The number of adults who attend a music festival, measured in hundreds of people, is represented by the function a(d)=−0.3d2+3d+10, where d is the number of days since the festival opened.

The number of teenagers who attend the same music festival, measured in hundreds of people, is represented by the function t(d)=−0.2d2+4d+12, where d is the number of days since the festival opened.

What function, f(d) , can be used to determine how many more teenagers than adults attend the festival on any day?


f(d)=−0.1d2+d+22

f(d)=0.1d2+d+2

f(d)=−0.1d2+7d+2

f(d)=0.1d2+7d+2

Answer:

4 weeks = 105

16 weeks = 42

24 weeks = 0

Step-by-step explanation:

the function is missing the 'w'

it should be : C(w) = 126 - 5.25w

'w' is the number of weeks

Substitute number of weeks in the 'w' spot

first one is 4 weeks, so

C(w) = 126 - 5.25(4)

= 126 - 21

= 105

Answer:

OK

Step-by-step explanation:

The first screenshot is for #7 and the second screenshot is for #8

Answer:

c. -x + 3x + 7  = 2x+7

Step-by-step explanation:

f(x) = 3x +1 and g(x) = x - 6

f-g = 3x +1 - ( x - 6)

Distribute the minus sign

     = 3x+1 - x+6

     = 2x +7

Answer:

The answer is 4.

Step-by-step explanation:

Edge 2021

Answer:

4

Step-by-step explanation:

EDGE2021

Answer: 0.2

Step-by-step explanation:

1 divided by 5 = 0.2

Answer:

0.2

Step-by-step explanation:

1/5 = 1 divided by 5.

This will also apply to any fraction

Fraction = Numerator divided by Denominator

Given : Scale drawing of Angel's rectangular room is 5cm by 7 cm

We know that, Area of a rectangle is given by : Length × Width

⇒   Area of Angel's rectangular room = (5 cm × 7 cm) = 35 cm²

Given : The scale is 1 cm = 4 feet

⇒   Area of Angel's rectangular room in square feet = 35 × (4 feet)²

⇒   Area of Angel's rectangular room in square feet = 35 × 16 feet²

⇒   Area of Angel's rectangular room in square feet = 560 feet²

Answer:

B. 4/3pi (7^3)

Step-by-step explanation:

The volume of a sphere is given by

V = 4/3 pi r^3

We know the radius is 7

V = 4/3 pi 7^3

Answer:

Given:

Cost = £ 800

Tax = 20%

To find:

The total cost

Solution:

Total cost = Cost + Tax

Tax = 20 % of cost

20 / 100 * 800

Tax = £ 160

Hence,

Total cost =  £ 800 + £ 160

Total cost = £ 960

Answer:

C) f(x) = 1500(2.15)x

Step-by-step explanation:

Got it right on Edge :)

Answer:

5328.78

Step-by-step explanation:

formula:

[tex]P(1+\frac{i}{n})^{n*t}\\2600(1+\frac{.08}{12})^{12*9}\\\\2600(1.006667)^{108}=5328.77861305[/tex]

this rounds to 5328.78

Answer:

(-3,-2)

(-3,4)

(3,4)

(3,-3)

Step-by-step explanation:

Answer:

cant see nun mind showing it

Answer:

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

We have that:

The mean number of penalties per game is [tex]\mu[/tex] and the standard deviation is [tex]\sigma[/tex].

Sample of n games:

This means that [tex]s = \frac{\sigma}{\sqrt{n}}[/tex]

What is the probability that, for a sample of college games to be played next week, the mean number of holding penalties will be X penalties per game or less?

The probability that the mean number of holding penalties per game is of X or less is the p-value of [tex]Z = \frac{X - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex], in which [tex]\mu[/tex] is the mean number of penalties per game, [tex]\sigma[/tex] is the standard deviation and n is the number of games that will be sampled.

Answer:

[tex]3\sqrt{5}i[/tex]

Step-by-step explanation:

[tex]\sqrt{-45}[/tex]

[tex]\sqrt{-9*5}[/tex]

[tex]\sqrt{-9}\sqrt{5}[/tex]

[tex]3i\sqrt{5}[/tex]

[tex]3\sqrt{5}i[/tex]

Answer:

21%

Step-by-step explanation:

Area of one sprinkler

a = πr²

a = π10²

a = 314.159 ft²

8 sprinklers

a = 8 * 314.159

a = 2,513.272

---------------------

area of field

a = lw

a = 80 * 40

a = 3200

------------------------

area not watered

a = 3200 - 2,513.272

a = 686.728

------------------

percentage not watered

p = 686.728 / 3200 * 100%

p = 21.46025%

Rounded

21%

Answer:

Step-by-step explanation:

Given that:

[tex]P = \left[\begin{array}{ccc}0.22&0.20&0.65\\0.62&0.60&0.15\\0.16&0.20&0.20\end{array}\right][/tex]

For a steady-state of a given matrix [tex]\bar X[/tex]

[tex]\bar X = \left[\begin{array}{c}a\\b\\c\end{array}\right][/tex]

As a result P[tex]\bar X[/tex] = [tex]\bar X[/tex] and a+b+c must be equal to 1

So, if P[tex]\bar X[/tex] = [tex]\bar X[/tex]

Then;

[tex]P = \left[\begin{array}{ccc}0.22&0.20&0.65\\0.62&0.60&0.15\\0.16&0.20&0.20\end{array}\right]\left[\begin{array}{c}a\\b\\c\end{array}\right] =\left[\begin{array}{c}a\\b\\c\end{array}\right][/tex]

[tex]\implies \left\begin{array}{ccc}0.22a+&0.20b+&0.65c\\0.62a+&0.60b+&0.15c\\0.16a+&0.20b+&0.20c\end{array} \right = \left \begin{array}{c}a ---(1)\\b---(2)\\c---(3)\end{array}\right[/tex]

Equating both equation (1) and (3)

(0.22a+ 0.2b + 0.65c) - (0.16a + 0.2b + 0.2c) = a - c

0.06a + 0.45c = a - c

collect like terms

0.06a - a = -c - 0.45c

-0.94 a = -1.45 c

0.94 a = 1.45 c

[tex]c =\dfrac{ 0.94}{1.45}a[/tex]

[tex]c =\dfrac{ 94}{145}a --- (4)[/tex]

Using equation (2)

0.62a + 0.60b + 0.15c = b

where;

c = 94/145 a

[tex]0.62a + 0.60b + 0.15(\dfrac{94}{145}) a= b[/tex]

[tex]0.62a + 0.15(\dfrac{94}{145}) a= -0.60b+b[/tex]

[tex]0.62a + (\dfrac{141}{1450}) a= 0.40b[/tex]

[tex](0.62+\dfrac{141}{1450}) a= 0.40b[/tex]

[tex](\dfrac{62}{100}+\dfrac{141}{1450}) a= 0.40b[/tex]

[tex](\dfrac{1043}{1450})a= 0.40b[/tex]

[tex](\dfrac{1043}{1450})a= \dfrac{4}{10} b[/tex]

[tex](\dfrac{1043 \times 10}{1450 \times 4})a = \dfrac{4}{10} \times \dfrac{10}{4}[/tex]

[tex]b = (\dfrac{1043}{580}) a --- (5)[/tex]

From a + b + c = 1

[tex]a + \dfrac{1043}{580}a + \dfrac{94}{145} a = 1[/tex]

[tex]a + \dfrac{1043}{580}a + \dfrac{94*4}{145*4} a = 1[/tex]

[tex]a + \dfrac{1043}{580}a + \dfrac{376}{580} a = 1[/tex]

[tex]\dfrac{580+ 1043+376 }{580} a= 1[/tex]

[tex]\dfrac{1999}{580} a= 1[/tex]

[tex]a = \dfrac{580}{1999}[/tex]

∴

[tex]b = \dfrac{1043}{580} \times \dfrac{580}{1999}[/tex]

[tex]b = \dfrac{1043}{1999}[/tex]

[tex]c = \dfrac{94}{145} \times \dfrac{580}{1999}[/tex]

[tex]c= \dfrac{376}{1999}[/tex]

∴

The steady matrix of [tex]\bar X[/tex] is:

[tex]\bar X = \left[\begin{array}{c}\dfrac{580}{1999} \\ \\ \dfrac{1043}{1999}\\ \\ \dfrac{376}{1999}\end{array}\right][/tex]

Answer:

9.68*10^-10

Step-by-step explanation:

The problem above can be solved using the binomial probability relation :

Where ;

P(x = x) = nCx * p^x * q^(n-x)

n = number of trials = 25

p = 1/4 = 0.25

q = 1 - p = 0.75

x = 20

P(x > 20) = p(x = 21) + p(x = 22) +.. + p(x = 25)

Using the binomial probability calculator to save computation time :

P(x > 20) = 9.68*10^-10

Answer:

136 mm²

Step-by-step explanation:

[tex]A=a^{2} +2a\sqrt{\frac{a^{2} }{4} } +h^{2}[/tex]

[tex]A=6^{2} +2(6)\sqrt{\frac{6^{2} }{4} } +8^{2}[/tex]

[tex]A=36 +12\sqrt{\frac{36 }{4} } +64[/tex]

[tex]A=36 +12\sqrt{9 } +64[/tex]

[tex]A=36 +12(3)+64[/tex]

[tex]A=36 +36+64[/tex]

A = 136

The answer would be 30 because the triangle is 10, the circle is 5, and each black triangle is 2 which would be 10 plus 5 which is 15 then times 2 which is 30.

Answer:

20?

Step-by-step explanation:

If 3 triangles = 30 they we could assume that each triangle = 10

10 + 10 + 10 = 30

If one triangle = 10 then the 2 circles would = 5 in the 2nd equation

10 + 5 + 5 = 20

If 1 circle = 5 then the 1 full squares would = 4

5 + 4 + 4 = 13

1 triangle = 10 , 1 circle = 5, Half a square = 2

10 + 5 * 2 = ?

Using PEMDAS we would multiply 2 and 5 first to get 10

10 + 10 = 20

Answer:

1/13

Step-by-step explanation:

there are total no of 52 cards

out of that there are 4 queen

propability = tatal no of favorable outcomes / total no of possible outcomes

=4 / 52

=1/13

Answer:

1/13

Step-by-step explanation:

Total cards = 52

Number of Queen = 4

Probability of the chosen card to be queen

                                                                   [tex]=\frac{Number \ of \ queen}{total \ number \ of \ cards}\\\\=\frac{4}{52} \\\\= \frac{1}{13}[/tex]

Answer:

530.929158457

Step-by-step explanation:

13x13= 169 x pi= 530.929158457

answer is

(Y)=-23,-14, -5,4,13

hope this will help you

Answer:

y = -x + 8

Step-by-step explanation:

First, plug in the slope.

y = mx + b

y = -1x + b

y = -x + b

Then, plug in the point.

7 = -(1) + b

7 = -1 + b

8 = b

Answer:

b open down and have a maximum

Step-by-step explanation:

A negative value for a will make the quadratic function open down

A downward facing parabola will have a maximum

Answer:

18°

Step-by-step explanation:

Know that the intersection of two lines and the angles opposite each other are equal

3t+12=66

Subtract 12 from both sides

3t=54

Divide 3 from both sides

t=18

Answer:

The time-mean speed of the minivans is of 105.8 seconds.

Step-by-step explanation:

Mean of a data-set:

The mean of a data-set is the sum of all values in the data-set divided by the number of values.

Five minivans, times of: 98.0, 108.0, 113.0, 108.0, 102.0, in seconds.

Thus, the mean is:

[tex]M = \frac{98 + 108 + 113 + 108 + 102}{5} = 105.8[/tex]

The time-mean speed of the minivans is of 105.8 seconds.

Answer:

the volume of the solid is 1024/3 cubic unit

Step-by-step explanation:

Given the data in the question,

radius of the circular disk = 4

Now if the center is at ( 0,0 ), the equation of the circle will be;

x² + y² = 4²

x² + y² = 16

we solve for y

y² = 16 - x²

y = ±√( 16 - x² )

{ positive is for the top while the negative is for the bottom position }

A = b²

b = 2√( 16 - x² )           { parallel cross section }

A = [2√( 16 - x² )]²

A = 4( 16 - x² )

Now,

VOLUME = [tex]\int\limits^r -rA dx[/tex]

= [tex]\int\limits^4_4 {-4(16-x^2)} \, dx[/tex]

= 4[ 16x - (x³)/3 ]           { from -4 to 4 }

= 4[ ( 64 - 64/3 ) - (-64 = 64/3 0 ]

= 4[ 64 - 64/3 + 64 - 64/3 ]

= 4[ (192 - 64 + 192 - 64 ) / 3 ]

= 4[ 256 / 3 ]

= 1024/3 cubic unit

Therefore,  the volume of the solid is 1024/3 cubic unit

Answer:

D. V=314.2cm³

Step-by-step explanation:

The volume of the cone is:

V=pi×r²×h/3=pi×5²×12/3=100×pi=314.2cm³

Answer: D) 314.2 [tex]cm^3[/tex]

Step-by-step explanation:

The formula for finding the volume of a right cone is [tex]V=\pi r^2\frac{h}{3}[/tex]

r is the radius and h is the height/altitude.

We can sub these values in and solve

[tex]V=\pi (5^2)(\frac{12}{3} )\\V=\pi (25)(4)\\V=100\pi[/tex]

Let's sub in 3.14 for [tex]\pi[/tex] since that is a close estimate

[tex]V=(100)(3.14)\\V=314[/tex]

The volume is about 314.

Our closest answer to that is D so that is the correct choice.