Find an ordered pair (x,y) that is a solution to the equation

The side length x of the triangle rounded to the nearest tenth is 31.3.

The figure in the image is a right triangle.

To determine the value of x, use trigonometric ratio.

Tangent = Opposite / Adjacent

tan( 38° ) = x / 40

Solve for x

x = tan( 38° ) × 40

x = 0.781285 × 40

x = 31.3

Therefore, the value of x is 31.3.

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The amount of sand needed for every 100 square yard of surface would be 1. 1 cubic yards.

The amount of sand needed for 280 square yards would be 4 .18 cubic yards of sand.

The question says that 1. 1 cubic yards of sand are needed for every 100 square yards of surface so this is the amount of sand needed per 100 square yards.

As for 380 square yards, the amount of sand needed can be found by the formula :

= ( 380 square yards of surface x 1. 1 cubic yards of sand ) / 100 square yards of surface

= 418 / 100

= 4 .18 cubic yards of sand

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Using simple division we know that 86 people or citizens dies each day in 2015.

One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division.

The other operations are multiplication, addition, and subtraction.

Division in mathematics is the process of dividing an amount into equal parts.

For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

So, we know that:

31,500 people died in 2015.

We also know that 2015 had 365 days.

Then, people died easily day would be:

= 31,500/365

= 86.30

Rounding off: 86 people

Therefore, using simple division we know that 86 people or citizens dies each day in 2015.

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The required length of the third side of the right-angle triangle is 15 units.

In a right-angled triangle, its sides, such as the hypotenuse, are perpendicular and the base is Pythagorean triplets.

Here,
For the right triangle lenght of the two legs to be 9 and 12 units, a measure of the third side is to be determined.

So, Applying the Pythagoras theorem,
h² = p² + b²
h = √9² + 12²
h = √225
h = 15

Thus, the required length of the third side of the right-angle triangle is 15 units.

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Answer:

The cost of 3 tennis balls and 2 golf balls is $7. The cost of 6 tennis balls and 3 golf balls is$12. Find the cost of 1 tennis ball and 1 golf ball.

Step-by-step explanation:

The shortest distance between the two skew lines is equal to 11√38 / 38 units.

According to linear algebra, lines are defined by vectorial equations of the form:

(x, y, z) = P(x, y, z) + t · T(x, y, z)

Where:

And the shortest distance between two skew lines is determined by the following expression:

[tex]d = \frac {|[P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)]|}{|T_{1} (x, y, z) \times T_{2} (x, y, z)|}[/tex]

First, determine the points contained in each line:

P₁(x, y, z) = (3, 2, 1)

P₂(x, y, z) = (2, 4, - 1)

Second, find each vector slope:

T₁(x, y, z) = (2, 1, 0) - (3, 2, 1)

T₁(x, y, z) = (- 1, - 1, - 1)

T₂(x, y, z) = (3, 0, - 2) - (2, 4, - 1)

T₂(x, y, z) = (1, - 4, - 1)

Third, determine the vector subtraction:

P₂(x, y, z) - P₁(x, y, z) = (2, 4, - 1) - (3, 2, 1)

P₂(x, y, z) - P₁(x, y, z) = (- 1, 2, - 2)

Fourth, determine the cross product:

T₁(x, y, z) × T₂(x, y, z) = (- 1, - 1, - 1) × (1, - 4, - 1)

T₁(x, y, z) × T₂(x, y, z) = (- 3, - 2, 5)

Fifth, use the dot product:

[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = (- 1, 2, - 2) \,\bullet\,(- 3, - 2, 5)[/tex]

[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = 3 - 4 - 10[/tex]

[tex][P_{2} (x, y, z) - P_{1}(x, y, z)] \bullet [T_{1} (x, y, z) \times T_{2} (x, y, z)] = - 11[/tex]

Sixth, calculate the norm of the cross product:

|T₁(x, y, z) × T₂(x, y, z)| = √[(- 3)² + (- 2)² + 5²]

|T₁(x, y, z) × T₂(x, y, z)| = √38

Finally, determine the shortest distance between the two skew lines:

d = |- 11| / √38

d = 11 / √38

d = 11√38 / 38

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The statement of statistics "the statistical methods of analysis of variance assume that the populations are normally distributed" is true. So the correct answer is (a)True.

Statistics is a branch of applied mathematics that involves collecting, describing, analyzing, and drawing conclusions from quantitative data. It  gives us information to figure out how things work. Statistics are used to conduct research, evaluate results, develop critical thinking, and make informed decisions. Statistics can be used to examine nearly any area of ​​research to find out when and why things happen, and whether their recurrence is predictable. 

Statistics are used in many different applications and professions. Statistics are generated each time data is collected and analyzed. This ranges from government agencies to academic research to investment analysis. 

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Let V be an inner product space, S and S0 be subsets of V, and W be a finite-dimensional subspace of V. To prove the other side,

1 ) Suppose (e1,…,en) is basis for W. Suppose x∈(W⊥)⊥. Consider the projection w of x onto W, specifically:

w=⟨x,e1⟩e1+…+⟨x,en⟩en∈W.

Then, x−w is perpendicular to each ei, since

⟨x−w,ei⟩=⟨x,ei⟩−∑j=1n⟨⟨x,ej⟩ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩⟨ej,ei⟩=⟨x,ei⟩−∑j=1n⟨x,ej⟩δij=⟨x,ei⟩−⟨x,ei⟩=0.

Since the linear map ⟨⋅,x−w⟩ is constantly 0 on the basis of W, it is constantly zero on all of W, hence x−w∈W⊥.

But then, since x∈(W⊥)⊥, we have ⟨x−w,x⟩=0, and since ⟨x−w,w⟩=0,

∥x−w∥2=⟨x,x−w⟩−⟨w,x−w⟩=0,

i.e. x=w∈W, completing the proof.

2 ) Suppose that w∈(W⊥)⊥

then ⟨w,x⟩=0

for all x∈W⊥

If w∉W, then w=v+v′ where v∈W and v′∈W⊥∖{0}.

Then.

0=⟨w,x⟩=⟨v,x⟩+⟨v′,x⟩=⟨v′,x⟩

for all x∈W⊥.

However, v′∈W⊥ and ⟨v′,v′⟩≠0 so it is a contradiction.

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The effective annual rate (EAR) is the actual rate of interest that is earned or paid over a given period of time, taking into account the compounding of interest. For example, a stated rate of 7.80% with 4 compounding periods per year would result in an EAR of 15.30%.

The effective annual rate (EAR) is a measure of the actual rate of interest that is earned or paid over a given period of time. It takes into account the effect of compounding, which is the process of earning interest on both the principal and the accumulated interest. This means that the rate of return can increase over time. The EAR is calculated by taking the stated rate of interest, which is the rate of interest stated by the lender, and multiplying it by the number of compounding periods per year. For example, if the stated rate is 7.80% and the compounding periods per year are 4, then the EAR would be 15.30%. Similarly, if the stated rate is 12.40% and the compounding periods per year are 365, then the EAR would be 11.40%. If the compounding period is infinite, then the EAR will be the same as the stated rate, in this case 12.40%. Therefore, the EAR is the actual rate of return that is earned or paid over a given period of time.

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Answer:

[tex]\frac{(s + 15.4)(8.1)}{2}[/tex] = 81

8.1s + 124.74 = 162

8.1s = 37.26

s = 4.6

Answer: qt=0.6

Step-by-step explanation:

3.5=

60%=0.6

qt=0.6

Answer:

$72

Step-by-step explanation:

300

4% per year

so 12$ per year,

6 years = 12*6 = 72

In this matrix question where percentages are listed, answers to all these questions are written below.

In the matrix given in the image, we can calculate following things:

a. S32 is a value that represents the percentage of sick students in the third grade of the elementary school. From data we can say it is 10%

b. P22 is a value that represents the number of middle school students in the second grade. From data we can say there are 795 such boys.

c. To find[tex][s] * [p][/tex] we need to multiply the percentage of students in each category by the corresponding population in each grade level.

      [tex]\left[\begin{array}{ccc}1190.75&1311.75\\1194&1366.25\\1233&1405.5\end{array}\right][/tex]

Columns: Girls, Boys

Rows: Susceptible, Sick, Infected

d. [tex][[s] * [p]]21[/tex] represents the number of sick students in the second grade of the elementary school.

It represents that 1194 girls are sick.

e. To find the number of sick girls, we need to multiply the number of girls in each grade level by the corresponding percentage of sick students.

1194

f. To find the number of infected boys, we need to multiply the number of boys in each grade level by the corresponding percentage of infected students.

1406

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Complete Question: Image is uploaded for it.

a. Describe what S32 value is and what it will represent

b. Describe what P22 value is and what it will represent

c. Find [tex][s] * [p][/tex]

d. Describe what[tex][[s] * [p]]21[/tex] value is and what it will represent

e. How many sick girls are present?

f. Number of boys infected?

Answer: We can solve the system of equations using the substitution method.

First, we'll isolate "y" in one of the equations and substitute it into the other equation:

Y = x - 11

7x + 7y = -21

Substituting the first equation into the second equation:

7x + 7(x - 11) = -21

7x + 7x - 77 = -21

14x = 56

x = 4

Now that we have found the value of x, we can substitute it back into one of the original equations to find the value of y:

Y = x - 11

Y = 4 - 11

Y = -7

The solution to the system of equations is (x, y) = (4, -7).

Step-by-step explanation:

The value of x and y in the equation is 4 and -7 respectively

Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.

Using substitution method to solve the system,

y = x-11 equation 1

7x+7y = -21 equation 2

substitute x-11 for y in equation 2

7x + 7( x-11) = -21

7x + 7x -77 = -21

14x = -21+77

14x = 56

divide both sides by 14

x = 56/14

x = 4

substitute 4 for x in equation 1

y = 4-11

y = -7

therefore the value of x and y is 4 and -7 respectively

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Mr. Garcia's homeroom had a more consistent collection of canned goods.

Ms. Vicario's homeroom varied more widely with the collection of canned goods.

An interquartile range is a measure of the difference between the upper and lower quartiles of a dataset.

W can find the values of the upper and lower quartile and median from a box plot.

The middle line is the median and the first line is the lower quartile and the last line is the upper quartile.

The formula used is Upper quartile - Lower quartile.

We have,

The two daily food drives:

Mr. Garcia:

The mean number of canned goods collected = 18.75.

The median number of canned goods collected = 18.

The range of data for Mr. Garcia's homeroom = 11.

The IQR (interquartile range) of data = 4.25.

Ms. Vicario's homerooms:

The range of data = greater than 11.

The IQR of data = greater than 4.25.

The number of canned goods collected = more variable than the number of canned goods collected by Mr. Garcia's homeroom.

Based on these observations.

We can conclude that,

Mr. Garcia's homeroom had a more consistent collection of canned goods. i.e

Smaller range and IQR.

Ms. Vicario's homeroom varied more widely with the collection of canned goods.

i.e

Wider range and IQR

Thus,

Mr. Garcia's homeroom had a more consistent collection of canned goods.

Ms. Vicario's homeroom varied more widely with the collection of canned goods.

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A phase change occurs when the kinetic energy decrease enough so that the attraction between molecules pulls them together.

A substance with weaker molecular attraction will freeze at a lower temperature because it requires more energy to be taken out before the attraction pulls the molecules together.

A substance with stronger molecular attraction will evaporate at a higher temperature because it requires less energy to be added to overcome attraction between the molecules.

In Science, a phase change refers to the change in the state of matter of a given chemical compound or substance. Additionally, some examples of a phase change include the following;

Generally speaking, a change in the state (phase) of matter that results in the release of energy is known as an exothermic reaction and they include:

In conclusion, sublimation, melting, and evaporation are other processes that are associated with a change in the state (phase) of matter.

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a)The events A1, A2, and A3 are pairwise independent.

b)  The events are not mutually independent.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Observe the given numbers:

Out of 4 numbers, 2 have 1 at first position

so outcomes in event A1 is

A1 ={ 110, 101}

Similarly, possible outcomes in A2 is

A2 ={110, 011}

A3 = {101,111}

The probabilities of events are

P(A1) = 2/4 = 0.5

P(A2) = 2/4 = 0.5

P(A3) = 2/4 = 0.5

Also,

(A1 and A2) = {110}

(A1 and A3) = {101}

(A2 and A3) = {011}

The probabilities are

P(A1 and A2) = 1 /4 = 0.25

P(A1 and A3) = 1 /4 = 0.25

P(A2 and A3) = 1 /4 = 0.25

a)

From above we have

P(A1 and A2) = P(A1)P(A2) = 0.25

P(A1 and A3) = P(A1)P(A3) = 0.25

P(A2 and A3) = P(A2)P(A3) = 0.25

So events A1, A2, and A3 are pairwise independent.

b)

Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.

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a)The events A1, A2, and A3 are pairwise independent.

b)  The events are not mutually independent.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Observe the given numbers:

Out of 4 numbers, 2 have 1 at first position

so outcomes in event A1 is

A1 ={ 110, 101}

Similarly, possible outcomes in A2 is

A2 ={110, 011}

A3 = {101,111}

The probabilities of events are

P(A1) = 2/4 = 0.5

P(A2) = 2/4 = 0.5

P(A3) = 2/4 = 0.5

Also,

(A1 and A2) = {110}

(A1 and A3) = {101}

(A2 and A3) = {011}

The probabilities are

P(A1 and A2) = 1 /4 = 0.25

P(A1 and A3) = 1 /4 = 0.25

P(A2 and A3) = 1 /4 = 0.25

a)

From above we have

P(A1 and A2) = P(A1)P(A2) = 0.25

P(A1 and A3) = P(A1)P(A3) = 0.25

P(A2 and A3) = P(A2)P(A3) = 0.25

So events A1, A2, and A3 are pairwise independent.

b)

Since P(A1 and A2), P(A1 and A3) and P(A2 and A3) are not equal to zero so events are not mutually independent.

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The correct option that can be used to prove that ∠ABC = ∠FDE is option (A). It is done using rules of congruency.

What is meant by congruency?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

For the construction of the congruent angle, the compass measurement used is the same for both figures.

Now we draw a line through points A and C and another line through points F and E.

We can then say that

AB = FD

BC = DE

CA = EF

These are the sides of the triangles ΔABC and ΔFDE

As all sides are equal, we can say that

ΔABC ≅ ΔFDE by SSS congruency rule.

Now CPCTC rule says that "corresponding parts of congruent triangles are congruent". This means that the corresponding angles and sides of two or more triangles must also be identical in order for them to be considered congruent.

So ∠ABC ≅ ∠FDE by CPCTC as they are corresponding angles.

Therefore the correct congruency rules that can be used to prove that

∠ABC = ∠FDE is option (A).

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Statistics is a discipline, principally within applied mathematics, concerned with the systematic study of the collection, presentation, analysis, and interpretation of data.

The measures used in statistics are mean, range, standard deviation, variance etc.

The range can be calculated by finding the difference between the lowest and highest observation i.e. 23 - 12 = 11.

Variance is a measure of dispersion of data points from the mean. In the above given data, the variance is 9.389.

Standard deviation is the square root of the variance, hence, is 3.06.

Mean = sum of data divided by no of observations (10).

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The intersection in the below problem is 13

Given equation is

[1,13] ∩ [13,19]

We need to simplify the expression and tell the intersection of the expression

After doing the intersection, we will  take all the common elements in two sets

so , we have

[1,13] ∩ [13,9 ] = 13

therefore we get the intersection of the given expression by simplifying it as 13.

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The percentages of the weights are given as follows:

a) Over 15.5 pounds: 2.07%.

b) Under 11.9 pounds: 75.8%.

c) Between 11.9 pounds and 15.9 pounds: 22.13%.

The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The parameters for this problem are given as follows:

[tex]\mu = 10, \sigma = 2.7[/tex]

The proportion over 15.5 pounds is one subtracted by the p-value of Z when X = 15.5, hence:

Z = (15.5 - 10)/2.7

Z = 2.04

Z = 2.04 has a p-value of 0.9793.

1 - 0.9793 = 0.0207.

The proportion under 11.9 pounds is the p-value of Z when X = 11.9, hence:

Z = (11.9 - 10)/2.7

Z = 0.7

Z = 0.7 has a p-value of 0.7580.

The proportion between is the subtraction of the p-values, hence:

0.9793 - 0.7580 = 0.2213 = 22.13%.

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The best estimate of the difference between the two numbers is 31/12 or 2 7/12.

A mixed fraction is one that is represented by both its quotient and remainder. A mixed fraction is, for instance, 2 1/3, where 2 is the quotient and 1 is the remainder. An amalgam of a whole number and a legal fraction is a mixed fraction.

to transform a mixed fraction into an incorrect fraction.

By denominator, divide the numerator.

Take the quotient as a whole number and use the remaining amount as the proper fraction's numerator while maintaining the original denominator.

Covert the mixed fraction into improper fractions:

5 5/6 = 35/6

3 1/4 = 13/4

The difference between the two numbers is:

35/6 - 13/4

Take the LCM.

70/13 - 39/12

(70 - 39) / 12

31/12 = 2 7/12

Hence, the best estimate of the difference between the two numbers is 31/12 or 2 7/12.

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37.96 is the average atomic mass of the element in the data table .

What does average mean?

The average is calculated by dividing the total number of values by the total number of values. It can also be described as mean. The mean in statistics is the average value across the specified sample or data set.

                                      Mean, median, and mode are the three primary categories of average. Each of these methods operates a little bit differently and frequently yields values that diverge a little bit from the norm. The most popular type of average is the mean.

the average atomic mass = 35.97 + 37.96 + 39.96/3

                                          = 113.89/3

                                           =  37.96

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Answer:

39.96

Step-by-step explanation: I think

The required values of the given composite functions follow as:

(a) fog(x) = 4x², (b) gof(x) = 2x², and (c) gog(x) = x⁴.

Composite functions are mathematical functions that are formed by taking the output of one function and using it as the input for another function.

(a) To find fog(x), we need to evaluate g(f(x)).

Since function f(x) = 2x, we have:

g(f(x)) = g(2x) = (2x)² = 4x²

Therefore, fog(x) = 4x².

(b) To find gof(x), we need to evaluate f(g(x)).

Since g(x) = x², we have:

f(g(x)) = f(x²) = 2(x²) = 2x²

Therefore, gof(x) = 2x².

(c) To find gog(x), we need to evaluate g(g(x)).

Since function g(x) = x², we have:

g(g(x)) = g(x²) = (x²)² = x⁴

Therefore, gog(x) = x⁴.

Thus, the required values of the given composite functions follow as:

(a) fog(x) = 4x², (b) gof(x) = 2x², and (c) gog(x) = x⁴.

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The solution of the system of equations is equal to (3, 4).

In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.

By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant II and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-coordinate (y-axis), which is given by  ordered pair (3, 4).

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Answer:

Step-by-step explanation:

The number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is calculated as follows:

The number of ways the hospital can receive exactly 2 defective machines is C(4,2) = 6, where C(n, k) is the number of combinations of n things taken k at a time.

The number of ways the hospital can receive exactly 3 defective machines is C(4,3) = 4.

The number of ways the hospital can receive exactly 4 defective machines is C(4,4) = 1.

So, the total number of ways the hospital can purchase 5 machines and receive at least 2 of the defective machines is 6 + 4 + 1 = 11.

The ratio of circular chips to square chips is 1:4.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

A box contains 16 square chips, 12 triangular chips, and 4 circular chips.

The ratio of circular chips to square chips,

= Circular chips / square chips

= 4 / 16

= 1/4

= 1: 4

Therefore, the ratio is 1:4.

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Well, most books define critical values of a function as x-values where f'(x)=0 or f'(x) is undefined, so they occur there because that's the definition of what a critical value is.

But the reason we define it that way is that when you're looking for local extrema (local mins and/or local maxs), these must occur when f'(x)=0 or f'(x) is undefined.  

If f has a local extremum at a point x=c, then f'(c)=0 or f'(c) is undefined.