A boy owns 7 pairs of pants, 7 shirts, 8 ties, and 3 jackets. How many different outfits can he wear to school if he must wear one of each item
Answers
The total number of ways to choose outfits = 7 x 7 x 8 x 3= 1176
Therefore, he can wear 1176 different outfits to school if he must wear one of each item.
Given, a boy owns 7 pairs of pants, 7 shirts, 8 ties, and 3 jackets.
To find, the number of different outfits he can wear to school.
Let's solve it step by step.
Pick one pair of pants out of 7.
So, the number of ways to pick one pair of pants out of 7 = 7 ways
Pick one shirt out of 7.
So, the number of ways to pick one shirt out of 7 = 7 ways
Pick one tie out of 8.
So, the number of ways to pick one tie out of 8 = 8 ways
Pick one jacket out of 3.
So, the number of ways to pick one jacket out of 3 = 3 ways
By the Fundamental Counting Principle, we can find the number of ways to choose the outfits.
The Fundamental Counting Principle states that:
If one event can happen in m ways and another event can happen in n ways, then both events together can happen in m x n ways. In other words, if there are 'n' operations and the first operation can be performed in 'a' ways, the second operation can be performed in 'b' ways, the third operation can be performed in 'c' ways, and so on. Then, the total number of ways of performing the n operations is:
a x b x c x ... x n
Hence, by the Fundamental Counting Principle,
the total number of ways to choose outfits = 7 x 7 x 8 x 3= 1176
Therefore, he can wear 1176 different outfits to school if he must wear one of each item.
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Related Questions
In a sequence of numbers, the first term is x and each term thereafter is twice the previous term. the fifth term is 160. what is the value of x ?
Answers
The value of x in sequence of number is 10.
Here, first term of sequence is x and each term there after is twice the previous term. Also Fifth term is 160.
What is geometric series?
Geometric series is an infinite series of the form:
\(a+ar+a r^{2} +ar^{3} +..........\)
where r is known as common ratio.
Now, first term is x and each term there after is twice the previous term.
So the series will be;
x , 2x , 4x , 8x, ..........
Clearly this series is geometric series with common ratio 2.
And the nth term of geometric series is \(ar^{n-1}\)
⇒ fifth term is 160
\(ar^{5-1} = 160\\ar^{4} = 160\\a 2^{4} =160\\a=\frac{160}{16} \\a=10\)
Here, first term is x.
The value of x in sequence of number is 10.
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A cell phone company uses the equation C=$0.15t+$35.00 to determine the total cost, C, for a month of service based on the number of text messages, t. Identify the slope.
Answers
Slope is $0.15 of the equation of cost C=$0.15t+$35.00.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
Given that A cell phone company uses the equation C=$0.15t+$35.00
C is the total cost for a month of service.
t is the number of text messages.
We have to find the slope of the equation.
slope is 0.15 and 35.00 is the y intercept of the equation given.
Hence, slope is $0.15 of the equation of cost C=$0.15t+$35.00.
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A right triangle has a leg lengths of 9 units and 12 units. Write an equation that can be used to determine the length of the hypotenuse, c.
Answers
Answer:
a^2+b^2=c^2
c=15 units
Step-by-step explanation:
You can use the pythagorean theorem to solve this equation. a^2+b^2=c^2.
If you substitute the leg lengths in, the new equation will be 9^2+12^2=c^2, c being the hypotenuse.
Next, you can simplify it to get 81+144=c^2. Simplifying it further, you get 225=c^2, which means that the length of the hypotenuse is 15. Hope this helped! :)
Answer:
15
Step-by-step explanation:
9^2+12^2=c^2
81+144=c^2
225=c^2
15=c
or you can see that this is a 3,4,5 triangle (just 3 times bigger)
hope this helps :)
In order to estimate the amount of time students spend on homework, the principal at a high school plans to survey a sample of students. Because the principal believes that different grade levels have different amounts of homework, the plan is to take separate random samples of freshmen, sophomores, juniors, and seniors. What type of sample did the principal perform
Answers
Answer: Stratified Random sampling
Step-by-step explanation:
Stratified Random sampling simply refers to a sampling technique or strategy whereby random selection of observation of samples are made from a population or larger sample by first arranging or splitting the population of interest into smaller groups or separate catagory based on a certain criteria or criterias. Random samples are then taken from each of the groups also called strata. This technique is aimed at ensuring a more even distribution of samples across the various available groups within a population of interest. In the scenario above the stratas or groups are ; Sophomores, Junior, Senior and freshmen.
Use the graph to complete the follow statement. _____ cm of rain fell in total on Tuesday.
Answers
Tiffany is filling her daughter’s pool with water from a hose. She can fill the pool at a rate of 1/10 gallon/seconds.How many gallons of water can she fill in 50 seconds
Answers
Answer:
5 gallons
Step-by-step explanation:
If she can do 1/10 gallon per seconds, that means she can do 5/50.
You can write it as this ratio:
1/10 = x/50.
You know that 10 * 5 = 50.
Since it is a constant ratio, it has to be 1 * 5 = x
Since 1 * 5 = 5, Tiffany can fill the pool 5 gallons per 50 seconds.
The spinner above is used in a game. What is the theoretical probability of the given event with one spin? P (5)
Answers
Answer:
1 /8
Step-by-step explanation:
Given that :
Number of sections on spinner = (1,2,3,4,5,6,7,8) = 8
Number of 5's = 1
Recall :
Probability of event A = number required outcome / Total possible outcomes
P(5) = 1/8
A. If a spacecraft was parked on Venus and needed to make a flight to Jupiter, how far would it need to travel? Show your work and provide your answer in scientific notation.
Answers
Answer:
Distance for the spacecraft to travel from Venus to Jupiter = Distance of Jupiter from Sun - Distance of Venus from Sun
Step-by-step explanation:
⇒ Distance for the spacecraft to travel from Venus to Jupiter = 4.838 × 10⁸ - 6.724 × 10⁷
⇒ Distance for the spacecraft to travel from Venus to Jupiter = 483,800,000 - 67,240,000
⇒ Distance for the spacecraft to travel from Venus to Jupiter = 416,560,000
⇒ Distance for the spacecraft to travel from Venus to Jupiter = 4.1656 × 10⁸
Instantaneous vs Average Rate of change
PLEASE AND THANKSSS:))
Answers
Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos. Fabio scored 31 points in the game.
How many points did Carlos score?
Answers
The number of points that Carlos score based on the information is 19 points.
How to illustrate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It demonstrates the equality of the relationship between the expressions written on the left and right sides. We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
In this.case, Fabio and Carlos play on a basketball team together. In the last game, Fabio had 7 points less than 2 times as many points as Carlos.
Let Carlos point = x
Fabio point will be = 2x - 7
The equation will be:
2x - 7 = 31
2x = 31 + 7.
2x = 38
Divide
x = 19
Carlos had 19 points
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What form of deductive reasoning is used in the given argument?
If it’s raining outside, I’ll wear my raincoat.
I am not wearing my raincoat.
It is not raining outside.
A.
law of detachment
B.
law of syllogism
C.
law of contrapositive
D.
identification of counterexample
Answers
Answer:
C.
law of contrapositive
Answer:
law of contrapositive
Step-by-step explanation:
2. Let L be the line in R 3 passing through the origin in the direction of the vector u=(2,1,0). Consider the following two linear transformations S:R 3 →R 3
given by the projection onto the xy-plane. That is, S(x,y,z)=(x,y,0). T:R 3 →R 3
given by the reflection along the line L. (a) Find the standard matrix for S. (b) Find the standard matrix for T. (c) Find the standard matrix for the composition T∘S of the linear transformation S followed by T.
Answers
(a) To find the standard matrix for S, we need to apply S to each of the standard basis vectors in R^3. The standard basis vectors are:
e1 = (1, 0, 0)
e2 = (0, 1, 0)
e3 = (0, 0, 1)
Applying S to each vector gives:
S(e1) = (1, 0, 0)
S(e2) = (0, 1, 0)
S(e3) = (0, 0, 0)
Therefore, the standard matrix for S is:
[ 1 0 0 ]
[ 0 1 0 ]
[ 0 0 0 ]
(b) To find the standard matrix for T, we need to use the formula for a reflection matrix. The reflection of a vector v across a line with unit direction vector u is given by:
v' = 2proj_u(v) - v
where proj_u(v) is the projection of v onto u. In this case, the line L has direction vector u = (2, 1, 0), so we can write:
u / ||u|| = (2/√5, 1/√5, 0)
Using this, we can find the projection of a vector v onto u as:
proj_u(v) = ((v · u)/||u||^2)u
= ((2v1 + v2)/5)(2/√5, 1/√5, 0)
where · denotes the dot product.
Therefore, the reflection of a vector v across the line L is:
v' = 2((2v1 + v2)/5)(2/√5, 1/√5, 0) - (v1, v2, v3)
= ((4v1 + 2v2)/5, (2v1 + v2)/5, -v3)
This gives us the action of T on each standard basis vector:
T(e1) = (4/5, 2/5, 0)
T(e2) = (2/5, 1/5, 0)
T(e3) = (0, 0, -1)
Therefore, the standard matrix for T is:
[ 4/5 2/5 0 ]
[ 2/5 1/5 0 ]
[ 0 0 -1 ]
(c) To find the standard matrix for the composition T∘S, we need to multiply the standard matrices for S and T. Since the standard matrix for S has a column of zeros, we can just ignore that column when performing the multiplication. Therefore, we have:
[T∘S] = [ 4/5 2/5 ] [ 1 0 ]
[ 2/5 1/5 ] * [ 0 1 ]
[ 0 0 ] [ 0 0 ]
Which simplifies to:
[T∘S] = [ 4/5 2/5 ]
[ 2/5 1/5 ]
[ 0 0 ]
Therefore, the standard matrix for the composition T∘S is:
[ 4/5 2/5 ]
[ 2/5 1/5 ]
[ 0 0 ]
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Select the correct answer. Which expression is equivalent to the given expression?
Answers
Answer:
B
Step-by-step explanation:
2x times x = 2x²
2x times -6 = -12x
1 times x = x
1 times -6 = -6
= 2x² - 12x + x - 6
= 2x² - 11x -6
do any of yall know the questions
Answers
Answer:
In a election of municipality two candidates P and Q stood for the post of mayor and 35000 people were in voter list. Voters were supposed to cast for a single candidate .22000 people cast vote for P, 5500 people cast for Q and 1500 cast vote even for both. How many people didn't cast vote find it
13. It’s an obtuse angle
14. It’s a reflex angle …
Hope it helps :)
Find the distance between the following pair of points.
A(-3,1), B(7,13)
Answers
Answer:
15.6 units (3 s.f.)
Step-by-step explanation:
The distance between 2 points is given by the formula below, where \((x_1, y_1)\) is the first coordinate and \((x_2, y_2)\) is the second coordinate.
\(\boxed{{\text{Distance between 2 points}= \sqrt{(y_1 - y_2)^{2} + (x_1 - x_2)^{2} } }}\)
Using the distance formula above,
distance between A(-3, 1) and B(7, 13)
= \(\sqrt{(13-1)^{2} + [7-(-3)]^{2} } }}\)
= \(\sqrt{12^2+(7+3)^2}\)
= \(\sqrt{244}\)
= 15.6 units (3 s.f.)
Additional:
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Simplify each expression 2m+6(2/3-m);m=4
Answers
Answer:
3 (m-2)-5=8-2 (m-4)
Step-by-step explanation:
please mark me as brainliest.
Answer:
-12
Step-by-step explanation:
a packing lot has a rectangular area of 40,000yd2. the length is 200 yd more than twice the width. find the dimensions of the lot.
Answers
the dimensions of the lot is 100 yards by 400 yards. In this problem, a parking lot has a rectangular area of 40,000 square yards, and the length is 200 yards more than twice the width.
Determining the dimensions of a rectangular area, such as a parking lot, can be a useful task for many purposes, such as planning and designing a new lot or estimating the amount of space available for parking.
Let's call the width of the parking lot "w". Then, the length of the parking lot can be represented as 2w + 200.
The total area of the parking lot is 40,000 square yards, so we can set up an equation to solve for w: w * (2w + 200) = 40,000.
Solving for w, we get w = 100. This means that the width of the parking lot is 100 yards and the length is 2 * 100 + 200 = 400 yards.
The dimensions of the parking lot are 100 yards by 400 yards.
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A robin is flying 11 metres away from a bird
box that is on top of a pole.
The angle of depression from the robin to the
base of the pole is 38°.
What is the distance between the robin and
the base of the pole?
Give your answer to 2 d.p.
Not drawn accurately
Answers
The distance between the robin and the base of the pole is 6.77 meters
How to determine the valueTo determine the distance, we need to know the different trigonometric identities in mathematics.
These identities are given as;
sinetangentsecantcosinecotangentcosecantFrom the information given, we have that;
The angle of depression, θ = 38 degrees
The distance is unknown
The hypotenuse side is 11 meters
Now, using the sine identity, we have;
sin 38 = d/11
Cross multiply the values
d = 0. 6156(11)
multiply the values
d = 6. 77 meters
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Select the graph of the solution. Click until the correct graph appears. {x | x < 4} ∩ {x | x > -2}
Answers
Answer:
It converges
Step-by-step explanation:
dx/dy = x∧4 + 9x∧21
f(x) = ∫(x∧4 + 9x∧21)dy 0 > f(x) > ∞
= x∧5/5 + 9x∧22/22 + c
x = ∞ and x = 0
∴ c = 1 /5 + 9/22 = 27/22
i have so much work and im am sad plz help me for geometry or I'm going to fail
Answers
Answer: First option, “22”
Step-by-step explanation:
Graph the line given the point (4, 3) and the slope m = − 1/3
Answers
The line passes through the point (4, 3)
The line has a slope of m=-1/3
The equation of the line can be written in the form
\(y=mx+c\)Since the slope is -1/3
Then the equation becomes
\(y=-\frac{1}{3}x+c\)Since the line passes through the point (4, 3)
Substitute x = 4, y= 3 into the equation
\(3=-\frac{1}{3}(4)+c\)Simplify the equation and solve for c
\(\begin{gathered} 9=-4+3c \\ 9+4=3c \\ 13=3c \\ c=\frac{13}{3} \end{gathered}\)Hence, the equation becomes
\(y=-\frac{1}{3}x+\frac{13}{3}\)Using an online graphing calculator.
The graph of the line is shown
Need D, E and F thank you
Answers
Answer:
I'm assuming you meant to put a picture of your problem. I will answer it when you post a picture (If I know the answer lol). Have a good day ;)
Answer:
D)= angle F= 105
angel G= 34
angel J= 41
Step-by-step explanation:
PLEASE HELP im to stupid
Answers
Answer:
line BC, 4 units right, and down 1 unit!
Hope This Helps!
Answer:
1. BC
2. 4
3. 1
Step-by-step explanation:
Find the volume of a cylinder if the radius is 3 and the height is 9
Answers
Answer:
81pi
Step-by-step explanation:
pi3^2=9pi
9pi * 9 = 81pi
Answer:
254.34 un³
Step-by-step explanation:
π × 3² × 9
π × 9 × 9
3.14 × 9 × 9
254.34
What are the terms in the expression 2d+7+5f
Answers
Answer:
3 terms 2d,7 and 5f
Step-by-step explanation:
Answer:
The answer would be 2d 7 5f hope this helps
Step-by-step explanation:
Identify the zeros of the graphed function
Answers
Answer:
-4,-2,1
Step-by-step explanation:
It crosses the x-axis at -4,-2 and 1
What is the shortest time it takes it to collect a container of water?
Answers
Answer:
45 minutes
Step-by-step explanation:
The minimum of a box-and-whisker plot is the leftmost endpoint, called the "whisker". This minimum is the smallest value collected in the data.
I’ve been stuck on this khan for hours already can’t seem to figure it out, it’s just adding and subtracting polynomials but it’s supposed to equal a polynomial in standard form :( please help me !!
Answers
= p^2 - 5p + 4 - 4p^2 + 9p - 11
= p^2 - 4p^2 -5p + 9p + 4 - 11
= -3p^2 + 4p - 7
Think about your daily experience how is probability utilized in news papers, television, shows, and radio programs that interest you? What are your general impression of the ways in which probability is used in the print media and entertainment industry
Answers
Probability is frequently used in news reports to convey the possibility of an event occurring.
Generally, in my opinion, probability is used well in the media space.
How Probability is Utilized?Probability is frequently used in news reporting to demonstrate the likelihood of an event occurring. A news story, for example, might mention that there is a 50% chance of rain tomorrow. Similarly, sports writers may use probability to forecast the outcome of games and goals to be scored.
Overall, I feel probability is utilized fairly responsibly in the media and entertainment industries, with a focus on informing or entertaining audiences rather than misleading them. However, in some cases, such as political polling or advertising, the use of probability may be incorrect or exploited to influence audiences.
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In the Sweet Sprouts Farm U-Pick Berry Patch,
Brenda picks 3.21 pounds of strawberries and
2.76 pounds of blueberries. How many pounds
of berries does Brenda pick in all?
Answers
The number of pounds that Brenda pick in all is 5.97 pounds.
What is a pound in weight?
One pound is equivalent to 0.4535 kilograms and is referred to as an imperial unit of mass or weight measurement. Pound is a metric unit of measurement of mass. Both the pound and the kilogram are weight or mass measurement units. The imperial unit of mass or weight is the pound.
What is meaning of mass?
The amount of matter in a particle or object is represented by the dimensionless quantity mass (symbolised m). The kilogramme is the International System's (SI) preferred unit of mass (kg).
Given that Brenda picks 3.21 pounds of strawberries and 2.76 pounds of blueberries.
Total number of pound of berries is (3.21 + 2.76) pounds = 5.97 pounds.
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