In a 1995 Corporation for Public Broadcasting poll of TV viewership, one question was, "A recent study by a psychology professor at a leading university concluded that the amount of violence children see on television has an effect on their likelihood of being aggressive and committing crimes. From what you have seen or heard about this subject, do you agree strongly with that conclusion, agree somewhat, or disagree strongly?" Is this question appropriate, or is it flawed in some way? Comment briefly.

Answer:

Maximum = 540 at (6,14)

Minimum = 300 at (0,10) or (12,2).

Step-by-step explanation:

The given linear programming problem is

Minimize and maximize: P = 20x + 30y

Subject to constraint,

[tex]2x+3y\ge 30[/tex]            .... (1)

[tex]2x+y\le 26[/tex]            .... (2)

[tex]-2x+3y\le 30[/tex]            .... (3)

[tex]x,y\geq 0[/tex]

The related equation of given inequalities are

[tex]2x+3y=30[/tex]

[tex]2x+y=26[/tex]

[tex]-2x+3y=30[/tex]

Table of values are:

For inequality (1).

x      y

0     10

15     0

For inequality (2).

x      y

0     26

13     0

For inequality (3).

x      y

0     10

15     0

Pot these ordered pairs on a coordinate plane and connect them draw the corresponding related line.

Check each inequality by (0,0).

[tex]2(0)+3(0)\ge 30\Rightarrow 0\ge 30[/tex]    False

[tex]2(0)+(0)\le 26\Rightarrow 0\le 26[/tex]     True

[tex]-2(0)+3(0)\le 30\Rightarrow 0\le 30[/tex]    True

It means (0,0) is included in the shaded region of inequality (2) and (3), and (0,0) is not included in the shaded region of inequality (1).

From the below graph it is clear that the vertices of feasible region are (0,10), (6,14) and (12,2).

Calculate the values of objective function on vertices of feasible region.

Point           P = 20x + 30y

(0,10)           P = 20(0) + 30(10) = 300

(6,14)           P = 20(6) + 30(14) = 540

(12,2)           P = 20(12) + 30(2) = 300

It means objective function is maximum at (6,14) and minimum at (0,10) or (12,2).

Answer:

Spearman's correlation

Step-by-step explanation:

A researcher records each student’s rank in his/her high school graduating class and the student’s rank in the college graduating class.

The correlation that should be used to measure the relationship between these two variables is - Spearman's correlation

This correlation gives a statistical measure of similar relationship between paired data.

This is used to evaluate relationships involving ordinal variables.

Answer:

The answer is 1.

Answer:

1

Step-by-step explanation:

any variable of power 0 equal to 1

Answer:

[tex]f(x)=3^{3x-1}[/tex].

The domain of the function is the set of all real number and the range is [tex](0,\infty)[/tex]

Step-by-step explanation:

Given:

The function is  given as:

[tex]f(x)=\frac{1}{3}(81)^{\frac{3x}{4}}[/tex]

Using the rule of the exponents, [tex]a^{mn}=(a^m)^n[/tex],

[tex]f(x)=\frac{1}{3}((81)^{\frac{1}{4}})^{(3x)}\\f(x)=\frac{1}{3}(\sqrt[4]{81} )^{3x}\\f(x)=\frac{1}{3}(3)^{3x}\\f(x)=\frac{3^{3x}}{3^1}[/tex]

Using the rule of the exponents,[tex]\frac{a^m}{a^n}=a^{m-n}[/tex],

[tex]f(x)=3^{3x-1}[/tex]

Therefore, the simplified form of the given function is:

[tex]f(x)=3^{3x-1}[/tex]

Key aspects:

The given function is an exponential function with a constant base 3.

Domain is the set of all possible values of [tex]x[/tex] for which the function is defined.

The domain of an exponential function is a set of all real values.

The range of an exponential function is always greater than zero.

Therefore, the domain of this function is also all real values and the range is from 0 to infinity.

Domain: [tex]x \epsilon (-\infty,\infty)[/tex]

Range: [tex]y\epsilon (0,\infty)[/tex]

Answer: 1/3 27 all real numbers y>0

Step-by-step explanation:

Answer:

  12 mph

Step-by-step explanation:

The relationship between jogging speed and walking speed means the time it takes to walk 4 miles is the same as the time it takes to jog 8 miles. Then the total travel time (0.75 h) is the time it would take to jog 1+8 = 9 miles. The jogging speed is ...

  (9 mi)(.75 h) = 12 mi/h . . . average jogging speed

__

Check

1 mile will take (1 mi)/(12 mi/h) = 1/12 h to jog.

4 miles will take (4 mi)/(6 mi/h) = 4/6 = 8/12 h to walk.

The total travel time is (1/12 +8/12) h = 9/12 h = 3/4 h. (answer checks OK)

_____

Comment on the problem

Olympic race-walking speed is on the order of 7.7 mi/h, so John's walking speed of 6 mi/h should be considered quite a bit faster than normal. The fastest marathon ever run is on the order of a bit more than 12 mi/h, so John's jogging speed is also quite a bit faster than normal. No wonder he got tired.

Answer: The clock skip 0.25 seconds every 30 minutes.

Step-by-step explanation:

Since we have given that

Clock was correct on Wednesday at 4 pm.

At 2 pm , on saturday, the clock was running late by 35 seconds.

From 4 pm wednesday to 4 pm thursday = 24 hours

From 4 pm thursday to 4 pm friday = 24 hours

From 4 pm friday to 2 pm saturday = 22 hours

So, total hours = 24+24+22 = 70 hours

We need to find the number of seconds that the clock skip every 30 minutes.

So, it becomes

[tex]\dfrac{70}{0.5}=\dfrac{35}{T}\\\\70T=35\times 0.5\\\\T=\dfrac{35\times 0.5}{70}\\\\T=0.25[/tex]

Hence, the clock skip 0.25 seconds every 30 minutes.

The clock was 35 seconds late over a period of 70 hours, which equals 140 intervals of 30 minutes. Therefore, the clock skipped an average of 0.25 seconds every 30 minutes.

To determine the average number of seconds the clock skipped every 30 minutes, we first need to calculate the total time difference and then divide by the number of 30-minute intervals.

The clock was showing the correct time on Wednesday at 4 pm.

It was 35 seconds late by Saturday at 2 pm.

Time elapsed from Wednesday 4 pm to Saturday 2 pm is 2 days and 22 hours, which equals (2×24 + 22) hours = 70 hours.

Converting 70 hours into minutes: 70×60 = 4200 minutes.

Number of 30-minute intervals in this period: 4200 / 30 = 140 intervals.

Average seconds skipped per 30-minute interval: 35 seconds / 140 intervals = 0.25 seconds.

Thus, the clock skipped an average of 0.25 seconds every 30 minutes.

Answer:

Step-by-step explanation:

We want to find 95% confidence interval for the mean of the weight of of textbooks.

Number of samples. n = 28 textbooks weight

Mean, u =76 ounces

Standard deviation, s = 12.3 ounces

For a confidence level of 95%, the corresponding z value is 1.96. This is determined from the normal distribution table.

We will apply the formula

Confidence interval

= mean +/- z ×standard deviation/√n

It becomes

76 +/- 1.96 × 12.3/√28

= 76 +/- 1.96 × 2.3113

= 76 +/- 4.53

The lower end of the confidence interval is 76 - 4.53 =71.47

The upper end of the confidence interval is 76 + 4.53 = 80.53

Therefore, with 95% confidence interval, the mean textbook weight is between 71.47 ounces and 80.53 ounces

Amount of down payment = $46000

Mortgage needs = $184000

Solution:

From the given,

Cost of the house = [tex]\$230000[/tex]

Percentage of down payment = [tex]20\%[/tex]

Number of years of fixed loan = 30

[tex]\text { Total down payment }=\text { cost of the house } \times \text { Percentage of down payment }[/tex]

[tex]\Rightarrow \frac{230000 \$\times 20}{100} \rightarrow 46000 \$[/tex]

[tex]\text {Mortgage needs}=\text { Total cost - Total down payment }[/tex]

[tex]\Rightarrow 230000 \$-46000 \$=184000 \$[/tex]

It can be concluded that the total down payment for the house and mortgage needs would be [tex]\$46000 \text{ and } \$184000[/tex]

Her total sales was $3695.33

Step-by-step explanation:

Osmin had a gross pay of $624.86 last week

She wants to know what was her total sales

Assume that her total sales is $x

∵ Her gross pay = $624.86

∵ She earns 12.85 per hour plus a 3% commission on all sales

∵ She worked for 40 hrs last week

∵ Her total sales was $x

- Put all of these in an equation represents her gross pay

∵ Her gross pay = her rate per hour × the number of hours + 3% of x

∴ 624.86 = 12.85 (40) + 3% (x)

∴ 624.86 = 514 + [tex]\frac{3}{100}[/tex] x

∴ 624.86 = 514 + 0.03 x

- Subtract 514 from both sides

∴ 110.86 = 0.03 x

- Divide both sides by 0.03

∴ 3695.33 = x

∴ Her total sales = $3695.33

Her total sales was $3695.33

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Let the number of bikes = x and total money = y.

Set  up two equations:

The first equation is the cost function, which would be rent plus 60 times the number of bikes:

y = 1800 + 60x

The second equation would be revenue, where total money would be equal to 120 times the number of bikes sold:

y = 120x

Now you can graph both equations by setting the equations to equal each other. The point on the graph, where the loib=ne crosses the X axis is the break even point

Graph

120x = 1800 +60x

See attached picture for the graph and you can see the break even point is 30 bikes.

You can check by replacing X with 30 to see if the equations equal each other:

1800 + 60(30) = 1800 +1800 = 3600

120(30) = 3600

Answer:

The mean of a binomial distribution is given  by  mean  = n x p where n = the number of items and p equals the probability of success.  Here we have:

mean =  1632 x 0.57  =   930.2

Step-by-step explanation:

The mean for a binomial substitution = n x p

Mean = 1632 x 0.57 = 930.24

The answer would be D.

Picture:

Multiply P(x) by X, then add those together:

0 x 0.42 = 0

1 x 0.12 = 0.12

2 x 0.34 = 0.68

3 x 0.05 = 0.15

4 x 0.07 = 0.28

Mean = 0 + 0.12 + 0.68 + 0.15 + 0.28 = 1.23

Answer:

d is the correct answer

Answer:75

Step-by-step explanation:

Answer:

16.78 seconds

Step-by-step explanation:

speed = Distance Traveled / time

thus speed =29.79 Km/sec

time =distance Traveled/speed (from above formula)

time taken=500 km ÷ 29.79 Km/sec

∴time taken=16.78 seconds

Answer:

Yes, it will reach or exceed 141 degree F

Step-by-step explanation:

Given equation that shows the temperature T in degrees Fahrenheit x minutes after the machine is put into operation is,

[tex]T = 0.005x^2 + 0.45x + 125[/tex]

Suppose T = 141°F,

[tex]\implies 141 = 0.005x^2 + 0.45x + 125[/tex]

[tex]\implies 0.005x^2 + 0.45x + 125 - 141 =0[/tex]

[tex]\implies 0.005x^2 + 0.45x - 16=0[/tex]

Since, a quadratic equation [tex]ax^2 + bx + c =0[/tex] has,

Real roots,

If Discriminant, [tex]D = b^2 - 4ac \geq 0[/tex]

Imaginary roots,

If D < 0,

Since, [tex]0.45^2 - 4\times 0.005\times -16 = 0.2025 + 32 > 0[/tex]

Thus, roots of -0.005x² + 0.45x + 125 are real.

Hence, the temperature can reach or exceed 141 degree F.

The temperature of the part will exceed 141°F during the manufacturing process.

To determine if the temperature of the part will ever reach or exceed 141°F, we need to find the value of x when the temperature T equals 141°F. We can do this by setting the equation T = 0.005x² + 0.45x + 125 equal to 141 and solving for x using the quadratic formula.

The quadratic formula is given by x = (-b ± √(b² - 4ac))/(2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 0.005, b = 0.45, and c = 125 - 141 = -16.

Calculating the discriminant, which is the value inside the square root in the quadratic formula, we get b² - 4ac = 0.45² - 4(0.005)(-16) = 0.2025 + 0.32 = 0.5225. Since the discriminant is positive, the quadratic equation has two real and distinct solutions, which means the temperature of the part will exceed 141°F at some point during the manufacturing process.

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Answer:

Optical axis

Step-by-step explanation:

Optical axis is the rotational symmetry axis of the surfaces.

A line with a certain degree of rotational symmetry is called as the optical axis in an optical system.

It is the straight line that passes through the geometric center of the lens and joins two curvature centers of its surfaces.

It is also called as the principal axis.

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

Solution:

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is [tex]\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }[/tex]

If they work together they can do the entire prospectus in five hours

[tex]\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}[/tex]

On cross-multiplication we get,

[tex]\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}[/tex]

[tex]\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}[/tex]

On cross multiplication ,we get

[tex]\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}[/tex]

using quadratic formula:-

[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]

[tex]x=\frac{12 \pm \sqrt{144-40}}{2}[/tex]

[tex]\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}[/tex]

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

Answer:

The answers should be c. 120° and e. 240°

Step-by-step explanation:

Consider the provided information.

Equilateral triangle has 3 equal sides.

Now we need to rotate the equilateral triangle so that the equilateral triangle to map it onto itself.

For this we need to rotate each of those sides to an adjacent side. (Shown in figure)

This can be happen 3 times as there are 3 sides,

A circle has 360° and [tex]\dfrac{1}{3}\times 360^{\circ}=120^{\circ}[/tex].

Thus, a 120° rotation map it onto itself.

Any other angle multiple of 120° will do the same.

Hence, the answers should be c. 120° and e. 240°

Answer:

28.27 cm/s

Step-by-step explanation:

Though Process:

Solution:

the area of the exposed circle is

[tex]A =\pi a^2 [/tex]

the rate of change of this area can be, (using chain rule)

[tex]\frac{dA}{dt} = 2 \pi a \frac{da}{dt}[/tex] we can call this Eq(2)

what we are really concerned about is how [tex]a[/tex] changes as the punch is being poured into the bowl i.e [tex]\frac{da}{dh}[/tex]

So we need another formula: Using the property of hemispheres and pythagoras theorem, we can use:

[tex]r = \frac{a^2 + h^2}{2h}[/tex]

and rearrage the formula so that a is the subject:

[tex]a^2 = 2rh - h^2[/tex]

now we can derivate a with respect to h to get [tex]\frac{da}{dh}[/tex]

[tex]2a \frac{da}{dh} = 2r - 2h[/tex]

simplify

[tex]\frac{da}{dh} = \frac{r-h}{a}[/tex]

we can put this in Eq(1) in place of [tex]\frac{da}{dh}[/tex]

[tex]\frac{da}{dt} = \frac{r-h}{a} . \frac{dh}{dt}[/tex]

and since we know [tex]\frac{dh}{dt} = 1.5[/tex]

[tex]\frac{da}{dt} = \frac{(r-h)(1.5)}{a} [/tex]

and now we use substitute this [tex]\frac{da}{dt}[/tex]. in Eq(2)

[tex]\frac{dA}{dt} = 2 \pi a \frac{(r-h)(1.5)}{a}[/tex]

simplify,

[tex]\frac{dA}{dt} = 3 \pi (r-h)[/tex]

This is the rate of change of area, this is being asked in the quesiton!

Finally, we can put our known values:

[tex]r = 5cm[/tex]

[tex]h = 2cm[/tex] from the question

[tex]\frac{dA}{dt} = 3 \pi (5-2)[/tex]

[tex]\frac{dA}{dt} = 9 \pi cm/s// or//\frac{dA}{dt} = 28.27 cm/s[/tex]

Answer:

D= -16

E= 0

F= 0

Step-by-step explanation:

The given equation is [tex]x^{2} + y^{2} + Dx + Ey + F = 0[/tex]

It is also given that the circle passes through (0,0) (16,0) and (8,8).

Inserting (0,0) in the equation, it gives

[tex]0 + 0 + 0 + 0 + F = 0[/tex]

This gives F = 0 .

Now inserting (16,0) , it gives

[tex]16^{2} + 0^{2} + D(16) + E(0) + 0 = 0[/tex]

[tex]D(16) = -256[/tex]

[tex]D = \frac{-256}{16}[/tex]

D = -16

Now inserting (8,8) , it gives

[tex]8^{2} + 8^{2} + (-16)(8) + (E)(8) + 0 = 0[/tex]

[tex]-16 + E = -16[/tex]

E = 0

Thus the equation of circle is

[tex]x^{2} + y^{2} + (-16)x  = 0[/tex]

We can draw the following graph and thus verify that points (0,0) (8,8) and (16,0) lie on graph.

The equation of the circle passing through points (0, 0), (8, 8), and (16, 0) is x^2 + y^2 - 16x - 16y = 0. Solving the system of equations derived from substituting the given points into the circle equation confirms these coefficients for D and E.

To find the equation of the circle that passes through the points (0, 0), (8, 8), and (16, 0), we can use the standard form of a circle's equation:

x

2

+

y

2

+ D

x

+ E

y

+ F = 0

Because the circle passes through the origin (0,0), we know that F = 0. With the remaining points (8, 8) and (16, 0), we can substitute these coordinates into the equation to form a system of equations.

Using point (8,8), the equation becomes:

64 + 64 + 8D + 8E + F = 0

Using point (16,0), the equation becomes:

256 + 16D + F = 0

Since F = 0, the system of equations is:

Solving these equations, we get:

The equation of the circle is therefore:

To verify the result, plotting the points and the graph of the circle on a graphing utility should show that the points lie on the circumference of the circle.

Both jewelers used 26104 beads altogether while making necklaces.

Step-by-step explanation:

No. of necklaces made by Gemma = 106

Necklaces made by Leah = 106+39 = 145 necklaces

Total necklaces made = Gemma's + Leah's

Total necklaces made = [tex]106+145 = 251\ necklaces[/tex]

Beads used in 1 necklace = 104 beads

Beads used in 251 necklaces = 104*251 = 26104

Both jewelers used 26104 beads altogether while making necklaces.

Keywords: multiplication, addition

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Answer: length of the drive way = 56 feet

Width of the driveway = 12 feet

Step-by-step explanation:

The rectangular driveway has two equal lengths and two equal widths. The area of the driveway is expressed as

length,l × width,w

The area is 672 feet squared. It means that

L×W = 672

The length of the rectangular driveway is four feet less than five times the width. It means that

L = 5W - 4

Substituting L = 5W - 4 into LW = 672

W(5W - 4) = 672

5W^2 - 4W - 672 = 0

5W^2 + 56W - 60W - 672 = 0

W(5W + 56) - 12(5W + 56) = 0

(W - 12)(5W + 56) = 0

W - 12 = 0 or 5W + 56 = 0

W = 12 or 5W = -56

W= 12 or W = - 56/5

The Width cannot be negative , so

W = 12

LW = 672

12L = 672

L = 672/12 = 56

Answer:

0.9953, 3.3629<x<4.0371

Step-by-step explanation:

Given that slader the internal revenue service claims it takes an average of 3.7 hours to complete a 1040 tax form, assuming th4e time to complete the form is normally distributed witha standard devait of the 30 minutes:

If X represents the time to complete then

X is N(3.7, 0.5) (we convert into uniform units in hours)

a) percent of people would you expect to complete the form in less than 5 hours

=[tex]100*P(x<5)\\= 0.9953[/tex]

b) P(b<x<c) = 0.50

we find that here

c = 4.0371 and

b = 3.3629

Interval would be

[tex](3.3629, 4.0371)[/tex]

Answer:

C

Step-by-step explanation:

(2x + 3)^5 = C(5,0)2x^5*3^0 +

C(5,1)2x^4*3^1 + C(5,2)2x^3*3^2 + C(5,3)2x^2*3^3 + C(5,4)2x^1*3^4 + C(5,5)2x^0*3^5

Recall that

C(n,r) = n! / (n-r)! r!

C(5,0) = 1

C(5,1) = 5

C(5,2) = 10

C(5,3) = 10

C(5,4) = 5

C(5,5) = 1

= 1(2x^5)1 + 5(2x^4)3 + 10(2x^3)3^2 + 10(2x^2)3^3 + 5(2x^1)3^4 + 1(2x^0)3^5

= 2x^5 + 15(2x^4) + 90(2x^3) + 270(2x^2) + 405(2x) +243

= 32x^5 + 15(16x^4) + 90(8x^3) + 270(4x^2) + 810x + 243

= 32x^5 + 240x^4 + 720x^3 + 1080x^2 + 810x + 243

Answer:

the answer is C

Step-by-step explanation:

Answer:

Step-by-step explanation:

For given points (t1, y1), (t2, y2), I like to write the exponential function as ...

  y(t) = y1·(y2/y1)^((t-t1)/(t2-t1))

This can be converted to other forms (such as a·b^t or a·e^(kt)) fairly easily, but those tend not to reproduce the given numbers exactly as this form does.

Using (15, 300) and (35, 1900) as our data values, the exponential function can be written as ...

  y(t) = 300·(19/3)^((t-15)/20)

__

a) The initial size of the culture is the value of y(0).

 y(0) = 300·(19/3)^(-15/20) ≈ 75.144

  y(0) ≈ 75 . . . initial population

__

b) The doubling period will be the value of t that satisfies ...

  (19/3)^(t/20) = 2

Taking logarithms, we have ...

  (t/20)·log(19/3) = log(2)

  t = 20·log(2)/log(19/3) ≈ 7.5104 . . . . minutes

The doubling time is about 7.51 minutes.

__

c) Evaluating the formula for t=115, we have ...

  y(115) = 300·(19/3)^(100/20) ≈ 3056912.346

The count after 115 minutes will be about 3,056,900.

__

d) Solving y(t) = 11,000, we have ...

  11000 = 300·(19/3)^((t-15)/20)

  11000/300 = (19/3)^((t-15)/20)

  log(110/3) = (t-15)/20·log(19/3)

  t = 20·log(110/3)/log(19/3) + 15 ≈ 54.027

It will take about 54.03 minutes for the count to reach 11,000.

_____

I find a graphing calculator to be a nice tool for solving problems like this.

Answer:

The answer to your question is 43

Step-by-step explanation:

                  2x³  + 8x² - 5x + 5 / x - 2

Process

1.- Use synthetic division

                      2   8    -5    5     2

                           4    24  38                          

                      2  12    19   43

Quotient    2x² + 12x + 19

Remainder     43

Answer:

Volume of wax for 210 candles=18463.2 cubic inches

Step-by-step explanation:

Each wax candle has a cylindrical shape with

Number of candles to be made=210

Volume of one wax candle =π × [tex]r^{2}[/tex] × h

                                             =π ×[tex]2^{2}[/tex] × 7

                                             =3.14×4×7

                                             =87.92 cubic inches

Volume of 210 wax candles=210×87.92

                                              =18,463.2 cubic inches

Answer:

18,471.6

Step-by-step explanation:

Answer:

The number of pitchers produced by each container = 16 .

Step-by-step explanation:

Given,

⇒∴ The number of cups of mix in brand A = [tex]x+4[/tex];

Number of pitchers produced by the containers :

Since both are equal:

⇒[tex]2x+8 = 4x\\8=2x\\x=4[/tex]

Thus the number of cups of mix in Brand B = [tex]x=4[/tex];

The number of pitchers produced by each container :

= [tex]\frac{4}{\frac{1}{4} } \\= 4*4\\=16[/tex]

∴The number of pitchers produced by each container = 16.

Each container can make 16 pitchers.

In mathematics, a fraction is used to denote a portion or component of the whole. It stands for the proportionate pieces of the whole.

As per the given data:

For making a pitcher of brand, A 1/2 cup of a mix is required.

For making a pitcher of brand, B 1/4 cup of a mix is required.

For brand A, 4 more cups than brand B .

Let's assume the number of cups for brand B as x

∴ Number of cups for brand A = x + 4

Total number of pitchers = Total number of cups / cups for one pitcher

For brand A number of pitchers:

= [tex]\frac{x + 4}{\frac12}[/tex] = 2(x + 4)

For brand B number of pitchers:

= [tex]\frac{x}{\frac14}[/tex] = 4x

The number of pitchers will be same for both brand A and B

∴ 2(x + 4) = 4x

= 2x + 8 = 4x

x = 4

The number of pitchers = [tex]\frac{4}{\frac14}[/tex] = 16

Hence, each container can make 16 pitchers.

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Final answer:

To find the probability that the first to arrive waits no longer than 5 minutes and the probability that the man arrives first, follow the provided detailed steps.

Explanation:

To find the probability that the first to arrive waits no longer than 5 minutes:

Man arrives first: 1/6

Woman arrives first: 1/4

Man and Woman arrive simultaneously within 5 minutes: 1/12

The probability that the man arrives first: 1/6

Answer:

Step-by-step explanation:

The right triangle has three sides which can be called legs. The legs are; shorter leg. Longer leg and hypotenuse

Let the longer leg be x

One leg of a right triangle is 4 mm shorter than the longer leg. This means

The shorter leg = x - 4

the hypotenuse is 4 mm longer than the longer leg. This means

The hypotenuse = x + 4

So the legs of the triangle are

Shorter leg or side = x-4

Longer leg or side = x

Hypotenuse = x + 4

The lengths of the sides of the triangle are 12 mm, 16 mm, and 20 mm.

Let's use variables to represent the lengths of the sides:

According to the Pythagorean theorem, in a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse:

a² + b² = c²

Plugging in the values, we have:

x² + (x + 4)² = (x + 8)²

Expanding and simplifying, we get:

x² + x² + 8x + 16 = x² + 16x + 64

Combining like terms, we get:

x² - 8x - 48 = 0

Factoring the quadratic equation, we find:

(x - 12)(x + 4) = 0

Therefore, x = 12 or x = -4. We discard the negative value, so the lengths of the sides of the triangle are: