Answers
Answer:i think it is c
Step-by-step explanation:
Related Questions
Entries for Sale of Fixed Asset
Equipment acquired on January 8 at a cost of $212,000 has an estimated useful life of 15 years, has an estimated residual value of $14,000, and is depreciated by the straight-line method.
a. What was the book value of the equipment at December 31 the end of the fifth year?
b. Assume that the equipment was sold on April 1 of the sixth year for $105,800.
1. Journalize the entry to record depreciation for the three months until the sale date.
2. Journalize the entry to record the sale of the equipment.
Answers
The journal entry to record the sale of the equipment would be:Cash $105,800,Loss on Sale of Equipment $35,650,Equipment $212,000
Accumulated Depreciation $66,000
How to solve the question?
a. To calculate the book value of the equipment at December 31 of the fifth year, we need to determine the accumulated depreciation for the first five years. The annual depreciation expense is calculated as follows:
Depreciation Expense = (Cost - Residual Value) / Useful Life
Depreciation Expense = ($212,000 - $14,000) / 15
Depreciation Expense = $13,200 per year
The accumulated depreciation for five years is therefore:
Accumulated Depreciation = Depreciation Expense x Number of Years
Accumulated Depreciation = $13,200 x 5
Accumulated Depreciation = $66,000
The book value of the equipment at December 31 of the fifth year is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - $66,000
Book Value = $146,000
b.
To record depreciation for the three months until the sale date, we need to calculate the depreciation expense for the sixth year. The annual depreciation expense remains the same at $13,200, but since the equipment was sold on April 1, we need to prorate the depreciation for the first three months of the year.
Depreciation Expense for the Sixth Year = Depreciation Expense x (Months Remaining / 12)
Depreciation Expense for the Sixth Year = $13,200 x (9 / 12)
Depreciation Expense for the Sixth Year = $9,900
The journal entry to record depreciation for the three months until the sale date would be:
Depreciation Expense $9,900
Accumulated Depreciation $9,900
To record the sale of the equipment, we need to compare the sale price to the book value of the equipment at the time of the sale.
The book value of the equipment at the time of the sale is calculated as follows:
Book Value = Cost - Accumulated Depreciation
Book Value = $212,000 - ($13,200 x 5.25)
Book Value = $141,450
Since the sale price of $105,800 is less than the book value of $141,450, we need to record a loss on the sale of the equipment. The journal entry to record the sale of the equipment would be:
Cash $105,800
Loss on Sale of Equipment $35,650
Equipment $212,000
Accumulated Depreciation $66,000
The cash received from the sale is debited, and the difference between the sale price and the book value is recorded as a loss on the sale of the equipment. The equipment and its accumulated depreciation are removed from the books.
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The radius of the wheel is 1.2 feet. What is the distance traveled when the wheel turns 20 time?
Answers
The distance traveled by the wheel when it turns 20 times is 150.7964 feet.
What is circumference?
The circumference of a wheel can be calculated as:
Circumference = 2 x π x radius
where π (pi) is a mathematical constant approximately equal to 3.14159.
The distance traveled by a wheel when it turns is equal to the circumference of the wheel multiplied by the number of times it turns.
Given that the radius of the wheel is 1.2 feet, the circumference of the wheel is:
Circumference = 2 x π x radius
Circumference = 2 x 3.14159 x 1.2
Circumference = 7.53982 feet (rounded to 5 decimal places)
Therefore, each time the wheel turns, it travels a distance of 7.53982 feet. To find the distance traveled when the wheel turns 20 times, we can multiply the distance traveled each time by the number of times the wheel turns:
Distance traveled = Circumference x Number of turns
Distance traveled = 7.53982 feet x 20
Distance traveled = 150.7964 feet (rounded to 4 decimal places)
Therefore, the distance traveled by the wheel when it turns 20 times is 150.7964 feet.
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a rectangular field has a perimeter of 400 yards the length of the field is 3 times the width what is the length of the field and what is the width of the field
Answers
The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.
what is perimeter ?A this double shape's perimeter is the space encircling its outside edge. It is the length of the object's sides. As an illustration, the perimeter of a rectangle is equivalent to the total of its four sides' lengths.
given
Assume that the rectangular field has a width of "x" yards.
The problem states that the field's length is three times its breadth, or three times yards.
The lengths of all the sides make up the rectangle's perimeter, therefore we can write:
[tex]Perimeter = 2 (length + width).[/tex]
In place of the values we hold:
[tex]400 = 2(3x + x)\\400 = 2(4x) (4x)\\400 = 8x\\x = 50[/tex]
The field's length is therefore three times its breadth, or 3(50), or 150 yards, and its width is 50 yards.
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Suppose a(x) takes integers as inputs (so x=-4 is in the domain, but x=1/2 isn't, for example) and returns 1 if x is odd and 0 otherwise. Is a(x) a function? Is it a one-to-one function? Why?
Answers
Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function.
Describe function.A mathematical item called a function accepts an input and creates an output. It looks like an apparatus with an input and an output. A formula or a graph can both be used to express a function. For instance, the function f(x) = x² returns the square of an input x as output.
Because it gives exactly one output value for each input value, a(x) is a function, hence the answer is yes. Since several input values might result in the same output value, it is not a one-to-one function. A(x) is not one-to-one, for instance, because a(1) and a(3) are both equal to 1.
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4x4x4x5x5 (I’ve tried 4^3 x 5^2 and it’s not write)
Answers
Answer:
1600
Step-by-step explanation:
The answer you tried is equivalent.
Dean ran 2.3 fewer kilometers than Sam. If Dean ran 6.8 km, how far did Sam run? A 2-column table with 4 rows. Column 1 is labeled Situation with entries increasing, difference, finding part of a total, sharing or grouping. Column 2 is labeled Operation with entries +, minus, times, divided by. Select all that apply. You know the difference in the distances the boys ran, so this is a subtraction problem. You are finding the total distance the boys ran, so this is an addition problem. Dean ran part of the distance Sam ran, so this is a multiplication problem. The correct equation is s + 2.3 = 6.8. The correct equation is s – 2.3 = 6.8. The correct equation is 2.3s = 6.8.
Answers
The correct equation to use is "s - 2.3 = 6.8", where s represents the distance Sam ran.
What is distance?Distance is a measurement of how far apart two objects or points are from each other. It is usually measured in units such as meters, kilometers, miles, or feet. Distance can refer to physical space between two points, or it can be used to describe the extent of an abstract concept, such as a difference in opinion or a cultural divide.
According to question:The Situation column should have two entries: "finding part of a total" and "difference".
The Operation column should have only one entry: "minus".
The right formula is "s - 2.3 = 6.8", where s stands for the distance Sam ran.
To solve for s, we can add 2.3 to both sides of the equation:
s - 2.3 + 2.3 = 6.8 + 2.3
s = 9.1
Therefore, Sam ran 9.1 kilometers.
So, the Situation entries are: "difference" and "finding part of a total".
The Operation entry is: "minus".
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HELP ASAP!!
A company sends every item of mail by second class post.
Each item of mail is either a letter or a packet.
The tables show information about the cost of sending a letter by second class post and the cost of sending a packet by second class post.
Letter
Packet
Weight range
Second Class
Weight range
Second Class
0 – 100 g
61p
0 – 100 g
£1.17
101 – 250 g
£1.51
251 – 500 g
£1.95
501 – 750 g
£2.36
751 – 1000 g
£2.84
Worked example
The company sent 1225 items by second class post.
The ratio of the number of letters sent to the number of packets sent was 8:27
fraction numerator 2 over denominator 7 end fractionof the packets sent were in the weight range 0 – 100 g.
The other packets sent were in the weight range 101 – 250 g.
Work out the total cost of sending the 1225 items by second class post.
Calculation
The total number of items sent was 1225, to proportion the items according to the ratio we first need to work out how many items there are in 1 part of the ratio. So in this example the ratio is 8:27 so there are a total of 8 + 27 = 35 parts.
So, dividing 1225 by 35 will give us the number of items per part of the ratio
1225 over 35 equals 35
We can now multiply each part of the ratio by the number of items per part to give us the number of letters and packets
letters = 35 space cross times space 8 space equals
Total Letters =
Answer for part 1
packets = 35 space cross times space 27 space equals
Total Packets =
Answer for part 2
For the next part of the question we need to work out the total cost of sending all the items. We can easily work out the cost of the letters, as we know how many we have and that the cost is 61p
How much does it cost to send all the letters?
Cost to send all letters = £
Answer for part 3
We know that the ratio of small to large packets is 2:7, so to calculate the number of small packets we need to first work out the number of parts of the ratio adding 2 and 7 together
This gives us 2+7=9
We can now multiply each part of the ratio by the number of items per part to give us the number of small and large packets
For small packets fraction numerator 2 over denominator 9 end fraction
No. packets 0 - 100g =
Answer for part 4
For large packets fraction numerator 7 over denominator 9 end fraction
No. packets 101 - 250g =
Answer for part 5
We can now use these figures to calculate the cost for each type of packet
Cost of packets 0 - 100g =£
Answer for part 6
Cost of packets 101 - 250g =£
Answer for part 7
And we can now calculate the total cost of letters and packets
Total cost of letters and packets =£
Answer for part 8
Answers
Tje number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.
How to calculate the valueTo find out how many items there are in 1 part of the ratio, we need to add together the two parts of the ratio. In this case, 8+27 = 35.
To proportion the items according to the ratio, we need to divide the total number of items (1225) by the number of parts in the ratio (35).
This gives us:
1 part of the ratio = 1225 / 35 = 35
To find out how many items there are in each part of the ratio, we need to multiply this value by the corresponding part of the ratio.
For the part that corresponds to 8, we have:
8 parts of the ratio = 8 x 35 = 280 items
For the part that corresponds to 27, we have:
27 parts of the ratio = 27 x 35 = 945 items
Therefore, the number of items in the ratio 8:27, proportioned according to the total number of items sent (1225), is 280 items in the 8 part and 945 items in the 27 part.
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Find sin(B).
1. a/b
2. a/c
3. b/a
4. b/c
5. c/a
6. c/b
Answers
Answer:
4. b/c
Step-by-step explanation:
In a right-angled triangle with sides of lengths a, b, and c, where c is the hypotenuse (the side opposite the right angle), the sine of the angle opposite side b (angle B) is given by:
Sin theta : Opposite/hypotenuse
sin(B) = b/c
Therefore, the answer is 4. b/c
How many lines of symmetry does a rhombus have
Answers
Answer: 2
Step-by-step explanation:
Answer:
2 lines of symmetry.
can you answer these two questions
Answers
The confidence interval can be expressed as a trilinear inequality: 82.9% < p < 95.7%.
The confidence interval in interval form is (0.1864, 0.3026).
How to calculate confidence interval?The given confidence interval, 89.3% ± 6.4%, means that we are 89.3% confident that the true value of the population parameter lies within a range of 6.4% above and below the sample estimate.
To express this in the form of a trilinear inequality, first find the upper and lower bounds of the interval.
Upper bound = 89.3% + 6.4% = 95.7%
Lower bound = 89.3% - 6.4% = 82.9%
Therefore, the confidence interval 89.3% ± 6.4% can be expressed in the form of a trilinear inequality as:
82.9% < p < 95.7%
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HELPP PLEASE ANSWER :)brainless! In Urge
I'll give brainliest!
Answers
1. The value of Angle STR is 19°
2. The value of arc ST is 134°
What Is circle geometry?A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.
Part of circle theorem states that: The angle in the same segment are equal.
1. Therefore the value of angle STR is calculated as;
= 180- ( 90+71)
= 180- 161
= 19°
2. The value of arc ST is calculated as;
Since arc SR = QR = 46°
representing the value of arc ST by x
therefore,
46+46+x+x = 360
92 +2x = 360
2x = 360-92
2x = 268
divide both sides by 2
x = 268/2
x = 134°
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Find the number of different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together (i.e. maximum two Es next to each other).
Answers
The eight letters in the word DECEIVED may be arranged in 4200 distinct ways, with two Ds grouped together and three Es not all together.
The following approach may be used to determine how many different ways there are for the eight letters in the word DECEIVED to be arranged such that two Ds are together and three Es are not altogether:
Treat the two Ds as a single object, which we can call DD. Now we have 7 objects to arrange: DD, E, E, C, V, I, and E.First, we count the total number of arrangements of these 7 objects, without considering any restrictions. This is simply the number of permutations of 7 objects, which is 7! = 5040.Next, we count the number of arrangements in which the three Es are all together. We can treat the three Es as a single object, which we can call EEE. Now we have 6 objects to arrange: DD, EEE, C, V, I, and an extra E. The number of arrangements of these objects is 6!, since we can treat the EEE as a single object.However, we have overcounted the arrangements in which the two Es are together with the EEE object. To correct for this, we can treat the two Es as a single object, which we can call EE. Now we have 5 objects to arrange: DD, EEE, EE, C, V, and I. The number of arrangements of these objects is 5!, since we can treat the EEE and EE as single objects.Therefore, the number of arrangements in which the three Es are not all together is the difference between the total number of arrangements and the number of arrangements in which the three Es are all together, minus the number of arrangements in which the two Es are together with the EEE object:7! - 6! - 5! = 5040 - 720 - 120 = 4200
Therefore, there are 4200 different arrangements of the 8 letters in the word DECEIVED, in which two Ds are together and the three Es are not all together.
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the libarian tracked how many books she checked out on selected days in January and Feburary .She displayed her information in the two dot plots shown. Find the median, mode and range for both dot plots.
Answers
The median, mode and range for both dot plots are:
Median = 7.5 and 5Mode = 7 and 8 & 4 and 5Range = 3 and 7Finding the median, mode and range for both dot plots.The median
This is the middle value
From the dot plots, we have the middle values to be
Group A = (7 + 8)/2 = 7.5
Group B = 5
So, we have
Median Group A = 7.5
Median Group B = 5
The mode
This is the number of books with the highest dots
From the dot plots, we have the modal values to be
Mode Group A = 7 and 8
Mode Group B = 4 and 5
The range
This is the difference between the smallest and highest number of books with the highest dots
From the dot plots, we have the range to be
Group A = 9 - 6 = 3
Group B = 10 - 3 = 7
So, we have
Range Group A = 3
Range Group B = 7
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In the 1992 Winter Olympic trials, John Jennings pushed the USA bobsled with a force of 110 N at an angle of 42with the horizontal. Find the horizontal and vertical components of the force
Round to the nearest hundredth!!!!!!
Answers
The horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.
How to determine the horizontal and vertical components of the forceThe force can be broken down into its horizontal and vertical components using trigonometry.
Horizontal component:
cos(42) = adjacent/hypotenuse
adjacent = cos(42) * 110 N
adjacent ≈ 80.34 N
Vertical component:
sin(42) = opposite/hypotenuse
opposite = sin(42) * 110 N
opposite ≈ 74.62 N
Therefore, the horizontal component of the force is approximately 80.34 N, and the vertical component of the force is approximately 74.62 N.
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Cuantos subconjuntos tiene A={a, r, i, t, m, e, t, i, c, a}
Answers
The number of subsets that the set has are 128 subsets.
How to find the number of subsets?First, let's remove the duplicates from the set A. The distinct elements in set A are:
A = {a, r, i, t, m, e, c}
Now, we can find the number of subsets. For each element in the set, we have two choices: either it is included in the subset, or it is not. Therefore, there are 2^n subsets for a set with n distinct elements.
In our case, n = 7, so there are 2^7 = 128 subsets for the given set A.
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a) Calculate the scale factor from shape A to shape B. b) Find the value of t. Give each answer as an integer or as a fraction in its simplest form.
Answers
80% or a dilation rate of .8
t = 5.6 cm
Explanation
Take your similar side measurement of your image and divide it by the pre image to get your dilation rate
4 / 5 = .8
12 / 15 = .8
.8 is your dilation rate
Your unknown “t” can be found using
7 cm x .8 dilation rate = 5.6 cm
Answer:
a) The scale factor is [tex]\frac{4}{5}[/tex]
b) [tex]t=5\frac{3}{5}[/tex]
Step-by-step explanation:
The scale factor from shape A to shape B is the value that is multiplied by the side measures of shape A to arrive at the side measures of shape B.
In other words, 5 times a certain value is 4, 15 times a certain value is 12. and 7 times a certain value is t.
Let's start by calling our "certain value" k.
[tex]5k=4=\\k=\frac{4}{5}[/tex]
Let's check 15 to make sure k is 4/5, like so:
[tex]15(\frac{4}{5})=\\\frac{60}{5} =\\12[/tex]
Since 15 times 4/5 is twelve, our initial answer was correct.
So, the scale factor, or k, is 4/5.
Following this logic, we know that 7 multiplied by the scale factor is equal to t.
Let's set up an equation and solve for t:
[tex]7(\frac{4}{5} )=t=\\\frac{28}{5} =t=\\5\frac{3}{5} =t[/tex]
So, [tex]t=5\frac{3}{5}[/tex]
Use the properties of logarithms to write the logarithm in terms of
log5(2) and log5(7).
The logarithm is
log5(98)
Answers
By using the properties of logarithms, The logarithm "log₅(98)" can be written as log₅(2) + log₅(7) + log₅(7).
We use the "product' and "quotient" logarithmic identities to write log₅(98) in terms of log₅(2) and log₅(7):
⇒ logₐ(b × c) = logₐ(b) + logₐ(c) ....(product rule)
⇒ logₐ(b/c) = logₐ(b) - logₐ(c) ...(quotient rule)
First, we write the number "98" as the product of 2 and 7, which is :
⇒ log₅(98) = log₅(2 × 7 × 7),
Using the product rule, we can split this into three logarithms;
⇒ log₅(2 × 7 × 7) = log₅(2) + log₅(7) + log₅(7),
So, we have,
⇒ log₅(98) = log₅(2) + log₅(7) + log₅(7),
Therefore, log₅(98) is equal to log₅(2) + log₅(7) + log₅(7).
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The given question is incomplete, the complete question is
Use the properties of logarithms to write the logarithm in terms of log₅(2) and log₅(7).
The logarithm is log₅(98).
You pick a card at random.
4567
What is P(odd or less than 5)?
Answers
Answer:
9/13
Step-by-step explanation:
P(odd or less than 5) = number of odd cards + number of cards less than 5 / total number of cards
P(odd or less than 5) = (20 + 16) / 52
P(odd or less than 5) = 36 / 52
P(odd or less than 5) = 9 / 13
Therefore, the probability of picking an odd card or a card less than 5.
Answer is 9/13
Write as a logarithm with a base of 4. -4
Answers
Answer:
4 cannot be written as a logarithm with a base of 4. A logarithm is an exponent that tells us how many times we need to multiply a base by itself to get a certain number. For example, log2(8) = 3 because 2^3 = 8. We can write this as an equation: logb(x) = y means b^y = x.
-4 cannot be written as a logarithm with a base of 4 because there is no exponent that can make 4 equal to -4. In other words, there is no y such that 4^y = -4. This is because any positive number raised to any power will always be positive. Therefore, log4(-4) is undefined or does not exist.
Therefore, -4 cannot be written as a logarithm with a base of 4.
Step-by-step explanation:
Solve the system of equations using substitution. y = 3x y = 6x + 3 (2, 15) (1, 3) (−1, −3) (−2, −6)
Answers
We are given the system of equations:
y = 3x
y = 6x + 3
We can use substitution to solve this system. Since both equations are equal to y, we can set them equal to each other:
3x = 6x + 3
Subtracting 3x from both sides, we get:
0 = 3x + 3
Subtracting 3 from both sides, we get:
-3 = 3x
Dividing both sides by 3, we get:
x = -1
Now that we know x, we can use either equation to find y. Let's use the first equation:
y = 3x = 3(-1) = -3
Therefore, the solution to the system of equations is (-1, -3).
To check our solution, we can substitute these values back into both equations:
y = 3x gives us -3 = 3(-1), which is true
y = 6x + 3 gives us -3 = 6(-1) + 3, which is also true
Therefore, our solution is correct.
We can also plug in the other given points to check that they do not satisfy both equations, which means they are not solutions to the system.
1. Which set of ordered pairs DOES NOT represent a function?
a. (0, 1), (2,3), (3,4), (5,6)
b. (1, 1), (2, 2), (3,3), (4,4)
c. (1,4), (1, 5), (1,6), (1,8)
d. (0,7), (2, 4), (4,7), (5,7)
Answers
Answer:
C.
Step-by-step explanation:
because x value cannot be repeated in an ordered pair
Mohawk Skywalkers are iron workers who helped build skyscrapers, bridges, and other structures for over 120 years. Which of the following is a statistical question about the Mohawk Skywalkers?
A. How many construction sites has each of the current Mohawk Skywalkers worked on in their lifetime?
B. How many New York City skyscrapers were built with the help of Mohawk Skywalkers?
C. How many generations of the Martin family have worked as Mohawk Skywalkers?
D. How many Mohawk Skywalkers helped build the Empire State Building?
Answers
How many construction sites has each of the current Mohawk Skywalkers worked on in their lifetime? is a statistical question about the Mohawk Skywalkers. Option A.
What are statistical questions?A statistical question is a question that can be answered by collecting and analyzing data. It involves variability and asks about the distribution of a population, rather than just a single value or specific instance.
Option A is a statistical question because it asks about the variability of the number of construction sites each of the current Mohawk Skywalkers worked on in their lifetime.
Option B is also a statistical question as it asks about the distribution of New York City skyscrapers built with the help of Mohawk Skywalkers.
Option C is not a statistical question because it asks for a specific value, the number of generations of the Martin family who have worked as Mohawk Skywalkers, which does not involve variability or a population.
Option D is not a statistical question as it asks for a specific value, the number of Mohawk Skywalkers who helped build the Empire State Building, which does not involve variability or a population.
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Which of the following is equivalent to the quantity two thirds end quantity to the power of 2 times x?
the quantity four thirds end quantity to the power of x
the quantity four sixths end quantity to the power of x
the quantity four ninths end quantity to the power of x
the quantity three halves end quantity to the power of x
Answers
The equivalent expressions is solved to give the quantity four ninths end quantity to the power of x. Option C
What is an algebraic expression?An algebraic expression can be described as an expression that is made up of terms, factors, coefficient, variables and constants.
These expressions are also composed of mathematical operations.
Also note that index forms are mathematical forms used to represent numbers too large or too small.
From the information given, we have that;
(2/3)²⁽ˣ⁾
expand the bracket, we get;
(2/3)²ˣ
Find the square of both the numerator and denominator, we get;
(4/9)ˣ
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I need help with this
Answers
Answer: B
Step-by-step explanation: You can subtract 21 from 245 11 times but some will remain
Please help solving this
Quite urgent, thanks :)
Answers
The measure of arc angle QT is determined as 142 ⁰.
The measure of m∠STR is determined as 23⁰.
What is the measure of arc angle QT?The measure of angle subtended by the arc QT is calculated by applying the following formula.
Based on the angle of intersecting chord theorem, we will have the following equation.
m∠QST = ¹/₂( arc QT )
arc QT = 2 (m∠QST)
arc QT = 2 x 71⁰
arc QT = 142⁰
m∠STR = ¹/₂( arc SR )
m∠STR = ¹/₂ x 46⁰
m∠STR = 23⁰
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100 Points! Two multiple choice algebra questions. Photo attached. Thank you!
State the domain and range of the function.
Stats the end behavior of the function.
Answers
Answer:
7.D
8.A
Step-by-step explanation:
For the function f(x) = √x+2+5:
(D) D= {x|x≥2}, R= {y|y≥5}
The domain is restricted to x values greater than or equal to 2 because the function contains the square root of x+2, which cannot be negative. The range starts at y = 5 because the lowest possible output of the function is √2+2+5 = 5.
(A) f(x)+∞o as x→ +∞o; f(x) +∞ as x――∞
As x approaches positive infinity, the output of the function approaches infinity as well. As x approaches negative infinity, the function is undefined since it involves taking the square root of negative numbers. However, the limit of the function as x approaches negative infinity from the right is positive infinity.
Write a formula for the nth term of each sequence. first term 7 and common difference 15
Answers
As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.
what is sequence ?An ordered set of number with a pattern or rule regulating their values is referred to as a sequence in mathematics. A word is used to characterize each number in a sequence. There are many various kinds of sequences, but a few of the most popular ones are as follows: A common differential, or constant number, is added to the respective period to produce an arithmetic series, each term of which is obtained. One arithmetic series with a following differences of three is 1, 4, 7, 10, 13, etc.
given
Given an arithmetic series with a first term (a1) and a common difference (d), the formula for the nth term (an) is as follows:
[tex]a = a1 + (n - 1) * d[/tex]
In this instance, the common difference (d) is 15, and the first term (a1) is 7. When these values are added to the formula, we obtain:
[tex]a = 7 + (n - 1) * 15[/tex]
As a result, a = 7 + (n - 1) * 15 is the formula for the nth term of the series with first term 7 and common difference.
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From a standard deck of 52 cards, in how many ways can 7 cards be drawn?
Answers
there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.
How to solve the question?
The number of ways to draw 7 cards from a standard deck of 52 cards can be calculated using the combination formula, which is:
C(52, 7) = 52! / (7! * (52-7)!)
where "!" represents the factorial function.
To simplify this expression, we can use the property that n! / k! = n * (n-1) * (n-2) * ... * (n-k+1) for positive integers n and k such that k ≤ n.
Using this property, we can rewrite the above expression as:
C(52, 7) = (52 * 51 * 50 * 49 * 48 * 47 * 46) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
Simplifying this expression, we get:
C(52, 7) = 133,784,560
Therefore, there are 133,784,560 ways to draw 7 cards from a standard deck of 52 cards.
To understand why this is the case, we can think of each draw as a separate event with no replacement. The first card can be drawn in 52 ways, the second card can be drawn in 51 ways (since one card has already been drawn), the third card can be drawn in 50 ways (since two cards have already been drawn), and so on. Therefore, the total number of ways to draw 7 cards is the product of the number of ways to draw each individual card, which is 52 * 51 * 50 * 49 * 48 * 47 * 46. However, since the order in which the cards are drawn does not matter, we need to divide by the number of ways to arrange 7 cards, which is 7 * 6 * 5 * 4 * 3 * 2 * 1 (i.e., 7 factorial). This gives us the final answer of 133,784,560.
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please help me answer this
Answers
The ice rink is 14.42 units away from the origin and other solutions are added below
Completing the table of valuesFirst, we have the library at (7,8), which is 7 units to the right of the origin and 8 units up from the origin.
Next, we have the market at (3,6), which is 4 units to the left of the library (7-4=3) and 2 units down from the library (8-2=6).
Then, we have the bank at (3,8), which has the same x-coordinate as the market (3) and a y-coordinate of 8.
We have the school at (10,8), which has the same y-coordinate as the bank (8) and an x-coordinate of 10.
The pool is located at (7,3), which is 5 units down from the school (8-5=3) and 3 units to the left from the school (10-3=7).
Finally, the park is located at (7,1), which has the same x-coordinate as the pool (7) and a y-coordinate of 1.
The completed table is:
Point Ordered Pair (x, y)
Library (7,8)
Market (3,6)
Bank (3,8)
School (10,8)
Pool (7,3)
Park (7,1)
Bao's movements and distancesBao's new location can be found by moving 5 blocks down from his current location of (3,13) and then 2 blocks right.
This gives us the new coordinates of (5,8) for Boo.
The new location is 5 units right and 8 units up of the origin
To get to the baseball diamond, he traveled 3 blocks to the right from his starting point (3 - 3 = 0) and 8 blocks down (15 - 8 = 7), which gives us the new coordinates of (3, 15) for the baseball diamond.
Bao's starting point was (0, 7).
Bao's starting point can be found by moving 5 blocks to the left from his current location of (14, 13) and then 10 blocks down.
This gives us the new coordinates of (9,3) for Bao's starting point.
The distance between the ice rink and the origin can be found using the distance formula:
d = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, we have:
d = √((12 - 0)^2 + (8 - 0)^2) = √(144 + 64) = √(208) ≈ 14.42
So the ice rink is approximately 14.42 units away from the origin.
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Find the surface area of the figure. Round to the nearest hundredth when necessary.
Answers
The surface area of the cylinder is approximately 3015.93square inches when rounded to the nearest hundredth.
What is the Surface Area of a Cylinder?To find the surface area of a cylinder, we need to add the areas of the top and bottom circles, and the area of the lateral surface, which is the curved part of the cylinder.
The formula for the surface area of a cylinder is:
S.A. = 2πr² + 2πrh
where r is the radius of the cylinder, h is the height, and π is approximately equal to 3.14.
Given that the diameter is 32 inches, we can find the radius by dividing by 2:
r = d/2 = 32/2 = 16 inches
Now we can substitute the values into the formula and simplify:
S.A. = 2πr² + 2πrh
S.A. = 2π(16)² + 2π(16)(14)
S.A. = 2π(256) + 2π(224)
S.A. = 512π + 448π
S.A. = 960π
To approximate the answer to the nearest hundredth, we can use the value of π rounded to two decimal places (3.14):
S.A. ≈ 960(3.14)
S.A. ≈ 3015.93 square inches
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The surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.
How to evaluate the surface area of a cylinderThe surface area of a cylinder can be calculated using the formula:
Surface Area = 2πr² + 2πrh
Where r is the radius of the base of the cylinder, h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14159.
From the figure we have that:
r = 16 in
h = 14 in
surface area = 2 × 3.14 × 16 in × 16 in + 2 × 3.14 × 16 in × 14 in
surface area = 1607.68 in² + 1406.72 in²
surface area = 3014.40 in²
Therefore, the surface area of the cylinder figure is derived to be equal to 3014.40 square inches rounded to the nearest hundredth.
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