100 POINTS
Triangle ABC with vertices at A(−8, −8), B(12, 12), C(0, 12) is dilated to create triangle A′B′C′ with vertices at A′(−2, −2), B′(3, 3), C′(0, 3). Determine the scale factor used.

6
one sixth
4
one fourth

Answer: I think a

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

When two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

We need to find the type of correlation when two variables vary along with each other but the data points are loosely scattered around the line of best fit.

A scatter plot helps find the relationship between two variables. This relationship is referred to as a correlation. Based on the correlation, scatter plots can be classified as follows.

A weak positive correlation indicates that, although both variables tend to go up in response to one another, the relationship is not very strong. A strong negative correlation, on the other hand, indicates a strong connection between the two variables, but that one goes up whenever the other one goes down.

Therefore, when two variables vary along with each other but the data points are loosely scattered around the line of best fit, the correlation is weak correlation.

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If the diagonal of the quadrilateral bisect each other at a right angle. Then the quadrilateral will be a rhombus.

It is a polygon with four sides. The total interior angle is 360 degrees. A rhombus's opposite sides are parallel and equal.

The diagonal of the rhombus will intersect at a right angle.

From the diagram, the diagonal of the rhombus will intersect at a right angle.

That means the diagonals bisect each other.

Thus, if the diagonal of the quadrilateral bisect each other at a right angle. Then the quadrilateral will be a rhombus.

The diagram is given below.

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Upper

daysThe(a) The time for an individual to recover from an infectious disease, is estimated to be between 4.02 and 5.98 days. (d) The structured SIR model assumes homogeneous mixing, constant population, recovered immunity.

(a) To calculate the time for an individual to recover with a 95% confidence level, we can use the properties of the normal distribution. The 95% confidence interval corresponds to approximately 1.96 standard deviations from the mean in both directions.

Given:

Mean (μ) = 5 days

Standard deviation (σ) = 0.5 days

The confidence interval can be calculated as follows:

Lower limit = Mean - (1.96 * Standard deviation)

Upper limit = Mean + (1.96 * Standard deviation)

Lower limit = 5 - (1.96 * 0.5)

= 5 - 0.98

= 4.02 days

Upper limit = 5 + (1.96 * 0.5)

= 5 + 0.98

= 5.98 days

Therefore, the time for an individual to recover from the infectious disease with a 95% confidence level is between approximately 4.02 and 5.98 days.

(b) To simulate the epidemic using the SIR model, we need additional information about the transmission rate and the duration of infectivity.

(c) Without the transmission rate and duration of infectivity, we cannot determine the fraction of the total population that will have come down with the infectious disease once the epidemic is over.

(d) The structured model in this case is the SIR (Susceptible-Infectious-Recovered) model, which is commonly used to study the dynamics of infectious diseases. The major assumptions associated with the SIR model include:

Homogeneous mixing: The model assumes that individuals in the population mix randomly, and each individual has an equal probability of coming into contact with any other individual.

Constant population: The model assumes a constant population size, without accounting for birth, death, or migration rates.

Recovered individuals develop immunity: The model assumes that individuals who recover from the infectious disease gain permanent immunity and cannot be reinfected.

No vaccination or intervention: The basic SIR model does not incorporate vaccination or other intervention measures.

These assumptions simplify the model and allow for mathematical analysis of disease spread dynamics. However, they may not fully capture the complexities of real-world scenarios, and more sophisticated models can be developed to address specific contexts and factors.

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Answer:

( x-7) (x+3)

Step-by-step explanation:

X^2- 4x- 21

What two numbers multiply to -21 and add to -4

-7 * 3 = -21

-7+3 = -4

( x-7) (x+3)

Answer:

Parallelogram

Step-by-step explanation:

Since the opposite sides are parallel in the given polygon, it is parallelogram.

the radius of the distance between the middle point of the circle and the outside, we have the diameter which is 6 so the radius will be 3

slant height is

\(\sqrt{r^2+h^2}\)

h is 4.7 and r is 3

\(\sqrt{3^2+4.71^2} \\5.58427\)

slant height is 5.58427

lateral surface area

\(\pi r\sqrt{h^2+r^2}\)

\(\pi (3)\sqrt{4.71^2+3^2} \\52.63053\)

lateral surface area is 52.63053

total surface area

\(\pi r(r+\sqrt{h^2+r^2})\)

\(\pi 3(3+\sqrt{4.71^2+3^2})\)

\(80.90486\)

total surface area is 80.90486

The slant height of the cone is 5.6km, the total surface area is 50.4πkm, the lateral surface area is 16.8π km.

A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreases to a certain point.

The volume of a cone is (1/3)πr²h.

The total surface area of a cone is πr(r + l).

The curved surface area is πrl.

In the given question radius of the cone is (6/2) km = 3 km.

The slant height of the cone is 5.6 km.

The total surface area of the cone is = π×3(3 + 5.6) km.

= 3π(16.8) km.

= 50.4π km.

lateral surface area is = π×3×5.6 km.

= 16.8π km.

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Answer:

-3 ⅛

Step-by-step explanation:

Based on the price the computer was reduced by and the profit the shopkeeper still made, if the computer was sold at full price, the profit percentage would have been 50%.

First assume a price the computer was sold at. We'll go with $100.

At this price, the shopkeeper still made a profit of 20% which means that the cost price was;

= 100 / (1 + 20%)

= $83.33

Based on the discounted price of $100, the full price was:

= 100 / (1 - 20%)

= $125

The profit the shopkeeper would have made is:

= (Full price - Cost price) / Cost price x 100%

= (125 - 83.33) / 83.33 x 100%

= 50%

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The functions that approach negative infinity as x approaches negative infinity are a, b and d.

What is the definition of a function?

In mathematics, a function is a rule that assigns to each element in a set (called the domain) a unique element in another set (called the range). In other words, a function is a relationship between two sets of values in which each input value maps to exactly one output value.

Formally, we can define a function f as follows:

Let A and B be two sets. A function f from A to B is a rule that assigns to each element x in A a unique element f(x) in B. We write f(x) = y to indicate that the element y in B is the image of the element x in A under the function f.

Now,

The function that approach negative infinity as x approaches negative infinity are:

a. f(x) = (4x + 1)(3x + 5)(x - 2)

b. f(x) = -4.8x(2x + 3)(x - 9)(x + 5)

d. f(x) = -0.5x(3x - 7)(4x + 1)(x + 9)(x - 3)

To see why, note that as x approaches negative infinity, the dominant term in the function will be the term) with the highest power of x. For functions a, b, and d, the dominant term have a negative coefficient and a power of x that is either 3 or higher, which means that these functions will approach negative infinity as x approaches negative infinity.

Functions c, e, and f have dominant terms with positive coefficients and/or powers of x that are less than 3, so they do not approach negative infinity as x approaches negative infinity.

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Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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Answer:

E

Step-by-step explanation:

Answer: 45

Step-by-step explanation:

15 - 1/6n = 1/6n

1. multiply everything by 6

90 - n = n

2. add n to the right-side

90 = 2n

3. divide

n = 90/2

n = 45

Answer:

24 boys & 20 girls

Step-by-step explanation:

Last year:

Number of boys = x

Total number = 45

Number of girls = 45 - x

An increase of 20% is the same as multiplying by 1.2

A decrease of 10% is the same as multiplying by 0.8

This year:

New number of boys: 1.2x

New number of girls: 0.8(45 - x)

New total number = 45 - 1 = 44

1.2x + 0.8(45 - x) = 44

1.2x + 36 - 0.8x = 44

0.4x + 36 = 44

0.4x = 8

x = 20

Last year there were 20 boys and 25 girls.

This year there are 20 * 1.2 = 24 boys

and 44 - 24 = 20 girls

Answer: 24 boys & 20 girls

x = 5

z = 118°

Step-by-step explanation:

opposite angles are equal

(6x + 32)° = 62°

6x = 62° - 32°

6x = 30°

x = 5°

angles on a straight line add up to 180

180° = 62° + z

z = 180° - 62°

z = 118°

Let the score she needs be x.

\(\frac{79+82+74+59+96+2x}{7}=80 \\ \\ 79+82+74+59+96+2x=560 \\ \\ 2x=170 \\ \\ \boxed{x=85}\)

Answer:

1521 pi in^3

radius x radius x height x pi = volume

13 x 13 x 9 = 1521

We do not multiply by pi because it is already included

Hope this helps

Step-by-step explanation:

The finance charge is $285

Suppose the value of which a thing is expressed in percentage is "a'

Suppose the percent that considered thing is of "a" is b%

Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).

Thus, that thing in number is

\(\dfrac{a}{100} \times b\)

Given;

An installment loan that has an APR of 16 percent

The motor scooter sells for $1,687

The store financing requires a 20 percent down payment

Monthly payments are for 30months

Now,

Downpayment= cost of scooter*20%

=1687*20%

=$337.4

Amount of finance = Cost of scooter - Down payment

=1687-337.4=1349.6

Interest rate=16%*1/12=1.3% per month

Monthly payment = Amount of finance*I/[1-(1+I)^-n]

=1349.6*1.3%/[1-(1+1.3%)^-30]

=1349.6*0.013(1-0.6780)

=17.5448/0.322

=54.486

Total amount paying for loan over a period = Monthly payment * Term

=54.486*30=1634.6

Amount of finance charge = Total amount paying for loan - Amount of loan

Amount of finance charge =1634.6-1349.6

=285

Therefore, the finance charge by given percent will be $285

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Answer:

If Samuel drives a compact car, he would need to buy 243.75 gallons of gas per year. If he drives a pickup truck, he would need to buy 250.25 gallons of gas per year. So he would need to buy 6.5 more gallons of gas per year if he drives a pickup truck compared to a compact car.

Step-by-step explanation:

According to Descartes' Rule of Signs, the given polynomial function\(f(x) = 10x^10 + 3x^5 + 8x^6 + 14x^4 + 12\) can have at most 2 positive real zeros and either 0 or 2 negative real zeros.

To apply Descartes' Rule of Signs, we need to examine the signs of the coefficients of the polynomial function.

1. Counting the positive real zeros:

2. Counting the negative real zeros:

Based on Descartes' Rule of Signs, the possible number of positive real zeros is 0 or 2, and the possible number of negative real zeros is 0 or 2.

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Mu X is a statistical concept used to measure the difference between two means.

It is calculated by subtracting the mean of one group from the mean of another group. Mu X is often used to compare the means of two or more groups, or to compare the means of two subgroups within a group. It can also be used to measure the relative size of a group's mean compared to the grand mean or the size of a group's mean compared to the mean of another group. Mu X is a useful tool for distinguishing between true and false differences between two means. It is also useful for understanding the relative importance of different factors in a study. Mu X is sometimes referred to as the difference in means or the mean difference, and it is an important concept in inferential statistics.

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Answer:

55.5 as a fraction is 111/2.

Answer: 55.5 as a fraction is 111/2.

Step-by-step explanation:

Answer:

a. $1669

Step-by-step explanation:

Price in 1994 = [ (CPI in 1994) / (CPI 1973) ] * (Price in 1973) =

[ 148.2 / 44.4 ] * 500 =  1668.91891892 = $1669 rounded to the nearest dollar.

Answer:

y=-1/4x +0

Step-by-step explanation:

Add 4y to left side of =

subtract X to right side

divide all terms by 4 to get Y alone

Slope- -1/4x,

Y-intercept- 0

that's what I got at least

Answer:

B = 82 c = 82

Step-by-step explanation:

These add up to 360 and since 98 + 98 + 82 + 82 = 360 b and c = 82 Hope this helps!

Answer:

\(\sqrt{2^{5} }\) is correct

Step-by-step explanation:

Answer:

False cuase 5 is in thousands