There are 3,256 ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores, assuming that only apples have inedible cores.
To solve this problem, we need to first identify which fruits have inedible cores. We know that apples have cores, but we don't know about the other fruits. Let's assume that only apples have inedible cores for the purposes of this problem.
We want to buy 10 pieces of fruit, but we can only buy at most 2 pieces with inedible cores. This means that we can buy either 0, 1, or 2 apples.
Case 1: 0 apples with inedible cores
If we buy 0 apples with inedible cores, then we can buy any combination of bananas, pears, and strawberries. This is a classic stars and bars problem, and the solution is (10 + 3 - 1) choose (3 - 1) = 66.
Case 2: 1 apple with inedible core
If we buy 1 apple with inedible core, then we need to choose one of the 10 pieces of fruit to be an apple with inedible core. We can then buy any combination of the remaining 9 fruits, which is again a stars and bars problem. The solution is 10 * (9 + 2 - 1) choose (2 - 1) = 220.
Case 3: 2 apples with inedible cores
If we buy 2 apples with inedible cores, then we need to choose two of the 10 pieces of fruit to be apples with inedible cores. We can then buy any combination of the remaining 8 fruits, which is once again a stars and bars problem. The solution is (10 choose 2) * (8 + 3 - 1) choose (3 - 1) = 2,970.
Finally, we add up the number of ways to buy 10 pieces of fruit with at most 2 pieces with inedible cores: 66 + 220 + 2,970 = 3,256.
Therefore, there are 3,256 ways to buy 10 pieces of fruit so that you buy at most 2 pieces with inedible cores, assuming that only apples have inedible cores.
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The coefficient of [tex]x^{10}[/tex] in the expanded polynomial, which represents the total number of ways to buy 10 pieces of fruit with at most 2 inedible cores.
The number of each type of fruit as a polynomial.
Let B(x), A(x), P(x), and S(x) be the generating functions for bananas, apples, pears, and strawberries, respectively.
We can write:
[tex]B(x) = 1 + x + x^2 + x^3 + ...[/tex]
[tex]A(x) = 1 + x + x^2 + x^3 + ...[/tex]
[tex]P(x) = 1 + x + x^2 + x^3 + ...[/tex]
[tex]S(x) = 1 + x + x^2 + x^3 + ...[/tex]
The coefficient of [tex]x^n[/tex]in each polynomial represents the number of fruits of that type you can buy with n selections.
The 1 term in each polynomial represents the possibility of buying 0 fruits of that type.
To count the number of ways to buy 10 pieces of fruit with at most 2 inedible cores, we need to find the coefficient of[tex]x^{10}[/tex] in the polynomial:
[tex](B(x) + A(x) + P(x) + S(x))^{10}[/tex]
Combination of 10 fruits from the total pool of bananas, apples, pears, and strawberries, subject to the constraint that we can only choose up to 2 fruits with inedible cores.
Polynomial using the binomial theorem:
the binomial theorem (or binomial expansion) describes the algebraic expansion of powers of a binomial.
According to the theorem, it is possible to expand the polynomial. [tex](x + y)^n[/tex]into a sum involving terms of the form. [tex]ax^by^c,[/tex] where the exponents b and c are nonnegative integers with b + c = n, and the coefficient a of each term is a specific positive integer depending on n and b.
For example, for n = 4,
[tex]{\displaystyle (x+y)^{4}=x^{4}+4x^{3}y+6x^{2}y^{2}+4xy^{3}+y^{4}.}[/tex]
The coefficient a in the term of[tex]ax^by^c[/tex] is known as the binomial coefficient. [tex](^n_b)[/tex] or [tex](^n_c)[/tex] (the two have the same value).
These coefficients for varying n and b can be arranged to form Pascal's triangle.
These numbers also occur in combinatorics, where.
[tex](^n_b)[/tex] gives the number of different combinations of b elements that can be chosen from an n-element set.
Therefore
[tex](^n_b)[/tex] is often pronounced as "n choose b".
[tex](B(x) + A(x) + P(x) + S(x))^{10} = (B(x) + A(x) + P(x) + S(x))^8(B(x) + A(x) + P(x) + S(x))^2[/tex]
The right-hand side has the coefficient of [tex]x^8[/tex] in each term as the number of ways to choose 8 fruits from the total pool with at most 2 inedible cores.
The second factor has the coefficient of [tex]x^2[/tex]in each term as the number of ways to choose 2 fruits from the total pool with at most 2 inedible cores. We can expand each of these factors using the binomial theorem, then multiply the resulting polynomials together and find the coefficient of [tex]x^{10}[/tex].
Cumbersome calculation, but it can be simplified by using some algebraic manipulations to group like terms and reduce the number of calculations needed.
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the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule (as presented in the book), what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?
Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.
Explain about the bell-shaped curve:A bell curve is a form of graph that is used to show how a collection of selected values are distributed; it often has a peak at the centre that tends to be normal, with low and high extremes tapering out rather symmetrically on either side.
Given that:
Mean = 42 with standard deviation of 4.
Now,
If mean = 42,
1 standard deviation (+1σ) above that mean = 42 + 4 =48
1 standard deviation (-1σ) below that mean = 42 - 4 = 38
By the empirical rule 68-95-99.7 rule:
68% of the given normal distribution data lies between -1σ and +1σ: That is between 38 - 48 requests.
And,
In the range 42 - 50 requests (between that mean and +1σ) is half of the given 68% : 68/2 = 34%
Thus, the approximate percentage of lightbulb replacement requests numbering between 42 and 50 is 34%.
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Correct question:
the physical plant at the main campus of a large state university recieves daily requests to replace florecent lightbulbs. the distribution of the number of daily requests is bell-shaped and has a mean of 42 and a standard deviation of 4. using the empirical rule 68-95-99.7 rule, what is the approximate percentage of lightbulb replacement requests numbering between 42 and 50?
marvin company sells pens ($6) and flashlights ($10). if total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold?
If total sales were $624 and customers bought 7 times as many pens as flashlights, then the number of pens sold is 84.
Let's start by assigning variables to represent the unknown quantities.
Let x be the number of flashlights sold.
Then, since "customers bought 7 times as many pens as flashlights," the number of pens sold would be 7x.
The total sales can be expressed as the sum of the sales of each item:
10x (sales from flashlights) + 6(7x) (sales from pens) = 624
Simplifying this equation
10x + 42x = 624
52x = 624
x = 12
So, the number of flashlights sold is 12.
And the number of pens sold would be 7x = 7(12) = 84.
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In circle C, FG and FE are tangent segments, m
Choose the two answers that represent the angle measures of the central and circumscribed angles.
The angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
What is angle?Angle is a geometric term used to describe the measure between two lines or surfaces that intersect each other. It is measured in degrees, and is typically represented by the Greek letter θ (theta). Angles can be acute, obtuse, right, reflex, or straight. Acute angles are angles that are less than 90°, obtuse angles are angles that are greater than 90°, and right angles are angles that measure exactly 90°. Reflex angles are angles that measure greater than 180°, and straight angles measure exactly 180°.
The two correct answers are 83° and 79°. The angle measure of the central angle GFE is 3x + 11. Therefore, 3x + 11 = 83°, and x = 26. The angle measure of the circumscribed angle GCE is 5x - 23. Therefore, 5x - 23 = 79°, and x = 26. As both equations have the same value for x, the two angle measures are 83° and 79°.
In conclusion, the angle measures of the central angle GFE and the circumscribed angle GCE in circle C are 83° and 79° respectively.
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can yall help me with this question this would rlly help me out!
Answer:
59.5[tex]cm^{2}[/tex]
Step-by-step explanation:
You have two shape: a square and a triangle
Square:
The area of a square is the sides squared
a = [tex]s^{2}[/tex] The side length is 7 (7 x 7 = 49)
a = [tex]7^{2}[/tex]
a = 49
Triangle:
a [tex]\frac{bh}{2}[/tex] The base times the height divided by 2
The base is 7 and the height is 3.
a = [tex]\frac{7x3}{2}[/tex] = [tex]\frac{21}{2}[/tex] = 10.5
Add the two areas together: 49 + 10.5 = 59.5
Helping in the name of Jesus.
It costs $50 every two days to rent a bike. The amount y is proportional to the number x of days the bike is rented. a. Find the rate of change (slope) in simplest form. b. Write an equation that represents the situation. c. How many dollars will you pay for renting the bike 6 days?
Therefore , the solution of the given problem of equation comes out to be the cost of renting the bike for six days is $150.
What is equation?Variable words are frequently used in complex algorithms to show consistency between two competing arguments. Academic expressions called equations are used to show the equality of various academic figures. Think on the details connected to those x + 7 proposals. In contrast to another method that involved splitting 12 identical components into two halves, elevating in this case yields b + 7 while building y + 7 and integrating.
Here,
The amount y changes in relation to how many days x the bike is rented; this is known as the rate of change (slope).
The rate of change (slope) is $50 every two days, or $25 per day, because renting a bike costs $50 every two days.
b. The scenario is represented by the equation
=> y = 25x.
c. You can enter x = 6 into the equation to get the price for renting the bike for six days:
=> y = 25(6)
=> y = 150
Therefore, the cost of renting the bike for six days is $150.
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Teachers at Arcadia Elementary School asked students to name their favorite desserts.
Ice cream
1
3
Frozen yogurt
2
9
Cookies
1
9
Candy
1
9
Pudding
1
9
Brownies
1
9
Favorite desserts
If there were 99 students voting, how many of them named brownies as their favorite dessert?
Out of 99 students, 11 of them named brownies as their favorite dessert.
What is proportion?
A proportion is a statement that two ratios are equal. In other words, when two ratios have the same relationship between their corresponding values, they are said to be in proportion. Proportions are commonly used in mathematics to solve problems involving equivalent ratios and to scale quantities up or down. They can also be used to represent real-world situations, such as calculating the ratio of ingredients in a recipe or determining the scale of a map.
According to the chart, 1 out of 9 students named brownies as their favorite dessert.
To find the actual number of students who named brownies, you can set up a proportion,
1/9 = x/99
Where x represents the number of students who named brownies.
To solve for x, you can cross-multiply,
9x = 1 × 99
Simplifying,
9x = 99
x = 11
Therefore, out of 99 students, 11 of them named brownies as their favorite dessert.
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Correct question is "Teachers at Arcadia Elementary School asked students to name their favorite desserts.
Ice cream -1/3
Frozen yogurt - 2/9
Cookies - 1/9
Candy - 1/9
Pudding - 1/9
Brownies - 1/9
If there were 99 students voting, how many of them named brownies as their favorite dessert?"
PLEASE HELP AND SHOW YOUR WORK . I WILL MARK YOU BRAINLIEST IF YOU EXPLAIN.
The approximation of √300 to the nearest integer is 17
What is an integer?An integer is a whole number that can be positive or negative or zero. Examples of integers are 0, -5, 10, 15, 1000. e.t.c. Decimal numbers are not integers.
Since the value of √300 can not give a whole number because 300 is not a perfect square. This means that the answer given will not be an integer. Therefore saying that we should approximate to integer means approximation to whole number.
√ 300 = 17.32. Therefore the approximation of the value of √300 to the nearest integer = 17.
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I NEED HELP ASAP IT'S DUE IN 20MIN
Question 2
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
Question 5
A recent conference had 900 people in attendance. In one exhibit room of 80 people, there were 65 teachers and 15 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 820 principals in attendance.
There were about 731 principals in attendance.
There were about 208 principals in attendance.
There were about 169 principals in attendance.
Question 6
A teacher was interested in the subject that students preferred in a particular school. He gathered data from a random sample of 100 students in the school and wanted to create an appropriate graphical representation for the data.
Which graphical representation would be best for his data?
Stem-and-leaf plot
Histogram
Circle graph
Box plot
Question 7
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sports Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 8
A New York City hotel surveyed its visitors to determine which type of transportation they used to get around the city. The hotel created a table of the data it gathered.
Type of Transportation Number of Visitors
Walk 120
Bicycle 24
Car Service 45
Bus 30
Subway 81
Which of the following circle graphs correctly represents the data in the table?
circle graph titled New York City visitor's transportation, with five sections labeled walk 80 percent, bus 16 percent, car service 30 percent, bicycle 20 percent, and subway 54 percent
circle graph titled New York City visitor's transportation, with five sections labeled walk 40 percent, bicycle 8 percent, car service 15 percent, bus 10 percent, and subway 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 40 percent, bus 8 percent, car service 15 percent, bicycle 10 percent, and walk 27 percent
circle graph titled New York City visitor's transportation, with five sections labeled subway 80 percent, bicycle 20 percent, car service 30 percent, bus 16 percent, and walk 54 percent
Question 9
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the scoops of ice cream the college will need?
The college will have about 480 students who prefer ice cream.
The college will have about 640 students who prefer ice cream.
The college will have about 1,280 students who prefer ice cream.
The college will have about 1,440 students who prefer ice cream.
2. The appropriate measure of center for the given data is the median, and it equals 19.
5. We can predict that there were about 169 principals in attendance at the conference.
6. The best graphical representation for the teacher's data would be a bar graph.
7. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
8. The correct circle graph to represent the data is titled "New York City Visitor's Transportation"
9. We can predict that the college will need about 1440 scoops of ice cream.
Median, bar chart, histogramAnswer 2:
The appropriate measure of center for the given data is the median, and it equals 19. We can determine this from the box plot since the line inside the box represents the median of the data, and the box itself represents the middle 50% of the data. Since the box extends from 17 to 21, we know that half of the data falls below 19 and half above, making it the median. The mean is not a good measure of center for this data because it can be influenced by outliers, which are present in this dataset.
Answer 5:
Since we know that 15 out of 80 people in the exhibit room were principals, we can assume that about 15/80 (or about 0.1875) of the attendees were principals. To estimate the number of principals in attendance, we can multiply this fraction by the total number of attendees:
0.1875 x 900 ≈ 169
Therefore, we can predict that there were about 169 principals in attendance at the conference.
Answer 6:
The best graphical representation for the teacher's data would be a bar graph. A bar graph is a useful way to display categorical data, such as the subject preferences of the students. Each subject can be represented by a bar, with the height of the bar representing the frequency or percentage of students who prefer that subject.
Answer 7:
The correct graph to display the data is a bar graph with the title "Favorite Sport" and the x-axis labeled "Sport" and the y-axis labeled "Number of Students". The bars should be labeled "Basketball" with a value of 17, "Baseball" with a value of 12, "Soccer" with a value of 27, and "Tennis" with a value of 44. A histogram is used to display continuous data, while a bar graph is used to display categorical data.
Answer 8:
The correct circle graph to represent the data is titled "New York City Visitor's Transportation" and has five sections labeled "Walk" at 30%, "Bicycle" at 6%, "Car Service" at 11.25%, "Bus" at 7.5%, and "Subway" at 20.25%. To calculate the percentages, we can divide the number of visitors for each mode of transportation by the total number of visitors (i.e., 300), then multiply by 100% to get the percentage.
Answer 9:
To estimate the number of students who prefer ice cream, we can add up the number of students who chose ice cream, which is 81. Then, we can set up a proportion:
81/225 = x/4000
where x represents the number of students who prefer ice cream out of the total population of 4000. Solving for x, we get:
x = 81 x 4000 / 225 = 1440
Therefore, we can predict that the college will need about 1440 scoops of ice cream.
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Which table represents a function?
Answer:
Table 4 represents a function because each x-value corresponds to exactly one y-value.
g you are dealt a hand of three cards from a standard deck of 52 cards. a. how many different combinations of 3 cards can you possibly have? b. how many different combinations of 3 aces can you possibly have?
a) There are 22,100 possible combinations of 3 cards that can be drawn from a standard deck of 52 cards.
b) There are only 4 possible combinations of 3 aces that can be drawn from a standard deck of 52 cards.
How to find the possible combinations of 3 cards?a) The number of different combinations of 3 cards from a deck of 52 cards is given by the combination formula:
C(52, 3) = 52! / (3! * (52-3)!) = 22,100
Therefore, there are 22,100 possible combinations of 3 cards from a deck of 52 cards.
How to find the possible combinations of 3 aces?b) Since there are 4 aces in a standard deck of 52 cards, the number of different combinations of 3 aces is given by the combination formula:
C(4, 3) = 4! / (3! * (4-3)!) = 4
Therefore, there are only 4 possible combinations of 3 aces from a deck of 52 cards.
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Correct 0.00025 to one Significant figure
Answer:
0.0003
Step-by-step explanation:
u don't count the zeros as a significant figure
5 rounds 2 up to 3
Find the measures of angle and B. Round to the nearest degree.
The measure of angle A and angle B are 30° and 60° respectively.
What is the measure of angle A and angle B?The figure in the image is a right-triangle.
To find the measure of angle A and angle B, we use the trigonometric ratio.
Solving for the measure of angle A:
sinθ = opposite / hypotenuse
opposite of angle A = 8
hypotenuse = 16
Plug in the values
sinθ = 8/16
sinθ = 1/2
θ = sin⁻¹( 1/2 )
θ = 30°
Solving for angle B
cosB = adjacent / Hypotenuse
adjeacent of angle B = 8
Hypotenuse = 16
Plug in the given values
cosB = 8/16
cosB = 1/2
B = cos⁻¹( 1/2 )
B = 60°
Therefore angle A is 30 degrees and angle B is 60 degree.
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Jamie was working on his math homework with his friend, Kent. Jamie looked at the following problem. −9. 5 − (−8) − 6. 5 He told Kent that he did not know how to subtract negative numbers. Kent said that he knew how to solve the problem using only addition. What did Kent mean by that? Explain. Then, show your work, and represent the answer as a single rational number
The value of the expression as a single rational number is -8.
Kent was likely referring to the idea that subtracting a negative number is the same as adding a positive number. Specifically, to subtract a negative number, we can add the opposite of that number (i.e., the positive version of that number). In this case, we can rewrite the expression as:
= -9.5 - (-8) - 6.5
= -9.5 + 8 - 6.5 (replacing -(-8) with its positive equivalent 8)
= (-9.5 - 6.5) + 8 (grouping like terms)
= -16 + 8 (simplifying)
= -8
Therefore, the value of the expression is -8, which is a single rational number.
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A right triangle has a side length of 10,6 and x. Find x if it is one of the legs show your work
Answer:
The missing side of the right triangle is 8, and it is one of the legs.
Step-by-step explanation:
Step 1: Write down the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. In equation form, it looks like this:
a^2 + b^2 = c^2
where a and b are the lengths of the legs (the shorter sides) and c is the length of the hypotenuse.
Step 2: Identify which sides are the legs and which is the hypotenuse.
In our triangle, we are given the lengths of two sides, 10 and 6. We don't know which one is the hypotenuse and which one is a leg. However, we can use the fact that the hypotenuse is always the longest side to figure it out. Since 10 is longer than 6, we know that 10 is the hypotenuse.
Step 3: Apply the Pythagorean theorem to find x.
Now that we know which side is the hypotenuse, we can use the Pythagorean theorem to find x. We substitute the values we know into the formula and solve for x:
a^2 + b^2 = c^2
6^2 + x^2 = 10^2
36 + x^2 = 100
x^2 = 100 - 36
x^2 = 64
x = √64
x = ±8
Step 4: Choose the positive value of x.
Since x represents a length of a side of a triangle, it must be a positive value. Therefore, x = 8.
Step 5: Verify that the answer is correct.
We can check that our answer is correct by substituting x = 8 into the Pythagorean theorem and seeing if it holds true:
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100
What is the value of the expression 8w−4j2 when w=0. 25 and j=0. 5?
The value of the expression 8w - 4j² when w = 0.25 and j = 0.5 is 1.
The expression 8w - 4j² is a combination of variables, w and j, and a constant, 8 and 4. In order to evaluate the expression when w = 0.25 and j = 0.5, we substitute these values for w and j in the expression and perform the necessary calculations.
First, we substitute w = 0.25 and j = 0.5 in the expression:
8(0.25) - 4(0.5)²
Next, we simplify the expression by performing the calculations in the parentheses first. Since 0.5² = 0.25, we can simplify 4(0.5)² to 4(0.25) = 1. We can then simplify 8(0.25) - 4(0.5)² to:
= 2 - 1
= 1
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The given question is incomplete, the complete question is:
What is the value of the expression 8w−4j² when w=0. 25 and j=0. 5?
Determine the number of real solutions of the system
y=X^2 + 8
y= X + 15
Answer:
2
Step-by-step explanation:
Graphing the system shows that the lines intersect twice, meaning there are two real solutions.
Consider a circle whose equation is x2 + y2 – 2x – 8 = 0. Which statements are true? Select three options. The radius of the circle is 3 units. The center of the circle lies on the x-axis. The center of the circle lies on the y-axis. The standard form of the equation is (x – 1)² + y² = 3. The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.
Answer:
The radius of the circle is 3 units.
The center of the circle lies on the y-axis.
Step-by-step explanation:
The circle equation is :
x² + (y-1)² = 3²
center: (0, 1) The center of the circle lies on the y-axis.
Radius: 3 The radius of the circle is 3 units.
A road is inclined at an angle of 4°. After
driving 5,164 feet along this road, find
the driver's increase in altitude. Round to
the nearest foot.
5,164 ft
a=?
Answer:
Step-by-step explanation:
Sin = Opposite/Hypotenuse
(5,164) x sin (4°) =
5164 x .0698 ≈ 360.4472
Round to nearest foot ≈ 360'
which measure of variation is affected most by a few extreme scores? which measure of variation is affected most by a few extreme scores? standard deviation mode range median mean
Standard deviation and median are less affected by extreme scores, while mode is not affected at all since it represents the most frequently occurring value.
The measure of variation affected most by a few extreme scores is the range, as it considers only the difference between the highest and lowest values in a dataset. However, the mean can also be influenced by extreme scores, causing it to deviate from the central tendency. Standard deviation and median are less affected by extreme scores, while the mode is not affected at all since it represents the most frequently occurring value.
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The measure of variation affected most by a few extreme scores is the range. The range is the difference between the
highest and lowest values in a data set. Extreme scores significantly increase the range, making it a sensitive measure
of variation.
The measure of variation that is affected most by a few extreme scores is the standard deviation.
The reason for this is that the standard deviation is calculated by taking the square root of the sum of squared
deviations from the mean, and the squared deviations from the mean are particularly sensitive to extreme scores.
On the other hand, the mode, range, median, and mean are less affected by a few extreme scores.
The mode is simply the most frequently occurring value in a dataset and is not affected by extreme scores.
The range is the difference between the highest and lowest values in a dataset and can be affected by extreme scores, but only to a limited extent.
The median is the middle value in a dataset, and it is also not affected by extreme scores unless they are extreme
enough to change the position of the middle value.
The mean is the average value in a dataset, and while it can be influenced by extreme scores, its effect is typically less
pronounced than on the standard deviation.
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What is -7(7-2p)=-22+5p
Step-by-step explanation:
-49+14p=-22+5p
-49+22=5p-14p
-27=-9p
p=3
A net of a rectangular prism is shown.
A net of a rectangular prism with dimensions 5 and three-fourths centimeters by 4 centimeters by 11 and three-fourths centimeters.
What is the surface area of the prism?
five hundred fifty and one-fourth cm2
four hundred twelve and three-fourths cm2
two hundred seventy-five and one-eighth cm2
one hundred thirty-seven and nine-sixteenths cm2
Answer:
surface area of the rectangular prism is 278( 1/4) cm^2,
Step-by-step explanation:
To calculate the surface area of a rectangular prism, we need to find the area of all six faces and add them together.
The formula for the surface area of a rectangular prism is:
Surface area = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the rectangular prism.
Given that the dimensions of the rectangular prism are 5 and three-fourths cm by 4 cm by 11 and three-fourths cm, we can substitute these values in the formula to get:
Surface area = 2(5 3/4 x 4) + 2(5 3/4 x 11 3/4) + 2(4 x 11 3/4)
Simplifying this expression, we get:
Surface area = 2(23) + 2(69 1/8) + 2(47)
Surface area = 46 + 138 1/4 + 94
Surface area = 278 1/4 cm^2
Therefore, the surface area of the rectangular prism is 278 1/4 cm^2, which is closest to the option: two hundred seventy-five and one-eighth cm^2.
Briana Ralph is married and claims 2 allowances. Her gross weekly salary is $450. Each week she pays federal, Social Security, and Medicare taxes, $21.20
for medical insurance, and $5.00 for the credit union. What is her net pay?
Answer:
423.8
Step-by-step explanation:
you have to add the taxes and insurance together then subtract it by the gross salary and then you get your answer brainly please
School: Date Assignment: Directions: Solve the following equation. Write the complete solutions on a 1 whole sheet of paper. 1) y + 6 = 20 2) x-12 = 18 3) c + 15 = 25 4) 5y-2 = 18 5)3 + 2x = 17 6) 5x (12 + 5) = 85 7) 96-4b = 28 8) 5h + (-55) = 20 9)-12 + y + (-25) = 45 10) y-(-18) = 14 +11
You seem to have made a typo.
Answer:
y = 14
x = 30
c = 10
y = 4
x = 7
x = 3
b = 17
h = 15
y = 82
y = 32
This is not an equation and cannot be solved.
Explanation:
To solve each equation, we need to isolate the variable (the letter that we are solving for) on one side of the equation. To do this, we perform the same operation on both sides of the equation until the variable is alone on one side. Here are the steps for each equation:
y + 6 = 20
Subtract 6 from both sides: y = 14
x-12 = 18
Add 12 to both sides: x = 30
c + 15 = 25
Subtract 15 from both sides: c = 10
5y-2 = 18
Add 2 to both sides: 5y = 20
Divide both sides by 5: y = 4
3 + 2x = 17
Subtract 3 from both sides: 2x = 14
Divide both sides by 2: x = 7
5x (12 + 5) = 85
Simplify the left side: 5x (17) = 85
Divide both sides by 85: x = 3
96-4b = 28
Subtract 96 from both sides: -4b = -68
Divide both sides by -4: b = 17
5h + (-55) = 20
Add 55 to both sides: 5h = 75
Divide both sides by 5: h = 15
-12 + y + (-25) = 45
Add 12 and 25 to both sides: y = 82
y-(-18) = 14
Simplify the left side: y + 18 = 14
Subtract 18 from both sides: y = -4
This is not an equation and cannot be solved.
7. Suppose that there is a rumour going around
your school that next year all weekends will
be extended to three days. Initially, on day 0,
five students know the rumour. Suppose that
each person who knows the rumour tells two
more students the day after they hear about
it. Also assume that no-one hears the rumour
more than once.
a) How many people will learn about the
rumour
i) on day 1?
ii) on day 2?
On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.
a) How many people will learn about the rumour
i) on day 1?a) Let's first consider how the number of people who know the rumor grows each day:
On day 0, 5 people know the rumor.
On day 1, each of the 5 people tells 2 more people, so 5 x 2 = 10 people now know the rumor, including the original 5.
On day 2, each of the 10 people tells 2 more people, so 10 x 2 = 20 people now know the rumor, including the original 5 and the 10 from day 1.
i) Therefore, on day 1, a total of 10 people will know the rumor.
ii) On day 2, a total of 20 people will know the rumor.
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Find the missing measures in each diagram.
Answer:
X = 65°
Y = 75°
Z = 65°
Step-by-step explanation:
Hello!
Angle Y and the angle measuring 75 degrees are corresponding angles, and corresponding angles are congruent to each other in degree measure.
There is also another set of corresponding angles, and those are Angle Z and Angle X.
Since Angle Y and 75° are corresponding, we can state that Angle Y is also 75°. We can now find Angle Z by subtracting 40° and 75° from 180°. This is because the sum of angles in a triangle is 180°.
Angle Z:180° - 40° - 75°180°-115°65°The measure of Angle Z is 65°. We know that Z and X are corresponding, so X is also 65°.
Gia made a garden stone shaped like a regular octagon with the dimensions shown. Find the area of the octagon.
5.5 in.
4.6 in.that is the area of the octagon but what is the answer???
Area of the octagon is 85.5591 in².
What is octagon?
The fundamental characteristics of a regular octagon. There are 8 interior angles and 8 sides. Both the length of each side and the measurement of each angle are equal. A regular octagon has a total of 20 diagonals. Each inner angle is 135 degrees in length. This means that (135 x 8) = 1080 degrees is the total of all interior angles. An octagon is a polygon that has 8 sides. An octagon is referred to as a regular octagon if all 8 of its sides are equal in length and all of its angles are equal.
Area of rectangular octagon = 2a² (1 + √2) , where a is side
= 2 * (5.5)² ( 1+√2)
= 2 * 30.25(1+√2)
= 60.5 (1+√2)
= 60.25(1 + 1.4142)
= 60.25 * 2.4142
= 85.5591 in²
Therefore, Area of the octagon is 85.5591 in².
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Solve the triangle
A
B
C
Maureen bought 3/4 of a pound of small binder clips and 3/4 of a pound of jumbo binder clips. How much did she spend
If Alice has $50 and spends 4/5 of her money, she spends $40.
A fraction is a mathematical expression that represents a part of a whole or a ratio between two quantities. Fractions are commonly represented using two numbers separated by a horizontal line, where the top number is called the numerator and the bottom number is called the denominator.
Alice spends 4/5 of her money, which is equivalent to 0.8 of her money.
To find out how much Alice spends, we can multiply her total money ($50) by 0.8
= $50 x 0.8
Multiply the numbers
= $40
Therefore, Alice spends $40.
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I have solved the question in general, as the given question is incomplete.
The complete question is:
Alice has $50 and spends 4/5 of her money. How much does Alice spend?
what does it mean to be 90% confident in this problem? use the definition of confidence level. there is a 90% chance that the confidence interval contains the population mean 90% of all simple random samples of size 8 from this population will result in confidence intervals that contain the population mean the confidence interval contains 90% of all samples
Being 90% confident in a problem means that there is a 90% chance that the confidence interval calculated from a sample contains the true population mean.
In other words, if we take 100 different samples of the same size from the population and calculate a confidence interval for each sample, then we can expect that 90 of those intervals will contain the true population mean.
This is the definition of a confidence level. Therefore, we can say that there is a 90% chance that the confidence interval we have calculated includes the true population mean.
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3. In raising a 7000 N motorcycle with a pulley system, the workers note that for every 3 m of rope pulled down- ward, the piano rises 0. 3 m. Show that 700 N is required to lift the motorcycle
If workers note that for every "3 m" of rope pulled down-ward, the piano rises 0.3 m, then we have shown that 700 N is required force to lift the motorcycle.
The term "Mechanical advantage" (MA) is defined as ratio of "output-force" to "input-force" in a machine.
In this case, the output force is the weight of the motorcycle (7000 N) and the input force is the force applied to pull the rope downward.
We use the formula for mechanical advantage in a pulley system, which is given by:
⇒ MA = (distance moved by the effort) / (distance moved by the load),
In this case, the distance moved by the effort is 3 m, and
The distance moved by the load is 0.3 m,
Substituting the values,
We get,
⇒ MA = 3/0.3,
⇒ MA = 10,
So, mechanical advantage of "pulley-system" is 10.
Now, we use mechanical advantage to calculate the required force to lift the motorcycle.
Since mechanical advantage is defined as the ratio of output force to input force, we can rearrange the formula as:
⇒ Input force = (Output force)/(Mechanical advantage),
Substituting values for "output-force" as 7000 N and "mechanical-advantage" as 10,
We get,
⇒ Input force = 7000/10,
⇒ 700 N,
Therefore, the required force to lift motorcycle is 700 N.
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