Which of the following shows the extraneous solution to the logarithmic equation below? log Subscript 3 Baseline (18 x cubed) minus log Subscript 3 Baseline (2 x) = log Subscript 3 Baseline 144

The volume of rotation of region R is [tex]192\pi[/tex] cubic units.

Given information:

Region R is bounded by the lines y=4, x=6, the y-axis and the x-axis.

Region R is rotated about the line y=-2.

So, the region R is a rectangle with length 6 units (x=0 to x=6), and the height of the rectangle is 4 units (y=0 to y=4).

After rotating this rectangle about y=-2, we will get a hollow cylinder.

The outer radius of the cylinder will be,

[tex]R=4-(-2)=6[/tex]

The inner radius of the cylinder will be,

[tex]r=0-(-2)=2[/tex]

And the length of the cylinder is 6 units.

So, the volume of the solid formed after the rotation will be,

[tex]V=\pi R^2L-\pi r^2L\\V=\pi L(R^2-r^2)\\V=\pi \times 6(6^2-2^2)\\V=\pi\times 6 \times 32\\V=192\pi[/tex]

Therefore, the volume of rotation of region R is [tex]192\pi[/tex] cubic units.

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To find the volume of the solid formed by rotating region R about the line y=-2, we use the washer method which results in a volume of 216π cubic units.

The problem involves calculating the volume of a solid of revolution, which is formed when a two-dimensional region is rotated around a line that does not intersect the region.

Region R is defined as the area bounded by y=4, x=6, the y-axis, and the x-axis. The volume of the solid formed by rotating this region around the line y=-2 can be calculated using the washer method, which involves integrating over the area of concentric washers.

The general formula for the volume V of a washer is given by V = π∫[R2(x) - r2(x)]dx , where R(x) and r(x) are the outer and inner radii of the washers, respectively. In this case, the outer radius is R(x) = 4 - (-2) = 6 and the inner radius is r(x) = -2 - (-2) = 0.

Therefore, the volume V is:

V = π∫06[62 - 02 ]dx = π∫0636dx = 36π∫06dx = 36π[6] = 216π cubic units.

Answer:

The hourly rate she worked to pay for the new bike is $18.84.

Step-by-step explanation:

Given:

Sis worked 14.4 hours and saved $271.30 for a new bike.

The equation 14.4x=271.30 could be used to represent how much she earned per hour.

Now, to find the hourly rate she worked to pay for the new bike.

The hourly rate = [tex]x[/tex].

Number of hours = 14.4.

Money she saved = $271.30.

According to the question, the equation used to represent she earned per hour is:

[tex]14.4x=271.30[/tex]

Now, to solve the equation to get the hourly rate:

[tex]14.4x=271.30[/tex]

Dividing both sides by 14.4 we get:

[tex]x=\$18.840.[/tex]

Thus, the hourly rate rounding to the nearest hundredths place is $18.84.

Hence, the hourly rate she worked to pay for the new bike is $18.84.

Answer:

this question is really easy

so 20 + 27 + 34 + 41 ........ and we have to find out the 16th term so...

your answer is = 132

I hope this would help you

thank u

Answer:

1272

Step-by-step explanation:

The series can be written as (20+7*0)+(20+7*1)+...+(20+7*n).

Therefore, the sum of the first 16 terms would be as follows:

20*16 + 7*0 + 7*1 + 7*2 +...+ 7*16 = 320 + 0 + 7 + 14 + 21 +  ... + 112 = 320 + 952 =

= 1272

There are many ways to calculate the underlined bit, I'm just not showing it (on this occasion I just put it in my calculator).

Answer:

-0.95

Step-by-step explanation:

cos(theta) = sqrt(1 - sin²(theta))

= sqrt(1 - 0.312²)

= sqrt(0.902656)

= +/- 0.9500821017

Since cos is negative in quadrant 2,

cos(theta) = -0.95

To approximate the value of cos0, we can use the given value of sin0 and the Pythagorean identity. The approximate value of cos0 is -0.95022.

Since the given angle 0 lies in Quadrant II where cos0 is negative, we can approximate the value of cos0 using the given value of sin0.

Using the Pythagorean identity sin^2(0) + cos^2(0) = 1, we can find cos0.

sin^2(0) + cos^2(0) = 1

0.312^2 + cos^2(0) = 1

0.097344 + cos^2(0) = 1

cos^2(0) = 1 - 0.097344

cos^2(0) = 0.902656

cos0 = √0.902656

cos0 ≈ -0.95022

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Final answer:

The probability of selecting a red marble followed by a yellow marble from a bag, without replacement, is 1/5. Option B)  1/5 is correct.

Explanation:

The probability of selecting a red marble and then a yellow marble without replacement from a bag is determined by multiplying the probability of the first event by the probability of the second event, given the first has occurred.

First, calculate the probability of drawing a red marble (P(red)). With 3 red marbles out of 6 total marbles, that probability is 3/6 or 1/2.

Next, calculate the probability of drawing a yellow marble after a red one has been drawn (P(yellow | red)). Now there are only 5 marbles left in the bag, 2 of which are yellow, so that probability is 2/5.

Finally, multiply these two probabilities to find the probability of both events occurring in sequence: P(red then yellow) = P(red) × P(yellow | red) = (1/2) × (2/5) = 2/10 or 1/5.

The probability of selecting a red and then a yellow marble from a bag containing 3 red, 1 blue, and 2 yellow marbles, without replacement, is 1/5.

Therefore, the probability of selecting a red marble and then a yellow marble without replacement is 1/5, which corresponds to option b).

Final answer:

The volume of the cylinder with a base diameter of 16 inches and a height of 7 inches is approximately 1407.36 cubic inches. This is calculated using the formula V = πr²h.

Explanation:

To calculate the volume of a cylinder with a base diameter of 16 inches and a height of 7 inches, we use the volume formula V = πr²h. First, find the radius r by halving the diameter, which gives us 8 inches. Then, square the radius and multiply by π (approximately 3.1416) and the height.

V = π × (8 inches)² × (7 inches)

V = π × 64 inches² × 7 inches

V = π × 448 inches³

V ≈ 3.1416 × 448 = 1407.36

The volume of the cylinder is approximately 1407.36 cubic inches.

Final answer:

The volume of a cylinder with a base diameter of 16 inches and a height of 7 inches is 1,408 cubic inches, calculated using the formula V = πr²h.

Explanation:

To calculate the volume of a cylinder with a base diameter of 16 inches and a height of 7 inches, we first need to find the radius of the cylinder's base. The radius (r) is half of the diameter, so for this cylinder, the radius is 8 inches. We then apply the formula for the volume of a cylinder, which is V = πr²h.

Using the values provided:

Calculate the radius: radius = diameter / 2 = 16 inches / 2 = 8 inches.

Compute the volume: V = π * (8 inches)² * 7 inches.

Since π is approximately 3.14159, the calculation is V = 3.14159 * 64 inches² * 7 inches = 1,408 cubic inches.

Therefore, the volume of the cylinder is 1,408 cubic inches.

Answer:

9

Step-by-step explanation:

Total letters in word 'COUNTING'=8

Number of vowels in word 'COUNTING'=3(O,U,I)

Total letter in word 'PRIME'=5

Number of consonants in word 'PRIME'=3(P,R,M)

We have to find the total number of outcomes.

Number of choice for O=3(P,R,M)

Number of choice for U=3(P,R,M)

Number of choice for i=3(P,R,M)

Number of outcomes of choosing a vowel from the word 'COUNTING' and a consonant from the word 'PRIME'=3+3+3

Total number of outcome=9

Answer:

Shelly paid $215 for the desk

Step-by-step explanation:

In this question, we are asked to calculate the price a particular desk was bought given the price at which it was sold and the percentage of profit associated with the sales of the desk. In other words, we are calculating the cost price

Mathematically,

% profit = (selling price - cost price)/cost price * 100%

Our percentage profit here is 35% and our selling price is $290.25, we are left with calculating the selling price. let’s input these values into the equation;

Before that, let’s say the cost price is $x

35 = (290.25-x)/x * 100

100(290.25-x) = 35x

29025 -100x = 35x

135x = 29025

x = 29025/135

x = $215

Answer:

A) (x²/127806.25) + (y²/76956) = 1

B) 451 miles

C) 715 miles

Step-by-step explanation:

Center is at (0,0) and focus is at (c,0) while vertex is at (a,0)

Thus, a - c = 132 miles

and a + c=583 miles

Adding both equations together, we have;

2a= 715 miles

Thus, a = 715/2

a = 357.5 miles

Since a+c=583

Thus, c = 583-357.5 = 225.5 miles

Now, for an ellipse it is defined by; a² = b² + c²

a² = 357.5² = 127806.25

c² = 225.5² = 50850.25

So, b² = 127806.25 - 50850.25

b² = 76956

b = √76956

b = 277.409

A) Equation of tangent to ellipse which is equation of orbit would be;

(x²/a²) + (y²/b²) = 1

Thus,

(x²/127806.25) + (y²/76956) = 1

B) distance between the earth and the other focus is = 2c = 2 x 225.5 = 451 miles

C) Length of other major axis = 2a = 2 x 357.5 = 715 miles

a) The equation of the orbit is \(\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\). b) The distance from the center to the other focus is calculated using the formula \(c = \sqrt{(583+3963)^2 - 132^2}\). c) The length of the major axis is \(2(583+3963)\).

a) To find an equation of the orbit, we can use the standard form equation for an ellipse:
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2} = 1\] where \((h,k)\) represents the center of the ellipse, \(a\) represents the distance from the center to the vertices along the major axis, and \(b\) represents the distance from the center to the co-vertices along the minor axis. In this case, the center of the ellipse is the Earth's center, which is at the origin \((0,0)\). The highest point of the orbit is 583 miles above the Earth's surface, so the distance from the center to the vertices along the major axis is 583 miles + the radius of the Earth. The radius of the Earth is approximately 3963 miles. The lowest point of the orbit is 132 miles above the Earth's surface, so the distance from the center to the co-vertices along the minor axis is 132 miles. Substituting the values into the equation:
\[\frac{x^2}{(583+3963)^2}+\frac{y^2}{132^2} = 1\]

b) The distance from the center to the other focus can be found using the relationship \(c = \sqrt{a^2 - b^2}\), where \(c\) represents the distance from the center to the foci. Substituting the values into the equation:
\[c = \sqrt{(583+3963)^2 - 132^2}\]

c) The length of the major axis can be found using the formula \(2a\), where \(a\) represents the distance from the center to the vertices along the major axis. Substituting the values into the equation:
\[2a = 2(583+3963)\]

Answer:

Voluntary response sample

Step-by-step explanation:

They constitute voluntary response sample. Voluntary response sample is a sample that is made up of volunteers.

Apart from voluntary response sample, it can also be called or known as self-selected sample.

A good example of this sample is the typical phone in polls u can witness on radio or tv stations where people call to air their views or make their stands known.

The voluntary response sample is most times chosen or selected by the people that will respond rather than the administrator of the survey.

One of the standout advantages or benefit of the voluntary response sampling is the convenience and probably the ethical considerations as well. The demerit is that this self-selected samples are sometimes subject to bias.

Answer:

1. 2a

2. Vertex

3. Center

4. (c-a)

Step-by-step explanation:

The missing black in the paragraph will be 2a, vertex, center, and (c – a).

The hyperbola is the locus of a point such that the difference of distance from point P to two non-movable points. These two points are called foci of hyperbola.

In the derivation, the difference between the distances from any point P on a branch of the hyperbola to foci of the hyperbola is set equal to the constant value of 2a.

2a is used in the equation because the Vertex is a point on the hyperbola, and it is the difference in the distances from this point to the foci.

This can be shown algebraically if we let a be the distance from the Center to the vertex. Then, the difference of the distances is (c + a) – (c – a).

More about the hyperbola link is given below.

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Answer:

Sales Price = $21.00

New Price = $39.00

Step-by-step explanation:

Convert 35% into a decimal and multiply that with the $60.00. After you get the product, which is $21.00, you then need to subtract $21.00 from $60.00 and that gets you $39.00.

Answer:

19.20 seconds.

Step-by-step explanation:

Given:

She invited 150 friends.

But she only had 5 activities for her friends and her party only lasted 4 hours.

Question asked:

How much time will each friend get on each activity ?

Solution:

First of all convert 4 hours into seconds:-

1 hour = 3600 seconds

4 hours = 3600 [tex]\times[/tex] 4 = 14400 seconds

By unitary method:

150 friends get time in 5 activities = 14400

1 friend get time in 5 activities = 14400 [tex]\div[/tex] 150 = 96 seconds

That means each friend get 96 seconds in all 5 activities.

Each friend get time on each activity = ?

Each friend get time on 5 activities = 96

Each friend get time on 1 activity = 96 [tex]\div[/tex] 5 = 19.20 seconds

Thus, each friend will get 19.20 seconds on each activity.

Answer:

(a) 288 students

(b) 249 students

(c) 121 students

Step-by-step explanation:

(a) 39 + 124 + 125 = 288

(b) 81 + 39 + 52 + 77 = 249

Without access to the Venn diagram, it's not possible to provide specific numerical answers. However, guidance on reading the diagram to answer these type of questions is given.

I apologize, but without the actual Venn diagram, I can't provide accurate numbers for your questions. However, I can guide you on how to read the diagram if you have it. To find the students who drink exactly two of the three drinks, you will sum the numbers in the intersections of the circles that exclusively represent two drinks. For students who don’t drink tea, count all the students who fall outside of the tea circle. Lastly, for students drinking only tea, refer to the number that lies exclusively within the tea circle and not within the circles representing coffee and soda.

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Answer:

1)

80 = 2×2×2×2×5

2)

21 -- 11 -- 8 -- 40

21 -- 15 -- 24 -- 60

Step-by-step explanation:

80 = 2×2×2×2×5

Half Tuna white: 21

Half brown: 21

25% of 32

25/100 × 32 = 8

32-8 = 24

Total brown: (100-20)/2 = 40

Total white = 60

Cheese:

40 - 21 - 8 = 11

60 - 21 - 24 = 15

21 -- 11 -- 8 -- 40

21 -- 15 -- 24 -- 60

Answer:

I think it is 38 centimeters.

Step-by-step explanation:

Answer:

It is A

Step-by-step explanation:

It will be undefined if something is divided by 0.

So if you divided 0/6, it will be 0. But if you did 6/00 it will not work because 0 is not a number.

Answer: The volume is 40 cubic inches

Step-by-step explanation: Each toy block is 1 cubic inch, which means each toy block is a cube with all sides (Length, width and height) measuring 1 inch. That makes the volume of each cube or block to be derived as;

Volume = L x W x H

Volume = 1 x 1 x 1

Volume = 1 cubic inch

The first 3 floors are made up of six rows of four blocks. This means, the first 3 floors has six by four blocks, that is, six times four blocks and that gives us 24 blocks.

The fourth to eighth floors are made up of four rows of four blocks. This also means four by four blocks, that is, four times four blocks and that gives us 16 blocks.

Having determined the amount of blocks used in the total model building as

1st - 3rd = 24 blocks

4th - 8th = 16 blocks

The total number of blocks used is 24 plus 16 which equals 40. Having been told that each block has a volume of 1 cubic inch, the volume of the model building equals 40 cubic inches.

Answer:

B

Step-by-step explanation:

I got it correct

Answer:

38.2º

hope you have a good day!

Answer-

for a shape to be a square, you need to make sure that all size are equal. then you will need to see if the angels are all the same (they need to be 90 degrees). all the sides must be parallel with each other. that is what makes a shape a square. this doesn't fit will all quadrilateral shapes.

Answer:

a)   0.71

b)   0.9863

Step-by-step explanation:

a. Given the mean prices of a house is $403,000 and the standard deviation is $278,000

-The probability the probability that the selected house is valued at less than $500,000 is obtained by summing the frequencies of prices below $500,000:

[tex]P(X<500,000)=P(X=0)+P(X=500)\\\\=0.34+0.37\\\\=0.71[/tex]

Hence, the probability of a house price below $500,000 is 0.71

b. -Let X be the mean price of a randomly selected house.

-Since the sample size 40 is greater than 30, we assume normal distribution.

-The probability can therefore be calculated as follows:

[tex]P(X<x)=P(z<\frac{\bar X-\mu}{\sigma/\sqrt{n}})\\\\P(X<500,000)=P(z<\frac{500-403}{278/\sqrt{40}})\\\\=P(z<2.2068)\\\\\\=0.9863[/tex]

Thus, the probability  that the mean value of the 40 houses is less than $500,000 is 0.9863

When you write URGENT the Brainly cops think you may be taking a test.

y = ax² + c thru (-1,4) and (0,8)

Substituting in the coordinates of each point for x and y gives two equations:

4 = a  (-1)² + c

8 = a (0²) + c = c

From the second one we see c=8.  Substituting into the first one,

4= a + 8

a = 4-8 = -4

Answer: a=-4, c=8

Check:

f(x) = -4x² + 8

f(0) = 8, good

f(-1) = -4(1) + 8 = 4, good

Final answer:

To find the values of a and c for the parabola through points (-1, 4) and (0, 8), we substitute these points into the equation y = ax² + c. This gives us two equations, and by solving them, we find that a = -4 and c = 8.

Explanation:

To find the values of a and c for the parabola y = ax² + c that passes through the points (-1, 4) and (0, 8), we can use these points to set up two equations:

1. For the point (-1, 4), substituting into the equation y = ax² + c, we get: 4 = a(-1)² + c 4 = a + c

2. For the point (0, 8), substituting into the equation y = ax² + c, we get: 8 = a(0)² + c 8 = c

From the second equation, we can see that c = 8. Using this information in the first equation, we substitute c to find a: 4 = a + 8 -4 = a

Therefore, the values for the parabola that passes through the given points are a = -4 and c = 8.

Answer:

80 minutes

Step-by-step explanation

24/3=8

8mins/1 mile

8 minsx10 miles= 80 mins for 10 miles

The first step in simplifying is to distribute the -b and -1 to the terms in the parentheses.

The abbreviation PEMDAS stands for parentheses, exponents, multiply or divide, add or subtract, which stands for the sequence of operations in mathematics. To achieve the right result when an expression contains many operations, it's crucial to compute them in the correct sequence (exponents after the parenthesis, etc.).

Given equation 3-b(7b+ 2) + 3b - (11 - b). As we can see that in this equation there is nothing complicated inside the bracket to simplify. so we will jump to the next step which is to distribute the -b.

Hence, in equation 3-b(7b+ 2) + 3b - (11 - b) first step in simplifying is to distribute the -b and -1 to the terms in the parentheses.

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Answer: 408/x

Step-by-step explanation:

Total number of people = 816

after 1 song = 816/2 people remained

after 2 songs = 816/4 people remained

after 3 songs = 816/8 people remained

after x songs = 816/x*2 people remained

People that remained = 816/2x

where x is the number of songs

Simplified = 408/x

Answer:

try using this it might help out with the question

Step-by-step explanation:

Y=2x+3

Gracie needs 2 cups of flour to make 2 batches of muffins as each batch requires 1 cup of flour.

The subject of this question is Mathematics as it involves multiplication of fractions to find the total amount of flour needed. As the question states, Gracie is making 2 batches of muffins and each batch needs 1 cup of flour.

To find the total amount of flour, we simply multiply the number of batches by the amount of flour per batch. In this case, that's 2 (batches) * 1 (cup of flour per batch). Therefore, Gracie needs 2 cups of flour to make 2 batches of muffins.

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In the process of making muffins, if one batch requires 1 cup of flour, then two batches would require 2 cups of flour.

The question is asking about how much flour Gracie requires to bake 2 batches of muffins when one batch requires 1 cup of flour. This is a question about proportionality. If one batch of muffins needs 1 cup of flour, then 2 batches of muffins will require 2 cups of flour. This is because the amount of flour Gracie needs is directly proportional to the number of batches she bakes.

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Answer:

0.2x

Step-by-step explanation:

Answer:

0.2x---------------------------------------------------------------------------------------

Answer:

Interest: $390 | Total: $715

Step-by-step explanation:

To answer the first question, we can use the simple interest formula provided:

[tex]I=Prt[/tex]

P = initial balance

r = annual interest rate

t = time

First, change 8% into the decimal form:

8% -> [tex]\frac{8}{100}[/tex] -> 0.08

Now, plug in the values:

[tex]I=325(0.08)(15)[/tex]

[tex]I=390[/tex]

Charlie made $390 of interest. To find the total, just add that number to $325.

[tex]390+325=715[/tex]

Charlie's total money made was $715.

Final answer:

Charlie earns $390 in simple interest over 15 years. The total future amount, including the initial investment, is $715 after 15 years.

Explanation:

To determine how much interest Charlie's initial investment will earn over the 15-year period, we apply the simple interest formula, I = P rt, where I stands for interest, P is the principal amount, r is the rate of interest per year, and t is the time in years. Plugging in Charlie's investment details: I = $325(0.08)(15).

First, calculate the annual interest: $325  imes 0.08 = $26 per year. Then, multiply the annual interest by the number of years: $26  imes 15 = $390.

Therefore, the total simple interest earned over the 15-year period is $390.

To calculate the total future amount, add the interest earned to the initial investment: Total future amount = Principal amount + Interest = $325 + $390 = $715.

After 15 years, Charlie will have $715 in his account.