(10) The population of bacteria an experiment can be modeled by d p(d)= 400(1.56)^d , where d is the number of days the population has been growing.

(a) Find the average rate the population has been growing over the interval 0≤d≤7.
Round to the nearest integer and include appropriate units.

(b) If the population of bacteria was modeled as a function of the number of hours, h,
such that h p(h)= 400b^h then what would be the value of b to the nearest thousandth?
Show or explain how you found your answer.

The sum of all the angles of any triangle is 180 degrees

     -->  Therefore the missing angle is:

                  x = 180 - 60 - 75 = 45

Hope that helps!

The sum of the angles of a triangle is 180 degrees

   --> to put that into mathematical terms

                       Angle O + Angle K + Angle C = 180

                                 60 + 75 + Angle C = 180

                                         Angle C = 45 degrees

Therefore the missing angles' measure is 45 degrees

Hope that helps!

Answer:

Step-by-step explanation:

hello :

the sum is : Sn = n/2(U1 + Un )     and U n = U1+(n-1)r    

given :    U1 = 1      r=4-1=7-4=...= 3      n= 32

so :  U 32 = 1+(32-1)3= 94

S32 = 32/2 (1+94) = 1520

When creating a histogram it is best to create a range for the different variables that are available.

So for the sake of covering all the possible ranges from 1 - 22, let's divide it into 5 categories.

0 - 5        6 - 10   11 - 15   16 - 20   21 - 25

Now that we have set ranges for the different variables, we then find the frequencies.

0 - 5  : 3 

6 - 10 : 2

11 - 15 : 3

16 - 20 : 1

21 - 25 : 3

Now that we have all the values we can then create our histogram.

Taken from https://brainly.com/question/12197869

All rights reserved.

I can give you a hint. So when we do the composition of functions, if we plug 2 functions into each other and get x by itself, that means the functions are inversely related.

For this problem, simply find the inverse of f(x).

If you are stuck, I could provide you with a solution below...

f(x) = 8x³ - 2

y = 8x³ - 2

y + 2 = 8x³

(y + 2)/8 = x³

cube root((y + 2)/8) = x

g(x) = cube root((x + 2)/8)

The value of function g(x) after solving will be ∛(x + 2) / 2.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The value of function,

f(x) = 8x³ − 2

And, f(g(x)) = x and g(f(x)) = x

Now,

Since, f(g(x)) = x

And, f(x) = 8x³ − 2

The substitute x = g (x) in above equation we get;

f (g(x)) = 8 (g(x))³ - 2

x = 8 (g(x))³ - 2

Add 2 both side;

x + 2 = 8 (g(x))³  

Divide by 8;

(x + 2)/8 = (g(x))³

Take cube root both side;

∛(x + 2)/8 = g(x)

g(x) = ∛(x + 2) / 2

So, The value of function g(x) after solving will be ∛(x + 2) / 2.

Learn more about the function visit:

https://brainly.com/question/24748644

#SPJ2

Answer:

[tex]\dfrac{1}{102}[/tex]

Step-by-step explanation:

Average rate of change of function [tex]f(x)[/tex] over the interval [tex]a \leq x \leq b[/tex] is:

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

Given function:

[tex]f(x)=\dfrac{2x-2}{5x-6}[/tex]

Given interval [tex]0\leq x\leq 8[/tex] :

when [tex]x=0[/tex]:

[tex]f(0)=\dfrac{2(0)-2}{5(0)-6}=\dfrac13[/tex]

when [tex]x=8[/tex]:

[tex]f(8)=\dfrac{2(8)-2}{5(8)-6}=\dfrac{7}{17}[/tex]

Therefore, average rate of change:

[tex]\dfrac{f(8)-f(0)}{8-0}=\dfrac{\frac{7}{17}-\frac13}{8}=\dfrac{1}{102}[/tex]

Answer:

2,184

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Answer:

(x+5)(2x+7)

Step-by-step explanation:

x(2x+7) + 5(2x+7)

(x+5)(2x+7)

I hope this helps!!

Answer:

1750

Step-by-step explanation:

If you flip a coin, you should theoretically get heads 50% of the time and tails 50% of the time. So in this case you would get heads 1,750 times.

Answer:

A

Step-by-step explanation:

Got it right on Khan Academy.

Hope this helps!

Please mark as brainliest!

Answer:

  13

Step-by-step explanation:

Estimates are often made by rounding the operands to 1 or 2 significant digits. Here, that is accomplished by rounding each number to the nearest hundred.

__

Rounded to hundreds, the problem becomes ...

  3900 ÷ 300

  = 39/3 = 13

An estimate of the quotient is 13.

Answer:

ok sure wait

Step-by-step explanation:

Answer:

11 13 15

Step-by-step explanation:

n + n + 2 + n + 4 = 39

3n + 6 =39

3n = 33

n = 11

the three odd integers are 11 , 13 ,15

Step-by-step explanation:

only the circle

as cylinder is neither oval nor triangle not a rectangle..

so cylinder has circle as the cross section

Answer:

This is for a different question but hope this helps too!

Step-by-step explanation:

Hey there!

Option A.

(4 + 5) * 3^2 - 9 ÷ 3^2

= 9 * 9 - 9 ÷ 9

= 81 - 1
= 80

Thus, that answer is: [incorrect]

Option B.
4 + 5 * (3^2 - 9) + 3^2

= 4 + 5 * (9 - 9) + 9

= 4 + 5 * (0) + 9

= 4 + 5(0) + 9

= 4 + 0 + 9

= 4 + 9

= 13

Thus, that answer is also [incorrect]

Option C.

4 + 5 * 3^2(-9 ÷ 3^2)

= 4 + 5 * 3^2(-9 ÷ 9)

= 4 + 5 * 3^2(-1)

= 4 + 5 * 9(-9)

= 4 + 5(9) * -1

= 4 + 45 * -1

= 4 - 45

= -41

Thus, that answer is also [incorrect]

Option D.
4 + 5 * 3^2 - 9 ÷ 3^2

= 4 + 5(9) - 9 ÷ 9

= 4 + 45 - 9 ÷ 9

= 49 - 9 ÷ 9

= 49 - 1

= 48

Therefore, your answer is: Option D.

Good luck on your assignment & enjoy your day l!

~Amphitrite1040:)

Answer:

Option D

Step-by-step explanation:

To find out which expression has a value of 48, we need to recall the PEMDAS (where: P = Parenthesis, E = Exponents, M/D = Multiplication or Division, A/S = Addition or Subtraction).

A) [4 + 5] × 3² - 9 ÷ 3²

First, simplify the expression in the parenthesis as PEMDAS

⇒ [9] × 3² - 9 ÷ 3²

Pull the "9" out of the parenthesis

⇒ 9 × 3² - 9 ÷ 3²

Simplify the exponents as PEMDAS

⇒ 9 × 9 - 9 ÷ 9

Multiply the first two terms in the expression as PEMDAS

⇒ 81 - 9 ÷ 9

Divide the last two terms as PEMDAS

⇒ 81 - 1

Finally, simplify the expression.

⇒ 80

⇒ 48 ≠ 80

B) 4 + 5 × (3² - 9) ÷ 3²

First, simplify the expression in the parenthesis as PEMDAS.

We can see here that the expression in the parenthesis includes a constant with a negative sign and an exponent. To simplify the expression, we need to simplify the exponent. Once the exponent is simplified, we can simplify the expression in the parenthesis.

⇒ 4 + 5 × (3² - 9) ÷ 3²

⇒ 4 + 5 × (9 - 9) ÷ 3²

⇒ 4 + 5 × (0) ÷ 3²

Pull the "0" out of the parenthesis

⇒ 4 + 5 × 0 ÷ 3²

Simplify the exponent as PEMDAS

⇒ 4 + 5 × 0 ÷ 9

Multiply the middle two terms as PEMDAS

⇒ 4 + 0 ÷ 9

Divide the last two terms as PEMDAS

⇒ 4 + 0

Add the two terms in the expression as PEMDAS

⇒ 4

⇒ 4 ≠ 48

C) 4 + 5 × 3²(-9 ÷ 3²)

First, simplify the expression in the parenthesis as PEMDAS

⇒ 4 + 5 × 3²(-9 ÷ 3²)

⇒ 4 + 5 × 3²(-9 ÷ 9)

⇒ 4 + 5 × 3²(-1)

*3²(-1) can also be written as 3² × -1*

⇒ 4 + 5 × 3² × -1

Simplify the exponent as PEMDAS

⇒ 4 + 5 × 9 × -1

Multiply the last three terms as PEMDAS

⇒ 4 + 5 × 9 × -1

⇒ 4 + (-45)

Add/Subtract the last two terms as PEMDAS

⇒ 4 - 45

⇒ -41

D) 4 + 5 × 3² - 9 ÷ 3²

Since there are no parenthesis in the expression, we can start simplifying this expression by simplifying the exponents.

⇒ 4 + 5 × 3² - 9 ÷ 3²

⇒ 4 + 5 × 9 - 9 ÷ 9

⇒ 4 + 5 × 9 - 9 ÷ 9

Multiply the second and the third terms as PEMDAS

⇒ 4 + 45 - 9 ÷ 9

Divide the last two terms as PEMDAS

⇒ 4 + 45 - 1

Add/Subtract the terms as PEMDAS

⇒ 4 + 44

⇒ 48

⇒ 48 = 48 ✔✔

In conclusion, we can say that option D is correct because the expression of Option D has a value of 48.

Answer:

25[tex]\pi[/tex]

Step-by-step explanation:

because area is pi r^2

Answer:

78.54 or 25π (if in terms of pi)

Step-by-step explanation:

A = πr² = π*5² ≈ 78.53982

Answer:

4320

Step-by-step explanation:

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Answer: $7401.22

Step-by-step explanation: it’s right just trust me

Answer:

3

Step-by-step explanation:

Divide 12 by 4 since the ratio is 12 to every 4 inches

Answer:

[tex]c = 15[/tex]

Step-by-step explanation:

[tex]b = 2a - 7[/tex]

[tex]b = 2(-4) -7[/tex]

[tex]b = (-8)-7[/tex]

[tex]b = (-15)[/tex]

[tex]c = -(-15)[/tex]

[tex]c = 15[/tex]

Answer:

a∥b, Converse of the Alternate Interior Angles Theorem

well, let me not bore you to death on how we test it and test it.

[tex]\underline{\textit{testing for symmetry to the }\frac{\pi }{2}~line\qquad \qquad r=-r~~,~~\theta =-\theta } \\\\\\ r=5-sin(11\theta )\implies (-r)=5-sin[11(-\theta )]\implies -r=5-sin(-11\theta ) \\\\\\ \stackrel{symmetry~identity}{-r=5-\stackrel{\downarrow }{[-sin(11\theta )]}}\implies\implies r=-5-sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underline{\textit{testing for symmetry to the polar axis}\qquad \qquad \theta =-\theta} \\\\\\ r=5-sin(11\theta )\implies r=5-sin[11(-\theta )]\implies r=5-sin(-11\theta ) \\\\\\ r=5-[-sin(11\theta )]\implies r=5+sin(11\theta )\impliedby \textit{no dice} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\underline{\textit{testing for symmetry to the pole}\qquad \qquad r=-r} \\\\\\ r=5-sin(11\theta )\implies -r=5-sin(11\theta )\implies r=-5+sin(11\theta )\qquad \textit{no dice}[/tex]

so the symmetry tests didn't pass, notice the picture below though, looks a bit deceiving, it looks as if it'd have π/2 symmery, but it doesn't show in the test.

Using the Central Limit Theorem, it is found that the condition that applies to this test is:

C. The sample includes at least 30 employees from each department.

It states 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 sampling distribution is also approximately normal, as long as n is at least 30.

From this, since we have a skewed variable, it is found that a sample size of at least 30 is needed, hence option C is correct.

More can be learned about the Central Limit Theorem at https://brainly.com/question/24663213

Answer:

Domain: -5,6,2,1,-3

Range: 13,18,-7,4,-1

Step-by-step explanation:

Domain is the independent value/ x / input

Range is the dependent value/ y / output

Answer:

12

Step-by-step explanation:

60% of 30 is 18 (girls)

40% of 30 is 12  (boys)

Answer:

12 boys

Step-by-step explanation:

60% is the same as 6/10, and if you make the denominator 30, you must make the denominator multiply by three as well as the numerator.  this makes the number 18/30 girls in a class. if you subtract the girls from the total number of people, you get 12 boys, or 40% of the class.

you can also find that 100% - 60% = 40%, which is equal is equal to 4/10. After it's multiplied by 3 again, it becomes 12/30 or 12 boys.

Answer:

x= 6, -4

Step-by-step explanation:

x^2 - 2x - 24 = 0

(x-6) (x+4) = 0

x = 6, x= -4

We are given the equation of circle (x - 7)² + (y - 3)² = 64² , but let's recall the standard equation of circle i.e (x - h)² + (y - k)² = r², where (h, k) is the centre of the circle and r being the radius ;

So, consider the equation of circle ;

[tex]{:\implies \quad \sf (x-7)^{2}+(y-4)^{2}=(64)^{2}}[/tex]

On comparing this equation with the standard equation of Circle, we will get, centre and radius as follows

Answer:

Step-by-step explanation:

A = [tex]\frac{b_{1} +b_{2} }{2}[/tex] × h

~~~~~~~~

[tex]b_{1}[/tex] = 15 in.

[tex]b_{2}[/tex] = 6 + 15 + 6 = 21 in.

h = 18 in.

A = [tex]\frac{15+21}{2}[/tex] × 18 = 324 in.²

Answer:

3

Step-by-step explanation:

You just divide 13.5 by 4.5, and you get 3 yards per second.

[tex]======================================[/tex]

Perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, flop it over, and change its sign.

So the slope of the given line is -2

Flop it over:

-1/2

Change its sign:

1/2

Now, let's write the equation in point-slope form:

y-y1=m(x-x1)

y-(-5)=1/2(x-(-4)

y+5=1/2(x+4)

y+5=1/2x+2

y=1/2x+2-5

[tex]\bold{y=\displaystyle\frac{1}{2} x-3}}[/tex]

[tex]==========================================[/tex]

~DnomaiD

;)

Answer:

2816

Step-by-step explanation:

Cm to m is divide by 100

10 / 100 = 0.1.

0.1 x 8 = 0.8

40 x 88 = 3520

3520 / 0.8 = 2816