At the beginning of an experiment, a scientist has 300 grams of radioactive goo. After 150 minutes, her sample has decayed to 37.5 grams.




What is the half-life of the goo in minutes?


________



Find a formula for


G(t),


the amount of goo remaining at time T.


G= _________



How many grams of goo will remain after 32 minutes?

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

Here, we have,

From the provided 95% confidence interval, we can make the following conclusions:

The point estimate of the difference between the mean student loans for females and males is 516.74334 dollars.

The standard error of the difference between the means is 368.41116 dollars.

The degrees of freedom (DF) associated with the confidence interval is 907.34739.

The lower limit of the confidence interval is -206.29374 dollars.

The upper limit of the confidence interval is 1239.7804 dollars.

The confidence interval does not contain zero.

Since zero is not within the interval, we can conclude that the difference between the mean student loans for females and males is statistically significant at the 95% confidence level.

Based on the information given, these are the conclusions we can draw from the 95% confidence interval.

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The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Based on the 95% confidence interval provided for the difference in means between the loans of female and male StatCrunchU students, we can draw the following conclusions:

The sample difference in means is 516.74334.

The standard error of the difference is 368.41116.

The degrees of freedom (DF) for the analysis is 907.34739.

The lower limit of the confidence interval is -206.29374.

The upper limit of the confidence interval is 1239.7804.

Therefore, we can conclude the following:

The estimated difference in the mean student loans between females and males is 516.74334.

There is a 95% confidence that the true difference in means falls within the range of -206.29374 to 1239.7804.

Note: Since the confidence interval includes both positive and negative values, we cannot conclude with certainty whether there is a significant difference or not in the mean student loans between females and males. The confidence interval suggests that the difference could be positive, negative, or even zero.

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Answer:

E) 0.99

Step-by-step explanation:

100 recruits x 0.4 chance of retiring as police officer = 40 officers

probability of being married at time of retirement = (1 - 0.25) x 40 = 30 officers

each new recruit will result in either 0, 1 or 2 new pensions

mean = µ = E(Xi) = (0 x 0.6) + (1 x 0.1) + (2 x 0.3) = 0.7

σ²  = (0² x 0.6) + (1² x 0.1) + (2² x 0.3) - µ² = 0 + 0.1 + 1.2 - 0.49 = 0.81

in order for the total number of pensions (X) that the city has to provide:

the normal distribution of the pension funds = 100 new recruits x 0.7 = 70 pension funds

the standard deviation = σ = √100 x √σ² = √100 x √0.81 = 10 x 0.9 = 9

P(X ≤ 90) = P [(X - 70)/9] ≤ [(90 - 70)/9] =  P [(X - 70)/9] ≤ 2.22

z value for 2.22 = 0.9868 ≈ 0.99

Answer:

Step-by-step explanation:

REcall that given a set A, * is a equivalence relation over A if

- for a in A, then a*a.

- for a,b in A. If a*b, then b*a.

- for a,b,c in A. If a*b and b*c then a*c.

Consider A the set of all ordered pairs of positive integers.

- Let (a,b) in A. Then a+b = a+b. So, by definition (a,b)R(a,b).

- Let (a,b), (c,d) in A and suppose that (a,b)R(c,d) . Then, by definition a+d = b+c. Since the + is commutative over the integers, this implies that d+a = c+b. Then (c,d)R(a,b).

- Let (a,b),(c,d), (e,f) in A and suppose that (a,b)R(c,d) and (c,d)R(e,f). Then

a+d = b+c, c+f = d+e.  We have that f = d+e-c. So a+f = a+d+e-c. From the first equation we find that a+d-c = b. Then a+f = b+e. So, by definition (a,b)R(e,f).

So R is an equivalence relation.

[(a,b)] is the equivalence class of (a,b). This is by definition, finding all the elements of A that are equivalente to (a,b).

Let us find all the possible elements of A that are equivalent to (2,4). Let (a,b)R(2,4) Then a+4 = b+2. This implies that a+2 = b. So all the elements of the form (a,a+2) are part of this class.

Answer:

3. 72.9%

Step-by-step explanation:

Let's call M the event that the customer is male and C the event that the customer prefer chocolate chips Scones.

So, the probability P(M∪C) that a customer chosen at random will be a male or prefer the Chocolate Chip Scones is calculated as:

P(M∪C) = P(M) + P(C) - P(M∩C)

Then, there are 145 males (317 customer - 172 females = 145 males), so the probability that the customer is a males is:

P(M) = 145/317 = 0.4574

There are 167 customers that prefer chocolate chips Scones ( 317 customers - 150 customers that prefer the Cranberry Walnut Scones = 167), so the probability that a customer prefer chocolate chips Scones is:

P(C) = 167/317 = 0.5268

Finally, 81 customers were males and prefer the Chocolate Chip Scones, so the probability that a customer will be a male and prefer chocolate  chip scones is:

P(M∩C) = 81/317 = 0.2555

Therefore,  P(M∪C) is equal to:

P(M∪C) = 0.4574 + 0.5268 - 0.2555

P(M∪C) = 0.7287

P(M∪C) = 72.9%

Answer:

3. 72.9%

Step-by-step explanation:

A probability is the number of desired outcomes divided by the number of total outcomes.

Desired outcomes:

Male or prefers the Chocolate Chip Scones. That is, males and females who prefer the Chocolate Chip Scones.

There are 172 female customers and 317-172 = 145 male customers.

150 customers prefer the Cranberry Walnut Scones. So 317 - 150 = 167 customers prefer the Chocolate Chip Scones.

81 of those are male, so 167 - 81 = 86 are female.

So the total of desired outcomes is 86 + 145 = 231

Total outcomes:

317 total customers.

Probability:

231/317 = 0.729

So the correct answer is:

3. 72.9%

Answer:

The probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.

Step-by-step explanation:

The complete question is:

There are 103 students in a physics class. The instructor must choose two students at random.

Students in a Physics Class

Academic Year          Physics majors           Non-Physics majors

Freshmen                              17                                     15

Sophomores                         20                                    14

Juniors                                   11                                      17

Seniors                                   5                                       4

What is the probability that a senior Physics major and then a sophomore Physics major are chosen at random? Express your answer as a fraction or a decimal number rounded to four decimal places.

Solution:

There are a total of N = 103 students present in a Physics class.

Some of the students are Physics Major and some are not.

The instructor has to select two students at random.

The instructor first selects a senior Physics major and then a sophomore Physics major.

Compute the probability of selecting a senior Physics major student as follows:

[tex]P(\text{Senior Physics Major})=\frac{n(\text{Senior Physics Major}) }{N}[/tex]

                                        [tex]=\frac{5}{103}\\\\=0.04854369\\\\\approx 0.0485[/tex]

Now he two students are selected without replacement.

So, after selecting a senior Physics major student there are 102 students remaining in the class.

Compute the probability of selecting a sophomore Physics major student as follows:

[tex]P(\text{Sophomore Physics Major})=\frac{n(\text{Sophomore Physics Major}) }{N}[/tex]

                                        [tex]=\frac{20}{102}\\\\=0.1960784314\\\\\approx 0.1961[/tex]

Compute the probability that a senior Physics major and then a sophomore Physics major are chosen at random as follows:

[tex]P(\text{Senior}\cap \text{Sophomore})=P(\text{Senior})\times P(\text{Sophomore})[/tex]

                                     [tex]=0.0485\times 0.1961\\\\=0.00951085\\\\\approx 0.0095[/tex]

Thus, the probability that a senior Physics major and then a sophomore Physics major are chosen at random is 0.0095.

Answer:

X^6

Step-by-step explanation:

Answer:

y - x = 16

Step-by-step explanation:

Explanation:-

Step(i):-

Given data set A  is  9,5,y,2,x

Mean of the Data set A

                         =   [tex]\frac{9 + 5 + y + 2 +x}{5}[/tex]

                         = [tex]\frac{16 +x+y}{5}[/tex]

Given data set B is 8, x, 4, 1, 3

Mean of the Data set B

                         =   [tex]\frac{8+ x+4+1+3}{5}[/tex]

Step(ii):-                          

Mean of the Data set A  = 2 X Mean of the Data set B

              [tex]\frac{16 +x+y}{5} = 2 X \frac{16+x}{5}[/tex]

On simplification , we get

           16 +x + y = 2( 16 +x)

           16 + x + y = 32 + 2 x

            16 + x + y - 32 - 2 x = 0

            y - x -16 =0

           y - x = 16

Answer:

x = 75

Step-by-step explanation:

Assuming the angles are equal  ( bisected means divided in half)

2x-5 = 145

Add 5 to each side

2x-5+5 = 145+5

2x = 150

Divide by 2

2x/150/2

x = 75

Answer:

x=75

Step-by-step explanation:

∠BAD is bisected by AC and measurement of BAC is equal to 2x - 5 and measurement of CAD is equal to 145. Since they are bisected, they are equal and the solution is shown below:

m ∠ BAC = m ∠ CAD

2x - 5 = 145 , transpose -5 to the opposite side such as:

2x = 145 + 5 , perform addition of 145 and 5

2x = 150

2x / 2 = 150 / 2 , divide both sides by 2

x = 75

The answer is 75 for the x value.

Answer:  The correct answer is:  

_________________________  

The given "graph" in the bottom right, lowest corner

Step-by-step explanation:

_________________________

Note:  When there is only one (1) equation give for a graph;

          and/or:  only one (1)  "inequality given";  

         we  look for the symbol.

If the symbol is "not" an "equals" symbol (i.e. not an:  =  symbol) ;

 we check for the type of "inequality" symbol.

If there is a:  "less than" (<) ;  or a "greater than" (>) symbol;  the graph of the "inequality" will have "dashed lines" (since there will be a "boundary").

If there is an "inequality" that is a: "less than or equal to" (≤) ;

                                                 or a: "greater than or equal to" (≥) ;

       →   then there will be not be a dashed line when graphed;

          but rather—a "solid line" ;  since "less than or equal to" ;

          or "greater than or equal to" —is similar to:

          "up to AND including"; or: "lesser/fewer than AND including".).

 _________________________  

Note:  We are given the "inequality" :

            →   " y <  x²  + 4x  "  .

_________________________________

Note that we have a "less than" symbol (< ) ; so the graph will have a:

   "solid line" [and not a "dotted line".].

_________________________________

Note that all of the graphs among our 4 answer choices have "dotted lines".

Not that all values (all x and y coordinated) within the "shaded portion" of the corresponding graph are considered part of the graph.  

As such, given any point within the shaded part,  the x and y coordinates must match the inequality (i.e. the given inequality must be true when one puts in the "x-coordinate" and "y-coordinate" into the "given inequality" :

→   " y <  x²  + 4x "  .

_________________________

Likewise, we can take any point within the "white, unshaded" portion of any of the graph, and take the "x-coordinate" and "y-coordinate" of that point, and the inequality: →   " y <  x²  + 4x  "  ;  will not hold true when the "x-coordinate" and "y-coordinate" values of that point— are substituted into the "inequality".  

_________________________

{Note:  Answer is continued on images attached.}.

Wishing you the best!

Answer:

plot a point at 6 up from (0,0) and then go down one and over three places then plot another point- and so on - and so on

Step-by-step explanation:

To graph the line using the slope and intercept, first understand what the slope and intercept mean:

Slope is how steep or flat the line appears on the graph.

The y-intercept is the point at which the line hits the y-axis. In this equation, the line hits the y-axis at positive 6, which means that the point is (0, 6).

You can use a method called "rise over run" to graph. The slope is negative one over three, so the line will "rise" negative one units after "running" three units.

So, for every one unit down, the line will travel three units to the right.

Graph this from the point (0, 6), your y-intercept, and plot the points according to the slope:

The correct question is:

A study of consumer smoking habits includes 167 people in the 18-22 age bracket (59 of whom smoke), 148 people in the 23-30 age bracket (31 of whom smoke), and 85 people in the 31-40 age bracket (23 of whom smoke). If one person is randomly selected from this sample, find the probability of getting someone who is age 23-30 or smokes

Answer:

The probability of getting someone who is age 23-30 or smokes = 0.575

Step-by-step explanation:

We are given;

Number consumers of age 18 - 22 = 167

Number of consumers of ages 22 - 30 = 148

Number of consumers of ages 31 - 40 = 85

Thus,total number of consumers in the survey = 167 + 148 + 85 = 400

We are also given;

Number consumers of age 18 - 22 who smoke = 59

Number of consumers of ages 22 - 30 who smoke = 31

Number of consumers of ages 31 - 40 who smoke = 23

Total number of people who smoke = 59 + 31 + 23 = 113

Let event A = someone of age 23-30 and event B = someone who smokes. Thus;

P(A) = 148/400

P(B) = 113/400

P(A & B) = 31/400

Now, from addition rule in sets which is given by;

P(A or B) = P (A) + P (B) – P (A and B)

We can now solve the question.

Thus;

P(A or B) = (148/400) + (113/400) - (31/400)

P(A or B) = 230/400 = 0.575

Answer:

676

Step-by-step explanation:

lxw

14x35

4x24

6x15

676

Answer:

[tex]Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]

[tex]Area\ of\ the\ garden\ =l1*b1[/tex]

Step-by-step explanation:

Let assume the l1 is the length of the garden and b1 is the breadth of garden then

[tex]Perimeter\ of\ the\ Garden\ = 2 ( L ength + Breadth )\\Perimeter\ of\ the\ Garden\ =2(l1*b1)[/tex]

Now,

[tex]Area\ of\ Garden\ = Length * Breadth[/tex]

[tex]Area\ of\ the\ garden\ =l1*b1[/tex]

Answer:

  10.5 ft high

  5.3 ft horizontally

Step-by-step explanation:

The equation can be written in vertex form to answer these questions.

  f(x) = -0.2(x² -10.5x) +5

  f(x) = -0.2(x² -10.5x +5.25²) +5 +0.2(5.25²)

  f(x) = -0.2(x -5.25)² +10.5125

The vertex of the travel path is (5.25, 10.5125).

The maximum height is 10.5 feet, which occurs 5.3 feet (horizontally) from the point of release.

Answer:

Step-by-step explanation:

=20

This take 30 minutes to finish filling the remaining jugs.

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.

Now,

Let the time to finish filling the remaining jugs = x

Since, A person needs to fill 20 water jugs with a hose. Filling the first 2 jugs has taken 3 minutes.

Hence, By definition of proportion we get;

⇒ 20 / x = 2 / 3

⇒ 20 × 3 / 2 = x

⇒ x = 30

Thus, The time to finish filling the remaining jugs =  30 minutes

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Answer:

a) We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

b) We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

c) [tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]  

d) Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Step-by-step explanation:

Information provided

[tex]\bar X=23400[/tex] represent the sample mean

[tex]s=1412[/tex] represent the sample standard deviation

[tex]n=18[/tex] sample size  

[tex]\mu_o =22100[/tex] represent the value to verify

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

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value

Part a

We want to conduct a hypothesis in order to see if the true mean is 22100 or not, the system of hypothesis would be:  

Null hypothesis:[tex]\mu = 22100[/tex]  

Alternative hypothesis:[tex]\mu \neq 22100[/tex]  

Part b

We need to find the degrees of freedom given by:

[tex] df =n-1 = 18-1=17[/tex]

And the critical values for this case are:

[tex] t_{\alpha/2}= 2.110[/tex]

Part c

The statistic is given by:

[tex]t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}[/tex]  (1)  

Replacing the info we got:

[tex]t=\frac{23400-22100}{\frac{1412}{\sqrt{18}}}=3.906[/tex]    

Part d

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true mean is significantly different from 221100 mi

Answer:

[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl

Step-by-step explanation:

For each bead that you draw, there are only two possible outcomes. Either it is a pearl bead, or it is not. The sum of these probabilities = 100% = 1.

So

2/3 probability of drawing a pearl bead.

p probability of drawing a non pearl bead.

What is the probability of drawing a bead which is not a pearl?

[tex]p + \frac{2}{3} = 1[/tex]

[tex]p = 1 - \frac{2}{3}[/tex]

[tex]p = \frac{3*1 - 2}{3}[/tex]

[tex]p = \frac{1}{3}[/tex]

[tex]\frac{1}{3}[/tex] probability of drawing a bead which is not a pearl

Answer:

c) 5√2 cm

Step-by-step explanation:

A square with side length l has a perimeter given by the following equation:

P = 4l.

In this question:

P = 20

So the side length is:

4l = 20

l = 20/4

l = 5

Diagonal

The diagonal forms a right triangle with two sides, in which the diagonal is the hypothenuse. Applying the pytagoras theorem.

[tex]d^{2} = l^{2} + l^{2}[/tex]

[tex]d^{2} = 5^{2} + 5^{2}[/tex]

[tex]d^{2} = 50[/tex]

[tex]d = \pm \sqrt{50}[/tex]

Lenght is a positive meausre, so

[tex]d = \sqrt{50}[/tex]

[tex]d = \sqrt{2 \times 25}[/tex]

[tex]d = \sqrt{2} \times \sqrt{25}[/tex]

[tex]d = 5\sqrt{2}[/tex]

So the correct answer is:

c) 5√2 cm

Answer:

9.8

Step-by-step explanation:

updated

9^2=x^2+4^2

9*9=x*x+4*4

81=x*x-16

+16. +16

97=x*x

√97=√x*x

√97=x

So the answer is √97, but the question wants it rounded so it's actually 9.8

Answer:

Quantitative variable

Step-by-step explanation:

The objective in this study is to find the of variable used to conduct the study. The type of variable used to conduct this study is Qualitative variable.

There are majorly two types of variable. These are:

Categorical variables are types of variables that are grouped based on some similar characteristics. The nominal scale and the ordinal scale falls under this group of variable.

The nominal scale is an act of giving name to a particular object or concept in order to identify or classify that particular thing.

On the other hand, The ordinal scale possess all the characteristics of nominal scale but here the variables can be ordered. It can be used to determine whether the item is greater or less. It express the indication of order and magnitude.

In Qualitative variables; variables are measured on a numeric scale. From the given question , This type of variable is used to measure the high levels of vitamin C (measured in mg) which were associated with a 30 percent lower risk of allergies in the infants.

The levels of vitamin C could range from 0 mg to certain mg therefore we can measure vitamin C in numerical values of measurement (Quantitative variable).

Answer:

630 milliliters.

Step-by-step explanation:

The statement tells us that the final product is 14 jars of honey peanut butter and that in each jar use 45 mliliters of honey. This means that to know the total honey to be used, the required quantity for each jar must be multiplied by the total number of jars, that is:

14 * 45 = 630

Which means that he would spend a total of 630 milliliters.

Step-by-step explanation:

Ares uses 630 ml of honey, because 14×45=630

Answer:

  [tex]F^{-1}(x)=\dfrac{x-7}{4}[/tex]

Step-by-step explanation:

To find the inverse function, solve for y the relation ...

  F(y) = x

  4y +7 = x

  4y = x - 7

  y = (x -7)/4 . . . . the inverse function

  [tex]\boxed{F^{-1}(x)=\dfrac{x-7}{4}}[/tex]

Answer:

The probability that the next mattress sold is either king or queen-size is P=0.8.

Step-by-step explanation:

We have 3 types of matress: queen size (Q), king size (K) and twin size (T).

We will treat the probability as the proportion (or relative frequency) of sales of each type of matress.

We know that the number of queen-size mattresses sold is one-fourth the number of king and twin-size mattresses combined. This can be expressed as:

[tex]P_Q=\dfrac{P_K+P_T}{4}\\\\\\4P_Q-P_K-P_T=0[/tex]

We also know that three times as many king-size mattresses are sold as twin-size mattresses. We can express that as:

[tex]P_K=3P_T\\\\P_K-3P_T=0[/tex]

Finally, we know that the sum of probablities has to be 1, or 100%.

[tex]P_Q+P_K+P_T=1[/tex]

We can solve this by sustitution:

[tex]P_K=3P_T\\\\4P_Q=P_K+P_T=3P_T+P_T=4P_T\\\\P_Q=P_T\\\\\\P_Q+P_K+P_T=1\\\\P_T+3P_T+P_T=1\\\\5P_T=1\\\\P_T=0.2\\\\\\P_Q=P_T=0.2\\\\P_K=3P_T=3\cdot0.2=0.6[/tex]

Now we know the probabilities of each of the matress types.

The probability that the next matress sold is either king or queen-size is:

[tex]P_K+P_Q=0.6+0.2=0.8[/tex]

Answer:

-13c-6

Step-by-step explanation:

-3(6c + 2) + 5c

Distribute

-18c -6 +5c

Combine like terms

-13c-6

Answer:

-13c -6

Step-by-step explanation:

-3 (6c) -3x2+5c

multiply 6 by -3

-18c-3x2+5c

multiply -3 by 2

-18c -6+ 5c

add 18c and 5c

-13c -6

Answer:

15.86%

Step-by-step explanation:

When the distribution is normal, we use 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.

Percent of area between the mean and 0.20 standard deviations from the mean:

pvalue of Z = 0.2 subtracted by the pvalue of Z = -0.2

Z = 0.2 has a pvalue of 0.5793

Z = -0.2 has a pvalue of 0.4207

0.5793 - 0.4207 = 0.1586

So this percentage is 15.86%

Answer:

A and B

Step-by-step explanation:

1) Distance to the focus

From (x,y) to the focus(2,-4) {using distance formula}

=√(x-2)²+(y+4)²

2) Distance to the directrix

Is, y+p where P here is (-6)

So

d2 = y+p

= y+(-6)

= y-6

Answer:

A) 15

B) 0.9

Step-by-step explanation:

Use the correct order of operations.

A) 40 − 5 ÷ 1/5 =

= 40 − 5 * 5

= 40 - 25

= 15

B) (4.8 − 1.8 ÷ 6) ÷ 5 =

= (4.8 − 0.3) ÷ 5

= 4.5 ÷ 5

= 0.9

Answer:

Step-by-step explanation:

Let us assume that x is normally distributed. The sample size is greater than 30. Since the the population mean and population standard deviation are known, we would apply the formula,

z = (x - µ)/(σ/√n)

Where

x = sample mean

µ = population mean

σ = standard deviation

n = number of samples

From the information given,

µ = 50

σ = 7

n = 36

If x is within 0.5 of the population mean, it means that x is between (50 - 0.5) and (50 + 0.5)

the probability is expressed as

P(49.5 ≤ x ≤ 50.5)

For x = 49.5

z = (49.5 - 50)/(7/√36) = - 0.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.334

For x = 49.5

z = (50.5 - 50)/(7/√36) = 0.43

Looking at the normal distribution table, the probability corresponding to the z score is 0.666

Therefore,

P(49.5 ≤ x ≤ 50.5) = 0.666 - 0.334 = 0.332