How wide is each annual ring (springwood and summerwood combined)? Disregard the bark and pith in your calculations. Show your work. Write your answer in inches

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Work Shown:

For now focus on triangle ABC. Since this is a right triangle, we can use the pythagorean theorem to find the hypotenuse BC.

a^2 + b^2 = c^2

(AC)^2 + (AB)^2 = (BC)^2

8^2 + 10^2 = (BC)^2

(BC)^2 = 164

BC = sqrt(164)

BC = 12.806248 approximately

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Move onto triangle ABD. Find the missing side BD through the pythagorean theorem

a^2 + b^2 = c^2

(AD)^2 + (AB)^2 = (BD)^2

5^2 + 10^2 = (BD)^2

125 = (BD)^2

(BD)^2 = 125

BD = sqrt(125)

BD = 11.1803399 which is approximate

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Move onto triangle ADC. We'll use the pythagorean theorem again

a^2 + b^2 = c^2

(AC)^2 + (AD)^2 = (CD)^2

8^2 + 5^2 = (CD)^2

89 = (CD)^2

(CD)^2 = 89

CD = sqrt(89)

CD = 9.433981 also approximate

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Focus on triangle BCD. We have the following side lengths

Let

Note the use of uppercase letters for angles and lowercase letters for side lengths.

We can then use the law of cosines to find the angle we're after

d^2 = b^2 + c^2 - 2*b*c*cos(D)

12.806248^2=9.433981^2+11.1803399^2-2*9.433981*11.1803399*cos(D)

163.999987837504=213.999997787893-210.950228380284*cos(D)

-210.950228380284*cos(D) = -50.000009950389

cos(D) = (-50.000009950389)/(-210.950228380284)

cos(D) = 0.237022781792173

cos(D) = arccos(0.237022781792173)

D = 76.2891111084541

D = 76.3

The size of the angle ∠BDC of the tetrahedron can be determined by

cosine rule.

The size of angle ∠BDC is approximately 71.1°

Reasons:

A tetrahedron is a pyramid with triangular faces.

By Pythagoras's theorem, we have;

[tex]\overline{DC}[/tex]² = [tex]\mathbf{\overline{AD}}[/tex]² + [tex]\mathbf{\overline{AC}}[/tex]²

∴ [tex]\overline{DC}[/tex]² = 8² + 5² = 89

[tex]\overline{DC}[/tex]² = 89

[tex]\overline{BC}[/tex]² = [tex]\overline{AB}[/tex]² + [tex]\overline{AC}[/tex]²

∴ [tex]\overline{BC}[/tex]² = 10² + 8² = 164

[tex]\overline{BC}[/tex]² = 164

[tex]\overline{DB}[/tex]² = [tex]\mathbf{\overline{AD}}[/tex]² + [tex]\mathbf{\overline{AB}}[/tex]²

[tex]\overline{DB}[/tex]² = 5² + 10² = 150

[tex]\overline{DB}[/tex]² = 150

By cosine rule, we have;

[tex]\overline{BC}[/tex]² = [tex]\overline{DB}[/tex]² + [tex]\overline{DC}[/tex]² - 2 ×  [tex]\mathbf{\overline{DB}}[/tex] × [tex]\mathbf{\overline{DC}}[/tex] × cos(∠BDC)

Therefore;

164 = 150 + 89 - 2 × √(150) × √(89) × cos(∠BDC)

2 × √(150) × √(89) × cos(∠BDC) = 150 + 89 - 164 = 75

[tex]cos( \angle BDC) = \mathbf{\dfrac{75}{2 \times \sqrt{150} \times \sqrt{89} }}[/tex]

[tex]\angle BDC = arccos \left(\dfrac{75}{2 \times \sqrt{150} \times \sqrt{89} } \right) \approx \mathbf{71.1 ^{\circ}}[/tex]

∠BDC ≈ 71.1°

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Answer:

well, they all give you answers as fractions,

A.=1/9

B.=1/64

C.=1/64

Step-by-step explanation:

Answer:

[tex] {p}^{2} - 13p - 30 \\ \\ {p}^{2} - 15p - 2p - 30 \\ \\ p(p - 15) + 2(p - 15) \\ \\ (p + 2)(p - 15)[/tex]

# Jerry Don is here#

Answer:

[tex]\displaystyle [p + 2][p - 15][/tex]

Explanation:

Find two quantities that when differed to 13, they also multiply to 30. Those will be 2 and 15. The TINIER quantity gets the plus sign because the B-value is −13, therefore 15 gets the minus sign, leaving 2 with the plus sign.

I am joyous to assist you at any time.

Answer:

Delay

Step-by-step explanation:

Because you are multiply x into 0.99, every time the multiplication takes place it will only become 99% of the value of the product of x and 400.

Answer:

144 is the l.c.m of 16 and 18

explanation:

multiples:

16 - 16, 32, 48, 64, 80, 96, 112, 128, 144

18 - 18, 36, 54, 72, 90, 108, 126, 144

Therefore,  144 is the l.c.m of 16 and 18 which is divisible by both numbers.

Answer:

144

Step-by-step explanation:

First, prime factorize the numbers.

16 = 2⁴

18 = 3² x 2

LCM (16, 18) = 2⁴ x 3²

= 16 x 9

= 144

Solution :-

144

Answer:

The answer is 60!

Answer:

100cm = 0.001km

Step-by-step explanation:

100 divided by 100,000=0.001

Answer:

1/100th part of the whole part.

Step-by-step explanation:

Hope this helps :)

Answer:

441

Step-by-step explanation:

I think

Answer:

Lowest term

Step-by-step explanation:

you can write a ratio using a fraction form, a colon form, and a word form. The lowest term is just a part of an answer.

Answer:

34°

Step-by-step explanation:

sum interior measure = (n-1)*180 ; n is the number of sides

of the polygon

(n-1)*180

(4-2)*180

2*180

360° ( sum interior measure )

The angles of the quadrilateral are ( 90 , 90 , w , 146 )

90+90+146+w = 360

326+w = 360

w = 360-326

w = 34°

Hope you get benefit from it

Answer:

2

Step by step explanation:

Given: The average mass of all the students in the class was 35.1 kg. After 1 student left the class, whose mass is 32.3kg, the average mass of the remaining students became 36.3kg, how many students were there in the class room now?

Find out: how many students were there in the class room after one student left

Solution: Let the total number of remaining student be= n

Let the total number of remaining student be= nAnd the sum of mass of all the students be = x kg

So,

[tex] \frac{x}{n + 1} = 35.1[/tex]

Make x the subject of formula

[tex]--› \: x = 35.1(n + 1)[/tex]

And

[tex]--› \: \frac{x - 32.3}{n} = 36.3[/tex]

[tex]--›x - 32.3= 36.3n[/tex]

[tex]--› \: 35.1(n + 1) - 32.3 = 36.3n[/tex]

[tex]--› \: 35.1n + 35.1 - 32.3 = 36.3n[/tex]

[tex]--› \: 2.8 = 1.2n[/tex]

divide both side by n

[tex]n = \frac{2.8}{1.2} [/tex]

N = 2.333

so total number of students remaining is 2

The answer might be c. not 100% sure sorry

Answer:

B. A(r(t)) = 25πt²

Step-by-step explanation:

Find the completed question below

The radius of a circular pond is increasing at a constant rate, which can be modeled by the function r(t) = 5t where t is time in months. The area of the pond is modeled by the function A(r) = πr². The area of the pond with respect to time can be modeled by the composition . Which function represents the area with respect to time? A. B. C. D.

Given

A(t) = πr²

r(t) = 5t

We are to evaluate the composite expression A(r(t))

A(r(t)) = A(5t)

To get A(5t), we will replace r in A(t) with 5t and simplify as shown

A(5t) = π(5t)²

A(5t) = π(25t²)

A(5t) = 25πt²

A(r(t)) = 25πt²

Hence the composite expression A(r(t)) is 25πt²

Option B is correct.

Answer:

Step-by-step explanation:

B . Correct

Answer:

[tex]ML=27\\LN=27\\MN=54[/tex]

Step-by-step explanation:

Since L is the midpoint of MN, by the definition of midpoint:

[tex]ML=LN[/tex]

We can picture the following segment:

M----------L----------N

We know that [tex]ML=2x+7[/tex] and [tex]LN=3x-3[/tex]. Since the two segments are equivalent, we can set them equal to each other:

[tex]2x+7=3x-3[/tex]

Now, let's solve for x. Subtract -7 from both sides:

[tex]2x=3x-10[/tex]

Subtract 3x from both sides:

[tex]-x=-10[/tex]

Divide both sides by -1:

[tex]x=10[/tex]

So, the value of x is 10.

With this, we can find the remaining lengths.

We know that ML is [tex]2x+7[/tex].

Substitute 10 for x. So, the length of ML is:

[tex]ML=2(10)+7=20+7=27[/tex]

We know that LN is [tex]3x-3[/tex]. So, the length of LN is:

[tex]LN=3(10)-3=30-3=27[/tex]

Finally, MN will be the combined lengths of ML and LN. So:

[tex]MN=ML+LN=27+27=54[/tex]

And we're done!

Answer:

jdjssusaudisjdssdIes

Tanisha lives with her older sister and helps with the rent by paying $500 per month. Her annual salary as a child care specialist is $14,700 after taxes. So  to save money for her college classes her monthly budget should be less than 725 .

Budget is total plan of income and expenditure of a period .

Here given that Her annual salary as a child care specialist is $14,700 after taxes. and she lives with her older sister and helps with the rent by paying $500 per month.

So money she have after rent can be calculated as:

[tex]14700-12\times500\\\\14700-6000\\\\=8700[/tex]

So her monthly saving after rent is

[tex]\frac{8700}{12} \\\\\\=725[/tex]

So her  monthly budget should be less than 725

Tanisha lives with her older sister and helps with the rent by paying $500 per month. Her annual salary as a child care specialist is $14,700 after taxes. So  to save money for her college classes her monthly budget should be less than 725 .

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Answer:

B

Step-by-step explanation:

Edge 2022

have a great day!

Answer:

subtract 180 from the other two angles

Step-by-step explanation:

triangle involves 3 angles with x's in the equation, set the 3 angles = to 180 and solve

Answer:

The slope-intercept form

Here m is the slope and b is y-intercept

When b= 0

and

In this case Avery's method works

When b≠0

In this case Avery's method brings wrong outcome

Answer:

Step-by-step explanation:

Answer:

The normal force is the force that a surface makes on an object that lies on that surface.

As the book rest flat in the table, the force acting on the book will be the gravitational force. This force pulls down the book against the table, then the normal force will be opposite to this, then the direction of this force is upwards. Being more exact, the normal force always acts on the normal direction to a given surface, to find the normal of a surface, you need to find the plane of the surface, then any perpendicular line to that surface will be "normal" to the surface (and the normal direction points away from the surface) then if the book is resting on top of the table, the direction of the normal will be upwards..

Then the force that acts on the book is normal to the surface of the table,

Answer:

53.5

Step-by-step explanation:

Answer:

she drove b 53.5 mi

Step-by-step explanation:

214 divided by 4

Answer:

y = 2/3x - 3

Step-by-step explanation:

Given equation :-

Transformations :-

Solving :-

Answer:

It's 14% p.a simple interest

Step-by-step explanation:

Simple interst:

Answer:

I = $ 649.60

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 14%/100 = 0.14 per year,

then, solving our equation

I = 2320 × 0.14 × 2 = 649.6

I = $ 649.60

The simple interest accumulated

on a principal of $ 2,320.00

at a rate of 14% per year

for 2 years is $ 649.60.

Compound interest

Answer:

A = $2,945.78

A = P + I where

P (principal) = $2,320.00

I (interest) = $625.78

Calculation Steps:

First, convert R as a percent to r as a decimal

r = R/100

r = 12/100

r = 0.12 rate per year,

Then solve the equation for A

A = P(1 + r/n)nt

A = 2,320.00(1 + 0.12/12)(12)(2)

A = 2,320.00(1 + 0.01)(24)

A = $2,945.78

Summary:

Answer:

the <5 = 28

because if u add <1 and <5 it will be a 180°

so....if u 180 - 152 ( which is the angle of 1< )

and

same goes to 2< and <3 but its a 90°

so....<2 = 90° - 36°

= 54

u should get the <4 too....

hope u get it

please mark me brilliant

The expected frequencies from the data conducted to investigate the differences in the length of stay of a trip will be 221.7097, 72.471, 49.3881, and 25.7677.

From the complete question, the expected frequencies from the data about the trip will be calculated thus:

E(240) = (379 × 413) ÷ 706

=221.7097

E(83) =(379 × 153) ÷ 706

=72.471

E(40) = (379 × 92) ÷ 706

=49.3881

E(16) =(379 × 48) ÷ 706

=25.7677

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Step-by-step explanation:

I don't see all the options.

I only see the options under "angles", as it seems.

anyway, the way to prove this is :

the official definition of similar triangles is :

two triangles are said to be similar if their corresponding angles are congruent (and the corresponding sides are in proportion - but that is automatically true, when all 3 angles are matching).

so, if two pairs of corresponding angles in a pair of triangles are congruent, then the triangles are similar. we know this, because if two angle pairs are the same, then the third pair must also be equal (remember, the sum of all angles in a triangle is always 180°). When the three angle pairs are all equal, the three pairs of sides must also be in proportion.

now, we look at the 2 triangles.

the angles QPR and STR are congruent (the same size).

we know also the angles QRP and SRT : they are both 90° and therefore congruent.

and that means that also the third angles PQR and RST are equal and therefore congruent (due to the 180° sum rule).

so, we have all 3 pairs of angles to be congruent, and the two triangles are therefore similar.

Answer:(-1,7)

Step-by-step explanation:

Answer:

(a) The unit rate for car B is greater because the slope is greater than the slope for car A.

Step-by-step explanation:

We have been given a graph that represents the distance cars A and B travel. We are asked to choose the correct option about our given graphs.

Since slope represents the change in y-value with respect to change in per unit x value, so slope is also unit rate of the graph.

Let us find the slope of car A using points (8,5) and (0,0).

Let us find the slope of car B using points (5,8) and (0,0).

We can see that slope of car B is greater than slope of car A, therefore, option A is the correct choice.

Step-by-step explanation:

Step-by-step explanation:

the answer is the last one, because if you plug in (5, -6) to both equations you would get equal answer.

Answer:

D

Step-by-step explanation:

5=x and -6=y so 5+-6 or 5-6=-1 so it makes the first equation true. Then plug it in to the second equation. (3)(5)--6 or (3)(5)+6 which = 15+6. 15+6=21. So both are true. Btw Im new to this hope this helps!

Answer:

Your answer is: k = 5+12/x

Isolate the variable by dividing each side by factors that don't contain the variable.

Step-by-step explanation:

Hope this helped : )

Answer:

50,000 pounds

Step-by-step explanation:

1 ton = 2,000 pounds