The probability of drawing two consecutive Jacks without replacement is
1/221
Two events A and B are independent if the knowledge that one occurred does not affect the chance the other occurs. For example, the outcomes of the two roles of a fair die are independent events. The outcome of the first roll does not change the probability of the outcome of the second roll. To show two events are independent, you must show only one of the above conditions. If two events are NOT independent, then we say that they are dependent
The probability of drawing two consecutive Jacks without replacement is
1/221
The probability of drawing the initial Jack is 4 out of 52 as there are 4 Jacks in a deck of 52 cards.
Since you are not replacing the Jack the Deck now has 51 cards and 3 Jacks making that 3 out of 51.
1st Jack = 4/52
2nd Jack = 3/51
To find the probability of consecutive events we would multiply the individual probabilities.
(4/52)(3/51)=12/2652
=1/221
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A square piece of cloth with an area of 324 square inches is folded in half twice to form the napkin shown. What is
the area of the folded napkin?
Answer:
I think it is 4.5 length
area= 20.25
Step-by-step explanation:
Step 1: I square rooted 324 to get 18
Step 2: I divided that number by 2 twice to get 4.5
18/2 = 9/2 = 4.5
multiply 4.5 by 4.5 to get 20.25!
Hope this is correct!
15. a) Graph the following equation: 2x−y=−8
The graph of the function is added as an attachment
How to graph the equationFrom the question, we have the following parameters that can be used in our computation:
2x−y=−8
Make y the subject
y = 2x + 8
The above equation is a linear equation
A linear equation is represented as
y = mx + c
Where
slope = m
y-intercept = c
This means that the slope is 2 and the y-intercept is 8
Next, we plot the graph of the equation
See attachment for the graph
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let $0, a, b, c$ be the vertices of a square in counterclockwise order. then enter $b/a$ and $c/a$ in that order in rectangular form.
The square is shown in the complex plane, where each vertex can be represented as a complex number.
If we let the first vertex be 0, then the next vertex [tex]$a$[/tex] is at a distance of 1 unit along the real axis. The complex number representing [tex]$a$[/tex] is [tex]$1 + 0i$[/tex]. The vertex [tex]$b$[/tex] is at a distance of 1 unit along the imaginary axis, so its complex representation is [tex]$0 + 1i$[/tex]. Finally, the vertex [tex]$c$[/tex] is at a distance of 1 unit along the negative real axis, so its complex representation is [tex]$-1 + 0i$[/tex].
To find [tex]$b/a$[/tex], we divide the complex number representing [tex]$b$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$b/a = (0 + 1i) / (1 + 0i) = 0 + 1i$[/tex].
Similarly, to find [tex]$c/a$[/tex], we divide the complex number representing [tex]$c$[/tex] by the complex number representing [tex]$a$[/tex]. We get [tex]$c/a = (-1 + 0i) / (1 + 0i) = -1 + 0i$[/tex].
So, the values of [tex]$b/a$[/tex] and [tex]$c/a$[/tex] in rectangular form are [tex]0 + 1i[/tex] and [tex]-1 + 0i[/tex], respectively.
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the only research method that allows us to determine whether two variables are causally related is to conduct a(n) _______
Given point O(0, 1) and point P(5, 3), what is the slope of the line that passes through points P and Q
Answer:
Step-by-step explanation:
y = mx +c
1 = m0 + c
1=0+c
c=1
5-1=4
3-1=2
4/2=2
m=2
y=2x+1
The table shows the numbers of cars manufactured by a company for selected years. Identify a polynomial function for cars manufactured in thousands where x represents the years since 1990.
P(x) = 0.5x3 + 0.2x2 + 0.3x + 0.4
P(x) = 0.5x3 + 0.5x2 + 0.4x + 0.4
P(x) = 0.2x3 + 0.2x2 + 0.3x + 0.3
P(x) = 0.2x3 + 0.5x2 + 0.4x + 0.3
The polynomial function for the cars manufactured in thousands since 1990, where x represents the number of years since 1990 the fourth option
P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3
What is a polynomial?A polynomial consists of an expression that has two or more terms of (the same) variables with different powers or index.
The possible table in the question, obtained from a similar question on the internet is presented as follows;
Year; [tex]{}[/tex] 1991 1993 1995 1997 1999
Cars Manufactured; [tex]{}[/tex] 1.4 11.4 39.8 96.2 190.2
(thousands)
The details in the table indicates that we get;
When x = 1991 - 1990 = 1, P(x) = 1.4
Which, based on the coefficients of x³, x², and x, corresponds with the first and the fourth polynomial.
p(x) = 0.5·x³ + 0.2·x² + 0.3·x + 0.4...(1)
p(1) = 0.5 × 1³ + 0.2 × 1² + 0.3 × 1 + 0.4 = 1.4
P(x) = 0.2·x³ + 0.5·x² + 0.4·x + 0.3...(4)
p(1) = 0.2 × 1³ + 0.5 × 1² + 0.4 × 1 + 0.3 = 1.4
When x = 1993 - 1990 = 3, we get in equation (1);
p(3) = 0.5 × 3³ + 0.2 × 3² + 0.3 × 3 + 0.4 = 16.6
The polynomial in equation (4) indicates that we get;
p(3) = 0.2 × 3³ + 0.5 × 3² + 0.4 × 3 + 0.3 = 11.4
Therefore, the polynomial in the fourth equation best represents the polynomial function for the cars manufactured in thousands where x represents the years since 1990
Verifying, we get;
When x = 5; p(5) = 0.2 × 5³ + 0.5 × 5² + 0.4 × 5 + 0.3 = 39.8
When x = 7; p(7) = 0.2 × 7³ + 0.5 × 7² + 0.4 × 7 + 0.3 = 96.2
When x = 9; p(9) = 0.2 × 9³ + 0.5 × 9² + 0.4 × 9 + 0.3 = 190.2
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wenty-five randomly selected students were asked the number of movies they watched the previous week. the results are as follows:
The sample mean of the number of movies watched by 25 students is 2.8 and the approximate sample standard deviation is 1.15.
(a) The sample mean X can be calculated by taking the average of the number of movies watched by all 25 students.
Step 1: Sum up the number of movies watched by all 25 students:
[tex]0 * 1 + 1 * 2 + 2 * 4 + 3 * 10 + 4 * 6 + 3 * 2 = 0 + 2 + 8 + 30 + 24 + 6 = 70[/tex]
Step 2: Divide the sum from Step 1 by the number of students (25):
70 / 25 = 2.8
So the sample mean X = 2.8
(b) The sample standard deviation s can be calculated using the formula:
[tex]s = \sqrt{\frac{ \sum(X - X_{mean})^2}{(n-1)} }[/tex]
Where [tex]X_{mean}[/tex] is the sample mean, n is the sample size, and Σ represents the sum of all values.
Step 1: Calculate [tex](X - X_{mean})^2[/tex]for each data point and sum up the values:
[tex](0 - 2.8)^2 * 1 + (1 - 2.8)^2 * 2 + (2 - 2.8)^2 * 4 + (3 - 2.8)^2 * 10 + (4 - 2.8)^2 * 6 + (3 - 2.8)^2 * 2\\ = 7.84 + 3.24 + 0.64 + 9.6 + 1.44 + 7.84\\ = 31.36[/tex]
Step 2: Divide the sum from Step 1 by (n - 1) = 24:
31.36 / 24 = 1.31
Step 3: Take the square root of the result from Step 2:
[tex]\sqrt{1.31} = 1.15[/tex]
So the approximate sample standard deviation s = 1.15 (rounded to two decimal places).
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Find the length of each arc. Round to the nearest tenth.
The arc lengths of the given circles are 8π/3, 14π/3 and 4π
What is the arc length of a circle?Arc length is the distance between two points along a section of a curve.
Given are circles, with radii 4, 3 and 3 units, we need to find the arc length of each,
Since, angles are in radian, convert them into degree by multiply them by π/180°
1) radius = 2π/3 × 180°/π
= 120°
2) radius = 7π/6 × 180°/π
= 210°
3) radius = 4π/3 × 180°/π
= 240°
Arc length = θ/360° × 2π × radius, where θ is the central angle,
1) Arc length = 120°/360° × 2π × 4
= 8π/3
2) Arc length = 210°/360° × 2π × 3
= 14π/3
3) Arc length = 240°/360° × 2π × 3
= 4π
Hence, the arc lengths of the given circles are 8π/3, 14π/3 and 4π
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you are given two arrays of integers a and b, and an array queries, the elements of which are queries you are required to process. every queries[i] can have one of the following two forms: [0, i, x]. in this case, you need to assign a[i] the value of x (a[i]
A dynamic array is an array with a big improvement: automatic resizing.
How does dynamic array works?
A random access, variable-size list data structure called a dynamic array, growable array, resizable array, dynamic table, or array list allows elements to be added or removed. It comes with standard libraries for many current, widely used programming languages.
A value of type array is stored in a static array variable. A pointer to an array value is stored in a dynamic array variable. The code you write to use either type of array differs very little because of automatic pointer dereferencing and automatic index padding.
Resizable dynamic arrays offer random access to its elements. They can have variable size initializations, and the software can change their size at a later time.
Initial Values:
n = 2
arr[0] = [ ]
arr[1] = [ ]
Query 0: Append 5 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]
last answer = 0
arr[0] = [5]
arr[1] = [ ]
Query 1: Append 7 to arr[( 1 ⊕ 0 ) % 2 )] = arr[1]
arr[0] = [5]
arr[1] = [7 ]
Query 2: Append 3 to arr[( 0 ⊕ 0 ) % 2 )] = arr[0]
last answer = 0
arr[0] = [5, 3]
arr[1] = [7 ]
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half as many pages as george read. define a variable and write each phrases as an algebraic expression
The variable that can be used to represent the number of points scored before is x and the algebraic expression would be equal to (3x - 2).
How to write algebraic expression?Algebra refers to the system for computation using letters or other symbols to represent numbers, with rules for manipulating these symbols.
let the Number of points scored before = x
3 times the number of points scored before
= 3 × x
= 3x
Thus, two points fewer than 3 times the number of points scored before;
= 3x - 2
The examples of algebraic expression are:
2t - 5 + 3t
65x + y - 8y + 5x
In conclusion, the expression can be written as; 3x - 2
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The graph shows the position (distant from home) of a bicycle rider on a 42-minute trip. Letters A through E are time intervals during the trip. The key defines the length of each interval.
The point D on the graph shows that the rider has stopped moving.
What is a graph?
Graph is a line or curve of a line with represents the relation between two quantities.
There are two axis in graph each axis represents different quantity in a graph.
Two axis are X-axis and Y-axis. Generally quantity which increases gradually is kept on X-axis.
By using graph we can calculate many different things like in distance time graph if we calculate the area of the graph we can get the speed for that region.
Graph is a very helpful took as its a pectoral representation of data and we all know action speak louder than words so graphs can explain more information with less data.
Now for the given question:
In graph section D shows that bicycle rider has stopped because the distance of rider from its house is not increasing while the time increases due to of which this interval has a straight line.
Hence, rider has stopped moving at region D.
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The complete Question is:
The graph shows the position (distance from home) of a bicycle rider on a 42-minute trip. Letters A through E are time intervals during the trip. The key defines the length of each interval. Which of the following best explains how the graph shows that the rider stopped during time interval D?
true/false. prove that any field if is also a vector space over itself, with the field addition used as vector addition, and the field multiplication used as scalar multiplication.
Any field if is also a vector space over itself, with the field addition used as vector addition, and the field multiplication used as scalar multiplication is True.
A set whose elements, frequently termed vectors, can be added to and multiplied ("scaled") by figures known as scalars is referred to as a vector space (also known as a linear space). Real numbers make up scalars most of the time, but they can also be complex numbers or, more broadly, components of any field.
If V and W are both sub spaces of the vector space U, then their intersection is also a subspace of U.
According to the definition of a subspace, we can say that {0} belongs to both V and W.
So, {0} will also belong to the intersection of V and W.
That is, {0} ∈ V ∩ W.
Now, let a, b are scalars and v, w∈ V ∩ W.
So, we get
v, w ∈ V and v, w ∈ W.
Since V and W are sub spaces of V and W, so we get
av + bw ∈ V and av + bw ∈ W.
Therefore, av + bw ∈ V ∩ W.
Thus, V ∩ W is also a subspace of U.
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0°≤ theta ≤ 180° and cos theta = -3/7, find tan theta, and csc theta. Include a sketch as a part of your solution. Rationalize denominators.
The trigonometry ratios are tan(∅) = 2/3√10 and
csc(∅) = 7√10/20
How to determine the trigonometry ratiosFrom the question, we have the following parameters that can be used in our computation:
0°≤ ∅ ≤ 180°
Also, we have
cos(∅) = -3/7
The tangent is calculated as
tan(∅) = √[1/cos²(∅) - 1]
Substitute the known values in the above equation, so, we have the following representation
tan(∅) = √[1/(-3/7)² - 1]
So, we have
tan(∅) = √[49/9 - 1]
This gives
tan(∅) = √40/9
So, we have
tan(∅) = 2/3√10
Also, we have
cos²(∅) + sin²(∅) = 1
So, we have
(-3/7)² + sin²(∅) = 1
Evaluate
sin²(∅) = 1 - (-3/7)²
sin²(∅) = 1 - (9/49)
sin²(∅) = 40/49
Take the inverse of both sides
csc²(∅) = 49/40
So, we have
csc(∅) = 7/(2√10)
Rationalize
csc(∅) = 7√10/20
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uhhh help please
I JUST DONT KNOW WHAT TO DO IM SO SLOW
By using trigonometry formula, The value of variable y is 63.6396103.
What is trigonometry?In the field of mathematics known as trigonometry, correlations between angles and length ratios are studied.
Trigonometry has a wide variety of identities. In order to simplify an expression, identify a more practical version of an expression, or solve an equation, trigonometric identities are frequently employed to rewrite trigonometrical expressions.
Given that, the angle is 45°.
the height is 45.
from the formula Sin A = height/ hypotenuse
⇒ Sin45° = 45/ y
⇒ y = 45 / Sin45°
⇒ y = 45 / 0.7071067
⇒ y = 63.6396103
The value of variable y is 63.6396103.
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factor the expression completely 16x^3-20x^2+28x-35
The expression can be factored as:
(16x^3 - 20x^2 + 28x - 35) = 4x(4x^2 - 5x + 7) = 4x(x - 1)(4x - 7)
consider your eight-digit student id as a set of single-digit integers. for example, if your student id is the number 01238586, then it represents the set , shown in roster notation. for your student id, construct the set and use it to determine the truth set, , for the statement in your answer, show both your set and your set in roster notation.
The set is {0, 1, 2, 3, 5, 6, 8}. and the truth set is {0, 1, 2, 3, 5}
How to determine the set roaster notationFrom the question, we have the following parameters that can be used in our computation:
ID = 01238586
So, the roster notation for the set is
{0, 1, 2, 3, 5, 6, 8}.
Constructing the truth setWe have:
The statement is x ∈ S, (x prime) ∨ (x + 1 ∈ S)
This means that
Prime numbers satisfy the first condition.If x + 1 is an element of the set, then it satisfies the second condition.Using the above as a guide, we have the following:
0: Fails the first, but satisfies the second1: Fails the first, but satisfies the second2: Passes the first3: Passes the first5: Passes the first6: Fails both8: Fails bothSo, the truth set is {0, 1, 2, 3, 5}
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pls help I don't know the answer
Answer: w=-7/4, x = 3 , z = 8.
You were only incorrect on one which I will provide an image on how I solved that one so you can maybe see what you did wrong. hope it helps !
manny made a scale drawing of a swimming pool he used the scale 8 millimeters = 1 meter the pool is 28 meters long in real life how long is the pool on the drawing
Answer:
224 millimeters
or
2.24 cm
Step-by-step explanation:
Scale is 8 millimeters = 1 meter
So 28 meters = 28 x 8 millimeters = 224 millimeters
224 millimeters = 224/10 cm = 22.4 cm
Write expressions for r and h so that the volume of the cone can be represented by the expression 27πx^8.
The expression for r and h are 9 and x⁸ respectively.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, The volume of a cone is 27πx⁸.
We know, The volume of a cone is (1/3)πr²h.
Therefore, (1/3)πr²h = 27πx⁸.
r²h = 81x⁸.
h = x⁸ and r² = 81 ⇒ r = 9
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PLS HELP QUICK ITS IN THE PHOTO BTW
Question 1 What is the total number of minutes spent reading?
A 170 minutes
B 195 minutes
C 205 minutes
D 220 minutes
Question 2
What is the mode of the data set?
18, 23, 12, 21, 23
A 12
B 18
C 21
D 23
Question 3 What is the median of the data table? ITS IN THE PICTURE BTW
A 20
B 25
C 30
D 35
Question 4 Select the data set with more than one mode.
A 19, 23, 15, 23, 15
B 19, 40, 22, 26, 22
C 26, 23, 19, 25, 23
D 26, 34, 27, 29, 30
Question 5 Select the expression that shows how much more time was spent reading on Thursday than Saturday. ITS IN THE PICTURE BTW
A 35 – 20
B 35 – 30
C 45 – 20
D 45 – 30
Question 6 Select the data set with no mode
A 38, 17, 24, 25, 17
B 38, 34, 26, 29, 40
C 24, 17, 21, 17, 21
D 24, 30, 22, 24, 25
Question 7 What is the range of the data set?
28, 32, 22, 20, 25
A 12
B 25
C 32
D 48
Question 8 What is the median of the data set? LAST QUESTION
44, 32, 18, 25, 32
18
25
32
44
Answer:
1.D
2.D
3.D
4.A
5.A
6.B
7.A
8.B
hope those are right
Step-by-step explanation:
1.D
2.D
3.B
4.A
5.A
6.B
7.A
8.B
a 6 inch personal pizza has 606 calories. estimate the number of calories in one slice of a 16 inch pizza. round your answer to the nearest calorie. assume the pizza is cut into eight slices.
Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).
The diameter of a circle is equal to the number of inches in a pizza's size.
The area of a circle is calculated using the formula: [tex]\pi r^{2} = \pi (d/2)^{2}[/tex].
Assume that a pizza's calories are evenly distributed over its surface (even though we know there is a crust ring around the outsize). C calories per square inch, as an illustration.
The number of calories in a 6-inch pizza is
[tex]CA_{6} = C\pi (6/2)^{2} =9C\pi =590[/tex] [eq1]
Calories in a 16-inch pizza are calculated as follows:
[tex]CA_{16}=C\pi (6/2)^{2} =64C\pi[/tex]
The number of calories in one of those pizza's eight slices is:
[tex]X=CA_{16} /8=8C\pi[/tex] [eq2]
math:
[tex]C\pi =590/9[/tex] [from eq1]
[tex]X=8(C\pi )[/tex] [from eq2]
[tex]X=8(590/9)[/tex]
[tex]X=524[/tex] [estimated]
Approximately 524 calories are contained in each of the eight slices of a 16-inch pizza (note: this makes good sense since it has a little less than the area as a complete 6-inch pizza).
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5.638 divided by 32.791
Answer: 0.17193742185
Step-by-step explanation:
Answer:
0.171937422
Step-by-step explanation:
Without performing any algebraic manipulations, can you define the relation between x and y?
The equation of the relation between x and y is y= 2x
How to determine the equationFrom the question, we have the following parameters that can be used in our computation:
The table of values
On the table of values, we can see that
y is twice of x
When represented as an equation, we have
y = 2x
Hence, the equation is y = 2x
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Complete question
Without performing any algebraic manipulations, can you define the relation between x and y?
X (input) 7 8 9 10
y (output) 14 16 18 20
given AC || DF and m
Applying the corresponding angles theorem, m<DEG = 33°.
What is the Corresponding Angles Theorem?The Corresponding Angles Theorem states that if two lines are cut by a transversal, then corresponding angles are equal. This means that if two lines intersected by a transversal form a pair of corresponding angles, then those angles are congruent (have the same measure).
Given that:
m<HBC = 33 degrees
m<ABE = m<HBC [vertical angles are congruent]
m<ABE = 33° [substitution property]
Therefore, based on the corresponding angles theorem, we have:
m<DEG = m<ABE
Substitute:
m<DEG = 33°
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Management Development and Consultancy Bureau (MDCB) conducted research on the daily expenses of civil servants traveling to various cities throughout the world. In particular, MDCB published appropriate per diem totals, which represent the average costs for the typical civil servant at the management level including three meals a day in business-class restaurants and single-rate lodging in business-class hotels. If 86.65% of the per diem costs in Nairobi, Kenya, are less than $449, and if the standard deviation of per diem costs is $36, what is the average per diem cost in Nairobi?
The average per diem cost in Nairobi is $417.806.
What is standard deviation?Standard deviation is the positive square root of the variance. Standard deviation is one of the basic methods of statistical analysis. Standard deviation is commonly abbreviated as SD and denoted by 'σ’ and it tells about the value that how much it has deviated from the mean value.
Given that, 86.65% of the per diem costs in Nairobi, Kenya, are less than $449, and if the standard deviation of per diem costs is $36.
z=(x-μ)/σ
z= standard score
x= raw observed data point
μ= population mean
σ= population standard deviation.
Here, 0.8665 =(449-μ)/36
0.8665×36=449-μ
31.194=449-μ
μ=449-31.194
μ=$417.806
Therefore, the average per diem cost in Nairobi is $417.806.
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A pair of boots with an original price of $34.70 is discounted 10%. What is the sale price?
Answer:
hi !!
Step-by-step explanation:
34.70 - 34.70/100*10 = 34.70 - 3.47 = $31.23
cc[tex]\frac{p-8}{p^2-12p+32} ÷\frac{1}{10}[/tex]
Using Factorization, The solution of the algebraic fraction is [tex]\frac{10}{p-4}[/tex].
An algebraic equation is what?Due to the fact that they have polynomials on both sides of the equality sign, algebraic equations are also known as polynomials. Variables, coefficients, constants, and algebraic operations like addition, subtraction, multiplication, division, and exponentiation are all components of algebraic equations.
Factorization: what is it?Numbers are factored using formulas for factorization. Decomposing an entity into the result of another entity or factors that, when multiplied together, produce the original number is known as factorization. Simple factorization formulas are used in factorization procedures to simplify algebraic or quadratic equations. Instead of expanding parentheses, expressions are expressed as the sum of their constituent parts. Each equation may have factors that are algebraic expressions, variables, or .
[tex]\frac{p - 8}{8 p²-12p+32} \div \frac{1}{10}[/tex]
first we factorize the denominator and using invert Endo to the other fraction.
[tex]\frac{p - 8}{8 p²-12p+32} \times \frac{10}{1}\\\frac{p - 8}{(p - 8)(p - 4)} \times 10[/tex]
= [tex]\frac{10}{p-4}[/tex]
Hence the simplified fraction is [tex]\frac{10}{p-4}[/tex]
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Kaylee is working two summer jobs, making $6 per hour walking dogs and $13 per hour landscaping. Last week Kaylee worked a total of 8 hours and earned a total of $83. Determine the number of hours Kaylee worked walking dogs last week and the number of hours she worked landscaping last week
The number of hours spent walking dogs is 3 hours and 5 hours was spent landscaping.
How many hours was spent carrying out each activity?The first step is to form a system of equations using the information provided in the question:
x + y = 8 equation 1
6x + 13y = 83 equation 2
Where:
x = number of hours spent walking dogs y = number of hours spent landscaping.The elimination method would be used to solve the equations.
Multiply equation 1 by 6
6x + 6y = 48 equation 3
Subtract equation 3 from equation 2:
7y = 35
Divide both sides of the equation by 7:
y = 35 / 7
y = 5
Substitute for y in equation 1:
x + 5 = 8
8 - 5 = x
x = 3
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which of the following is the largest unit? group of answer choices meter micrometer kilometer millimeter decimeter
A kilometer is the largest unit.
In the International System of Units, a kilometer represents one mile (SI). The symbol for it is km. Km is typically used to describe a location's or a piece of land's distance. It is possible to measure length and distance in kilometers or "km." The measurement unit "kilometer," which is also used to measure geographic distances, is comparable to the measurement unit "mile." Kilometers are a common measurement unit for length and distance in many nations. 1000 meters make up one kilometer.
the distance between two points along an object's longest side or length; often used to describe a specific component of an object: a length of rope; the boat is 20 feet long.
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a group of five students is being selected for a leadership group. they are being selected from a group of 12 nominees.
The probability of selecting a group of five students from a group of 12 nominees is 2.32 or 792 possible combinations.
The formula used to calculate the probability of a group of five students being selected from a group of 12 nominees is C(12,5) which is equal to 792. This can be calculated using the formula n!/(r!(n-r)!), where n is the number of nominees (12) and r is the number of students in the group (5).
To calculate C(12,5), first calculate 12!/5!7!. This is equal to 12x11x10x9x8/5x4x3x2x1, which is equal to 11,664. Then divide 11,664 by 7! (7x6x5x4x3x2x1) which is equal to 5040. This is equal to 2.32, which is the probability of selecting a group of five students from a group of 12 nominees.
Therefore, the probability of selecting a group of five students from a group of 12 nominees is 2.32 or 792 possible combinations.
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