Solve each system in Exercises 1 - 4 by using elementary row operations on the equations or on the augmented matrix. Follow the systematic elimination procedure described in this section. 2x_1 + 4x_2 = -4 5x_1 + 7x_2 = 11

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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the data y = (y1,..., yn) are a sample from a normal distribution with unknown mean θ and known standard deviation σ = 2. Our prior distribution p(θ) is normal with mean 0 and standard deviation σ0.

y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1 y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1

We have two cases for Ф,

1.  Ф=1; it implies that Pr(Ф=1)=0.5, while y~N(1,α²)

2. Ф=2; it implies that Pr(Ф=2)=0.5, while y~N(2,α²)

Now,

For 1st case of α=2,

We have marginal probability density formula

p(y)=∑p(yIФ)p(Ф)

=p(yIФ=1)p(Ф=1)+p(yIФ=2)p(Ф=2)

=N(yI1,2²)(1/2)+N(yI2,2²)(1/2)

=(1/2)[N(yI1,2²)+N(yI2,2²)]

Now.

For Pr(Ф=1Iy=1) at α=2

We have,

=p(Ф=1Iy=1)

=[p(y=1,Ф=1)]/[p(y=1)]

=[p(y=1IФ=1)p(Ф=1)]/[p(y=1)]

={(1/)exp[(-1/(2*2²))(1-1)²(1/2)]}/{(1/)(1/2)[exp[(-1/(2*2²))(1-1)²]+exp[(-1/(2*2²))(1-2)²]}

=0.53 Answer

Now, to describe the changes in shape of Ф when α is increased and decreased deviation

The formula for posterioir density is p(ФIy)=p(yIФ)p(Ф)/p(y)

=exp[(-1/(2α²)(y-Ф)²]/{exp[(-1/(2α²)(y-1)²]+exp[(-1/(2α²))(y-2)²]}

Now at Ф=1 and solving the equation, we get

p(Ф=1Iy)=1 / {1+exp[(2y-3)/2α²]}

Similarly at Ф=1 and solving the equation, we get

p(Ф=2Iy)=1 / {1+exp[(2y-3)/2α²]}

Conclusion:

α² → ∞ ⇒p(ФIy) → p(Ф) = 1/2

α² → 0 ⇒ two cases

y > 3/2, α² → 0 ⇒p(Ф=2Iy) → 1

y < 3/2, α² → 0 ⇒p(Ф=1Iy) → 1

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The table that represents the equation of the proportional relationship is; Table 4

A proportional relationship is defined as a mathematical relationship that exists between two variables in which their ratio is always equal.

We have that the equation s equals three fourths times f. This is expressed as;

s = ³/₄f

where;

s is the amount of sugar

f is the amount of flour

Table 1;

when f = 1

s = ³/₄(1)

s = ³/₄

when f = 2

s = ³/₄(2)

s = 6/4

Thus, table 4 is correct

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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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Answer:

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

Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.

Punnett square is a diagrammatic representation of genotypes of a distinct cross in organisms.

It is used to know the result of the genotype of the offspring having either having single or multiple traits.

The correct answers are:

1.Option C. 0%

In the Punnett square the cross is between the purebred dominant and purebred recessive parent.

This will result in all the offspring having a heterogeneous genotype trait carrying purple color. Hence 0% will carry white color.

2. Option D. 25%

It can be explained as:

Due to the presence of heterogenous parent species. It will result in 25% of offspring carrying white color.

Therefore, in question 1, 0% of plants will be white while in another question 25% of the offspring will carry the white color trait.

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Answer:

7.77

Step-by-step explanation:

49.77 - 42 = 7.77

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.

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:

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:

Hope this helps!! :)). Mark me brainliest! :))

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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A distribution that has both mean and median of (-15) is referred to as a perfectly symmetrical distribution.

This is referred to as a type of distribution in which the values of the mean and the median are the same as they are the central component of inferential statistics.

In this scenario, we were given the mean and median to be of the same value which is (-15) which therefore denotes that the type of distribution is a perfectly symmetrical one.

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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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They are the set of numbers and symbols that are related by the different mathematical operation signs such as addition, subtraction, multiplication, division among others.

According to the data problem,

At the end of 46 week the city will have: 132 streetlight + (4 streetlight/ week * 46 weeks)

At the end of 46 week the city will have: 132 streetlight  + 184 streetlight

At the end of 46 week the city will have: 316 streetlight

232 streetlight at the end of the week = (232 streetlight - 132 streetlight) / 4 streetlight /week

232 streetlight at the end of the week = 100 streetlight /4 streetlight /week

232 streetlight at the end of the week = 25 weeks

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Correctly written question:

A city currently has 132 streetlights. As part of an urban renewal program, the city council has decided to install 4 additional streetlights at the end of each week for the next 52 weeks. Use this information to complete the following statements. Round to the nearest whole number as needed. The city will have (blank) streetlights at the end of 46 weeks. The city will have 232 streetlights at the end of (blank) week

No, u is not in the plane spanned by the columns of A.

To check if u is in the plane spanned by the columns of A, we first need to construct the augmented matrix of the system A · x = u, where x is the vector of unknowns. The augmented matrix is:

[−5 9 | 26 4 −2]

The reduced row echelon form of this augmented matrix is:

[1 0 | 2 -1]

This is an inconsistent system,the reduced row echelon form of the augmented matrix is , which is an inconsistent system so it does not have any solutions. This means that u cannot be written as a linear combination of the columns of A, so it is not in the plane spanned by the columns of A.

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Solution is in the attachment!!

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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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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The system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.

The stability of a linear system can be determined by analyzing the magnitude of its impulse response −

|h[n]| ≤ M for some finite M

In this case, the impulse response is h[n] = 0.25nu[n], where nu[n] is the unit step function. Since the magnitude of h[n] is 0.25 for all n, the system is stable since 0.25 is a finite number that is less than any M.

To summarize, the system is stable since the magnitude of its impulse response is 0.25, which is a finite number that is less than any M.

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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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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

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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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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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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In order to determine the practical significance requires considering both the effect size measures and the context of the study

One way to determine practical significance is by using effect size measures. Effect size is a standardized measurement of the magnitude of a treatment or intervention.

A common equation used to calculate effect size is Cohen's d, which is the difference between the means of two groups divided by the standard deviation.

Another equation used is the odds ratio, which is the ratio of the odds of an event occurring in one group compared to another.

Additionally, it is important to consider the context of the study when evaluating practical significance.

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Answer: option b. 71%

Step-by-step explanation:

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:

f(x) = 100 (3)^x  <===> C

f(x) = 100 (3.5)^x  <===> B

f(x) = 100 (4)^x <===> A

Step-by-step explanation:

Since the base of each of the exponential functions is the same, the higher the base, the higher up the graph will be with respect to another base with a lower value

This can be easily determined by choosing a specific value for x for each equation and seeing what the f(x) value is

Let's choose x = 2

For f(x) = 100 (3)^x, at x = 2 we get f(2) = 100(3)^2 = 100 x 9 = 900

For f(x) = 100 (3.5)^x, at x = 2 we get f(2) = 100(3.5)^2 = 100 x 12.25 = 12.25

For f(x) = 100 (4)^x, at x = 2 we get f(2) = 100(4)^2 = 100 x 16 = 1600

So for a specific value of x, the higher the base, the higher the graph is relative to the x-axis

So the matches are:

f(x) = 100 (3)^x  <===> C

f(x) = 100 (3.5)^x  <===> B

f(x) = 100 (4)^x <===> A

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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