Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the reflected function will change because the input values will be the opposite sign from the reflected function. Simon disagrees with Alissa. He states that if an exponential function is reflected across the y-axis, the domain will still be all real numbers.

Which student is correct and why?

Alissa is correct because the domain will change from negative to positive x-values.
Alissa is correct because a reflection across the y-axis will change the possible input values of the reflected function.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.
Neither student is correct.

The height of the cylinder is (a) 8.75 meters

The given parameters are:

Volume = 315[tex]\pi[/tex]

Radius, r = 6

The volume of a cylinder is:

[tex]V = \pi r^2 h[/tex]

So, we have:

[tex]315\pi = \pi * 6^2 * h[/tex]

Divide both sides by 36[tex]\pi[/tex]

h = 8.75

Hence, the height of the cylinder is (a) 8.75 meters

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The graph that matches the function f(x) = 2(x – 1)2(x + 1)(x + 2) is shown in the attached file

A function assigns the value of each element of one set to the other specific element of another set.

We want to draw the graph of the function f(x) = 2(x – 1)2(x + 1)(x + 2). Using relevant coordinates input into the function and the generated output, the graph of the given function is as attached below.

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0.385 is the probability under given conditions.

Lets simplify the above problem,

Given n=20, p=0.05, q=0.95

Probability that in a sample of 20 window frames:

None will need adjustments.

P(x=0)= 0.95^20 = 0.3585

At least one will need adjustment?

P(x>=1) = 1 - P(x=0)

= 1 - 0.3585

= 0.6415

More than two will need adjustment?

P(x>2) = 1 - P(x=0) -P(x=1) -P(x=2)

= 1 - 0.3585 - 20C1(0.05)^1*(0.95)^19 - 20C2(0.05)^2*(0.95)^18

= 0.6415 - 20*0.05*0.3774 - 190*0.0025*0.3972

= 0.2641-0.18868

= 0.0755

Hence 0.385 is the solution of the given problem.

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The minimum possible distance that Fyodor could be from Alyosha is 4 meters.

Given Information and Deduction

It is given that Fyodor is 3 meters in distance away from Dmitri and 5 meters from Ivan.

Now, since we know that the longest side of a right angle triangle formed by the dividing the rectangular room into two parts using a diagonal is the hypotenuse. Thus, if we want to find the minimum possible distance between Fyodor and Alyosha, we will have to assume that Ivan is standing diagonally opposite to Fyodor, as shown in the figure below.

Calculating the Minimum Distance

According to Pythagoras Theorem,

(hypotenuse)² = (base)² + (perpendicular)²

Here, the hypotenuse is the distance between Fyodor and Ivan.

Perpendicular and the base are the distances between Fyodor and Dmitri, and Fyodor and Alyosha respectively.

⇒ base = √(hypotenuse)² -(perpendicular)²

⇒ base = √(5)²-(3)²

⇒ base = √(25-9)

⇒ base = √16

⇒ base = 4 meters

Therefore, the minimum possible distance between Fyodor and Alyosha is 4 meters.

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Answer:

a(b+c) = a into b + a*c

So, 79(457+35) = 79*457 + 79*35

Step-by-step explanation:

One accurate statement amount Arab Americans is that b. Arab Americans include both Muslims and Christians.

Arab Muslims are known to include both Muslims and Christians and indeed it is estimated that more Arab Americans are Christians as opposed to Muslims.

They are also quite urbanized and have very high rates of education which has given then access to more income.

Options for this question include:

a. Arab Americans are not urbanized.

b. Arab Americans include both Muslims and Christians.

c. Arab Americans rank relatively low in terms of income and occupation

d. Arab Americans tend to have low levels of education and skills.

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Question 11

1) [tex]\overline{BA} \cong \overline{FA}[/tex], [tex]\angle 1 \cong \angle 2[/tex] (given)

2) [tex]\angle A \cong \angle A[/tex] (reflexive property)

3) [tex]\triangle AEB \cong \triangle ACF[/tex] (ASA)

4) [tex]\overline{AC} \cong \overline{AE}[/tex] (CPCTC)

Question 12

1) Isosceles [tex]\triangle ACD[/tex] with [tex]\overline{AC} \cong \overline{AD}[/tex], [tex]\overline{BC} \cong \overline{ED}[/tex] (given)

2) [tex]\angle ACD \cong \angle ADC[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle ACB[/tex] and [tex]\angle ACD[/tex] are supplementary. [tex]\angle ADC[/tex] and [tex]\angle ADE[/tex] are supplementary (angles that form a linear pair are supplementary)

4) [tex]\angle ACB \cong \angle ADE[/tex] (supplements of congruent angles are congruent)

5) [tex]\triangle ABC \cong \triangle AED[/tex] (SAS)

6) [tex]\overline{AB} \cong \overline{AE}[/tex] (CPCTC)

7) [tex]\triangle ABE[/tex] is an isosceles triangle (a triangle with two congruent sides is isosceles)

Note: I changed the names of the segments in Question 11 because of the word filter.

The time it will take for the block of ice to melt if the temperature is 45 degrees is 3 hours.

The cost to travel 22 miles is 55 dollars.

let

time it takes for ice to melt = x

air temperature = y

Therefore,

x ∝ 1 / y

x  = k / y

when x = 2.5 hours and y = 54 degrees

Hence,

k = 2.5 × 54

k = 135

The time it will take for the block to melt at 45 degrees = 135 / 45 = 3 hours

It costs $35 for a ride from the city centre to the airport, 14 miles away.

where

c = cost

m = number of miles

Therefore, the equation is as follows:

35 / 14 = 2.5

c = 2.5m

Hence, when you travel 22 miles,

c = 22(2.5)

c = 55 dollars

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Answer:

A

Step-by-step explanation:

The rule for a 180 degree clockwise rotation is (-x, -y). After applying this to the figure, it must be translated one unit right to match the image.

Add up the number of students within the random sample data:
32+26+28+22 = 108

We can then use proportional fractions / cross-multiply to answer the question.

In a sample size of 108 students, 32 of them preferred Movie A.
There are 900 students in total.

[tex]\frac{32}{108} =\frac{x}{900}[/tex]

32*900 = 28800

108*x = 108x

108x = 28800

x = [tex]266\frac{2}{3}[/tex] or [tex]\frac{800}{3}[/tex]

In decimal form that is approximately 266.667 and round that to the nearest whole number, you get 267 students who would prefer Movie A.

Labor productivity is normally measured by (c) dividing total real domestic output by the number of workers or by the number of labor hours.

What is labour productivity in India?

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The amplitude is 6 and vertical translation is 2. Therefore Option C is correct

For the transformation of y=f(x) to f(x)+k, for k>0, f(x) is moved k upwards and for transformation of f(x) to f(ax) it depends upon the value of a If |a|>1 then f(ax) is f(x) squashed horizontally by a factor of a and If 0<|a|<1 then f(x) is stretched horizontally by a factor of a.

So by the graph it is clearly visible that amplitude of the graph is 6 as the distance from the centre line (or the still position) to the top of a crest or to the bottom of a trough is 6 and the vertical translation is 2 as distance moved by the graph upwards is 2.

Thus the amplitude is 6 and vertical translation is 2.

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Based on the speed of the plane, the number of hours it will take to fly 3,008 miles is 5.47 hours.

The speed of the plane is given as 550 miles per hour

In order to reach 3,008 miles, the plane should travel for:

= Distance / Speed

= 3,008 / 550

= 5.47 hours

Rest of the question is:

how many hours will it take a plane to go 3 008 miles if it travels at 550 mph

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The value of du becomes 4 by integration.

According to the statement

we have given a two statement which are u - 4x and  u = x + 1.

And we have to find the value of du by the use of integration.

An Integral assigns numbers to functions in a way that describes the data.

So,

From u  - 4x

here du becomes by derivative

du - 4dx/du

du = 4dx/du.  -(1)

And in u = x + 1.

here du becomes

du = dx/du  -(2)

by comparing both terms from equation (1) and (2) we get the value of du

du = 4.

the value of du is 4.

So, The value of du becomes 4 by integration.

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Answer:

1251 cm

Step-by-step explanation:

Perimeter is just adding the side lengths together.

Answer:

f(-x) = -4x^3 + 9x, f(x) is an odd function

Step-by-step explanation:

We are given that f(x) = 4x^3 - 9x. In order to solve this problem, we first need to understand what an odd function is and what an even function is. When we have an odd function, f(-x) = -f(x). Meaning, that if we plug -x in for x, we should get -f(x). On the other hand, with an even function, f(-x) = f(x). Even if you change the sign, when you simplify, you will get back the same function. In either case, we have to first find f(-x) to figure this problem out:

[tex]f(-x)=4(-x)^3-9(-x)\\f(-x)=-4x^3+9x[/tex]

We can see from our answer for f(-x) that it is equal to -f(x). We can verify this below:

[tex]-f(x)=-(4x^3-9x)\\-f(x)=-4x^3+9x[/tex]

Since f(-x) = -f(x), our function f(x) is an odd function

By using the triple integral, the wedge's volume is 4/15.

A parabolic cylinder is a three-dimensional quadratic surface (sometimes known as a quadric surface) in mathematics, specifically analytical geometry, and is defined by the equation x 2 + 2 a y = 0 x2+2ay=0. A parabola serves as the directrix of a parabolic cylinder, to put it another way.

The wedge's volume, which the parabolic cylinder encloses, must be determined.

Consequently, as a result of the z=y form,

In addition to the specified boundary, the plane y=0 x = 0, z = 0.

For all of this, we are therefore in the first octant. additionally, the plane

x + y = 1 is a constraint.

Triple integrals are three independent integrations that are done one after the other to calculate a volume or to integrate across three independent dimensions in a fourth dimension.

The following would be written as a triple integral:

∫x=0 ∫y=0

∫z=0 dy dz dx

Once the values have been entered and the problem has been solved, we obtain the

[−4/15(1−x)^5/2] at x=0

The answer will then change to 4/15.

As a result, using the triple integral, the wedge's volume comes out to 4/15.

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The value "x = 3" and "x = -1/2" are part of the solution set.

We can represent any linear inequality using any of the following forms:

Now, if the sign is pointing towards x, it means that x is greater than b., so, the line under the greater sign means that x can also equal b.

The options given are:

Hence, the value "x = 3" and "x = -1/2" are part of the solution set.

Therefore, the Option A and C is correct.

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The inference that can be made from the dot plot is the range of each round is the same.

A dot plot is a graph that shows the frequency of a number using dots. The greater the number of dots above a number, the greater its frequency.

Range is the difference between the largest number and smallest number.

Range of round 1 = 8 - 5 = 3

Range of round 2 = 9 - 6 = 3

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The exact value of sin 5π/4 is 0. 0677

It is important to note that π = 3. 142

Let's find sin 5π

Substitute the value

sin 5π = sin (5 × 3. 142) = sin 15. 71

= [tex]\frac{sin 15. 71}{4}[/tex]

Find the sine of the number

= [tex]\frac{0. 27076}{4}[/tex]

= [tex]0. 0677[/tex]

Thus, the exact value of sin 5π/4 is 0. 0677

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Answer:

-  sqrt2/2

Step-by-step explanation:

The Law of sines defines that in a triangle, (Sin A)/a = (Sin B)/b = (Sin C)/c and as per law of sines the length of BC is 24.

The given triangle is ΔABC, we split the given triangle into two right-angled triangle ΔABD and ΔBCD.

In the triangle ΔABD,

sin θ = opposite side/hypotenuse

sin A=BD/AB

BD=(sin A)/AB

And in the triangle ΔBCD,

sin θ = opposite side/hypotenuse

sin B=BD/BC

BD=(sin B)/BC

Hence, BD=(sin A)/AB=(sin B)/BC

Let say, (sin A)/a=(sin B)/b

As per law of sine, (sin A)/a=(sin B)/b

Then,

(sin 46°)/a=(sin 31°)/17

a=(17 × sin 46°)/(sin 31°)

a=23.74

a=24

Hence, the value of BC, rounded to the nearest tenth of a unit is 24.

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Answer:

12

Step-by-step explanation:

Well they are similar I assume so 5 / 3.5 = roughly 1.43 and 8.4 x this number gives you 12 so I would say 12

Answer:

2n^3 + 6n^2 + 8n

Answer: It's 2n^3 + 6n^2 + 8n

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

I'm quite positive its b hopefully:)!

Answer:

B.b if you follow the formula and chances are very high for it to be b

Last option. The correct statement about the graph is g(x) is an odd degree polynomial with a positive leading coefficient.

We have the function as

[tex]f(x) = x^2 - 2x + 1[/tex]

The polynomial that we have here is of an even degree. The highest degree we have here is 2. The coefficient that has the highest degree is 1.

Hence all of the options that have f(x) are incorrect.

The answer to the question is option 4.

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The mean could be used to describe a data set by itself, while interquartile range would almost never be used to describe a data set by itself.

Brief Description of Mean and Interquartile Range

While interquartile range only assesses the middle half of the data, mean and range deal with the entire set of data. The mean is significant in statistics because it helps us determine where a dataset's "center" is. The mean contains information from each observation in a dataset as a result of how it is calculated.

The interquartile range in descriptive statistics reveals the spread of your distribution's middle half. Any distribution that is sorted from low to high is divided into four equal portions using quartiles. The second and third quartiles, or the center half of your data set, are contained in the interquartile range (IQR).

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Answer: C. the graph contains (1, 1/10)

Step-by-step explanation:

When x=1, [tex]y=(1/10)^1=1/10[/tex].

68% of the daily phone calls answered by the company are between 47 and 53.

Empirical rule states that for a normal distribution, 68% of the data are within one standard deviation from the mean, 95% of the data are within two standard deviation from the mean and 99.7% of the data are within three standard deviation from the mean.

Given mean of 50 and a standard deviation of 3

68% are within one standard deviation from mean = mean ± standard deviation = 50 ± 3 = (47, 53)

68% of the daily phone calls answered by the company are between 47 and 53.

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Using it's concept, the probabilities are given as follows:

19. A. 1/3.

20. F. 1/6.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there are 1 + 1 + 3 + 4 + 3 = 12 papers. 4 have a score of 6, hence, in item 19, the probability is:

p = 4/12 = 1/3.

Which means that option A is correct.

2 papers have a score greater than 12, hence the probability in item 20 is given by:

p = 2/12 = 1/6.

Which means that option F is correct.

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