Find the volume of a block of woods

Answer:Simplifying

5(x + 2) = 3(x + 8)

Reorder the terms:

5(2 + x) = 3(x + 8)

(2 * 5 + x * 5) = 3(x + 8)

(10 + 5x) = 3(x + 8)

Reorder the terms:

10 + 5x = 3(8 + x)

10 + 5x = (8 * 3 + x * 3)

10 + 5x = (24 + 3x)

Solving

10 + 5x = 24 + 3x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3x' to each side of the equation.

10 + 5x + -3x = 24 + 3x + -3x

Combine like terms: 5x + -3x = 2x

10 + 2x = 24 + 3x + -3x

Combine like terms: 3x + -3x = 0

10 + 2x = 24 + 0

10 + 2x = 24

Add '-10' to each side of the equation.

10 + -10 + 2x = 24 + -10

Combine like terms: 10 + -10 = 0

0 + 2x = 24 + -10

2x = 24 + -10

Combine like terms: 24 + -10 = 14

2x = 14

Divide each side by '2'.

x = 7

Simplifying

x = 7

Step-by-step explanation:

Answer:

The new volume would be 14,850cm³.

Step-by-step explanation:

The volume of a rectangular prism is:

[tex]V = l*w*h[/tex]

In which l is the length, w is the width and h is the height.

Dimensions tripled.

So [tex]l = 3l, w = 3w, h = 3h[/tex]

The modified volume will be:

[tex]V_{m} = 3l*3w*3h = 27*l*w*h = 27V[/tex]

Volume of 550 cm³ before the dimensions are tripled.

This means that [tex]V = 550[/tex]

New volume:

[tex]V_{m} = 27*550 = 14850[/tex]

The new volume would be 14,850cm³.

Answer: 5/11

Step-by-step explanation:

The probability of picking a dime is [tex]\frac{2}{11}[/tex].

The measure of happening or non-happening of the outcomes of a random experiment is called probability.

P(E) = Number of favorable outcomes/ total number of outcomes

Where,

P(E) is the probability of an event.

According to the given question.

Total number of quarters coins = 5

Total number of dimes coins = 2

Total number of pennies coins = 4

Therefore,

The total number of coins in a bag = 5 + 4 + 2 = 11

⇒ Total number of outcomes = 11

So, the probability of picking a dime coin is given by

P(E) = total number of dime coins/ total number of coins in a bag

⇒[tex]P(E) = \frac{2}{11}[/tex]

Hence, the probability of picking a dime is [tex]\frac{2}{11}[/tex].

Find out more information about probability here:

https://brainly.com/question/11234923

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Answer:

Sin A= − 12/37

Step-by-step explanation:

tan ⁡ A = − 12/35

Reason for minus sign is because of it's in the fourth quadrant.

12 = opposite

35 = adjacent

? = Hypotenuse

12² + 35² = hypotenuse ²

1369 = hypotenuse ²

hypotenuse = √1369

hypotenuse= 37

Sin = -12/37

Reason for minus sign is because of it's in the fourth quadrant.

Answer:

Moving the decimal 3 places to the right in a decimal number is the same as multiplying the number by 1000.

Answer:

  108 square feet

Step-by-step explanation:

When you say "triangular prism" it means the base is a triangle and the lateral faces are all rectangles. It doesn't matter which side is lying on the ground.

So, we see this is a triangular prism with a 3-4-5 right triangle as a base, and a "height" of 8 feet.

Its total surface area is the area of the two triangle bases plus the area of the three rectangular faces:

  A = 2(1/2)(4·3) +8(3 +4 +5) = 12 +96 = 108 . . . . . square feet

Answer:

its C

Step-by-step explanation:

Answer:

e = 10

Step-by-step explanation:

In this problem we are told to solve for e. This means we need to isolate the variable e, leaving it completely by itself on one side of the equation.

9e + 4 = -5e + 14 + 13e

We can do this multiple ways, but I will show you how I would do it.

First I would subtract 4 from both sides.

9e + 4 = -5e + 14 + 13e

9e = -5e + 14 + 13e - 4

We can simplify the right side of the equation down by subtracting four from 14.

9e = -5e + 10 + 13e

Next, let's simplify our algebraic expressions. We can subtract 5e from 13e (or add -5e to 13e whatever tickles your fancy)

-5e + 13e = 8e

9e = 8e + 10

Now we subtract algebraic expression 8e from both sides

9e - 8e = 10

All of our expressions with the variable e are now on one side but we aren't done yet. Compute 9e - 8e.

9e - 8e = 10

1e = 10

or

e = 10

We have isolated e! Our final answer is e = 10

Answer:

0.004

Step-by-step explanation:

Since 4/10 is 0.4 and 4/100 is 0.04, 4/1000 must be 0.004

Answer:

0.004

Step-by-step explanation:

[tex]\frac{4}{1000}[/tex] is basically [tex]4 \cdot 10^{-4[/tex] (if you've learned scientific notation), so all you have to do is move the decimal to the left four times. That gives us

[tex]4.0\\0.4\\0.04\\\boxed{0.004}[/tex]

More depth:

[tex]10^{-4[/tex] also equals 0.001, so [tex]4 \cdot 0.001 = \boxed{0.004.}[/tex]

*You may do division and find the answer too. However, these ways are quicker.

Answer:20

Step-by-step explanation:

Since it is a right angled triangle we can use Pythagoras principle to get the missing length

Let the missing length be h

h=√(16^2+12^2)

h=√(16x16+12x12)

h=√(256+144)

h=√(400)

h=20

Answer:

The true statements are:

The cost of 9 magnets is $3.

The cost of 6 magnets is $2.

The cost of 3 magnets is $1.

Step-by-step explanation:

equivalents ratios are two or more ratios that express the same relationship between the numbers involved. In order to calculate the equivalent ratios that are equal, when the numbers involved are divided, they ought to give the same result. In the answer chosen above the ratios in each case are equivalent because:

if the cost of 9 magnets is $3;

9 magnets = $3

∴ 1 magnet = 3/9 = $ 1/3 = 1:3

if the cost of 6 magnets is $2;

6 magnets = $2

1 magnet = 2/6 = $1/3 = 1:3

if the cost of 3 magnets is $1;

3 magnets = $1

∴ 1 magnet = $ 1/3 = 1:3

From the answers obtained, the equivalent ratio of 1 : 3 is the same in all case.

Answer:

square feet

Step-by-step explanation:

1/2 a feet is the full square is half

Answer:

the second answer

Step-by-step explanation:

cause 0+0.8 is 0.8 and 0.8+0.3 is 1.1

Answer:

A

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

21-9=12 hope this helps :)

Answer:

Yes it does provide strong evidence

Step-by-step explanation:

Answer:

12, 13, 14, 15, 16

Step-by-step explanation:

Let the five consecutive integers be (x - 2), (x - 1), x, (x + 1) & (x + 2)

According to the given condition:

[tex](x - 2) + (x - 1) + x + (x + 1) + (x + 2) = 70 \\ 5x = 70 \\ x = \frac{70}{5} \\ x = 14 \\ \implies \\ (x - 2) = (14 - 2) = 12 \\ (x - 1) = (14 - 1) = 13 \\ x = 14 \\ (x + 1) = (14 + 1) = 15 \\ (x + 2) = (14 + 2) = 16\\ [/tex]

Answer:

1024

Step-by-step explanation:

I don't know what this superscript is but the answer is above.

Answer:OPTION D: 2^10 = 1024

Step-by-step explanation: I just took the quiz on edge.hope this helps :)

Answer: You add 9 each time

Step-by-step explanation:

19 + 9 = 28 + 9 = 37 + 9 = 46 + 9 = 55

hope this helps mark me brainliest if it did

Answer:4 and 5

Step-by-step explanation:

√(20) is approximately 4.5 so it is between 4 and 5

Answer:

Step-by-step explanation:

Hello!

A pilot study was conducted to test if three food rewards are equally appealing to the participants.

Of 60 participants surveyed:

16 preferred cupcakes (CC)

26 preferred candy bars (CB)

18 preferred dried apricots (DA)

If the three types of food are equally appealing for the participants, you'd expect that their proportions will be equal: P(CC)=P(CB)=P(DA)= 1/3

1.

The objective of this pilot study is to test if the observed frequencies follow a theoretical model/ distribution. To analyze this, you have to apply a Chi Square Goodness to Fit test. [tex]X^2=sum \frac{(O_i-E_i)^2}{E_i} ~~X^2_{k-1}[/tex] Where k= number of categories of the variable.

For this example the statistical hypotheses are:

H₀: P(CC)=P(CB)=P(DA)= 1/3

H₁: At least one of the proportions isn't equal to the others.

2.

To calculate the expected frequencies for each category you have to use the formula: [tex]E_i= n* P_i[/tex] where Pi represents the theoretical proportion for the i category, stated in the null hypothesis.

[tex]E_{CC}= n* P(CC)= 60*1/3= 20[/tex]

[tex]E_{CB}= n*P(CB)= 60*1/3= 20[/tex]

[tex]E_{DA}= n* P(DA)= 60* 1/3= 20[/tex]

3.

The cutoff or critical value indicates the beginning of the rejection region for the hypothesis test. For the Chi-Square tests, the rejection region is always one-tailed to the right, meaning that you'll reject the null hypothesis if the value of the statistic is big. For the goodness to fit test you have k-1 degrees of freedom, so the critical value will be:

Assuming α: 0.05

[tex]X^2_{k-1;1-\alpha /2}= X^2_{2;0.975}= 7.378[/tex]

The rejection region is then X²₂ ≥ 7.378

4.

[tex]X^2_{H_0}= \frac{(O_{CC}-E_{CC})^2}{E_{CC}} + \frac{(O_{CB}-E_{CB})^2}{E_{CB}} + \frac{(O_{DA}-E_{DA})^2}{E_{DA}} = \frac{(16-20)^2}{20} +\frac{(26-20)^2}{20} +\frac{(18-20)^2}{20}= \frac{14}{5}= 2.8[/tex]

I hope this helps!

Answer:

Step-by-step explanation:

It is assumed the first winner is part of the second drawing as well

There are 4 people and two prizes

The probability of each person to win is 1/4

The first winner has 1/2 probability to get a mug

The second winner, if it is Jack, gets either prize

The combined probability is:

Answer:

The probability is 37.5%

Step-by-step explanation:

There are eight total outcomes, but we only need to focus on three. Ang winning a mug and Jack winning either a t-shirt or a mug, that makes three. Write that as a fraction: 3/8, and then divide. 3 divided by 8 gives us 0.375. But we need a percent so multiply that by 100, that now gives us 37.5.

So, the probability that either Ang wins and is given a mug, or Jack wins is 37.5%. If it makes you feel more confident in this, I put the same exact answer for my assessment and I got it correct.

Also, “The monks named me aOng.”

Answer:

The solution

[tex]Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3 t}[/tex]

Step-by-step explanation:

Explanation:-

Consider the initial value problem y′+3 y=9 t,y(0)=7

Step(i):-

Given differential problem

                           y′+3 y=9 t

Take the Laplace transform of both sides of the differential equation

                L( y′+3 y) = L(9 t)

 Using Formula Transform of derivatives

                L(y¹(t)) = s y⁻(s)-y(0)

   By using Laplace transform formula

              [tex]L(t) = \frac{1}{S^{2} }[/tex]

Step(ii):-

Given

             L( y′(t)) + 3 L (y(t)) = 9 L( t)

            [tex]s y^{-} (s) - y(0) + 3y^{-}(s) = \frac{9}{s^{2} }[/tex]

            [tex]s y^{-} (s) - 7 + 3y^{-}(s) = \frac{9}{s^{2} }[/tex]

Taking common y⁻(s) and simplification, we get

             [tex]( s + 3)y^{-}(s) = \frac{9}{s^{2} }+7[/tex]

             [tex]y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}[/tex]

Step(iii):-

By using partial fractions , we get

[tex]\frac{9}{s^{2} (s+3} = \frac{A}{s} + \frac{B}{s^{2} } + \frac{C}{s+3}[/tex]

  [tex]\frac{9}{s^{2} (s+3} = \frac{As(s+3)+B(s+3)+Cs^{2} }{s^{2} (s+3)}[/tex]

 On simplification we get

  9 = A s(s+3) +B(s+3) +C(s²) ...(i)

 Put s =0 in equation(i)

   9 = B(0+3)

   B = 9/3 = 3

  Put s = -3 in equation(i)

  9 = C(-3)²

  C = 1

 Given Equation  9 = A s(s+3) +B(s+3) +C(s²) ...(i)

Comparing 'S²' coefficient on both sides, we get

  9 = A s²+3 A s +B(s)+3 B +C(s²)

  0 = A + C

put C=1 , becomes A = -1

[tex]\frac{9}{s^{2} (s+3} = \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}[/tex]

Step(iv):-

[tex]y^{-}(s) = \frac{9}{s^{2} (s+3}+\frac{7}{s+3}[/tex]

[tex]y^{-}(s) =9( \frac{-1}{s} + \frac{3}{s^{2} } + \frac{1}{s+3}) + \frac{7}{s+3}[/tex]

Applying inverse Laplace transform on both sides

[tex]L^{-1} (y^{-}(s) ) =L^{-1} (9( \frac{-1}{s}) + L^{-1} (\frac{3}{s^{2} }) + L^{-1} (\frac{1}{s+3}) )+ L^{-1} (\frac{7}{s+3})[/tex]

By using inverse Laplace transform

[tex]L^{-1} (\frac{1}{s} ) =1[/tex]

[tex]L^{-1} (\frac{1}{s^{2} } ) = \frac{t}{1!}[/tex]

[tex]L^{-1} (\frac{1}{s+a} ) =e^{-at}[/tex]

Final answer:-

Now the solution , we get

[tex]Y (s) = 9( -1 +3 t + e^{-3 t} ) + 7 e ^{-3t}[/tex]

Answer:

Rows are the steps - they go left to right and are numbered 1,2,3,... Columns are the columns - they go up and down and are lettered A,B,C,... Cells are defined by the row and column they are in.

Step-by-step explanation:

Answer:

C. (x + 8) (x + 7)

Step-by-step explanation:

To factor this trinomial, you must split the middle term (15x) into two terms that can be added to get 15x, and multiplied to get 56:

[tex]x^2 + 15x + 56[/tex]

[tex]x^2 + 7x + 8x + 56[/tex]

Group:

[tex](x^2 + 7x) (8x + 56)[/tex]

Take out the GCF (Greatest Common Factor):

x(x + 7)  8(x + 7)

(x + 8) (x + 7)

Answer: -18h^2 + 85h - 18

Step-by-step explanation:

(-2h+9)(9h-2)

Open brackets

(-2h x 9h) + (-2h x -2) + (9 x 9h) + (9 x -2)

-18h^2 + 4h + 81h - 18

Add like terms 4h + 81h

-18h^2 + 85h - 18

x = amount (in L) of 0.04% solution

y = amount (in L) of 0.2% solution

x + y = 1

Each liter of p% salt solution contributes 0.01*p L of salt to the mixture. In the new solution, the lab tech wants to end up with a concentration of 0.12%, which comes out to 0.0012 * (1 L) = 0.0012 L of salt:

0.0004x + 0.002y = 0.0012

Solve for y in the first equation:

y = 1 - x

Substitute this into the other equation and solve for x, then y:

0.0004x + 0.002(1 - x) = 0.0012

0.0008 = 0.0016x

x = 0.5 L

y = 1 - 0.5 = 0.5 L

Answer:

exponential decay...................

Answer:

exponential decay

Step-by-step explanation:

If the amount is 1/2 every half hour, it is getting smaller, so it is decreasing, leaving choices a and b

We start with 100 items

100, 50 ,25, 12.5

this is not linear so it must be exponential decay

Answer:

The center is (2,6) and the radius is 8

Step-by-step explanation:

The answer is center: (2,6); radius: 8

Answer:

$3900.

Step-by-step explanation:

If retirement is taken at the age of 67 years, income  = $1300 per month.

% Loss, if retirement taken at the age of 62 years = 25% per month

Loss in dollars per month if retirement taken at the age of 62 years = 25% of Monthly income if retirement is taken at the age of 67 years

[tex]\Rightarrow \dfrac{25}{100} \times 1300\\\Rightarrow \dfrac{1300}{4}\\\Rightarrow 325 \$[/tex]

We know that there are 12 months in an year.

So, annual loss in total annual income over one year:

Loss in dollars per month [tex]\times[/tex] 12 :

325 [tex]\times[/tex] 12 = 3900$

Answer: $3,900

Step-by-step explanation:

What you usually make:

$1300 * 12 months = $15600

What you make with the cut:

$1300 * 0.75 = $975

* 12 months = $11700

15600-11700 = $3900