Each interval (a, a), [a, a), and (a, a] represents the empty set, whereas [a, a] denotes the singleton set {a}
What do you meant by interval?
The empty set is represented by the intervals (a, a), [a, a), and (a, a, while the singleton set an is denoted by [a, a]. All four notations are often taken to denote the empty set when a > b. Both notations may be used in conjunction with other mathematical parentheses and brackets.For instance, in analytic geometry, linear algebra, and set theory, the notation (a, b) is frequently used to represent an ordered pair, the coordinates of a point or vector, or (sometimes) a complex number.Bourbaki created the notation]a, b[to signify the open interval for this reason. For ordered pairings, the notation [a, b] is also occasionally used, particularly in computer science.a ) [0, 2]
The empty set is represented by the intervals (a, a), [a, a), and (a, a, while the singleton set an is denoted by [a, a].
b ) iv
If a function f(x) is continuous on a closed interval [ a, b], then f(x) has both a maximum and minimum value on [ a, b].
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A data analyst wants to demonstrate how the population in Charlotte has increased over time. They create the chart below. What is this type of chart called?
Line chart
Area chart
Column chart
Bar chart
The Line chart should be used by the data analyst.
Option (A) is correct.
What is a line chart?
A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.
Line chart
This type of chart is called a line chart. A line chart is a type of chart that is used to display a series of data points over time. It shows how a variable changes over time by connecting data points with lines. The line chart is commonly used to display trends, patterns and changes over time in continuous data.
It uses a horizontal x-axis and a vertical y-axis, with the data points connected by a line. It is great for visualizing trends and changes in data over a period of time, and it can be used to compare multiple variables at once.
Hence, the Line chart should be used by the data analyst.
Option (A) is correct.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
Step-by-step explanation:
The area of a rectangular room is given by the formula A = l * w, where l is the length and w is the width. In this case, we know that A = 750 square feet and w = l - 5 feet. We can use this information to create equations to solve for the length of the room.
Three options that can be used to solve for y are:
y(y + 5) = 750
This equation can be obtained by substituting the given information into the formula for the area of a rectangular room.
y(l - 5) = 750
y(l) - 5y = 750
y2 – 5y = 750
This equation can be obtained by expanding the first equation and moving all the terms to one side of the equation.
y(l) - 5y = 750
y2 - 5y = 750
(y + 25)(y - 30) = 0
This equation can be obtained by factoring the second equation, in which you get two solutions, y = -25 and y = 30. The first solution is not a valid solution because the length of a room can not be negative but the second one is a valid solution.
Note that 750 - y(y - 5) = 0 and y(y - 5) + 750 = 0 are not valid options as they are not equation that can be used to solve for y.
Find the standard parametrization for the line segment joining the points below. Draw coordinate axes and sketch the segment, indicating the direction of increasing t for the
parametrization. (0,0,0) and (5,3,7/2)
The parameterization equation for (0,0,0) and (5,3,7/2) is[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]. Equation of parameterization is what it is.
How do you calculate parametrization?mathematical formulas
[tex]$$\begin{aligned}& x=0+5 t \\& y=0+3 t \\& z=0+3.5 t\end{aligned}$$[/tex]
Equations with symmetry
[tex]\frac{x}{5}=\frac{y}{3}=\frac{z}{3.5}[/tex]
A straight line is the most straightforward curve to parametrize. It is possible to parametrize a line that passes through the origin along the vectors a, b. X is equal to AT and Y is BT. Two vectors parallel to the plane and a point on the plane must be located in order to find a parametrization. On the plane, finding a location is simple. We may use any number for x and y to determine z using the plane's equation. In the event when x and y are both 0, equation (1) states that
z= 18 x + 2 y 3 = 180 + 2 (0) 3= 6.
The process of locating parametric equations of a curve, a surface, or, more generally, a manifold or a variety, described by an implicit equation, is known as in mathematics, and is most commonly used in geometry.
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If r = 2 units and h = 8 units, then what is the surface area of the cylinder
The surface area of the cylinder is 125.66
What is the area of a cylinder?The surface area of a cylinder is the area occupied by its surface in a three-dimensional space. A cylinder is a three-dimensional structure having circular bases which are parallel to each other. It does not have any vertices. Generally, the area of the three-dimensional shapes refers to the surface area.
The surface area of a cylinder is calculated with the formula:
= 2π × r × h + 2πr2= 2πr (h + r) Square units
A=2πrh+2πr2
With the following parameters from the question:
r = 2
h = 8
Substituting the parameters into the formula
A = 2πrh+2πr2=
A = 2·π·2·8+2·π·22
A = 125.66371
Hence, the surface area of the cylinder is 125.66371
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Given the following histogram for a set of data, how many values in the data set are greater than 6.5 and less than 9.5?
Given the following histogram (image now attached), for a set of data, the number of values in the data set that are greater than 6.5 and less than 9.5 is: 14 (Option D)
What is a histogram?A histogram is a rough depiction of the numerical data distribution. Karl Pearson was the first to coin the phrase.
A histogram is a graph that depicts the frequency distribution of a few data points from a single variable. Histograms frequently divide data into "bins" or "range groups" and count the number of data points that belong to each of those bins.
Between 6.5 and 9.5 there are 3 bars. Their heights are:
3, 6, 5, 4, and 3. Adding the values, we have:
3 + 6 + 5 = 14
Thus, the values in the data set are greater than 6.5 and less than 9.5 are 14.
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Full Question:
See attached image.
A recent poll of 738 randomly selected customers of a major U.S. cell-phone carrier found that 170 of them had walked into something or someone while talking on a cell phone. Show that the conditions for calculating a confidence interval for a proportion are satisfied.
Yes, the conditions to calculate a confidence interval for a proportion are satisfied.
n = 738
p = 170/738 = 0.2297
np ≥ 10 and n(1-p) ≥ 10
np = 0.2297*738 = 169.686 ≥ 10
n(1-p) = 738(1-0.2297) = 568.314 ≥ 10
Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.
Yes, the conditions for calculating a confidence interval for a proportion are satisfied. The sample size of the poll was 738 randomly selected customers of a major U.S. cell-phone carrier. Out of these 738 customers, 170 had walked into something or someone while talking on a cell phone. This gives us a population proportion of 170/738 or 0.2297. We need to ensure that np ≥ 10 and n(1-p) ≥ 10. Calculating these values, np = 0.2297*738 = 169.686 which is greater than 10 and n(1-p) = 738(1-0.2297) = 568.314 which is also greater than 10. Therefore, the conditions for calculating a confidence interval for a proportion are satisfied.
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the united states mint produces coins in 1-cent, 5-cent, 10-cent, 25-cent, and 50-cent denominations. if a jar contains exactly 100 cents worth of these coins, which of the following could be the total number of coins in the jar?
The total number of coins in the jar is 10.
The total number of coins in the jar can be determined using the following formula:
Number of Coins = (1-cent coins) + (5-cent coins) + (10-cent coins) + (25-cent coins) + (50-cent coins)
Since the jar contains a total of 100 cents, we can calculate the number of coins in the jar by solving the following equation:
1x + 5x + 10x + 25x + 50x = 100
The solution to this equation is x = 2. This means that the jar contains 2 coins of each denomination, for a total of 10 coins in the jar. Therefore, the total number of coins in the jar is 10.
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Which inequality is true when the value of p is -1
When the value of p is - 1, then p- 1 ≤ 0.5 is the required inequality.
What is an inequality?In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.
Given:
We have the inequalities;
(A). p- 1 ≤ 0.5
When p = -1,
-2 ≤ 0.5.
(B). -p - 1 ≤ -0.5
When p = -1,
0 ≤ -0.5.
This is contradiction.
(C). p - 1 ≥ 0.5
When p = -1,
-2 ≥ 0.5.
This is contradiction.
(D). -p -1 ≥ 0.5
When p = -1,
0 ≥ 0.5.
This is contradiction.
Therefore, p- 1 ≤ 0.5 is the required inequality.
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The complete question:
Which inequality is true when the value of p is -1?
(A). p- 1 ≤ 0.5
(B). -p - 1 ≤ -0.5
(C). p - 1 ≥ 0.5
(D). -p -1 ≥ 0.5
Find the Area of the figure below, composed of a rectangle and two semicircles. Round to the nearest tenths place.
Answer:
44.57
Step-by-step explanation:
area of two semicircles = πr²
3.142×2×2= 12.568
area of rectangle=L×W2
4×8=32
32+12.568
44.568
=44.57
(1.3) (2.5) (2,7) (4,9) does it represent a function
This doesn’t represent a function because the x value 2 repeats
Hope this helped =)
simplify 4x to the power of 3 to power of 5
The simplified form of the given expression is 1073741824x¹⁵.
What is the exponent?Exponent is defined as the method of expressing large numbers in terms of powers. That means, exponent refers to how many times a number multiplied by itself.
The given expression is ((4x)³)⁵
= (4x)¹⁵
= 1073741824x¹⁵
Therefore, the simplified form of the given expression is 1073741824x¹⁵.
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refer to exhibit 1-3. according to the data provided in this table, what is the approximate slope of the line between points c and d (if these data were graphed with x on the horizontal axis and y on the vertical axis)? a. -6.00 b. -1.00 c. -0.17 d. 6.00 e. 0.17
If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.
E. 0.17
The approximate slope between points C and D can be calculated by taking the difference in the y-values (9-15) and dividing it by the difference in the x-values (4-2). This yields a slope of -0.17.
The approximate slope between points C and D can be determined by first calculating the change in y-values (9-15) and the change in x-values (4-2). Then, the change in y-values is divided by the change in x-values to calculate the slope. In this case, the slope is -0.17. This means that for every unit of increase in x-values, the corresponding y-values decrease by 0.17. If the data were graphed with x on the horizontal axis and y on the vertical axis, this would be the approximate slope of the line between points C and D.
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Write the equation of the line with a slope of 3/2 that contains the point ( − 2, – 4). A-y=3/2x-1 B-y=3/2x+4 C-y= 3/2x−7 D-y= 3/2x−4
Answer:
A) y = 3/2 x - 1
Step-by-step explanation:
y + 4 = 3/2 (x + 2) This is the point slope form of a line.
y + 4 = 3/2 x + 3 Subtract 4 from both sides
y = 3/2 x -1
HELP FAST WILL MARK BRAINLYIST! You are a housekeeper in a hotel. It takes you 15 minutes to clean 1 room. In the floor you are assigned, there are 26 rooms. At that rate, how many hours will it take you to clean all 26 rooms?
3.75
3.9
6.5
9.0
15.6
Answer:360 minutes
Step-by-step explanation: 15 x 26 = 360
360 minutes = to 6 HOURS
Answer: 390 minutes
Step-by-step explanation:
which of the following are magnitudes for rotational symmetry of the isosceles trapezoid below about the marked point?
The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.
The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.
The isosceles trapezoid has rotational symmetry about the marked point. This means that when the trapezoid is rotated by an angle of 360°, it will look the same as it did before. Since the trapezoid has 4 sides, the rotational symmetry is 4-fold, or 4 magnitude. Therefore, the answer is b) 4.
The correct answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.The answer is b) 4, as the isosceles trapezoid has 4-fold rotational symmetry about the marked point.
The complete question is :
Which of the following are magnitudes for rotational symmetry of the isosceles trapezoid below about the marked point?
a) 2
b) 4
c) 6
d) 8
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If 25% of a number is 60 and 90% of the same number is 216, find 65% of that number?
Answer:
Step-by-step explanation:
Let's call the number we're trying to find "x".
We know that:
25% of x is 60 (0.25x = 60)
90% of x is 216 (0.9x = 216)
We can use the first equation to solve for x:
x = 60 / 0.25 = 240
Now we can use this value of x to find 65% of it:
65% of x = 0.65 * 240 = 156
So, 65% of that number is 156.
One number is 6 times a first number. A third number is 100 more than the first number. If the sum of the three numbers is 780. Find the numbers
Answer: 156, 56, 336
Answer:
85,510 and 185.
Step-by-step explanation:
let the first number be "a"
let the second number be "b"
let the third number be "c"
we know that
b=6a
c=100+a and
a+b+c=780
If we substitute the first 2 equations on the third one we get:
a+6a+100+a=780
8a+100=780
8a=780-100
8a=680
8 8
a=85
b=6a
b=6×85
b=510
c=100+a
c=100+85
c=185
Please find k value
The value of k is -1 in the given matrix.
What is matrix?In mathematics, a matrix is a rectangular array or table of digits, characters, or expressions that is used to represent a mathematical object or a characteristic of one.
Matrixes represent linear maps and allow for explicit linear algebraic calculations in the absence of additional information.
Due to the fact that matrices can be used to express the majority of abstract linear algebra's properties and operations, a significant portion of linear algebra is devoted to their study. Matrix multiplication, for instance, can be used to represent how linear maps are put together.
the det(Y)=|Y| value is 0. Expanding through third column we get
[tex]0 - 7 \times \left[\begin{array}{ccc}2&-1\\k&2\\\end{array}\right] + 3 \times \left[\begin{array}{ccc}2&-1\\-1&4\\\end{array}\right][/tex]
0 - 7(4 -(-k)) + 3(8 -(1)) = 0
- 7(4 +k) + 3(8 -1) = 0
-28 - 7k + 24 -3 = 0
-7k -7 = 0
-7k = 7
k = -7/7
k = -1
Thus, The value of k is -1 in given matrix.
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Find ∥u∥2 if u=⟨−6,−3,−3⟩.
Answer:
Solution in attached photo.
Step-by-step explanation:
SolutionSteps are in the attached photo, do note for this question, the units for vectors are called 'units'. Also do note that square roots and squared will cancel out each other (Power 2 x Power Half = Power 1).
Edit: I have included solutions for both scenarios for reference.
Identify the value of x that makes each pair of ratios equivalent.
5. x to 50 and 16 to25
32
34
41
The value of x that makes the given pair of ratios equivalent is: A. 32.
What is a ratio?In Mathematics, a ratio simply refers to a mathematical expression that is typically used to denote the proportion of two (2) or more quantities with respect to one another and the total quantities.
What is a proportion?In Mathematics, a proportion can be defined as an equation which is typically used to represent the equality of two (2) ratios.
This ultimately implies that, proportions can be used to establish that two (2) ratios are equivalent and solve for all unknown quantities as follows;
x/16 = 50/25
Cross-multiplying, we have the following:
25x = 16 × 50
25x = 800
x = 800/25
x = 32.
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Noah opens a savings account which gives compound interest of 2.5% per
year. He puts £4000 into it.
a) How much money will Noah have in the account after 9 years?
b) How much interest will Noah have earned from this account after
9 years?
Give your answers in pounds (L) to the nearest 1p.
The answer of the given question based on the compound interest is (a) Noah will have £4995.45 in the account after 9 years. (b) Noah will have earned £995.45 in interest from this account after 9 years.
What is Compound interest?Compound interest is type of the interest that is calculated on the both principal (initial amount) and any accumulated interest from the previous periods. In other words, interest is earned not only on the initial investment, but also on the interest earned in previous periods.
a) The formula for compound interest is given by:
A = P(1 + r/n)^(n*t)
In this case, P = £4000, r = 0.025 (2.5% as a decimal), n = 1 (since the interest is compounded annually), and t = 9. Substituting the values into formula, we will get:
A = £4000(1 + 0.025/1)⁽¹*⁹⁾ = £4995.45
Therefore, Noah will have £4995.45 in the account after 9 years.
b) The amount of interest earned is simply the difference between the amount at the end of the time period and the initial deposit, i.e.,
Interest = A - P = £4995.45 - £4000 = £995.45
Therefore, Noah will have earned £995.45 in interest from this account after 9 years.
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Select the correct answer. Consider these functions: Which statements, if any, are true about these functions? I. The function f(g(x)) = x for all real x. II. The function g(f(x)) = x for all real x. III. Functions f and g are inverse functions. A. I only B. II only C. I, II, and III D. None of the statements are true.
Based on the functions, the statements that are true about these functions include the following: C. I, II, and III.
What is an inverse function?In Mathematics, an inverse function simply refers to a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine the inverse of any function, you should swap both the input value (x-value) and output value (y-value) as follows;
x = 3y³ + 2
3y³ = x - 2
y³ = (x - 2)/3
y = ∛[(x - 2)/3]
Therefore, the function f(g(x)) is given by:
Function, f(g(x)) = 3[∛((x - 2)/3)]³ + 2
Function, f(g(x)) = 3[(x - 2)/3] + 2
Function, f(g(x)) = x
For the function g(f(x)), we have:
Function, g(f(x)) = ∛[(3x³ + 2 - 2)/3]
Function, g(f(x)) = ∛x³
g(f(x)) = x
In conclusion, the input value (x-value) and output value (y-value) of these functions are interchangeable.
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Raelyn has 33 red beads and 21 blue beads. She mixes the
beads together and uses 6 beads for each key chain she
makes. What multiplication equation and division equation can
help Raelyn determine how many key chains she can make?
The multiplication equation and division equation can
help Raelyn determine how many key chains she can make is 9
What is multiplication equation?When solving multiplication equations, these equations may have the form ax = c, bx = d, or cx = f
The question says that Raelyn has 33 red beads and 21 blue beads. She mixes the
beads together and uses 6 beads for each key chain she
makes.
Based on the given conditions, formulate:: (33+21) /6
Calculate the sum or difference: 54/6
Cross out the common factor: 9
Therefore, the multiplication equation and division equation gives 9
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Evaluate this expression for the given values of x and y 2xy x=5 y= -3 FAST QUICK I WILL GIVE BRAINLIEST
Find the indicated real nth root(s) of a. n=6,a=-729
There is no real nth root. Option C
What is indicated real nth root(s)?
You should understand that a square root of a number is a number that when multiplied by itself yields the original number.
Also, to indicate that we want both the positive and the negative square root of a radicand we put the symbol ± (read as plus minus) in front of the root. ... Zero has one square root which is 0. ... Negative numbers doesn't have real square roots since a square is either positive or 0.
The formula is
nth root of x
Where x ≥0
-729≥0
In conclusion there is no real root for the figure -729
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. Fractions less than 1/2
Answer:
[tex]\frac{1}{x} ; x > 2[/tex]
Step-by-step explanation:
A fraction less than one half would have to be one out of a larger number than two.
Basically, let's change the denominator to "x"
[tex]\frac{1}{x}[/tex] -> for this fraction to be less than 2, x always has to be greater than two
in alphabetical order, the six most common last names in the united states in 2018 were brown, garcia, johnson, jones, smith, and williams (united states census bureau website). assume that a sample of
Based on the information given in the bar chart, it should be noted that the most popular last names are Smith, Johnson, and Williams.
What is meant by bar chart?A bar chart, often known as a bar graph, is a diagram that displays categorical data as rectangular bars with heights or lengths proportional to the values they stand for. You can plot the bars either vertically or horizontally. A vertical bar chart may also be referred to as a column chart. One of the various methods used to convey data in a visual format so that the reader can easily spot patterns or trends is the usage of bar charts. Typically, discrete, continuous, or categorical variables are presented in bar charts in class intervals.The information provided in the question is needed to solve the bar chart and pie chart, it should be highlighted.Miller is the name with the smallest population. On the other hand, Smith, Johnson, and Williams are the most common last names.The complete question is,
Most Popular Last Names. In alphabetical order, the six most common last names in the United States in 2018 are Brown, Garcia, Johnson, Jones, Smith, and Williams (United States Census Bureau website). Assume that a sample of 50 individuals with one of these last names provided the following data:
Brown Williams Williams Williams Brown
Smith Johnson Williams Smith Miller
Johnson Williams William Johnson Jones
Miller Jones Jones Smith Smith
Miller Johnson Smith Jones Jones
Johnson Smith Brown Smith Johnson
Jones Smith Smith Williams Brown
Johnson Johnson William Smith Brown
Smith Miller Johnson Brown Johnson
Brown Jones Miller Smith Miller
Summarize the data by constructing the following:
A. Relative and percent frequency distributions
B. A bar chart
C. A pie chart
D. Based on these data, what are the three most common last names?
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Mrs. Smith is upgrading all 6 of the family phones and wants them to be
protected. New phone cases cost $45 each and screen protectors cost $25
each. Write an expression and use the distributive property to find how
much Mrs. Smith will spend to protect the new phones.
Answer:
6(45 + 25)
Step-by-step explanation:
Suppose that 20,000 married adults in a country were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.
x P(x) xP(x)
0 0.10
1 0.25
2 0.30
3
4 0.10
5 0.05
6 (or more) 0.05
(a) Find the probability that a married adult has three children. (Enter your answer to two decimal places.)
(b) In words, what does the expected value in this example represent?
the number of children adults in the country have
the number of children married adults in the country have
the average number of children married adults in the country have
the average number of children adults in the country have
(c) Find the expected value. (Enter your answer to two decimal place.)
children
(d) Is it more likely that a married adult will have two to three children or four to six children? How do you know?
it is more likely to have four to six children, with p = 0.2
it is more likely to have two to three children, with p = 0.45
it is more likely to have four to six children, with p = 0.8
it is more likely to have two to three children, with p = 0.3
it is more likely to have four to six children, with p = 0.1
In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).
a) The probability that a married adult has three children is 0.30.
b) The expected value in this example represents the average number of children married adults in the country have.
c) The expected value is 1.90 children.
d) It is more likely that a married adult will have two to three children, with p = 0.55. This is because the probability of having two to three children (0.30 + 0.25 = 0.55) is greater than the probability of having four to six children (0.10 + 0.05 = 0.15).
In this example, the expected value is 1.90 children, and it is more likely that a married adult will have two to three children (with a probability of 0.55) than four to six children (with a probability of 0.15).
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Question 7, I am quite unsure
Answer: 137000 cm³
Step-by-step explanation:
formula to find the volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³
formula to find the volume of a cylinder= πr²×h
both the shapes will have the same radius therefore to get the radius you should divide the diameter by two *you probably already know abt it*
so 46/2= 23 (the radius of both the shapes)
In order to get the height of the cylinder you should subtract the radius of the hemisphere from the total height given as the radius is the same all around the hemisphere **but remember not to mistake the diameter as the radius when subtracting a hemisphere's height from a total height**
height of the cylinder= 90cm- 23cm= 67
Therefore now substitute the values into the formulas and find the volumes of the two shapes separately...
volume of a hemisphere= [tex]\frac{2}{3}[/tex] x πr³
= [tex]\frac{2}{3}[/tex]× π × 23³
= 25482.5 cm³
volume of a cylinder= πr²×h
= π × 23² × 67 (including the height calculated above)
= 111347.5 cm³
Now add the volumes you found which will give you the volume of water that the tank holds when it if full.
volume of a cylinder + volume of a Hemisphere
111347.5 + 25482.5
136830
137000 cm³ (make sure to estimate the final answer to 3s.f or else you'll lose your accuracy mark)
