1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
krok68 [10]
3 years ago
8

45 POINTS At a high school football game, 4 out of every 7 students in line to buy a ticket wore a hat. If 350 students bought a

ticket, how many students wore a hat? How many students did not wear a hat?Be sure to answer both questions in sentence form. Also, describe how you got your answers in sentence form.
Mathematics
2 answers:
son4ous [18]3 years ago
8 0

Answer:

(:

Step-by-step explanation:

nataly862011 [7]3 years ago
6 0

Step-by-step explanation:

Number of students who wore a hat

= 4/7 * Number of students who bought a ticket

= 4/7 * 350 students

= 200 students.

Number of students not wearing a hat

= Number of students who bought a ticket - Number of students who wore a hat

= 350 students - 200 students

= 150 students.

You might be interested in
we want to build a box with square base of side x and height and in such a way that the volume is 128 cubic inches. If we know t
sergij07 [2.7K]

Answer:

4 in × 4 in × 8 in or  

6.47 in × 6.47 in × 3.06 in

Step-by-step explanation:

Data:

(1)                  V = 128 in³

(2)                  l = w = x

(3) 4(l + w + h) = 64 in  (There are 12 edges)

Calculation:

The formula for the volume of the box is

(4)                 V = lwh

(5)              128 = x²h          Substituted (1) and (2) into (4)

(6)                  h = 128/x²     Divided each side by x²

          l + w +h = 16            Divided (1) by 4

          x + x + h = 16           Substituted (2) into 6

(7)          2x + h = 16           Combined like terms

     2x + 128/x² = 16           Substituted (6) into (7)

        2x³ + 128 = 16x²        Multiplied each side by x²

2x³ - 16x²+ 128 = 0            Subtracted 16x² from each side

    x³ - 8x² + 64 = 0           Divided each side by 2

According to the Rational Zeros theorem, a rational root must be a positive or negative factor of 64.

The possible factors are ±1, ±2, ±4, ±8, ±16, ±32, ± 64.

After a little trial-and-error with synthetic division (start in the middle and work down) we find that x = 4 is a zero.              

4|1   -8     0   64

 <u>|      4  -16  -64 </u>

   1  -4  -16      0

So, the cubic equation factors into (x - 4)(x² - 4x + 16) = 0

We can use the quadratic formula to find that the roots of the quadratic are

x = 2 - 2√5 and x = 2+ 2√5

We reject the negative value and find that there are two solutions to the problem.

x = 4 in and x = 2 + 2√5 ≈ 6.472 in

Case 1. x = 4 in

h = 128/x² = 128/4² = 128/16 = 8 in

The dimensions of the box are 4 in × 4 in × 8 in

Also, 4(l + w + h) = 4( 4 + 4 + 8) = 4 × 16 =  64 in

Case 2. x = 6.472 in

h = 128/x² = 128/6.472² = 128/41.89 = 3.056 in

The dimensions of the box are 6.47 in × 6.47 in × 3.06 in

Also, 4(l + w + h) = 4( 6.47 + 6.47 + 3.06) = 4 × 16.00 =  64 in

The two solutions are

(a) 4 in       × 4 in      × 8 in

(b) 6.47 in × 6.47 in × 3.06 in    

7 0
3 years ago
What is the sum of the series? 4 ∑k=1 (2k^2−4)
larisa86 [58]

The sum of the series \sum_{k=1}^{4}\left(2 k^{2}-4\right) is 44.

Step-by-step explanation:

The given series is \sum_{k=1}^{4}\left(2 k^{2}-4\right)=44

To find the sum of the series, we need to substitute the values for k in the series.

\sum_{k=1}^{4}\left(2 k^{2}-4\right)=\left[2(1)^{2}-4\right]+\left[2(2)^{2}-4\right]+\left[2(3)^{2}-4\right]+\left[2(4)^{2}-4\right]

Now, simplifying the square terms, we get,

[2(1)-4]+[2(4)-4]+[2(9)-4]+[2(16)-4]

Multiplying the terms,

[2-4]+[8-4]+[18-4]+[32-4]

Subtracting the values within the bracket term, we get,

-2+4+14+28

Now, adding all the terms, we get the sum of the series,

\sum_{k=1}^{4}\left(2 k^{2}-4\right)=44

Thus, the sum of the series is \sum_{k=1}^{4}\left(2 k^{2}-4\right)=44

8 0
3 years ago
Find two consecutive whole numbers that the square root of 47<br> lies between.
ella [17]
\sqrt{47}\approx6.9

So those two consecutive whole numbers will be 6 and 7.
3 0
3 years ago
2√m^2 if m is greater than or equal to 0
iris [78.8K]

Answer:

\displaystyle  \boxed{|2m| }

Step-by-step explanation:

we are given that

\displaystyle 2 \sqrt{  {m}^{2} }

since m is greater than or equal to 0 it's a positive number therefore, the square root of m is defined and recall that √x²=|x| thus

\displaystyle  \boxed{2 |m|}

remember that,|a|•|x|=|ax| hence,

\displaystyle  \boxed{ |2m|}

and we're done!

3 0
3 years ago
Read 2 more answers
Find the value of x and y​
ra1l [238]

Answer:

here is the answer

Step-by-step explanation: x = 120, y = 150

hope this helped:)

6 0
3 years ago
Other questions:
  • How many solutions can be found for the linear equation?<br><br> 3(x + 4) = 3x + 4
    5·1 answer
  • Catherine has $54. She plans to spend more than $20 of the money for a painting canvas. The rest will go toward paints. Each tub
    13·1 answer
  • A digital video recorder (DVR) records television shows on an internal hard drive. To use a DVR, you need a subscription with a
    8·1 answer
  • • Which multiplication expression is equivalent to
    12·2 answers
  • What would be the original cost? $99.50?
    9·1 answer
  • Y = 2x – 6 y = –4x + 3<br> will give brainliest
    13·1 answer
  • Expand and simplify the following<br> 1<br> 2(4x - 3) + 5x + 4
    14·1 answer
  • The Franklin Family went on
    15·1 answer
  • PLS HELP ASAP!tysm if u help me!&lt;3
    14·1 answer
  • A line passes through the point (-2,6) and has a slope of 5/2 write an equation in slope-intercept form for this line
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!