A company has been forced to reduce its number of employees. Today the company has 33% fewer employees than it did a year ago. If there are currently 268 employees, how many employees did the company have a year ago?

Answer:

x³-3x²-40x+84

Step-by-step explanation:

y = (x-7)(x-2)(x+6)

 = (x²-9x+14)(x+6)

 = (x³-9x²+14x)+(6x²-54x+84)

 = x³-3x²-40x+84

Answer:

k = 5.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope, and b is the y-intercept(y when x = 0).

Perpendicular lines

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to the line y=x−285.

This line has slope 1, so the line we want to find the equation has slope [tex]m = -1[/tex]

Then

[tex]y = -x + b[/tex]

Passes through (7, 0)

This means that when [tex]x = 7, y = 0[/tex]. So

[tex]y = -x + b[/tex]

[tex]0 = -7 + b[/tex]

[tex]b = 7[/tex]

So

[tex]y = -x + 7[/tex]

Find the value of k given that the line through (k, 2)

This means that when [tex]x = k, y = 2[/tex]. So

[tex]y = -x + 7[/tex]

[tex]2 = -k + 7[/tex]

[tex]k = 7 - 2 = 5[/tex]

The value of k is k = 5.

Answer:   [tex]2(\dfrac{1-e}{\pi})[/tex] or StartFraction 2 (1 minus e) Over pi EndFraction

Step-by-step explanation:

The average rate of function f(x) over the interval [a,b] is given by:-

[tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

Given  : [tex]f(x)=e^{\sin x}[/tex]

The average rate of change over [tex][\dfrac{\pi}{2},\pi][/tex] will be:

[tex]\dfrac{f(\pi)-f(\dfrac{\pi}{2})}{\pi-\dfrac{\pi}{2}}=\dfrac{e^{\sin \pi}-e^{\sin \dfrac{\pi}{2}}}{\dfrac{\pi}{2}}\\\\=\dfrac{e^0-e^1}{ \dfrac{\pi}{2}}\\\\=2(\dfrac{1-e}{\pi})[/tex]

Hence, the average rate of change over [tex][\dfrac{\pi}{2},\pi][/tex]  is [tex]2(\dfrac{1-e}{\pi})[/tex].

Answer:

2 (1 minus e) Over pi

Step-by-step explanation:

edge 2023

Answer:

Difference = 5 meters

Step-by-step explanation:

Given that:

Length of shadow of building = 20 meter

Height of woman = 1.8 meters

Shadow length of woman = 2.4 meters

Height of building = x

Ratio of building's height to shadow = x : 20

Ratio of woman's height to shadow = 1.8 : 2.4

x : 20 :: 1.8 : 2.4

Product of mean = Product of extreme

20 * 1.8 = 2.4x

2.4x = 36

Dividing both sides by 2.4

[tex]\frac{2.4x}{2.4}=\frac{36}{2.4}\\x=15[/tex]

Difference in height and shadow = 20 - 15 = 5 meters

Hence,

Difference = 5 meters

Answer:

[tex]\huge\boxed{y=5-\frac{2}{3}x}[/tex]

Step-by-step explanation:

With the equation [tex]\displaystyle 2x+3y=15[/tex], we can solve for y by algebraically manipulating the question until we have y isolated on one side.

It's important to note that if we do something to one side, we have to do it to another. Just as [tex]5=5[/tex], adding two to both sides still makes it true [tex]5+2=5+2, 7=7[/tex].

Therefore, this equation for y is [tex]\displaystyle y = 5 - \frac{2}{3}x[/tex] .

Hope this helped!

2x + 3y = 15

3y = 15 - 2x

y = 15 - 2x/3

Answer:

12.8 seconds

Step-by-step explanation:

Create a proportion where x is the number of seconds for 80 feet

[tex]\frac{25}{4}[/tex] = [tex]\frac{80}{x}[/tex]

Cross multiply and solve for x

25x = 320

x = 12.8

So, the answer is 12.8 seconds

Step-by-step explanation:

6/10*300=180

60% of 500 is 300

6/10x=300 x=500

60/300=1/5=20%

Answer:

The answer is 40.

Step-by-step explanation:

Calculate within the parenthesis. After calculate the outside by the inside.

Answer:

-6

Step-by-step explanation:

hey laudu

[tex]3a + b + 4[/tex]

[tex]3( - 2) + ( - 4) + 4[/tex]

[tex] - 6 - 4 + 4[/tex]

[tex] - 6[/tex]

Step-by-step explanation:

❀ [tex] \underline{ \underline{ \text{Given}}} : [/tex]

❀ [tex] \underline{ \underline{ \text{To \: find}}} : [/tex]

✏ [tex] \underline{ \underline{ \text{Solution}}} : [/tex]

All you need to do is plug the value and simplify !

⟶ [tex] \tt{3 \times ( - 2) + ( - 4) + 4}[/tex]

⟶ [tex] \tt{ - 6 + ( - 4) + 4}[/tex]

⟶ [tex] \tt{ - 6 - 4 + 4}[/tex]

⟶ [tex] \tt{ - 10 + 4}[/tex]

⟶ [tex] \boxed{ \tt{ - 6}}[/tex]

[tex] \red{ \boxed{ \boxed{ \tt{Our \: final \: answer : \boxed{ \underline{ - 6}}}}}}[/tex]

Hope I helped ! ♪

Have a wonderful day / night ! ♡

▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁▁

Answer:

We have point P(-3,-6).

Step-by-step explanation:

We want to find a point P(x,y).

Since it is on the directed line segment AB in the ratio 3:4, it means that:

[tex]P - A = \frac{3}{3+4}(B - A)[/tex]

So

[tex]P - A = \frac{3}{7}(B-A)[/tex]

We apply this to both the x-coordinate and y-coordinate of P.

x-coordinate:

x-coordinate of A: -9

x-coordinate of B: 5

x-coordinate of P: x

So

[tex]P - A = \frac{3}{7}(B-A)[/tex]

[tex]x - (-9) = \frac{3}{7}(5-(-9))[/tex]

[tex]x + 9 = \frac{3}{7} \times 14[/tex]

[tex]x + 9 = 6[/tex]

[tex]x = -3[/tex]

y-coordinate:

y-coordinate of A: -9

y-coordinate of B: -2

y-coordinate of P: y

So

[tex]P - A = \frac{3}{7}(B-A)[/tex]

[tex]y - (-9) = \frac{3}{7}(-2-(-9))[/tex]

[tex]y + 9 = \frac{3}{7} \times 7[/tex]

[tex]y + 9 = 3[/tex]

[tex]y = -6[/tex]

We have point P(-3,-6).

Answer: Set A is greater than set B

Step-by-step explanation:

You can see that the scale of set A is larger than the scale of set B. Therefore making set A greater than set B

Answer:

the y-intercept is -2, hope this helps! :]

(0, -2)

Hope it helps.

Do comment if you have any query.

Answer:

0.86

Explanation:

He answered 43 out of 50 questions.

As a fraction this is written  

43

50

To convert this fraction to a decimal fraction divide 43 by 50 .This

can be done on a calculator to obtain 0.86

Step-by-step explanation:

Brainliest?

The required probability is [tex]\dfrac{1}{12}[/tex].

Important information:

Total number of marbles is:

[tex]4+3+2=9[/tex]

The probability of getting a blue marble is [tex]\frac{2}{9}[/tex].

After removing a marble, the number of remaining marbles is 8. So, the probability of getting a green marble is [tex]\frac{3}{8}[/tex].

Now, the probability that the first marble is blue and the second marble is green is:

[tex]P=\dfrac{2}{9}\times \dfrac{3}{8}[/tex]

[tex]P=\dfrac{1}{12}[/tex]

Therefore, the required probability is [tex]\dfrac{1}{12}[/tex].

Find out more about 'Probability' here:

https://brainly.com/question/10697254

Answer:

35+4x+5+6x=180

10x=180-40

x=140/10

x=14

Answer:

reflection and rotation

Step-by-step explanation:

Answer:

(0,2)

Step-by-step explanation:

X=0 and y=2

Answer:

930m

Step-by-step explanation:

It says they were 900 feet in the air below him is the ocean so thats 900 meters away from him and the shark is 30 feat below the surface of the ocean so you would do 900+30=930m so the shark is 930m away from him

Answer:

12.54m by 12.54 and 8.54m by 8.54m

Step-by-step explanation:

Area of a square = L²

L is the side length of the room

The total area of the two square room = A₁+A₂

T = A₁+A₂

T = L₁²+x²

If the two square rooms have a total floor area of 230 m², then;

L₁²+x² = 230. ..... 1

If one room is 4 meters bigger each way than other, then;

L₁ = x + 4 .... 2

where x is the length of the smaller room

Substitute equation 2 into 1;

From 1: L₁²+x² = 230

(x+4)²+x² = 230

x²+8x+16+x² = 230

2x²+8x+16-230 = 0

2x²+8x-214 = 0

x²+4x-107 = 0

x = -4±√16-4(-107)/2

x = -4±√16+428/2

x = -4±21.07/2

x = 17.07/2

x = 8.54m

L₁ = x+4

L₁ = 8.54+4

L₁ = 12.54m

Hence the dimensions of the room is 12.54m by 12.54 and 8.54m by 8.54m

Answer:

answer is A

Step-by-step explanation:

hope this helps!

Answer:

18

Step-by-step explanation:

Solve for c by cross multiplying

Answer:

7 seconds

Step-by-step explanation:

Distance of the coin above the water is modeled by the equation

[tex]y=-16x^2+96x+112[/tex]

where [tex]x[/tex] is time taken to cover the distance

Now equating with zero.

[tex]0=-16x^2+96x+112\\\Rightarrow 16x^2-96x-112=0\\\Rightarrow x=\dfrac{-\left(-96\right)\pm \sqrt{\left(-96\right)^2-4\times \:16\left(-112\right)}}{2\times \:16}\\\Rightarrow x=7, -1[/tex]

So, time taken by the coin to hit the water is 7 seconds.

Answer:

86 thousand 5 hundred and 3

Step-by-step explanation:

Answer:

15% probability that 7 adults selected at random from the town all have health insurance.

Step-by-step explanation:

(sample/population)^number of times selected

(76/100)^7 = (0.76)^7 = 0.15 = 15%

The correct model of the height of rocket above water is;

h(t) = -16t² + 96t + 112

Answer:

time to reach max height = 3 seconds

h_max = 256 ft

Time to hit the water = 7 seconds

Step-by-step explanation:

We are given height of water above rocket;

h(t) = -16t² + 96t + 112

From labeling quadratic equations, we know that from the equation given, we have;

a = -16 and b = 96 and c = 112

To find the time to reach maximum height, we will use the vertex formula which is; -b/2a

t_max = -96/(2 × -16)

t_max = 3 seconds

Thus, maximum height will be at t = 3 secs

Thus;

h_max = h(3) = -16(3)² + 96(3) + 112

h_max = -144 + 288 + 112

h_max = 256 ft

Time for it to hit the water means that height is zero.

Thus;

-16t² + 96t + 112 = 0

From online quadratic formula, we have;

t = 7 seconds

Answer:

b) False, all integers are whole numbers, but not all whole numbers are integers

a. The concentration of the solution is  0.05 kg/L. b. The amount of salt is   154 kg after 4.5 hours. c. The concentration of salt in the solution in the tank approaches 0 as the time approaches infinity.

a. The concentration of the salt in the tank initially is given by the amount of salt divided by the volume of water:

0.025 kg/L = 100 kg / 2000 L = 0.05 kg/L

b. Let t be the time in minutes. The amount of salt in the tank after t minutes is given by:

100 kg + 0.025 kg/L × 8 L/min × t

To find the amount of salt after 4.5 hours, we convert the time to minutes:

4.5 hours × 60 minutes/hour = 270 minutes

And substitute this value of t into the equation:

100 kg + 0.025 kg/L × 8 L/min × 270 min = 100 kg + 54 kg = 154 kg

c. The concentration of salt in the solution in the tank as the time approaches infinity is given by:

154 kg / (2000 L + 8 L/min × t) as t approaches infinity

As t approaches infinity, the volume of water in the tank approaches infinity, so the concentration of salt in the solution approaches 0.

So, the concentration of salt in the solution in the tank approaches 0 as the time approaches infinity.

Learn more about the concentration of the salt here:

https://brainly.com/question/14177007

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