The nucleus of a 125xe atom (an isotope of the element xenon with mass 125 u ) is 6. 0 fm in diameter. It has 54 protons and charge q=+54e.

The independent variable in this relationship is the radius (r) and the dependent variable is the circumference (C). This is because the circumference is dependent on the radius of the circle, meaning that if the radius changes, the circumference will change accordingly.

Step-by-step explanation given below

Step 1: The rule states that the relationship between the circumference (C) and the radius (r) is C = 6.3r.

Step 2: This means that the circumference of a circle is a function of its radius.

Step 3: The independent variable in this relationship is the radius (r) because it is what is used to determine the circumference.

Step 4: The dependent variable in this relationship is the circumference (C) because it is what is being determined by the radius.

This is because the circumference is dependent on the radius of the circle, meaning that if the radius changes, the circumference will change accordingly.

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The statement which is true is D. 65% of the seventh-grade students prefer the water park.

Percentage is defined as the parts of a number per fraction of 100. We have to divide a number with it's whole and then multiply with 100 to calculate the percentage of any number.

A : Total number of students = 120

Number of students who prefer amusement park = 14 + 16 = 30

Percentage of students who prefer amusement park = 30 / 120 = 0.25 = 25%

B : Total number of eighth grade students = 80

Number of eighth grade students who prefer amusement park = 16

Percentage = 16 / 80 = 0.2 = 20%

C : Total number of students = 120

Number of students who prefer water park = 26 + 64 = 90

Percentage = 90 / 120 = 0.75 = 75%

D : Total number of seventh grade students = 40

Number of seventh grade students who prefer water park = 26

Percentage = 26 / 40 = 0.65 = 65%

Hence the option D is the correct percentage.

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9 i think

i’m pretty sure it’s 9 i just done it

The electric field at this point is given by E = k * q/r^2 = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C where  q is the charge (4.89e-9 C), and r is the distance from the charge (2.79e-2 m).

1. First calculate the electric field, E, using the equation E = k * q/r^2, where k is Coulomb's constant (8.99e9 N * m^2/C^2), q is the charge (4.89e-9 C), and r is the distance from the charge (2.79e-2 m).

2. Plugging in the values, we get E = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C.

The electric field at this point is given by E = k * q/r^2 = (8.99e9 N * m^2/C^2) * (4.89e-9 C) / (2.79e-2 m)^2 = 7.76e6 N/C.

The complete question is :

Consider a point at a location 2.79 cm away from a 4.89-nc charge. What is the electric field at this point?

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Based on the IUCN Red Data list of species, by solving the data we get the number of species in each category as

The answer which has been provided above gives the number of species that are present in each of the 7 categories of the IUCN Red Data List.

The IUCN Red Data List is a list of species that are globally threatened.

The categories that are present in the IUCN Red Data List are

Extinct in the Wild, Extinct, Critically Endangered, Endangered, Threatened, Vulnerable, Near Threatened, and Least Concern.

The number of species in each category is calculated based on the given information:

There are 78 species that are extinct in the wild.

Hence,

11 times that many have gone extinct since 1500 AD.

Hence,

6 and 9 times as many species have gone extinct are on the critically endangered and endangered lists respectively.

Hence,

24,570 species are listed as threatened In the IUCN Red Data list.

Hence,

According to the list, the number of near-threatened species is 468 more than a third of the number which is vulnerable.

Hence,

According to the data, there are 7,098 more species on the least

The total number of species on the IUCN Red Data List is calculated by adding up the number of species in each category:

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Answer: 529/8

Step-by-step explanation:

Part A: The perimeter of the tree house floor is 32 m.

Part B: The area of the tree house floor is 40 m².

Part A: The perimeter of the rectangular floor can be found by adding up the lengths of all four sides.

Part B: The area of the rectangular floor can be found by multiplying the length by the width.

This is about a tree house design using a coordinate plane in which the coordinates are measured in meters (m). The task is to calculate the perimeter and the area of the rectangular floor of the tree house, given the vertices of the floor. The perimeter is found by adding up the lengths of all four sides of the rectangular floor, and the area is found by multiplying the length by the width.

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Suppose a deck of 52 cards is shuffled and the top two cards are dealt..

[tex]\left \P {{52} \atop {2}} \right.[/tex] =52!50! = 52 ×51 = 2652.

Now assuming each of the pairs has the same chance, calculate the probabilities for the following events

the chance that the first card is an ace;

There are 4aces in a deck, so the probability is

P (A)=

[tex]\frac{4}{52}\\ =\frac{1}{13}[/tex]

the chance that the second card is an ace

Again, there are 4aces in a deck, so the probability is

P(B)=

[tex]\\ \\ \frac{4}{52}\\ =\frac{1}{13}[/tex]

the chance that both cards are aces

There are 4aces in the deck. We already have the number ofpossible ordered pairs from P(A), each of which is equally likely. How many different ordered pairs give both aces? The answer is the number of permutations of two cards among four.

= [tex]\left \ P{4} \atop {2}} \right. \\\frac{4!}{2!}[/tex]

= 4*3

= 12

The probability that both cards are aces is therefore

[tex]\frac{\left \P {{4} \atop {2}} \right. }{\left \P{{52} \atop {2}} \right. }[/tex]

=12 /2652

=1/221

the chance of at least one ace among the two cards.

How many different permutations of the first two cards give at least one ace? The number that give two aces is P42, from above. The number that give an ace as the first card but not the second card is 4×48, since there are4aces, and after choosing one ace, there are 48 that possible non-aces for the second card. Likewise there are 48 ×4ways to choose an ace as the second card, but not the first. Thus the total number of ways that the two cards can have at least one ace is

P42+ 4 ×48 + 4 ×48 = 396.

The probability of of selecting at least one ace among the first two cards

= 396/3652

P (D)= 33 /221

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To find the total monthly mortgage payment, we need to calculate the monthly payments for both the first (80%) and second (20%) mortgages and then add them together.

First, we'll find the monthly payment for the first mortgage:

Loan amount: $140,000 x 80% = $112,000

Interest rate: 4.75% / 12 months = 0.0395%

Loan term: 30 years x 12 months/year = 360 months

Monthly payment: $112,000 * (0.0395% / (1 - (1 + 0.0395%)^-360)) = $527.64

Next, we'll find the monthly payment for the second mortgage:

Loan amount: $140,000 x 20% = $28,000

Interest rate: 7.525% / 12 months = 0.0627%

Loan term: 30 years x 12 months/year = 360 months

Monthly payment: $28,000 * (0.0627% / (1 - (1 + 0.0627%)^-360)) = $184.07

Finally, we'll add the monthly payments for both mortgages to get the total monthly payment:

Total monthly payment: $527.64 + $184.07 = $711.71

So, the total monthly mortgage payment for Pablo's house is $711.71.

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Scarlett typically rides her bike for around 1 and a half hours per day, thus she covered a distance of 7/12.

The overall uninspired velocity of an object will be its distance. Distance is the amount of space an object has traveled, regardless of where it began or ended. Distance would be the measurement of said size or extent of the separation between two places. It is important to keep in mind that the distance between two spots and the traveled between them aren't the same thing. Distance traveled is the sum of a line's length joining various places. Distance refers to the actual travel path of a body. Path length is another term for it. For instance, if an object is traveling from board to point P, the path's length will be similar to OP = 360 m.

given

We are aware of: t = 1 1/5   d = 7/8

Write down and replace 7/8 = v * (1* 1/5)

Remove the connecting element: 7/4 * 1/3

As a single fraction, write:

7 / 4*3

Determine the quotient or product: 7/12

Response: 7/12

Scarlett typically rides her bike for around 1 and a half hours per day, thus she covered a distance of 7/12.

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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.

This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

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The probability of rolling a 5 with two 6-sided dice is 1/9 or approximately 0.11.

This can be found by calculating the number of combinations that add up to 5. There are 2 combinations that add up to 5: (1, 4) and (2, 3). Out of 36 possible combinations of rolling 2 dice (6 x 6), there are only 2 combinations that give us a sum of 5, so the probability is 2/36 or 1/18 or approximately 0.11.

Probability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 means the event is impossible, and 1 means the event is certain to happen. A probability of 0.5 means that the event has an equal chance of happening or not happening.

The probability of an event is calculated by dividing the number of favorable outcomes by the number of possible outcomes. For example, if you flip a fair coin, the probability of getting heads is 1/2 because there are two possible outcomes (heads or tails) and only one of them is favorable (heads).

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The time in minutes until there are 280 grams of the element remaining is given as follows:

16 minutes.

A decaying exponential function is modeled as follows:

y = a(1 - r)^t.

In which the parameters are given as follows:

The parameter values for this problem are given as follows:

a = 660, r = 0.051.

Hence the function is modeled as follows:

y = 660(0.949)^t.

The time until there are 280 grams remaining is given as follows:

280 = 660(0.949)^t.

(0.949)^t = 280/660

tlog(0.949) = log(280/660)

t = log(280/660)/log(0.949)

t = 16 minutes.

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The No Of ways are there to distribute the donuts = 34650

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!

Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.

Hence,

Total number of ways to distribution the donuts

= 12/4*4*4

= 34650

Total number of ways = 34650

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The No Of ways there to distribute the donuts = 34650

What is Probability?

Probability is an area of mathematics that deals with numerical descriptions of how probable an event is to occur or how likely a statement is to be true. The probability of an event is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty.

Number of ways to distribute 12 donuts in 12 kids so that each kid got one donut = 12!

Though, there are 4 chocolate, 4 jelly and 4 glazed donuts.

Hence,

Total number of ways to distribute the donuts

= 12/4*4*4

= 34650

Total number of ways = 34650

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Answer:

12.82

Step-by-step explanation:

6.4/49.92

multiply both the numerator and denominator with 100 since the denominator is to hundredth place

6.4×100/49.92×100

640/49.92=

compute in the calculator to get answer as;

12.82

Answer:

This is an approximate answer so I not sure if it is accurate.

0.1282051282

Hoped it helped and was the right answer

Answer:

9 : 7

Step-by-step explanation:

given the ratio

4.5 : 3 [tex]\frac{1}{2}[/tex] , that is in decimal form

4.5 : 3.5 ( multiply both parts by 10 to clear the decimal )

= 45 : 35 ( divide both parts by 5 )

= 9 : 7 ← in simplest form

Answer:

9:7

Step-by-step explanation:

Convert all the numbers to either decimal or fraction. The operation becomes simple.

Simplifying after converting to decimal

Convert 3 1/2 to decimal 3 1/2 = 3 + 1/2

1/2 = 0.5

3 + 1/2 = 3 + 0.5 = 3.4

Ratio 4.5:3.5 = 4.5/3.5

Divide by 5 to give
[tex]\dfrac{4.5 /5 }{3.5/5} = 0.9/0.7\\\\[/tex]

Multiply both numerator and denominator by 10
0.9 x 10 = 9

0.7 x 10 = 7

So the ratio becomes 9/7 = 9:7

Simplifying after converting to fraction

4.5 = 4 + 0.5

0.5 = 1/2

5.5 = 4 + 1/2 = 4 1/2

Convert to mixed fraction:
4 1/2 = (4 x 2 + 1)/2 = 9/2

Convert 3 1/2 to fraction

3 1/2 = (3 x 2 + 1)/2 = 7/2

So 4.5 : 3 1/2 = 9/2 : 7/2

Multiplying by 2 we get the same answer: 9:7

Choose whichever approach you feel comfortable with

The statement that identifies the scale used in this map would be = 1 inch equals 19 miles. That is option C.

A map is a diagram that can be used to represent the location and distance of various areas of a country or state.

In the map, there are 4 towns which are separated by 3 inches apart.

The actual distance apart = 57 miles

Therefore the actual scale that was used is calculated as follows;

3 inches = 57 miles

1 inch = X miles

make X mile the subject of formula;

X miles = 57/3 = 19 miles.

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Answer:

9.5

Step-by-step explanation:

72 + 10t = 34 + 14t

72 - 34 = 14t - 10t

38/4 = 4t/4

9.5 = t

The expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?

An arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

The nth term of an arithmetic sequence is derived using; aₙ = a + (n - 1)d where a is the first term and d the common difference

Given the first term as 37, we have that;

a₁ = a + (1 - 1) d = 37

a₁ = a = 37

for the second term 42, substituting 37 for a;

a₂ = 37 +(2 - 1)d = 42

37 + d = 42

d = 42 - 37 {subtract 37 from both sides}

d = 5

Therefore, the arithmetic sequence increase by a common difference 5 and the expression aₙ = 37 + (n - 1)5 can be used to determine the nth term of the arithmetic sequence pattern?

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The first value of the given exponential expression would be 3.

What is an exponential function?

An exponential function is a mathematical function of the form f(x) = aˣ, where "a" is a positive constant and x is a real number. The function represents an exponential growth or decay, depending on the value of "a". If "a" is greater than 1, the function increases rapidly as x increases. If "a" is between 0 and 1, the function decreases as x increases.

In the exponential expression y = 3 * q⁵, the first value is 3.

Hence, the first value of the given exponential expression would be 3.

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Answer:

118000

Step-by-step explanation:

cash out flow = beg balance - end balance

= 24 -14 =10K

128K - 10K =118K

actual pay out is 118K

Yes, the three lines have a common point of intersection. This point is located where all three equations equal the same value, which in this case is (4,-4).

Yes, the three lines 3x1−12x2=4, 6x1 39x2=−76, and −3x1−51x2=80 have a common point of intersection. This point is located where all three equations equal the same value. To find this point, one must solve the three equations simultaneously. First, one can subtract the first equation from the third equation, which will result in a new equation equal to −3x1 + 48x2 = 76. From there, one can subtract the second equation from the new equation, resulting in a new equation equal to −45x2 = 132. From this equation, one can solve for x2 and the result is x2 = -4. Then, one can substitute the value of x2 into any of the original equations to solve for x1 and the result is x1 = 4. Therefore, the common point of intersection for these three equations is (4, -4).

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The proof of divisibility is correct in this question.

The capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.

According to the question

It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.

The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes 75^30 = 31 * 52^30 = 3^30 * 5^60. Similar to how 45 may be expressed as 3^2 * 5^1, 3^90 * 5^45 is equal to 45^45 = (3^2 * 5^1)^45. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.

75 = 3^1 * 5^2,

∴ 75^30 = (3^1 * 5^2)^30 = 3^30 * 5^60.

It follows that 75^30, or 3^30 * 5^60, divides 45^45 * 15^15, or 3^90 * 5^45 * 3^15 * 5^15, as 3^30 divides 3^90 and 5^60 divides 5^45.

45 = 3^2 * 5^1,

∴ 45^45 = (3^2 * 5^1)^45 = 3^90 * 5^45.

15 = 3^1 * 5^1,

∴ 15^15 = (3^1 * 5^1)^15 = 3^15 * 5^15.

In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.

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The proof of divisibility is correct in this question.

Divisibility

The capacity of one integer (the divisor) to divide another integer (the dividend) equally and without leaving a residual is known as divisibility in mathematics. Alternatively said, if a dividend is divisible by a divisor, the division will produce a whole number or an integer. The formula for this connection is "dividend divisor = integer." Using divisibility criteria, which are based on the characteristics of numbers and their prime factorizations, is a typical method of checking for divisibility. In subjects such as number theory, cryptography, and others, the ability to divide a number by another number can have significant ramifications.

According to the question,

It is necessary to demonstrate that the phrase 45*45*15*15 may be divided by 75*30. We must first comprehend the characteristics of the numbers' prime factorization in order to do this.

The number 75 may be represented as 31 * 52, and when it is raised to the 30th power, it becomes [tex]75^{30}=(31*52^{30})=(3^{30}*5^{60})[/tex]. Similar to how 45 may be expressed as [tex](3^2*5^1)[/tex]. [tex](3^{90}*5^{45})[/tex] is equal to [tex]45^{45}=(3^2*5^1)^{45}[/tex]. Additionally, 15 may be written as 3 * 5 1, which means that 15 = 3 * 5 * 15.

[tex]75=3^1*5^2[/tex],

∴ [tex]75^{30}=(3^1*5^2)^{30}=3^{30}*5^{60}[/tex].

It follows that [tex]75^{30}[/tex], or [tex](3^{30}*5^{60})[/tex], divides [tex](45^{45}*15^{15})[/tex] or [tex](3^{90}*5^{45}*3^{15}*5^{15})[/tex], as [tex]3^{30}[/tex] divides [tex]3^{90}[/tex] and [tex]5^{60}[/tex] divides [tex]5^{45}[/tex].

[tex]45=3^2*5^1[/tex]

∴ [tex]45^{45}=(3^*5^1)^{45}=3^{90}*5^{45}[/tex]

[tex]15=3^1*5^1[/tex]

∴ [tex]15^{15}=(3^1*5^1)^{15}=3^{15}*5^{15}[/tex]

In other words, the equation 45*45*15*15 may be evenly divided by 75*30 without any residual, proving that it is divisible by 75*30. The division may be used to confirm this, but it can also be demonstrated by the fact that all of the dividend's prime factors—45*45*15*15—are included in the divisor's prime factorization, 75*30, in the multiples necessary to divide it evenly.

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n−4  out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex],  [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.

Now, According to the question:

It is easy to show that a tree with  n ≥ 9 can have at most one vertex of degree n - 3. It is [tex]v_0[/tex].

Now, there are n - 1 - (n - 3) = 2 vertices that are not adjacent to [tex]v_0[/tex], it is also

[tex]v_n_-_1[/tex] and [tex]v_n[/tex]

Then a desired tree can be of 3 possible forms:

1. n - 4 out of n - 3  neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 2 and is adjacent to both [tex]v_0[/tex] and [tex]v_n_-_1[/tex]. [tex]v_n_-_1[/tex] has degree 2 and is adjacent to [tex]v_k[/tex] and [tex]v_n.v_n[/tex] is a leaf.

2. n − 5  out of the n − 3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_j[/tex] and [tex]v_k[/tex]. [tex]v_j[/tex]has degree 2 and is adjacent to [tex]v_0[/tex] and  [tex]v_n_-_1[/tex]. [tex]v_k[/tex] also has degree 2 and is adjacent to[tex]v_0[/tex] and [tex]v_n[/tex]. [tex]v_n[/tex] and  [tex]v_n_-_1[/tex] are both leaves.

3. n−4  out of the n−3 neighbors of [tex]v_0[/tex] are leaves, except for [tex]v_k[/tex], which has degree 3 and is adjacent to [tex]v_0[/tex],  [tex]v_n_-_1[/tex]. and [tex]v_n[/tex] . [tex]v_n[/tex] and [tex]v_n_-_1[/tex] are both leaves.

It is then easy to computer the number of trees in each form and sum them up.

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The number of 2 letter codes that can be formed is 6 with no letter repeated using Permutation.

A permutation of a set is, broadly speaking, a rearranging of its elements if the set is already sorted, or arranging its members into a sequence or linear order. The act or procedure of altering the linear order of an ordered set is referred to as a "permutation."

A permutation is a combination and an ordered arrangement of possible outcomes. For instance, there are 5 chairs, and 3 people should occupy them. There are five different methods to seat the first person, four ways to sit the person after them, and three ways to seat the third. As a result, we multiply the alternatives at our disposal to get the total number of configurations for seating 3 people in 5 seats. 5 4 3 are the methods we carry it out. It can be done in 60 different ways. You may write 5 4 3 as (5!) / (2!) (or) (5!) / (5 - 3), as you can see. .

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

The first 3 letters of alphabet are a, b and c

The number of 2 letter codes that can be formed is 3*2 = 6 with no letter repeated.

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Answer:

39°

Step-by-step explanation:

Information we need to know

As we know, one of the angles in this triangle is 39° this means that the angle opposite it would also be 39°! This is because as the triangle is SAS v and the given 39 has to be equal

Have a lovely day :)

Answer:

39°

Step-by-step explanation:

Triangle HJI is an isosceles triangle.

In isosceles triangles the base angles are congruent which means their measures are equal.

So the measure of m∠HIJ = 39°

The depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units is 15000.

Cost of machine = Rs. 1,70,000; Scrap value = Rs. 20,000;

Depreciation in production during the first year =  6,000 units;

Production units during the life of the machine = 60,000 units

Depreciation rate per unit = (Rs. 1,70,000 -  Rs. 20,000)/ 60,000 units

=  Rs. 2.5

Depreciation of first year =  6,000 * Rs. 2.5 = Rs. 15,000

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Complete question

If the original cost of a machine is Rs. 170,000, estimated scrap value Rs. 20,000, what is the depreciation if production during the first year is 6,000 and total estimated production during the working life of the machine is 60,000 units.

The width of the box of books which Mr. Lin recieved which is in the shape of Rectangular Prism is (486/l*h) units.

A three-dimensional solid form having six sides, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

According to the face form or the angle the faces make with the base, there are two different varieties of rectangular prisms.

Below are several characteristics of a rectangular prism that make it simple to recognize one.

The length of the rectangular Prism is l.

Width is w , height is h

Therefore,

Volume (V) = lbh

We know Volume is 486

so we casn find the width of the rectangular prism as 486/lh

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The process of converting repeating, non-terminating decimal to a fraction has been explained below. On conversion of 0.1515…, we get the fraction as 5/33.

What is a non-terminating decimal?

Non-terminating decimals are those decimal numbers that never reach an end since there is no endpoint in their decimal digits.

We are given a repeating, non-terminating decimal as 0.1515…

So, let x = 0.1515151515  ...(1)

Here, .15 is repeating

So, we will move one set of the repeating digits in front of the decimal.

By this, we get

100x = 15.1515151515     ...(2)

Now, on subtracting (1) from (2), we get

⇒100x - x = 15.1515151515 - 0.1515151515

⇒99x = 15

⇒x = 15/99

⇒x = 5/33

Hence, this way we can convert repeating, non-terminating decimal to a fraction.

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The standard parameterization for the tangent line  is x = 12t + 18 , y = 3t + 13 , z = 54t + 54

Equation of this type is known as a parametric equation; it uses an independent variable known as a parameter (commonly represented by t) and dependent variables that are defined as continuous functions of the parameter and independent of other variables.

Given that,

Given that, t = t0 = 3, I + (3t + 4) j + (2t 3) k

In order to get the tangent line to the curve at t=3, (x, y, z) = 18, 13, and 54,

r'(t) = 4t, 3, > and r'(t=3) = 12, 3, 54>. (18, 13, 54)

finally,

x = 12t + 18

y = 3t + 13

z = 54t + 54

The tangent line's usual parameterization is as follows:

x=12t+18, y=3t+13, and z=54t+54

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