Answer:
50
Step-by-step explanation:
To find the number of students, we can use the formula: average = (sum of marks) / (number of students).
Substituting the given values: 40 = 2000 / number of students
Solving for the number of students: number of students = 2000 / 40 = 50
So, there are 50 students in the series.
Plastic parts produced by an injection-molding operation are checked for conformance to specifications. Each tool contains 14 cavities in which parts are produced, and these parts fall into a conveyor when the press opens. An inspector chooses 1 part(s) from among the 14 at random. Two cavities are affected by a temperature malfunction that results in parts that do not conform to specifications.
Round your answers to four decimal places.
(a) What is the probability that the inspector finds exactly one nonconforming part?
(b) What is the probability that the inspector finds at least one nonconforming part?
The probability values
(a) P(X=1) = 0.2696(b) P(at least one nonconforming part) = 0.8845The probability that the inspector finds exactly one nonconforming partFrom the question, we have the following parameters that can be used in our computation:
n = 14
p = 2/14
The probability P(x =1) can be calculated as
P(x) = C(n, x) * p^x * (1 - p)^(n - x)
In this case, we have
P(x = 1) = C(14, 1) * (2/14)^1 * (1 - (2/14))^(13
Evaluate
P(x = 1) = 0.2696
The probability that the inspector finds at least one nonconforming partThe probability P(x >= 1) can be calculated as
P(x) = 1 - P(0)
In this case, we have
P(x >= 1) = 1 - [C(14, 0) * (2/14)^0 * (1 - (2/14))^(14)]
Evaluate
P(x >= 1) = 0.8845
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Dina has a circular table. she wants to paint around the edge of the table. If the table has a radius of 3.5 feet, how long is the part of the table she will be painting?
The length of the part of the table that Dina will be painting is 21.991595 feet.
What do you mean by Circumference?Circumference refers to the distance around the edge of a circle. It is the length of the perimeter of a circle and is defined as the product of the circle's radius and its constant pi (π). The formula for the circumference of a circle is:
C = 2πr
where C is the circumference, π is approximately equal to 3.14, and r is the radius of the circle.
The circumference of a circle is an important concept in geometry, trigonometry, and engineering, as it provides a measure of the size and shape of a circular object. Circumference is used in many applications, such as determining the size of wheels, gears, and other circular objects, as well as in the calculation of areas and volumes of circular shapes.
To find the length of the part of the circular table that Dina will be painting, we need to find the circumference of the circle.
Circumference = 2 * π * r
Where r is the radius of the circle. In this case, the radius is 3.5 feet, so:
Circumference = 2 * π * 3.5
Circumference = 2 * 3.14159 * 3.5
Circumference = 21.991595 feet (to 4 decimal places)
So, the length of the part of the table that Dina will be painting is 21.991595 feet.
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What is the weighted average length of the nails in the drawer?
A. 350 cm
B. 333 cm
C. 5.00 cm
D. 3.50 cm
100-40+10-100-20+20-+10
Answer:
-40
Step-by-step explanation:
100-40+10-100-20+20-(+10)
=60+10-100-20+20-10
=70-100-20+20-10
=-30-20+20-10
=-50+20-10
=-30-10
=-40
What is the total length of 3km, 464m, 8km, 550m and
The total length of 3km, 464m, 8km, 550m and 900m in kilometre is 12.914 km. Thus Option d is correct
The total length of 3km, 464m, 8km, 550m and 900m in kilometre
As we know that 1000m = 1 km, now
= 3000 + 464 + 8000 + 550 + 900
= 12914 m
= 12.914 km
Thus, the total length of 3km, 464m, 8km, 550m and 900m in kilometre is 12.914 km
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What is the central angle(pic included)
Answer:
72
Step-by-step explanation:
circumference = 20
arc = 4
4/20 =1/5
a circle = 360°
1/5 * 360 = 72
What is AB in the figure?
A) An Altitude
B) A Median
C) An Angle Bisector
D) None Of The Above
Answer:
option C
Step-by-step explanation:
line AB bisects the angle, so it is an angle bisector.
Simplify 25a/7 times 2a/5
Give your answer as a single fraction in its simplest form.
Answer:
10a²/7
Step-by-step explanation:
25a/7×2a/5
50a²/35
10a²/7
Answer:
lamohehsphbejrokrbbrjirorvv!hskosbbbwjoajwwjorvvrjfoisbbsiosbwbddpsba hzidb djfofvdjododvowjwwjfpgrdhvrjforvveif fbbrhfjvrjdoddvririvrhrHieojeh
The graph shows a scatter plot for a set of data.
Scatter plot with x-axis labeled width in centimeters and y-axis labeled with length in centimeters. The 20 points graphed are 1.3 and 1.7, 1.4 and 1.9, 1.4 and 1.8, 1.5 and 1.9, 1.9 and 2.3, 2.1 and 3.5, 2.1 and 2.8, 2.1 and 2.7, 2.2 and 3, 2.2 and 2.7, 2.3 and 3, 2.4 and 3.2, 2.4 and 2.9, 2.5 and 3.5, 2.5 and 3.3, 2.6 and 3.5, 2.6 and 3.4, 2.6 and 3.4, 2.7 and 3.2, and 2.8 and 3.8.
What type of correlation exists? Is the model linear or non-linear?
The graph shows a negative correlation, and it is a linear model.
The graph shows a positive correlation, and it is a linear model.
The graph shows a negative correlation, and it is a non-linear model.
The graph shows a positive correlation, and it is a non-linear model.
An equation for the line of best fit that models the data points is
y = 1.31x + 0.02.
How to determine a line of best fit for the data?We would utilise a scatter plot on Microsoft Excel to find a linear equation for the line of best fit that models the data points mentioned above.
In this case, the scatter plot's x-axis would be used to plot the width (in centimetres), and its y-axis would be used to plot the length (in centimetres).
A linear equation for the line of best fit can be derived from the scatter plot (see attachment), which depicts the relationship between the width and length as
y = 1.31x + 0.02.
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Answer: The graph shows no correlation, and it is neither linear nor exponential.
Step-by-step explanation:
try doing a line of fit you're ALWAYS. gonna be ignoring other dots/points/coorids.
Why it's not a correlation is because nothing is together. You could consider a lot of dots on the edge.
If that doesn't make sense to you lets go through each answer
The graph shows a negative correlation, and it is a linear model.
The coordinates don't form any specific line
None of the coordinates are together
there's no slope since there's no line of fit.
it's THE SAME FOR THE OTHER ANSWER CHOICES BESIDES:
'The graph shows no correlation, and it is neither linear nor exponential.'
Question 8
Imagine you are planning to use circles to visually compare the populations of North
Carolina (10,300,000), California (39,800,000), and Ohio (11,600,000). The size of each
population will be represented by the area of each circle, not the radius. The circle for
Ohio will have a radius of 8. Round each answer to the nearest tenth.
What should the area of the circle representing the population of California? Round
your answer to one decimal place.
Area =
cm²
Hint
Create a proportion to find the area of Ohio first. Then use the area formula to find the
radius.
The area of the circle representing the population of California is 689.5 units
What is area of the circle?
Area of the circle is is them measure of size of circle. The area of circle is given by pi* r^2. where r is the radius of the circle which is equal to half the diameter. and pi is a mathematical constant. its value is 3.14.
We are given that the radius representing a circle for ohio is 8
Area of circle = 3.14 * (8^2)
Area of circle = 200.96
Now the area of the circle representing the population of California
given by,
= (39800000*200.96)/11600000
= 689.5
Hence the area of the circle representing population of California is 689.5
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How much water do you add to make each concentration? 1% sugar syrup using 12g sugar
Please help with this answer I will give you Brainly
Answer:
x=1
Step-by-step explanation:
up we have the answer of the question
Answer:
the number is 4.
Step-by-step explanation:
The number is 4 because 3 × 4 = 12 and 4^2 = 16.
16 - 12 = 4
Thanks for Brainly.
Hope I could help in time.
10. Kara's grandmother is knitting a baby
cap. She knitted 1/5 of the cap yesterday
morning. By evening, she had knitted 7/10
of the cap. Estimate how much of the cap
she knitted during the afternoon.
Kara's grandmother knitted the cap during the afternoon is [tex]\frac{1}{2}[/tex].
What is a Fraction?A fraction is a number that represents the part of a whole. It is in the form of [tex]\frac{a}{b}[/tex] , in which upper 'a' part denotes numerator and the lower part 'b' denotes the numerator.
Kara's grandmother knitted the cap,
In the morning = [tex]\frac{1}{5}[/tex]
In the evening = [tex]\frac{7}{10}[/tex]
She knitted during the afternoon = [tex]\frac{7}{10} -\frac{1}{5}[/tex]
= [tex]\frac{7}{10} - \frac{2}{10}[/tex]
= [tex]\frac{5}{10} = \frac{1}{2}[/tex]
Hence, Sara's grandmother knitted the cap during the afternoon =[tex]\frac{1}{2}[/tex].
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Giai PT: xy'=y+xe^{\frac{y}{x}}
Can someone answer this?
Answer:
Step-by-step explanation:
1+1=2 your welcome
4p divided by 6,
where p= 12
The value of the expression 4p ÷ 6 when p = 12 is 8
What is the value of the expression when p = 12?Given the expression in the question;
4p ÷ 6
p = 12To determine the value of the expression, substitute p = 12 for all values of p in the expression and simplify.
4p ÷ 6
Plug in p = 12
4( 12 ) ÷ 6
Multiply 4 and 12
48 ÷ 6
Divide 48 by 6
8
Therefore, the value is 8.
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Need help with this question pls
Answer:
[tex]\huge\boxed{\sf SA \approx 967.1\ cm\²}[/tex]
Step-by-step explanation:
Given data:Radius = r = 7 cm
Height = h = 15 cm
Required:Surface Area = SA = ?
Formula:Surface Area of a cylinder = 2πrh + 2πr²
Solution:Using 3.14 for π
Now, Put the given data in the above formula.
SA = 2(3.14)(7)(15) + 2(3.14)(7)²
SA = 659.7 + 2(3.14)(49)
SA = 659.4 + 307.72
SA ≈ 967.1 cm²[tex]\rule[225]{225}{2}[/tex]
Use algebraic methods to find as many intersection points of the following curves as possible. Use graphical methods to identify the remaining intersection points. R = 6 sin theta and r = 6 cos theta the intersection point(s) is/are_______
(Type an ordered pair. Type exact answer for each coordinate, using phi as needed. Type the coordinate for theta in radians between 0 and phi. Use a comma to separate answers as needed)
The intersection points are (6, 6) and (-6, -6).
What is Intersection points?
The point at which two lines or curves intersect is referred to as the point of intersection. The point at which two curves intersect is crucial because it is the point at which the two curves take on the same value.
The given curves are the polar equations of two circles with radii 6. To find their intersection points, we can set the two equations equal to each other and solve for Ф.
6 sin(Ф) = 6 cos(Ф)
Dividing both sides by 6 and rearranging terms, we get:
tan(Ф) = 1
This equation has infinitely many solutions, but we are only interested in those that lie in the interval [0, π/2].
Ф = π/4 satisfies this condition and corresponds to the point (6, 6) in Cartesian coordinates.
Since the two curves are circles, they are symmetrical about the origin. Therefore, we can deduce that the other intersection point is (-6, -6).
Therefore, the intersection points are (6, 6) and (-6, -6).
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A ball is thrown from an initial height of 6 feet with an initial upward velocity of 37ft/s . The ball's height h (in feet) after t seconds is given by the following. h=6+23t-16t^2 Find all values of t for which the ball's height is 26 feet. Round your answer(s) to the nearest hundredth
The value of t for which the ball's height is 26 feet is given as follows:
t = 0.33 seconds.
How to model the situation?The quadratic equation that models a projectile's height is given as follows:
y = -16t² + v(0)t + h(0).
In which the parameters are given as follows:
v(0) is the initial velocity.h is the initial height.The coefficients for this problem are given as follows:
h(0) = 6, v(0) = 37.
Hence the function is given as follows:
y = -16t² + 37t + 6.
The height is of 26 feet when:
-16t² + 37t + 6 = 20
Hence:
-16t² + 37t - 14 = 0.
The coefficients of the quadratic function are given as follows:
a = -16, b = 37, c = -14.
Inserting these coefficients into a quadratic function calculator, the time is given as follows:
t = 0.33 seconds.
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Find the GCF of 35x^5y and 42x^5y^3.
Answer:
x^5y
Step-by-step explanation:
To find the greatest common factor (GCF) of 35x^5y and 42x^5y^3, we need to find the largest expression that divides into both of these polynomials.
The common factor in both of these polynomials is x^5y, which is the GCF. So, the GCF of 35x^5y and 42x^5y^3 is x^5y.
write an exponential function that has a y-intercept of -4 and passes through the points (1, -1.6) and (2, -0.64)
The function can be used to model the exponential growth or decay that occurs in real-life situations that fit this particular pattern is y = 4(-0.4)ˣ + -4
An exponential function is a mathematical function that has the form
=> y = abˣ,
where a is a constant and b is the base of the exponential.
To start, we will use the first point, (1, -1.6), to write an equation that relates x and y. Let's call the constant a in our exponential function "k". Using the point (1, -1.6), we can write the equation:
=> -1.6 = k * b¹
Next, we will use the second point, (2, -0.64), to write another equation that relates x and y. Using the point (2, -0.64), we can write the equation:
=> -0.64 = k * b²
Now that we have two equations, we can solve for the two unknowns, k and b, by dividing the two equations:
=> (-0.64) / (-1.6) = k * b² / k * b¹
b = (0.64 / -1.6)¹
b = -0.4
With b determined, we can substitute it back into one of the equations and solve for k:
=> -1.6 = k * (-0.4)¹
=> k = -1.6 / (-0.4)
=> k = 4
So our exponential function that passes through the points (1, -1.6) and (2, -0.64) and has a y-intercept of -4 is:
y = 4 * (-0.4)ˣ + -4
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Richard and Teo have a combined age of 36. Richard is 15 years older than twice Teo's age. How old are Richard and Teo?
Teo is 10.5 years old and Richard is 25.5 years old.
How old are Richard and Teo?Represent Teo's age with x.
Using the above as a guide, we have the following:
Richard = x + 15
Their combined age is 36
So, we have the following representation
x + (x + 15) = 36
Evaluate the like terms
2x + 15 = 36
2x = 21
x = 10.5
Recall that
Richard = x + 15
So, we have
Richard = 10.5 + 15
Richard = 25.5
So Teo is 10.5 years old
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an upward opening parabola beginning with closed circle at negative 2 comma 4, which decreases to a vertex at 0 comma 0 and then increases to an open circle at 3 comma 9
What is the range of the function?
{x | −2 ≤ x < 3}
{x | −2 < x ≤ 3}
{y | 0 ≤ y < 9}
{y | 0 < y ≤ 9}
The range of the quadratic function is {y |0 ≤ y < 9}
What is the range of a function?The range of a function is the set of output values of the graph. In other words mean the range of a function is the set of y values of the graph.
Given,
Parabola opens from
Closed circle point = (-2, 4) , then decreases
y ≤ 4
vertex = (0,0)
at vertex y = 0
then increases to
Open circle point = (3, 9)
y < 9.
It can be concluded,
value of y is such that 0 ≤ y < 9.
Range = {y | 0 ≤ y < 9}
Hence, the range of the function is {y | 0 ≤ y < 9}
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HELP FAST WILL GIVE 60 POINTS For THE RIGHT ANSWER
A repeating decimal like 0.2222222.... is a rational number and can be written as the fraction 2/9.
A stopping decimal like 0.22 is a rational number and can be written as the fraction 22/100.
A non-stopping and non-repeating decimal like 0.1234567891011... or 0.121121112... is an irrational number that can be written as the fraction 1514013912/5000000
The square root of a perfect square is a rational number and also a whole number.
The square root of a prime number is an irrational number.
What are rational and irrational numbers?
The definition of a rational number is one that may be stated as a fraction or as a portion of a whole number. For example -7, 2/3, 3.75 Numbers that cannot be stated as a fraction or ratio of two integers are referred to be irrational numbers. There is no limit to how one might convey them. For example √2, √3, e
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3. ABCD is
a. Congruent
b. Similar
c. Neither
to A'B'C'D'.
Answer:
Step-by-step explanation:
A. Congruent
Let f(x) = √x-5 for x ≥ 5
Find f^-1(2)
Answer: To find the inverse of the function f(x), we need to switch the roles of x and y, so that x becomes the dependent variable and y becomes the independent variable. Then, we need to solve for x in terms of y.
Let y = √x - 5, then x = y^2 + 5.
To find f^-1(2), we need to substitute 2 for y in the equation x = y^2 + 5:
x = 2^2 + 5 = 9
So f^-1(2) = 9.
This means that the inverse of f(x) at 2 is 9. In other words, if f(x) = 2, then x = 9.
Step-by-step explanation:
what is (-5,-3) reflected over the Y axis
The point (-5,-3) reflected over the y-axis is (5, -3).
What is a reflection?There are two ways of reflection.
Along x-axis:
(x, y) – (x, -y)
Along y-axis:
(x, y) - (-x, y)
We have,
(-5, -3)
Now,
Along y-axis:
(x, y) → (-x, y)
So,
(-5, -3) → (-(-5), -3) = (5, -3)
Thus,
(5, -3) is the reflected point.
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[tex]\sqrt{11x-5}=7[/tex]
solve for x and explain how you know if this equation is extraneous or not.
The value of the variable x is 4. 90
How to determine the value of the expressionAlgebraic expression are expressions composed of variables, terms, coefficients, factors and constants.
They are also made up of mathematical operations.
From the information given, we have that;
[tex]\sqrt{11x - 5}[/tex] = 7
To solve the equation
Find the square of both sides, we get;
11x - 5 = 7²
find the square
11x - 5 = 49
collect like terms
11x = 49 + 5
add the values
11x = 54
Make 'x' the subject
x = 4. 90
Hence, the value is 4. 90
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The points (14,8) and (28,16) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.
the answer to your problem is y = 4/7x
Use this pattern when a binomial
can be written as the square of
one number minus the square of
another number.
4x² - 49 = (2x-7)(2x + 7)
2
A pattern when a binomial can be written as the square of one number minus the square of another number will be 4x² - 9 = (2x-3)(2x + 3)
What is a binomial?Binomial is the name for an algebraic expression with only two terms. It is a polynomial with two terms. It is sometimes referred to as the sum or difference of two or more monomials. It is a polynomial's most basic form.
It should be noted that a binomial is an algebraic expression that has two non-zero terms. Examples of a binomial expression: a2 + 2b is a binomial in two variables a and b. 5x³ – 9y² is a binomial in two variables x and y.
In this case, the illustration for 4x² - 9 = (2x-3)(2x + 3) depicts this.
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