Triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:
AB || DC, as required.
What is the congruent angle?
When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal and in matching corners will be congruent.
Corresponding Parts of Congruent Triangles are Equal
AD || BC, AD = CB
Given
1 = 4
From statements 1 and 5, we can conclude that:
ACD is congruent to CAB because they are corresponding angles of parallel lines AD and BC.
If Lines are Parallel, then Alternate Interior Angles are Equal.
ACD = CAB
From statement 4, we know that angles ACD and CAB are equal because AD is parallel to BC. Therefore:
ACD = CAB
Reflexive Property of Equality
AC = AC
From statement 2, we know that segment AC is equal to itself because of the reflexive property of equality. Therefore:
AC = AC
If Alternate Interior Angles are Congruent, then Lines are Parallel.
2 = 3
From statement 3, we know that if alternate interior angles are congruent, then the lines are parallel. Therefore, since ACD = CAB (statement 4) and AC = AC (statement 2), we can apply the SAS (Side-Angle-Side) congruence theorem to triangles ACD and CAB to conclude that they are congruent.
SAS (Side-Angle-Side)
AB || DC
Hence, As a result, since triangles ACD and CAB are congruent by SAS, their corresponding sides are equal, so we have:
AB || DC, as required.
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What is an equation of the line that passes through the points (-6, 1) and (6, 7)?
Answer:y = (1/2)x + 4
Step-by-step explanation:
The equation of the line that passes through the points (-6, 1) and (6, 7) can be found using the slope-intercept form of a line. The slope m is calculated as (y2 - y1)/(x2 - x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Plugging in the values for these points gives us a slope of m = (7-1)/(6-(-6)) = 1/2.
Now that we have the slope, we can use point-slope form to find the equation of the line: y - y1 = m(x - x1). Substituting one of our points and our calculated slope into this equation gives us y - 1 = (1/2)(x + 6). Simplifying this expression gives us y = (1/2)x + 4, which is the equation of our line in slope-intercept form.
So, an equation for this line is y = (1/2)x + 4.
Answer:
y = [tex]\frac{1}{2}[/tex] x + 4
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 1 ) and (x₂, y₂ ) = (6, 7 )
m = [tex]\frac{7-1}{6-(-6)}[/tex] = [tex]\frac{6}{6+6}[/tex] = [tex]\frac{6}{12}[/tex] = [tex]\frac{1}{2}[/tex] , then
y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (6, 7 )
7 = [tex]\frac{1}{2}[/tex] (6) + c = 3 + c ( subtract 3 from both sides )
4 = c
y = [tex]\frac{1}{2}[/tex] x + 4 ← equation of line
A square wall is 81 square meters. What are the dimensions of the wall?
The wall is 9 meters long and 9 meters wide.The area of a square is equal to the length multiplied by the width.
The area of a square is equal to the length multiplied by the width. Therefore, in order to determine the dimensions of the wall, we must solve the equation 81 = l x w, where l and w represent the length and width of the wall, respectively. By dividing both sides of the equation by 9, we get that l = w = 9, meaning that the wall is 9 meters long and 9 meters wide.
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when may you want to use lower gears when driving
They should be used carefully because they can potentially increase fuel consumption and engine damage.
what is distance ?The space or length separating two points or objects is measured as distance. It is used to define the distance between objects in space or their relative position in space, and it is a fundamental idea in mathematics and physics. The distance formula, which is based on the Pythagorean theorem, is typically used in mathematics to calculate distance. In a two-dimensional coordinate system, the distance between two locations is calculated as the square root of the sum of the squares of the disparities between their x and y coordinates.
given
While travelling at slower speeds, ascending hills, or travelling down or up steep inclines, lower gears are often employed. When driving, you might want to shift into a lower gear in the following circumstances:
Driving on ice or snow Using a lower gear can provide you more traction and help you keep control of the car when driving in slick conditions.
Driving on windy roads: Using a lower gear while driving on winding roads might help you keep a steady speed and prevent the car from accelerating too quickly.
In general, when the engine needs to work harder than usual, using lower ratios might provide you greater power and control.
They should be used carefully because they can potentially increase fuel consumption and engine damage.
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What is 1. 2 x 10 ^5 in standard form?
Answer:
120,000
Step-by-step explanation:
1.2 x 10^5 in standard form is 120,000.
To convert a number from scientific notation (with a power of 10) to standard form, you simply move the decimal point to the right or left depending on the sign of the exponent.
In this case, the exponent is positive, so we move the decimal point to the right by 5 places, filling in any empty spaces with zeros. This gives us the final answer of 120,000 in standard form.
The population of a city in Arizona is 3200 in 2010. The city's population is increasing at a rate of 3% per decade. Using this information, predict the population of the city in the year 2030. Round your answer to the nearest person.
The predicted population of the city in the year 2030 is 5,780 person.
How to determine the population of the city in the year 2030?In Mathematics, a population that increases at a specific period of time represent an exponential growth. This ultimately implies that, a mathematical model for any population that increases by r percent per unit of time is an exponential function of this form:
P(t) = I(1 + r)^t
Where:
P(t ) represent the population.t represent the time or number of years.I represent the initial value of car.r represent the exponential growth rate.Years = 2030 - 2010 = 20 years.
By substituting given parameters, we have the following:
[tex]P(t) = I(1 + r)^t\\\\P(t) = 3200(1 + 3/100)^{20}\\\\P(t) = 3200(1 + 0.03)^{20}[/tex]
P(t) = 5,779.56 ≈ 5,780 person.
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if you calculated the standard deviation for a distribution of 20 scores, removed the 5 highest scores and recalculated, the value of the standard deviation would select one: a. increase b. stay the same c. decrease d. be reduced by five
Whatn the 5 highest is removed then standard deviation will decrease. (C)
The standard deviation is a measure of how spread out numbers are from the mean. Removing the 5 highest scores from the distribution of 20 scores will cause the numbers to become more concentrated around the mean, thus decreasing the standard deviation.
This is because the 5 highest scores are further away from the mean than the other numbers and by removing them, the average distance between the numbers and the mean decreases.
Mathematically, the formula for standard deviation is the square root of the sum of squared deviations from the mean divided by the number of scores minus 1.
When the 5 highest scores are removed, this means the sum of squared deviations from the mean is reduced, and since the number of scores is also reduced, the overall standard deviation value decreases.(C)
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10. Jack bought the fishing gear pictured. The
sales tax was calculated by multiplying the
total cost of the fishing gear by 0.07 and
rounding to the nearest cent. How much
did Jack pay for the fishing gear including
sales tax?
So, the total cost including sales tax is 1.07 times the cost before tax.
What is percent?Percent is a way of expressing a number as a fraction of 100. It is denoted by the symbol "%". It is commonly used to represent proportions, rates, and changes in quantity. For example, if 50 out of 100 students in a class passed an exam, the pass rate is 50%, which means that 50% of the students in the class passed the exam.
Here,
Let's say the cost of the fishing gear before tax was $X. Then, the sales tax would be 0.07*X. To get the total cost, we add the cost before tax and the sales tax:
Total cost = cost before tax + sales tax
Total cost = X + 0.07X
Total cost = 1.07X
So, the total cost including sales tax is 1.07 times the cost before tax. If you know the cost before tax, you can calculate the total cost by multiplying it by 1.07.
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the time needed to complete a final examination in an introductory microeconomics mba course at the college of williamsburg follows a normal probability distribution with a mean of 80 minutes 0 seconds and a standard deviation of 10 minutes 0 seconds. 1. (10 points) what is the probability that a student will complete the exam in between 60 minutes 0 seconds and 75 minutes 0 seconds?
With the help of probability we can solve our question-
What is Probability?The idea of probability describes the possibility of an event happening.
We frequently have to make forecasts about the future in real life.
We may or may not be aware of the outcome of an event.
When this happens, we declare that there is a chance the event will take place.
In summary, probability has a wide range of fantastic applications in entertainment, business, and this recently expanding branch of artificial intelligence.
The probability formula can be used to determine the likelihood of an event by only dividing the favorable number of possibilities by the entire number of possible outcomes.
s=d/t
75 minutes
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An icicle in the shape of a cone is hanging from a gutter. It is 12 in. long and has a radius of 1 in. What is the volume of the icicle? Round
answer to the nearest hundredths place.
As a result, the icicle has a volume of about 4.19 cubic inches.
. The formula V = (1/3)r2h, where r is the radius of the base and h is the height of the cone, determines the volume of a cone.
Define radius?The distance between a circle's center to any other point on the circle is known as the radius. It is frequently represented by the letter "r."
The radius of a sphere, in this example, is the separation between any two points on its surface from the sphere's centre.
In this instance, the icicle is shaped like a cone with a 1 in. radius and a 12 in. height.
As a result, the icicle's volume is:
V = (1/3)π(1 in.)²(12 in.)
V ≈ 4.19 cubic inches
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find the area of the shaded region
Answer:
196
Step-by-step explanation:
Which expression is equivalent to 4/9x2?
4x2/9
2x9/2
4x9/2 or
2x2/9
4x2/9
Both will result to 8/9
BAN
ANA
NAN
In how many different ways can the word BANANA be read from the following table by moving from one cell to another cell with which it shares an edge? Cells may be visited more than once
10. Jade accidentally dropped a candy wrapper from the top of a building that was 600 feet tall.
The height of the wrapper in feet, f(x), can be represented using f(x) = -16x² - 2x + 600 where x
is the time in seconds.
o. If the candy wrapper is now 450 feet in the air, set up an equation that could be used to find
the amount of time since dropping the wrapper.
b. Solve the equation using the quadratic formula.
c. Which solution makes the most sense in the context of the situation? Explain.
After answering the provided question, we can conclude that As a result, equation the wrapper must have been dropped around 4.875 seconds ago.
What is equation?An equation in mathematics is a statement that states the equality of two expressions. An equation is made up of two sides that are separated by an algebraic equation (=). For example, the argument "2x + 3 = 9" asserts that the phrase "2x + 3" equals the value "9". The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements. The variable x is raised to the second power in the equation "x2 + 2x - 3 = 0." Lines are utilised in many different areas of mathematics, such as algebra, calculus, and geometry.
a) Set f(x) to 450 and solve for x to find the amount of time since dropping the wrapper when it is 450 feet in the air:
-16x² - 2x + 600 = 450
b)
-16x² - 2x + 150 = 0
[tex]x = (-(-2) + \sqrt((-2)^2 - 4(-16)(150))) / (2(-16))\\x = (2 + \sqrt(4 + 9600)) / (-32)\\x = (2 + \sqrt(9604)) / (-32)\\x = (2 + 98) / (-32)\\x = -3.125\\ or\\ x = 4.875\\[/tex]
c) Because time cannot be negative and the candy wrapper cannot have been at a height of 450 feet before it was dropped, the solution that makes the most sense in the context of the circumstance is x = 4.875. As a result, the wrapper must have been dropped around 4.875 seconds ago.
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What is the point (5,4) rotated 90 degrees clockwise
Answer: (-4,5)
Step-by-step explanation:
The vertices of triangle PQR are P(3,4), Q(5,8) and R(7,4). Find the length of QS and deduce the area of the triangle PQR
Check the picture below.
Find the area of the following shapes:
Answer:
30cm²
Step-by-step explanation:
If yu remove the triangle FED and replace it in place ABC, you will recive a rectangle of side a=AC=6cm and b=DC=5cm. And the area of rectangle is a*b.
Area=a*b=6cm*5cm=30cm²
Find the volume & surface area of each figure. Round your answers to the nearest hundredth, if
necessary.
We can conclude by answering the provided question that As a result, Figure B has a capacity of approximately 226.19 cubic centimetres and a surface area of approximately 94.25 square centimetres.
what is surface area ?The surface area of an object indicates the total volume filled by its surface. The surface area of a three-dimensional shape is the entire quantity of space that surrounds it. The surface area of a three-dimensional object refers to its total surface area. By adding the areas of each face, the surface area of a cuboid with six rectangular sides can be determined. As an alternative, you can use the following algorithm to identify the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total quantity of room occupied by the surface of a three-dimensional shape (a three-dimensional shape is a shape that has height, width, and depth).
For each figure, we will compute the volume and surface area individually.
Diagram A:
Figure A is a rectangle pyramid in form. It measures 10 centimetres long, 6 cm wide, and 4 cm tall.
Diagram B:
Figure B is a cylindrical in form. It has a radius of 3 centimetres and a height of 8 cm.
Image B volume = x radius2 x height = x 32 x 8 cm3 = 226.19 cubic centimetres
Figure B surface area = 2 x radius x height + 2 x radius2 = 2 x 3 cm x 8 cm + 2 x 32 cm2 = 94.25 square centimetres
As a result, Figure B has a capacity of approximately 226.19 cubic centimetres and a surface area of approximately 94.25 square centimetres.
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in a class, there are 18 girls and 14 boys. if the teacher selects two students at random to attend a party with the principal, what is the probability that the two students are the same sex? 0.49 0.50 0.51 0.52 0.53
In a class, there are 18 girls and 14 boys. If the teacher selects two students at random to attend a party with the principal, the probability that the two students are the same sex is 0.49.
For getting, the total number of students in the class. There are 18 girls and 14 boys.Therefore, the total number of students = 18 + 14 = 32
Find the number of ways of choosing two students from 32 students.This can be calculated by using the combination formula: ⁿC₂ = n! / ((n - r)! r!).
Here, n = 32 (total number of students), and r = 2 (number of students that we have to select).
ⁿC₂ = 32C₂ ⇒ 32! / ((32 - 2)! 2!) ⇒ (32 × 31) / (2 × 1) ⇒ 496
Find the number of ways of selecting two students of the same sex.The number of ways of selecting two girls = ¹⁸C₂ ⇒ 153
The number of ways of selecting two boys = 14C₂ ⇒ 91
Find the probability of selecting two students of the same sex.Total number of ways of selecting two students of the same sex = 153 + 91 = 244
Probability of selecting two students of the same sex = (Number of ways of selecting two students of the same sex) / (Total number of ways of selecting two students)
⇒ 244 / 496 ⇒ 0.49
Therefore, the probability that the two students are the same sex is 0.49.
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The area of a door is 3024 scare inches the the length of the door is 48 inches longer than the width of the door what is the width of the door
Answer:
Let's assume the width of the door is x inches. Then, according to the problem, the length of the door is 48 inches longer than the width, which means the length is x+48 inches.
The area of the door is given as 3024 square inches, so we can set up an equation:
Area = width x length
3024 = x(x+48)
Simplifying the equation, we get:
x^2 + 48x - 3024 = 0
Now we can solve for x using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = 48, and c = -3024
x = (-48 ± √(48^2 - 4(1)(-3024))) / 2(1)
x = (-48 ± √(2304 + 12096)) / 2
x = (-48 ± √14400) / 2
We take the positive root since the width of a door cannot be negative:
x = (-48 + 120) / 2
x = 36
Therefore, the width of the door is 36 inches.
Step-by-step explanation:
A large rectangle has sides 8 cm and 10 cm. Two small rectangles are removed from this large rectangle. This leaves the shaded shape. What is the perimeter of the shaded shape?
Answer:
To find the perimeter of the shaded shape, we need to determine the length of the sides of the shaded shape.
First, we need to find the area of the two small rectangles that were removed from the large rectangle:
Area of small rectangle 1: length x width = 4 cm x 3 cm = 12 cm²
Area of small rectangle 2: length x width = 4 cm x 2 cm = 8 cm²
The total area of small rectangles: 12 cm² + 8 cm² = 20 cm²
Now we can find the area of the shaded shape by subtracting the area of the small rectangles from the area of the large rectangle:
Area of large rectangle: length x width = 10 cm x 8 cm = 80 cm²
Area of shaded shape: 80 cm² - 20 cm² = 60 cm²
Since the shaded shape is rectangular, we can find the length and width by dividing the area by a factor pair:
60 cm² ÷ 6 cm = 10 cm
60 cm² ÷ 10 cm = 6 cm
So the shaded shape has sides of 6 cm and 10 cm.
Finally, we can find the perimeter of the shaded shape by adding up the lengths of all four sides:
Perimeter = 6 cm + 10 cm + 6 cm + 10 cm = 32 cm
Therefore, the perimeter of the shaded shape is 32 cm.
Step-by-step explanation:
Triangle ABC
maps to triangle XYZ
by a rotation of 90∘
counterclockwise about the origin followed by a reflection across the line y=x.
In triangle ABC,
m∠A=45∘,
m∠B=55∘,
and m∠C=80∘.
What is the measure of ∠Y?
First, we need to find the coordinates of each vertex of triangle ABC. Let's assume that A is located at (a,b), B is located at (c,d), and C is located at (e,f). Since we know the measures of the angles, we can also determine the slopes of the lines connecting the vertices:
The slope of line AB is (d-b)/(c-a), which is equal to tan(55°).
The slope of line BC is (f-d)/(e-c), which is equal to tan(80°).
The slope of line AC is (f-b)/(e-a), which is equal to tan(55°-45°) = tan(10°).
Using these slopes, we can find the equations of the three lines and solve for the coordinates of the vertices:
Line AB: y-b = tan(55°)(x-a)
Line BC: y-d = tan(80°)(x-c)
Line AC: y-b = tan(10°)(x-a)
Solving these equations simultaneously, we get:
A = (b + (c-a)tan(55°), b + (c-a)tan(55°-45°))
B = (c + (f-d)/tan(80°), d + (f-d))
C = (e + (b-f)/tan(10°), f + (e-a)tan(10°))
Next, we need to apply the rotation and reflection to these vertices to find the corresponding vertices of triangle XYZ. The rotation by 90° counterclockwise about the origin transforms a point (x,y) into (-y,x), while the reflection across the line y=x transforms a point (x,y) into (y,x). So:
Vertex A of ABC is mapped to vertex X of XYZ: (a,b) → (-b,a) → (a,-b)
Vertex B of ABC is mapped to vertex Y of XYZ: (c,d) → (-d,c) → (c,d)
Vertex C of ABC is mapped to vertex Z of XYZ: (e,f) → (-f,e) → (e,f)
Now we need to find the measure of angle Y. Since we don't know the exact coordinates of the vertices of XYZ, we'll use the fact that the rotation by 90° counterclockwise about the origin preserves angles and the reflection across the line y=x changes the orientation of angles but not their measure. Therefore:
m∠Y = m∠ZOX, where O is the origin
m∠ZOX = 90° - m∠XOZ
m∠XOZ = m∠COA = 55° + 45° = 100°
Therefore, m∠Y = 90° - 100° = -10°, but since angles can't have negative measures, we add 360° to get m∠Y = 350°.
So the measure of angle Y in triangle XYZ is 350°.
Question 1
1/1
Triangle ABC
maps to triangle XYZ
by a rotation of 90∘
counterclockwise about the origin followed by a reflection across the line y=x.
In triangle ABC,
m∠A=45∘,
m∠B=55∘,
and m∠C=80∘.
What is the measure of ∠Y?
Enter your answer as the correct value, like this: 42
55 is the answer I'm not joking try it lol
A hockey coach recorded the number of shots taken by the home team and the number taken by the visiting team in 20 games. He displayed the results in the box plots below.
A box plot titled Number of Shots Taken by home team players. The number line goes from 10 to 32. The whiskers range from 16 to 32, and the box ranges from 20 to 23. A line divides the box at 22.
Number of Shots Taken by Home Team Players
A box plot titled Number of Shots Taken by visiting team players. The number line goes from 10 to 32. The whiskers range from 14 to 32, and the box ranges from 16 to 24. A line divides the box at 18.
Number of Shots Taken by Visiting Team Players
Which describes an inference that the coach might make after comparing the medians of the two data sets?
Answer:The most accurate inference from this boxplot is that: The visiting team had more variability in the number of shots taken.
Step-by-step explanation:
The box and whiskers plot is a way of presenting data that gives 5 major information about the distributionFrom the whiskers of the plot, one can read- The minimum value - The maximum value Then, from the boxplot, one can read- The Median, represented by the middle line of the boxplot.- The first Quartile or 25th percentile, represented by the lower end of the boxplot.- The third quartile or 75th percentile, represented by the upper end of the boxplot.Other variables that can be obtained from these five data points include- The range of the distribution (maximum value minus minimum value)- The interquartile range (a measure of variation, which is the difference between the third and first quartile of the distribution)For the two boxplots that the coach madeHome teamWhiskers range from 16 to 32Minimum value = 16maximum value = 32the box ranges from 20 to 23. A line divides the box at 22.First quartile = 20Third quartile = 23Median = 22IQR = 23 - 20 = 3For the visiting teamWhiskers range from 14 to 32Minimum value = 14maximum value = 32the box ranges from 16 to 24. A line divides the box at 18.First quartile = 16Third quartile = 24Median = 18IQR = 24 - 16 = 8Since the median only represents the midpoint of the distribution, one cannot conclude with certainty that home team took more shots than the visiting team, information on the mean would confirm that. A less controversial and evident inference is that the visiting team had more variability in their shots as their distribution has a higher Interquartile Range (IQR of 8 > 3) which is a direct measure of variation for distributions.
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if all else remains constant and the values of two variables move in the same direction it indicates a
If all else remains constant and the values of two variables move in the same direction, it indicates a positive correlation.
What is correlation?Correlation is a statistical measure that expresses the relationship between two variables. The correlation coefficient, which ranges from -1 to +1, is used to quantify the correlation.
A positive correlation is when the values of the variables move in the same direction. A correlation of +1 indicates that the variables are perfectly positively correlated, implying that as one variable increases, the other also increases.
A correlation of -1 indicates that the variables are perfectly negatively correlated, implying that as one variable increases, the other decreases. A correlation of zero indicates that there is no correlation between the variables.
Hence a positive correlation exists when the values of two variables move in the same direction while all other factors remain constant.
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The mean cost of a box of Cheerios Out Crunch is $4.00. If the price increases by 10% what is the new mean? None of the other choices is correct $410 $400 $440
The new mean cost of a box of Cheerios Out Crunch is $4.40. This means that, on average, customers can expect to pay $0.40 more for a box of cereal after the price increase.
The new mean cost of a box of Cheerios Out Crunch after a 10% increase in price would be $4.40.
To see why, we can start with the original mean cost of $4.00 per box. To calculate a 10% increase, we can multiply the original mean cost by 1.10 (or 110% as a decimal), which gives:
$4.00 x 1.10 = $4.40
The mean cost is the proportion of the cost of the multitude of items to the absolute number of items. In Maths, we likewise have the term called "normal". The normal of some random arrangement of information is known as the mean of information.
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2d+7.5d≥ 5.5d +3
solve for d
Answer: d
≥
3/4
Step-by-step explanation:
2d+7.5d≥ 5.5d +3
9.5d≥ 5.5d +3
9.5d-5.5d ≥ 3
4d ≥ 3
***Divide 4 on both sides
d
≥
3/4
The mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is .35. If the price increases by 25 cents a box, what is the new variance?
The new variance is 0.35.
The variance of a random variable measures how spread out the values are from the mean.
The formula for the variance is Var(X) = E[(X - E[X])²], where E[X] is the expected value (or mean) of X.
If the price of a box of Cheerios Oat Crunch increases by 25 cents, the new mean cost would be $4.25. To find the new variance, we can use the formula Var(aX + b) = a²Var(X), where a is a constant and b is a constant. In this case, a = 1 (because we are not changing the units of measurement) and b = 0.25 (because we are adding 25 cents to the price).
Therefore, the new variance is Var(X + 0.25) = Var(X) = Var(X) x 1² = Var(X) = 0.35.
This means that the variance remains the same even though the price has increased. This is because the variance is a measure of how spread out the values are from the mean, and the mean has shifted by the same amount as the price increase. Therefore, the distance between the values and the new mean is the same as the distance between the values and the old mean, so the spread is unchanged.
The variance is a measure of how spread out a set of data is from its mean. It is calculated as the average of the squared differences between each value and the mean. The formula for variance is Var(X) = E[(X - E(X))²], where E is the expected value or mean of X.
In this case, we are given that the mean cost of a box of Cheerios Oat Crunch is $4.00 and the variance is 0.35. This means that the average squared difference between each box's cost and the mean cost is 0.35.
Now, if the price of each box increases by 25 cents, this means that the new mean cost will be $4.25. However, this does not affect the variance directly. This is because the variance only measures how spread out the data is from the mean, and the mean has shifted by the same amount as the price increase.
To see this more clearly, imagine a set of data that has a mean of 4 and a variance of 0.35. If we add 0.25 to each value, we get a new set of data that has a mean of 4.25. However, the spread of the data is still the same; that is, the distance between each value and the new mean is the same as the distance between each value and the old mean. Therefore, the variance remains the same even though the price has increased.
In summary, the variance measures how spread out a set of data is from its mean, and a shift in the mean does not affect the variance directly.
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PLEASE HELP I NEED THE ANSWER
What is the correct numerical expression for "subtract the sum of 2 and 9 from the product of 4 and 3?"
2 + 9 − 4 x 3
(2 + 9) − 4 x 3
(4 x 3) − (2 + 9)
4 x (3 − 2) + 9
Answer: (4 x 3) - (2 + 9)
The correct numerical expression is:
(4 x 3) - (2 + 9)
A toy shop purchases 125 identical stuffed animals for a total cost of $321.50 and sells them for $7 each. What is the percent markup?
A toy shop purchases 125 identical stuffed animals for a total cost of $321.50 and sells them for $7 each. The percent markup is 171.9%.
The total cost of purchasing 125 identical stuffed animals is $321.50.
To find the cost per stuffed animal, we divide the total cost by the number of stuffed animals:
Cost per stuffed animal = Total cost / Number of stuffed animals
Cost per stuffed animal = $321.50 / 125
Cost per stuffed animal = $2.572
The toy shop sells each stuffed animal for $7.
To find the markup, we need to calculate the difference between the selling price and the cost price, and then express that difference as a percentage of the cost price:
[tex]Markup = (Selling price - Cost price) / Cost price * 100%[/tex]
Markup = ($7 - $2.572) / $2.572 x 100%
Markup = $4.428 / $2.572 x 100%
Markup = 1.719 x 100%
Markup = 171.9%
Therefore, the percent markup is 171.9%.
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The points C, D, E and F all lie on the same line segment, in that order, such that the ratio of
C
D
:
D
E
:
E
F
CD:DE:EF is equal to
1
:
6
:
3. 1:06:03. If
C
F
=
20
,
CF=20, find
E
F. EF
Given the ratio of CD:DE:EF as 1:6:3 and CF as 20, we can use the sum of segment lengths equation to find the length of EF to be 12 units.
We're given that points C, D, E, and F lie on the same line segment in that order, with the ratio CD:DE:EF equal to 1:6:3. This means that the length of segment CD is 1x, the length of segment DE is 6x, and the length of segment EF is 3x, for some common factor x.
We're also given that CF (the total length of the segment from C to F) is equal to 20. So that we can set an equation:
CD + DE + EF = CF
Substituting the values we know from the ratio and CF:
1x + 6x + 3x = 20
Combining like terms:
10x = 20
Solving for x:
x = 2
Now we can use this value of x to find the lengths of each segment:
CD = 1x = 1(2) = 2
DE = 6x = 6(2) = 12
EF = 3x = 3(2) = 6
So the length of segment EF is 12 units.
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if (0.57, 0.63) is a 50% confidence interval for p, what does n k equal, and how many observations were taken?
The number of observation taken to obtain confidence interval of 50% is equal to 484.
Confidence interval for p = 50%
Use the formula for the confidence interval of a proportion to find the sample size n,
p ± z√(p×(1-p)/n) = (0.57, 0.63)
where z is the z-score corresponding to a 50% confidence interval, which is 0.674.
Midpoint of the interval is,
(p1 + p2) / 2
= (0.57 + 0.63) / 2
= 0.60
Rewrite the equation as,
0.60 ± 0.674√(0.60(1-0.60)/n) = (0.57, 0.63)
Simplifying this equation, we get,
⇒ 0.674√(0.60(1-0.60)/n) = 0.03/2
⇒ 0.674√(0.60(1-0.60)/n) = 0.015
Squaring both sides and solving for n, we get,
⇒n = 0.60×(1-0.60)×(0.674/0.015)^2
⇒n = 483.84
Rounding up to the nearest integer, the sample size is n = 484.
Therefore, n k equals 484 k, and 484 observations were taken to obtain the 50% confidence interval of (0.57, 0.63) for p.
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