The relation between a and r is 2r
How to write a function describing the relationship of the given variables?According to the given information
a varies directly with r
a = 8
r = 4
a is directly proportional to r
a ∝ r
a = k r
where k is constant of proportionality
k = [tex]\frac{a}{r}[/tex]
k = [tex]\frac{8}{4}[/tex]
k = 2
so,
a = k r
putting the value of k in the above equation
we get
a = 2r
The relation between a and r is 2r
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Which of the following statements are true?
i. It is okay to use the median to estimate the mean since both are a measure of the center of a
distribution.
ii. It is okay to use the standard deviation to estimate the IQR since both are measures of variability.
iii. Point estimates based on a sample are sometimes far from a parameter's value.
Oi only
O ii only
O iii only
Oi and ii
Oi and iii
O i, ii, and iii
Check Answer
The correct answer is c) iii only as statement 1 and statement 2 are false.
What do mean and standard deviation tell us?
In statistics, the measurement of variability known as the standard deviation (SD) is frequently utilized. It demonstrates how different things are from the norm (mean). While a high SD shows that the data are dispersed throughout a wide range of values, a low SD suggests that the data points tend to be close to the mean.
What is relationship between mean and standard deviation?
The standard deviation is a measure that summarizes how far away from the mean each observation is. The positive would exactly balance the negative if the discrepancies themselves were totaled together, making their aggregate equal to zero. The squares of the discrepancies are then added as a result.
What is median?
The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
Statement 1: False, it only works if distributiion is syummetric, for non- symmetric distribution, median is not unbiased estimator population in mean.
Statement 2: False standard deviation is not equal to IQR, and is heavily influenced by sample mean and outliers.
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Find the intercept of the line 4x−3y=17
Answer:
see attachment
Step-by-step explanation:
(sec²0 - 4/3) (2sin0 + 1)=0
csc³0 + 2csc²0 - 4/3csc²0 - 8/3=0
2sin²0 + 2sin0 + 1/2 =0
Answer:
2sin²0 + 2sin0 - 1/2 = 0
(2sin0 + 1)(sin²0 - 1/2)= 0
2sin0 + 1 = 0 or sin²0 - 1/2 = 0
2sin0 = -1 or sin0 = ±1/√2
How do I take an antiderivative of the following equation?
[tex]dy/dx+ky-77k=0[/tex]
The required anti derivative of given function is -(ky^2)/2 + 77ky.
What is integration(anti-derivative)?Anti-differentiation or integration is the converse interaction to separation. For instance, if f (x) = 2x, we realize that this is the subordinate of f(x) = x^2.
According to question:We have,
dy/dx +ky - 77k = 0
dy/dx = -ky + 77k
Integrate with respect to x
∫dy/dx = ∫(-ky + 77k)
∫dy/dx = -∫ky +∫77k
y = -(ky^2)/2 + 77ky
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The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
What is antiderivative?
In calculus, a differentiable function F whose derivative is identical to the original function f is known as an antiderivative, inverse derivative, primitive function, primitive integral, or indefinite integral of a function f. F' = f can be used to represent this.
[tex]\frac{dy}{dx} = 77k - ky\\\\dx=\frac{dy}{77k-ky} \\\\dx = \frac{dy}{77-y} \times \frac{1}{k} \\\\kdx = \frac{dy}{77-y} \\\\-\frac{dy}{y-77} =kdx\\\\log(y-77)=-(kx+c)\\\\y=e^{-(kx+c)} +77[/tex]
Hence, The required antiderivative is [tex]y=e^{-(kx+c)} +77[/tex]
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(100 POINTS AND BRAINLYEST GURANTEE PLEASE I NEED HELP)
Answer everything in the image listed below please.
To prove parallelograms is a parallelograms we have show that, diagonals cut each other in half, and one angle adds to both following angles .
What is parallelograms ?One particular type of quadrilateral that is created by parallel lines is a parallelogram. A parallelogram can have any angle between its adjacent sides as long as its opposite sides are parallel.
The sum of all the sides' lengths determines a rhombus' perimeter. A rhombus's perimeter is equal to four times the length of each side because all of its sides are equal. A diamond's perimeter is given in 4x units, for instance, if one of its sides is x units.
P=4a
The two opposing side pairs must be parallel, the two opposite side pairings must coincide, the two opposite angle pairs must coincide, the diagonals must cut each other in half, the first angle must add to both the following angles, and one set of opposing sides must be both parallel AND congruent. These are the six basic properties of parallelograms.
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ABCD is a rhombus and side AE Is congruent to EC prove triangle AEB is congruent to CEB
ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
What is a rhombus?A rhombus is one type of parallelogram and has 4 sides and 4 vertices.
Every side is equal in length and opposite angles are equal.
Given that the side AE is congruent to EC of rhombus.
That means, AE ≅ EC.
And the diagonals of rhombus bisects each other.
Both the triangle AEB and triangle CEB share the same side which is BE.
That means BE ≅ BE, by the reflexive property.
And the sides AB and BC are the sides of rhombus.
So, AE ≅ BC.
Therefore, if ABCD is a rhombus and side AE Is congruent to EC. Then triangle AEB is congruent to CEB.
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The perimeter of a playing field for a certain sport is 302 ft. The field is a rectangle, and the length is 47 ft longer than the width. Find the dimensions. What is the width?
Answer:
To find the dimensions of a rectangle
Step-by-step explanation:
perimeter=302
let width=x
length=x+47
p=2(L+W)
302=2(x+x+47)
302=2(2x+47)
302=4x+94
subtracting 94 from the other side we have
302-94=4x
208=4x
x=52
length=99
width=52
x^-3=1/343 what does x equals please show all work.
Answer:
Step-by-step explanation:
X^-3=1/343
X^-3=1/7^3
X^-3=7^-3
Since the powers are equal, the bases should also be equal.
Therefore, X=7
A table of 1,022 guests are attending a reception. If each table can seat exactly 12 people,what is the least number of tables needed to seat all guests?
Answer:
86
Step-by-step explanation:
If you did 1,022 divided by 12, you would get something crazy like 85.16666666666. So round up.
What is mZQPR?
I need help please help me
Answer: 68
Step-by-step explanation:
Angles in a triangle add to [tex]180^{\circ}[/tex], meaning that [tex]m\angle TRS +m\angle TSR=136^{\circ}[/tex].
Furthermore, since [tex]\triangle TSR[/tex] is isosceles, [tex]m\angle TRS=m\angle TSR[/tex].
Therefore, [tex]m\angle TSR=68^{\circ}[/tex].
Carlos sells tickets for a concert. He earns $200 plus
$2.50 per ticket he sells. So far, Carlos has earned
$300. How many more tickets does Carlos need to sell
to earn $350?
A. 20
B. 50
C. 125
D. 150
Answer:
A. 20
Step-by-step explanation:
300 ÷ 2.5= 120
So
50÷2.5 = 20
PLEASE HELP ASAP HURRY PLEASE!! I'LL GIVE BRAINLIEST TO FIRST PERSON TO ANSWER!!!
4y = 164, solve for y.
The value of y that satisfies the equation is 41.
What is the arithmetic operation?
Arithmetic operations involve the study of numbers, the operation of numbers that are useful in all the other branches of mathematics. It basically comprises operations such as Addition, Subtraction, Multiplication, and Division.
To solve this equation for y, you can divide both sides by 4:
4y/4 = 164/4
This simplifies to:
y = 41
Hence, the value of y that satisfies the equation is 41.
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A container is a hemisphere of radius 30cm.
Sand fills the container at a rate of 4000 cm³ per minute.
Does it take less than a quarter of an hour to fill the container?
You must show your working.
Since the time is 0.24 hour. Yes, it takes less than a quarter of an hour to fill the container
How to determine if it takes less than a quarter of an hour to fill the container?Given: A container is a hemisphere of radius 30cm
Sand fills the container at a rate of 4000 cm³ per minute
A hemisphere is half a sphere. Thus:
The volume of a hemisphere = 1/2 × 4/3 πr³ = 2/3 πr³
The volume of a hemisphere = 2/3 × π × 30 = 56548.67 cm³
Rate = Volume / Time
Time = Volume/Rate
Time = 56548.67 /4000 = 14.14 minutes
In hours: Time = 14.14/60 = 0.24 hour
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Please help! :] 50 Points and awarding Brainliest. Consider the following right pyramid and right prism. Both figures have a base that is a regular pentagon.
Heidi tried to use Cavalieri's principle to show that the two figures have the same volume.
"The base areas are the same. Therefore, corresponding cross-sections have the same area. The figures have the same height. So the volumes must be the same."
What is the first mistake Heidi made?
Choose 1 answer:
(Choice A)
A
The base areas are not the same.
(Choice B)
B
It isn’t true that corresponding cross-sections have the same area.
(Choice C)
C
The heights are not the same.
Answer:
The answer to your question is,
B) It isn’t true that corresponding cross-sections have the same area.
Step-by-step explanation:
They have the same areas and the same heights. but the corresponding cross-section is not the same
{The top of the first figure is a point, but the second one is a flat}
I hope this helps :)
Answer:
B) It isn’t true that corresponding cross-sections have the same area.
Step-by-step explanation:
Cavalieri's principle
If two three-dimensional figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.
From inspection of the given diagram:
The base area of both figures is the same.The height of both figures is the same.The cross-sectional area at every point along the height is not the same in both figures.
find the circumference of the circle use 3.14 r=6
The circumference of the circle with the dimensions radius = 6 and π = 3.14 is 37.68
What is the circumference of a circle?The circumference of a circle refers to the line that bounds a circle or other two-dimensional figure.
Circumference of a circle = 2πr
Where,
π = 3.14Radius, r = 6Circumference of a circle = 2πr
= 2 × 3.14 × 6
= 37.68
Therefore, the circumference of the circle is given by 37.68
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Solve the system of equations by using the addition method.
5x+-7y=-2
10x+5y=15
Answer:
y=1, x=1
Step-by-step explanation:
no need for step by step cause i know
From question 28 -29
Help please
By using the concept of vector, it can be calculated that
28) First option is correct
29) Fourth option is correct
What is vector?
Anything that has both magnitude and direction and follow the vector addition law is called vector.
28) The vectors are
[tex]\vec{v} = -2i-5j,[/tex]
[tex]\vec{w} = -3i+j[/tex]
[tex]\vec{v}. \vec{w} = (-2i-5j).( -3i+j) = 6 - 5 = 1\\|\vec{w}|^2 = (-3)^2+(1)^2 = 9 + 1 = 10\\\vec{v_1} = \frac{1}{10}( -3i+j) = \frac{-3}{10}i+\frac{1}{10}j[/tex]
[tex]\vec{v_2} = (-2i-5j) - (-\frac{3}{10}i - \frac{1}{10}j)\\\vec{v_2}= (-2+\frac{3}{10})i+(-5 - \frac{1}{10}j)\\\vec{v_2}=-\frac{17}{10}i - \frac{51}{10}j\\[/tex]
First option is correct
29) P = (1, 2) and Q = (-6, -1)
Position vector = (-6-1)i + (-1-2)j = -7i - 3j
Fourth option is correct
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Describe the graph of the proportional relationship represented by the equation y = 7.5x.
The graph is a line that goes through points (0, 0) and (7.5, 7.5).
The graph is a line that goes through points (0, 0) and (15, 2).
The graph is a line that goes through points (0, 0) and (7.5, 1).
The graph is a line that goes through points (0, 0) and (1, 7.5).
The graph of the proportional relationship represented by the equation y = 7.5x is The graph is a line that goes through points (0, 0) and (1, 7.5)
What is a graph of linear function?A linear function consists of functions where the variables has exponents of 1.
The graph of linear functions is a straight line graph and the relationship is expressed in the form.
y = mx + c
definition of variable to suit the problem
y = output variable
m = slope
x = input variable
c = y intercept
considering the given equation y = 7.5x.
c = 0
hence the graph passed through (0, 0)
substituting x = 1 gives y = 7.5 hence (1, 7.5) is another point
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Determine algebraically whether the given function is even, odd, or neither.
f(x) = -5x² + |2x|
well, as you already know, to check if a function is EVEN, we simply check what's f( -x ), if f( -x ) = f( x ), then voila!!. and if f( -x ) = -f( x ), then oddly enough, is an ODD function.
well, let's plug in " -x " to see what we get anyway
[tex]f(x)=-5x^2 + |2x|\implies \boxed{f(x)=-5x^2 + 2x} \\\\[-0.35em] ~\dotfill\\\\ f(-x)=-5(-x)^2 + |2(-x)|\implies f(-x)=-5(-x)(-x) + |-2x| \\\\\\ f(-x)=-5(+x^2) +2x\implies \boxed{f(-x)=-5x^2 + 2x}~\hfill \stackrel{\textit{\LARGE Even}}{f(-x)=f(x)}[/tex]
In the diagram below of triangle PQR, S is the midpoint of PR and T is the midpoint of Q R. If ST=-2x+32, and PQ=7x-2, what is the measure of PQ ?
The measure of PQ in the given triangle is 24.
What is triangle?
Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.PQ = ST
7x-2 = -2x+32
7x + 2x = 32 + 2
9x = 34
x = 34/9
The measure of PQ:
PQ = 7x-2
= 7(34/9) - 2
= (238 - 18) / 9
= 24.4
PQ ≅ 24
Hence, the measure of PQ in the given triangle is 24.
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Please hurry please help me but correct answer
Answer:
increase of 100%
Step-by-step explanation:
50 cents to 1 dollar is an increase.
The percent increase can be calculated by dividing the increased amount by the original amount.
$1.00 - $0.50 = $0.50 increase
% increase = 100%
If ABTS = AGHD, BS = 25, IS = 14, BT = 31, GD = 4x - 11, m2S = 56, mLB = 21°, and mLH = (7y + 5)°, find the values of x and y.
Answer:
x = 8
y = 2
Step-by-step explanation:
Solve the equation A = L • W for W.
Answer:
[tex]W=\frac{A}{L}[/tex]
Step-by-step explanation:
Divide both sides of the equation by [tex]L[/tex].
Divide. Give the quotient and remainder.
133 2
Answer:
Quotient: 66
Remainder: 1
Step-by-step explanation:
133/2 = 66.5
66.5 =
66 + 0.5 =
66 + 1/2 = 66 1/2
1/2 * 2 = 1 ==> Remainder: 1
Whole number : 66
Quotient: 66
Remainder: 1
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High school students across the nation compete in a financial capability challenge each year by taking a National Financial Capability Challenge Exam. Students who score in the top 18 percent are recognized publicly for their achievement by the Department of the Treasury. Assuming a normal distribution, how many standard deviations above the mean does a student have to score to be publicly recognized?
The top 18 percent of scores fall within two standard deviations of the mean.
What is publicly recognized?Publicly recognized refers to something that is well-known or acknowledged by the public or by a large segment of the population. This could include a famous person, a popular business, or an important event or achievement. Public recognition is often seen as an indicator of success, as it shows that the person or thing being recognized has achieved something noteworthy or has had a positive influence on the public. Examples of publicly recognized things include awards, honors, and other achievements.
Assuming a normal distribution, a student needs to score at least two standard deviations above the mean to be publicly recognized. This is because the top 18 percent of scores fall within two standard deviations of the mean. This can be expressed mathematically as:
P(x > μ + 2σ) = 0.18
where μ is the mean and σ is the standard deviation.
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Liam works at a zoo. He was looking at some data showing the masses of their
5
55 African elephants. The mean mass of the elephants was
3
,
800
kg
3,800kg3, comma, 800, start text, k, g, end text, and the median mass was
3
,
600
kg
3,600kg3, comma, 600, start text, k, g, end text. The smallest elephant, named Lola, weighed
2
,
700
kg
2,700kg2, comma, 700, start text, k, g, end text.
Lola then got very sick and lost weight until her mass reached
1
,
800
kg
1,800kg1, comma, 800, start text, k, g, end text.
How will Lola's mass decreasing affect the mean and median?
Median won't change, however Mean will fall by 180.
What do mean and median?By summing all the numbers in a data collection and dividing by the total number of values in the set, one may get the mean (average) of the data set. When a data collection is sorted from least to largest, the median represents the midpoint value.
African elephants total 555 in number.
Elephants had a 3800 kg average mass.
Elephants had a 3600 kg median mass.
Lola, the elephant that was the smallest, weighed 2700 kg.
Later, Lola became really ill and lost a lot of weight, reaching a mass of 1800 kg.
What effect will Lola's weight loss have on the mean and median as well as Currently, the median is 3600 and the lowest is 2700.
now 2700 becomes 1800
so Median remains the same as 3600
No change in Median
The mean mass of the elephants was 3800 kg
=> total weight = 5 x 3800 = 19000 kg
2700 kg becomes 1800 kg
Hence new total mass = 19000 - 2700 + 1800 = 181000 kg
New Mean = 18100/5 = 3620 kg
Mean reduced by 3800 - 3620 = 180 kg
No change in Median weight
Mean reduced by 180 kg
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You brake your car from a speed of 55 mph. The table shows data that represent your car's speed versus the amount of time elapsed from the moment that you began to brake.
Elapsed Time (seconds)
Speed (mph)
1
47
2
39
3
31
4
23
5
23
6
23
Evaluate the following graph based on the data in the table.
A graph has elapsed time (seconds) on the x-axis, and speed (miles per hour) on the y-axis. A line goes through points (1, 47), (2, 39), (3, 31), (4, 23), (5, 23), (6, 23).
For what interval of time is the speed increasing?
For what interval of time is the speed decreasing?
For what interval of time is the speed constant?
a.
None
0 to 4 seconds
4 to 6 seconds
c.
None
0 to 5 seconds
5 to 6 seconds
b.
0 to 5 seconds
None
5 to 6 seconds
d.
0 to 4 seconds
None
4 to 6 seconds
Answer:
Step-by-step explanation:
d. 0 to 4 seconds, None, 4 to 6 seconds.
Based on the data in the table, the speed of the car is increasing for the interval of time from 0 to 4 seconds. After 4 seconds, the speed remains constant at 23 mph for the remainder of the time period. Therefore, the speed is not decreasing at any point in the given time interval.
Solve for x. 4 (x + 1 1/3) = 9 2/3 Enter your answer as a mixed number in simplest form in the box.
An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
The value of x is 6.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4(x + 11/3) = 9(2/3)
Divide both sides by 4.
x + 11/3 = 29/3
Subtract 11/3 on both sides.
x = 29/3 - 11/3
x = (29 - 11) / 3
x = 18/3
x = 6
Thus,
The value of x is 6.
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5
ARK
Simplify each of the following expressions:
4+ (-9) + 3 =
16) How many more line segments will be needed to be added to Step 3 to create Step 4 of the
sequence?
Step 1
Step 2
Step 3