the volume of an expanding sphere is increasing at a rate of 12 cubic feet per second. when the volume of the sphere is 36 pi cubic feet, how fast, in square feet per second, is the surface area increasing?

answer:

I believe it's D

Answer: 14 Adult tickets

Step-by-step explanation:

The equation for the total number of tickets would be

x+y=18

5x+3y=82

y=18-x

5x+3(18-x)=82

2x=28

x=14

x= Number of adult tickets

Recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]     where n>1

What do you mean by recursive realtion?

A recursive sequence is one in which terms are defined by reference to one or more previously defined terms.

The recursive formula [tex]a_{n+1}=a_{n}[/tex] + d  can be used to find the (n+1)th term of an arithmetic series if you know the nth term and the common difference, d.

It is given that cost of midisze car is $50.00

Rent per day = $19.99

We need to find the sequence of costs to rent the car for 1 day, 2 days, 3 days, and so on.

According to the question:

Cost become = 50.00 + 19.99n where n represents the number of days

Recursive formula become:

[tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]      where n>1

Therefore, recursive relation is [tex]a_{n-1}= 50.00 + 19.99~a_{n}[/tex]     where n>1

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Answer: (-84, 272)

x = -84

y = 272

Hope this helps!

Answer:

Below

Step-by-step explanation:

-6x - 2y = - 40       <====multiply this entire equation by -1 to get:

6x + 2y = 40      <=====   then add it to the second equation

-7x -2y = -44         to get:

-x = -4    

          so x = 4     use this value in one of the equations to compute y

-6(4) - 2y = -40

-2y = -16

y = 8                    (4,8)

Answer:

y = 100 - 10x

Step-by-step explanation:

Let y₀ be the original water level before any marbles were removed

Let y = water level after x marbles are removed.

Let d be the water level drop for every marble removed

Then we have the general equation:

y = y₀ - x.d  

We have to find d and y₀

So we get one equation for the water level after removal of 2 marbles

80 = y₀ - 2d     [1]

After 4 more marbles were removed, the water level drops to 40ml. That means for 4 marbles removed, the water level drops from 80 to 40. So drop in water level for 4 marbles = 80-40 = 40ml

For each marble then, water level drop = 40/4 = 10ml. This is the value of d

Plug this value of d into [1] to get the original water level y₀

80 = y₀ - 2( 10)

80 = y₀ - 20

100 = y₀

or,

y₀ = 100

So original water level is 100ml and the equation for water level after x marbles are removed is

y = 100 - 10x

The area of the Rhombus ABCD is 1.2 square meter.

What is Rhombus?

A quadrilateral with four equal-length sides is known as a Rhombus in plane Euclidean geometry. Another name for this shape is an equilateral quadrilateral because all of its sides are equal in length.

Let ABCD be the given Rhombus of Perimeter = 52 cm.

Since all the sides are equal to each other.

Therefore, each side of Rhombus measures = 13 cm

So,

AD = CD = 13 cm and AC = 24 cm.

Area of the triangle ACD = √[ s (s - a) (s - c) (s - d) ] ….. Heron’s Formula.

where s = semi-perimeter,

a, c, and d are side measures.

s = (1/2) [ 13 + 13 + 24 ] = 25

Area (A) = √[ 25 (25 – 13) (25 – 13) (25 - 24) ] = 60

Hence Area of the entire Rhombus = 2 * 60 = 120 cm²

Convert 120 cm^2 into meter square

⇒ 120 cm^2 = 1.2 m^2

Hence, the area of the Rhombus ABCD is 1.2 square meter.

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A real-valued function defined on an interval with the property that its epigraph—the collection of points on or above the function's graph—is a convex set—is said to be convex. The challenge of minimizing convex functions over convex sets is the subject of the optimization discipline known as convex minimization.

A mathematical model whose needs are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming. When a linear function is subjected to various constraints, it is maximized or minimized using the mathematical modeling technique known as linear programming. In business planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.

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Answer:

below

Step-by-step explanation:

density  *   volume = mass

7.92 g / cm^3    *   60 cm^3 = 475.2 g

Answer: -9/2

Let's solve this equation step-by-step.

−8+2(3+8)=−4(g+1)

Step 1: Simplify both sides of the equation.

−8+2(3+8)=−4(g+1)

−8+2(3+8)=(−4)(g)+(−4)(1) (Distribute)

−8+22=−4g+−4

(−8+22)=−4g−4 (Combine Like Terms)

14=−4g−4

Step 2: Flip the equation.

−4g−4=14

Step 3: Add 4 to both sides.

−4g−4+4=14+4

−4g=18

Step 4: Divide both sides by -4.

−4g/−4 = 18/−4

g = −9/2

The number of ft that Luke climbed, given the elevation he started from, and the summit, is 5, 050 ft

The number of feet that Luke climbed, can be found by the formula:

Number of feet climbed = Summit of K2 - Luke's starting elevation

Summit of K 2 = 28, 251 ft

Luke's starting elevations = 23, 201 ft

Elevation climbed by Luke was therefore:

= 28, 251 - 23, 201

= 5, 050 ft

In conclusion, the total elevation that Luke climbed from his starting point to the summit of K2 is 5, 050 ft.

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The constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.

The value of the proportionality constant is determined by the type of proportion between the two specified values.

Proportional relationships are written in the form y = kx

where k is the constant of proportionality.

As per the given table, the constant of proportionality will be

k = (1 - 2/3)/(3-2)

k = (1/3)/1

k = 1/3

So, the equation is y = (1/3)x.

Thus, the constant of proportionality is 1/3, and the equation is y = (1/3)x represents the relationship.

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Answer:

5/2 or 2.5

Step-by-step explanation:

Slope is rise/run. We take the difference of the y-coordinates and divide it by the difference of the x-coordinates.

From this, we get [tex](7--3)/(5-1)[/tex], or [tex]10/4[/tex], which can be simplified to 5/2, or 2.5.

The probability of  first drawing a red card, then a jack, and then a black card is 0.0612

First we will describe the standard deck of 52 cards in terms of black, red and face cards found in a standard deck

Following is a table of distribution of colored and face card found in a standard deck:

                Type                   Number of cards

                1 - 10                                40

                Black                               26

                Red                                 26

                Face                                12

The numerical cards from digit ( 1 to 10 ) are found in all 4 suits ( Clubs, Diamonds, Spades, and Hearts ). Hence, 10 x 4 = 40

- The entire deck is split in two colors ( Red and Black ) equally. So, the number of Black and Red cards are = 52 / 2 = 26 cards.

- The face cards are of three types ( King, Queen and Jack ). These three face cards are found in each of the 4 suits. Hence, Total number of face cards are = 4 * 3 = 12

- We will now consider the probabilities associated with each type. We will define 3 events and write down their probability as expressed:

Event ( A ): First draw is a red card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 red card in a standard deck of 52 cards. Hence,

           p ( A ) = [ Number of red cards ] / [ Total cards in a deck ]

           p ( A ) = [ 26 ] / [ 52 ]

           p ( A ) = 1 / 2

- After we make the first draw of a red card. Our deck distribution is changed to Number of Red cards remaining = 25 and total deck now has 51 cards remaining.

- We will define the next event as:

Event ( B ): The second draw is a face card.

- The probability of this event can be determined with the help of the table given above. There are a total of 12 face cards in a standard deck of 52 cards which is now down to 51 cards. Hence,

           p ( B ) = [ Number of face cards ] / [ Total cards in a deck ]

           p ( B ) = [ 12 ] / [ 51 ]

           p ( B ) = 4 / 17

- After we make the first draw of a face card. Our deck distribution is changed to Number of Face cards remaining = 11 and total deck now has 50 cards remaining.

- We will define the next event as:

Event ( C ): The third draw is a black card.

- The probability of this event can be determined with the help of the table given above. There are a total of 26 black cards in the deck. The total number of cards are down to 50 cards only. Therefore,

           p ( C ) = [ Number of black cards ] / [ Total cards in a deck ]

           p ( C ) = [ 26 ] / [ 50 ]

           p ( C ) = 13 / 25

- The entire drawing process consists of 3 events which are dependent on each draw. However, for the overall event to occur i.e drawing a red card , then a face card, and then a black card. We will multiply all three outcomes as follows:

         p ( T ) = p ( A ) * p ( B ) * p ( C )

         p ( T ) = [ 1 / 2 ] * [ 4 / 17 ] * [ 13 / 25 ]

         p ( T ) =  [ 26 / 425 ] ≈ 0.0612

Hence we get the required answer.

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Answer:

Where is the equation? It's ok but still.

Step-by-step explanation:

There are 360 different skirt-blouse-shoe outfits can she wear.

What is outfits?

A group of clothes that have been specifically chosen or designed to be worn together is known as an outfit. The term "outfit" can also refer to a business, an association, or a team of people who collaborate frequently. It can be used as a verb to mean "provide with the necessary gear."

A dress is different from a blouse and a skirt!  So I'll rephrase this as how many ways can she dress, to wear one blouse, one skirt and one pair of matching shoes.

You just multiply the number of blouses, the number of skirts, and the number of pairs of shoes;

= 5*9*8 = 360

Hence, there are 360 different skirt-blouse-shoe outfits can she wear.

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We concluded that whenever x changes by 1, the value of y becomes 1.7 units larger than its previous value.

What is the growth factor?

The rate at which a quantity multiplies itself over time is known as its growth factor. A quantity's growth rate is the factor by which it grows (or shrinks) over time.

Here, we have

The required expression for y with respect to x is:

y = (1.7)ˣ.......(1)

Where, 1.7 = 1-unit growth factor

Now we check,

Whenever x changes by 1

x →x +1 .....(2)

Now we put Equation (2) in (1) and we get

y' = (1.7)ˣ⁺¹

y' = (1.7)ˣ (1.7).....(3)

Taking the ratio of equations 3 & 1, we get

y'/y =   (1.7)ˣ (1.7)/(1.7)ˣ

y' = 1.7y

Hence, we observe that whenever x changes by 1, the value of y  becomes 1.7 units larger than its previous value.

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Answer: Brian payed $24.00

How u do it:

Discount= original price x discount%/100

Discount = 40 × 40%/100

Discount = 40 x 0.4 

You save = $16.00

Final Price = Original Price - Discount

Final Price = 40 - 16

Final Price = $24.00

The given statement that Diagonal WY bisects angles ZWX and ZYX has been proven below to be true.

Bisection of an angle is simply defined as dividing an angle into two equal parts.

We are given that Diagonal WY bisects angles ZWX and ZYX.

Now, from the image attached, we can see that side XY is congruent to side ZY and so; XY ≅ ZY.

Similarly, XW is congruent to ZW and as such; XW ≅ ZW

Since XY is congruent to ZY and XW is congruent to ZW, then the statement that  diagonal WY bisects angles ZWX and ZYX is true

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[tex]z = \frac{0.08 - 0.083}{\sqrt{0.083 * 0.917/100} }[/tex]

  = 0.108

pₐ = P( z < -0.108 ) = 0.4562

So the p-value obtained was a very high value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%)

Data given and notation

n = 100 represent the random sample taken

X=8 represent the people with depression or a depressive illness

p = 8/100 = 0.08 estimated proportion of people with depression or a depressive illness

p₀ = 0.083  is the value that we want to test

α = 0.05 represent the significance level  assumed

Confidence = 83% or 0.83  assumed

z  would represent the statistic (variable of interest)

pₐ represent the p value (variable of interest)  

Concepts and formulas to use  

We need to conduct a hypothesis in order to test the claim that the true proportions of people with depression or a depressive illness is lower than the general adult population value of 8.3% or 0.083:  

Null hypothesis:  

p ≥ 0.083

Alternative hypothesis:  

p < 0.083

When we conduct a proportion test we need to use the z statistic, and the is given by:

[tex]z = \frac{p- p_{0} }{\sqrt{p_{0} ( 1 - p_{0} )/ n } }[/tex]                       ---------------------  (1)  

The One-Sample Proportion Test is used to assess whether a population proportion  is significantly different from a hypothesized value .

Calculate the statistic  

Since we have all the info requires we can replace in formula (1) like this:  

[tex]z = \frac{0.08- 0.083 }{\sqrt{0.083 ( 1 - 0.083 )/ 100 } }[/tex]

 =  - 0.083 / √ 0.0076

 = -0.083 / 0.028

 = -0.108

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.  

The significance level assumed is α = 0.05 . The next step would be calculate the p value for this test.  

Since is a left tailed test the p value would be:  

     pₐ = P( z < -0.108 ) = 0.4562

So the p value obtained was a very high value and using the significance level given  we have  so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of people with depression or a depressive illness is not significantly lower than 0.083 (8.3%).

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Answer:

8x^2-14xy+3y^2 (I think)

Step-by-step explanation:

You probably don't need it now but like here

Answer:

394.527

Step-by-step explanation:

Divide the total number of beads by the number he needs to make each necklace and you will have your answer.

The graph of the proportional relationship d = 4t is given by:

Graph B.

The general model of a proportional relationship is given as follows:

y = kx.

Meaning that it's graph is that of a linear function, in which:

The relation between velocity, distance and time is given as follows:

v = d/t.

Then the equation for the distance as a function of time is given as follows:

d = vt.

Meaning that the slope is the velocity.

Trey walks 12 miles in 3 hours, hence the slope of the graph is of:

v = 12/3 = 4 miles per hour.

Among the options given by the image shown at the end of the answer, the correct option is:

Graph B.

As it goes through point (4,16).

The options are given by the image shown at the end of the answer.

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Differentiation reverses the parity of a function, means if f(x), is an even function, then its derivative f'( x ) is odd which is true i.e f(x) is even function implies f'(x) is odd and if f(x) is odd function implies f'(x) is even .

First, let's we start with the definition of even and odd functions.

f is even if and only if f(x) = f(-x) --(1)

f is odd iff f(x) = -f(-x) ---(2)

If f is even and differentiating equation (1) we get,

f'(x) = f'(-x)× (-1) = -f'(-x).

f'(x) = - f'(-x).

Since, f'(x) is some function, then let

g(x) = f'(x) So, we see g(x) = -g(-x) which shows that the derivative of an even function is an odd function.

If f is odd then: f(x) = -f(-x)

differentiating above function with respect to x we get ,

f'(x) = -f'(-x)× (-1 ) = f'(-x).

Let g(x) = f'(x), then g(x) = g(-x) which shows that the derivative of an odd function is an even function.

Hence, Differentiation reverses the parity is hold.

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Answer:

58

Step-by-step explanation:

72 + 1 - 5 x 3

= 72 + 1 - 15

= 73 - 15

= 58

14t-5t is another way to write the expression ​t⋅(14−5)

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

The given expression is t(14-5)

An expression is combination of variables, numbers and operators.

t times of fourteen minus five

Here t is the variable

We need to find other way to write this expression

t(14-5)

Apply distributive property

14t-5t

9t

Hence, 14t-5t is another way to write the expression ​t⋅(14−5)

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The graph of the solution of the inequality is shown in figure.

What is Inequality?

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

The inequality is,

⇒ x + 5 ≥ 2

Now,

Since, The inequality is,

⇒ x + 5 ≥ 2

Hence, Simplify the inequality as;

⇒ x + 5 ≥ 2

Subtract 5, we get;

⇒ x + 5 - 5 ≥ 2 - 5

⇒ x  ≥ - 3

Thus, The graph of the solution of the inequality is shown in figure.

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The physics student predicted that a force of 377.28N would be needed to stretch the spring by 15 cm using the regression model.

The relevant points from the regression model are

B. He predicted something that was outside the range of forces seen.

C. He predicted something that was outside the range of stretched distances that were observed.

D. His data contained outliers or significant points.

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Given that there are six blue marbles in the bag out of a total of 16, there is a 3/8 chance that the marble selected will be blue.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a proposition is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here,

Total number of marbles in bag,

=3+6+5+2

=16 marbles

Number of blue marbles=6

Probability of selecting blue marbles,

=6/16

=3/8

The probability that the marble chosen is blue will be 3/8 as the bag contains 6 blue marbles when total number of marbles is 16.

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The tottal number of ways to selct  15 cookies is 15504 and the ways are there to select 15 cookies if at least three is 6188.

What is combination?

A combination is a choice made in mathematics from a group of different elements when the order of the choices is irrelevant (unlike permutations). For instance, if three fruits, such as an apple, an orange, and a pear, are supplied, there are three possible pairings of the two: an apple and a pear. Formally speaking, a k-combination of a set S is a subset of S's k unique components. In other words, two combinations are the same if and only if they have the same members. (It is not important how the individuals in each set are arranged.) The quantity of k-combinations for a set with n components

we have to select 15 Cookies from 6 varieties so we can think an n₁+n2+n3+n4 + N5 +N6=15 with each o≤ni ≤15

C([tex]\frac{20}{12}[/tex]) = 15504

NOW we have One category is fixed let K Chocolate chips are Selected in I way The A we have to (15-K) Cookies from the varieties

C([tex]\frac{19-k}{15-5}[/tex])

So for k=0, C1=3876

k=1, C2 =3060

k=2, C3=2380

So C =C1+C2+C3=9316.

So the number of ways 15504-9316= 6188.

Hence, The tottal number of ways to selct  15 cookies is 15504 and ways are there to select 15 cookies if at least three is 6188.

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