Vc,vvevecvvcusl lol here it is

The triangular prism has a volume of 27 cubic units.

Levart [38]

Given:

The volume of the triangular prism = 27 cubic units

To find the volume of the prism if each side is dilated by $\frac{1}{3}$

Formula

The volume of a triangular prism

$V = \frac{1}{2} ach$

where, a be the height of the triangle

c be the base of the triangle

h be the height of the prism

Let us take after dilation the we get,

$a \rightarrow \frac{1}{3} a$

$c \rightarrow \frac{1}{3} c$ and

$h \rightarrow \frac{1}{3} h$

So,

After dilation the volume will be

$V_{1} =\frac{1}{2} (\frac{a}{3} )(\frac{c}{3} )(\frac{h}{3} )$

or, $V_{1} =\frac{1}{9} (\frac{1}{2} ach)$

or, $V_{1}=\frac{1}{9} (27)$ [Since, $V = \frac{1}{2} ach = 27$ ]

or, $V_{1} = 3$

Hence,

After dilation the volume of the prism will be 3 cubic unit.

8 0

3 years ago

Read 2 more answers

What is the distance between the points R (5,7) and S (-2,3) 1: 25 2:33 3:55 or 4:65

Shtirlitz [24]

$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$
$d = \sqrt{(-2 - 5)^{2} + (3 - 7)^{2}}$
$d = \sqrt{(-7)^{2} + (-4)^{2}}$
$d = \sqrt{49 + 16}$
$d = \sqrt{65}$

The answer is 4, √(65).

6 0

3 years ago

-4x = -1/2(10x + 18)

frosja888 [35]

Answer:

x = -9

Step-by-step explanation:

-4x = -1/2(10x + 18)

Distribute

-4x= - 5x -9

Add 5x to each side

-4x+5x = -5x+5x -9

x = -9

5 0

3 years ago

ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. Show your work OR give an explaination.

love history [14]

Answer:

$\boxed{D. 3 {x}^{2} - x - 6}$

Given:

$f(x) = 3{x}^{2} - 4 \\ \\ g(x) = x + 2$

To Find:

$(f - g)(x) = f(x) - g(x)$

Step-by-step explanation:

$= > f(x) - g(x) = (3{x}^{2} - 4) - (x + 2) \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 3{x}^{2} - 4 -(x) - (2)\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3{x}^{2} - 4 - x - 2\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: =3 {x}^{2} - x - 6$

8 0

3 years ago

2) The results of a 2012 Pew Foundation survey of high school and middle school teachers is given in the pie chart. A student as

Serggg [28]

Answer:

The calculated value z = 9.4451 > 1.96 at 5% level of significance.

Null hypothesis is rejected at 5% level of significance

yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance

Step-by-step explanation:

Explanation:-

Step:- (1)

The results of a 2012 Pew Foundation survey of high school and middle school teachers is given in the pie chart.

A student asked a random sample of teachers in 2018 and found 165 had smart-phones, 80 had a cell phone

The first sample proportion

$p_{1} = \frac{80}{165} = 0.4848$

A student asked a random sample of teachers in 2018 and found 165 had smart-phones,5 had no cell phone

The second sample proportion

$p_{2} = \frac{5}{165} = 0.03030$

Step :-(ii)

Null hypothesis :H₀: Assume that there is no difference in the distribution of types of cell phones for the teachers in 2018

H₀ : p₁ = p₂

Alternative hypothesis :H₁

H₁ : p₁ ≠ p₂

Level of significance : ∝=0.05

The tabulated value z=1.96

Step:-(iii)

The test statistic

$Z = \frac{p_{1} -p_{2} }{\sqrt{pq(\frac{1}{n_{1} } } +\frac{1}{n_{2} } )} }$

where $p = \frac{n_{1}p_{1} +n_{2} p_{2} }{n_{1} + n_{2} }$

q = 1-p

In given data n₁ = n₂ = n

$p = \frac{165 (0.4848)+165 (0.03030 }{165 + 165}$

on calculation , we get p = 0.2655

q =1-p = 1-0.2655

q = 0.7345

$Z = \frac{0.4848 -0.030}{\sqrt{0.2655X0.7345(\frac{1}{165 } } +\frac{1}{165} )} }$

Z = 9.4451

The calculated value z = 9.4451 > 1.96 at 5% level of significance.

Conclusion:-

Null hypothesis is rejected at 5% level of significance

yes there is difference in the distribution of types of cell phones for the teachers in 2018 at a 5% level of significance

6 0

4 years ago