6-4(a+2)=8+a
What dose a equal

Answer:

Step-by-step explanation:

The probability that the flight would be delayed when it is not raining is 12.15%.

Since at LaGuardia Airport, for a certain nightly flight, the probability that it will rain is 0.19 and the probability that the flight will be delayed is 0.15, while the probability that it will not rain and the flight will leave on time is 0.74 , to determine what is the probability that the flight would be delayed when it is not raining, the following calculation must be performed:

Probability that it will not rain = 1 - probability that it will rain

X = 1 - 0.19

X = 0.81

Probability that the flight would be delayed when it is not raining = probability that it is not raining x probability that the flight will be delayed

X = 0.81 x 0.15

X = 0.1215

0.1215 x 100 = 12.15

Therefore, the probability that the flight would be delayed when it is not raining is 12.15%.

To find the absolute maximum and minimum values of a function that is continuous on a closed interval, you need to follow these steps:

1. Determine the interval of the function. The closed interval should be defined as [a, b], where a and b are real numbers.

2. Find the critical points of the function within the interval. Critical points are where the derivative of the function is equal to zero or does not exist.

3. Evaluate the function at the critical points and the endpoints of the interval.

4. The highest value of the function among the critical points and endpoints is the absolute maximum, and the lowest value is the absolute minimum.

It is important to note that the function must be continuous on the interval to have an absolute maximum and minimum. This means that the function is uninterrupted and has no holes, jumps, or breaks. If the function is not continuous on the interval, then it may not have an absolute maximum or minimum.

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By following these steps, you can effectively find the absolute maximum and minimum values of a continuous function on a closed interval.

Identify the given function and closed interval, Find the critical points, Check endpoints of the interval, Compare function values,

Identify the given function and closed interval: First, you need to know the specific function working with and the closed interval, which will be in the form [a, b],

where a and b are the endpoints.
Find the critical points: Determine the derivative of the function, f'(x), and then set f'(x) equal to zero to find the critical points within the given interval.

These points are where the function may have local maximum or minimum values.
Check endpoints of the interval:

In addition to critical points, absolute maximum and minimum values can also occur at the endpoints of the closed interval.

So, be sure to evaluate the function at both endpoints, f(a) and f(b).
Compare function values:

Evaluate the function at each critical point and the endpoints to determine the function values at these points.

The largest function value will represent the absolute maximum, while the smallest function value will represent the absolute minimum.

Identify the absolute maximum and minimum values:

Based on the comparisons in step 4, we can now identify which points correspond to the absolute maximum and minimum values of the function on the given closed interval.

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Answer:

71.8

Step-by-step explanation:

74*0.97=71.78

Rounds up to 71.8

The five-number summary for the given data set is: Minimum: 19.5, Q1: 51.4, Q2 (Median): 54.5, Q3: 56.6, Maximum: 58.3

To calculate the five-number summary for the given data set, we need to find the minimum, the first quartile (Q1), the median (Q2), the third quartile (Q3), and the maximum.

1. Arrange the data in ascending order:

19.5, 23.2, 50.1, 52.7, 52.9, 54.5, 55.6, 55.6, 57.6, 58.3, 58.3

2. Obtain the minimum:

The minimum value is 19.5.

3. Obtain Q1 (the first quartile):

Q1 is the median of the lower half of the data set.

In this case, we have 11 data points, so the lower half consists of the first 5 data points:

19.5, 23.2, 50.1, 52.7, 52.9

To obtain Q1, we need to calculate the median of these data points:

Q1 = (50.1 + 52.7) / 2 = 51.4

4. Obtain Q2 (the median):

Q2 is the median of the entire data set.

In this case, we have 11 data points, so the median is the middle value:

Q2 = 54.5

5. Obtain Q3 (the third quartile):

Q3 is the median of the upper half of the data set.

In this case, we have 11 data points, so the upper half consists of the last 5 data points:

55.6, 55.6, 57.6, 58.3, 58.3

To obtain Q3, we need to calculate the median of these data points:

Q3 = (55.6 + 57.6) / 2 = 56.6

6. Obtain the maximum:

The maximum value is 58.3.

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Answer:

\(2^{4} x 2^{-4} ---- 2^{0} \\2^{-4} x 2^{5} ---- 2^{1} \\\frac{2^{4} }{2^{5}} ---- 2^{-1} \\\\\frac{2^{4} }{2^{4}} ---- 2^{0}\)

Step-by-step explanation:

(pretend the x's are multiplication signs)

hope this helps you!

Answer:

The formula A=12bh is used to find the area of the top and bases triangular faces, where A = area, b = base, and h = height.

Hope this helped :)

Step-by-step explanation:

Answer:

Find the area to all sides.

Step-by-step explanation:

Find the area of all the triangles (b*h*1/2), and find all the area's of the squares/rectangles (b*h), then add all the areas together.

Answer:

2 hours

Step-by-step explanation:

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a) The distance of the boat from its starting point is 20 km.

b. The nearest degree  is 63°

c. The bearing g that the boat should travel on to return to the starting point is 360° - 63° = 297°.

To find the distance of the boat from its starting point, we can use the Pythagorean theorem.

x^2 + y^2 = d^2

Substituting the values for x and y, we get:

12^2 + 16^2 = d^2

d^2 = 144 + 256

d^2 = 400

d = 20

Hence, the distance of the boat from its starting point is 20 km.

b) To find the bearing that the boat should travel on to return to the starting point, we must calculate the angle between the two legs of the journey.

b = arctan (y / x) = arctan (16 / 12) = 63.43°

To the nearest degree  is 63°.

c) The bearing that the boat should travel on to return to the starting point is the opposite direction of the angle formed by the two legs of the journey. Therefore, the bearing is 360° - 63° = 297°.

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Answer:

8 inches

Step-by-step explanation:

Nacho cheese

v= Pi×radius×2×height

v = 3.14×8×2×4 = 200.96

jalapeño

3.14×4×2=25.12

200.96÷25.12=8

the height is 8

to check your work you can do

(multiply by 8 and see if it equals 200.96)

3.14×4×2×8 = 200.96

since the volume is the same as the volume for nacho cheese we can say that 8 inches for height is correct

Answer:

x = -1.59

Step-by-step explanation:

We are here given a equation and we need to solve out for x. The given equation is ,

\(\sf\longrightarrow 4^{( x +3)}= 7\)

Take log to the base " e " on both sides , so that we can remove the variable from the exponent .

\(\sf\longrightarrow log_e 4^{x+3}= log_e 7\)

Simplify using the property of log , \(\sf log a^m = m log a \) , we have ,

\(\sf\longrightarrow (x + 3) ln 4 = ln 7 \)

Distribute by opening the brackets ,

\(\sf\longrightarrow x ln 4 + 3 ln 4 = ln 7\)

This can be written as ,

\(\sf\longrightarrow x ln 4 = ln 7 - 3ln4 \)

Divide both sides by ln 4 ,

\(\sf\longrightarrow x = \dfrac{ ln7}{ln 4 } - \dfrac{ 3ln4}{ln4} \)

Simplify ,

\(\sf\longrightarrow x = \dfrac{ ln4 }{ln7 } -3\)

On simplifying , we will get ,

\(\sf\longrightarrow \boxed{\blue{\sf x = -1.59 }}\)

Given that

The point is (-2, 4) and the slope is 3.

And we have to find the point-slope equation for this data.

Explanation -

First, we will write the formula to find the point-slope equation and then we will substitute the values to find the required equation.

The general point-slope equation is given as

We have slope, m = 3 and point (x1, y1) = (-2, 4)

Hence the required equation is

So the correct option is B.

Final answer -

The exponential growth function will be:  y = 4000(1 + 0.04)⁴

An exponential equation is an equation with exponents where the exponent (or) a part of the exponent is a variable.

We are given;,

Initial population = 4000

Rate of increase = 4%

Let current population be p.

Let number of years passed be t.

Thus, the exponential growth function will be:

y = 4000(1 + 0.04)⁴

Complete question is;

A town has a current population of 4,000. The population increased 4 percent per year for the past four years, Emergency response professionals make up 3 percent of the town's population.

Part A

Write a function that represents the population (p) of the town in terms of the number of years (1) for the last four years.

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Answer:

number of emergency response professionals = 3% of population

e = 0.03p

e is a function of p

e(p) = 0.03p

Step-by-step explanation:

edumentum

A circle chord exists a straight line segment with both endpoints on a circular arc.

SU goes through the center, R, so SU is a diameter.

Any straight line segment that traverses a circle's center and has ends on the circle exists said to have that circle's diameter in geometric terms. It exists even comprehended as the longest chord of the circle. Both definitions apply to the diameter of a sphere.

The line segment joining any two points on a circle's circumference exists known as the chord. A circle's diameter exists described as the lengthiest chord that passes through its center.

A circle chord exists a straight line with circular arcs at both ends. A secant line, or simply secant, is the infinite line extension of a chord. A chord exists a segment of a line that connects two points on a curve, such as an ellipse.

SU goes through the center, R, so SU is a diameter.

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To solve for x in: \(2x + 8 = 3x + 10\)

Collect like terms

\(→8 - 10 = 3x - 2x \\ - 2 = x\)

Therefore:

\(x = - 2\)

The angle (in radians) between vectors u and v is approximately 1.66 radians, rounded to two decimal places.

To find the angle between two vectors, we can use the dot product formula and the magnitudes of the vectors. Let's calculate the angle between vectors u and v:

Given:

u = 4i - 6j

v = 5i + 4j

Step 1: Calculate the dot product of u and v.

The dot product of two vectors u and v is given by:

u · v = |u| |v| cosθ

where |u| and |v| are the magnitudes of vectors u and v, respectively, and θ is the angle between them.

To calculate the dot product, we multiply the corresponding components of u and v and sum them:

u · v = (4 * 5) + (-6 * 4) = 20 - 24 = -4

Step 2: Calculate the magnitudes of vectors u and v.

The magnitude of a vector is given by:

|u| = √(u₁² + u₂²)

For vector u:

|u| = √((4)² + (-6)²) = √(16 + 36) = √52 ≈ 7.21

For vector v:

|v| = √((5)² + (4)²) = √(25 + 16) = √41 ≈ 6.40

Step 3: Calculate the angle θ.

Using the dot product formula mentioned earlier, we have:

-4 = (7.21)(6.40)cosθ

Solving for cosθ:

cosθ = -4 / (7.21 * 6.40) ≈ -0.086

To find θ, we can take the inverse cosine (arccos) of cosθ:

θ ≈ arccos(-0.086) ≈ 1.66 radians

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Answer:

Step-by-step explanation:

a) The system of planes is represented by the following equations:

3x + 2y - z = -2

2x + y - 2z = 7

2x - 3y + 4z = -3

To solve this system, we can use various methods such as substitution, elimination, or matrix methods. Here, we'll use the elimination method to find the solution:

Step 1: Multiply the second equation by 2 and the third equation by 3 to create a cancellation:

3x + 2y - z = -2

4x + 2y - 4z = 14

6x - 9y + 12z = -9

Step 2: Subtract the first equation from the second equation and the first equation from the third equation:

4x + 2y - 4z - (3x + 2y - z) = 14 - (-2)

6x - 9y + 12z - (3x + 2y - z) = -9 - (-2)

Simplifying, we get:

x - 3z = 16 (Equation 4)

3x - 11y + 13z = -7 (Equation 5)

Step 3: Multiply Equation 4 by 3 and add it to Equation 5:

3(x - 3z) + (3x - 11y + 13z) = 16(3) - 7

Simplifying, we have:

6x - 2y + 4z = 37 (Equation 6)

Step 4: Now we have the following two equations:

6x - 2y + 4z = 37 (Equation 6)

2x + y - 2z = 7 (Equation 2)

Step 5: We can now solve this system of equations. One way is to multiply Equation 2 by 2 and add it to Equation 6:

2(2x + y - 2z) + (6x - 2y + 4z) = 2(7) + 37

Simplifying, we get:

10x = 51

Dividing both sides by 10, we find:

x = 5.1

Step 6: Substituting the value of x into Equation 2, we can solve for y:

2(5.1) + y - 2z = 7

Simplifying, we have:

y - 2z = -3.2 (Equation 7)

Step 7: Substituting the values of x and y into Equation 6, we can solve for z:

6(5.1) - 2y + 4z = 37

Simplifying, we get:

4z = 1.8

Dividing both sides by 4, we find:

z = 0.45

Therefore, the solution to the system of planes is x = 5.1, y = -3.2, and z = 0.45.

b) The system of planes is represented by the following equations:

3x - 4y + 2z = 1

6x - 8y + 4z = 10

15x - 20y + 10z = -3

To solve this system, we'll again use the elimination method:

Step 1: Multiply the first equation by 2 and the second equation by 5 to create a cancellation:

6x - 8y + 4z = 2

30x -

I hope this is right!! :)

Answer:

2) 1885 km

3) 795 h 46 m 29 s

Step-by-step explanation:

2)

C = 2πr

C = 2 × 3.14159 × 300 km

C = 1885 km

3)

(1000000 km)/ (1885 km/tour) = 530.16477 tours

1 tour = 1 h 30 m = 1.5 h

530.16477 tours = 530.16477 × 1.5 h = 795.7747155 h = 795 h 46 m 29 s

Hello there, today we will solve your problem

First off we can right our ratio being 2:3

which can be phrased as 2x:3x

since 3x equals 15 we can say 1x equals 5

2*5=10

meaning she would have 10 guavas.

The equation of the line is y=4x-54.

To get the slope of the line parallel to the provided equation, which is necessary to solve this issue. In order to get the equation's slope, we must first transform the equation into slope-intercept form. Now that the parallel lines are equal in slope, both will be equal in slope.

The slope of parallel lines is the same. In the formula for the slope-intercept, y = mx + b, variable m stands for the slope and variable b for the y-intercept.

The slope of the equation y = 4 x +12 is 4. Consequently, any parallel line's slope will also equal 4.

Next, get the y-intercept of the new line by substituting the x and y coordinates for the given point (-8,18):

y=mx+b

y=4x+b

18=4×18+b

18=72+b

-54=b

Thus the equation of the new line is y=4x-54

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The cost of CDs has been decreasing for the past five years. The correct option is A.

Regression analysis is a group of statistical procedures used in statistical modeling to determine the relationships between a dependent variable and one or more independent variables.

A scatter plot is a particular kind of plot or mathematical diagram that displays values for typically two variables for a collection of data. It uses Cartesian coordinates. When the points are coded, a further variable can be seen.

In the given scatter plot it is observed that the vertical line is represented by the amount of the CDs and the horizontal line is represented by years.

The amount of CDs is decreasing with time on yearly basis therefore, the cost of CDs has been decreasing for the past five years.

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Answer:

Step-by-step explanation:

The compound interest at the end of 14 years compounded annually at a rate of 5% is $98,996.58

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. In Mathematics, compound interest is usually denoted by C.I.

The formula is given as

C.I = P(1 + r/n)^nt

Substituting the values into the formula

A = 50000(1 + 0.05/1)^1 * 14

A = 98,996.58

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Answer:

360 pupils

Step-by-step explanation:

7/8 = 168/x

168 divided by 7 is 24, so if you multiply 8 by 24 you will get the amount of girls in the school.

7/8= 168/192    

168 +192= 360

Answer:

720

Step-by-step explanation:

The lock requires that repetition is not allowed.

The possibles numbers are 0 - 9, that is, 10 digits.

The first number in the combination can be picked from the 10 digits.

This means that there are 10 possible choices.

The second number in the combination can now only be picked from 9 digits.

This means that there are 9 possible choices.

The third number in the combination can now only be picked from 8 digits.

This means that there are 8 possible choices.

Therefore, the number of possible outcomes in the combination is:

10 * 9 * 8 = 720 outcomes

Volume of beach ball or the amount of air will the beach ball hold is 2304π in³.

Formula

Volume of Sphere is 4/3πr³

The volume, V, of a sphere with radius r is  4/3πr³

By employing a technique that roughly represents the surface area of a sphere using square pyramids, it is possible to obtain the formula for the volume of a sphere using the formula for its surface area, which is 4πr^2.

Where r is the radius of the sphere .

As given

12 inches is the radius of a beach ball.

r = 12 in

Substitute the r in above volume equation,

V =4/3πr³

V=4/3π(12)³

V= 2304π in³

Therefore, the amount of air will the beach ball hold is 2304π in³.

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The possible first coordinate x with a slope of 3 is equal to -13/3.

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Based on the information provided, we can logically deduce the following data points and slope on the line:

Substituting the given data points into the slope formula, we have the following;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

3 = (4 - 8)/(x + 3)

3x + 9 = -4

3x = -13

x = -13/3

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Answer: \(y=-2x+6\)

Step-by-step explanation:

The slope of line l is

\(\frac{5-1}{0-2}=-2\)

Since parallel lines have the same slope, the slope of the line we need to find is -2.

Substituting into point-slope form,

\(y=-2(x-3)\\\\y=-2x+6\)

Answer:

3 pieces

I hope this helps

Step-by-step explanation:

X(1/3) = 1

x/3 = 1

X= 1×3 = 3

The value of n in the equation n/5 + 0.6 = 2 is 7.

It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

In this case, n/5 + 0.6 = 2

0.2n + 0.6 = 2

Collect the like terms

0.2n = 2 - 0.6

0.2n = 1.4

Divide

n = 1.4 / 0.2

n = 7

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Complete question

Solve for n

n/5 + 0.6 = 2

The required value of x is 22 degrees for the given figure.

Adjacent angles are a sort of additional angle. Adjacent angles share a common side and vertex, such as a corner point. Their points do not overlap in any manner.

As we know that supplementary angles are defined as when pairing of angles addition to 180° then they are called supplementary angles.:

According to the given figure, it can be written as follows:

2x + 24 + 6x - 20 = 180

8x + 4 = 180

8x = 180 - 4

8x = 176

x = 176/8

x = 22

Therefore, the required value of x is 22 degrees for the given figure.

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The complete question is as follows:

Find the value of x for the below figure.