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3 years ago

Which equation can pair with 3x + 4y = 8 to create a consistent and independent system?

1 answer:

6 0

There isn't any choices given in this problem but I can give you a tip to answer these kinds of problem. When you say independent, it means that the equation cannot be algebraically altered to result to 3x + 4y = 8. So the equation 6x + 8y = 16 is not an independent equation since when you divide each side by 2 it will result to 3x + 4y =8. You get the idea.

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In 1998, as an advertising campaign, the Nabisco Company announced a "1000 Chips Challenge," claiming that every 18-ounce bag of

Phoenix [80]

Answer:

A 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

Step-by-step explanation:

We are given that statistics students at the Air Force Academy (no kidding) purchased some randomly selected bags of cookies and counted the chocolate chips.

Some of their data are given below; 1219, 1214, 1087, 1200, 1419, 1121, 1325, 1345, 1244, 1258, 1356, 1132, 1191, 1270, 1295, 1135.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean number of chocolate chips = $\frac{\sum X}{n}$ = 1238.2

s = sample standard deviation = $\sqrt{\frac{\sum (X-\bar X)^{2} }{n-1} }$ = 94.3

n = sample of car drivers = 16

$\mu$ = population mean number of chips in a bag

Here for constructing a 95% confidence interval we have used a One-sample t-test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.131 < $t_1_5$ < 2.131) = 0.95 {As the critical value of t at 15 degrees of

freedom are -2.131 & 2.131 with P = 2.5%}

P(-2.131 < $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ < 2.131) = 0.95

P( $-2.131 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X-\mu}$ < $2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.131 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X+2.131 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = [ $\bar X-2.131 \times {\frac{s}{\sqrt{n} } }$ , $\bar X+2.131 \times {\frac{s}{\sqrt{n} } }$ ]

= [ $1238.2-2.131 \times {\frac{94.3}{\sqrt{16} } }$ , $1238.2+2.131 \times {\frac{94.3}{\sqrt{16} } }$ ]

= [1187.96, 1288.44]

Therefore, a 95% confidence interval for the mean number of chips in a bag of Chips Ahoy Cookies is [1187.96, 1288.44].

7 0

3 years ago

How many milliliters of syrup are in a 100-ml sample containing 6.55 g of syrup per 20 mL if the syrup's specific gravity is 1.3

sashaice [31]

Answer:

25 milliliters

Step-by-step explanation:

Given:

volume of sample = 100 ml

Syrup present in sample = 6.55 g per 20 mL

Therefore in 100 mL, amount of syrup present = $\frac{\textup{6.55}}{\textup{20}}\times100$

amount of syrup present in 100 mL sample = 32.75 grams

Now,

Specific gravity of the syrup = 1.31

also,

Specific gravity of the syrup = $\frac{\textup{Density of syrup}}{\textup{Density of water}}$

1.31 = $\frac{\textup{Density of syrup}}{\textup{1 g/mL}}$

Density of syrup = 1.31 g/mL

also,

Density = $\frac{\textup{Mass}}{\textup{Volume}}$

therefore,

1.31 = $\frac{\textup{32.75}}{\textup{Volume of syrup in the sample}}$

Volume of syrup in the sample = $\frac{\textup{32.75}}{\textup{1.31}}$

Volume of syrup in the sample = 25 milliliters

8 0

3 years ago

Jessica packed 1-inch cubes into a box with a volume of 144 cubic inches how many layers of 1-inc cubes did Jessica pack

alexdok [17]

Maybe 3 or 6 or 8, the formula for the volume of a rectangular prism = a * b * c. A, B, C are the length, width, and height. and 3*6*8=144

7 0

3 years ago

The cost of a one-way ticket to Muscat is 487.75 QR and the cost of a return trip is 909 QR. How much cheaper is it to buy a ret

Brums [2.3K]

Answer:

Price of (1) One way ticket = 487.75 QR

Price of (2) One way tickets = 487.75*2= 975.5 QR

Price for Return trip = 909 QR

Difference = 975.5-909 = 66.5 QR

There for Its is cheaper to buy to buy a return trip ticket by 66.5 QR

Ans: 60.50 QR

6 0

3 years ago

Isabella works at Baker's Book company. If she earned a commission of $63.75 on her sales of $850, what was Isabella's rate of c

Westkost [7]

Rate = 63.75/850=.075*100%= 7.5%

7.5% is Isabella's rate of commission.

8 0

3 years ago