Answer:
a
Step-by-step explanation:
to find a proportion they must equal each other
8/4 in its simplest form is just 2
to make r/3 = 2 r must be 6
6/3 is 2
On the first day, you pay $5 for 2 boxes of popcorn.
The next day you pay $7.50 for 3 boxes. Are the ratios
equivalant.
Answer:
10 5
Step-by-step explanation:
Answer: Yes
Step-by-step explanation:
First find the unit rate by find the cost per box.
To find the cost per post you will divide the cost by the number of boxes.
5/ 2 = 2.5
7.50/ 3 = 2.5
2.5 is indeed equal to 2.5 so they are equivalent.
Within the year, a city in Texas recorded 50,000 new cases of a common disease. The year before, the city saw 40,000 cases of the same disease. The city has a population of 250,000 people. The amount of people in this city that have this disease is 90,000 people which shows a prevalence rate of 0.36, a little over 1 in 3 people. This is an example of what kind of rate
The given situation is an example of a point prevalence rate.
The point prevalence rate is the proportion of people in a population who have a particular disease or condition at a particular point in time. In this given situation, the city has a population of 250,000, with 90,000 of them having the disease, so the point prevalence rate would be calculated as follows:
Point Prevalence Rate = (Number of People with the disease / Total Population) x 100%
Point Prevalence Rate = (90,000 / 250,000) x 100%
Point Prevalence Rate = 0.36 x 100%
Point Prevalence Rate = 36%
Therefore, the given situation is an example of a point prevalence rate as it indicates the proportion of people in a population who have the disease at a specific point in time
The given situation is an example of a point prevalence rate.
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Let $F,$ $G,$ and $H$ be collinear points on the Cartesian plane such that $\frac{FG}{GH} = 1.$ If $F = (a, b)$ and $H = (7a, c)$, then what is the $x$-coordinate of $G$?
F, G, and H all lie on the same line. If FG/GH = 1, then FG = GH, which is to say the distance between F and G is equal to the distance between G and H. This means either F and H are the same point, or G is the midpoint of F and H.
They're not the same point, because the x-coordinate of H is 7 times that of F. So G must be halfway between F and H.
Then the x-coordinate of G is
(a + 7a)/2 = 8a/2 = 4a
Find the rectangular coordinates of the point(s) of intersection of the polar curves =2sin(2) and =2sin().
The rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.
To find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form, the rectangular coordinates of the above points are given below:
For the equation r = 2sin(2θ):
x = 2sin(2θ)cos(θ)
y = 2sin(2θ)sin(θ)
For the equation r = 2sin(θ):
x = 2sin(θ)cos(θ)
y = 2sin^2(θ)
The rectangular coordinates of the point(s) of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ) can be found by converting the polar equations to rectangular form and solving for the x and y coordinates.
To convert the polar equations to rectangular form, we can use the relationships x = rcos(θ) and y = rsin(θ). Substituting these expressions into the given polar equations, we get:
For the equation r = 2sin(2θ):
x = 2sin(2θ)cos(θ)
y = 2sin(2θ)sin(θ)
For the equation r = 2sin(θ):
x = 2sin(θ)cos(θ)
y = 2sin^2(θ)
To find the points of intersection, we need to set the x and y coordinates of both equations equal to each other and solve for θ. However, solving this system of equations algebraically can be complex due to the trigonometric functions involved.
Graphing the polar curves and visually inspecting the points of intersection may provide a more intuitive approach to finding the rectangular coordinates. By plotting both polar curves on a graph, the points where the curves intersect can be determined by their shared coordinates.
In summary, to find the rectangular coordinates of the points of intersection of the polar curves r = 2sin(2θ) and r = 2sin(θ), the equations can be converted to rectangular form. However, solving the resulting system of equations algebraically may be challenging. Alternatively, graphing the polar curves and visually identifying the points of intersection can provide an effective method.
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Someone plz help me
A rotation ____________ a figure around a fixed point called the center of
________________.
Answer:
A rotation ____on the coordinate plane________ a figure around a fixed point called the center of
___rotation_____________.
questions: 27.32 x 48.97step bye step: Answer:
27.32 x 48.97
multiplying this will give 1337.8604
Kenji drives 18.4 miles in 16 minutes. He passes a sign, which gives the speed limit as 60 mph. By how much, in mph, did Kenji's average speed exceed the speed limit?
The amount of speed by which kendri exceeded the speed limit is; 9 mph
We are given;
Distance; d = 18.4 miles
Time; t = 16 minutes = (16/60) hours
Now, the formula for speed is;
Speed = distance/time
Thus, let's Calculate kenji's speed;
Kenji's speed = 18.4/(16/60)
Kenji's speed = 69 mph
We are told that the speed limit is to be 60 mph, this means that kendri exceeded the speed limit by;
69 - 60 = 9 mph
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What is the circumference of a circle with the radius of 9 inches? Use 3.14 for pi or put pi in your answer for an exact answer.
The circumference of the circle with a radius of 9 inches is approximately 56.52 inches if we use 3.14 to approximate pi.
The circumference of a circle is the distance around the edge of the circle. It can be calculated using the formula C = 2πr, where r is the radius of the circle and π is the mathematical constant pi.
In this problem, we are given the radius of the circle, which is 9 inches. We can substitute this value into the formula C = 2πr and simplify:
C = 2π(9)
C = 18π
Since we are asked to use 3.14 for pi, we can approximate the value of 18π by substituting 3.14 for π:
C ≈ 18 × 3.14
C ≈ 56.52
So, the circumference of the circle with a radius of 9 inches is approximately 56.52 inches if we use 3.14 to approximate pi. However, as I mentioned earlier, pi is an irrational number, and the exact circumference of the circle cannot be expressed as a finite decimal.
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what is the value of x?
Answer:
127
Step-by-step explanation:
There are 720 degrees in hexagon 720-112-133-128-100-120 = 127 so x=127
The random variable x is known to be uniformly distributed between 3.19 and 9.58. Compute the standard deviation of x.
Group of answer choices:
1.845
3.195
6.385
4.518
2.527
3.403
the standard deviation of the random variable x, which is uniformly distributed between 3.19 and 9.58, is 1.845.
To compute the standard deviation of a uniformly distributed random variable x between 3.19 and 9.58, follow these steps:
Step 1: Determine the range of the random variable x. In this case, it is given as 3.19 to 9.58.
Step 2: Calculate the difference between the upper limit (b) and the lower limit (a).
b = 9.58
a = 3.19
Difference = b - a = 9.58 - 3.19 = 6.39
Step 3: Use the formula for the standard deviation of a uniformly distributed random variable, which is:
Standard Deviation (σ) = √((b - a) ²/ 12)
Step 4: Plug in the values from step 2 into the formula:
σ = √((6.39)/ 12)
Step 5: Calculate the result:
σ = √((40.8321) / 12) = √(3.402675) = 1.845
So, the standard deviation of the random variable x, which is uniformly distributed between 3.19 and 9.58, is 1.845.
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5. State if the following statements are true or false. If true, give a 1-3 line explanation; otherwise, provide a counter example or explanation. No rigorous formal justification needed. (a) The set {x∈R
n
∣Ax=b} is convex, where A∈R
m×n
,b∈R
m
. (b) The set {(x
1
,x
2
)∣x
2
≤3x
1
2
} is convex. (c) All polygons on the R
2
plane are convex. (Hint: A polygon is a plane figure formed with straight line segments.) (d) If S⊆R
2
is convex, then S must enclose a region of finite area. (e) If S
1
,S
2
⊆R
2
and S
1
∩S
2
=ϕ, then S
1
∪S
2
must be non-convex. (f) If S
1
,S
2
⊆R
2
and both S
1
,S
2
are closed, then S
1
∪S
2
must be non-convex.
(a) False. The set {x∈R^n | Ax=b} is not necessarily convex. It depends on the matrix A and the vector b. For example, if A is a non-convex matrix, then the set of solutions {x∈R^n | Ax=b} will also be non-convex.
(b) True. The set {(x₁,x₂) | x₂ ≤ 3x₁²} is convex. The inequality defines a downward parabolic region, and any line segment connecting two points within this region will lie entirely within the region. (c) False. Not all polygons on the R² plane are convex. For example, a polygon with a concave portion, such as a crescent shape, would not be convex.
(d) True. If S⊆R² is convex, then it must enclose a region of finite area. Convex sets do not have "holes" or disjoint parts, so they form a connected and bounded region. (e) False. If S₁⊆R² and S₂⊆R², and S₁∩S₂=ϕ (empty set), then S₁∪S₂ can be convex. If S₁ and S₂ are both convex sets that do not overlap, their union can still be a convex set. (f) True. If S₁⊆R² and S₂⊆R² are both closed sets, then their union S₁∪S₂ must also be closed. However, it may or may not be convex. The convexity of the union depends on the specific sets S₁ and S₂.
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Help plsss............
Answer:
The answer would be $50.
Step-by-step explanation:
$5 per session
They come 10 times
$5 x 10 = $50
I need help solving this question x=.
Answer:
X=45
Step-by-step explanation:
90 - 45 = 45
Look at image please help me
Answer:
75 cents
Step-by-step explanation:
3 dollars divided by 4 lemons would equal 75 cent per lemon.
In decimal form it is 0.75 dollars :)
Find the measures of the interior angles of the triangle.
Answer:
see explanation
Step-by-step explanation:
the 3 interior angles of Δ ABC sum to 180°
sum the 3 angles and equate to 180
x - 44 + x + 48 = 180
2x + 4 = 180 ( subtract 4 from both sides )
2x = 176 ( divide both sides by 2 )
x = 88
Then
∠ A = 48°
∠ B = x = 88°
∠ C = x - 44 = 88 - 44 = 44°
urn a contains six white balls and seven black balls. urn b contains five white balls and three black balls. a ball is drawn from urn a and then transferred to urn b. a ball is then drawn from urn b. what is the probability that the transferred ball was white given that the second ball drawn was white?
Using the Bayes' theorem, we find the probability that the transferred ball was white given that the second ball drawn was white to be 52/89, or approximately 0.5843.
To solve this problem, we can use Bayes' theorem, which relates the conditional probability of an event A given an event B to the conditional probability of event B given event A:
P(A|B) = P(B|A) * P(A) / P(B)
where P(A|B) is the probability of event A given that event B has occurred, P(B|A) is the probability of event B given that event A has occurred, P(A) is the prior probability of event A, and P(B) is the prior probability of event B.
In this problem, we want to find the probability that the transferred ball was white (event A) given that the second ball drawn was white (event B). We can calculate this probability as follows:
P(A|B) = P(B|A) * P(A) / P(B)
P(B|A) is the probability of drawing a white ball from urn b given that the transferred ball was white and is now in urn b. Since there are now six white balls and three black balls in urn b, the probability of drawing a white ball is 6/9 = 2/3.
P(A) is the prior probability of the transferred ball being white, which is the number of white balls in urn a divided by the total number of balls in urn a, or 6/13.
P(B) is the prior probability of drawing a white ball from urn b, which can be calculated using the law of total probability:
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
where P(B|not A) is the probability of drawing a white ball from urn b given that the transferred ball was black and P(not A) is the probability that the transferred ball was black, which is 7/13.
To calculate P(B|not A), we need to first calculate the probability of the transferred ball being black and then the probability of drawing a white ball from urn b given that the transferred ball was black.
The probability of the transferred ball being black is 7/13. Once the transferred ball is moved to urn b, there are now five white balls and four black balls in urn b, so the probability of drawing a white ball from urn b given that the transferred ball was black is 5/9.
Therefore, we can calculate P(B) as follows:
P(B) = P(B|A) * P(A) + P(B|not A) * P(not A)
= (2/3) * (6/13) + (5/9) * (7/13)
= 89/117
Now we can plug in all the values into Bayes' theorem to find P(A|B):
P(A|B) = P(B|A) * P(A) / P(B)
= (2/3) * (6/13) / (89/117)
= 52/89
Therefore, the probability that the transferred ball was white given that the second ball drawn was white is 52/89, or approximately 0.5843.
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What is the measure of Boc
Answer:
BOC, since angle B and angle C are bisected, sum of angle OBC and OCB will be half of sum of angles B and C which is 108 degrees.
C = dh + e
Solve for e
Answer: C-dh
Step-by-step explanation: Need to get e on its own
C=dh+e
take dh from both sides
allows you get e on its own
C-dh=dh-dh+e
C-dh=e
Select the equation of the line, in standard form, that passes through (4,2) and is parallel to the line shown on the coordinate grid to the right
The equation of the line that passes through (4,2) and is parallel to the line shown is 3x + y = -10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The slope intercept form of a line is:
y = mx + b
where m is the slope and b is the y intercept
Two lines are said to be parallel if they have the same slope.
The line shown passes through point (0, 1) and (-1, -2). Hence:
Slope = (-2 - 1) / (-1 - 0) = 3
The line parallel will also have a slope of 3. It then passes through (4, 2). Hence:
y - y₁ = m(x - x₁)
y - 2 = 3(x - 4)
y = -3x - 10
3x + y = -10
The equation of the line is 3x + y = -10
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A recent study found that people with insomnia are more likely to experience heart problems than people without insomnia.
a. What are the explanatory and response variables in this study?
b. Explain why amount of caffeine consumed might be a confounding variable in this study by explaining how caffeine consumption fits the two properties of confounding variables given in the box on page.
a. The explanatory variable in this study is insomnia and the response variable is the likelihood of experiencing heart problems. b. Amount of caffeine consumed could be a confounding variable in this study because it fits the two properties of confounding variables.
In this study, the explanatory variable is "insomnia" and the response variable is "heart problems." A confounding variable, such as "amount of caffeine consumed," might affect the relationship between insomnia and heart problems. Caffeine consumption fits the two properties of confounding variables as it is related to both the explanatory variable (insomnia) and the response variable (heart problems). Consuming more caffeine can lead to insomnia, and it can also increase the risk of heart problems independently. Therefore, caffeine consumption could be a confounding variable in this study, potentially influencing the observed relationship between insomnia and heart problems.
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Michael has a bag of marbles. The frequency of selecting each color is recorded in the table below.
Outcome Frequency
Green 4
Black 6
Orange 5
Based on the given frequency, determine the experimental probability of selecting an orange marble.
0.27
0.33
0.40
0.67
The probability of selecting an orange marble is 0.33.
Option B is the correct answer.
What is probability?It is the chance of an event to occur from a total number of outcomes.
The formula for probability is given as:
Probability = Number of required events / Total number of outcomes.
We have,
The number of times each marble is selected.
Green = 4
Black = 6
Orange = 5
Total number of times all marbles are selected.
= 4 + 6 + 5
= 15
Now,
The probability of selecting an orange marble.
= 5/15
= 1/3
= 0.33
Thus,
The probability of selecting an orange marble is 0.33.
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HELPPP!!!! ASAPPPP!!!
1. TRUE
2. FALSE
Answer:
False You just multiply the numbers by 5/3 I am pretty sure.
Hope it helps Have an wonderful day! :)
16. What is the equation in slope-intercept form of a line
passing through points (0,0) and (2, 4)?
Answer:
y= 2x
Step-by-step explanation:
(0,0) and (2, 4)
m= (y2-y1)/ (x2-x1)
m= (4-0)/(2-0)
m= 4/2
m=2
y- y1= m(x -x1)
y - 4= 2(x - 2)
y-4= 2x - 4
y= 2x
Answer:
Step-by-step explanation:
y=mx+b where m is the slope and b is the y intercept. Since there is point (0,0) we know that b=0 so we only need to find m
m=(y2-y1)/(x2-x1)
m=(4-0)/(2-0)=4/2=2 so the line is
y=2x
Joe, Bill, and Hank run different legs of a relay race. Their combined time is 29 minutes. Bill's time is 1 minute more
than three times Joe's time. The sum of Bill's time and twice Joe's time is equal to Hank's time. How much time
did it take each runner to run his leg of the race?
The time it took Joe, Bill and Hank to run the leg of the race is 3, 10 and 16 minutes respectively.
How to determine the valueLet Joe's leg be x
Bill's leg by y
Hank's leg by z
x + y + z = 29 (1)
3x + 1 = y (2)
y + 2x = z (3)
Substitute into equation (1)
x + 3x + 1 + (3x + 1) + 2x = 29
x + 3x + 1 + 3x + 1 + 2x = 29
collect like terms
9x = 29 - 2
9x = 27
Make 'x' the subject of formula
x = 27/9
x = 3 minutes
y = 3x + 1
y = 3(3) +1
y = 10 minutes
z = y + 2x
z = 10 + 2(3)
z = 10 + 6
z = 16 minutes
Thus, the time it took Joe, Bill and Hank to run the leg of the race is 3, 10 and 16 minutes respectively.
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2. ) Write an equation of the line that is perpendicular to the line y = 4x - 10 that passes through the point (-16, 2).
A) y = -1/4 x - 2
B) y - 4 x + 6
C) y = -1/4 x + 2
D) y-4 x +2
3) Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)
A) y = -3x + 2
B) y = -3x + 3
C) y = -1/3x + 2
D) y = -1/3x + 3
4) Consider the line in the coordinate plane that passes through the point (-5, 2) and the origin. Find the slope of a line perpendicular to the line described
A) -2/5
B) -5/2
C) 1/2
D) 5/2
Answer:
2) The negative reciprocal of 4 is -1/4.
Using the point-slope form of a line (y - y1 = m(x - x1)), where (x1, y1) is the given point (-16, 2) and m is the slope:
y - 2 = -1/4(x - (-16))
y - 2 = -1/4(x + 16)
y - 2 = -1/4x - 4
y = -1/4x - 2
Therefore, the equation of the line perpendicular to y = 4x - 10 that passes through the point (-16, 2) is y = -1/4x - 2. So, the correct answer is A.
3) The given equation is y - 3x = -8. To find the equation of a line perpendicular to this, we need to determine the negative reciprocal of the slope of the given line, which is 3. The negative reciprocal of 3 is -1/3.
Using the point-slope form with the point (3, 2) and the slope -1/3:
y - 2 = -1/3(x - 3)
y - 2 = -1/3x + 1
y = -1/3x + 3
Therefore, the equation of the line perpendicular to y - 3x = -8 that passes through the point (3, 2) is y = -1/3x + 3. So, the correct answer is D.
4) The given line passes through the point (-5, 2) and the origin (0, 0). The slope of a line passing through two points can be found using the formula (y2 - y1) / (x2 - x1).
slope = (0 - 2) / (0 - (-5))
slope = -2 / 5
slope = -2/5
The negative reciprocal of -2/5 is 5/2. Therefore, the slope of a line perpendicular to the line passing through (-5, 2) and the origin is 5/2. So, the correct answer is D.
do you know the answer to this question 4x16+3-1
Answer:
66
Step-by-step explanation:
use
P- parenthesis
E- Exponents
M-multiplication
D-Division
A- addition
S- subtraction
NOTE THAT MULTIPLICATION IS NOT MORE IMPORTANT THAN DIVISION AND SAME GOES FOR ADDITION AND SUBTRACTION.
This means that that we do it from left yo right
4×16+3-1 --> 64+3-1 --> 67-1 = 66
Aisha has $100 saved from her job. She wants to buy as many charms for her bracelet, at $4 each on earrings at $5 per set as she can without spending all of her money. The inequality represents her spending where x is the number of charm,s and y is the number of sets of earrings.
The inequality representing Aisha's spending is 4x + 5y ≤ 100, where x is the number of charms and y is the number of sets of earrings.
To determine the maximum number of charms and sets of earrings Aisha can buy without spending all of her $100, we need to solve the inequality. The left-hand side of the inequality, 4x + 5y, represents the total cost of her purchases. The inequality states that the total cost must be less than or equal to $100.
By substituting different values for x and y, we can find combinations that satisfy the inequality. We can also use trial and error or graphing methods to find the valid combinations within the given constraint. The maximum number of charms and sets of earrings Aisha can buy will depend on the specific values of x and y that satisfy the inequality, ensuring she doesn't spend more than $100.
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Is 4 +y=2x linear or not linear
Answer:
The equation 4 + y = 2x is a linear equation.
Step-by-step explanation:
The equation 4 + y = 2x is a linear equation. Linear equations have a constant rate of change and can be represented by a straight line when plotted on a graph. In this equation, y is a linear function of x, as it changes at a constant rate (y increases by 2 units for every unit increase in x).
A linear equation is characterized by having only one variable raised to the first power and no higher powers. In this equation, both y and x are only raised to the first power, making it a linear equation.
It is also important to note that linear equations have no exponents or absolute value signs, and only involve additions, subtractions, multiplications, and divisions of variables and constants. The equation 4 + y = 2x fits these criteria, making it a linear equation.
1. a certain college wants to estimate the amount of time students, who live off campus, spend commuting to classes each week. a random sample of 45 off-campus students is surveyed. a) identify the population and sample for this study. b) what data is being collected? what type of data is this? c) what type of study is this?
The objective of this research is to collect data on a specific component of the off-campus student population.The amount of time they spend travelling to courses each week.
a) The population for this study is all off-campus students at this college, and the sample is a random sample of 45 off-campus students who are polled. The sample is chosen at random to be representative of the entire population.
b) The data being gathered is the amount of time the surveyed students spend each week travelling to school. Because it reflects a numerical measurement, this is quantitative data. This information will be used to calculate the average commuting time for off-campus students and to identify any possible concerns or areas for improvement in commuting.
c) This is a descriptive research, since it seeks to characterise and summarise the features of the off-campus student population in terms of commuting time. The study's purpose is to better understand off-campus students' commuting patterns and gather ideas into how to enhance their commuting experience.
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