Casey went too movie for 4 times and Darnell went to movie for 7 times.
Casey and Darnell went to the movies a total of 11 times last month, Darnell went one less than twice as many times as Casey did.
Let us say that Casey went to movie for X times,
So, the amount of times that Darnel went for movie is 2X-1
It is given that they went for a total of 11 times.
We can make a simple algebraic equation by using the above data.
X + 2X - 1 = 11
3X = 12
X = 4
So, Casey went to movie for 4 times and Darnell went to movie for 7 times.
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BRAINLIEST AND POINTS
The stem-and-leaf plot displays the distances that a heavy ball was thrown in feet.
2 0, 1, 3
3 1, 1, 5
4 1, 3, 4
5 0, 8
6 2
Key: 4|1 means 4.1
What is the mean, and what does it tell you in terms of the problem?
4.59 feet; The value means that a typical throw of the ball results in 4.59 feet.
4.1 feet; The value means the furthest the ball went.
3.825 feet; The value means that a typical throw of the ball results in 3.825 feet.
3.1 feet; The value means this measurement had the most occurrences.
The mean and the meaning is
C. 3.825 feet; The value means that a typical throw of the ball results in 3.825 feet.What is mean?The mean is a measure of central tendency that gives us the average value of a set of numbers.
To calculate the mean of the distances that the ball was thrown, we add up all the values and divide by the number of values. In this case, the mean is calculated as:
= (2.0 + 2.1 + 2.3 + 3.1 + 3.1 + 3.5 + 4.1 + 4.3 + 4.4 + 5.0 + 5.8 + 6.2) / 12
= 45.9 / 12
= 3.825
This value of 3.825 feet tells us that on average, the ball was thrown a distance of approximately 3.825 feet. This value gives us an idea of what a typical throw of the ball looks like, and can help us understand the distribution of the data.
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Six different colored dice are rolled. Of interet i the number of dice that how a one. Find the probability that all ix dice how a one
The fundamental colours of red, blue, and yellow, as well as orange, purple, and green, are most frequently present on six dice.
What is probability?The area of mathematics known as probability deals with numerical descriptions of how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty. Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.Six dice most likely have the primary colours of red, blue, and yellow as well as orange, purple, and green.
Despite the possibility of black and white, unseen hues are highly improbable: the infrared and ultraviolet
Each dice has 6 possible results, numbered from 1 to 6. There are only the possible outcomes of 1, 2, 3, 4,5, or 6.
On each die, a 5 has a 1/6 chance. divided by the total number of possible outcomes, by one way to achieve a five.
The likelihood of all 6 having is 1/6^5s
About 0.00002 is equal to 5 = 1/6 x 1/6 x 1/6 x 1/6.
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Write the slope-intercept form of the ec
3x-2y=-16
The equation in the slope-intercept form is:
y = 8 + (3/2)x
How to write the line in the slope-intercept form?Herewe have the linear equation:
3x - 2y = -16
And we want to write it in the slope-intercept form.
To do that, we need to isolate the variable y.
We will get:
3x - 2y = - 16
-2y = -16 - 3x
y = (-16/-2) + (-3/-2)x
y = 8 + (3/2)x
That is the equation written in the slope-intercept form.
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Nondisclosure of the treatment an experimental unit is receiving.
Blinding refers to nondisclosure of the treatment an experimental unit is receiving
What is Non discloure Treatment?
Medical NDAs are written agreements in which a patient agrees not to post negative reviews of a medical professional on the internet. Medical NDAs, like any other type of contract, vary widely.
Concept:
Blinding is the practice of not disclosing the treatment that an experimental unit is getting. A single-blind experiment is one in which the experimental unit (or subject) is unaware of the therapy being administered.
A single-blind experiment is one in which the experimental unit (or subject) is unaware of the therapy being administered.
A double-blind experiment is one in which neither the experimental unit nor the researcher who comes into touch with it knows which treatment it is receiving.
Blinding is the practice of not disclosing the treatment that an experimental unit is getting.
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Blinding refers to nondisclosure of the treatment an experimental unit is receiving
What is Nondisclosure Treatment?
Medical NDAs are written agreements in which a patient agrees not to post negative reviews of a medical professional on the internet. Medical NDAs, like any other type of contract, vary widely.
Concept:
Blinding is the practice of not disclosing the treatment that an experimental unit is getting. A single-blind experiment is one in which the experimental unit (or subject) is unaware of the therapy being administered.
A single-blind experiment is one in which the experimental unit (or subject) is unaware of the therapy being administered.
A double-blind experiment is one in which neither the experimental unit nor the researcher who comes into touch with it knows which treatment it is receiving.
Blinding is the practice of not disclosing the treatment that an experimental unit is getting.
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three groups of participants are asked to read a short story and then take a multiple-choice test on the content of the story. one group is given 10 minutes to read the story, a second is given 15 minutes, and a third 20 minutes. the independent variable in this study is
Independent variable t is time given to read story, dependent variable y is test scores, relationship modeled as y = f(t).
What is variable ?
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Let's denote the amount of time given to read the story as t. The independent variable t has three levels: t = 10 minutes, t = 15 minutes, and t = 20 minutes.
The dependent variable y is the test scores on the content of the story. The purpose of the study is to determine the relationship between the independent variable t and the dependent variable y.
The problem can be mathematically represented as:
y = f(t)
where f is a function that represents the relationship between the independent variable t and the dependent variable y.
Independent variable t is time given to read story, dependent variable y is test scores, relationship modeled as y = f(t).
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Independent variable t is time given to read story, dependent variable y is test scores, relationship modeled as y = f(t).
variable, In algebra, a symbol (usually a letter) standing in for an unknown numerical value in an equation. Commonly used variables include x and y (real-number unknowns), z (complex-number unknowns), t (time), r (radius), and s (arc length).
Let's denote the amount of time given to read the story as t. The independent variable t has three levels: t = 10 minutes, t = 15 minutes, and t = 20 minutes.
The dependent variable y is the test scores on the content of the story. The purpose of the study is to determine the relationship between the independent variable t and the dependent variable y.
The problem can be mathematically represented as:
y = f(t)
where f is a function that represents the relationship between the independent variable t and the dependent variable y.
Independent variable t is time given to read story, dependent variable y is test scores, relationship modeled as y = f(t).
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a fair coin is tossed 26 times. what is the probability that at most 23 tails occur?
The probability that at most 23 tails occurs is 46/52.
Describe probability.Probability is a measure of how likely something is to occur. It is a branch of mathematics that studies the occurrence of random events. The value is between 0 and 1. Mathematics has incorporated probability to forecast the possibility of events happening. The probability of something happening is referred to as its likelihood. The probability distribution is based on this fundamental idea of probability. We must first identify the total number of possibilities in order to calculate the probability that a specific event will occur.
Probability that an event will occur P(E) is the proportion of favourable outcomes to all outcomes.
Now,
Total no. of times coin tossed=26
Total outcomes=26 × 2=52
the probability that at most 23 tails occur=1-probability that 24,25 and 26 tails occured
=1- × [tex]\frac{25}{52}[/tex] × [tex]\frac{26}{52}[/tex]
=1-15600/140608
=89/100≈46/52
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3.) Make up a word problem for this expression. 3(8a + 5c + 6e)
Answer: A math teacher writes 3(8a + 5c + 6e) on the board and asks her students to simplify the expression. If a student has values of a = 2, c = 3, and e = 4, what is the result of simplifying the expression?
Step-by-step explanation:
Suppose 50% of recent college graduate plan on pursuing a graduate degree. 14 recent college graduates are randomly selected
The probability that not more than 5 graduates plan to pursue a graduate degree is 0.0191.
Given Information
Percentage of college graduates that plan on pursuing a graduate degree=50%
Number of graduates selected=14
Let us consider the event that a college graduate plans on pursuing a graduate degree as a success.
The probability of getting success is p = 0.50
Let X denotes the event of success.
We have, n = 14.
Then,
X∼Bin(14,0.50).
The pmf of X is given as,
[tex]P(X)= ^nC_xP^x(1-P)^n^-^x\\\\P(X)= ^1^4C_x(0.50)^x(0.50)^1^4^-^x[/tex]
The probability that not more than 5 graduates plan to pursue a graduate degree can be computed as,
P(X≤5)=5∑¹⁴Cₓ(0.50)x(0.50)¹⁴⁻ˣ
=0+0.00001+0.00012+0.00081+0.00396+0.01425
P(X≤5)=0.01914
Hence, the probability that not more than 5 graduates plan to pursue a graduate degree is 0.0191.
The probability that exactly 7 of the college graduates plan to pursue a graduate degree can be computed as,
P(X=7)=¹⁴C₇(0.5)⁷(0.5)⁹
P(X=7)=0.08395
Therefore, the probability that exactly 7 of the college graduates plan to pursue a graduate degree is 0.0840.
The probability that at least 9 but not more than 14 of the college graduates plan to pursue a graduate degree can be computed as,
P(9≤X≤14)=14∑x=9 ¹⁴Cₓ(0.50)x(0.50)¹⁴⁻ˣ
P(9≤X≤14)=0.18889+0.19833+0.16227+0.10142+0.04681+0.01505
P(9≤X≤14)=0.71277
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How many integrals would be required in the shell method?
The number of integrals required in the shell method is one or two, depending on the axis of rotation and the dimension of the solid of revolution.
The number of integrals required in the shell method depends on the dimension of the solid of revolution being generated. The shell method generates a solid of revolution by rotating a region about an axis.
For a solid of revolution generated by rotating a two-dimensional region about a vertical axis (i.e., a vertical shell), two integrals are required: one to find the volume of the shell and another to add up the volumes of all the shells to get the total volume of the solid.
For a solid of revolution generated by rotating a two-dimensional region about a horizontal axis (i.e., a horizontal shell), one integral is required to find the volume of the solid.
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Write a quadratic function h whose only zero is -10
only has one zero/root, and it's a quadratic, means that that only zero has a multiplicity of 2, namely is there twice, so
[tex]\begin{cases} x = -10 &\implies x +10=0\\ x = -10 &\implies x +10=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{( x +10 )( x +10 ) = \stackrel{0}{h}}\implies x^2+20x+100=h[/tex]
Circle F is centered at the origin. If the radius of circle Q is 7, which of the following statements is TRUE?
Circle on grid
A.) If the distance from the origin to a given point is 7, then that point lies on circle F.
B.) If the distance from the origin to a given point is less than 7, then that point lies outside circle F.
C.) If the distance from the origin to a given point is greater than 7, then that point lies on circle F.
D.) If the distance from the origin to a given point is greater than 7, then that point lies inside circle F.
Answer:
The statement that is true is B. This can be determined by using the information from openstax.org, which states that the measure of an angle is the amount of rotation from the initial side to the terminal side. Since the radius of circle Q is 7, any point with a distance from the origin that is less than 7 will lie outside of circle F.
Step-by-step explanation:
4x-37 2x + 7 pleasee helpppppppppp
The solution of the linear equation, 4·x - 37 = 2·x + 7, found using the collection of like terms, is; x = 22
What is a linear equation?A linear equation is an equation of the form, y = m·x + c, that has the highest index or power of one (1), and for which the graph of the equation is a straight line.
The expressions, 4·x - 37 and 2·x + 7 are linear expressions
Whereby the equation is 4·x - 37 = 2·x + 7, we get;
4·x - 37 = 2·x + 7
Collecting like terms, produces
4·x - 2·x = 7 + 37 = 44
2·x = 44
Dividing both sides by 2, we get;
2·x/2 = x = 44/2 = 22
x = 22
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data collected over several years shows that of all patients that come to the doctor's office with a sore throat, 220 patients are being sampled with a sore throat are tested for this virus. 5% (or 11 patients) of them have a contagious virus. a) the population is [ select ] . the parameter of interest is [ select ] and the value of the parameter is [ select ] . b) the central limit theorem (clt) holds for the sample proportion of patients with a contagious virus, because [ select ] . c) the mean of the sample proportion of patients with sore throat who have the virus is [ select ] and standard deviation the sample proportion is [ select ] . d) the probability that between 7.5% and 9% of these 220 patients in the sample with sore throat that have the virus is: [ select ] e) [ select ]
A sample of 220 patients with sore throats is tested for a contagious virus (5% positive). The central limit theorem holds and the mean of the sample proportion is 5% with a standard deviation of 0.0096. The probability of 7.5-9% positive is 68.3%.
a) the population is all patients who come to the doctor's office with a sore throat. The parameter of interest is the proportion of patients with a contagious virus in the population. The value of the parameter is 5%.
b) the central limit theorem (CLT) holds for the sample proportion of patients with a contagious virus because the sample size of 220 patients is large enough (more than 30) and the sample is being drawn randomly from the population.
c) the mean of the sample proportion of patients with a sore throat who has the virus is 5% and the standard deviation of the sample proportion is √(0.05 * 0.95) / 220 = 0.0096.
d) the probability that between 7.5% and 9% of these 220 patients in the sample with a sore throat have the virus is approximately 68.3% (based on a normal distribution).
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A sample of 220 patients with sore throats is tested for a contagious virus (5% positive). The central limit theorem holds and the mean of the sample proportion is 5% with a standard deviation of 0.0096. The probability of 7.5-9% positive is 68.3%.
a) the population is all patients who come to the doctor's office with a sore throat. The parameter of interest is the proportion of patients with a contagious virus in the population. The value of the parameter is 5%.
b) the central limit theorem (CLT) holds for the sample proportion of patients with a contagious virus because the sample size of 220 patients is large enough (more than 30) and the sample is being drawn randomly from the population.
c) the mean of the sample proportion of patients with a sore throat who has the virus is 5% and the standard deviation of the sample proportion is √(0.05 * 0.95) / 220 = 0.0096.
d) the probability that between 7.5% and 9% of these 220 patients in the sample with a sore throat have the virus is approximately 68.3% (based on a normal distribution).
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If c intersects b what is m<2
The measure of angle 2 from the given figure is 90°.
What are angles of parallel lines?Angles in parallel lines are angles that are created when two parallel lines are intersected by another line called a transversal.
Given that, c is perpendicular to b.
Sice, c⊥b angles formed with lines c and b are equal to 90°.
Now, m∠2=90°
Therefore, the measure of angle 2 from the given figure is 90°.
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Divide the sum of `(-12)/(5) and (-18)/(15)` by their difference.
Dividing the sum of `(-12)/(5) and (-18)/(15)` by their difference. The answer is 3.
How did we get the value?To divide the sum of two numbers by their difference, we first need to find the sum and the difference of the two numbers.
The sum of (-12)/(5) and (-18)/(15) is:
(-12)/(5) + (-18)/(15) = (-12)/(5) + (-6)/(5) = -18/5
The difference of (-12)/(5) and (-18)/(15) is:
(-12)/(5) - (-18)/(15) = (-12)/(5) - (-6)/(5) = -6/5
Finally, dividing the sum by the difference, we get:
(-18/5) / (-6/5) = -18/-6 = 3
So, the answer is 3.
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Consider the two functions shown below. Assume the blue line represents afx) and the pink line represents b(x). Which statement is true about these functions at x-3? O O 2 (3) (3) but (3) = (3) and 3 O (3) -(3) but O a(3) (3) and O I DON'T KNOW YET
The statement that is true about these functions at x = 3 is that a(3) = b(3).
At x = 3, the value of a(x) is equal to the value of b(x) because the lines representing the two functions intersect at x = 3. Therefore, a(3) = b(3).
The two functions shown, a(x) and b(x), intersect at x = 3. This means that the values of the two functions are equal at x = 3. Therefore, a(3) = b(3).
The two functions, a(x) and b(x), represent mathematical expressions that can be graphed on a coordinate plane. When two lines intersect, they meet at exactly one point. In this case, the lines representing the two functions intersect at x = 3. This means that the two functions have the same value at x = 3. Therefore, a(3) is equal to b(3), which can be mathematically expressed as a(3) = b(3). This is an important property of intersecting lines and is commonly used in mathematics, engineering, and other related fields. It provides a way to find the common value between two functions at a specific point.
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How do you find the missing side of the right triangle with legs: a = 5, b = 12?
The missing side of the triangle is known as the hypotenuse. The length of the missing side is 13.
What is a right triangle?
A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or formerly rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and other angles of the right triangle.
A right triangle has two legs and one hypotenuse.
The length of the legs is 5 and 12.
The sum of the square of the legs is equal to the square of the hypotenuse.
Therefore,
Hypotenuse² = 5²+ 12²
Hypotenuse² = 25+ 144
Hypotenuse² = 169
Hypotenuse = 13
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The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:.
A. The slope of the line is 40
B. The equation of the line is 40x - y + 600 = 0
C. The equation is g(x) = 4x + 600
The balance is 628 Rs.
The formula of the slope of line = Δy/Δx
= 720 - 600 / 3 - 0
= 120/3
= 40
The equation of a line is given as y - y₁ = m(x - x₁)
m = 40 which is the slope.
When we substitute we have
y - 600 = 40(x - 0)
We have to substitute x as 0
y - 600 = 0
y = 600
therefore y = 40x + 600
This implies that 40x - y + 600 = 0
c. y - 600 = 40x
g(x) - 600 = 4x
hence
g(x) = 4x + 600
d. x is 7 days
g(x) = 4*7 + 600
= 628
The balance in the bank after 7 days is 628Rs.
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The complete question is:
The table of values represents a linear function g(x), where x is the number of days that have passed and g(x) is the balance in the bank account:
x g(x)
0 $600
3 $720
6 $840
Part A: Find and interpret the slope of the function. (3 points)
Part B: Write the equation of the line in point-slope, slope-intercept, and standard forms. (3 points)
Part C: Write the equation of the line using function notation. (2 points)
Part D: What is the balance in the bank account after 7 days? (2 points)
Distance and Dot Products: Consider the vectors u=〈−3,10,9〉 and v=〈9,−5,7〉.
The dot product of u and v is -64. The distance between u and v is 16.
The dot product of two vectors u and v is calculated by multiplying the corresponding components of each vector and then summing the results. Therefore, the dot product of u and v is:
u•v = (−3)(9) + (10)(−5) + (9)(7) = −27 − 50 + 63 = −64
The distance between two vectors u and v is calculated by taking the square root of the dot product of the two vectors. Therefore, the distance between u and v is:
Distance(u,v) = √(u•v) = √(−64) = 16
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what are the values of a b and c in the quadratic equation 0=-15 9x^2 13
-15,9,13 are the quadratic equation values of a,b and c is 231.3.
How do you solve a quadratic equation for B and C?The equation for the quadratic function is f(x) = a * x2 + b * x + c. The center figure, the one right next to the x, is the b-value. Both a and c are numbers, just like the other letters. Any number may be used for each of them. They provide information about the graph of the quadratic function when taken together.
Graphs, A quadratic function is one that has the formula f(x) = ax2 + bx + c, where a, b, and c are all integers with a not equal to zero. T
Our ability to solve any quadratic equation is aided by the quadratic formula. First, we change the equation's form to read as ax2+bx+c=0, where a, b, and c are the coefficients.
As a result, we enter these coefficients into the formula:
(-b(b2-4ac))/(2a).
(-b(b2-4ac))/(2a).
-9(9-4*-15*13)/2*-15
-9(9-780)/-30 = -9(-771)/-30 =6939/-30 = -231.3.
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Complete question:
What are the values of a, b and c in the quadratic equation 9x² -15x + 13 = 0?
Which angle is 120 degree?
Answer:
wrong ?
Step-by-step explanation:
show us crycle or a picture man
Given that 120 is a number between 90 and 180, it is an obtuse angle. This angle's measurement is therefore 90º < 120º < 180º.
What is angle?Two lines converge at a common point to form an angle. They are expressed by the sign ° and are measured in degrees. Acute, right, obtuse, and reflex angles are four crucial types. There are 360° in a circle. It has completed two full rotations if you observe an angle of 720°. An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays—known as the vertex—is referred to as an angle's sides.Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet.To learn more about angle, refer to:
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The quadratic function d = -2x^2+ 10 models a skateboarders distance,
in feet, from the bottom of a hill, x seconds after the skateboarder starts moving down the hill.
After how many seconds, is the skateboarder 1 ft from the bottom of the hill?
Answer:
2.1 seconds
Step-by-step explanation:
Note we are told that d = -2x² + 10, where d is distance (in feet) and x is time (in seconds).
After how many seconds is the skateboarder 1 ft from the bottom of the hill? => What is x when d=1?
To do this, sub 1 in for d and solve for x:
d = -2x² + 10
1 = -2x² + 10
-9 = -2x²
4.5 = x²
x = [tex]\sqrt{4.5}[/tex] ≈ 2.12132
A car aleperon earn a bae alary of $1,400 per month plu a commiion of 5% on ale. The aleperon earned $4500 thi month. Write an equation to repreent the amount of ale made
The car salesperson made $62,000 in sales for the month
Let us say the amount of sales the car salesperson made in a month is x. Then, the total income can be represented as:
$1,400 + 0.05x = $4,500
The equation represents the total income of the car salesperson as the base salary of $1,400 per month plus a commission of 5% on sales. To find the amount of sales made, we have to solve x.
Subtracting $1,400 from both sides:
0.05x = $4,500 - $1,400 = $3,100
Dividing both sides by 0.05:
x = $3,100 / 0.05 = $62,000
So the car salesperson made $62,000 in sales for the month.
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Complete the statement comparing Manuel’s and Gretchen’s data.
Select the correct answer from each drop-down menu.
Gretchen’s data values Manuel’s data values because the are for Manuel’s data.
The correct statement about the comparison between Manuel’s and Gretchen’s data is: Gretchen’s data values are more spread out than Manuel’s data values because the mean and median and interquartile range mean and standard deviation and interquartile range are larger for Gretchen's data than for Manuel’s data.
What is Interquartile Range?The interquartile range is a measure of statistical dispersion, or the spread of the data, in descriptive statistics.
The middle 50%, fourth spread, or H-spread are further names for the IQR. It is described as the spread between the data's 75th and 25th percentiles.
Hence, from the data gotten from both Manuel and Gretchen shows differences in them.
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If 5 dates cost 25 cents, how many can be bought for USD 5?
Step-by-step explanation:
25 cents = $0.25
the ratio is 5/0.25 (5 dates for $0.25)
now we need to convert this to $5 in the denominator. and we need to multiply the numerator with the same factor.
and then the numerator will tell us how many dates we get for $5 in the denominator.
0.25 × x = 5
x = 5/0.25 = 20
indeed, 20 quarters = $5
so, we do
5/0.25 × 20/20 = 100/5
that means we can buy 100 dates for $5.
Explain with an example what an even number is
The explanation of an even number is mentioned below
What is an Even number?A number that is a multiple of two is said to be "even." Any integer that can be divided in half by two is considered to be an even number.
Explanation:
An illustration will enable you to understand this.
Let's say John has six balls.
He can couple up all 6 balls and create 3 pairs if he attempts to organize them.
There are no unpaired balls remaining.
He can thus deduce that 6 is an even number.
Let's split 6 by 2 now.
The number of pairs that are created, 3, is the quotient that we arrive at. The number of balls that cannot be matched is equal to the remainder, which comes out to be 0.
Every time John attempts to pair
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Following is a statement of a theorem which can be proven using the quadratic formula. For this theorem, a, b, and c are real numbers.Theorem - If f is a quadratic function of the form f(x) = ax2 + bx + c and ac < 0,then the function f has two x-intercepts.Using only this theorem, what can be concluded about the functions given by the following formulas?(a) g(x) = -8x2 + 5x - 2(b) h(x) = (-1/3)x2 + 3x(c) k(x) = 8x2 - 5x - 7
(a) The function g(x) = -8[tex]x^2[/tex] + 5x - 2 doesn't have two x-intercepts because ac > 0.
(b) The function h(x) = (-1/3)[tex]x^2[/tex] + 3x doesn't have two x-intercepts because ac = 0.
(c) The function k(x) = 8[tex]x^2[/tex] - 5x - 7 have two x-intercepts because ac < 0.
In the theorem, a, b, and c are real numbers.
Theorem - If f is a quadratic function of the form f(x) = a[tex]x^2[/tex] + bx + c and ac < 0, then the function f has two x-intercepts.
(a) The function is g(x) = -8[tex]x^2[/tex] + 5x - 2
On comparing the equation by f(x) = a[tex]x^2[/tex] + bx + c, we get a = -8, b = 5 and c = -2.
To check the two x-intercepts, we put values in ac and compare with ac<0
ac = (-8)(-2)
ac = 16 > 0
As the value of ac is greater than 0. So we can say that it doesn't have two x-intercepts.
(b) The function is h(x) = (-1/3)[tex]x^2[/tex] + 3x
On comparing the equation by f(x) = a[tex]x^2[/tex] + bx + c, we get a = -1/3, b = 3 and c = 0.
To check the two x-intercepts, we put values in ac and compare with ac<0
ac = (-1/3)(0)
ac = 0 = 0
As the value of ac is equal to 0. So we can say that it doesn't have two x-intercepts.
(c) The function is k(x) = 8[tex]x^2[/tex] - 5x - 7
On comparing the equation by f(x) = a[tex]x^2[/tex] + bx + c, we get a = 8, b = -5 and c = -7.
To check the two x-intercepts, we put values in ac and compare with ac<0
ac = 8(-7)
ac = -56
ac < 0
As the value of ac is less than 0. So we can say that it have two x-intercepts.
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Use the distributive property to write an expression that is equivalent to 2s 1 3s with 2 as the exponent
The equivalent expression of the given expression is 6s^2
How to determine the equivalent expressionFrom the question, we have the following parameters that can be used in our computation:
2s 1 3s
Rewrite the expression properly
So, we have the following representation
2s * 3s
Evaluate the product
So, we have the following representation
6s^2
Hence, the equivalent expression is 6s^2
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Is u in the plane in R3 spanned by the columns of A? I was able to reduce the matrix and see that there is a solution and it is consistent. However my last row doesn't have a pivot and is 000=0, how can the answer be yes if each row doesn't have a pivot and doesnt follow theroem 4?
Yes, the solution to the system of linear equations represented by the matrix A lies in the plane spanned by the columns of A.
If the last row of the reduced matrix is [0, 0, 0, 0], it means that the system of linear equations represented by the matrix is consistent, but not necessarily unique. This is because the last row corresponds to an equation of the form 0 = 0, which is always true.
However, the presence of a non-zero row in the reduced matrix that corresponds to a non-trivial equation (i.e., an equation that is not of the form 0 = 0) is sufficient to guarantee that the solution exists and is unique, and that the solution lies in the plane spanned by the columns of A.
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when is 9^3n - 5^3n divisivle by 2^n
9³ⁿ - 5³ⁿ will not be divisible by 2ⁿ for any positive integer value of n.
The expression 9³ⁿ - 5³ⁿ is divisible by 2ⁿ if and only if 9³ⁿ and 5³ⁿ have the same number of factors of 2. In order to check this, we can write 9³ and 5³ as powers of 2:
9³ = 729 = 9² × 9 = (3²)² × 3² = (2² × 3)² × 3²
5³ = 125 = 5² × 5 = (5²)²
Since 9³ has three more factors of 2 than 5³, 9³ⁿ - 5³ⁿ will not be divisible by 2ⁿ for any positive integer value of n.
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