Ashley needs new batteries for the flashlights at her house. Each flashlight takes 4
batteries. Write an equation to show how the number of batteries needed, b, depends on the number of flashlights, f.

Answer:  Choice C

The fraction 1/16

In other words the "StartFraction 1 Over 16 EndFraction"

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Work Shown:

[tex]\displaystyle L = \lim_{x \to -2}4^x\cos(\pi x)\\\\\\L = 4^{-2}\cos(\pi (-2))\\\\\\L = \frac{1}{4^2}\cos(-2\pi)\\\\\\L = \frac{1}{16}\cos(2\pi)\\\\\\L = \frac{1}{16}(1)\\\\\\L = \frac{1}{16}\\\\\\[/tex]

The limit of the function f(x)=[tex]4^{x}[/tex]cos(πx) is 1/16 which is start fraction 1 over 16 end fraction.

The limit is the extent to which the value of function exists.

The function which is given is f(x)=[tex]4^{x}[/tex]cos(πx) and we have to find the limit of f(x).

L.H.L of f(x)

[tex]\lim_{x \to \-2} 4^{x}cos([/tex]πx)

Put x=-2-h

[tex]\lim_{h \to \0} 4^{-2-h}cos([/tex]π(-2-h)

put h=0

=[tex]4^{-2} cos(2[/tex]π)

=[tex]4^{-2}*1[/tex]  {cos(2π)=1}

=1/16

R.H.L of f(x)

[tex]\lim_{x \to \-2} 4^{x}[/tex] cos(πx)

Put the value of x=-2+h

=[tex]\lim_{h \to \0}4^{-2+h}[/tex] cos{π(-2+h)}

Put the value of h=0

=[tex]4^{-2}*cos(2[/tex]π)

=1/16

L.H.L=R.H.L

Hence the limit of the function [tex]4^{x}cos([/tex]πx) is 1/16.

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Answer:

Step-by-step explanation:

First find the volume of the Cylinder, plug in the Radius (3), and the height (14) into the formula.

V= 3 x (3 squared) 9 x 14

V of Cylinder = 378 cm^3

V of Cone use the formula given,

V = [tex]\frac{3*9*5}{3}[/tex]

V = 45 cm^3

Add them together and you get 423 cm^3

Answer:

16 quarters

Step-by-step explanation:

4 x 4 = 16

$1 = 4 quarter

Flynn has 16 quarters.

Answer:

[tex]3.14 \times 10 ^{3} < 2.6 \times 10^{3} [/tex]

Step-by-step explanation:

[tex]3.14 \times 10 ^{3} [/tex]

[tex]3140[/tex]

[tex]2.6 \times 10 ^{4} [/tex]

[tex]26000[/tex]

Answer:

∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE  are the additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS.

The additional information to prove that ΔXYZ ≅ ΔFEG using ASA or AAS

is ∠Z ≅ ∠G and XY ≅ FE

Option E is the correct answer.

It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.

We have,

ΔXYZ ≅ ΔFEG

We see that,

∠X and ∠F are equal

To prove that ΔXYZ ≅ ΔFEG using ASA or AAS.

We need one more congruent angle and one corresponding side.

∠Z ≅ ∠G and XY ≅ FE can be used to prove this.

Now,

∠X = ∠F (angle)  (given)

∠Z ≅ ∠G (angle)

XY ≅ FE (side)

ΔXYZ ≅ ΔFEG

Thus,

The additional information is:

∠Z ≅ ∠G and XY ≅ FE

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Answer: It is the third to the top

Step-by-step explanation:

90's block each other out add you rotate it 180 degrees you get this.  

Answer:

79.8

Step-by-step explanation:

Answer:

n=9M, when m is 6,n=18

Step-by-step explanation:

If n is proportional to M

n=kM

27=3k

k=27/3

k=9

the formula on terms of n and M is

n= 9M

2) If m= 6,

n= 3M

n=3(6)

n=18

Answer:

n = 108

Step-by-step explanation:

given n is proportional to m² then the equation relating them is

n = km² ← k is the constant of proportion

to find k use the condition n = 27 when m = 3 , then

27 = k × 3² = 9k ( divide both sides by 9 )

3 = k

n = 3m² ← equation of proportion

when m = 6 , then

n = 3 × 6² = 3 × 36 = 108

Answer:

Step-by-step explanation:

According to definition of the function, each input must have exactly one output.

One of the given relationships - T-shirt prices reveals two outputs.

All the rest show one-to-one relationship.

Answer:

14.28%

Step-by-step explanation:

I'm not sure if it's right but this is how I worked it out,

the box's contents are 4.2 pounds in total,

therefore in a fraction it would be 6/42

you turn a fraction into a percentage you do the numerator divided by the denominator

6÷42=0.142857(decimal form)

now you just turn it into a percentage

14.28%

please correct me if I'm wrong

Answer:

6 * 1.2 = 7.2

7 * 1.2 = 8.4

8 * 1.2 = 9.6

now find the Area and Perimeter of the enlarged triangle:

A = 1/2bh

A = 1/2 * 9.6 * 8.4

A = 40.32

P = a + b + c

P = 7.2 + 7.2 + 9.6

P = 24

So, the Area is 40.32 and the Perimeter is 24.

Answer:

28620

Step-by-step explanation:

→ Find the multiplier

( 100 + 6 ) ÷ 100 = 1.06

→ Multiply by the original amount

27000 × 1.06 = 28620

Answer:

27.8 nearest tenth pints

To find, divide the value by 16

Answer:

I am positve it 2mph

Step-by-step explanation:

becuase for evry hr u drive 2 miles

Answer:

15.

Step-by-step explanation:

1) property:

m(∠B)+m(∠D)=180°;

2) according to the property:

3x+9x=180°; ⇒ x=15°

The value of x is 15 degree in the trapezoid ABCD.

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles

A trapezoid is a quadrilateral with one pair of opposite sides parallel.

ABCD is a trapezoid.

We have to find the value of x in the given quadrilateral.

The sum of opposite angles of a quadrilateral is 180 degrees.

m(∠B)+m(∠D)=180°

From the figure m(∠B) is 3x and m(∠D) is 9x

3x+9x=180°

Combine the like terms

12x=180

x=15 degrees.

Hence, the value of x is 15 degree in the trapezoid ABCD.

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Answer:

Step-by-step explanation:

given that a bag contains 6 balls labelled A to F.

Given that a ball is drawn at random and its letter is recorded as outcome.

Since each ball is equally likely to be drawn the sample space for one ball drawing is

S = {A,B,C,D,E,F} and n(S) = 6

Let G be the event of choosing a lable from D to F

G = The event of choosing a label from D to F= {D,E,F}  n(A) = 3

A sample space is a set which contains the set of all the possible outcomes or results that could occur while performing an experiment.

i.e. the sample space while flipping a coin is: {H,T}

The sample space while tossing a six-sided die is: {1,2,3,4,5,6}

Here it is given that:

A bag has six balls labeled:  A,B,C,D,E,F

One ball will be randomly picked, and its letter will be recorded as the outcome.

       This means that the sample space is given by:

                     Sample space={ A,B,C,D,E,F}

Now, when the event is choosing a letter from   D to F.

            Then the sample space is:

                     Sample space= {D,E,F}

Answer: D. Subtraction property of equality

Step-by-step explanation:

They are subtracting 6 from both sides of the equality.

Answer:

66

Step-by-step explanation:

It's given that

Tn = 5n + 16

The 10th term is

T10 = 5(10) + 16

= 66

The 10th term of the sequence is 66.

In mathematics, a sequence is a list of numbers arranged in a specific order. Each number in the sequence is called a term. Sequences can be finite, meaning they have a specific number of terms, or they can be infinite, continuing indefinitely.

We have the rule: 5n + 16

Now, To find the 10th term of the sequence, we can substitute n = 10 into the given rule:

5n + 16 = 5(10) + 16 = 50 + 16 = 66

Therefore, the 10th term of the sequence is 66.

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Answer:

7176

Step-by-step explanation:

23 is a prime factor.

3 & 13 are the prime factors of 39.

2, 2, & 2 are the prime factors of 8.

Determine the max. number of times each prime factor occurs.

Calculate: 2^3 x 3 x 13 x 23 = 7176

Answer:

7,176

Step-by-step explanation:

The LCM of these numbers is found when you multiply the three numbers together: 23*39*8 = 7,176

Hope this helps!

Using the Newton's law of cooling, the time it takes to cool to 100°F is 116 mins.

According to the Newton's law of cooling, the when an object is exposed to the surrounding it looses heat rapidly untill it is at a thermal equilibrium with the suurroundings.

Now;

T(t) = T(s) + (To - Ts)e^-kt

T(t) = temperature at time T

To = initial temperature

Ts = temperature of the surrounding

k = colling constant

t = time taken

200 = 68 + (230 - 68)e^-15k

200 = 68 + 162e^-15k

200 - 68/162 = e^-15k

ln(0.815) = -15k

k = ln(0.815)/-15

k = 0.014 min-1

Now;

100 = 68 + (230 - 68)e^-( 0.014t)

100 -68/162 = e^-( 0.014t)

0.198 =e^-( 0.014t)

ln(0.198) = -( 0.014t)

t = ln(0.198)/-0.014

t = 116 mins

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Answer:

x=1 y=4
x=2 y=7
x=3 y=10

Step-by-step explanation:

To find the answer, you have to plug in the x-value for the equation to find y.

You will then find out that every time x increases by 1, y increases by 3.

The number of marbles in the bag illustrates probability

The conclusion about the number of marbles in the bag is that the bag can only contain one type of marble

The probabilities are given as:

P(Red) = 1

P(Green) = 1

For a distribution, the sum of all probabilities must equal to 1.

This means that:

P(Red) + P(Green) = 1

So, we have:

1 + 1 = 1

This gives

2 = 1

The above equation is false because 2 does not equal to 1.

So, the conclusion about the number of marbles in the bag is that the bag can only contain one type of marble i.e. either red marbles are in the bag or blue marbles are in the bag

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Answer:

Step-by-step explanation:

Finding the angles of quadrilateral:

Sum of all angles of quadrilateral = 360

2x + 10 + 3x + 3x + 5 + 5x +20 =360

2x + 3x + 3x + 5x + 10 + 5 + 20 = 360

Combine like terms

                    13x + 35 = 360

Subtrace 35 from both sides

                            13x = 360 - 35

                           13x  = 325

Divide both sides by 13

                               x = 325/13

                               x = 25

5x +20 = 5*25 +20

            = 125 +20

             = 145°

Measeure of largest angle : 145°

Using the vertex of the quadratic equation, it is found that a maximum height of 78.75 feet is reached after 2.13 seconds.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

In this problem, the height is modeled by:

h(t) = -16t² + 68t + 6.5.

The coefficients are a = -16, b = 68, c = 6.5, and the vertex will be given by:

[tex]x_v = -\frac{b}{2a} = -\frac{68}{-32} = 2.13[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a} = -\frac{68^2 - 4(-16)(6.5)}{-64} = 78.75[/tex]

A maximum height of 78.75 feet is reached after 2.13 seconds.

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Answer:

0.8L = red

0.64L = yellow

0.06L = white

Step-by-step explanation:

R : Y : W

20 : 16 : 1.5

20 + 16 + 1.5 = 37.5

1.5 ÷ 37.5 = 0.04

0.04 × 20 = 0.8L = red

0.04 × 16 = 0.64L = yellow

0.04 × 1.5 = 0.06L = white