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Alik [6]
3 years ago
5

John and his friends but four bags of popcorn and three sodas at a movies for a total of $13.50 at the next movie John and his f

riends bought two bags of popcorn and 5 sodas for a total of $12 how much will John and his friends pay in dollars for 5 bags of popcorn and two sodas
Mathematics
1 answer:
Aleonysh [2.5K]3 years ago
5 0
To answer this question you will set up a system of equations to represent each scenario.  Solve for one variable and substitute that in to the other equation to find the missing value.  This example will have you solving for p, the price of popcorn.

4p + 3s = 13.50    and 2p + 5s = 12

2p + 5s = 12
      -2p    -2p
5s = 12 - 2p
5         5
s = 2.4 - 0.4p

4p + 3s = 13.50 
4p + 3(2.4 - 0.4p) = 13.50
4p +7.2 - 1.2p = 13.5
 2.8p +7.2 = 13.5
       -7.2       -7.2 
   <u>2.8p</u> = <u>6.3</u>
   2.8      2.8
   p = 2.25

The price of popcorn is 2.25 and the soda is (2.4 - 0.4 x 2.25) $1.50.

5 popcorn and 2 sodas will cost (2.25 x 5 + 1.50 x 2) = $14.25.

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In the past, the population proportion of consumers preferring orange juice with no pulp was equation. To test if this populatio
geniusboy [140]

Answer:

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

a) For the null hypothesis,

P = 0.45

For the alternative hypothesis,

P ≠ 0.45

b) For the decision rule, we would reject H0 if 0.1 > p value and accepth H0 if 0.1 < p value

Considering the population proportion, probability of success, p = 0.45

q = probability of failure = 1 - p

q = 1 - 0.45 = 0.55

Considering the sample,

Sample proportion, p = x/n

Where

x = number of success = 52

n = number of samples = 120

p = 52/120 = 0.43

c) We would determine the test statistic which is the z score

z = (p - P)/√pq/n

z = (0.43 - 0.45)/√(0.45 × 0.55)/120 = - 0.44

Recall, population proportion, P = 0.45

The difference between sample proportion and population proportion(P - p) is 0.45 - 0.43 = 0.02

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.45 - 0.02 = 0.43

the p for the right tail is 0.45 + 0.02 = 0.47

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.3336

We would double this area to include the area in the right tail of z = 0.44 Thus

p = 0.3336 × 2 = 0.67

d) Since alpha, 0.1 < than the p value, 0.67, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the​ null hypothesis

4 0
2 years ago
Find the mean of these numbers:<br> 5,11,2,12,4,2
givi [52]

Answer:

6

Step-by-step explanation:

Add all the  numbers together which you get 36.

next divide 36 by the total of number you have.

so 36 divided by 6 equals 6.

6 0
2 years ago
A quadrilateral has two angles that measure 120° and 140°. The other two angles are in a ratio of 2:3. What are the measures of
Furkat [3]
40 degrees and 60 degrees
8 0
2 years ago
Prove that can you please prove and explain it plz ​
Alexandra [31]

Answer:

Step-by-step explanation:

LHS = Sin² ∅ + Sin² ∅*tan² ∅

        = Sin² ∅ [1 + tan² ∅ ]                 {Sec² ∅ - tan² ∅  = 1}

         = Sin² ∅ *Sec² ∅

         = Sin² ∅ * \frac{1}{Cos^{2} }

         = Sin² ∅ /Cos² ∅

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8 0
3 years ago
Read 2 more answers
Which ordered pair makes both inequalities true? y &lt; 3x – 1 y &gt; –x + 4 On a coordinate plane, 2 straight lines are shown.
Katen [24]

Answer:

(4,0)

Step-by-step explanation:

we have

y< 3x-1 ----> inequality A

y \geq -x+4 ----> inequality B

we know that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities (makes true both inequalities)

Verify each ordered pair

case 1) (4,0)

<em>Inequality A</em>

0< 3(4)-1

0< 11 ----> is true

<em>Inequality B</em>

0 \geq -(4)+4

0 \geq 0 ----> is true

so

the ordered pair makes both inequalities true

case 2) (1,2)

<em>Inequality A</em>

2< 3(1)-1

2< 2 ----> is not true

so

the ordered pair not makes both inequalities true

case 3) (0,4)

<em>Inequality A</em>

4< 3(0)-1

4< -1 ----> is not true

so

the ordered pair not makes both inequalities true

case 4) (2,1)

<em>Inequality A</em>

1< 3(2)-1

1< 5 ----> is true

<em>Inequality B</em>

1 \geq -(2)+4

1 \geq 2 ----> is not true

so

the ordered pair not makes both inequalities true

5 0
3 years ago
Read 2 more answers
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