Answer:
the product of 6 and 23 is more than 126
Step-by-step explanation:
You want to know how to tell that 6 is too high an estimate for the first digit of the quotient of 126 and 23.
Trial dividendWhen the trial quotient value of 6 is multiplied by the actual divisor of 23, we are computing 6(20 +3) = 120 +18. This is more than 126, so the trial quotient value is too large.
__
Additional comment
Another way to tell is to consider the dual problem that 120/20 = 6 represents: 120/6 = 20. It is easy to see that 126/6 = 21, so we know that a divisor of 23 (larger than 21) will give a quotient less than 6.
the following is a listing of the amount of sugar in six popular snacks found on a high school campus: 35g 35g 43g 49g 52g 53g what is the median?
The median is 43 g. By using median formula and by simple observation method we can find median of the given data.Hence median is 43 g.
What is median?The middle number ,by ordering all data points and picking out the one in the middle.Arrange the all values from lowest to highest.Then we can find easily.Median is also type of average which is used to find centre value.
What is the formula we use to find median?There are the following formula we use to find median.
Median= (n+1)th/2 terms (if n is odd)
Where n is the number of observations.
So,if n is even then we use
Median= (n/2)th terms
if number of term is even,then the median is the simple average of the middle two numbers.
So we can find median by two methods
median= n/2 -th term
median =6/2 -th term
median = 3-th term
Hence our third term is 43 g so our median will be 43 g.
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James was also measured at 23 inches long. How many centimeters long was he at birth
The length of the birth in centimeters will be 58.42 centimeters.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
James was also measured 23 inches long.
We know that, in one inch, there are 2.54 centimeters.
The length of the birth in centimeters is calculated as,
⇒ 23 inches
⇒ 23 x 2.54 centimeters
⇒ 58.42 centimeters
The number of birth in centimeters will be 58.42 centimeters.
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Mark car can travel 22 km per liter of gas gas cost 200 per liter how many kilometers can mark travel on 1000 worth of gas
Mark can travel a distance of 110 km on 1000 worth of gas.
Mathematical operations:The operations that we use in daily life are problems like adding, subtracting adding multiple times, and dividing things are called Mathematical operations.
The four basic mathematical operations are
1. Adding, 2. Subtracting, 3. Multiplication, and 4. Division.
Here in this problem, we use Multiplication and Division to solve the
Here we have
Mark car can travel 22 km per liter of gas costs 200 per liter
Here we need to find how many kilometers can mark travel on 1000 worth of gas
Given the cost of 1 liter of gas = 200 Rs
=> Amount gas that can be worth 1000 = 1000/200 = 5 liter
Given Mark can travel 22 km with 1 liter
The distance can be travel with 5 liters = 5 × 22 = 110 km
Therefore,
Mark can travel a distance of 110 km on 1000 worth of gas.
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Given a number n, for each integer i in the range from 1 to n inclusive, print one value per line as follows: if i is a multiple of both 3 and 4, print FizzBuzz. If i is a multiple of 3 (but not 5), print Fizz. If i is a multiple of 5 (but not 3), print Buzz. If i is not a multiple of 3 or 5, print the value of i.
To begin, let’s create a for loop to account for the first line of the question. We know that the value of i is always either equal to or less than n, so let’s write that in.
Taking two count variables, say count3 and count5, to store the count of numbers divisible by 3 and 5 respectively.
Iterate over the range [1, N] using a variable, say i, and perform the following steps:
If the value of count3 and count5, print “FizzBuzz”.
If the value of count3 is equal to 3, print “Fizz”.
If the value of count5 is equal to 5, print “Buzz”.
If none of the above conditions match, then print i.
What is FizzBuzz?In a typical coding challenge during an interview, candidates are asked to create a solution that prints integers from 1 to N, designating any integers that are divisible by 3 as "Fizz," any integers that are divisible by 5 as "Buzz," and any integers that are both divisible by 3 and 5 as "FizzBuzz." Good coding practises can be reinforced by knowing how to solve it.
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
// Function to generate FizzBuzz sequence
void fizzBuzz(int N)
{
// Stores count of multiples
// of 3 and 5 respectively
int count3 = 0;
int count5 = 0;
// Iterate from 1 to N
for (int i = 1; i <= N; i++) {
// Increment count3 by 1
count3++;
// Increment count5 by 1
count5++;
// Initialize a boolean variable
// to check if none of the
// condition matches
bool flag = false;
// Check if the value of count3
// is equal to 3
if (count3 == 3) {
cout << "Fizz";
// Reset count3 to 0, and
// set flag as True
count3 = 0;
flag = true;
}
// Check if the value of count5
// is equal to 5
if (count5 == 5) {
cout << "Buzz";
// Reset count5 to 0, and
// set flag as True
count5 = 0;
flag = true;
}
// If none of the condition matches
if (!flag) {
cout << i;
}
cout << " ";
}
}
// Driver Code
int main()
{
int N = 15;
fizzBuzz(N);
return 0;
}
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The map of a walking trail is drawn on a coordinate grid with three points of interest. The trail starts at R(−1, 4) and goes to S(5, 4) and continues to T(5, −2). What is the total walking trail of units?
Answer:
Exact answer 12 + 6[tex]\sqrt{2}[/tex]
Answer rounded to the nearest whole number 20
Step-by-step explanation:
find the interval of convergence of the power series. (be sure to include a check for convergence at the endpoints of the interval.) (7x)^n/(10n)!
The interval of convergence of the power series is (-10/7, 10/7).
What does Interval of convergence tell you?
A group of x-values on which a power series converges is known as the interval of convergence. In order to create a convergent series, you can plug in this interval of x-values.
The interval of convergence of a power series is the set of values of x for which the series converges. To find the interval of convergence of the given power series, we can use the ratio test.
The ratio test states that if the series [tex]∑ a_nx^n[/tex] has a positive radius of convergence R, then the series converges for |x| < R and diverges for |x| > R. The radius of convergence is given by the formula
[tex]R = 1/limsup|a_n+1/a_n|.[/tex]
In the given power series, the coefficient [tex]a_n[/tex] is given by [tex]a_n = (7x)^n/(10n)!.[/tex]
We can rewrite this as [tex]a_n = x^n(7/10)^n/n!.[/tex]
Taking the limit of the ratio [tex]a_n+1/a_n[/tex] as n goes to infinity, we get:
[tex]limsup|a_n+1/a_n| \\\\= limsup|x^(n+1)(7/10)^(n+1)/(n+1)!/(x^n(7/10)^n/n!)|\\\\= limsup|x(7/10)/(n+1)|\\\\= |x(7/10)|[/tex]
Therefore, the radius of convergence R is [tex]1/|x(7/10)|[/tex].
This means that the interval of convergence is [tex]|x| < 1/|7x/10| = 10/7.[/tex]
We can check the endpoints of the interval to see if the series converges at these points. At x = 10/7, the series becomes [tex](7(10/7))^n/(10n)! = 1^n/(10n)!.[/tex]
This series is a geometric series with first term 1 and common ratio 1/10, and it converges because [tex]|1/10| < 1.[/tex]
At x = -10/7, the series becomes[tex](7(-10/7))^n/(10n)! = (-1)^n/(10n)![/tex]. This series is an alternating series with first term 1 and common ratio (-1/10), and it also converges because [tex]|-1/10| < 1.[/tex]
Therefore, The interval of convergence of the power series is (-10/7, 10/7).
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2x - y = 20
2x + y = 48
Answer:
Below
Step-by-step explanation:
2x-y = 20
2x + y = 48 add the two equations to get
4x = 68
x = 17 <==== use this value in either equation to calculate y = 14
tessa needs 1,450 yards of yarn to knit a blanket. she buys 9 balls of yarn, which are each 185 yards long. tessa hopes there will be enough leftover yarn to knit a scarf for her younger brother. a childs scarf takes 125 yards of yarn.
There will be enough leftover yarn to knit a scarf for her younger brother If the child scarf takes 125 yards of yarn.
What is Unit conversion ?
Unit conversion is a necessary step in many mathematical problems. Calculations must be performed using mathematical conversions.
Tessa has bought 9 balls of yarn which are each 185 yards long.
So, She has total 1665 (185 × 9) yards of yarn.
She needs 1450 yards of yarn to knit a blanket.
So, The leftover yarn = 1665 - 1450
= 215.
She needs 125 yards of yarn to knit a scarf for her brother.
So, She has enough yarn to knit the scarf for her brother because the leftover yarn is greater than the yarn needed for scarf.
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125x ^ 3 - 27 = 0
Solve this by grouping
The solution to the equation 125x³ - 27 = 0 is (5x−3)(25x ^2 +15x+9)
What is an equation?An equation is a mathematical expression that contains an equals symbol. Equations often contain algebra. Algebra is used in mathematics when you do not know the exact number in a calculationsolving the equation 125x³ - 27 = 0 by grouping
Rewriting 125x^ 3 −27 as (5x) ^3 −3³
The difference of cubes can be factored using the rule:: a ^3 −b^ 3 =(a−b)(a^ 2 +ab+b^ 2 )
Polynomial 25x^ 2 +15x+9 is not factored since it does not have any rational roots.
Hence, (5x−3)(25x ^2 +15x+9)
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A researcher is examining the effects of income (X1) and number of friends (X2) on personal happiness (Y) and finds an R2 of 0.45. Which of the following is a correct interpretation of this result?A.Friends are more important than money for happiness. B.Money CAN buy happiness. C.Taken together, income and number of friends explain 0.45% of the variance in happiness. D.Taken together, income and number of friends explain 45% of the variance in happiness.
Correct interpretation of this result is together, income and friend count account for 45% of the variation in happiness.
Define variation.Variation refers to this relationship between the change in a variable's value when the values of the linked variables change. An example of a straightforward equation, y = mx, in which m is a constant, can be used to show this. The equation becomes y = 5x if we suppose that the value of m is 5. A function in which the variables are related by how they alter in relation to one another is known as a variation function. In this function, for instance, if x rises or falls, D follows suit. Direct and inverse variation functions are the two different categories of variation functions.
Given
A researcher is examining the effects of income (X1) and number of friends (X2) on personal happiness (Y) and finds an R2 of 0.45.
Here, the independent variables of income (X₁) and friend count account (X₂) for 45% of the variation in happiness.
Correct interpretation of this result is:
D) Together, income and friend count account for 45% of the variation in happiness.
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9. If point Q is reflected across x = 1, what are the coordinates of its reflection image?
The coordinates of reflection image are (-1, -2).
What is point reflection?
A particular kind of Euclidean space isometry is known as a point reflection in geometry. A thing is said to have point symmetry if it is invariant under a point reflection; if it is invariant under a point reflection through its center, it is said to have central symmetry or to be centrally symmetric.
Given:
point Q is reflected across x = 1.
From graph the point Q is (3, -2).
We have to find the coordinates of its reflection image.
x = 1 is a vertical line passing through all points with an x- coordinate of 1.
(3, - 2) is 2 units to the right of x = 1 ( 3 - 1 ), thus
The reflection is 2 units to the left of x = 1 ( 1 - 2 = - 1 )
Q(3, - 2 ) → Q'(- 1, - 2 )
This is because the x-coordinate goes 2 units left to the line x = 1 and the y-coordinate remains the same.
Hence, the coordinates of reflection image are (-1, -2).
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Expand the polynomial (x + y)7 and write the coefficients of the terms.
Answer:
7x+7y siuuuuuuuuuuuuuuuuu
Write a fraction in simplified form that expresses the ratio of 0.27 to 0.06.
Answer: 9/2
Step-by-step explanation:
To express 0.27 and 0.06 as fractions, we first need to convert them to fractions with denominators that are powers of 10. We can do this by multiplying 0.27 by 100 to get 27/100, and multiplying 0.06 by 100 to get 6/100. The ratio of 0.27 to 0.06 is then equal to the ratio of 27/100 to 6/100, which simplifies to 27/6. To express this ratio in simplest form, we can divide both the numerator and denominator by the greatest common factor of 27 and 6, which is 3. This gives us a simplified fraction of 27/6 = 9/2.
How many liters are in 4 quarts of milk? Round to the nearest tenth if needed. 1 quart = 0.95 liters.
Answer:
3.8
Step-by-step explanation:
4 x 0.95 = 3.8
There are three different sections to sit at a stadium. The number if people who can sit in each section is described below.
~ Red section seats 200 people
~ Blue section seats 20 fewer people than the red section
~ Green section seats 2 times as many people as the blue section
What is the total number of people who can sit in the stadium when it is full?
How did you get your answer?
Answer:
740
Step-by-step explanation:
R = 200
Blue = 200-20 = 180
Green = 2(200-20) = 2( 180) = 360
200 + 180 + 360
740
Answer:
Red section (full)=200 people
Blue section (full)=200-20=180 people
Green section (full)=2×blue section ( full)=2×180=360 people
Stadium (full)=(200+180+360) people=740 people
The equation y−k = a(x−h) ^2 has graph a parabola with vertex (h, k).
Suppose a > 0. A horizontal line 1 unit above the vertex intersects the
graph at two points. Find the distance between these two points.
The distance between these two points is given as follows:
[tex]d = 2\sqrt{1 - a}[/tex]
How to obtain the distance between these two points?The equation of the parabola is given as follows:
y - k = a(x - h)².
Hence:
y = a(x - h)² + k.
The horizontal line one unit above the vertex has the equation given as follows:
y = k + 1.
(as k is the y-coordinate of the vertex).
Then the intersection of this line with the graph is obtained as follows:
k + 1 = a(x - h)² + k.
a(x - h)² = 1
(x - h)² = 1 - a
[tex]x - h = \pm \sqrt{1 - a}[/tex]
[tex]x = \pm \sqrt{1 - a} + h[/tex]
Then the points are given as follows:
[tex]x = -\sqrt{1 - a} + h[/tex][tex]x = \sqrt{1 - a} + h[/tex]The distance between these two points is of:
[tex]d = \sqrt{1 - a} + h - (-\sqrt{1 - a} + h)[/tex]
[tex]d = 2\sqrt{1 - a}[/tex]
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PLEASE HELP!! I will mark Brainliest
The expression to the scenario it's represent is as follows:
The price of a USB memory stick selling at 21% discount off it marked price(m) → 0.21m
The price of Cd that sells for 21% more than the amount (m) needed to manufacture the CD → 1.21m.
The final value of painting after the initial value, m increases by 2 / 5 → 7 / 5 m.
The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy → 3 / 5 m
What is expression?An algebraic expression is made up of variables and constants, along with algebraic operations like subtraction, addition, multiplication and division.
Therefore, let's match the algebraic expression with the scenario.
The price of a USB memory stick selling at 21% discount off it marked price(m).
Hence, the expression is 21% of m = 21 / 100 m = 0.21m
The price of Cd that sells for 21% more than the amount (m) needed to manufacture the CD.
Hence, the expression is 21%m + m = 0.21m + m = 1.21m.
The final value of painting after the initial value, m increases by 2 / 5.
Hence, the expression is 2 / 5 m + m = 7 / 5 m.
The total number of markers Nancy have if she gives away 2 / 5 of her m markers to Amy.
Hence, the expression is m - 2 / 5 m = 3 / 5 m.
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The graph of the linear function passes through points (2, 44) and (5, 80). What is the equation of the function?
Step-by-step explanation:
the slope-intercept form is in general
y = ax + b
a being the slope, b being the y-intercept (the y-value when x = 0).
the slope is the ratio (y coordinate difference / x coordinate difference) when going from one point on the line to another.
we got 2 points identified, so, let's use them.
(2, 44) and (5, 80)
x changes by +3 (from 2 to 5).
y changes by +36 (from 44 to 80).
the slope is +36/+3 = 12.
so, we got "a" for our equation. to get "b" we need to use the coordinates of one of the given points as x and y.
I usually use the one with the smaller numbers.
here : (2, 44).
44 = 12×2 + b = 24 + b
b = 44 - 24 = 20
our equation is
y = 12x + 20
A recipe requires 3 cups of flour to make 15 servings and 7 cups of flour to make 35 servings how many cups of flour are needed to make 20 servings?
Answer:
a = 8
b = 2
c = 48
Step-by-step explanation:
3 cups of flour is needed to make 24 servings.
3:24
Simplify. First, divide 3 from both sides of the ratio.
(3)/3 : (24)/3
1:8
Next, solve for b. You multiply 2 to 8 to get 16. Next, multiply 2 to 1
1 x 2 = b = 2
Finally, multiply 8 to 6 to get c.
8 x 6 = c = 48
~
Write an inequality for the graph
The inequality that represents the line in the figure will be y > - (2/3) x + 3.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
From the figure, the points of the line are (0, 3) and (3, 1). And the region above the line is a consideration. Then the equation of the line is given as,
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
Simplify the equation, then we have
(y - 3) > [(3 - 1) / (0 - 3)](x - 0)
(y - 3) > - (2/3)x
y > - (2/3) x + 3
The disparity that addresses the line in the figure will be y > - (2/3) x + 3.
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NO LINKS!!
The inverse function of the exponential function f(x) = a^x is the (a. transcendental, b. logarithmic, c. rational, d. polynomial, e. algebraic) function with base a.
Answer:
The inverse function of the exponential function f(x) = a^x is the logarithmic function with base a.
The inverse function of a function f is a function that "undoes" the original function, meaning that it reverses the transformation applied by the original function. In the case of the exponential function, the inverse function is the logarithmic function, which "undoes" the transformation applied by the exponential function.
For example, suppose we have the exponential function f(x) = 2^x. The inverse function of this function is the logarithmic function with base 2, which is written as y = log_2 x. If we apply the inverse function to 2^x, we get:
y = log_2 (2^x)
Solving for x gives:
x = 2^y
This means that the inverse function of the exponential function f(x) = a^x is the logarithmic function with base a, which is written as y = log_a x.
The other options (a. transcendental, c. rational, d. polynomial, e. algebraic) are not correct, since they do not describe the inverse function of the exponential function.
Answer:
b. logarithmic
Step-by-step explanation:
Given exponential function:
[tex]f(x)=a^x[/tex]
The inverse of the given function is the logarithmic function with base a.
To find the inverse of a function, replace f(x) with y:
[tex]\implies y=a^x[/tex]
Swap the x and y:
[tex]\implies x=a^y[/tex]
Take logs with base a of both sides of the equation:
[tex]\implies \log_ax=\log_aa^y[/tex]
Apply the log power law: logₐ xⁿ = n logₐ x
[tex]\implies \log_ax=y\log_aa[/tex]
Apply the log law: logₐ a = 1
[tex]\implies \log_ax=y[/tex]
[tex]\implies y=\log_ax[/tex]
Replace y with f⁻¹(x):
[tex]\implies f^{-1}(x)=\log_ax[/tex]
Thus proving that the inverse of the exponential function f(x) = aˣ is the logarithmic function with base a.
Please answer my quistion in math the quistions are in the picture
Step-by-step explanation:
i hope this helps u get an idea how to solve the problems, sorry for the bad handwriting though
Good luck!!
Which expression is equivalent to 3(−4.2y − 13.6)?
1.2y − 13.6
1.2y − 10.6
−12.6y − 13.6
−12.6y − 40.8
Answer:
D) - 12.6y - 40.8-----------------------------------
Given:
Expression 3(−4.2y − 13.6)Distribute and simplify it to get equivalent expression:
3(−4.2y − 13.6) = 3(-4.2y) - 3(13.6) = - 12.6y - 40.8This is matching the last option.
Abby owns a square plot of land. She knows that the area of the piot is between 2200 and 2400 square meters. Which of the following answers is a possible value for the side length of the plot of land? O 50 meters
O 44 meters
O 48 mefers
O 46 meters
The possible value for the side length of the plot of land is 46 meters.
What is area?Area is a measurement of the size of a two-dimensional space or shape. It can be measured in square feet, square meters, and other units of measurement. Area is often used to measure the size of a room, a garden, a piece of land, and many other objects. In mathematics, area is a concept used to calculate the size of a shape or figure. It is calculated by multiplying the length of a shape by its width. Area can also refer to the total amount of space a shape takes up, such as the area of a circle or triangle.
The area of a square is calculated by multiplying the length of one of its sides by itself. Therefore, the side length of Abby's plot of land can be calculated by taking the square root of the area. The square root of 2200 is 46.89, and of 2400 is 48.98. Therefore, the possible side lengths of Abby's plot of land are 46 meters and 48 meters.
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The following graph shows a system of inequalities. Is the point (-4,-4) a solution to the system?
Yes, the point is a solution.
No, the point is not a solution.
Two members of the Math Competition Team solve 13 problems in 1 hour. Assume all team members solve problems at the same rate. How many team members are needed to solve in 1 hour 39 problems
Two members of the maths competition team solve 13 problems in 1 hour.
Person=13
Time=1 hour
Then.
Rate=13/1 (person/time)
With the help of question,
Let us consider,
x team members are needed to solve in 1 hour 39 problems,
2M×1/13=1×xM/39
2M/13=x M/39
2M=x M/13
M=26
26 team members are needed to solve in 1 hour 39 problems,
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A two-part question....
(i). Set up, but do not evaluate, a triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0.
(ii). Set up, but do not evaluate, a triple integral that gives the volumes of the right circular cylinder above with a hemisphere sitting atop the cylinder.
(i) The triple integral that gives the volume of the right circular cylinder enclosed by the surfaces x^2 + y^2 = 4 , z=-10 and z=0 is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10.
This triple integral gives the volume of the right circular cylinder which is enclosed by the given surfaces and extends from z = 0 to z = -10.
(ii) The triple integral that gives the volume of the right circular cylinder with a hemisphere sitting atop the cylinder is:
∫∫∫dV = ∫∫∫dx dy dzwhere the limits of the integration are:
0 ≤ x ≤ 2*sqrt(2), -2*sqrt(2) ≤ y ≤ 2*sqrt(2), 0 ≤ z ≤ -10, and 0 ≤ r ≤ sqrt(x^2 + y^2).
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Evaluate (if possible) the six trigonometric functions of the angle (0).
-5pi/6
Answer:
sin(-5π/6) = -1/2cos(-5π/6) = -√3/2tan(-5π/6) = √3/3csc(-5π/6) = -2sec(-5π/6) = -2√3/3cot(-5π/6) = √3Step-by-step explanation:
You want the 6 trig functions of the angle -5π/6.
QuadrantThe angle is in the 3rd quadrant, so all trig functions are negative except the tangent and cotangent. The reference angle is -5π/6 +π = π/6.
Trig functionsSince you have memorized the values of the trig functions for multiples of π/6, you know ...
sin(-5π/6) = -1/2
cos(-5π/6) = -√3/2
tan(-5π/6) = sin/cos = √3/3
csc(-5π/6) = 1/sin = -2
sec(-5π/6) = 1/cos = -2√3/3
cot(-5π/6) = 1/tan = √3
Answer/Step-by-step explanation:
Use a Unit Circle, you may have access to (hopefully) or have been asked to memorize.
To find -5pi/6 count clockwise the sixths to 5. Or add:
-5pi/6 + 2pi
= -5pi/6 + 12pi/6
= 7pi/6
-5pi/6 is the same as 7pi/6 on the Unit Circle.
Use the coordinates at that spot
(-root3/2 , -1/2)
to find the six trig ratios.
The Unit Circle is a big, giant, Answer Key. It has all the trig answers on it all in one place. It looks like a scary math pizza, but really its all the answers all in one place.
Once you find your angle, the sine is the y-coordinate.
sin theta = -1/2
The cosine is the x-coordinate.
cos theta = -root3/2
Tangent theta is the sine over the cosine, sin/cos,
= y/x
= (-1/2) / (-rt3/2)
Use Keep-Change-Flip to simplify this.
see image.
= root3/3
Sec is cos flipped over. Csc is sin flipped over. Cot is tan flipped over (the math word is reciprocal)
Yes, just flip over sin to get csc:
sintheta = -1/2
csctheta = - 2/1 = -2
Flip over cos to get sec:
costheta = -rt3/2
sectheta = 2/-rt3
Then rationalize, see image.
= -2rt3/3
Flip over tan to get cot.
tantheta = 1/rt3
Use a form that's easy to flip.
cottheta = rt3/1 = rt3
see image.
There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean
B. Because the standard deviation is unaffected by a change in a single data value, it will remain unchanged.
A change in a single data value has no impact on the standard deviation, which measures the spread of a data collection. As a result, even if the single data value changes, the standard deviation won't.
The variability of a data set is measured by the standard deviation. It is calculated by taking the square root of the average of the sum of the squares of the differences between each value in a data set and the mean. When a single value in a data set is changed, the mean of the data set will change, but the standard deviation will not be affected. This is because the standard deviation is not calculated based on individual data points, but on the overall variability of the data set. Therefore, when a single data value is changed, the standard deviation of the data set will remain the same.
Let x be one of the students in the class
Mean = (76.9 + 82)/2 = 79.4
Standard Deviation = sqrt(((76.9 - 79.4)^2 + (82 - 79.4)^2)/2) = 3.2
The complete question is : There are 40 students in a college statistics class. After the first exam, their instructor told them that the class scores were normally distributed with a 10 points mean of 76.9 and a standard deviation of 3.2. However, one of the students pointed out that the instructor recorded 28 for his score when he actually earned 82. The class recalculates the mean and standard deviation The mean is now 78.1. Which of the following is true about the standard deviation? A. The standard deviation will increase because the value of an exam score increased. B. The standard deviation will stay the same because it is not affected by a change in a single data value C. The standard deviation will decrease because the change moved an exam score closer to the mean D. The standard deviation will increase because the change moved an exam score further from the mean
Learn more about standard deviation here
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Question 5 of 20:
Select the best answer for the question.
5. What's the sum of 667 and 23?
OA. 644
OB. 29
OC. 690
D. 15,341
Mark for review Will be highlighted on the review pagel
Answer:
C). 690
Step-by-step explanation:
When you see the word "sum" that means you add the numbers together
667 + 23 = 690
Answer:
OC. 690
Step-by-step explanation:
To find the sum of 667 and 23, you need to add the two numbers together. When you do this, you get 690 as the result. Therefore, the sum of 667 and 23 is 690.
This can be written as an equation: 667 + 23 = 690. The symbol "+" is used to represent the operation of addition, and the equals sign "=" is used to show that the value on the right side of the equation is the result of the operation on the left side.
In general, when you add two or more numbers together, you find their sum by combining their values and counting the total. For example, to find the sum of the numbers 3 and 4, you would add them together to get 7. To find the sum of the numbers 5, 6, and 7, you would add them together to get 18.
I hope this helps to clarify the concept of addition and the meaning of the term "sum." Let me know if you have any further questions.