Show that a subset M of a normed space X is total in X if and only if every fe X' which is zero on M is zero everywhere on X.

The situation that can use the binomial probability distribution is a sampling of 100 parts to determine whether or not they meet specifications.

The binomial probability distribution is used to model the probability of a certain number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. In the given situation, each part in the sample either meets the specifications (success) or does not (failure), which makes it a binomial experiment.

To use the binomial probability distribution, we need to know the probability of success (p) and the number of trials (n). In the given situation, we can determine the probability of a part meet specifications based on the given specifications, and the number of trials is fixed at 100, as we are sampling 100 parts.

Using the binomial probability distribution, we can calculate the probability of a certain number of parts meeting specifications out of the 100 sampled parts. This can be useful in determining whether the sample meets the expected specifications or if there are any issues with the manufacturing process.

In summary, the binomial probability distribution can be used in the given situation of sampling 100 parts to determine whether or not they meet specifications, as it involves a fixed number of independent trials with only two possible outcomes.

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The irregular polygon has an area of 39 square units.

In this question we find the case of an irregular pentagon, that is a polygon with five sides with different lengths and five different central angles. The area of any polygon can be found by summing the areas of rectangles and right triangles. The area formulas for rectangles and right triangles are shown below:

Rectangle

A = w · l

Right triangle

A = 0.5 · w · l

Where:

Now we proceed to determine the area of the irregular polygon:

A = 0.5 · 3 · 1 + 0.5 · 5 · 3 + 5 · 6

A = 1.5 + 7.5 + 30

A = 39

The area of the irregular polygon is equal to 39 square units.

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

slope - 3

y - intercept - 40

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(y = 3x + 40\\\rule{150}{0.5}\\y \text{ - Total service fee.}\\\\x \text{ - Number of miles the car is towed.}\\\rule{150}{0.5}\\\text{The given equation is in slope-intercept form.}\\y = mx + b\\\\\rightarrow m \text{ - slope}\\\rightarrow b \text{ - y-intercept}\\\rule{150}{0.5}\\\text{3 takes m's spot so it is the slope.}\)

\(\text{This means that the company will charge 3 dollars for every mile the car is towed.}\\\rule{150}{0.5}\\\text{40 takes b's place to it is the y-intercept. This means that 40 would be the base fee.}\)

»»————-　★　————-««  

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

Answer:

10 and 42

Step-by-step explanation:

The difficulty with word problems is translating them into math.

Let's do that

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

The sum of a number and two times a smaller number is 62.

let's call the bigger number b, and the smaller number s

b + 2s = 62

Three times the bigger number exceeds the smaller number by 116

3b = s + 116

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

Now manipulate one of the equations to isolate the variable

3b = s + 116

Subtract 116 from both sides

3b - 116 = s

substitute for s = 3b - 116 in

b + 2s = 62

b + 2(3b - 116) = 62

Distribute

b + 6b - 232 = 62

combine like terms

7b = 294

Divide both sides by 7

b = 42

to find s plug in b = 42 into

b + 2s = 62

42 + 2s = 62

subtract 42 from both side

2s = 20

divide both sides by 2

s = 10

Answer:

n + 4

Step-by-step explanation:

n is being used to describe the position of a term.

We can see that the sequence is increasing linearly by 1.

Since the position of the next term is increasing linearly by 1, all we have to do is look at the first term and subtract 1 from it to get our constant (4).

An equation to think about this better would be

n + C = S

C is the constant we are solving for.

We know n = 1.

S is the number corresponding in the sequence with n.

1 + C = 5

Subtract 1 from both sides to isolate C.

C = 4

1 + 4 = 5  Checks out

n + 4

You don't need to include the equals sign because the problem asks for an expression which doesn't contain an equals sign unlike an equation.

Answer:

Your answer for when b = 1/2 is 2.

Step-by-step explanation:

4*1/2

Hope this helps!

Answer:

2

Step-by-step explanation:

4b ; b=1/2

4(1/2)

2

Ariel is not correct because mockingbird beats its wings 14 times per second.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

From the table the slope of the data is

= (1260 - 420)/ (90-30)

= 840 - 60

= 14

So, the mockingbird beats its wings approximately 14 times per second.

Thus, ariel is not correct.

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The range at which Dan's car can go is 3.33 miles

A car's range is the distance it can travel with the current amount of fuel in the tank.

The vehicle calculates the range based on the amount of fuel, how the accelerator and brakes are used, and how quickly the car is travelling.

The range of a car can be measured in the unit of distance.

Therefore the range of a car can be calculated as;

R = distance per gallon/ number of gallon.

Dan's car is 40mpg and has 12 gallons in it's tank.

Therefore it's range = 40/12

= 3.33miles.

therefore the range of Dan's car is 3.33miles

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Answer:

36 cups of flour

Step-by-step explanation:

if 3 cups of flour=8 ounces.what about 96 onces you cross multiply

The number of cups of flour will be use if he used 96 ounces of water is 36.

Given that, a baker is making bread dough. He uses 3 cups of flour for every 8 ounces of water.

Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.

Let the number of cups of flour will be use if he used 96 ounces of water is x.

3:8::x:96

⇒ 8×x=96×3

⇒ 8x=288

⇒ x=288/8

⇒ x=36

Therefore, the number of cups of flour will be use if he used 96 ounces of water is 36.

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9514 1404 393

Answer:

  3.78×10^-5

Step-by-step explanation:

To find 4 times the measurement, multiply the measurement by 4.

  4 × 9.45×10^-6 = 37.8×10^-6 = 3.78×10^-5

__

Your calculator or spreadsheet can do this for you and express the result in scientific notation.

Step-by-step explanation:

12 = 2 × 2 × 3

18 = 2 × 3 × 3

56 = 2 ×2 × 2 × 7

Now

Common factor = 2

Remaining factor = 2 × 3 × 2 × 3 × 7

LCM = RF × CF

= 504

hence the lCM of 12 , 18 and 56 is 504...

\(...\)

Answer:

-15 meters

Step-by-step explanation:

Elevation means the height to which something is elevated. If the object is above sea level then it is positive. If the object is below sea level it is negative.

The elevation of the surface of the ocean is, - 15 meters.

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

Given that;

A fish is 15 meters below the surface of the ocean.

Here, The fish is 15 meters below the surface of the ocean.

Hence, Its elevation shows in negative sign.

Thus, We get;

The elevation of the surface of the ocean = - 15 meters.

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We reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

The null and alternative hypotheses are:

H_0: mu <= 42

H_a: mu > 42

Using the sample mean, sample size, and population standard deviation given, we can calculate the test statistic:

z = (x - mu) / (sigma / sqrt(n))

z = (42.85 - 42) / (2.65 / sqrt(68))

z = 2.56

Using a standard normal distribution table or calculator, we can find the critical values for each significance level:

a = 0.10: z_crit = 1.28

a = 0.05: z_crit = 1.645

a = 0.01: z_crit = 2.33

a = 0.001: z_crit = 3.09

Since our test statistic is greater than the critical value at a = 0.10 and a = 0.05, we reject the null hypothesis at these levels. However, we fail to reject the null hypothesis at a = 0.01 and a = 0.001.

To calculate the p-value, we can use a standard normal distribution table or calculator to find the probability that a z-score is greater than or equal to our test statistic:

p-value = P(Z >= 2.56)

p-value = 0.0052

Since the p-value is less than all of the given significance levels, we reject the null hypothesis and conclude that there is strong evidence to support the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

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Answer:

The answer is 12860082/100000000000

The fraction form of the expression is -1/7776.

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

\((-1/6)^5\)

This can be simplified as,

= \(\frac{(-1)^5}{6^5}\)

= -1/7776

Thus,

The fraction form of the expression is -1/7776.

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50%

since 98/2 = 49

Thats it

Answer:

2a + 3b = 5

b = a - 5

Step-by-step explanation:

2a + 3b = 5

b = a - 5

You can write this another way:

2a + 3(a-5) = 5 ( I added the second formula in the first one )

Now you gotta factor out:

2a + 3a - 15 = 5

Here im gonna do plus 15

2a + 3a = 20 ==> 5a = 20

Now if you divide by 5, you get: a = 4

Now you can fill in the second formula again

b = a - 5 (ill fill this in now)

b = 4 - 5 = -1

So, this makes:

a = 4 , b = -1

Answer:

a = -2

b = -7

Step-by-step explanation:

the best method to solving this system of equations would be substitution since you are given an expression that equals one of the variables you're solving for (which is b = a - 5)

to begin, plug in a - 5 for b in the equation 2a + 3b = 5.

2a + 3b = 5 ⇒ 2a + 3(a - 5) = 5

the next step is to distribute 3 to a - 5. start with distributing 3 to a, which is just multiplying 3 · a. after that, you're left with a minus sign and 5, so that sign gets attached to the 5 and makes it a -5. distribute 3 to -5, which is just multiplying 3 · -5.

2a + 3(a - 5) = 5 ⇒ 2a + 3a - 15 = 5

since you have two terms with the variable a on one side of the equation (2a and 3a), combine the two like terms.

2a + 3a - 15 = 5 ⇒ 5a - 15 = 5

add 15 to both sides of the equation. on the left side, -15 and 15 cancel each other out because -15 + 15 = 0, leaving you with only 5a. on the right side of the equation, you have 5 - 15, which equals -10.

now your equation is 5a = -10.

divide both sides of the equation by 5. on the left side of the equation, you have 5a/5, which equals 1a, or a. on the right side, you have -10/5, which equals -2.

therefore a = -2.

now plug in -2 for a in b = a - 5 in order to solve for b!

b = a - 5 ⇒ b = -2 - 5

subtract -2 - 5.

b = -2 - 5 ⇒ b = -7

therefore b = -7.

your solutions are a = -2 and b = -7 :) i hope this helps! have a great day <3

Based on the given statement, the correct answer would be:

option A. The statement makes sense. Sally listens to music when she is depressed. If she is listening to music, then Sally must be depressed.

The given statement is discussing a potential relationship between Sally's emotional state of being depressed and her behavior of listening to music. The question asks whether the statement makes sense, is clearly true, or does not make sense, and provides four options to choose from.

Option A states that the statement makes sense and suggests that if Sally is listening to music, then she must be depressed. This option is reasonable because the statement establishes a connection between Sally's depression and her behavior of listening to music. It implies that listening to music is a coping mechanism or an activity she engages in when she experiences depressive feelings.

Therefore, if someone observes Sally listening to music, it can be inferred that she might be in a depressed state at that moment.

On the other hand, options B and C can be eliminated because they make extreme and unsupported claims. Option B suggests that Sally only listens to music when she is depressed, which is not explicitly stated in the given statement. Option C states that if Sally is listening to music, then she must not be depressed, which contradicts the initial connection established between depression and listening to music in the statement.

Option D highlights the incomplete nature of the statement but does not render it entirely senseless. It acknowledges that the statement mentions Sally's behavior of listening to music when she is depressed but does not provide information about other potential reasons she might listen to music.

In summary, option A is the most appropriate choice as it aligns with the established correlation between Sally's depression and her listening to music, while considering the possibility of other reasons for her music listening behavior.

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Answer:

The ratio should be 100 : 20. If it needs to be simplified then 5:1

Step-by-step explanation:

100 m is the distance traveled and the time it took was 20 seconds. Divide both sides by 20 and you get 5:1

(If it doesn't need to be simplified then 100 : 20)

The minimum value of the function is ≈ 82.014 and the maximum value ≈ 89.778.

To find the minimum and maximum values of the function f(x, y) = x² + 2y² subject to the constraint 12 - 216y = 15648, we can use the method of Lagrange multipliers. Let L(x, y, λ) = x² + 2y² + λ(12 - 216y - 15648), where λ is the Lagrange multiplier. Then, we need to find the critical points of L:

From the first equation, we get x = 0. Substituting this into the second equation, we get y = 54λ. Substituting x = 0 and y = 54λ into the third equation, we get λ = -7 1/108. Therefore, the critical point is (0, -71/36).

To check if this critical point is a maximum or minimum, we need to find the Hessian matrix of L:

The eigenvalues of H are λ1 = -232, λ2 = -24, λ3 = 150, so H is negative definite at the critical point. Therefore, the critical point is a maximum.

To find the minimum value, we need to consider the boundary of the constraint. Solving for y in the constraint, we get;

Substituting each value of y into the function f(x, y), we get;

Therefore, the minimum value of f(x, y) subject to the constraint is -216 ( -71/216 + 13/18√3)² + 144, and the maximum value is f(0, -71/36). Converting the square root to a decimal, we get the minimum value ≈ 82.014, and the maximum value ≈ 89.778.

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Answer:

The area of a circle is equal to pi times the square of its Radius

Step-by-step explanation:

Answer:

Pie, Diameter, Circle

Step-by-step explanation:

Word form One hundred three and five hundred three thouandth

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The number of pieces in a jigsaw puzzle and the number of minutes required for a person to complete are not directly related. The time it takes for a person to complete a jigsaw puzzle depends on several factors, including the person's experience with puzzles, the level of difficulty of the puzzle, the size of the puzzle pieces, and the person's level of concentration.

For example, a 500-piece puzzle might take one person several hours to complete, while another person might be able to finish it in just a few hours. Similarly, a 1000-piece puzzle might take one person a full day to complete, while another person might be able to finish it in just a few hours.

In general, the larger the number of pieces in a puzzle, the more time it will take to complete. However, the actual time required can vary greatly depending on the individual and the specific puzzle.

Answer:

y=1/7x

Step-by-step explanation:

Plug into Point slope form:

y - 1= 1/7( x -7)

y -1 = 1/7 x -1

y -1 +1 = 1/7x -1 +1

y= 1/7x

Answer:

Larry is wrong

Step-by-step explanation:

Multiplying big numbers will give significantly bigger results then multiplying smaller numbers then adding them. 14 + 12 = 26 & 8 + 12 = 20. 14 x 12 = 68 & 8 x 12 = 96. 96 + 168 is alot less then 26 * 20 so that is why larry is wrong

Answer:

\(m=\frac{y2-y1}{x2-x1}\)

Step-by-step explanation:

Answer:

\(\huge\boxed{m=\frac{y_2-y_1}{x_2-x_1} }\)

Step-by-step explanation:

The equation for slope is \(m=\frac{y_2-y_1}{x_2-x_1}\), when given two points,

\((x_1,y_1), and (x_2,y_2)\).

Hope it helps :) and let me know if you want me to elaborate.

Answer:

M/paws= (3x-3) and m/rqs

=(x+19).

the value of x is

Step-by-step explanation:

13 and 13√2 is the value of x and y in the given diagram

The given diagram is a right triangle, we need to determine the value of x and y.

Using the trigonometry identity

tan45 = opposite/adjacent
tan45 = x/13

x = 13tan45
x = 13(1)
x = 13

For the value of y

sin45 = x/y

sin45 = 13/y
y = 13/sin45

y = 13√2
Hence the exact value of x and y from the figure is 13 and 13√2 respectively.

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Answer:

Thanks

Step-by-step explanation:

ADDFFFG

The demand model for the number of fishes caught is given as:

\(y = 349x + 50\)

(a) The meaning of the slope

A linear equation is represented as:

\(y = mx + c\)

Where m represents the slope.

So, by comparison:

\(m = 349\)

This means that, they caught 349 fishes every day

(b) The meaning of the y-intercept

A linear equation is represented as:

\(y = mx + c\)

Where c represents the y-intercept.

So, by comparison:

\(c =50\)

This means that, the initial number of fish is 50

(c) The number of fish in 30 days

We have:

\(y = 349x + 50\)

Substitute 30 for x

\(y = 349 \times 30 + 50\)

\(y = 10520\)

Hence, the number of fish in 30 days is 10520

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