use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.

Given that we have to find the probability of each of the following when we roll a pair of fair dice:

Probability of getting a sum of 1 = 0

Probability of getting a sum of 5= {4}/{36}=0.1111

Probability of getting a sum of 12= {1}/{36}= 0.0278

Explanation: When we roll a pair of dice, there are 36 possible outcomes or events. When we roll the dice, the number on the dice will be an integer from 1 to 6.

The following table represents the possible outcome when we roll a pair of dice.

There is only one way to obtain the sum of 1, i.e., when both dice show 1. As there is only one way, the probability is 0.

There are 4 possible ways to obtain the sum of 5. They are (1,4),(2,3),(3,2),(4,1). The probability is 4/36.

There is only one way to obtain the sum of 12, i.e., when both dice show 6. As there is only one way, the probability is 1/36.

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Answer:

  3(x +2)

Step-by-step explanation:

If the number is represented by x, then "the sum of a number and 2" is ...

  x + 2

Three times that sum is ...

  3(x +2)

\( \huge \tt\dag \: Answer : \)

\( \tt \dfrac{ {r}^{ - 8} {s}^{ - 1} {t}^{ - 1} {u}^{7} }{ {r}^{6} {s}^{0} {t}^{ - 9} u \: • \: {r}^{ - 1} {s}^{ - 7} {t}^{0} {u}^{0} } \)

Now, put every term with power 0 = 1 i.e,

\( \tt : \implies\dfrac{ {r}^{ - 8} {s}^{ - 1} {t}^{ - 1} {u}^{7} }{ {r}^{6} \times 1 \times {t}^{ - 9} u \: • \: {r}^{ - 1} {s}^{ - 7} \times 1 \times 1 } \\ \tt : \implies\dfrac{ {r}^{ - 8} {s}^{ - 1} {t}^{ - 1} {u}^{7} }{ {r}^{6} {t}^{ - 9} u \: • \: {r}^{ - 1} {s}^{ - 7} }\)

Now, move all terms with negative powers from numerator to denominator and denominator to numerator to make their powers positive.

\(\tt : \implies\dfrac{ {r}^{ 1} {s}^{ 7} {t}^{ 9} {u}^{7} }{ {r}^{6} {t}^{ 1} u \: • \: {r}^{ 8} {s}^{ 1} }\)

Now, cancel the terms that are getting cancelled.

\(\tt : \implies\dfrac{ \cancel{{r}^{ 1}}{s}^{ \cancel{7}} {t}^{ \cancel{9}} {u}^{ \cancel{7}} }{ {r}^{ \cancel{6}} \cancel{{t}^{ 1}} \cancel{u} \: • \: {r}^{ 8} \cancel{{s}^{ 1}} } \\ \tt : \implies\dfrac{ {s}^{ 6} {t}^{ 8} {u}^{6} }{ {r}^{5} \: • \: {r}^{ 8}}\)

Now, add the powers of of exponential expression having same base.

\(\tt : \implies\dfrac{ {s}^{ 6} {t}^{ 8} {u}^{6} }{ {r}^{(5 + 8)}} \\ \tt : \implies\dfrac{ {s}^{ 6} {t}^{ 8} {u}^{6} }{ {r}^{13}}\)

Hence, the answer is \dfrac{ {s}^{ 6} {t}^{ 8} {u}^{6} }{ {r}^{13}}.

\( \large \tt Hence, \: the \: answer \: is \: \dfrac{ {s}^{ 6} {t}^{ 8} {u}^{6} }{ {r}^{13}}.\)

Answer: To find the discount, simply multiply the original selling price by the %discount:

ie:  39 x 33/100= $12.87

So, the discount is $12.87.

Step-by-step explanation: To find the sale price, simply minus the discount from the original selling price:

ie: 39- 12. 87=  26.13

So, the sale price is $26.13

Answer:

The answer is

\( \sqrt[3]{ {x}^{2} } \)

Step-by-step explanation:

\( \frac{ {x}^{ \frac{5}{6} } }{ {x}^{ \frac{1}{6} } } \)

Since they have the same base and are dividing we can use the rules of indices

That's

subtract the exponents

So we have

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

\( {x}^{ \frac{4}{6} } \)

\( = {x}^{ \frac{2}{3} } \)

Rewriting it in radical form

We have the final answer as

\( \sqrt[3]{ {x}^{2} } \)

Hope this helps you

From law of cosine formula, the width of lake for which Julia wants to determine the distance at certain points across a lake is equals to the 4023.4 meters.

Law of cosine in triangle is used to determine the length of third side of triangle when two other sides and angle between them is known. Cosine formula is c² = a² + b² - 2ab cosC , where

Julia wants to determine the distance at certain points across a lake. See the above figure and reconigse the measurements. Here, the width of lake is represented by AB. There is formed a triangle ABC, with following details,

Length of side AC = 2.82 mi

Length of side BC = 3.86 mi

Measure of angle C = 40.3°

We have to determine value of AB. Using the law cosine formula, AB² = BC² + AC² - 2AC× BC cosC

=> AB² = 2.82² + 3.86² - 2×2.82×3.86 ×cos( 40.3°)

=> AB² = 7.9524 + 14.8696 - 21.7764 ×cos( 40.3°)

=> AB² = 22.852 - 16.603

=> AB ² = 6.2485

=> AB = 2.4996

Hence, required width is 2.5 miles. But we needs answer in meter then convert miles into meters, 1 mile = 1609.344 m

so, 2.5 miles = 2.5 × 1609.344 meters = 4023.36 m ~ 4023.4 meters.

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Complete question:

The above figure complete the question.

julia needs to determine the distance at certain points across a lake. her crew and she are able to measure the distances shown on the diagram below. find how wide the lake is to the nearest tenth of a meter.

Answer:

15

Step-by-step explanation:

The probability of getting at least one head is 15/16.

What is probability?

The ratio of positive outcomes to all possible outcomes of an event is known as the probability.

Formula for probability = favourable outcomes/ total outcomes

Main body:

if 4 coins are tossed , total no. of outcomes = 2⁴ = 16

In a toss there are 2 outcomes T or H

so, Probability of getting Head = 1/2

The probability of getting at least 1 head = 1- probability of getting no heads

⇒1 - Probability of getting tail in 4 tosses

⇒ 1 - (1/2)⁴

⇒ 1 - 1/16

⇒ 15/16

So the probability of getting at least one head is 15/16.

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Answer: x=\(p^{9}\)

nah nah nvm give charpriv brainliest

The statement is true - Independent variables are beyond the experimenter's control.

The statement is true. Independent variables are those factors that cannot be manipulated by the experimenter. They are the variables that are naturally occurring and cannot be changed. For example, age, gender, or genetics are independent variables that are beyond the experimenter's control. In contrast, dependent variables are those variables that can be manipulated by the experimenter, such as the amount of light, the temperature, or the dosage of a drug. Understanding the difference between independent and dependent variables is crucial in designing and conducting experiments.

Independent variables are those variables that are beyond the control of the experimenter. They are naturally occurring factors that cannot be manipulated, whereas dependent variables are those that can be manipulated.

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Answer:

Around 140

Step-by-step explanation:

It's over 90 degree angle

The best description of the passenger's linear and angular velocity while passing point A is option d) Linear Velocity Constant, Angular Velocity Constant.

When the passenger is at point A, which is the highest point of the ride, the seat exerts a normal force with a magnitude of 0.8F, where F represents the person's weight. This normal force provides the necessary centripetal force to keep the person moving in a circular path. At this point, the passenger's linear velocity remains constant, as there is no change in speed.

Since the passenger releases a small rock without hitting anything, there are no external torques acting on the system. Therefore, according to the law of conservation of angular momentum, the passenger's angular velocity remains constant as well. The angular velocity is determined by the rotational motion of the wheel and does not change as the passenger passes point A.

Therefore, the passenger's linear velocity is constant, and their angular velocity is also constant while passing point A, resulting in the most accurate description being d) Linear Velocity Constant, Angular Velocity Constant.

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you add the fractions together

1 5/12+1 3/4+2 1/3 is 4 3/1 which simplifies to 7

multiply 7 by 10.50 and get 73.5

ANSWER= $73.50

The values of x in f(x) = 3|x - 2| + 6 when f(x) = 18 are 6 and -2

The function is given as:

f(x) = 3|x - 2| + 6

The value of f(x) is

f(x) = 18

So, we have:

3|x - 2| + 6 = 18

Subtract 6 from both sides

3|x - 2| = 12

Divide both sides by 3

|x - 2| = 4

Remove the absolute bracket

x - 2 = 4 or x - 2 = -4

Add 2 to both sides

x = 6 or x = -2

Hence, the values of x are 6 and -2

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Answer:

6/11.

Step-by-step explanation:

1 5/6 = (6+5) / 6

= 11/6.

Its reciprocal = 1 / 11/6

= 6/11.

Check the picture below.

\(\cos(\theta )=\cfrac{\stackrel{adjacent}{3}}{\underset{hypotenuse}{3.4}}\implies \theta =\cos^{-1}\left( \cfrac{3}{3.4} \right)\implies \theta \approx 2807^o\)

Make sure your calculator is in Degree mode.

Answer:

4/13

Step-by-step explanation:

A fraction is a fragment of a whole number, used to define parts of a whole. The whole can be a whole object, or many different objects. The number at the top of the line is called the numerator, whereas the bottom is called the denominator.

Nyla owns 13 films in total, out of which 9 are romance films. To solve for how many films are not romance, we can subtract the number of romance films from the total amount of films:

This means that the remaining 4 films are not romance films.

The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

In this case, the number of favorable outcomes is the number of non-romance films (4) and the total number of possible outcomes is the total number of films (13).

4 ÷ 13 = \(\frac{4}{13}\)

Therefore, the probability that Nyla chooses a non-romance film at random is \(\frac{4}{13}\). This fraction is already in its simplest form.

The acceleration components of point D are, ax = 3.6 m/s², ay = 6.4 m/s², az = -1.14 m/s²

At the instant shown, the shaft and plate rotates with an angular velocity of 19 rad/s and angular acceleration of 9 rad/s2. The given diagram is shown below. Angular velocity (w) = 19 rad/sAngular acceleration (α) = 9 rad/s²Plate dimension AB = 0.6 m, BC = 0.2 m, CD = 0.4 m, DA = 0.3 m, AE = 0.3 m and EF = 0.4 m.

Determine the wocl and Dsea of Enter the ", y, and Z components of the velocity separated by commas vec m/sThe velocity components for point D can be calculated using the following formula.Vd = R x wWhere R is the position vector of D relative to the origin.

According to the given diagram, the position vector of point D relative to the origin is, R = 0.2i + 0.4j + 0.3kThe velocity of point D can be calculated as follows.Vd = R x w = 0.2i + 0.4j + 0.3k x 19The cross product of R and w can be calculated as follows.i j k 0.2 0.4 0.3 0 19 0 = [(0.4 × 0) - (0.3 × 19)] i - [(0.2 × 0) - (0.3 × 0)] j + [(0.2 × 19) - (0.4 × 0)] kVd = -5.7i + 6.8kThus, the velocity components of point D are, Vx = -5.7 m/s, Vy = 0 m/s, Vz = 6.8 m/s

Determine the acceleration of point D located on the corner of the plate at this instant. Enter the, y, and Z components of the velocity separated by commas vec m/sThe acceleration components of point D can be calculated using the following formula.aD = R x α + w x (w x R)Where R is the position vector of D relative to the origin.

According to the given diagram, the position vector of point D relative to the origin is, R = 0.2i + 0.4j + 0.3kThe acceleration of point D can be calculated as follows.aD = R x α + w x (w x R) = (0.2i + 0.4j + 0.3k) x 9 + 19 x (19 x (0.2i + 0.4j + 0.3k)) = (0.4k - 0.3j) x 9 + 19 x (0.4 x (0.4j - 0.3k))aD = 3.6i + 6.4j - 1.14k.

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Answer:

5 m/s²

Step-by-step explanation:

To find the acceleration we apply Newton's second law of motion

F = ma   where F is the net force in Newtons, m the mass of the object (kg) and a the acceleration in  meters/second² (m/s²)

Given

F = 200 N

m = 40 kg

we have 200 = 40a

So a = 200/40=5 m/s²

Answer:

4x-3

Step-by-step explanation:

Yea

The statement is incorrect. When researchers obtain a high p-value, like 0.30, it indicates that there is not enough evidence to reject the null hypothesis.

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

The p-value serves as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

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Answer:

The correct answer is C.

Step-by-step explanation:

C. ✓ No, the Large Counts condition is not met.

in a class of 12 boys and 9 girls, the teacher selects three students at random to write problems on the board then the probability that all the students selected are boys is 0.165

given that a class consists of 12 boys and 9 girls. The teacher picks three students to present their work to the rest of the class  and says that the three students are being selected at random

Here selecting any 3 students from the group of total 21 students is combination because order does not matter.

Total no of ways of selecting any 3 from total 21 = 21C3 = 1330

No of ways of selecting only 3 boys = No of ways of selecting random 3 boys from total 12 boys

= 12C3 =220

the probability be that all three students

selected are boys=220/1330 = 0.165

Hence , the probability that all the students selected are boys is 0.165

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The plane intercepts on the x,y, z axes are 1, ∞, and 1/2. Hence, the Miller indices for the plane inside the cubic unit cell is (102).

Miller indices are used to specify planes and directions. These planes and directions could be in lattices or crystals. The number of indices will correspond to the size of the lattice or crystal.

In the given graph, the plane intercepts are:

x-intercept : 1

y-intercept : ∞  (since the planes does not intercept y-axes)

z-intercept = 1/2

Take the reciprocal:

1/1 = 1

1/∞ = 0

1/(1/2) = 2

Hence, the miller indices are (102)

The graph in your question is missing. Most likely it was like on the attached picture.

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Answer:

3

Step-by-step explanation:

Because if you multiply 12x75 you get 900, and if 1 gallon of paint covers 400 square feet then you will need 3 gallons to get to 900.

Answer:

3

Step-by-step explanation:

Thus, the amount of money Celine will save in 7 years is 200 cents.

To estimate the amount of money Celine will save in 7 years, we can first find the average amount of money she saves per year. To do this, we will add the total money saved and divide by the number of years.

Total money saved: 50 + 175 + 10 + 130 + 212 + 90 = 667 cents
Total number of years: 2 + 5 + 5 + 4 + 6 + 3 = 25 years

Average money saved per year: 667 cents / 25 years ≈ 26.68 cents per year

Now we can estimate the amount of money she will save in 7 years by multiplying the average money saved per year by 7 years.

Estimated money saved in 7 years: 26.68 cents/year * 7 years ≈ 186.76 cents

Among the given options, 200 cents is the closest to our estimation. So, the approximate amount of money Celine will save in 7 years is 200 cents.

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The point estimate of the difference in the population mean exercised between underclassmen and upperclassmen is 0.16 hours.

In this case, we are estimating the difference in population means between two groups - upperclassmen and underclassmen. The point estimate is calculated by subtracting the sample mean of the underclassmen from the sample mean of the upperclassmen, which gives us

0.76 - 0.60 = 0.16.
the point estimate of the difference in population mean exercised between underclassmen and upperclassmen is 0.16 hours, which was calculated by subtracting the sample mean of underclassmen from the sample mean of upperclassmen.
Point Estimate = (Sample Mean of Upperclassmen) - (Sample Mean of Underclassmen)
Point Estimate = (0.76) - (0.60)
Point Estimate = 0.16

Hence, the point estimate of 0.16 suggests that, on average, upperclassmen exercised 0.16 hours more than underclassmen in the past 24 hours. This is a rough estimate of the difference between the two population means based on the provided sample data.

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