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3 years ago

Please help me!!!!!!!

Mathematics

1 answer:

dusya [7]3 years ago

5 0

Answer:

544 units²

Step-by-step explanation:

The surface area is the sum of the areas of the three rectangular faces and the two triangular bases.

SA = 10×14 +10×14 +12×14 + 2(1/2)(12)(8)

= 14×(10+10+12) +12×8

= 448 +96

= 544 . . . . square units

_____

The area of a rectangle is the product of its dimensions:

A = LW

The area of a triangle is half the product of its base and height:

A = (1/2)bh

Here, both triangles have the same area, so we multiplied the area of one of them by 2 to get the area of both of them.

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Put Them in The box They Go in

pav-90 [236]

Answer:

$\frac{1}{3} \times r - 4 \\ 3 \times r - 4 \\ \frac{1}{3} \times r + 4 \\ 3(r + 4)$

5 0

3 years ago

The nicotine content in a single cigarette of a particular brand has a distribution with mean 0.9 mg and standard deviation 0.1

Ad libitum [116K]

Answer:

The answer to the question is;

The probability that the resulting sample mean of nicotine content will be less than 0.89 is 0.1587 or 15.87 %.

Step-by-step explanation:

The mean of the distribution = 0.9 mg

The standard deviation of the sample = 0.1 mg

The size of the sample = 100

The mean of he sample = 0.89

The z score for sample mean is given by

$Z =\frac{X-\mu}{\sigma/ \sqrt{n} }$ where

X = Mean of the sample

μ = Mean of the population

σ = Standard deviation of the population

Therefore Z = $\frac{0.89-0.90}{0.1/\sqrt{100} }$ = -1

From the standard probabilities table we have the probability for a z value of -1.0 = 0.1587

Therefore the probability that the resulting sample mean will be less than 0.89 = 0.1587 That is the probability that the mean is will be less than 0.89 is 15.87 % probability.

7 0

3 years ago

Given the formula A = 5h (B + b); solve for B. 2

stellarik [79]

Answer:

B = A/5h - b; You could use

B = (A - 5hb)/5h This just puts everything over a common denominator.

Step-by-step explanation:

A = 5h (B + b) Divide both sides by 5h

A/5h = B + b Subtract b from both sides.

A/5h - b = B

6 0

3 years ago

What is the solution to the equation 1.6m − 4.8 = −1.6m?

Alla [95]

1.6m − 4.8 = −1.6m
- 1.6m -1.6m
 -4.8 = -3.2m

divide both sides by -3.2

m = 1.5

7 0

2 years ago

The indefinite integral can be found in more than one way. First use the substitution method to find the indefinite integral. Th

Fantom [35]

Answer:

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C$

Step-by-step explanation:

To find:

∫ $6x^5(x^6-2)\,dx$

Solution:

Method of substitution:

Let $x^6-2=t$

Differentiate both sides with respect to $t$

$6x^5\,dx=dt$

[use $(x^n)'=nx^{n-1}$ ]

So,

∫ $6x^5(x^6-2)\,dx$ = ∫ $t\,dt$ = $\frac{t^2}{2}+C_1$ where $C_1$ is a variable.

(Use ∫ $t^n\,dt=\frac{t^{n+1} }{n+1}$ )

Put $t=x^6-2$

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1$

Use $(a-b)^2=a^2+b^2-2ab$

So,

∫ $6x^5(x^6-2)\,dx$ = $\frac{1}{2}(x^6-2)^2+C_1=\frac{1}{2}(x^{12}+4-4x^6)+C_1=\frac{x^{12} }{2}-2x^6+2+C_1=\frac{x^{12} }{2}-2x^6+C$

where $C=2+C_1$

Without using substitution:

∫ $6x^5(x^6-2)\,dx$ = ∫ $6x^{11}-12x^5\,dx$ = $\frac{6x^{12} }{12}-\frac{12x^6}{6}+C=\frac{x^{12} }{2}-2x^6+C$

So, same answer is obtained in both the cases.

7 0

2 years ago