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3 years ago

Which expressions are equivalent to -6z+ (-5.5) +3.5z + 5y - 2.5?

Mathematics

2 answers:

TiliK225 [7]3 years ago

4 0

Answer:

-2.5z + 5y -8

Step-by-step explanation:

-6z+ (-5.5) +3.5z + 5y - 2.5

[-6z +3.5z] + 5y + [-2.5+ (-5.5)] Combine like terms.

[-2.5z] + 5y + (-8)]

-2.5z + 5y -8

Molodets [167]3 years ago

3 0

Answer:

what the heck its too much to me

Step-by-step explanation:

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John buys a new motorcycle for $1,420.00 and a helmet for $75.00. If there is an 8% sales tax, how much will John pay when purch

m_a_m_a [10]

He will pay 2,340 dollars

3 0

3 years ago

The surface area of a right circular cone of radius r and height h is S = πr√ r 2 + h 2 , and its volume is V = 1 3 πr2h. What i

kirill115 [55]

Answer:

Required largest volume is 0.407114 unit.

Step-by-step explanation:

Given surface area of a right circular cone of radious r and height h is,

$S=\pi r\sqrt{r^2+h^2}$

and volume,

$V=\frac{1}{3}\pi r^2 h$

To find the largest volume if the surface area is S=8 (say), then applying Lagranges multipliers,

$f(r,h)=\frac{1}{3}\pi r^2 h$

subject to,

$g(r,h)=\pi r\sqrt{r^2+h^2}=8\hfill (1)$

We know for maximum volume $r\neq 0$ . So let $\lambda$ be the Lagranges multipliers be such that,

$f_r=\lambda g_r$

$\implies \frac{2}{3}\pi r h=\lambda (\pi \sqrt{r^2+h^2}+\frac{\pi r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}r h= \lambda (\sqrt{r^2+h^2}+\frac{ r^2}{\sqrt{r^2+h^2}})\hfill (2)$

And,

$f_h=\lambda g_h$

$\implies \frac{1}{3}\pi r^2=\lambda \frac{\pi rh}{\sqrt{r^2+h^2}}$

$\implies \lambda=\frac{r\sqrt{r^2+h^2}}{3h}\hfill (3)$

Substitute (3) in (2) we get,

$\frac{2}{3}rh=\frac{r\sqrt{R^2+h^2}}{3h}(\sqrt{R^2+h^2+}+\frac{r^2}{\sqrt{r^2+h^2}})$

$\implies \frac{2}{3}rh=\frac{r}{3h}(2r^2+h^2)$

$\implies h^2=2r^2$

Substitute this value in (1) we get,

$\pi r\sqrt{h^2+r^2}=8$

$\implies \pi r \sqrt{2r^2+r^2}=8$

$\implies r=\sqrt{\frac{8}{\pi\sqrt{3}}}\equiv 1.21252$

Then,

$h=\sqrt{2}(1.21252)\equiv 1.71476$

Hence largest volume,

$V=\frac{1}{3}\times \pi \times\frac{\pi}{8\sqrt{3}}\times 1.71476=0.407114$

3 0

3 years ago

A random sample of 250 juniors majoring in psychology or communication at a large university is selected. These students are ask

fenix001 [56]

Solution :

It is given that :

Number of students in a random sample majoring in communication or psychology at an university = 250

Total number of students majoring in psychology = 100

Number of students majoring in psychology those who are happy = 80

So number of students majoring in psychology those who are not happy = 20

Total number of students majoring in communication = 250 - 100 = 150

Number of students majoring in communication those who are happy = 115

So number of students majoring in psychology those who are not happy = 35

a). Probability of the students happy with their major choices are

$=\frac{80+115}{250}$

= 0.78

b). Psychology major $=\frac{80+20}{250}$

= 0.4

c). Probability of the students who are happy with the communication as the choice of major = $\frac{115}{250}$ = 0.46

d). Students unhappy with their choice of major given that the student is psychology major = $\frac{20}{250}$ = 0.018

8 0

3 years ago

When 142 is added to a number, the result is 64 more than 3 times the number. Find the number.

pishuonlain [190]

Answer:

x + 142 =3x + 64

2x = 78

x = 39

5 0

3 years ago

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What is the slope in the equation:<br> y= 3/4x - 1

Basile [38]

Answer: the slope is 3/4.

y=mx+b and m is always the slope.

3 0

3 years ago

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