What is the volume of a cube of side 2cm ?

The derivative of f(x) = 4x² using the definition of the derivative can be proven to be f'(x) = 8x.

To prove this, we start with the definition of the derivative:

f'(x) = lim(h->0) [(f(x + h) - f(x)) / h]

Substituting f(x) = 4x² into the equation, we have:

f'(x) = lim(h->0) [(4(x + h)² - 4x²) / h]

Expanding and simplifying the numerator, we get:

f'(x) = lim(h->0) [(4x² + 8xh + 4h² - 4x²) / h]

Canceling out the common terms, we are left with:

f'(x) = lim(h->0) [(8xh + 4h²) / h]

Factoring out h, we have:

f'(x) = lim(h->0) [h(8x + 4h) / h]

Canceling out h, we get:

f'(x) = lim(h->0) (8x + 4h)

Taking the limit as h approaches 0, the only term that remains is 8x:

f'(x) = 8x

Therefore, the derivative of f(x) = 4x² using the definition of the derivative is f'(x) = 8x.

To sketch the graph of the function f(x) = 4x², we recognize that it represents a parabola that opens upward. The coefficient of x² (4) determines the steepness of the curve, with a larger coefficient leading to a narrower parabola. The vertex of the parabola is at the origin (0, 0) and the curve is symmetric about the y-axis. As x increases, the function values increase rapidly, resulting in a steep upward slope. Similarly, as x decreases, the function values increase, but in the negative y-direction. Overall, the graph of f(x) = 4x² is a U-shaped curve that becomes steeper as x moves away from the origin.

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The solution for the given equation is x=6.

The given equation is 17.95x + 24 = 18.95x + 18.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 17.95x + 24 = 18.95x + 18

⇒ 18.95x-17.95x=24-18

⇒ x=6

Hence, the solution for the given equation is x=6.

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The probability that she selects the route of three specific capitals is 97290/1.

The probability that she selects the route of three specific capitals can be calculated by taking the total number of possible routes and dividing it by the total number of routes that involve the three specific capitals. To calculate the total number of possible routes, multiply the number of states (47) by the number of routes that could be selected from each state (2). This gives 94 total possible routes.

47 x 46 x 45 ways = 97290 ways

= 1/97290

Now, calculate the number of routes that involve the three specific capitals. Since the president is selecting three states, the total number of routes will be 3. Therefore, the probability that she selects the route of three specific capitals is 3/94, which can be simplified to 97290/1.

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Answer:

=11

Step-by-step explanation:

= -1 - 2(8)+7(4)

=-1-16+7(4)

= -1-16+28

=11

Step-by-step explanation:

-1^2-16+28

-1^2+12

-1+12=11

Answer:

C = 14.99n + 9.99

Step-by-step explanation:

From the information given in the question, we already have the slope which is 14.99.

To find the y-intercept (which in this case represents the same delivery fee no matter how many Blu-rays are purchased) we can use the order for 10 Blu-rays.

Multiply 14.99 by 10 to get the cost of all the DVDs.

(14.99)(10) = 149.90

To find the value of the delivery fee we can minus 149.90 from 159.89:

159.89 - 149.90 = 9.99

The cost of delivery is $9.99

Therefore, we can write the final equation like this:

C = 14.99n + 9.99

I hope this helps!!

- Kay :)

There are several statistics that are robust to outliers: Median, Interquartile range, Winsorized mean and Trimmed mean.

These statistics are more suitable for datasets that contain outliers as they are less influenced by the extreme values and provide more accurate information about the central tendency and variability of the data.

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The inequality that shows the possible distances of house A from house C is x ≥ 5

Inequality is defined as the relation which makes a non-equal comparison between two given functions.

An inequality is a mathematical statement that compares two values or expressions using a relational operator, such as less than (<), greater than (>), less than or equal to (≤), greater than or equal to (≥), or not equal to (≠). Inequalities are used to describe relationships between quantities or to express constraints or conditions.

We are given that;

Distance= 4miles

Let x be the distance of house A from house C. Since house B is 4 miles from house A, and house C is at least 1 mile from house B, we can write an inequality that relates x, 4, and 1:

x ≥ 4 + 1

This inequality means that the distance of house A from house C is greater than or equal to the sum of the distances of house A from house B and house B from house C.

To solve this inequality, we need to simplify it by adding 4 and 1:

x ≥ 5

Therefore, by inequality the answer will be x ≥ 5.

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If Jim has to run faster than 80% of adult then he need to run with speed 5.89 mph.

A Normal Distribution is defined as the distribution where the random variable values are distributed symmetrically.

In the Question it is given  that

mean (μ) = 5.3                                                   ...(i)

standard deviation (σ) = 0.7                             ...(ii)

and Jim runs faster than 80% of adult men,

and the group follows a normal distribution.

For Normal Distribution

Jim runs faster than 80% of adult men, is represented by

P(x<z)=0.80

z=φ(0.80)

z=0.842    ( from z table )                                  ...(iii)

we know that

\(z=\frac{x-\mu}{\sigma}\)                                         ...(iv)

Substituting the values of (i),(ii) and (iii)  in (iv) we get

\(0.842=\frac{x-5.3}{0.7} \\ \\ x-5.3=0.842*0.7\\ \\ x-5.3=0.5894\)

\(x=0.5894+5.3\\x=5.8894\)

x≅5.89

Therefore , if Jim has to run faster than 80% of adult then he need to run with speed 5.89 mph.

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Answer:

D is the correct equation.

\(2500 = 125( {2}^{w} )\)

The probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

According to the given question.

Total number of cards in a deck is 52.

As we know that total number of red cards in a well shuffled deck is 26.

Since, Eric first draws a red card, places it back in the deck, shuffles the deck, and then draws another card. Which means there is a replacement of cards.

So, the probability of drawing the first card is red = 26/52 = 1/2

And the probability of drawing the another card is red = 26/52 = 1/2

Therefore,

The probability of drawing a red card, placing it back in the deck, and drawing another red card

= 1/2  × 1/2

= 1/4

Hence, the probability of drawing a red card, placing it back in the deck, and drawing another red card is 1/4.

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Answer:

x = 32.7

Step-by-step explanation:

High school geometry can throw you off really hard. One year, you're learning about transformations, then the next you have to write PROOFS. But it's alright because we can take this problem.

We can observe that we have a right triangle. Sadly, we can't use the Pythagorean Theorem to solve for x because we're not given the length of the hypothenuse. But, we could use one other thing: trigonometric functions.

Trigonometric functions are functions that relate sides of a triangle to an angle θ on that triangle. The three main trigonometric functions are sine, cosine, and tangent, and all three are defined as follows:

Sine θ  = Opposite / Hypothenuse

Cosine θ = Adjacent / Hypothenuse

Tangent θ = Opposite / Adjacent

You can memorize this by remembering the phrase: SOHCAHTOA. Note that an angle is opposite to a side if it's directly opposite from it and is adjacent to a side if the side is not the opposite side nor the hypothenuse, the longest side on a right triangle.

So, how do we use trigonometry to solve the problem.

First, let's find our θ, the angle of our triangle. We can see that we have an angle of 61 degrees, so we can say that θ is 61 degrees. We can also say that θ is opposite to the side of 59 and adjacent to the side of x. We can put this into an equation and solve for x.

IMPORTANT: IF YOU ARE USING DEGREES, SET YOUR CALCULATOR TO DEGREES AND NOT RADIANS WHEN DOING CALCULATIONS.

tan θ = opposite / adjacent

tan(61) = 59 / x

x = 59 / tan(61)

x = 32.7

Therefore, we can say that x = 32.7.

Answer:

-6

Step-by-step explanation:

The number line represents an inequality. The inequality is x  ≥ -3.

What is a number line?

A number line is a picture of a graduated straight line that serves as a visual representation of real numbers in primary mathematics. Every number line point is considered to correspond to a real number and every real number to a number line point.

If a number line contains a close circle, then the number includes in the inequality.

If a number line contains an open circle, then the number does not include in the inequality.

In the graph, there is a close circle on -3.

The line represents all real numbers greater than -3.

Since there is a close circle on -3, thus -3 include in the inequality.

The given variable is x.

The graph represents all real numbers greater than or equal to -3.

The inequality is x  ≥ -3.

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Answer:

the correct answer is 2/200

Step-by-step explanation:

The probability that a randomly chosen person from the survey is female and at least 6 feet tall is 2/200

The probability of an event is a number that indicates how likely the event is to occur.

It is expressed as a number in the range from 0 and 1, or, using percentage notation, in the range from 0% to 100%.

The more likely it is that the event will occur, the higher its probability.

Given that, the result of a survey of 200 adults are shown in the table,

We need to find the probability that a randomly chosen person from the survey is female and at least 6 feet tall,

P(E) = favorable outcomes / total outcomes

= 2 / 200

Hence, the probability that a randomly chosen person from the survey is female and at least 6 feet tall is 2/200

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The probability that he misses the train today is 0.135 or 13.5%.

P(Class runs late)=30%=0.30

P(Miss train ∣ Class runs late)=45%=0.45

General multiplication rule:

P(A and B)=P(A)×P(B ∣ A)

Using the general multiplication rule, we then obtain (and using that the student always catches his train if the class ends on time) :-

P( Miss train)=P( Miss train and Class runs late)=P(Class runs late)×P(Miss train ∣ Class runs late)

= 0.30×0.45

= 0.135

= or 13.5%.

So, the the probability that he misses the train today is 0.135 or 13.5%.

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Two crucial tasks inherent in the initial stage of group therapy are orientation and establishing group norms.Ambiguity and lack of a structured approach in groups often lead to confusion, inefficiency, and potential challenges.

Orientation involves providing essential information to group members about the purpose, goals, and guidelines of the therapy group.

It helps individuals understand what to expect, builds trust, and creates a sense of safety and predictability within the group. Orientation may include discussing confidentiality, group rules, expectations, and addressing any questions or concerns.

Establishing group norms involves collaboratively developing shared guidelines and expectations that govern the behavior and interactions within the group. This process allows group members to contribute to the creation of a supportive and respectful group climate. Group norms help set boundaries, encourage open communication, and foster a sense of cohesion among members.

Without clear structure and guidance, group members may struggle to understand their roles, goals, or the process of the group therapy. Ambiguity can hinder progress, create frustration, and impede meaningful communication.

Lack of structure may also result in difficulty managing conflicts, decision-making, or time management within the group. It can lead to unequal participation, power struggles, and a lack of accountability.

To address these issues, it is important for group therapy to provide a clear framework, establish ground rules, and facilitate structured activities or interventions that promote clarity, engagement, and progress. A structured approach helps create a supportive environment, enhances group dynamics, and maximizes the therapeutic benefits of the group process.

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Answer:

what is the question?

Step-by-step explanation:

Answer: Infinite

Step-by-step explanation: You can substitute the number x with anything and get the same answer, so it’s an infinite amount.

Answer:

Hilda had 35$ before purchase.

Answer:

$35

Step-by-step explanation:

Given:

Spend $35

After Purchase No More Money

So Hilda Had $35 then she Spend $35 at last had no more money so Before purchasing she had $35

Answer:

The measure of ∠A = 107.5°

Step-by-step explanation:

Given that

ABCD is a kite such that

AB = BC and AD = DC

Join A and C

Since AB = BC

→ ∠BAC = ∠BCA

Since , the angles opposite to equal sides are equal.

Let ∠BAC = ∠BCA = x°

and

Since AD = DC

→ ∠CAD = ∠ACD

Since , the angles opposite to equal sides are equal.

Let ∠CAD = ∠ACD = y°

Now

In ∆ ADC ,

∠ADC + ∠CAD + ∠ACD = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 30° + y°+ y° = 180°

⇛ 30°+2y° = 180°

⇛ 2y° = 180°-30°

⇛ 2y° = 150°

⇛ y° = 150°/2

⇛ y° = 75°

Therefore, ∠CAD = ∠ACD = 75°

and

In ∆ ABC,

∠ ABC + ∠BAC + ∠BCA = 180°

Since , the sum of the all angles in a triangle is 180°

⇛ 115° + x° + x° = 180°

⇛ 115°+2x° = 180°

⇛ 2x° = 180°-115°

⇛ 2x° = 65°

⇛ x° = 65°/2

⇛ x° = 32.5°

Therefore, ∠BAC = ∠BCA = 32.5°

Now, ∠ A = ∠BAC + ∠CAD

⇛ ∠A = 32.5° + 75°

⇛ ∠A = 107.5°

Therefore, ∠A = 107.5°

Answer:-

Read more:

Similar Questions

ABCD is a kite with AD=AB A= 116° B=2x° D=(5x-147)° Find the size of the smallest angle of the kite.

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Answer:

x = 1

Step-by-step explanation:

Horizontal asymptotes are the y-values for which a particular function is undefined;

Finding the horizontal asymptote for linear reciprocal function is quite simple;

For this kind of function, where there is no x term in the numerator, the horizontal asymptote is just equivalent to the constant added to the fraction (note: having no added constant is the same as having an added 0);

so:

f(x) = 1/(x - 1) = (1/( - 1 )) + 0

The horizontal asymptote is y = 0 for this function.

If it was F(x) = (1/(x - 1)) + 1, the horizontal asymptote would be  y = 1

hope it help!! :)

-y+4x=19

I think that's it but I'm not sure

Answer:

2x-y=20 I hope this is right!

Step-by-step explanation:

2*x

=2x

2*4

=8

y=2x-8(2)

y=2x-16-3

y=2x-20

20+y=2x

-y       -y

20=2x-y

H0: The distribution of lunch preferences is 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza.

Ha: The distribution of lunch preferences is not 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place.

In hypothesis testing, we have a null hypothesis (H0) and an alternative hypothesis (Ha). The null hypothesis represents the claim or assumption we want to test, while the alternative hypothesis represents the opposite or alternative claim.

In this case, the null hypothesis (H0) states that the distribution of lunch preferences is 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place. The alternative hypothesis (Ha) states that the distribution of lunch preferences is not 70% cafeteria, 10% hut, 10% taco wagon, and 10% pizza place.

To test these hypotheses, a random sample of 150 students is selected, and their lunch preferences are recorded. The goal is to determine if the observed distribution of lunch preferences in the sample provides enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

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Answer:

The equation is:

\(409 = T - 223\)

And the solution is:

\(T = 632\)

Step-by-step explanation:

Given

Represent Kiran with K and Tyler with T

Kiran score is represented as:

\(K = 409\)

Also, Kiran scored 223 less than Tyler.

This is represented as:

\(K = T - 223\)

Substitute 409 for K

\(409 = T - 223\)

Make T the subject

\(T = 409 +223\)

\(T = 632\)

The probability that the sample mean will be greater than 57.95 is 0.0495.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. This is the basic probability theory, which is also used in the probability distribution.

To solve this question, we need to know the concepts of the normal probability distribution and of the central limit theorem.

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z=\dfrac{X-\mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The Central Limit Theorem establishes that, for a random variable X, with mean \(\mu\) and standard deviation \(\sigma\), a large sample size can be approximated to a normal distribution with mean \(\mu\) and standard deviation \(\frac{\sigma}{\sqrt{\text{n}} }\).

In this problem, we have that:

The probability that the sample mean will be greater than 57.95

This is 1 subtracted by the p-value of Z when X = 57.95. So

\(Z=\dfrac{X-\mu}{\sigma}\)

By the Central Limit Theorem

\(Z=\dfrac{X-\mu}{\text{s}}\)

\(Z=\dfrac{57.95-53}{3}\)

\(Z=1.65\)

\(Z=1.65\) has a p-value of 0.9505.

Therefore, the probability that the sample mean will be greater than 57.95 is 1-0.9505 = 0.0495

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Given function is,

To find the Horizontal and vertical shift.

Horizontal shift is defined as any changes which is made by adding or substracting to the variable x in the function.

Vertical shift is defined as any changes which is made by adding or substracting to the variable y in the function.

So in the given function the value inside the root is ( x+2 ). so the horizontal shift is two unit left side.

So in the given function the value out side the root is -3, which directly add it to the variable y.

So the vertical shift is three unit down ( Downwards since negative side ).

So the required answer is 2 units left side and 3 units downwards.

The equation below correctly represents the situation. Therefore, it's true.

A mathematical statement known as an equation is made up of two expressions joined together by the equal sign. a formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign.

It should be noted that Jill's bowl of pudding contains 12 ounces, and she eats 0.1of an ounce each second and Barb's bowl of pudding contains 0.1 of an ounce, and she adds 2 ounces each second.

The appropriate equation will be:

12 - 0.1(x) = 2 + 0.1(x)

12 - 0.1x = 2 + 0.1x.

Therefore, the answer is yes.

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Determine whether or not the equation below correctly represents each situation. If so, write "yes". If not, write the correct equation for the situation described.

12 - 0.1x = 2 + 0.1x.

Jill's bowl of pudding contains 12 ounces, and she eats 0.1of an ounce each second. Barb's bowl of pudding contains 0.1 of an ounce, and she adds 2 ounces each second. After how many seconds will the two bowls contain the same amount of pudding?

It will take about 5.18 years for the car to be worth 8,200.

We can use the given formula to find the value of the car after x years:

\(V = 20,000(0.8)^x\)

We want to know how long it will take for the car to be worth 8,200. So we can set V equal to 8,200 and solve for x:

\(8,200 = 20,000(0.8)^x\)

Dividing both sides by 20,000 gives:

\(0.41 = (0.8)^x\)

Taking the logarithm of both sides with base 0.8, we get:

\(log0.8(0.41) = x\)

Using a calculator, we can find:

x ≈ 5.18

Therefore, it will take about 5.18 years for the car to be worth 8,200.

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The answer is closest to 0.196. This means that if we repeat the experiment many times, we would expect to draw the blue marble twice in approximately 19.6% of the trials.

We can solve this problem using the hypergeometric probability distribution. The hypergeometric distribution is used when we have a finite population and we want to calculate the probability of drawing a certain number of objects of a specific type without replacement.

In this case, the population consists of 8 marbles, one of which is blue. We want to calculate the probability of drawing the blue marble twice when we draw 5 marbles without replacement. The number of ways to choose 5 marbles out of 8 is given by the binomial coefficient:

C(8,5) = 56

The number of ways to choose the blue marble twice and the other three marbles from the remaining 7 is:

C(1,2) * C(7,3) = 35

Therefore, the probability of drawing the blue marble twice is:

P = 35/56 = 0.625.

The closest answer choice to this probability is 0.196. Therefore, the answer is closest to 0.196. This means that if we repeat the experiment many times, we would expect to draw the blue marble twice in approximately 19.6% of the trials.

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