#8: Expand the logarithm shown below. *
log981xy

The surface area of the sphere, to the nearest whole number, is 1318 cm².

A sphere is simply a three-dimensional geometric object that is perfectly symmetrical in all directions.

The volume of a sphere is expressed as:

Volume =  (4/3)πr³

The surface area of a sphere is expressed as:

SA = 4πr²

Where r is the radius of the sphere and π is the mathematical constant pi.

Given that the volume V is 4500 cm³.

First, we solve for the radius:

Volume =  (4/3)πr³

4500 = (4/3)πr³

4500 × 3 = 4πr³

13500 = 4πr³

r³ = 13500/4π

r = ∛( 13500/4π )

Now that we have the radius, we can calculate the surface area of the sphere using the formula:

SA = 4πr²

Substituting the radius we found:

SA = 4 × π × ∛( 13500/4π )²

SA = 1318 cm²

Therefore, the surface area is approximately 1318 cm².

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Answer:

What is the question asking for?

Step-by-step explanation:

I'm not sure what is it asking

The compound inequality representing the range for the skull size of cats is: 39.32 ≤ x ≤ 43.01.

To find the compound inequality that represents the range for the skull size of cats, we need to solve the given compound inequality:

8 ≤ 1.03x - 32.4 ≤ 12

Let's solve it step by step:

Add 32.4 to all parts of the compound inequality:

8 + 32.4 ≤ 1.03x - 32.4 + 32.4 ≤ 12 + 32.4

40.4 ≤ 1.03x ≤ 44.4

Divide all parts of the compound inequality by 1.03 (the coefficient of x):

40.4/1.03 ≤ (1.03x)/1.03 ≤ 44.4/1.03

39.32 ≤ x ≤ 43.01

Therefore, the range for the skull size of cats can be represented by the compound inequality:

39.32 ≤ x ≤ 43.01

Rounded to the nearest hundredth, the compound inequality representing the range for the skull size of cats is:

39.32 ≤ x ≤ 43.01

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Answer:

6

Step-by-step explanation:

Answer: 6
The factors of 12 are: 1, 2, 3, 4, 6, 12

The factors of 18 are: 1, 2, 3, 6, 9, 18

The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30

Then the greatest common factor is 6.

Answer:

Step-by-step explanation:

-15-9 = -24

I would think about it as adding 15 and 9, but just make the answer negative.

Answer:

MAD would be more similar than mean

Step-by-step explanation:

Without doing any calculations, I assumed that the average value for each neighbor is different since their dot plots surround different areas. The MAD is the mean absolute deviation where it shows how distributed are the dot plots compared to the average value. In this case, I can tell that both neighborhoods having a very similar distribution of dot plots relative to their average/mean. Hope this helps!

Answer: 2/3

Step-by-step explanation:

Answer:

m=−3

Step-by-step explanation:

There is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

To find the probability that a box of cereal is underfilled by 5 g or more, we need to calculate the probability of obtaining a weight measurement below 345 g.

First, we can standardize the problem by using the z-score formula:

z = (x - μ) / σ

Where:

x = the weight value we want to find the probability for (345 g in this case)

μ = the mean weight (350 g)

σ = the standard deviation (4 g)

Substituting the values into the formula:

z = (345 - 350) / 4 = -1.25

Next, we can find the probability associated with this z-score using a standard normal distribution table or a statistical calculator.

The probability of obtaining a z-score less than -1.25 is approximately 0.1056.

However, we are interested in the probability of underfilling by 5 g or more, which means we need to find the complement of this probability.

The probability of underfilling by 5 g or more is 1 - 0.1056 = 0.8944, or approximately 89.44%.

Therefore, there is approximately an 89.44% probability that a box of cereal is underfilled by 5 g or more.

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The average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

To determine the average rate of change of the school's enrollment during the given time period, we can use the formula:

Average rate of change = (Change in enrollment) / (Change in time)

The change in enrollment is calculated by subtracting the initial enrollment from the final enrollment, while the change in time is calculated by subtracting the initial year from the final year.

Given that in 2004 there were 975 students enrolled and in 2009 there were 730 students enrolled, we can calculate the change in enrollment:

Change in enrollment = 730 - 975 = -245 students

The change in time can be calculated as:

Change in time = 2009 - 2004 = 5 years

Now we can calculate the average rate of change:

Average rate of change = (-245 students) / (5 years) = -49 students per year

Therefore, the average rate of change of the school's enrollment during this time period is -49 students per year. This means that on average, the enrollment at the college has been decreasing by 49 students per year.

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The range of the function on the graph is C. all the real numbers greater than or equal to –3 .

We can see by the graph maximum value of y of function is -3 and the graph continues to extend upward .

So, the range contain all the real numbers greater than or equal to –3 .

Therefore, the range contain all the real numbers greater than or equal to –3 .

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Answer:

BD = 30√2 yd

Step-by-step explanation:

The shape of the land is a square with 30 yd side length on each side.

The fence to he built is the diagonal of the square BD.

Apply pythagorean theorem to find the number of yards of fencing (BD) he needs.

Thus:

BD² = BC² + CD²

BD² ° 30² + 30²

BD² = 1800

BD = √1800

BD = √(900*2)

BD = 30√2 yd

The right response is 400%. In other words, Johnny moves at four times the pace of Jane.

We must compare the speeds of Johnny and Jane in relation to one another in order to get their ratio. According to the issue, Jane moves at a pace that is 1/4 that of Johnny. In other words, Jane moves at a speed that is one-fourth that of Johnny.

We may compare the speeds as a fraction to figure out the ratio:

Johnny's speed divided by Jane's speed equals 4/1.

This indicates that Johnny is moving at a speed that is four times that of Jane. We can express Johnny's speed as 400% of Jane's speed in percentage terms.

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Answer:

Fixed

x=5.66

Step-by-step explanation:

This is an around about way since it's not a right triangle.

lets call the segment line that bisects the lower right angle= M.

The two triangles created would be similar. So:

4/6=M/(x+3)

4x+12=6M

M=(4x+12)/6

and

(x+3)/(x+4)=M/6

(6x+18)=Mx+4M

M=(6x+18)/(x+4)

since M=M

(4x+12/6=(6x+18)/(x+4)

(x+4)(4x+12)=6(6x+18)

4x^2+12x+16x+48=36x+108

4x^2+28x+48=36x+108

4x^-12x-60=0

x^2-3x-15=0

Factor

(x+2.65)(x-5.66)=0

x=5.66

Answer:

80

Step-by-step explanation:

You need to divide 20 by 1/4 as 1/4 of the people support it, and you need 20. 20/(1/4)=80.

Using equivalent angles, the correct options are given as follows:

Negative 25 degrees is on the fourth quadrant, with the positive angle measure being given by:

360 - 25 = 335º.

The equivalent angle on the first quadrant is of 360º - 335º = 25º, and the cosine on the first quadrant is positive, just like in the fourth, hence:

cos(-25°) = cos(25º).

The positive angle measure is given as follows:

360 - 136 = 224º.

Which is on the third quadrant, in which both the sine and the cosine are negative.

The equivalent angle on the first quadrant is given as follows:

224º - 180º = 44º.

Hence the expression is:

sin(-136º) = -sin(44º).

The positive angle measure is given as follows:

360 - 212 = 148º.

Which is on the second quadrant, in which the tangent is negative.

The equivalent angle on the first quadrant is given as follows:

180º - 148º = 32º.

Hence the expression is:

tan(-212º) = -tan(32º).

The positive angle is given as follows:

360 - 315 = 45º.

Which is already on the first quadrant, hence the expression is given as follows:

cot(-315º) = cot(45º).

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The time is taken by the 8 gardeners to landscape the same garden will be 30 hours.

A ratio is an ordered set of integers a and b expressed as a/b, with b never equaling 0. A proportional is a mathematical expression in which two things are equal.

It takes 5 gardeners 48 hours to landscape a garden.

Then the time taken by the 8 gardeners to landscape the same garden will be

The relationship between the gardeners and time is inversely proportional. Then we have

Let x be the time taken by the 8 gardeners. Then we have

8x = 5×48

 x = 30 hours

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The term 'expression' in mathematics refers to a combination of symbols that follows certain rules and represents an idea that can be completely abstract or have an equivalent in the tangible world.

We already have a picture of an expression

When an expression finds its place in the 'real world' it can be used to model something, like the velocity of a falling rock or the changes in a population of animals. When this happens, we are trying to 'imitate' what we see in nature with mathematical expressions, and that imitation can be quite precise or not so. It's like trying to sculpt the face of a person, depending on our tools, abilities, and knowledge, we can almost perfectly copy his/her face or not so accurately.

We can use a simple example from physics. A falling object towards the center of the Earth has for its equation:

Where v is its velocity, t is the time, and g a constant.

This is an attempt at modeling that phenomena, and it's more or less accurate depending on whether we consider wind, how distant we are from the center of the Earth, etc.

It's important to notice that math by itself does not pursue that its concepts apply to the so-called 'real world, its ideas can be purely abstract and it's only when we try to use a mathematical expression to describe something that they become 'real'.

Using the normal distribution, we have that:

a) The sketch of the situation is given at the end of this answer.

b) The probability is:

\(P(2.8 \leq X \leq 7) = 0.8284\)

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

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

In this problem:

Item a:

The part between 2.8 and 7 years is shaded on the sketch given at the end of this answer.

Item b:

The probability is the p-value of Z when X = 7 subtracted by the p-value of Z when X = 2.8, thus:

X = 7:

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

\(Z = \frac{7 - 4.1}{1.3}\)

\(Z = 2.23\)

\(Z = 2.23\) has a p-value of 0.9871.

X = 2.8:

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

\(Z = \frac{2.8 - 4.1}{1.3}\)

\(Z = -1\)

\(Z = -1\) has a p-value of 0.1587.

0.9871 - 0.1587 = 0.8284, thus:

\(P(2.8 \leq X \leq 7) = 0.8284\)

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Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Step-by-step explanation:

Answer:

Magnitude of force is \(||v||\approx16.12\text{ lbs}\)

Step-by-step explanation:

\(||v||=\sqrt{x^2+y^2}\\||v||=\sqrt{(-8)^2+(14)^2}\\||v||=\sqrt{64+196}\\||v||=\sqrt{260}\\||v||\approx16.12\text{ lbs}\)

Answer:B

Step-by-step explanation:

The length of AD is 1 unit.

A triangle is a three-sided polygon that consists of three edges and three vertices.

Let us solve the question

In Δ ABC

∠B is a right angle

BD is perpendicular to the hypotenuse AC

(AB)² = AD × AC ⇒ rule

AB = 3 units

AC = 9 units

Let AD = x

Substitute them in the rule above

(3)² = x × 9

9 = 9x

Divide both sides by 9

x=1

Hence, the length of AD is 1 unit.

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Question

Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 3 and AC = 9, what is the length of AD? (Note: the figure is not drawn to scale.)

Answer:

1. 5x - 15

2. 5x - 3

Step-by-step explanation:

The first one is f(g(x)), which means that you substitute g(x) into f(x).

5(x - 3)

5x - 15

Vice versa for the 2nd one.

(5x) - 3

5x - 3

Hope this helps! :)

Answer: Area of Polygon Q is  \(\dfrac14\)  of  Area of Polygon

Step-by-step explanation:

Given: Polygon Q is a scaled copy of Polygon P using a scale factor of \(\dfrac12\) .

According to the property of scale factor ,

Area of the image = (scale factor )²x (Area of the original figure)

So, Area of Polygon Q = \((\dfrac12)^2\)  x (Area of Polygon P)

⇒ Area of Polygon Q = \(\dfrac14\)  x (Area of Polygon P)

Hence,  Area of Polygon Q is   \(\dfrac14\)  of  Area of Polygon P.

Answer:

1/4

I did on khan

Step-by-step explanation:

Answer:

Answer is 96%

Step-by-step explanation:

298-152/152 ×100

The percent increase in the number of people attending the exhibit will be 96%. Then the correct option is D.

The quantity of anything is stated as though it were a fraction of a hundred. A quarter of 100 can be used to express the ratio. Per 100 is what the term percent signifies. The symbol ‘%’ is used to symbolize it.

The percentage is given as,

Percentage (P) = [Initial value - Final value] / Initial value x 100

One weekend, 152 people attended an art exhibit.

The following weekend, 298 people attended.

Then the percent increase in the number of people attending the exhibit will be

P = [(298 - 152) / 152] x 100

P = (146 / 152 x 100)

P = 0.96 x 100

P = 96%

The percent increase in the number of people attending the exhibit will be 96.05%.

Then the correct option is D.

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a. The number of red roses left t hours after the store opens \(R(t) = 400/2^{t/2}\)    

b. The number of boxes of chocolate left t hours C(t) = 200 - 0.15t

c. One possible solution is t ≈ 7.546 hours after the store opens.

d. there are 194 boxes of chocolates left.

e. you need to arrive at the store no later than 7.504 hours after it opens.

a. The proportion (relative frequency) of times an event is anticipated to occur when an experiment is repeated a large number of times under identical conditions is known as the probability of the event.:

\(R(t) = 400/2^{t/2}\)

b. Let C(t) be the quantity of boxes of chocolate left t hours after the store opens. At first, there are 200 boxes, of which 15% are purchased every hour. We can therefore write:

C(t) = 200 - 0.15t

c. We must solve the equation R(t) = C(t) in order to determine the time at which the number of boxes of chocolates and the number of roses are equal. We obtain: by substituting the formulas we discovered in parts a and b:

\(400/2^{t/2} = 200 - 0.15t\)

Simplifying this equation, we get:

\(2^{t/2 + 1} + 0.15t - 400 = 0\)

We can solve this equation numerically, using a calculator or a computer program. One possible solution is t ≈ 7.546 hours after the store opens.

d. At 12:30 in the early evening, which is 3.5 hours after the store opens, we can utilize the recipe we tracked down to some extent b to work out the quantity of boxes of chocolates left:

C(3.5) = 200 - 0.15(3.5) = 194.25

We ought to adjust this solution to appear to be legit with regards to the issue. Since we cannot have a fraction of a box, we can round to the nearest integer and state that there are 194 chocolate boxes remaining.

e. To buy 36 red roses, we need to solve the equation R(t) = 36. Substituting the formula we found in part a, we get:

\(400/2^{t/2}= 36\)

Simplifying this equation, we get:

2^(t/2) ≈ 11.111

Taking the logarithm of both sides, we get:

t/2 ≈ log2(11.111)

t ≈ 2 log2(11.111)

Using a calculator, we get:

t ≈ 7.504 hours after the store opens.

Therefore, you must arrive at the store no later than 7.504 hours after it opens in order to purchase 36 red roses.

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