1) The permutation that is the next one in lexicographic order after (4, 6, 2, 7, 3, 1, 5) is (4, 6, 2, 7, 3, 5, 1). Therefore answer is a. (4, 6, 2, 7, 3, 5, 1).
2) The 5-subset from {1, 2, 3, 4, 5, 6, 7, 8, 9} that is the next one in lexicographic order after {2, 3, 7, 8, 9} is {2, 4, 7, 8, 9}. Therefore the answer is d. {2, 4, 7, 8, 9}.
The next permutation in lexicographic order is the one that comes immediately after the given permutation when the permutations are listed in numerical order. To find the next permutation, we need to find the rightmost pair of elements that are in decreasing order. In this case, that pair is (5, 1). We then need to find the smallest element to the right of 1 that is larger than 1, which is 3. We swap 1 and 3 to get (4, 6, 2, 7, 3, 5, 1).
To find the next 5-subset in lexicographic order, we need to find the rightmost element that can be increased. In this case, that element is 9. We then replace 9 with the smallest element to its right that is larger than 9, which is 4. We then need to rearrange the remaining elements in increasing order to get {2, 4, 7, 8, 9}.
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Select the correct answer. Camille is saving for a laptop that costs about $850. To model her savings plan and determine how many more months it will take her to reach her goal, she recently created this equation, where y represents the total amount saved and x represents the number of months. Which statement about her work is true?' Step Calculation Step 1: y = 80 + 70x Step 2: y − 80 = 80 + 70x − 80 Step 3: y − 80 = 70x Step 4: = Step 5: = x Step 6: = x Step 7: 11 = x A. Camille used the associative property in step 3. B. Camille used the multiplication property of equality in step 4. C. Camille used the subtraction property of equality in step 5. D. Camille used the substitution property in step 6.
Answer:
C. Camille used the subtraction property of equality in step 5.
Step-by-step explanation:
In step 2, Camille subtracted 80 from both sides of the equation. In step 3, she simplified the equation by combining like terms. In step 4, Camille divided both sides of the equation by 70 to isolate the variable x. In step 5, she subtracted y-80 from both sides of the equation to isolate x. In step 6, Camille simplified the equation by dividing both sides by -1/70. Finally, in step 7, she calculated the value of x.
Therefore, option C is the correct answer.
81x 1 please help !!!!!!1
Answer:
The answer would 81, LOLOLOLOL
Step-by-step explanation:
If Gretchen randomly chooses one of the boxed lunches, what is the probability that she will get a roast beef sandwich on wheat bread and popcorn in her box?
To calculate the probability of Gretchen getting a roast beef sandwich on wheat bread and popcorn in her boxed lunch, we need to know the total number of possible boxed lunch combinations and the number of boxed lunches that contain roast beef on wheat bread and popcorn.
Let's assume there are 4 different types of sandwiches available: roast beef on wheat bread, turkey on white bread, ham on rye bread, and vegetarian on whole wheat bread. Also, let's assume there are 3 different snack options available: popcorn, chips, and fruit.
If each boxed lunch contains one sandwich and one snack, then there are 4 x 3 = 12 possible boxed lunch combinations.
Out of these 12 combinations, we need to determine how many contain roast beef on wheat bread and popcorn. Let's say there are 2 boxed lunches that contain roast beef on wheat bread and popcorn.
Therefore, the probability of Gretchen randomly choosing a boxed lunch with roast beef on wheat bread and popcorn is 2/12, which simplifies to 1/6, or approximately 0.1667.
So, there is a 16.67% chance that Gretchen will get a roast beef sandwich on wheat bread and popcorn in her box.
Find the volume of this sphere use 3 for pi 2ft
The volume of the sphere is 32/3 cubic feet.
What is Volume ?
Volume is a measure of the amount of space that a three-dimensional object takes up. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.
To find the volume of a sphere, we use the formula:
V = (4/3) * pi * [tex]r^{3}[/tex]
where V is the volume of the sphere, pi is the constant pi (3.14...), and r is the radius of the sphere.
In this case, the radius of the sphere is given as 2ft. So, substituting this value into the formula, we get:
V = (4/3) * 3 * [tex](2ft)^3[/tex]
= (4/3) * 3 * 8[tex]ft ^ 3[/tex]
= 32/3 [tex]ft ^ 3[/tex]
Therefore, the volume of the sphere is 32/3 cubic feet.
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When x is 4 y is a equal to 20 what is the value of y when x is equal to 10
The value of y when x is equal to 10 is 60.
Describe value-Value in math is the numerical representation of a given quantity. It can be a literal number, a variable, or an expression. Values are used to solve equations, calculate statistics, and determine patterns. They can be used to measure physical quantities such as length, area, volume, and force. Values are also used to measure abstract concepts such as money, probability, and time. Values help us understand and make sense of the world around us.
The value of y when x is equal to 10 can be calculated by using y = mx + c, where m is the gradient and c is the y-intercept of the line. Using the given values, we can calculate the equation of the line to be y = 5x + 10.
Therefore, when x = 10, y = 5(10) + 10 = 60.
Therefore, the value of y when x is equal to 10 is 60.
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Please help me figure this out! Im working on a quiz, please simplify
Answer:
2/7 is the right answer
14 and 21 are both divisible by 7, their GCF, so if you divide the numerator and the denominator by 7, you get the fraction 2/7
The following data have been gathered for Syncronics, Inc.:
a. The July 31 bank balance was $4,000,
b. The bank statement included $65 in service charges.
c. There was an EFT deposit of $900 on the bank statement for the monthly rent from
the tenant.
d. Checks #541 and #543 for $205 and $320, respectively, were not among the canceled
checks returned with the statement, therefore the checks are outstanding.
e. The July 31 deposit of $350 did not appear on the bank statement
f. The bookkeeper had erroneously recorded a $50 check as $500. The check was
written to a vendor to pay- off an accounts payable.
g. Included with the canceled checks was a check written by Syncronize
Corporation for $200 which was deducted from Syncronics' account. .
h. The bank statement also included an NSF check written by Multimedia, Inc for a $460
payment on accounts receivable
i. The cash account showed a balance of $3,200 on July 31.
REQUIRED:
1. Prepare the July 31 bank reconciliation for Syncronics Inc.
2. Adjust the Cash Balance (using Journal Entries, T accounts, or the Accounting Equation)
·
After answering the provided question, we can conclude that Following expression the completion of the necessary journal entries, the T-account for Cash would show an adjusted balance of $2,575.
What is expression ?An expression in mathematics is a collection of representations, octal, and huge corporations that resemble a clear association or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include inclusion, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
Starting Balance: $4,000
Addition: $900 EFT deposit from tenant
Less: ($65) service charges
Less: ($460) NSF check
$4,375 in adjusted bank balance
Book Balance according to Company Records:
Starting Balance: $3,200
Addition: $350 deposit not yet recorded
($525) in outstanding checks [$205 + $320]
Less: Erroneous $500 check recorded: ($450) [$500 - $50]
$2,575 in Adjusted Book Balance
Bank Reconciliation: Modified $4,375 in bank balance
$2,575 in Adjusted Book Balance
The difference is $1,800. (overdraft)
a. Not yet recorded deposit:
Debit: $350 in cash
Credit: $350 in earnings
b. Uncollected checks:
Debit: $525 Accounts Payable
Credit: $525 in cash
c. Incorrectly recorded $500 check:
Debit: $450 Accounts Payable
Credit: $450 in cash
Following the completion of the necessary journal entries, the T-account for Cash would show an adjusted balance of $2,575.
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complete question
the following data gathered the latest details for Synchronic, Inc.:
A. The bank amount as of July 31 was $4,000.
a. There have been $65 in service fees on the bank statement.
c. The bank statement showed an EFT deposit of $900 for the tenant's monthly rent.
d. The cancelled checks that were included with the statement were not checks #541 and #543, which were for amounts of $205 and $320, respectively.
g. The $350 deposit made on July 31 did not show up on the bank statement.
f. A $50 cheque was mistakenly reported as $500 by the bookkeeper. A seller received the check as payment for a debt.
g. A check from Synchronize Corporation for $200 that was taken out of Synchronic' account was included with the cancelled checks.
h . An NSF check for a $460 payment to an account that was written by Multimedia, Inc. was also included in the bank statement.
i. As of July 31, the bank had a $3,200 balance in the cash account.
1. Complete the bank reconciliation for Synchronic, Inc. on July 31.
2. Modify the company's cash position.
Need help will give brainliest and 5 stars for the fastest answers with work.
The point (2, 2) would end up at the point (1, 1) after the transformations.
Describe Function?Functions can be represented in different ways, including graphs, tables, and equations. A graph of a function is a visual representation of the relation between the inputs and outputs, usually plotted on a coordinate plane. A table of values lists the inputs and corresponding outputs of a function. An equation of a function expresses the rule for calculating the output in terms of the input variable.
To sketch the graph of the new function h(x), we can start by considering the effect of each transformation on the original function f(x).
First, we have a horizontal shift of 1 unit to the left, since we are subtracting 1 from the argument of f(x). This means that the graph of f(x+1) will be shifted 1 unit to the left compared to the graph of f(x).
Next, we have a vertical stretch by a factor of 2, since we are multiplying the output of f(x+1) by 2. This means that the graph of 2f(x+1) will be twice as tall as the graph of f(x+1).
Finally, we have a vertical shift downwards by 3 units, since we are subtracting 3 from the output of 2f(x+1). This means that the graph of h(x) will be shifted 3 units downwards compared to the graph of 2f(x+1).
To find where the point (2, 2) ends up after these transformations, we can first apply the horizontal shift of 1 unit to the left, which gives us the point (1, 2). Next, we apply the vertical stretch by a factor of 2, which gives us the point (1, 4). Finally, we apply the vertical shift downwards by 3 units, which gives us the point (1, 1).
Therefore, the point (2, 2) would end up at the point (1, 1) after the transformations.
To sketch the graph of h(x), we can start with the graph of f(x) and shift it 1 unit to the left, stretch it vertically by a factor of 2, and shift it 3 units downwards. The resulting graph will have the same shape as the graph of f(x), but will be shifted and scaled as described above. The point (1, 1) will be on this graph as well.
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A. Regardless of the values of b and c, the point (-2,2) is included in the curve of g(x).
B. On the graph of h(x), the point (2,2) would be changed into the point (2,1).
What is graph?A graph is a graphical representation of data, functions, or variable connections. It is a method of displaying information that is simple to analyse and comprehend.
Graphs are widely used in a variety of disciplines, including science, economics, business, engineering, and others. They make it simpler for researchers and analysts to visualise data and identify trends or patterns, allowing them to draw conclusions and make educated choices based on the data.
A. To include the spot (-2,2), we must shift the f(x) graph two units to the right and two units up. So far, we have:
g(x) = a f(x - (-2)) + 2
g(x) = a f(x + 2) + 2
We must now determine the worth of "a." Because the point (3,4) on the f(x) graph is transferred to the point (2,2) on the g(x) graph, we have:
g(3) = a f(3 + 2) + 2 = 2
4a + 2 = 2
4a = 0
a = 0
Therefore, the function g(x) is:
g(x) = 0 f(x + 2) + 2
g(x) = 2
As a result, independent of the values of b and c, the point (-2,2) is included in the graph of g(x).
B. The function h(x) has a slope of 2 and a y-intercept of -1. We plug x=2 into h(x) to determine where the point (2,2) would end up after the transformations and get:
h(2) = 2(2+1)-3 = 1
As a result, the point (2,2) on the graph of h(x) would be changed to the point (2,1).
The transformations applied to f(x) to produce h(x) are a one-unit horizontal shift to the left (x+1), a two-unit vertical stretch (2(x+1)), and a three-unit vertical shift downwards (-3).
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Complete question and graph attached below,
100 points!! brainliest.
The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:
Angle 1 is an acute angle that is adjacent to angle 2.Angle 2 is a right angle formed by the intersection of lines m and n.Angle 3 is an obtuse angle that is adjacent to angle 2.Angle 4 is a vertical angle to angle 2 and is congruent to angle 2.Angle 5 is an acute angle that is adjacent to angle 4.Angle 6 is a straight angle formed by the collinear extension of lines m and n.
Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.
Answer:
If the scale factor is -5, it means that the new image will be a reflection across the origin (negative scale factor means reflection) and enlarged by a factor of 5.If the scale factor is 1/2, it means that the new image will be half the size of the original image.If the scale factor is 0.4, it means that the new image will be 40% of the size of the original image.If the scale factor is 3/2, it means that the new image will be enlarged by a factor of 3/2 or 1.5 times the size of the original image.If the scale factor is 1, it means that the new image will be the same size as the original image.II. The diagram shows two intersecting lines, labeled line m and line n. Line m intersects line n at a point labeled point P. There are several angles labeled in the diagram:Angle 1 is an acute angle that is adjacent to angle 2.Angle 2 is a right angle formed by the intersection of lines m and n.Angle 3 is an obtuse angle that is adjacent to angle 2.Angle 4 is a vertical angle to angle 2 and is congruent to angle 2.Angle 5 is an acute angle that is adjacent to angle 4.Angle 6 is a straight angle formed by the collinear extension of lines m and n.Note that angles 1, 3, 5 are all alternate interior angles formed by the intersection of line m and line n.
Step-by-step explanation:
What is the cost price if the selling price = $980 and the loss = 12%?
Therefore, the cost price is $1113.64 if the selling price is $980 and the loss is 12%.
What is cost price?Cost price (also known as CP) is the amount of money that is required to produce or purchase a particular product or service. It includes all the expenses incurred in the production or purchase of a product, such as the cost of raw materials, labor, transportation, rent, and other overhead expenses. The cost price is an important factor in determining the profit margin of a business, as it is used to calculate the selling price of a product or service. In general, the cost price is the amount that a seller pays to acquire a product, while the selling price is the amount that a buyer pays to purchase the same product.
Let's assume that the cost price is "C".
We know that the selling price (S) is $980, and the loss percentage is 12%.
We can use the formula for calculating the cost price:
C = S / (1 - Loss%)
where Loss% is expressed as a decimal (i.e., 12% = 0.12).
Substituting the values, we have:
C = $980 / (1 - 0.12)
C = $980 / 0.88
C = $1113.64
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Think of letters A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z. if BAD=10,DAC=,11andCGI=22 what is PAD?
A quick quiz consists of a multiple-choice question with 5 possible answers followed by a multiple-choice question with 6 possible answers. If both questions are answered with random guesses, find the probability that both responses are correct.
The probability that the submitted responses to the questions were correct will be 2/11.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
Mathematics' study of random events is known as probability, and there are four primary types of probability: axiomatic, classical, empirical, and subjective.
So, the probability formula is as follows:
Probability = Favourable events/Total events
Now, insert values as follows:
Probability = Favourable events/Total events
Probability = 1+1/5+6
Probability = 2/11
Therefore, the probability that the submitted responses to the questions were correct will be 2/11.
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(Scale Factor HC)
A rectangular oil painting is 14 inches wide and 24 inches long. A museum wants to create a larger print of the painting using a scale factor of 3.
Part A: What are the dimensions of the print, in feet? Show every step of your work. (2 points)
Part B: What is the area of the print, in square feet? Show every step of your work. (2 points)
Part A:
First, we need to find the dimensions of the print by multiplying the dimensions of the original painting by the scale factor of 3.
The width of the print is 14 inches x 3 = 42 inches
The length of the print is 24 inches x 3 = 72 inches
To convert these dimensions into feet, we need to divide by 12 (since there are 12 inches in a foot):
Width of print = 42 inches / 12 = 3.5 feet
Length of print = 72 inches / 12 = 6 feet
Therefore, the dimensions of the print are 3.5 feet by 6 feet.
Part B:
To find the area of the print, we need to multiply the width by the length:
Area of print = (3.5 feet) x (6 feet) = 21 square feet
Therefore, the area of the print is 21 square feet
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Explain why domain restrictions are necessary to create inverse trigonometric functions rather than relations.
This would make the inverse function a relation rather than a function, and it would fail the vertical line test.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It focuses on the study of trigonometric functions, which are functions that relate the angles of a triangle to the ratios of the lengths of its sides.
Inverse trigonometric functions are used to find the angle whose trigonometric ratio is given. For example, if we know that sin θ = 1/2, we can use the inverse sine function to find the angle θ, which is sin^-1(1/2) = 30°.
However, inverse functions must be functions, meaning that they must pass the vertical line test, where each input (x) produces exactly one output (y). To ensure that inverse trigonometric functions meet this criteria, we need to restrict the domain of the original trigonometric functions.
Trigonometric functions are not one-to-one functions, which means that multiple angles can produce the same value of a trigonometric ratio. For example, sin 30° = sin 150° = 1/2. If we were to define the inverse sine function as the inverse of the sin function without a domain restriction, we would have multiple possible outputs for the same input.
Therefore, this would make the inverse function a relation rather than a function, and it would fail the vertical line test.
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Solve for x. 3(3x - 8) - 12x < 30
- x < -18
- x > -18
- x < 18
- x > 18
Answer: x>-18
Step-by-step explanation:
simplify
9x-24-12x<30
-3x-24<30
-3x>54
-x>18
x>-18
a jar contains 30 coins, all dimes and quarters. the value of the coins is $4.80. how many of each coin is in the jar
Answer:
Step-by-step explanation:
1 quarter = 25 cents
1 dime = 10 cents
Let
q = the number of quarters, q>=0, q is integer
d = the number of dimes, d>=0, d is integ
30 coins totaling $4.80 = 480 cents:
q + d = 30
25q + 10d = 480
q = 12 quarters
d = 18 dimes
12 quarters and 18 dimes.
Answer:
Let x be the number of dimes in the jar.
Then the number of quarters in the jar would be 30 - x.
The total value of the dimes in the jar would be 0.10x, and the total value of the quarters would be 0.25(30 - x) = 7.50 - 0.25x.
We know that the total value of the coins is $4.80, so we can set up the equation:
0.10x + 7.50 - 0.25x = 4.80
Simplifying and solving for x, we get:
0.15x = 2.70
x = 18
Therefore, there are 18 dimes and 30 - 18 = 12 quarters in the jar.
Step-by-step explanation:
42 E This histogram shows battery life (in hours) of 40 batteries of the same brand. When reading a histogram, it is important to look at the shape, center and spread of the data. Relative Frequency 0.30 100 110 120 130 Battery Life (hours) 140 150 Complete the following statements about the shape of the data shown.
A. The distribution of the data is approximately
B. The mean battery life is
The answer of the given question based on the histogram that shows battery life is, (A). The distribution of the data is approximately symmetric. (B). The mean battery life is around 125 hours.
What is Data distribution?Data distribution refers to pattern or shape of how data is spread out or distributed over range of values. It is important to understand distribution of data because it can provide insights into nature of the data and inform statistical analysis.
There are several ways to describe distribution of data, including measures of center (like mean, median, and mode) and measures of spread (like range, variance, and standard deviation)
A. The distribution of the data is approximately symmetric.
B. The mean battery life can be estimated by finding the center of the histogram, which appears to be around 125 hours. However, without knowing the exact bin widths or the midpoint of each bin, it is difficult to estimate the mean precisely.
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Based on the histogram that displays energy life, the following is the response to the question:
a). The data are distributed in a roughly symmetrical manner.
b). An average charge lasts for about 125 hours.
What is Data distribution?Data distribution describes the way that data is dispersed or distributed across a variety of values. Understanding data distribution is crucial because it can shed light on the character of the data and help with statistical analysis.
Measures of the center (like mean, median, and mode) and measures of spread are two methods to describe data distribution. (like range, variance, and standard deviation).
A). The facts are distributed in a roughly symmetrical manner.
B). You can determine the average battery life by locating the histogram's center, which looks to be 125 hours.
It is challenging to calculate the mean exactly without knowing the precise bin widths or the midpoint of each bin, though.
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The image of the question attached below,
A motorboat travels 205 kilometers in 5 hours going upstream. It travels 275 kilometers going downstream in the same amount of time. What is the rate of the
boat in still water and what is the rate of the current?
Answer:
205:275
300:
Find the answer
A parabola opening up or down has vertex (0, 1) and passes through (8, 17). Write its
equation in vertex form.
Answer: y = (1/4)x^2 + 1
Step-by-step explanation:
The equation of a parabola in vertex form is given by:
y = a(x-h)^2 + k
Where (h,k) is the vertex of the parabola and "a" is a coefficient that determines the shape of the parabola.
In this case, the vertex is given as (0,1), so h=0 and k=1. Also, the parabola passes through the point (8,17), which means that when x=8, y=17. We can use this information to solve for "a".
Substituting the values of h, k, x, and y in the equation, we get:
17 = a(8-0)^2 + 1
Simplifying this equation, we get:
17 - 1 = 64a
16 = 64a
a = 16/64
a = 1/4
Now that we know the value of "a", we can substitute it in the vertex form equation to get the final equation of the parabola:
y = (1/4)(x-0)^2 + 1
Simplifying this equation, we get:
y = (1/4)x^2 + 1
Therefore, the equation of the parabola in vertex form is y = (1/4)x^2 + 1.
Explanation:
We start with the general equation of a parabola in vertex form and substitute the given values of the vertex and the point that the parabola passes through. Then, we solve for the coefficient "a" by simplifying the resulting equation. Once we have the value of "a", we substitute it in the vertex form equation to obtain the final equation of the parabola.
Which graph shows a proportional relationship? (Check Screenshot)
Also I need answers ASAP, I’m already behind in this subject :(
7.
Kermit solved the equation below and got x = 5, but he isn't sure he solved correctly.
Show Kermit how he can check his equation using his solution. Let him know if he
solved the equation correctly or not, explaining how you know.
5(x - 4) + 20 = 14
The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
To check if Kermit's solution is correct, we can substitute x = 5 back into the original equation and see if it makes a true statement:
5(x - 4) + 20 = 14
5(5 - 4) + 20 = 14
5(1) + 20 = 14
25 ≠ 14
Hence, The statement "25 = 14" is clearly false, so Kermit's solution of x = 5 is not correct. Therefore, Kermit made a mistake in solving the equation.
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what signs are sin(100°) and tan(100°)?
A)sin(100°) >0 and tan (100°) < 0
B) they both positive
c) sin(100°) < 0 and tan (100°) > 0
d) they both negative
Answer:
A)sin(100°) >0 and tan (100°) < 0
Step-by-step explanation:
You want to know the signs of sin(100°) and tan(100°).
Quadrant100° is an angle in the 2nd quadrant, where angles between 90° and 180° lie.
In that quadrant, the sine function is positive, and the cosine function is negative. The tangent is the ratio of sine to cosine, so the tangent is negative in the 2nd quadrant.
sin(100°) > 0tan(100°) < 0__
Additional comment
Of course, your calculator can help you figure this out. Be sure it is in degrees mode.
The second attachment shows you sine is positive above the x-axis; cosine is positive to the right of the y-axis. Everything else derives from this.
The vertex of a parabola is (0, 0) and the focus is(1/8,0).What is the equation of the parabola?
The equation of the parabola is
[tex]y = \frac{1}{32} {x}^{2} [/tex]
What is the vertex form of the equation of a parabola?
[tex]y = a {(x - h)}^{2} + k[/tex]
where (h, k) is the vertex and 'a' is a constant that determines the shape of the parabola. For a parabola with a horizontal axis of symmetry (opening to the right or left), the focus is (h + c, k), where c is the distance from the vertex to the focus, and the directrix is the line x = h - c.
Given,the vertex of a parabola is (0, 0) and the focus is(1/8,0).
We want to find equation of the parabola.
Given by In this problem, the vertex is at (0,0) which means h=0 and k=0. Also, the focus is at (1/8,0) which means c=1/8. So, the directrix is the line x = -1/8.
Since the parabola opens to the right, the equation of the parabola can be written as:[tex]y = {(x - 0)}^{2} + 0[/tex]
or simply: [tex]y = a {x}^{2} [/tex]
To find the value of 'a', we need to use the distances formula between the vertex and the focus:
[tex]c = \frac{1}{8} = \sqrt{ \frac{4a}{2} } \\ a = \frac{1}{32} [/tex]
Therefore, the equation of the parabola is:
[tex]y = \frac{1}{32} {x}^{2} [/tex]
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A rectangular park measuring 200m by 100m has a 2m flower border constructed around the two longer sides and one shorter side. Also a circular fish pond of diameter 20m is in the center of the park and the remainder of the park is grassland. Calculate the following areas correct to the nearest square meters. a) the fish pond. b) the flower borders. c) the grassland. d) the perimeter of the park.
Step-by-step explanation:
a) The area of the fish pond is given by the formula:
Area = πr^2
where r is the radius of the pond (which is half of the diameter). So, in this case, r = 10m.
Area = π(10m)^2
Area = 100π m^2
Area ≈ 314 m^2 (rounded to the nearest square meter)
b) The flower border has a width of 2m on the two longer sides and one shorter side of the rectangular park. So, we need to find the area of three strips of land, each of which is 2m wide and has a different length.
The length of the two longer sides is 200m, so the total length of the two strips along these sides is:
2 × 200m = 400m
The length of the shorter side is 100m, but we need to subtract the width of the fish pond (which is 20m) from it, since the flower border does not extend around the pond. So, the length of the strip along this side is:
100m - 20m = 80m
Therefore, the total area of the flower border is:
2m × 400m + 2m × 80m = 960m^2
c) The grassland is the remaining area of the rectangular park after we subtract the area of the fish pond and the flower border from the total area of the park.
The total area of the park is:
200m × 100m = 20,000m^2
The area of the fish pond is:
π(10m)^2 ≈ 314m^2
The area of the flower border is:
960m^2
So, the area of the grassland is:
20,000m^2 - 314m^2 - 960m^2 = 18,726m^2
d) The perimeter of the park is the sum of the lengths of all its sides.
The two longer sides have a length of 200m each, but we need to add the lengths of the two flower borders (each of which is 2m wide), so the total length of the two longer sides is:
200m + 2m + 2m = 204m
The shorter side has a length of 100m, but we need to add the length of the flower border (which is 2m wide), so the total length of the shorter side is:
100m + 2m = 102m
The perimeter of the park is:
204m + 204m + 102m = 510m
Therefore, the perimeter of the park is 510 meters.
A baker uses food coloring to color cake batter he needs 4 1/8 ounces of green food coloring the baker only has 2 1/2 ounces how much more green food coloring does he need is the baker only find one ounce of food coloring at the store how many more ounces does the baker need
The baker needs 13/8 more ounces of green food color.
What is Subtraction?Subtraction can be done for any numbers or algebraic expressions. It is the process of taking out certain value from a given amount of number.
The process of subtraction can also be termed as finding difference.
Given that,
A baker uses food coloring to color cake batter.
He needs 4 1/8 ounces of green food coloring.
Total amount of food color needed for the batter = 4 1/8 ounces
= (4 × 8 + 1) / 8
= 33/8 ounces
The baker only has 2 1/2 ounces.
Amount of food color he has = 2 1/2 ounces
= (2 × 2 + 1) / 2
= 5/2 ounces
Amount of color he need = 33/8 ounces - 5/2 ounces
= 13/8 ounces
= 13/8 ounces
Hence the baker needs 13/8 more ounces of color.
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What is the surface area, in square centimeters, of the toy box?
The surface area of the toy box is 846 [tex]cm^2[/tex].
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here the given toy is form of rectangular prism.
Length = 15 cm , width w = 9 cm and height h = 12 cm
Surface area of the rectangular prism is,
=> A = 2( lw+ wh+ lh) square unit.
=> A = 2( 15*9+9*12+12*15)
=> A = 2(135+108+180)
=> A = 2(423)
=> A= 846 [tex]cm^2[/tex].
Hence surface area of the rectangular prism is 846 [tex]cm^2[/tex].
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Find the measure of X
Answer:
X=18.88
Step-by-step explanation:
This is a 90 degree triangle which means that you can use Sin, Cos, Or Tan. In this case you have to use Tan as you don't know the hypotenuse length. Which means you would set up an equation that looks like Tan(42°)=17/x as tangent is opposite over adjacent. Then if you were to solve for X eventually you'll get X= 17/Tan(42°) and if you plug it in a calculator you would get that X= 18.88 or 19 if you round to a whole number.
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
Pyramid ABCD is similar to pyramid WXYZ. The perimeter of triangle BCD is 16, and the perimeter of triangle XYZ is 32. What is the scale factor
to dilate ABCD to WXYZ?
The scale factor is
N
Answer:
The scale factor to dilate ABCD to WXYZ is 1/sqrt(2) or (sqrt(2))/2.
The scale factor to dilate ABCD to WXYZ is k = 2.
Given data:
To find the scale factor between two similar figures, compare the corresponding side lengths.
The perimeter of triangle BCD is 16 and the perimeter of triangle XYZ is 32. Since corresponding sides of similar triangles are proportional, the ratio of their perimeters to determine the scale factor.
The scale factor is calculated by dividing the perimeter of triangle XYZ by the perimeter of triangle BCD:
Scale factor = Perimeter of XYZ / Perimeter of BCD
Scale factor = 32 / 16 = 2
Hence, the scale factor to dilate pyramid ABCD to WXYZ is 2.
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Jerry and his friends are celebrating Jerry's birthday at Adventure Zone, which has trampolines, mini golf, laser tag, and an arcade. Jerry's mom gives 14 arcade tokens to each kid at the party. In all, she gives out 126 tokens.
Zendaya randomly selected marbles from a bag during a probability experiment. She completed 50 rounds and recorded the results in the table shown. Based on the information from her experiment, in how many of the next 200 rounds would she pick a blue marble?
We can expect her to pick about 70 blue marbles in the next 200 rounds.
How many of the next 200 rounds would she pick a blue marble?We must divide the number of blue marbles by the total number of marbles to determine the likelihood of selecting a blue marble in a single round:
P(blue) = 14/40 = 7/20
Since the experiment has been conducted 50 times, we may anticipate that the proportion of blue marbles will eventually be around 7/20. This suggests that in the subsequent 200 rounds, Zendaya will likely choose to focus on:
70 blue marbles result from P(blue) 200 = (7/20) 200.
So, in the following 200 rounds, we can anticipate her choosing roughly 70 blue marbles.
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