7 engineering students are lined up to give presentations at a hiring fair. one person demands to be either first or last. in how many ways can these students line up? (enter an integer.)

Para encontrar el equivalente decimal de una fracción, divide el numerador por el denominador. Debido a que el número en el numerador es más pequeño que el número en el denominador, debe colocar el punto decimal después y agregar ceros.

Un número decimal es un número formado por números enteros y fraccionarios, que al escribirse entre enteros y fracciones se separan por una coma, lo que se denomina punto decimal.

En números enteros, estamos familiarizados con los términos miles, centenas, decenas y unidades. Sin embargo, estos números aún pueden continuar con números más pequeños, a saber, décimas, centésimas, milésimas, etc.

En los números decimales, la parte cuyo valor es menor que el número de la unidad se coloca a la derecha de la coma, siempre que el número a la derecha del decimal sea un número de décimas, y cada número a la derecha sea una décima menor que el anterior.

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The probability is 0, 1/9, and 1/36 for getting a sum of 1, the sum of 5, and the sum of 12 occurs.

Probability is something that is to happen or a chance that an event will occur.

For two rolled dice, the total outcome is 6² = 36

Probability = Expected outcome/Total outcome

a) Pr of getting a sum of 1 = 0/36 = 0

we have a pair of dice, the least sum we can have is 2

b) The event that occurs a sum of 5 are (1, 4), (4, 1), (3, 2), (2, 3)

n(E) = 4

Pr of getting a sum of 5 = 4/36 = 1/9

c)The probability of getting a sum of 12 is (6, 6)

n(E) = 1

Pr of getting a sum of 12 = 1/36

Therefore, the probability that occurs a sum of 1, the sum of 5, and the sum of 12 are 0, 1/9, and 1/36 respectively.

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The measure for x is 1.414 units.

The area of mathematics that deals with particular angles' functions and how to use those functions in calculations. There are six popular trigonometric functions for an angle. Sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant are their respective names and acronyms (csc).

Given:

Hypotenuse= 2

angle= 45

Using Trigonometry

cos 45 = B/ H

1/√2 = B/ 2

B = 2/√2

B = √2

Hence, the measure of x is 1.414 unit.

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Answer:

No, it is not an infinite solution.

Step-by-step explanation:

4x-4=4              

Add 4 to each side

4x=8

Divide 4 on each side

x=2

Answer:

No

Step-by-step explanation:

An infinite solution has both sides equal. For example, 6x + 2y - 8 = 12x +4y - 16. If you simplify the equation using an infinite solutions formula or method, you'll get both sides equal, hence, it is an infinite solution.

The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10

The proof of this statement is constructive, as it will provide a way to explicitly construct a positive integer which is equal to the sum of the positive integers not exceeding it.

To prove this, we will use the following formula:

Let n = the positive integer

Let S = the sum of the positive integers not exceeding n

n = 1 + 2 + ... +n-1 + n

S = 1 + 2 + ... +n-1

Therefore, n = S + n

For example, let n = 5. The sum of the positive integers not exceeding 5 is 1 + 2 + 3 + 4 = 10. Therefore, 5 = 10 + 5, which is true. This proves that for any positive integer, n, it is equal to the sum of the positive integers not exceeding it.

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He answers the same number of questions correctly as he answers incorrectly in each round.

Equation is a physical and mathematical statement that describing physical phenomena and the relationship between different physical quantity typically consist of variable simple presenting physical quantity and then it personal variable may be pointed such as your energy.

For the pair of equations to be a system of equations, the number of questions answered correctly must equal the number of questions answered incorrectly in each round. Therefore, the equation 5x - 3y = 22 must have the same number of x and y variables, and the equation 10x - 4y = 46 must also have the same number of x and y variables. This is the only condition that must be true for the pair of equations to be a system of equations.

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4 square 6 in surd form​ is  4√6

A number system is defined as a system of writing to express numbers.

4 square 6 in surd form​

Any number of the form n √a, which cannot be written as a fraction of two integers is called a surd.

4 square 6 in surd form​ is 4√6

Decimal Form is 9.8

Hence, 4 square 6 in surd form​ is  4√6

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The speed of the car travelled after converting 85 meter per hour into feet per second is equal to ( 0.08 feet per seconds )(round to 2 decimal places)

Speed of the car in meter per hour is equal to 85 mph.

Conversion of unit  meter per hour in feet per second is :

1 meter = 3.28084 feet

1 hour = 60 minutes

          = 3600 seconds

85 mph = ( 85 × 3.28084 feet ) / ( 3600 seconds )

⇒ 85 mph = ( 278. 8714 feet ) / ( 3600 seconds )

⇒ 85 mph = ( 0.07746 feet per seconds )

⇒ 85 mph = ( 0.08 feet per seconds )( round to 2 decimal places )

Therefore, the car travelled in feet per seconds is equal to ( 0.08 feet per seconds ).

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The required correct answer is A. the five-number summary.

A box and whisker plot, often known as a box plot, shows a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary. A box is drawn from the first quartile to the third quartile in a box plot. At the median, a vertical line passes through the box.

The correct answer is A. the five-number summary. A boxplot is a graphical representation of the distribution of a set of data, and it provides information about the shape, spread, and skewness of the data. The five-number summary is used to construct a boxplot and includes the minimum value, first quartile (Q1), median, third quartile (Q3), and maximum value.

The boxplot uses these five values to display the range of the data and highlight any outliers or unusual observations. Knowing the five-number summary is sufficient to create a boxplot, while knowing all of the individual observations or the mean and standard deviation is not necessary.

Final answer: A. the five-number summary.

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The tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate, After 20 minutes, the amount of salt in the tank is still 50 grams.

In order To calculate the amount of salt in the tank after 20 minutes, we basically use the formula:  Salt (in grams) = (Amount of salt in the tank x Time) / Total volume.So, after 20 minutes, the amount of salt in the tank is:  (50 grams x 20 minutes) / 240 liters = 8.33 grams.    

As we can see, both methods produce the same result, confirming that the amount of salt in the tank after 20 minutes is still 50 grams. since the rate of pumping in salt water is equal to the rate of pumping out salt water, so the total amount of salt remains the same.

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A tank contains 240 liters of fluid in which 50 grams of salt is dissolved. pure water is then pumped into the tank at a rate of 6 l/min; the well-mixed solution is pumped out at the same rate. find the number of grams of salt in the tank after 20 minutes

The solution to the given Inequality |2x − 3| ≥ 7 is; x ≤ −2 or x ≥ 5

An absolute value inequality is defined as an expression with absolute functions as well as inequality signs. For example, the expression |x + 4| > 2 is an absolute value inequality containing a greater than symbol.

The absolute value inequality we want to solve is;

|2x − 3| ≥ 7

What this means is;

2x - 3 ≥ -7   or 2x - 3 ≥ 7

Thus;

2x - 3 ≥ -7

Add 3 to both sides to get;

2x ≥ -4

Divide both sides by 2 to get;

x ≤ -2

For 2x - 3 ≥ 7

Add 3 to both sides to get;

2x ≥ 10

Divide both sides by 2 to get;

x ≥ 5

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Answer:

Option D: x ≤ −2 or x ≥ 5

Step-by-step explanation:

i took the test xx

Answer:

the solution to the system is x = 1 and y = 5/2.

Step-by-step explanation:

To find the values of x and y, we can simplify each equation in the system and then substitute the value of x into the other equation to find y.

Starting with the first equation:

y - 1 = 3x / 2

2 * (y - 1) = 3x

3x = 2y - 2

Next, we substitute the value of 3x/2 from the first equation into the second equation:

5x + 1 = 4x

x = 1

Finally, we can substitute the value of x = 1 into the first equation to find y:

y - 1 = 3 * 1 / 2

y - 1 = 3 / 2

y = 5 / 2

So the solution to the system is x = 1 and y = 5/2.

Answer: Tony

Step-by-step explanation: What I did is I took the 7.02 and multiplied it by 4 to make the 50 200 and I got 28.08 so since the time for Simon is larger than the time for Tony, tony went faster because it look him less time. Hope this helps!

Answer: Tony was faster

Step-by-step explanation: To find who ran faster we multiply Tony's time by 4. If it took Tony 7.02 seconds for 50 yards we can multiply that by for to find how long it would have taken him at that speed to run 200 yards.

7.02 x 4 = 28.08

If circuit boards are randomly selected for testing, the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833. So, the correct option is b .

This is a geometric distribution problem, where we are trying to find the probability of the number of trials (inspections) until the first success (defective board). The probability of success (finding a defective board) on each trial is 0.02 and the probability of failure (not finding a defective board) on each trial is 0.98.

The formula for the probability of exactly k trials until the first success is given by:

P(X = k) = (1 - p)^(k-1) * p

where p is the probability of success and k is the number of trials.

Plugging in p = 0.02 and k = 10, we get:

P(X = 10) = (1 - 0.02)^(10-1) * 0.02 = 0.9833

So the probability it takes 10 circuit boards to be inspected before a defective board is found is 0.9833.

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The height of the plant A would be 95cm, while the height of the plant B would be 87 cm

We can use an equation to represent the height of each plant as a function of time t:

Plant A: h_A = 75 + 10t

Plant B: h_B = 55 + 12t

We want to find the time t at which the two plants will be the same height, so we can set the two equations equal to each other:

75 + 10t = 55 + 12t

Solving for t, we get:

10t = 20

t = 2

So, after 2 months, the two plants will be the same height. To find the height at that time, we can substitute t = 2 into either equation:

h_A = 75 + 10t = 75 + 10 * 2 = 95

h_B = 55 + 12t = 55 + 12 * 2 = 87

So, after 2 months, the plants will both be 95 cm tall.

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The most appropriate measure of spread for this data is standard deviation, because the boxplot is skewed to the right.

The most appropriate measure of spread for this data is standard deviation. The data is represented by a boxplot, which is a graphical representation of the data that shows the median, quartiles, and range of the data. In this case, the boxplot is skewed to the right, meaning that the data is not normally distributed. When the data is not normally distributed, the standard deviation is the best measure of spread to use. Standard deviation measures the spread of data by calculating the distance between each data point and the mean, and then taking the average of these distances. This allows us to accurately measure the spread of data that is not normally distributed. Therefore, standard deviation is the most appropriate measure of spread for this data.

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we can look at this as some exponential growth, now, the page hit 10,000 views in the first day, that is, at the end of the 1st day and the beginning of the 2nd day, so the compounding of 30% will occur only for the next 4 days, that is, the 2nd, 3rd, 4th and 5th days, so we can say starting initially with 10000, how much will it be 4 days later?

[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &10000\\ r=rate\to 30\%\to \frac{30}{100}\dotfill &0.3\\ t=\textit{elapsed time}\dotfill &4\\ \end{cases} \\\\\\ A = 10000(1 + 0.3)^{4} \implies A=10000(1.3)^4\implies \boxed{A = 28561}[/tex]

The perimeter of the trapezoid is 50 cm.

A trapezoid, commonly referred to as a trapezium, is a quadrilateral or a polygon with four sides. It has a set of parallel opposing sides and a set of non-parallel sides. The bases and legs of the trapezoid are known as the parallel and non-parallel sides, respectively.

Given the trapezoid,

let us consider ABCD be the trapezoid,

so given angle B = 90°

AB = 12 cm, AD = 10 cm, and BC = 15 cm

let us draw a perpendicular from D on BC parallel to AB

which forms the right triangle DEC

from the Pythagorean theorem, from the figure attached in the image.

DC² = DE² + EC²

DC² = 12² + 5²

DC² = 144 +25

DC² = 169

DC = 13 cm

perimeter is the sum of all sides,

P = AB + BC + AD + DC

P = 12 + 15 + 10 + 13

P = 50 cm

Hence perimeter is 50 cm.

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Answer:

x = 50

Step-by-step explanation:

50 + 2x = 150

2x = 100

x = 50

answer is c because i did math and got it right

Explanation:

The common ratio is calculated by dividing each term by its previous one.

The nth term formula for this particular geometric sequence is:

[tex]a_n = a*r^{n-1}\\\\a_n = 7*4^{n-1}\\\\[/tex]

The last step is to plug n = 8 into that formula.

[tex]a_n = a*r^{n-1}\\\\a_n = 7*4^{n-1}\\\\a_8 = 7*4^{8-1}\\\\a_8 = 7*4^{7}\\\\a_8 = 7*16384\\\\a_8 = 114688\\\\[/tex]

The 8th term is 114688

Avoid using commas to separate out the digits. This is because commas are used to separate each term of the geometric sequence.

8th term of this geometric sequence is 114,688.

In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the 8th term, we need to know the common ratio and the first term. Given that the first term is 7 and the second term is 28, we can find the common ratio as follows:

r = 28/7 = 4

Now that we know the common ratio, we can find the 8th term by multiplying the first term by the common ratio raised to the power of 7:

a_8 = 7 * r^(8-1) = 7 * 4^7 = 7 * 16,384 = 114,688

Therefore, the 8th term of the sequence is 114,688.

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The area of the shaded region of the semicircle is 108π mm²

Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.

Given that, a semicircle with a diameter of 24 mm, a circle is fitted in it, we need to find the measurement of the area which is shaded.

The diameter of the smaller circle = radius of semicircle.

Therefore,

Radius of smaller circle = 24/4 = 6 mm

To find the area of shaded region, we will subtract the area of the smaller circle from the area of semicircle.

Area of a circle = π × radius² {area of semicircle is just half of it}

Area of shaded region = π × 12² - π × 6²

= π(144-36)

= 108π

Hence, the area of the shaded region of the semicircle is 108π mm²

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The sphere has a volume of 113 cubic units, the sphere's radius is 2.99 units.

Volume is the quantity of space a thing occupies, whereas capacity is a measure of the substance it can store, such as a solid, a liquid, or a gas. While capacity can be measured in virtually any other unit, such as liters, gallons, pounds, etc., volume is measured in cubic units.

the sphere's diameter.

Having said that,

The sphere's volume is equal to[tex]4/3 \pi r^3.[/tex]

The volume is already known.

[tex]113 = 4/3 (3.14) r^3[/tex]

339 = 4 (3.14) r³

339/4 = 3.14 r³

84.75 = 3.14 r³

84.75/3.14 = r³

26.99 = r³

r = ∛26.99

r = 2.99

Consequently, the sphere's radius is 2.99 units.

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Complete question -

Consider a sphere whose volume is 113 cubic units what will be the radius of the mirror?

The length of the candle was 13.5 inches before it was lit.

Let the length of candle in the beginning be c.

Constant rate of change in length of candle=  1.2 inches per hour

Since rate of change is constant so the length of candle can be represented by a linear function [Linear function has constant rate of change.]

Linear function : f(x)= mx+c , where x= independent variable.

m= constant rate of change and c= initial value of function.

Let x = Number of hours after the candle was lit.

Put m=  1.2 , x= 3 and f(x)= 10.5 , we get

c= 13.5

Hence, the length of the candle was 13.5 inches before it was lit.

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The flower associated to the given probability is the sunflowers.

We want to find the probability of randomly choosing a flower is:

Now, remember that the probability of randomly selecting a type of flower is equal to the quotient between the number of that type of flower and the total number of flowers.

Here we know that the probability is:

P = 0.5

We can rewrite that as:

P = 1/2

If we rewrite the denominator as 16, we will get:

P = 8/16

And we know that there are 8 sunflowers, then sunflower is the correct option.

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The complete question is:

There are 16 flowers in a vase. Four flowers are daisies, 1 is rose, 3 are tulips and the rest are sunflowers. Suppose the probability of randomly choosing a flower is 0.5

Which of the following flowers could it be?

The first five terms will be -4, 3, 10, 17 and 24.

The 34th term will be 227

An arithmetic sequence is one in which each phrase grows by adding or removing a certain constant, k. The difference between consecutive terms in an arithmetic series is always the same and is known as the common difference d.

Based on the information, it should be noted that the AP is given as An = - 11 + 7b

First term = -11 + 7(1) = -4

Second term = -11 + 7(2) = 3

Third term = -11 + 7(3) = 10

Fourth term = -11 + 7(4) = 17

Fifth term = 24

The 34 term will be:

= -11 + 7(34)

= 227

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Given the explicit formula for an arithmetic sequence find the first five terms and the term named in the problem. An=-11+7b. Find a34

On dilating the point X(6,5) with scale factor of -2, the value is obtained as X(-12,-10).

What is dilation?

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial shape should be stretched or contracted during a dilatation.

The coordinate point for X is given as X(6,5).

The dilation is centered at the origin (0,0).

The dilation scale factor is given as -2.

To find the value of X' use the formula -

X(a,b) → X[(a×(-2)) , (b×(-2))]→ X'

Substitute the values in expression -

X(6,5) → X[(6×(-2)) , (5×(-2))]

X(6,5) → X'(-12,-10)

Therefore, the coordinate point is X'(-12,-10).

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The following binary number has the value of 157 in decimal form.

Step 1: Compose the binary number in writing. 10011101

Multiplying each binary digit by the corresponding power of two in step two:

1x27 + 0x26 + 0x25 + 1x24 + 1x23 + 1x22 + 0x21 + 1x20

Solve the powers in Step 3:

1x128+0x64+0x32+1x16+8+4+0x2+1x1=128+0 + 0 + 0 + 16+8+4+0 + 0 + 1

Step 4: Add the figures listed above:

128 + 0 + 0 + 16 + 8 + 4 + 0 + 1 = 157.

A binary number is a number that is expressed in the binary system or base 2 numeral system, according to digital technology and mathematics. It talks about numerical values.by the two distinct digits 1 (one) and 0 (zero). The base-2 system is the positional notation that uses 2 as the radix.

A number that has been divided into a whole and a fraction is called a decimal. To express the numerical value of entirely and partially entire quantities between integers, decimal numbers are used.

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The initial value of the first investment was M = Rs.12,000,000 and the initial value of the second investment was N = Rs.16,000,000.

Let's assume the initial investment in the first investment be M and the initial investment in the second investment be N.

We know that the annual return from the first investment is 3% of M and the annual return from the second investment is 5% of N.

So, the total annual return (T) is:

T = 0.03M + 0.05N = 1160000

The investor increases his investment in the first investment by 25%, so the new investment in the first investment becomes:

M1 = M + 0.25M = 1.25M

And the new annual return from the first investment becomes:

R1 = 0.03 * 1.25M = 0.0375M

Similarly, the new investment in the second investment becomes:

N1 = N + 0.40N = 1.40N

And the new annual return from the second investment becomes:

R2 = 0.05 * 1.40N = 0.07N

So, the new total annual return (T1) is:

T1 = R1 + R2 = 0.0375M + 0.07N

And the increase in the total annual return is:

410,000 = T1 - T

We have 2 equations with 2 variables (M and N), so we can solve for them.

0.0375M + 0.07N = 0.03M + 0.05N + 410000

Expanding and solving the equation we get:

M = 12,000,000

N = 16,000,000

So, the initial value of the first investment was M = Rs.12,000,000 and the initial value of the second investment was N = Rs.16,000,000.

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