Write a paragraph proof for the following conjecture:
Given: m∠1 +m∠2=m∠4
Prove: m∠3 +m∠1 +m∠2=180°

The equations should be matched with the correct transformation rule as follows;

In Mathematics and Geometry, the translation of a graph to the left means subtracting a digit from the numerical value on the x-coordinate of the pre-image;

g(x) = f(x + N)

y = |x + 1|

In Mathematics and Geometry, the translation of a graph downward means a digit would be subtracted from the numerical value on the y-coordinate (y-axis) of the pre-image:

g(x) = f(x) - N

y = x² - 1

In Mathematics and Geometry, a reflection over or across the x-axis is represented by this transformation rule (x, y) → (x, -y);

y = -|x|

In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y);

y = (-x)²

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The magnitude of the resultant vector is approximately 30.77 kilometers. We need to use the Pythagorean theorem. We can start by drawing a diagram of the balloon's path. From the starting point, we can draw a right-angled triangle with the East and North distances as the two sides.

Using the Pythagorean theorem, we can find the hypotenuse, which is the magnitude of the resultant vector.
So, the first step is to square the East distance (18.5 km) and the North distance (24.6 km) separately:
18.5 km^2 = 342.25 km^2
24.6 km^2 = 605.16 km^2
Next, we add the two squared distances:
342.25 km^2 + 605.16 km^2 = 947.41 km^2

Finally, we take the square root of the sum to get the magnitude of the resultant vector: √947.41 km^2 ≈ 30.78 km
Therefore, the magnitude of the resultant vector is approximately 30.78 kilometers. In conclusion, to find the magnitude of the resultant vector when a balloon floats 18.5 kilometers East then 24.6 kilometers North, we need to use the Pythagorean theorem by squaring the East and North distances separately, adding them together, and then taking the square root of the sum. This gives us a resultant vector of approximately 30.78 kilometers.

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Answer:

4.5 hours in minutes = 270

Every 45 minutes, bacteria triples

You start with 50

Divide 270 (total time) by 45 (every time bacteria triples)

270/45 = 6

36,450 bacteria

Answer:

The properties of trapezoid apply by definition (parallel bases).

The legs are congruent by definition.

The lower base angles are congruent.

The upper base angles are congruent.

Any lower base angle is supplementary to any upper base angle.

The diagonals are congruent.The bases are parallel by definition.

Each lower base angle is supplementary to the upper base angle on the same side.

Answer: b

Step-by-step explanation:

The equation in slope-intercept form of the line that passes through the point is y = -2x+4 , Option B is the correct answer.

The equation of a straight line is given by the equation

y= mx+c

Where m is the slope and

c is the intercept on y axis.

The given data is

line passes through the point (3,-2) with slope -2.

m = -2

y = -2x + c

-2 = - 2 * 3 +c

-2 = -6 +c

c = +4

y = -2x+4

Therefore Option B is the correct answer.

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Answer:

324 in^2

Step-by-step explanation:

If you transfer the 9 ft to inches you get 108 in

108x3=324

Answer:

21

Step-by-step explanation: 9 + 9 = 18 , 3 + 3 = 6 , 18 + 6 = 21.

Answer:

$9.60

Step-by-step explanation:

The question above is a simple interest question.

The formula for the amount of money after a given period of time using simple interest is given as:

A = P(1 + rt)

Where

P = Initial Amount saved or invested = $8

R = Interest rate = 5%

t = Time in years = 4

Calculation:

First, converting R percent to r a decimal

r = R/100 = 5%/100 = 0.05 per year.

Solving our equation:

A = 8(1 + (0.05 × 4)) = 9.6

A = $9.60

The amount of money that will be in a bank account after 4 years is $9.60

The percent of change is an increase in altitude of the weather balloon.

Change in altitude = New altitude - Original altitude

= 103 ft - 100 ft

= 3 ft

Percentage change = Change in altitude / Original altitude × 100

= 3 / 100 × 100

= 3%

Therefore, the percentage change in the altitude of the weather balloon is 3%.

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Answer:

The answer is 0.3

Step-by-step explanation:

Here,

1.5 × 20/100 = 0.3

Thus, The answer is 0.3

-TheUnknownScientist 72

30

The statement ''the symbol μ ˆ p represents the proportion of a sample of size n, not the proportion of a sample of size n.'' is false because the symbol "μ ˆ p" does not represent the proportion of a sample of size n.

In statistical notation, the symbol "μ ˆ p" typically represents the sample proportion, which is an estimate of the population proportion. The sample proportion is obtained by dividing the number of occurrences of a specific event in the sample by the sample size.

On the other hand, the population proportion, denoted by "p," represents the proportion of the entire population that exhibits a certain characteristic or has a specific attribute.

The symbol "μ ˆ p" could be a typographical error or a confusion between different symbols used in statistics. The correct symbol to represent the sample proportion is usually denoted as "p ˆ" or "p-hat." The symbol "μ" typically represents the population mean.

Therefore, it is incorrect to state that "μ ˆ p" represents the proportion of a sample of size n.

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If in a certain​ chemical, the ratio of zinc to copper is 4 to 13 A jar of the chemical contains 507 grams of copper The number of grams of zinc that it​ contain is:  156 grams of zinc.

Using this formula to determine the number of gram of zinc it contain

Number of gram of zinc=Number of gram of copper/ 13 Ratio of zinc to copper  ×4

Let plug in the formula

Number of gram of zinc=507 grams/13×4

Number of gram of zinc=39×4

Number of gram of zinc= 156 grams of zinc

Therefore if in a certain​ chemical, the ratio of zinc to copper is 4 to 13 A jar of the chemical contains 507 grams of copper The number of grams of zinc that it​ contain is:  156 grams of zinc.

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Answer:

6x+2

Step-by-step explanation:

Answer:combine your like terms and solve to get the width .

Step-by-step explanation:

Answer:

Step-by-step explanation:

this is a ratio of 2cm to 3km

this can be written as a fraction 2/3

now we can set this up and solve for x

2cm/3km = 8cm/xkm

2x = 8(3)

2x = 24

x = 24/2 km

or 12km

Answer: The answer is 12 km.

Step-by-step explanation:

Answer:

For one year the fee would be,

C = $120 + $5l

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The polynomial function of least degree with integral coefficients is equal to f(x) = x³ - 4x² + x + 6 with the given zeros 3, 2, -1.

As given in the question,

Given zeros of the polynomial function are :

3, 2, -1

⇒ ( x - 3 ) =0 or ( x - 2 ) = 0 or ( x + 1 ) = 0

Polynomial function of the given factors  ( x - 3 ) =0 or ( x - 2 ) = 0 or

( x + 1 ) = 0 is given by :

f (x ) = ( x - 3 )( x - 2 )( x + 1 )

⇒ f(x) = ( x² - 3x - 2x + 6 ) ( x + 1 )

⇒ f(x) = ( x² - 5x + 6 ) ( x + 1 )

⇒ f(x) = x³ + x² -5x² - 5x + 6x + 6

⇒f(x) = x³ - 4x² + x + 6

Therefore, the required polynomial function of least degree with integral coefficients using given zeros is equal to f(x) = x³ - 4x² + x + 6.

The complete question is:

Write a polynomial function of least degree with integral coefficients that has the given zeros 3, 2, -1?

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If a fair die is rolled six times, the probability that each score is obtained exactly once is (1/6)^6 or 0.0001286. This is because there is a 1/6 chance of getting any given score in a single roll of the die.

Therefore, the probability of getting each score exactly once in six rolls is the product of the individual probabilities of each roll, which is equal to 1/6 x 1/6 x 1/6 x 1/6 x 1/6 x 1/6.

If a fair die is rolled seven times, the probability that a 6 is not obtained at all is (5/6)^7 or 0.0859375. This is because there is a 5/6 chance of not obtaining a 6 in a single roll of the die. Therefore, the probability of not obtaining a 6 in seven rolls is the product of the individual probabilities of each roll, which is equal to 5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 5/6 x 5/6.

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The distributor can say that the maximum error of the mean with 95% confidence is 0.639 ounces for standard-deviation 2.0 ounces.

We can use the formula for maximum error of the mean:

\($E = \frac{t_{\alpha/2} \cdot s}{\sqrt{n}}$\),

where \($t_{\alpha/2}$\) is the critical value for the desired level of confidence,

s is the sample standard deviation, and

n is the sample size.

n = 40 (sample size)

σ = 2.0 oz (standard deviation)

We want to find the maximum error of the mean with 95% confidence, which means α = 0.05/2

                          = 0.025 (for a two-tailed test).

To find \($t_{\alpha/2}$\), we need to look up the t-distribution table with n-1 = 39 degrees of freedom (df).

For a 95% confidence level, the critical value is t0.025,39 = 2.021.

Now, we can substitute the values in the formula:

E = \($\frac{t_{\alpha/2} \cdot s}{\sqrt{n}}$$= \frac{(2.021) \cdot 2.0}{\sqrt{40}}$$= \frac{4.042}{6.324}$$= 0.639$\)

Therefore, the distributor can say that the maximum error of the mean with 95% confidence is 0.639 ounces.

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Answer:

156

Step-by-step explanation:

209x18.50=3866.5

5700-3866.5=1833.5

1833.5÷11.75=156.04

Answer:

58.03 ft

Step-by-step explanation:

To solve for the total circumference of circle F, we can create a ratio of section angle measure to circumference. We know that these two attributes of a circle have a linear relationship because the formula for arc length (\(S = 2\pi r \cdot \frac{\theta}{360\°}\)) relies proportionately on the radius and angle measure of the section.

angle measure : circumference

               290°   :   46.75 ft

We can multiply this ratio by \(\frac{360}{290}\) to get the corresponding circumference for a 360° section (which is the entire circle).

\(\frac{360}{290}(290\° : 46.75 \text{ ft})\)

\(= 360\° : \boxed{58.03 \text{ ft}}\)

Therefore, the circumference of circle F is approximately 58.03 ft.

Answer:

c=-12

Step-by-step explanation:

Let's solve your equation step-by-step.

2/3c−2=2+c

Step 1: Simplify both sides of the equation.

2/3c−2=2+c

2/3c+−2=2+c

2/3c−2=c+2

Step 2: Subtract c from both sides.

2/3c−2−c=c+2−c

−1/3c−2=2

Step 3: Add 2 to both sides.

−1/3c−2+2=2+2

−1/3c=4

Step 4: Multiply both sides by 3/(-1).

(3/−1)*(−1/3c)=(3/−1)*(4)

c=−12

Answer:

c=−12

Answer:

f(2) = -2

General Formulas and Concepts:

Step-by-step explanation:

Step 1: Define

f(x) = 5x - 12

f(2) is x = 2

Step 2: Solve

Answer:

f ( 2 ) = - 2

Step-by-step explanation:

Step 1:

f ( x ) = 5x - 12            Function

Step 2:

f ( 2 ) = 5 ( 2 ) - 12          Input x

Step 3:

f ( 2 ) = 10 - 12        Multiply

Answer:

f ( 2 ) = - 2

Hope This Helps :)  

Answer:

X= -6 (B)

Step-by-step explanation:

-3x=18

X=18/-3

X= -6

The diver collected water samples at every 3 meters, starting from 5 meters below the water surface, up to a final depth of 35 meters.

We can find the number of samples collected by dividing the total depth range by the distance between each sample and then adding 1 to include the first sample.

The total depth range is:

35 m - 5 m = 30 m

The distance between each sample is 3 m, so the number of samples is:

(30 m) / (3 m/sample) + 1 = 10 + 1 = 11

Therefore, the diver collected a total of 11 water samples.

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The origin of the number zero is believed to be ancient India, where it was invented as a placeholder in the decimal system around the 5th century CE. The concept of zero as a number in its own right was a revolutionary idea that greatly advanced mathematical understanding and allowed for much more efficient mathematical calculation. From India, the use of zero spread to the Islamic world and eventually to the West. The modern representation of zero as a circle or a digit was introduced in the 13th century in India.

(f + g)(6) = 39 represents the total number of animals adopted by both shelters in 6 months, based on the combined adoption rates of the two shelters.

Part A:

To find (f + g)(x), we add the functions f(x) and g(x):

(f + g)(x) = f(x) + g(x)

= (3x + 10) + (x + 5) (substitute the given functions)

= 4x + 15 (combine like terms)

Therefore, (f + g)(x) = 4x + 15.

Part B:

To evaluate (f + g)(6), we substitute x = 6 into the (f + g)(x) function:

(f + g)(6) = 4(6) + 15

= 24 + 15

= 39

Therefore, (f + g)(6) = 39.

Part C:

The value of (f + g)(6) represents the combined number of animals adopted by both shelters after 6 months. The function (f + g)(x) gives us the total adoption rate of the two shelters at any given time x. When x = 6, the combined adoption rate was 39 animals.

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