The piecewise function h(x) is shown on the graph.
What is the value of h(3)?
-2
ch
0-1
0 1
02
2.
-5 4 -3 -2 -14
2 3 4 5 x
-2
2
-3
-5

Answer:

Zero, based on the information provided.

Step-by-step explanation:

The output rate of the teller machine is (1 transaction/6 minutes).  The input rate is (1 customer/10 minutes).  This means that the machine completes a cycle faster than the customers arrive, on the average.  I don't know how an average can be calculated without more information.  If we assume customers arrive every 10 minutes, and no one screws up the machine, that there should be no waiting line.   Is there more information about when the customers arrive?  E.g., 50 arrive in the first hour the machine is open.

If the average transaction at an automatic teller can be completed in six minutes and customers arrive at the average rate of one every ten minutes. The average number of customers in the queue is: B. 0.900 customers.

M represent Markovian (memoryless) arrivals and service times

1 represents a single server.

Arrival rate (λ) is 1 customer every 10 minutes and the service rate (μ) is 1 customer every 6 minutes.

The formula to determine the average number of customers in the queue (Lq) is:

Lq = (λ^2) / (μ * (μ - λ))

Plugging in the values:

λ = 1/10

μ = 1/6

Lq = ((1/10)^2) / ((1/6) * ((1/6) - (1/10)))

Lq = (1/100) / ((1/6) * (10 - 6)/60))

Lq = (1/100) / ((1/6) * (4/60))

Lq = (1/100) / ((1/6) * (1/15))

Lq = (1/100) / (1/90)

Lq = (1/100) * (90/1)

Lq = 90/100

Lq = 0.9

Therefore, the correct option is B.

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Step-by-step explanation:

To find the derivative of

3x+5, apply sum rule

[tex] \frac{d}{dx}(3x + 5) = \frac{d}{dx} 3x + \frac{d}{dx} 5[/tex]

The derivative of

[tex] \frac{d}{dx} kx = k[/tex]

And

[tex] \frac{d}{dx} c = 0[/tex]

So we have

[tex] \frac{d}{dx} 3x + 5 = 3[/tex]

So the derivative of the function is 3,

Since linear equations have a constant slope, the slope at any point will be 3.

So the slope of the tangent line is 3.

Answer:

[tex]7000[/tex]

Step-by-step explanation:

Recall the form of the difference of squares.

[tex]x^2 - y^2 = (x+y)(x-y)\\\\\\[/tex]

Now let's apply it to your numbers:

[tex]85^2 - 15^2 = (85 + 15)(85 - 15)[/tex]

Simplify:

[tex](100)(70) = 7000[/tex]

Answer: it would be 34

Step-by-step explanation:

Answer:

See below for proof

Step-by-step explanation:

[tex]\tan^2x\sin^2x\\\\(\sec^2x-1)(\sin^2x)\\\\(\frac{1}{\cos^2x}-\frac{\sin^2x}{\sin^2x})(\sin^2x)\\\\(\frac{\sin^2x-\sin^2x\cos^2x}{\sin^2x\cos^2x})(\sin^2x)\\\\\frac{\sin^2x-\sin^2x\cos^2x}{\cos^2x}\\\\\frac{\sin^2x}{\cos^2x}-\sin^2x\\\\\tan^2x-\sin^2x[/tex]

Hence, the identity is proven

Answer:

Approximately 32

Step-by-step explanation:

8.1 is closest to 8

4.2 is closest to 4

Thus, you can estimate the product to be 8*4=32

The actual product is 8.1*4.2=34.02, so it's about 2 greater than the estimated product

Answer:

35 cm²

Step-by-step explanation:

Area of the 2 triangles combined:

1/2 x 4 x 5 = 10

Area of the square:

5 x 5 = 25

10 + 25 = 35

4×4 or 4×5 perimeter times area

Tax the assesed home would increase the total amount paid

The tax of a home assesed at $150,000 is $1500

The given parameter can be represented using the following ratio:

Ratio = Tax : Amount

So, we have:

$10 : $1000 = Tax : $150000

Express as fraction

10/1000 = Tax/$150000

Multiply both sides by $150000

Tax = $1500

Hence, the tax of a home assesed at $150,000 is $1500

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Answer:a=10 b=35

Step-by-step explanation:

1*8=8  1.25*8=10

1*28=28 1.25*28=35

Answer:

400

Step-by-step explanation:

[tex] \huge\mathbb\orange{ANSWER} [/tex]

[tex] \mathsf \purple{c) \: 400}[/tex]

Answer:

[tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]

Step-by-step explanation:

Notice that [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=\frac{12(0)e^{0}-12(0)}{cos(5(0))-1}=\frac{0}{0}[/tex], which is in indeterminate form, so we must use L'Hôpital's rule which states that [tex]\lim_{x \to c} \frac{f(x)}{g(x)}=\lim_{x \to c} \frac{f'(x)}{g'(x)}[/tex]. Basically, we keep differentiating the numerator and denominator until we can plug the limit in without having any discontinuities:

[tex]\frac{12xe^x-12x}{cos(5x)-1}\\\\\frac{12xe^x+12e^x-12}{-5sin(5x)}\\ \\\frac{12xe^x+12e^x+12e^x}{-25cos(5x)}[/tex]

Now, plug in the limit and evaluate:

[tex]\frac{12(0)e^{0}+12e^{0}+12e^{0}}{-25cos(5(0))}\\ \\\frac{12+12}{-25cos(0)}\\ \\\frac{24}{-25}\\ \\-\frac{24}{25}[/tex]

Thus, [tex]\lim_{x \to 0} \frac{12xe^x-12x}{cos(5x)-1}=-\frac{24}{25}[/tex]

Step-by-step explanation:

3)

25% of 15.99=0.25×15.99=3.9975

Nope you will save about 4 dollars.

4)

12$ is 100% of its price

If there is a 25% discount, it will cost 75% of its original value.

75% of 12=0.75×12=9

It will cost 9 dollars

5)

You have 40% left of 150

so, 0.4(150)=60

You ANSWERED 90 but you still have 60 remaining.

6)

60% of 1350 lived since 40% died

0.6×1350=810

about 810 lived

7)

40% of the angelfish died

0.4×230=92

92 angelfish died

8)

The collected 125% of what they expected

1.25×1200=1500

They collected 1500 cans

Answer:52.8

Step-by-step explanation:

Answer:

The answer is indeed 52.8

Step-by-step explanation:

Here is proof: I got the same answer.

Answer:

0.9524

Step-by-step explanation:

Since the probability of a baby being a girl is 0.467, then the probability of a baby being a boy is 1 - 0.467 = 0.533

By the Binomial Theorem, the probability of at least one baby out of four being a boy is 1 - (0.467)^4 = 1 - 0.0476 = 0.9524

The equation x^2−2x+c=0 is an illustration of a quadratic equation

The value of c is 1

The equation is given as:

x^2 -2x + c = 0

A quadratic equation is represented as:

ax^2 + bx+ c = 0

When the quadratic equation  has two roots of one sign, the following equation is true

b^2 =4ac

So, we have:

(-2)^2 =4 * 1 * c

Evaluate the exponent and the product

4 = 4c

Divide both sides by 4

c= 1

Hence, the value of c is 1

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The answer to this problem is:

0<c<1

The age group that represents 25% of the people at the family reunion as displayed by the bar graph is: B. 20 - 29.

A bar graph can be described as a graphical representation of a data distribution usin bars/bins to display the frequency of a group or data points.

First, find the total number of people at the family reunion:

Total number of people = 8 + 10 + 19 + 15 + 5 + 13 + 3 + 5 = 78 people.

25% of 79 = 25/100 × 78 = 19.5

19.5 is closer to 19.

People in the age group 20 - 29 from the bar graph represents 19 people, therefore, the age group that represents 25% of the people at the family reunion as displayed by the bar graph is: B. 20 - 29.

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Answer: B

Step-by-step explanation: I took the test in K12

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

The value of third side should be lesser than the the sum of other two sides ~

[tex]\qquad \sf  \dashrightarrow \:x < 2.8 + 2.8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x < 5.6[/tex]

and, value of third side should also be greater than the difference of other two sides ~

[tex]\qquad \sf  \dashrightarrow \: x> 2.8 - 2.8[/tex]

[tex]\qquad \sf  \dashrightarrow \:x > 0[/tex]

Now, combine the two inequalities, we will get ~

[tex]\qquad \sf  \dashrightarrow \:0 < x < 5.6[/tex]

I hope you got the required Answer ~

Answer:

so here we minus 5 from 255 to get to 250 and we do it again to get to 245. for reaching the 40th term we should do it 39 times.

so, 255+ (-5) (39) = 255 - 195 = 60

which is our 40th term.

The 40th term of  (255, 250, 245...) is 60.

Calculations :

The formula to find the nth term = [tex]a_{n}[/tex]  =  -5n + 260

                                                      = [tex]a_{40}[/tex] x 5n = 260

                                                      = 260 - 200 = 60

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Answer:

B

Step-by-step explanation:

This statement is false because quadrilaterals just mean a polygon with 4 sides, but a parallelogram is a shape with two sides of opposite length. For example, a scalene quadrilateral has 4 sides, but none are the same length.

The value of the derivative at the maximum or minimum for a continuous function must be zero.

So, remember that the derivative at a given value gives the slope of a tangent line to the curve at that point.

Now, also remember that maximums or minimums are points where the behavior of the curve changes (it stops going up and starts going down or things like that).

If you draw the tangent line to these points, you will see that you end with horizontal lines. And the slope of a horizontal line is zero.

So we conclude that the value of the derivative at the maximum or minimum for a continuous function must be zero.

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Answer:

4/10 = 2/5

2/5 is thr probability of her wearing coat with purple hat, black boots and purple mittens

Answer:

9 or 9 months (if you have to add units)

Step-by-step explanation:

Subtract 15 from his savings:

420-15 = $405

This is the amount left he has to  pay the monthly membership

405/45 = 9

9 is the number of months

Answer:

9 months

Step-by-step explanation:

Set up and solve the equation 15 + 45x = 420.  Begin by subtracting 15 from both sides.  After paying 15 dollars for the deposit, He will have $405 dollars left.  Divide both sides of the equation by 45.  When you divide 405 by 45 that will tell you how many months the membership can be paid.

Answer:

[tex]x=-\frac{4}{9}[/tex]

Step-by-step explanation:

2x + 1 - 4x = 7x +5

First, take 7x to the left side.

2x + 1 - 4x - 7x = 5

Now take 1 to the right side.

2x - 4x - 7x = 5 - 1

Now combine like terms.

-2x - 7x = 4

-9x = 4

Now divide both sides by -9.

x = - 4/9

Answer:

2x+1-4x=7x+5

-->2x-4x-7x=5-1

-->-2x-12x=4

-->-9x=4

-->x=-4/9

-->x=-4/9

Answer:

Below in bold.

Step-by-step explanation:

g(x) = x^2 – 8x + 12

Convert to vertex form:

g(x) = (x - 4)^2 - 16 + 12

g(x) = (x - 4)^2 - 4.

So the vertex is at (4, -4).

y-intercept (when x = 0) is ((0-4)^2 - 4 = 16 - 4

- that is (0, 12).

Zeros:

(x - 4)^2 - 4 = 0

(x - 4)^2 = 4

x - 4 = +/- 2

x = 2 + 4 = 6 or x = -2 + 4 = 2.

= 2, 6.

Answer:

  frequency = 1/(2π)

Step-by-step explanation:

The frequency of the function is found by comparing the argument of the cosine function to (2πfx), where f is the freuqency.

  2πfx = x . . . . the argument of the cosine is x in f(x)=2cos(x) -4

  2πf = 1 . . . . . . divide by x

  f = 1/(2π) . . . . . the frequency of the function f(x)

Answer:

Explanation:

use compound interest formula:  [tex]\sf \boxed{ \sf P ( \sf 1 + \dfrac{r}{100} )^n}[/tex]

[tex]\rightarrow \s \sf 10( 1 + \dfrac{1.4}{100} )^n = 20[/tex]

[tex]\rightarrow \sf ( 1.014) ^n = 2[/tex]

[tex]\rightarrow \sf n( ln( 1.014) ) = ln(2)[/tex]

[tex]\rightarrow\sf n = \dfrac{ln(2)}{ln( 1.014)}[/tex]

[tex]\rightarrow\sf n = 49.8563 \ years[/tex]

Answer:

General form of an exponential equation:  [tex]y=ab^x[/tex]

where:

Given information:

⇒ growth factor = 100% + 1.4% = 101.4% = 1.014

Inputting these values into the equation:

[tex]\implies y=10(1.014)^x[/tex]

where y is the population (in millions) and x is the number of years since 1992

Now all we need to do is set y = 20 and solve for x:

[tex]\implies 10(1.014)^x=20[/tex]

[tex]\implies 1.014^x=2[/tex]

[tex]\implies \ln 1.014^x=\ln 2[/tex]

[tex]\implies x\ln 1.014=\ln 2[/tex]

[tex]\implies x=\dfrac{\ln 2}{\ln 1.014}[/tex]

[tex]\implies x=49.85628343...[/tex]

1992 + x = 2041.8562....

Therefore, the population will reach 20 million during 2041, so the population will reach 20 million by 2042.

Answer:

68 units

Step-by-step explanation:

Given:

As the x-values of points A and B are the same (x = -3), the line through points A and B is vertical.

Therefore, to find the distance between the two points, simply subtract the y-value of point B from the y-value of point A:

[tex]\sf distance=y_A-y_B=80-12=68 \ units[/tex]

Answer:

D

Step-by-step explanation:

f(x) = 10x - 5 → x = 10g(x) - 5 → x + 5 = 10g(x) →

g(x) = (x + 5)/10

Step-by-step explanation:

let's first convert feet to inches

4 ft = 48 inches ( width )

6.5 ft = 78 inches ( length )

12.5 ft = 150 inches ( height )

each cube is 1/4 x 1/4 x 1/4

x-axis ( length )

78 ÷ 1/4 = 78 x 4 = 312 cubes

y-axis ( width )

48 x 4 = 192 cubes

z-axis ( height )

150 x 4 = 600 cubes

the total number of cubes fit in the closet is :

312 x 192 x 600 = 35,942,400 cubes