30% of students mean 30 students wear contact lenses from a random selection of 100 students studying in a university.
What is meant by percentage?Percentage is a fraction or a ratio of a random sample in which the value of whole is always 100. For example, if Sam received 30% on his arithmetic test, he received 30 points out of 100. It is expressed as 30/100 in fractional form and 30:100 in ratio form.
Percentage is defined as a certain fraction or number out of a hundred. It is a fraction with the denominator 100, and the sign for it is "%."
Finding the proportion of a whole in terms of 100 is the goal of percentage calculations. There are two methods to calculate a percentage:
Use the unitary approach or try adjusting the fraction's denominator to 100.
How to solve?
30 % = 30/100 of a sample = 0.3 of a sample
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slope=6 y-intercept=-3
The equation of the line with a slope of 6 and a y-intercept of -3, is y = 6x - 3
Determining the equation of a line with slope and interceptFrom the question, we are to determine the equation of the line that has the given slope and y-intercept
From the slope-intercept form of the equation of a straight line, we have that
y = mx + b
Where m is the slope
and b is the y-intercept
From the given information,
The slope of the line is 6
and
The y-intercept is -3
That is,
m = 6
b = -3
Substitute the values into the equation
y = mx + b
y = 6(x) + (-3)
Simplify
y = 6x - 3
Hence, the equation is y = 6x - 3
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(2x² + 3x − 9)
Factor
I am thinking of a number. When I divide my number by $7$ and subtract $\dfrac{3}{5},$ I get back my original number. What is my number?
A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point.
The area of the triangle as the function of x is [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)
The point on the line = (2, 1)
The give three points are (0, y), (2, 1) and (x, 0)
The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line
Consider the point (0, y) and (2, 1)
Slope = (1-y) / (2-0)
= (1-y) /2
Consider the point (2, 1) and (x, 0)
Slope = (0-1) / (x-2)
= -1/x-2
Both slopes are equal
(1-y) /2 = -1/x-2
(1-y) = -2 / (x-2)
y = 1 + (2/(x-2))
y = x / (x-2)
The area of the triangle = (1/2)bh
Where b is the base
h is the height
The area of the triangle = (1/2) × x × (x / (x-2))
= [tex]x^2[/tex] / 2x - 4
The domain is x∈(2, ∞)
Hence, the area of the triangle is [tex]x^2[/tex] / 2x - 4 and the domain of the function is x∈(2, ∞)
The complete question is
A right triangle is formed in the first quadrant by the x- and y-axes and a line through the point (2,1). Write the area of the triangle as a function of x, and determine the domain of the function.
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A partial payment is made on the date indicated. Use the United States rule to determine the balance due on the note at the date of maturity. (The Effective Date is the date the note was written.) Assume the year is not a leap year.Principal Rate Effective Date Partial Payment Maturity Date Amount Date $2000 4% April 1 $1000 May 1 June 1 The balance due on the note at the date of maturity is $nothing.(Round to the nearest cent as needed.)
The balance due on the note at the date of maturity is $1010.13.
What is meant by partial payment?The offering of a payment by cheque for less than the whole amount sought by the creditor is known as partial payment. It is standard practice to grant debt forgiveness in exchange for the tender of a "payment-in-full" check.
Given permission to apply the US rule
In the United States, a year is deemed to have 360 days for the purposes of calculating interest.
Given that the principal is $ 2000,
Interest rate = 4% = 0.04
The effective date is April 1.
The whole amount is $1,000.
May 1 = partial payment
Duration = 30 days (May 1 - April 1)
Therefore, interest = PTR = 2000 * 0.04 * 30/360 = $6.67
So value = $ 2000 + $6.67 = $6.67
Partial payment received = $1,000
As a result, value = $ 1006.67 = $2006.67 - $ 1000
Time T= 31
Interest = PTR * 31/360 * 0.04 = 3.46
So the total value is $1006.67 + $3.47 = $1010.13.
The note's outstanding balance at maturity is $1010.13.
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why are t statistics more variable than z-scores?
T statistics are more unpredictable than z scores since they employ sample variance rather than population variance.
Explain the term t statistics?The t-value, also known as the t-score, is a ratio of the variance present within the sample sets to the difference between their respective means. The discrepancy between the means of the two tested samples serves as the numerator value.When data sets have a normal distribution however the population variance is unknown, the t test is typically performed. If you flip a coin 1,000 times, for instance, you can discover that the outcome is distributed normally over all trials.The correlation between both the response as well as the predictor factors can be found using the t-test statistic.In linear regression, the null hypothesis that slope or coefficient is equal to 0 will be tested using a one-sample t-test.Thus, because the t statistic employs the sample variance rather than the population variance, it is more volatile than z scores.
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Consider the differential equation dy/dx = 2x - y. dx Find d^2 y/d x^2.\ Determine the concavity of all points in Quadrant Determine the slope of the function if f(2) = 3.
The second derivative, inflation point and slope of differential equation are explained below.
Explain differential equation.differential equation states how a pace of progress (a "differential") in one variable is connected with different factors. For example, when the position is zero (ie. the spring is neither extended nor compacted) then the velocity isn't evolving.
According to question:We have,
dy/dx = 2x-y
Suppose f'(x) = 2x - y
d^2y/dx^2 = d(2x - y)/dx
⇒ 2
(b) To find the inflection points, equate f(x) to zero and solve for x.
f"(0) =0
f" (x)=2
So, the function defined on the interval (- ∞, 2) (2, ∞)
In the interval (- ∞, 2), when x-1
f"(1)=2>0
So, the concave up wards on this interval.
In the interval (2,∞) when x=2
f"(2)=2>0
the concave up wards on this interval
Now, the slope of the function,
f(2)=3
here x-2y=3
Then, x = 2, y = 3
[tex]\frac{dy}{dx}|_{2, 3}[/tex] = 2(2) - 3 = 1
Thus, the slope of the function is 1.
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Alex and Debbie took an afternoon walk through the city. Alex practiced his map making skills along the way, and drew an accurate picture of each turn they took. When he got home, he measured the angles of their turns with a protractor. His drawings are shown below. If they started their walk going north, what direction did they end up facing?
Answer:
connect with a tour
Step-by-step explanation:
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I NEED HELP ASAP PLS HURRY
Answer: C
Step-by-step explanation: The slope of Function A is 6 and the slope of Function B is 5.
Determine whether ∆MNO=∆QRS. Explain using rigid motions.
M(4, 7), N(5, 4), O(2, 3), Q(2, 5), R(3, 2), S(0, 1)
∆MNO and ∆QRS are congruent with each other.
What are rigid motions in congruency of triangles?
Two plane figures are congruent if and only if one can be obtained from the other through a series of rigid motions (that is, reflections, translations, and/or rotations). A landscape architect designs the landscape around a mall using a grid. Trace the landscape elements to ensure that they are congruent.
For the given coordinates M(4, 7), N(5, 4), O(2, 3), Q(2, 5), R(3, 2), S(0, 1).
Let's draw the triangles on graph paper,
You can map MNO to QRS with a translation left 2 units and
down 2 units. The planters are congruent because there is a rigid
transformation that maps one to the other.
Hence, ∆MNO and ∆QRS are congruent with each other.
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TRUE OR FALSEfor 95% of the samples from the population, the confidence interval we compute will contain the true mean.
The statement if true, for 95% of the samples from the population, the confidence interval we compute will contain the true mean.
In the given question we have to check whether the given statement is TRUE or FALSE.
The given statement is:
For 95% of the samples from the population, the confidence interval we compute will contain the true mean.
Because the underlying approach succeeds on 95% of random samples, we have a 95% confidence that this confidence interval contains the population mean.
Approximately 95% of the estimated intervals will contain the actual value of the population mean if samples are taken frequently and 95% confidence intervals are generated.
So the given statement is true.
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The graph represents the relationship between the number of hours Jane babysits and the amount of money she earns.
Which of the following statement describes the graph represented?
The statement that best describes the relationship in the graph is Jane earns $8 for every hour she babysits
How to know the correct statementIn the graph, the x directions shows the number of hours. while the y directions show the amount earned
At point 1, in the x directions trace up to meet the line, then at the point of intersection with the line, trace to the left to meet the y directions
Following the description shows that at 1 hour (in x direction) the corresponding value in the y direction is $8
Therefore we say that Jane earns $8 per hour
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PLEASE HELP ASAP!!
Geometry Help!!
5) <OSL
Vertical pair angles are equal angles formed by intersecting lines
6) <MSN (or <LOS)
Supplementary angles are angles that add up to 180 degrees
Write an equation of the line that passes through (18, 2) and is parallel to the line 3y−x=−12.
Answer: No solution
Step-by-step explanation:
3y - x = (3 * 2 - 18) = 6 - 18 = -12
3y - x = -12
x - 3y = 12
since parallel lines, by definition, have NO point of intersection, there is no solution.
Calculate how far each of the following travels. A helicopter flies at a speed of 72miles per hour for 10 minutes
Answer:
12 miles
Step-by-step explanation:
72 x [tex]\frac{10}{60}[/tex] = 12
Tom and rosie are designing a game. In each turn, a player rolls five 666-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=51+1+1+1+1=51, plus, 1, plus, 1, plus, 1, plus, 1, equals, 5 points, and the highest is 6+6+6+6+6=306+6+6+6+6=306, plus, 6, plus, 6, plus, 6, plus, 6, equals, 30 points.
Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
Based on the expected value, Rosie's statement is correct.
The expected value, denoted as E(X), represents the average or mean value of a random variable, in this case, the sum of points in a given turn when rolling the five dice.
Tom's statement, "A player will most likely get 17.5 points in any given roll," is not accurate. The expected value of 17.5 points does not necessarily mean that a player is most likely to get exactly 17.5 points in any single roll. Instead, it indicates that over many rolls, the average value of points earned in a turn is 17.5 points.
On the other hand, Rosie's statement, "Over 100 turns, we can expect a total of about 175 points," is correct. Since the expected value is 17.5 points per turn, over 100 turns, we can expect the total sum of points to be approximately 100 turns × 17.5 points/turn = 1750 points.
In summary, the expected value of 17.5 points represents the average outcome over multiple rolls, and based on this value, Rosie's statement about expecting a total of about 175 points over 100 turns is accurate.
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The complete question:
Tom and Rosie are designing a game. In each turn, a player rolls five 6-sided dice and adds the numbers showing on each face to determine how many points they get that turn. For example, the lowest number of points in a given turn is 1+1+1+1+1=5 points, and the highest is 6+6+6+6+6=30 points.
They let X represent the sum in a given turn, and they find the expected value of X is E(X) = 17.5 points.
Tom says, "A player will most likely get 17.5 points in any given roll."
Rosie says, "Over 100 turns, we can expect a total of about 175 points."
Whose statement is correct based on the expected value?
carla's cell phone company charges $35 a month for phone service plus $0.50 for each text message. carla's bill was $52 this month.
The number of text messages sent by carla in a month is 34.
What is an algebric equation ?
An algebraic equation is a mathematical statement that sets two expressions equal to each other. An algebraic equation is typically made up of a variable, coefficients, and constants.
For given question,
Phone service = $35
For each text message = $0.50
Total bill = $52
Let x be the no. of total text messages.
Equation: 52 = 35 + 0.50x
Solving for x,
52 - 35 = 0.50x
17 / 0.50 = x
34 = x
The number of text messages sent by carla in a month is 34.
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Fill in the blank with an appropriate word, phrase, or symbol(s). Measures of dispersion are used to indicate the spread or _ of the data.
Measures of dispersion are used to indicate the spread or variability of the data.
What is measure of dispersion?Measures of dispersion are crucial for representing the spread of the data, or its fluctuation around a central value, whereas measures of central tendency are used to assess a dataset's "normal" values.
The four main measure of dispersion include
Range Standard deviationInterquartile rangeVarianceThe range in statistics refers to the distribution of data between the lowest and greatest value in the distribution. It is a widely used indicator of variation.
The standard deviation deals with how much the data is away from the mean
The variance is standard deviation squared
These measures the spread, variability or distribution of data
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In the diagram, A and B are points
on the circle AC and BC are
tangents to the circle and meet
at C. Work out the angle ACB.
The angle ACB would be 80 degrees.
What is tangent to a circle?
The tangent always makes a single-point contact with the circle. It never intersects the circle twice. Tangents from an external point to a circle have the same length.
In the given figure,
angle AOB = 40.
So angle OBA = 40.
Then the angle AOB = 180 - 40 -40
AOB = 100.
By the theorem of circles,
AOB + ACB = 180
100 + ACB = 180
ACB = 80.
Hence, the angle ACB would be 80 degrees.
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In a school there are 1,970 pupils. If there are 799 boys, how many more girls are there than boys?.
If in the school of 1970 pupils, there are 799 boys, there are 372 girls more than the boys.
What do you understand by linear equation?A linear equation is an equation with the maximum degree of one. No variable in a linear equation, thus, has an exponent greater than 1. The graph of a linear equation is always a straight line.
Both linear equations with one variable and those with two variables exist. This is already taught in schools. Let's use the examples below to understand how to distinguish between linear and non-linear equations.
y = 8x - 9 Linear
y = x2 - 7 Non-Linear, the power of the variable x is 2
√y + x = 6 Non-Linear, the power of the variable y is 1/2
y + 3x - 1 = 0 Linear
How to solve?
total number of pupils = 1970
number of boys = 799
number of girls = 1970 - 799 = 1171
number of girls more than the boys = 1171 - 799 = 372
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determine the zeros of f(x)=28x^2−7
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The function is given below.
f(x) = 28x² - 7
For the zeroes of the function, put f(x) = 0, then we have
f(x) = 0
28x² - 7 = 0
x² = 1/4
x = ± 1/2
The zeroes of the function f(x) = 28x² - 7 will be 1/2 and negative 1/2.
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Alejandro and some friends are going to the movies. At the theater, they sell a bag of popcorn for $3. 50 and a drink for $4. How much would it cost if they bought 3 bags of popcorn and 8 drinks? how much would it cost if they bought pp bags of popcorn and dd drinks?.
Answer:
3.50 × 6 = $21.004.50 × 4 = $18.00
But to Add These Two Numbers up The Cost Would $39.00 All Together :D
And pp+ dd+ =$39.00
Step-by-step explanation:
Drew's grandmother is 72 years old. Drew's mother is y years younger than Drew's grandmother, and she is 45 years old. Write an equation using subtraction that represents this situation.
The population of a city increases by 0. 8% per year. If this year's population is 108,000, what will next year's population be, to the nearest individual?.
The population of the next year will be, 108,864.
What is population?
The term "population" refers to all citizens who are either permanently residing in a nation or are just temporarily absent from it. This indicator displays the population of a given area on a regular basis. Growth rates are the yearly changes in population brought on by births, deaths, and net migration.
Given:
The population of a city increases by 0. 8% per year.
This year's population is 108,000.
0.8% of 108,000 is,
108,000 x 0.008 = 864
The population increased by 864 people.
So, the next year's population will be,
108,000 + 864 = 108,864.
Hence, the next year's population will be 108,864.
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y=-2x+2 y=-2x-5 y=3/2x+5 label them to the correct ones
Answer:
y=-2x+2: second graph
y=-2x-5: third graph
y= 3/2x+5: first graph
Step-by-step explanation:
we can just look at the y intercept since each equation has different ones
The graphs are left to right so I’ll call it by 1st graph 2nd graph and last graph
y=mx+b is slope intercept formula where big y intercept
The first equation b or the y intercept is 2 and the only graph where the Line intersects with the y axis at 2 is the second one
The second equation has a y intercept of -5 so the last graph is the only one that line intersects with the y axis at -5
the last equation has a y intercept of 5 so the first graph is the only one where the line intersects with 5
Hopes this helps please mark brainliest
Solve the equation and verify the solution using substitution.
-5(2r-0.3)+0.5(4r+3)=-64
Solve the following equation. 25x + 3 = 14 (Type an exact answer.)
Answer:11/25
Step-by-step explanation:
Write the following expression using the fewest possible terms.
the expression quantity two fifths times t minus 7 plus two thirds times t end quantity minus quantity five sixths times t plus 14 end quantity
The rewritten form of the given expression using the fewest possible terms as required is; 7/30t - 21.
What is the rewritten form of the given expression?It follows from the task content that the given expression is to be rewritten using the fewest terms.
Since the given expression is;
( 2/5t - 7 + 2/3t ) - (5/6t + 14)
By getting rid of the parentheses; we have;
2/5t - 7 + 2/3t - 5/6t - 14.
By collecting like terms; we have;
2/5t + 2/3t - 5/6t - 7 - 14
7/30t - 21.
Therefore, the required rewritten form of the given expression is; 7/30t - 21.
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What is irrational number and is 4/3 a irrational number??
Answer: 4/3 is not irrational, it is rational
Explanation:
A rational number is a ratio, or fraction, of two integers. The denominator cannot be zero.
4/3 is rational since it's the ratio of the integers 4 over 3.
Since it is rational, it is not irrational. The term "irrational" literally means "not rational". Therefore, a real number is either of those options, but not both simultaneously.
A famous example of an irrational number is [tex]\pi \approx 3.14...[/tex] because it cannot be written as a fraction of two integers. We can get approximations like 22/7, but never manage to capture the full value of [tex]\pi[/tex] with a single fraction.
Another example of an irrational number is [tex]\sqrt{2}[/tex]
[tex]\displaystyle\\Answer: \ \frac{4}{3} \ isn`t\ an\ irrational\ number[/tex]
Step-by-step explanation:
An irrational number is an infinite non-periodic fraction
[tex]\displaystyle\\\frac{4}{3}=1\frac{1}{3} \\\\\frac{4}{3} =1.333333...\\\\\frac{4}{3}=1.(3)[/tex]
1.(3) - is an infinite periodic fraction
[tex]\displaystyle\\Hence,\ \frac{4}{3} \ isn`t\ an\ irrational\ number[/tex]
In a multiple regression problem involving two independent variables, if b1 is computed to be +2.0, it means thatthe estimated mean of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.the estimated mean of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constantthe estimated mean of Y is 2 when X1 equals zero.the relationship between X1 and Y is significant.
The solution is y will increase by 2 units with every unit increase in x1
What do you mean by multiple regression?A single dependent variable and several independent variables can be analyzed using the statistical technique known as multiple regression. In order to predict the value of the single dependent value, multiple regression analysis uses independent variables whose values are known.
What is the difference between multiple and single regression?X and Y variables are the sole ones in simple linear regression. Two or more x variables and one y variable make up multiple linear regression. For instance, basic linear regression is used when we forecast rent using only square footage.
In the above question:-
Interpretation of b1=2
it means that y will increase every 2 units for every unit increase in x1
holding x2 constant.
Hence option B is the correct answer.
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