Fill in the blank with a constant, so that the resulting quadratic expression is the square of a binomial.
\[x^2 + 22x + \underline{~~~~}.\]

The criminal will go down the rope safely if his acceleration is less than 9.81 m/s^2.

To get down safely without breaking the rope, a criminal who wants to escape from the third storey window of a jail, by going down a rope to the road below and has a mass of 75 kg while the rope can only support 65 kg without breaking can use the following method :Step-by-step explanation:

Calculate the acceleration produced by the criminal and find the maximum tension the rope can withstand.

According to Newton's second law, F = ma .Frictional force (f) acts upward and it opposes the weight of the criminal. Therefore, F = mg - f. If the criminal is accelerating downwards at a constant rate, a, the tension in the rope (T) is given by T = m(g - a).

If a is positive, then the tension in the rope is greater than mg and the rope breaks.

If a is negative, then the tension in the rope is less than mg and the rope is safe.

Let's assume that the tension in the rope is just equal to the breaking point.

Then:65*9.81 = 75* a + 65 *9.81a = 6.74 m/s^2

The criminal will go down the rope safely if his acceleration is less than 9.81 m/s^2.

This means that he should create additional friction by wrapping the rope around his legs, to increase the force of friction acting upwards. By doing this, he will decrease the net force acting downwards and thus reduce his acceleration.

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Answer: y=4/3x-8/3

Step-by-step explanation:

Slope-intercept form is y=mx+b.

Solve for m (the slope) first.

m=4/3

(you can use the points to solve for slope)

The y-intercept is -8/3 (as seen on the graph)

y=4/3x-8/3

The length of the side opposite the angle of 53.1 degrees in a right triangle with a hypotenuse of 10 cm is 8 cm.  (A)

This can be found using trigonometry and the Pythagorean theorem. The trigonometric function sine can be used to find the ratio of the length of a side to the length of the hypotenuse given an angle in a right triangle.

In this case, the sine of the angle 53.1 degrees is the ratio of the length of the side opposite the angle to the length of the hypotenuse, which is 10 cm.

Therefore, the length of the side opposite the angle 53.1 degrees can be found by multiplying the sine of the angle by the length of the hypotenuse, which is 10 cm * sin(53.1) = 8 cm.

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Any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

Given that S is a non-empty subset of Rⁿ such that any linear combination of vectors in S is again a vector in S. Therefore, to prove that S is a subspace of Rⁿ, we have to show that S satisfies three conditions. These conditions are as follows;

The condition for being a subspace of Rⁿ

Firstly, a subspace must be closed under addition. In other words, if x and y are any two vectors in S, then their sum x + y must be in S.

Secondly, a subspace must be closed under scalar multiplication. In other words, if x is any vector in S and c is any scalar, then cx must be in S.

Finally, a subspace must contain the zero vector, denoted by 0.S is a subspace of Rⁿ

From the conditions mentioned above, we can show that S is indeed a subspace of Rⁿ, since S satisfies all the required conditions.

Therefore, we can say that any non-empty subset of Rⁿ, where any linear combination of vectors in S is again a vector in S, is a subspace of Rⁿ.

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Answer:

6 r10

Step-by-step explanation:

If you do 215 divided by 32 you get 6.71875 so i just rounded your answers and got B) if not be its D)

Answer:

C

Step-by-step explanation:

When data is collected in a statistical study for only portion or subset of all element of interest we are using a sample.

We frequently collect data from samples, or smaller subsets of the population, as opposed to the entire population as a whole.

A sample is a subset of units chosen to represent all the individuals in the population. Because just a portion of the population was counted, it is only a partial enumeration. To estimate the characteristics for the total population of interest, data from the sampled units is used.

For instance, a medical study looks at how a certain disease spreads among city's stray canines. The population of interest in this case are the city's street dogs. This sample or population of interest corresponds to the overall population on which you want to draw conclusions.

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The height of the cylinder for the given volume is 12 yards and option 1 is the correct answer.

The density of a cylinder is determined by its volume, which represents how much material may be immersed in it or carried inside of it. The formula πr²h, where r is the radius of the circular base and h is the height of the cylinder, determines the volume of a cylinder. Any substance that can fill the cylinder consistently with liquid or another material may be used as the material.

Given that,

diameter = 8 yards

radius = 8/2 = 4 yards.

Volume = 602.88 cubic yard

The volume of the cylinder is given as:

V = πr²h

602.88 = (3.14)(4)²h

h = 12 yd

Hence, the height of the cylinder for the given volume is 12 yards and option 1 is the correct answer.

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Answer:

12!

Step-by-step explanation:

You got this!!

As per the volume of a rectangular prism, it is found that 34.76% of the container is empty.

Volume of a rectangular prism

The volume of the rectangle prism is calculated by multiplying the length, breadth and height of the prism.

The formula for the volume of rectangle prism is

V = l x w x h

where

l represents the length

w represents the width

h represents the height

Given,

A shipping container is in the form of a right rectangular prism, with dimensions of 30 ft by 8 ft by 7 ft 3 in.

Here we need to find if the container holds 1096 cubic feet of shipped goods, what percent is empty

According to the given question,

Let us consider the length is 30ft, Width is 8ft and Height is 7ft.

Here the value 3ft refers the depth.

That one is also multiplied with the volume.

Therefore, the volume of the container is

=> 8 x 7 x 30

=> 1680

Therefore, the volume of the container is 1680 cubic feet.

So, here we have to percentage of the empty space for that we have to find the difference of them and convert it into percentage,

=> 1680 - 1096

=> 584

The percent of empty space is,

=> x% of 1680 = 584

=> x% = 584/1680

=> x% = 0.3476

=> x = 34.76

Therefore, 34.76% of rectangular prism container is empty.

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Answer:

c

Step-by-step explanation:

The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c

The lighthouse keeper should land approximately 3 miles from the point on the shore nearest to the lighthouse in order to make the fastest possible time to the restaurant.

To determine the fastest possible time for the lighthouse keeper to reach the restaurant, we need to calculate the time it takes for him to row to the shore and then walk to the restaurant. The key is to minimize the total time taken.

Let's denote the distance from the landing point to the restaurant as x miles. The time taken to row to the shore can be calculated as 7 miles divided by the rowing speed of 2.7 mph, which is approximately 2.59 hours.

The time taken to walk from the landing point to the restaurant can be calculated as (14 + x) miles divided by the walking speed of 4 mph.

To minimize the total time, we need to find the value of x that minimizes the sum of the rowing time and the walking time. So, we can set up the equation:

Total time = 2.59 hours + (14 + x) miles / 4 mph

To find the value of x that minimizes the total time, we can take the derivative of the equation with respect to x, set it equal to zero, and solve for x.

However, given that we are asked to round the answer to the nearest whole number, we can simplify the problem by considering the value of x that yields the smallest whole number total time.

By trying different values of x, we can find the value that minimizes the total time.

When x = 0, the total time is 2.59 + 14 / 4 = 6.59 hours.

When x = 1, the total time is 2.59 + 15 / 4 = 6.84 hours.

When x = 2, the total time is 2.59 + 16 / 4 = 7.09 hours.

Continuing this process, we find that the smallest whole number total time occurs when x = 3.

Therefore, the lighthouse keeper should land approximately 3 miles from the point on the shore nearest to the lighthouse in order to make the fastest possible time to the restaurant.

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The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.

The correct option is A.

Place value, which is related to a digit's location in a number, is the amount that each digit is worth.

Given:

We have a decimal number 25.381.

From the given choices;

We have number 52.

In the number 52:

The place value of 2 is 2.

The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in 52.

Therefore, the number is 52.

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The complete question:

The value of the digit 2 in the number 25.381 is 10 times greater than the value of the digit 2 in which of the following numbers:

A) 52.

B) 25534.675

Answer:

36

Step-by-step explanation:

Conjugate of z = -3-5i

Therefore the expression is equivalent to (-3+5i)(-3-5i).

(-3+5i)(-3-5i)

=(-3)^2-(5i)^2

=9-(-25)

=36

Answer:

z (the conjugate of z) = 34

Answer:

La fórmula para calcular el balance (en dólares) de una inversión con una

A = P(1 + r/n)^(nt)

Donde:

A es el balance total después de t años

P es el depósito inicial

r es la tasa de interés anual expresada como decimal (5% = 0.05)

n es la frecuencia de capitalización por año (en este caso, 4 para compuestos trimestrales)

t es el tiempo en años

Sustituyendo los valores dados, la función que representa el balance después de t años es:

A(t) = 5000(1 + 0,05/4

b. Para encontrar el balance actual, podemos simplemente evaluar la función A en t = 0, lo que nos da:

A(0) = 5000(1 + 0,05/4

Por lo tanto, el balance actual de la cuenta es de $5000.

c. Supongamos que el costo de la matrícula y los gastos de su primer año en la universidad suman $20,000. Para determinar si la inversión cubrirá el costo, podemos evaluar la función A en t = 12 (es decir, después de 12 años desde el depósito inicial) y compararla con el costo de la matrícula y los gastos.

A(12) = 5000(1 + 0.05/4)^(4(12)) = $10,768.49

Como el balance de la cuenta después de 12 años es menor que el costo de la matrícula y los gastos, se necesitará más dinero para cubrir el costo del primer año de universidad. La cantidad adicional requerida será:

$20,000 - $10,768.49 = $9,231.51

Por lo tanto, se necesitarán $9,231.51 adicionales para cubrir el costo del primer año de universidad.

Step-by-step explanation:

tal vez te sirve esto

Answer:

y=0.20p + 0.15n

Step-by-step explanation:

I believe this is correct I am 90% positive that it is right.

The algebraic expression will be C = 0.20 p + 0.15 n

It is given that a pen cost $0.20 and a pencil cost $0.15.

We have to give expression for total cost of p pens and n pencils.

What will be the value if 2 times of x is added to x ?

The value will be 3x.

Cost of 1 pen = $0.20

Cost of p pens will be ;

= 0.20 p

Cost of 1 pencil = $0.15

Cost of n pencils = 0.15 n

If total cost is represented by C then ;

C =  0.20 p + 0.15 n

Thus , the algebraic expression will be C = 0.20 p + 0.15 n

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The coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.

A transformation can be defined as the movement of a point on a cartesian coordinate from its original (initial) position to a new location.

In Geometry, there are different types of transformation and these include the following:

Based on the information provided, triangle UVW would be rotated counterclockwise through an angle of 270 degree at origin to produce triangle U'V'W', we have:

\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\)

Therefore, the image of triangle UVW would be given by this matrix:

\(\left[\begin{array}{ccc}0&1\\-1&0\end{array}\right]\) \(\left[\begin{array}{ccc}-3&8&6\\8&4&-8\end{array}\right]\)

Image = \(\left[\begin{array}{ccc}8&4&-8\\3&-8&-6\end{array}\right]\)

Based on the image above, we can logically deduce that the coordinates of triangle U'V'W' include U'(8, 3), V'(4, -8) and W'(-8, -6) and this is represented by graph A shown in the image attached below.

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Answer:

hi friend

Step-by-step explanation:

Answer:

y=-1/2x+4

Step-by-step explanation:

the slope is -1/2x and y intercept is 4

Answer:

Fraction: \(\frac{1}{4}\)

Decimal: 0.25

Percentage: 25%

Step-by-step explanation:

Have a good day :)

Answer: (5, 7)

Step-by-step explanation: Midpoint formula is ((x1 + x2)/2, (y1+y2)/2) where (x1, y1) and (x2, y2) are points on a line. Thus

(3+7/2, 8+6/2) = (5, 7)

Answer: \(\Large\boxed{2}\)

Concept:

Here, we need to know the idea of the PEMDAS method.

PEMDAS is an acronym for the order of operations.

Solve:

Given expression

\(\dfrac{3^3~-~13}{11~-~2^2}\)

Simplify the exponents

\(=\dfrac{27~-~13}{11~-~4}\)

Simplify by subtraction

\(=\dfrac{14}{7}\)

Simplify the fraction

\(\Large\boxed{=2}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

11/2is the answer hope it helps

Answer:

0.41666666666

Step-by-step explanation:

Answer:

The value is 5/12

Answer:

y-4=3(x-2)

Step-by-step explanation:

y-y1=m(x-x1)

Answer:

-4

Step-by-step explanation:

The probability that the student drinks soda, given that they drink coffee, is 0.25.

Let's designate the proportion of students who regularly consume soda as "S," those who frequently consume coffee as "C," and those who regularly consume both as "B."

Since 40% of students frequently consume soda, there are 0.4S kids who do the same.

Additionally, there are 0.3S students who consume coffee because 30% of students do it frequently.

Additionally, since 10% of students consume both beverages, there are 0.1S students who also consume soda and coffee.

Students in the class S = 0.4S + 0.1S = 0.5S either drink soda or both.

The pupils in C = 0.3S + 0.1S = 0.4S either consume coffee or both.

So, given that the student drinks coffee, the probability of drinking soda is:

P(soda | coffee) = P(soda and coffee) / P(coffee)

                          = 0.1S / 0.4S

                          = 0.25.

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The probability that the number 6 will appear between 150 and 200 times inclusively is 0.926.

In the given question, one thousand independent rolls of a fair die will be made.

We have to compute an approximation to the probability that the number 6 will appear between 150 and 200 times inclusively.

Let n=1000 are independent trails.

The probability of success is constant, p=1/6

The probability of success is not constant,

q=1-1/6 = 5/6

let X be the number of times the die shows a 6.

μ = np

μ = 1000*1/6

μ = 166.7

σ=√npq

σ=√1000*1/6*5/6

σ=√5000/36

σ=11.785

Now we used the correlation continuity for finding the probability that number 6 will appear between 150 and 200 times is

P(150≤X≤200)=P(X≤200)-P(X<150)

P(150≤X≤200)=P(Z≤(200+0.5-166.7)/11.785)-P(Z≤(150-0.5-166.7)/11.785)

P(150≤X≤200)=P(Z≤2.87)-P(Z≤-1.46)

P(150≤X≤200)=0.998-0.072

P(150≤X≤200)=0.926

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Answer:

8

Step-by-step explanation:

I attached an image below. Basically the symbols || means absolute value, meaning the distance between that number and 0. It will always be a positive number. Then, I solved the equation as normal using PEMDAS, multiplying first then going left to right, then I got 8.

Hope this helps !!

-Ketifa

Answer:

The answer would be (-2, -5)

Step-by-step explanation:

3x - 8y= 34

2(7x + 4y = -34)

3x - 8y=34

14x + 8y= -68

----------------------

     17x= -34    divided by 17

       x = -2

3(-2) -8y= 34

-6 -8y =34 add 6

   -8y= 40  divide by -8

      y = -5

if you want to check the answer replacing -2 for x and -5 for y

7(-2) + 4(-5)= -34

-14 + (-20) = -34

-34 = -34

I hope this help sorry I'm not good explaining