In which interval is the median?
A sample of 50 students was surveyed about their time
spent in front of a screen (laptop, tablet, phone, etc.).
Each interval contains the left endpoint but not the
right endpoint.
[4,5)
[5,6)
[6,7)
[7,8)
Hours of Screen Time per Day
10
B
Frequency
2
6
8
10 12
Answer:
B is correct! Took the quiz 2021 <3. Yall b safe!
Step-by-step explanation:
More on Slope Question 9, 2.4.5 Part 1 of 2 Use the given conditions to write an equation for the line in point -slope form and in slope -intercept form. Passing through (-4,-7) and parallel to the line whose equation is y=-4x+2
The equation of the line in slope-intercept form is: y = -4x - 23
To obtain the equation of a line parallel to the line y = -4x + 2 and passing through the point (-4, -7), we can use the fact that parallel lines have the same slope.
The provided line has a slope of -4. Therefore, the parallel line will also have a slope of -4.
1. Point-slope form:
The point-slope form of a linear equation is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Using the point (-4, -7) and the slope -4, we can write the equation in point-slope form:
y - (-7) = -4(x - (-4))
Simplifying:
y + 7 = -4(x + 4)
2. Slope-intercept form:
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Using the slope -4 and the point (-4, -7), we can substitute these values into the slope-intercept form:
y = -4x + b
Now, to obtain the value of b, substitute the coordinates of the provided point (-4, -7):
-7 = -4(-4) + b
Simplifying:
-7 = 16 + b
b = -7 - 16
b = -23
Therefore, the equation of the line in slope-intercept form is:
y = -4x - 23
Both the point-slope form and the slope-intercept form describe the same line passing through (-4, -7) and parallel to the line y = -4x + 2.
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Circle A is located at (6, 5) and has a radius of 4 units. What is the equation of a line that is tangent to circle A from point C (2, 8)
Answer:
x = 2 (One of many options)
Step-by-step explanation:
See attached worksheet.
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:
Answer:
0 ≤ x ≤ 30
Step-by-step explanation:
In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:
f(x) = 250(1.25)ˣ
Which of the following is a reasonable domain for the function?
0 ≤ x ≤ 250
0 ≤ x ≤ 30
All positive integers greater than 100
All real numbers
Solution:
Given that f(x) = 250(1.25)ˣ, where x is the number of days and f(x) is the population of the birds after x days. This means that at the beginning of the month of September (i.e. at x = 0), the population of the birds was 250. And as each day goes by, the population of the bird increases by a factor of 1.25.
The domain of a function is the set of all possible independent variables. In this case the number of days (x) is the independent variable. Since in the month of September there are 30 days, therefore the domain is:
0 ≤ x ≤ 30
the 3rd term of an A.P is 6 and the 16th term is 32 find the common difference and the sum of the first 20 term
Answer:
2 and 420
Step-by-step explanation:
The n th term of an AP is
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Given a₃ = 6 and a₁₆ = 32 , then
a₁ + 2d = 6 → (1)
a₁ + 15d = 32 → (2)
Subtract (1) from (2) term by term
13d = 26 ( divide both sides by 13 )
d = 2
Substitute d = 2 into (1) for corresponding value of a₁
a₁ + 2(2) = 6
a₁ + 4 = 6 ( subtract 4 from both sides )
a₁ = 2
The sum of n terms of an AP is
\(S_{n}\) = \(\frac{n}{2}\) [ 2a₁ + (n - 1)d ] , thus
\(S_{20}\) = \(\frac{20}{2}\) [(2 × 2) + (19 × 2) ]
= 10(4 + 38) = 10 × 42 = 420
a rectangle has width that is 2 feet less than the length the arrea of the rectangle is 80 square feet find the dimensions of the rectangle
The dimensions of the rectangle are 10 feet (length) and 8 feet (width).
To find the dimensions of the rectangle with an area of 80 square feet and a width that is 2 feet less than the length,
follow these steps:
1. Let the length of the rectangle be L feet and the width be W feet.
2. According to the given information, W = L - 2.
3. The area of a rectangle is calculated by multiplying its length and width: Area = L × W.
4. Substitute the given area and the relationship between L and W into the equation: 80 = L × (L - 2).
5. Solve the quadratic equation: 80 = L² - 2L.
6. Rearrange the equation: L² - 2L - 80 = 0.
7. Factor the equation: (L - 10)(L + 8) = 0.
8. Solve for L: L = 10 or L = -8 (since the length cannot be negative, L = 10).
9. Substitute L back into the equation for W: W = 10 - 2 = 8.
So, the dimensions of the rectangle are 10 feet (length) and 8 feet (width).
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4cm
6cm
7cm
9cm
Finley says "the two triangles are similar because 3cm has been added to both the height and
base of the smaller triangle. "
Explain why Finley is incorrect
Finley's statement is incorrect because adding the same amount to the height and base of a triangle does not necessarily guarantee similarity between the two triangles. Similar triangles have corresponding angles that are congruent and corresponding sides that are proportional.
In this case, adding 3cm to both the height and base of the smaller triangle changes its proportions, but it does not guarantee that the resulting triangle is similar to the larger triangle. The ratios of corresponding sides in the two triangles may not be equal, which is a necessary condition for similarity.
To determine if the two triangles are similar, we need to compare the ratios of corresponding sides. Simply adding the same value to the height and base does not provide enough information to conclude similarity between the triangles.
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If x² is =169, what is x-5?
Answer:
\(\sqrt{169}=13\)
\(13-5=8\)
HELP I WILL GIVE BRAINIEST
nine hundred fifteen and sixty five thousandths in number form i please please help will ggive points or brainly for right answer!!!!!!!!!!!!!!!
Answer:
It is 0.0091565
hope that helps !
a bakery made 20 loaves of bread for the dinner rush. They sold 17 of the loaves during dinner and had 3 left. What is the decimal equivalent of the fraction of loaves they sold? What is the decimal equivalent of the fraction of loaves they didn't sell.
Your firm uses a continuous review system and operates 52 weeks per
year. One of the SKUs has the following characteristics. Refer to
the standard normal table for z-values.
PLEASE ANSWER SECTIONS
Certainly! You didn't provide the characteristics of the SKU, but here is a general answer that includes the terms "continuous" and "characteristics."Your firm uses a continuous review system and operates 52 weeks per year.
A continuous review system is a perpetual inventory system in which the inventory level for an item is continuously monitored, and a reorder is generated when the inventory level reaches a particular point, known as the reorder point (ROP).
As for the characteristics of an SKU, this can include various factors such as demand, lead time, safety stock, and so on. In order to determine the optimal reorder point and the order quantity for an SKU, you need to consider the characteristics of that particular item.
As for the standard normal table for z-values, this is used to determine the probability of a random variable taking a value within a certain range. The table is typically used in statistics and probability courses and can be used to determine probabilities for a variety of continuous distributions.
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in a pitch black room you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. how many socks do you take out to ensure you get a pair that is not navy?
There is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.
What is probability?Simply put, the probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes.
Statistics is the study of events that follow a probability distribution.
So, we know that:
27 black socks.
18 grey socks.
9 navy socks.
Probability formula: P(E) = Favouravle events/Total events
Now, insert values in the formula as follows:
P(E) = Favouravle events/Total events
P(E) = 27+18/27+18+9
P(E) = 45/54
P(E) = 15/18
P(E) = 5/6
Therefore, there is a 5/6 probability that you will remove pairs of socks to make sure you obtain a pair that is not navy.
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Correct question:
in a pitch-black room, you have a drawer with 27 black socks, 18 grey socks, and 9 navy socks. What is the probability that you take out pairs of socks to ensure you get a pair that is not navy?
the volume of a cube is decreasing at a constant rate of 1327 cubic feet per second. at the instant when the volume of the cube is 528528 cubic feet, what is the rate of change of the surface area of the cube? round your answer to three decimal places (if necessary).
The required rate of change of the surface area of the cube is 66 sq,feet/second.
Explain Rate change with respect to time.The momentum of a variable is represented by the rate of change, which is used to mathematically express the percentage change in value over a specified period of time. R = (D2 - D1)/T is a general formula for calculating the rate of change.
According o question:\(\frac{V}{dt}\) = 1327 cubic feet per second
volume(V) = 528528 cubic feet
We know that
V = a^3
528528 = a^3
a = 80.85
Differentiate w, r, t
\(\frac{V}{dt}\) = 3a^2\(\frac{da}{dt}\)
1327 = 3(80.85)^2da/dt
da/dt = 0.068
Now,
Surface area(S) = 6a^2
Differentiate w, r, t
dS/dt = 12a(da/dt)
dS/dt = 12(80.85)(0.068)
dS/dt = 66 Sq.feet/second
Thus, required rate of change of the surface area of the cube is 66.
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Help plz anyone who’s good with slope?
Answer:
-3
Step-by-step explanation:
you go down from the dot left most and you count towards the line that the second dot falls on and count over too it
Answer:
slope = - 3
Step-by-step explanation:
Calculate the slope m using the slope formula
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = (1, 2) and (x₂, y₂ ) = (2, - 1) ← 2 points on the line
m = \(\frac{-1-2}{2-1}\) = \(\frac{-3}{1}\) = - 3
Valeria wants to ride her bicycle 48 miles this week. She has already ridden 18 miles. If she rides for 4 more days, what is the average number of miles she would have to ride each day to meet her goal?
Subract what she rode already from total:
48-18 = 30
Divide by number of days:
30/4 = 7.5
she will need to ride 7.5 miles per day
What is the Square root of 39
Answer:
The square root would be something that multiplies twice by itself to get 39.
Step-by-step explanation:
In this case it is a decimal
6.244997998
We can round to
6.24
Plssss helppp w this maths question!
Shrina is selling cookie dough for her soccer team. She sold 2 tubs of
Oatmeal Raisin and 2 tulbs of Peanut Butter.
How much money did she make?
Oatmeal Raisin
$6 a tub
$22
$24
Peanut Butter
$5 a tub
$20
$11
Answer: 22
Step-by-step explanation:
She sold two tubs of Oatmeal Raisins and it's 6 dollars a tub so we can do 6*2 or 6+6 (doesn't matter). We get $12. Then, she also sells 2 tubs of Peanut Butter, and since it's $5 a tub, then we do 5*2 or 5+5 to get 10. We add 12 and 10 (12+10) and get 22.
I'm not sure if this is right because you added $22, $24, $20, and $11 and I'm not sure what the purposes of those are.
The length of a rectangular vegetable bed is 3 feet more than twice the width. The length of the fence around the bed is 36 feet. Find the length and with.
a) If the width of the rectangle is x, the equation is_.
b) The width of the vegetable bed is __, the length is __
Answer:
b) The width of the vegetable bed is 2x__, the length is 2x+3__
width = 5 feet
length = 13 feet
Step-by-step explanation:
length of a rectangular vegetable bed is 3 feet more than twice the width
l = 2x + 3
length of the fence around the bed is 36 feet
p = 2(l + x)
36 = 2(l + x)
18 = l + x
Substitute for l
18 = (2x + 3) + x
18 = 3x + 3
15 = 3x
x = 5
l = 2(5) + 3 = 13
its in the file below
According to the information we can infer that Dora's conclusion may be incorrect because the information provided only states that the number of people who spent time reading falls within specific ranges (0-2 hours, 2-4 hours, and 2-10 hours), but it does not give a specific count for those who spent at least 4 hours. Therefore, Dora's assumption that "most people spent at least 4 hours a week reading" is not supported by the given data.
How to calculate the range of the time that Dora's friends spent reading?The range of the time spent reading cannot be determined from the information provided because the ranges are overlapping. For example, a person who spent exactly 2 hours reading could fall into both the first range (0-2 hours) and the second range (2-4 hours). Without more specific data or non-overlapping ranges, it is not possible to determine the exact range of time spent reading.
To estimate the mean time spent reading by Dora's friends, we can calculate the midpoint of each range and use it as an approximate value. The midpoint for the first range (0-2 hours) is 1 hour, for the second range (2-4 hours) is 3 hours, and for the third range (2-10 hours) is 6 hours. We can then calculate the estimated mean by taking the weighted average of these midpoints using the respective number of people as weights.
Estimated mean = [(4 * 1) + (5 * 3) + (11 * 6)] / (4 + 5 + 11) = 4.53 hours (approximately)
So, an estimate of the mean time spent reading by Dora's friends is approximately 4.53 hours.
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If Z is a standard normal random variable, then P(-1.75 ZS -1.25) is: O a. 0.106 O b. 0.040 OC. 0.854 O d. 0.066
The answer is option B: 0.040. When Z is a standard normal random variable, it means that Z has a mean of 0 and a standard deviation of 1. Therefore, P(-1.75 < Z < -1.25) represents the area under the standard normal curve between -1.75 and -1.25 standard deviations from the mean.
Using a standard normal distribution table or calculator, we can find that the area under the curve between -1.75 and -1.25 is approximately 0.040. Hence, the answer is option B: 0.040.
To solve your question, we need to find the probability P(-1.75 ≤ Z ≤ -1.25) where Z is a standard normal random variable.
Step 1: Identify the given values
Z1 = -1.75
Z2 = -1.25
Step 2: Look up the Z-values in a standard normal table or use a calculator to find the corresponding probabilities
P(Z ≤ -1.75) = 0.0401
P(Z ≤ -1.25) = 0.211
Step 3: Use the properties of probabilities to find the required probability
P(-1.75 ≤ Z ≤ -1.25) = P(Z ≤ -1.25) - P(Z ≤ -1.75)
P(-1.75 ≤ Z ≤ -1.25) = 0.211 - 0.0401
P(-1.75 ≤ Z ≤ -1.25) = 0.1709
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Exhibits
Sandra makes an income of $10,000 a month. She pays $24,000 for
mortgage annually. What percent of Sandra's income pays for her
mortgage? Enter the percent in the box provided.
Answer:
20%
Step-by-step explanation:
a couple has two children. one is a son. what is the probability that the other child is a daughter?
Answer:
1/2 it’s like flipping a coin it can either come up heads or tails.
Step-by-step explanation:
The probability that the other child is a daughter is 1/2 or 50%.
The gender of each child is independent, and there are two equally likely outcomes for each child (male or female). Therefore, the probability of having a son is 1/2 and the probability of having a daughter is also 1/2. Since one child is already known to be a son, that does not affect the probability of the other child being a daughter. Thus, the probability of having a daughter as the other child is also 1/2 or 50%.
Therefore, the answer to the question is that the probability that the other child is a daughter is 1/2 or 50%
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All solutions to the new system can be obtained by multiplying solutions from the original system by constant c if each equation in a consistent linear system is multiplied through by that constant c. True False
The given statement is false. The correct option is (B) False.
The given statement "All solutions to the new system can be obtained by multiplying solutions from the original system by a constant c if each equation in a consistent linear system is multiplied through by that constant c" is false.
Explanation :A consistent system is one that has one or more solutions. If the linear system is multiplied by a nonzero constant c, then each equation is multiplied through by c.
This means that every coefficient is multiplied by c and the constant term on the right-hand side is also multiplied by c. If this happens, then there is a new linear system formed, which is obtained from the original system by multiplication.
Here's an example to better explain the concept:Let's suppose that we have a linear system as follows
:x + y = 3 (1)2x - y = 4 (2)
If we multiply the first equation by 3 and the second equation by 2, we obtain:3x + 3y = 9 (3)4x - 2y = 8 (4)
This system is equivalent to the original system. To solve the new system, we need to multiply the solution(s) of the original system by the constant c. But, not all solutions to the new system can be obtained by multiplying the solutions from the original system by a constant c.
So, the given statement is false. Hence, the correct option is (B) False.
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Solve the following maximisation problem by applying the Kuhn-Tucker theorem: Max xy subject to –4x^2 – 2xy – 4y^2 x + 2y ≤ 2 2x - y ≤ -1
By applying the Kuhn-Tucker theorem, the maximum value of xy is: 18/25
The constraints are:-4x² - 2xy - 4y²x + 2y ≤ 22x - y ≤ -1
Let us solve this problem by applying the Kuhn-Tucker theorem.
Let us first write down the Lagrangian function:
L = xy + λ₁(-4x² - 2xy - 4y²x + 2y - 2) + λ₂(2x - y + 1)
Then, we find the first order conditions for a maximum:
Lx = y - 8λ₁x - 2λ₁y + 2λ₂ = 0
Ly = x - 8λ₁y - 2λ₁x = 0
Lλ₁ = -4x² - 2xy - 4y²x + 2y - 2 = 0
Lλ₂ = 2x - y + 1 = 0
The complementary slackness conditions are:
λ₁(-4x² - 2xy - 4y²x + 2y - 2) = 0
λ₂(2x - y + 1) = 0
Now, we solve for the above equations one by one:
From equation (3), we can write 2x - y + 1 = 0, which implies:y = 2x + 1
Substitute this in equation (1), we get:
8λ₁x + 2λ₁(2x + 1) - 2λ₂ - x = 0
Simplifying, we get:
10λ₁x + 2λ₁ - 2λ₂ = 0 ... (4)
From equation (2), we can write x = 8λ₁y + 2λ₁x
Substitute this in equation (1), we get:
8λ₁(8λ₁y + 2λ₁x)y + 2λ₁y - 2λ₂ - 8λ₁y - 2λ₁x = 0
Simplifying, we get:
-64λ₁²y² + (16λ₁² - 10λ₁)y - 2λ₂ = 0 ... (5)
Solving equations (4) and (5) for λ₁ and λ₂, we get:
λ₁ = 1/20 and λ₂ = 9/100
Then, substituting these values in the first order conditions, we get:
x = 2/5 and y = 9/5
Therefore, the maximum value of xy is:
2/5 x 9/5 = 18/25
Hence, the required answer is 18/25.
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Which of the following parameters is required to convert a computer-generated random variable into a uniform random variable?
a. Variance of the distribution
b. Mean of the distribution
c. Moments of the distribution
d. Range of the distribution
The range of the distribution is the parameter that is required to convert a computer-generated random variable into a uniform random variable. Below are more than 100 words explaining this in detail:A uniform random variable is a random variable with a probability distribution function that is uniform across all possible values.
The probability density function of a uniform distribution is constant over the range of values of the variable. Therefore, it has equal probability of taking any value within the range of values that it is defined.The process of converting a computer-generated random variable into a uniform random variable is known as uniform random number generation. The process of uniform random number generation is an important aspect of computer simulation and statistical analysis of data.
It is used to generate random numbers that follow a uniform distribution, which is a common distribution in many applications.The range of the distribution is the parameter that is required to convert a computer-generated random variable into a uniform random variable. This is because the range of the distribution defines the possible values that the variable can take. By mapping the computer-generated random variable to the range of the uniform distribution, we can convert it into a uniform random variable.
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the variables y and x have a proportional relatinship and y=9 when x=2 what is the value of y when x=30
The value of y for proportional relationship when x = 30 is y = 135.
What is proportional relationship?Relationships among two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relation, one variable is consistently equal to the other's constant value.
A "constant of proportionality" is the name of this constant.
the importance of proportional relationship are-
Students' grasp of numerous areas in science and maths depends on their ability to use ratios and proportions. They play a crucial role in the development of slopes, uniform rate of change and other concepts and abilities that are essential to understanding and mastering algebra.Calculation the for the value of y.
According to the question,
The variables y and x have a proportional relationship.
Where, y=9 when x=2
Thus,
y/x = 9/2
Cross multiplying the above result;
2y = 9x
The value of y when x = 30.
2y = 9×30
2y = 270
y = 135
Therefore, the value of y when x=30 is 135.
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What is a fraction equivalent to the mixed number 3 3/4
Answer:
15/4
Step-by-step explanation:
Answer:
15/4
Step-by-step explanation:
Which triangle is a translation of triangle P?
D
4
5
A
--5--4--3--2--2₁
O triangle A
O triangle B
O triangle C
4
3
2
4
-2
-3
€
2 3 4 5 x
to
A triangle that is a translation of triangle P include the following: C. triangle C.
What is a translation?In Mathematics and Geometry, a translation can be defined as a type of rigid transformation which moves every point of the object in the same direction, as well as for the same distance.
This ultimately implies that, geometric figures that are translated would always have the same size, shape, and orientation.
In this context, we can reasonably infer and logically deduce that triangles A, B, and D have different shape, so, only triangle is a translation of triangle P.
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Complete Question:
Which triangle is a translation of triangle P?
triangle A
triangle B
triangle C
triangle D