A.

B.

C.

D.

look at the picture ^^

A.B. C.D. Look At The Picture ^^

Answers

Answer 1

Answer:

C, he did not divide properly .

Step-by-step explanation:


Related Questions

Find the equation of a line parallel to y + 9 = -3/2x that passes through the point (-8,9)

Find the equation of a line parallel to y + 9 = -3/2x that passes through the point (-8,9)

Answers

Parallel lines have equal slope but different y-intercepts.

slope intercept form:
y = mx + b (where m = slope
and b = y-intercept)

simply subtract 9 from both sides of the given equation to get slope intercept form of the first line:
y + 9 = -3/2x
y + 9 - 9 = -3/2x - 9
y = -3/2x - 9

so the slope (m) = -3/2

the problem tells us a point on the second line (x,y) or (-8,9)

and we now know slope is -3/2

so let’s plug those in and solve for the y-intercept (b) of the second line.

y = mx + b
9 = -3/2(-8) + b
9 = 12 + b
9 - 12 = 12 - 12 + b
-3 = b

so now we know the slope (m) of both lines is -3/2 and the y-intercept (b) of the second line is -3

all we have to do is use the information to establish slope intercept form of the equation of the second line:

y = mx + b
y = -3/2x - 3

The answer is: y = -3/2x - 3

check your answer by plugging the point (-8,9) back in to your equation

9 = -3/2(-8) - 3
9 = 12 - 3
9 = 9 [TRUE]

Determine the area of the shaded region below. ​

Determine the area of the shaded region below.

Answers

Answer:

the answer is 19square units

Answer:

big square -small rectangle

(5×5)-(2×3)

25-6

19 sq units

4(m+3)=36 what’s the value of m

Answers

Answer:

m=6

Step-by-step explanation:

4(m+3) = 36

4m + 12 = 36

4m + (12 -12) = (36 -12)

4m = 24

4m/4 = 24/4

m = 6

Which inequality is equivalent to this one?
y minus 8 less-than-or-equal-to negative 2

y minus 8 + 8 greater-than-or-equal-to negative 2 + 8

y minus 8 + 8 less-than negative 2 + 8

y minus 8 + 2 less-than-or-equal-to negative 2 + 8

y minus 8 + 2 less-than-or-equal-to negative 2 + 2

please help very fast! Will mark brainliest!

Answers

Answer:

(D) The Last Option

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

If the black cloth absorbs heat energy, why was the ice cube at room temperature covered with the black cloth the slowest to melt?

Answers

The cloth acts as insulation it doesn't matter the colour . And as to Black cloth attracting Heat this is only partially true if you put a black cloth in the room with no windows and the temperature of the room was 70° the cloth will not get any hotter black cloth absorbs infrared energy this makes it feel warmer


Based on the data, what is the probability that the hen will lay
exactly 6 eggs next week?

Based on the data, what is the probability that the hen will layexactly 6 eggs next week?

Answers

The needed inequality is (6 X)   > (12 Y) .6 hens x 200 eggs per year = 1,200 eggs per year, or 23+ eggs per week.

How to calculate hen will lay exactly next 6 week?

According to the given data:

The number of eggs laid by first hen per week = 6 eggs

So, the number of eggs laid by first hen in X weeks

= (Eggs Laid per week) x  (X)   = 6 X

So, the first hen lays a total of (6 X) eggs in X weeks.

Similarly,

The number of eggs laid by second hen per week =  9 eggs

So, the number of eggs laid by second hen in Y weeks

= (Eggs Laid per week) x  (Y)   = 9 Y

So, the second hen lays a total of (9 Y) eggs in Y weeks.

As given:

The total number of eggs laid by the first hen >  The total number of eggs laid by the second hen.

⇒ (6 X)   > (9 Y)  

Hence, the needed inequality is (6 X)   > (9 Y) .

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An ice cube weighs 20 grams. How much will it weigh after it melts?

Answers

Answer:well if a ice cub melts its probally gonna be 0

Step-by-step explanation:

im not so good sorry

Let f(x) = 7x - 2, g(x) = -x + 4, and h(x) = -4x + 1.
Perform the indicated operation.

1. f(x) + g(x)
2. f(x) + h(x)
3. h(x) + g(x)
4. f(x) - g(x)
5. h(x) - f(x)
6. g(x) - h(x)

Answers

Answer:

Explanation:

1.
f(x) + g(x)
= (7x - 2) + (-x + 4)
= 7x - 2 - x + 4
= 6x + 2

2.
f(x) + h(x)
= (7x - 2) + (-4x + 1)
= 7x - 2 - 4x + 1
= 3x - 1

3.
h(x) + g(x)
= (-4x + 1) + (-x + 4)
= -4x + 1 - x + 4
= -5x + 5

4.
f(x) - g(x)
= (7x - 2) - (-x + 4)
= 7x - 2 + x - 4
= 8x - 6

5.
h(x) - f(x)
= (-4x + 1) - (7x - 2)
= -4x + 1 - 7x + 2
= -11x + 3

6.
g(x) - h(x)
= (-x + 4) - (-4x + 1)
= -x + 4 + 4x - 1
= 3x + 3

HELP URGENT PLEASE !!!!!!!!!!!!!!!!!!

HELP URGENT PLEASE !!!!!!!!!!!!!!!!!!

Answers

Answer:

y=69*43

Step-by-step explanation:

this is not correct because the words are writen

A manager of a clothing store always orders 2 small shirts and 3 large shirts for
every 4 medium shirts ordered. The manager plans to order 24 medium shirts.
How many small shirts and large shirts will the manager order? Show your work.
SOLUTION
GRADE 7 Lesson
classroom use.
Authorized for use by school personnel only. This resource expires on 6/30/2022.
Curriculum Associates, LLC Copying permitted

Answers

Taking into account the rule of three, the manager will order 12 small shirts ans 18 large shirts for every 24 medium shirts.

Rule of three

The rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.

That is, what is intended with it is to find the fourth term of a proportion knowing the other three.  

If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.

To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:

a ⇒ b

c ⇒ x

So: x= (c×b)÷a

Amount of small shirts and large shirts ordered

In this case, you can applied the rule of three as follow:

A manager of a clothing store always orders 4 medium shirts ordered for every 2 small shirts, for every 24 medium shirts how many small shirts does he order?

amount of small shirts= (24 medium shirts× 2 small shirts)÷4 medium shirts

amount of small shirts= 12

A manager of a clothing store always orders 4 medium shirts ordered for every 3 large shirts, for every 24 medium shirts how many large shirts does he order?

amount of large shirts= (24 medium shirts× 3 large shirts)÷4 medium shirts

amount of large shirts= 18

In summary, the manager will order 12 small shirts ans 18 large shirts for every 24 medium shirts.

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solve the equation. –9x + 1 = –x + 17. Multiple choice A) x=-8 B) x=-2 C) x=2 D) x=8

Answers

We divide both sides by 8, which yields -2 = x. This means that x is equal to -2, the correct answer is B) x = -2.

To solve the equation -9x + 1 = -x + 17, we can simplify and isolate the variable x.

First, let's combine like terms by adding 9x to both sides:

-9x + 9x + 1 = -x + 9x + 17

Simplifying further:

1 = 8x + 17

Next, let's isolate the variable x by subtracting 17 from both sides:

1 - 17 = 8x + 17 - 17

Simplifying again:

-16 = 8x

To solve for x, we divide both sides by 8:

-16/8 = 8x/8

-2 = x

Therefore, the solution to the equation -9x + 1 = -x + 17 is x = -2.

To solve the equation, we want to isolate the variable x on one side of the equation. We start by combining like terms. By adding 9x to both sides, we eliminate the variable terms on the left side, resulting in 1 = 8x + 17.

Next, we isolate the variable x by subtracting 17 from both sides. This simplifies the equation to -16 = 8x.

To solve for x, we divide both sides by 8, which yields -2 = x. This means that x is equal to -2. Therefore, the correct answer is B) x = -2.

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3x²+1/x-5
solve this.

Answers

Answer:

Step-by-step explanation:

3x+1/x-5solve this.

please solve! thank you so much.

please solve! thank you so much.

Answers

A - Growth (25%)

B- Growth (75%)

C - Growth

D - Growth (100%)

E - Growth (99%)

What is a growth or decay function?

An rise in the resultant quantity for a given quantity is referred to as exponential growth, and a decrease in the resultant quantity for a given quantity is referred to as exponential decay.

The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.

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Which is a correct first step in solving the inequality –4(2x – 1) > 5 – 3x? answers are a.Distribute –4 to get –8x + 4 > 5 – 3x. b.Distribute –4 to get –8x – 1 > 5 – 3x. c.Subtract 2x from both sides of the inequality. d.Add 1 to both sides of the inequalit

Answers

Answer:

a. Distribute –4 to get –8x + 4 > 5 – 3x

Step-by-step explanation:

–4(2x – 1) > 5 – 3x-8x+4 > 5- 3x-8x+3x >5-4-5x> 1x< -1/5

Correct first step is:

a. Distribute –4 to get –8x + 4 > 5 – 3x

The first step to solve the given expression is to distribute -4 over 2x and -1 to get –8x + 4 > 5 – 3x

Inequality expressions

Inequality are expressions not separated by an equal sign. Given the inequality;

–4(2x – 1) > 5 – 3x

The first step to solve the given expression is to distribute -4 over 2x and -1 to get –8x + 4 > 5 – 3x

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Suppose that y(t) solves the ordinary differential equation dy/dt = (4 - 4y) / (5 + 3y) y(0) = 0 Find (d^2 y / dt^2) (0)

Answers

The (d^2 y / dt^2) (0) = -28/125.

The ordinary differential equation given is dy/dt = (4 - 4y) / (5 + 3y) with the initial condition y(0) = 0. To find (d^2 y / dt^2) (0), we need to find the second derivative of y with respect to t at t = 0.

First, let's find the first derivative of y with respect to t at t = 0. Using the initial condition y(0) = 0, we can plug in t = 0 into the equation to find dy/dt at t = 0:

dy/dt = (4 - 4y) / (5 + 3y)

dy/dt = (4 - 4(0)) / (5 + 3(0))

dy/dt = 4/5

So the first derivative of y with respect to t at t = 0 is 4/5.

Next, we need to find the second derivative of y with respect to t at t = 0. To do this, we can take the derivative of the first derivative with respect to t:

d^2 y / dt^2 = d/dt (dy/dt)

d^2 y / dt^2 = d/dt (4 - 4y) / (5 + 3y)

Using the quotient rule, we can find the derivative of the right hand side of the equation:

d^2 y / dt^2 = [(5 + 3y)(-4dy/dt) - (4 - 4y)(3dy/dt)] / (5 + 3y)^2

Now we can plug in t = 0 and dy/dt = 4/5 into the equation to find the second derivative at t = 0:

d^2 y / dt^2 = [(5 + 3(0))(-4(4/5)) - (4 - 4(0))(3(4/5))] / (5 + 3(0))^2

d^2 y / dt^2 = (-16/5 - 12/5) / 25

d^2 y / dt^2 = -28/125

So the second derivative of y with respect to t at t = 0 is -28/125.

Therefore, (d^2 y / dt^2) (0) = -28/125.

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Hi can you please help me

Hi can you please help me

Answers

The probability that student chosen at random is 16 years is 0.28.

How to find the probability of the student chosen?

The table shows the distribution of student by age in a high school with 1500 students. Therefore, the probability that randomly chosen student is  16 years can be found as follows:

Therefore,

probability = number of favourable outcome to age / total number of possible outcome

Hence,

probability that student chosen at random is 16 years =  420 / 150

probability that student chosen at random is 16 years = 0.28

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Use the RK4 method with h = 0.1 to obtain a four-decimal approximation of the indicated value. y' = (x - y), y(0) = 0.6; y(0.5) y(0.5) = 0.5714 x

Answers

Approximation of y(0.5) using RK4: 0.5714 (4 decimal places).

Find the RK4 method approximation for y(0.5)?

To approximate the value of y(0.5) using the fourth-order Runge-Kutta (RK4) method with a step size of h = 0.1 and the initial condition y(0) = 0.6, we perform iterative calculations.

Starting with x = 0 and y = 0.6, we calculate k1, k2, k3, and k4 using the given differential equation y' = (x - y).

Then, we update x and y using a weighted average of these values. Repeating these steps until x reaches 0.5, we obtain the approximate value of y(0.5) as 0.5714 (rounded to four decimal places), which matches the given value. The RK4 method provides a reliable numerical approximation for solving differential equations.

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Write an Equation in Slope Intercept form for the line described:

passes through (2.5, 0) and (0, 5)

Answers

Answer:

y=-2x+5

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-0)/(0-2.5)

m=5/-2.5

m=-2

y-y1=m(x-x1)

y-0=-2(x-2.5)

y=-2(x-2.5)

y=-2x+5

Please mark me as Brainliest if you're satisfied with the answer.

Please Help It is for my hw

Please Help It is for my hw

Answers

Answer:

step 1: distribute -1

step 2: combine like terms

step 3: subtract 4 on both sides

step 4: divided both sides by -8, so u can isolate M alone

M=-2

Step-by-step explanation:

suppose you are asked to guess a number between 1 and 15 (inclusive), and after each guess you are told whether it is higher or lower. what is the minimum number of guesses required to guarantee that you know the number?

Answers

3 is the minimum number of guesses required to guarantee that you know the number.

If we use a binary search approach, we can guess the number in a minimum number of steps.

First, we guess the middle number, which is 8. If the answer is higher, we can eliminate all the numbers from 1 to 8, because they are lower than the answer.

Then we guess the middle number of the remaining numbers, which is 12. If the answer is lower, we can eliminate all the numbers from 12 to 15, because they are higher than the answer.

We have now eliminated half of the remaining numbers, and we are left with 6 and 7. We can guess either of these numbers, and we will know the answer with a total of three guesses.

Therefore, we can guarantee that we know the number in three guesses using this binary search approach.

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If g(x)=4x-5 find g(-3).

Answers

Answer: -17

Explanation: If g(x) = 4x - 5, then g(-3) = 4(-3) - 5 which simplifies to -17.

Help me please ?? If u can

 Help me please ?? If u can

Answers

Answer:

1) 35

2)-270

3)-12

Step-by-step explanation:

The 35th floor is above ground

Descending means going down

If you owe someone money that money being taken out of your account

Answer: Thanks For points

Consider sets a = { x | x is a prime number less than 7} and b = { y | y is perfect square of an integer and y is less than 29}. what is the cardinality of the cartesian product of a and b ?

Answers

The cardinality of the cartesian product of A and B is 18.

Cartesian Product of two sets A and B is defined as the set of all ordered pairs (a,b) where a∈A & b∈B.

Cardinality of a set is defined as the number of elements in that particular set.

For example,  for a set A={2,6,4} , the cardinality is 3.

Given set A= { x | x is a prime number less than 7}

A={2,3,5}

set B =  { y | y is perfect square of an integer and y is less than 29}

B={0,1,4,9,16,25}

The cartesian product of A and B denoted by AxB will be

AxB={(2,0),(2,1),(2,4),(2,9),(2,16),(2,25),(3,0),(3,1),(3,4),(3,9),(3,16),(3,25),(5,0),(5,1),(5,4),(5,9),(5,16),(5,25)}

The number of elements in AxB is 18.

Therefore , the cardinality of the cartesian product of A and B is 18.

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A student writes the equation for a line that has a slope of -6 and passes through the point (2, –8).

y -(-8) = -6(x - 2)

y -(-8) = -6x + 12

y -(-8) + 8 = -6x + 12 + 8

y = -6x + 20

Explain why the work is not correct.

Answers

Answer:

y-(-8)= -6(x-2)

y+8= -6x+12

y = -6x+ 4

you're mistake was you did +8 in 3rd step but you need to -8 both side becoz y-(-8)= y+8

Step-by-step explanation:

brainliest?

The student has incorrectly added 8 on both sides of the equation instead of subtracting it.

The general form of an equation is given as,

(y ₋ y₁)=m(x ₋ x₁)

where (x₁,y₁) is the point through which the line passes and m is the slope of the line.

Given that a line has a slope of -6 and passes through the point (2, –8). Therefore, substitute the slope and point in the above general form of the line and simplify.

(y ₋ y₁)=m(x ₋ x₁)

[y ₋ (-8)] = (-6)(x ₋ 2)

y + 8 = -6x + 12

Subtract 8 from both sides of the equation,

y + 8 - 8 = -6x + 12 - 8

y = -6x + 4

Now, if the steps are compared it can be seen that parenthesis are not opened properly and instead of subtracting 8, it is added to both sides of the equation.

Hence, the student has incorrectly added 8 on both sides of the equation.

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For the given points P, Q, and R, find the approximate measurements of the angles of triangle PQR being angle P, angle Q, and angle R.
P(0,-1,5), Q(3,3,1), R(-4,4,6)

Answers

To find the approximate measurements of the angles of triangle PQR, we can use the dot product formula and the Law of Cosines.

First, let's find the vectors PQ and PR:

Vector PQ = Q - P = (3, 3, 1) - (0, -1, 5) = (3, 4, -4)

Vector PR = R - P = (-4, 4, 6) - (0, -1, 5) = (-4, 5, 1)

Next, we'll find the lengths of vectors PQ and PR:

|PQ| = sqrt((3)^2 + (4)^2 + (-4)^2) = sqrt(9 + 16 + 16) = sqrt(41)

|PR| = sqrt((-4)^2 + (5)^2 + (1)^2) = sqrt(16 + 25 + 1) = sqrt(42)

Now, we can find the dot product of vectors PQ and PR:

PQ · PR = (3)(-4) + (4)(5) + (-4)(1) = -12 + 20 - 4 = 4

Using the dot product and the lengths of PQ and PR, we can calculate the cosine of each angle using the Law of Cosines:

cos(angle P) = (PQ · PR) / (|PQ| |PR|)

cos(angle Q) = (QR · QP) / (|QR| |QP|)

cos(angle R) = (RP · RQ) / (|RP| |RQ|)

Substituting the values:

cos(angle P) = 4 / (sqrt(41) sqrt(42))

cos(angle Q) = -4 / (sqrt(41) sqrt(42))

cos(angle R) = 8 / (sqrt(42) sqrt(41))

Finally, we can calculate the approximate measurements of the angles using the inverse cosine function:

angle P ≈ arccos(cos(angle P))

angle Q ≈ arccos(cos(angle Q))

angle R ≈ arccos(cos(angle R))

Note: The angles will be in radians. To convert to degrees, you can multiply by (180 / π).

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Which sets of side lengths could from a triangle?
choose all that apply.​

Which sets of side lengths could from a triangle? choose all that apply.

Answers

Answer:

E

Step-by-step explanation:

Answer:

d and e

Step-by-step explanation:

for them to be possible side lengths of a triangle the two shorter sides added together have to be greater than the longest side and an answer D and e 6 + 4 is greater than 9 and 5 + 5 is greater than 9 to so those are possible side lengths

What is the measure of ZSPQ in the figure below?
10
P
S
28°
10
R
Q
A. 14°
B. 62°
OC. 56°
D. 28°
E. 15°
F. Cannot be determined

What is the measure of ZSPQ in the figure below?10PS2810RQA. 14B. 62OC. 56D. 28E. 15F. Cannot be determined

Answers

The measure of angle SPQ is 56°

What is trigonometric ratio?

the trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Sin(θ) = opp/hyp

cosθ = adj/hyp

tanθ = opp/adj

To calculate the hypotenuse , we have known the adjascent to angle 28°.

Therefore;

cos 28 = 10/x

0.883 = 10/x

x = 10/0.883

x = 11.3

Represent angle SPR by y

cos x = 10/11.3

cos x = 0.883

x = 28°

Therefore the measure of angle SPQ is 28+28 = 56°

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which of the following ordered pairs could be placed in the table below and still have the relation qualify as a linear function ? -5,7,-3,15,-1,23, ?, ?

Answers

(1,31)
Subtract 2 from x, add 8 to y

If I remember correctly, the answer is (1, 31).

Hope this helps! :3

A bakery makes cylindrical mini muffins that measure 2 inches in diameter and 1 and three fourths inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.

103 and 5 over 7 in2
84 and 6 over 7 in2
66 and 1 over 7 in2
17 and 2 over 7 in2
Question 9(Multiple Choice Worth 2 points)
(Scale Factor MC)

The state of Colorado is 4 centimeters long and 3 centimeters wide on a map. A cartographer wants to use a scale factor of 2.5 to enlarge the map. What is the area of the enlarged map?

12 cm2
30 cm2
35 cm2
75 cm2
Question 10(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures LC)

An image of a rhombus is shown.

A rhombus with a base of 21 inches and a height of 19 inches.

What is the area of the rhombus?

160.5 in2
80 in2
399 in2
199.5 in2
Question 11(Multiple Choice Worth 2 points)
(Circumference MC)

A race car drove around a circular track that was 0.4 mile. If 1 mile = 5,280 feet, what is the radius of the track, in feet? Use π = 3.14 and round to the nearest hundredth.

107.11 feet
214.21 feet
336.31 feet
672.61 feet
Question 12(Multiple Choice Worth 2 points)
(Scale Factor MC)

The distance between two cities on a map is 25 inches. The actual distance between the two cities is 400 miles. How many miles would 35 inches be on the map?

560 miles
285 miles
16 miles
11 miles
Question 13(Multiple Choice Worth 2 points)
(Surface Area of Cylinders LC)

Which equation would calculate the amount of wrapping paper, in square centimeters, needed to completely cover the cylinder shown?

a cylinder with the diameter labeled 2.6 centimeters and the height labeled 3.8 centimeters

SA = 2π(1.3)2 + 1.3π(3.8)
SA = 2π(2.6)2 + 2.6π(3.8)
SA = 2π(2.6)2 + 1.3π(3.8)
SA = 2π(1.3)2 + 2.6π(3.8)
Question 14(Multiple Choice Worth 2 points)
(Area of Polygons and Composite Figures MC)

A family has a unique pattern in their tile flooring on the patio. An image of one of the tiles is shown.

A quadrilateral with a line segment drawn from the bottom vertex and perpendicular to the top that is 6 centimeters. The right vertical side is labeled 3 centimeters. The portion of the top from the left vertex to the perpendicular segment is 4 centimeters. There is a horizontal segment from the left side that intersects the perpendicular vertical line segment and is labeled 5 centimeters.

What is the area of the tile shown?

34.5 cm2
45 cm2
54 cm2
57.5 cm2
Question 15(Multiple Choice Worth 2 points)
(Area of Circles LC)

A circle with a diameter of 36 inches is shown.

circle with diameter of 36 inches

What is the area of the circle using π = 3.14?

113.04 in2
452.16 in2
1,017.36 in2
4,069.44 in2
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Answers

The area of the circle with a Diameter of 36 inches,  π = 3.14, is 1017.36 square inches.

The surface area of one mini muffin and multiply it by 6. The surface area of a cylindrical mini muffin can be calculated as 28 and 2/7 square inches. Multiplying by 6, we get a total of 169 and 1/7 square inches. Approximating the answer, we get 169 and 1/7 169.14 square inches.  the correct answer is 169 and 1/7 square inches.      

The area of the enlarged map, we need to scale up the dimensions of the state of Colorado by the scale factor of 2.5.

The length of the enlarged map would be 4 cm * 2.5 = 10 cm.

The width of the enlarged map would be 3 cm * 2.5 = 7.5 cm.

Area = length * width

Area = 10 cm * 7.5 cm

Area = 75 cm²

Therefore, the area of the enlarged map is 75 cm².

The area of a circle can be calculated using the formula:

Area = π * (radius)^2

the diameter of the circle is 36 inches, we can find the radius by dividing the diameter by 2:

Radius = 36 inches / 2 = 18 inches

Now, we can calculate the area using π = 3.14:

Area = 3.14 * (18 inches)^2

    = 3.14 * 324 square inches

    = 1017.36 square inches

the area of the circle with a diameter of 36 inches, using π = 3.14, is 1017.36 square inches.

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Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.
1. N ⊃ O
2. N ⊃ P / N ⊃ (O • P)

Answers

The conclusion of the symbolised argument is that N implies (O and P). This can be proven using conditional proof and the eighteen rules of inference, or using the rule of conjunctive simplification.

The symbolic argument's conclusion is that N implies (O and P). This can be demonstrated using conditional proof and the eighteen inference rules.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (3-6 Conditional Proof)

8. N ⊃ (O•P) (2,7 Disjunctive Syllogism)

This leads us to the conclusion that N implies (O and P).

Without the use of conditional proof, the identical result can be reached. The conjunctive simplification rule can be used to do this.

Proof:

1. N ⊃ O (Premise)

2. N ⊃ P (Premise)

3. N (Assumption)

4. O (1,3 Modus Ponens)

5. P (2,3 Modus Ponens)

6. O•P (4,5 Conjunction)

7. N ⊃ (O•P) (Conjunctive Simplification)

Therefore, we have derived the conclusion that N implies (O and P).

Complete Question:

Use conditional proof and the eighteen rules of inference to derive the conclusions of the following symbolized arguments. Having done so, attempt to derive the conclusions without using conditional proof.

1. N ⊃ O

2. N ⊃ P / N ⊃ (O • P)

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