The formula for the Lateral Surface Area of a pyramid is LSA = (1/2) Pl; where 'P' is the perimeter of the base and 'l' is the slant height.
a. true
b. false

Alisha needs to use a fraction of 3/8 of each of the ingredients on the recipe.

We know that a pancake recipe calls for 8 eggs and some other ingredients.

But Alisha only has 3 eggs, so she needs to adjust the recipe.

The fraction of each one of the other ingredients that she needs to use is equal to the fraction between the number of eggs that she has and the number of eggs that the recipe calls, it is:

N = 3/8

So she needs to use 3/8 of each of the ingredients that the recipe calls.

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The speed of Joshua's skating rate is given by the equation A = 7 m/s

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

The rate of Joshua's skating is given by S = 35 meters / 5 seconds

So , the rate S = 35/5

And , the unit rate of Joshua's skating rate is given by A = 35/5

On simplifying the equation , we get

The unit rate of Joshua's skating rate is given by A = 7 meters per second

The unit rate of Joshua's skating rate is given by A = 7 m/s

Hence , the skating rate of Joshua's skating is 7m/s

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The constant of proportionality is 7.

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

A four-sided figure is resized to create a scaled copy.

The proportional relationship between any given side length in the original figure f, and the corresponding side length in the scaled copy, s, can be represented by the equations s=1/7f.

To find the constant of proportionality from side lengths in the original figure to side lengths in the scaled copy

The equation we get as, f=7s

Therefore, the constant of proportionality is 7.

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So, if they plan to practice a total of 45 minutes and have only completed 18.5 minutes that means they have 26.5 minutes of practice remaining (45-18.5).

Answer:

Step-by-step explanation:

The values of the letters are:

A =  $37.5

B = $16.95

C = 5

D = $15.34

A sales tax is a tax paid to the government for the sales of certain goods and services.

Total price = Quantity * Unit Price

Unit price = Total price / Quantity

Quantity = Total price / Unit price

A = Total price = 3 * 12.5 = $37.5

B = Unit price = 33.90 / 2 = $16.95

C = Quantity = 31.00 / 6.20 = 5

15% VAT = 15% of Total Price

D = 15/100 * 108.28 = $15.34

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Answer:

Area of a circle= 1/4*π d^2

A=1/4*π*12^2=

A=1/4*π*144=113.1

Step-by-step explanation:

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The solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:

x = -4 or x = 8

What is inequality?

A solution for an inequality in x is a number such that when we substitute that number for x we have a true statement. So, 4 is a solution for example 1, while 8 is not. The solution set of an inequality is the set of all solutions.

We can solve this absolute value equation by first isolating the absolute value term on one side of the equation and then solving for both possible cases. Here are the steps:

|4 − 2x| + 6 = 18

|4 − 2x| = 12 (subtract 6 from both sides)

Now we have an absolute value equation with no constant term. We can split this equation into two cases: one where the expression inside the absolute value is positive, and one where it is negative. For each case, we can solve for x:

Case 1: 4 - 2x > 0

If 4 - 2x is positive, then we can drop the absolute value bars and write:

4 - 2x = 12

-2x = 8

x = -4

So one solution is x = -4.

Case 2: 4 - 2x < 0

If 4 - 2x is negative, then we must flip the inequality when dropping the absolute value bars:

-(4 - 2x) = 12

-4 + 2x = 12

2x = 16

x = 8

So the other solution is x = 8.

Therefore, the solutions to the equation |4 − 2x| + 6 = 18, in order from least to greatest, are:

x = -4 or x = 8

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Jay is given 65% discount

Percentage discount is a discount that is given to a product or service that is given as an amount per hundred

Percentage discount can be gotten with the formula below:

Discount % = (Discount/Original Price) × 100.

From the question,

Jay pays 27300, instead of 42000

Using the percentage discount above

Percentage Discount = 27300/42000 x 100

Percentage Discount = 65%

Hence, jay got 65% discount from the school

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The number of tones of the black plastic that is required here is 9567.3 tones .

The volume of one meter of piping can be calculated as follows:

V = π * (r^2) * l

Where r is the radius of the pipe (6.5 mm), and l is the length (1 meter).

So, the volume of one meter of piping is:

V = π * (6.5^2) * 1 = 134.96 mm^3

Since 1 m^3 = 10^9 mm^3, the volume in m^3 of one meter of piping is:

V = 134.96 / 10^9 = 0.00013496 m^3

Therefore, the total volume of 81000 km of piping is:

V = 0.00013496 * 81000 * 10^3 = 11,124.16 m^3

And the total weight of the piping is:

W = V * 0.86 tones/m^3 = 9567.3 tones

So, 9567.3 tones of black plastic is required.

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Normally distributed residuals is not an assumption of the general linear model and hence option b is correct

Linear regression models relate to some assumptions about the distribution of error terms. If they are violated violently, the model is not suitable for drawing conclusions. Therefore, it is important to consider the suitability of the model for information before further analysis can be performed based on this model.

The fit of the model is related to the remaining behavior complying with the basic assumptions for error values in the model. When a regression model is constructed from a series of data, it should be shown that the model responds to the standard statistical assumptions of the linear model because of conducting inference. Residual analysis is an effective tool to investigate hypotheses. This method is used to test the following statistical assumptions for a simple linear regression model:

-Regression function is linear in parameters,

-Error conditions have constant variance,

-Error conditions are normally distributed,

-Error conditions are independent.

Normally distributed residuals is not an assumption of the general linear model and hence option b is correct

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The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."

The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.

The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.

Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.

In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.

Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

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The statement that is not a characteristic of the normal probability distribution is "the graph of the curve is the shape of a rectangle."

The normal probability distribution is a continuous probability distribution that is symmetrical and bell-shaped. It is described by its mean and standard deviation, and its graph can be used to represent the distribution of a continuous random variable. The total area under the curve of the normal distribution is equal to 1, which represents the probability of observing any value within the range of the distribution.

The mean, median, and mode of a normal distribution are equal and located at the center of the distribution. This is why the normal distribution is often referred to as the "bell-shaped" distribution. The shape of the curve is a smooth, symmetrical shape that slopes gently and then becomes more steep as it approaches the tails of the distribution.

Finally, it's true that a random variable that follows a normal distribution assumes a value within plus or minus three standard deviations of its mean 99.72% of the time. This is a property of the normal distribution known as the empirical rule or the 68-95-99.7 rule.

In summary, the statement "the graph of the curve is the shape of a rectangle" is not a characteristic of the normal probability distribution, while the other statements are.

Therefore, the degrees of freedom are a feature of statistics that reflect the number of independent observations in a sample that can be used to make inferences about the population.

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The rate of change of f'(x) at (1, 13) is 25.

We have,

To find the rate of change of the derivative f'(x) at point (1, 13), we first need to find the derivative of the function f(x).

Given: f(x) = 14x² - x³

To find f'(x), we differentiate f(x) with respect to x:

f'(x) = d/dx (14x² - x³)

= 28x - 3x²

Now, to find the rate of change of f'(x) at x = 1,

we substitute x = 1 into the derivative expression f'(x):

f'(1) = 28(1) - 3(1)²

= 28 - 3

= 25

Therefore,

The rate of change of f'(x) at (1, 13) is 25.

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P ( A or B ) ≠ P(A) + P(B) Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true for the given events

Two events are called mutually exclusive they are independent to each other.

Also, If A and B are any two events,

Then they are called mutually exclusive,

If P(A ∪ B ) = P(A) + P(B)

Or P ( A or B ) = P(A) + P(B)

Here, P(A) = 0.37, P(B) = 0.38 and P(A or B) = 0.27

Since,

0.27 ≠ 0.37 + 0.38

⇒  P ( A or B ) ≠ P(A) + P(B)

Hence, A and B are not mutually exclusive.

therefore the given condition is not true and hence statement is not true

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Answer:

y = [tex]\frac{3}{2}[/tex] x

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

here slope m = [tex]\frac{3}{2}[/tex] and y- intercept c = 0 , then

y = [tex]\frac{3}{2}[/tex] x + 0 , that is

y = [tex]\frac{3}{2}[/tex] x

The total surface area of the rectangular prism is 103.12 square inches.

The surface area of the rectangular prism can be calculated using the formula which is given as: 2 * (lw + lh + wh), where:

w = width of the prism

h = its height

l = its length.

Given the following:

Length = 7.1 in

Width = 2.8 in

Height = 3.2 in

Therefore:

Total surface area = 2 * (7.1 * 2.8 + 7.1 * 3.2 + 2.8 * 3.2)

= 2 * (19.88 + 22.72 + 8.96)

= 2 * 51.56 in^2

= 103.12 square inches.

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Answer:

7.77

Step-by-step explanation:

49.77 - 42 = 7.77

If q² – 4pr > 0, the roots of the quadratic equation px² + qx + r = 0 will be: "negative, if p, q, and r are positive". Therefore, Suman answered correctly.

In Mathematics, a quadratic function can be defined as a mathematical expression which defines and represent the relationship that exists between two (2) or more variable on a graph, with a maximum exponent of two.

Generally speaking, the standard form of a quadratic function is given by ax² + bx + c = 0.

Assuming the roots of the quadratic function are a and b. Therefore, the sum of the roots of the quadratic function would be equal to -q/p;

a + b = -q/p

ab = r/p

This ultimately implies that, the nature of the roots would depend on the value of p, q and r, which make Zain's answer to be wrong.

Additionally, if p, q, and r are positive, a + b would be negative, and one or both roots must be negative, which make Vipul's to be wrong.

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Answer:

15 prints

Step-by-step explanation:

Let's call the number of small prints sold as "x".

The number of medium prints sold is then (52 - x) prints.

We know that the total revenue from all the prints sold is $2,975, so we can set up the following equation:

$2975 = (x * $50) + ((52 - x) * $75)

Expanding and solving for x:

$2975 = $50x + $3900 - $75x

$2975 = $3900 - $25x

$-925 = -$25x

x = 37

So, Catori sold 37 small prints and (52 - 37) = 15 medium prints

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Solution is in the attachment!!

Answer:

sup dudes pls what state is this and plus is this logarithms

Total Utility of Harry remains the same and so he would indifferent to this exchange.

Now, According to the question:

MUa(H) = ∂UH/∂a = ∂(2ab)/∂a = 2b

MUb(H) = ∂UH/∂b = ∂(2ab)/∂b = 2a

"Information available from the question"

a = 3 apples  and b = 2 bananas

For a = 3 and b = 2

MUa(H) = 2b = 4; MUb(H) = 2a = 6

Total Utility(H) = MUa(H) + MUb(H) = 4 + 6 = 10

New distribution after exchange --> a = 2 and b = 3.

MUa(H) = 2b = 6; MUb(H) = 2a = 4

Total Utility(H) = MUa(H) + MUb(H) = 6 + 4 = 10

Total Utility of Harry remains the same and so he would indifferent to this exchange.

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The given quesion is incomplete, complete question is:

Tom, Jim , and Harry, the only three people on a desert island with two consumption goods, apples and bananas, have utility functions UT, UD, and UH, respectively, where:

UT(xa,xb) = 6xa+9xb

UD(xa,xb) = 8xa+12xb

UH(xa,xb) = xaxb2

a)Suppose harry has 3 apples and 2 bananas. would he be willing to trade an apple for a banana? show why or why not.

Answer:=1±√5

Step-by-step explanation:

aight so bassically i looked this shi up and yeah thats what what i got bro

Answer: option b. 71%

Step-by-step explanation:

Kelvin's solution is correct because he multiplies the base of the triangle by the height of the triangle.

Area of triangle= base × height

The base of the triangle= 5 in

The height of the triangle = 8 in

Area of triangle= base × height

= 5 in × 8 in

= 40 square inches

Consequently, the area of the triangle as calculated by kelvin is correct.

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The value of the correlation coefficient would not change.

The following would be the correlation change if the stopping distances were recorded in meters, rather than feet.

Hence, option (A) is the correct choice.

Correlation is a statistical number derived based on historical data (profitability), and, contrary to popular belief, it is not constant and can change over time.

Correlation is a statistical term that reflects how much two or more variables vary in relation to one another.

The correlation coefficient is evaluated on a scale ranging from + 1 to - 1. The degree of correlation between two variables is denoted by + 1 or -1. When one variable rises as the other rises, the correlation is positive; when one falls as the other rises, the correlation is negative.

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Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.

The QR factorization is the factorization of a matrix A into an orthogonal matrix Q and an upper triangular matrix R. Given matrices A and Q, the matrix R can be calculated as:

R = Q^T * A

Where Q^T is the transpose of Q.

Note that this calculation assumes that Q is an orthogonal matrix, meaning that its transpose is equal to its inverse. If Q is not orthogonal, it will not have an inverse and the QR factorization cannot be calculated in this manner.

Therefore, Given matrices A and Q, the matrix R can be calculated as: R = Q^T * A.

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Answer:

52 cats

Step-by-step explanation:

Let d be the number of dogs, then c = 2d + 10 is the number of cats.

The total number of animals is 73, so we have d + c = 73.

Substituting c = 2d + 10 into this equation, we get d + 2d + 10 = 73.

Combining like terms, we get 3d + 10 = 73.

Solving for d, we have 3d = 63, so d = 21.

Thus, there are 21 dogs and 2 * 21 + 10 = 52 cats up for adoption.

$0.80 required for a 200g packet cost and $0.01 required for a 100g packet cost

To find the cost of a 200g packet,

you can use the unit price,

which is the cost per gram of the biscuits.

To get the unit price, divide the cost of the 600g packet by its weight: $2.40 / 600g = $0.004/g.

Then multiply the unit price by the weight of the 200g packet to get its cost:

$0.004/g * 200g = $0.80.

To find the cost of a 100g packet of Orea's,

Use the same process as above:

$2 / 200g = $0.01/g.

Then multiply the unit price by the weight of the 100g packet to get its cost:

$0.01/g * 100g = $0.01.

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The correct way to report the length of the rectangle in centimeters would be (b)"15.6 cm".

A rectangle in Euclidean plane geometry is a quadrilateral with four right angles. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°).

The general practice is to report measurements to the appropriate number of significant digits. In this case, "15.6 cm" accurately reflects the measurement to the nearest tenth of a centimeter and uses the proper unit symbol (cm). "15.600 cm" and "15.60 cm" include more significant digits than are necessary and "16 cM" uses an incorrect unit symbol.

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A and B are each represented by an oval:IV LT III regions make up

the answer is (d) II.

What is Venn diagram ?

A Venn diagram uses overlapping circles or other shapes to illustrate the logical relationships between two or more sets of items. Often, they serve to graphically organize things, highlighting how the items are similar and different.

The set (A union B) complement is defined as the set of all elements in the universal set that are not in A union B. In set notation, it can be expressed as (A union B)^c = U - (A union B), where U is the universal set and c represents the complement.

In a Venn diagram, the complement of a set is represented by the region outside of the set. In the given Venn diagram, the region outside of A and B is represented by region IV, so (A union B) complement = IV.

Therefore, A and B are each represented by an oval:IV LT III regions make up the answer is (d) II.

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