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2 years ago

Solve each of the following system of equations by substitution!!! x-5y=-49 y=-2x+1

Mathematics

1 answer:

miss Akunina [59]2 years ago

4 0

Answer:

x = -4, y = 9

(-4, 9)

Step-by-step explanation:

x - 5y = -49

y = -2x + 1

substitute y for -2x + 1

x - 5(-2x + 1) = -49

x + 10x - 5 = - 49

add 5 to both sides

x + 10x - 5 + 5 = - 49 + 5

x + 10x = -44

11x = -44

divide both sides by 11

11x/11 = -44/11

x = -4

substitute x for -4 in any of the original equations

y = -2x + 1

y = -2 * -4 + 1

y = 8 + 1

y = 9

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Air-USA has a policy of booking as many as 24 persons on an airplane that can seat only 22. (Past studies have revealed that onl

Alex17521 [72]

Answer:

B. no, it is not low enough

A. no, it is not low enough

Step-by-step explanation:

Given that Air-USA has a policy of booking as many as 24 persons on an airplane that can seat only 22.

Prob for a random person booked arrive for flight = 0.86

No of persons who books and arrive for flight, X is binomial, since there are two outcomes and each person is independent of the other

The probability that if Air-USA books 24 persons, not enough seats will be available

= P(X=23)+P(x=24)

= 0.1315

B. no, it is not low enough

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The prob we got is >10% also

A. no, it is not low enough

7 0

3 years ago

A cellular phone company monitors monthly phone usage. The following data represent the monthly phone use of one particular cust

Fiesta28 [93]

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given set of values

$321,397,559,454,475,324,482,558,369,513,385,360,459,403,498,477,361,366,372,320$

STEP 2: Write the formula for calculating the Standard deviation of a set of numbers

$\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ where\text{ }x_i\text{ are data points,} \\ \bar{x}\text{ is the mean} \\ \text{n is the number of values in the data set} \end{gathered}$

STEP 3: Calculate the mean

$\begin{gathered} \bar{x}=\frac{\sum ^{}_{}x_i}{n} \\ \bar{x}=\frac{\sum ^{}_{}(321,397,559,454,475,324,482,558,369,513,385,360,459,403,498,477,361,366,372,320)}{20} \\ \bar{x}=\frac{8453}{20}=422.65 \end{gathered}$

STEP 4: Calculate the Standard deviation

$\begin{gathered} S\tan dard\text{ deviation=}\sqrt[]{\frac{\sum^{}_{}(x_i-\bar{x})^2}{n-1}} \\ \sum ^{}_{}(x_i-\bar{x})^2\Rightarrow\text{Sum of squares of differences} \\ \Rightarrow10332.7225+657.9225+18591.3225+982.8225+2740.52251+9731.8225+3522.4225+18319.6225+2878.3225 \\ +8163.1225+1417.5225+3925.0225+1321.3225+386.1225+5677.6225+2953.9225+3800.7225 \\ +3209.2225+2565.4225+10537.0225 \\ \text{Sum}\Rightarrow108974.0275 \\ \\ S\tan dard\text{ deviation}=\sqrt[]{\frac{111714.55}{20-1}}=\sqrt[]{\frac{111714.55}{19}} \\ \Rightarrow\sqrt[]{5879.713158}=76.67928767 \\ \\ S\tan dard\text{ deviation}\approx76.68 \end{gathered}$

Hence, the standard deviation of the given set of numbers is approximately 76.68 to 2 decimal places.

STEP 5: Calculate the First and third quartile

$\begin{gathered} \text{IQR}=Q_3-Q_1 \\ \\ To\text{ get }Q_1 \\ We\text{ first arrange the data in ascending order} \\ \mathrm{Arrange\: the\: terms\: in\: ascending\: order} \\ 320,\: 321,\: 324,\: 360,\: 361,\: 366,\: 369,\: 372,\: 385,\: 397,\: 403,\: 454,\: 459,\: 475,\: 477,\: 482,\: 498,\: 513,\: 558,\: 559 \\ Q_1=(\frac{n+1}{4})th \\ Q_1=(\frac{20+1}{4})th=\frac{21}{4}th=5.25th\Rightarrow\frac{361+366}{2}=\frac{727}{2}=363.5 \\ \\ To\text{ get }Q_3 \\ Q_3=(\frac{3(n+1)}{4})th=\frac{3\times21}{4}=\frac{63}{4}=15.75th\Rightarrow\frac{477+482}{2}=\frac{959}{2}=479.5 \end{gathered}$

STEP 6: Find the Interquartile Range

$\begin{gathered} IQR=Q_3-Q_1 \\ \text{IQR}=479.5-363.5 \\ \text{IQR}=116 \end{gathered}$

Hence, the interquartile range of the data is 116

3 0

1 year ago

Find the equation in terms of x of the line through the points (-4,-4) and (5,-5)

zhuklara [117]

Answer:

The answer to your question is: y = -1/9 x - 40/9

Step-by-step explanation:

Data

A (-4 , -4)

B (5, -5)

Formula

m = (y2 - y1) / (x2 - x1)

y = mx + b

(y - y1) = m(x - x1=

Process

m = (-5 + 4) / (5 + 4)

m = -1 / 9

( y +4) = -1/9 (x + 4)

y + 4 = -1/9 x - 4/9

y = -1/9 x - 4/9 - 4

y = -1/9 x - 4/9 - 36/9

y = -1/9 x - 40/9

5 0

3 years ago

HELP ME ASAP PLS

Katarina [22]

Answer:

Tommy had 56 cents in start and Loren had 7 cents in start.

Step-by-step explanation:

Let,

x be the money Tommy have.

y be the money Loren have.

According to given statement;

Tommy had 8 times more money than Loren.

x = 8y Eqn 1

Parents gave 35 cents to Loren and Tommy spent 14 cents, therefore

x-14=y+35 Eqn 2

Putting x=8y in Eqn 2

$8y-14=y+35\\8y-y=35+14\\7y=49$

Dividing both sides by 7

$\frac{7y}{7}=\frac{49}{7}\\y=7$

Putting y=7 in Eqn 1

$x=8(7)\\x=56$

Hence,

Tommy had 56 cents in start and Loren had 7 cents in start.

6 0

3 years ago

What is the volume of the cuboid in cm3 ?<br><br> What is the volume of the cuboid in mm3

KengaRu [80]

Answer:

3150mm

Step-by-step explanation:

1cm is 10mm you convert it then times it together l x b x h will equal 3150

7 0

1 year ago