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?

Answers

Answer 1

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 2

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


Related Questions

Use Pythagorean theorem to solve the following right triangles, put your answer in simplest radical form:

Answers

Answer:

Step-by-step explanation:I found the answer on this web[tex]^{}[/tex]site. It seems correct! Link Below!ly/3fcEdSx

bit.[tex]^{}[/tex]

The net of a solid figure is shown below:

The net of a solid figure is shown below:
Which calculation will give the total surface area of the solid figure?


A) 3 x 6 x 6 square inches
B) 6 x 3 x 3 x 3 square inches
C) 3 x 6 x 6 x 6 square inches
D) 6 x 3 x 3 square inches

Answers

Answer:

D, 6 x 3 x 3

Step-by-step explanation:

One area of a square is 3 x 3 there are 6 squares so we multiply by 6 too.

The city is planting new trees in its downtown to make the streets more comfortable for visitors. They are planting each tree 12 feet apart. How many trees can they plant on 2 miles of streets? Hint is that 5280= 1 mile. Please help

Answers

Step-by-step explanation:

let's make T= the number if trees...

If we're placing one tree every 12 feet for two miles, then:

T×(space between trees) = (number of miles)×(1mi.)

T×12ft. = 2×1mi. = 2×5280ft.

Dividing by 12ft. to isolate T gives us:

T=(2×5280)/12 = 880

So that'll be 880 trees for 2 miles of street.

The number of trees that they plant on 2 miles of streets will be 880 trees.

What is division?

Division means the separation of something into different parts, sharing of something among different people, places, etc.

The city is planting new trees in its downtown to make the streets more comfortable for visitors.

They are planting each tree 12 feet apart.

Then the number of trees that they plant on 2 miles of streets will be  

We know the conversion of miles into feet.

  1 mile = 5280 feet

2 miles = 10560 feet

Then the number of trees will be

Number of trees = 10560 / 12

Number of trees = 880

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Ali runs 6 miles in 55 minutes. At the same rate, how many miles would he run in 44 minutes?

Answers

Answer:

4

Step-by-step explanation:

Correct answer: in 44 minutes, he would run 4.8 miles

Which of the following are solutions to the equation below?
Check all that apply.
(3x - 5)2 = 19

Answers

Answer:

Take the square root of each side of the equation to set up the solution for

x

(

3

x

5

)

2

1

2

=

±

19

Remove the perfect root factor

3

x

5

under the radical to solve for

x

.

3

x

5

=

±

19

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

x

=

19

3

+

5

3

,

19

3

+

5

3

The result can be shown in multiple forms.

Exact Form:

x

=

19

3

+

5

3

,

19

3

+

5

3

Decimal Form:

x

=

3.11963298

,

0.21370035

The solutions of the of the equation are,

⇒ x = 3.12

⇒ x = 0.21

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ (3x - 5)² = 19

Now,

We can simplify the expression for the solutions as;

⇒ (3x - 5)² = 19

Take square root both side,

⇒ √(3x - 5)² = √19

⇒ (3x - 5) = √19

Add 5 both side,

⇒ 3x - 5 + 5 = √19 + 5

⇒ 3x = √19 + 5

⇒ 3x = ± 4.36 + 5

⇒ 3x = 4.56 + 5

⇒ 3x = 9.36

Divide by 3;

⇒ x = 9.36 / 3

⇒ x = 3.12

And, 3x = - 4.56 + 5

3x = 0.64

x = 0.64/3

x = 0.21

Thus, The solutions of the of the equation are,

⇒ x = 3.12

⇒ x = 0.21

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Help with this please!!

Answers

Answer:

the first answer

Step-by-step explanation:

well first ofc u have to graph both equations to be able to compare them and if u don't have a graphing calculator just search up Desmos graphing calculator it will help A LOT

Norma needs to find the sum of the fractions below. 3/8 +5/6 Norma starts by multiplying the first fraction by 3/3.
By which number should she multiply the second fraction?
A.8/8
B.4/4
c.3/3
d.undefined

Answers

Answer:

Its A

Step-by-step explanation:

Because if you add 3+5 that is 8 so 8/8

Can someone plz help me plz I beg u plz

Answers

Answer:

A.... X=3

Step-by-step explanation:

The answer is 3
X = 3 cuz 3x3 is 9 which would be equal to the other side when you add it with the other 2 blocks

Convert (4, 3π/2) to rectangular form.
A) (0,4)
B) (0, -4)
C) (-4,0)
D) (4,0)

Answers

Answer:

(0, -4)

Step-by-step explanation:

The rectangular form is expressed as;

x = rcos theta

y = rsin theta

Given the coordinate  (4, 3π/2)

r = 4

theta = 3π/2

Substitute

x = 4cos3π/2

x = 4cos270

x = 4(0)

x = 0

y= 4sin3π/2

y = 4sin270

y = 4(-1)

y = -4

Hence the required coordinate is (0, -4)

PLSSSSS HELPPPPP REWARD BRAINLEISTTT

Answers

ANSWER:

number 1 is D, it moves to the right 4 times

number 2 is B, its a vertical stretch of 2

Tomorrow the last day of school how ya feel?
-franz:)

Answers

Answer:

Ours is today. Feels weird how we came a long way with the pandemic presiding our academic studies.

Step-by-step explanation:

You sold your friend a raffle ticket for $1. If his ticket is selected from the 1000 sold, he will win
$500. What is the expected value of his net gain?
0 -$0.10
-$0.99
0 -$0.50
0 $0.05

Answers

They are expected to win back on average 50 cents back, which is a bad investment.

simplify 3+4(y-7)+5y​

Answers

Answer:

9y-25

Step-by-step explanation:

Answer:

9y-25

Step-by-step explanation:

Math

What is the probability of spinning an even number?

Answers

Answer:

3/5

Step-by-step explanation:

there are 6 even numbers and 4 odd so 10 in total which is 6/10 and that simplified is 3/5 PLS give me brainliest i beg

HELP ASAPPPP, FIRST PERSON TO HAVE THE CORRECT ANSWER WILL HAVE BRAINLIEST

What is the distance between points (8,3) and (3, 1) on the coordinate plane?


OA. 3 units
OB. 21 units
OC.29 units
OD. 7 units

Answers

Answer:

√29

Step-by-step explanation:

You would use the distance formula in this case to solve the problem:

(8-3)^2+(1-3)^2=29

Now square root 29, leaving you with √29.

Answer:

5.39

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(3 - 8)² + (1 - 3)²

√(-5)² + (-2)²

√25 + 4

√29

= 5.39


Asif and Ben share $2100 in the ratio Asif: Ben = 3:7.
Work out how much Asif receives.
$2100

Answers

Answer:

$630 for Asif

Step-by-step explanation:

Asif gets 3/10ths

So

2100 x 3/10 =  $630 for Asif

Identify who is correct
Describe the mistake that was made

Answers

Jack is wrong because he used the distributive property wrong. On the top equation, you see 2(4k - 3). The 2 multiplies into the (), so basically you have

2 x 4k - 2 x 3

which gives you

8k - 6

Answer:

Taniyah

Step-by-step explanation:

Taniyah is correct because you need to:

diistribute : 8k - 6 - 6k = 14

combine like terms : 2k - 6 = 14

add 6 to both sides : 2k - 6 + 6 = 14 + 6

simplify : 2k = 20

divide both sides by the same factor : 2k/2 = 20/2

simplify : k = 10

Find the sum of the first 8 terms of the following sequence. Round to the nearest hundredth if necessary. 20,40,80,...

Answers

Answer:

5100

Step-by-step explanation:

the geometric sequence is

f(n) = 20(2)^(n-1)

add up the first 8 to get

All dimensions of a cylinder are multiplied by 1.5. Which statement is true?

A. The total surface area is multiplied by 3.375.
The volume is multiplied by 2.25.

B. The total surface area is multiplied by 2.25.
The volume is multiplied by 3.375.

C. The total surface area is multiplied by 3.
The volume is multiplied by 4.5.

D. The total surface area is multiplied by 4.5.
The volume is multiplied by 3.

Answers

Answer:

The true statement is;

B. The total surface area is multiplied by 2.25

The volume is multiplied by 3.375

Step-by-step explanation:

By scale drawing proportionality, we have;

The amount by which all the dimensions of the cylinder are multiplied to create an image of the cylinder = 1.5

∴ The scale factor between the original cylinder and the image of the cylinder, S.F. = 1.5

By rule, we have;

The area factor of the surface area = S.F.² = 1.5² = 2.25

Therefore;

The total surface area of the original cylinder is multiplied by 2.25 to get the total surface area of the image of the cylinder

By rule, we have;

The volume factor = S.F.³ = 1.5³ = 3.375

Therefore;

The volume of the original cylinder is multiplied by 3.375 to find the volume of the image of the cylinder.

Answer:

B

Step-by-step explanation:

Ravi and Hasan bought 13⁄4 of pies , Ravi ate 1/3 and Hasan ate 2/3 of it
. How much pie is left?

Answers

Answer:

The final answer is 0

Step-by-step explanation:

1/3 + 2/3 = 1 which means Ravi and Hasan ate the whole thing

Can I have brainliest? It would help me out, if not thanks anyways! Hope this helped and have a nice day!

find the volume of the irregular figure

Answers

Answer:

V = 672cm^3

Step-by-step explanation:

V of irregular figure = lwh + lwh

V = 7(3)(2) + 10(7)(9)

V = 42 + 630

V = 672cm^3

3 feet
4 feet
inches
6 inches
Is Inches
What is the volume, in cubic feet, of the
cement used to make the steps? Show or
explain all of the steps you used to determine
your answer.

Answers

Answer: 12 for the main square

Step-by-step explanation:

take the 4 and the 3 and multiply it, makes 12. you see how each stair is 6 inches and there is 3 full steps which makes it 1.50 feet. 12 x 1.50 is 18. that makes your main square. I'm sorry but I cant really help you with the steps but that was also confusing to me.

Use elimination/linear combination to solve the following.
please help

Answers

Answer:

Step-by-step explanation:

3x + 4y = 17

5x - 4y = 7

you can thus cancel out 4y

Hence

8x = 24

Hence x = 3

Substituting’

3(3) + 4y = 17

9 + 4y = 17

Hence 17 - 9/4

= y = 2

Hope this helps

which of the following tables does NOT represent a function ? (i can’t get this wrong please help) (15 points)

Answers

Answer:

C

Step-by-step explanation:

the answer is c because there is more then one y value for 5

Three boys were playing balls. Ben's ball bounced eight more times than Menard's . Menard's ball bounced half as many times as Diego's. Diego's ball bounced eight times. How many times did Ben's ball bounced?

Answers

Answer:

12 bounce

Step-by-step explanation:

Let :

Number of Menard's bounce = x

Ben's bounce = x + 8

Diego's bounce = 2x

If Diego's bounce = 8

Then ;

2x = 8

x = 8/2

x = 4

Ben's bounce = x + 8

Ben's bounce = 4 + 8 = 12

y=x
2
+3x+2 & y=4x+4

Answers

Answer:

Step-by-step explanation:pho;np9yil.gboil k,

Find the area of the given regular polygon
Round your answer to the nearest tenth, if necessary.
A. 221.7
B. 665.1
C. 280.6
D. 2660.4

Answers

Answer:

A.221.7

Step-by-step explanation:

god bless

[tex]a[/tex]

HELPPPPPPPPPPPP THIS IS A MEGA TEST Felicia pours 3/4 of a 2 1/2-liter bottle of chlorine solution into a swimming pool. Then, she measures out the liter of the remaining solution to use to clean the pool filter. How much chlorine solution is left in the bottle?

Answers

Answer:

1/4 L

Step-by-step explanation:

2 1/2=10/4  10/4*3/4=30/16= 1 7/8

1 7/8=15/8        10/4*2=20/8          20/8-15/8=5/8

5/8-3/8=2/8 or 1/4 L

Answer: 1/4 L

In bottle 1/4 of chlorine solution is left in bottle.

What is an expression?

Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Given that;

Felicia pours 3/4 of a 2 1/2-liter bottle of chlorine solution into a swimming pool.

And, then she measures out 3/8 liters of the remaining solution to use to clean the pool filter.

Now,

Chlorine solution in bottle = 2 1/2 × ( 1 - 3/4 ) - 3/8

                                        = 5 / 2 × 1/4 - 3/8

                                        = 5 / 8 - 2 / 8

                                        = 1 / 4

Thus, In bottle 1/4 of chlorine solution is left in bottle.

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The complete question is this;

Felicia pours 3/4 of a 2 1/2-liter bottle of chlorine solution into a swimming pool then she measures out 3/8 liters of the remaining solution to use to clean the pool filter how much chlorine solution is left in the bottle?

Find the circumference of the circle to the nearest hundredth
11cm

Answers

Question: Find the circumference of the circle to the nearest hundredth

d = 11cm

Answer:

34.54 cm

Step-by-step explanation:

Applying,

P = πd...................... Equation 1

Where P = Circumference of perimeter of the circle, d = diameter of the circle, π = pie

From the question

Given: d = 11 cm

Constant: π = 3.14

Substitute these values into equation 1

P = (3.14×11)

P = 34.54 cm

How many reflectional symmetries does this figure have?

Enter your answer in the box.

_ reflectional symmetries


How many rational symmetries does this figure have?

Enter your answer in the box.

_ rotational symmetries

Answers

Answer:

1 & 1

Step-by-step explanation:

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