What is the solution Ofsimultaneous equations 5x 3y 8 and 3x Y 2?

From the proof below, we have been able to prove that IK bisects ∠HIJ by CPCT postulate

Congruent angles are defined as angles that have equal measure.

Now, we are given that;

IK bisects ∠HKJ

HK ≅ JK

Thus, since IK bisects ∠HKJ, then it means that by definition of angle bisector that;

∠HKI = ∠JKI

Now, we are also told that HK ≅ JK.

Now, by reflexive property of congruence, we can say that IK is congruent to itself.

Thus, we now have 2 congruent sides and an include angle and as such both triangles are congruent by SAS Congruency postulate.

Thus, we can conclude that ∠HIK = ∠JIK by CPCT which states that Corresponding parts of Congruent Triangles are congruent.

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No , cousin is not correct because when 5,953 is rounded  to the nearet hundred the value should be 6000 .

Given :

What is rounding to the nearest hundred ?

Rounding a number to the nearest hundred means to write down the multiple of 100 that is nearest to the number .

so here given number = 5,953

so here the number 53 is greater than 50 .

We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

so the number after rounded = 6000

so his cousin is incorrect .

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Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".

What is judicial activism?

Judicial activism is a judicial philosophy that is sometimes referred to as "legislating from the bench". It is an exercise of judicial review and generally refers to the willingness of a judge to strike down legislative or executive actions regarding constitutional issues. Judicial restraint is generally thought of as the opposite of judicial activism.[1]

Earlier in the january of 1947 ,Arthur Schlesinger Jr. introduced the term "judicial activism" .An article by Keenan Kmiec says that in its early usage, it was sometimes used with a positive connotation akin to the term "civil rights activist".

Thus , Arthur Schlesinger Jr. introduced the term "judicial activism" in a January 1947 Fortune magazine article titled "The Supreme Court: 1947".

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Mavis is interested in whether military dependency is related to gender in american samoa. then Male = 0.4193 and Female = 0.5087

What does distribution mean in work?

Distribution is the activity of both selling and delivering products and services from manufacturer to customer. This can also be called product distribution. As businesses become more global it becomes important to improve distribution to ensure that customers and all members of the distribution channel are happy.

To obtain the marginal distribution of gender :

Total number of civilians (male + female)

(26393 + 27330) = 53,723

Male :

P(male) = number of male / total

P(male) = 26393 / 53,723 = 0.4912793

P(Female) = number of Female / total

P(Female) = 27330 / 53,723 = 0.5087206

Complete question :

Mavis is interested in whether military dependency is related to gender in American Samoa. Here is data she collected about the population of American Samoa in 2010.

Millitary status _________ female ____ Male

In armed forces _________ 28 _______ 59

Millitary dependent ______ 928 ______ 781

Civilian _______________ 26393 ___27330

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Answer:

9

Step-by-step explanation:

add all the numbers: 6+12+10+8=36

then divide by the amount of numbers there are: 36/4=9

Answer:

(b) mean=95, standard deviation=7.2.

Step-by-step explanation:

To find the new mean and standard deviation, we first need to apply the transformation to the original mean and standard deviation.

The new mean is given by: x*=65+0.6x

Substituting in the original mean of 50, we get: x*=65+0.6(50) = 95

The new standard deviation is given by: s*=0.6s

Substituting in the original standard deviation of 12, we get: s*=0.6(12) = 7.2

Therefore, the new mean and standard deviation are (b) mean=95, standard deviation=7.2.

Answer:c

Step-by-step explanation:

Answer: C) 5 years

Step-by-step explanation:

Formula for the simple interest is: I = P * r * t, where: I = $500, P = $2,500, r = 0.04 and t stays for the number of the years. 500 = 2,500 * 0.04 * t; 500 = 100 * t; t = 500 : 100; t = 5.

The correct answer is b). Yes, the p-value for testing for a positive correlation between age and body fat percentage is 0.039. Since the p-value is small we reject the null hypothesis of no relationship.

In statistics, the p-value is used to determine the likelihood that the observed relationship between two variables occurred by chance. If the p-value is small, it means that the relationship is statistically significant and unlikely to have occurred by chance. In this case, the p-value of 0.039 indicates that there is a statistically significant positive relationship between age and body fat percentage.

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Graphs and the correlation coefficients are mentioned below-

A scatter plot uses dots to represent values for two different numeric variables. There are three types of scatter plots or charts -

There are the three most important correlations as -

Given are the scatter plots and the associated correlation coefficient.

        [tex]$r =\frac{\sum\left(x_{i}-\bar{x}\right)\left(y_{i}-\bar{y}\right)}{\sqrt{\sum\left(x_{i}-\bar{x}\right)^{2} \sum\left(y_{i}-\bar{y}\right)^{2}}}[/tex]

        r = correlation coefficient

        [tex]$x_{i}[/tex] = values of the x-variable in a sample

        [tex]$\bar x[/tex] = mean of the values of the x-variable

        [tex]$y_{i}[/tex] = values of the y-variable in a sample

 [tex]\bar y[/tex] = mean of the values of the y-variable

The graph and their corresponding values of [r] are mentioned below -

Therefore, graphs and the correlation coefficients are mentioned below-

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The minimum and maximum heights accepted for NASA astronauts are 62 inches and 75 inches, respectively. These values can be represented by the following equation: 62 <= height <= 75

This equation can be read as "the height must be greater than or equal to 62 inches and less than or equal to 75 inches."

Alternatively, you can represent the minimum and maximum heights using the following inequality:

62 < height < 75

This inequality can be read as "the height must be greater than 62 inches and less than 75 inches."

Either of these equations can be used to represent the minimum and maximum heights accepted for NASA astronauts.

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SSS congruence of triangles is proved when all three sides of considered two triangles are congruent(that is, of equal measures).

If two considered triangles have corresponding side pairs congruent(for all three sides), then both the triangles are congruent. This proof of congruence is triangle is done by SSS congruence of triangles (Side Side Side congruence)

Since it is given that the sides CB and FE are congruent, and since it is given that sides AB and DE are congruent too.

Thus, for SSS congruence of both considered triangles, we need the third side pair of the given triangles to be congruent too.

Thus, we need the line segment DF congruent to the line segment AC.

We can write it symbolically as:

[tex]$\overline{D F} \cong \overline{A C}$[/tex] (remember that order doesn't matter here. This can be written as [tex]$\overline{A C} \cong \overline{D F}$[/tex] .)

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The outcome of the complex number given is 7i+8/10 in its most basic form. Option C

Complex numbers are referred to as the square root of negative numbers. For instance √-1 = i.

In this expression 'i" is a complex number.

Given the expression below;

-7+8i / 10i

Rationalise

-7+8i / 10i * 10i/10i

= 10i(-7+8i)/10(i²)

= -70i+18(-1)/10(-1)

= -70i - 18/-10

= 7i+1.8

Hence the result of the given complex number in its simplest form is 7i+8/10

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Answer:

A cuboid is a 3-dimensional shape with six rectangular faces, four of which are the sides or lateral faces, and the other two are the base and the top. To solve the problem, we can first find the perimeter of the base of the cuboid by dividing the lateral surface area by the height. In this case, the perimeter of the base is 26 cm.

To find the dimensions of the base, we can set up an equation using the given information. Let x be one of the sides of the base, and let y be the other side. Since one of the sides is 3 cm smaller than the other, we can write the equation as:

x + x - 3 + x + x - 3 = 26 cm

We can simplify the equation by combining like terms:

4x - 6 = 26 cm

Next, we can solve the equation by adding 6 to both sides and then dividing by 4:

4x = 32 cm

x = 8 cm

Therefore, the dimensions of the base of the cuboid are 8 cm x 11 cm (since one side is 3 cm smaller than the other). The perimeter of the base is 26 cm, and the height of the cuboid is 10 cm.

Step-by-step explanation:

The velocity of Rosie when running is 2 meters per second

From the question, we have the following parameters that can be used in our computation:

Time = 1/3 of 78 seconds

Distance covered = 52 meters

The velocity can be calculated using the following equation

Velocity = Distance covered/Time

Substitute the known values in the above equation, so, we have the following representation

Velocity = 52/(1/3 * 78)

Evaluate the quotient

Velocity = 2

Hence, the velocity is 2 meters per second

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Step-by-step explanation:

first of all, remember for life :

the sum of all angles in a triangle is always 180°.

so, in this right-angled triangle we have therefore

180 = b + 90 + 71

b = 180 - 90 - 71 = 19°

and then regarding a and b :

the sum of all angles around a single point on one side of a line is also always 180°.

why ? because the line can be seen as the extended diameter of a circle, with that point being the center of the circle. and one side of the line is representing half of that circle. and a half-circle is 180°.

so,

a + b = 180

a + 19 = 180

a = 180 - 19 = 161°

FYI, the reason for the first principle (all angles in a triangle are together 180°) is also based on a half-circle concept : any right-angled triangle can be seen as inscribed into a half-circle, with the Hypotenuse (the baseline opposite of the 90° angle) being the diameter of the circle, and the center of the circle being the midpoint of the Hypotenuse.

Linear algebra is too hard because it is not very intuitive, it places a powerful emphasis on rigorous proofs, and its concepts are very different and difficult to visualize.

Linear algebra is difficult because it is naturally different from most high school and college courses you have taken until now.

Linear algebra is a branch of mathematics that deals with mathematical structures closed under the operations of addition and scalar multiplication and that comprises the theory of systems of linear equations, matrices, determinants, vector spaces, and linear transformations.

Linear algebra is hard to study. Linear algebra is one of the most difficult courses that most STEM majors will study in university.

Linear algebra is not a simple class because it is a very abstract course, and it requires strong analytical and logical skills.

Linear algebra is considered a demanding course by STEM majors since it gets exponentially complex and perplexing as the term progresses.

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The two solutions to the equation x² + 5x + 6 = 0 are x = -2 and x = 3. This means that when we substitute either of these values into the equation, the left-hand side of the equation will be equal to 0.

To find the roots of a quadratic equation, we need to set the equation equal to 0 and then solve for x. In this case, we have the equation x² + 5x + 6 = 0. we can use the quadratic formula. The quadratic formula states that the two solutions for x are given by x = (-b ± √(b² - 4ac))/2a. For our equation, this gives us x = (-5 ± √(5² - 4(1)(6)))/2(1). Once we simplify this, we get x = (-5 ± √(-19))/2. Since the square root of a negative number is not real, we can discard this solution. This leaves us with x = -2 and x = 3. This means that when we substitute either of these values into the equation, the left-hand side of the equation will be equal to 0.

x = (-5 ± √(5² - 4(1)(6)))/2(1)

= (-5 ± √(-19))/2

= (-5 ± i√19)/2

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Answer:

Step-by-step explanation: 44/59 = 0.74576271186 so that means the answer is around 74.5% or 74.6%

Answer: 25 weeks

Step-by-step explanation:

Let W represent the number of weeks

Judy equation is

12W + 300

Cassie equation is

20W + 100

Now let's solve it! Our system of equation is

12W + 300 = 20W + 100

Subtract 300 from both sides

12W = 20W -200

Subtract 20W from both sides

-8W = -200

W = 25 weeks

So, it takes 25 weeks for Judy and Cassie to have the same amount saved.

Answer:

let judy = 300 + 12W

cassie = 100 + 20W

300 + 12W =  100 + 20W

300 - 100 = 20W - 12W

200 = 8W

W = 25

300 +  12(25) = 100 + 20(25)

300 + 300 = 100 + 500

600 = 600

Therefore, it will take 25 days for Judy and Cassie so that they have the same amount saved.

THE GRAPH IS IN THE PICTURE,line graph

Step-by-step explanation:

The quotient of 1065 ÷ 33 is [tex]32\ \frac{3}{11}[/tex] .

1065 ÷ 33 = 32.2727272727

Dividend = 1065

divisor = 33

quotient = 32

balance = 9

answer as a mixed number  [tex]32\ \frac{9}{33} = 32\ \frac{3}{11}[/tex]

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The volume of a cone is given by the formula:

V = (1/3) * π * r² * h

Where V is the volume, r is the radius, and h is the height.

In this case, we know the radius (4.96) and the volume (102), so we can use the formula to solve for the height.

Substituting the known values into the formula, we get:

102 = (1/3) * π * (4.96)² * h

Dividing both sides by (1/3) * π * (4.96)², we get:

h = 102 / [(1/3) * π * (4.96)²]

Substituting in the value for π, we get:

h = 102 / [(1/3) * 3.14 * (4.96)²]

Which simplifies to:

h = 102 / [(1/3) * 3.14 * 24.1952]

Which simplifies to:

h = 102 / (0.7853 * 24.1952)

Which simplifies to:

h = 102 / 19.1268

Which is approximately 5.33.

Therefore, the estimated height of the cone is approximately 5.33.

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Answer:

Step-by-step explanation:

The volume of a clone = 1/3 × π × r^2 × h

Volume, v = 102
Radius r = 4.96
r^2 = 4.96^2 = 24.6016  
Approximately = 24.6

π = 3.142
v = 1/3  x π x r^2 x h

Cross multiply

3v = π x r^2 x h

h = (3 x 102) / 24.6 x 3.142

h = 3.959 cm

I hope this was helpful

As per the given function, the equation of tangent line is y - e = e(x -1)

The term tangent line in math referred as a function y=f(x) can be calculate the slope by taking derivative m=f′(x) then at a given point (x1,y1) equation of tangent line is given by the formula y−y1=m(x−x1)

Here we have given the expression y = eˣ/x

Now, we have to calculate the tangent line for the given function,

Let us consider, Slope of the tangent line is written as,

=> m = dy/dx

Now, we have written it as,

=> dy/dx = eˣ/x

then the equation is equate with the slope, then  we get,

=> m = eˣ/x

When we put the value of x as 1, then we get

=> m = e

Here we know that the point value is (1, e)

Therefore, the equation of the tangent line is written as,

=> y - e = e(x -1)

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The mean and the median of the given data are 210 and 170.

A data set's mean (average) is calculated by summing all of the numbers in the set, then dividing by the total number of values in the set. When data collection is ranked from least to greatest, the median is the midpoint. The number that appears most frequently in a data set is called the mode.

The four-hour service call costs

$30  + $40(4) = $90

(a) The given table summary details and finds the cost of the service cells

Statics      Hour of service call       cost of service call

Mean          4.5                                  30 + 40(4.5) = 210

Median       3.5                                  30 + 40 (3.5 = 170

SD               1.2                                  30 + 40 (1.2) = 78

TQR            2.0                                  30 + 40 (2.0) = 110

Minimum    0.5                                  30 + 40 (0.5) = 50

(b) The service call corresponding score is 1.50

z score = 138-4.5/1.2 = 113.75

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The zero of the graph is x = -4

From the question, we have the following parameters that can be used in our computation:

Major points on the graph are (minus 4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).

Express the points, properly

So, we have the following representation

Major points on the graph are (-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).

Write out the points

(-4, 0), (0, 1), (2, 2), (4, 5.5), and (6, 6).

The zeros of the graph are the point where y = 0

In this case, the points are

(-4, 0)

So, we have

x = -4

Hence, the zero is x = -4

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The property scale factor make the similar shapes similar one.

The term shape in math refers the outline or the boundary of an object.

Here we need to find the property that makes the similar shape similar.

As per the definition of shape we have identified that the shape has the following property, they are listed as,

=> Length

=> Breadth

=> height.

All these are collectively called scaling factor,

Based on these values we have take the two similar shapes such as similar triangles, similar rectangles, similar square, are the shapes whose dimensions are in equal or common ratio but the size or length of their sides vary.

Therefore the common ratio is called the scale factor.

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The value of the function (f o g )(11) is -1

Applying composite function formula,

(f o g )(x) = f [g (x)]

Here ,f(x) = [tex]\sqrt{x} - 3[/tex]

g (x ) = x - 7

(f o g )(x)  =f [x - 7 ]

                =[tex]\sqrt{x-7} -3[/tex]   --(1)

Substitute x = 11 in the given function in (1)

 [tex](f o g )(11) =\sqrt{11-7} -3\\(f o g )(11) =\sqrt{4} - 3\\(f o g )(11) = 2 -3 = -1[/tex]

The value of the function (f o g )(11) is -1

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The dot plots show that the lowland areas experienced significantly more rainfall than the highland area during spring storms, with a larger range and maximum rainfall.

The dot plots show the rainfall totals for several spring storms in both highland and lowland areas. The dots representing the lowland areas are more spread out and have a larger range compared to the dots representing the highland areas. This indicates that the lowland areas experienced more rainfall than the highland areas during these storms. Additionally, the maximum rainfall for the lowland areas is greater than the maximum rainfall for the highland areas, further emphasizing the difference in rainfall between the two areas. This could be due to a number of factors, such as the higher elevation of the highland areas resulting in less moisture being able to accumulate, or the lower temperature of the highland areas resulting in less evaporation and thus less rainfall. Additionally, the lower elevation of the lowland areas could result in more moisture being able to accumulate, and the higher temperature of the lowland areas could result in more evaporation, leading to increased rainfall. Regardless of the cause, the data from the dot plots clearly show that the lowland areas experienced more rainfall than the highland areas during these spring storms.

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The fractions equivalent to 3/5 are 6/10, 9/15, 12/20, etc.

Now, According to the question:

Equivalent fractions can be written by multiplying or dividing both the numerator and the denominator by the same number. This is the reason why these fractions get reduced to the same number when they are simplified.

Let us understand the two ways in which we can make equivalent fractions:

Hence, the equivalent fractions for 3/5 are:

(3/5) × (2/2) = (3 × 2) / (5 × 2) = 6/10

(3/5) × (3/3) = (3 × 3) / (5× 3) = 9/15

(3/5) × (4/4) = (3 × 4) / (5 × 4) = 12/20

Thus, 6/10, 9/15, 12/20 are equal to 3/5,

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The associative property looks like a + (b + c) = (a + b) + c.

According to the associative property, if 3 numbers are added or multiplied then the grouping of numbers does not change the final result.

The associative property is applicable in addition as well as in multiplication.

According to the associative property in addition - when 3 numbers, say a, b, and c are being added then their sum will not change even if the grouping of numbers is changed. It can be presented as:

(a + b) + c = a + (b + c)

According to the associative property in multiplication - when 3 numbers, say a, b, and c are being multiplied then their product will not change even if the grouping of numbers is changed. It can be presented as:

(a × b) × c = a × (b × c)

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Answer:

Step-by-step explanation

So in the fraction 3/8 the numerator is 3. In the fraction 1/9 the numerator is 1.