Dr. Lopez gives students 90 minutes to complete the final exam for her course. Most students use almost all the
time allowed, and relatively few students finish early, so the distribution of times that it takes students to finish
the exam is strongly skewed to the left. The mean and standard deviation of the finishing times are 85 and 10
minutes, respectively.
Suppose we took random samples of 40 students and calculated as the sample mean finishing time. We can
assume that the students in each sample are independent.
What would be the shape of the sampling distribution of ??
Choose 1 answer:
Skewed to the left
Skewed to the right
No

The correct answer is: mean = 10.44/30 = 0.348, standard error (9.2/30)^2 = 0.094

When you take random samples of 30 pennies and find the mean age in each sample, the distribution of the sample means will have a mean that is equal to the mean of the population (10.44 years in this case) divided by the sample size (30 in this case). This is known as the sampling distribution of the mean.

The standard error is a measure of the spread or dispersion of the sampling distribution. It is calculated as the standard deviation of the population divided by the square root of the sample size. In this case, the standard error would be (9.2/30)^2 = 0.094.

The other options do not correctly describe the center and spread of the sampling distribution of the means. Option A gives the mean and standard deviation of the population, not the sampling distribution. Option B gives the correct standard error, but the mean is incorrect. Option D gives the correct mean, but the standard error is incorrect.

∴ The correct answer is: mean = 0.348, standard error = 0.094.

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Answer:

Step-by-step explanation:

[tex]s=ut+\frac{1}{2}gt^2\\if ~the~body~falls~freely,~then~at~t=0,d=0\\s_{n}=d_n=\frac{1}{2}gn^2\\S_{n-1}=\frac{1}{2}g(n-1)^2\\distance~covered ~in~nth~second\\S(n)=d(n)-d(n-1)=\frac{1}{2}gn^2-\frac{1}{2}g(n-1)^2=\fracg[n^2-(n-1)^2]\\=\frac{1}{2}g{(n+n-1)(n-n+1)]\\=\frac{1}{2}g(2n-1)[/tex]

Answer: C its C

Step-by-step explanation:

GOT DANG JUST READ THE ANSWER ITS CCCCCCCCCCCCCCCCCCCCCCCCCCCCC

The complete statement is "After 80 years, the town will have more than 96 people."

Generally,  A population is the whole set of people in a group, whether that group is a country or a collection of people who share a certain trait. A population is the group of people from whom a statistical sample is taken in statistics.

Here is the pattern:

After 80 years, the town will have more than 96 people.

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The probability of not drawing a 5 from the deck is 48/52.

What is probability?

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

There are 4 number 5's in the deck of 52 cards.

They are as follows:

The 5 of clubs, the 5 of spades, the 5 of hearts, and the 5 of diamonds.

Using the formula,

Probability = (Number of possible outcomes)/(Total number of outcomes)

The probability of drawing a 5 from the deck is 4/52.

The probability of not drawing a 5 from the deck is 48/52.

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The probability that the student is

(a) enrolled in mathematics is equal to [tex]\frac{3}{10}[/tex]

(b) enrolled in English is equal to [tex]\frac{11}{20}[/tex].

(c) enrolled in both is equal to [tex]\frac{11}{80}[/tex].

(d) enrolled in mathematics or English is equal to [tex]\frac{57}{80}[/tex].

(e) enrolled in English but not in mathematics is equal to [tex]\frac{33}{10}[/tex].

(f) not enrolled in English or is enrolled in mathematics is equal to [tex]\frac{23}{80}[/tex].

What is probability?

A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The total number of students in college is 400.

Students enrolled in Mathematics = 120.

Students enrolled in English = 220.

Students enrolled in both Mathematics and English = 55.

(a) The probability that the student is enrolled in mathematics is the Number of students enrolled in mathematics divided by the total number of students which is equal to [tex]\frac{120}{400} =\frac{3}{10}[/tex].

(b) The probability that the student is enrolled in English is the Number of students enrolled in English divided by the total number of students which is equal to [tex]\frac{220}{400} =\frac{11}{20}[/tex].

(c) The probability that the student is enrolled in Both is equal to the number of students enrolled in Both divided by the total number of students which is equal to [tex]\frac{55}{400} =\frac{11}{80}[/tex].

(d)  The probability that the student is enrolled in mathematics or English is the Number of students enrolled in mathematics or English that is the Number of students in (Maths+English - Both) divided by the total number of students which is equal to [tex]\frac{120+220-55}{400} =\frac{285}{400}=\frac{57}{80}[/tex].

(e) The probability that the student is enrolled in English but not in mathematics is the Number of students enrolled in (English- enrolled in both) divided by the total number of students which is equal to [tex]\frac{220-55}{400} =\frac{165}{400}=\frac{33}{80}[/tex].

(f) The probability that the student is neither enrolled in mathematics nor English is the Total Students - (Maths+English-both) divided by the total number of students which is equal to [tex]\frac{400-(120+220-55)}{400} =\frac{115}{400}=\frac{23}{80}[/tex].

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Passive solar heating systems use solar collectors. This is false.

An apparatus that gathers and/or concentrates solar radiation from the Sun is called a solar collector. These gadgets enable the heating of water for personal use and are primarily used for active solar heating.

Through the absorption of sunlight, a solar thermal collector gathers heat. Commonly, a solar hot water heater is referred to as a "solar collector," but the term can also refer to large power generation facilities like solar parabolic troughs and solar towers or non-water heating equipment like solar air heaters.

In conclusion, it's false.

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Answer:

Using the inclusion and exclusion principle, we can calculate the percentage of members who play all three sports as follows:

60% of members play Tennis, 50% of members play Cricket, and 70% of members play Football.

Therefore, 60% + 50% + 70% = 180% of members play at least one of the sports.

However, this count includes members who play more than one sport, so we need to subtract out the members who play two sports and add back in the members who play all three sports.

20% of members play Tennis and Cricket, 40% of members play Cricket and Football, and 30% of members play Football and Tennis.

Therefore, 20% + 40% + 30% = 90% of members play at least two sports.

Subtracting this number from the total number of members who play at least one sport gives us 180% - 90% = 90% of members who play at least one sport but not all three sports.

To find the number of members who play all three sports, we need to subtract this number from the total number of members who play at least one sport:

180% - 90% = 90% of members who play at least one sport but not all three sports

180% - 90% = 90% of members who play all three sports

Therefore, according to the inclusion and exclusion principle, 90% of members play all three sports.

If someone claimed that 20% of members play all three sports, this would be incorrect based on the calculations using the inclusion and exclusion principle. The correct number of members who play all three sports is 90%, not 20%. This can be verified by using the given information about the percentage of members who play each individual sport and the percentage of members who play two sports in combination.

To clarify, the inclusion and exclusion principle states that to find the number of elements in a union of sets (in this case, the number of members who play at least one sport), we can add the number of elements in each set (the percentage of members who play each individual sport) and then subtract the number of elements that are counted multiple times (the percentage of members who play two sports in combination). We then add back in the elements that were subtracted out in the previous step (the percentage of members who play all three sports).

Using this principle, we were able to calculate that 90% of members play all three sports, rather than the 20% claimed by someone.

Step-by-step explanation:

Answer:

Only X = X - ( (X∩Y - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )

Only X = 600 - ( (200-200) + 200 + ( 300-200) )

Only X = 600 - (0 + 200 + 100)

Only X = 600 - (300)

Only X = 300

Only Y = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (X∩Y - X∩Y∩Z) )

Only Y = 500 - ( (400-200) + 200 + ( 200-200) )

Only Y = 500 - (200 + 200 + 0)

Only Y = 500 - (400)

Only Y = 100

Only Z = Y - ( (Y∩Z - X∩Y∩Z) + X∩Y∩Z + (Z∩X - X∩Y∩Z) )

Only Z = 500 - ( (400-200) + 200 + ( 300-200) )

Only Z = 500 - (200 + 200 + 100)

Only Z = 500 - (500)

Only Z = 200

Step-by-step explanation:

Penny currently budgeted for her trip, in US dollars is $993.95.

What is  Penny currently?

Pennies are constructed of copper-coated zinc. Only nickels—that identical alloy of 75% copper and 25% nickel—are one solid substance.

Given: Exchange rate of the US dollar to Egyptian pound is 1:5.3841

Item Cost Currency Plane ticket =

[tex]3,241.77 £=\frac{3,241.77}{5.3841}=\$ 602.100629632 \approx \$ 602.10[/tex]

Passport =  $65.00

Tour guide [tex]$=494.25 £=\$ 91.7980721012 \approx \$ 91.80$[/tex]

International phone card [tex]$=\$ 41.38$[/tex]

Hotel reservation [tex]$=398.26 £=\frac{398.26}{5.3841}=\$ 73.9696513809 \approx \$ 73.97$[/tex]

Car rental [tex]$=644.48 £=\frac{644.48}{5.3841}=\$ 119.700599915=\$ 119.70$[/tex]

Therefore, the total budgeted for her trip, in US dollars= [tex]602.10+91.80+41.38+73.97+119.70+65$ $=\$ 993.95$[/tex]

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Answer:

Step-by-step explanation:

If the weight of Ram and Sam are in the ratio 4:7, and the weight of Aari and Ram are in the ratio 3:2, you can use this information to set up a system of equations to represent the weights of the three people. Let's say that Ram weighs x kilograms. Then, the weight of Sam is 7x/4 kilograms, and the weight of Aari is 3x/2 kilograms.

The maximum difference in weight between any two people is 15 kilograms, so we can set up the following equation to represent this constraint:

|x - (7x/4)| <= 15

|x - 3.5x| <= 15

|-2.5x| <= 15

|x| <= 6

This equation tells us that the weight of Ram (x) must be less than or equal to 6 kilograms or greater than or equal to -6 kilograms.

Since the weight of a person cannot be negative, the maximum weight for Ram is 6 kilograms. Therefore, the maximum weight for Sam is 7x/4 = 76/4 = 10.5 kilograms, and the maximum weight for Aari is 3x/2 = 36/2 = 9 kilograms.

Thus, the maximum weight of the three people is 6 + 10.5 + 9 = 25.5 kilograms.

Answer:

A) -3

Step-by-step explanation:

To evaluate this mathematical expression, we must follow the following steps:

Perform the operation between parentheses: (0-1) = -1

Multiply the previous result by 2: -1 * 2 = -2

Add 1.5 to the previous result: -2 + 1.5 = -0.5

Therefore, the correct answer to the mathematical expression is A) -3.

Answer: 15

Step-by-step explanation:

To solve this problem, we first need to translate the given information into a system of equations. Let's call the first number x and the second number y. Since the sum of the two numbers is 22, we know that x + y = 22.

The second statement says that three times one number increased by five is the same as twice the other number decreased by four. We can translate this into an equation by substituting x and y for the two numbers and using the given information:

3x + 5 = 2y - 4

Now that we have a system of equations, we can solve for x and y. First, we'll solve for x by adding four to both sides of the second equation:

3x + 9 = 2y

Then, we can divide both sides by three to get the value of $x$:

x = {2y - 9} / {3}

Next, we can substitute this expression for x into the first equation to solve for y:

y + {2y - 9} / {3} = 22

We can simplify this equation by multiplying both sides by three:

3y + 2y - 9 = 66

Combining like terms on the left side, we get:

5y - 9 = 66

Then, we can add nine to both sides to solve for y:

5y = 75

Finally, we can divide both sides by five to find the value of y:

y = 15

Now that we know the value of $y$, we can substitute it back into the expression for $x$ to find the value of $x$:

x = \frac{2 \cdot 15 - 9}{3} = \frac{27}{3} = 9

Since we want the larger of the two numbers, the answer is 15

The length of the larger filter is 6 inches.

What is area of rectangle ?

The area of a rectangle is the product of its length and width. That is, A = l x w where l is the length and w is the width

Given:

Small heater :  Length = 20 inches , width = 16 inches

larger heater :  Length = ?, width = 56 inches

Since, larger heater requires a similar filter

∴Area of  small heater = Area of  larger heater

(length * width) of smaller heater = (length * width) of larger heater

20 * 16 = length * 56

length = 20*16/56 = 320/56

length = 5.714

0r , length = 6 inches

Hence , the length of the larger filter is 6 inches.

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Answer:

Step-by-step explanation:

Look at the original value of the gallons of water =12568 this is in July

Look at the value of the gallons of water in August =11,562

Find the difference between the two values=12568-11562=1006

Place the larger value of gallons of water first, as you are going from a large number to a small number you are decreasing by 1006

We put this value of the difference over the original gallons of water and then multiply by 100%

1006/12568 x100%=

This can be done on your calculator

1006÷12568 x100=8.004455761

Rounding to the nearest whole percent gives 8% decrease

Therefore, number of pages of study guide Gloria have=9

In mathematics, an equation is a formula that uses the equals symbol (=) to represent how two expressions are equivalent. the act of comparing two things or "the equation of science with objectivity."

given

no. of  study guides for language art= 3

no. of  pages in each study guides=3

so no. of pages of study guides= no. of  study guides for language art*

no. of  pages in each study guides

3*3=9

therefore, number of pages of study guide Gloria have=9

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Answer: x=-3

Step-by-step explanation:

-4=3x+5

isolate x by moving all other variables  to the right

-4-5=3x+5-5

-9=3x

x=-3

Answer:

-7

Step-by-step explanation:

To find the solution you'd have to plug in the -4 for every x you see but in this solution there is only one x so then you'd plug it in for that x. So then you'd have f(-4= 3(-4) + 5 and then you'd solve it. To solve it you would first multiply the 3 with the -4 because when something is in a parenthesis and there is a number beside with no sign that means you multiply. When you multiply you should get -12. After you get -12 you add 5 and your answer is -7.

When they give you an equation with an f(x) they sometimes give you inputs which you plug in to get your output. -4 was an input and -7 (your answer) is an output.
(hopefully you understood how i solved..)

The slope of the equation is 0.50 and its interpretation in the context of the problem is that Emily will spend 0.50 dollars, or 50 cents, for each minute of use.

The slope-intercept form of a straight line is used to get the equation of a line. To utilize the slope-intercept formula, we need to know the line's slope and the point at which it crosses the y-axis, or intercept. For a straight line with slope "m" and y-intercept "b," the slope-intercept form equation is: y = mx + b.

Given equation,

C = 9 + 0.50t

Here, c = 0.50

Hence, the slope is 0.50.

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This is a case of Compound Interest.

It takes around 3.22 years for investment to grow to 1500$ from 1000$.

The interest charged on a loan or deposit is known as compound interest. It is the idea that we employ the most frequently on a daily basis. Compound interest is calculated for an amount based on both the principal and cumulative interest. The major distinction between compound and simple interest is this.

The interest that is calculated using both the principal and the interest that has accrued during the previous period is called compound interest. It differs from simple interest in that the principal is not taken into account when determining the interest for the subsequent period with simple interest. Compound interest is commonly abbreviated C.I. in mathematics.

Annual amount, A=P(1+[tex]\frac{r}{n}[/tex])∧nt

Given,

P=1000$

A=1500$

r=13%=0.13

A=P(1+[tex]\frac{r}{n}[/tex])∧nt

n=2(Compounded semi-annually)

⇒1500=1000(1+[tex]\frac{0.13}{2}[/tex])^2t

⇒[tex]\frac{1500}{1000}[/tex]=(1.065)^2t

⇒1.5=(1.065)^2t

Taking log on both sides

㏒(1.5)=2t㏒(0.625)

⇒t=[tex]\frac{log(1.5)}{2log(0.625)}[/tex]

⇒t=3.219years≈3.22years

This is a case of Compound Interest.

It takes around 3.22 years for investment to grow to 1500$ from 1000$.

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Using the principle of proportional relationship, the time taken by the turtle to walk one mile is 2.1667 hours

What is proportional relationship?

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is know as the "constant of proportionality".

Creating a system of proportional expression :

Cross multiply :

1.5t = (3.25 × 1)

1.5t = 3.25

Divide both sides by 1.5

t = (3.25 ÷ 1.5)

t = 2.1667 hours

Therefore, the time taken per mile is 2.1667 hours

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The turtle needs 2.16 hours to move a mile using the proportional relationship principle.

What does the word "proportional" mean?

Proportional relationships form when the ratios of two variables are equal. The fact that one variable is consistently equal to the constant value of the other in a proportionate connection is another way to think of them. The "constant of proportionality" is the name of this constant.

For instance, the time it takes a train to travel 50 kilometers per hour is equal to the time it needs to travel 250 kilometers in 5 hours. e.g., 250km/5 hours at 50 km/h.

Establishing a proportional expression system

Cross multiply :

1.5t = (3.25 × 1)

1.5t = 3.25

t = (3.25 ÷ 1.5)

t equals 2.16 hours

Consequently, the time required for each mile is 2.16 hours.

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Albert's total earnings for the last two weeks is $320.82.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Albert got a regular salary of $312 every two weeks.

Also given, he makes 9% of the commission on sales and he sold worth $98.

So, His total earnings of Albert is the sum of his fixed earnings and the percentage of commission he made which is,

= $[312 + (9/100)×98].

= $[312 + 8.82].

= $320.82.

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The value of x in the parallelogram is zero.

A parallelogram is a two-dimensional geometrical shape(quadrilateral) whose sides are parallel to each other.

Therefore, the properties of a parallelogram are as follows:

Therefore, let's find the value of x using the properties of a parallelogram.

Hence,

ST = RU

2x + 15 = x + 15

2x - x = 15 - 15

Therefore,

x = 0

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The upper control limit(UCL) is 160

sample mean X =35

sample size n   =25

sample size n=25, average sample standard deviation is 5

Upper control limit is shown by the top dashed line (UCL). The data that is plotted on the control chart is used to calculate the upper control limit. It is positioned 3 sigma off the average line (of the data being plotted).

A control chart is made up of various components. It has an average line and two control limits. The lower control limit is represented by the dashed bottom line (LCL). The statistic's average is represented by the solid center line. The higher control limit appears as the top dashed line (UCL).

a)

Upper control limit(UCL) =X+A2R =160

Control line (CL) = X=35

Lower control limit (LCL)=X-A2R =90

Hence, The upper control limit (UCL) is 160

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The correct option is (b) i.e. f(0) > f(2).

What is Domain?

The entire range of independent variable values is the domain of a function. In straightforward terms, this definition means The collection of all x-values that can cause the function to "work" and produce actual y-values is known as the domain.

We have,

f(x) =         (x+2)^2 - 1        ,  -4 ≤ x ≤ 0

                      -x + 1          ,  0 ≤ x ≤ 2

        5/2 log ( -x +5) - 1    , 2 < x < 5

Now, f(0) =   (x+2)^2 - 1  

               =   (0+2)^2 - 1

               = 4 - 1 = 3

Similarly, f(2) =  - x +1

                     = - 2 + 1

                     = - 1.

Hence, f(0) > f(2)  because 3 > -1.

∴ The correct option is (b).  

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Answer:

D 13 [tex]\frac{3}{5}[/tex]

Step-by-step explanation:

I’m ur math man

In the given equation, Y = 3x is at (0, 3) and a line passes through (-3, 0).

A mathematical statement known as equation is given by joining two expressions with the equal sign. For instance, 3x - 5 = 16 is an equation. This equation can be solved, and the result shows that the value of the variable x is 7.

A mathematical equation links the two phrases on either side of the sign. It typically only contains an equal sign and one variable. similar to 2x - 4 = 2.

Either identities or conditional equations can be used to classify equations. Each value of the variables corresponds to a specific identity. A conditional equation can only be true for a certain range of variable values. An equation is represented by two expressions being separated by the equals sign ("=").

A line goes through (- 3, 0) and (0, 3)

The equation is

y - y1 = y2 - y1/ x2- x1

y - 0 = 3 - 0 / 0 - (-3) (x - (-3)

y = x + 3

y = 3x

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0.4166667 is the difference between 2/ 3 and 1 /4.

A fraction is a symbol used in mathematics to represent a part or element of the whole. It represents the proportional components of the whole. A fraction is made up of the denominator and the numerator. The top number is the numerator, and the lower number is the denominator.

More manageable pieces of a whole are represented by fractions. The components could be combined to make one thing or several things. In any instance, they come together to create the concept of a whole. As parts of wholes or sets, as the result of dividing two numbers, as the ratio of two quantities, as operators, and as measures are only a few examples of how to use fractions, they are all examples of fractions.

= 2/3 - 1/4

= 512

= 0.4166667

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Answer:

-----------------------

Initial number of sports team:

Number after new members joined:

60% of 150 members are men, number  of men is:

Number of women:

Number of newly joined women:

Perimeter of the rectangle:

Area of rectangle:

New dimensions:

New perimeter:

New area:

New perimeter is same as previous one but new area is smaller.

Answer:

C. Translation [tex](x,y) \longrightarrow (x-7, y+0)[/tex], Reflection in the [tex]y[/tex]-axis

The exact value of the expression cos(arcsin(15/17)) is 1.

The inverse sine function, denoted as arcsin, gives the angle whose sine is a given value. Since the range of the sine function is -1 to 1, the range of the arcsin function is -90 degrees to 90 degrees.

In this case, the value of the expression is given by cos(arcsin(15/17)). To find the exact value of this expression, we can first use the definition of the inverse sine function to find the value of arcsin(15/17). Since the sine of an angle is equal to the opposite side divided by the hypotenuse in a right triangle, we can set up the following equation:

Since the sine function has a period of 180 degrees, we can add or subtract multiples of 180 degrees to the angle x to find the value of the expression for all possible angles. For example,

Using this information, we can find the values of the expression for all possible angles:

x = arcsin(15/17) => cos(arcsin(15/17)) = cos(x)

                                                           = √(1 - sin^2(x))

                                                           = √(1 - (15/17)^2)

                                                           = √(289/289)

                                                           = 1

x + 180 = arcsin(15/17) + 180 => cos(arcsin(15/17) + 180) = cos(x + 180)

                                                                                         = -cos(x)

                                                                                         = -1

x - 180 = arcsin(15/17) - 180 => cos(arcsin(15/17) - 180) = cos(x - 180)

                                                                                       = -cos(x)

                                                                                       = -1

Since the cosine function has a period of 360 degrees, the values of the expression for all possible angles can be expressed as:

cos(arcsin(15/17) + 360k) = 1 for all integers k

cos(arcsin(15/17) + 180 + 360k) = -1 for all integers k

Therefore, the exact value of the expression cos(arcsin(15/17)) is 1.

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