Using the Empirical Rule, it is found that the interval in which approximately 978 students scored was:
A. 72 < x < 88.5.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.The percentage that 978 is of 1200 is:
978/1200 x 100% = 81.5%.
Considering the symmetry of the normal distribution, two outcomes are possible involving 81.5% of the measures:
Between one standard deviation below the mean and two above, which in the context of this problem is between 77.5 and 94.Between two standard deviations below the mean and one above, which in the context of this problem is between 72 and 88.5, which is option A in this problem.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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Solutions
2
1) f(x) = x, and the transformed version of the function, g(x)
=
f(2(x + 1)) - 10
Answer:
Step-by-step explanation:
its 6
please help me with this question thank you
Answer:
2): x - $31 = $69
Step-by-step explanation:
See attached worksheet. The derivation of the answer, x - $69 = $31 (then x = $100) is shown. Convert the written question into an equation: If x is the amount given the cashier, then once $69 is subracted, Lemon receives $31:
x - $69 = $31
This can be rearranged to: x - $31 = $69, the second answer option. Other options have errors, noted by the red circles. There are no reasons that inequalities are involved, and seemingly random values of $61 and $30 have no relationship to the problem.
Answer:
B) Let x = amount paid to cashier
x - $31 = $69
x = $100
Step-by-step explanation:
We want to determine the amount Lemon paid the cashier. Therefore, the unknown variable is:
Let x = the amount he paid the cashier.If Lemon received $31 in change, then the amount he paid the cashier less the change is equal to the cost of the walnuts:
x - $31 = $69To solve the equation, add $31 to both sides:
x - $31 + $31 = $69 + $31x = $100Therefore, the amount Lemon paid the cashier was $100.
Are the following expressions equivalent? How do you know?
-2(x-1)+3(x+2) and x+8
Yes, these expressions are equivalent.
What are equivalent expressions?Expressions that are equivalent do the same thing even when they have distinct appearances.
When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
We may be given equations with algebraic expressions on both sides in some situations.
The two expressions on either side of the equation must be comparable in order for the equation to hold true for all values of the variable. F
According to our question-
-2(x-1)+3(x+2)
further solving gives;
x+8
Hence, Yes, these expressions are equivalent.
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How many congruent triangles can be made by joining the midpoints of the sides of triangle?
It is proved that a triangle is divided into four congruent triangles by the line segments connecting the middle points of its sides.
What are triangle?A triangle in geometry is a three-sided polygon with three edges and three vertices.
The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.
This characteristic is known as the triangle's angle sum property.
If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.
In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.
A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.
The vertex is the intersection of two straight lines. The triangle therefore has three vertices.
Hence, It is proved that a triangle is divided into four congruent triangles by the line segments connecting the middle points of its sides.
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Determine whether quadrilateral ABCD is a rhombus, a rectangle, a square, or none. Select all that apply. Explain. A(−9, 1), B(2, 3), C(12, −2), D(1, −4)
The quadrilateral ABCD indicates that it is a rhombus.
What is rhombus?A quadrilateral with four equal-length sides is known as a rhombus in plane Euclidean geometry (plural rhombi or rhombuses). Another name for this object is an equilateral quadrilateral because all of its sides are equal in length.
The rhombus is frequently referred to as a "diamond" after the diamonds suit in playing cards, which resembles the projection of an octahedral diamond, or as a "lozenge," though the former term is occasionally used to refer specifically to a rhombus with a 60° angle which some authors refer to as a calisson after the French sweet , and the latter term is occasionally used to refer specifically
Lets mark the given points onto a graph
As you can see in the graph,
The points given for quadrilateral ABCD indicates that its is a rhombus
As, All sides are equal
opposites sides are parallel
Thus, The quadrilateral ABCD indicates that it is a rhombus.
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How do you know if a set of ordered pairs is a function?
The set of ordered pair (x,y) is a function If each value of x has exactly only one corresponding value of y .
What are Function ?
The Function is defined as a relation that associates each element 'a' from a non empty set A to at least a single element 'b' from another non-empty set B.
For Example : Consider the ordered pairs , F = [tex][(0,4) , (2,3)][/tex] ;
the element 0 has the image as 4 , and the element 2 has the image as 3 .
So , we can see that , the each value of x has exactly only one corresponding value of y .
Therefore , the given ordered pair can be considered as a function .
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Which of Newton's Laws explain why the table moves at 0.25 m/s/s when you push on it
Answer:
First Newton's Law of motion
Step-by-step explanation:
a body will remain in it's constant motion or at rest unless acted upon by an external force.
Lat Friday Scott had $26. Over the weekend he received ome money for babyitting. He now ha $39. How much money did he receive?
Scott receive 39-26= 13 dollar when Lat Friday Scott had $26. Over the weekend he received ome money for babyitting. He now ha $39.
Money is defined as something that serves as a medium of exchange.
Money has three functions that distinguish it from the rest of the assets: 1) It is a means of change; 2) It is a unit of account; and 3) It is a store of value.
1.- MEANS OF PAYMENT OR CHANGE: basically, it consists of the use of money to make any type of transaction, thus facilitating the exchange of goods, products and services. Deliver one thing for another.
2.- ACCOUNT UNIT: this fulfills the function of determining the units of value, or prices, that the goods, products and services have. It is related to the prices.
3.- DEPOSIT OF VALUE: it consists of being able to buy something in the future. Money has the capacity to remain stable over time, which allows a person who has a capital today to invest it in the following months, or even years
Lat Friday Scott had $26.
Over the weekend he received ome money for babyitting.
He now ha $39.
Scott receive 39-26= 13 dollar
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Taub is a high school basketball player. In a particular game, she made some three point shots and some two point shots. Taub made a total of 11 shots altogether and scored a total of 30 points. Graphically solve a system of equations in order to determine the number of three point shots made, x, and the number of two point shots made, y.
john is making a poster for safety awareness week. His poster has 2 sides of equal length. Which math words and numbers are important in this problem
Answer:
2 sides of equal length meaning the poster is a rectangle
Find the volume of a pyramid with a square base, where the perimeter of the base is 12. 8\text{ m}12. 8 m and the height of the pyramid is 12. 5\text{ m}12. 5 m. Round your answer to the nearest tenth of a cubic meter.
A pyramid with a square base has a volume of 42.67 cubic meters.
What is perimeter?A perimeter is a closed route that covers, surrounds, or outlines a two-dimensional form or length. The circumference of a circle or an ellipse is its perimeter. There are various practical applications for calculating the perimeter. The perimeter of a shape is the distance around its edge. A shape's perimeter is always computed by summing the lengths of each of its sides. The perimeter of a thing is the distance surrounding it. Your house, for example, has a fenced-in yard. The perimeter of the barrier is its length.
Here,
perimeter=12.8 m
side=12.8/4
=3.2 m
volume=1/3*3.2²*12.5
=1/3*128
=42.67 m³
The volume of a pyramid with a square base is 42.67 m³.
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Monsieur le Gacy supports Paris St Germain Football Club. He went to twenty games last season.
They either played their matches at home or away.
• 60% of the games he attended were at home,
●
. The team won 2/3 of the home games,
They won 50% of all games Monsieur le Gacy attended.
●
How many games of the twenty did they win away from home?
The number of games that the team won away from home is given as follows:
2 games.
How to obtain the number of wins away from home?The number of games that the Paris Saint Germain team won away from home is obtained applying the proportions given in the context of this problem.
60% of the 20 games he attended were at home, hence 40% of the games were away games, hence the number of away games attended by Monsieur is given as follows:
0.4 x 20 = 8 games.
The team also won 2/3 of the home games, hence the number of wins at home is given as follows:
2/3 x 12 = 8 games.
They won 50% of all games Monsieur le Gacy attended, hence the number of wins is given as follows:
0.5 x 20 = 10 wins.
The wins are then divided as follows:
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Nathan bought a wallet for 5% off its full price. What was the full price of the wallet if nathan paid $17. 67 before sales tax?.
The full price of the wallet that Nathan bought before the discount is $18.60
In this case, we are given that:
The total price after the discount = $17.67
Let’s assume that the full price of the wallet is X
The discount = 5% off = 0.05 X
We can find the full price by using this following formula:
Full price – discount price = total price after discount
X – 0.05X = 17.67
0.95X = 17.67
X = 17.67 : 0.95
X = 18.6
Therefore, the full price of the wallet before the discount is $18.6
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PLEASE PLEASE HELP ME!!! Question
Let f(x)=8x. The graph of f(x) is transformed into the graph of g(x) by a vertical stretch of 4 and a translation of 7 units down.
What is the equation for g(x)?
Enter your answer by filling in the box.
g(x)=
the equation for g(x)= 32x-7
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
EXPLANATION
We want to find the equation for g(x).
First, the function is stretched vertically by a factor of 4. This means that the function changes as follows:
f(x)→4f(x)
Therefore, the function becomes:
4(8x)
=32x
Then, it is translated 7 units down. This means that the function changes as follows:
f(x)→f(x)-7
Therefore, the equation for g(x) is:
g(x)=32x-7
Hence, the equation for g(x)= 32x-7.
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2) You go out to breakfast and order a meal that costs $7.24
and a coffee that costs $2.65. You want to leave a 15% tip.
How much will you leave for a tip?
Amount is paid for a tip = $1.48 that is 15% of the total cost.
What is tip?
Amount of money paid by the customer himself to express the gratitude.
towards the hospitality made by the certain service sector.
How much you leave for tip?cost of meal = $7.24
cost of coffee = $2.65
total cost including meal and coffee = $(7.24+2.65) = $9.89
tip is given by customer 15 % of total cost
the amount of tip paid = 15/100×9.89 =$1.48
The customer paid $1.48 along with total cost $9.89.
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Point A has coordinates A(2,1). What is the image after a dilation centered at the origin with a scale factor of 2?
The image of Point A, after a dilation which is centered at the origin with a scale factor of 2 is ( 4, 2 )
How to find the dilated coordinates ?When a dilation is centered at the origin with a scale factor of 2, the coordinates of a point are multiplied by 2.
Given a point A(2,1) , the image of point A after a dilation centered at the origin with a scale factor of 2 is:
Point X :
= 2 x 2
= 4
Point Y:
= 1 x 2
= 2
So the image of point A after the dilation is the point A' with coordinates ( 4, 2 )
It's important to note that dilation either expands or contracts the figure and the center of dilation is the fixed point around which the expansion or contraction occurs.
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"Complete the table of values and answer these questions. Which function has the greater rate of change between 0 and 1? Which function has the greater rate of change between 1 and 2? Which function has the greater rate of change between 0 and 2?"
1. The complete table is:
x | f(x) | g(x)
0 1 0
1 3 3
2 9 6
2. g(x) has the greater rate of change between 0 and 1 is: g(x).
3. f(x) has the greater rate of change between 1 and 2 is: f(x).
4. f(x) is greater.
How to Find the Rate of Change between an Interval?The rate of change = f(b) - f(a) / b - a.
Given the following functions as:
f(x) = 3^x
g(x) = 3x
1. Complete the table by plugging in each of the values of x:
x | f(x) | g(x)
0 f(0) = 3^0 = 1 g(0) = 3(0) = 0
1 f(1) = 3^1 = 3 g(1) = 3(1) = 3
2 f(2) = 3^2 = 9 g(2) = 3(2) = 6
2. Rate of change between 0 and 1:
a = 0
b = 1
For function f(x) = f(b) - f(a) / b - a = 3 - 1 / 1 - 0 = 2
For function g(x) = g(b) - g(a) / b - a = 3 - 0 / 1 - 0 = 3
The function with the greater rate of change between 0 and 1 is: g(x).
3. Rate of change between 1 and 2:
a = 1
b = 2
For function f(x) = f(b) - f(a) / b - a = 9 - 3 / 2 - 1 = 6
For function g(x) = g(b) - g(a) / b - a = 6 - 3 / 2 - 1 = 3
The function with the greater rate of change between 1 and 2 is: f(x).
4. Rate of change between 0 and 2:
a = 0
b = 2
For function f(x) = f(b) - f(a) / b - a = 9 - 1 / 2 - 0 = 4
For function g(x) = g(b) - g(a) / b - a = 6 - 0 / 2 - 0 = 3
The function with the greater rate of change between 0 and 2 is: f(x).
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Write the equation of the line in standard form:
4y=2x+9
2x - 4y + 9 is the equation of the line in standard form.
What is standard form?Ax + By=C is the typical form for linear equations involving two variables. A linear equation in standard form is, for instance, 2x + 3y=5.
Finding both intercepts of an equation in this format is fairly simple (x and y). When resolving systems of two linear equations, this form is also really helpful.
Lets write the equation of the line in standard form:
4y=2x+9
We know that standard form = Ax + By=C
⇒ 4y = 2x + 9
⇒ 2x - 4y + 9
Here,
Ax = 2x
By = -4x
C = 9
Thus, 2x - 4y + 9 is the equation of the line in standard form.
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Juan bought 7.8 pounds of grapes for 2.85 per pound how much did Juan spend on grapes
Juan needs to spent 22.23 to buy 7.8 pounds of seedless red grapes.
What is a unitary method?A unitary method is a mathematical method for calculating the value of a single unit and then multiplying it by the number of given units.
Given that:
Juan purchased 7.8 pounds of seedless red grapes for $2.85 per pound.
The cost of the unit pound is already given here. To get the cost of 7.8 pounds, multiply the cost of the unit pound by the number of pounds, i.e.
= (7.8×2.85)
= 22.23.
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Which of these numbers lies between 8885 and 9885?
a}8875
b}8895
c} 9895
d}9975
Answer:
b
Step-by-step explanation:
The interactions of snakes and mice make up which ecological unit?
A. species
B. community
C. biome
D. population
Answer:
The interactions of snakes and mice make up which ecological unit?
A. species
B. community
C. biome
D. population
Step-by-step explanation:
The best answer here is community. Please see the explanation below.
Ecological UnitsA species is frequently defined in biology as the biggest group of creatures in which any two individuals of the appropriate sexes or mating types may create viable offspring, usually by sexual reproduction. Ex: "A rattlesnake and a cobra are two different species of a snake." OR "The male and female cows we found are the same species."A community, also known as a biological community, is a group or association of populations of two or more distinct species that occupy the same geographical region at the same time. Ex: "There are snakes, mice, and trees in the forest community."A biome is a community of plants and animals that live naturally in a certain region and have common traits. Ex: "The continent of Africa has rich biological diversity because it contains nine biomes."A population is the whole number of inhabitants occupying an area of the same species. Ex: "Ecologists are studying the decline of the red panda population in relation to ecotourism and zoos."Please let me know if this helped!!!
How do I convert 2D to 3D in Autocad 2022?
To convert 2D to 3D in AutoCAD 2022, install Microsoft 3D Builder.
Transform your 2D ideas and designs into 3D models with Autodesk® software. Autodesk software not only enables you to digitally design, visualize and simulate your most complex ideas, but it also eases the transition from 2D to 3D design and engineering processes.
Steps are:
1. Install Microsoft 3D Builder.
2. Uploading an image and converting it to 3D.
3. Which conversion method to choose.
4. Level selection and smoothing.
5. Scale your image to the size you want.
6. Save the image.
7. Export the 3D model for 3D printing or other 3D applications.
8. Rendering the 3D model.
9. Share the 3D model with others.
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the comparison of two quantities with different units is called a
The comparison of two quantities with different units is called a ratio and proportion. A ratio that specifically compares two quantities measured in different units.
Comparing amounts is done using a ratio. A ratio demonstrates how many times one amount fits inside another or how much larger one amount is than another.
If I need to mix some cement, I would add two parts cement to four parts sand. The two numbers are both portions of the entire. Hence, the 2:4 ratio (6 parts in total). The written version is crucial; 4:2 would produce a different blend.
Ratios are expressed in their most basic form. There are five green and fifteen red dots in the figure on the right. The ratio is 15:5, but like with fractions, this can be boiled down to its most basic form.
If you look at the relationship between the numbers 15:5 as is 3:1, you can see that 3 is multiplied by 5 to obtain 15 and that 1 is multiplied by 1 to get 5. The ratio, as we can see in the image, is also 3:1.
Therefore,
The comparison of two quantities with different units is called a ratio and proportion. A ratio that specifically compares two quantities measured in different units.
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Find the measure of angles T and V.
Answer:
m<T = 36*
m<V = 54*
Step-by-step explanation:
2x + 90 + 3x = 180
5x + 90 = 180
5x = 90
x = 18
<T = 2x = 18 * 2 = 36
<V = 3x = 18 * 3 = 54
Hope this helps!
How do you find the end behavior of a graph with Asymptotes?
To find the equation of an asymptote from a graph, look for the line that the graph approaches but never touches. Then calculate the slope of the line and the y-intercept. This will give you the equation of the asymptote.
How to find an asymptote?To find the equation of an asymptote from a graph, look for the line that the graph approaches but never touches. Asymptotes usually run parallel to the x-axis or the y-axis, so look for a straight line that is horizontal or vertical.
Once you have identified the line, calculate the slope of the line and the y-intercept. The slope of the line is the ratio of the change in the y-values to the change in the x-values.
Once you have found the slope and the y-intercept, you can use the slope-intercept form of a line to find the equation of the asymptote: y = mx + b, where m is the slope and b is the y-intercept. This will give you the equation of the asymptote.
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rewrite (-4)^2/7 in radical form
The expression (-4)^2/7 can be written as seventh root 16
What are radicals?The √ symbol that is used to denote square root or nth roots. A radical expression is an expression containing a square root. Radicand is a number or expression inside the radical symbol. Radical equation is an equation containing radical expressions with variables in the radicands.
For example, x^2/3, 3 is the root while 2 is the power of x . therefore the x^2/3 can be written as cube root of x squared.
Similarly in (-4)^2/7 2 is the power of (-4), this means (-4)² = 16
7 is the root of (-4)²
Therefore (-4)^2/7 can be written in radical for seventh root 16.
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which statement best describes the liquid state of matter
a) it has define shape but indefinite volume
b) it has define shape and definite volume
c) it has indefinite shape and indefinite volume
d) it has indefinite shape but define volume
D) it has indefinite shape but define volume
Liquids take shape of whatever container you put them in but flow freely if un-restrained, it has a volume because it doesn't grow or disappear unless acted upon
Solve for x:
1. 3 (x-12) =15
2. -5 (-2×+10) =10
3. 8(6-4x) = 12
4. 3 (2+6X) = 18
Step-by-step explanation: hi I also need help with this when the answer is posted pls let me know
Answer:
1. 17
2. 6
3. (9/8)
4. (2/3)
Step-by-step explanation:
1. 3(x-12) =15
3x-36=15
3x = 51
x = 17
2. -5(-2×+10) =10
10x - 50 = 10
10x = 60
x = 6
3. 8(6-4x) = 12
48 -32x = 12
-32x = -36
x = (-36/-32)
x = (9/8)
4. 3(2+6X) = 18
6 + 18x = 18
18x = 12
x=(12/18)
x = (2/3)
A bushel of apples weighs about 42
pounds.
There are 4 pecks in a bushel. It takes
2 pounds of apples to make one pie. How
many pies can you
make with one peck of
apples?
Answer:5
Step-by-step explanation: 42 divided by 4 = 10.5
10.5 divided by 2 = 5.25
round it and you get 5 pies per peck of apples
if triangle KLJ ~ to triangle VWU, find the value of x. (LK=25, KJ=4x-23, UV=2x+2, WV=20)
In the given diagram, using similar triangles theorem, the value of x is 17
Similar triangle: Calculating the sides of a triangleFrom the question, we are to determine value of x in the given diagram
From the similar triangles theorem, we can write that
JK/KL = UV/VW
From the given information,
JK = 4x - 23
KL = 25
UV = 2x + 2
VW = 20
Thus,
(4x - 23)/25 = (2x + 2)/20
20(4x - 23) = 25(2x + 2)
80x - 460 = 50x + 50
80x - 50x = 50 + 460
30x = 510
x = 510/30
x = 17
Hence, x is 17
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