SCALCET8 3.8.001.MI. A population of protozoa develops with a constant relative growth rate of 0.6137 per member per day. On day zero the population consists of two members. Find the population size after seven days. (Round your answer to the nearest whole number.) P(7)

Answer:

The general equation for a parabola is:

y = f(x) = a*x^2 + b*x + c

And the vertex of the parabola will be a point (h, k)

Now, let's find the values of h and k in terms of a, b, and c.

First, we have that the vertex will be either at a critical point of the function.

Remember that the critical points are the zeros of the first derivate of the function.

So the critical points are when:

f'(x) = 2*a*x + b = 0

let's solve that for x:

2*a*x = -b

x = -b/(2*a)

this will be the x-value of the vertex, then we have:

h = -b/(2*a)

Now to find the y-value of the vertex, we just evaluate the function in this:

k = f(h) = a*(-b/(2*a))^2 + b*(-b/(2*a)) + c

k =  -b/(4*a) - b^2/(2a) + c

So we just found the two components of the vertex in terms of the coefficients of the quadratic function.

Now an example, for:

f(x) = 2*x^2 + 3*x + 4

The values of the vertex are:

h = -b/(2*a) = -3/(2*2) = -3/4

k = -b/(4*a) - b^2/(2a) + c

=  -3/(4*2) - (3)^2/(2*2) + 4 = -3/8 - 9/4 + 4 = (-3 - 18 + 32)/8 = 11/8

Step-by-step explanation:

Let us take a nominal square of area 25 cm².

So, in this question, we can say that:-

a. The length of one of its sides will be less than 5 cm.

b. Its perimeter will be less than 20 cm.

Hope it helps :)

Step-by-step explanation:

area= 25cm squared

length of one side = 5cm as 5*5 =25

perimeter= 5*4= 20cm

But since the area is less than 25cm squared

we can say that the length of one side is less than 5cm and we can also say that the length of the perimeter is less than 20cm.

Hope this helps.

9514 1404 393

Answer:

  p > 3

Step-by-step explanation:

  3p -4 -8p < -19 . . . . . . given

  -5p -4 < - 19 . . . . . . . . collect terms

  -5p < -15 . . . . . . . . . . . add 4

  p > 3 . . . . . . . . . . . . . . divide by -5 (reverses the inequality symbol)

Answer:

1/6 < 2/11

Step-by-step explanation:

1/6 = 2/12

2/11 >2/12

So that means 1/6 < 2/11

Answer:  1/6 < 2/11

This is the same as saying 11/66 < 12/66

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Explanation:

1/6 is the same as 11/66 when multiplying top and bottom by 11.

2/11 is the same as 12/66 when multiplying top and bottom by 6.

The 6 and 11 multipliers are from the original denominators (just swapped).

We can see that 11/66 is smaller than 12/66, simply because 11 < 12, so that means 1/6 is smaller than 2/11

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

Here's one way you could list out the steps

11 < 12

11/66 < 12/66

1/6 < 2/11

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Here's another way to list out the steps. First assume that 1/6 and 2/11 are equal. Cross multiplication then leads to

1/6 = 2/11

1*11 = 6*2

11 = 12

Which is false. But we can fix this by replacing every equal sign with a less than sign

1/6 < 2/11

1*11 < 6*2

11 < 12

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

Yet another way to see which is smaller is to use your calculator or long division to find the decimal form of each value

1/6 = 0.1667 approximately

2/11 = 0.1818 approximately

We see that 0.1667 is smaller than 0.1818, which must mean 1/6 is smaller than 2/11.

Answer:

The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 24 - 1 = 23

98% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 23 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.98}{2} = 0.99[/tex]. So we have T = 2.5

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.5\frac{2}{\sqrt{24}} = 1.02[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 42 - 1.02 = $40.98.

The upper end of the interval is the sample mean added to M. So it is 42 + 1.02 = $43.02.

The 98% confidence interval for the mean amount spent on their child's last birthday gift is between $40.98 and $43.02.

Answer:

2

Step-by-step explanation:

8*8 is 64

Since it looks like the empty box is an exponent, and there are 2 8s being multiplied, the answer is 2

Answer:

Step-by-step explanation:

l -> length

b -> width

h -> height

Find the area of four walls and ceiling. then subtract the area of four windows and a door form that area.

Area of four walls + ceiling = 2( lh + bh) +lb

 = 2*(20*5 + 15*5) + 20*15

= 2( 100 + 75) + 300

= 2* 175 + 300

= 350 +300

= 650 sq m

Area of window = 2 *3 = 6 sq.m

Area of four windows = 4*6 = 24 sq.m

Area of door = 2 * 1 =  2 sq.m

Area of four walls excluding 4 windows and door = 650 - 24 - 2 = 624 sq.m

Cost of painting = 624 * 6.50

                          = $ 4056

Answer:  1950 dollars to paint the ceiling only (ignoring the walls)

The cost to paint the walls only is 2106 dollars.

The cost to paint the walls and ceiling is 4056 dollars.

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Explanation:

It seems a bit strange how your teacher mentions the windows and doors, but then asks about the ceiling only. Perhaps this is a red herring, but I'm not sure.

Anyway, to directly answer the question, we'll need to find the area of the ceiling first. The ceiling is a rectangle of dimensions 20 m by 15 m, so its area is 20*15 = 300 square meters.

Since paint costs 6.50 dollars per square meter, the total cost for the ceiling alone is 6.50*300 = 1950 dollars

If your teacher only cares about the ceiling, then you can stop here (and ignore the next section below).

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

If you wanted to find the cost to paint the walls, then we need to find the area of the walls.

For now, ignore the windows and door. Two opposite walls have area of 20*5 = 100 m^2 each. That accounts for 2*100 = 200 m^2 of wall area so far.

The other pair of opposite walls have area 15*5 = 75 m^2 each. That's another 2*75 = 150 m^2 of wall area.

In all, the total wall area without considering the windows or door is 200+150 = 350 m^2.

Now we consider the windows. Each window is 2 m by 3 m, yielding an area of 2*3 = 6 m^2. Four such windows have a total area of 4*6 = 24 m^2.

The door is 2 m by 1 m, so its area is 2*1 = 2 m^2

We'll subtract the wall area and the combined window+door areas to get

wallArea - windowArea - doorArea = 350-24-2 = 324

So after accounting for the windows and door, the amount of wall to paint is 324 m^2, which leads to a cost of 6.50*324 = 2106 dollars.

Therefore, painting the walls and ceiling gets us a total cost of 1950+2106 = 4056 dollars

This section is entirely optional if your teacher only cares about the ceiling.

Answer:

3.15 seconds is the answer.

Explanation

when the ball touches the ground, h =0

hence,

0=255-21t-16t²

16t²+21t-225=0

here a=16 ,b=21, c= -225

[tex]t= \frac{ - b± \sqrt{ {b }^{2} - 4ac} }{2a} \\ \\ t= \frac{ - 21± \sqrt{ {21}^{2} - 4 \times 16 \times - 225} }{2 \times 16} \\ = \frac{ - 21 ± \sqrt{441 - ( - 14400)} }{32} \\ = \frac{ - 21± \sqrt{14841} }{32} \\ = \frac{ - 21±121.82}{32} \\ \\ t = \frac{ - 21 + 121.82}{32} \: or \: \: t = \frac{ - 21 - 121.82}{32} \\ t = 3.15 \: \: or \: \: t = - 4.46[/tex]

time cannot be negative, hence t = -4.46 can be avoided

The ball takes 3.15 seconds to hit the ground.

Answer:

65 km/hr

Step-by-step explanation:

The average of numbers can be calculated by adding them up and dividing that by how many numbers there are.

Here, we have two numbers. Therefore, we first add them (55+75 = 130) and then divide by 2 because there are 2 numbers, so 130/2 = 65

Answer:

x = ±i√2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Multiplication Property of Equality

Division Property of Equality

Addition Property of Equality

Subtraction Property of Equality

Algebra II

Imaginary root i

Step-by-step explanation:

Step 1: Define

Identify

5x² - 2 = -12

Step 2: Solve for x

Answer:

8.50 cm²

Step-by-step explanation:

The dimension of each square is given as 0.5cm by 0.5cm

The area of the a square is, a²

Where, a = side length

Area of each square = 0.5² = 0.25cm

The number of blue colored squares = 34

The total area of the blue colored squares is :

34 * 0.25 = 8.50cm²

Explanation:

This is known as a cyclic quadrilateral since all four points are on the circle's edge, and the quadrilateral is entirely inside the circle (no parts of the quadrilateral spill outside the circle). Another term is "inscribed quadrilateral"

Since we have an inscribed quadrilateral, this means the opposite angles of the quadrilateral are supplementary.

B+D = 180

120+x = 180

x = 180-120

x = 60

Answer:

[tex]P(x < 3) = 25\%[/tex]

[tex]E(x) = 3[/tex]

Step-by-step explanation:

The given parameters can be represented as:

[tex]\begin{array}{ccccccc}x & {5} & {4} & {3} & {2} & {1}& {0} & P(x) & {25\%} & {30\%} & {20\%} & {15\%} & {5\%} & {5\%} \ \end{array}[/tex]

Solving (a): P(x < 3)

This is calculated as:

[tex]P(x < 3) = P(x = 0) + P(x = 1) + P(x =2)[/tex] ----- i.e. all probabilities less than 3

So, we have:

[tex]P(x < 3) = 5\% + 5\% + 15\%[/tex]

[tex]P(x < 3) = 25\%[/tex]

Solving (b): Expected number of events

This is calculated as:

[tex]E(x) = \sum x * P(x)[/tex]

So, we have:

[tex]E(x) = 5 * 25\% + 4 * 30\% + 3 * 20\% + 2 * 15\% + 1 * 5\% + 0 * 5\%[/tex]

[tex]E(x) = 125\% + 120\% + 60\% + 30\% + 5\% + 0\%[/tex]

[tex]E(x) = 340\%[/tex]

Express as decimal

[tex]E(x) = 3.40[/tex]

Approximate to the nearest integer

[tex]E(x) = 3[/tex]

Answer:

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1-p)}{n}}[/tex]

A hotel manager believes that 23% of the hotel rooms are booked.

This means that [tex]p = 0.23[/tex]

Sample of 610 rooms

This means that [tex]n = 610[/tex]

Mean and standard deviation:

[tex]\mu = p = 0.23[/tex]

[tex]s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.23*0.77}{610}} = 0.017[/tex]

What is the probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%?

p-value of Z when X = 0.23 + 0.03 = 0.26 subtracted by the p-value of Z when X = 0.23 - 0.03 = 0.2. So

X = 0.26

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.26 - 0.23}{0.017}[/tex]

[tex]Z = 1.76[/tex]

[tex]Z = 1.76[/tex] has a p-value of 0.9608

X = 0.2

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{0.2 - 0.23}{0.017}[/tex]

[tex]Z = -1.76[/tex]

[tex]Z = -1.76[/tex] has a p-value of 0.0392

0.9608 - 0.0392 = 0.9216

0.9216 = 92.16% probability that the proportion of rooms booked in a sample of 610 rooms would differ from the population proportion by less than 3%

Answer:

cos(∝) = 1/√3

cos(β) = 1/√3

cos(γ) = 1/√3

∝ = 55°

β = 55°

γ = 55°

Step-by-step explanation:

Given the data in the question;

vector is z = < c,c,c >

the direction cosines and direction angles of the vector = ?

Cosines are the angle made with the respect to the axes.

cos(∝) = z < 1,0,0 > / |z|

so

cos(∝) = < c,c,c > < 1,0,0 > / √[c² + c² + c²] = ( c + 0 + 0 ) / √[ 3c² ]

cos(∝) = c / √[ 3c² ] = c / c√3 = 1/√3

∝ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

cos(β) = < c,c,c > < 0,1,0 > / √[c² + c² + c²] = ( 0 + c + 0 ) / √[ 3c² ]

cos(β) = c / √[ 3c² ] = c / c√3 = 1/√3

β = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

cos(γ) = < c,c,c > < 0,0,1 > / √[c² + c² + c²] = ( 0 + 0 + c ) / √[ 3c² ]

cos(γ) = c / √[ 3c² ] = c / c√3 = 1/√3

γ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

Therefore;

cos(∝) = 1/√3

cos(β) = 1/√3

cos(γ) = 1/√3

∝ = 55°

β = 55°

γ = 55°

Answer:

D. 34

Step-by-step explanation:

Because this is a right triangle we can use sin, cos, tan.

Use cosine because the values of the adjacent side and hypotenuse are already given.

cos(θ) = 72/87

Because we are solving for the angle measure (and not the measure of the side) we need to use inverse cos.

cos⁻¹ = 72/87

put into a calculator and answer is approximatelyn34 degrees.

Step-by-step explanation:

x intercept=(-1,0) because the graph is passing this point on the x axis

y intercept=(0,-3)

Answer:

4th option

Step-by-step explanation:

The x- intercept is where the graph crosses the x- axis.

This is at (- 1, 0 )

The y- intercept is where the graph crosses the y- axis.

This is at (0, - 3 )

Answer:

Step-by-step explanation:

a) 52 is divisible by 4 and 5 - 2 = 3

b) 63 is divisible by 9 and 3*2 = 6 -> ten digit

c) 50 is divisible by 10 and 5 + 0 = 5

d) 72 is divisible by 6 and 7*2 = 14

Step-by-step explanation:

[tex]\tan^2 \theta - 3\tan \theta + 2 = 0[/tex]

Let [tex]x = \tan \theta[/tex]

We can then write

[tex]x^2 -3x + 2 = 0\:\:\Rightarrow\:\:(x - 2)(x - 1) = 0[/tex]

or

[tex](\tan \theta - 2)(\tan \theta - 1) = 0[/tex]

The zeros occur when

[tex]\tan \theta = 2\:\:\:\text{or}\:\:\:\tan \theta = 1[/tex]

or when [tex]\theta = 63.4°[/tex] or [tex]\theta = 45°[/tex].

The answer is D

Hope that was fast enough

Answer:

Please find the complete question in the attached file.

Step-by-step explanation:

Total quantities of plant-produced pollutants:

[tex]=(10.88+15.82+0.92) \ L\\\\=27.62\ L[/tex]

We are three medicinal plants here, Pinecrest, Macon, and Ogala. The average number of contaminants produced by plants would be

[tex]\to 27.62\div 3 \\\\\to \frac{27.62}{3} \\\\ \to 9.206 \ L[/tex]

( solution at pic)

Answer: 75%

Step-by-step explanation:

Answer:

the car travels 10km then 15km 60* north of east

Step-by-step explanation:

Answer:

6.09 is the answer rounded to nearest hundredths.

Step-by-step explanation:

It gives you n=150, p=0.55, and q=1-p.

If p=0.55 and q=1-p, then by substitution property we have q=1-0.55=0.45.

It ask you to evaluate the expression sqrt(npq).

So npq means find the product of 150 and 0.55 and 0.45. So that is 150(0.55)(0.45)=37.125.

The sqrt(npq) means we need to find the square root of that product. So sqrt(37.125)=6.093 approximately .

Answer:

= x^2 + 3 + √3x^2 - 1

Step-by-step explanation:

Remove parentheses: (a) = a

= x^2 + 3 + √x . 3x - 1

x . 3x = 3x^2

= x^2 + 3 + √3x^2 - 1

Answer:

270 plates

Step-by-step explanation:

First, you need to find how much one plate costs.

6x = 54

----    ----

6       6

x = 9

Now, multiply 30 plates with x, which is 9.

30(9) = 270

The answer is 270.

Answer:

270

Step-by-step explanation:

54($)÷6= 9 then 9×30=270

Answer:

In general gf(x) is not equal to fg(x)

Some pairs of functions cannot be composed. Some pairs of functions can be composed only  for certain values of x.

Only with they can be composed some values of x are the ranges of g(x) and f(x) are the same, and their domains are also the same. Or else lies inside it.

Step-by-step explanation:

g(x) = 3x + 6 - 8, f(x) = √x.

The domain of a composed function is either the same as the domain of the first function, or  else lies inside it

The range of a composed function is either the same as the range of the second function, or else lies inside it.

Or vice versa

Now only positive numbers, or zero, have real square roots. So g is defined only for numbers

greater than or equal to zero. Therefore g(f(x)) can have a value only if f(x) is greater than or

equal to zero. You can work out that

f(x) ≥ 0 only when x ≥3/2

.