g a spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min. at what rate is the volume of the snowball decreasing when the radius is 12 cm. (note the answer is a positive number).

The function has its graph to be represented by graph (a)

Table:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

The equation that represents the function is given as

f(x) = (3/4)ˣ

Next, we extract the x values from the given table

These x values are represented as

x = -2, -1, 0, 1 and 2

Solving further, we need to calculate the function at the x values

So, we have the following computations

f(-2) = (3/4)⁻² = 16/9

f(-1) = (3/4)⁻¹ = 4/3

f(0) = (3/4)⁰ = 1

f(1) = (3/4)¹ = 3/4

f(2) = (3/4)² = 9/16

When these values are presented on a table, we have:

x  -2       -1      0     1      2

y  16/9   4/3   1     3/4   9/16

Some of the points on the table are

(0, 1), (1. 3/4) and (2. 9/16)

The graph that passes through these points is graph (a)

So, the

Hence, the graph of the function is graph (a)

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Answer:

D 50 minutes

Step-by-step explanation:

If the customer is the fifth car in line then x = 5, so

f(5) = 7(5) + 15

f(5) = 35 +15

f(5) = 50

The required number of two positive consecutive integers are 35 and 36.

Consecutive integers are the whole numbers that follow each other without gaps. consecutive  integers are even, and odd integers.

consecutive even integers that differ from previous integer by difference of 2 and each integer is divisible by 2.

consecutive odd integers that differ from previous integer by difference of 2 and each integer is an odd number.

let the first positive integer be x

Therefore the second positive integer be (x+1)

Given that the sum of two consecutive positive integer is 71:

x+(x+1)=71

open the bracket

x+x+1=71

Add the similar terms

2x+1=71

2x=71-1

2x=70

x=35

Finding the second integer Substituate the value of x=35 in (x+1):

x+1=35+1

x+1=36

The required number of two positive consecutive integers are 35 and 36.

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Answer:

y=-3/4x+3

Step-by-step explanation:

(See picture)

The angles in a circle are called inscribed angles, which can be formed by passing the line through the center.

What is a Central Angle?

The central angle is the angle that a circle's arc occupies in its center. The arms of the central angle are formed by the radius vectors. In other words, it's an angle whose vertex is the center of a circle and whose arms, which have the circle's two radii as their arms, cross at two separate positions. These two points make an arc when they are combined. The angle that this arc at the circle's center subtends is known as the central angle.

An arc's angle at the circle's center is twice as large as its angle at any other point along the circle's circumference. the angle subtended by the arc in the opposite segment of the circle is twice as large as the angle at the center of the circle.

When two chords intersect on a circle, an inscribed angle is an angle that is created inside the circle. It can alternatively be described as the angle formed at a particular point on a circle by two specified points.

Hence,

The angles in a circle are called inscribed angles, which can be formed by passing the line through the center.

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The prime multiples of 8 are number 2 and 4

The multiples of 8 are 1, 2, 4, 8.

The prime numbers are the numbers who can be divided only by 1 and itselves.

First we need the multiplies of 8

And then find their factors, if the number of factors is exactly two( that is 1 and the number itself) then it is prime.

The factors of 1 is 1

The factors of 2 are 1 and 2

The factors of 4 are 1, 2and 4

The factors of 8 are 1, 2, 4 and 8

The numbers which have only two factors are prime.

2 and 4 are prime multiples of 8

Therefore, the number 2 and 4 can be said as the prime multiples of 8

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2500 positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits

A number system is defined as a system of writing to express numbers.

The smallest 5 digit even integer is 10000. The largest is 99998.

The difference between these numbers is 89998. Half of these are even, or about 45000 numbers.

But, we want all of the digits to be even. So, the digits can only be 0, 2, 4, 6, or 8. 0 cannot be the first digit.

4×5×5×5×5=2500

Hence, 2500 positive integers with 5 or less digits are even or divisible by 5 and do not contain any repeated digits

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The surface area of the given rectangular prism with a length 7cm , width 2cm and height 6cm is equal to 136cm².

As given in the question,

Dimensions for a given rectangular prism are:

Length = 7cm

Width = 2cm

Height = 6cm

Surface area of the given rectangular prism is equal to

= 2 ( length × width + width × height + height × length )

Substitute the value in the formula we get,

= 2 ( 7 × 2 + 2 × 6 + 6 × 7 )

= 2 ( 14 + 12 + 42 )

= 2 ( 68 )

= 136 cm²

Therefore, the surface area of the rectangular prism is equal to 136cm².

The complete question is :

Hannah has a rectangular prism with a length of 7 cm, a width of 2 cm,

and a height of 6 cm.

What is the surface area of Hannah's rectangular prism?

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There are 99 students preferred pizza.

The students preferred pizza can be calculated as follows.

First, let’s make the equation.

Students preferred pizza is symbolized as P

Students preferred hotdogs is symbolized as H

P = 2.25H

Second, let’s put the number of student preferred hotdogs.

P= 2.25 x 44

= 99

Hence, there are 99 students preferred pizza.

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Solution of the given expression 6a + 18ab after rewriting using a common factor is equal to :

A. 6a(1 + 3b).

As given in the question,

Given expression is equal to :

6a + 18ab

Find common factors of both the terms we get.

6 = 1, 2, 3, 6

18 = 1, 2, 3, 6, 9, 18

Highest common factor of 6 and 18 is equal to 6.

Now take 6a as a common factor from both the terms we get,

6a + 18ab

= ( 6a × 1 ) + ( 6a × 3b )

= 6a × ( 1 + 3b )

= 6a ( 1 + 3b )

Therefore, solution of the given expression 6a + 18ab after rewriting using a common factor is equal to :

A. 6a(1 + 3b).

The complete question is :

Rewrite 6a + 18ab using a common factor.

A.6a(1 + 3b)

B. 6a(0 + 3b)

C.6ab(0 + 3)

D. 6ab(1 + 18ab)

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Answer:  6a(1 + 3b)

Step-by-step explanation:  I took the test

a) List the next two terms of the sequence as 28,36

b) [tex]A_{n} =A_{n-1} +n, A_{0} =0, n\geq 1[/tex]

c) [tex]P_{n} =P_{n-1} +n, P_{0} =0, n\geq 1[/tex]

consider the given sequence,

0,1,3,6,10,15,21,.........

= (0), (0+1), (1+2), (3+3), (6+4), (10+5),(15+6), (21+7), (28+8),......

therefore,

a) next two terms =28, 36

b)

[tex]A_{1} =0, A_{2}=1, A_{3} =3, A_{4} =6, A_{5} =10, A_{6} =15\\A_{n+1} = A_{n} +n, A_{1} =0, n\geq 1[/tex]

c)

[tex]P_{0} =0, P_{1} =1, P_{2} =3, P_{3} =6, P_{4} =10, P_{5} =15, P_{5} =21\\P_{n} =P_{n-1} +n, P_{0} =0, n\geq 1[/tex]

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The 'base angles' are the angles that involve the base of an isosceles triangle.

What is the vertex angle of a isosceles triangle?

Vertex angle: The 'vertex angle' is the angle formed by two equal sides of an isosceles triangle. ∠BAC is a vertex angle of the isosceles triangle. 4. Base angles: The 'base angles' are the angles that involve the base of an isosceles triangle.

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The required solution of the given expression is given as x = 5 and x = -3.

Given that,
To solve x² - 2x=15,

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
x² - 2x - 15 = 0
x² -5x + 3x - 15 = 0
x (x - 5) + 3 (x - 5) = 0
(x + 3)(x - 5) = 0
So,
x = -3 and x = 5

Thus, the required solution of the given expression is given as x = 5 and x = -3.

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The ratio of tubes of blue paint to all of the tubes of paint used was 75/10000 = 0.0075.

A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other.

A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.

Given,

          red paint= 666 tubes

          yellow paint = 222 tubes

          white paint = 131313 tubes

          blue paint= 999 tubes  

Total paint tubes = 666+222+131313+999 = 133200

The ratio of blue paint tubes to all of the paint tubes = 999/133200

                                                                                        = 75/10000.

The ratio of tubes of blue paint to all of the tubes of paint used = 75/10000 = 0.0075.

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The line integral in both cases is  52/3

Given,

a) The line integral; L = ∫c xy dx + x² y³ dy

 Where C is counterclockwise around the triangle with vertices (0, 0),

(1, 0)  and (1, 4)

Our first line integral is

L₁ = ₁∫₍₀, ₀₎ ⁽¹ ⁰⁾ xy dx + x² y³ dy

The equation of this line is y = 0,  x varies from 0 to 1.

L₁ = 0

Our second line integral is

L₂ = ₁∫₍₁, ₀₎ ⁽¹ ⁴⁾ xy dx + x² y³ dy

The equation of this line is x = 0  and y varies from 1 to 4.

L₂ = 64/3

The third line integral is

L₃ = ∫₁⁰ xy dx + x² y³ dy

The equation of this line is y = 4x  and x varies from 0 to 1.

L₃ = -4

The value of the line integral is

L = L₁ + L₂ + L₃ = 0 + 64/3 + (-4) = 52/3

b) The second part requires the use of Green's Theorem to evaluate:

This is given by:

∫c Pdx + Qdy = ∫ ∫ R Qy - Px dA

∫c xy dx + x² y³ dy = ∫ ∫R 3x² y² - ydA

We choose our region of integration parallel to the y-axis.

∫c xy dx + x² y³ dy

= ∫¹₀ ∫⁴ˣ₀ 3x² y² - y dy dx

= ∫¹₀ x² y³ - 1/4 |y²|²ˣ₀ dx

=  ∫¹₀ 64x⁵ - 4x² dx = 52/3

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The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.

A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x).

Given,

Function,

Region = [0,1] × [0,1]

Lˣ = 1/area of region ∫¹₀ ∫₀¹ f(xy) dx dy

Differentiating,

Lˣ

= 1/1 ∫₀¹ tan⁻¹ xy dxdy

= ∫¹₀ [ ∫¹₀ tan⁻¹(xy) dx ] dy

= ∫₀¹ [{x tan⁻¹ (xy) ¹₀ - 1/2 ∫ 2(x+y)/ 1 + xy₂ dx] dy

= ∫¹₀ tan⁻¹ y dy - ¹₀ log(y² + 1) 2y dy

= [ytan⁻¹ y - 1/2 log( y² + 1) ∫¹₀ - [1/4 log (y² +1) log y² +1/4log(y²+1)

= π/4 - 1/2 log 2 -π²/48

L = 1/4( π - log4) - π²/48

The average value of the function over the given rectaf (x,y) = arctan (xy), R = [0,1] x [0,1] is 1/4( π - log4) - π²/48.

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There are 100, 4-digit positive integers that are divisible by 5 between  1000 and 9999.

A integer is divisible by 5 if it ends with 0 or 5. 35, 790, and 55, for instance, are also all divisible by 5.

We then multiply all the computed ways to fill in the corresponding spaces (4 x 5 x 5 x 1 = 100).

Therefore, there are 100 potential 4-digit positive integers.

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When a pair of dice rolled, the probability that the sum is either a multiple of 3 or a multiple of 4 is 5/9.

If an event A and an event B is independent to each other, then the probability A or B is:

P(A or B) = P(A∪B) = P(A) + P(B)

In the given problem:

The possible outcomes or the sample space of rolling a pair of dice = 6 x 6 = 36.

The maximum sum is 6 + 6 = 12

Multiple 3 or multiple 4 that ≤ 12 is {3, 4, 6, 8, 9, 12}

Possible outcomes for Sum = 3 are 1 + 2 and 2 + 1

Hence,

P(3) = 2/36

Possible outcomes for Sum = 4 are 1 + 3, 3 + 1, 2 + 2

Hence,

P(4) = 3/36

For Sum = 8,  2 + 6, 6 + 2, 3 + 5, 5 + 3, 4 + 4

Hence,

P(8) = 5/36

Similarly,

P(6) = 5/36

P(9) = 4/36

P(12) = 1/36

Therefore,

P(Multiple 3 or multiple 4) = P(3, 4, 6, 8, 9, 12)

                                          = 2/36+3/36+5/36+5/36+4/36+1/36

                                          = 20/36

                                          = 5/9

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The least-square regression line between data fuel efficiency and speed is  In(Fuel Efficiency) = 1.437 + 0.541 In(Speed).  The fuel efficiency when the speed 60 mph is 38.55 mpg

Least square regression is a representation of data in a linear equation:

y = ax + b

where x, y are data variables.

The least-squares regression line is obtained by minimizing  the distance from  regression line to each data points.

In the given problem, the given least-squares regression line is:

In(Fuel Efficiency) = 1.437 + 0.541 In(Speed)

In this case,

y =  In(Fuel Efficiency)

x = ln(Speed)

Where ln is the natural logarithmic operator.

When speed = 60 mph, then,

In(Fuel Efficiency) = 1.437 + 0.541 In(60)

In(Fuel Efficiency) = 1.437 + 2.215

In(Fuel Efficiency) = 3.65

Fuel efficiency = e^(3.65) = 38.55

Hence, the fuel efficiency when the speed 60 mph is 38.55 mpg

Your question is incomplete, but most probably your question was:

Data were recorded for a car's fuel efficiency, in miles per gallon (mpg), and corresponding speed, in miles per hour (mph). Given the least-squares regression line, In(Fuel Efficiency) = 1.437 + 0.541 In(Speed), what is the fuel efficiency for a speed of 60 mph? 3.65 mpg 33.90 mpg 36.52 mpg 38.55 mpg

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One of the two identical halves of a chromosome that has been replicated in preparation for cell division is referred to as a chromatid. The two "sister" chromatids are united at the centromere, a restricted portion.

A chromatid is an individual of two together alike halves of a deoxyribonucleic acid that has been copied imminent for the formation of cells by dividing. The two “twin” chromatids are linked at an inhibited domain of the chromosome named the centromere. The establishment of chromatids is a main become involved in cellular division guaranteeing that each new girl cell has the correct complement of DNA at the end of the formation of cells by dividing.

Cell division is the process by which a person's container divides into two woman cells. Cell division frequently happens as few the best container phase at which point the cell evolves and replicates allure deoxyribonucleic acid before separating.

There are two types of cell division: the formation of cells by dividing and the formation of cells by dividing. Most of the time when nations are concerned with “cellular division,” they mean the formation of cells by dividing, the process of making new carcass containers.

Sister chromatids differ from chromatids in that sister chromatids are two copies of a single chromosome and are products of the S phase of the cell cycle. The centromere links sister chromatids together.

During the early stages of cell division, chromatids are produced. Non-sister chromatids appear during metaphase I of meiosis, whereas sister chromatids replicate from the same chromosome.

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There are basically three to four rules for angles of a triangle.

sum of all interior angle of triangle is 180°.

.

Angle in triangle

Triangles are one of the most basic geometric shapes and have a variety of well-studied properties. Triangle: Largest interior angle and sides facing each other. The same rules apply for minimum angles and sides, medium angles and medium sides.

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Answer:

  The ratio (center to focus)/(semi-major axis) is the greatest

Step-by-step explanation:

Given various foci coordinates and major axis lengths, you are asked to identify the ellipse with the highest eccentricity.

The eccentricity of an ellipse can be defined as the ratio of distance between foci to the length of the major axis. A high value of eccentricity corresponds to a longer, narrower ellipse.

The attached graph plots the locations of the given foci. They are color coded to correspond with the color of the resulting ellipse. (We have used the given r-value as the semi-major axis, not the major axis.)

The blue focal points (A, A') of the blue ellipse give the "flattest" of the bunch, so corresponds to the highest eccentricity. Its parameters are those of the first answer choice.

If we assume the given r-value is the semi-major axis, the eccentricity represented by each of the answer choices is ...

The numerator in each case is the distance from the center (0, 0) to one focus.

The gravitational force increases four times when the space between the items is cut in half.

What exactly does gravity mean?

Who made the discovery of gravity?

It is said that after observing an apple fall and wondering why it fell straight down rather than sideways or even upward, Isaac Newton developed the theory of gravitation in 1665 or 1666.

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Answer:

x >= 2.25

x is greater than or equal to 2.25

Step-by-step explanation:

8x - 3 >= 15

add 3 to both sides

8x >= 18

divide 8 from both sides

x >= 2.25

Answer:

x≥6

Step-by-step explanation:

8x

3 less goes to 8x-3

then there is at least 15 which changes to

8x-3≥15

Then solve for x:

add 3 to the sides--> 3x≥15+3

3x≥18

Divide both of the sides by 3

x≥6

Hope this helped!

The probability that he selects at least 4 green peppers is 0.0024

A cook has 10 red peppers and 5 green peppers

If the cook selects 6 peppers at random, what is the probability that he selects at least 4 green peppers

Event of getting green peppers be X

We need to find the probability that he selects at least 4 green peppers. This can be when the cook selects either 4 green peppers or 5 green peppers.

This can be found by binomial probabilty distribution.

P(X ≥ 4) = P(X = 4) + P(X = 5)

6C4(5/15)⁴(10/15)¹¹ + 6C5(5/15)⁵(10/15)¹⁰

15 x (1/3) ⁴ x (2/3) ¹¹ + 6 (1/3⁵) (2/3)¹⁰

= 0.002 + 0.0004

= 0.0024

Therefore, the probability that the cook selects at least 4 green peppers out 6 peppers he picked from 10 pred peppers and 5 green peppers is is 0.0024

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he got the same answer i did

Step-by-step explanation:

The solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,

u''x^6 u'x^5

Given, a differential equation

u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2

we have to find the solution of the given differential equation

on integrating both the sides, we get

u''x^6 u'x^5

So, we get u''x^6 u'x^5 as a solution of the given differential equation on solving by the reduction method.

Hence, the solution of the given differential equation u'x^4 4ux^3 u''x^4 8u'x^3 12ux^2 be,

u''x^6 u'x^5

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Answer:

c. ( 5, 3)

Step-by-step explanation:

y = 6x - 27

y = 4x - 17

6x - 27 = 4x - 17

2x = 10

x = 5

y = 4x - 17

y = 4(5) - 17

y = 3

x = 5; y = 3

Answer: c. ( 5, 3)

The coordinates of the point where y-4x=1 crosses on the axis is (0, 1).

The value of K is 6.5

An equation is an expression that shows the relationship between two or more numbers and variables.

a)  The graph will cross the y-axis at the y-intercept. We can find the value by putting the given equation into slope-intercept form (y = mx + b).

y - 4x = 1

y = 4x + 1

The y-intercept is (0,1).

b) We need to find c, or the y-intercept. This is given to us on the graph, where the line crosses the y-axis at (0,-3).

Therefore, our line is;

y = 2x - 3.

Then, we can plug in 10 for y from the point (k,10) and solve for k as;

10 = 2x - 3

13 = 2x

x = 6.5

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Yes, there is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.

We have,

There is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.

The calculated P-value of approximately 0.023, which is less than the significance level of 0.05.

The P-value indicates the probability of observing a test statistic as extreme as or more extreme than the observed value of -2.00 under the null hypothesis.

Since the P-value is smaller than the significance level, we reject the null hypothesis and conclude that the proportion of parts with an error is significantly less than 20%.

The fact that 16% is less than 20% also supports this conclusion.

Thus,

Yes, there is sufficient evidence at the α = 0.05 level to conclude that less than 20% of the parts are being painted with an error.

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