A software development company is voting to elect a president, a secretary, a treasurer, and three directors. If a total of 11 qualified candidates applied for these positions, in how many ways can the positions be filled?

The limit of the function as x approaches -2 is 20.To find the limit of the function (if it exists), we can substitute the given value into the function and simplify. Given function: f(x) = 4x² + 5x - 6x + 2

To find the limit as x approaches -2, we substitute -2 into the function:

f(-2) = 4(-2)² + 5(-2) - 6(-2) + 2
      = 4(4) - 10 + 12 + 2
      = 16 - 10 + 12 + 2
      = 20

Therefore, the limit of the function as x approaches -2 is 20.

To write a simpler function that agrees with the given function at all but one point, we can use a graphing utility. By plotting the given function and observing its behavior, we can create a simpler function that matches the original function except at one point.

However, without further information about the specific behavior of the given function, it is not possible to provide a more detailed explanation or a graph of the simpler function.

For more question on function

https://brainly.com/question/11624077

#SPJ8

Answer:

C.18

Step-by-step explanation:

at the rate 18 buses would have departed

The the smallest positive solution to the Trigonometry sin(5x)cos(9x) - cos(5x)sin(9x) = - 0.25 is x = 3.617degree

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles

sin(5x)cos(9x) - cos(5x)sin(9x) = -0.25

sin(5x)cos(5x + 4x) - cos(5x)sin(5x + 4x) = -0.25

-sin( 5x - 9x) = -0.25

-sin (9x -5x) = -0.25

sin ( 4x) = 0.25

Using the sine inverse

arcsin(0.25) = x = 0.25268 rad ≅ 14.47 degree

so dividing this angle by 4

x = 3.617degree

Therefore, the smallest positive solution to the Trigonometry is x = 3.617degree

Learn more about trigonometric here;  https://brainly.com/question/24349828

#SPJ1

Answer:

10 fire hydrants

Step-by-step explanation:

(15)(5)= 17+15+21+12+x

x= 10

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

hope it helps...

have a great day!!

Answer:

10

Step-by-step explanation:

\(~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})\qquad (\stackrel{x_2}{7}~,~\stackrel{y_2}{6}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 7 -5}{2}~~~ ,~~~ \cfrac{ 6 -4}{2} \right) \implies \left(\cfrac{ 2 }{2}~~~ ,~~~ \cfrac{ 2 }{2} \right)\implies (1~~,~~1)\)

Answer:

1.58 ish

Step-by-step explanation:

For a logx y = z, x^z = y
So here, log4 9= 1.58 or so
1.5849625007

Answer:

We can use the property of similar triangles to solve this problem. The triangles formed by the tree, its shadow, the fence post, and its shadow are similar. Let's call the length of the tree's shadow "x". Then we can set up the following proportion:

(tree height) / (tree shadow length) = (fence post height) / (fence post shadow length)

Plugging in the given values, we get:

27 / x = 5 / 2

Cross-multiplying, we get:

27 * 2 = 5 * x

Simplifying, we get:

54 = 5x

Dividing both sides by 5, we get:

x = 10.8

Therefore, the length of the tree's shadow is 10.8 feet. Answer: (B) 10.8 feet.

The missing variables on item 2 are given as follows:

The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:

For the angle of 60º, we have that:

Hence the length o is given as follows:

tan(60º) = o/12.

\(\sqrt{3} = \frac{o}{12}\)

\(o = 12\sqrt{3}\)

Applying the Pythagorean Theorem, the length i is given as follows:

i² = 12² + \((12\sqrt{3})^2\)

i² = 576

i² = 24²

i = 24.

A similar problem, also about trigonometric ratios, is given at brainly.com/question/24349828

#SPJ1

Answer:

o = 12√3

i = 24

Step-by-step explanation:

From observation of the given right triangle, we can see that two of its interior angles measure 60° and 90°. As the interior angles of a triangle sum to 180°, this means that the remaining interior angle must be 30°, since 30° + 60° + 90° = 180°. Therefore, the triangle is a special 30-60-90 triangle.

The side lengths in a 30-60-90 triangle have a special relationship, which can be represented by the ratio formula a : a√3 : 2a, where "a" represents a scaling factor that can be any positive real number.

In triangle #2, the shortest leg is 12 units.

As "a" is the shortest leg, the scale factor "a" is 12.

The side labelled "o" is the longest leg opposite the 60° angle. Therefore:

\(o = a\sqrt{3}=12\sqrt{3}\)

The side labelled "i" is the hypotenuse of the triangle. Therefore:

\(i= 2a = 2 \cdot 12=24\)

Therefore:

Answer:

its true

Step-by-step explanation:

Answer:

Im sorry I don't quite understand but here's but I'm going by:

Step-by-step explanation:

4 blue tiles + 8 blue tiles, represents the sun 4+8. Which equals 12.

sorry if this doesn't help!

Answer:

the volume of the square pyramid is 2430 cubic cm

Answer:

1296 cm³

Step-by-step explanation:

V = a² x [√s²- (a/2)²] / 3

a = 18 cm

s = 15 cm

V = 18² x [√15²-(18/2)²] / 3 = 18² x [√225-81] / 3

V = 324 x (√144/3) = 1296 cm³

We can rewrite:

525 =  3*5*5*7

And the highest common factor of 525 and 70 is 35.

We want to write the number 525 as a product of the prime factors, to do so, just try to divide it by prime numbers (2, 3, 5, etc..) until you find the factors.

We can write:

525 = 5*105 = 5*5*21 = 3*5*5*7

Now we want to find the HCF of 525 and 70, we can rewrite 70 as:

70 = 7*10 = 2*5*7

The greatest common factor between the two is (5*7) = 35

Learn more about common factors at:

https://brainly.com/question/219464

#SPJ1

Answer:

-1.615 is the answer...

Step-by-step explanation:

Hope this helps....

Answer:

6

Step-by-step explanation:

to find the perimeter of a trapezoid you add all the sides together

therefore we do it backwards

24-3-6-9=6

Solution :-

We know that perimeter is the sum of all sides, and here we have been provided with perimeter and the length of three sides. Now, we can assume the length of other side as any variable, say x. And develop a linear equation, and solve it. Thus,

A/Q,

→ 3yd + 6yd + 9yd + x = 24yd

→ 18yd + x = 24yd

→ x = 24yd - 18yd

→ x = 6yd

Thus, the length of the fourth side is 6yd.

Hope that helps :)

Answer:

2 is the gcf.

Answer:

In order to find the GCF of no.'s we need to first look at the smallest no (which is 8, in this case)

Next, list down all the factors of 8.

1*8

2*4

4*2

8*1

Now, once you have listed all the factors for 8, find which factor of 8 goes with 18 and 70.

2 is the answer; because 2 goes into 8, 18 and 70.

Answer:

LOL i dont need money jus mark me brainliest :P

Step-by-step explanation:

\(distance = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)

\(AB = \sqrt{(6--2)^2 + (2-4)^2} = \sqrt{8^2 + 2^2} = \sqrt{68}\\\\BC = \sqrt{(1-6)^2 + (-1-2)^2} = \sqrt{5^2 + 3^2} = \sqrt{34}\\\\AC= \sqrt{(1--2)^2 + (-1-4)^2}} = \sqrt{3^2 + 5^2 } = \sqrt{34}\)

\(Clearly, this\ satisfies \ the\ Pythagoras\ theorem : AC^2 = AB^2 + BC^2\)

                                                                      \((\sqrt{68})^2 = (\sqrt{34} )^2 + (\sqrt{34} )^2\\\\68 = 34 + 34 \\68 = 68\\Hence\ satisfies .\)

Therefore,  the triangle ABC is a right angle triangle.

Answer:

- 6x² -x⁴/6 -1 because 6x² is co effectient

#a

#b

That be x and y

So

So

from eq(1)

Put in second one

Put in third one

Take it positive

Answer:

(a) (i)  Factorize \(\sf 4p-6pq+9q-6\)

Rewrite by swapping the order of the first two terms:

⇒ -6pq + 4p + 9q - 6

Factorize the first two terms and the last two terms separately:

⇒ -2p(3q - 2) + 3(3q - 2)

Factor out the common term (3q - 2):

⇒ (3q - 2)(-2p + 3)

(ii)

Square of the binomial: \((a+b)^2=a^2+2ab+b^2\)

Rewrite \(9.9\) as \(10 - 0.1\)

Therefore, \(a = 10\) and \(b = -0.1\)

Also, remember that multiplying a number by 0.1 is the same as dividing it by 10.  (when dividing a decimal number by 10, simply move the decimal point 1 place to the left).

\(\begin{aligned}\implies 9.9^2 & =(10-0.1)^2\\ & =10^2-2 \cdot 10 \cdot 0.1+0.1^2\\& = 100-\dfrac{2 \cdot 10}{10}+\dfrac{0.1}{10}\\& =100-2+0.01\\ & =98 + 0.01\\ & = 98.01\end{aligned}\)

(b) (i)

Let x = number of motor bicycles

Let y = number of cars

Given:

⇒ x + y = 15

Given:

⇒ 2x + 4y = 64

(ii)  Rewrite   x + y = 15  to make x the subject:

⇒ x = 15 - y

Substitute into 2x + 4y = 64  and solve for y:

⇒ 2(15 - y) + 4y = 64

⇒ 30 - 2y + 4y = 64

⇒ 30 + 2y = 64

⇒ 2y = 34

⇒ y = 17 cars

Substitute found value of y into  x = 15 - y  to find x:

⇒ x = 15 - 17 = -2 motorbikes

**There must be an error in the question, as with the given information, the number of motorbikes is -2, which is impossible.**

Here are the possible combinations of number of motorbikes (M) and number of cars (C) whose sum of tires is 64.  As you can see, there is no combination that sums to 15 vehicles:

0 M +  16 C = 16 vehicles

2 M +  15 C = 17 vehicles

4 M +  14 C = 18 vehicles

6 M +  13 C = 19 vehicles

8 M +  12 C = 20 vehicles

10 M +  11 C = 21 vehicles

12 M +  10 C = 22 vehicles

14 M +  9 C = 23 vehicles

16 M +  8 C = 24 vehicles

18 M +  7 C = 25 vehicles

20 M +  6 C = 26 vehicles

22 M +  5 C = 27 vehicles

24 M +  4 C = 28 vehicles

26 M +  3 C = 29 vehicles

28 M +  2 C = 30 vehicles

30 M +  1 C = 31 vehicles

32 M +  0 C = 32 vehicles

Answer:

The rate of change is 28.

Step-by-step explanation:

The equation is in slope-intercept form,  y = mx + b, where m is the slope, and b is the y-intercept.

Answer:

-3

Step-by-step explanation:

For an expression to be undefined,. the denominator must be equal to 0

Therefore, in order to make that expression undefined, we must equate the denominator to 0

6 + 2v = 0

2v = 0 - 6

2v = -6

v = -6/2

v = -3

So in order to make the expression to be equal to 0, v must be -3

Answer:

The choice D. r= - 45

Step-by-step explanation:

\( \frac{r}{15} = ( - 3) \\ \\ r = ( - 3) \times 15 \\ \\ r = - 45\)

Answer:

16y1yg1gyyq717177171716161yggqg1g2y2gqgq62g2gtqy2g

1jwjqhwhwjmnbhokmbhiknb

Answer:

x = 31°

Step-by-step explanation:

the sum of the 3 angles in a triangle = 180° , that is

x + 54° + 95° = 180°

x + 149° = 180° ( subtract 149° from both sides )

x = 31°

Based on the given information, the second brand, Cola, is the more affordable option in terms of cost per milliliter compared to Co Fizz.

To determine which brand of cola is more expensive, we need to compare the cost per unit volume for each brand.

For the first brand, Co Fizz, a pack contains 4 bottles, and each bottle has a volume of 500 ml. The cost of the pack is $2.50. Therefore, the total volume in a pack is 4 * 500 ml = 2000 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2.50 / 2000 ml = $0.00125 per ml.

For the second brand, Cola, a pack contains 10 bottles, and each bottle has a volume of 330 ml. The cost of the pack is $2. Therefore, the total volume in a pack is 10 * 330 ml = 3300 ml. To find the cost per milliliter (ml), we divide the total cost by the total volume: $2 / 3300 ml ≈ $0.000606 per ml.

Comparing the two brands, we can see that the cost per milliliter for Co Fizz is $0.00125, while the cost per milliliter for Cola is approximately $0.000606.

Since the cost per milliliter for Co Fizz is higher than the cost per milliliter for Cola, it can be concluded that Co Fizz is more expensive in terms of price per unit volume.

For more such question on brand. visit :

https://brainly.com/question/29129317

#SPJ8

Answer:

2hrs 30 mins

Step-by-step explanation:

if the buoy Is 12 up and 16 right than you can use Pythagorean theorem

a²+b²=c²

144+256=c²

400=c²

√400=√c²

20=c

20/8=2.5

2 hrs 30 mins

Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

Answer:

Z score is a statistical that corresponds to the standarization of the regular score to a normal dsitribution

The formula for Z score is Z = [X - mean ]./ (standar deviation)

Here X = 930.00; mean = 900.00; and standard deviation = 15.00

Then, Z = [930.00 - 900.00] / 15.00 = 30.00 / 15.00 = 2.00

Answer: 2.00

Step-by-step explanation:

Answer:

D. An infinite number of real solutions

Step-by-step explanation:

3(2x + 1) = 2(3x + 5) - 7

6x + 3 = 6x + 10 - 7

6x + 3 = 6x + 3

I hope this helps!