Answer:
\(\frac{33}{8}\)
Step-by-step explanation:
4.125 = \(\frac{4125}{1000}\) because if you take 4125 divided by 1000, you will get 4.125.
Now we simplify the fraction by 125
\(\frac{4125}{1000}\) = \(\frac{33}{8}\)
So, the answer is \(\frac{33}{8}\)
This rectaglular frame is made from 5 straight pieces of metal the weight
The metal in the frame weighs 70.5 kg in total. If a rectangular frame measuring 5 metres in length and 12 metres in width is constructed from five straight pieces of metal.
Get the diagonal
d² = 52 + 122
d² = 25+ 144
d² = 169
d = 13m
Get the perimeter of the rectangular frame:
Perimeter of the frame = 2(5+12) + 13
Perimeter of the frame = 2(17) + 13
Perimeter of the frame = 34 + 13
Perimeter of the frame = 47m
If the weight of the metal is 1.5 kg per metre, the total weight will be expressed as:
Total weight = 47×1.5
Total weight = 70.5kg
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The complete question is
This rectangular frame is made from 5 straight pieces of metal.
5 m
12 m
The weight of the metal is 1.5 kg per metre.
Work out the total weight of the metal in the frame.
: Prove that a) X'Y' + X'Y +XY = X' +Y b) A'BC' + ABC' + BC'D = BC' Find the complement of the following function a) WX(Y'Z+YZ') + W'X'(Y' +Z)(Y+Z') b) (A+B'+C') (A'B' +C)(A + B'C') Find Dual of question 2 (a, b),
a) X'Y' + X'Y + XY simplifies to X' + Y.
b) A'BC' + ABC' + BC'D simplifies to BC'.
Complement of the functions:
a) Complement is W' + X' + YZ.
b) Complement is (A' + B + C)(A'B' + C' + A'B).
a) To prove X'Y' + X'Y + XY = X' + Y, we can use Boolean algebra identities:
X'Y' + X'Y + XY
= Y'(X' + X) + XY(Distributive Law)
= Y' + XY(X + X' = 1)
= X' + Y(Commutative Law)
Therefore, X'Y' + X'Y + XY simplifies to X' + Y.
b) To prove A'BC' + ABC' + BC'D = BC', we can simplify the expression using Boolean algebra:
A'BC' + ABC' + BC'D
= BC'(A' + A) + BC'D (Distributive Law)
= BC' + BC'D(A + A' = 1)
= BC'(BC' + BC'D = BC' + BC'(1) = BC')
Hence, A'BC' + ABC' + BC'D simplifies to BC'.
Complement of the given functions:
a) The complement of WX(Y'Z + YZ') + W'X'(Y' + Z)(Y + Z') is W' + X' + YZ.
b) The complement of (A + B' + C')(A'B' + C)(A + B'C') is (A' + B + C)(A'B' + C' + A'B).
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consider the relation | on s = {1,2,3,5,6}. find al l linear ex- tensions of | on s
The linear extension of l on s is {(1,3), (2,6), (5,), (1,5), (3,5)}.
The relation | on s = {1,2,3,5,6} means that two elements are related if they have the same parity (i.e., they are both even or both odd).
To find all linear extensions of | on s, we can first write down the pairs that are already related by |:
(1,3), (2,6), (5,)
We can then consider each remaining pair of elements and decide whether they should be related or not in a linear extension of |. For example, we could choose to relate 1 and 5, since they are both odd and do not currently have a relation.
One possible linear extension of | on s is:
{(1,3), (2,6), (5,), (1,5), (3,5)}
Note that there are several other possible linear extensions, depending on which pairs we choose to relate.
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Evaluate | x+y, for x = 8 and y=-15.
7
23
-7
-23
in a shooting match, eight clay targets are arranged in two hanging columns of three targets each and one column of two targets. a marksman is to break all the targets according to the following rules: 1) the marksman first chooses a column from which a target is to be broken. 2) the marksman must then break the lowest remaining target in the chosen column. if the rules are followed, in how many dierent orders can the eight targets be broken?
Therefore, there are 72 different orders in which the eight targets can be broken according to the given rules.
To find the number of different orders in which the eight targets can be broken, we can consider the arrangement of the columns and the targets within each column. Since there are three targets in each of the first two columns and two targets in the third column, we can focus on the relative order of breaking the targets within each column. Let's represent the columns as follows:
Column 1: T T T
Column 2: T T T
Column 3: T T
To calculate the number of different orders, we can count the permutations of breaking the targets within each column and then multiply them together.
For Column 1, there are 3 targets, so there are 3! = 3 × 2 × 1 = 6 possible orders.
For Column 2, there are also 3 targets, so there are 3! = 6 possible orders.
For Column 3, there are 2 targets, so there are 2! = 2 possible orders.
To find the total number of different orders, we multiply the number of orders for each column:
Total number of orders = 6 × 6 × 2
= 72
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help i hate maath
4 2/8+9 4/8
13 6/8 or 13 3/4 they are both right answers
Ashley babysits for 6 hours for $73.50 on Friday and for 3 hours for $36.75 on Sunday. What constant of proportionality relates the number of hours and total pay?
Group of answer choices
$13.50
$12.25
$11.75
$14.25
Answer:
12.25
Step-by-step explanation:
40 Which scatterplot does NOT suggest a linear relationship between x and y?
9
9
8
0
2
7
9
6
H
5
4
5
4
3
2
2
1
1
1 2 3 4 5 6
6
0
0
1 2 3 4 5 6 7 8 9
6
.
2
3
D
5
5
4
4
3
2
2
1
1
0
0
3 4 5 6 7 9
1 2 3 4 5 6 7 8 9
1 2
Answer:
D
Step-by-step explanation:
the last graph
Can someone help me with this problem? 3 + (-7 + y)
Answer:
−4+y
Step-by-step explanation:
3+(−7+y)
Subtract 7 from 3 to get −4.
−4+y
Which of the following expressions cannot be written as an integer?
Square 49
-3^0
1.2x10^-2
18/3
Answer:
18/3 cannot be written as an integer
a department store sells a pair of shoes with an 87% markup. If the store sells the shoes for 193.21 then what is there non markup price
Answer: 74%
sorry but i cant tell you my way their would be copyright claims
60 minutes is 20% of
minutes.
Answer:
60 minutes is 20% of 300 minutes
Step-by-step explanation:
let x be the number of total minutes
60 = 20% of x
20% = 1/5
60 = 1/5x
multiply both sides by 5
300 = x
x = 300 minutes
Function g is represented by the equation.
g(x) = 4(1/4)^x +2
Which statement correctly compares the two functions?
OA.
They have different y-intercepts but the same end behavior.
B. They have the same y-intercept but different end behavior.
C. They have the same y-intercept and the same end behavior.
D.
They have different y-intercepts and different end behavior.
Answer:
A. They have different y-intercepts but the same end behavior.
Step-by-step explanation:
I used Desmos to graph the function g(x)=4(1/4)^x+2
They have different y-intercepts because function f(x) is 4, while the y-intercept on graph is 6
But they have the same end behavior at 2.
They have different y-intercepts but the same end behavior.
The correct option is A.
What are intercepts in graph?
The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.
If we look at the graph of the function
\(g\left(x\right)=\ 4\left(\frac{1}{4}\right)^{x\ }+4\)
Then we can see that they have different intercept.
Function f(x) has y-intercept 4 while the graph has y-intercept is 6.
But if we look at the behavior, they have the same behavior.
Hence, They have different y-intercepts but the same end behavior.
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There are 5 blue pencils and 3 gold pencils in a container. If 2 pencils are drawn randomly without replacement, what is the probability that both pencils drawn are gold? Simplify the fraction into the lowest terms.
13/28
3/28
5/28
1/28
If 2 pencils are drawn randomly without replacement, the probability that both pencils drawn are gold is 3/28.
There are 8 pencils in total, and 3 of them are gold.
When we draw the first pencil, there are 8 options. If we draw a gold pencil, there will be 2 gold and 7 total pencils left. If we draw a blue pencil, there will be 3 gold and 6 total pencils left.
If the first pencil drawn is gold, the probability of drawing another gold pencil on the second draw is 2/7.
If the first pencil drawn is blue, the probability of drawing a gold pencil on the second draw is 3/7.
Therefore, the probability of drawing two gold pencils without replacement is:
(3/8) * (2/7) = 6/56
This fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 2:
6/56 = 3/28
So, the probability that both pencils drawn are gold is 3/28.
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Solve the systems using substitution.
Answer:
1. (-1,3)
2. (2,-5)
3. (6,4)
4. (5,-3)
5. (7,-4)
Step-by-step explanation:
hope this helps and also math .way answers any math problem. can u mark me as brainly
Wallace writes the number 72,204 in a
place-value chart. Select the places that
will be filled on the chart.
Ones
Tens
Thousands
Ten thousands
Hundred thousands
Can anyone help
looks like the answer C. Thousands.
In the number 72,204 the ones, tens, thousand, and ten thousand will be 4,0,2, and 7 respectively.
What are digits?In a positional numeral system, a numerical digit is a single sign that can be used singly or in combination to represent numbers.
A digit is a part of a set that, when combined, makes up a numeration system.
For example 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are digits.
The place value of a general abcd digit is given by
d = ones
c = tens
b = hundreds
a = thousands
So,
In the given number 72,204
4 = ones
0 = tens
2 = hundreds
2 = thousands
7 = hundred thousand
Hence "In the number 72,204 the ones, tens, thousand, and ten thousand will be 4,0,2, and 7 respectively".
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?Eric conducted an experiment in his science class and recorded the data in a table.
Eric’s science experiment, time (seconds), 3, Six, 9, 12, 15, 18, distance (ft), 18, 36, 54, 72, 90, 108.
What is the constant of proportionality that relates the distance traveled, y, to the elapsed time in seconds, x, represented by this data?
The constant of proportionality that relates the distance traveled to the elapsed time represented by this data will be 6.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
Eric conducted an experiment in his science class and recorded the data in a table.
Eric’s science experiment, time (seconds), 3, 6, 9, 12, 15, 18, distance (ft), 18, 36, 54, 72, 90, 108.
Let x be the time and y be the distance.
Let the distance and time be linear to each other. Then the linear equation is given as
y - 36 = [(36 - 18) / (6 - 3)] (x - 6)
y - 36 = 6 (x - 6)
y = 36 + 6x - 36
y = 6x
Then the constant of proportionality that relates the distance traveled to the elapsed time represented by this data will be 6.
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Assume a file consisting of 200 blocks, which we need to sort. (a) Assume we only have 5 memory buffers available What is the total number of I/Os to sort the entire file? How many sorted runs (lists) are there after the 1st merge step? How many sorted runs (lists) are there after the 2nd merge step? (b) Assume we only have 8 memory buffers available What is the total number of I/Os to sort the entire file? How many sorted runs (lists) are there after the 1st merge step? How many sorted runs (lists) are there after the 2nd merge step? .
Total number of I/Os: Read (200) + Write (200) = 400 I/Os
Sorted runs after 1st merge step: 4
Sorted runs after 2nd merge step: Not applicable, as the file is sorted after the 1st merge step.
(a) With 5 memory buffers available to sort a file consisting of 200 blocks:
1.Divide the 200 blocks into 40 equally sized runs (200 / 5 = 40), each with 5 blocks.
2. Perform 1st merge step, using 4 buffers for input and 1 for output. Merge 2 runs at a time: 40 runs / 2 = 20 sorted runs.
3. Perform 2nd merge step, again using 4 buffers for input and 1 for output. Merge 2 runs at a time: 20 runs / 2 = 10 sorted runs.
Total number of I/Os: Read (200) + Write (200) = 400 I/Os
Sorted runs after 1st merge step: 20
Sorted runs after 2nd merge step: 10
(b) With 8 memory buffers available to sort a file consisting of 200 blocks:
1. Divide the 200 blocks into 25 equally sized runs (200 / 8 = 25), each with 8 blocks.
2. Perform 1st merge step, using 7 buffers for input and 1 for output. Merge 7 runs at a time: 25 runs / 7 ≈ 3.57 => 4 sorted runs (3 runs with 8 blocks each, and 1 run with 5 blocks).
3. Perform 2nd merge step, not required as the file is already sorted after the 1st merge step.
Total number of I/Os: Read (200) + Write (200) = 400 I/Os
Sorted runs after 1st merge step: 4
Sorted runs after 2nd merge step: Not applicable, as the file is sorted after the 1st merge step.
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Now you will attempt to copy your original triangle using one of its angles:
Draw a line segment, DE of any length anywhere on the coordinate plane, but not on top of ∆ABC.
Choose one of the angles on ∆ABC. From point D, create an angle of the same size as the angle you chose. Then draw a ray from D through the angle. You should now have an angle that is congruent to the angle you chose on ∆ABC.
Create a point anywhere outside the mouth, or opening, of the angle you created. The point will initially be named F by the tool, but you should rename it point G. Now draw a ray from E through G such that it intersects the first ray. Your creation should be a closed shape resembling a triangle.
Label the point of intersection of the two rays F, and draw ∆DEF by creating a polygon through points D, E, and F.
Click on point G, and move it around. By moving point G, you can change
DEF and EFD while keeping FDE fixed.
Take a screenshot of your results for one position of G, save it, and insert the image in the space below.
The construction of similar triangles are given in attached figure.
What is a triangle?A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.
Similar shapes are shapes whose lengths are in an equivalent ratio. Triangle ABC and triangle DEF are similar because the side lengths of both triangles are in an equivalent ratio (refer to the attachment).
Step 1: Draw a random triangle ABC
The lengths of two sides and an angle are:
AB=10
BC=6
C=90
Step 2: Draw and measure the length of DE
DE=15
Step3: Calculate the ratio
The corresponding line segment to DE is line segment AB.
So, the ratio (k) is:
k= DE/AB
k= 15/10
k=1.5
Step 4: Multiply the ratio by the other line segment in step 1
In (1), we have:
BC=6
So,
EF=k*BC
EF=1.5*6
EF=9
Step 4: Draw a circle with center F and radius EF
The center of the circle is point F and the radius of the circle is 9 units
Step 5: Draw a ray from the center (i.e. point F) to DE
Refer to the attached image for
Triangle ABC
Triangle DEF
Circle with center F and radius 9
Ray from F to DE
Therefore, construction of similar triangles are given in attached figure.
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how to subtract mixed fractions with whole numbers
The process to subtract the mixed fractions with the whole numbers is explained below.
The Mixed Fractions are defined as type of fraction that consists of a whole number and a proper fraction.
Step(i) : We multiply whole number by denominator of fraction and add numerator.
For example, if mixed fraction 2(1/3), we multiply 2 by 3 and add 1 to get 7. So, 2(1/3) is equivalent to improper fraction 7/3.
Step(ii) : Find a common denominator for fractions. We find least common multiple (LCM) of denominators.
For example, if you want to subtract 2(1/3) from 5, denominators are 3 and 1, and LCM is 3.
Step(iii) : Convert whole number to a fraction with same denominator as common denominator.
For example, if LCM is 3 and we want to subtract 2(1/3) from 5, we will convert 5 to fraction 15/3.
Step(iv) : Rewrite each fraction with common denominator.
For example, if we want to subtract 2(1/3) from 5, we rewrite 2(1/3) as 7/3 and 15/3 as 5.
Step(v) : Subtract the fractions.
For example, to subtract 7/3 from 5, we subtract numerators and keep the denominator: 15/3 - 7/3 = 8/3.
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How do you find the angle of a slope?
The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.
What is the angle of the slope?The angle of slope shows the departure of your climb from the idealistic flat surface of the course (remember, it's an idealized flat surface that ignores elevation change). In order to figure this out, divide the increase by the run and then find the inverse tangent of the outcome.The angle between a horizontal plane and a specific location on the land surface is known as the slope angle (degree).The term "slope" describes the incline's angle or grade. You might have an upward or downhill slope. The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.To learn more about angle of slope refer,
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the levels of a(n) variable have meaning and order. a. prescriptive b. categorical c. analytical d. continuous
The correct answer is (c) analytical. Levels of a variable can have meaning and order when the variable is analytical variable.
Analytical variables are variables that have a meaningful order or ranking, such as height or weight. For example, height is an analytical variable because people can be ranked from shortest to tallest, and each height value is meaningful in relation to other height values.
Prescriptive variables describe the desired or prescribed behavior, such as in a set of rules or guidelines. Categorical variables divide data into categories or groups, such as gender or hair color. Continuous variables have an infinite number of values and can take on any value within a given range, such as temperature or time.
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what can you say about any two consecutive angles in a parallelogram? A. they are always congruent B. They are always supplymentary C. They are sometimes complementary D. They are both right angles
Answer:
B
Step-by-step explanation:
Adjacent angles sum to 180 degrees <====supplementary
Expand and simplify
(7 + V 6 )^2
Give your answer in the form b+ c V 6
Answer:
55 + 14\(\sqrt{6}\)
Step-by-step explanation:
Given
(7 + \(\sqrt{6}\) )² = (7 + \(\sqrt{6}\) )(7 + \(\sqrt{6}\) )
Each term in the second factor is multiplied by each term in the first factor, that is
7(7 + \(\sqrt{6}\) ) + \(\sqrt{6}\) (7 + \(\sqrt{6}\) ) ← distribute both parenthesis
= 49 + 7\(\sqrt{6}\) + 7\(\sqrt{6}\) + 6 ← collect like terms
= 55 + 14\(\sqrt{6}\)
b +cV 6 ÷12a
Step-by-step explanation:
let meknow 8i I am wrong
Pls solve with all steps
The results of the expressions involving logarithms are listed below:
Case 1: 1 / 2
Case 2:
Subcase a: 0
Subcase b: 11 / 2
Subcase c: - 11 / 2
How to simplify and evaluate expressions involving logarithmsIn this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:
㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c
㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c
㏒ₐ cᵇ = b · ㏒ₐ c
Now we proceed to determine the result of each case:
Case 1
㏒ ∛8 / ㏒ 4
(1 / 3) · ㏒ 8 / ㏒ 2²
(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)
㏒ 2 / (2 · ㏒ 2)
1 / 2
Case 2:
Subcase a
㏒ [b / (100 · a · c)]
㏒ b - ㏒ (100 · a · c)
㏒ b - ㏒ 100 - ㏒ a - ㏒ c
3 - 2 - 2 + 1
0
Subcase b
㏒√[(a³ · b) / c²]
(1 / 2) · ㏒ [(a³ · b) / c²]
(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²
(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c
(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c
(3 / 2) · 2 + (1 / 2) · 3 + 1
3 + 3 / 2 + 1
11 / 2
Subcase c
㏒ [(2 · a · √b) / (5 · c)]⁻¹
- ㏒ [(2 · a · √b) / (5 · c)]
- ㏒ (2 · a · √b) + ㏒ (5 · c)
- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c
- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c
- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c
- 1 - 2 - (1 / 2) · 3 - 1
- 4 - 3 / 2
- 11 / 2
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Given mn, find the value of x.
Answer:
(2x+5)° (8x+5)°
Submit Answer
m
00
Step-by-step explanation:
2x+(-8x) +5-5
-5=0. u Wii collect like terms and if u do that that's the answer if am wrong let me know
Using trigonometry, work out the length y Give your answer in centimetres to 1 d.p. Y 6.1 cm 39° Not drawn accurately
The length of y is given as follows:
y = 7.8 cm.
What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent, and they are defined as follows:
Sine of angle = length of opposite side to the angle divided by the length of the hypotenuse.Cosine of angle = length of adjacent side to the angle divided by the length of the hypotenuse.Tangent of angle = length of opposite side to the angle divided by the length of the adjacent side to the angle.In the context of this problem, we have that y is the hypotenuse, while 6.1 cm is the side length adjacent to the angle of 39º, hence:
cos(39º) = 6.1/y
y = 6.1/cosine of 39 degrees
y = 7.8 cm.
Missing Information6.1 cm is adjacent to the angle of 39º, while y is the hypotenuse.
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Colin is training for a triathlon and needs to swim a certain distance for today's workout. If he swims at the rec center pool, he will complete a 264-yard warmup and then swim laps in a lane that is 34 yards long. If Colin swims at the indoor pool at his gym, he will complete a 120-yard warmup, plus a main set that consists of 35 yards per lap. If Colin swims the correct number of laps, he can complete the same distance in either pool. How long will Colin's workout be in total? How many laps will that take?
Answer:
Jason is training for a triathlon and needs to swim a certain distance for ... If he swims at the rec center pool, he will complete a 200-yard warmup and then swim laps in a lane that is 20 yards long. If Jason swims at the indoor pool at his gym, he will complete a ... How long will Jason's workout be in total? 1.
Step-by-step explanation:
A house is 49.0ft long and 42.0ft wide and has 8.0-ft-high ceilings. What is the volume of the interior of the house in cubic meters and cubic centimeters? m^3, cm^3
Given: Length of house = 49 ft, Width of house = 42 ft, Height of house = 8 ftWe know that: Volume of the house = Length x Width x HeightFor conversion,
Volume of the house = Length x Width x Height= 49 ft x 42 ft x 8 ft= 16464 cubic feet= 16464 x 0.3048 x 0.3048 x 0.3048 cubic meters= 466.78 cubic metersTherefore, the volume of the interior of the house in cubic meters is 466.78 m³.To calculate the volume of the house in cubic centimeters,
we first convert the dimensions into centimeters:Length of house = 49 ft x 12 in/ft x 2.54 cm/in = 1493.52 cmWidth of house = 42 ft x 12 in/ft x 2.54 cm/in = 1280.16 cmHeight of house = 8 ft x 12 in/ft x 2.54 cm/in = 243.84 cmVolume of the house = Length x Width x Height= 1493.52 cm x 1280.16 cm x 243.84 cm= 466.78 x 10^9 cubic centimetersTherefore,
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Justin is designing a new board game, and is trying to figure out all the possible outcomes. How many different possible outcomes are there if he spins a spinner with 5 equal-sized sections labeled Monday, Tuesday, Wednesday, Thursday, Friday and rolls a fair die in the shape of a cube that has six sides labeled 1 to 6?