twice a number added to 4 is 28

Answer:

The answer is 440 pieces of checked luggage

Step-by-step explanation:

Mean = 380

Standard deviation = 20

No. of pieces of checked luggage for 1 standard deviation = 20 pieces

Therefore, Mean for 3 standard deviations above the mean = 3 × 20 = 60

Now, number of pieces of checked luggage 3 standard deviations above the mean = Mean for 1 standard deviation + Mean for 3 standard deviations above the mean

⇒ 380 + 60 = 440 pieces

To solve the equation 2x - 10 / 4 = 3x, multiply both sides by 4, simplify, and solve for x to find its value as -1.

Step 1: Multiply both sides of the equation by 4 to get rid of the fraction:
4 * (2x - 10) / 4 = 4 * 3x

Step 2: Simplify the equation:
2x - 10 = 12x

Step 3: Rearrange the equation to solve for x:
2x - 12x = 10
-10x = 10
x = -1

The standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]

Further Explanation:

The random variable X follows binomial distribution.

[tex]\boxed{X \sim {\text{Bin}}\left( {n,p} \right)}[/tex]

Here, n represents the total number of experiments and p denotes the probability of the event.

Apply central limit theorem.

[tex]\boxed{X \sim {\text{Normal}}\left( {np,np\left( {1 - p} \right)} \right)}[/tex]

The mean of the binomial distribution can be calculated as follows,

[tex]\boxed{{\text{Mean}} = n \times p}[/tex]

The standard deviation of binomial distribution can be calculated as follows,

[tex]\boxed{{\text{Standard deviation}} = \sqrt {np\left( {1 - p} \right)} }[/tex]

Given:

Coin is tossed 72 times.

Explanation:

Consider X is the random variable that head will occur.

The probability of head occur is [tex]p = \dfrac{1}{2}.[/tex]

The mean can be calculated as follows,

[tex]\begin{aligned}{\text{Mean}}&= 72\times \frac{1}{2}\\&= 36\\\end{aligned}[/tex]

The standard deviation of the number of heads can be calculated as follows,

[tex]\begin{aligned}{\text{Standard deviation}}&= \sqrt {72 \times \frac{1}{2}\left( {1 - \frac{1}{2}} \right)} \\&= \sqrt {72 \times\frac{1}{2} \times \frac{1}{2}}\\&=\sqrt{\frac{{72}}{4}}\\&= \sqrt {18}\\&= 4.24\\\end{aligned}[/tex]

Hence, the standard deviation for the number of heads that will be tossed is [tex]\boxed{4.24}.[/tex]

Learn more:

1. Learn more about normal distribution https://brainly.com/question/12698949

2. Learn more about standard normal distribution https://brainly.com/question/13006989

3. Learn more about confidence interval of mean https://brainly.com/question/12986589

Answer details:

Grade: College

Subject: Statistics

Chapter: Binomial Distribution

Keywords: coin, tossed 72 times, number of heads, binomial distribution, standard normal distribution, standard deviation, test, measure, probability, low score, mean, repeating, indicated, normal distribution, percentile, percentage, proportion, empirical rule.

Final answer:

To find when the population of the city will reach 140 thousand, the formula a = 118e⁰.⁰²⁴t must be solved, resulting in approximately 3.52 years after 1998.

Explanation:

The formula a = 118e^0.024t models the population of a city, in thousands, t years after 1998. To find when the population reaches 140 thousand, set the formula equal to 140 and solve for t:
a = 118e⁰.⁰²⁴t
140 = 118e⁰.⁰²⁴t
t = (ln(140/118)) / 0.024 ≈ 3.52 years after 1998.

The degree of a monomial is the sum of the exponents of the variables.

For example:

monomial: 257 x^3 y^5 z^21.

The degree is the sum of the exponents of x, y and z, this is 3 + 5 + 21 = 29.

When a monomial is just a number, it means that the exponents of the variables are zero. For example:

- 9 x^0 y^0 z^0 = - 9 * 1 * 1 * 1 = - 9.

This is your case, the monomial -9 has degree 0, which is the option B.

Final answer:

Sasha reads a total of 2775 minutes over 30 days, calculated using the formula for the sum of an arithmetic sequence.

Explanation:

To calculate the total number of minutes Sasha reads over 30 days, we note that she starts with 20 minutes on the first day and reads 5 minutes more each subsequent day. This is an arithmetic sequence where the first term (a1) is 20 minutes, the common difference (d) is 5 minutes, and the number of terms (n) is 30.

We can use the formula for the sum of an arithmetic sequence: Sn = n/2 (2a1 + (n - 1)d).

Plugging in the given values gives us S30 = 30/2 (2(20) + (30 - 1)(5)).

Now we calculate: S30 = 15(40 + 29(5)) = 15(40 + 145) = 15(185) = 2775 minutes.

Therefore, Sasha reads a total of 2775 minutes over the course of 30 days.

Answer:

-14

Step-by-step explanation:

khan academy

Final answer:

To calculate the amount of cardboard used for each box, we need to find the surface area of the hexagonal base and the lateral surface area. We can use the formula for the surface area of a hexagon to find the base area. Then, we multiply it by the height of the box and add the two areas together.

Explanation:

To find the amount of cardboard used for each box, we need to calculate the surface area of the hexagonal base and the lateral surface area. The surface area of a hexagon can be found using the formula:

Surface Area = 3 x √3 x s^2

where s is the length of the side of the hexagon. Given that the side length is 39 cm, we can substitute this into the formula to find the surface area of the hexagonal base. Once we have the surface area, we can calculate the lateral surface area by multiplying it by the height of the box, which is 4.7 cm. Adding the two areas together will give us the total amount of cardboard used for each box.

The distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10.

The distance between two points can be found using the distance formula: d = √((x2 - x1)^2 + (y2 - y1)^2). In this case, the coordinates of the two points are (3,8) and (-9,8). Plugging these values into the formula, we get:

d = √((-9 - 3)^2 + (8 - 8)^2)
d = √((-12)^2 + (0)^2)
d = √(144 + 0)
d = √144
d = 12

Therefore, the distance between the points (3,8) and (-9,8) is 12. The correct answer is option B) 10

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Bella's actual room dimensions are 18 feet by 12 feet, resulting in an actual area of 216 square feet. This was determined by applying the scale factor from the drawing to the actual room size.

To determine the actual dimensions of Bella's room based on her drawing, we first need to use the provided scale factor. According to the scale, 1 inch on the drawing is equal to 3 feet in actual size. We can calculate the actual dimensions by multiplying the length and width of the drawing by the scale factor.

The drawing is 6 inches long by 4 inches wide.

Actual length: 6 inches × 3 feet/inch = 18 feet

Actual width: 4 inches × 3 feet/inch = 12 feet

Now, to determine the actual area of Bella's room, we multiply the actual length by the actual width:

Actual area = actual length × actual width

Actual area = 18 feet × 12 feet = 216 square feet

Z= k/x

when x is 6, Z= 2

2=k/6

k=2*6

k=12

Z=12/X

when x = 13

Z=12/13

Z=0.923

To drive 500 miles, taking into account both driving time and oil stop time, it would take 11 hours and 15 minutes.

The length of the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.

In a 30-60-90 triangle, the ratio of the lengths of the sides is as follows:

- The length of the shorter leg is x.

- The length of the longer leg is x[tex]\sqrt{3}[/tex].

- The length of the hypotenuse is 2x.

Given that the hypotenuse of the larger triangle is 16 centimeters, we can set up the equation:

2x = 16

Solving for x:

x = [tex]\frac{16}{2}[/tex] = 8

Now, we know that the length of the longer leg of the larger triangle is x[tex]\sqrt{3}[/tex] = 8[tex]\sqrt{3}[/tex] centimeters.

Since the hypotenuse of the larger triangle becomes the longer leg of the smaller triangle, the longer leg of the smaller triangle is 8[tex]\sqrt{3}[/tex] centimeters.

The question is:

There are two triangles. Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. the hypotenuse of the larger triangle is 16 centimeters. What is the number of centimeters in the length of the longer leg of the smaller triangle?

Answer:

The Answer Is 1/4

Step-by-step explanation:

Ur brain xd

Answer:

six divided by the square root of thirteen

Step-by-step explanation:

hey there,

< sin θ = [tex]\frac{O}{H}[/tex]

So that means O = 2 and H = 3. In order to find cot θ, first let's find tan θ.

tan θ = [tex]\frac{O}{B}[/tex]

We only know what O is equal to, not B. So let's draw out a triangle.

7  

◢   6

 B

As you can see (sorry for the poor triangle), this is a right triangle. In order to find an unknown part, use [tex]a^2 + b^2 = c^2[/tex]!

[tex]6^2 + B^2 = 7^2[/tex]

B = ±√13

Obviously, a side of a triangle can't be negative, so it stays positive. Now we can find tangent!

tanθ =  [tex]\frac{6}{\sqrt{13} }[/tex]

But, we're not done here. We're trying to find cotθ.

cotθ = [tex]\frac{1}{tan}[/tex]θ

[tex]\frac{1}{\frac{6}{\sqrt{13} } }[/tex] = [tex]\frac{\sqrt{13} }{6}[/tex]

That's your final answer! >

Hope this helped! Feel free to ask anything else.

Answer:

The correct equation is [tex]-3.7n-4=-11.9[/tex]

Step-by-step explanation:

Let

n-------> the number

we know that

The equation that represent the expression “four less than [tex]-3.7[/tex] times a number is [tex]-11.9[/tex] " is equal to

[tex]-3.7n-4=-11.9[/tex]  

The equation that Daniella wrote represents the expression "[tex]-3.7[/tex] less than four times a number is [tex]11.9[/tex] "

Answer:

The coefficient of the variable should be -3.7 because of the word “times.” The words “four less than” mean that 4 will be subtracted from 3.7n. “Is” represents the equals sign, and “-11.9” is the second expression. The correct equation is -3.7n – 4 = -11.9.

Step-by-step explanation:

Edg math

The expression -3(6.3x + 7y - 2.5) expands to -18.9x - 21y + 7.5 using the distributive property by multiplying each term inside the parentheses by -3.

To use the distributive property to expand the expression -3(6.3x + 7y - 2.5), you multiply each term inside the parentheses by -3. The distributive property lets you reverse the distributive law and turn it into factors (multiples).

-3 × 6.3x = -18.9x
-3 × 7y = -21y
-3 ×-2.5 = 7.5

Once each term is multiplied, the expanded expression is:   -18.9x - 21y + 7.5

Final answer:

To prove lines are parallel, their slopes must be equal, and to prove they are perpendicular, their slopes must be negative reciprocals. To write an equation for a parallel line, use the same slope as the original; for a perpendicular line, use the negative reciprocal of the original line's slope. Manipulating a line involves changing either its slope or intercept.

Explanation:

To use slope to prove that lines are parallel or perpendicular, you need to compare their slopes. Two lines are parallel if their slopes are equal. Conversely, two lines are perpendicular if their slopes are negative reciprocals of each other, meaning that one slope is the negative inverse of the other (e.g., the slope of one line is 2 and the other is -1/2).

To write an equation of a line so that it is parallel to a given line, you must use the same slope as the given line. If the equation of the given line is y = mx + b, then the equation of a parallel line will be y = mx + c, where c is a different y-intercept. To write an equation of a line so that it is perpendicular to a given line, you use the negative reciprocal of the slope of the given line. If the slope of the given line is m, then the slope of the perpendicular line will be -1/m.

For example, consider a line with the equation y = 3x + 9, which signifies a slope of 3 and a y-intercept of 9 based on Figure A1. A parallel line would have a slope of 3 but could have a different y-intercept, such as y = 3x + 4. A perpendicular line would have a slope of -1/3, so it could be something like y = -1/3x + 5.

Manipulating a line involves changing its slope (m) or intercept (b). Changing the slope will tilt the line, while changing the intercept will shift the line up or down on the graph. Understanding how to read and manipulate a graph is crucial for visualizing these changes.