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1 year ago

2x-10/4=3x −10 −1 2 11

Mathematics

1 answer:

evablogger [386]1 year ago

6 0

Answer:

Step-by-step explanation:

$\dfrac{2x-10}{4}=3x\qquad\text{multiply both sides by 4}\\\\2x-10=12x\qquad\text{subtract}\ 2x\ \text{from both sides}\\\\-10=10x\qquad\text{divide both sides by 10}\\\\-1=x\to x=-1$

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If we were to make a poset of the form (A, |), where is the symbol for divisibility, which of the following sets A would yield a

Marrrta [24]

Answer:

IV. A+{1, 2, 3, 6, 12}

Step-by-step explanation:

The set of natural numbers form a poset number under relation of > or =. The discrete variables are used to form a poset. The symbols for divisibility in poset form are when an integer is divided by the variable without integer. The correct answer is therefore 4th option.

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2 years ago

In a statewide soccer competition, 36 games were played. Each team participating in the competition played once with every other

Tomtit [17]

Answer:

9 teams

Step-by-step explanation:

If the total games played was 36 and no team played each other twice, we need to ensure there isn't any double counting.

36 = (n-1) + (n-2) + (n-3) ... + (n-(n-1))

using this knowledge, we can then count up:

1+2+3+4+5+6+7+8 = 36

If our highest number is 8, then we know there must be 9 teams, because no team can play themselves.

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1 year ago

Read 2 more answers

Mateus’s bank issued an advertisement saying that 90\%90%90, percent of its customers are satisfied with the bank’s services. Si

densk [106]

Answer:

The probability of getting a sample with 80% satisfied customers or less is 0.0125.

Step-by-step explanation:

We are given that the results of 1000 simulations, each simulating a sample of 80 customers, assuming there are 90 percent satisfied customers.

Let $\hat p$ = <u><em>sample proportion of satisfied customers</em></u>

The z-score probability distribution for the sample proportion is given by;

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

where, p = population proportion of satisfied customers = 90%

n = sample of customers = 80

Now, the probability of getting a sample with 80% satisfied customers or less is given by = P( $\hat p \leq$ 80%)

P( $\hat p \leq$ 80%) = P( $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ $\leq$ $\frac{0.80-0.90}{\sqrt{\frac{0.80(1-0.80)}{80} } }$ ) = P(Z $\leq$ -2.24) = 1 - P(Z < 2.24)

= 1 - 0.9875 = <u>0.0125</u>

The above probability is calculated by looking at the value of x = 2.24 in the z table which has an area of 0.9875.

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2 years ago

Two cross sections of a right hexagonal pyramid are obtained by cutting the pyramid with planes parallel to the hexagonal base.

Tanya [424]

Answer:

The larger cross section is 24 meters away from the apex.

Step-by-step explanation:

The cross section of a right hexagonal pyramid is a hexagon; therefore, let us first get some things clear about a hexagon.

The length of the side of the hexagon is equal to the radius of the circle that inscribes it.

The area is

$A=\frac{3\sqrt{3} }{2} r^2$

Where $r$ is the radius of the inscribing circle (or the length of side of the hexagon).

Now we are given the areas of the two cross sections of the right hexagonal pyramid: $A_1=216\:ft^2\: \:\:\:A_2=486\:ft^2$

From these areas we find the radius of the hexagons:

$r_1=\sqrt{\frac{2A_1}{3\sqrt{3} } } =\sqrt{\frac{2*216}{3\sqrt{3} } }=\boxed{9.12ft}$

$r_2=\sqrt{\frac{2A_2}{3\sqrt{3} } } =\sqrt{\frac{2*486}{3\sqrt{3} } }=\boxed{13.68ft}$

Now when we look at the right hexagonal pyramid from the sides ( as shown in the figure attached ), we see that $r_1$ $r_2$ form similar triangles with length $H$