Using z-scores, it is found that due to the higher z-score, Luna did better on the exam.
What are z-scores?The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.From the two bullet points, it is found that the student who did "better" is the one whose grade has the higher z-score.
For Hazel, the parameters are given as follows:
[tex]X = 93, \mu = 80, \sigma = 8[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (93 - 80)/8
Z = 1.625.
For Luna, the parameters are given as follows:
[tex]\mu = 68, X = 40, \sigma = 15[/tex]
Hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
Z = (68 - 40)/15
Z = 1.87.
Due to the higher z-score, Luna did better on the exam.
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10. Write an algebraic expression that represents the perimeter of the figure shown below.
Simplify completely. Show your work.
3x
X
8x
4x
10x
2x
The perimeter of the given figure is 56x.
What do we mean by perimeter?A closed path that encompasses, encircles, or outlines a one-dimensional length or a two-dimensional shape is called a perimeter. A circle's or an ellipse's circumference is referred to as its perimeter. There are numerous uses in real life for perimeter calculations.So, perimeter: sum of all the sides
Then, according to the given figure:
Algebraic expression: 3x + x + 8x + 4x + 10x + 2x + (10x + 8x + 3x) + (x + 4x + 2x)28x + (10x + 8x + 3x) + (x + 4x + 2x)28x + 21x + 7x49x + 7x56xTherefore, the perimeter of the given figure is 56x.
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An isolated agricultural country has two distinct regions: a lowland plain and an upland of rugged hills. On one unit of land on the PLAIN, a farmer can raise 10 bushels of grain or graze 10 sheep. On one unit of land in the HILLS, a farmer can raise 2 bushels of grain or graze 4 sheep.
Determine which region has the absolute advantage for sheep production. Explain your answer.
Because food grows more quickly in the hills when exposed to heat and rain rather than sunlight all day. Then for 1 sheep 1 bushel is required in the hills.
What are statistics?
The practice or science of organizing and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.
Given that a remote agricultural nation is divided into two distinct geographic areas: a lowland plain and an upland of rough hills. A farmer can grow 10 bushels of grain or pasture 10 sheep on one unit of land on the plain. A farmer in the hills can pasture 4 sheep or grow 2 bushels of grain on one unit of land.
As opposed to being exposed to sunlight all day, food develops more quickly in the hills when it is exposed to heat and rain.
For uphill = 10 sheep = 10 bushels
For uphill = 1 sheep = 1 bushels
For down plain = 4 sheep = 2 bushels
For down plain = 1 sheep = (1 / 2 ) bushels
Therefore, then for 1 sheep 1 bushel is required in the hills.
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The marching band needs to create rows for its performance. There are 48 instruments and 32 flag bearers. Only one type of performer can be in each row. What is the maximum number of performers in each row so that all the rows are equal in length?
48
32
16
2
The maximum number of performers in each row so that all the rows are equal in length is C. 16.
How to calculate the value?It should be noted that there are 48 instruments and 32 flag bearers and only one type of performer can be in each row.
The maximum number of performers in each row so that all the rows are equal in length will be the highest common factor between both numbers.
It should be noted that the highest common factor between 32 and 48 is 16
Therefore the correct option is C.
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The probability density of a random variable X is given in the figure below. The random variable is uniformly distributed between 0 and 2. From this density, find the probability that X is at least 0.48.
The probability that X is at least 0.48 given the information about the density of a random variable X is 0.76.
How to calculate the probability?Given that x is uniformly distributed between 0 and 2.
Therefore, the probability density function:
f(x)= 1 / (b-a) = 1 / (2-0)
= 0.5
This will be illustrated as:
P(X<=x)=(x-a)/(b-a)=(x-0)/(2-0)=x/2
Now, we have to find:
P(x >= 0.48)
= 1 - P(x<=1.68)
= 1-(0.48 / 2)
= 1 -0.24
= 0.76
Therefore, the probability that X is at least 0.48 given the information about the density of a random variable X is 0.76.
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There's a roughly linear relationship between the number of times a species of cricket will chirp in one minute and the temperature outside. For a certain type of cricket, this relationship can be expressed using the formula T=0.33c+38T=0.33c+38, where TT represents the temperature in degrees Fahrenheit and cc represents the number of times the cricket chirps in one minute. What could the number 38 represent in the equation?
The temperature at which the crickets do not chirp is represented by the number 38, which serves as the y-intercept of the linear equation.
The equation is as follows:
T = 38 + 0.3*c
The temperature is denoted by T, while the number of chirps in a minute is denoted by c.
We want to know what the number 38 means.
Take c = 0 to demonstrate this as there are no chirps.
Then:
T = 38 + 0.33*0 = 38
T = 38
This is the temperature where crickets cease to chirp.
The temperature at which the crickets do not chirp is represented by the number 38, which is the y-intercept of the linear equation.
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Find the cost of 12¼ m of cloth, if 1 m of cloth costs rupees 17⅓
The cost of 12¼ m of cloth is 212.3 rupees.
What is Ratio?A ratio is defined as a relationship between two quantities, it is expressed as one divided by the other
We have been given that 1 m of cloth costs rupees 17⅓.
We have to determine the cost of 12¼ m of cloth.
Let the cost of 12¼ m of cloth would be x rupees
We can write this as a ratio as
1 m : rupees 17⅓ = 12¼ m : x rupees
[17⅓ = 52/3 = 17.3 and 12¼ = 49/4 = 12.25]
1 m : 17.3 rupees = 12.25 m : x rupees
⇒ 1 /17.3 = 12.25 /x
⇒ (1)(x) = (12.25 )×(17.3)
⇒ x = 212.3
Therefore, the cost of 12¼ m of cloth is 212.3 rupees.
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Explanation? I’ll give brainliest
Answer:
Step-by-step explanation:
you add all of that up and you get your answer then you subtract that answer to 100 then that’s your answer.
Answer:
First what you want to do is start with the socks.
Socks cost $9.00 so if he is buying 3 pair you would multiply by 3.
9 times 3 is 27. = $27
He bought 2 belts and the belts cost $10.00 so you would multiply that by 2.
10 times 2 is 20. = $20
He bought 1 hoodie which amounts to $29.99 and a pair of shoe laces that amounts to $1.50.
Now what you do is add all thew prices together.
$27 + $20 + $29.99 + $1.50 = $78.49
Final, since he is paying with a hundred dollar bill you want subtract that from the total amount.
$100 - #78.49 = $21.51
So he would get back a total of $21.51.
Step-by-step explanation:
Hope it helps! =D
The first week of January, there are
49 dogs and 28 cats in an animal shelter.
Throughout the month, the ratio of dogs
to cats remains the same. The last week
of January, there are 20 cats in the
shelter. How many dogs are there?
To pass a course with a C grade, a student must have an average of 70 or greater. A students grades on three test are 60,71, and 63. Find what score the student must get on the next test to get a C average or better
The score the student must get on the next test to get a C average or better is 86.
How to calculate the average?From the information given the pass a course with a C grade, a student must have an average of 70 or greater and students grades on three test are 60,71, and 63.
The next score will be calculated as x.
60 + 71 + 63 + x = (70 × 4)
194 + x = 280
x = 280 - 194
x = 86
Therefore, the next score must be 96.
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A quarterback is sacked for a loss of 7 yards. On the next play, his team loses 12 yards. Then the team gains 5 yards
on the third play. Write an expression to represent the word problem. What is the total number of yards lost or gained?
The total number of losses is 14.
What are expressions?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions.So, let the total number of lost and gains be 'x'.
Then, the expression:
-7 - 12 + 5 = x- 19 + 5 = x-14 = xSo, x has a value that is negative so it is a loss.Therefore, the total number of losses is 14.
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100 POINTS!!!!
An airplane travels at 145 km/hr for 2 hours in a direction of 220 degrees. At the end of this time, how far south of the airport is the airplane?
Note: Directions are given in degrees clockwise from north.
Answer:
53.83 km.
Step-by-step explanation:
53.83 km.
give the person above me brainliest
The average American woman self-reports consuming 1.785×103 kcal/day. For a 147.0 lb woman, express this value in joules per second per kilogram of body mass (watts per kilogram).
Energy consumed equals 0.133 W/kg
What is energy?
Energy is described as the "capacity to accomplish work, which is the ability to apply a force that causes an object to move." Despite this perplexing terminology, the meaning is straightforward: energy is just the force that causes objects to move. Potential energy and kinetic energy are the two forms of energy.
Weight = 147 lb = 66.68 kg (since, 1 lb = 0.453 kg)
Energy consumed = 1.785 x 103 kcal/day
In Watts = 1.785 x 103 x 0.0484 = 8.9 W/day
Energy consumed watts per kilogram = 8.9/66.68 = 0.133 W/kg
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A bag contains 10 red, 5 yellow, and 6 blue marbles. What is the probability of pulling out one blue marble and then one red marble without replacing the first blue marble?
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
How to determine the probability?The given parameters are
Red = 10
Yellow = 5
Blue = 6
The probability of pulling out one blue marble and then one red marble without replacing the first blue marble is
P = P(Blue) * P(Red Having selected Blue)
So, we have
P = 6/21 * 10/20
Evaluate
P = 1/7
Hence, the probability of pulling out one blue marble and then one red marble without replacing the first blue marble is 1/7
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What is the result, when the decision is to reject a null hypothesis
The underlying assumption is that the observed difference is just the result of chance. It is feasible to determine the probability that the null hypothesis is correct using statistical testing.
What is the null hypothesis?The observed difference is thought to be the sole product of chance, which is the underlying premise. Statistical testing can be used to calculate the likelihood that the null hypothesis is true.
As part of hypothesis testing, the null hypothesis is a made-up assertion that is intended to see if it can be rejected. It is incorrect to draw the conclusion that a result supports the null hypothesis when it is not extreme enough to do so.
This is because the research hypothesis is true, but the result in the particular sample was not extreme enough to enable the null hypothesis to be rejected.
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The given signs denote the following operations/relationships:
A+B means A is greater than B.
A-B means A is less than B.
A-B means A is greater than or equal to B.
A*B means A is not equal to B.
A/B means A is equal to B.
Which of the two conclusions I and II is/are definitely true based on the information
provided?
Statements:
E*F, F/G, G-H
Conclusions:
1. E*G
II. F-H
Based on the given information, the EFG GH Findings.
Refer to the symbols and their associated meanings below.
The symbols shown signify the following.
operations/relationships:
A+B denotes that A is bigger than B.
A-B indicates that A is less than B.
A is more than or equal to 8 when A=B.
A B denotes that A and B are not equal.
A = B is expressed as A/B.
Which of the two conclusions is unquestionably true?based on the details offered?
Statements: EFG GH Findings
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slope-intercept form? proper fractions, and improper
Answer:
y = 3x
Step-by-step explanation:
slope intercept form is y = mx + b with m as the slope and b as the y-intercept
to find the slope you can see where the line intersects at (1, 3) and (0,0) If you look at the graph you count up three spaces over one so the slope is 3
since the y-intercept intersects at (0,0) The y-intercept is 0 and you do not have to add that to the answer
Answer:
y=3x I think if not sorry
Step-by-step explanation:
have great evening,day,night,morning!
In a math class of 48 students, eight students are studying less than
one hour a night. Six students claim they never study. The rest say they
study more than one hour a night. What fraction of the students are
studying more than one hour each night? (2 marks)
Type a sentence answer in the field provided. Then, submit a picture of
your work to be graded by the instructor.
Fraction of the students are studying more than one hour each night is 17/24.
What is fraction?An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction.
Total student in the class = 48
students studying less than 1 hour = 8
students that don't study at night = 6
students studying more than one hour a night = 48 - (8+6) = 34
fraction of the students studying more than one hour -
= 34/48
= 17 / 24
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Let X be the number of students who show up for a professor's office hour on a particular day, pmf of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15, what is the probability at least 2 students show up? I tried doing P(p(1) u p(2)) = P(p(1)) + P(p(2)) - (P(p(1) n p(2))) what would be the correct formula?
The probability of at least 2 students showing up is .70 or 70%
Let X be the number of students who show up for a professor's office hour on a particular day, probability of X is p(0) = 0.10, p(1) = 0.20, p(2) = 0.25, p(3) = 0.30 and p(4) = 0.15
If we add the probability of 1 student showing up, 2 students to show up, 3 students to show up, and 4 students showing up
We get 0.10+ 0.20+ 0.25+ 0.15 =1
As the sum of these individual 4 possibilities is 1 that means these are the only possibilities to exit
Now we need to find out the probability of at least 2 students showing up which means the probability of two or more students showing up
Which can be written as
p(≥2) = p(2) + p(3) + p(4)
p(≥ 2) = 0.25+0.30+0.15
p(≥2) = 0.70
Hence, the probability of at least 2 students showing up is .70 or 70%
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Edwin needs to buy a car, a truck, and a motorcycle for his shipping business. He wants the car to be red or yellow; the truck to be black, white, or silver; and the motorcycle to be green, blue, or orange. Help pls
Answer:
The answer is that there are 18 different combinations of vehicles.
Step-by-step explanation:
We are given that the number of vehicles for his business = 3.
The vehicles are a car, truck, and motorcycle.
So we know that there is two possibilities for car: Red and yellow.
Three possibilities for truck: Black, white, and silver.
Three possibilities for motorcycle: Green, blue and orange.
So now we can make an equation of the different combinations of vehicles that Edwin have to chose from.
So 3 x 3 x 2 = 18
Therefore, there are 18 different combinations of vehicles.
I hope this helps, have a good day!! :D
Sam and Bethan share £54 in the ratio 5:4 how much does each person get
Answer:add 5 and 4, you get 9. divide 54 by 9, and you get 6. this is because for every 5 sam gets bethan will get 4. if you add, that, you will get the total amount for 1 share.
Step-by-step explanation:
Answer:
Sam gets £30
Bethan gets £24
Step-by-step explanation:
Since they split the money in a ratio of 5:4, that means for every 5 parts of the money that Sam gets, Bethan gets 4 parts. The total of 5 parts and 4 parts is 9 parts.
To find how much each part is, we divide £54 by 9.
£54/9 = £6
Each part is £6.
Sam gets 5 parts: 5 × £6 = £30
Bethan gets 4 parts: 4 × £6 = £24
Assume the cards are drawn sequentially and without replacement. In how many ways can 5 spades be drawn from a standard deck of 52 cards?
The number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement = 154440
In this question we have been given a standard deck of 52 cards.
We need to find the number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement.
We use the permutation formula.
We know that the number of ways to choose r elements from a set of n distinct objects where order does matter and replacements are not allowed.
^n(P_r) = n! / (n - r)!
We know that, in a standard deck of 52 cards, there are 13 spade cards.
So, n = 13
5 spades to be drawn
So, r = 5
Using the formula of permutation,
^13(P_5)
= 13! / (13 - 5)!
= 154440
Therefore, the number of ways 5 spades can be drawn from a standard deck of 52 cards without replacement = 154440
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given then functions: f(x)=4x+9 and g(x)=7x-5
Part 1
[tex](f+g)(x)=f(x)+g(x) \\ \\ =4x+9+7x-5 \\ \\ =11x+4[/tex]
Part 2
[tex](f-g)(x)=f(x)-g(x) \\ \\ =(4x+9)-(7x-5) \\ \\ =4x+9-7x+5 \\ \\ =-3x+14[/tex]
Part 3
[tex](f \cdot g)(x)=f(x) \cdot g(x) \\ \\ =(4x+9)(7x-5) \\ \\ =28x^2-20x+63x-45 \\ \\ =28x^2+43x-45[/tex]
Part 4
[tex]\left(\frac{f}{g} \right)(x)=\frac{f(x)}{g(x)} \\ \\ =\frac{4x+9}{7x-5}[/tex]
Francesca wants to
convert 1 cubic foot to cubic centimeters. Use
what you know about customary units to explain
how she can do this.
The value of 1 Cubic Foot is said to be 28316.85 Cubic Centimeters.
A cubic foot is a unit used to measure the volume of a cube with one foot-long sides. It is a unit to measure a unit volume and is symbolically represented as [tex]ft^{3}[/tex]. It is primarily used in the customary and imperial systems of measurement in the United States.
The volume of a cube with sides that are each one centimeter long is measured in cubic centimeters. It is a unit for measuring a unit volume that is symbolically represented as [tex]cm^{3}[/tex] and is typically used to measure lower volumes.
Conversation: The value of 1 cubic foot is approximately equal to 28316.85 cubic centimeters. So, to convert cubic feet to cubic meters, we have to multiply the given foot value by 28316.85 cubic centimeters.
Hence 1 Cubic Foot = 28316.85 Cubic Centimeters.
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A circle has a circumference of 25. Find the length of an arc whose central angle is 50
Answer:
19.625 units
Step-by-step explanation:
[tex]\text{ Arc length } = 2 \pi r \times \frac{\theta}{360}[/tex]
Substituting the given values,[tex]\begin{gathered}\text{Arc Length } = 2\times 3.14 \times 12.5 \times \frac{50}{360}\\\\\text{Arc length } = 78.5 \times \frac{1}{4}\\\\\text{Arc Length } = 19.625\end{gathered}[/tex]
Thus length of arc is 19.625 units
Type an equation for the following pattern.
Answer:
y=28x+0
Step-by-step explanation:
In each row of the table, y is 28 times the value of x.
PLS PLS PLS PLS PLS PLS PLS PLS HELP ME write the ratios 25:4 and 45:10 as a complex fraction
Answer: =−13 1/3
Step-by-step explanation:
Write an expression that represents the area of the rectangle below.
2x 1
X-6
The expression that represents the area of the given rectangle is: 2x² - 11x - 6.
How to Find the Area of a Rectangle?The area of a rectangle is the product of its width and its length. A rectangle's area is calculated using the formula below:
Area = (length)(width)
Given the following:
Length of the rectangle = 2x + 1
Width of the rectangle = x - 6
Therefore, substituting these into the formula, we have:
Area of the rectangle = (2x + 1)(x - 6)
Area of the rectangle = 2x(x - 6) +1(x - 6)
Area of the rectangle = 2x² - 12x + x - 6
Combine like terms
Area of the rectangle = 2x² - 11x - 6
Therefore, the expression that represents the area of the given rectangle is: 2x² - 11x - 6.
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The rectangular floor of a classroom is 30 feet in length and 21 feet in width. A scale drawing of the floor has a length of 10 inches. What is the area, in square inches, of the floor in the scale drawing? this is for a lot of points and please answer correctly or i will be reporting.
The width of the drawing maintaining the given scale factor will be 70.83 inches².
What is the scale factor?You must specify the extent of the shape's enlargement when describing one.
The scale factor is the ratio between two dimensions that determines how big or tiny a given figure is.
The length of the floor in actuality = 30 feet
⇒ 30 × 12 = 360 inches
Length of the floor in drawing = 10 inches
Scale factor = 10/360 = 1/36
By maintaining this scale factor
Width of the floor in drawing = (21 × 12)/36
⇒ 7.083 inches
Area = length × width
Area = 10 × 7.083
⇒ 70.83 inches²
Hence "The width of the drawing maintaining the given scale factor will be 70.83 inches²".
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PLEASE HELP<33333
(A): describe in words a sequence of transformation that maps ABC to A”B”C (hint, there are two different transformations.
(B): Write an ordered pair rule for each transformation in the sequences.
one negative two and then shifted to the rights, that's the translation to the right two units.
What is the sequence of transformation?
A certain order of transformational occurrences is referred to as a transformational sequence. This indicates that more than one transformation is handled by a series of transformations, and the order in which they happen is important.its a 180 Degree Rotation.
And let's see With a 180 degree rotation.
, we can say coordinates is that X. Y. Two negative X. Negative Y.
It goes to one negative two and he goes to two negative five And c goes to 5 -2.
So if one negative two and then shifted to the rights, that's the translation to the right two units.
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Consider the statements in the table shown. Select True or False for
each statement about the sequences of transformations that can
verify that triangle ABC is congruent to triangle A'B'C'.
The sequences of transformations can verify that triangle ABC is congruent to triangle A'B'C'. which is the correct answer would be (D)
What are congruent triangles?Two triangles are said to be congruent if their corresponding sides and angles are equal.
Triangle ABC has translated 12 units to the right, followed by a reflection across the x-axis. Which is a true statement
Triangle ABC is reflected across the y-axis, followed by a translation 12 units down. Which is a false statement
Triangle ABC is reflected across the x-axis, followed by a translation of 12 units to the right. Which is a true statement
Therefore, the sequences of transformations can verify that triangle ABC is congruent to triangle A'B'C'.
Hence, the correct answer would be (D)
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