Answer: Q.a Arun thinks that -29/36 is exactly halfway between -8/9 and -13/18. We can check if this is true by finding the midpoint between -8/9 and -13/18 and seeing if it equals -29/36.
To find the midpoint between two numbers, we take the average of the two numbers. So the midpoint between -8/9 and -13/18 is:
((-8/9) + (-13/18))/2 = (-16/18 + (-13/18))/2 = -29/36
Since -29/36 is the same as the midpoint, Arun is correct.
Q.b To find the fraction exactly halfway between -1 3/4 and -11/6, we can start by converting the mixed number to an improper fraction:
-1 3/4 = -7/4
-11/6
To find the midpoint between -7/4 and -11/6, we take the average:
((-7/4) + (-11/6))/2 = (-21/12 + (-22/12))/2 = -43/24
Therefore, -43/24 is the fraction exactly halfway between -1 3/4 and -11/6 on the number line.
Step-by-step explanation:
Sandra is selling root beer in 300 mL bottles. She makes 2 batches of root beer. Each batch makes 3.2 L of root beer. How much root beer will she have left over, after filling her bottles?
Step-by-step explanation:
3.2 liters divided by 300 ml / bottle is
3200 ml / 300 ml/bottle = 10 2/3 bottles
10 full bottles plus 2/3 of a bottle left over
2/3 bottle * 300 ml/bottle = 200 ml left over
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The angles that form a linear pair is 6 and 8.
option C.
What are linear pair angles?
Linear pair angles are two adjacent angles formed by two intersecting lines. These two angles are always supplementary, which means that their sum is equal to 180 degrees. In other words, if we add the measure of one angle to the measure of the other angle, we will get a total of 180 degrees.
A linear pair of angles can be easily identified by observing the angles formed when two straight lines intersect each other. For example, if line AB intersects line CD at point E, then the two pairs of adjacent angles formed are:
∠AED and ∠DEB∠CEB and ∠BEDEach pair of adjacent angles in a linear pair is supplementary, which means that ∠AED + ∠DEB = 180 degrees and ∠CEB + ∠BED = 180 degrees.
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An Electronic store donated a percentage of every sale to charity. The total sales were seven dollars, 150, of which the store donated $429 What percentage of seven dollars, 150 was donated to charity?
Answer:
6.00 %
Step-by-step explanation:
Percent = amount donated/total sales × 100 %
= 429/7150 × 100 %
= 6.00 %
The store donated 6.00 % of its sales to charity.
$1000 is deposited in an account with a 8.5% interest rate, compounded continuously. what is the balance after 5 years?
Answer:
$1529
Step-by-step explanation:
The formula for continuous compounding is:
A = Pe^(rt)
Where:
A = the final amount (balance) in the account
P = the initial principal (deposit)
e = Euler's number (approximately 2.71828)
r = the annual interest rate (as a decimal)
t = the time period (in years)
Plugging in the given values, we get:
A = 1000e^(0.0855)
A = 1000*e^0.425
A = 1000*1.529
A = 1529
Therefore, the balance after 5 years with continuous compounding at 8.5% interest rate is $1529.
I NEED HELP ON THIS ASAP! IT'S DUE TODAY!!!
Answer:
b = 8.485
c = 23.995 ≈ 24
Step-by-step explanation:
Part b:
[tex]\sqrt{(10-4)^2+(9-3)^2}[/tex]
√(36 + 36)
= 8.485
Part c:
Base = [tex]\sqrt{(6-2)^2+(1-5)^2}[/tex]
Base = 5.656
Area = Base x Height x 0.5
Area = 5.656 x 8.485 x 0.5
Area = 23.995 ≈ 24
DUE TODAY PLEASE HELP WELL WRITTEN ANSWERS ONLY
Here is a point at the tip of a windmill blade. The center of teh windmill is 6 feet off the ground and the blades are 1.5 feet long. Write an equation giving the height h of the point P after the windmill blade rotates by an angle of a. Point P is currently rotated π/4 radians from the point directly to the right of the center of the windmill.
the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.
What is Trigonometric Functions?
Trigonometry uses six fundamental trigonometric operations. Trigonometric ratios describe these operations. The sine function, cosine function, secant function, co-secant function, tangent function, and co-tangent function are the six fundamental trigonometric functions. The ratio of sides of a right-angled triangle is the basis for trigonometric functions and identities. Using trigonometric formulas, the sine, cosine, tangent, secant, and cotangent values are calculated for the perpendicular side, hypotenuse, and base of a right triangle.
To find the height h of point P, we can use the sine function, which relates the opposite side of a right triangle (in this case, the height h) to the hypotenuse (in this case, the length of the windmill blade, which is 1.5 feet). The angle between the opposite side and the hypotenuse is the complement of the angle of rotation a, which is π/4 radians minus the angle between the ground and the windmill blade, which is arctan(6/1.5) or approximately 1.3258 radians.
So, the equation for the height h of point P after the windmill blade rotates by an angle of a is: h = 1.5 sin(π/4 - arctan(6/1.5))
Therefore, the height of point P after the windmill blade rotates by an angle of a is approximately 1.1908 feet.
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3 of 5
→
Find the first three terms of the sequence below.
Tn = 2n^2-4n-3
T1=
T2=
T3=
Answer:
- 5 , - 3 , 3
Step-by-step explanation:
to find the first three terms, substitute n = 1, 2, 3 into the explicit formula
[tex]T_{n}[/tex] = 2n² - 4n - 3
T₁ = 2(1)² - 4(1) - 3
= 2(1) - 4 - 3
= 2 - 7
= - 5
T₂ = 2(2)² - 4(2) - 3
= 2(4) - 8 - 3
= 8 - 11
= - 3
T₃ = 2(3)² - 4(3) - 3
= 2(9) - 12 - 3
= 18 - 15
= 3
the first three terms are - 5, - 3 , 3
How does the diction in Aylmer’s dialogue enhance the meaning of Passage 2?
The author's purpose is enhanced through the arrogant word choice that suggests science is foolproof.
The literal meaning is enhanced by the informal word choice that conveys Aylmer's trust in his own scientific skills.
The tone is enhanced through the playful word choice that highlights the author’s humorous attitude toward marriage.
The mood is enhanced through the sympathetic word choice that emphasizes the sorrowful feeling evoked in the reader.
The passage and Aylmer's dialogue describe his obsession with perfection and his attempts to remove a birthmark from his wife's face.
What is the diction in Aylmer’s dialogue?Aylmer's language is formal and scientific, using technical terms and precise language to describe his work. This enhances the meaning of the passage by highlighting Aylmer's belief in the power of science and his desire to control nature.
For example, Aylmer says, “Georgiana, I have spent much thought upon the subject,” and “I feel myself fully competent to render this dear cheek as faultless as its fellow.”
This language conveys Aylmer's confidence in his abilities and his belief that he can achieve perfection through scientific means. The precise language also reinforces the idea that Aylmer sees his wife's birthmark as a flaw that needs to be eradicated.
Therefore, the diction in Aylmer's dialogue enhances the meaning of Passage 2 by highlighting the theme of obsession with perfection and the power of science to control nature.
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which of the following statements is not true? a) the mean of the sampling distribution of sample mean is always the same as that of x, the distribution from which the sample is taken. b) the larger the sample size, the better will be the normal approximation to the sampling distribution of sample mean. c) the standard deviation of the sampling distribution of sample mean
The statement "a) the mean of the sampling distribution of sample mean is always the same as that of x, the distribution from which the sample is taken" is not necessarily true.
While the mean of the sampling distribution of the sample mean is an unbiased estimator of the population mean, it is not always equal to the mean of the original distribution from which the sample is taken. This is because the sample mean will vary from sample to sample, and the sampling distribution will reflect this variability.
For example, if the population distribution is skewed or has outliers, the sampling distribution of the sample mean may be more symmetrical and have a different mean. However, as the sample size increases, the sampling distribution of the sample mean will approach a normal distribution with a mean equal to the population mean. This is known as the Central Limit Theorem.
Therefore, the incorrect statement is a).
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Which of the following expressions is equal to 9? 4 x (one-half x 6) ÷ 3 6 ÷ (one-fourth x 3 x one and one-fourth) 8 + (one-third x 6) ÷ 5 10 − (one-fifth x 10) + 1
The expression that is equal to 9 is 10 − (one-fifth x 10) + 1.
What are arithmetic operators?Basic mathematical procedures known as arithmetic are used to calculate using numbers. Addition, subtraction, multiplication, and division are the four fundamental arithmetic operations. Finding the sum of two or more numbers is done using addition, finding the difference between two numbers is done using subtraction, finding the product of two or more numbers is done using multiplication, and finding the quotient of two numbers is done using division. There are more operations outside these four, such as square root and exponentiation (increasing a number to a power) (finding the root of a number).
For the given expressions we have:
4 x (one-half x 6) ÷ 3 = 4 x 3 ÷ 3 = 4 --> not equal to 9
6 ÷ (one-fourth x 3 x one and one-fourth) = 6 ÷ (3/4 x 5/4) = 6 ÷ (15/16) = 96/15 --> not equal to 9
8 + (one-third x 6) ÷ 5 = 8 + 2 ÷ 5 = 8.4 --> not equal to 9
10 − (one-fifth x 10) + 1 = 10 - 2 + 1 = 9 --> equal to 9
Hence, the expression that is equal to 9 is 10 − (one-fifth x 10) + 1.
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Aaron has tried to construct the perpendicular bisector for line AB.
a) Write a sentence to explain how you know this is not a perpendicular bisector.
b) Which of the possible mistakes below has Aaron made in his construction?
A-
-B
Possible mistakes
He did not use a ruler to draw his line
The width of his pair of compasses
changed between drawing his arcs
He did not use a pair of compasses to
draw his arcs
A sentence to explain how I know this is not a perpendicular bisector is that line AB was not divided into two equal halves.
A possible mistake which Aaron made in his construction is: C. he did not use a pair of compasses to draw his arcs.
What is a perpendicular bisector?In Mathematics and Geometry, a perpendicular bisector can be defined as a type of line that bisects or divides a line segment exactly into two (2) equal halves and forms an angle that has a magnitude of 90 degrees at the point of intersection.
This ultimately implies that, the steps taken by Aaron for the construction of the perpendicular bisector for line AB is incorrect because it was not divided into two equal halves, even though it formed an angle that has a magnitude of 90 degrees at the point of intersection.
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A monument is 50 meteres high.What is the length of the shadow cast by the monument if the angle of elevation of the sun is 60 degree?
As a result, the monument's shadow is approximately 28.9 metres long as the monument's height is on the other side .
what is length ?The length of an object or the separation of two points is a measurement of its size in one dimension. It is an important physical quantity that is employed in many disciplines, including physics, technology, and daily life. Depending on the situation, length is typically expressed in quantities like metres (m), centimetres (cm), feet (ft), inch (in), and miles (mi).
given
Assume that the monument's shadow extends "x" metres in length.
Because we are aware of the monument's height and the sun's elevation angle, we can use the tangent function to get "x":
tan(60) = adjacent/opposite
where the monument's height is on the other side, and the shadow's length is right next to it.
Adding the values we obtain:
tan(60) = 50/x
To solve for "x," we obtain:
x = 50/tan(60) (60)
(Using the value of the tangent of 60 degrees, which is 3 or 1.732) x = 50/1.732
28.9 metres x
As a result, the monument's shadow is approximately 28.9 metres long as the monument's height is on the other side .
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Here is a graph of the equation y = 2sin(Θ) - 3. Use the graph to find the amplitude of this sine equation.
Answer:
The amplitude of this graph is 4.
Write an equation for the nth term of each geometric sequence.
-1, -5, -25,...
Oa. an = (5)-¹-1
Ob. a , = - 1¹( 3 ) - ²
5
Oc. an =-1(5)n-1
Od. an = 1(5)n-1
Answer:
C
Step-by-step explanation:
the nth term of a geometric sequence is
[tex]a_{n}[/tex] = a₁ [tex]r^{n-1}[/tex]
where a₁ is the first term and r the common ratio
here a₁ = - 1 and r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-5}{-1}[/tex] = 5
then nth term is
[tex]a_{n}[/tex] = - 1 [tex](5)^{n-1}[/tex]
What number is equal to 580 tenths and 17 thousandths?
580.017
58.017
5.817
0.5817
580.017 is equivalent to 580 tenths and 17 thousandths.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that can contain variables, constants, and mathematical operations such as addition, subtraction, multiplication, division, and exponentiation. Algebraic expressions are used to represent and solve problems in many areas of mathematics, science, engineering, and finance.
The number that is equal to 580 tenths and 17 thousandths is 580.017.
To understand this, we need to understand the place value system used in decimal notation. Each digit in a decimal number has a place value that is a power of 10. The rightmost digit represents the ones place, the next digit to the left represents the tens place, and so on.
In the number 580.017, the digit in the ones place is 0, the digit in the tens place is 1, the digit in the hundreds place is 7, the digit in the thousands place is 0, the digit in the ten-thousands place is 8, and the digit in the hundred-thousands place is 5.
Thus, the number 580.017 can be written as the sum of the digits multiplied by their corresponding place values:
580.017 = 5 x 100,000 + 8 x 10,000 + 0 x 1,000 + 0 x 100 + 1 x 0.1 + 7 x 0.01
Simplifying this expression, we get:
580.017 = 500,000 + 80,000 + 0 + 0 + 0.1 + 0.17
580.017 = 580,000 + 0.017
Therefore, 580.017 is equivalent to 580 tenths and 17 thousandths.
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A field is shaped like a trapezoid with the dimensions shown in the image.
7.2 meters
13.4 meters
There are 320 laying hens living in this field. What is the bird population density?
A Approximately 4 hens per square meter
More than 5 hens per square meter
c. Approximately Sens per square meter
Less than 2 hens per square meter
B
D
10.6 meters
Answer:
C. Approximately 3 hens per square meter
When the pressure is 2.6 g/m² then the depth is 3.9 m.
What is proportionality?The term proportionality describes any relationship that is always in the same ratio. The number of apples in a crop, for example, is proportional to the number of trees in the orchard, the ratio of proportionality being the average number of apples per tree.
Given that
the pressure varies directly with the depth. When the pressure is 320 g/m² the depth is 480 m.
We need to find the depth if the pressure is 2.6 g/m².
So, here we will use the concept of proportionality,
Let the unknown depth be x,
So,
320 / 480 = 2.6 / x
2 / 3 = 2.6 / x
2x = 7.8
x = 3.9
Hence when the pressure is 2.6 g/m² then the depth is 3.9 m.
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complete question:
Pressure varies directly with the depth. When the pressure is 320 grams per square meter the
depth is 480 meters. What is the depth, in meters, when the pressure is 2.6 grams per square
meter? (Round to the nearest tenth)
A 1.7 grams
B 1.9 grams
C 3.7 grams
D 3.9 grams
If you don't mind helping me with Antoher problem dealing with geometry
The coordinates of the image based on the transformation rule (x, y) → (x - 2, y) include the following:
A' (2, -4).
B' (3, -4).
C' (3, -1).
D' (2, -1).
What is a translation?In Mathematics, the translation of a graph to the left is a type of transformation that simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation of a graph to the right is a type of transformation that simply means adding a digit to the value on the x-coordinate of the pre-image.
By translating the pre-image of quadrilateral ABCD horizontally right by 4 units, the coordinates of quadrilateral ABCD include the following:
(x, y) → (x - 2, y)
A (4, -4) → (4 - 2, -4) = A' (2, -4).
B (5, -4) → (5 - 2, -4) = B' (3, -4).
C (5, -1) → (5 - 2, -1) = C' (3, -1).
D (4, -1) → (4 - 2, -1) = D' (2, -1).
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Explain why S is not a basis for R3. S = {(1, 1, 1), (0,1,1), (1,0,1), (0, 0, 0)} a. S is linearly dependent. b. S does not span R3. c. S is linearly dependent and does not span R3.
S is not a basis for R3 because: c. S is linearly dependent and does not span R3.
What's basis for a vector spaceA basis for a vector space is a set of vectors that are linearly independent and span the space.
Let's check if S = {(1, 1, 1), (0,1,1), (1,0,1), (0, 0, 0)} satisfies this definition of the basis or not.
Here, we have to find if the set is linearly dependent or not. If the set is linearly dependent, then it can't be a basis. To check the linearity of the set, we will set the equation for the linear combination of vectors of set S.
Then α1(1, 1, 1) + α2(0,1,1) + α3(1,0,1) + α4(0, 0, 0) = 0
For the above equation to hold true, α1 + α3 = 0α1 + α2 = 0α1 + α3 = 0
By solving the above equations, we get
α1 = -α3α2 = -α1α4 = 0
The above equation shows that α4 = 0 means there is always a trivial solution which makes it linearly dependent.
Therefore, it is not a basis.
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Simplify this fraction
1^22 / 1^7
Answer:
1
Step-by-step explanation:
One to any exponent is just 1 so this fraction simplifies to 1/1 or just simply 1
Answer:
1 or 1 / 1.
Step-by-step explanation:
Square the numbers:
1^22 / 1^7
Any number squared with 1 is always 1:
1 / 1
= 1 or 1 / 1
Allison gas a poster that is 15 in by 18 in. what will the dimension of the Poster be if she scales it down by a factor pf 1/3
The new dimensions of the poster will be 5 in by 6 in.
What is scaling?In mathematics, scaling is the process of adjusting a geometric form or figure's size by a predetermined factor or ratio. With scaling, a shape's dimensions are all multiplied by the same quantity. Depending on whether the scaling factor is more than 1 or less than 1, respectively, scaling can either make the form larger or smaller. In addition to science, engineering, and computer graphics, scaling is frequently utilised in trigonometry, geometry, and other areas of mathematics.
Given that the scale factor = 1/3.
Thus, the new dimensions are:
New length = 15 in x (1/3) = 5 in
New width = 18 in x (1/3) = 6 in
Hence, the new dimensions of the poster will be 5 in by 6 in.
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Equation of curve y=2x-5/x+1, given that x increases at a rate of 0.02 unit/sec. Find rate of change of y. When x=1
The rate of change of y when x = 1 is 0.005 unit/sec.
To find the rate of change of y when x = 1 and given that x increases at a rate of 0.02 unit/sec, we'll first find the derivative of the equation y = (2x - 5)/(x + 1) with respect to x, and then multiply it by the rate of change of x (0.02 unit/sec). Differentiate the equation with respect to x:
y = (2x - 5)/(x + 1)
To differentiate this function, we'll use the quotient rule: [tex](u'/v) - (uv')/v^2[/tex], where u = (2x - 5) and v = (x + 1).
u' = derivative of (2x - 5) = 2
v' = derivative of (x + 1) = 1
Now, apply the quotient rule:
dy/dx =[tex](2\times(x + 1) - (2x - 5)\times1) / (x + 1)^2[/tex]
Plug in x = 1:
dy/dx =[tex](2\times(1 + 1) - (2\times1 - 5)\times1) / (1 + 1)^2[/tex]
dy/dx = (4 - 3) / 4
dy/dx = 1/4
Multiply the derivative by the rate of change of x:
The rate of change of x is 0.02 unit/sec, so the rate of change of y when x = 1 is:
Rate of change of y = (dy/dx) × (rate of change of x)
Rate of change of y = (1/4) × 0.02 = 0.005 unit/sec
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of the 13,500 savings accounts in a bank, 4,675 belong to people younger than 40 years old. the bank president would like to increase her institution's marketing strategy to younger customers, so she is examining the population proportions in order to create a statistical study. find the population proportion, as well as the mean and standard deviation of the sampling distribution for samples of size n
Population proportion: The proportion of people aged under 40 who have savings accounts is the population proportion. This can be calculated as follows:Population proportion = (number of savings accounts belonging to people under 40) / (total number of savings accounts).
Population proportion = 4675/13500Population proportion = 0.3463 (rounded to four decimal places)Mean and standard deviation of the sampling distributionFor a given sample size, the mean and standard deviation of the sampling distribution can be calculated as follows:
Mean of sampling distribution = population proportionStandard deviation of sampling distribution = sqrt[(population proportion * (1 - population proportion)) / n]where n is the sample size.For this question, the sample size is not given, so we cannot calculate the mean and standard deviation of the sampling distribution.
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Here is a wheel with radius 1 foot. List three different counterclockwise angles the wheel can rotate so that point P ends up at position Q.
Below are the three angles listed out in both radians and degrees:
pi/2 radians (or 90 degrees)5π /2 radians (or 450 degrees)9π /2 radians (or 810 degrees)What is the rotation?Let us assume that point P is initially at the topmost point of the wheel, and Q is directly to the right of P.
When the wheel rotates counterclockwise, point P moves along a circle with radius 1 foot, centered at the center of the wheel. To end up at position Q, point P needs to move a quarter of the way around the circle, or pi/2 radians. Therefore, one angle that the wheel can rotate is pi/2 radians (or 90 degrees).
Another angle that the wheel can rotate is 5*pi/2 radians (or 450 degrees), which corresponds to rotating the wheel counterclockwise almost all the way around the circle, but stopping just short of completing a full rotation.
A third angle that the wheel can rotate is 9*pi/2 radians (or 810 degrees), which corresponds to rotating the wheel counterclockwise almost twice around the circle, but stopping just short of completing two full rotations.
Therefore, Note that there are a lot of many other angles that the wheel can rotate to end up at position Q, but these three examples give an idea of the possibilities.
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What i the answer this is a geometry homework?
Answer: 21
In order to find the answer you have to multiply FJ and JH which is equal to 6x+24.
After, multiply GJ and JE which is equal to 90.
After doing all these steps equal your findings:
6x+24= 90
x= 11
The length of FH is asked so, you have found x, which is equal to 11
FH= 6+(11+4)= 21
A nationa
l sampling of cookie preferences showed that 75% of people like chocolate chip, 50% like peanut butter, and only 3% like coconut. The use of this information makes sense in which of the following scenarios?
The information makes sense in different scenarios like manufacturing, baking, researching survey, etc.
What is sample?A sample is a portion of a population that is used to represent the full population in statistics. Researchers frequently utilise samples to draw conclusions about the population since it might be difficult or impossible to collect data from the complete population. In order for the conclusions made from the sample to be applicable to the entire population, it is important to pick a sample that is representative of the wider population. Many techniques, such as cluster sampling, stratified sampling, and random sampling, can be used to choose samples.
The knowledge of biscuit preferences may come in handy in a variety of situations. Here are three potential instances:
A biscuit manufacturer wants to launch a brand-new taste. They may opt to create a chocolate chip or peanut butter flavor as those are the most popular ones based on the preferences data.
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Complete question -
A national sampling of cookie preferences showed that 75% of people like chocolate chip, 50% like peanut butter, and only 3% like coconut. The use of this information makes sense in which of the following scenarios? A. The school cafeteria decides to make 3 coconut cookies for each 100 students who buy lunch, even though it puts them over budget for desserts. B. A national cookie company is thinking of changing the recipe in their peanut butter cookies. C. A national cookie company decides to spend $5 million in advertising to convince people to eat coconut cookies. D. Tom is about to open a small bakery and is using the result of the sampling to decide what kind of cookies to offer.
Point B has coordinates (5,1). The x-coordinate of point A is 2. The distance between point A and point B is 5 units. What are the possible coordinates of point A?
According to the solution we have come to find that, The possible coordinates of point A are (2,-2) and (2,4).
what is geometry?Geometry is a branch of mathematics that deals with the study of spatial relationships and properties of objects. It is concerned with the study of shape, size, position, and relative orientation of objects, as well as their properties such as angles, lines, curves, surfaces, and solids. Geometry is used extensively in various fields, including architecture, engineering, physics, astronomy, and computer graphics. The study of geometry involves using logic and reasoning to analyze and solve problems related to shapes and spatial relationships. It is an important subject that has practical applications in many areas of everyday life.
To find the possible coordinates of point A, we need to use the distance formula and the fact that the x-coordinate of point A is 2.
The distance formula is:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) are the coordinates of point A, (x2, y2) are the coordinates of point B, and d is the distance between the two points.
We know that the distance between point A and point B is 5 units:
5 = √((5 - 2)² + (1 - y1)²)
Squaring both sides:
25 = (5 - 2)²+ (1 - y1)²
Simplifying:
9 = (1 - y1)²
Taking the square root of both sides:
3 = 1 - y1 or 3 = y1 - 1
Solving for y1 in each case:
y1 = -2 or y1 = 4
Therefore, the possible coordinates of point A are (2,-2) and (2,4).
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Can someone help me ASAP it’s due tomorrow. I will give brainliest if it’s all done correctly. Show work.
The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
What is probability?
The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.
The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.
To find the probability of both events occurring together, we multiply the probabilities:
P(blue and even number) = P(blue) x P(even number)
P(blue and even number) = (1/3) x (1/2)
P(blue and even number) = 1/6
Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
What is spinner?
A spinner is a device or a toy used to randomly select or generate a value or outcome. It consists of a circular board or disc, often divided into sections of different colors or with different values or symbols, and a pointer or arrow that is spun around the disc to land on a particular section. Spinners are commonly used in games, educational activities, and statistical experiments to create random outcomes or to simulate probability distributions.
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Complete question is: The probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
Answer:
Step-by-step explanation:
The probability of the spinner landing on blue is 2/6, which simplifies to 1/3.
The probability of rolling an even number on a six-sided die is 3/6, which simplifies to 1/2.
To find the probability of both events occurring together, we multiply the probabilities:
P(blue and even number) = P(blue) x P(even number).
P(blue and even number) = (1/3) x (1/2).
P(blue and even number) = 1/6.
Therefore, the probability of the spinner landing on blue and rolling an even number on a six-side die is 1/6.
Find measure AD. Please hurry due at midnight
mAD is 74 ° .we can get this answer by using properties of chord and also using fact that the sum of angles in a quadrilateral is 360 degrees
what is properties of chord?
A chord is a straight line segment that joins two points on the circumference of a circle. Here are some properties of chords
1)The length of a chord is less than the diameter of the circle.
2) A chord that passes through the center of the circle is a diameter, which is the longest chord in a circle.
In the given question,
angle CAD = 180 - angle ADC - angle DCA
= 180 - 102 - 62
= 16 degrees
Now, we can use the fact that angles that subtend the same arc are equal. In particular, angles CAD and ABD subtend the same arc AD, so we have:
angle ABD = angle CAD = 16 degrees
Similarly, angles ADB and ACB subtend the same arc AB, so we have:
angle ACB = angle ADB
Now, we can use the fact that the sum of angles in a quadrilateral is 360 degrees. In particular, we have:
angle ABD + angle BAC + angle CAD + angle ACB = 360
Substituting the values we know, we get:
16 + angle BAC + 16 + angle ADB = 360
Simplifying, we get:
angle BAC + angle ADB = 328
But we also know that angle BAC + angle ADB + angle BAD = 180 degrees (since they form a triangle). Substituting the value we just found, we get:
328 + angle BAD = 180
Solving for angle BAD, we get:
angle BAD = 180 - 328 = -148 degrees
Wait, a negative angle? What's going on here? Well, it turns out that angles are usually measured in a counterclockwise direction, so if we go clockwise instead, we can end up with negative angles. In this case, we can think of angle BAD as a clockwise rotation from DB to BA, which is why it's negative.
But we can fix this by adding 360 degrees to angle BAD, which will bring it back into the range of 0 to 360 degrees. So:
angle BAD = -148 + 360 = 212 degrees
Now, we can use the fact that angles that subtend the same arc are equal again. In particular, angles ABD and ACD subtend the same arc AD, so we have:
angle ABD = angle ACD
Substituting the values we know, we get:
16 = angle ACD
Finally, we can use the fact that the sum of angles in a triangle is 180 degrees again. In particular, we have:
angle ADC + angle ACD + angle CDA = 180
Substituting the values we know, we get:
102 + 16 + angle CDA = 180
Simplifying, we get:
angle CDA = 62 degrees
But we also know that angles ACD and ADB subtend the same arc AD, so they're equal. Therefore:
angle ADB = angle ACD = 16 degrees
Now we can use the fact that the sum of angles in a triangle is 180 degrees again to find mAD:
angle ADB + angle ABD + angle BAD = 180
Substituting the values we know, we get:
16 + 16 + 212 = 180
Simplifying, we get:
mAD = (180 - 32) / 2 = 74 degrees
Therefore, mAD is 74 degrees
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a manufacturing machine has a 40% defect rate. if 101 items are chosen at random, answer the following. a) which is the correct wording for the random variable? select an answer b) pick the correct symbol: ?
Approximately 40.4 defective items in a sample of 101 items from this manufacturing machine with a 40% defect rate. The correct symbol for this random variable is X.
For this specific question, the random variable can be described as the number of defective items in a sample of 101
items taken from a manufacturing machine with a 40% defect rate. The correct wording for the random variable in this
case is "the number of defective items in a sample of 101 items."
The correct symbol for this random variable is X, which is often used to represent an unknown variable. Therefore, the
random variable can be written as X = the number of defective items in a sample of 101 items.
To find the expected number of defective items in this sample, we can use the formula for the expected value of a
discrete random variable: E(X) = np, where n is the sample size and p is the probability of the event of interest (in this
case, the probability of an item being defective).
Using this formula, we can calculate the expected number of defective items in the sample as:
E(X) = (101)(0.4) = 40.4
Therefore, we would expect to find approximately 40.4 defective items in a sample of 101 items from this manufacturing
machine with a 40% defect rate.
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Find x
a(x+2) = b(x-1)
For expression a(x+2) = b(x-1), x will be (-b - 2a)/(a - b).
What exactly are expressions?
In mathematics, an expression is a combination of numbers, variables, operators, and/or functions that can be evaluated to produce a numerical value. Expressions can range from simple calculations involving only arithmetic operations such as addition, subtraction, multiplication, and division, to more complex combinations of algebraic expressions and functions.
Now,
To solve for x in the equation a(x+2) = b(x-1), we can use algebraic manipulation:
a(x+2) = b(x-1)
ax + 2a = bx - b [distribute the terms]
ax - bx = -b - 2a [subtract bx and 2a from both sides]
x(a - b) = -b - 2a [factor out x]
x = (-b - 2a)/(a - b)
Therefore,
x = (-b - 2a)/(a - b).
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