We are arranging ten beads in different formations (call them A, B, C, D, E, F, G, H, I, J). You may use any of the techniques introduced from the week's material.
a. If we put them in a line with no other restrictions, how many ways are there to arrange the beads?
b. If we put them in a line, but B must be placed somewhere the right (but not necessarily immediately next to) of A and also somewhere to the left (but not necessarily immediately next to) C, how many ways are there to arrange the kids?
c. If we arrange the beads in a necklace with no other restrictions, how many ways are there to arrange the beads?
d. If we arrange the beads in two necklaces of five beads each, how many ways are there to arrange the beads?
Answers
a. The number of ways to arrange the ten beads in a line with no other restrictions is 10! (10 factorial), which is equal to 3,628,800.
Determine the number of ways?When arranging the beads in a line with no restrictions, the first bead can be chosen in 10 ways, the second bead in 9 ways (as one bead has already been placed), the third bead in 8 ways, and so on until the last bead, which has only 1 choice.
Therefore, the total number of arrangements is the product of all these choices, which is 10! = 10 × 9 × 8 × ... × 2 × 1 = 3,628,800.
b. If B must be placed somewhere to the right of A and also somewhere to the left of C, the arrangement of the beads is restricted. In this case, there are 8! (8 factorial) ways to arrange the remaining 8 beads.
Determine the number of ways?Since B must be placed somewhere to the right of A and also somewhere to the left of C, we can treat A, B, and C as a single unit. This unit can be arranged in 3! = 3 × 2 × 1 = 6 ways (ABC, ACB, BAC, BCA, CAB, CBA). The remaining 8 beads can then be arranged in 8! ways.
Therefore, the total number of arrangements is 6 × 8! = 241,920.
c. When arranging the beads in a necklace with no other restrictions, the total number of ways is (10!)/(10) = 9!, which is equal to 362,880.
Determine the number of ways to arrange the beads?Arranging the beads in a necklace means that rotations of the same arrangement are considered equivalent.
So, we divide the total number of linear arrangements (10!) by the number of possible rotations (10). This gives us (10!)/(10) = 9!.
d. If we arrange the beads in two necklaces of five beads each, the number of ways is [(10!)/(2 * 5!)]/2, which simplifies to 181,440.
Determine the number of ways?Since each necklace contains five beads, we divide the total number of linear arrangements of 10 beads (10!) by the number of ways we can arrange the beads within each necklace (5!).
However, we divide by 2 since the order of the two necklaces does not matter.
Therefore, the total number of ways to arrange the beads in two necklaces of five beads each is [(10!)/(2 * 5!)]/2 = 181,440.
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Related Questions
When planning a well-balanced long hair design, consider the proportional relationships between size, shape, texture and:
Answers
A well-balanced long hair design should consider the proportional relationships between size, shape, texture, and color to create a harmonious and visually pleasing hairstyle that flatters the client's features and personal style.
When planning a well-balanced long hair design, it is important to consider the proportional relationships between size, shape, texture, and color. These four elements work together to create a harmonious and visually pleasing hairstyle.
Size refers to the overall scale of the hairstyle, which can range from small and delicate to large and voluminous. It's important to consider the size of the client's head and face, as well as the desired level of impact.
Shape refers to the outline or silhouette of the hairstyle, which can be angular or rounded, symmetrical or asymmetrical. The shape should be chosen to flatter the client's face shape and features, as well as to create a balanced overall look.
Texture refers to the surface quality of the hair, which can be smooth or rough, sleek or tousled. Texture can be used to add interest and movement to the hairstyle, and should be chosen to complement the client's natural hair texture and the overall design.
Color refers to the hue, saturation, and tone of the hair, which can range from natural to bold and vibrant. Color can be used to enhance the shape and texture of the hairstyle, and should be chosen to flatter the client's skin tone and personal style.
In summary, a well-balanced long hair design should consider the proportional relationships between size, shape, texture, and color to create a harmonious and visually pleasing hairstyle that flatters the client's features and personal style.
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write down the rational number
whose numerator = 8 , denominator = 9
Answers
Answer:
8/9
Step-by-step explanation:
8 numerator
______________
9 denominator
david has d books, which is 3 times as many as jeff and i as many as paula. how many books do the three of them have altogether, in terms of d?
Answers
David, Jeff, and Paula have (7d)/3 books.
To find out how many books David, Jeff, and Paula have altogether in terms of d, we can use the given information as follows:
1. David has d books.
2. David has 3 times as many books as Jeff, so Jeff has d/3 books.
3. David has the same number of books as Paula, so Paula also has d books.
Now, to find the total number of books for all three of them, we simply add the number of books each person has:
Total books = David's books + Jeff's books + Paula's books
Total books = d + d/3 + d
To combine these terms, we can find a common denominator (in this case, 3):
Total books = (3d + d + 3d) / 3
Now, we can simplify the expression:
Total books = (7d) / 3
So, altogether, David, Jeff, and Paula have (7d)/3 books in terms of d.
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5. The scale on the map of a park is 5 in.: 3 mi. The distance from the entrance of the park to the playground is 9 miles. How many inches long is the distance on the map?
Answers
Answer:
15 inches
Step-by-step explanation:
Here, we have a scale of 5 inches to 3 miles
We have 9 miles here, we now want to get the amount of corresponding inches
Let the corresponding inches be x
5 inches to 3 miles
x inches to 9 miles
That means ;
x * 3 = 5.* 9
x = 45/3
x = 15 inches
Mr. King left 1/2 of his estate to his wife and 1/3 of the remainder to his granddaughter. What part of his estate is not accounted for in this statement?
Answers
Answer:
3/5 of his estate is not accounted for.
Step-by-step explanation:
You can figure out by adding the two fractions together:
1/2 + 1/3 = 2/5.
That means there is still 3/5 of the estate remaining.
Brainliest please! I am so close to getting my next rating! I would really appreciate it, and it would make my day! Thank you so much, and have a wonderful rest of your day!
true or false: every set of 15 socks chosen among 14 pairs of socks contains at least one matched pair. explain why.
Answers
The statement of the given question is True.
True. This is because there are only 14 different types of socks to choose from, so if you choose 15 socks, there must be at least one pair of socks that match. This is known as the Pigeonhole Principle, which states that if there are more pigeons than pigeonholes, at least one pigeonhole must contain more than one pigeon. In this case, the socks are the pigeons and the different types of socks are the pigeonholes.
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Help me with this question please
Answers
An associate in a scatter plot tells us the relation between the two variables. The points that are true about the given scatter plot are C and F.
What is an associate?An associate in a scatter plot tells us the relation between the two variables. There are 4 types of associates:
Positive associate: If the value of one variable is increasing the value of another increase as well, but the relation is not linear.
Negative associate: If the value of one variable is decreasing with the value of another increasing as well, but the relation is not linear.
Linear Associate: If the value of one is dependent on the other such that they follow a function of line, and all the data points are on that function line.
Non-linear Associate: If the data points of the plot are scattered and random, such that there is no relationship between the points.
The points that are true about the given scatter plot are:
C.) There appears to be a positive association.
F.) A cluster appears to be at the bottom left corner.
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Len bought 12.3 ounces of cashews and 15.2 ounces of almonds.
He calculates that if he and four friends share all the nuts equally,
each person will receive 5.1 ounces of nuts.
Which is the best explanation for whether or not his answer is reasonable?
A. Not reasonable; 12.3 + 15.2 = 25.5 and 25.5 ÷ 5 = 4.5.
B. Not reasonable; 12.3 + 15.2 = 27.5 and 27.5 ÷ 5 = 5.5.
C. Reasonable; 12.3 + 15.2 = 27.5 and 27.5 ÷ 5 = 5.1.
D. Reasonable; 12.3 + 15.2 = 25.5 and 25.5 ÷ 5 = 5.1.
Answers
Answer:
B
Step-by-step explanation:
Total ounces of nuts is cashews (12.3 ounces) plus almonds (15.2 ounces) is 27.5 ounces. If you divide 27.5 ounces by 5 people, 27.5 / 5 = 5.5 ounces each.
the average manufacturing work week in a particular city was 40.1 hours last year. it is believed that a recession has led to a reduction in the average work week. to test the validity of this belief, which is the correct hypotheses?
Answers
The following is the null and alternate hypothesis:
H₀ = u = 40.1
H₁ = u < 40.1
The null hypothesis should read as follows if we want to test the assertion that the average workweek has decreased:
The claim that there is a decrease in the typical work week should be made in the alternative hypothesis. The genuine mean is smaller than 40.1 can be used to express this.
The null hypothesis should assert that the average work week has not been significantly reduced, which is the opposite of the alternative. This can be expressed mathematically as 40.1 as the genuine mean.
Therefore, The alternative and null hypothesis are then:
H₀ = u = 40.1
H₁ = u < 40.1
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Suppose you have a part-time job delivering packages. Your employer pays you a flat rate of $9.50 per hour. You discover that a competitor pays employees 2 per hour plus 3 per delivery. How many deliveries would the competitor's employees have to make in four hours to earn the same pay you earn in a four-hour shift?
- How can you interpret the solution in the context of the problem?
Answers
The competitor's employees would earn a total of $8 + ($3 * D) in four hours. the competitor's employees would need to make 10 deliveries in four hours to earn the same pay as you do in a four-hour shift.
To interpret the solution in the context of the problem, we need to compare the earnings of the two different payment structures.
In your case, you earn a flat rate of $9.50 per hour for delivering packages. So, in a four-hour shift, you would earn 4 hours * $9.50/hour = $38.
On the other hand, the competitor's employees earn $2 per hour plus $3 per delivery. To determine how many deliveries the competitor's employees would have to make in four hours to earn the same pay as you, we need to calculate their earnings.
Let's assume that the competitor's employees also make deliveries at the same speed as you do. If they work for four hours, they would earn 4 hours * $2/hour = $8 from their hourly wage. In addition, they would earn $3 per delivery, so we'll call the number of deliveries they need to make "D."
Therefore, the competitor's employees would earn a total of $8 + ($3 * D) in four hours.
To find out how many deliveries they would need to make to earn the same pay as you, we can set up an equation:
$8 + ($3 * D) = $38
Simplifying the equation, we get:
$3 * D = $38 - $8
$3 * D = $30
Dividing both sides of the equation by $3, we find:
D = $30 / $3
D = 10
So, the competitor's employees would need to make 10 deliveries in four hours to earn the same pay as you do in a four-hour shift.
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all the ratios that are equivalent to the ratio 12:3.
Answers
Answer:
Step-by-step explanation:
12:3 = 12 divide by 3 = 4
3 divide by 3 = 1
if h + 12 =22, then h= 10. name the property
Answers
Answer:
substitution
Step-by-step explanation:
For the following right triangle, find the side length x.
A = 40
X
B = 9
Answers
Answer:
41
Step-by-step explanation:
Use the Pythagorean Theorem to find the hypotenuse.
\(a^{2} +b^{2} =c^{2}\)
Plug in the values.
\(40^{2} +9^{2} =c^{2}\)
Simplify.
\(1600+81=c^{2}\)
Add.
\(1681=c^{2}\)
Take the square root of both sides.
\(\sqrt{1681}=\sqrt{ c^{2}\)
41=c
Which equation describes the pattern shown in the table?Х- 4-21y5-30O A. y = x2 – 11OB. y = x2 + 3x - 1O C. y = x2 – 1OD. y = x2 + 2x - 3O E. y=x²-x-1Which equation shows
Answers
the equation describes the pattern shown in the table is y = x² + 2x - 3 (option D)
Explanation:
To determine which of the equation describes the pattern shown in the table, we need to insert the values of x and confirm if we will get corresponding value of y in any of the equation.
Let's check the equations in the options: when x = -4, -2
a) y = x² – 11
when x = -4
y = (-4)² - 11
y = 16 - 11 = 5
when x = -2
y = (-2)² - 11
y = 4 - 11 = -7
equation is wrong
b) x² +3x -1
when x = -4
y = (-4)² -3(-4) - 1
y = 16 + 12 -1 = 27
when x = -2
y = (-2)² -3(-2) - 1
y = 4 + 6 -1 = 9
equation is wrong
c) y = x² – 1
when x = -4
y = (-4)² - 1
y = 16 - 1 = 15
equation is wrong
d) y = x² + 2x - 3
when x = -4
y = (-4)² +2(-4) - 3
y = 16 - 8 -3 = 5
when x = -2
y = (-2)² +2(-2) - 3
y = 4 - 4 - 3
y = -3
equation is right
e) y=x²-x-1
when x = -4
y = (-4)² -(-4) - 1
y = 16 +4 -1
y = 19
equation is wrong
Therefore, the equation describes the pattern shown in the table is y = x² + 2x - 3 (option D)
The arithmetic sequence a_ia i a, start subscript, i, end subscript is defined by the formula: a_1 = 15a 1 =15a, start subscript, 1, end subscript, equals, 15 a_i = a_{i - 1} -7a i =a i−1 −7a, start subscript, i, end subscript, equals, a, start subscript, i, minus, 1, end subscript, minus, 7 Find the sum of the first 660660660 terms in the sequence.
Answers
Answer:
-1,512,390
Step-by-step explanation:
Given
a1 = 15
\(a_i = a_{i-1} -7\)
Let us generate the first three terms of the sequence
\(a_2 = a_{2-1}-7\\a_2 = a_1 - 7\\a_2 = 15-7\\a_2 = 8\)
For \(a_3\)
\(a_3 = a_{3-1}-7\\a_3 = a_2 - 7\\a_3 = 8-7\\a_3 = 1\)
Hence the first three terms ae 15, 8, 1...
This sequence forms an arithmetic progression with;
first term a = 15
common difference d = 8 - 15 = - -8 = -7
n is the number of terms = 660 (since we are looking for the sum of the first 660 terms)
Using the formula;
\(S_n = \frac{n}{2}[2a + (n-1)d]\\\)
Substitute the given values;
\(S_{660} = \frac{660}{2}[2(15) + (660-1)(-7)]\\S_{660} = 330[30 + (659)(-7)]\\S_{660} = 330[30 -4613]\\S_{660} = 330[-4583]\\S_{660} = -1,512,390\)
Hence the sum of the first 660 terms of the sequence is -1,512,390
Write an equation of each line in standard form with integer coefficients. y=7 x+0.4 .
Answers
The equation of the line y = 7x + 0.4 in standard form with integer coefficients is 70x - 10y = -4.
To write the equation of the line y = 7x + 0.4 in standard form with integer coefficients, we need to eliminate the decimal coefficient. Multiply both sides of the equation by 10 to remove the decimal, we obtain:
10y = 70x + 4
Now, rearrange the terms so that the equation is in the form Ax + By = C, where A, B, and C are integers:
-70x + 10y = 4
To ensure that the coefficients are integers, we can multiply the entire equation by -1:
70x - 10y = -4
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This class uses weighting, which you will need to account for in the calculation. test are worth 80% of the grade, and the class project is worth 20% of the grade. To calculate the final grade percentage you will need to add up the test scores; then divide by the total number of test points and then multiply by the weighted percentage. In a similar manner, calculate the percentage for the project. Then add the two totals together to get the final grade. Remember, students cannot earn more than 100%!
What is Student 3's numeric grade percentage? Use one decimal place and include the percent sign in your answer.
Answers
The student 3's numeric grade percentage is 95.6%.
The final grade for the students is calculated based on the test scores and the class project score.
The test is worth 80% and the project is worth 20% of the grade. To calculate the final grade percentage, the individual percentages of test and project are computed, then added together.
The result cannot exceed 100%.Let us calculate the weighted test score for student 3.
There were three tests each worth 100 points. The scores of student 3 are 91, 78, and 83.
We have to add up the test scores; then divide by the total number of test points and then multiply by the weighted percentage.
The weighted test score is:(91+78+83)/300 * 80% = 76.6%
We can now calculate the percentage for the project. Student 3 received a grade of 95%.
Therefore, the percentage for the project is: 95% * 20% = 19%.
Now, we add the weighted test score to the weighted project score to find the final grade for student 3. 76.6% + 19% = 95.6%.
Therefore, The final grade of student 3 is 95.6%
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variables that indicate the distance a target is from the level achieved are called
Answers
Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators.
Variables that indicate the distance a target is from the level achieved are called performance metrics or progress indicators. These variables help measure and track progress towards a goal by providing a quantitative or qualitative measure of how far the target is from the desired level of achievement.
Performance metrics can be represented in various forms, such as distance covered, percentage completed, points earned, or even subjective evaluations. For example, in a fitness program, a performance metric could be the number of miles run or the number of push-ups completed.
These metrics enable individuals or organizations to assess their progress and make necessary adjustments to reach their desired outcomes.
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Lisa earns $81 washing 9 windows. At this rate, how much does Lisa earn washing 5 windows?
Answers
So, this is simple, but needed to be one step at a time. We need to find out how much she earns by washing one window, and to do that we need to divide $81 by 9, and after that division she earns $9 per window. If she washes 5 windows, multiply $9 by 5 as that's how much she's going to earn. So, when she washes 5 windows, she earns $45.
Answer:
45
Step-by-step explanation:
81÷9=9
9×5=45
..............
WILL GIVE 200 BRAINLY POINTS FOR AWSNERING THIS CORRECTLY!!!!
Answers
Take 2 points
(5,3)(6,4)Slope:-
\(\\ \sf\longmapsto m=\dfrac{1}{1}=1\)
Equation in point slope form
\(\\ \sf\longmapsto y-3=x-5\)
\(\\ \sf\longmapsto y=x-2\)
Or
f(x)=x-2Answer:
Take 2 points(5,3)(6,4)Slope:-Equation in point slope formOr f(x)=x-2
Step-by-step explanation:
What is the value of x in the product of powers below
6 (to the power of 9) • 6 (to the power of X) = 6 (to the power of 2)
-11
-7
7
11
Pls help
Answers
Answer: 7
Step-by-step explanation:
Step 1: 6^9 * 6^x = 6^2
Step 2: 9 + x = 2
Step 3: x = 2 - 9
Step 4: x = -7
Step 5: Since the power of a number cannot be negative, x must be 7.
Hannah bought 3 magazines for $2.50 each, $17.40 worth of food, and $4.40 worth of cleaning supplies. The state tax rate is 6.5% on non-food items. What is Hannah’s total bill?
Answers
Answer:
The bill is 30.07
Step-by-step explanation:
First find the total of the non-food items
3 *25.0 for the magazines = 7.50 plus 4.40 for the cleaning supplies
11.90
Multiply this by 6.50% to find the tax
11.90*.065 =.77
Add the tax to the total of the non food items
11.90+.77=12.67
Now add the food items
12.67+17.40
30.07
The bill is 30.07
Find the value of this expression and show ur work
Answers
Answer:
-30/49
Step-by-step explanation:
You multiply the numbers, then add the negative symbol, when you multiply the numbers, you get:
10/7*3/7 which equals 30/49, which means the answer is -30/49
Please solve in a big hurry!:
will name the Brainliest!!!
Answers
Answer:
B.
4x+9 = 2x-1
Step-by-step explanation:
Answer:
Third one
Step-by-step explanation:
nine more than four times a number:
4x+9
x is the "mystery number"
"is the same as" is just another way of saying "equals"
one less than twice the number ("the number" is just x):
2x-1
put them all together:
4x+9=2x-1
don't over look it; break it down
<3
to remain on the cheerleading squad,Lakita must attend at least 3/5 of the study table sessions offered . she attends 15 sessions . if Lakita met the requirements, what is the maximum number of study table sessions ?
Answers
Find the exact length of the curve.
x = e^t − 9t, y = 12e^t/2, 0 ≤ t ≤ 3
Answers
The exact length of the curve defined by the parametric equations \(x = e^t - 9t, y = 12e^(t/2) (0 ≤ t ≤ 3)\)is approximately 29.348 units.
To find the length of a curve defined by a parametric equation, we can use the arc length formula. For curves given by the parametric equations x = f(t) and y = g(t), the arc length is found by integration.
\(L = ∫[a, b] √[ (dx/dt)^2 + (dy/dt)^2 ] dt\)
Then \(x = e^t - 9t, y = 12e^(t/2)\)and the parameter t ranges from 0 to 3. We need to calculate the derivative values dx/dt and dy/dt and plug them into the arc length formula.
Differentiating gives \(dx/dt = e^t - 9, dy/dt = 6e^(t/2)\). Substituting these values into the arc length formula yields:
\(L = ∫[0, 3] √[ (e^t - 9)^2 + (6e^(t/2))^2 ] dt\)
Evaluating this integral gives the exact length of the curve. However, this is not a trivial integral that can be solved analytically. Therefore, numerical methods or software can be used to approximate the value of the integral. Approximating the integral gives a curve length of approximately 29.348 units.
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Please helppppp!! Find the midpoint of the segment with the following end points (-2,7) and (2,3)
Answers
Answer:
\( \huge{ \boxed{ \bold{ \tt( \: 0 \: ,5 \: )}}}\)
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☞ First, Let's explore about Midpoint :
Midpoint of the segment simply means middle point of a line segment. Formula of Midpoint :
\( \boxed{ \sf{(x _{ \: m \: } ,\: y_{m}) = ( \frac{x_{1} + x_{2}}{2} ,\: \frac{y_{1} + y_{2}}{2} )}}\)
where ,
\(( \sf{x_{ \: m \: } ,\: y _{ \: m \: })}\) = co-ordinates of the midpoint\(( \sf{ x_{ \: 1 \: }, \: y_{ \: 1 \: }})\) = co-ordinates of the first point\( \sf{(x _{ \: 2 \: } ,\: y_{ \: 2 \: })}\) = co-ordinates of the second pointThe Midpoint Formula is used to find the exact center point between two defined points in a line segment. The Midpoint formula is quite simple , so you should easily be able to remember it. It won't matter which point you pick to be the 'first" point you plug in. Just make sure that you're adding both an x to an x and a y to a y. Hence, keep in mind , in order to find the midpoint of a line segment, the first step is to add both ' x - co-ordinates' and divide it by 2 and then the second step is to add both ' y - co-ordinates ' and divide it by 2.
Now, Let's solve it!
☯ Question :
Find the midpoint of the segment with the following end points ( - 2 , 7 ) and ( 2 , 3 ).☯ Step - by - step explanation :
Let P ( x , y ) divide the line joining the points A ( - 2 , 7 ) and B ( 2 , 3 ). Now, let :
A ( - 2 , 7 ) → ( x₁ , y₁ )B ( 2 , 3 ) → ( x₂ , y₂ )Apply midpoint formula , then plug the values and lastly simplify it :
\( \sf{ midpoint \: = \: ( \frac{x _{ \: 1 \: } + x _{ \: 2 \: }}{2} , \: \frac{y_{ \: 1 \: } + y _{ \: 2\: }}{2} })\)
➺ \( \sf{midpoint = ( \frac{ - 2 + 2}{2}, \: \frac{7 + 3}{2} )}\)
➺ \( \sf{midpoint = ( \frac{0}{2} , \: \frac{10}{2} )}\)
➺ \( \boxed{ \sf{ midpoint = ( \: 0 \: , 5})}\)
Hence , The midpoint of the segment with the end points A ( - 2 , 7 ) and B ( 2 , 3 ) is ( 0 , 5 ) .
Hope I helped!
Have a wonderful time ッ
~TheAnimeGirl ♡
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Work out length AC.
10 cm
Not drawn
accurately
120
7 cm
Answers
Step-by-step explanation:
Well. Let's call α the 120° angle, and β its supplementary angle (80°). Let's draw also the height of the triangle. We'll call it CH. We know, from goniometric relations, that BC * sinβ = CH and BC * cosβ = BH. We just apply the pythagorean theorem so we get: AC = \(\sqrt{(AB+BH)^2+CH^2}.\) By inserting all the values you'll get the result.
If the common differences of an Ap is 5, the value of a18-a13 is
Answers
Answer:
25
Step-by-step explanation:
The n th term of an AP is
\(a_{n}\) = a₁ + (n- 1)d
where a₁ is the first term and d the common difference
Here d = 5, then
a₁₈ = a₁ + 17d = a₁ + 85
a₁₃ = a₁ + 12d = a₁ + 60
Thus
a₁₈ - a₁₃
= a₁ + 85 - a₁ - 60
= 25
Sales tax is a function of the price of an item. the amount of sales tax is 0.08 times the price of the item. use h to represent the function. a. h (x) = 0.08 h b. x (h) = 0.08 h c. h (x) = 0.08 x d. x (h) = 0.08 x
Answers
The correct representation of the function is h(x) = 0.08x
What is function?
In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.
Solution:
Given data:
Sales tax is a function of the price of an item.
Let h be the function.
Take x be the price of an item.
Amount of sales tax = 0.08 times price of the item
= 0.08 × x
Amount of sales tax = 0.08x
⇒ h(x) = 0.08x
Hence the function is h(x) = 0.08x.
Option C is the correct answer.
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