Help, this is my math hw and I don't get it!


Pictures are attached below...

I need to show my work too, so i need a file to your work!

I'll mark brainliest if you can answer it.

Help, This Is My Math Hw And I Don't Get It!Pictures Are Attached Below...I Need To Show My Work Too,
Help, This Is My Math Hw And I Don't Get It!Pictures Are Attached Below...I Need To Show My Work Too,

Answers

Answer 1
For question #25. Just split the shape into smaller shapes, and find the area of those shapes, then combine.
Answer 2
For question 26, MLN = 2 times KLM.

So 3x KLM = 72 deg.

KLM = 72 / 3 = 24 deg

MLN = 2x KLM = 24 x 2 = 48 deg.

Related Questions

There are 110 calories per 28.4 grams of Cereal X. Find how many calories are in 39.76 grams of this cereal

Answers

Step-by-step explanation:

28.4 g there are 110 calories

1 g there are 110/28.4 = 3.87 calories

39.76 g there are 3.87 × 39.76 = 153.87

The expression cosine of pi over 2 times cosine of pi over 5 plus sine of pi over 2 times sine of pi over 5 can be rewritten as which of the following?
cosine of 7 times pi over 10
cosine of 3 times pi over 10
sine of 7 times pi over 10
sine of 3 times pi over 10


(The clear version of the question is in the picture below)

Answers

Answer:

  (b)  cos(3π/10)

Step-by-step explanation:

The given expression matches the trig identity form for the cosine of the difference of two angles:

  cos(α-β) = cos(α)cos(β) +sin(α)sin(β)

__

To match the given expression exactly, we can choose ...

  α = π/2

  β = π/5

Then the difference is ...

  α -β = π/2 -π/5 = (5/10)π -(2/10)π = 3π/10

The given expression can be shortened to ...

  cos(3π/10)

__

Additional comment

Sometimes it can be difficult to remember when the signs in trig identities match, and when they differ. The fact that cosines of smaller angles have larger values can be a peg on which to hang that hat.

2) Which situation ONLY describes a purchase made with a credit card?
A) Natalie purchased a new computer with her card. The money came straight out of her checking account
B) Jackie loves using her card to make purchases because it is convenient to use, and she doesn't have to carry cash
David paid for dinner with his card. Each time he uses this card his checking account decreases by the purchase amount
D) Maggie took her mother to the movies and paid for it with her card. This charge appeared on a bill she received two weeks later,

Answers

Answer:

D is the correct answer. This charged appeared on a bill

Solve for x

2x3=x2+6x

please help me. Thanks

Answers

Answer:

heya! ^^

[tex]2x {}^{3} = x {}^{2} + 6x \\ \\ 2x {}^{3} = x(x + 6) \\ \\ dividing \: both \: sides \: by \: x \\ \\ \frac{2\cancel{x} {}^{3} }{\cancel{x}} = \frac{\cancel{x}(x + 6)}{\cancel{x}} \\ \\ 2x {}^{2} = x + 6 \\ \\ 2x {}^{2} - x - 6 = 0 \\ \\ by \: splitting \: the \: middle \: term \: ( - x) \\ \\ 2x {}^{2} - 4x + 3x - 6 = 0 \\ \\ 2x(x - 2) + 3(x - 2) = 0 \\ \\ 2x + 3 = 0 \: \: \: or \: \: \: (x - 2) = 0 \\ \\ x = \frac{ - 3}{2} \: \: \: \: or \: \: \: \: x = 2[/tex]

hope helpful :D

Find the next two numbers in the sequence 5,2,-1,…

Answers

Answer:

The answer is (-4) and (-7).

Step-by-step explanation:

Given;a₁ = 5a₂ = 2a₃ = (-1)To Find;a₄ = ?a₅ = ?Formula;aₙ = a + (n 1) × d

Now, for common difference (d)

d = a₂ – a₁ = 2 – 5 = -3

d = a₃ – a₂ = (-1) – 2 = -3

Here, common difference is same everywhere.

So, for fourth term or n = 4

aₙ = a + (n – 1) × d

a₄ = 5 + (4 – 1) × (-3)

a₄ = 5 + 3 × (-3)

a₄ = 5 – 9

a₄ = -4

Then, for fifth term or n = 5

a₅ = 5 + (5 – 1) × (-3)

a₅ = 5 + 4 × (-3)

a₅ = 5 – 12

a₅ = -7

Thus, The fourth term is (-4) and fifth term is (-7).

You have been selected by the members of White House to participate in a one-mile race (1 mile = 5,280 feet) on Sports Day. Another student from Blue House will race against you. You know from some trials in PE that you run at an average rate of 12 feet per second. Since the student from Blue house runs 10 feet per second, you have been asked to let him have a 1000-ft. head start.

If both of you maintain the estimated rates, would you be able to beat your opponent in the one-mile race?

REASONING: If both of you maintain the estimated rates, would you be able to beat your opponent in a one-mile race?

Answers

Answer:

Blue wins

Step-by-step explanation:

Blue runner   4280 ft / 10 ft/sec = 428 sec to finish

Red                5280 / 12 =    440 sec     Blue will win

Find the distance between the two points in simplest radical form.
(9,-1,) and (3,3)

Answers

Hey there!

The distance will be 7.21 units

Step-by-step explanation:Here,

x1 = 9, x2 = 3

y1 = -1, y2 = 3

By using Distance formula

[tex] \sqrt{ {(x2 - x1) + (y2 - y1)}^{2} } \\ \\ \sqrt{ {(3 - 9)^{2} + (3 - ( - 1))}^{2} } \\ \\ \sqrt{ {( - 6)}^{2} + {(4)}^{2} } \\ \\ \sqrt{ 36 + 16 } \\ \\ \sqrt{52} \\ \\ 7.21 \: units[/tex]

Hope it helps

A function of x containing four ordered pairs of
the form (x, y) is shown below.
{(2,0),(4,0), (6,0), (8,0)}
What is the domain of the function?

Answers

Answer:

{2, 4, 6, 8}

Step-by-step explanation:

The domain refers to all the possible x values of a function.

Our ordered pairs :

(2,0)(4, 0)(6, 0)(8, 0)

As they are in the form (x, y), the domain is :

{2, 4, 6, 8}

=
15. Given a rectangle ABCD with AD 12. The diagonals AC and BD intersect at point O such that
mZDOC = 30°. Find the area of the rectangle.

Answers

Answer:

To find the area, we need to find the side length AB (and DC).

The easiest way to approach this is to draw a sketch with all the given information (see attached).

As point O is the center point of the rectangle, we can draw a horizontal line from point O to the center point of BC (point M on the diagram) and create a right triangle.  We can then use the Sine rule to find the shortest leg of the triangle (marked as x on the diagram).  This will be half of the side length AB, and so to find the side length, simply multiply it by 2.

To find the missing angles of the right triangle:

m∠COM = (180° - 30°) ÷ 2 = 75°

m∠OCM = 180° - 90° - m∠COM = 90° - 75° = 15°

Sine rule

[tex]\sf \dfrac{a}{sinA}=\dfrac{b}{sinB}=\dfrac{c}{sinB}[/tex]

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

[tex]\implies \dfrac{x}{\sin(15)}=\dfrac{6}{\sin(75)}[/tex]

[tex]\implies x=\sin(15)\cdot \dfrac{6}{\sin(75)}[/tex]

[tex]\implies x=12-6\sqrt{3}[/tex]

As AB = [tex]2x[/tex]

[tex]\begin{aligned} \implies AB & =2x\\ & =2(12-6\sqrt{3})\\ & =24-12\sqrt{3}\end{aligned}[/tex]

Now we have both side lengths of the rectangle, we can easily calculate the area.

Area of a rectangle = width × length

                                = (24 - 12√3) × 12  

                                = 288 - 144√3

                                = 38.5846837...

                                = 38.585 units² (nearest thousandth)

HELPPPPPP PLEASEEE PLEASEEEEEEEEEEEEEEEEEE

Answers

Answer:

31.63495408

Step-by-step explanation:

Find area of trinagles and semicurucles and then add up

Answer:

31.625 ft²

Step-by-step explanation:

It is assumed we need to find the area of shaded figure.

The figure comprises of two semicircles and a triangle.

The two semicircles add to one full circle with the diameter of 5 ft.

Area of circle

A = πr² = 3.14*(5/2)² = 19.625 ft²

Area of triangle

A = 1/2bh = 1/2(6)(4) = 12 ft²

Total area

19.625 + 12 = 31.625 ft²

Which of the following are not polynomials?

Answers

Answer:

D

I really wish is right!!!

Which expression is equivalent to 20 + 8y − 9y − 21

Answers

Answer:

-y-1

Step-by-step explanation:

4 pounds of apples cost $6. how much will 6 pounds cost​

Answers

Answer:10 bucks

Step-by-step explanation:

have a good day

$9
One pound costs $1.5, as 6/4 equals 1.5. So, you would do 6 x 1.5, which results in 9.

having issues with this question

Answers

Answer:

[tex]5q^8y^{16}\sqrt{5qy}[/tex]

Step-by-step explanation:

[tex]\sqrt{125q^{17}y^{33}} =\sqrt{5*5^2*q*q^{16}*y*y^{32}}=5q^8y^{16}\sqrt{5qy}[/tex]

URGENT I HAVE ALMOST 0 TIME LEFT I NEED LAST MINUTE HELP
A parabola has zeros of 7 and 1 and passes through the point (3,4). Determine the equation of the parabola.

Answers

Answer:

The zeros are the points where the parabola intercepts the x-axis.

[tex]\sf x = 7 \implies x - 7 = 0[/tex]

[tex]\sf x = 1 \implies x - 1 = 0[/tex]

[tex]\sf \implies y = a(x - 7)(x - 1)[/tex]  where a is some constant

If the parabola passes through point (3, 4) then:

[tex]\sf \implies a(3 - 7)(3 - 1) = 4[/tex]

[tex]\sf \implies a(-4)(2) = 4[/tex]

[tex]\sf \implies -8a = 4[/tex]

[tex]\sf \implies a = -\dfrac12[/tex]

So the equation of the parabola is:

[tex]\sf y = -\dfrac12(x - 7)(x - 1)[/tex]

Or in standard form:

[tex]\sf y = -\dfrac12x^2+4x-\dfrac72[/tex]

Spot the quadratic equation:-

(x-1)(x-7)x(x-7)-1(x-7)x²-7x-x+7x²-8x+7

Find a through (3,4)

a(x²-8x+7)=4a(9-24+7)=4a(-8)=4a=-1/2

Equation:-

y=-1/2(x-7)(x-1)

Compound Shapes
Find the area of each figure, round your answer to one decimal place if necessary
12 ya
30
1)
3)
2)
3
12 yd
18
12 ya
3
20 yd
24
Area
Area
Area
4)
5)
6)
17 cm
4 cm
7.5 m
8 orn
12 cm
10 m
5 m
Area:
Area:
Area:
9)
7)
8)
35 m
3.5 m
20 in
TO in
18 in
21 m
21 in
18 in
20 in
3.5 m
21 m
Area:
Area:
Area:

Answers

Applying the formula for areas of rectangle, triangle, & circle, area of each figure is:

1. 27

2. 537.9

3. 384

4. 168.5

5. 96.3

6. 73.1

7. 357.1

8. 1,029

9. 744

What is the Area of a Circle?

Area of a circle = πr², where r is its radius.

What is the Area of a Rectangle?

Area of a rectangle = length × width

What is the Area of a Triangle?

Where b is the height and b is the base length, area of triangle = 1/2bh.

What is the Area of a Square?

Area = s², where s is the side length.

1. Area of the figure = area of square + area of rectangle = s² + length × width

Area of the figure = 3² + 6 × 3 = 27 ft²

2. Area of the figure = area of circle + area of rectangle = πr² + length × width

Area of the figure = π(7²) + 24 × 16 = 537.9 ft²

3. Area of the figure = area of smaller rectangle + area of bigger rectangle

Area = 12 × 12 + 20 × 12 = 384 yd²

4. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh

Area of the figure = 1/2π(8²) + 1/2(8)(17) = 168.5 cm²

5. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh

Area of the figure = (10)(7.5) + 1/2(7.5)(5) = 96.3 m²

6. Area of the figure = area of 1/2circle + area of triangle = 1/2πr² + 1/2bh

Area of the figure = 1/2π(4²) + 1/2(8)(12) = 73.1 cm²

7. Area of the figure = area of 1/2circle + area of rectangle = 1/2πr² + 1/2bh

Area of the figure = 1/2π(10²) + (20)(10) = 357.1 in.²

8. Area of the figure = area of rectangle + area of triangle = (l)(b) + 1/2bh

Area of the figure = (35)(21) + 1/2(28)(21) = 1,029 m²

9. Area of the figure = area of square + area of rectangle = s² + length × width

Area of the figure = 18² + 21 × 20 = 744 in.²

Learn more about the area of rectangle, triangle and circle on:

https://brainly.com/question/14487364

A company sells confetti in boxes in the shape of a triangular
pyramid. Each box contains a volume of 240 cubic centimeters of confetti, If
the height of the box is 15 centimeters, which of the following
could be the area of the base of the box?
Volume Formula:
V number:
h of the 3-D shape number:

Answers

Answer:

who is William afton family?

Beryllium-li decomposes into boron-li with a half-life of
13.8 seconds. How long will it take 2400 g of beryllium-il
to decompose into 75 g of beryllium-il? (3 marks)

Answers

[tex]\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{current amount}\dotfill &75\\ P=\textit{initial amount}\dotfill &2400\\ t=seconds\\ h=\textit{half-life}\dotfill &13.8 \end{cases} \\\\\\ 75=2400\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{75}{2400}=\left( \frac{1}{2} \right)^{\frac{t}{13.8}}\implies \cfrac{1}{32}=\left( \frac{1}{2} \right)^{\frac{1}{13.8} t}[/tex]

[tex]\log\left( \cfrac{1}{32} \right)=\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8} t} \right]\implies \log\left( \cfrac{1}{32} \right)=t\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right] \\\\\\ \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \left( \frac{1}{2} \right)^{\frac{1}{13.8}} \right]}=t\implies \cfrac{\log\left( \frac{1}{32} \right)}{\log\left[ \sqrt[13.8]{\frac{1}{2}} \ \right]}=t\implies 69\approx t[/tex]

help pls it’s due soon :/
Chord AB subtends two arcs with measures in the ratio of 1:5. Line PQ is tangent
to the circle at point B. Find the measure of the angle between the tangent and secant AB.

Answers

Answer:

acute: 30°obtuse: 150°

Step-by-step explanation:

The angle between the secant and the tangent will be half the measure of the intercepted arc. The two intercepted arcs total 1+5=6 ratio units and 360°. That means each ratio unit represents 60° of arc. The two arcs are 60° and 300°.

Then the two angles at the tangent and secant are ...

  60°/2 = 30° . . . . . . . the one marked in the attache drawing

  300°/2 = 150°

Which expressions are equivalent. Circle your answer.
a. 10x - 6x
b. 7x + 3x
C. 12x + 2x - 10x
d. X - X + 2x

Answers

Answer: a) 10x-6x and c) 12x+2x-10x

Step-by-step explanation:

Lets start by simplifying all the expressions

a) 10x-6x=4x

b)7x+3x=10x

c)12x+2x-10x=14x-10x=4x

d)x-x+2x=2x

As you can see a and c both simplify to 4x meaning that is our answer.

Answer:

Options A and C

Solution:In order to simplify these expressions, we should combine like terms:10x-6x=4x7x+3x=10x12x+2x-10x=14x-10x=4x (so expressions A & C are equivalent)x-x+2x=0x+2x=2x

Hope it helps.

Do comment if you have any query.

which expression is equivalent to

Answers

Answer:

Option D

Step-by-step explanation:

[tex]6\dfrac{3}{5}*\dfrac{5}{8}=\dfrac{5}{8}*6\dfrac{3}{5}[/tex]

Poperty : Commutative property of multiplication.

When two numberes are multiplied, changing the order of numbers  will not change the result.

Total price: The sales tax is 4.25% and the sales tax is $17.55, what is the purchase price? (Round to the nearest cent)

The purchase price is ________

The total price is__________ (Round to the nearest cent)

Answers

Answer:

Purchase price = $412.94 (nearest cent)

Total price = $430.49 (nearest cent)

Step-by-step explanation:

Purchase price

If 4.25% = $17.55

⇒ 100% = (17.55 ÷ 4.25) × 100 = 412.9411765...

⇒ Purchase price = $412.94 (nearest cent)

Total price

total price = purchase price + sales tax

                 = $412.94 + $17.55

                 = $430.49

So let the original price be x

4.25% of x=17.550.0425x=17.55x=17.55÷0.0425$412.94

Total price:-

412.94+17.55$430.49

Find the surface area of a square pyramid with side length 2 km and slant height 2 km

Answers

given:

side length 2 km and slant height 2 km.

to find:

the surface area of the pyramid.

solution:

area of 4 triangle= 1/2 × 2 × 2 × 4

= 8km

area of rectangle= 2×2

= 4km

area= 4+8

= 12km

so, the surface area of the pyramid is 12km.

How many ounces are in 4 pounds?

4 ounces
56 ounces
64 ounces
72 ounces

Answers

Answer:

64

Step-by-step explanation:

16 ounces per pound

16 x 4

The answer would be C. 64

what is the circumference of a circle with a diameter of 7 in

Answers

Answer:

22 inches

Step-by-step explanation:

Given:

Diameter - 7 inches Radius  - 3.5 inches

Circumference of circle = πd , where d is the diameter of a circle.

= 22/7  * 7 inches

Circumference = 22 inches

The equation c = 0.20t +3.50 shows the relationship between the charge, c. in dollars for renting a kayak for t minutes
What is the meaning of the slope?
O Every 0.2 minutes you have to pay $1.
You have to pay $0.20 up front before sing the kayak at all.
For $1.00. you can rent a kayak for 20 minutes,
It costs $0.20 per minute to rent the kayak

Answers

Answer:

O It costs $0.20 per minute to rent the kayak

Step-by-step explanation:

c = 0.20t + 3.50→ $3.50 is the fixed cost→ $0.20 is the rate per minute use of the kayakOption 4

Answer:

It costs $0.20 per minute to rent the kayak

Step-by-step explanation:

The equation is a linear equation in the form  y = mx + b

x is the independent variabley is the dependent variablem is the slope/gradient and tells us the rate of changeb is the y-intercept and tells us the initial value (when x = 0)

Given equation:  c = 0.20t + 3.50  

Therefore,

t is time (in minutes) and is the dependent variable.c is the total charge (in dollars) and is the independent variable.$0.20 is the slope (rate of change) and tells us that the charge (c) increases by this amount for every increase of 1 unit of the value of t (1 minute).$3.50 is the initial charge and is not dependent on the value of t.

Therefore, the meaning of the slope is:

It costs $0.20 per minute to rent the kayak

Having trouble with the question!

Answers

Answer:

C) [tex]6r^2-9r-6[/tex]

Step-by-step explanation:

Open the parentheses, you get:

[tex]-3r^2-2r-4+9r^2-7r-2[/tex]

Then combine like terms:

[tex]-3r^2+9r^2=6r^2\\-2r-7r=-9r\\-4-2=-6\\[/tex]

Then right as a polynomial:

[tex]6r^2-9r-6[/tex]

So the answer would be C)

Answer:

6r² - 9r - 6

Step-by-step explanation:

(-3r² - 2r - 4) - (-9r² + 7r + 2)

Multiply to remove the parenthesis:

(-3r² - 2r - 4) - (-9r² + 7r + 2)

1(-3r² - 2r - 4) - 1(-9r² + 7r + 2)

1(-3r²) +1(-2r) + 1(-4) + -1(-9r²) + -1(7r) + -1(2) <== remember that multiplying 2 negatives, makes a positive

-3r² - 2r - 4 + 9r² - 7r - 2

Combine any like terms:

-3r² - 2r - 4 + 9r² - 7r - 2

6r² - 9r - 6 <== make sure that your answer is in Standard form (in decreasing degrees)

Hope this helps!

The C major key, starting with the middle C, consists of seven notes (white keys on the piano) with the following frequencies.

Note
C
D
E
F
G
A
B
Frequency(Hz)
261.6
293.7
329.6
349.2
392.0
440.0
493.9

Determine the ratio of the note E to middle C.
a.
1.1224
c.
1.434
b.
1.2599
d.
1.3454

Answers

Answer:

  b.  1.2599

Step-by-step explanation:

The ratio of the two frequencies is found by dividing the first by the second.

__

  (Freq of E)/(Freq of C) = 329.6/261.6 = 1.2599

a pentagon is shown what is the area, in square inches of the pentagon

Answers

Answer:   37

=========================================================

Explanation:

Along the top row, label the two triangles A and B.

In the bottom row, label the figures as C, D, E. We have C and E as the two surrounding triangles and D as the rectangle.

To find the area of triangle A, we need to find the horizontal side first. Use the pythagorean theorem to get 3 inches across the horizontal portion. We have a 3-4-5 right triangle. The area of triangle A is base*height/2 = 3*4/2 = 6 square inches. Triangle B is a reflected copy of triangle A, so it has the same area.

Triangle C has an area of base*height/2 = 1*5/2 = 2.5 square inches, so does triangle E because it is a mirrored congruent copy.

The rectangle D has an area of base*height = 4*5 = 20 square inches.

-----------------------

We have these areas:

Triangle A = 6 square inchesTriangle B = 6 square inchesTriangle C = 2.5 square inchesRectangle D = 20 square inchesTriangle E = 2.5 square inches

To wrap things up, add up those areas

A+B+C+D+E = 6+6+2.5+20+2.5 = 37 square inches

Type your answer in the box. You may use numbers, a decimal point (.), and/or a negative sign (-) in
your answer.
In one design being considered for the container shaped like a cylinder, the container will have a height
of 12 inches. What will be the radius of the container, to the nearest tenth of an inch?

Answers

Answer
Radius = 2.62 in

Solution in picture
Other Questions
last paragraph of the article?Despite the impressive crowds thatturned out for the Women's Marchevents, organizers were criticized for alack of a clear vision and for notincluding enough women of color.A.having meaningless goalsB.having unfair goalshaving impossible goalsDhaving vague goalsSubmitBack MAX POINTS Help please and thanksWhat is the period and frequency of the function graphed and how would the equation be written? There are 15 students on the debate team. Four will attend the debate. How many groups of four can be selected from the 15 students? Which shows how to determine the volume of the pyramid?10 cm8 cm12 cmV-3(1268)(10)OV-2(12)(10)8V-=(12(B)(10) What is the main goal in creating the federal budget? managing businesses and increasing spending on all programs deciding how to manage the governments tax revenue and expenditures finding a way to allow the economy to run on its own finding a way to slow down rapid economic growth I need a word after the sub- please help Please help me????22pts CAN SOMEONE HELP ME PLEASE ASAP!? Compare the chromosome number of the parent cell with that of each daughter cell. Select the correct answers.Which two sentences use definition 3 of the word "strike"?strike /strk/ verbto hit forciblyto occur suddenly with harmful or damaging effectsto refuse to work as a form of protestto attack suddenlyA.The weather forecaster mentioned that the storm was expected to strike before midnight.B.The carpenter tried to strike the plank with an enormous axe but failed in chopping the board in half.C.The transit strike yesterday made it difficult for people to get to work.D.The workers called for a strike when the promise to increase their daily wages was not fulfilled.E.The soccer teams plan was to strike early and score the first goal. Mark chose two cards randomly from a deck. What is the probabity of getting an Ace or King? 2. A baby weighs 8 pounds, 1 ounce. How much does she weigh in ounces? Question 2 of 10Which of the following is an example of a value?A. SportsB. Public speakingC. Coding skillsD. ResponsibilitySUBMIT A square pyramid is shown. What is the surface area of the pyramid? Enter your answer in the box. 100 points The sum of two numbers is 30 and their difference is 10. What are the two numbers? explain the distinction between a real address and a virtual address? Common factor of 20,88,40 PLEASE ANSWER QUICKLY!The figure shows a right prism.1. What is the volume of the figure?2. If the dimensions of the prism are decreased by a factor of 1/4, how will the volume of the new prism compare to the volume of the original prism? (ANSWER IN A SIMPLIFIED FRACTION). The volume of the prism is decreased by a factor of: ______ Although _____ studied the digestive system of dogs, he is best known for his pioneering work on classical conditioning Theodosius left a will instructing the Romans to do what after his death?