Linda is adding padding to all of the surfaces inside her attic for extra warmth in the winter.
She needs to find the approximate surface area of the attic, including the walls, floor, and
ceiling. The attic is in the shape of a triangular prism. Linda draws the net and writes
the expression below to represent the surface area of the attic. Are Linda's net and
expression correct?

Step-by-step explanation:

Given that,

∠PSQ = 13x+7

∠QSR = 42x+8

We need to find the measure of angles.

We can use the property of linear pair. ATQ,

13x+7 + 42x+8 = 180 (Linear pair)

Taking like terms,

13x+42x = 180 - 7-8

55x = 165

x = 3

So,

∠PSQ = 13x+7 = 13(3) + 7 = 46°

∠QSR = 42x+8 = 42(3) + 8 = 134°

Hence, this is the required solution.

Answer:

12

Step-by-step explanation:

~Turn the percentage into a decimal

4% -> 0.04

~Multiply

300 * 0.04 = 12

Best of Luck!

Answer:

f^-1(x) = (x² + 21)/7

Step-by-step explanation:

Since f(x) = y = √(7x – 21), to find the inverse of f(x) we have to write x in terms of y in order to make x the dependent variable and y the independent variable. The steps involved are:

Step 1: square both sides of the equation, y = √(7x – 21). Doing that, we have:

y² = 7x – 21

Step 2: Add 21 to both sides of the resulting equation. Doing that, we have:

y² + 21 = 7x

Step 3: Divide both sides of the equation by 7. Doing that we have:

x = (y² + 21)/7

Step 4: Replace x with f^-1(x) and y with x. Doing that, we have:

f^-1(x) = (x² + 21)/7

Answer:look at explanation

Step-by-step explanation:

Answer:

see answer above for your question

Answer:

105

Step-by-step explanation:

9 + (1/2)4 x 48

9 + 96 = 105

Answer:

105

Step-by-step explanation:

SO, based on the way you worded it, the equation is

[tex]9 + 1/2 *4*48[/tex]

You multiply [tex]1/2 * 4[/tex] first.

This gives you 2.  [tex]2*48=96[/tex]

96 + 9 =105

Answer:

19.5

Step-by-step explanation:

we will multiply the distance 6.5 miles per hour by 3 hours .. thenanswer is 19.5 miles

Answer:

shouldn't it be u-107=191 because if 107 LESS then u is 191 then you would subtract 107 from u to get the 191

Answer:

Yes, there will be with a probability of 0.4096

Step-by-step explanation:

Given,

p = 0.2

1 - p = 0.8

Number of trials, n = 5

P(x = 1)

Using the binomial probability formula :

P(x =x) = nCx * p^x * (1 - p)^(n - x)

P(x = 1) = 5C1 * 0.2^1 * 0.8^4

P(x = 1) = 5 * 0.2^1 * 0.8^4

P(x = 1) = 0.4096

Yes, there will be with a probability of 0.4096

Answer:

No. If Aaron tunes into this station at 5 randomly selected times, there will not necessarily be exactly one time when a commercial is playing.

Step-by-step explanation:

trust

Answer:

75%

Step-by-step explanation:

1/4 is 25

2/4 is 50

3/4 is 75

4/4 is 100

Answer:

Step-by-step explanation:

Answer: 33.8

Step-by-step explanation:

Answer:

Prof B and Prof D

Step-by-step explanation:

Step-by-step explanation:

From the question  we are told that

Sample size 100  

Instructor    Number of Failures  

Prof. A         13

Prof. B         0

Prof. C         11

Prof. D         16

Confidence level= 0.95

From Z table

Z=1.96

Generally proportion for failure is mathematically given as

  [tex]Proportion\ of\ Failure\ P=\frac{Number\ of\ Failure\ N}{Sample\ size\ S}[/tex]

  [tex]P=\frac{N}{S}[/tex]

For Prof A

    [tex]P_A=\frac{N_A}{S}[/tex]

    [tex]P_A=\frac{13}{100}[/tex]

    [tex]P_A=0.13[/tex]

For Prof B

    [tex]P_B=\frac{N_B}{S}[/tex]

   [tex]P_B=\frac{0}{100}[/tex]

    [tex]P_B=0[/tex]

For Prof C

    [tex]P_C=\frac{N_C}{S}[/tex]

    [tex]P_C=\frac{11}{100}[/tex]

   [tex]P_C=0.11[/tex]

For Prof D

     [tex]P_D=\frac{N_D}{S}[/tex]

   [tex]P_D=\frac{16}{100}[/tex]

   [tex]P_D=0.16[/tex]

Generally the average proportional failure is mathematically given as

    [tex]P_a_v_g=\frac{0.13+0+0.11+0.16}{4}[/tex]

   [tex]P_a_v_g=0.10[/tex]

Therefore  having this we calculate for the control limits

Generally the upper control limit UCl is mathematically given as

Upper control limits:

  [tex]UCL =P_a_v_g +Z\sqrt{\frac{P_a_v_g(1-P_a_v_g) }{S} }[/tex]

  [tex]UCL =0.1 +1.96\sqrt{\frac{0.1(1-0.1) }{100}}[/tex]

  [tex]UCL =0.1 +1.96*0.03[/tex]

  [tex]UCL =0.1 +0.0588[/tex]

  [tex]UCL =0.1588[/tex]

Generally the upper control limit UCl is mathematically given as

Lower limit control limits:

 [tex]UCL =P_a_v_g _Z\sqrt{\frac{P_a_v_g(1-P_a_v_g) }{S} }[/tex]

 [tex]UCL =0.1 -1.96\sqrt{\frac{0.1(1-0.1) }{100}}[/tex]

  [tex]UCL =0.1 -1.96*0.03[/tex]

  [tex]UCL =0.1 -0.0588[/tex]

  [tex]UCL =0.0412[/tex]

Therefore the Range is 0.0412 to 0.1588

Given the range 0.0412 to 0.1588 Prof B and Prof D are outside the Range making them the correct options

Answer:

Step-by-step explanation:

The formula for the volume is given by

(side)3=volume

Since we have the volume, we must take the cube root of the volume to find the length of any one side (since it is a cube, all of the sides are equal).

(side)3−−−−−−√3=side=volume−−−−−−√3

Plugging in 216 for the volume, we end up with

side=6 cm

Answer:

a = ∛v

Step-by-step explanation:

Edge (a) volume (v)

v = a³

a = ∛v

Answer:

umumumuykik.iu.fg

Step-by-step explanation:

lui;iou;uyfluylfuy;lui;uy;

Answer:

Second option!!!

Step-by-step explanation:

Hope it helps you:)

Answer:

y=7

Step-by-step explanation:

Answer:

2^6 * 3

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

25% is half of 50%, half of 30 is 15

Answer:

H

Step-by-step explanation:

Because I’m decimal if it is negative the greater the number in negative the less it is

Answer:

60 more cubes are needed

its 3 shorts

Step-by-step explanation:

11×5= 55 82-55= 27 27÷9= 3

Answer:

Step-by-step explanation:

Given this information, we can set up an equation

[tex]11x + 9y = 82[/tex], where x is the amount of shirts bought, and y is the amount of shorts bought. Since we know she bough 5 shirts, we can replace x with 5

[tex]11 (5) + 9y = 82[/tex]   Now, we have to find for y.

Step 1. Simplify

[tex]55+9y=82[/tex]

Step 2. Subtract 55 from both sides

[tex]55-55+9y=82-55\\9y=27[/tex]

Step 3. Divide both sides by 9

[tex]\frac{9y}{9}=\frac{27}{9}\\y=3[/tex]

If y = 3, this means that Jiyoung bought 3 shorts.

Answer: 3(2(8-2x4)+25divided by 5 )-(2(8 divided by 4x2)-7(7-2x3

The answer is 14

Answer:

7.) 1 (1,1)

8.) not sure

9.) 1 (-2,-2)

Step-by-step explanation:

I used rise over run

Answer:

7) Slope is 1

8) unidentified

9)  i can't really see the picture but i suggest you grab two points from the line and plug them into the equation (y2 - y1) / (x2 - x1).

Step-by-step explanation:

Answer:

B and D

Step-by-step explanation:

Hope this helped :)

Answer:

144

Step-by-step explanation:

-0- Easy :D

Answer:

Hi...

59+4=63

63/7=9

So Nina will be 9 years old

9514 1404 393

Answer:

  AE = 3

Step-by-step explanation:

First of all, we need to find corresponding sides that are defined in both figures. The table below shows the given values.

From the table, we can write the proportion ...

  EA/RS = BC/TU . . . corresponding sides are proportional

  EA/6 = 4/8 . . . . . . . substitute given lengths

  EA = 6(4/8) = 3

The length of AE is 3 units.

Answer:

12b + 36

Step-by-step explanation:

multiply the outside of the bracket by the inside

12(b + 3)

12b + 36

Answer:

-32

Step-by-step explanation:

-4 + f(8) + 3 x g(-7) = ?

To find f(8), look at each of the f(x) function and find x = 8. The y value is the answer you will plug in for f(8). The same goes for g(-7), but you will be looking at the g(x) function at x = -7.

f(8) = -4

g(-7) = -8

Make sure you solve in the correct order using PEMDAS.

-4 + (-4) + 3 x (-8) = -32