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Shalnov [3]
2 years ago
10

Hannah mixed 6.83 lb of pretzels with 3.57 lb of popcorn. After filling up 6 bags that were the same size with the mixture, she

had 0.35 lb left. What was the weight of each bag cant figur it out 5th grade math
Mathematics
1 answer:
liubo4ka [24]2 years ago
8 0

Answer:

1.675 lb

Step-by-step explanation:

Given that Hannah mixed 6.83 lb of pretzels with 3.57 lb of popcorn.

So, after mixing, the total amount of mixture is

6.83 lb + 3.57 lb = 10.40 lb.

After filling up 6 bags that were the same size with the mixture, she had 0.35 lb left, so 0.35 lb of the mixture is not in the bag.

So,he total amount of mixture in 6 bags = 10.40 lb - 0.35 lb=10.05 lb, which is the weight of 6 bags.

The weight of one bag =\frac {10.05}{6} lb

=1.675 lb

As all the bags are of the same size, so the weight of all the bags are same,

Hence, the weight of each bag is 1.675 lb.

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What is the completely factored form of f(x)=x3+5x2+4x−6?
Gre4nikov [31]
f(x)=x^3+5x^2+4x-6
f(-3)=(-3)^3+5(-3)^2+4(-3)-6=0\implies x+3\text{ is a factor of }f(x)

Synthetic division yields

-3  |  1   5   4   -6
.    |      -3  -6    6
- - - - - - - - - - - - -
.    |  1   2  -2    0

which translates to

\dfrac{x^3+5x^2+4x-6}{x+3}=x^2+2x-2

with remainder 0. Now by the quadratic formula,

x^2+2x-2=0\implies x=\dfrac{-2\pm\sqrt{2^2-4(1)(-2)}}2=-1\pm\sqrt3

and so

f(x)=x^3+5x^2+4x-6=(x+3)(x-(-1+\sqrt3))(x-(-1-\sqrt3))
3 0
2 years ago
A standardized test consists of 100 multiple-choice questions. Each question has five possible answers, only one of which is cor
Nady [450]

Answer:

a) S ~ N ( 0 , 48 )

b) P ( S > 10 ) = 0.0745

Step-by-step explanation:

Given:-

- We have n = 100 MCQs

- 5 options for every MCQs

- probability to guess each MCQ correct is independent from one another.

- Right Answer points= +4

- Wrong answer points= -1

Find:-

a) Find ????(S).

b) Find P(S>10). Write your answer as a math expression, then use the code cell below to find its numerical value and provide it along with your math expression.

Solution:-

- The probability (p) of guessing a correct answer for each question is:

                             p ( correct answer ) = 1 / 5 = 0.2

- The mean number of correct and incorrect answers can be determined by:

                             ( Mean correct answers) = n*p = 100*0.2 = 20

                             ( Mean incorrect answers) = n*(1-p) = 100*0.8 = 80

- The mean score for correct answers would be:

                            Sc ( u ) = (Points for right answer)*(Mean correct answers)

                            Sc ( u ) = ( +4 )*(20)

                            Sc ( u ) = 80 points

The mean score for incorrect answers would be:

                            Si ( u ) = (Points for wrong answer)*(Mean incorrect answers)

                            Si ( u ) = ( -1)*(80)

                            Si ( u ) = -80 points.

- The mean score attained by a student would be S (u):

                           S (u) = Sc(u) + Si(u)

                           S (u) = 80 - 80 = 0

- The variance of the correct and incorrect answers can be determined by:

                           Var ( correct answers ) = n*p*q = 100*0.2*0.8 = 16

                           Var ( in-correct answers ) = n*p*q = 100*0.2*0.8 = 16

- The variance of points of correct answers can be:

                           Sc (Var) = Var ( correct answer ) * (Points for right answer)

                           Sc (Var) = 16*(+4) = +64 points

- The variance of points of incorrect answers can be:    

                          Si (Var) = Var ( incorrect answer ) * (Points for wrong answer)

                          Si (Var) = 16*(-1) = -16 points  

- Since the probabilities of guessing correct answers are independent. Then as per law of independence:

                         S ( Var ) =  Sc (Var) + Si (Var)

                                       = 64 - 16

                                       = +48 points

- The standard deviation for the distribution (s.d) of points (S) is:

                         S ( s.d ) = √S (Var)  = √48 = 6.9282            

- The number of points (S) attained by a student by guessing on the test containing MCQs would have a mean u = 0 points and s.d = + 48 points.

- The random variable (S) can be modeled by normal distribution as follows:

                         S ~ N ( 0 , 48 )      

- To find the required probability P(S>10).

Compute the Z-value of S = 10 points:

                        Z - value =  ( S - u ) / s.d

                                        =  ( 10 - 0 ) / 6.9282

                                        = 1.4434

Use the standardized Z-table for normal distribution:

                       P ( Z > 1.4434 ) = 0.0745

The probability is:

                       P ( S > 10 ) = P ( Z > 1.4434 ) = 0.0745

5 0
2 years ago
It takes 36 minutes to manually package 400 candles into boxes for shipment. When an automated packaging system works together w
Fittoniya [83]

Answer:

12 minutes

Step-by-step explanation:

Candles can be manually packed at the rate of ...

... (400 candles)/(36 minutes) = 11 1/9 candles/minute

The two systems together pack candles at the rate of ...

... (400 candles)/(9 minutes) = 44 4/9 candles/minute

Then the machine's packing rate is the difference between the total and the manual rates:

... machine rate = (44 4/9 candles/minute) - (11 1/9 candles/minute)

... = 33 1/3 candles/minute.

At this rate, the machine working alone can pack 400 candles in ...

... (400 candles)/(33 1/3 candles/minute) = (400/(100/3)) minutes

... = 400 × 3/100 minutes = 12 minutes

4 0
2 years ago
Point T is at (–3, 7). What are the coordinates of point T' after Ry-axis ∘ Rx-axis?
dimaraw [331]

Given:

The point is T(-3,7).

To find:

The image T' after R_{y-axis}\circ R_{x-axis}.

Solution:

R_{y-axis}\circ R_{x-axis}, it means reflection across x-axis is followed by reflection across y-axis.

If a point is reflected across the x-axis, then

(x,y)\to (x,-y)

T(-3,7)\to T_1(-3,-7)

Then point is reflected across the y-axis. So,

(x,y)\to (-x,y)

T_1(-3,-7)\to T'(3,-7)

Therefore, the coordinates of point T' are (3,-7).

6 0
2 years ago
A travel agency charges $64 for each bus ticket and $82 for each train ticket. Aaron has $520 to purchase tickets. If he buys 3
Firlakuza [10]

Answer:

The total number of train tickets Aaron can buy=4

Step-by-step explanation:

a). Determine first expression

Let the number of each mode of transport be as follows;

bus ticket=b

train ticket=t

b). Determine the second expression

Let the total cost be expressed as shown;

total cost=(cost per bus ticket×number of bus tickets)+(cost per train ticket×number of train tickets)

where;

total cost=$520

cost per bus ticket=$64

number of bus tickets=b=3

cost per train ticket=$82

number of train tickets=t

replacing;

(64×3)+(82×t)=520

192+82 t=520

82 t=520-192

82 t=328

t=328/82=4

t=4

The total number of train tickets Aaron can buy=4

8 0
2 years ago
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