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Andreyy89
3 years ago
9

Solve the system of equations 3y + 2z = 12 and y – z= 9. 

Mathematics
1 answer:
dangina [55]3 years ago
3 0
\left\{\begin{array}{ccc}3y+2z=12\\y-z=9&|multiply\ both\ sides\ by\ 2\end{array}\right\\\underline{+\left\{\begin{array}{ccc}3y+2z=12\\2y-2z=18\end{array}\right}\\.\ \ \ \ 5y=30\ \ \ |divide\ both\ sides\ by\ 5\\.\ \ \ \ y=6\\\\subtitute\ the\ value\ of\ y\ to\ the\ equation\ y-z=9\\\\6-z=9\ \ \ |subtract\ 6\ from\ both\ sides\\-z=3\ \ \ |change\ signs\\z=-3\\\\Answer:\left\{\begin{array}{ccc}y=6\\z=-3\end{array}\right
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What is the difference between a proper and an improper subset?
lutik1710 [3]

A proper subset describes the set in full.  An improper subset strays from the original set.

4 0
3 years ago
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wilhelmina has 8.3 ounces of peanut butter.if she makes 5 sandwijes with an equal amount ofbpeanut butter on each,how much peanu
kotykmax [81]

Peanut butter: 8.3 ounces

Sandwich: 5

Divide 8.3 by 5, for equal amount of peanut butter on each sandwich.

8.3/5 = 1.66

She puts 1.66 ounces of peanut butter on each sandwich.

3 0
3 years ago
HELPPP PLZZZ IM CRYINGGGG HELPPPPPPPP
Goryan [66]

1) Experimental probability of drawing a Club = 9 / 40

The experimental probability is the probability of the event occurring in the experiment. You use your results to find the experimental probability. This is over the total amount of trials. In this experiment, 9 clubs were drawn. Thus, the experimental probability of drawing a club is 9 / 40.

2) Relative frequency of drawing a Spade = 1 / 5

Relative frequency is the same as experimental probability. You use your results and set the experiment number over the total number of trials. Thus, the relative frequency of drawing a Spade is 8 / 40, or 1 / 5.

3) Theoretical probability of drawing a Heart = 1 / 4

The theoretical probability is the expected probability. There are 13 hearts out of a full deck of 52 cards. Thus, the theoretical probability of drawing a heart is 13 / 52 or 1 / 4.

4) Theoretical probability of drawing a Club or Diamond = 1 / 2

The theoretical probability is the probability that is expected. In this scenario, it will be the number of clubs plus the number of diamonds in a deck of cards over the total number of cards in a full deck. And, or means that either probability could occur and we should add. Thus, the theoretical probability of drawing a club or diamond is 26 / 52 or 1 / 2.

5) The difference between experimental and theoretical probability is that experimental probability is the probability of an event occurring based on your experiment and results. The theoretical probability is the expected probability of an event occurring. It is not based on your experiment, and in a completely fair experiment, would be the probability of an event occurring. For example, flipping a coin. The theoretical probability of getting heads when you flip a coin is 0.5. But say in your experiment of 50 trials you get heads 15 times. The experimental probability would be 15 / 50.

Hope this helps!! :)

5 0
3 years ago
Suppose the force acting on a column that helps to support a building is a normally distributed random variable X with mean valu
Sauron [17]

Answer:

(1) 0.4207

(2) 0.7799

Step-by-step explanation:

Given,

Mean value,

\mu = 15.0

Standard deviation,

\sigma = 1.25

(1) P(X ≥ 17.5) = 1 - P( X ≤ 17.5)

= 1- P(\frac{x-\mu}{\sigma} \leq \frac{17.5-\mu}{\sigma})

=1-P(z\leq \frac{17.5 - 15}{1.25})

=1-P(z\leq \frac{2.5}{1.25})

=1-P(z\leq 2)

=1- 0.5793   ( By using z-score table )

= 0.4207

(2) P(14 ≤ X ≤ 18) = P(X ≤ 18) - P(X ≤ 14)

=P(z\leq \frac{18 - 15}{1.25}) - P(z\leq \frac{14 - 15}{1.25})

=P(z\leq \frac{3}{1.25}) - P(z\leq -\frac{1}{1.25})

=P(z\leq 2.4) - P(z\leq -0.8)

= 0.9918 - 0.2119

= 0.7799

8 0
3 years ago
“I had a pretty normal day,” “I have little confidence in our ability to win today,” and “That’s so random!” are statements you
Nesterboy [21]

Answer:

Yes

Step-by-step explanation:

I would say that yes, they do. The concepts are being described as normal, confident, and random. Those are describing the statistical concept the sentence is placed around.

7 0
3 years ago
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