A study called the Nelson study researched the number of text messages teenagers made from 2010 to 2012. In 2010, the study reported that teens sent an average of 2,380 text messages per month. In 2012, the study reported that teens sent an average of 3,213 texts per month. Complete this sentence: The relative change in the number of text messages from 2010 to 2012 was

Answer:

x+4→AB=7+4=11

Step-by-step explanation:

Answer:

the domain(s) are 7, 5,-3, and -6.

Step-by-step explanation:

the domain is the x which can repeat. the range is the y which can't repeat.

1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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The final answer is (f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

To find the composite functions (f o g)(x) and (g o f)(x), we need to substitute one function into the other.

(f o g)(x):

To find (f o g)(x), we substitute g(x) into f(x):

(f o g)(x) = f(g(x))

Let's substitute g(x) = x^2 - 8 into f(x) = x^2 + 8:

(f o g)(x) = f(g(x)) = f(x^2 - 8)

Now we replace x in f(x^2 - 8) with x^2 - 8:

(f o g)(x) = (x^2 - 8)^2 + 8

Simplifying further:

(f o g)(x) = x^4 - 16x^2 + 64 + 8

(f o g)(x) = x^4 - 16x^2 + 72

Therefore, (f o g)(x) = x^4 - 16x^2 + 72.

(g o f)(x):

To find (g o f)(x), we substitute f(x) into g(x):

(g o f)(x) = g(f(x))

Let's substitute f(x) = x^2 + 8 into g(x) = x^2 - 8:

(g o f)(x) = g(f(x)) = g(x^2 + 8)

Now we replace x in g(x^2 + 8) with x^2 + 8:

(g o f)(x) = (x^2 + 8)^2 - 8

Simplifying further:

(g o f)(x) = x^4 + 16x^2 + 64 - 8

(g o f)(x) = x^4 + 16x^2 + 56

Therefore, (g o f)(x) = x^4 + 16x^2 + 56.

(f o g)(2):

To find (f o g)(2), we substitute x = 2 into the expression (f o g)(x) = x^4 - 16x^2 + 72:

(f o g)(2) = 2^4 - 16(2)^2 + 72

(f o g)(2) = 16 - 64 + 72

(f o g)(2) = 24

Therefore, (f o g)(2) = 24.

In summary:

(f o g)(x) = x^4 - 16x^2 + 72

(g o f)(x) = x^4 + 16x^2 + 56

(f o g)(2) = 24

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Answer:

X = 14.48528137

Step-by-step explanation:

Solution: Better buy $ 19.24 for 20 packs of gum.

Analysis: As we want to compare two purchase options of packs of gum, we need to find the rate of each option. In this case, we want to find the rate: Price per 1 pack of gum. We find it calculating the total price between the number of packs of gum.

Option 1:

Option 2:

After we find both rates, let's compare them:

For that reason, we can assume the best purchase option is $ 19.24 for 20 packs of gum.

The p-value (0.036) is less than the significance level (α = 0.01), we reject the null hypothesis.

To determine if there is sufficient evidence to support the claim that more than 10% of ABM B students wear glasses, we can conduct a hypothesis test using the p-value approach.

Null hypothesis (H0): The proportion of ABM B students wearing glasses is equal to or less than 10%.

Alternative hypothesis (Ha): The proportion of ABM B students wearing glasses is greater than 10%.

Let p be the true proportion of ABM B students wearing glasses. We want to test if p > 0.10.

Given that we have conducted a survey of 35 students and found that 8 of them are wearing glasses, we can calculate the sample proportion, denoted by \(\bar p\), as 8/35 ≈ 0.229.

Next, we calculate the test statistic, which follows an approximate standard normal distribution under the null hypothesis.

Test statistic: z = (\(\bar p\) - p) / sqrt(p * (1 - p) / n)

= (0.229 - 0.10) / sqrt(0.10 * (1 - 0.10) / 35)

≈ 1.798

To determine the p-value, we find the probability of observing a test statistic greater than or equal to 1.798 assuming the null hypothesis is true.

Using a standard normal distribution table or a calculator, we find that the probability of observing a test statistic as extreme as 1.798 is approximately 0.036.

Since the p-value (0.036) is less than the significance level (α = 0.01), we reject the null hypothesis.

Therefore, we have sufficient evidence to support the claim that more than 10% of ABM B students wear glasses based on the survey results.

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Answer:

Question 1:

A) Parallelogram

B) Right Angled Triangle

Question 2:

Using parallelogram to use properties of parallel lines. To find whether a quadrilateral is parallelogram, first we will write it's coordinates. After writing coordinates, we find slope of each line by slope formula. After this , we compare the slope of equal lines through which we come to know whether they are parallel to eachother or not. After that, if two pairs of lines are parallel, then the given quadrilateral is a parallelogram.

Answer:

3) Obtuse

4) Right

Step-by-step explanation:

3)

11 + 13 > 25 It is a triangle

11² + 13² = 25²

121 + 169 = 625

290 ≠ 625

Since hypotenuse is larger, the triangle is obtuse

4)

21 + 28 > 35 It is a triangle

21² + 28² = 35²

441 + 784 = 1225

1225 = 1225

Since the hypotenuse is equal to the legs, it's a Right triangle

Answer:

B.

Step-by-step explanation:

factored form actually contains the x intercepts right in it. Basically whatever sets the whole equation equal to zero.

On the graph you can see that it passes through both positive and negative 4. so (x+4)(x-4) is the answer because plugging in 4 for x will make it zero. Same for plugging in negative 4

Hope this helps!

Answer:

Step-by-step explanation:

With reference < H

perpendicular (p) = 12

base (b) = 5

so now

tangent of < H

= p / b

= 12 / 5

hope it helps :)

We kindly invite to check the image attached below to see the triangle constructed on Cartesian plane.

The measure of angle A is approximately equal to 46.102° and the measure of side AC is equal to 2√13 centimeters.

Triangles are figures generated by three distinct points set on Cartesian plane, with three line segments (AB, BC, AC) and three internal angles. In this problem we show all steps to construct a triangle with the help of a graphing tool. First, set point B at origin.

B(x, y) = (0, 0)

Second, add point C along x-axis:

C(x, y) = (6, 0)

Third, determine point A and add it on Cartesian plane:

A(x, y) = (8 · cos 60°, 8 · sin 60°)

A(x, y) = (4, 6.928)

Fourth, draw all line segments in triangle ABC. The result is shown in the image attached below.

Finally, we determine the measure of angle A and side AC by trigonometry:

Angle A:

First, determine the length of line segment AC by law of cosine:

AC = √(AB² + BC² - 2 · AB ·BC · cos B)

AC = √(8² + 6² - 2 · 8 · 6 · cos 60°)

AC = 2√13

Second, calculate the angle A by law of cosine:

cos A = (BC² - AB² - AC²) / (- 2 · AB · AC)

cos A = [6² - 8² - (2√13)²] / [- 2 · 8 · 2√13]

A ≈ 46.102°

Side AC:

AC = 2√13

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Answer:

C

Step-by-step explanation:

1.7 squared

1.7*1.7= 2.89

or 1.7^2

Answer: B

Step-by-step explanation:

Answer:

x+6=y

Step-by-step explanation:

Answer:

The distance from John's house to Bill's house is 5 units

Step-by-step explanation:

John's house is located at the point (-5,7) and Bill's house is located at (-2,3) in a map of the town of Springville.

We need to find the distance from John's house to Bill's house. We use the formula of the distance between two points:

Given two points A(x,y) and B(w,z), the distance between them is:

\(d=\sqrt{(w-x)^2+(z-y)^2}\)

Applying the formula:

\(d=\sqrt{(-2+5)^2+(3-7)^2}\)

\(d=\sqrt{3^2+4^2}\)

\(d=\sqrt{9+16}=\sqrt{25}\)

d=5

The distance from John's house to Bill's house is 5 units

Answer:

\(Measure \: of \: angle \: z = \boxed{ \tt{ 19.5\degree}}\)

Statistics is referred to as a discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.

This is referred to as information that has been translated into a form that is efficient for movement or processing.

Statistics involves using information that has been translated into a form that is efficient for movement or processing through different tools such as mean standard deviation etc.They help to provide more details about a set of data which makes it use very important.

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The angle m∠JIX is 90 degrees.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90 degrees.

IG bisect CIJ. Hence,

m∠CIG ≅ m∠GIJ

Therefore,

m∠CIX = 150 degrees

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90 degrees because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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The measure of angle m∠JIX is  estimated to be 90⁰.

You should understand that an angle is a figure formed by two straight lines or rays that meet at a common endpoint, called the vertex.

IX is perpendicular to IJ. Therefore, angle m∠JIX is 90⁰.

Frim the given parameters,

IG⊥CIJ.

But;  m∠CIG ≅ m∠GIJ

⇒ m∠CIX = 150⁰

Hence, let's find m∠JIX.

Therefore, m∠JIX is 90⁰ because IX is perpendicular to IJ. Perpendicular lines forms a right angle.

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Answer:

\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx = \boxed{ \frac{4x^7}{7} - \frac{x^4}{2} + \frac{7x^2}{2} - 4x + C }\)

General Formulas and Concepts:
Calculus

Integration

Integration Rule [Reverse Power Rule]:
\(\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C\)

Integration Property [Multiplied Constant]:
\(\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx\)

Integration Property [Addition/Subtraction]:
\(\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx\)

Step-by-step explanation:

Step 1: Define

Identify given.

\(\displaystyle \int {4x^6 - 2x^3 + 7x - 4} \, dx\)

Step 2: Integrate

∴ we have found the given integral.

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Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Integration

Answer:

11

Step-by-step explanation:

Answer:

Step-by-step explanation:

-3x + 10 = 43

-3x = 33

x = -11

The data contained in the foodindustry file can be expressed mathematically by calculating the average sales per store for each restaurant chain.

This can be done by dividing the total sales of all stores in the chain by the total number of stores in the chain. Mathematically, this could be expressed as follows:

Average Sales per Store = Total Sales of all Stores / Total Number of Stores

For example, if a chain had 10 stores with a total sales of $100,000, the average sales per store would be $10,000 ($100,000/10). This calculation can be used to compare the performance of different restaurant chains, as well as to identify potential areas of improvement.

The data contained in the foodindustry file can be expressed mathematically by calculating the average sales per store for each restaurant chain, which is done by dividing the total sales of all stores in the chain by the total number of stores in the chain.

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By using the concept of dilation factor, length of BC obtained is 3 units

What is dilation factor?

Dilation is a transformation which changes the size of a figure by a certain factor.

That factor is called the scale factor

In the figure, A'B'C'D' is the image of ABCD under dilation with a scale factor of 3

A'B'C'D' is the dilated figure

Length of B'C' = 9 units

Length of BC = \(9 \div 3\) = 3 units

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Complete Question

The figure has been attached here

The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.

The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.

The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.

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Answer:

-0.825

Step-by-step explanation:

Did not know the options so do not know if this is right or not.

Here is ur answer.

- BRAINLIEST answerer

Answer:

\(\dfrac{5e^2}{2}\)

Step-by-step explanation:

Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.

Given function:

\(y=x^2\ln(2x)\)

Differentiate the given function using the product rule.

\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)

\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)

\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)

Input the values into the product rule to differentiate the function:

\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)

To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:

\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)

Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:

\(\boxed{\dfrac{5e^2}{2}}\)

On solving the provided question, we can say that -  here in graph we have on solving equation  \(2x^2+ 9y^2 \\\) = \(8 + 9 = 17\)

An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.

here,

from graph, x= 2

y = 1

\(2x^2+ 9y^2 \\\)

\(8 + 9 = 17\)

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Total water bill for the month is $62.37.

It seems that you may have accidentally left out the total amount of your water bill.

The total amount by simply adding the amounts of the individual bills together:

Total water bill =\($36.34 + $26.03\)

= \($62.37\)

You have not provided enough information to determine your total water bill.

You have only given the amounts of your individual bills from Metro Water Services and Madison Suburban Utility District.

To find your total water bill, you simply need to add the two bills together.

So, the total amount you owe for water this month would be:

Total water bill = \($36.34 + $26.03\)

= \($62.37\)

It appears that you may have forgotten to include the full amount of your water bill by accident.

Simple addition of the separate bill amounts yields the following sum:

Water bill total = \($36.34 + $26.03\)

= \($62.37\)

Your total water bill cannot be calculated because not enough information has been given.

Only the amounts of your individual Metro Water Services and Madison Suburban Utility District bills have been provided.

You just need to combine the two invoices together to get your total water bill.

As a result, this month's total water bill for you would be:

Water bill total =  \($36.34 + $26.03\)

= \($62.37\)

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Answer: (3, 1)

Step-by-step explanation: Plug in (3,1) to get -2x3 -1 to get -7≤-4, and -7 is less than -4