march madness movies served 23 lemonades out of a total of 111 fountain drinks. based on this data, what is a reasonable estimate of the probability that the next fountain drink ordered is a lemonade?

Use Hooke's law... (just kidding)

Break down each force vector into horizontal and vertical components.

[tex]\vec F_1=(1000\,\mathrm N)(\cos30^\circ\,\vec x+\sin30^\circ\,\vec y)\approx(866.025\,\mathrm N)\,\vec x+(500\,\mathrm N)\,\vec y[/tex]

[tex]\vec F_2=(1500\,\mathrm N)(\cos160^\circ\,\vec x+\sin160^\circ\,\vec y)\approx(-1409.54\,\mathrm N)\,\vec x+(513.03\,\mathrm N)\,\vec y[/tex]

[tex]\vec F_3=(750\,\mathrm N)(\cos195^\circ\,\vec x+\sin195^\circ\,\vec y)\approx(-724.444\,\mathrm N)\,\vec x+(-194.114\,\mathrm N)\,\vec y[/tex]

The resultant force is the sum of these vectors,

[tex]\vec F=\displaystyle\sum_{i=1}^3\vec F_i\approx(-1267.96\,\mathrm N)\,\vec x+(818.916\,\mathrm N)\,\vec y[/tex]

and has magnitude

[tex]|\vec F|\approx\sqrt{(-1267.96\,\mathrm N)^2+(818.916\,\mathrm N)^2}\approx1509.42\,\mathrm N[/tex]

The closest answer is D.

To determine the magnitude of the resultant force acting on a hook when three forces are applied, you can use vector addition. If you have the information of the forces and the angles between them, you can calculate the resultant force using trigonometric functions.

To determine the magnitude of the resultant force when three forces act on a hook, you must realize that forces are vector quantities. This means that they have both a magnitude (how much force is being applied) and a direction (the direction the force is being applied in).

If the forces are concurrent (i.e., they act at the same point), one usually uses the parallelogram law or the triangle rule to find the resultant force. You can add two forces to create a resultant, then add the third force to that resultant to find the total resultant. If the forces and the angles between them are known, you can use trigonometric functions to calculate the resultant force.

For instance, if the three forces are F1, F2, and F3, and the angles between them are θ1, θ2, and θ3, the resultant force R can be found using the following equation:

R = √[ (F1 + F2cosθ2 + F3cosθ3)^2 + (F2sinθ2 + F3sinθ3)^2 ]

This equation will give the magnitude of the resultant force. Please note that to use this equation, you must have enough information about the forces and the angles between them.

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Answer:

(3; - 4)

Step-by-step explanation:

Blue: y = -x - 1

Red: y = -2x + 2

The given system of linear equations have solution as  x = 3 and y = -4.

To represent a straight line on a graph consider two points namely x and y intercepts of the line. To find x-intercept put y = 0 and for y-intercept put x = 0. Then draw a line passing through these two points.

The system of equations are given as,

y =−2x + 2          (1)

y = −x − 1            (2)

The above equations are linear equation in two variables.

Their graph are straight lines which  shows their intersection at point (3, -4).

Hence, the solution of the given system of linear equations is x = 3 and y = -4.

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Given:

Given that two similar cylinder have surface areas 24π cm² and 54π cm².

The volume of the smaller cylinder is 16π cm³

We need to determine the volume of the larger cylinder.

Volume of the larger cylinder:

The ratio of the two similar cylinders having surface area of 24π cm² and 54π cm², we have;

[tex]\frac{24 \pi}{54 \ pi}=\frac{4}{9}[/tex]

       [tex]=\frac{2^2}{3^2}[/tex]

Thus, the ratio of the surface area of the two cylinders is [tex]\frac{2^2}{3^2}[/tex]

The volume of the larger cylinder is given by

[tex]\frac{2^2}{3^2}\times \frac{2}{3}=\frac{16 \pi }{x}[/tex]

where x represents the volume of the larger cylinder.

Simplifying, we get;

[tex]\frac{2^3}{3^3}=\frac{16 \pi }{x}[/tex]

[tex]\frac{8}{27}=\frac{16 \pi }{x}[/tex]

Cross multiplying, we get;

[tex]8x=16 \pi \times 27[/tex]

[tex]8x=432 \pi[/tex]

 [tex]x=54 \pi \ cm^3[/tex]

Thus, the volume of the larger cylinder is 54π cm³

Answer:

54π cm³

Step-by-step explanation:

Given:

Given that the table with values of x and y.

We need to determine the relationship between x and y.

Slope:

The slope of the relation can be determined using the formula,

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Substituting the points (2,11) and (4,9), we get;

[tex]m=\frac{9-11}{4-2}[/tex]

[tex]m=\frac{-2}{2}[/tex]

[tex]m=-1[/tex]

Thus, the slope of the relation is m = -1.

y - intercept:

The y - intercept of the relation is the value of y when x = 0.

Hence, from the table, it is obvious that when x = 0, the value of y is 13.

Thus, the y - intercept of the relation is b = 13.

Relationship between x and y:

The relationship between x and y can be determined using the formula,

[tex]y=mx+b[/tex]

Substituting m = -1 and y =13, we get;

[tex]y=-x+13[/tex]

Thus, the relationship between x and y is [tex]y=-x+13[/tex]

Answer:

[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]  

[tex]p_v =2*P(z>0.264)=0.792[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] 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 students said that blue is their favorite color is not different from 0.24

Step-by-step explanation:

Data given and notation

n=75 represent the random sample taken

X=19 represent the students said that blue is their favorite color

[tex]\hat p=\frac{19}{75}=0.253[/tex] estimated proportion of  students said that blue is their favorite color

[tex]p_o=0.24[/tex] is the value that we want to test

[tex]\alpha=0.05[/tex] represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

[tex]p_v[/tex] 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 proportion is different from 0.24.:  

Null hypothesis:[tex]p=0.24[/tex]  

Alternative hypothesis:[tex]p \neq 0.24[/tex]  

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

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

The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].

Calculate the statistic  

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

[tex]z=\frac{0.253 -0.24}{\sqrt{\frac{0.24(1-0.24)}{75}}}=0.264[/tex]  

Statistical decision  

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 provided [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.  

Since is a bilateral test the p value would be:  

[tex]p_v =2*P(z>0.264)=0.792[/tex]  

So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] 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 students said that blue is their favorite color is not different from 0.24

Answer:

0.792

Step-by-step explanation:

Answer:

The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

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

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

For this problem, we have that:

[tex]n = 51, \pi = \frac{19}{51} = 0.373[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 - 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.24[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.373 + 1.96\sqrt{\frac{0.373*0.627}{51}} = 0.506[/tex]

The 95% confidence interval for the proportion of young adults with pierced tongues who have receding gums is (0.24, 0.506).

The probability of first selecting a chocolate chip cookie and then selecting a sugar cookie from a box containing 24 cookies in total is 6/46 or approximately 0.1304.

The question refers to calculating the probability of selecting cookies of different flavors one after the other without replacement from a box. To begin with, we must find the probability of selecting a chocolate chip cookie followed by the probability of selecting a sugar cookie after one chocolate chip cookie has been removed.

Firstly, the total count of cookies is 12 chocolate chip + 6 peanut butter + 6 sugar cookies = 24 cookies. The probability (P) of selecting a chocolate chip cookie first is P(chocolate chip) = 12/24 = 1/2. After eating the chocolate chip cookie, there are 23 cookies left and the probability of then selecting a sugar cookie is P(sugar) = 6/23 since there are 6 sugar cookies left out of the remaining 23 cookies.

Since these events are sequential without replacement, we can find the combined probability of both events by multiplying the probabilities of each event. Thus, the combined probability is P(chocolate chip then sugar) = P(chocolate chip) *P(sugar) = (1/2) * (6/23) = 6/46.

The combined probability of first selecting a chocolate chip cookie and then selecting a sugar cookie is therefore 6/46 or about 0.1304.

the answer is 89

Step-by-step explanation:

it does not matter if the number is negative the absolute value is the number inside the lines

Answer:

The absolute value of this one is 89. Because for example: |-3|=3 because any number is in that sign || the number will turn to positive. For example, If it is |-3| it will turn to 3

Answer:

i think it's -0.0608

Step-by-step explanation:

Answer:

[tex]3,125[/tex]

Step-by-step explanation:

If you want to fill a pool, you will use the formula for finding the volume:

[tex]v=l*w*h[/tex]

In this case, height being depth:

[tex]v=l*w*d[/tex]

Insert values

[tex]v=50*25*2.5[/tex]

Simplify

[tex]v=1,250*2.5\\v=3,125[/tex]

You would need a lot of water.

Answer:

3125000 liter

Step-by-step explanation:

hope i helped

if i can be brainliest that would be great

Answer:

2/5

Step-by-step explanation:

The total number of candies are 2+1+2 = 5 candies

P (peppermint) = number of peppermints/total

                        =2/5

Answer:

2/5

Step-by-step explanation:

The probability is 2/5.There are five in all and two peppermint.Put it as a fraction and you get 2/5.

Given:

The given parent function is [tex]f(x)=x^2[/tex]

We need to determine the equation of the new translated (shifted) function g(x).

Vertical stretch:

The general rule to shift the graph f(x), to shift c units upward is [tex]g(x)=f(x)+c[/tex]

From the graph, it is obvious that the graph f(x) is shifted 1 unit upwards.

Thus, applying the above rule, we get;

[tex]g(x)=x^2+1[/tex]

Horizontal stretch:

The general rule to shift the graph f(x) to shift c units to the left is [tex]g(x)=f(x+c)[/tex]

From, the graph, it is obvious that the graph f(x) is shifted 2 units to the left.

Thus, applying the above rule, we have;

[tex]g(x)=(x+2)^2[/tex]

Equation of the new function g(x):

From the figure, it is obvious that the graph g(x) is shifted 1 unit upwards and 2 units to the left.

Thus, we have;

[tex]g(x)=(x+2)^2+1[/tex]

Therefore, the equation of the new function g(x) is [tex]g(x)=(x+2)^2+1[/tex]

The day when they would meet first time after joining the gym together will be 12.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

Kirk goes to the gym every 3 days.

Deshawn goes to the gym every 4 days.

If they join the gym on the same day.

Then the day when they would meet first time after joining the gym together will be

LCM of 4, 3 will be 12.

Then the day will be 12.

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Final answer:

Kirk and Deshawn will be at the gym together on the 12th day since they joined.

Explanation:

Gym memberships for Kirk and Deshawn occur every 3 days and 4 days respectively. To find the first day they'll be at the gym together, we need to find the lowest common multiple of 3 and 4.

LCM(3, 4) = 12. Therefore, Kirk and Deshawn will be at the gym together on the 12th day since they joined the gym.

Answer:

Approximately 20,579 units.

Answer:

a) 30.50% probability that  at least 150 stay on the line for more than one minute.

b) 0% probability that more than 200 stay on the line for more than one minute.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

[tex]E(X) = np[/tex]

The standard deviation of the binomial distribution is:

[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]

Normal probability distribution

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].

In this problem, we have that:

[tex]n = 800, p = 0.18[/tex]

So

[tex]\mu = E(X) = np = 800*0.18 = 144[/tex]

[tex]\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{800*0.18*0.82} = 10.87[/tex]

a. at least 150 stay on the line for more than one minute.

Using continuity correction, [tex]P(X \geq 150 - 0.5) = P(X \geq 149.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 149.5. So

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

[tex]Z = \frac{149.4 - 144}{10.87}[/tex]

[tex]Z = 0.51[/tex]

[tex]Z = 0.51[/tex] has a pvalue of 0.6950

1 - 0.6950 = 0.3050

30.50% probability that  at least 150 stay on the line for more than one minute.

b. more than 200 stay on the line.

Using continuity correction, [tex]P(X \geq 200 + 0.5) = P(X \geq 200.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 200.5. So

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

[tex]Z = \frac{200.5 - 144}{10.87}[/tex]

[tex]Z = 5.2[/tex]

[tex]Z = 5.2[/tex] has a pvalue of 1

1 - 1 = 0

0% probability that more than 200 stay on the line for more than one minute.

It's a parallelogram, opposite sides congruent.

6x - 7 = 2x + 9

4x = 16

x = 4

12 = y + 3

9 = y

Answer: x=4, y=9

Answer:

x = 4 and y = 9

Step-by-step explanation:

This is a parallelogram, which we can tell because of the arrows. Basically, opposite sides are parallel. By definition, then, opposite sides of this polygon are equal: LM = ON and LO = MN. That means we can set the various expressions equal to each other:

LM = ON  ⇒  6x - 7 = 2x + 9  ⇒  4x = 16  ⇒  x = 4

LO = MN  ⇒  12 = y + 3  ⇒  y = 9

Thus, x = 4 and y = 9.

Hope this helps!

Answer:

a. length  = 0.7211 ft

b. width  = 0.7211 ft

c. height = 140.3846 ft

Step-by-step explanation:

This is an optimiztion with restriction problem.

We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.

As the cost for the sides is constant, we know that length and width are equal.

Then, we can express the volume as:

[tex]V=x\cdot y\cdot z=x^2z=73[/tex]

being x: length and z: height

We can express the height in function of the length as:

[tex]x^2z=73\\\\z=73x^{-2}[/tex]

Then, the cost of the box can be expressed as:

[tex]C=0.62(x^2)+4*0.15(xz)+0.18(x^2)=(0.62+0.18)x^2+0.60xz\\\\C=0.8x^2+0.60x*x^{-2}=0.8x^2+0.6x^{-1}[/tex]

To optimize C, we derive and equal to zero

[tex]\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211[/tex]

The height z is then

[tex]z=73x^{-2}=\dfrac{73}{0.7211^2}=\dfrac{73}{0.52}=140.3846[/tex]

Answer:

It is shown in the explanation

Step-by-step explanation:

p(s) = s² + bs + c

a = 1

b = b

c = c

We get Δ as follows

Δ = (b²-4*a*c) = b² - 4*1*c = b² - 4c > 0  ⇒   b² > 4c  ⇔ c > 0

s = (-b + √(b² - 4c))/2(1)

⇒   s₁ = (-b + √(b² - 4c))/2

s₂ = (-b - √(b² - 4c))/2(1)

⇒   s₂ = (-b - √(b² - 4c))/2

We have that -b < 0  ⇔ b > 0

then s₁ < 0 and s₂ < 0 ⇔ c > 0 and b > 0

Answer:

For roots to lie on the left half plane, b ⊃ 0 and c ⊃0

Step-by-step explanation:

From quadratic formula, we have;

x = -b±√(b²-4ac)/2a

From the given expression p(s) = s² + bs + c,

x = s

a = 1

b = b

c = c

The quadratic formula can then be written as;

s =  -b±√(b²-4*1*c)/2*1

   =  -b±√(b²-4c)/2

s₁ =  -b+√(b²-4c)/2

s₂ =  -b±√(b²-4c)/2

From the equation above,

Sum of root = -b

Product of root = c

If both the root lie on left side of the s-plane, then sum of roots will be negative. Hence, -b ∠0. That is, b ⊃0

Also, the product root will be positive, c ⊃ 0

Hence, for roots to lie on the left half plane, b ⊃ 0 and c ⊃0

Answer:

x = 4

Step-by-step explanation:

14x - 15 + 139 = 180

(Alternate & Supplementary angles)

14x = 56

x = 4

The Answer is : ABC = 40

Answer:

Step-by-step explanation:

if you have 1/4 of a rope and you need to give 7/16 to your friend how much rope did you give to your friend?

Final answer:

Divide 1/4 by the reciprocal of 7/16 to get 4/7. A real-world example is when needing ¼ cup of sugar with only a 7/16 cup measure, fill it approximately 4/7 full to obtain the needed amount of sugar.

Explanation:

To calculate 1/4 divided by 7/16, you would multiply 1/4 by the reciprocal of 7/16, which is 16/7. This would give you (1/4) * (16/7) = 16/28, which can be simplified to 4/7 after dividing both numerator and denominator by 4. A real-world situation involving this expression could be as follows: Imagine you have a recipe that requires 1/4 of a cup of sugar, but you only have a measuring cup that measures 7/16 of a cup.

To find out how many times you need to fill the 7/16 cup to get the 1/4 cup needed, you would calculate 1/4 divided by 7/16, which will give you 4/7. So, you would fill the 7/16 measuring cup approximately 4/7 of the way full to have 1/4 cup of sugar for your recipe.

Answer:

  no solution

Step-by-step explanation:

First inequality:

  12x < -18 . . . . subtract 7

  x < -18/12 . . . divide by 12

  x < -1.5 . . . . . . write as decimal

__

Second inequality:

  5x -8 ≥ 40

  5x ≥ 48 . . . . . . add 8

  x ≥ 9.6 . . . . . . . divide by 5

__

There are no solutions to this pair of inequalities. No value of x can be both less than -1.5 and greater than 9.6.

Answer:

it is 61.3

Step-by-step explanation:

Answer:

8b+7p=20

p=2b

Step-by-step explanation:

You're welcome. Thou shall complete thou work without any trouble.

Answer:

The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.

The  sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.

Step-by-step explanation:

The Central Limit Theorem estabilishes 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 [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

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

In this problem

The sample size is smaller than 30, so we need to assume that the underlying population is normally distributed.

If it is:

[tex]\mu = 63, \sigma = 18, n = 10, s = \frac{18}{\sqrt{10}} = 5.69[/tex]

The  sampling distribution of x overbar will be approximately normally distributed with mean 63 and standard deviation 5.69.

Answer:

The player should be required to pay $5 to make this a fair game.

Step-by-step explanation:

U ~ Uniform(0, 10)

E[U] = (0 + 10)/2

         = 5

X | U ~ Poisson(U)

E[X | U] = U

By law of total probability for expectations,

E[X] = E[E[X|U]] = E[U] = $5

Therefore the player should be required to pay $5 to make this a fair game.

Answer:

240°

Step-by-step explanation:

[tex] \frac{4\pi^{c} }{3} = \frac{4 \times 180 \degree}{3} = 4 \times 60 \degree = 240 \degree \\ [/tex]