rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
How to calculated dimensions of a rectangular Persian rug?Let's say that the Persian rug is rectangular, with length "l" and width "w".
The total of a rectangle's four sides is known as the perimeter, and it can be calculated as follows:
Perimeter = 2l + 2w
Given that the distance around it is 22 feet, we can write:
2l + 2w = 22
When we simplify this equation, we obtain:
l + w = 11
A rectangle's area is determined by the product of its length and breadth, which may be written as follows:
l x w = area
Given that the space is 10 square feet, we can write:
l x w = 10
Two equations with two variables are now available:
L+W = 11, and L x W = 10.
To find l and w, we can utilise substitution or elimination. For instance, we can solve for w from the first equation in terms of l:
w = 11 - l
Using this expression as w's replacement in the second equation, we obtain:
l x (11 - l) = 10
The result of expanding and rearrangement is a quadratic equation:
l² - 11l + 10 = 0
Using the quadratic formula or factoring, we can solve this quadratic problem. Factoring results in:
(l - 10)(l - 1) = 0
so either l = 10 or l = 1 is true.
w = 1 if l = 10, otherwise. w equals 10 if l = 1.
As w is always smaller than l, we have
The rectangular Persian rug's measurements are 10 ft in length and 1 ft in width.
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help pls i will give brainliest to correct answer
The length of segment YS within the square QRST is equal to 6.
How to determine the length of a line segment within a diagonal in a square
Squares are quadrilaterals with four sides of equal length and two diagonals of equal length, in that order, diagonals QS and RT are the diagonals of square QRST. Besides, we have the following information:
VY = 13, RV = 19
The length of segment YS can be found by means of the following formula:
RV = VY + YS
YS = RV - VY
YS = 19 - 13
YS = 6
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please help me ive been struggling for a little bit
Using Pythagorean theorem, The value of cos(S) rounded to the nearest hundredth is approximately 0.78.
What is Triangle like?It is the simplest polygon and a key component in many branches of science and mathematics.
A triangle's three sides can be equilateral, isosceles, scalene, or any other combination of lengths and kinds. An isosceles triangle has a third side that is a different length from the other two sides, while an equilateral triangle has three sides that are all the same length. All three of the sides of a scalene triangle are different lengths.
In triangle STU, right angled at T, we have:
[tex]ST = 6UT = \sqrt{(22)}[/tex]
We can use the Pythagorean theorem to find the length of TU:
[tex]TU^2 = ST^2 + UT^2\\TU^2 = 6^2 + (\sqrt{(22)})^2\\TU^2 = 36 + 22\\TU^2 = 58\\TU = sqrt(58)\\[/tex]
Now, we can use the definition of cosine:
cos(S) = adjacent/hypotenuse
In this case, the adjacent side to angle S is ST and the hypotenuse is TU. Therefore:
[tex]cos(S) = ST/TU\\cos(S) = 6/\sqrt{(58)}[/tex]
To round to the nearest hundredth, we can divide 6 by the rounded value of sqrt(58):
cos(S) ≈ 0.78 (rounded to the nearest hundredth)
Therefore, the value of cos(S) rounded to the nearest hundredth is approximately 0.78.
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Maria is renting kayaks from a local shop that charges a $7 fee, plus an hourly rate of $5. 50. For how long can maria rent the kayak if she pays a total of $40?.
The number of hours Maria rent the kayak for the paid amount of $40 when hourly rate is $5.50 is equal to 6 hours.
Fees of renting charges paid for kayaks from a local shop = $7
Hourly rate = $5.50
Let 't' be the number of hours Maria rent kayak.
Total fees paid by Maria for renting kayak for 't' hours is equal to $40
Required equation to represents the above condition is
$40 = $7 + $5.50t
Simplify the expression to get the value of 't'
⇒ 5.50t = 40 - 7
⇒ t = 33 / 5.50
⇒ t = 6 hours
Therefore, for the number of hours Maria rent kayak by paying total of $40 is equal to 6 hours.
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[tex] {x}^{\frac{2}{3} }{ } = 64 [/tex]
Solve the following equation
The value of x in the given equation using laws of exponents is; x = 512
How to use Laws of Exponents?The different laws of exponents include;
1) Product of powers rule.
2) Quotient of powers rule.
3) Power of a power rule.
4) Power of a product rule.
5) Power of a quotient rule.
6) Zero power rule.
7) Negative exponent rule.
We have the equation as;
x^(2/3) = 64
We can write 64 as (∛512)²
This can be further expressed as;
512^(2/3)
Thus, we have;
x^(2/3) = 512^(2/3)
Thus, by identity rule;
x = 512
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Problem 1. Compute the complex norm |z|= √zz for the following complex numbers z:
1. z = −i
2. z = (2 + i)2
3. z = (3 −4i)3
4. z = (3 + 4i)3
Recall that the complex norm (or modulus) of a complex number z = a + bi is defined as the nonnegative square root of the product of the complex number and its conjugate, i.e., |z| = √(z × z*), where z* is the complex conjugate of z.
Using this definition, we can calculate the complex norm of each of the given complex numbers as follows:
[tex]z = -i\\z* = i (conjugate of -i)\\|z| = √(z z*) = √(-i i) = √1 = 1Therefore, |z| = 1.[/tex][tex]z = (2 + i)^2\\z* = (2 - i)^2 (conjugate of (2 + i)^2)\\|z| = √(z z*) = √((2 + i)^2 (2 - i)^2) = √((2^2 + 2i + i^2) (2^2 - 2i + i^2))= √((4 + 4i - 1) (4 - 4i - 1)) = √(9 * 9) = 9Therefore, |z| = 9.[/tex][tex]z = (3 - 4i)^3\\z* = (3 + 4i)^3 (conjugate of (3 - 4i)^3)\\|z| = √(z z*) = √((3 - 4i)^3 (3 + 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex][tex]z = (3 + 4i)^3\\z* = (3 - 4i)^3 (conjugate of (3 + 4i)^3)\\|z| = √(z z*) = √((3 + 4i)^3 (3 - 4i)^3) = √((3^2 - (4i)^2)^3) = √(25^3) = 125Therefore, |z| = 125.[/tex]What is complex number?A complex number is a number that can be expressed in the form [tex]a + bi[/tex], where a and b are real numbers, and i is the imaginary unit defined by [tex]i^{2} = -1[/tex]. The real part of the complex number is a, and the imaginary part is bi.
Complex numbers can be added, subtracted, multiplied, and divided in a manner similar to real numbers. They can also be graphed on a complex plane, where the horizontal axis represents the real part and the vertical axis represents the imaginary part.
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question 4 i need help with
Answer:
$3.00
Step-by-step explanation:
The drinks for the first family were 4, and the drinks for the second were 3. They were 2 numbers apart in price and so that means that they costed around $1. Minus a drink on the first to get $17.00. Now tell how far apart it is.
Mark and John work the same amount of hours babysitting and tutoring. Mark gets paid $6 per hour for babysitting and $15 an hour tutoring. He makes $150 in one week. John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114. How many hours were spent babysitting and tutoring?
The requried hours spent babysitting and tutoring are 5 and 8 hours respectively.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
Let the hours spent babysitting and tutoring be x and y respectively,
According to the quesiton,
Mark gets paid $6 per hour for babysitting and $15 an hour for tutoring. He makes $150 in one week.
6x + 15y = 150 - - - -(1)
John Makes $10 an hour babysitting and $8 an hour tutoring and gets paid a total of $114.
10x + 8y = 114 - - - - -(2)
Solving above equations 1 and 2 by elimination method we get x = 5 and y = 8
Thus, the requried hours spent for babysitting and tutoring are 5 and 8 hours respectively.
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Calculate the range and interquartile range for the following set of scores from a continuous variable: 5, 1, 6, 5, 4, 6, 7, 12. Identify the score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile. Why is the interquartile range a better description of variability in the data than the S range?
The range and interquartile range is 11 and 2 respectively. The score that corresponds to the 75th percentile and the score that corresponds to the 25th percentile is 7 and 4 respectively.
To calculate the range, we subtract the smallest value from the largest value:
Range = Largest Value - Smallest Value = 12 - 1 = 11
To calculate the interquartile range, we first need to find the first and third quartiles. We can do this by ordering the scores from lowest to highest and finding the median of the lower half and upper half of the scores, respectively:
1, 4, 5, 5, 6, 6, 7, 12
The median of the lower half (Q1) is the middle value of the numbers 1, 4, 5, and 5, which is 4.5 (the average of the two middle values).
The median of the upper half (Q3) is the middle value of the numbers 6, 6, 7, and 12, which is 6.5.
Interquartile Range = Q3 - Q1 = 6.5 - 4.5 = 2
To find the score that corresponds to the 75th percentile, we first need to find the index corresponding to the 75th percentile. We can do this by multiplying 0.75 by the total number of scores, which is 8. This gives us an index of 6, meaning the 75th percentile score is the 6th score in the ordered list:
1, 4, 5, 5, 6, 6, 7, 12
The score that corresponds to the 75th percentile is 7.
To find the score that corresponds to the 25th percentile, we can follow the same procedure. The index corresponding to the 25th percentile is 0.25 times the total number of scores, or 2. The 2nd score in the ordered list is 4.
The interquartile range is a better description of variability in the data than the range because the range is heavily influenced by outliers. In this case, the range is 11, which is largely driven by the outlier score of 12. The interquartile range, on the other hand, only considers the middle 50% of the scores and is therefore less affected by outliers. It gives a more accurate measure of the spread of the scores around the median.
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Help solve please !!
Answer:
2+1=3, 7+8=15, 0+1=1, 8+7=15, 2+9=11, 1+3=4, 2+0=0, 4+5=9, 3+4=7
Find the surface area of the pyramid. The side lengths of the base are equal.
The surface area of the pyramid is 116.4 sq. ft.
What is surface area?The area is the area occupied by a two-dimensional flat surface. It has a square unit of measurement. The surface area of a three-dimensional object is the space taken up by its outer surface. Square units are used to measure it as well.
For each three-dimensional geometrical shape, surface area and volume are determined. The area or region that an object's surface occupies is known as its surface area. Volume, on the other hand, refers to how much room an object has.
The surface area of the pyramid is calculated by adding the area of all the faces of the pyramid.
The area of the triangle is given as:
A = 1/2 (b)(h)
For the face of the pyramid:
b = 12 and h = 9
Substituting the values we have:
A = 1/2 (12)(9)
A = 54 sq. ft
The pyramid consists of three faces thus,
A = 3(54) = 162 sq ft
For the base of the pyramid:
b = 12 and h = 10.4 ft
A = 1/2(12)(10.4)
A = (6)(10.4)
A = 62.4 sq ft
The surface area of the pyramid is:
SA = 54 + 62.4
SA = 116.4 sq. ft
Hence, the surface area of the pyramid is 116.4 sq. ft.
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question is in the picture
The formula of the area of the trapezium as subject to x is,
x = 2A/h - y.
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Given:
The area of the trapezium,
A = (1/2)h(x + y)
To make x the subject of the equation:
2A/h = (x + y)
2A/h - y = x
x = 2A/h - y
Therefore, the formula is x = 2A/h - y.
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One cubic foot holds 7.48 gallons of water, and 1 gallon of water weighs 8.33 pounds. How much does 4.3 cubic feet of water weigh in pounds? In tons?
Answer:
268 pounds
Step-by-step explanation:
Two unit multipliers to be used for this unit conversion:
[tex]\frac{7.48 gallons}{1ft^{3}}[/tex] and [tex]\frac{8.33 pounds}{1 gallon}[/tex]
4.3 cubic feet = [tex](4.3ft^{3})[/tex]×[tex](\frac{7.48 gallons}{1ft^{3}})[/tex] ×[tex](\frac{8.33 pounds}{1ft^{3}})[/tex]
The cubic feet units in the numerator and denominator will cancel each other out. The gallons units in the numerator and denominator will cancel each other out.
= 268 pounds of water (Rounded to 3 significant figures)
In a particular metal mixture there are:
1 part mercury to 5 parts copper,
3 parts tin to 10 parts copper,
You would need how many parts mercury to how many parts tin?
A) 1:3
B) 2:3
C) 6:13
D) 4:15
Answer:
B) 2:3
Step-by-step explanation:
If you have mercury : copper = 1 : 5 and tin : copper = 3 : 10, you want the ratio of mercury to tin.
RatioThe ratios can be compared or combined when common components are represented by the same number. Doubling the values in the first ratio, we will have two ratios that both have 10 parts copper.
mercury : copper = 1 : 5 = 2 : 10
Then ...
mercury : tin : copper = 2 : 3 : 10
You need 2 parts mercury to 3 parts tin.
mercury : tin = 2:3 . . . . . . choice B
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There is a pair of vertical angles where ∠1=106° and ∠2=3x−75. What equation can you write to solve for x
The solution is, the value is, x = 49.6.
What is an angle?In Plane Geometry, a figure which is formed by two rays or lines that shares a common endpoint is called an angle. The two rays are called the sides of an angle, and the common endpoint is called the vertex.
here, we have,
given that,
There is a pair of vertical angles where ∠1=106° and ∠2=3x−75
so, 1 + 2 = 180
or, 106 + 3x - 75 = 180
or, 3x = 149
or, x = 49.6
Hence, The solution is, the value is, x = 49.6.
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14,125 ÷ 18 = ? With a remainder
Answer:
784 R 13
Hope this helps!
Step-by-step explanation:
WILL MARK BRAINLY IF SOMEONE CAN GIVE ME THE CORRECT ANSWER PLEASE.
The x-coordinate of P is given as follows:
x = 4.
How to obtain the x-coordinate of P?The x-coordinate of P is obtained applying the proportions in the context of this problem.
The partition ratio is 2:4, hence the equation to obtain the coordinates is given as follows:
P - A = 2/6(B - A)
P - A = 1/3(B - A).
Then the x-coordinate of P is obtained as follows:
x - 10 = 1/3(-8 - 10)
x - 10 = -6
x = 4.
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The pto is selling raffle tickets to raise money for classroom supplies. A raffle ticket costs $4. There is 1 winning ticket out of the 200 tickets sold. The winter gets a prize worth $76.
Answer:
Step-by-step explanation:
The profit the PTO makes from selling raffle tickets can be calculated by subtracting the cost of the tickets from the total revenue generated from ticket sales.
Let's first calculate the total revenue:
Number of tickets sold = 200
Price per ticket = $4
Total revenue = 200 * $4 = $800
Next, let's calculate the cost of the tickets:
Number of tickets sold = 200
Price per ticket = $4
Total cost = 200 * $4 = $800
Finally, we can calculate the profit by subtracting the cost of the tickets from the total revenue:
Profit = Total revenue - Total cost
Profit = $800 - $800 = $0
So, the PTO makes no profit from selling the raffle tickets. This is because the cost of the tickets and the prize are equal, and there are no other expenses. In this scenario, the prize money of $76 is given away to the winner, so the PTO does not get to keep the money for classroom supplies.
A bag contains 4 white marbles, 3 red marbles, and 5 blue marbles. Miko takes one marble from the bag, replaces it, and then takes another. Find P(red, then white).
Answer:
To find the probability of Miko taking a red marble first, then a white marble, we can use the formula for joint probability:
P(red, then white) = P(red) * P(white | red)
Where P(red) is the probability of Miko taking a red marble first and P(white | red) is the probability of Miko taking a white marble second, given that he took a red marble first.
P(red) = 3/12 = 1/4
P(white | red) = 4/12 = 1/3
So,
P(red, then white) = 1/4 * 1/3 = 1/12
Therefore, the probability of Miko taking a red marble first, then a white marble is 1/12.
I really need help on this question. I have attached it thx. Do all the questions I have put on it so the answer and units.
Answer:
14 cm
Step-by-step explanation:
The formula for circumference of a circle is 2πr, where r is the radius. In this problem, the circumference would be 2π * 7cm = 14 cm
Pat deposits $ 600 in a savings account at a simple interest rate of 6% per year for 5
years. how much will pat have earned in interest by the end of 5 years
Answer:
will earn in interest $ 180
A function is given.
g(x) =
4
x + 5
; x = 0, x = h
(a) Determine the net change between the given values of the variable.
(b) Determine the average rate of change between the given values of the variable.
A function is given net change and the average rate of change between the given values of the variable.
A. = - [tex]\frac{4h}{7h + 49}[/tex]
B. = - [tex]\frac{4}{7h + 49}[/tex]
What exactly is a sample average rate?Examples of average rates of change include: 80 kilometres per hour is the average speed of a bus. At a pace of 100 each week, a lake's fish population grows. For every 1 volt drop in voltage, the current in an electrical circuit reduces by 0.2 amps.
According to given information:a) The net change is just the difference between g(h) and g(0). This is found below.
g(h) - g(0) = [tex]\frac{4}{h + 7}[/tex] - [tex]\frac{4}{0 + 7}[/tex]
= [tex]\frac{28 - 4h -28}{7h + 49}[/tex]
= - [tex]\frac{4h}{7h + 49}[/tex]
b) The average rate of change is the net change divided by the length of the interval. This is:
[tex]\frac{g(h) - g(0)}{h - 0}[/tex] = - [tex]\frac{{4h}/{7h + 49}}{h - 0}[/tex]
= - [tex]\frac{4}{7h + 49}[/tex]
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what is the substitution for -3x+5y=21
Answer:
5
_ y - 7
3
the five is floating for some reason its supposed to be under the line
Samuel took a survey of people entering several random ice cream shops to find out who liked vanilla and who liked chocolate ice cream.
biased or unbiased
Answer:
ummmm i would say unbiased fam only bc i love ice cream and i always wonder whichwtch one does people like more.
Step-by-step explanation:
The circumference of a circle is 81.64 feet. What is the radius of the garden? Use 3.14 for π and do not round your answer
Answer:13
Step-by-step explanation:
r = circumference/2pi
81.64/6.28 = 13
The radius of the garden is 13 units.
In a class of 30 students x +10 study algebra, 10+3 study statistics, 4 study both algebra and statistics. 2x study only Algebra and 3 study neither algebra nor statistics
1. Illustrate the information one a Venn diagram.
2. How many students study;
A. Algebra
B. Only statistics
1. The Venn diagrams are attached
2. When the statistics students number = 10·x + 3, we have;
The number of students that study
a. Algebra = 128/11b. Statistic = 213/11When the statistics students number = 2·x + 3, we have;
The number of students that study
a. Algebra = 16b. Statistic = 15How to solve thisThe parameters given are;
Total number of students = 30
Number of students that study algebra n(A) = x + 10Number of students that study statistics n(B) = 10·x + 3Number of student that study both algebra and statistics n(A∩B) = 4Number of student that study only algebra n(A\B) = 2·xNumber of students that study neither algebra or statistics n(A∪B)' = 3Therefore;
The number of students that study either algebra or statistics = n(A∪B)
From set theory we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 10·x + 3 - 4 = 2711·x+13 = 27 + 4 = 31=11·x = 18x = 18/11The number of students that study
a. Algebra
n(A) = 18/11 + 10 = 128/11
b. Statistic
n(B) = 213/11
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 128/11 - 4 = 84/11
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 213/11 - 4 = 169/11
However, assuming n(B) = (2·x + 3), we have;
n(A∪B) = n(A) + n(B) - n(A∩B)
n(A∪B) = 30 - 3 = 27
Therefore, we have;
n(A∪B) = x + 10 + 2·x + 3 - 4 = 27
2·x+3 + x + 10= 27 + 4 = 31
3·x = 18
x = 6
Therefore, the number of students that study
a. Algebra
n(A) = 16
b. Statistics
n(B) = 15
Hence, we have;
n(A - B) = n(A) - n(A∩B) = 16 - 4 = 12
Similarly, we have;
n(B - A) = n(B) - n(A∩B) = 15 - 4 = 11
The Venn diagrams can be presented as follows;
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A faucet gives 20 gallons of water in 5 seconds. How many gallons does it give in 7 seconds?
Answer:
28
Step-by-step explanation:
IF 20 GALLONS IS EQUIVALENT TO 5 SECONDS WHAT ABOUT 7 SECONDS
CROSS MULTIPLY
Answer:
20 gallons / 5 seconds = 4 gallons / second
Therefore, In 7 seconds you get (7 x 4 ) or 28 gallons.
Step-by-step explanation:
Which is the solution of [tex]-\frac{6}{x} -\frac{x-2}{4} \ \textgreater \ \frac{3-x}{3}[/tex]?
Multiple choice question.
A)
x= −6, x= 12, or x ≠ 0
B)
−6 < x < 0 or x > 12
C)
x < −6 or x > 12
D)
−12 < x < 0 or x > 6
Answer:
C) x < −6 or x > 12----------------------
Given inequality:
- 6/x - (x - 2)/4 > (3 - x)/3Consider x ≠ 0 and multiply all terms by x, 4 and 3:
- 6*12 - 3x(x - 2) > 4x(3 - x)-72 - 3x² + 6x > 12x - 4x²4x² - 3x² + 6x - 12x - 72 > 0x² - 6x - 72 > 0 x² - 12x + 6x - 72 > 0x(x - 12) + 6(x - 12) > 0(x + 6)(x - 12) > 0The x-intercepts are:
x = - 6 and x = 12This quadratic function has a positive leading coefficient and two zeros, and hence is positive when:
x < - 6 and x > 12, the x = 0 is excluded from the given interval, therefore the above is the solution.The matching choice is C.
Determine the Domain and Range for the graph below. Write your answer in interval notation and as an inequality.
Domain written in Interval Notation:
Domain written as an Inequality:
Range written in Interval Notation:
Range written as an Inequality:
Points on the graph are:
(0,1) (1,2) (2,3) (3,4) (4,5)
(-1,0) (-2,-1) (-3,-2) (-4,-3)
The domain and the range of the ordered pairs in interval notations are as follows: 1) Domain = [0,4], Range = [1,5] ; (2) Domain [-1,-4], Range =[0,-3]
Domain and Range of a set of Ordered pairsThe domain of a function is the collection of all conceivable values that may be used as inputs, or alternatively, it is the whole array of possible values for independent variables.
The range of a function is the set of every possible value for the dependent variable's outcomes, or the whole set of all possible values when the domain is substituted.
In a set of ordered pairs (x,y), the domain (input) refers to all the x-values and the range refers to all the y-values.
From the points on the graph given:
(0,1) (1,2) (2,3) (3,4) (4,5)
Domain: (0, 1, 2, 3, 4)
In interval notation: = [0,4]Range: (1, 2, 3, 4, 5)
In interval notation: = [1, 5](-1,0) (-2,-1) (-3,-2) (-4,-3)
Domain: ( -1, -2, -3, -4)
In interval notation: = [-1, -4]Range: (0, -1, -2, -3)
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Sara can type 90 words in
4 minutes. About how many words
would you expect her to type in
10 minutes at this rate?
[tex]\begin{array}{ccll} words&minutes\\ \cline{1-2} 90 & 4\\ x& 10 \end{array} \implies \cfrac{90}{x}~~=~~\cfrac{4}{10} \\\\\\ \cfrac{ 90 }{ x } ~~=~~ \cfrac{ 2 }{ 5 }\implies 450=2x\implies \cfrac{450}{2}=x\implies 225=x[/tex]
A population mean is normally distributed with a mean of 56 and a standard deviation of 12.
The mean of the sampling distribution (p) and The standard error of the mean (o) are 56 and 2 respectively.
What is normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
According to question:(a) The mean of the sampling distribution (p) is equal to the population mean, which is 56.
(b) The standard error of the mean (o) is calculated as the standard deviation of the population divided by the square root of the sample size. So for a sample of 36 participants:
o = 12 / √36 = 2
(c) The distribution of the sample means (p) will be approximately normal with a mean of 56 and a standard deviation of 2. To sketch this distribution with M ± 3 SEM, we would plot a normal distribution with mean 56 and standard deviation 2, and shade the region that is 3 standard errors away from the mean on either side.
This region would capture approximately 99.7% of the data if the samples were selected randomly and independently from the population.
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