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3 years ago

Solve this application problem using a system of equations: A grocery store recently sold a

Mathematics

1 answer:

seraphim [82]3 years ago

5 0

Answer:

19 bags of peanuts and 31 bags of pistachios were sold.

Step-by-step explanation:

This question is solved by a system of equations.

I am going to say that:

x is the number of bags of peanuts sold.

y is the number of bags of pistachios sold.

50 bags of peanuts and pistachios were sold

This means that $x + y = 50$ , that is: $x = 50 - y$

A grocery store recently sold a bag of peanuts for $0.76 and a bag of pistachios for $3.68. Were sold for a total of $128.52.

This means that:

$0.76x + 3.68y = 128.52$

Since $x = 50 - y$

$0.76(50 - y) + 3.68y = 128.52$

$2.92y = 90.5$

$y = \frac{90.5}{2.92}$

$y = 31$

$x = 50 - y = 50 - 31 = 19$

19 bags of peanuts and 31 bags of pistachios were sold.

You might be interested in

How do you solve a linear inequality and graph on a number line?

tiny-mole [99]

This is very similar to solving linear equations except for one thing, If we multiply or divide by a negative number, we must flip the inequality sign.

<h3>What is linear inequality?</h3>

In mathematics, inequality occurs when a non-equal comparison is made between two mathematical expressions or two numbers. In general, inequalities can be either numerical inequality or algebraic inequality or a combination of both.

To better understand it, let's examine the example.

2x - 5 < 3

So, when we solve, let's just consider the inequality sign like a regular equal sign.

Let's start by adding 5 to each sides.

2x - 5 + 5 < 3 + 5

To find the value of x , we must divide it by two.

2x/2 <8/2

And the final result is x= 4.

This is our answer.

So if we need to graph it, let’s draw a number line and draw an open circle at 4. Open circle because x is not equal to 4. Then make an arrow going to the left.

to know more about linear inequality and graph:

brainly.com/question/21103162

#SPJ4

5 0

1 year ago

A simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week

Levart [38]

Answer:

99% confidence interval for the population proportion of employed individuals is [0.104 , 0.224].

Step-by-step explanation:

We are given that a simple random sample of size n=250 individuals who are currently employed is asked if they work at home at least once per week.

Of the 250 employed individuals surveyed, 41 responded that they did work at home at least once per week.

Firstly, the pivotal quantity for 99% confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of individuals who work at home at least once per week = $\frac{41}{250}$ = 0.164

n = sample of individuals surveyed = 250

<em>Here for constructing 99% confidence interval we have used One-sample z proportion statistics.</em>

So, 99% confidence interval for the population proportion, p is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99 {As the critical value of z at 0.5%

level of significance are -2.5758 & 2.5758}

P(-2.5758 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 2.5758) = 0.99

P( $-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

P( $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.99

<em>99% confidence interval for p</em> = [ $\hat p-2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+2.5758 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.164-2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ , $0.164+2.5758 \times {\sqrt{\frac{0.164(1-0.164)}{250} } }$ ]

= [0.104 , 0.224]

Therefore, 99% confidence interval for the population proportion of employed individuals who work at home at least once per week is [0.104 , 0.224].

7 0

3 years ago

What did the triangle say to the circle

Arte-miy333 [17]

You're so pointless ... duh XD

8 0

3 years ago

Read 2 more answers

Plot a point on the coordinate plane to represent each of the

Juli2301 [7.4K]

(1,4) you go right 1 time, and than go up 4.