A direct variation equation that shows the relationship between x and y is,
y = 8x.
What is proportional relationship?A proportional relationship is a relationship between two expressions and where changes in one expression means some constant change in the other expression as well. Generally, it is represented as x/y = k, where x and y are two expressions and k is constant.
Given:
In a direct variation, y=16 when x=2.
The proportional relationship between x and y:
y ∝ x.
y = kx, where k is constant.
When x = 2,
16/2 = k
k = 8.
Therefore, the relationship is y = 8x.
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At summer camp, 60 students are divided in two groups for swimming or hiking. Each camper flips a coin, where heads represents swimming and tails represents hiking.
Outcome Frequency
Swimming 26
Hiking 34
Compare the probabilities and determine which statement is true.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 34 over 60.
The theoretical probability of swimming, P(swimming), is 26 over 34, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is 26 over 60, but the experimental probability is one half.
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 26 over 60
The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 26 over 60.
How to calculate the probabilityThe ratio between the number of favorable events and the total number of conceivable outcomes is known as the theoretical probability.
The experimental probability can be calculated mathematically using the following formula: Probability of an Event P(E) = Number of Times an Event Occurs / Total Number of Trials.
The experimental probability will be:
= Frequency for swimming / Total frequency
= 26 / 60
Therefore, it should be noted the correct option is D.
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Which function is the inverse of g(x)=4x−12‾‾‾‾‾‾‾√2+4?
Change the variables and find the value of y for the equation g(x)=4x12 2+4 f1(x)=and inverse is (x2)/42x+7
what is function ?Math deals with figures and their variants, calculations and parts, shapes and their regions, and locations places where they could be found. The term "function" describes the connection between a group various inputs, each of which has a corresponding output. A task is an association between inputs and outputs which each input results in a single, unique output. A domain and a codomain, or scope, are assigned toward each function. Functions are typically designated by the letter f. (x). The input is an x. Inside functions, one-to-one activities, many-to-one functions, within functions, and even on functions are the four main categories of functions that are available.
given
f(x)= [tex]\sqrt[2]{4x - 12} + 4[/tex]
f(-1)= 4x/2 - 12/2 + 4
= f−1(x)=(x^2)/4−2x+7
Change the variables and find the value of y for the equation g(x)=4x12 2+4 f1(x)=and inverse is (x2)/42x+7 .
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the picture has the question
Answer:
Step-by-step explanation:
Noah answered 16 questions and is informed that he's completed 80% of the survey.
To find t, you are given 16/t = 80% or 16/t = 0.8.
Switch t and 0.8 to get 16/0.8 or 16/80% to find t.
t = 20 questions.
five people gather for a dinner party. what is the probability that no two of them have the same birthday
The probability of no two people having the same birthday at a dinner party with 25 people is 0.1389.
The probability of no two people having the same birthday is calculated using the Birthday Paradox. This paradox states that if there are n people gathered in a room, the probability that at least two people have the same birthday is 1 − (365/365) * (364/365) * (363/365) *...* ((365-n+1)/365).
For a dinner party with 25 people, the probability of no two people having the same birthday is 1 − (365/365) * (364/365) * (363/365) *...* (341/365) = 0.1389.
This means that there is a 13.89% chance that no two people at the dinner party have the same birthday. The probability of no two people having the same birthday at a dinner party with 25 people is 0.1389.
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Answer any of these questions pls some of them I started already
Step-by-step explanation:
I guess for #9
An exponent to an exponent is multiplication
[tex] {x {}^{ \\ y} }^{z} = {x}^{y \times z} [/tex]
So that first part...
[tex] {2}^{5 {}^{2} } = {2}^{5 \times 2} = {2}^{10} [/tex]
Doing the same for the other parts, you'll get a final of
273 246
[tex] \frac{ {2}^{10 } \times {2}^{21} }{ {2}^{24} } [/tex]
Now solving those
[tex] \frac{1024 \times2097152 }{16777216} = 128[/tex]
The Cooking Club made some pies to sell during lunch to raise money for a field trip. The cafeteria helped by donating 2 pies to the club. Each pie was cut into 4 pieces and then sold. There were a total of 64 pieces sold. How many pies did the club make?
The number of pies made by cooking club to raise the money for field trip is equal to 14 .
Number of pies given by cafeteria = 2
Number of pieces each pie cut into = 4
Total pieces donated by cafeteria = 8
Total number of pieces sold by cooking club = 64
Number of pieces made by cooking club = 64 - 8
= 56
Total number of pies made by cooking club to raise the money
= 56 / 4
= 14
Therefore, the total number of pies made by cooking club to raise the money is equal to 14.
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A spinner has 10 equal sized sections labeled 1 through 10. In 40 spins, the spinner lands 3 times in section 5. How does this compare to the number of times the pointer is expected to land in section 5?
a. Find the experimental probability that teh pointer lands in section 5. / which equals %
b. Find the theoretical probability that the pointer lands in section 5. / which equals %
c. How does the actual number of times the pointer landed in section 5 compare to the expected number?
(less often or more often) then expected
a) The experimental probability that the pointer lands in section 5 is 7.5%
b) The theoretical probability that the pointer lands in section 5 is 10%.
c) The actual number of times is lower than the expected number, so we can say that the spinner landed in section 5 less often than expected.
a. Experimental probability:
The experimental probability is found by dividing the number of times the spinner lands in section 5 by the total number of spins.
In this case, the spinner landed in section 5 3 times in 40 spins, so the experimental probability is:
Experimental probability = 3/40 = 0.075 or 7.5%
b. Theoretical probability:
The theoretical probability is the expected probability based on the assumption that the spinner is fair and each section has an equal chance of being selected.
With 10 equal sections, the theoretical probability that the spinner lands in section 5 is:
Theoretical probability = 1/10 = 0.1 or 10%
c. Comparison between actual and expected:
The actual number of times the spinner landed in section 5, 3, is compared to the expected number of times, 4 (based on the theoretical probability of 10% and 40 spins).
The actual number of times is lower than the expected number, so we can say that the spinner landed in section 5 less often than expected.
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Daryl Mattingly bought a rental property in Lake Arrowhead for $185,900. After a $40,000 down payment, he mortgaged the rest. His annual expenses totaled $19,850 and he rented the condo for $3,875 per month for 6 months. Determine a) the annual net income and b) the annual yield.
The annual net income and annual yield are $3400 and 2.335 respectively
What is the annual net incomea) To find the annual net income, we need to subtract the annual expenses from the annual rental income. The annual rental income can be calculated as follows:
$3,875 * 6 months = $23,250
The annual net income would be:
$23,250 - $19,850 = $3,400
b) The annual yield can be calculated as the annual net income divided by the total cost of the property, including the down payment:
$3,400 / ($185,900 - $40,000) = 0.023 or 2.33%
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a survey conducted on 1,000 canadians found that 700 of them refused to receive the h1n1 vaccination. construct a 95% confidence interval of the estimated proportion of canadians who refused the vaccination.
A 95% confidence interval for the estimated proportion of Canadians who refused the H1N1 vaccination can be calculated as follows:
Let p be the true proportion of Canadians who refused the vaccination.
The sample proportion is estimated by:
p_hat = 700 / 1000 = 0.7
The standard error of the sample proportion is:
SE = sqrt(p_hat * (1 - p_hat) / 1000) = sqrt(0.7 * 0.3 / 1000) = 0.0247
Using a normal approximation and a z-score of 1.96 (corresponding to a 95% confidence level), the confidence interval can be calculated as:
p_hat +/- z * SE = 0.7 +/- 1.96 * 0.0247 = [0.6511, 0.7489]
So, with 95% confidence, we can estimate that the true proportion of Canadians who refused the H1N1 vaccination lies between 0.6511 and 0.7489.
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The unequal angle of kite is 64 and 88 find the equal angle
15.42 in terms of pi
The approximate value of π for 15.42 is 3.855.
What is the Pi?
π (Pi) is a mathematical constant that represents the ratio of a circle's circumference to its diameter. It is an irrational number, which means that its decimal representation never terminates or repeats.
In a study of Mathematics, the number π read as pi is used.
The value of π is 3.1415926535 is the approximate value of 22/7
For this, in consideration of calculation, we take π as 22/7
The approximate value of π (pi) for 15.42 can be calculated as:
15.42 / 4 = 3.855
Hence, the approximate value of π for 15.42 is 3.855.
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if researchers use statistical tests and determine that there is a low probability that their experimental results occurred purely by chance, then their results are .
If researchers use statistical tests and determine that there is a low probability that their experimental results occurred purely by chance, then their results are considered statistically significant.
Statistically significant results suggest that the observed effects in the experimental group are unlikely to have happened by chance and are likely to reflect a real effect of the treatment or intervention being tested.
However, it's important to note that statistical significance does not necessarily mean practical significance or real-world importance. For example, a small effect may be statistically significant but still not large enough to have practical implications.
Additionally, it's important to be aware of potential sources of error and bias in the experimental design and data analysis, and to consider the results in the context of other relevant evidence. Statistical significance should not be used as the sole criterion for accepting or rejecting research results, and should always be accompanied by a thorough evaluation of the quality of the evidence and the implications of the results.
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The probability of rain on any particular day is 0. 2. However, the probability of rain on a day after a rainy day is 0. 85, whereas the probability of rain on a day after a non-rainy day is 0. 1.
a) On two consecutive days, find the probability of having:
i. Two rainy days
ii. Exactly one rainy day
iii. At least one dry day
b) On three consecutive days, find the probability of having:
i. Three rainy days
ii. Exactly one dry day
iii. At most two rainy days
a) i. the probability of two rainy days is 0.2 * 0.85 = 0.17.
ii. The total probability of having exactly one rainy day is the sum of these two probabilities is 0.18.
iii. probability of having At least one dry day is 0.83.
b)i. The probability of having Three rainy days is 0.1447.
ii. The probability of having Exactly one dry day is 0.1881
iii. The probability of having At most two rainy days is 0.35
a) On two consecutive days, the probability of having:
i. Two rainy days: The probability of two rainy days can be found by multiplying the probabilities of rain on each day, given that the previous day was rainy. In this case, the probability of two rainy days is 0.2 * 0.85 = 0.17.
ii. Exactly one rainy day: There are two ways to have exactly one rainy day in two consecutive days: either the first day is rainy and the second day is dry, or the first day is dry and the second day is rainy. The total probability of having exactly one rainy day is the sum of these two probabilities, which can be calculated as:
P(rainy day first) * P(dry day second) + P(dry day first) * P(rainy day second) = 0.2 * 0.9 + 0.8 * 0.1 = 0.18
iii. At least one dry day: To find the probability of at least one dry day, we can subtract the probability of two rainy days from 1, since the only possibility in which there is no dry day is if both days are rainy:
1 - P(two rainy days) = 1 - 0.17 = 0.83
b) On three consecutive days, the probability of having:
i. Three rainy days: The probability of three rainy days can be found by multiplying the probabilities of rain on each day, given that the previous day was rainy. In this case, the probability of three rainy days is 0.2 * 0.85 * 0.85 = 0.1447.
ii. Exactly one dry day: To have exactly one dry day in three consecutive days, we need two rainy days followed by a dry day, or a rainy day followed by two dry days, or two dry days followed by a rainy day. The total probability of having exactly one dry day can be calculated as:
P(rainy day first, rainy day second, dry day third) + P(rainy day first, dry day second, dry day third) + P(dry day first, rainy day second, rainy day third)
= 0.2 * 0.85 * 0.9 + 0.2 * 0.9 * 0.9 + 0.8 * 0.1 * 0.1 = 0.1881
iii. At most two rainy days: To find the probability of at most two rainy days, we need to add up the probabilities of two rainy days and one rainy day.
P(at most two rainy days) = P(two rainy days) + P(one rainy day) = 0.17 + 0.18 = 0.35
So, the probability of having at most two rainy days in three consecutive days is 0.35.
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Which of the following answers is correct?
The function d/dx (f/g) = 2 gives the value of c as -4.
What is Quotient Rule?The denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator, is how the Quotient Rule defines the derivative of a quotient.
Given:
f(x) = 1/2x and g(x) = 1/ (3x + c)
Using Quotient rule
d/ dx (f/g)
= g f' - f g- / g²
So, d/dx ( 3x+c / 2x )
= [3x -1(3x+c)] / 2x²
= -c/ 2x²
Now out x= 1
Also, d/dx (f/g)= 2
-c/ 2 = 2
c= -4.
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Why does everyone need to follow the order of operations when evaluating expressions?
Answer:
They make sure everyone gets to the same answer. Many people memorize the order of operations as PEMDAS (parentheses, exponents, multiplication/division, and addition/subtraction). The order of operations are one set of agreements for how to evaluate expressions. They make sure everyone gets to the same value.
Step-by-step explanation:
Use sets to solve the problem.
Monticello residents were surveyed concerning their preferences for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen,
100 support both Moore and Allen, and 250 support only Moore. How many residents support Moore?
The number of residents that support more are 350
What is set?Sets are a collection of well-defined objects or elements. A set is represented by a capital letter symbol and the number of elements in the finite set is represented as the cardinal number of a set in a curly bracket {…}.
The number of residents that support more will be number of residents that support Moore only plus the number of residents that support both Moore and Allen
therefore ;
the number of residents that support Moore =
250+100 = 350 residents
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a unit vector lies in the xy plane, at an angle of 156 degrees from the x axis, with a positive y component. what is the unit vector? (it helps to draw a diagram.)
Components of the unit vector are (cos(156), sin(156)) = (-0.41, 0.91). Drawing a vector with a positive y-component and an angle of 156 degrees with the x-axis in the xy plane will help you see it.
The unit vector has a positive y component and is located in the xy plane at a 156 degree angle to the x axis. Drawing a vector with a positive y-component and an angle of 156 degrees with the x-axis in the xy plane will help you visualise this. Components of the unit vector are (cos(156), sin(156)) = (-0.41, 0.91). This shows that the unit vector has both a positive y-component and a negative x-component. Since the unit vector's magnitude is 1, it has a length of 1, and it points in the same general direction as the 156-degree angle. In light of this, the unit vector is (-0.41, 0.91). Any vector with the same magnitude and direction as the unit vector but a different length can be represented by this vector.
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**I WILL GIVE 50 POINTS AND BRAINLIEST**
A paperweight, the shape of a hemisphere, fits snugly inside a cylinder-shaped box with a radius of 9 cm. A cone fits snugly inside the paperweight hemisphere.
What is the volume of the cylinder in terms of π? Show all work.
What is the volume of the cone in terms of π? Show all work.
Estimate the volume of the hemisphere in terms of π by calculating the average of the volumes of the cylinder and cone. Show all work.
Answer:
V = πr^2h = πr^2(2r) = 2πr^3
Volume of the cone: The volume of a cone with height h and base radius r is given by the formula V = (1/3)πr^2h. In this case, the height of the cone is equal to the radius of the hemisphere, so h = r. Substituting this into the formula, we have:
V = (1/3)πr^2h = (1/3)πr^2r = (1/3)πr^3
Volume of the hemisphere: To estimate the volume of the hemisphere, we'll average the volumes of the cylinder and cone.
So:V = (2πr^3 + (1/3)πr^3) / 2 = (5/3)πr^3 / 2 = (5/6)πr^3
So the volume of the hemisphere is approximately equal to (5/6)πr^3, where r is the radius of the hemisphere (and equal to the radius of the cylinder).
Step-by-step explanation:
What is 5 x 3 1/5 please with solution
Please Help, step by step needed
Using the double angle property of the trigonometric functions the value of tan 2θ = 4/3.
What is Pythagoras theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse. Due to its position opposite the 90° angle, the hypotenuse in this case is the longest side. When the positive integer sides of a right triangle (let's say sides a, b, and c) are squared, the result is an equation known as a Pythagorean triple.
Given that the value of cos θ = 2√5 / 5.
The cosine is given as:
Cos θ = adjacent side / Hypotenuse
So, the value of adjacent side = 2√5 and the value of hypotenuse = 5.
To find the value of opposite side we use the Pythagorean theorem:
a² + b² = c²
a² + (2√5)² = (5)²
a² + 4(5) = 25
a² = 25 - 20
a = √5
Now, the value of tan θ = opposite side / adjacent side so,
tan θ = √5 / 2√5 = 1/2
The tan 2θ is given as:
tan 2θ = 2(tan θ) / 1 - tan² θ
Substituting the value of tan θ:
tan 2θ = 2(1/2) ÷ (1 - (1/2)²)
tan 2θ = 1 ÷ (3/4)
tan 2θ = 4/3
Hence, using the double angle property of the trigonometric functions the value of tan 2θ = 4/3.
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as a result of control testing, a cpa has decided to increase control risk. what is the impact on substantive testing sample size if all other factors remain constant?
Increasing control risk will not have an impact on substantive testing sample size if all other factors remain constant.
If all other factors remain constant, then the substantive testing sample size will remain the same. The increase in control risk will affect the auditor’s overall assessment of risk and may result in the auditor deciding to perform more tests of controls, but it will not necessarily affect the substantive testing sample size.
Increasing control risk will not have an impact on substantive testing sample size if all other factors remain constant.
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which expression uses the commutative property of addition and the associative property of multiplication to rewrite the expression (3x2) x 5 7?
The expression used by commutative property of addition and the associative property of multiplication to rewrite the expression (3x2) x 5+7 is 7+3.(2.5).
The commutative property or commutative law of mathematics states that while executing mathematical operations, the order of terms is irrelevant.
Only addition and multiplication operations are under the purview of the commutative property. As a result, it means that while adding or multiplying any two integers, we can swap the positions of the numbers. One of the main characteristics of integers is this.
According to the commutative property of multiplication, even if the positions of the two integers are switched around, the result of multiplying two integers will still be the same.
Suppose A and B are two integers;
A × B = B × A
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How many of the scores (from the group that studied in Question #8).
Studied: 87, 100, 94, 79, 92, 100, 95, 83, 89, 99, 100, 91, 89, 95, 100, 93, 96, 83
Did Not Study: 82, 72, 45, 91, 58, 83, 65, 87, 90, 77, 73, 89
. Are within one mean absolute deviation of the mean? Which scores are within one mean absolute deviation of the mean? (Please show all work). Worth a ton of points!!!!!!
Answer:
Mean Of Students Who Studied: 92.5
Absolute Deviation: 5.2
Answer: 100
Step-by-step explanation:
The area of the base of the nonagonal prism below is 40 square
meters. Its volume is 320 cubic meters. What is the height of the
prism?
The height of the prism with base area of 40 square meters and volume of 320 cubic meters is 8 meters
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
The volume of the prism is the amount of space that the solid figure occupies.
The volume of prism = area of base * height
The area of the base of the nonagonal prism below is 40 square meters. Its volume is 320 cubic meters. Hence:
The volume of prism = area of base * height
Substituting:
320 m³ = 40 m² * height
height = 8 m
The height of the prism is 8 meters
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Londyn and Landen are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 43.98 (about 14π ) cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?
Answer:
Step-by-step explanation:
The volume of a cone can be calculated as (1/3)πr^2h, so we can set that equal to 43.98:
(1/3)πr^2h = 43.98
Dividing both sides by (1/3)π:
r^2h = 43.98 * 3 / π
Solving for one of the variables in terms of the other requires choosing specific values for either radius or height. Here are two examples:
Example 1: Let's say r = 3.
Then
h = 43.98 * 3 / (π * 9) = 4.43
So one possible cone has height 4.43 and radius 3.
Example 2: Let's say h = 5.
Then
r^2 = 43.98 * 3 / (π * 5) = 25.51
So one possible cone has height 5 and radius 5.07.
19. Nomusa has 30 sweets.
She has
18 fruit sweets
7 aniseed sweets
5 mint sweets
Nomusa is going to take at random two sweets.
Work out the probability that the two sweets will not be the same type of sweet.
You must show all your working.
The probability that Nomusa will not take two of the same type of sweet is 0.35
How to find the probability?To find the probability that Nomusa will not take two of the same type of sweets, we need to find the total number of combinations of two sweets she can take, and then find the number of combinations where the two sweets are different.
First, let's find the total number of combinations of two sweets:
C(30, 2) = 435
This means there are 435 different combinations of two sweets she can take from her collection of 30 sweets.
Next, let's find the number of combinations where the two sweets are not the same:
C(18, 2) + C(7, 2) + C(5, 2) = 153
This means that there are 153 combinations where the two sweets are different fruit sweets, different aniseed sweets, or different mint sweets.
So, the probability that Nomusa will not take two of the same type of sweet is:
153 / 435 = 0.35
This means that there is a 35% chance that the two sweets she takes will not be the same type of sweet.
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the graph of contains the point . what point must be on the graph of each of the functions below? enter points as including the parentheses.
Based on the provided information, the graph of y = v(3x) - 4 must contain the point (-4, -8) and (b) the graph of y = 1/4 v(x) + 9 must contain the point (-12, 6).
As the graph of y = v(x) contains the point (−12, −7), point that must be on the graph of each of the functions below are:
(a) y = v(3x) - 4
3x = -12
x = (-12)/3= -4
y = -4 – 4 = -8
The graph of y = v(3x) - 4 must contain the point (-4, -8).
(b) y = 1/4 v(x) + 9
x = -12
y = 1/4 (-12) + 9 = 6
The graph of y = 1/4 v(x) + 9 must contain the point (-12, 6).
Note: The question is incomplete. The complete question probably is: The graph of y=v(x) contains the point (−12,−7). What point must be on the graph of each of the functions below? Enter points as (a,b) including the parentheses. (a) The graph of y = v(3x) - 4 must contain the point _ (b) The graph of y = 1/4 v(x) + 9 must contain the point _ .
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If JK=31, KI = 40, and NL=12, find the length of ‾MN‾. Round your answer to the nearest tenth if necessary. Figures are not necessarily drawn to scale.
Answer:
MN = 15.5 units
------------------------------
The triangles are similar since all three angles are equal on both.
We know corresponding sides of similar triangles are proportional.
Set up proportions and find the missing side length:
MN/KJ = NL/JKMN/40 = 12/31MN = 40*12/31MN = 15.4838 ≈ 15.5candidate a says that he is winning because current polling shows that he has 54% of the vote as opposed to his opponent who has 46% of the vote. the poll has a margin of error of plus or minus 5%. is candidate a giving an honest reading of the poll results? why or why not?
Candidate A may not be giving an honest reading of the poll results.
When interpreting poll results, it is important to consider the margin of error, which indicates the level of precision of the results. In this case, the margin of error is plus or minus 5%. This means that the true support for each candidate could be as much as 5% higher or lower than the reported numbers.
Based on this information, it is possible that candidate A's lead is not as large as he claims, or that his opponent is actually leading by a narrow margin. Furthermore, it is important to note that the results of a single poll should not be taken as the definitive outcome of an election. Instead, multiple polls should be considered and the results should be viewed in the context of other factors such as the demographic makeup of the polling sample and the timing of the poll.
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Which three-dimensional figure is formed by the rotation given?
A three-dimensional figure that is formed by the rotation given include the following: D. inverted-open cone.
What is a rotation?In Mathematics, a rotation can be defined as a type of transformation which moves every point of the geometric figure through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.
Generally speaking, the rotation of a plane figure around a straight line (axis of revolution) is referred to as a solid of revolution.
In this scenario, a right triangle with a side that matches the axis is rotated with respect to its hypotenuse (axis of revolution or straight line), by an angle of 360 degrees and through the origin in order to form an inverted-open cone.
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Answer: Bottom Left Corner, No Shading on the base.
Step-by-step explanation: Took the test