Five different awards are to be given to three students. Each student will receive at least one award. In how many different ways can the awards be distributed?

Answer:

B

D

D

Step-by-step explanation:

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Answer: 24

Step-by-step explanation: 6 x 4 = 24
24 - 8 = 16

Answer:

4:5:1

Step-by-step explanation:

so first of all the ratio will be 140:70:35 but after we simplify it with 35 we'll get the final simplified ratio which is 4:5:1

Answer:

The answer is "0.4329 ".

Step-by-step explanation:

P( three in favor of FA)

Select 3 out of 6 FA supporters then select 2 out of 5 FB supportive judges  

\(=\frac{^{6}_{C_{3}}\times ^{5}_{C_{2}}}{^{11}_{C_{5}}}\\\\=\frac{\frac{6!}{3!(6-3)!}\times \frac{5!}{2!(5-2)!}}{\frac{11!}{5!(11-5)!}}\\\\=\frac{\frac{6!}{3! \times 3!}\times \frac{5!}{2! \times 3!}}{\frac{11!}{5! \times 6!}}\\\\=\frac{\frac{6 \times 5 \times 4 \times 3!}{3 \times 2 \times 1\times 3!}\times \frac{5 \times 4 \times 3!}{2 \times 1 \times 3!}}{\frac{11 \times10 \times 9 \times 8 \times 7 \times 6! }{5 \times 4 \times 3 \times 2 \times 1 \times 6!}}\\\\\)

\(=\frac{ (5 \times 4) \times(5 \times 2)}{(11 \times 3 \times 2 \times 7 )}\\\\=\frac{ 20 \times 10 }{(11 \times 42)}\\\\=\frac{ 200 }{462}\\\\=\frac{100 }{231}\\\\=0.4329\)

James earned a $13 per hour rate and Alex earned a $12 per hour rate thus option (A) is correct.

The rate of change is the change of a quantity over 1 unit of another quantity.

Most of the time the rate of change is the change concerning time.

For example the speed 3meter/second.

As per the given number of hours and money earned table.

For James,

Rate of change or earned per hour = 26/2 = $13

For Alex,

Rate of change or earned per hour = 36/3 = $12

Hence "James earned a $13 per hour rate and Alex earned a $12 per hour rate".

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Answer:

It is a function

This is because a function is a mapping whose co-domain is a set of numbers

Answer:

Second quadrant

Step-by-step explanation:

Quadrant I ranges from \(0^\circ<\theta<90^\circ\)

Quadrant II ranges from \(90^\circ<\theta<180^\circ\)

Quadrant III ranges from \(180^\circ<\theta<270^\circ\)

Quadrant IV ranges from \(270^\circ<\theta<360^\circ\)

Answer:

f(x) = x³ - 4x + 6

f'(x) = 3x² - 4

a) f'(2) = 3(2²) - 4 = 12 - 4 = 8

6 = 8(2) + b

6 = 16 + b

b = -10

y = 8x - 10

b) 3x² - 4 = 0

3x² = 4, so x = ±2/√3 = ±(2/3)√3

= ±1.1547

f(-(2/3)√3) = 9.0792

f((2/3)√3) = 2.9208

c) 3x² - 4 = 8

3x² = 12

x² = 4, so x = ±2

f(-2) = (-2)³ - 4(-2) + 6 = -8 + 8 + 6 = 6

6 = -2(8) + b

6 = -16 + b

b = 22

y = 8x + 22

f(2) = 6

y = 8x - 10

The equation perpendicular to the tangent is y = -1/8x + 25/4

-The smallest slope on the curve is 2.92

The curve has the smallest slope at the point (1.15, 2.92)

The equations at tangent points are y = 8x + 16 and  y = 8x - 16

From the question, we have the following parameters that can be used in our computation:

y = x³ - 4x + 6

Differentiate

So, we have

f'(x) = 3x² - 4

The point is (2, 6)

So, we have

f'(2) = 3(2)² - 4

f'(2) = 8

The slope of the perpendicular line is

Slope = -1/8

So, we have

y = -1/8(x - 2) + 6

y = -1/8x + 25/4

We have

f'(x) = 3x² - 4

Set to 0

3x² - 4 = 0

Solve for x

x = √[4/3]

x = 1.15

So, we have

Smallest slope = (√[4/3])³ - 4(√[4/3]) + 6

Smallest slope = 2.92

So, the smallest slope is 2.92 at (1.15, 2.92)

Here, we set f'(x) to 8

3x² - 4 = 8

Solve for x

x = ±2

Calculate y at x = ±2

y = (-2)³ - 4(-2) + 6 = 6: (-2, 0)

y = (2)³ - 4(2) + 6 = 6: (2, 0)

The equations at these points are

y = 8x + 16

y = 8x - 16

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For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

What exactly is a linear inequality?

In mathematics, inequality denotes a mathematical statement with no equal sides. An inequality happens in mathematics when a connection results in a non-equal comparison of two expressions or two numbers. Any of the inequality symbols, such as greater than symbol (>), less than symbol (<), greater than or equal to symbol (≥), less than or equal to symbol (≤), or not equal to symbol (≠), replace the equal sign "=" in the sentence. In mathematics, inequalities are classified into three types: polynomial inequalities, rational inequalities, and absolute value inequalities.

The characters "< and >" denote severe inequalities, whereas ‘≤’ and ‘≥’  denote slack inequalities. A linear inequality looks to be a linear equation, however the formula is different.

Now,

As stated in Commutative property the order in addition does not matter and in addition property the value added on both sides does not affect the result.

In step 3 we can write this as 5x-x-5<11x+x-21

which will not change result and

in step 7, 21 is added both sides which will not change result.

Hence,

           For given linear inequalities in step 3 and 7 properties shown are Commutative property and addition property of inequality.

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Answer:

X=11

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Solve the equation backwards using a proportion, 80 - 14 = 66, now divde the 6 from 6x, meaning you also have to divide it from 66, leaving you with 11, now all there is, is x = 11, and that's your answer.

Answer:

1.5 MPH

Step-by-step explanation:

3/4 = 0.75

3/4 x 2 = 0.75 x 2 = 1.5

Answer: 8.06 Inches

The area of the circle is 28.26 ft². 3. The diameter of the circle is 8.06 inches.

The value of x in the triangles are 9.

For variable x : ax² + bx + c = 0, where a≠0 is a standard quadratic equation, which is a second-order polynomial equation in a single variable. It has at least one solution since it is a second-order polynomial equation, which is guaranteed by the algebraic basic theorem.

Given:

The triangles are congruent.

That means, their corresponding angles are also congruent.

In ΔJKL,

the sum of all the angles of the triangle is 180°.

So,

x²-2x + x + 29 + 3x + 52 = 180

x² + 2x - 99 = 0

Solving the quadratic equation,

x² +11x - 9x - 99 = 0.

x (x + 11) -9 (x + 11) = 0

x = 9 and x = -11

Here, we take x = 9.

Therefore, the value of x is 9.

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Answer:

x equals 8 due to 8^2 being 8x8=64

Step-by-step explanation:

Answer:

the answer is 105

Step-by-step explanation:

because 5×3=15 so 15×7 =105

Answer:

1. 3:2

2. 7:2

3. 63:56:24

4. 16:56:63

5. 84:56:16:63

the ages added up is 219

the uncle is the oldest

Step-by-step explanation:

I'm answering by ratios because I'm not exactly sure what you mean.

24:16 = 6:4 = 3:2

56:16 = 7:2

63:56:24 is already in its simplest form I think??

16:56:63  also in its simplest form

84:56:16:63

the ages added up is 219

the uncle is the oldest

Answer:

Y = -½x + 3/2

Y = -3x + 5

Y = 1/4x - 3¼

Step-by-step explanation:

Parallel implies they have the same gradient

Perpendicular implies the gradient is a negative reciprocal of the other.

This differential equation states that the rate of change of the amount of salt in the tank is equal to the difference between the rate at which brine containing salt is being added to the tank.

(a) The initial amount of salt in the tank is 50 lbs.

(b) The initial volume of solution in the tank is 100 gal.

(c) The concentration of salt being added to the tank is 1 lb of salt per gallon of brine.

(d) The rate at which the solution is being added to the tank is 5 gal/s.

(e) The rate at which the solution is being removed from the tank is 3 gal/s.

(f) The volume of the solution in the tank at time t can be represented by V(t) = 100 + (5 - 3)t = 100 + 2t gal.

(g) The concentration of salt in the tank at time t can be represented by C(t) = x(t) / V(t), where x(t) represents the number of pounds of salt in the tank at time t.

(h) A differential equation with initial conditions that models this mixture problem is:

dx/dt = 5 - 3 = 2 (lb/s), where x(0) = 50 lbs.

This differential equation states that the rate of change of the amount of salt in the tank is equal to the difference between the rate at which brine containing salt is being added to the tank and the rate at which brine is being removed from the tank. The initial condition x(0) = 50 lbs states that the initial amount of salt in the tank is 50 lbs. The units in this differential equation make sense as the rate of change of the amount of salt in the tank is in lbs/s and the amount of salt in the tank is in lbs.

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Answer:

the c.o.p is 14.25

Step-by-step explanation:

The Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.

For the stated question:

Relation :  x = b

Its absolute value of a negative is equal to the absolute amount of a positive alone.

Thus, the Y value can therefore be either positive or negative for every given X number, proving that this isn't a function.

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Answer:

(x + 5) and (x -1)

Step-by-step explanation:

Given

The attached graph

Required

The \(factors\) of the graph

The x \(values\) are where the \(curve\) \(touches\) the x-axis

The first is at:

\(x = -5\)

Add 5 to both sides

\(x +5= -5+5\)

\(x +5= 0\)

This implies that the first factor is: (x + 5)

The second is at:

\(x =1\)

Subtract 1 from both sides

\(x - 1 = 1 - 1\)

\(x - 1 = 0\)

This implies that the other factor is: (x - 1)

Answer:

-49

Step-by-step explanation:

\(\int _{-5}^{-2}\:\left(8\:w\left(r\right)-3\right)dr\) = \(\int _{-5}^{-2}\:8\:w\left(r\right)dr\) -3 (-2 -(-5)) = \(8 \int _{-5}^{-2}\:\:w\left(r\right)dr\) -9 =8(-5) -9 = -49

Sum of the interior angles of any triangle equal 180° .

Thus ;

\(x + 2x + x + 8 = 180\)

\(4x + 8 = 180\)

Subtract sides -8

\(4x + 8 - 8 = 180 - 8\)

\(4x = 172\)

Divided sides by 4

\( \frac{4}{4}x = \frac{172}{4} \\ \)

\(x = 43\)

So the angles are :

x = 43°

2x = 2 ( 43 ) = 86°

x + 8 = 43 + 8 = 51°

Thus the order from least to greatest ,

is : 43° , 51° , and 86°

_________________________________

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Answer:

12

Step-by-step explanation:

Answer : 12

Step-by-step explanation:

The method that i used here was FOIL

(2 - 2i)(3 + 3i)

2x3=6

2x3i=6i

-2ix3=-6i

-2ix3i=-6i^2

6 + 6i - 6i - 6i^2

6-6i^2

i^2 is also known as (-1)

6 - 6(-1)

6 + 6

= 12

The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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Answer: A

Step-by-step explanation:

Volume= LxWxH so we get 20x28x24 as given.

Volume= 13,440 which is the volume of the box given. ANd so if the box is 10,500cubic inches, we subtract to find the difference.

13,440-10,500= 2,940 Cubic Inches

Option A

Answer:

Part A:  13440 cubic inches.

Part B: A - 2940 cubic inches.

Step-by-step explanation:

The volume of the box = 24x20x28 = 13440 cubic inches.

The problem tells us that his gift is 10,500 cubic inches. So subtract that from the volume of the box.

13440-10500 = 2940 cubic inches. The answer is A.

Answer:

my answer would be m=-3/2

Step-by-step explanation:

given the coordinates

(0,0) - this is the origin and the first coordinate it will be treated as x1=0,y1=0

(-2,3)- this is the second given coordinate and will be treated as x2=-2,y2=3

To find the slope(m) we use the formula

m=y2-y1/x2-x1

m=3-0/-2-0

m=-(3/2)

m=-3/2

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