In Exercises 4 and 5. graph the polygon and its image after a reflection in the given line.
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24,48,72,96,120,144,168,192,216,240,264...360

90,180,270,360

LCM of 24 and 90 is 360

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hope it helps

Answer:

Step-by-step explanation:

Find the prime factorization of each number

24=2*2*2*3, 90=2*3*3*5

The LCM will be the product of highest occurring primes, in this case

2*2*2*3*3*5=360

So the LCM is 360

312.5 μCi is equivalent to 0.3125 mCi.

Conversion factors refer to a relationship between the value in one unit to the value in another unit. It is used to convert a quantity expressed in one unit to another unit.

The following conversion factors are needed to convert 312.5 μCi to millicuries (mCi):1 mCi = 1000 μCiUsing the above conversion factor, we can write the given value of 312.5 μCi as:312.5 μCi = (312.5/1000) mCi= 0.3125 mCi

Therefore, the value of 312.5 μCi can be converted to millicuries (mCi) using the above conversion factor. We can rearrange the formula as shown below.312.5 μCi × 1 mCi / 1000 μCi= (312.5/1000) mCi= 0.3125 mCi

Therefore, 312.5 μCi is equivalent to 0.3125 mCi. The calculation can be summarized in a sentence as follows: To convert 312.5 μCi to millicuries (mCi), we use the conversion factor 1 mCi = 1000 μCi.

The calculation shows that 312.5 μCi is equivalent to 0.3125 mCi. The answer can be expressed as follows: 312.5 μCi = 0.3125 mCi.

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Answer:

Distributive property

Step-by-step explanation:

With the distributive property, it is possible to simplify expressions that consist of an expression term such as (a + b) being multiplied by one singular term such as c given as follows

c ×(a + b) = c·a + c·b

Factoring, which is the reverse  use of the distributive property enables the difference or the sum of two products, each having a common factor to be the presented as the difference  or the sum of two numbers multiplied by the common factor as follows;

2·x - 2·y = 2·(x - y).

A big sample that should the experimenter take from the population is 256 and if the standard deviation and the width of the confidence interval are both doubled then the sample is also 256.

In the given question,

The confidence level = 99%

Given width = 0.5

Standard deviation of resistance(\sigma)= 1.55

We have to find a big sample that should the experimenter take from the population and what happens if the standard deviation and the width of the confidence interval are both doubled.

The formula to find the a big sample that should the experimenter take from the population is

Margin of error(ME) \(=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\)

So n \(=(z_{\alpha /2}\frac{\sigma}{\text{ME}})^2\)

where n=sample size

We firstly find the value of ME and \(z_{\alpha /2}\).

Firstly finding the value of ME.

ME=Width/2

ME=0.5/2

ME=0.25

Now finding the value of \(z_{\alpha /2}\).

Te given interval is 99%=99/100=0.99

The value of \(\alpha\) =1−0.99

The value of \(\alpha\) =0.01

Then the value of \(\alpha /2\) = 0.01/2 = 0.005

From the standard table of z

\(z_{0.005}\) =2.58

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{1.55}{0.25})^2\)

Simplifying

n=(3.999/0.25)^2

n=(15.996)^2

n=255.87

n≈256

Hence, the sample that the experimenter take from the population is 256.

Now we have to find the sample size if the standard deviation and the width of the confidence interval are both doubled.

The new values,

Standard deviation of resistance(\(\sigma\))= 2×1.55

Standard deviation of resistance(\(\sigma\))= 3.1

width = 2×0.5

width = 1

Now the value of ME.

ME=1/2

ME=0.5

The z value is remain same.

Now putting in the value in formula of sample size.

n=\((2.58\times\frac{3.1}{0.5})^2\)

Simplifying

n=(7.998/0.5\()^2\)

n=(15.996\()^2\)

n=255.87

n≈256

Hence, if the standard deviation and the width of the confidence interval are both doubled then the sample size is 256.

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To find the means, variances, covariance, and correlation coefficient of random variables X and Y with a joint PMF:

- Calculate the means: E[X] and E[Y].

- Compute the variances: Var(X) and Var(Y).

- Find the covariance: Cov(X, Y).

- Determine the correlation coefficient: ρ(X, Y).

Based on the covariance, we can determine if X and Y are independent or dependent.

Let the random variables X and Y have a joint probability mass function (PMF). We need to find the means (expected values), variances, covariance, and correlation coefficient of X and Y, and determine whether they are independent or dependent.

The mean of a random variable X is denoted by E[X] or μX, and it is calculated as the sum of all possible values of X weighted by their respective probabilities. Similarly, the variance of X, denoted by Var(X) or σ²X, measures the spread or dispersion of the values of X around its mean.

The covariance between two random variables X and Y, denoted by Cov(X, Y), measures the degree to which they vary together. It is calculated as the sum of the products of the differences of the values of X and its mean, and the differences of the values of Y and its mean, weighted by their joint probabilities.

The correlation coefficient between X and Y, denoted by ρ(X, Y), quantifies the strength and direction of the linear relationship between them. It is calculated by dividing the covariance of X and Y by the product of their standard deviations.

To determine the means and variances, we can use the following formulas:

E[X] = ∑x∑y x * P(X = x, Y = y)

E[Y] = ∑x∑y y * P(X = x, Y = y)

Var(X) = E[X²] - (E[X])²

Var(Y) = E[Y²] - (E[Y])²

To calculate the covariance, we use the formula:

Cov(X, Y) = E[XY] - E[X]E[Y]

Once we have the means and variances, we can calculate the correlation coefficient using the formula:

ρ(X, Y) = Cov(X, Y) / (√Var(X) * √Var(Y))

Based on the calculations of means, variances, covariance, and correlation coefficient, we can determine whether X and Y are independent or dependent. If the covariance is zero (Cov(X, Y) = 0), then X and Y are independent. Otherwise, they are dependent.

In summary, to find the means, variances, covariance, and correlation coefficient of X and Y, we use the formulas mentioned above. Based on the calculated values, we can determine whether X and Y are independent or dependent.

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\(m\angle E=\sin \dfrac{\sqrt{10}}{2\sqrt5}=\sin \dfrac{\sqrt2}{2}=45^{\circ}\)

On solving the given problem by help of mathematical operations, we got - After Ray poured 0.47L, he was left with 2.201L.

The term "operation" in mathematics refers to the process of calculating a value using operands and a math operator. For the given operands or numbers, the math operator's symbol has predetermined rules that must be followed.

In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

Total amount of tea Ray has - 2.671L

Amount of tea Ray poured - 0.47

Therefore,

amount he was left with was  = 2.671- 0.47 = 2.201L

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Suppose that a square of length s is cut out from each corner of the cardboard. The length of the box will be x - 2s and the width of the box will be y - 2s. The height of the box will be s. The volume of the box will be given by V = s (x - 2s) (y - 2s) or V = 4s³ - 2(x + y) s² + xy s.

To find the maximum volume, we need to take the derivative of V with respect to s and set it equal to zero. We get:

dV/ds = 12s² - 4(x + y) s + xy = 0

Solving for s, we get:

s = [(x + y) ± √(x² + y² - 2xy)] / 6

Since s must be less than x/2 and less than y/2, we choose:

s = min {[(x + y) ± √(x² + y² - 2xy)] / 6, x/2, y/2}

Plugging this value of s into the formula for V, we get:

V = (xy/6) [(x + y) - √(x² + y² - 2xy)]

Therefore, the maximum volume of the box is given by:

Vmax = (1/6)xy(x + y - √(x² + y² - 2xy))

Thus, the maximum volume of a box that can be made by cutting out squares from the corners of an inch by inch rectangular sheet of cardboard and folding up the sides is given by (1/6) cubic inch, which is 0.166666 cubic inch. The justification is based on the given formula for the volume of the box.

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Answer:

the correct answer would be p=nRt/v

Step-by-step explanation:

you would devide both sides by v to get the new equation

Answer:

456.29 miles

Step-by-step explanation:

Hope this helps!

Answer:

we invented it. it's a tool to help things make sense.

Answer:

Step-by-step explanation:

We invent it.  it was invented by Archimedes.

Answer:The slope of a line measures the steepness of the line. Most of you are probably familiar with associating slope with "rise over run". Rise means how many units you move up or down from point to point. Run means how far left or right you move from point to point. On the graph, that would mean a change of x values.

Step-by-step explanation:

The ordered pair that is a solution to the inequality:

y > (1/4)*x + 5

is (4, 7)

Here we have the inequality:

y > (1/4)*x + 5

To check if an ordered pair is a solution, we just need to replace the values of the ordered pair on the inequality and see if it is true.

For example, for (12, 8)

We will get:

8 > (1/4)*12 + 5

8 > 3 + 5

8 > 8

This is false, so (12, 8) is not a solution.

The pair that is a solution is:

(4, 7)

7 > (1/4)*4 + 5

7 > 1  + 5

7 > 6

This is true.

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Therefore, the two positive coterminal angles are 5π/4 and 13π/4, and the two negative coterminal angles are -11π/4 and -19π/4.

To find the coterminal angles, we can add or subtract multiples of 2π (or 360°) to the given angle to obtain angles that have the same initial and terminal sides.

For the angle -3π/4 radians, adding or subtracting multiples of 2π will give us the coterminal angles.

Positive coterminal angles:

-3π/4 + 2π = 5π/4

-3π/4 + 4π = 13π/4

Negative coterminal angles:

-3π/4 - 2π = -11π/4

-3π/4 - 4π = -19π/4

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Answer:

y = 1.5x

Step-by-step explanation:

in the graph you can see that when y=2, x= 3 and this graph is linares (im sorry if its not the right word). so this means for every 3gal of white paint youll need 2 gal of red paint. so 2y=3x: y = 3/2x

Answer:

$134.09

Step-by-step explanation:

you take 156.34 and minus 15.50, then you take that and minus it by 6.75

Answer $134.09

why 156.34 - 15.50+6.75=134.09

Answer:

a_48000cm^3

b_48000000mm^3

Step-by-step explanation:

first of all, let's find the base area:

Ab=((b+B)h)/2=((10cm+30cm)20cm)/2=400cm^2

then, to find the volume, we need to multiplicate the base area to the height of the prism:

V=Ab*H=400cm^2*120cm=48000cm^3=48000000mm^3

We would expect to find the middle 98% of most pregnancies in the small rural village in the range of approximately 237 to 303 days.

We can use the properties of the normal distribution to determine the range in which we would expect to find the middle 98% of most pregnancies in the small rural village.

First, we need to find the z-scores associated with the upper and lower tails of the distribution that exclude the middle 2%. We can use a standard normal distribution table or calculator to find these values:

For the upper tail, the z-score is 2.33 (corresponding to a probability of 0.01 or 1%).

For the lower tail, the z-score is -2.33 (corresponding to a probability of 0.01 or 1%).

Next, we can use the formula for transforming a z-score into an actual value:

z = (x - μ) / σ

where z is the z-score, x is the actual value, μ is the mean, and σ is the standard deviation.

Substituting the values we know, we can solve for the upper and lower limits of the range:

For the upper limit:

2.33 = (x - 270) / 14

x - 270 = 32.62

x = 302.62

For the lower limit:

-2.33 = (x - 270) / 14

x - 270 = -32.62

x = 237.38

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Answer:

Yes, it is y=mx+b

Step-by-step explanation:

Answer:

=The opposite angles of a parallelogram are equal

=(3x+4)

=(5x-2)

=-2x=-6

=x=6+2

=x=3=

1st angle=3x+4=13

3rd angle=5x-2=13

=sum of adjacent side of angle is 180°

=Let the adjacent (2nd angle ) be y=

y+13°=180°

=y=180°-13°

=y=167°=

2nd angle=4th angle

=2nd angle=167° 

=4th angle=167°

Step-by-step explanation:

This might be confusing, but I hope it helps <3

Answer:

58

Step-by-step explanation:

3x-14=58

+14 +14

3x=72

x=24

solved that now we'll input the factor

3(24)-14

72-14

"58" is your answer

If the temperature is -5 degrees in one city and it is four degrees less in another city, the temperature in the other city would be -9 degrees.

This is because subtracting four from -5 results in a decrease of four units, giving us -9 degrees.

In the given scenario, the temperature in the other city is four degrees less than the temperature in the first city. When we subtract four from the original temperature of -5 degrees, we obtain -9 degrees.

Thus, the temperature in the other city is -9 degrees, indicating that it is colder by four degrees compared to the first city.

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Answer:

1

Step-by-step explanation:

–6 − 8r = 8 − r

− 8r - r = 8 + 6

-9r = 14

r = -14/9

Answer:

r =-2

Step-by-step explanation:

–6 − 8r = 8 − r

Add r to each side

–6 − 8r+r = 8 − r+r

-6 -7r = 8

Add 6 to each side

-6+6 -7r = 8+6

-7r = 14

Divide each side by -7

-7r/-7 = 14/-7

r =-2

A sample size of 32 is necessary if the width of the 95% interval is to be 0.38.

To compute the confidence intervals (CI) for the true average porosity of coal seams, we can use the t-distribution since the sample sizes are relatively small (less than 30) and the true standard deviation is unknown. The formula for the confidence interval is:

CI = sample mean ± t_critical * (sample standard deviation / √(sample size))

where t_critical is the critical value of the t-distribution for the desired confidence level and degrees of freedom (sample size - 1).

(a) For the 95% CI of the true average porosity of the first seam with a sample mean of 4.85 and a sample size of 19, the t_critical value for a 95% confidence level with 18 degrees of freedom is approximately 2.101 (you can find this value from t-distribution tables or using a calculator/software). The sample standard deviation is not the true standard deviation, so we use the sample standard deviation instead, which is 0.71.

CI (95%) = 4.85 ± 2.101 * (0.71 / √19)

CI (95%) ≈ 4.85 ± 0.296

So, the 95% confidence interval for the true average porosity of the first seam is approximately (4.554, 5.146).

(b) For the 98% CI of the true average porosity of the second seam with a sample mean of 4.56 and a sample size of 13, the t_critical value for a 98% confidence level with 12 degrees of freedom is approximately 2.681.

CI (98%) = 4.56 ± 2.681 * (0.71 / √13)

CI (98%) ≈ 4.56 ± 0.365

The 98% confidence interval for the true average porosity of the second seam is approximately (4.195, 4.925).

(c) To find the necessary sample size for a 95% confidence level and a CI width of 0.38, we rearrange the CI formula:

Sample size = [(t_critical * sample standard deviation) / (CI width / 2)]^2

Given t_critical for a 95% confidence level and a sample standard deviation of 0.71:

Sample size = [(1.96 * 0.71) / (0.38 / 2)]^2 ≈ 31.52

Since the sample size must be a whole number, we round up to 32. Therefore, a sample size of 32 is necessary to achieve a 95% confidence interval with a width of 0.38.

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Answer:

The Great Chicago Fire was a conflagration that burned in the American city of Chicago during October 8–10, 1871. The fire killed approximately 300 people, destroyed roughly 3.3 square miles (9 km 2) of the city, and left more than 100,000 residents homeless. The fire began in a neighborhood southwest of the city center.

Step-by-step explanation:

Origin

The fire is claimed to have started at about 8:30 p.m. on October 8, in or around a small barn belonging to the O'Leary family that bordered the alley behind 137 DeKoven Street.

Spread

When firefighters finally arrived at DeKoven Street, the fire had grown and spread to neighboring buildings and was progressing toward the central business district.

Aftermath

Once the fire had ended, the smoldering remains were still too hot for a survey of the damage to be completed for many days. Eventually, the city determined that the fire destroyed an area about 4 miles (6 km) long and averaging ⁄4 miles (1 km) wide, encompassing an area of more than 2,000 acres (809 ha).

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The inequality that represents the situation where there are more students in Priscilla's class than Mrs. Roder's class using x for the number of students in Mrs. Roder's class is x + 1 < 24.

We know that there are more students in Priscilla's class than in Mrs. Roder's class, so the number of students in Mrs. Roder's class, represented by x, must be less than the number of students in Priscilla's class. If we add 1 to x to account for the fact that there are more students in Priscilla's class, the resulting inequality is x + 1 < 24. This means that the number of students in Mrs. Roder's class, x, must be less than 23 in order for there to be more students in Priscilla's class.

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Answer: A

Step-by-step explanation:

Answer:

x=1120-d

Step-by-step explanation:

Answer:

x = 1120 - d

Step-by-step explanation:

Hi there!

We can simplify this using orders of operations.

First, subtract 125 from both sides to get x + d = 1120.

To isolate x, just subtract d from both sides.

If you give me a value for d, i can solve the full problem.

I hope this helps!

Answer:

A and B

Step-by-step explanation:

simplify both sides of the equation

add 4x to both sides subtract 3 from both sides. Divide both sides by 9 and that's it

If the equation given a unique and single value of variable after solving then the equation is said one solution equation.

The equation which has only one solution are,

\(5x+3=-2(2x+3)\)

Thus, the option C is the correct option.

How to find one solution of equation?

If the equation given a unique and single value of variable after solving then the equation is said one solution equation.

Such equation gives exactly one solution.

Given information-

To find the equation we have to solve each equation one by one.

\(-7x+2&=-3(x-3)-4x-7\\\)

Solve it further,

\(-7x+2&=-3x+9-4x-7\\-7x+2&=-7x+2\\.\;\;\;\;\;\;\;\;\;\;\;0=0\)

Thus this equation has no solution. Hence the option A is the incorrect option.

\(14x&=7(2x+2)\)

Solve it further,

\(14x&=14x+14\\.\;\;\;0=14\)

Thus this equation has no solution. Hence the option B is the incorrect option.

\(5x+3=-2(2x+3)\)

Solve it further,

\(5x+3=-(4x+6)\\5x+3=-4x-6\)

Bring the same variable terms one side.

\(5x+4x=-6-3\\9x=-9\\x=-1\)

As the expression of equation gives the value of variable which is -1.Thus this equation has one solution.

Hence the option C is the correct option.

\(3(4x+2)-9=12x-3\)

Solve it further,

\(12x+6-9=12x-3\\2x-3=12x-3\\.\;\;\;\;\;\;\;0=0\)

Thus, this equation does not has one solution.

Hence the option D is the incorrect option.

Hence the equation which has only one solution are,

\(5x+3=-2(2x+3)\)

Thus, the option C is the correct option.

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