC = Jo + M * t, where Jo represents the one-time fee to join, M represents the monthly fee to remain a member, and t represents the number of months for which the membership is valid.

The slope of the graph is M, the monthly fee to remain a member. The interpretation of the slope in the context of the problem is that it represents the cost per month of remaining a member of the gym.

Answer:

2/3 + 2/3 + 1/3.

Step-by-step explanation:

You can use equivalent fractions. 6 is 2x more than 3. You can use three as the denominator.

Mark decompose 5/6 into three fractions using fractions : 1/3, 5/18, 2/9

In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Given, fraction

5/6

Multiplying 3 with both numerator and denominator

15/18

= (6 + 5 + 4)/18

= 6/18 + 5/18 + 4/18

= 1/3 + 5/18 + 2/9

Hence, 1/3, 5/18, 2/9 are fractions Mark used to decompose 5/6.

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Answer:

There are 7 fish in each tank.

Step-by-step explanation:

We know that there are 3 tanks and 21 fish and that each tank has the same number of fish. We need to divide the 21 fish evenly into the three tanks, so we use division for this problem. 21÷3=7

As P-value > significance level (i.e.,0.05), so, null hypothesis can't be rejected. There is no sufficient evidence to support our claim that there was a decrease in voter support for the new candidate after the unfortunate remarks were made.

We have two random samples related to election. For first Sample : Voters was interviewed 3 weeks before the start of a state-wide campaign for governor. Sample size, n₁ = 415

Sample mean, X₁ = 223

Sample proportion for sample one :

\(p₁ = \frac{X₁}{n₁ }= \frac{223}{ 415} = 0.537\)

Consider sample 2ⁿᵈ for several unfortunate remarks one week before the election.

Sample size, n₂ = 630

Sample mean, X₂ = 317

Let the significance level be 95% .

Sample proportion for sample two :

\(p₂ = \frac{X₂}{n₂ }= \frac{317}{630} = 0.503\)

A two-proportion Z-test is a statistical hypothesis test used to determine whether two proportions are different from each other. Consider the null and alternative hypothesis,

\(H₀ : p₂ = p₁

Hₐ : p₂ < p₁\)

Now, we have to check the hypothesis by two- proportion Z-test. Formula is,

\(Z = \frac{( p₁ - p₂)}{ \sqrt{p(1- p)( \frac{1}{n₁} + \frac{1}{ n₂}})}\)

p is mean of both the samples where k₁ is successes out of n₁ data in sample 1 and k₂ is successes out of n₂ data in sample 2.

\(p = \frac{k₂+ k₁} { n₂ + n₁} = 0.512\)

Now, plugging all known values in above formula,

\(Z = \frac{( 0.537 - 0.503)}{ \sqrt{0.512(1- 0.512)( \frac{1}{415} + \frac{1}{ 630}})}\)

\(Z = \frac{0.034}{ \sqrt{0.512(0.488)(0.00399 )}}\)

\(Z = \frac{0.034}{ 0.0316} = 1.076\)

The p-value or z-critical value for two tailed test is 0.2819. We see that 0.281>0.05 ( significance level). So, Null hypothesis can't be rejected. Therefore, null hypothesis is true i.e., there is no decrease in voter support for the new candidate.

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Answer:

15/50

Step-by-step explanation:

\(\frac{6}{20}\) = \(\frac{x}{50}\)  Cross multiply

20x = 6(50)

20x = 300   Divide both sides by 20

x = 15

Answer:

(x+2)^2 +(y-4)^2

Step-by-step explanation:

correct answer: ( x - ( -2 ) ) ² + ( y - 4 ) ² = 36

so put in -2 for the first blank, 4 for the second and 36 for the last blank!

btw it can be simplified to (x+2)² + (y-4)² = 6²

but thats not what theyre asking for ^^

Answer:

Kristi will pay $22.77 for the shirt.

Step-by-step explanation:

First, determine the sales price of the shirt. If the full price is $27.99, a 25% reduction is $7. Subtract the discount from the full price to get a sales price of $20.99 for the shirt.

Next, determine the amount of tax Kristi will pay for the shirt. In her state, the sales tax is 8.5% (0.085). Multiply $20.99 by 0.085 and you will see that the sales tax is $1.78. Add the amount of the tax, $1.78, to the sales price of the shirt, $20.99, and you will get $22.77 as the cost of the shirt after the sales tax is added.

The equation equivalent to the formula d = rt is t = d/r

What is equation ?

An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."

When two expressions are joined by an equal sign, a mathematical statement is called an equation. An equation is something like 3x - 5 = 16.

Equations can be classified as either conditional equations or identities. Any value of the variables results in an identity being true. Only certain values of the variables in a conditional equation result in truth. When two expressions are joined together by the equals sign ("="), the result is an equation.

The equation is d = rt

As we need the value of t we take t to the left hand side

∴ t = d/r

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The autocovariance function γ(h) of the linear process Xₜ is absolutely summable, as the sum of the absolute values of the autocovariance coefficients is finite. To show that the autocovariance function (ACVF) of the linear process Xₜ is absolutely summable, we need to demonstrate that the sum of the absolute values of the autocovariance coefficients is finite.

The autocovariance function of Xₜ is defined as γ(h) = Cov(Xₜ, Xₜ₋ₕ), where h is the time lag.

Expanding the expression, we have:

γ(h) = Cov(∑ⱼψⱼWₜ₋ⱼ, ∑ₖψₖWₜ₋ₖ₋ₕ)

Using the properties of covariance, we can rewrite this as:

γ(h) = ∑ⱼ∑ₖψⱼψₖCov(Wₜ₋ⱼ, Wₜ₋ₖ₋ₕ)

Since Wₜ is a white noise process with zero mean and constant variance, Cov(Wₜ₋ⱼ, Wₜ₋ₖ₋ₕ) = σ²wδⱼₖ, where δⱼₖ is the Kronecker delta function.

Substituting this back into the expression for γ(h), we get:

γ(h) = σ²w∑ⱼψⱼψₖδⱼₖ

Now, let's consider the absolute value of γ(h):

|γ(h)| = |σ²w∑ⱼψⱼψₖδⱼₖ|

Using the properties of the absolute value, we can remove the absolute value sign inside the summation:

|γ(h)| = σ²w∑ⱼ|ψⱼψₖδⱼₖ|

Since ∑ⱼ|ψⱼψₖδⱼₖ| < ∞ (as stated in the given condition), we conclude that |γ(h)| is absolutely summable.

Therefore, To show that the autocovariance function (ACVF) of the linear process Xₜ is absolutely summable, we need to demonstrate that the sum of the absolute values of the autocovariance coefficients is finite.

The autocovariance function of Xₜ is defined as γ(h) = Cov(Xₜ, Xₜ₋ₕ), where h is the time lag.

Expanding the expression, we have:

γ(h) = Cov(∑ⱼψⱼWₜ₋ⱼ, ∑ₖψₖWₜ₋ₖ₋ₕ)

Using the properties of covariance, we can rewrite this as:

γ(h) = ∑ⱼ∑ₖψⱼψₖCov(Wₜ₋ⱼ, Wₜ₋ₖ₋ₕ)

Since Wₜ is a white noise process with zero mean and constant variance, Cov(Wₜ₋ⱼ, Wₜ₋ₖ₋ₕ) = σ²wδⱼₖ, where δⱼₖ is the Kronecker delta function.

Substituting this back into the expression for γ(h), we get:

γ(h) = σ²w∑ⱼψⱼψₖδⱼₖ

Now, let's consider the absolute value of γ(h):

|γ(h)| = |σ²w∑ⱼψⱼψₖδⱼₖ|

Using the properties of the absolute value, we can remove the absolute value sign inside the summation:

|γ(h)| = σ²w∑ⱼ|ψⱼψₖδⱼₖ|

Since ∑ⱼ|ψⱼψₖδⱼₖ| < ∞ (as stated in the given condition), we conclude that |γ(h)| is absolutely summable.

Therefore, the autocovariance function γ(h) of the linear process Xₜ is absolutely summable, as the sum of the absolute values of the autocovariance coefficients is finite.

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Answer:

4

Step-by-step explanation:

10+6=16

16/4=4

Basic math

Answer: There are 1820 ways that a committee of 4 people can be formed from the 16 members of the ski club.

Step-by-step explanation: The number of ways that a committee of 4 people can be formed from the 16 members of the ski club is given by the combination formula:

C(16, 4) = 16! / (4! * (16 - 4)!) = (16 * 15 * 14 * 13) / (4 * 3 * 2 * 1) = 1820

Therefore, there are 1820 ways that a committee of 4 people can be formed from the 16 members of the ski club.

Answer:

32, 40, 48, 56

Step-by-step explanation:

\(a_n= 8(n+3)...(given) \\\\ a_1= 8(1+3) = 8 \times 4 = 32 \\ \\ \: a_2= 8(2+3) = 8 \times 5 = 40 \\ \\ a_3= 8(3+3) = 8 \times 6 = 48 \\ \\ a_4= 8(4+3) = 8 \times 7 = 56 \\ \)

The equation of the line passing through P(3,6,8) that is parallel to c=2i+5j+k is (z,y,z) = (2,5,1) + t(3,6,8) = (2t+2,5t+5,t) = (2z-9,5z-24,z)

The equation of a line in three-dimensional space can be represented in vector form as

r = r0 + tc

where

r is the position vector of any point on the line

r0 is the position vector of a known point on the line (in this case, P(3,6,8))

t is a parameter that represents the distance from r0 to any point on the line along the direction of the line

c is the direction vector of the line (in this case, c=2i+5j+k)

To find the equation of the line passing through P(3,6,8) that is parallel to c=2i+5j+k, we can substitute the values of r0 and c into the equation above

r = (3,6,8) + t(2,5,1)

This is the equation of the line in vector form, where (3,6,8) is the known point on the line and (2,5,1) is the direction vector parallel to c.

To represent the equation in the form (z,y,z), we can use the components of the vector

x = 3 + 2t

y = 6 + 5t

z = 8 + t

We can eliminate t by solving for it in terms of z

t = z - 8

Substituting this expression for t into the equations for x and y, we get

x = 3 + 2(z - 8) = 2z - 13

y = 6 + 5(z - 8) = 5z - 34

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Given that the initial height of the launcher was above ground, the function

created by the student should be transformed upwards.

Reasons:

The function created by the student = h(r), a model of the path of a T-shirt cannon

The part of the equation left out in the function = The initial height of the cannon

The given initial height of the cannon = 4 feet

Required:

The method of correcting the function to model the path of the T-shirt correctly

Solution:

Given that the function created by the student gives the height of the

cannon, and the initial height of the launcher is 4 feet above the ground

The initial function h(r) should be transformed 4 feet in the upward

direction.

The student should add 4 feet to the function by replacing h(r) with h(r) + 4, to account for the increase in all heights by 4 feet;

The correct option is; The student should replace h(r) with h(r) + 4

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0.05723 is 0.05223 greater than 0.005.

"Greater than" is a comparison term used to indicate that one quantity or value is larger or more than another quantity or value. It is represented mathematically by the symbol "&gt;".

"Lesser than" is a comparison term used to indicate that one quantity or value is smaller or less than another quantity or value. It is represented mathematically by the symbol "&lt;".

In the given question,

To find out how much greater 0.05723 is than 0.005, we can subtract 0.005 from 0.05723:0.05723 - 0.005 = 0.05223

Therefore, 0.05723 is 0.05223 greater than 0.005.

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To determine whether the set S is linearly independent or linearly dependent.The set is linearly independent. This is because the only way to make a linear combination of vectors equal to the zero vector is to have all the coefficients equal to zero.

A linear combination of vectors is the sum of a scalar multiple of each vector in the set. We must check if the equation a(-2,2,4) + b(1,9,-2) + c(2,3,-3) = (0,0,0) has only the trivial solution, i.e., a=b=c=0. This gives us the system of equations,-2a + b + 2c = 01a + 9b + 3c = 02a - 2b - 3c = 0We can solve the system of equations by using Gauss-Jordan elimination. The augmented matrix for the system is:[-2 1 2 0][1 9 3 0][2 -2 -3 0]Let's use elementary row operations to simplify the matrix.

We can swap the first and second rows since the first element in the second row is 1.[1 9 3 0][-2 1 2 0][2 -2 -3 0]We can then add twice the first row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][-2 1 2 0][0 16 3 0]We can then add nine times the first row to the second row to eliminate the leading coefficient in the second row.[1 9 3 0][0 17 15 0][0 16 3 0]We can then add -16/17 times the second row to the third row to eliminate the leading coefficient in the third row.[1 9 3 0][0 17 15 0][0 0 -117/17 0]We see that the only solution is a=0, b=0, and c=0. Therefore, the set S is linearly independent.

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A. pyramid has only one base, B. The base of a pyramid is a polygon, C. If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height, F. The slant height is used to calculate the lateral area.

Let’s verify all the options:

A) A pyramid has only one base.

By definition, a pyramid has only one base

So, A is TRUE

B) The base of a pyramid is a polygon.

By definition, a pyramid is a polyhedron formed by a polygonal base.

So, B is TRUE

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.  

Given, the right pyramid and if the length of the base is known. Then, we can find the half distance of the base and it will form a right-angled triangle. Hence Pythagorean theorem can be used to find its slant height.

So, C is TRUE

D) The slant height is always the same length as the base of the pyramid.

No, the slant height is not always the same as the base of the pyramid.

So, D is FALSE

E) The lateral faces of a pyramid are rectangles.  

By definition, the shape of the lateral faces of the pyramids is triangular.

So E is FALSE

F) The slant height is used to calculate the lateral area.

The formula for the lateral surface area of the pyramid is given:

Lateral Surface Area = (P × L), where

P is the perimeter of the base

L is the slant height.

So F is TRUE

Hence the true options are A, B, C, and F.

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

What information is true when calculating the surface area of a pyramid? Check all that apply.

A) A pyramid has only one base.

B) The base of a pyramid is a polygon.

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.

D) The slant height is always the same length as the base of the pyramid.

E) The lateral faces of a pyramid are rectangles.

F) The slant height is used to calculate the lateral area.

Your question was incomplete. Please refer the content below:

What information is true when calculating the surface area of a pyramid? Check all that apply.

A) A pyramid has only one base.

B) The base of a pyramid is a polygon.

C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.

D) The slant height is always the same length as the base of the pyramid.

E) The lateral faces of a pyramid are rectangles.

F) The slant height is used to calculate the lateral area.

The options that are correct about a pyramid will include option (A), option (B), option (C) and option (F).

Now, we will see all the options one by one:

option (A) A pyramid has only one base.

Yes, it is true as it can only have 1 base.

option (B) The base of a pyramid is a polygon.

Yes, it is true as the base will always be a polygon only.

option (C) If the altitude of a right pyramid and the apothem of the base is known, then the Pythagorean theorem can be used to find its slant height.  

Yes, it is true as Pythagoras theorem can be used in a right angles triangle which will be formed by the slant height.

option (D) The slant height is always the same length as the base of the pyramid.

No, it is false as it can be different according to the pyramids.

option (E) The lateral faces of a pyramid are rectangles.  

No, it can be triangular also.

option (F) The slant height is used to calculate the lateral area.

Yes, it is true as the formula for the lateral surface area of the pyramid is given as:

Lateral Surface Area = (P × L), where

L represents the slant height.

Therefore, the options that are correct about a pyramid will include option (A), option (B), option (C) and option (F).

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The probability a male's growth plate will fuse before age 17 is 0.1112, for this we have to learn probability.

Probability of an event is a number that shows what is the possibility of an event occur.

we have to take entire area under the standardized curve from and including the left tail up to the z-score for 17.

\(= \frac{(17 - 18.6 years)}{1.308333 years}\)

\(= \frac{(-1.6) }{1.308333}\)

\(= -1.22293\)

\(= approx. 1.22.\)

The area from the mean to +ve or -ve 1.22 is .3888

We have to subtract .3888 from area from the tail to the mean (.5000) to get area from the tail to 1.22.

So, the growth plates will fuse before age 17 \(= .5000-.3888 = 0.1112\)

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