A consumer wanted to compare two types of battery storage. One type is refrigerated and the other is room temperature. It is a common belief that refrigerated batteries last longer. This belief is tested by placing 10 fully charged batteries into each type of storage and then measuring the percentage of charge remaining after thirty days. A coin tip was used to determine which type of storage each battery would be placed in first. Results indicated that there was no difference in the two types of storage Complete parts (a) through in below.
What type of experimental design is this?
A) Matched pairs design
B) Completely randomized design
C) Randomized block design
D) Case-control study

Answer:

16.3 meters

Step-by-step explanation:

1 pi radian =180°

0.19 =?

(0.19×180)÷3.142=10.9°

cos 10.9=16/d

d cos 10.9 =16

d=16÷cos 10.9

d=16.3 meters

The integral\int(1/x^4 + 9x^2) dx converges by comparison to a convergent integral, and its value is 1/3

To determine whether the integral converges or diverges, we can use the limit comparison test with the integral:

Since for all x > 0, we have:

Thus, by the limit comparison test:

converges if and only if converges.

We can evaluate  using the power rule of integration:

where C is the constant of integration. Evaluating this integral from 1 to infinity, we get:

∫(1/x^4) dx from 1 to infinity = lim as b → infinity

=>

=> 0 - (-1/3)

=> 1/3

Since the integral  dx converges by comparison to a convergent integral, and its value is 1/3.

To learn more about  Convergent integral :

Note: The full question is

Determine whether the integral converges or diverges; if it converges, evaluate. (If the quantity diverges, enter DIVERGES. Do not use the [infinity] symbol in your answer.) [infinity] dx x4 + 9x2 1

Answer:

Step-by-step explanation:

½×6×8 = 24 cm²

We need to compare the number of bones in the arms and legs with the number of bones in the face.

The question says that there are 30 bones in the arms and legs.

The question also says that there are 14 bones on the face.

So, the difference between these will be how many more bones there are in the arms and legs than in the face:

Answer:

Depends on person to person.

Some may cry ( if it is a child or kid )

Some may get shout.

Some may come away from sleep, that is their sleep rhythm may get disturbed.

Some won't react, that is they continue to sleep even after they fall from the bed.

Step-by-step explanation:

In this case, I will continue to sleep, because on the floor another bed will be there.

Answer:

You COULD DIEEEE ._.

Step-by-step explanation:

Answer:

An acute angle

Step-by-step explanation:

An acute angle is smaller than an obtuse ad right angle.

hope this helps and hope it was right 'cause I really don't know what you meant. :)

Answer:

552 eggs

Step-by-step explanation:

A dozen is equal to 12

Solve:

Multiply 46 by 12

Answer:

hope this helps !

Step-by-step explanation:

1) ( 8 x- 16 ) / (x²- 13 x + 22 ) = ( 8 x- 16 ) ( x - 11) ( x -2 ) = 8 ( x-2) ( x-11) ( x- 2 ) = 8/(x-11)

Restriction x ≠ 11 & x ≠ 2

since both values render the denominator = to 0 & we can't divide by 0.

Answer:

Perimeters of Similar Figures

of their perimeters is equal to the ratio of their corresponding side lengths.

Step-by-step explanation:

Answer:

here it is

Perimeter is the distance around a two dimensional shape, a measurement of the distance around something; the length of the boundary.

Answer:

8

Step-by-step explanation:

9: 9, 18, 27, 36, 45, 54, 63, 72

12: 12, 24, 36, 48, 60, 72

72 is the first number that can be divided (evenly) by both 9 and 12

Answer:

8

Step-by-step explanation:

9: 9, 18, 27, 36, 45, 54, 63, 72

12: 12, 24, 36, 48, 60, 72

72 is the first number that can be divided (evenly) by both 9 and 12

Answer:

$ 4.86

Step-by-step explanation:

Subtract 7.19 and 2.33

7.19-2.33=4.86

Answer:

29.4°

Step-by-step explanation:

The equation can be rearranged to give C directly.

 C = arccos((a^2 +b^2 -c^2)/(2ab))

 C = arccos((90^2 +55^2 -50^2)/(2·90·55))

 C = arccos(8625/9900) ≈ 29.4002°

 C ≈ 29.4°

The measure of angle C is approximately 29.46 degrees.

To find the measure of angle C (cos(C)) using the given values a = 55, b = 90, and c = 50, we can use the Cosine Rule formula:

cos(C) = (a² + b² - c²) / (2 * a * b)

Substitute the given values:

cos(C) = (55² + 90² - 50²) / (2 * 55 * 90)

Now, calculate the numerator:

cos(C) = (3025 + 8100 - 2500) / (2 * 55 * 90)

cos(C) = 8625 / 9900

Now, divide to get the final value of cos(C):

cos(C) ≈ 0.8707

To find the measure of angle C itself, we can take the inverse cosine (arccos) of this value:

C ≈ arccos(0.8707)

Using a calculator, you'll find:

C ≈ 29.46 degrees (rounded to two decimal places)

So, the measure of angle C is approximately 29.46 degrees.

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First of all we are being asked about the probability of a car not needing repairs. We will have to work with the percentages like fractions, for example a 15% chance would be 0.15.

The probability of picking a car that doesn't need repairs ( P(nr) ) can be calculated using the probability of car needing at least one repair ( P(r) ). There are two possible outcomes when you pick a car: or the car needs no repairs or it needs at least one. This means that sum of the probabilities of both outcomes is 1:

Now, the probability of needing at least 1 repairs P(r) is given by the sum of the probabilities of needing 1, 2, 3 or more repairs. These probabilities are given to us so:

So the probability of needing no repairs is:

Writting as a percentage the probability of needing no repairs is 74%.

While solving this one we also find the solution for the third item since P(r) is the probability of needing some repairs. Since P(r)=0.26 then that probability is 26%.

For the second item we need to find the probability of needing no more than 1 repair. This probability is given by the probability of needing no repairs and the probability of needing one (and only one) repair. Then:

Therefore this probability is 89%.

In summary, the correct answers are 74%, 89% and 26% respectively.

Answer:

\( -\frac{1}{18} \)

Step-by-step explanation:

Average rate of change = \( \frac{f(b) - f(a)}{b - a} \)

Where,

a = -2,

f(a) = f(-2) = \( \frac{1}{(-2) - 7} = \frac{1}{-9} \) = -⅑

f(a) = -⅑

b = 5

f(b) = f(5) = \( \frac{1}{(5) - 7} = \frac{1}{-2} \) = -½

f(b) = -½

Plug in the values into the equation

Average rate of change = \( \frac{-\frac{1}{2} - (-\frac{1}{9}}{5 -(-2)} \)

\( = \frac{\frac{-9 - (-2)}{18}}{7} \)

\( = \frac{\frac{-7}{18}}{7} \)

\( = \frac{-7}{18} * \frac{1}{7} \)

\( = \frac{-1}{18} * \frac{1}{1} \)

\( = \frac{-1}{18} * 1 \)

\( = -\frac{1}{18} \)

A. Definition = (the third meaning.)

B. Postulate (axiom) = (the first meaning.)

C. Common notion = (the last meaning.)

D. Theorem = (The second meaning.)

E. Corollary = (the fourth meaning.)

Proof is evidence or an argument that helps to establish a fact or the truth of a statement. For example, most people won't accept new concepts or ideas without proof of its existence.

Part a.

The expected value is calculated by multiplying eacn of the possible outcomes by their respective probability and then summing all of those values. In our case, we have

then

which gives

Part b

On the other hand, the sample variance is computed as

where μ is the mean value. Given by

So we get

which gives

Therefore, the answers are:

a) E(X)= 4.6

b)

Var(X)=3.05

Answer:

-5.5

Step-by-step explanation:

After simplifying the given equation we get x as 150.

What is Algebraic expression ?

Algebraic expressions are the idea of expressing numbers using letters or alphabets without specifying their actual values. The basics of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are called here as variables. An algebraic expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is a coefficient.

here, it is given that :

4(x+15)=640 and we have to solve for x.

first, open bracket to multiply 4 :

4(x+15)=640

4x + 4.15 = 640

4x + 60 = 640

Now, subtract 60 both side :

4x + 60 - 60 = 640 - 60

4x = 600

Now, divide "4" both side to get value of x :

x = 600/4

x = 150

Therefore, after simplifying the given equation we get x as 150.

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The only interval with a negative rate of change is the last one:

[1, 2.5]

For an interval (a, b) and a function f(x), the rate of change is defined as:

\(r = \frac{f(b) - f(a)}{b - a}\)

So the rate of change is only negative when the function evaluated on the first value of the interval is larger than the function evaluated in the second one.

For example, on the interval [1, 2.5} we can see that:

f(1) = 3

f(2.5) = -1

Then on this interval, the rate of change will be negative, meaning that this is the correct option.

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Answer:

It's D: 1 to 2.5

Step-by-step explanation:

It's D: 1 to 2.5

The equation of the sinusoid function is:

3 Sin πx + 2.

Let's analyze the given options to find the correct equation:

a. 3 Cos πx + 2:

This option is a cosine function with a vertical shift of 2, but it does not have the correct amplitude or period. Therefore, it is not the correct equation.

b. 3 Sin x: This option is a sine function with the correct amplitude, but it does not have the correct vertical shift or period. Therefore, it is not the correct equation.

c. 3 Sin πx + 2: This option is a sine function with the correct amplitude and vertical shift. Let's check if it has the correct period:

To determine if the period is correct, we need to calculate the x-values when the function repeats itself.

In this case, we need to find x-values such that sin(πx) = 0, since the function will reach its maximum and minimum points again at those x-values.

sin(πx) = 0 when πx = 0, π, 2π, 3π, ...

Solving for x, we have:

πx = 0 ⟹ x = 0

πx = π ⟹ x = 1

πx = 2π ⟹ x = 2

πx = 3π ⟹ x = 3

From this, we can see that the function repeats itself every integer value of x, which matches the given information.

Therefore, option (c) is the correct equation: 3 Sin πx + 2.

Option (d) 3 Cos x does not have the correct vertical shift or period, so it is not the correct equation.

Hence, the equation of the sinusoid function is:

3 Sin πx + 2.

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The temperature at the bottom of the mountain is 50.9 °C.

Let's work through the given information step by step to find the temperature at the bottom of the mountain.

The temperature in the hotel is 21 °C.

The temperature in the hotel is 26.7 °C warmer than at the top of the mountain.

Let's denote the temperature at the top of the mountain as T_top.

So, the temperature in the hotel can be expressed as T_top + 26.7 °C.

The temperature at the top of the mountain is 3.2 °C colder than at the bottom of the mountain.

Let's denote the temperature at the bottom of the mountain as T_bottom.

So, the temperature at the top of the mountain can be expressed as T_bottom - 3.2 °C.

Now, let's combine the information we have:

T_top + 26.7 °C = T_bottom - 3.2 °C

To find the temperature at the bottom of the mountain (T_bottom), we need to isolate it on one side of the equation. Let's do the calculations:

T_bottom = T_top + 26.7 °C + 3.2 °C

T_bottom = T_top + 29.9 °C

Since we know that the temperature in the hotel is 21 °C, we can substitute T_top with 21 °C:

T_bottom = 21 °C + 29.9 °C

T_bottom = 50.9 °C

Therefore, the temperature at the bottom of the mountain is 50.9 °C.

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Answer:

I could help

Step-by-step explanation:

The english phrase "Seven less than four times a number" as an algebraic expression is 4x - 7

From the question, we have the following parameters that can be used in our computation:

seven less than four times a number

Represent the number with x

So:

four times a number means 4x

So, we have

seven less than 4x

seven less than means - 7

So, we have

4x - 7

Hence, the english phrase as an algebraic expression is 4x - 7

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Complete question

write the english phrase as an algebraic expression. Let x represent the number

Seven less than four times a number

Answer:

Step-by-step explanation:

Answer:

x² + 3 and x² + 4x + 5

Step-by-step explanation:

(a)

to find f(g(x)) substitute x = g(x) into f(x)

f(g(x))

= f(x² + 1)

= x² + 1 + 2

= x² + 3

(b)

to find g(f(x)) substitute x = f(x) into g(x)

g(f(x))

= g(x + 2)

= (x + 2)² + 1 ← expand factor using FOIL

= x² + 4x + 4 + 1

= x² + 4x + 5

The volume of the box is 99 unit cubes.

A cube is a three-dimensional object that has six faces, twelve edges and eight vertices. The length, width and height of a cube usually has equal dimensions. The volume of the box is a function of the dimension of the cubes in it and the number of layers.

Volume of a box = number of layers x amount of units

9 x 11 - 99 unit cubes

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Answer:

58.5

Step-by-step explanation:

the area for a square is l x l so 9

the area for a rectangle is l x w so 33

the area for a rectangle is l x w /2 so 33 /2 = 16,5

so after adding them all up you get 58.5

Answer:

Step-by-step explanation:

19 from pythagoras theorem

x^2 = 15^2 + 6^2

x^2 = 225 + 36

x^2 = 261

x = sq.root of 261

x=16.2

20 Using SOHCAHTOA

Cos theta = adj/ hypotenuse

cos y = 24/30

cos y = 0.8

y= arc cos 0.8

y = 36.9

The probability that it is raining if the flight has been delayed is 0.07, or 7%.

We can use the following formula to calculate the probability that it is raining if the flight has been delayed:

P(Rain|Delayed) = P(Rain and Delayed) / P(Delayed)

We are given that P(Rain) = 0.07 and P(Delayed) = 0.18. We can also use the fact that P(Rain and Delayed) = P(Rain) * P(Delayed):

= 0.07 * 0.18

= 0.0126.

Substituting these values into the formula, we get:

P(Rain|Delayed) = 0.0126 / 0.18 = 0.07

Therefore, the probability that it is raining if the flight has been delayed is 0.07, or 7%.

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Answer:

Based on the last digit discovered, which is 0, and the flavor of pie, which is cherry, the code to unlock the maze is "0 Cherry".

Answer:

45 degrees

Step-by-step explanation:

The 4 angles of a quadrilateral will add to 360.

We know 1 of them (angle B) is 90 degrees.

We can set up an equation to solve the others.

2x+3x+x+90 = 360

Now solve for x.

Start by combining the x terms together.

6x+90 = 360

6x = 360-90

6x = 270

(6x/6) = 270/6

x = 45 degrees

Check back to see if that makes sense and if the equation equals 360 when x is 45:

2x+3x+x+90 = 360

2(45)+3(45)+45+90=360.