Work out length x.
Give your answer to 1 d.p.

The points form a square is D. DA = AB = BC = CD = 6; DB = AC = 6.

For a set of points to form a square, the following conditions must be satisfied:

All four sides must have equal length

The opposite sides must be parallel

The diagonals must be equal in length and perpendicular to each other.

In option D, we have DA = AB = BC = CD = 6 and DB = AC = 6. This satisfies condition 1, as all four sides have equal length.

We can also see that opposite sides are parallel by observing that line AD is parallel to line BC, and line AB is parallel to line CD. Therefore, condition 2 is also satisfied.

To check condition 3, we can calculate the length of the diagonals. The length of diagonal AC is given by the Pythagorean theorem as:

AC^2 = AB^2 + BC^2

AC^2 = 6^2 + 6^2

AC^2 = 72

AC = sqrt(72) = 6sqrt(2)

Similarly, the length of diagonal BD is also 6sqrt(2). Therefore, both diagonals have equal length, and they are perpendicular to each other. Hence, condition 3 is also satisfied.

Since all three conditions for a square are satisfied, we can conclude that the four points form a square.

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The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

To solve the given initial-value problem, we start by rearranging the equation:
3 11 16 × -(: * *:)* X' = 1 1 3
-(: * *:)* X' = (1/16)  (1/11)  (1/3)
Integrating both sides with respect to t:
-(: * *:)* X = (1/16) t + C1, where C1 is the constant of integration.
Multiplying both sides by the inverse of the matrix -(: * *:) gives:
X = (-1/8) t + C1/8 + C2, where C2 is another constant of integration.
To find the values of C1 and C2, we use the initial condition X(0) = (0) - (5):
X(0) = (-1/8) (0) + C1/8 + C2 = -5
C1/8 + C2 = -5
Since X'(t) = (-3/8), we have X'(0) = (-3/8). Using the equation X'(t) = (-3/8) and the initial condition X(0) = (0) - (5), we can solve for C1:
X'(t) = (-1/8) => (-3/8) = (-1/8) + C1/8 => C1 = -2
Substituting C1 = -2 into C1/8 + C2 = -5 gives:
(-2)/8 + C2 = -5 => C2 = -39/8
Therefore, the solution to the initial-value problem is:
X = (-1/8) t - 1/4 - (39/8)

The solution to the given initial-value problem is X = (-1/8) t - 1/4 - (39/8). The constant of integration C1 was found by using the initial condition X'(0) = (-3/8), and the constant C2 was found by using the initial condition X(0) = (0) - (5).

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The goat can reach a circular region centered at the corner of the rectangular burn where it is tethered. The radius of the circle is 50 feet, the length of the goat's rope.

To visualize the region the goat can reach, we can draw a diagram of the rectangular burn and the circular region around the tethered goat. The center of the circle is at the corner of the rectangular burn where the goat is tethered. The radius of the circle is 50 feet, which is the length of the goat's rope. The circle intersects the sides of the rectangular burn, dividing them into two segments. The goat can move freely within the circular region, but it cannot reach any part of the rectangular burn that is outside the circle.

In summary, the region the goat can reach is a circular region centered at the corner of the rectangular burn where it is tethered. The radius of the circle is 50 feet, which is the length of the goat's rope. The circle intersects the sides of the rectangular burn, dividing them into two segments, and the goat cannot reach any part of the rectangular burn that is outside the circle.

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The required,
(a) it would cost Mandla R72.19 if he used 8.75 kl of water.
(b) it would cost Mandla R115.50 if he used 14 kl of water.

The table can be set up as follows:

Number of kilolitres used Tariff per kilolitre (RO/kl)

Less than 6                           R7.50/kl

6 - 10                                    R8.25/kl

More than 10                              R8.25/kl

a) Mandla used 8.75 kl of water, which falls in the second category of 6-10 kl. The cost per kilolitre for this category is R8.25. Therefore, the total cost for Mandla would be:

8.75 kl x R8.25/kl = R72.19

So it would cost Mandla R72.19 if he used 8.75 kl of water.

b) Mandla used 14 kl of water, which falls in the third category of more than 10 kl. The cost per kilolitre for this category is also R8.25. Therefore, the total cost for Mandla would be:

14 kl x R8.25/kl = R115.50

So it would cost Mandla R115.50 if he used 14 kl of water.

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If 72% of the coins Blake collected were foreign, then the remaining 28% of the coins were not foreign.

Let x be the number of coins that Blake collected that were not foreign. Then, we can write an equation based on the total number of coins he collected:

0.72(total number of coins) + 0.28(total number of coins) = x + 0.72(total number of coins)

Simplifying this equation, we get:

0.28(total number of coins) = 0.28x

Dividing both sides by 0.28, we get:

total number of coins = x

Therefore, the number of coins that Blake collected that were not foreign is equal to the total number of coins he collected, which is 275, multiplied by 0.28:

x = 0.28 * 275

≈ 77

Therefore, Blake collected approximately 77 coins that were not foreign.

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There is a significant effect of temperature and/or noise conditions on task performance, as well as any specific conditions that differ significantly from each other.

State the hypotheses: Before conducting any statistical analysis, it is important to state the null and alternative hypotheses.

In this case, the null hypothesis would be that there is no significant effect of temperature and noise conditions on task performance, while the alternative hypothesis would be that there is a significant effect.

Check assumptions: The validity of the ANOVA results relies on several assumptions being met, such as normality of the data, homogeneity of variance, and independence of observations.

These assumptions can be checked using statistical tests or graphical methods.

Conduct the analysis: To conduct a two-way ANOVA in a statistical software package, the data would be organized in a table with one column for the dependent variable (task performance),

Two columns for the independent variables (temperature and noise conditions). The software will then calculate the sum of squares, mean squares, and F-values for each main effect and the interaction effect, as well as the associated p-values.

Interpret the results: The ANOVA output will provide information on whether there are significant main effects of temperature and noise conditions, as well as whether there is a significant interaction effect.

If the p-value is less than the significance level (usually 0.05), then we can reject the null hypothesis and conclude that there is a significant effect. Post-hoc tests may be used to identify which specific conditions differ significantly from each other.

Report the results: The results of the ANOVA analysis should be reported in a clear and concise manner, including the F-value, degrees of freedom, and p-value for each effect.

It is also important to include any limitations or potential sources of error in the study.

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The probability that K will not be the letter Terry selects is 0.875.

We know that, probability of an event = Number of favourable outcomes/Total number of outcomes.

Given that, Jacob mixes the letters J, K, L, J, K, M, N, and P thoroughly.

Here, total number of outcomes = 8

Number of outcomes = 7

Probability of event = 7/8

In decimal

7/8= 0.875

In percentage = 0.875×100

= 87.5%

Therefore, the probability that K will not be the letter Terry selects is 0.875.

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The total distance between Theo and Jarvis from Cassidy is 3x units.

Let's say the distance between Cassidy and Jarvis is "x" units.

According to the problem, Theo lives twice as far from Cassidy as Jarvis. This means the distance between Theo and Cassidy is 2x units.

To find the total distance between Theo and Jarvis from Cassidy, we need to add their individual distances from Cassidy:

Total distance = Distance between Theo and Cassidy + Distance between Jarvis and Cassidy

Total distance = 2x + x

Total distance = 3x

Therefore, the total distance between Theo and Jarvis from Cassidy is 3x units.

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the sample is truly representative of all horses in the state, and that there are no biases or confounding factors that might affect the proportion of stallions in the sample.

If we assume that the horses constitute a random sample of all horses in the state, then we can estimate the probability that a randomly selected horse is a stallion by calculating the proportion of horses in the sample that are stallions. Let's assume that we have a sample of n horses, and that x of these horses are stallions. Then the estimated probability of selecting a stallion is:

x/n

For example, if we had a sample of 100 horses and 25 of them were stallions, the estimated probability of selecting a stallion would be:

25/100 = 0.25 or 25%

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The table marked 3 in the accompanying figure has a rules value of is "void".

The explanation behind this is that Table 3 in the figure does not have any specified rules value. Therefore, it is considered void. In conclusion, the rules value for Table 3 is "void".


The given question provides a table marked as "Table 3" with values A, B, C, D, E, F, G, H, and I. However, the question asks for a "rules value" which is not provided or explained in the context. Therefore, it is impossible to determine a specific value or any relation among the given terms.

Due to the lack of information and context, the answer to the question regarding the rules value of Table 3 is void.

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Borman famously quipped, "We're not very good at odds-making. But if I had to bet my life on it, I'd give the odds to us."

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence.

During the Apollo 8 mission, which launched on December 21, 1968, the three-man crew consisting of Frank Borman, James Lovell, and William Anders became the first humans to orbit the Moon. Prior to the mission, Borman was asked about the chances of the crew's survival given that the Saturn V rocket had only been tested twice before and never with a crew. In response, Borman famously quipped, "We're not very good at odds-making. But if I had to bet my life on it, I'd give the odds to us."

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The area of the given triangle is 87.55 square centimeter.

From the given triangle, base=17 cm and height=10.3 cm.

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.

Here, area of a triangle = 1/2 ×17×10.3

= 87.55 square centimeter

Therefore, area of the given triangle is 87.55 square centimeter.

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The probability of a child having type O blood is the same for both males and females and is given by 0.44.

Assuming that the inheritance of blood type follows the laws of Mendelian genetics, the probability of a child having type O blood when both parents have type B blood is 0.25. This is because each parent can contribute only one of two possible alleles for blood type, either B or O. Thus, there are four possible combinations for the alleles that the child can inherit: BB, BO, OB, and OO. Out of these four combinations, only one (OO) results in the child having type O blood.

Therefore, the probability of a son with type O blood for a couple with type B blood is 0.25 times the probability of having a son, which is 0.5, so:

P(son with type O blood) = 0.25 x 0.5 = 0.125

Therefore, the probability that a couple with type B blood will have a son with type O blood is 0.125 or 12.5%.

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The partial derivative of z with respect to s is :

(3 - 9t) / (v * (9s - 3t)) + (3s/3t-s)^2 * 9 / (v * (3t-s)^2)

The partial derivative of z with respect to t is :

-9 / (v * (9s - 3t)) + (3s/3t-s)^2 * 3 / (v * (3t-s)^2).

To find ∂z/∂s and ∂z/∂t using the chain rule, we can first find the partial derivatives of z with respect to u and v, and then use the chain rule to find the partial derivatives with respect to s and t.

∂z/∂u = sec^2(u/v) * 1/v

∂z/∂v = -sec^2(u/v) * u/v^2

Using the chain rule, we have:

∂z/∂s = (∂z/∂u) * (∂u/∂s) + (∂z/∂v) * (∂v/∂s)

∂z/∂t = (∂z/∂u) * (∂u/∂t) + (∂z/∂v) * (∂v/∂t)

Substituting the expressions for ∂z/∂u and ∂z/∂v, as well as the expressions for u and v in terms of s and t, we get:

∂z/∂s = sec^2(3s/9s-3t) * 1/(9s-3t) * (3 - 9t)

- sec^2(3s/9s-3t) * (3s/9s-3t)^2 * (-9)/(9s-3t)^2

∂z/∂t = sec^2(3s/9s-3t) * 1/(9s-3t) * (-9)

- sec^2(3s/9s-3t) * (3s/9s-3t)^2 * (3)/(9s-3t)^2

Simplifying these expressions, we get:

∂z/∂s = (3 - 9t) / (v * (9s - 3t))

+ (3s/3t-s)^2 * 9 / (v * (3t-s)^2)

∂z/∂t = -9 / (v * (9s - 3t))

+ (3s/3t-s)^2 * 3 / (v * (3t-s)^2)

Therefore, the partial derivative of z with respect to s is (3 - 9t) / (v * (9s - 3t))

+ (3s/3t-s)^2 * 9 / (v * (3t-s)^2), and the partial derivative of z with respect to t is -9 / (v * (9s - 3t))

+ (3s/3t-s)^2 * 3 / (v * (3t-s)^2).

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Using the Laplace inverse the answer is f(t) = sin(2(t-π/2))u(t-π/2).

Hi, I'm happy to help you with this Laplace inverse question.

To find f(t) for the given expression ℒ^(-1) (se^(πs/2))/(s^2+4), we need to follow these steps:

Step 1: Identify the Laplace inverse of the given expression.
The given expression is in the form ℒ^(-1) (se^(πs/2))/(s^2+4). Here, e^(πs/2) represents a time-shift property in the time domain.

Step 2: Apply the time-shift property of Laplace transforms.
The time-shift property states that if ℒ^(-1) {F(s) * e^(as)} = f(t-a)u(t-a), then ℒ^(-1) {F(s)} = f(t). In our case, F(s) = s/(s^2+4) and a = π/2.

Step 3: Find the Laplace inverse of F(s).
We have F(s) = s/(s^2+4).

This is similar to the Laplace transform of the sine function, ℒ{sin(at)} = a/(s^2+a^2). Here, a = 2. Thus, ℒ^(-1) {F(s)} = sin(2t).

Step 4: Apply the time-shift property to find f(t).
Now, we can apply the time-shift property from Step 2 to get f(t) = sin(2(t-π/2))u(t-π/2).

So, the answer is f(t) = sin(2(t-π/2))u(t-π/2).

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The interval that contains the root of f(x) = 2x − x3 + 0.5 is [-2, -1].

To find which interval contains the root of the equation f(x) = 2x − x3 + 0.5, we can use the intermediate value theorem. This theorem states that if a function is continuous on a closed interval [a, b], and takes on values f(a) and f(b) at the endpoints, then for any value y between f(a) and f(b), there exists a value c in [a, b] such that f(c) = y.

In this case, we can evaluate f(x) at the endpoints of the intervals [-2, -1], [-1, 0], [0, 1], and [1, 2], as follows

For [-2, -1]: f(-2) = -11.5 and f(-1) = 1.5
For [-1, 0]: f(-1) = 1.5 and f(0) = 0.5
For [0, 1]: f(0) = 0.5 and f(1) = 1.5
For [1, 2]: f(1) = 1.5 and f(2) = -11.5

From this, we can see that the function changes sign from negative to positive in the interval [-2, -1], which means there must be a root in this interval. We can also see that the function is positive throughout the interval [1, 2], so there cannot be a root in this interval. The intervals [-1, 0] and [0, 1] do not change sign, so we cannot conclude whether or not there is a root in these intervals.

Therefore, the interval that contains the root of f(x) = 2x − x3 + 0.5 is [-2, -1].

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Step-by-step explanation:

X + 78   = 145 degrees

x = 145 - 78  = 67 degrees

The probability of drawing a specific color in all 50 draws is (1/3)^50, which is approximately 1.41 x 10^-30.

Jenny pulls a tile out of a bag containing three different colored tiles (purple, pink, and orange) 50 times with replacement.

Since Jenny replaces the tile after each draw, the probability of drawing any one of the three colors remains constant at 1/3 for each draw. The probability of drawing a specific color on any single draw is therefore 1/3.

Assuming the draws are independent, the probability of drawing a specific color in all 50 draws is (1/3)^50, which is approximately 1.41 x 10^-30.

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Answer:

Step-by-step explanation:

first of all, the median is the value in the middle of a data set. If the data set has an odd number of data (same as here , it has 17 numbers), the middle one is selected. To find the median, first arrange the numbers in order, usually from lowest to highest:

21 24 25 32 33 40 46 48 49 51 54 54 54 56 62 63 70

then find the middle one like this :

(21 24 25 32 33 40 46 48) 49 (51 54 54 54 56 62 63 70)

and the middle one is 49.

Answer:A

Step-by-step explanation:

The equation of a line in slope-intercept form is y = mx + b, where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).

Out of the given options, only option A is in the slope-intercept form, with a slope of -1/3 and a y-intercept of -1. Therefore, the equation of the line in slope-intercept form is:

y = -1/3 x - 1

So the answer is A.

Answer:

Step-by-step explanation:

It is D.

The general form for line is " y=ax+b"

which a is slope.

We have 2 known points : (-1,2) and (1,-4)

We can find slope by writing this :

slope  = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}} = \frac{-4-2}{1-(-1)}=\frac{-6}{2} = -3\\[/tex]

⇒ y=-3x+b

in order to find b, let's try one of the given points :

if x=1 then y=-4 :

y=(-3×1)+b=-4 ⇒ -3+b=-4⇒ b=-4+3=-1⇒ b=-1

so let's complete the line equation :

y=-3x-1

Answer:

Step-by-step explanation:

it’s ca

For the company to practice price discrimination, there should not be any resale of its product, is not true if a public utility company is considered a monopolist. This is because price discrimination involves charging different prices to different groups of customers based on their willingness to pay. Resale of the product can actually facilitate price discrimination as it allows different customers to buy the product at different prices and then resell it to others. The other options are true for a monopolist, such as having upward sloping demand and supply curves, charging a price higher than its marginal revenue, and determining profit maximizing quantity at the point where marginal revenue equals marginal cost.

Let's analyze each statement:

A. The company's demand curve and supply curve are upward sloping.
This statement is NOT true for a monopolist. A monopolist faces a downward sloping demand curve, which means that they can increase the quantity sold by lowering the price. The supply curve does not apply in the traditional sense for monopolists, as they have the power to set both the price and quantity produced.

B. Its price must be higher than its marginal revenue.
This statement is true for a monopolist. Under a monopoly, the price charged by the company is higher than its marginal revenue due to the downward-sloping demand curve.

C. For the company to practice price discrimination, there should not be any resale of its product.
This statement is true. In order for a monopolist to successfully engage in price discrimination, they must prevent the resale of their product, ensuring that consumers cannot undercut the monopolist's pricing strategy.

D. Its profit maximizing quantity is determined where its marginal revenue equals its marginal cost.
This statement is true. A monopolist maximizes its profit by producing the quantity where marginal revenue equals marginal cost, and then setting the price based on the demand curve at that quantity.

So, the statement that is NOT true for a public utility company considered as a monopolist is: A. The company's demand curve and supply curve are upward sloping.

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The statement that knowing the value of x tells you nothing about the value of y can be explained by several scenarios. One possible scenario is when the values of x and y are not related in any way. In other words, there is no mathematical or logical connection between them.

Another scenario where knowing the value of x tells you nothing about the value of y is when there are multiple possible values of y for a given value of x. This occurs when the relationship between x and y is not one-to-one. For instance, if x represents a person's age and y represents their height, knowing someone's age does not determine their height since there are different heights for different ages.

Furthermore, it is possible that there is a relationship between x and y, but the value of y is affected by other factors besides x. For example, if x represents the amount of time a student spends studying and y represents their grade on a test, knowing the value of x does not completely predict the value of y because other factors like natural ability and test-taking skills may also play a role in determining the grade.

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Answer:

the answer to this mathematics question is B. 0.08

Answer:

Step-by-step explanation:

In Q

Answer:

It is in point p

. p is tge intersection of line AB and CD

The price elasticity of demand at any point on a demand curve with a slope equal to negative 1 is C greater than 1, but less than infinite. This is because price elasticity of demand measures the percentage change in quantity demanded in response to a percentage change in price.

The price elasticity of demand at any point on a demand curve with a slope equal to negative 1 would be C) greater than 1, but less than infinite. This is because a slope of negative 1 indicates that for every one unit increase in price, there is a one unit decrease in quantity demanded. This means that the demand curve is relatively steep, indicating that small changes in price will result in larger changes in quantity demanded. Therefore, the price elasticity of demand would be greater than 1, but not infinite, as there is still some level of responsiveness to price changes.

When the elasticity is greater than 1, it indicates elastic demand, where the quantity demanded is highly responsive to price changes.

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The difference in centigrade degrees between a temperature of 60 degrees F and a temperature of 78 degrees F is 11.11 degrees C.

To convert Fahrenheit temperature to centigrade, we use the formula C = 5/9(F-32), where C is the temperature in centigrade and F is the temperature in Fahrenheit. Using this formula, we can calculate the temperature in centigrade for each of the given Fahrenheit temperatures:

For a temperature of 60 degrees F:

C = 5/9(60-32)

C = 5/9(28)

C = 15.56 degrees C

For a temperature of 78 degrees F:

C = 5/9(78-32)

C = 5/9(46)

C = 25.56 degrees C

The difference in centigrade degrees between these two temperatures is: 25.56 - 15.56 = 10 degrees C

Therefore, the difference in centigrade degrees between a temperature of 60 degrees F and a temperature of 78 degrees F is 11.11 degrees C (rounded to two decimal places).

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The total number of cups of punch that can be made is: 8 Cups

Proportion is defined a mathematical comparison between two numbers.

Now, we are given that:

Percentage of Ginger Ale = 35%

Percentage of Orange Juice = 25%

Percentage of Pineapple Juice = 25%

Percentage of Sorbet = 15%

We are told that there are 2 cups of Pineapple Juice. Thus:

(25/100) * x = 2

x = 200/25

x = 8 cups

Thus, this represents the total number of cups of punch that can be made.

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(a) Yes, the new series will still diverge. This is because a divergent series has an infinite sum, meaning that removing a finite number of terms will not significantly impact the behavior of the series.

(b) Yes, the new series will still converge. This is because a convergent series has a finite sum, meaning that adding a finite number of terms will not significantly impact the behavior of the series.

(a) When you delete a finite number of terms from a divergent series, the new series will still diverge. This is because a divergent series is characterized by its inability to converge to a specific value, regardless of the number of terms included. Removing a finite number of terms will not significantly affect the overall behavior of the series, so it will continue to diverge.

(b) When you add a finite number of terms to a convergent series, the new series will still converge. A convergent series is one that approaches a specific value as the number of terms increases. Adding a finite number of terms will only affect the series by a fixed amount, and since the original series converges, the new series will also converge to a new limit that accounts for the added terms.

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