a spherical ball 8 inches in diameter is coated with a layer of ice of uniform thickness. if the ice melts at a rate of 10 cubic inches per min, how fast is the thickness of the ice decreasing when it is 2 inches thick? at the same rate of melting, how fast is the outer surface area of the ice changing?

Answer:

12

Step-by-step explanation:

h(-3)= -(-3)(1-(-3))=

3(4)=12

The length of each side of the courtyard is 25 meters. Then 35.36 meters long is each walkway.

In the given question, a school has a square courtyard and wants to create diagonal walkways.

The length of each side of the courtyard is 25 meters.

We have to find how long is each walkway.

By dividing the square in half to form a right triangle, you can find the solution. The Pythagorean theorem can then be used to find the hypotenuse.

According the Pythagorean Theorem

[tex]a^2+b^2 = c^2[/tex]

[tex](25)^2+(25)^2=c^2[/tex]

Now solving,

625 + 625 = [tex]c^2[/tex]

[tex]c^2[/tex] = 1250

Taking square root on both side, we get

c = 35.36 meters.

Hence, 35.36 meters long is each walkway.

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According to the given information Every 10th product in the line is selected.

Systematic sampling is a probabilistic strategy that includes selecting people from the general population at predetermined intervals, such as each 15th people on a list of the population. If the community is set up in a random order, this can replicate the benefits of simple random sampling.

Biased sample sizes and subpar survey results are reduced by systematic sampling. If there is a low chance that data will be manipulated: Data validity may be compromised if researchers rearrange a data set. The best strategy for surveys when there is little likelihood of data manipulation is systematic sampling.

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An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.

An equilateral triangle is one that has all three of its sides be in line with one another.A slash mark is used to indicate the congruent sides.An equilateral triangle always has angles that are 60° in length.

It is referred to as an isosceles triangle when a triangle's two sides are identical. When the corresponding sides and angles of two angles match, the angles are said to be congruent.

When stacked, two angles are also congruent if they match.

If they line up with each other after turning or moving it, then.

Also creating equivalent vertex angles are a parallelogram's diagonals.

Congruent sides - L and X, G and Y, and F and T.

Congruent angles - ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.

ΔLGF ≅ ΔXYT

Congruent angles are ∠L and ∠X, ∠G and ∠Y, and ∠F and ∠T.

Congruent sides are L and X, G and Y, and F and T.

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Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour. To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Answer: 2.5 miles : 4 milem/hour x 60 minutes/1 hour

Ishi walked on the treadmill time for 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

To find the time Ishi walked on the treadmill, we need to use the equation, Distance (miles) / Rate (miles/hour) x Time (hours) = Time (minutes).

Therefore, 2.5 miles / 4 miles/hour x 1 hour = 0.625 hour or 37.5 minutes.

Ishi walked on the treadmill for time 37.5 minutes, which is equivalent to 2.5 miles at a rate of 4 miles/hour.

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The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped. Answer is 8.212°.

The functions sin and cosine, sometimes known as sin() and cos(), show how a right triangle is shaped.

The ratio of the opposite side to the hypotenuse is called sin(), and the ratio of the adjacent side to the hypotenuse is called cos(), when viewed from a vertex with angle.

So, the Pythagorean identity-based formula for sin is sin²x = 1 - cos²x.

Hypotenuse²=base²+perp²

(8)²=(7)²+(perp)²

64=49+(perp)²

64/49=perp²

1.306=perp²

Now taking square root on both sides

Perp=√1.306

Perp=1.142

Sin C=opposite/hypotenuse

Sin =1.142/8

Sin C=0.14285

C=Sin^-1 0.14285

C=8.212°

Answer is 8.212°.

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The length of segment PX in this problem is given as follows:

PX = 9.

The theorem used to solve this problem is given as follows:

A line parallel to one side of a triangle divides the other two proportionately.

In this problem, all the horizontal lines are parallel, hence the side is divided proportionality, as the resulting triangles in the context of this problem are all similar.

PX is three-fourths of the length of the segment PW = 12, hence it's length is given as follows:

PX = 3 x 12/4

PX = 3 x 3

PX = 9 units.

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If the number of flu patients at the school is modelled by the equation [tex]F=10e^{0. 12d}[/tex] , then the number of days that it will take for the number of patients to reach 50 is 13 days .

The Exponential Growth equation is given as : [tex]F=10e^{0. 12d}[/tex] ;

We have to find How many days will it take for the number of new flu patients to equal 50 .

So , we substitute the value [tex]F=50[/tex] in the model equation ;

we get ;

⇒ [tex]50 = 10e^{0. 12d}[/tex] ;

dividing both side by 10 ,

we have ;

⇒ [tex]5=e^{0. 12d}[/tex] ;

taking [tex]\ln[/tex] on both sides ,

⇒ [tex]\ln 5 = 0.12d(\ln e)[/tex]   ,....we know that [tex]\ln e = 1[/tex] ;

⇒[tex]d= \frac{\ln 5}{0.12}[/tex] ⇒ 13.41198 ;

≈ 13 days .

Therefore , it will take 13 days for the number of patients to reach 50 .

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Answer:

Step-by-step explanation:

B

Zell invested $80,000 in two different types of stocks. Solving for x gives us the amount invested in the 9% stock:

x = $45000

Generally, Let x be the amount invested in the 9% stock.

Then (80,000 - x) is the amount invested in the 12% stock.

The profit on the 9% stock is 0.09 * x and the profit on the 12% stock is

0.12 * (80,000 - x).

We know that the profit on the 12% stock is $150 more than the profit on the 9% stock.

So we can set up the following equation:

0.12 * (80,000 - x)

= 0.09 * x + 150

x=45000

Therefore, Zell invested $80,000 in two different types of stocks. the amount invested in the 9% stock is $45000

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Answer:

$45,000

Step-by-step explanation:

The approximate arc length is 56.52mm.

The central angle that creates the intercepted arc's central angle, or the arc measure, is expressed in degrees. Arc length can be estimated as a percentage of the circle's circumference by multiplying the circle's diameter by the arc length, divided by 360.

The distance between two places along a segment of a curve is known as the arc length.

Given that, the bicycle wheel has a radius (r) = 225 mm

And number of equally spaced spokes (n) = 25

π = 3.14

Perimeter of the bicycle wheel (P) = 2*π*r

Perimeter of the bicycle wheel = 2 * 3.14 * 225 mm

Perimeter of the bicycle wheel = 1413 mm

The arc length = Perimeter of the bicycle wheel (P) / number of spokes (n)

The arc length = 1413 / 25 mm

The arc length = 56.52 mm

The approximate arc length is 56.52mm.

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So, on solving the provided question, we can say that percentage  = 1/15 X 100 = 15%

A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.

car gas mileage is normally distributed with a mean of = 25 miles per gallon

67% of cars get at least 23 miles per gallon

percentage of cars get less than 30 miles per gallon

25-23/30

2/30

1/15

percentage  = 1/15 X 100 = 15%

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Answer:x-5.50=20

Step-by-step explanation:

Using the law of sines, the length of l is: 12.1 cm.

The Law of Sines is a theorem in triangle geometry that relates the lengths of the sides of a triangle to the sine of its angles. It states that for any triangle, the ratio of the length of a side to the sine of the angle opposite that side is the same for all three sides.

Given the following:

k = 1.2 cm

m<L = 93°

m<M = 6°

m<K = 180 - 93 - 6 = 81°

Using the law of sines, sin K/k = sin L/l:

sin 81/1.2 = sin 93/l

Find l:

(sin 81)(l) = (sin 93)(12)

l = (sin 93)(12)/(sin 81)

l = 12.1 cm

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While some College Board math sections permit all students to use a calculator, other math portion do not. Students can prayer the use of a four-function calculator for use on Non calculator sections.

Four-function calculators are basic calculators that have functions limited to subtraction, addition, multiplication, square roots, division, and percentage.

Four-function calculators can only be used on test portion that need math calculations.

They must be put away during non-mathematical part.

Board policy on use of a calculator may vary by exam. Check by reading calculator rules for the PSAT/NMSQT and PSAT 10 and the SAT or visiting AP Students to read calculator policies for specific AP exams.

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The required number of containers are two.

105 minutes per process cycle.

We must first determine the utilization rate of the process in order to determine the number of containers required for the parts. Usage rate is the typical unit utilised each hour.

The scenario specifies that the procedure uses 88 components every hour.

The net cycle time per part per hour is determined as follows: (99/60) x 105 = 173.25

0.31 is the efficiency factor.

We can determine the total number of things Kanban can maintain using the information provided:

= 173.25/(1 - 0.31)

= 119.54

We may calculate the total number of containers required by dividing the container capacity by the entire number of parts after we know how many total pieces will be stored.

Each container can hold 8 dozens, or 96 pieces.

=  119.54

Consequently, two containers are required.

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The 4 in front of the formula is called a coefficient.A coefficient is a number that is multiplied by a variable or a constant in an algebraic expression.

In this case, the 4 is being multiplied by the formula, which makes it a coefficient.

A coefficient is a numerical value that is used in an algebraic expression or equation. It is placed in front of a variable or a constant, and it is multiplied by that particular element. The coefficient is used to adjust the value of the expression or equation, and it can be any number, including fractions, negative numbers, and decimals. For example, if a formula were written as 4x + 2 = 10, then the 4 in front of the x is the coefficient. This number is used to adjust the value of the expression, and it can be changed to any other number in order to alter the equation. Coefficients are very useful in mathematics, and they can be used to solve many types of equations and problems.

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Answer: The area under the curve refers to the area between the curve of a function and the x-axis. To find the area under the curve of a function, you would typically integrate the function with respect to x and then evaluate the definite integral between a set of limits.

For example, to find the area under the curve of f(x) = x^2 + 2x from x=0 to x=a, we would integrate the function with respect to x,

∫[0,a] (x^2 + 2x) dx = (1/3)x^3 + x^2 evaluated from x=0 to x=a,

Similarly, to find the area under the curve of g(x) = x + 2 from x=0 to x=a, we would integrate the function with respect to x,

∫[0,a] (x + 2) dx = (1/2)x^2 + 2x evaluated from x=0 to x=a

It's important to note that the definite integral is only defined if the function is continuous and has no vertical asymptotes on the interval.

Step-by-step explanation:

The length of the arc of the sector watered is 0.89π.

In the given question, a lawn sprinkler located at the corner of a yard rotates through 80 degrees and sprays water of 20 ft.

We have to find the length of the arc of the sector watered.

From the given question,

r = 20 ft, θ = 80 degree

A sector is referred to as a component of a circle made up of the circle's arc and its two radii. It is a section of the circle made up of the arc's circumference and the radii of the circle at its ends.

The formula for the length of the arc of the sector watered is

L = [tex]\frac{\theta}{360^{o}}\times 2\pi r[/tex]

Now putting the value

L = [tex]\frac{80^{o}}{360^{o}}\times 2\times\pi \times20[/tex]

Now simplifying the length

L = [tex]\frac{320^{o}}{360^{o}}\pi[/tex]

L = 0.89π

Hence, the length of the arc of the sector watered is 0.89π.

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Table A represents a function, but Table B does not represent a function.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.

As, each element of X is associated with unique element of Y, so this is a function.

Table A    

          X               Y

          3                 1

           2                 0

           1                  0

As, each element of X is associated with a unique element of Y, so this is a function.

Table B

X            Y

3           -2

5              1

5              2

Hence, Table A represents a function, but Table B does not represent a function.

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The solution to f(g(h(x))) = [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]

f(x) = [tex]x^{4} + 6[/tex]

g(x) = [tex]x-3[/tex]

h(x) = [tex]\sqrt{x}[/tex]

Therefore to find f(g(h(x))),

fogoh(x) = f(g(h(x)))

We first substitute the value of h(x) as above,

f(g([tex]\sqrt{x}[/tex]  ))   ....... as h(x) = [tex]\sqrt{x}[/tex]

Now, we substitute the value of g(x) where x is [tex]\sqrt{x}[/tex]

f([tex]\sqrt{x} -3[/tex]) ....... as g(x) =  [tex]x-3[/tex]

Then we substitute the value of x in f(x) with [tex]\sqrt{x} -3[/tex]

[tex](\sqrt{x} -3)^{4} + 6[/tex]

Now we further solve to find a simpler form of the equation,

[tex](\sqrt{x} -3)^{4} + 6[/tex]

= [tex](x^{2} -12x^{3/2} +54x- 108\sqrt{x} +81) + 6[/tex]

=  [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]

Therefore, fogoh(x) = f(g(h(x))= [tex]x^{2} - 12x^{3/2} + 54x -108\sqrt{x} + 87[/tex]

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The required function,which best describe the problem is split function.

By designating one of the given string's sub-strings as the delimiter, the split() method can be used to divide a given string or line. The output is the string that comes before and comes after the substring that was supplied as a delimiter.

a data analyst at an e-commerce company is working with a spreadsheet containing last month's sales.

the most expensive product their company sells costs $49.99, so they want to quickly confirm that all of the data in the sales column is $49.99 or less.

This situation is defined for split function, which is best describe it.

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The length of the two line segments together is 80 cm

Step 1: Convert 500mm into cm.

We know that the value of 1mm is equal to 0.1 cm.

Then,  500mm will be  500mm*0.1 = 50 cm.

Therefore, the second line segment is  50 cm long.

Step 2: Calculate total length.

Let the first line segment be L1= 30 cm long and the second line segment be L2= 50 cm long.

Now, the total length is

L = L1 + L2

Substitute the values L1= 30 cm and  L2= 50 cm in L = L1 + L2.

Hence, the length of the two line segments together is 80 cm

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23 minutes she will be devoting to weightlifting in week 10.

function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Formula represent the sequential increase in weight lifting time is :

f (n) = 2n + 5

f (n) = 2n + 5

f (10-1) = 2(10-1) + 5

f(9) = 2(9)

f(9) = 18

f(9) = 23

Therefore,23 minutes she will be devoting to weightlifting in week 10.

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Answer: its 1.6667.

Answer:

Step-by-step explanation

3*X=5

X=5/3

X=1.67

Answer: 1.7

Step-by-step explanation: First, let's see how many decimeters are in 1 cm. To find it, we must divide the cm by 10. So, we can do 17 / 10 or move the decimal one spot left. They should both = 1.7. I hope this helped!

Answer:

14x - y

Steps:

(9x + 3y) + (5x - 4y)

Determine the sign:

9x + 3y + 5x - 4y

Combine as terms:

14x - y

I hope it helps you :)

[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-3})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +3= -\cfrac{4}{3} (x -3) \\\\\\ y+3=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x+1 \end{array}}[/tex]

The inequality which can be used to determine too, the number of outfits Wyatt can purchase while staying within his budget is:

                         780 ≥ 472.44 + 46.60x

Inequality:

In mathematics, equations are not always balanced on both sides using equal signs. It can also be about "not equal" relationships, such as one being greater than the other or less than the other. In mathematics, an inequality refers to a relationship in which two numbers or other mathematical expressions do not compare equally. These formulas belong to algebra and are called inequalities.

An inequality means that two things are not the same. One of them may be less than, greater than, less than or equal to, greater than or equal to the other.

According to the question:

As based on the information,

he can't spent more than $780.

Four cycle reflector cost = 2 × $19.41

                                         = $38.82

Let maximum number of outfit = x

and Cost = 46.60x

and the the pair of glove is for $35.27.

Therefore,

New bicycle + Bicycle reflectors + Biker gloves + Biking Outfit  ≤ 780

⇒ $398.35 + $ 38.82 + $ 35.27 + $46.60 x ≤ 780

⇒  472.44 + $ 46.60x ≤ 780

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Answer:

Step-by-step explanation:

Given : In a GP the first term is 7

            the last term is              448

             and the sum                 889

To find : Common ratio ? The number of terms is 7.

The common ratio is 2

Answer:

common ratio (r) = 2

Step-by-step explanation:

solution in picture