Write the slope-intercept form of the equation of the line
12x + 4y = -48

Answer:

5. x=80°, y= 80°

Step-by-step explanation:

5.x=80 (Vertically opposite angle V.O.A)

y=80 (alternate angle)

Answer:

A² = 9

Step-by-step explanation:

substitute A = - 3 into A² , that is

A² = (- 3)² = - 3 × - 3 = 9

Using proportional relationships, we can say that They will walk 12 laps and run 20 laps for a total of 32 miles.

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

Given that we know this, they walk 3/8 of the 8 miles that make up the complete distance. Run 5/8 of the route.

The following are the proportional relationships for the distances:

For a total distance of 32 miles, the distances walked and run are given:

therefore, They will walk 12 laps and run 20 laps for a total of 32 miles as per the proportional relation.

Learn more about proportional relationships here: brainly.com/question/10424180

#SPJ1

The probability that at least 8 tadpoles survive the week in at least one of the two bodies of water is approximately 0.9298.

Let the probability that a tadpole in one body of water survives the week be denoted by P(A) = 0.9.Using the binomial distribution formula, we can determine the probability of x number of tadpoles surviving until the end of the week out of n total tadpoles.

P(x) = (nCx)(p^x)(1 - p)^(n - x) where n = 10 and p = 0.9. For at least 8 tadpoles to survive the week in at least one of the two bodies of water,

we need to calculate: P(at least 8) = P(8) + P(9) + P(10)P(8) = (10C8)(0.9^8)(0.1^2) ≈ 0.1937P(9) = (10C9)(0.9^9)(0.1^1) ≈ 0.3874P(10) = (10C10)(0.9^10)(0.1^0) ≈ 0.3487

Therefore, P(at least 8 tadpoles surviving the week in at least one of the two bodies of water) = P(8) + P(9) + P(10)≈ 0.9298 (rounded to four decimal places).

To Know more about  binomial distribution visit:

https://brainly.com/question/29137961

#SPJ11

Given: Tadpoles in two bodies of water are being monitored for one week. Each body contains 10 tadpoles, where the probability the tadpole survives until the end of the week is 0.9 (independently of each tadpole). The probability that at least 8 tadpoles survive the week in at least one of the two bodies of water is 0.9999.

Let event A be the event that at least 8 tadpoles survive the week in the first body of water and let event B be the event that at least 8 tadpoles survive the week in the second body of water.

Therefore, the probability that at least 8 tadpoles survive the week in at least one of the two bodies of water is P(A ∪ B).

We can solve for this probability using the principle of inclusion-exclusion: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

We know that the probability of survival for a tadpole is 0.9.

Therefore, the probability of 8 or more tadpoles surviving out of 10 is:

P(X ≥ 8) = (10C8 × 0.9⁸ × 0.1²) + (10C9 × 0.9⁹ × 0.1) + (10C10 × 0.9¹⁰)

≈ 0.9919

Using this probability, we can calculate the probability of at least 8 tadpoles surviving in each individual body of water:

P(A) = P(B)

= P(X ≥ 8)

≈ 0.9919

To calculate P(A ∩ B), we need to find the probability of at least 8 tadpoles surviving in both bodies of water.

Since the events are independent, we can multiply the probabilities:

P(A ∩ B) = P(X ≥ 8) × P(X ≥ 8)

≈ 0.9838

Now we can substitute these probabilities into our formula:

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

≈ 0.9999

Therefore, the probability that at least 8 tadpoles survive the week in at least one of the two bodies of water is approximately 0.9999.

To know more about Probability, visit:

https://brainly.com/question/30034780

#SPJ11

The coordinates of B when it is given that A(5,-2) and M(12,6) is (29, 14).

If M is the mid-point of line segment AB, and the coordinates of A = (5,-2) while the coordinates of B = (12,6), then the coordinates of M = (8.5,2), which is what you stated that you got.

You are provided with M = (12,6) so you need to identify the coordinates of B. So, just ask yourself how did I get from A to M ? The answer is move 7 right and 8 up since 5 + 7 = 12 while -2 + 8 = 6. All you have to do is add 7 more to the x-value and 8 more to the y-value to obtain the correct answer of (19,14).

Learn more about coordinate on;

https://brainly.com/question/17206319

#SPJ1

Find the coordinates of B when it is given that A(5,-2) and M(12,6),

The x-bar chart relies on the Normal Distribution due to the Central Limit Theorem, which states that the distribution of sample means will approach a normal distribution as the number of samples increases.


1. An x-bar chart is a type of control chart used to monitor the process mean of a continuous data set. It helps to determine whether a process is stable and under control.

2. The x-bar chart is based on the concept of sampling. In a process, multiple samples are taken, and their means (x-bar) are calculated.

3. According to the Central Limit Theorem, when a large number of samples are taken from a population, the distribution of the sample means will approach a normal distribution, regardless of the population's original distribution.

4. This is why the underlying statistical distribution for the x-bar chart is the Normal Distribution. The x-bar chart assumes that the sample means follow a normal distribution, allowing for the identification of process changes, shifts, or trends by monitoring the control limits and variation in the x-bar chart.

Learn more about sampling here:

brainly.com/question/31523301

#SPJ11

Answer:

p= -1 or -11

Step-by-step explanation:

if you mean (p+ 6)² = 25;

then we have that:

p + 6 = √ 25: gotten by squaring both sides of the equal sign

which makes

p + 6 = ±5

P= -6 ±5

therefore;

p = -6 + 5 or p = -6 -5

a.  The definite integral ∫|x|/(11 - x²) dx is 4.183

b. The area of the region bounded above by y = sin x (1 – cos x)? below by y = 0 and on the sides by x = 0, x = 0 is 1

a. To find the definite integral of |x|/(11 - x²) dx, we need to split the integral into two parts based on the intervals where |x| changes sign.

For x ≥ 0:

∫[0, 11] |x|/(11 - x²) dx

For x < 0:

∫[-11, 0] -x/(11 - x²) dx

We can evaluate each integral separately.

For x ≥ 0:

∫[0, 11] |x|/(11 - x²) dx = ∫[0, 11] x/(11 - x²) dx

To solve this integral, we can use a substitution u = 11 - x²:

du = -2x dx

dx = -du/(2x)

The limits of integration change accordingly:

When x = 0, u = 11 - (0)² = 11

When x = 11, u = 11 - (11)² = -110

Substituting into the integral, we have:

∫[0, 11] x/(11 - x²) dx = ∫[11, -110] (-1/2) du/u

= (-1/2) ln|u| |[11, -110]

= (-1/2) ln|-110| - (-1/2) ln|11|

≈ 2.944

For x < 0:

∫[-11, 0] -x/(11 - x²) dx

We can again use the substitution u = 11 - x²:

du = -2x dx

dx = -du/(2x)

The limits of integration change accordingly:

When x = -11, u = 11 - (-11)² = -110

When x = 0, u = 11 - (0)² = 11

Substituting into the integral, we have:

∫[-11, 0] -x/(11 - x²) dx = ∫[-110, 11] (-1/2) du/u

= (-1/2) ln|u| |[-110, 11]

= (-1/2) ln|11| - (-1/2) ln|-110|

≈ 1.239

Therefore, the definite integral ∫|x|/(11 - x²) dx is approximately 2.944 + 1.239 = 4.183 (rounded to three decimal places).

b. For the second question, to find the area of the region bounded above by y = sin x (1 - cos x), below by y = 0, and on the sides by x = 0 and x = π, we need to find the definite integral:

∫[0, π] [sin x (1 - cos x)] dx

To solve this integral, we can use the substitution u = cos x:

du = -sin x dx

When x = 0, u = cos(0) = 1

When x = π, u = cos(π) = -1

Substituting into the integral, we have:

∫[0, π] [sin x (1 - cos x)] dx = ∫[1, -1] (1 - u) du

= ∫[-1, 1] (1 - u) du

= u - (u²/2) |[-1, 1]

= (1 - 1/2) - ((-1) - ((-1)²/2))

= 1/2 - (-1/2)

= 1

Therefore, the area of the region bounded above by y = sin x (1 – cos x)? below by y = 0 and on the sides by x = 0, x = 0 is 1

Learn more about definite integral at https://brainly.com/question/31404387

#SPJ11

Answer: I think it's 0

The ratios that could be the lengths of the two legs in a 30-60-90 triangle are √3:3 (option E) and 12√3 (option D).

In a 30-60-90 triangle, the angles are in the ratio of 1:2:3. The sides of this triangle are in a specific ratio that is consistent for all triangles with these angles. Let's analyze the given options to determine which ones could be the ratio between the lengths of the two legs.

A. √2:√2

The ratio √2:√2 simplifies to 1:1, which is not the correct ratio for a 30-60-90 triangle. Therefore, option A is not applicable.

B. 15

This is a specific value and not a ratio. Therefore, option B is not applicable.

C. √√√√5

The expression √√√√5 is not a well-defined mathematical operation. Therefore, option C is not applicable.

D. 12√3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which simplifies to √3:3. Therefore, option D is applicable.

E. √3:3

This is the correct ratio for a 30-60-90 triangle. The ratio of the longer leg to the shorter leg is √3:1, which is equivalent to √3:3. Therefore, option E is applicable.

F. √2:√5

This ratio does not match the ratio of the sides in a 30-60-90 triangle. Therefore, option F is not applicable. So, the correct option is D. 1 √2.

For more such questions on lengths

https://brainly.com/question/28322552

#SPJ8

The risk of explosion in the process industry is 6.6594e-06 per year.

To calculate the risk of explosion, we need to consider the probability of a gas release, the probability of ignition, and the probability of fatal injury.

Step 1: Calculate the probability of an explosion.

The probability of a gas release per year is given as\(1.23 * 10^-^5\).

The probability of ignition is 0.54.

The probability of fatal injury is 0.32.

To calculate the risk of explosion, we multiply these probabilities:

Risk of explosion = Probability of gas release * Probability of ignition * Probability of fatal injury

Risk of explosion = 1.23 * \(10^-^5\) * 0.54 * 0.32

Risk of explosion = 6.6594 *\(10^-^6\) per year

Therefore, the risk of explosion in the process industry is approximately 6.6594 * 10^-6 per year.

Learn more about explosion  

brainly.com/question/16787654

#SPJ11

Answer:

see below

Step-by-step explanation:

Hi!

\(\frac{1}{21-20} \left[\begin{array}{ccc}-3&10&\\2&-7&\end{array}\right]\)

(Determinant is 1 in this case)

Hence the inverse is:

\(\left[\begin{array}{ccc}-3&10\\2&-7&\\\end{array}\right]\)

The type of variable for,

a. The number of counties in California: Quantitative discrete.

b. The stages of childhood: Qualitative ordinal.

c. In the scenario above, 23 minutes is a statistic, because 28 students is a sample.

d. Between 6 minutes and 8 minutes: Approximately 68% of the athlete's mile times are expected to be between 6 and 8 minutes, according to the empirical rule.

e. Between 4 minutes and 7 minutes: Approximately 68% of the athlete's mile times are expected to be between 4 and 10 minutes, according to the empirical rule.

f. Less than 9 minutes: Approximately 84% of the athlete's mile times are expected to be less than 9 minutes, according to the empirical rule.

In statistics, variables can be categorized into two types: qualitative and quantitative.

Qualitative variables describe characteristics or qualities that cannot be measured numerically, such as gender or hair color.

Quantitative variables, on the other hand, represent numerical values that can be measured or counted.

There are two types of quantitative variables: continuous and discrete. Continuous variables can take any numerical value within a range, such as age or weight.

Learn more about the type of a variable at

https://brainly.com/question/14501374

#SPJ4

Answer:

One solution

Step-by-step explanation:

They have isolated y for you in both equations so you can plug either one into the other.

y = 3x - 1

2x + 7 = 3x - 1

isolate the x

7 = x - 1

x = 8

Go back to the original and plug 8 into x to get y.

y = 2 (8) + 7

y = 16 + 7

y = 23

This means at (8, 23) y = 2x+7 is equal to y = 3x-1. In other words they share a point at (8, 23). This is the only solution because for any other x and y they'd not be equal.

The Answer:the answer is D

Step-by-step explanation:

Answer:

7x

Step-by-step explanation:

Theatre should conclude that majority of patrons were dissatisfied with performance quality.

Here, we have to use one sample z test for a population proportion.

Null hypothesis: H0: No majority of patrons are dissatisfied with performance quality.

Alternative hypothesis: Ha: The majority of patrons are dissatisfied with performance quality.

H0: p ≤ 0.5 versus Ha: p > 0.5

This is an upper-tailed or right-tailed test.

We assume a level of significance as α = 0.05.

The test statistic formula for this test is given as below:

Z = (p ^ - p)/sqrt(pq/n)

Where, p^ = Sample proportion, p is population proportion, q = 1 - p, and n is the sample size

n = sample size = 100

p^ = x/n = 0.70

p = 0.50

q = 1 - p = 0.50

Z = (p^- p) / sqrt ( p q / n)

Z = (0.70 – 0.50) / sqrt(0.50*0.50/100)

Z = 4.00

P-value = 0.00 (by using z-table)

P-value < a = 0.05

So, we reject the null hypothesis.

Therefore theatre should conclude that majority of patrons were dissatisfied with performance quality.

Learn more about the hypothesis here: https://brainly.com/question/15980493

#SPJ4

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Read more about area here:https://brainly.com/question/27440983

#SPJ1

Answer:

2

Explanation:

In short terms, there are two numbers that are reciprocals of themselves, 1 and -1.  According to euler's identity, e^(-i*2*pi) is a reciprocal of itself, but I believe that is beyond the scope of this question.

Answer:

A plane extends infinitely in two dimensions. It has no thickness. An example of a plane is a coordinate plane. A plane is named by three points in the plane that are not on the same line.

Step-by-step explanation:

\(\bf Step-by-step~explanation:\)

Remember: In math, a plane is a flat, two-dimensional surface that stretches infinitely far in all directions.

An example of a plane would be the photo below.

The purple rectangle is one plane, and the brown one is another one. If there are points there, then they would be on both planes if the points lie exactly on the intersection between the two planes.

We label planes when they have a letter (K, M, etc.), or if there are three non - collinear points on one plane, we take those letters and make them into the plane's name. (ex: Plane AGE, QDE, etc.)

Answer: 1.8 X 10^8

Step-by-step explanation: 6.0 X 10^7 times .3 = 1.8 X 10^8

Answer:

(37,23)

Step-by-step explanation:

1. 11+x divide 2 = 24

x= 37

2. 25+y divide 2= 24

y= 23

Answer:

Step-by-step explanation:

I think that the numbers 10-(2-3990

The normal distribution have an importance in statistics of whether or not out appears in nature, because it fits several natural phenomena.

For exa. measurement error, heights, IQ scores, and physical activity measures all follow the normal distribution.

In this question we need to describe why does the normal distribution have an importance in statistics of whether or not out appears in nature.

We know that if we plot the probability distribution and it forms a bell-shaped curve. If the mean, mode, and median of the sample are equal then the variable has normal distribution.

A normal distribution is dependent on two parameters of the data set: mean and the standard deviation of the sample.

This characteristic of the normal distribution makes it extremely simple.

Also, the normal distribution is important because of the Central limit theorem.

It makes math easy - like calculating moments, correlations between variables, and other calculations that are domain specific.

So, the normal distribution have an importance in statistics of whether or not out appears in nature.

Learn more about the normal distribution here:

https://brainly.com/question/29509087

#SPJ4

Answer:

Question 3

First option:
\(\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}\)

Question 4
Third option:
\(\dfrac{1}{4} \div \dfrac{2}{5}\)

Question 5

Second Option:
\(\dfrac{7}{10}\)

Step-by-step explanation:

Question 3

If  \(\dfrac{4}{5}\) inches of rain falls every  \(\dfrac{2}{3}\) hours then the unit rate in inches per hour is inches \(\div\) hours

This would be:
\(\dfrac{\ensuremath{\dfrac{4}{5}\;in}}{\dfrac{2}{3}\;hr}\)

This is the first option in Question 3 answer choices

Question 4

\(\dfrac{\dfrac{1}{4}\;km}{\dfrac{2}{5}\;min}\)

is nothing but the numerator ÷ denominator which would be:

\(\dfrac{1}{4} \div \dfrac{2}{5}\)

This is the third option in Question 4 answer choices

Question 5

\(\dfrac{1}{2} \div \dfrac{5}{7}\\\)

Flip the divisor \(\dfrac{5}{7}\); it comes \(\dfrac{7}{5}\)

Multiply:
\(\dfrac{1}{2} \times \dfrac{7}{5}\)

The result is
\(\dfrac{7}{10}\)

This is the second option in Question 4 answer choices

Answers:

Question 3: \(\frac{\frac{4}{5}in.}{\frac{2}{3}hr.}\)

Question 4: \(\frac{1}{4}\) ÷ \(\frac{2}{5}\)

Question 5: \(\frac{7}{10}\)

Explanations:

Question 3: We're told that rain is falling at a rate of  \(\frac{4}{5} in.\) every  \(\frac{2}{3} hr.\), and the unit rate we're looking for is inches per hour (or more precisely, inches per 1 hour). Based on these parameters, we know that you have to divide the unit inches by the unit hours. So using the numbers above, the correct complex fraction to represent this situation would be \(\frac{\frac{4}{5} in.}{\frac{2}{3} hr.}\) .

Question 4: In this question, we are given a complex fraction and asked to rewrite it as a simple division problem. The complex fraction is \(\frac{\frac{1}{4} km.}{\frac{2}{5} min.}\), so in order to write this as a division expression, you simply take the numerator fraction and divide it by the denominator fraction, which will end up being \(\frac{1}{4}\) ÷ \(\frac{2}{5}\). Therefore, that will be your answer.

Question 5: Now, we have a division expression and are asked to use the Keep, Change, Flip method to solve the problem. First and foremost, the Keep, Change, Flip method is essentially telling you that when you are dividing by a fraction, you keep the dividend the same, you change the divisor - specifically switching the numerator with the denominator, which is creating the reciprocal of that fraction - and multiply by the reciprocal of the original divisor instead.

                   A good example of the Keep, Change, Flip method from above would be \(\frac{1}{2}\) ÷ \(\frac{1}{3}\). You keep the dividend, change the divisor, specifically flip the function around to create its reciprocal, and instead multiply by the divisor's reciprocal. Following those steps, \(\frac{1}{2}\) ÷ \(\frac{1}{3}\)  will become \(\frac{1}{2}\) × \(\frac{3}{1}\) or \(\frac{1}{2}\) × \(3\).

                  Now that we understand how to use the Keep, Change, Flip method, we can use it to solve the expression \(\frac{1}{2}\) ÷ \(\frac{5}{7}\). We keep \(\frac{1}{2}\) the same, flip \(\frac{5}{7}\) to make its reciprocal, and multiply \(\frac{1}{2}\) by that instead. So the final answer will be \(\frac{1}{2}\) ÷ \(\frac{5}{7}\) = \(\frac{1}{2}\) × \(\frac{7}{5}\) = \(\frac{7}{10}\).

Have a great day! Feel free to let me know if you have any more questions :)

Answer:

\(y=\frac{3x}{4} +\frac{19}{4}\)

Step-by-step explanation:

Plug-in given to the point-slope form:

m = 3/4

(the slope is the same for the other line as the two are parallel to each other)

(3 , 7)

\(y - 7 = \frac{3}{4} (x - 3)\\ y-7 = \frac{3}{4} x - \frac{9}{4} \\4( y-7) =( \frac{3}{4} x - \frac{9}{4})4\\ 4y - 28 = 3x - 9\\ 4y - 28 +28 = 3x - 9 + 28\\4y = 3x + 19\\\frac{4y}{4} =\frac{3x+19}{4} \\y=\frac{3}{4}x +\frac{19}{4}\)

The derivative is a. y' = [7 * cos(7x) * tan(3x) - 3 * sin(7x) * sec²(3x)] / [tan²(3x)] and the derivative of second funtction is b. (ln(π) * \(\pi^(3x^2-7)\)) * (6x) + (9 - x²) / (x²+9)² - 32 / sqrt(1 - (32x+1)²).

a. y = sin(7x)/tan(3x)

To differentiate this function, we can use the quotient rule, which states that if we have a function in the form f(x) = g(x)/h(x), where g(x) and h(x) are differentiable functions, the derivative of f(x) is given by:

f'(x) = (g'(x) * h(x) - g(x) * h'(x)) / (h(x))²

In this case, g(x) = sin(7x) and h(x) = tan(3x). Let's differentiate both g(x) and h(x) first:

g'(x) = d/dx [sin(7x)] = 7 * cos(7x)

h'(x) = d/dx [tan(3x)] = 3 * sec²(3x)

Now we can substitute these derivatives into the quotient rule formula:

y' = [(7 * cos(7x) * tan(3x)) - (sin(7x) * 3 * sec²(3x))] / (tan(3x))²

Simplifying further, we get:

y' = [7 * cos(7x) * tan(3x) - 3 * sin(7x) * sec²3x)] / [tan²(3x)]

b. y = \(\pi^{(3x^2-7)\) + x/(x²+9) + cos⁻¹(32x+1)

To differentiate this function, we can use the sum and chain rules. Let's differentiate each term separately:

For the first term, y₁ = \(\pi^{(3x^2-7)\):

y₁' = d/dx [\(\pi^{(3x^2-7)\)]

Using the chain rule, the derivative is:

y₁' = (ln(π) * \(\pi^{(3x^2-7)\)) * (6x)

For the second term, y₂ = x/(x²+9):

y₂' = d/dx [x/(x²+9)]

Using the quotient rule, the derivative is:

y₂' = [(1 * (x²+9)) - (x * 2x)] / (x²+9)²

Simplifying further, we get:

y₂' = (9 - x²) / (x²+9)²

For the third term, y₃ = cos⁻¹(32x+1):

y₃' = d/dx [cos⁻¹(32x+1)]

Using the chain rule, the derivative is:

y₃' = -32 / sqrt(1 - (32x+1)²)

Now, we can add all the derivatives together to find the derivative of the function:

y' = y₁' + y₂' + y₃'

y' = (ln(π) * \(\pi^{(3x^2-7)\))) * (6x) + (9 - x²) / (x²+9)² - 32 / sqrt(1 - (32x+1)²)

The complete question is:
a. Differentiate the function: \(y=\frac{sin(7x)}{tan(3x)}\).

b. Differentiate the function: \(\pi^{(3x^2-7)\) + x/x²+9+cos⁻¹(32x+1)

To know more about derivative, refer here:
https://brainly.com/question/2159625#
#SPJ11

Answer:

7

Step-by-step explanation:

Answer:

7-8

Step-by-step explanation:

with this is basd

Answer:

Step-by-step explanation: y= x -2 i hope this helps