The perimeter (y) of a given shape is a function of its longest side (x). The equation for this function is y = 2.5x + 14. What does a solution of (15 feet, 51.5 feet) represent in the context of the problem?

The number of ways pets can be arranged in group according to the species is  in a row 288 ways.

Pets can be grouped by permutation concept as follows.

Total number of pets = 10

Number of dogs = 4

Number of cats = 3

Number of alpacas = 2

Number of bunny = 1

The number of ways pets can be arranged in group according to the species in a row as,

⇒ (4!)(3!)(2!)(1!)

⇒ (24)(6)(2)(1)

⇒ 288

Hence we can conclude that the number of ways pets can be arranged in group according to the species in a row is 288 ways.

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Answer:

$29.75

Step-by-step explanation:

If Lukas paid for the shoes with $50, and got $17.30 back, the total price of the shoes with the tax was $32.70. Because we are trying to find the price of the shoes without the 9% tax, we calculate what 91% of 32.70 is, which is $29.757

According to my calculation the answer is 188.

Answer:

m= -1/5

Step-by-step explanation:

slope formula to find it ^^

[tex]\tan 45^{\circ}=\frac{x}{2\sqrt{10}}\\\\1=\frac{x}{2\sqrt{10}}\\\\\boxed{x=2\sqrt{10}}\\\\\\\\\sin 45^{\circ}=\frac{2\sqrt{10}}{y}\\\\\frac{1}{\sqrt{2}}=\frac{2\sqrt{10}}{y}\\\\y=2\sqrt[20}\\\\\boxed{y=4\sqrt{5}}[/tex]

Answer:

see image

Step-by-step explanation:

The two circles will represent "starter" or "pudding" people and the overlap are both, but also don't forget people who chose neither. There must be 3-neither people. Because 6+7+8 only add to 21 and the question said there were 24 people.

I think you mean in terms of [tex]\sin(x)[/tex]?

Recall Euler's identity

[tex]e^{ix} = \cos(x) + i \sin(x)[/tex]

and de Moivre's theorem

[tex]\left(e^{ix}\right)^n = \left(\cos(x) + i \sin(x)\right)^n = \cos(nx) + i \sin(nx) = e^{inx}[/tex]

where [tex]i=\sqrt{-1}[/tex].

It follows that

[tex]\sin(4x) = \mathrm{Im}\left(\cos(x) + i \sin(x)\right)^4[/tex]

By the binomial theorem, expanding the right side gives

[tex]\cos^4(x) + 4i \cos^3(x) \sin(x) - 6\cos^2(x) \sin^2(x) - 4i \cos(x) \sin^3(x) + \sin^4(x)[/tex]

and so

[tex]\sin(4x) = 4\cos^3(x) \sin(x) - 4 \cos(x) \sin^3(x)[/tex]

We can factorize this as

[tex]\sin(4x) = 4 \cos(x) \sin(x) \left(\cos^2(x) - \sin^2(x)\right)[/tex]

and using the Pythagorean identity

[tex]\cos^2(x)+\sin^2(x) = 1 \implies \cos(x) = \pm \sqrt{1-\sin^2(x)}[/tex]

this reduces to

[tex]\sin(4x) = \pm 4 \sqrt{1-\sin^2(x)} \sin(x) (1 - 2 \sin^2(x))[/tex]

Answer:

62,500

Step-by-step explanation:

250,000 ÷ 4 = 62,500

∴ Each member would receive 62,500.

Answer:

Step-by-step explanation:

Solving    3x2-5x-1 = 0 by the Quadratic Formula .

According to the Quadratic Formula,  x, the solution for   Ax2+Bx+C  = 0, where  A, B, and  C number, often called coefficients, is given by :

           - B  ±  √ B2-4AC

 x =   ————————

                     2A

 In our case,  A   =     3

                     B   =    -5

                     C   =   -1

 B2  -  4AC   =

      25 - (-12) =

             37

Applying the quadratic formula :

              5 ± √ 37

  x  =    —————

                   6

 √ 37, rounded to 4 decimal digits, is   6.0828

So now we are looking at:

          x  =  ( 5 ±  6.083 ) / 6

Two solutions:

x =(5+√37)/6= 1.847

x =(5-√37)/6=-0.180

Using the z-distribution, considering the standard 95% confidence level, the margin of error is of 0.0486 = 4.86%.

A confidence interval of proportions is given by:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

The margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which:

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The sample size and the estimate are given by:

[tex]n = 350, \pi = \frac{240}{350} = 0.6857[/tex]

Hence the margin of error is:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

[tex]M = 1.96\sqrt{\frac{0.6857(0.3143)}{350}}[/tex]

M = 0.0486 = 4.86%.

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Answer:

99% - 0.06

95% - 0.05

90% - 0.04

Step-by-step explanation: i got it right

There were 2.07 times as much people that applied in the fourth month than in the first month.

An exponential function is one that grows or decreases in an exponential manner. Thus, for any exponential function we can write; f(x) = ax^±n. The term a is the initial value x is the rate of change while n is the time elapsed. The positive sign is used for an exponential increase while the negative sign is used for an exponential decrease.

Thus we have;

f(x) = 27(1.2)^4

This shows us that the time elapsed is four months and f(x) = 2.07.

Therefore, there were 2.07 times as much people that applied in the fourth month than in the first month.

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The statement that is true about Sheila's savings plan is that; C.

Sheila must save $60 per month to achieve her goal.

The price of bathroom remodeling is $ 810.

After 13 months , she has saved $ 510

This means that she has a $300 shortage to cover in 5 months.

This means that she need to save :

$300/5  = $60 / month in order to achieve her goal

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Answer: C

Step-by-step explanation: edge

8  is the largest possible value of the median of all nine numbers in this list.

Lets simplify it,

⇒  The given six numbers are 7,8,3,5,9 and 5.

⇒  Arrange the six numbers in order 3,5,5,7,8,9.

⇒  We have three more numbers to insert into the list, and the median will be the  highest 5(and 5 lowest) number on the list. If the three numbers are greater than 9, the median will be the highest it can possible be.

∴  The median is the 5th item of data which is 8.

∴  Median=8

Hence 8  is the largest possible value of the median of all nine numbers in this list.

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The probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

According to the question,

Alice and Bob each arrive at a party at a random time between 1.00 P.M and 2.00 P.M.

In probability theory, the sample space(s) of a random trial is the set all possible results of that trial.

Let 'x' be the arrival time of Alice and 'y' be the arrival time of Bob.

s = {(x, y) /1≤x≤2 and 1≤y≤2}

In order to find the probability of the Bob arrived before 1.30 P.M, if the Alice arrives after Bob.

Formula for Probability = [tex]\frac{Number of favorable events}{Total number of events}[/tex]

= 1/2

Hence, the probability of the Bob arrived before 1.30 P.M is 1/2 if the Alice arrives after Bob.

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Answer:

large pitcher, or from 2 small pitchers, 1 medium pitcher, and 3 la

or from 2 small pitchers, 1 medium pitcher, and 3 large pitchers. If we use only large pitchers of water, Root Tissues

Identify the root tissues. Record your answer under "Slide 5" on your lab report.

The measure of m<1, m<2 and m<3 are 90, 63 and 63 degrees respectively

A kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other.

The given figure is a kite with two intersecting lines that are perpendicular to each other.

Since the lines are perpendicular to each other, hence;

m<1 = 90 degrees

For the measure of m<2

m<2 + 90 + 27 =180

m<2 + 117 = 180

m<2 = 180 - 117

m<2 = 63degrees

Since the opposite sides are congruent, hence the measure of m<2 is congruent to m<3. Hence m<3 = 63 degrees

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Answer,

Leaves from home=22:15hour

get to destination=4:00hour

time taken on a journey,

from time 22:15hour to 24:00hour=2:45hour and,

time is taken form 22:00hour to 4:00hour=4:00hour
So, the total time taken to reach the destination is 2:45+4:00=6:45hour

Answer:

Step-by-step explanation:

(a)

      1 - Simplify 4 - 9 to -5.

         ⇒ | - 5 |

      2 - Simplify.

       ⇒ 5

  (b)  

   1 -  Simplify

 ⇒ -5

Answer:

30

Step-by-step explanation:

Let's start by multiplying the equation through bt the least common denominator so that we can clear the denominator:

[tex]\frac{2}{5}x+\frac{1}{3}y=1[/tex]

The least common of 3 and 5 is 15, so we can multiply through by 15:

[tex]15(\frac{2}{5}x+\frac{1}{3}y)=15(1)\\6x+5y=15[/tex]

We want the left side of the equation to be 12x + 10y. We can get this if we multiply the expression we currently have (6x + 5y) by 2. However, if we multiply the left side by 2, we must also multiply the right side by 2 to balance out the equation. If we do this, we will get our answer:

[tex]2(6x+5y)=2(15)\\12x+10y=30[/tex]

On the right side, we get 30. Therefore, the answer is 30

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

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

The graph of a quadratic equation has the shape of a parabola. The standard quadratic equation has the form:

y = ax² + bx + c

The equation of a parabola with vertex at (-2, 2) and passes through (-3, 5) and (-1, 5) is y = 3x² + 12x + 14. The value of a in the equation is 3.

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Answer:

The correct answer is A:3

Step-by-step explanation:

If the domain of the function y=-2/3 x+7 is {-12,-6,3,15} then the range of the function is {15,11,5,-3}.

Given that the domain of the sunction y=-2/3 x+7 is {-12,-6,3,15}.

We have to find the range of the function and complete the table.

Function is relationship between two or more variables expressed in equalto form. In a function each value of x has some value of y.

To complete the table we need to find the value of the function at different values of x.Domain is basically value of  x which satisfies the function.

We have to first put the value of x=-12 in y=-2/3+7

y--2/3*-12+7

=15

Now put x=-6 in the function.

y=-2/3 *-6+7

=3

Put the value of x=3 in the function.

y=-2/3*3+7

=5

Put the value of x=15.

y=-2/3*15+7

=-41/3.

Hence the range of function is {15,11,-41/2,5}.

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The Surface area of the triangular prism with the net shown below is 106 cm²

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

Surface area of the triangular prism = 2(0.5 * 5 * 3) + (7 * 3) + 2(7 * 5) = 106 cm²

The Surface area of the triangular prism with the net shown below is 106 cm²

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Answer:

6

Step-by-step explanation:

If you divide 78 by all of the numbers, only one, 6, is a whole number, making it the only factor. You can check this by multiplying 6 by 13, (you get 13 from the division) and you get 78.

I hope this helps!

Answer:

300

Step-by-step explanation:

25 choose 2 (exactly how it sounds like)

= (25*24)/(2*1)=600/2=300

The probability that exactly one tank in the sample contains high-viscosity material is P(A) = 0,4607 or P(A) = 46,07 %

P(A) = Number of favorable events/ Total number of events FE/TE

If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )!    ⇒  C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!  

C ( 24,4) = 24*23*22*21/4*3*2C ( 24,4) = 24*23*22*21/4*3*2    ⇒  C ( 24,4) =  10626

TE = 10626

Splitting the group of tanks in two 6 with h-v  and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3)  = 6 * 18! / 3!*15!  =  18*17*16*15!/15!

FE =  4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607     or   P(A) = 46,07 %

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Averagely, Ana practiced for a greater amount of time each day.

Mean for ana= (20 + 20 + 30 + 60 + 60 + 60 + 70 + 70 + 100 + 100 + 100 + 115 + 115 + 115)/14 = 69.6

Mean for tara= (20 + 20 + 30 + 30 + 45 + 45 + 45 + 70 + 70 + 70 + 75 + 90 + 90 + 120)/14 = 58.6

Median for ana= 70

Median for tara= (45 + 70)/2 = 57.5

Ana has the greater median and also has the greater mean.

Averagely, we can conclude that ana practiced for a greater amount of time each day.

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Answer:

Step-by-step explanation:

150 kilometers

60 kph

tank is 20 liters

6 km/l

150/6 = 25 liters needed

$60/l

5 more liters of fuel

total cost 25 x .60 =  $15

[tex] \frac{5}{6} \: of \: a \: number \: is \: 180[/tex]

[tex] \frac{1}{6} \: is \: 5 \: times \: less \: than \: \frac{5}{6} \\ \frac{1}{6} = \frac{180}{5} = 36[/tex]