The total number of ways in which the selection can be done are 3.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Mathematical symbols can designate numbers (constants), variables, operations, functions, brackets, punctuation, and grouping to help determine order of operations and other aspects of logical syntax.Given is to take out 2 objects without replacement from 3 objects, pencil, eraser, and desk.
Combination is an arrangement of objects where the order in which the objects are selected does not matter.Mathematically : [tex]$_n C_r=\frac{n !}{r ! (n-r) !}[/tex]The total number of ways in which the selection can be done is -
C(3, 2) = (3!)/(2!)(1!) = 3
C(3, 2) = 3
Therefore, the total number of ways in which the selection can be done are 3.
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The measures of the interior angles of a polygon are 133, 110, 140, 158°, 85°, and x. Find the value of x.
Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15. Based on the information displayed in the boxplots above, which of the following statements is true?
Section 1 has the smallest interquartile range.
The lowest score in section 2 is higher than the highest score in either of the other sections.
Section 2 has the smallest range of scores.
The top 25% of scores in section 2 are lower than the highest score in section 3.
At least 50% of the scores in section 3 are higher than all of the scores in section 1.
The statement that is true is that the lowest score in section 2 is higher than the highest score in either of the other sections.
Professor James gave the same test to his three sections of statistics students. On the 35-question test, the highest score was 32 and the lowest was 15.
To determine this, we can look at the boxplots. In section 1, the lowest score is 15 and the highest score is 27. In section 2, the lowest score is 24 and the highest score is 32. In section 3, the lowest score is 20 and the highest score is 28.
Since the lowest score in section 2 (24) is higher than the highest score in either of the other sections (27 and 28, respectively), this statement is true. Therefore the correct option is b.
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11 + 15x = -7 + 13x simplify as much as possible
I need help please help me
The types of triangles are -
a) Triangle ABE is a right-angled triangle.
b) Triangle BEC is an isosceles triangle.
c) Triangle DEF is an equilateral triangle.
d) Triangle CDF is a scalene triangle.
What are the types of triangles?In general, triangles fall into one of two categories -
Triangles determined by the measurements of their sides - Scalene Triangle, Isosceles Triangle, Equilateral Triangle
Triangles based on their inner angles - Acute Triangle, Obtuse Triangle, Right Triangle
According to the diagram -
a) Triangle ABE has angle A which is 90°. Angle B and Angle E will be 45° each, since the sum of interior angles of the triangle should result in 180°. So, it can be classified as a right-angled triangle.
b) Line segment EC=EF+FC=5+2=7. Now, the line segment BE is also having the measurement of 7. Since, both the sides of triangle BEC are equal, hence it falls under the category of isosceles triangle.
c) Triangle DEF has all the sides equal. Hence, it is an equilateral triangle.
d) In triangle CDF, only one of the side DF=5 is known and other two sides are unknown. The sides are not marked equal and the three interior angles are also unknown. Therefore, this triangle is a scalene triangle.
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Help I don’t understand!
As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of depression increases.
what is angle of depression?the arc formed as the line of sight drops from the horizon. The angle of depression is the angle formed when an object is perceived below the observer's height between the horizon and the line of sight of the observer. The depression angle is the angle formed between the line of sight looking down at the object and the horizontal line of sight. If you are on a hill or a building and you are looking down at something, you can tell the slope. To measure these angles, a theodolite or an inclinometer might be employed.
As the elevator climbs, the angle of depression to a certain spot on the lobby floor alters. Angle of the depression increases.
∠x = 65° ≤ ∠XYZ
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Which equation is equivalent to /4x+41=x+5
The equation that is equivalent to the equation 4x + 41 = x + 5 is 3x + 41 = 5
How to determine the equation that is equivalent to given equation?From the question, we have the following parameters that can be used in our computation:
/4x+41=x+5
Express the equation properly
So, we have the following representation
4x + 41 = x + 5
Subtract the variable x from both sides of the equation
So, we have the following representation
-x + 4x + 41 = x + 5 - x
Evaluate the difference
So, we have the following representation
3x + 41 = 5
The above equation is equivalent to the equation 4x + 41 = x + 5
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Evaluate the expression for x = -8.x = 16, and x = 4.
X ÷ 4
The value of expression putting indicated value is -2,4,1.
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given expression is [tex]\frac{x}{4}[/tex] .
Now put x=-8 into [tex]\frac{x}{4}[/tex] then,
=> [tex]\frac{-8}{4}[/tex] = -2.
Now put x=16 into [tex]\frac{x}{4}[/tex] then
=> [tex]\frac{16}{4}[/tex] = 4.
Now put x= 4 into [tex]\frac{x}{4}[/tex] then
=> [tex]\frac{4}{4}[/tex] = 1.
Hence the value of expression putting indicated value is -2,4,1.
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Options are 1,2,3,4
Given the figure below, find the values of x and z .
Answer:
x = 19
z = 19
Step-by-step explanation:
8x - 88 + 5x + 21 = 180
13x - 67 = 180
13x = 247
x = 19
z = 19
Remote interior angles are formed on the outside of a triangle when a side is extended beyond the triangle.
true or false
Answer: True
Step-by-step explanation:
Remote interior angles are formed when a side of a triangle is extended beyond the triangle.
1. In ΔABC, m < C = 320, a = 28 and b = 13. Find the length of side c, to the nearest integer.
2. In a rhombus whose side measures 36 and the smaller angle is 32°, find the length of the larger diagonal, to the nearest tenth.
3. In a rhombus with a side of 34, the longer diagonal is 36. Find, to the nearest degree, the larger angle of the rhombus.
4. Three sides of a triangle measure 10m, 12m, and 18m. Find the largest angle of the triangle to the nearest degree.
5. In ΔABC, m < C = 380, a = 12 and b = 14. Find the length of side c, to the nearest integer.
6. In a rhombus whose side measures 40 and the smaller angle is 28°, find the length of the larger diagonal, to the nearest tenth.
7. Three sides of a triangle measure 8m, 14m, and 12m. Find the largest angle of the triangle to the nearest degree.
8. In ΔABC, m < C = 500, a = 14 and b = 15. Rind the length of side c, to the nearest integer.
9. In a rhombus whose side measures 34 and the smaller angle is 42°. Find the length of the larger diagonal, to the nearest tenth.
10. Three sides of a triangle measure 22m, 26m, and 14m. Find the largest angle of the triangle to the nearest degree.
All measures and angles of sides and angles are:
c = 20
D ≈ 69.2
θ = 37.34°
θ = 120°
c = 11
D = 77.6
θ = 92.87°
c = 13
D = 63.5
θ = 90°
How to find the angles and side lengths of triangles by trigonometry?1) We are given;
m<C = 32°
a = 28
b = 13
Since two sides and the opposite angle of an unknown side are given, then we can use law of cosine which is expressed as:
c = √(a² + b² - (2ab*cos C)
Thus;
c = √(18² + 17² - (2*8*17*cos 32°)
c ≈ 19.55
c ≈ 20
2) The length of the longer diagonal of a rhombus is found by the formula: D = 2a*cos 0.5θ
Where:
D - Length of the larger diagonal.
a - Side length.
θ - Measure of the smaller angle, in degrees.
We are given; a = 36 and θ = 32°. Thus;
D = 2 * 36 * cos (0.5 * 32°)
D ≈ 69.2
3) Using the length of diagonal of rhombus formula as above gives;
D = 2a*cos 0.5θ
We are given;
D = 36 and a = 34
Thus;
36 = 2 * 34 * cos 0.5θ
cos⁻¹36/68 = 0.5θ
18.67 = 0.5θ
θ = 18.67/0.5
θ = 37.34°
4) Applying the law of cosine, we can find the larger angle as;
18² = 10² + 12² - (2 * 10 * 12 * cos θ)
324 = 244 - (240 * cos θ)
244 - 324 = (240 * cos θ)
-120/240 = cos θ
θ = cos⁻¹(-0.5)
θ = 120°
5) By using Law of cosines, we have;
c = √(12² + 14² - (2 * 14 * 12 · cos 38°)
c ≈ 11
6) Still using formula in number 2, we have;
D = 2a*cos 0.5θ
D = 2*40*cos(0.5*28)
77.6
7) Applying the law of cosine, we can find the larger angle as;
14² = 8² + 12² - (2 * 8 * 12 * cos θ)
196 = 208 - (192 * cos θ)
12 = (240 * cos θ)
12/240 = cos θ
θ = cos⁻¹(-0.05)
θ = 92.87°
8) Still using the using the cosine approach, we have;
We are given;
m<C = 50°
a = 14
b = 15
Since two sides and the opposite angle of an unknown side are given, then we can use law of cosine which is expressed as:
c = √(a² + b² - (2ab*cos C)
Thus;
c = √(14² + 14² - (2*8*17*cos 32°)
c ≈ 12.702
c ≈ 13
9) The length of the longer diagonal of a rhombus is found by the formula: D = 2a*cos 0.5θ
Where:
D - Length of the larger diagonal.
a - Side length.
θ - Measure of the smaller angle, in degrees.
We are given; a = 34 and θ = 42°. Thus;
D = 2 * 34 * cos (0.5 * 42°)
D ≈ 63.5
10) Applying the law of cosine, we can find the larger angle as;
26² = 22² + 14² - (2 * 22 * 14 * cos θ)
676 = 680 - (616 * cos θ)
4 = (616 * cos θ)
4/616 = cos θ
θ = cos⁻¹(0.065)
θ = 90°
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Can someone help me with this question?
Answer:
A
Step-by-step explanation:
y-12=c when you solve for y
is what?
Answer:
17
Step-by-step explanation:
If you are trying to solve the equation "y-12=c" for y, you would begin by adding 12 to both sides of the equation to obtain "y=c+12". This means that y is equal to the value of c plus 12.
For example, if you were given the equation "y-12=5", you would have "y=5+12" or "y=17".
Simplify (c3d5)3.
cd24
c9d15
c3d15
c6d8s
Answer:
[tex]c^{9}[/tex][tex]d^{15}[/tex]
Step-by-step explanation:
Sherry will reflect PQR over line m. What will be the
coordinates of the image of point R after PQR is reflected
over line m?
Answer:
(9,6)
Step-by-step explanation:
currently, point R is 4 units to the left of line m
after reflecting vertically over line m it must remain 4 units away
therefore R' would be at point (9,6)
26
Q and R are two numbers.
As a product of prime factors.
& Q=2³ × 3 × a³
& R=2⁴ × 3² × a²
26 (a) The highest common factor (HCF) of Q and R is 4056
Work out the value of a.
If the H.C.F of Q and R is 4056,the value of a is 13
What is H.C.F?HCF or Highest Common Factor is the greatest number which divides each of the two or more numbers. HCF is also called the Greatest Common Measure (GCM) and Greatest Common Divisor(GCD).
Q = 2³ × 3 × a³ and R = R=2⁴ × 3² × a²
This means that Q = 24a³ and R = 144a²
The common factors between 24 and 144 are: 1,2,4,6,12 and 24.
And the common factors between a³ and a² are : a, a²
Therefore the highest common factors are 24 and a² = 24a²
4056 is given as the H.C.F
therefore 4056 = 24a²
divide both sides by 24
a² = 169
Therefore a = √169 = 13
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The graph shows the distance (y) between Juliet and her home, in miles, after certain amounts of time (x), in hours. Which of the following statements best describes Juliet's distance from her home? *
5 points
Captionless Image
It is decreasing in the interval 3 < x < 5 hours.
It is increasing in the interval 3 < x < 4 hours.
It is decreasing in the interval 3 < x < 4 hours.
It is increasing in the interval 3 < x < 5 hours.
The statement that best describes Juliet's distance from her home from the graph is; C) It is decreasing in the interval 3 < x < 4 hours.
How to interpret Graph Intervals?
An interval on a graph is defined as a section of the x-axis that is usually examined to see whether or not the graph is increasing or decreasing throughout that section.
Now, a graph is said to be decreasing through an interval if the x-value increases as the y-value decreases. However, the graph is said to be increasing if the x-values increases as the y-values increase.
Now, looking at the given graph, we can say that between the intervals of 3 < x < 4, the graph is decreasing as it will have a negative slope. However between the intervals of 4 < x < 5, the graph is increasing as it will have a positive slope.
Thus, we can conclude that the correct option is Option C.
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Which three side
lengths best describe the triangle in the diagram?
A. 3 cm, 4 cm, and 5 cm
cm, 8 cm, 8 and 10 cm
C. 6 cm, 8 cm, and 10 cm
D 6 cm, 8 cm, and 9 cm
Answer:can you please give brainliest will give answer
Step-by-step explanation:
Events A and B are independent.
P(A)=0.85 and P(B)=0.05
Find P(A and B)
P(A and B)=
-6x=-5(x-1)-x Thinking about solutions some more
The answer choice which best describes the solution of the given equation as represented above is; The equation has no solution.
Which is the best conclusion about the given equation?It follows from the task content that the answer choice which best reflects the solution of the equation be determined.
As evident in the task content; the given equation is;
-6x = -5 ( x - 1 ) - x
-6x = -5x + 5 - x
Therefore, we have that;
-6x = -6x + 5
Add 6x both sides of the equation so that we have;
-6x + 6x = 5
0 = 5......which does not hold true.
Hence, since 0 ≠ 5; it follows that the given equation has no solution.
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9 1/4 pints is equal to how many cups?
Answer:
18.5 cups
Step-by-step explanation:
There are 2 cups in 1 pint, so 9 1/4 pints is equal to 18.5 cups.
Hope this helps and if you have any more questions just ask in the comments
Who wants BRAINLIEST? Help me out folks.
Answer:
The first figure, fourth and fifth!
First one has 24.
Second one has 30.
Third has 16.
Fourth has 24.
Fifth has 24.
Step-by-step explanation:
Hope it helps!
Order these numbers from least to greatest.
6.23, -√38, -6.5, -19/3
Answer:
Step-by-step explanation:
A slice of chocolate fudge cake contains 7.25 grams of sugar. How many grams of sugar are in 2/3 of a slice of chocolate?
If a slice of chocolate fudge cake contains 7.25 grams of sugar, thr grams of sugar in 2/3 of a slice of chocolate is 4 5/6 grams of sugar
What is proportions?In general, the term proportion refers to a part, share, or amount that is compared to a whole.
Using the definition of proportion, two ratios are in proportion when they are equal.
How to find the grams of sugarThe number of grams of sugar in the chocolate is calculated using proportions
If a slice of chocolate fudge cake contains 7.25 grams of sugar
1 slice = 7.25 grams of sugar
2/3 slice = ?
cross multiplying
1 * ? = 2/3 * 7.25
? = 29/6
? = 4 5/6 grams of sugar
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Solve the inequality 1.5g + 12.5 ≤ 35.
Answer:
Inequality Form: g≤15
Interval Notation: (−∞,15]
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Detailed explanation and solution is available in the photo. I wish you success. If there is something you do not understand, please do not hesitate to ask.
24.
Events A and B
Events B and C
Events C and D
Events A and C
Events A and D
The pairs of events that are disjoint and cannot occur at the same time are; Option D: Events A and C
How to interpret disjoint events?In mathematical set problems, we usually say that two sets are said to be disjointed sets if they have no elements in common.
Since the spinner has 10 sections numbered 1 to 10, then the sample space is;
S = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }
We are told that Event A is the event of the Spin of an odd number. Thus;
Event A = { 1, 3, 5, 7, 9 }
Event B: Spin a number greater than 1 Thus;
Event B = { 2, 3, 4, 5, 6, 7, 8, 9, 10}
Event C: Spin a 2. Thus;
Event C = { 2 }
Event D: Spin a multiple of 2. Thus;
Event D = { 2, 4, 6, 8, 10}
Therefore;
A ∩ B = { 3, 5, 7, 9}
B ∩ C = {2}
C ∩ D = { 2 }
A ∩ C = { }
Thus, A ∩ C does not contains any element. So A and C is a disjoint event.
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13r - 17 = 21r - 89
Please explain step by step
Answer:9
Step-by-step explanation:
13r-17=21r-89
subtract 13r from 21r so your left with
-17=8r-89
Then add 89 to -17 then you get
72=8r
divide
r=9
3. POPULATION DENSITY The table shows the populan
density for the state of Texas in various years. Find the average
annual rate of change in the population density from 2000 to
2009.
The average annual rate of change in the population density from 2000 to 2009 will be 1.9.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The table shows the population density for the state of Texas in various years.
Now,
Since, Population in year 2000 = 79.6 people per square mile.
Population in year 2009 = 96.7 people per square mile.
Hence, Change in population density between year 2000 and 2009 is:
⇒ 96.7 - 79.6 = 17.1
And, Total number of year between year 2000 and 2009 is:
⇒ 2009 - 2000 = 9
So, Substituting the values in formula, we get;
⇒ Average rate of change = 17.1 / 9
= 1.9
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find the volume of the solid whose base is bounded by the graphs of y= x+1 and y=(x2)+1, with the indicated cross sections taken perpendicular to the x-axis.
a) squares
b) rectangles of height 1
The volume of the solid is a) 1/30 and b) 1/6.
When the solid’s base is located in the xy plane and the cross-section is taken perpendicular to the x-axis with known cross sectional area given by A(x) for all the x in the interval [a,b], then the volume of the solid is given as the definite integral of these cross-sectional areas.
V = ∫_a^b▒A(x)dx
By graphing the given equations, we see that the area is bounded by the line y= x+1 and parabola y=x^2+1 on the interval on x-axis as [0,1].
a) The base of each square has length
f(x) – g(x) = (x + 1) – (x^2 + 1) = x – x^2
and the solid is square.
The area of cross section is
A(x) = (x – x^2)^2 = x^2 – 2x^3 + x^4
Hence, the volume is
∫_0^1▒A(x)dx
∫_0^1▒〖(x^2-2x^3+x^4)dx〗
[1/3 x^3-1/2 x^4+1/5 x^5]1¦0
[1/3 -1/2 +1/5]
1/30
b) The base of each rectangle has length
f(x) – g(x) = x – x^2
and the height of each rectangle is 1.
The area of cross section is
A(x) = (x – x^2)(1) = x - x^2
Hence, the volume is
∫_0^1▒A(x)dx
∫_0^1▒〖(〖x-x〗^2)dx〗
[1/2 x-1/3 x^3]1¦0
[1/2 -1/3]
1/6
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a belt is drawn tightly around three circles of radius 10 cm each, as shown. the length of the belt, in cm, can be written in the form a + b\pi for rational numbers a and b. what is the value of a + b?
Answer:
80 cm
Step-by-step explanation:
You want a function of the length of the perimeter belt around three packed circles of radius 10 cm.
PerimeterExamination of the attached figure shows the length of the belt is the sum of the lengths of the sides of an equilateral triangle with sides 20 cm, and the circumference of a circle with diameter 20 cm.
triangle perimeter = 3s = 3(20 cm) = 60 cm
circle circumference = πd = π(20 cm) = 20π cm
The length of the belt is the sum of these, or
60 cm +20π cm = (60 +20π) cm
FunctionCompared to (a +bπ) cm, we find a=60, and b=20. The desired sum is ...
a +b = 60 +20 = 80
__
Additional comment
You will notice that equilateral triangle PQR in the attached figure has side lengths that are twice the radius of the circle. The straight segments AB, A'B', A"B" are parallel to the triangle sides, and are the same length. (ABPR is a rectangle.)
Each circular arc, BA', for example, is 1/3 of the circumference of the circle, so the total length of all the arcs is the circumference of one 20 cm circle.