The length of the rectangular lot is 25 ft longer than twice the width. If the perimeter of the lot cannot exceed 350 ft, what is the greatest width possible?

It would take 11.1 hours to decay from 500 grams to 299 grams.

We know that for an element with an half-life T has a decay equation that can be written as:

f(t) = A*e^(-t*ln(2)/T)

Where A is the initial amount, and f(t) is the amount of the element t hours after.

Here we know that:

A = 500g

T = 15h

Then the function is:

f(t) = 500g*e^(-t*ln(2)/15h)

And we want to find the value of t such that f(t) = 299g, then:

299g =  500g*e^(-t*ln(2)/15h)

299/500 = e^(-t*ln(2)/15h)

ln(299/500) = -t*ln(2)/15h

-ln(299/500)*15h/ln(2) = t

11.1h = t

It will take 11.1 hours.

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The probability that the family had at least 3 girls is 0.6367

This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:

P(x = r) = nCr . p^r . q^n-r

Given: n= 8, probabibility of sucess (p) = 0.5, x≥3 (at least 3 girls)

The failures can be calculated using q = 1 - p = 1 - 0.5 = 0.5

P(x≥3) = 1 - P(x≤3) = 1 - ( P(x= 0) + P(x= 1) + P(x= 2) + P(x= 3) )

Using the formula:

P(x≥3)  = 1 - ( (8C0 x 0.5⁰  x 0.5⁸⁻⁰) +(8C1 x 0.5¹  x 0.5⁸⁻¹) + (8C2 x 0.5²  x 0.5⁸⁻²)  +  (8C3 x 0.5³  x 0.5⁸⁻³) )

          = 1 - ( (1/256) + (1/32) + (7/64) + (7/32) )

         = 0.6367

Therefore, the probability that the Wilson family had at least 3 girls is 0.6367

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Answer: 60 minutes

Step-by-step explanation:

x=time Madison spent at the mall

2x + 15 = 135

2x = 135-15

x = 120/2 = 60

Answer:god is good

Step-by-step explanation:if u put this 1 stars u hate god

if u give 5 stars u love god

The difference in the amount of money earned by Beth and Bartley is $40.25.

Given that, Beth makes $10.25/hour and Bartley makes $11.50 an hour.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

If Beth worked for 23 hours

Money earned by Beth is

10.25×23=$235.75

If Bartley worked for 17 hours

Money earned by Bartley is

11.50×17 =$195.5

So, difference of money = 235.75-195.5

= $40.25

Hence, the difference in the amount of money earned by Beth and Bartley is $40.25.

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Answer:

X - 111

Y - 104

Z - 76

Step-by-step explanation:

X - Just add 45 and 66

Y - 180 minus 76

Z - 119 minus 43

Answer:

2 people watch tv 3 hours a day, 3 people watch tv 0 hours a day, 2 people watch tv 1 hour a day, 2 people watch tv 2 hours a day, and 1 person watches tv 4 hours a day

Step-by-step explanation:

hope it helped :)

Answer:

  4.  121,800

  5.  591 3/32

  6.  1/4

Step-by-step explanation:

You want the sum of the first 200 terms of the arithmetic sequence starting 12, 18, 24, ....

The sum of the first n terms of an arithmetic sequence is given by the formula ...

  Sn = (2·a1 +d(n -1))(n/2)

where a1 is the first term and d is the common difference. Your sequence has first term 12 and common difference 18-12 = 6. The desired sum is ...

 S200 = (2·12 +6(200 -1))/(200/2) = (24 +1194)(100) = 121,800

You want the sum of the first 8 terms of the geometric sequence starting 12, 18, 27, ....

The sum of the first n terms of a geometric sequence is given by the formula ...

  Sn = a1·(r^n -1)/(r -1)

where a1 is the first term and r is the common ratio. Your sequence has first term 12 and common ratio 18/12 = 3/2. The desired sum is ...

  S8 = 12·((3/2)^8 -1)/(3/2 -1) = 24·6305/256 = 591 3/32

For this sequence, a1 = 1/12 and r = 2/3. When the sum is infinite and |r| < 1, the sum formula becomes ...

  S = a1/(1 -r)

The desired sum is ...

  S = (1/12)/(1 -2/3) = (1/12)/(4/12) = 1/4

Answer:

[tex]\textsf{4.} \quad 121,800[/tex]

[tex]\textsf{5.} \quad \dfrac{18915}{32}=591.09375[/tex]

[tex]\textsf{6.} \quad \dfrac{1}{4}[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given arithmetic sequence:

The first term of the given sequence is 12.

The common difference can be found by subtracting the first term from the second term:

[tex]\implies d=a_2-a_1=18-12=6[/tex]

Therefore:

To find the sum of the first 200 terms, substitute n = 200, a = 12 and d = 6 into the formula:

[tex]\begin{aligned}S_{200}&=\dfrac{1}{2}(200)[2(12)+(200-1)(6)]\\&=100[24+(199)(6)]\\&=100[24+1194]\\&=100[1218]\\&=121800\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]

Given geometric sequence:

The first term of the given sequence is 12.

The common ratio can be found by dividing the second term by the first term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{18}{12}=1.5[/tex]

Therefore:

To find the sum of the first 8 terms, substitute n = 8, a = 12 and r = 1.5 into the formula:

[tex]\begin{aligned}\implies S_{8}&=\dfrac{12(1-1.5^8)}{1-1.5}\\\\&=\dfrac{12\left(1-\frac{6561}{256}\right)}{-0.5}\\\\&=\dfrac{12\left(-\frac{6305}{256}\right)}{-0.5}\\\\&=\dfrac{-\frac{18915}{64}}{-0.5}\\\\&=\dfrac{18915}{32}\\\\&=591.09375\end{aligned}[/tex]

[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]

Given geometric sequence:

The first term of the given sequence is ¹/₁₂.

The common ratio can be found by dividing the second term by the first term:

[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{\frac{1}{18}}{\frac{1}{12}}=\dfrac{2}{3}[/tex]

Therefore:

To find the sum of the infinite geometric sequence, substitute a = ¹/₁₂ and r = ²/₃ into the formula:

[tex]\begin{aligned}\implies S_{\infty}&=\dfrac{\frac{1}{12}}{1-\frac{2}{3}}\\\\&=\dfrac{\frac{1}{12}}{\frac{1}{3}}\\\\&=\dfrac{1}{12} \times \dfrac{3}{1}\\\\&=\dfrac{3}{12}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]

The number which is as represented on the calculator display is; Choice A; 0.000001231151

It follows from the task content that the number which is represented on the calculator display is to be identified.

By checking, The display of the calculator is; 1.231151 E-⁶.

The number above can be represented as follows;

1.231151 × 10-⁶.

Since a negative exponent on the number ten indicates a shift leftwards, it follows that the number represented on the calculator display is;

0.000001231151.

Therefore, the correct number represented on the calculator display is; Choice A; 0.000001231151.

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Answer: 1. 0.1333 2. 1

Step-by-step explanation:

Step 1: 2/15 is the same as 2 divided by 15 which is 1.33333333333333333333333333333333333333333333333333 and so on.

Step 2: Clearly, the only number that is repeating is the 3.

The distance travelled before their first gas stop is 76.68 miles.

A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.

Consider that the distance covered before their first stop for gas be 'x'

The Total distance travelled is 372 miles

WE have given that after stopping for gas they travelled  65 1/4 miles and then tripled their distance. The equation is;

x + 261/4 + 3x = 372

4x + 261/4 = 372

16x + 261 = 1488

16x = 1227

x = 76.68 miles

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Considering the situation described, it is found that:

At the null hypothesis, it is tested if the mean is of 6 minutes, that is:

[tex]H_0: \mu = 6[/tex]

At the alternative hypothesis, it is tested if the mean is less than 6, hence:

[tex]H_1: \mu < 6[/tex]

The test statistic is obtained as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters of the equation are:

Using a calculator from the sample, the values of the parameters are:

[tex]\overline{x} = 5.39, \mu = 6, s = 1.22, n = 15[/tex]

Hence the test statistic is:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{5.39 - 6}{\frac{1.22}{\sqrt{15}}}[/tex]

t = -1.94.

The p-value is obtained with a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.94 and 15 - 1 = 14 df, hence it is of 0.0364.

Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected and there is not enough evidence that the mean is less than 6 days.

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Answer:

The Question is not Correct but answer is f 3 and g 3

Answer: [tex]6\\[/tex]

Step-by-step explanation:

[tex]\frac{(3+9) * 2}{4}[/tex]

Add 3 and 9 to get 12.

[tex]\frac{12 * 2}{4}[/tex]

Multiply 12 and 2 to get 24.

[tex]\frac{24}{4}[/tex]

Divide 24 by 4 to get 6.

[tex]6[/tex]

The measure of central angle is 45°

Here, arc length S = 5π/4

radius r = 5

We need to find central angle θ

Using the formula of arc length,

S = r * θ

5π/4 = 5 * θ

θ = π/4

θ = 45°

Therefore, the measure of central angle is 45°

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Answer:

Step-by-step explanation:

You want the steps to finding the equation of the hyperbola with center (1, 4), vertices (-7, 4) and (9, 4) and that includes the point (-11, -6).

The standard-form equation of a hyperbola with center (h, k) and semi-axes 'a' and 'b' is ...

  [tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]

The "linear eccentricity" 'c' is the distance from the center to a focus, and satisfies the equation ...

  c² = a² +b²

The vertices are (h±a, k) and the foci are (h±c, k).

The center of the hyperbola is given as (1, 4). The distance from the right vertex to the center is ...

  a = 9-1 = 8

The equation thus far is ...

  (x -1)/8² -(y -4)/b² = 1

The value of 'b' can be determined from the given point:

  (-11 -1)²/8² -(-6 -4)²/b² = 1

  9/4 -100/b² = 1

  5/4 = 100/b²

  b² = 100/(5/4) = 80

The linear eccentricity is ...

  c² = a² +b²

  c² = 64 +80 = 144

  c = √144 = 12

The foci are (1±12, 4) = (-11, 4) and (13, 4).

The equation is ...

  (x -1)²/64 -(y -4)²/80 = 1

Answer:

[tex]\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1[/tex]

Step-by-step explanation:

Standard equation of a horizontal hyperbola (opening left and right):

[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]

where:

Given:

Therefore:

Find the value of a using the x-values of the vertices:

[tex]\begin{aligned}\implies h-a &= -7\\1-a &= -7\\a &= 8\end{aligned}[/tex]

[tex]\begin{aligned}\implies h+a &= 9\\1+a &= 9\\a &= 8\end{aligned}[/tex]

Therefore, a = 8.

Substitute the values of h, k and a into the formula:

[tex]\implies \dfrac{(x-1)^2}{8^2}-\dfrac{(y-4)^2}{b^2}=1[/tex]

[tex]\implies \dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{b^2}=1[/tex]

Substitute the given point on the hyperbola (-11, -6) into the equation and solve for b²:

[tex]\implies \dfrac{(-11-1)^2}{64}-\dfrac{(-6-4)^2}{b^2}=1[/tex]

[tex]\implies \dfrac{(-12)^2}{64}-\dfrac{(-10)^2}{b^2}=1[/tex]

[tex]\implies \dfrac{144}{64}-\dfrac{100}{b^2}=1[/tex]

[tex]\implies \dfrac{144}{64}-1=\dfrac{100}{b^2}[/tex]

[tex]\implies \dfrac{144}{64}-\dfrac{64}{64}=\dfrac{100}{b^2}[/tex]

[tex]\implies \dfrac{80}{64}=\dfrac{100}{b^2}[/tex]

[tex]\implies \dfrac{5}{4}=\dfrac{100}{b^2}[/tex]

[tex]\implies b^2=\dfrac{4 \cdot 100}{5}[/tex]

[tex]\implies b^2=\dfrac{400}{5}[/tex]

[tex]\implies b^2=80[/tex]

Therefore, the equation of the hyperbola is:

[tex]\boxed{\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1}[/tex]

To find the foci, first find c where c² = a² + b²:

[tex]\implies c=\sqrt{a^2+b^2}[/tex]

[tex]\implies c=\sqrt{64+80}[/tex]

[tex]\implies c=\sqrt{144}[/tex]

[tex]\implies c=12[/tex]

Substitute the found value of c, along with the values of h and k into the foci formula:

[tex]\implies (h+c, k)=(1+12, 4)=(13,4)[/tex]

[tex]\implies (h-c,k)=(1-12,4)=(-11,4)[/tex]

Therefore, the foci are (-11, 4) and (13, 4).

The domain is  {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}

The given relation is {(−5,4), (−4, −1), (−2,1), (0,4), (1,3)

We need to find its domain and range

Domain of the set is {-5, -4, -2, 0, 1}

Range of the set is {4, -1, 1, 4, 3}

If in an relation every input has an single output, it is said to be a function

Here, every element of the domain has a single element in range, so it is a function

The given relation is  {(−3, −4), (−1,2), (0,0), (−3,5), (2,4)}

We need to find its domain and range

Domain of the set is {-3, -1, 0, -3, 2}

Range of the set is {-4, 2, 0, 5, 4}

If in an relation every input has an single output, it is said to be a function

Here, every element of the domain has a single element in range, so it is a function

Therefore, the domain is  {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}

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Answer:

$48.5

Step-by-step explanation:

From the question, we know that Jen and Kevin are definitely adults and the fee for adults

= $22.50

Jon is 14, and any number from 12 to 17 is classified as a youth, so his fee is

= $16.25

Beth is 8, classified as a child, her fee is

= $9.25

Joshua's age which is below 5 is granted free entry without a fee

Hence, the total cost of admission for the family is

$22.50 + $16.25 + $9.75

= $48.5

The given rational expression when added gives

[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]

Given:

[tex] \frac{5}{(x + 3)(x - 4)} + \frac{7}{(x + 2)(x - 4)} [/tex]

=

[tex] \frac{5(x + 2) + 7(x + 3)}{(x + 3)(x - 4)(x + 2)} [/tex]

=

[tex] \frac{5x + 10 + 7x + 21}{(x + 3)(x - 4)(x + 2)} [/tex]

=

[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]

So therefore, the addition of the rational expression is

[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]

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Answer of the why did George Washington caution against the formation of political parties?

What potential risks do political parties pose towards democracy? Do you think that the country should have followed his advice are as follows :  

(a) He believes that the government was undermined by differences between the political parties. Additionally, he argues that "the alternate domination" of one party over another and concurrent attempts to exact revenge on their rivals have resulted in terrible atrocities and "is itself a frightful despotism."

(b)The democratic theory's main tenet is that democracies force administrations to take citizens' preferences into account. Every contemporary democracy is organized by political parties, and some observers contend that parties are what makes democracies responsive. Others, however, contend that parties give extremists a platform and make governments less receptive to the needs of the populace. As newly established democracies around the world grapple with concerns of representation and governability, the discussion of parties and democracy assumes fresh prominence.

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The volume or the upper limit of the jellybean jar is 2,208.83cm³.

The space occupied within an object's borders in three dimensions is referred to as its volume.

It is sometimes referred to as the object's capacity.

Volume and mass are the two fundamental characteristics of matter.

Volume is only the amount of space that a thing occupies.

There are a few methods for determining an object's volume depending on its physical state.

So, the volume of the Jellybean jar:

Formula: πr²h

Now, insert values and calculate as follows:

πr²h

π(6.2)²18.3

π38.44(18.3)

π703.452

2,208.83

Therefore, the volume or the upper limit of the jellybean jar is 2,208.83cm³.

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Answer:

slope: 1

y-intercept: (0,2)

the second point to plot: (1,3)

Step-by-step explanation:

Points to plot

(0,2),(1,3),(-2,0)

Using the proportionality theorem, the values are:

x = 3

y = 2

The proportional theorem states that if two triangles are similar to each other, then their corresponding side lengths have the same ratios.

The triangles above are similar to each other, therefore, their corresponding sides will have lengths that are proportional or have the same ratios.

Therefore:

3/1.5 = 6/x

Cross multiple

3x = (1.5)(6)

3x = 9

3x/3 = 9/3

x = 3

Find y:

3/1.5 = 4/y

3y = (1.5)(4)

3y = 6

3y/3 = 6/3

y = 2

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The airplane is 359.12 feet high.

Given,

The distance between the observers = 1050 feet

When an aero plane crosses the line connecting them, each observer measures the plane's elevation angle.

Angle A = 40 degrees

Angle B = 30 degrees

We have to find the height of the airplane.

Here,

C = 180 - (40 + 30) = 110°

According to the sine rule :

Sin110 / 1050 = Sin40 / b = Sin 30 / a

1050 sin40 / sin 110 = b = 718.24 ft

1050 sin 30 / sin 110 = a = 558.69 ft

Sin 40 = h / 558.69

h = 558.69 × sin 40

h = 359.12 feet

That is,

The airplane is 359.12 feet high.

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Answer:

At this price, i would say the demand is: Unitary Inelastic Elastic Based on this, to increase revenue we should: Lower Prices Raise Prices Keep Prices

The measure of the required angle ∠VUT = 80 degrees

Given : A triangle with angle measures as :

∠RTU = 50°

exterior angle ∠UVR = 120°

To find : ∠VUT

In the given triangle we can use the exterior angle sum property

which states that the angle opposite to the inside of the triangle and the angle outside the triangle

The angle outside the triangle is 120 degrees

120 = ∠VUT  + 50

thus on subtracting 50 both sides we will get

∠VUT = 120 - 50

∠VUT = 80 degrees

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Answer: 48

Step-by-step explanation:  

         first you divide 25/2 and you get 12.5 and that is irrelevant but what is relevant is that you divide 96 by 2 and you get 48 thus giving you the answer to that question. :)

Answer:

Step-by-step explanation:

M is slope

B is y intercept

X and y are given

using the equation for the y intercept

b=y1-mx1

B=1−(1/2)⋅(−6)=4

Write in y=Mx+b

=12+4

The general equation of the line is −2+8=0

From the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .

As given in the question,

Given pair of lines,

Condition given that two angles are congruent ,

∠5 ≅ ∠7

Angle 5 is congruent to vertical opposite angle and to make a pair of parallel line Opposite angle should be congruent to angle 7.

Opposite angle and Angle 7 are pair of corresponding angles.

Line l should be parallel to the line m to satisfied the condition of

∠5 ≅ ∠7.

Therefore, from the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .

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