(Impossible) Twelve men are on a desert island. They all have identical weights except for one of them, who is either slightly lighter or slightly heavier than the others.

The only other thing on the island is a seesaw. There are no scales or means to measure weight otherwise. Can you determine which man has the different weight? You only get to use the seesaw three times.

Answers

Answer 1

Answer:

Yes, it is possible to determine which man has the different weight by using the seesaw three times. Here is one possible method

Divide the 12 men into three groups of four: A, B, and C.

Weigh group A against group B on the seesaw. (First use)

If the seesaw balances, then the odd man is in group C. Otherwise, he is in the heavier or lighter group (A or B).

Take two men from group C and weigh them against two men from group A or B that were balanced. (Second use)

If the seesaw balances again, then the odd man is one of the remaining two men from group C. Otherwise, he is one of the two men from group C that were weighed.

Weigh one of the suspected men against any other man. (Third use)

If the seesaw balances, then the odd man is the other one. Otherwise, he is the one that was weighed.

This method works because it eliminates half of the possible candidates at each step and identifies whether the odd man is heavier or lighter by comparing him with known balanced men.

Step-by-step explanation:


Related Questions

Jamal paints sceneries on canvas and sells them at art auctions. A large painting sells for $45.99 and a small one for $28.99. In six months he sold seven large paintings and four small ones. Calculate how much money Jamal made in six months.

Answers

Answer:

Step-by-step explanation: To calculate the total amount of money Jamal made in six months, we need to multiply the number of paintings sold by the price of each painting, and then add the results for the large and small paintings:

7 large paintings * $45.99/large painting = $321.93

4 small paintings * $28.99/small painting = $115.96

Total amount made = $321.93 + $115.96 = $437.89

Therefore, Jamal made $437.89 in six months by selling seven large paintings and four small ones.

If you make an initial deposit of $1000 in an account that yields 5% interest
Semi-annually
Find your balance at the end of a year.
Show your work !

Answers

The balance at the end of a year is $1051.56.

Describe Compound Interest?

To find the balance at the end of a year, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the balance after t years

P = the principal (initial deposit)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $1000, r = 0.05, n = 2 (since the interest is compounded semi-annually), and t = 1. Plugging these values into the formula, we get:

A = $1000(1 + 0.05/2)^(2*1)

= $1000(1.025)^2

= $1051.56

Therefore, the balance at the end of a year is $1051.56.

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What is the volume of this figure?

Answers

Answer: 186 cubic in

Step-by-step explanation:

Please heeelp i have 30 minutes

Answers

The mathematical model that can be used to express the verbal statement of the proportional relationships are;

10. y = k/x²

11. P = k/V

12. P = k·V·I

What are proportional relationships?

A proportional relationship is one in which the output variable is a multiple of the input variable and a constant (the constant of proportionality).

10. The verbal statement is; y varies inversely as the square of x

The inverse relationship indicates that a variable is related to the reciprocal of the other variable, therefore;

The mathematical model for the statement can be presented as follows;

y ∝ 1/x²

The constant of proportionality k can therefore be applied as follows;

y = k/x²

11. The verbal statement is; For a constant temperature, the pressure P of a gas is inversely proportional to the volume V of the gas

The mathematical model of the proportional relationship is; P ∝ 1/V

Therefore;

P = k/V


12. The verbal statement is; The electric power P of a direct current circuit is jointly proportional to the voltage V and the electric current I

The mathematical model is therefore;

P ∝ V·I

Therefore;

P = k·V·I

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Se compra medio galón de leche para poder llenar biberones de 5 onzas
¿cuantos biberones se podrán llenar?
¿Cuantos mililitros tendrá cada biberón?

Answers

Answer:

Step-by-step explanation:

here is a step-by-step explanation:

Convert half a gallon of milk to liters. There are 3.785 liters in a gallon, so half a gallon is 1.892 liters.

Convert 5 ounces to liters. There are 0.147868 liters in 5 ounces.

Divide the total volume of milk (1.892 liters) by the volume of each bottle (0.147868 liters) to find out how many bottles can be filled completely:

1.892 liters / 0.147868 liters per bottle = 12.8 bottles

Note that the answer is not a whole number, which means there will be some leftover milk after 12 bottles are filled.

To find out how many milliliters are in each bottle, we can convert 5 fluid ounces to milliliters:

5 fluid ounces x 29.5735 milliliters per fluid ounce = 147.868 milliliters

Therefore, each bottle will contain approximately 147.868 milliliters of milk.

So, in summary, with half a gallon of milk, you can fill 12 bottles completely and each bottle will contain about 147.868 milliliters of milk.

Ms. Wong sold 28 cars. She sold 8 fewer cars than 34 as many cars as Mr. Diaz. Which equation can be used to find the number of cars that Mr. Diaz sold, c?
Responses

Answers

So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

Which kinds of equations are feasible?

In algebra, a statement of mathematics that proves the equality of two mathematical expressions is known as an equation. Consider the equation 3x + 5 = 14, where the word "equal" is used to denote the relationship between the terms 3x + 5 and 14.

Let c be the number of cars that Mr. Diaz sold.

According to the problem statement, Ms. Wong sold 8 fewer cars than 34 times the number of cars Mr. Diaz sold, which can be written as:

Ms. Wong's cars sold = 34c - 8

We also know that Ms. Wong sold 28 cars, so we can set this expression equal to 28 to get:

34c - 8 = 28

To solve for c, we can add 8 to both sides and then divide both sides by 34:

34c - 8 + 8 = 28 + 8

34c = 36

c = 36/34

So the equation that can be used to find the number of cars that Mr. Diaz sold, c, is:

34c - 8 = 28

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Find an integer n so that the interval of the form [n, n+1] contains the solution to the equation x2+1x=1.
The integer is n = _____
(a) If f(x)=x2+1x−1
then f(n) = _____ and f(n+1) = _____
(b) The function f is continuous on the interval(s)
◯(−[infinity],[infinity])
◯(−[infinity],a)
◯(a,[infinity])
◯(−[infinity],a)∪(a,[infinity])
◯(−[infinity],b)∪(b,[infinity])
Choose the largest set possible and give the values for a and for b. Enter DNE in any empty blank.
a = _____
b = _____
The theorem that tells us that the solution must be in the interval [n, n+1] is that _____ (you must write out the full name, correctly spelled).

Answers

Answer:

Step-by-step explanation:

To find an integer n so that the interval of the form [n, n+1] contains the solution to the equation x^2 + 1/x = 1, we can first rewrite the equation as x^3 - x^2 + 1 = 0.

Next, we can use the Intermediate Value Theorem to find such an n. Since f(x) = x^3 - x^2 + 1 is a continuous function, if we can find two values of x, a and b, such that f(a) and f(b) have opposite signs, then there must exist a value of x between a and b for which f(x) = 0.

(a) Evaluating f(n) and f(n+1), we have:

f(n) = n^3 - n^2 + 1

f(n+1) = (n+1)^3 - (n+1)^2 + 1

(b) Since f(x) is a polynomial, it is continuous for all x, and so the largest possible interval on which f(x) is continuous is (-∞, ∞).

Thus, we want to find values a and b such that f(a) and f(b) have opposite signs. We can plot the function to get an idea of where the roots might be                          

   |                              

   |                 __          

   |                 /  \        

   |                /    \        

   |              ./      \.      

   |             /          \    

   |           ./            \.  

   |          /                \  

   |        ./                  \.

   |      ./                      \

   |    ./                          \

   |---------------------------------

        a                           b

From the graph, it appears that there is a root between 0 and 1, and another root between -1 and 0. We can use this information to choose a and b. Since we want the largest possible interval, we can take a = -1 and b = 1, so that the interval is (-∞, ∞).

Thus, the integer n such that [n, n+1] contains a root of x^2 + 1/x = 1 is given by n = 0.

The theorem that tells us that the solution must be in the interval [n, n+1] is the Intermediate Value Theorem.

Final answer:

The integer 'n' that fits the solution of the equation x^2 + 1/x = 1 within the interval [n, n+1] is 0. Using n=0 for the function f(x) = x^2 + 1/x - 1 it is undefined, but for n+1, it equals 1. The function f is continuous for all x ≠ 0 which is represented by the interval (-∞, 0) ∪ (0, ∞). This conclusion is established by the Intermediate Value Theorem.

Explanation:

The task involves solving the equation x2 + 1/x = 1 to find an integer 'n' such that the solution fits within the interval [n, n+1]. For this equation, rearranging to x2 - x + 1 = 0, we can use the quadratic formula to find x = (1±√(1-4))/2. This gives us two solutions x = 0.5 and x = -0.5.

However, only x=0.5 is found in the interval [0, 1], where n = 0.

For the function f(x) = x2 + 1/x - 1, at n = 0, the function is undefined. However, for f(n+1) it yields a value of 1.

The function f is continuous everywhere on its domain and the function is defined for all x ≠ 0, hence the function is continuous on the interval (-∞, 0) ∪ (0, ∞).

The theorem that ensures the solution is within the interval [n, n+1] is known as the Intermediate Value Theorem.

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X=6 y=1/2 what is the equation that represents the inverse variation

Answers

Answer:

The equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.

Step-by-step explanation:

Inverse variation is a type of relationship between two variables, in which the product of the variables is constant. The equation that represents inverse variation is:

y = k/x

where y and x are the variables, and k is the constant of proportionality.

To find the equation that represents inverse variation for the given values of x=6 and y=1/2, we can first substitute these values into the equation:

1/2 = k/6

To solve for k, we can multiply both sides by 6:

k = 6 * (1/2)

k = 3

Now that we know the value of k, we can substitute it back into the equation to get the final equation for the inverse variation:

y = 3/x

Therefore, the equation that represents inverse variation for the given values of x=6 and y=1/2 is y = 3/x.

Will award brainliest need help on a few questions.

Answers

Answer:

32 degrees

Step-by-step explanation:

We know that the two opposite angles are equivalent so we need to figure out what each one equals.

First we find what x equals so:

9x - 55 = 5x + 21

When we solve for x we get 19 so we can put this back into the expression to find out the first angle

5(19) + 21 = 116

Since we know both sides are 116 we can add them and get 232

We know now that since all sides all add to 360 we can do

360-232= 128

then split 128 in two for the left and right sides we get 64 degrees

Since the line VU bisects the left angle we know the angle WOV is half of 64 which is:

32 degrees

The electromagnetic spectrum contains more than just the visible light that you see.

Name one other form of energy that is in the electromagnetic spectrum other than ultraviolet or infrared light.

Answer in a complete sentence.

Answers

Another form of energy that is in the electromagnetic spectrum is X - rays

What is the electromagnetic spectrum?

The electromagnetic spectrum is the range of all the electromagnetic waves.

Since electromagnetic spectrum contains more than just the visible light that you see, its range is given by the pneumonic RMIVUXG where

R - RadiowavesM - MicrowavesI - InfraredV - Visible lightU - UltravioletX - X-rays andG - Gamma rays

So, the frequencies of the electromagnetic waves increase as we go from top to bottom and its wavelength decreases as we go from top to bottom.

So, another form of energy that is in the electromagnetic spectrum is X - rays

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Find the values of the sine, cosine, and tangent for LA-
A
4 m
B
3 m
с
Mark this and return
Save and Exit
Next
S

Answers

The sine, cosine and tangent are obtained applying the trigonometric ratios presented in this problem.

What are the trigonometric ratios?

The three trigonometric ratios are defined as follows:

Sine of angle = length of opposite side divided by the length of the hypotenuse.Cosine of angle = length of adjacent side divided by the length of the hypotenuse.Tangent of angle = length of opposite side divided by the length of the adjacent side.

The hypotenuse is the slanted segment connecting the horizontal and the vertical segment.

For the desired angle, you must identify the adjacent side(between the angle and the angle of 90º) and the opposite side.

Missing Information

The problem is incomplete, hence the concepts needed to obtain the sine, cosine and tangent were presented.

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Please help me!!!
Sharon factored the polynomial
x^2 + 81 as (x+9)(x-9)
using the difference of 2 squares method. Her teacher marked her andar wrong. Do you agree or disagree. Write a 1 sentence explaining why you agree or disagree with her teacher. You must write a sentence to earn a full credit.

Answers

Answer:

I agree with Sharon's teacher and I believe that the factoring of x^2 + 81 as (x+9)(x-9) is incorrect because the difference of two squares method can only be used to factor polynomials of the form x^2 - a^2, and not x^2 + a^2.

Step-by-step explanation:

The correct answer is x^2 + 81 can be factored as (x + 9)(x + 9) using the trinomial method.

3. Select all the expressions that are
equivalent to 9 + 7x - 3y.
9 + 7x + 3y
• 9-7x- 3у
Г•9 - 7x + 3y
П 9+7x + (-3y)
П 9-(-7)x -3у
m

Answers

There are D. 9+7x+(-3y) and E. 9-(-7)x-3y that equivalent to the given expression 9 +7x-3y.

What are the equivalent expressions?

Equivalent expressions are defined as mathematical statements that have containing identical variables or numbers.

The expression is given in the question, as follows:

9 + 7x - 3y

D. 9+7x+(-3y) is equivalent because the expression in the parentheses represents a negative value of 3y, so we can combine the 7x and the negative 3y terms to get 7x-3y, which when added to 9 gives the original expression of 9 +7x-3y.

E. 9-(-7)x-3y is equivalent because we can simply change the minus sign before the -7 to a plus sign, resulting in the original expression of 9 +7x-3y.

Thus, D. 9+7x+(-3y) and E. 9-(-7)x-3y are equivalent to the given expression 9 +7x-3y.

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The complete question would be as:

Select all the expressions that are equivalent to 9 +7x-3y.

A. 9+7x+3y

B. 9-7x-3y

C. 9-7x+3y

D. 9+7x+(-3y)

E. 9-(-7)x-3y

A number cube is rolled three times. An outcome is represented by a string of the sort oee (meaning an odd number on the first roll, an even number on the second roll, and even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability.

Answers

Answer:16/10

Step-by-step explanation:

add 4/5+4/5=16/10

so the answer is 16/10

find the value of a in the number 6a subtract 4 a+ 5a=210​

Answers

The value of "a" will be 30 for the given Algebraic expression.

What is algebraic Expression?

Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given, a algebraic expression 6a -4a +5a = 210

Simplifying the equation in terms of a

6a -4a +5a = 210

adding or subtracting the terms with the same variables

7a = 210

divide by 7 on both sides

a = 30

Therefore, the value of "a" will be 30 for the given Algebraic expression.

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I can’t get this right!!!!

Answers

Answer:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}=\dfrac{6\sqrt{61}}{61}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Step-by-step explanation:

Use Pythagoras Theorem to calculate the length of the hypotenuse of the given right triangle:

[tex]\implies a^2+b^2=c^2[/tex]

[tex]\implies 5^2+6^2=c^2[/tex]

[tex]\implies 25+36=c^2[/tex]

[tex]\implies c^2=61[/tex]

[tex]\implies c=\sqrt{61}[/tex]

Therefore:

The side opposite angle θ is 6 units.The side adjacent angle θ is 5 units.The hypotenuse is √(61) units.

[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric ratios}\\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\\\$\sf\csc(\theta)=\dfrac{H}{O}\quad\sec(\theta)=\dfrac{H}{A}\quad\cot(\theta)=\dfrac{A}{O}$\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]

Substitute the given values into each ratio:

[tex]\csc \theta=\dfrac{\sqrt{61}}{6}[/tex]

[tex]\sin \theta=\dfrac{6}{\sqrt{61}}[/tex]

[tex]\cot \theta=\dfrac{5}{6}[/tex]

Note: The sin θ ratio can also be written as:

[tex]\implies \sin \theta=\dfrac{6}{\sqrt{61}}\cdot \dfrac{\sqrt{61}}{\sqrt{61}}[/tex]

[tex]\implies \sin \theta=\dfrac{6\sqrt{61}}{61}[/tex]

How much more interest to your parents have to pay at the end of the first month because their rating is good rather than excellent?

Answers

The interest to pay at the end of the first month C. $18.71.

How to find the monthly interest?

To calculate the monthly interest rate, divide the annual percentage rate by 12. For excellent credit, the monthly rate is 4.75% / 12 = 0.3958%, and for good credit, the monthly rate is 5.00% / 12 = 0.4167%.

The total cost of the mobile home including sales tax is $92,738 ($89,000 x 4.2% sales tax). With a $3,000 down payment, the amount financed is $89,738.

For excellent credit, the monthly interest rate :

= 4.75% / 12

So, the interest charged in the first month is $89,738 x  4.75% / 12 = $355.21

For good credit, the monthly interest rate is 0.4167%. So, the interest charged in the first month is $89,738 x 0.004167 = $33.91.

The difference in interest charged between good and excellent credit is $373.91 - $355.21 = $18.71.

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The complete question is:

Your parents are purchasing a mobile home for $89,000. The sales tax is 4.2%, they make a $3,000 down payment. How much more interest do your parents have to pay at the end of the first month because their rating is good rather than excellent?

Secured Unsecured

Credit APR (%) APR (%)

Excellent 4.75 5.50

Good 5.00 5.90

Average 5.85 6.75

Fair 6.40 7.25

Poor 7.50 8.40

Options:

$29.39

$21.10

$18.71

$19.02

An electrician fixed 4 bulbs in a room how many rooms can 216 bulbs be fixed by him

Answers

Answer:

216÷4=54

Step-by-step explanation:

we have to divide the bulb he fixed in per room by how many he fixes I guess so

Answer: He can fix in a total of 54 rooms which makes 216 bulbs fixed by him.

Step-by-step explanation:

4 bulbs are present in = 1 room

thus, 216 bulbs are present in = 216/4 = 54 rooms

So, he fixes 54 rooms in total

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A movie website offers one free movie viewing to anyone that registers. The total number of people that register can be modeled by the function f(x)=−27x^3−135x^2−72x+220, where x is the number of months passed since starting the website. The number of free movies available to choose from can be modeled as 3x+11. Write an expression that can be used to determine the average number of people that watch each free movie. Simplify your answer.

Answers

The expression that can be used to determine the average number of people that watch each free movie is -

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

What is algebraic expression?

An algebraic expression is a combination of terms both constants and variables. For example -

2x + 3y + z

3x + y

Given is that a movie website offers one free movie viewing to anyone that registers. The total number of people that register can be modeled by the function f(x) = - 27x³ - 135x² - 72x + 220, where x is the number of months passed since starting the website. The number of free movies available to choose from can be modeled as 3x + 11.

The expression that can be used to determine the average number of people that watch each free movie can be written as -

y = (- 27x³ - 135x² - 72x + 220)(3x + 11)

y = 3x(- 27x³ - 135x² - 72x + 220) + 11(- 27x³ - 135x² - 72x + 220)

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

Therefore, the expression that can be used to determine the average number of people that watch each free movie is -

y = - 81x⁴ - 405x³ - 216x² + 660x - 281x³ - 1485x² - 792x + 2420

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For the following equation, determine the values of the missing entries. Reduce all fractions to lowest terms.

4x−2y=12
Note: Each column in the table represents an ordered pair. If multiple solutions exist, you only need to identify one.

Answers

Therefore , the solution of the given problem of equation comes out to be (1, -4) is a solution to the equation 4x - 2y = 12.

How do equations work?

The equivalent sign (=) is used in arithmetic equations to signify the equality of two propositions. It is shown that it is possible to compare various numerical factors by using mathematical techniques, which have served as manifestations of reality. For instance, the equal sign divides the number 12 even the solution y + 6 = 12 in two distinct portions. How many characters also are present from either end of such a character can be calculated. Conflicting symbol readings are prevalent.

Here,

To find the values of missing entries, we can pick any arbitrary value of x and solve for y. Let's take x=1.

4(1) - 2y = 12

Simplifying the equation, we get:

-2y = 8

Dividing both sides by -2, we get:

y = -4

So, when x=1, y=-4. Therefore, the missing entries in the table are (1, -4).

Using this value, we can also check that the equation 4x - 2y = 12 is satisfied:

4(1) - 2(-4) = 4 + 8 = 12

So, (1, -4) is a solution to the equation 4x - 2y = 12.

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Follow these steps to graph this parabola:
y = x
Plot the y-intercept
2
1. Find/Plot the vertex
2.
3. Find/plot one more point
4. Reflect #2 and #3 over the axis of symmetry
-10-9-8-7 -6 -5 -4 -3 -2
7
10
9
8
7
6
54
3
2
1
0 1 2 3 4 5 6 7 8 9 10
-1
2
4x + 4
-3
-4
-5
-6
-7
-8
-9
X

Answers

Please find attached the graph of the parabola, y = x² - 4·x + 4, created with MS Excel, showing the points;

The vertex, (2, 0)Y-intercept; (0, 4)One more point; (1, 1)What is a parabola?

A parabola is the locus of a point that moves such that its distance from a point (known as the focus) and a line (known as the directrix), are the same.

1. The quadratic function is; y = x² - 4·x + 4

The x-coordinates of the vertex of the quadratic function, f(x) = a·x² + b·x + c, can be found using the formula;

x = -b/(2·a)

The x-coordinates of the graph of the equation, y = x² - 4·x + 4, is the point;

x = -(-4)/(2 × 1) = 2

The y-value of the vertex is therefore;

y = 2² - 4 × 2 + 4 = 0

The coordinates of the vertex is therefore; (2, 0)

2. The y-intercept is the point the graph intersects the y-axis, which is the point the x-value is zero, therefore;

The coordinate of the y-value of the y-intercept is therefore;

y = 0² - 4 × 0 + 4 = 4

The y-intercept is therefore; (0, 4)

3. A point on a function can be plugging a value of the input as follows;

The point at x = 1 is; y = 1² - 4×1 + 4 = 1

Therefore, another point on the graph is; (1, 1)

4. The axis of symmetry is the vertical line passing through the vertex, with an equation which is the x-value of the vertex

The x-value of the vertex is; x = 2, therefore, the axis of symmetry is the line; x = 2

The reflection of a point (x, y) about the vertical y-axis is the point (-x, y)

Therefore, the image of the reflection of the y-intercept, (0, 4) about the line x = 2 will be the point (4, 4)

The reflection of the point (1, 1), about the line x = 2 is the point (3, 1)

The above points can be used to graph the parabola, y = x² - 4·x + 4.

Please find attached the graph of the parabola created with MS Excel.

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Find AnB if A= 3,6 9,12 and B = 2,4 6,8 10,12

Answers

Answer:

A ∩ B = {6, 12}

Step-by-step explanation:

A ∩ B means only the terms A and B have in common.

Therefore, A ∩ B = {6, 12}

If point C lies on the line x = −1, what is the y-value of point C? (1 point) −2 −1 0 1

Answers

In a parallelogram ABCD, if point C lies on the line x = −1, then the y-value of C is option C: 0.

What is a parallelogram?

A quadrilateral with two sets of parallel sides is referred to as a parallelogram. In a parallelogram, the opposing sides are of equal length, and the opposing angles are of equal size. Additionally, the interior angles that are additional to the transversal on the same side.

Since ABCD is a parallelogram, it is known know that opposite sides are parallel.

Therefore, the slope of side AB is the same as the slope of side CD, and the slope of side BC is the same as the slope of side AD.

The points B and C both lie on the line x = -1.

Therefore, the x-coordinate of point C is also -1.

Use the slope of side BC to find the y-coordinate of point C.

The slope of side BC can be found as -

slope of BC = (y-coordinate of C - y-coordinate of B) / (-1 - 1)

slope of BC = (y-coordinate of C - 2) / (-2)

Since side AD is parallel to side BC, it has the same slope.

The slope of side AD can be found as -

slope of AD = (y-coordinate of D - y-coordinate of A) / (-1 - 1)

slope of AD = (2 - 4) / (-2) = 1

Since the slopes of two parallel lines are equal so -

slope of AD = slope of BC

Therefore, equate the two slopes and solve for the y-coordinate of point C -

1 = (y-coordinate of C - 2) / (-2)

Multiplying both sides by -2 -

-2 = y-coordinate of C - 2

Adding 2 to both sides -

y-coordinate of C = 0

Therefore, the y-coordinate of point C is 0.

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Figure ABCD is a parallelogram. If point C lies on the line x = −1, what is the y-value of point C?

Hannah is taking out a loan in the amount
of $12,000. Her choices are a 3-year loan
at 6% simple interest and a 5-year loan at
7.5% simple interest. What is the difference
in the amount of interest Hannah would
have to pay on these two loans?
A. $2,290
B. $2,340
C. $2,410
D. $2,470

Answers

Answer:

Step-by-step explanation:

For the 3-year loan at 6% simple interest:

Interest = Principal x Rate x Time

Interest = 12,000 x 0.06 x 3

Interest = $2,160

For the 5-year loan at 7.5% simple interest:

Interest = Principal x Rate x Time

Interest = 12,000 x 0.075 x 5

Interest = $4,500

The difference in the amount of interest Hannah would have to pay on these two loans is:

$4,500 - $2,160 = $2,340

So the answer is (B) $2,340.

Round to the closest whole number. 32% of the animals were males. If the herd had 112 animals how many were female?

Answers

Using arithmetic operations it is obtained that there were approximately 76 female animals in the herd.

What is arithmetic operation?

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

If 32% of the animals were males, then 100% - 32% = 68% of the animals were female.

To find the number of female animals in the herd of 112 animals, multiply the total number of animals by the percentage that were female -

68% = 68/100 = 0.68

Number of female animals = 0.68 x 112

Number of female animals = 76.16

Rounding this to the closest whole number gives -

Number of female animals ≈ 76

Therefore, the number of female animals is 76.

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Questions 19 and 20 refer to the following information.
Every Saturday morning, three friends meet for breakfast at 9:00 AM. Andrea walks, Kellan bikes, and Joelle
drives.
19. Last Saturday, all three friends were exactly
on time. Andrea left her house at 8:30 AM and
walked at a rate of 3 miles per hour. Kellan
left his house at 8:15 AM and biked at a rate of
14 mph. Joelle left her house at 8:45 AM and
drove an average speed of 35 miles per hour.
How many miles from the restaurant does the
person who traveled the farthest live?
20. Kellan lives 12 miles away from Andrea. On
a different Saturday, Kellan biked at a rate of
15 miles per hour to Andrea's house. The two
then walked to the restaurant at a rate of
2.5 miles per hour, and they arrived five
minutes early. What time did Kellan leave his
house? Enter your answer as three digits and
ignore the colon. For example, if your answer
is 5:30 AM, enter 530.
0000000

Answers

Answer:

Question 19: The person who traveled the farthest lives 12 miles from the restaurant, which is the same distance as Kellan.

Question 20: Kellan would have left his house at 8:10 AM in order to arrive at Andrea's house at 8:30 AM and then walk to the restaurant with Andrea at a rate of 2.5 miles per hour, arriving at the restaurant at 8:50 AM, five minutes early. So the answer is 810.

The table shows a linear relationship between the variables x and y. What is the slope?.

Answers

Answer: 0

Step-by-step explanation:

Y2 - Y1

________.

X2 - X1

A linear slope means that the Ys are the same and you can't divide by zero.

You have your points (8,7) and (3,7)

Use the template like I have above.

7 - 7

______

3 - 8

which equals....

0

__

-5

I hope that makes sense for you :)

sorry about me mass uploading questions
im retaking a 25 question mid year test

Answers

Answer:

Step-by-step explanation:

o divide 6029 by 28, we can use long division:

             215

          ---------

28 |    6029

             56

             ---

            182

           168

             ---

           144

          140

           ---

            4

So 6029 divided by 28 is 215 with a remainder of 4. Therefore, the answer to the problem is:

6029/28 = 215 R 4

X-y=4


Work out the value of 3(x-y)

Answers

The value of the expression 3 (x - y) is 12

How to determine the value of the expression

From the question, we have the following parameters that can be used in our computation:

x - y = 4

Multiply both sides of the equation by 3

So, we have the following representation

3 * (x - y) = 4 * 3

Evaluate the products

This gives

3 (x - y) = 12

Hence, the soluton of 3 (x - y) is 12

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It is the morning of the day that senior class presidents Anna and Sean have worked toward for weeks: the Senior Class Picnic! Anna reads, with some distress, that there is a 60% probability of rain in their area today. Which of the following best describes the most likely way the probability was determined?

a. It rains 60% of the time on this date each year.
b. Historically, in the United States, it has rained 60% of the time on days with similar meteorological conditions as today.
c. Historically, it rains 60% of the days during this month.
d. Historically, in this area, it has rained 60% of the time on days with similar meteorological conditions as today.

Answers

Answer:

Step-by-step explanation:

When trying to determine the probability of rain on a given day, there are a variety of methods that could potentially be used, depending on the data available and the specific context. In the case of Anna and Sean's Senior Class Picnic, the probability of rain is stated to be 60%, which suggests that some kind of statistical analysis was used to arrive at this figure. The question asks which of the following methods was most likely used to determine this probability.

Option a suggests that the probability of rain is based on the frequency of rain on the same date each year. This method might be used if there is a long-term historical record of weather conditions on this particular date, which could be used to estimate the probability of rain. However, the question does not provide any information to suggest that this is the case. Additionally, even if there is historical data for this date, it may not be particularly relevant if the local climate has changed over time or if the weather patterns for this particular year are unusual.

Option b suggests that the probability of rain is based on historical data for days with similar meteorological conditions as today. This method might be used if there is a large database of weather information that can be used to identify patterns in weather conditions and predict the likelihood of rain based on those patterns. However, the question does not specify what kinds of meteorological conditions are being considered, so it is unclear whether this is a valid method for the current situation.

Option c suggests that the probability of rain is based on the historical frequency of rain during this month. This method might be used if there is a reliable historical record of weather conditions for this month, which can be used to estimate the likelihood of rain. However, this method does not take into account the specific conditions of the current day, which could be very different from the average conditions for the month.

Option d suggests that the probability of rain is based on historical data for days with similar meteorological conditions to the current day, in the specific area where Anna and Sean are located. This method is the most plausible option, as it takes into account the local climate and weather patterns, as well as the specific conditions of the current day. This type of analysis might involve looking at historical data for temperature, humidity, air pressure, and other relevant factors, and using that information to predict the likelihood of rain.

In summary, based on the information provided in the question, option d seems to be the most likely method for determining the probability of rain on the day of Anna and Sean's Senior Class Picnic.

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