Power Function:
Analyze and model the power function: Exercise 2

Answer:

Step-by-step explanation:

Circumference of a circle = 2πr

where

r is the radius

From the above question

radius = 25 in.

Substitute this value into the above formula

That's

Circumference = 2(25)π

= 50π

= 157.079

We have the final answer as

Hope this helps you

Answer:

8.33 hours

Step-by-step explanation:

120-45 = 75

75 ÷ 9 = 8.33

Answer:

Step-by-step explanation:

● h(x) = 2-2x

The domain is {-3,-2,1,5}

● h(-3) = 2-2×(-3) = 2+6 = 8

● h(-2) = 2 -2×(-2) = 2+4 = 6

● h(1) = 2-2×1 = 2-2 = 0

● h(5) = 2-2×5 = 2-10 = -8

The range is {-8,0,6,8}

Answer: There will 486 bacteria in 31 hours.

Step-by-step explanation:

The population decay in bacteria is exponential.

Exponential function : [tex]y=Ab^x[/tex], where A = initial population, b multiplication decay factor, t= time:

As per given:

Initial population: [tex]A=120,000[/tex]

After 36 hours, population = [tex]120000(b^{36})=200[/tex]

Divide both sides by 120,000 we get

[tex]b^{36}= 0.00167[/tex]

Taking natural log on both sides , we get

[tex]36\ln b=\ln 0.00167\\\\\Rightarrow\ b=e^{\left(\frac{\ln0.00167}{36}\right)}=0.83724629\approx0.8372[/tex]

At x= 31,

[tex]y=120000(0.8372)^{31}=120000\times0.00405234\approx486[/tex]

Hence, there will 486 bacteria in 31 hours.

Answer:

a. False

b. True

c. False

d. False

e.True

f. True

Step-by-step explanation:

The 95% is confidence interval its not a probability estimate. The probability will be different from the confidence interval. Confidence interval is about the population mean and is not calculated based on sample mean. Every confidence interval contains the sample mean. There is 95% confidence that the number of televisions per American household is between 1.15 to 4.20.

Answer:

Step-by-step explanation:

Total surface of the cardboard box is expressed as S = 2LW + 2WH + 2LH where L is the length of the box, W is the width and H is the height of the box. Since the cardboard box is without a lid, then the total surface area will be expressed as;

S  = lw+2wh+2lh ... 1

Given the volume V = lwh = 4ft³ ... 2

From equation 2;

h = 4/lw

Substituting into r[equation 1;

S = lw + 2w(4/lw)+ 2l(4/lw)

S = lw+8/l+8/w

Differentiating the resulting equation with respect to w and l will give;

dS/dw = l + (-8w⁻²)

dS/dw = l - 8/w²

Similarly,

dS/dl = w  + (-8l⁻²)

dS/dw = w - 8/l²

At turning point, ds/dw = 0 and ds/dl = 0

l - 8/w² = 0 and w - 8/l² = 0

l = 8/w²  and w =8/l²

l = 8/(8/l² )²

l = 8/(64/I⁴)

l = 8*l⁴/64

l = l⁴/8

8l = l⁴

l³ = 8

l = ∛8

l = 2

Hence the length of the box is 2 feet

Substituting l = 2 into the function l = 8/w² to get the eidth w

2 = 8/w²

1 = 4/w²

w² = 4

w = 2 ft

width of the cardboard is 2 ft

Since Volume = lwh

4 = 2(2)h

4 = 4h

h = 1 ft

Height of the cardboard is 1 ft

The dimensions of the box that requires the least amount of cardboard is 2ft by 2ft by 1 ft

Answer:

k = 5

Step-by-step explanation:

I will assume that your polynomial is

x^2 - 3x^2 + kx + 14

If x - a is a factor of this polynomial, then a is a root.

Use synthetic division to divide (x - 2) into x^2 - 3x^2 + kx + 14:

 2      /      1     -3     k     14

                        2     -2    2k - 4

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

               1        -1    (k - 2)   2k - 10

If 2 is a root (if x - 2 is a factor), then the remainder must be zero.

Setting 2k - 10 = to zero, we get k = 5.

The value of k is 5 and the polynomial is x^2 - 3x^2 + 5x + 14

Answer:

it should be 308,608. the comma is after every three in this scenario.

Step-by-step explanation:

Answer:

opposites

Step-by-step explanation:

9+-9 = 0

When they add to zero they are opposites

Answer:

Step-by-step explanation:

9 and -9 are examples of opposite integers

━━━━━━━☆☆━━━━━━━

▹ Answer

1 - 9/7n

▹ Step-by-Step Explanation

1/7 - 3(3/7n - 2/7)

Remove the parentheses (Distribute -3 among the parentheses):

1/7 - 9/7n + 6/7

Calculate:

1 - 9/7n

Hope this helps!

CloutAnswers ❁

━━━━━━━☆☆━━━━━━━

Answer:

1-9/7n

Step-by-step explanation:

[tex]\frac{1}{7}-3(\frac{3}{7}n-\frac{2}{7} ) \\=\frac{1}{7}-\frac{9}{7}n +\frac{6}{7} \\=\frac{1-9n+6}{7} \\=\frac{7-9n}{7}\\=1-\frac{9}{7}n[/tex]

Answer:

Hey there!

A is correct. The +2 means shifted up two units, 1/2 means compressed by a factor of 1/2, and the -3 means to the left of three units.

Let me know if this helps :)

Answer:

5x^3-2

[tex]ax^{3} +bx^{2} +cx+d\\5x^{3}-given\\ d=-2-given\\5x^{3} -2[/tex]

Explanation:

The two terms are [tex]5x^3[/tex] and [tex]2[/tex]. Terms are separated by either a plus or minus.

We can write it as [tex]5x^3+(-2)[/tex] which is an equivalent form. Here the two terms are [tex]5x^3[/tex] and [tex]-2[/tex]. This is because adding a negative is the same as subtracting.

The coefficient is the number to the left of the variable.

The degree is the largest exponent, which helps form the leading term.

The third degree polynomial written above is considered a cubic binomial. "Cubic"  refers to the third degree, while "binomial" means there are 2 terms.

We can write something like [tex]5x^3[/tex] as 5x^3 when it comes to computer settings.

Answer:

1078

Step-by-step explanation:

The product of 22 and 49 is 1078.

Answer:

1078 is the product

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:

There are a couple ways to solve this.  One would be by finding the least common denominator for each one with 2/3, subtracting, and seeing what is left over.  Another way is converting to decimals.

2/3=0.666666

————————-

7/8=0.875

8/9=0.88888

4/5=0.8

5/7=0.7143

They are all greater than 2/3 (0.6666666), but 5/7 is the closest, so would have the least waste.

Answer:

A square is a retangle

Step-by-step explanation:

Because a squre is a rectangle

Answer:

the number is 80

Step-by-step explanation:

let x be an unknown number so from the above question we deduce that

(70/100)*x=56

70x/100=56

70x=56*100

70x=5600

70x/70=5600/70

x=80

Answer:

The correct choice is option D. -1

Step-by-step explanation:

Find f(x) = - 3 on the table. When y = -3, what is the x value? Look on the right side, you can see it's -1, correct? So, f(x) = - 3 when x = - 1.

Answer:

  2/5

Step-by-step explanation:

  f(x) = 2(5/2)^-x = 2(2/5)^x

The multiplicative rate of change is the base of the positive exponent, 2/5.

Answer:

18/25

Step-by-step explanation:

Due to the fact that the fractions have the same denominator, we can multiply to numerators, and also the denominators. So we get 3x6/5x5.

Which becomes 18/25

Hope this helps!

Answer:

9/5 which simplifies to 1 4/5

Step-by-step explanation:

Answer:

Hey there!

You can think of the rate of change as the slope of a quadratic function- here we see that it is 9/-3, or - 3.

Let  me know if this helps :)

Answer:

–3 meters per second

Step-by-step explanation:

Answer:

4450878

Step-by-step explanation:

Answer:

52 units^2

Step-by-step explanation:

It's unclear what the leg lengths and the width are.  I must assume that the lengths are 12 units and 14 units and that the width of the trapezoid is 4 units.  You were given an illustration for this problem and should have shared it or described the trapezoid in words.  Please do this if the answer given below does not agree with any of your answer choices.

If the lengths are 12 units and 14 units and that the width of the trapezoid is 4 units, then the area is

      12 units + 14 units

A = ---------------------------- * 4 units = 52 units^2

                    2

Answer:

$96

Step-by-step explanation:

6(1/2) = 3 bushels of berries total

3(4) = 12 pecks of berries total

4(8) = 32 quarts of berries total

32(2) = 64 pints of berries total

64 x $1.50 = $96

Answer:

The farmer will make a total of $96 from selling 6 buckets of blueberries.

Step-by-step explanation:

The total price is determined by multiplying the 12 pecks down into pints. Each pint sells for 1.50 and he has 64 pints of blueberries.

64 x $1.50 = $96

Answer:

C

Step-by-step explanation:

The required equation that is rewritten and ready to solve is 4x² - 12x + x - 3 = 0. Option C is correct.

Given that,
The quadratic equation 4x² - 11x - 3 = 0 The equations is rewritten and ready to solve using factoring by grouping is to be determined.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
4x² - 11x - 3 = 0
4x² - 12x + x - 3 = 0
4x[x - 3] + 1[x - 3] = 0
[4x + 1][x - 3] = 0

Thus, the required equation that is rewritten and ready to solve is 4x² - 12x + x - 3 = 0. Option C is correct.

Learn more about simplification here:

https://brainly.com/question/12501526

#SPJ2

Answer:

4^8

Step-by-step explanation:

4^3 * 4^5

We know a^b * a^c = a^(b+c)

4^(3+5)

4^(8)

Hi there!  

»»————-　★　————-««

I believe your answer is:  

[tex]4^8[/tex]

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

[tex]\boxed{\text{Simplifying the answer...}}\\\\4^3 * 4 ^ 5\\-----------------\\\text{Recall the exponent rule:}\\\\a^x * a^y = a^{x+y}\\\\\rightarrow 4^3 + 4^5\\\\\rightarrow 4^{3+5}\\\\\rightarrow \boxed{4^8}[/tex]

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

Answer:

Step-by-step explanation:

Let REPEAT [tex]_{TM[/tex]= { | M is a TM, and for all s ∈ L(M), s = uv where u = v }

To prove that REPEAT [tex]_{TM[/tex]  is undecidable.

Let  REPEAT [tex]_{TM[/tex] {| M is a TM that does not accept M}

Then, we form a TM  u for L by applying TM v as a subroutine.

Assume Repeat   is decidable

Let M be the algorithm that  TM which decides the REPEATU = on input "s" simulate the M

Accept; if M ever enters the accept state

Reject; if M ever enters the reject state

U does not decide the REPEAT as it may loop over s

so REPEAT is undecidable

[tex]10[/tex] divisions between $20$ and $20.1$ so each division is $\frac{20.1-20.0}{10}=0.01$

A is 2nd division from $20.0$, so, A is $20.0+2\times 0.01=20.02$

similarly, C is one division behind $20.0$ so it is 19.99

and B is $20.14$

A rectangle can be constructed using a straightedge, and a setsquare or compass

Please find attached the drawing of rectangle ABCD

The steps to construct the rectangle ABCD are as follows:

Question:

The missing part of the question is the name of the rectangle = ABCD

The given parameters are;

The length of the side AB = 8 cm

The length of the diagonal of the rectangle ABCD = AC = 10 cm

The steps to construct a rectangle are;

h² = [tex]\overline{AC}[/tex]² - [tex]\overline{AB}[/tex]²

∴ h² = 10² - 8² = 36

h = √36 = 6

h = 6 cm = The length of the sides [tex]\mathbf{\overline{AD}}[/tex] and [tex]\mathbf{\overline{CB}}[/tex]

Learn more about the construction of basic shapes here;

https://brainly.com/question/17440931

Answer: Dimension = 27 inches by 39.75 inches

Concept:

A perimeter is a path that encompasses/surrounds/outlines a shape.

Perimeter (rectangle) = 2 (l + w)

l = length

w = width

Solve:

l = 2w - 14.25

w = w

P = 133.5

Given equation

P = 2 (l + w)

Substitute values into the equation

133.5 = 2 (2w - 14.25 + w)

Combine like terms

133.5 = 2 (3w - 14.25)

Distributive property

133.5 = 6w - 28.5

Add 28.5 on both sides

133.5 + 28.5 = 6w - 28.5 + 28.5

162 = 6w

Divide 6 on both sides

162 / 6 = 6w / 6

w = 27 in

l = 2w - 14.25 = 2 (27) - 14.25 = 39.75 in

Hope this helps!! :)

Please let me know if you have any questions