A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium hat costs $6.00. A large hat costs $7.00. He purchases three times as many medium hats as small hats. Using matrices, how many large hats did the coach purchase?
Answer:
The answer is below
Step-by-step explanation:
Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.
Since a total of 47 hats where purchased, hence:
x + y + z = 47 (1)
Also, he spent a total of $302, hence:
5.5x + 6y + 7z = 302 (2)
He purchases three times as many medium hats as small hats, hence:
y = 3x
-x + 3y = 0 (3)
Represent equations 1, 2 and 3 in matrix form gives:
[tex]\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] ^{-1} \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}6\\18\\23\end{array}\right][/tex]
Therefore he purchases 6 small hats, 18 medium hats and 23 large hats
Answer:
Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.
Since a total of 47 hats where purchased, hence:
x + y + z = 47 (1)
Also, he spent a total of $302, hence:
5.5x + 6y + 7z = 302 (2)
He purchases three times as many medium hats as small hats, hence:
y = 3x
-x + 3y = 0 (3)
Therefore he purchases 6 small hats, 18 medium hats and 23 large hats
Help I need help with this
Answer:
????
Step-by-step explanation:
square & cube numbers puzzle
| Using only square and cube numbers less than or equal to 100, can you fill in the circles to make these
| sums true? You can only use each number once and you must use all the numbers.
36) + (64
Square and cube numbers
Answer:
who friendhjcicivigigivigigogogig'g
what is the HCF of 3000 and 525 answer with process
Answer:
The HCF is 75
Step-by-step explanation:
Here, we want to get the highest common factors of the two numbers
To do this, we have to write the numbers as the product of their prime factors
We have;
3,000 = 2 * 2 * 2 * 3 * 5 * 5 * 5
525 = 3 * 5 * 5 * 7
now looking at this, we can see that in both numbers, we can have 3 * 5 * 5 taken out as it is common to both numbers
This represents the highest common factor of the two numbers
and that is 75
HELLLLLPP FASSTT PLZZZZ!!!!!! U ANSWER THIS THANNNKKK YOU
Answer:
1) No
2) 4/8 or 1/2
3) 2/8 or 1/4
4) 4/8 or 1/2
5) No
6) 1/8
7) No
Question Progress
Homework Progress
4/
Work out the size of angle x.
105
140
Answer:
Step-by-step explanation:
Sum of angles of a triangle = 180
x + (180 - 105) + (180 -140) = 180
x + 75 + 40 = 180
x = 180 -75 - 40
x = 65
Plot a triangle with vertices located at (4, -2) (1, -2) and (4,5) on this coordinate plane To graph the triangle, select the places on the coordinate plane to plot the vertices. Your vertices will be connected in the order that they are plotted Here is the grid.
Solve for x.
A) 13
B) 26
C) 11
Answer:
13
Step-by-step explanation:
Once again we are looking at inscribed angles and intercepted arcs. Like stated previously an inscribed angle is equal to half its intercepted arc
That being said we want to create an equation to solve for x
The equation would be 7x + 5 = 192/2
We now solve for x
step 1 simplify
192/2=96
now we have 7x + 5 = 96
step 2 subtract 5 from each side
5 - 5 cancels out
96 - 5 = 91
7x = 91
step 3 divide each side by 7
7x/7 = x
91 / 7 = 13
we're left with x = 13
For the trapezoid below, what is the correct term for RT?
R
E
1
1
TL
w
A. Leg
B. Apothem
C. Base
D. Altitude
HELPPP MEEE ASAPPPPP PLSSSS
4x-2
x=5
can someone help me with this?
Answer:
x= 5/2
Step-by-step explanation:
Evaluate the following expression when x=-5 and y=7: *enter numbers only
Answer
x+y
Step-by-step explanation:
helpppp pleaseee
NO LINK
Answer:
The graph increases
Step-by-step explanation:
The perimeter of a square is 36 centimeters.
What is the length of the diagonal of the square?
6√2 cm
9√2 cm
12√2 cm
18√2 cm
Who are some good you tubers to watch?
Answer:
Cocomelon
Their videos are pretty good!
673,000 in numeric help!!
Answer:
huh? explain better
Step-by-step explanation:
help me please!!! asap!
Answer: C
Explanation: 3(2) = 6
A rational number equivalent to 5/7 is
5/7 is 5÷7
so
5÷7 = 0.7142857143
ANSWER ASAP! MARK BRAINLIEST
3.) In triangle RST, RS = 4, ST = 5, and RT = 6. Which angle is largest?
Hint draw a picture!
A)
B)
C)
D) Cannot be determined
Answer:
So If you start with sinØ = .5
your calculator is programmed to always give the closest angle to 0, and that would be 30°
You probably used the cosine law to find the first angle. A suggestion is to always find the largest angle first. If that happens to be an obtuse angle, your calculator will find the correct angle.
Of course there can only be one obtuse angle in a triangle, so using the sine law for your second angle does not result in any problems
notice that in your solution 78 and 102 add up to 180 , and sin 78 = sin(180-78) = sin 102
I would have found angle S first, the largest angle always opposite the largest side.
7^2 = 5^2 + 4^2 - 2(5)(4)cosØ
40cosØ = -8
cosØ = -8/40 = -1/5
Ø = 101.537°
Now you can use the sine law and you will find the correct other angles.
Step-by-step explanation:
i need to find the square root of √16
Answer:
4
Step-by-step explanation:
I don't know how to explain this other than use a calculator.
Hope that this helps!
Please help :') Estimate 15 divided by 2.57
Answer:
5.83
Step-by-step explanation:
15 ÷ 2.57 = 5.8
mark as brainllest
the answer is 5.83
hope it's help
A town has a population of 2000 and grows at 4% every year. What will be the
population after 15 years, to the nearest whole number?
Answer:
[tex] \frac{4}{?100} \times \frac{2000}{?1} = 80 \\ \\ 2000 + 80 = 2080 \\ \\ 2080 \times 15 = 31200 [/tex]
Can someone explain this question which part of the class do you think you will apply to your life both now or in the future?
Which statement is true about the pattern above?
Answer:
The correct answer is "The next fraction in the pattern is 243/324". Each fraction is the other multipled by 3.
Step-by-step explanation:
help me pls! i'll mark u brainliest promised
Answer:
DF≅YZ
angle R≅angle N
XW≅TH
angle M ≅angle C
new coordinate=(2,1)
new coordinate=(0,2)
Reflection:
new coordinate=(5,-6)
new coordinate=(1,4)
Last one is already done
Step-by-step explanation:
Help me on this one
IM CONFUSED!!!!!!!!!
WINNER GETS BRAINLEST
A square has an area of 16 square ft what would be the measurement of its side
Answer:
4ft
Step-by-step explanation:
to get the area of a square you multiply the sides together so you just find the square root of the area
Answer:
4 feet would be the legth of the squares side
Step-by-step explanation:
t16 is the squares area and the area of a square is length X width, since all the sides of a square are equal, we can just take the square root of 16 which is 4 feet.
Please help will mark brainliest
Answer:
The answer is 36.9
Step-by-step explanation:
A boat is spotted in the water with an angle of depression of 25degrees from the top of a lighthouse that is 89 feet tall. How far away , to the nearest foot, is the boat from the lighthouse ?
Answer:
191 Feet.
Step-by-step explanation:
Answer: Your answer should be 191!
Of the clients who had their hair cut at Tanner's salon last month, 4 clients had black hair and
12 clients had hair in other colors. Considering this data, how many of the next 12 clients to
get haircuts should you expect to have black hair?
Answer: 3
Step-by-step explanation:
The number of getting the black hair color clients will be 4.
What is probability?Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Probability = Number of favorable outcomes / Number of samples
Given the of the clients who had their hair cut at Tanner's salon last month, 4 clients had black hair and 12 clients had hair in other colors.
The probability is:-
P = 4 / 12
The number of clients having black color hair is calculated as:-
Number = ( 4 / 12 ) x 12
Number = 4
Therefore, there will be 4 people getting black hair colors.
To know more about probability follow
https://brainly.com/question/24756209
#SPJ6
Taylor collected 4 white shells and 9 grey shells. If she put all the shells in a bucket and randomly pulled one out, what is the probability that the shell would be white?
Answer:
4/13
Step-by-step explanation:
Add the number of eggs which is 13 so it shows that 13 eggs are in the bag and there are 4 white eggs so the probability of taking a white egg is 4/13