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3 years ago

Solve the given equation x – 1 + 5x = 23

Mathematics

1 answer:

mina [271]3 years ago

7 0

Step-by-step explanation:

x - 1 + 5x = 23

6x - 1 = 23

6x = 23 + 1 = 24

6x = 24

x = 24/6

x = 4 ans.

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Round to the nearest hundredths 9.999

Sergio039 [100]

Answer:

10 or 9.9

Step-by-step explanation:

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3 years ago

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Suppose the radius of the sphere is increasing at a constant rate of 0.3 centimeters per second. At the moment when the radius i

elixir [45]

<h2>At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.</h2>

Step-by-step explanation:

We have equation for volume of a sphere

$V=\frac{4}{3}\pi r^3$

where r is the radius

Differentiating with respect to time,

$\frac{dV}{dt}=\frac{d}{dt}\left (\frac{4}{3}\pi r^3 \right )\\\\\frac{dV}{dt}=\frac{4}{3}\pi \times 3r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}$

Given that

Radius, r = 24 cm

$\frac{dr}{dt}=0.3cm/s$

Substituting

$\frac{dV}{dt}=4\pi r^2\times \frac{dr}{dt}\\\\\frac{dV}{dt}=4\pi \times 24^2\times 0.3\\\\\frac{dV}{dt}=2171.47cm^3/min$

At the moment when the radius is 24 centimeters, the volume is increasing at a rate of 2171.47 cm³/min.

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3 years ago

In the roof truss, line BG bisects ∠ABC and ∠DEF, m∠ABC= 112°, and ∠ABC≅∠DEF.

Dennis_Churaev [7]

In the given diagram, line BG bisects ∠ABC and ∠DEF, m∠ABC= 112°, and ∠ABC≅∠DEF. So the measure of angles are :

1. m∠DEF= 112° because ∠ABC≅∠DEF

2. m∠ABG= 56° because a straight line BG is bisecting ∠ABC in two equal parts. So, $\frac{112}{2} = 56$

3. m∠CBG= 56° because ∠ABG and ∠CBG are equal.

4. m∠DEG= 56° because ∠ABG ≅ ∠DEG

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3 years ago

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A family has j children with probability pj , where p1 = .1, p2 = .25, p3 = .35, p4 = .3. A child from this family is randomly c

aliya0001 [1]

Answer:

A) the conditional probability that the has only 1 child = 0.24

B) The conditional probability that the family has only 4 children = 0.18

Step-by-step explanation:

To answer the questions, we first start with defining each event. Let E be the event that the child selected is the oldest and let Fj be the event that the family has j children.

From this, we can deduce that the probability that the child is the oldest, given that there is j children is ; P(E | Fj ) = 1/j.

In addition, we know P(Fj ) = pj as given in the problem. In answering the 2 questions, we seek the probability P(Fj | E). Thus, by the Bayes’s formula;

P(Fj | E) = P(EFj )/P(E) which gives;

P(Fj | E) = {P(E | Fj )P(Fj )} / {Σ(4,i=1)P(E | Fj )P(Fj )}

= (1/j)/ Σ(4,i=1)(1/j)pj

= ((pj)/j) / {p1 + (p2)/2 + (p3)/3 +(p4)/4}

Therefore, the conditional probability that the family has only 1 child; P(F1 | E) = p1 / {p1 + (p2)/2 + (p3)/3 +(p4)/4} = 0.1/ (0.1 + (0.25/2) +(0.35/3) + (0.3/4) = 0.1/0.4167 = 0.24

The conditional probability that the family has only 4 children =

{(p4)/4} / {p1 + (p2)/2 + (p3)/3 +(p4)/4} = (0.3/4)/ (0.1 + (0.25/2) +(0.35/3) + (0.3/4) = 0.075/0.4167 = 0.18

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4 years ago

PLEASE HELP WITH THIS

olga_2 [115]

Answer:

7^3 = 343 is equivalent to 3 = log to base 7 343 so the base of the logarithm 7^3 is 7

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3 years ago