In how many ways can you select a committee of four students of a group of nine students?

The person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

To determine how high up the person was shot, we can use the principles of projectile motion and the dimensions of the blood drop. Since we have the horizontal distance and the dimensions of the blood drop, we can assume that the drop followed a parabolic trajectory.

First, let's convert the distance from feet to meters for consistency. 5.1 feet is approximately 1.554 meters. Now, we need to calculate the time of flight. Since there is no information about the drop's initial velocity or angle, we cannot calculate the exact time. However, we can estimate it by assuming a reasonable range of velocities.

Let's assume the drop was traveling between 5 and 20 meters per second. With a distance of 1.554 meters, the estimated time of flight would be between 0.0777 and 0.311 seconds.

Next, we need to calculate the vertical displacement. We have the dimensions of the blood drop, with a width of 0.8 mm and a length of 2.1 mm. Assuming the drop maintained a spherical shape while in motion, we can take the average of the width and length to find the diameter. So, the diameter is approximately 1.45 mm, which is 0.00145 meters.

Using the estimated time of flight, we can calculate the vertical displacement using the formula:

Vertical displacement = (1/2) * g * t^2

where g is the acceleration due to gravity (approximately 9.8 m/s^2). Plugging in the estimated values, the vertical displacement ranges from 0.0038 to 0.0301 meters (3.8 to 30.1 mm).

Therefore, based on the given information, the person was likely shot from a height between 3.8 and 30.1 mm above the location where the blood drop landed.

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Answer:

11

Step-by-step explanation:

we know this because there are 5 people saying they have 3 and 6 people saying they have between 4-7

Answer:

The scientific notation is a method of writing very large or very small numbers in a more compact and easy to read format. It is expressed in the form of a x 10^n, where "a" is a number between 1 and 10, and "n" is an integer.

To write 464000 in correct scientific notation, we need to move the decimal point to the left until we get a number between 1 and 10. We count the number of places we moved the decimal point, and that will be the exponent of 10.

So, we can write 464000 as:

4.64 x 10^5

Therefore, the correct scientific notation of 464000 is 4.64 x 10^5.

Step-by-step explanation:

Answer:

y=11x

Step-by-step explanation:

we use formula y2-y1/x2-x1 with 2 of the order pairs

22-11/2-1

11/1

11 is the slope

We find y intercept by finding when x is equal to zero and we subtract 11 until we find the 0 x unit since it goes down 11 every time

When x is zero y is zero so we write it like this

Y=11x

Hopes this helps please mark brainliest

On solving the provided question, we can say that - the range \(|x + 1| = 0\) \(x + 1 = 0 = > x = -1\) and \(y = 3\)

Finding the variable's greatest observed value (maximum) and deducting the least observed value will yield the range (minimum). Limits of variation or potential range: a variety of steel costs; several styles; The size or scope of an action or operation: insight. how far a weapon's projectile can or will travel. The number in a list or set between the lowest and maximum is referred to as a range. Line up all the numbers before locating the region. After that, take away (get rid of) the lowest number from the greatest number. The solution provides the list's range.

The regions where the absolute values are zero are known as the vertex points of an absolute value function.

\(|x + 1| = 0\\x + 1 = 0\\x = -1\)

\(y = |-1 + 1| + 3\\y= 0 + 3\\y = 3\)

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The coefficient of \(x^{7}\) is 16796160.

For this, we have to find the coefficient of \(x^{7}\) in \((3x+4)^{10}\)

General Term: This term symbolizes all of the terms in the binomial expansion of (x + y)^n.

The general term in the binomial expansion of (x + y)^n is

T(r+1) = nCr x^(n-r)y^r.

Here the r-value is one less than the number of the term of the binomial expansion. Also, nCr is the coefficient, and the sum of the exponents of the variables x and y is equal to n.

We can use the general term for this.

\(T_{r+1} = (nCr) a^{n-r} x^{r}\)

Since we have to find  \(x^{7}\),

\(T_{3+1} = (10C3)(3x)^{7} 4^{3} \\T_{3+1} = [(10C3)3^{7} 4^{3} ]x^{7}\)

This is the coefficients of \(x^{7}\)

Calculating,

10C3 = 120 (using combinations)

\(3^{7} = 2187\\4^{3} = 64\)

Therefore, multiplying the 3,

Coefficients of \(x^{7}\) = 120 * 2187 *64

= 16796160

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Answer:

Step-by-step explanation:

Answer: To calculate the expected value, we need to multiply each possible outcome by its probability and then add up the results.

The probability of selecting a gold marble is 3/41, the probability of selecting a silver marble is 8/41, and the probability of selecting a black marble is 30/41.

The winnings/losses associated with each outcome are $3 for gold, $2 for silver, and -$1 for black.

Step-by-step explanation:

Therefore, the expected value can be calculated as follows:

(3/41) x $3 + (8/41) x $2 + (30/41) x (-$1)

= $0.073

The expected value is $0.073, which means that on average, you can expect to win $0.073 per game if you play this game many times.

Therefore, if you play this game, you can expect to win a small amount of money on average, but it is not a guaranteed win.

References:

Grinstead, C.M. and Snell, J.L. (2006). Introduction to Probability. American Mathematical Society.

"Expected Value," Investopedia, accessed May 14, 2023, https://www.investopedia.com/terms/e/expectedvalue.asp.

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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Answer:

3.Yes, because triangle ABC has a 90 degree angle.

4.No, because triangle XYZ doesn’t have a 90 degree angle.

Step-by-step explanation:

7! = 5040 ways

You will have $50,000 in your account after 50 years.

We have,

Simple interest formula is given by:

I = Prt

Where:

I = interest earned

P = principal amount (initial investment)

r = interest rate

t = time (in years)

Here,

P = $10,000

r = 8%

t = 50 years

So, the interest earned after 50 years will be:

I = Prt

= 10000 x 0.08 x 50

= $40,000

The total amount in the account after 50 years will be the initial investment plus the interest earned:

Total amount = $10,000 + $40,000 = $50,000

Therefore,

You will have $50,000 in your account after 50 years.

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Answer:

1.5

Step-by-step explanation:

Answer:

1 1/2

Step-by-step explanation:

-2 1/4 = \(-\frac{(2*4)+1}{4}= -\frac{9}{4}\)

-1 1/2 = \(-\frac{(1*2)+1}{2}=-\frac{3}{2}\)

-2  1/4 ÷ -1 1/2 = \(-\frac{9}{4} * -\frac{2}{3}\)

                      = \(\frac{3}{2}\)

                     = 1 1/2

Use KCF method

Keep the first number.

Change division to multiplication

Flip the second number

Answer:

assuming you want to cover 18 ft x 15 ft:

18 x 15 = 270 ft²

1.5 x 1.5 = 2.25 ft² per tile

270 ft²/ 2.25 per tile = 120 tiles

Answer:

Answer is

1,2,3,4,5

5,10,15,20,25

just did the k12 test

Answer:

1,2,3,4,5

5,10,15,20,25

Step-by-step explanation:

Answer:

40\(\pi\) or 125.66

Step-by-step explanation:

Use the formula 2\(\pi\)r² + 2\(\pi\)rh

2\(\pi\)(2)² + 2\(\pi\)(2)(8)

8\(\pi\) + 32\(\pi\)

= 40\(\pi\) or 125.66

The coordinates of the reflected point P' will be (4, -3).

When a point is reflected over the x-axis, its y-coordinate changes sign.

In this case, the point P has coordinates (4,3).

To reflect it over the line x=3, we need to keep its x-coordinate the same and change its y-coordinate to its opposite.

So, the x-coordinate of the reflected point will still be 4, but the y-coordinate will become -3.

Therefore, the coordinates of the reflected point P will be (4, -3).

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Answer:

Step-by-step explanation:

In a case whereby Juan buys candy that costs $8 per pound and will spend at least $48 on candy  the possible numbers of pounds he will buy written in inequality is is p>5 (at least 5 pounds).

Inequality in math refers to a statement that one quantity is either greater than, less than, or not equal to another quantity. Inequalities are often represented using symbols such as "<" (less than), ">" (greater than), or "≤" (less than or equal to) and "≥" (greater than or equal to). For example, the inequality "x > 3" states that the variable "x" is greater than the value of 3. The inequality "y ≤ 5" means that the variable "y" is less than or equal to 5.

From the question, p = number of pounds Juan will buy.

candy=costs $8 per pound

$20/$4 = 5 pounds

p>5

at least 5 pounds

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The required area of the lune is (D) √3/4 - π/24.

The measurement that expresses the size of a region on a flat or curved surface is termed area.

Surface refers to the area of a surface or the boundary of a tri structure, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

So,

The lune's area is equal to the smaller semicircle's area minus the segment's area.

The area of the segment is equal to the sum of the areas of the sector and the triangle formed by the intersection points and the larger semicircle's center.

Additionally, because all of the sides are one unit, the triangle thus constructed is an equilateral triangle.

Area of the lune = π * 1/8 (60/360 * π * 1² - √3/4 * 1²)

Area of the lune = π/8 - π/6 + √3/4

= √3/4 - π/24

Therefore, the required area of the lune is (D) √3/4 - π/24.

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Answer: 2.5>9.5

Step-by-step explanation: maybe we should both pay attention to math

The journal entry for the sale of the bonds on June 1, 2022 would be:

Date           Account title and explanation                 Debit              Credit

June 1        Cash                                                     $ 343, 200

                 Premium on bonds payable                                          $ 13, 200  

                 Bonds payable                                                           $ 330, 000

When a company issues bonds, it needs to record the issuance in its accounting records. Determine the terms of the bond issuance, including the face value of the bonds, the interest rate, the maturity date, and any other terms that may apply.

Cash should be debited by the amount acquired from the sale of the bond which is :

= 330, 000 x 104 / 100

= $ 343, 200

If there is a premium, which means bond selling price is greater than par value, take this to the Premium on Bonds Payable account . The premium where is:

= 343, 200 - 330, 000

$ 13, 200

The rest should be credited to Bond Payable.

There is no given question in the first picture so please repost.

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As x tends to negative one from the left, the value of f(x) tends to positive infinity. As x → -1⁻, f(x) → ∞.

In Mathematics and Geometry, the vertical asymptote of a function simply refers to the value of x (x-value) which makes its denominator equal to zero (0).

By critically observing the graph of this rational function f(x) shown below, we can logically deduce that its vertical asymptote is at x = -1 and x = 2, and its horizontal asymptote is at y = 3.

In this context, we can logically deduce that the value of f(x) tends towards positive infinity, as x tends to negative one from the left;

As x → -1⁻, f(x) → ∞.

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Given:

p and q are the two distinct solutions to the equation

\((x-3)(x+3)=21x-63\)

To find:

The value of p-q if p>q.

Solution:

We have,

\((x-3)(x+3)=21x-63\)

\((x-3)(x+3)=21(x-3)\)

\((x-3)(x+3)-21(x-3)=0\)

\((x-3)(x+3-21)=0\)

\((x-3)(x-18)=0\)

Using zero product property, we get

\(x-3=0\text{ and }x-18=0\)

\(x=3\text{ and }x=18\)

Here, 18>3, so p=18 and q=3.

Now,

\(p-q=18-3\)

\(p-q=12\)

Therefore, the value of p-q is 12.

Answer:

The answer is 5, the "Expert Verified" is wrong :)

Step-by-step explanation:

First we try factoring the left side to simplify it. Now we can multiply both sides by (x+5)and solve.

Answer:

17.1

Step-by-step explanation

a^2+b^2=c^2

2^2 + 17^2 = c^2

4 + 289 = c^2

293 = c^2

square root of 293 or 17.1

Answer:

Step-by-step explanation:

x = −2 x = −1 x = 0 x = 1 x = 2

The amount of money she will have to pay for booking of the holidays would be = £220

The total amount of money that will cost Merrisa for booking of holidays = £660

The fraction of the total cost that she needs to deposit = 1/3

Therefore, the actual amount that she needs to deposit = 1/3 of £660

= 1/3× 660

= £220

Therefore, in conclusion, Merrisa would have to pay a total of £220 for booking of the holidays. This total amount is ⅓ of total cost of booking.

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Answer:

Step-by-step explanation:

You have to use the quadratic formula

x = -b +/- \(\sqrt{(b^{2} -4ac)/2a\)

and then you can simplify both answers so the first one would be -13/2 and the second would be -27/2

you usually have to reject an answer but since there is no equal sign in the question, you should be fine