For f to be continuous at x=2, b must be equal to 6. That is, when b=6, there is no break in the function at x=2, and the function is continuous.
To determine the value of b for which f is continuous at x=2, we need to first find the limit of f(x) as x approaches 2 from the left and from the right. From the left, the limit is 4b-4. From the right, it is 2b+2. To make the function continuous at x=2, we need to make sure that the left- and right-hand limits are equal. Setting the two limits equal to each other, 4b-4 = 2b+2, and solving for b yields b=6. Therefore, for f to be continuous at x=2, b must be equal to 6.
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Pick three answers for this question
Answer:
HOPE THIS HELPS YOUStep-by-step explanation:
0.25 L = 250 mL
12 000mL = 12 L
5 L 400mL = 5400mL
Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds (Morningstar Funds500, 2008).\begin{matrix} \text{Type of Fund} & \text{Number of Funds} & \text{Total Return (\\\%)}\\ \text{Domestic Equity} & \text{9191} & \text{4.65}\\ \text{International Equity} & \text{2621} & \text{18.15}\\ \text{Specialty Stock} & \text{1419} & \text{11.36}\\ \text{Hybrid} & \text{2900} & \text{6.75}\\ \end{matrix}Type of FundDomestic EquityInternational EquitySpecialty StockHybridNumber of Funds9191262114192900Total Return (%)4.6518.1511.366.75a. Using the number of funds as weights, compute the weighted average total return for the mutual funds covered by Morningstar.b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return for Morningstar in part (a)? Discuss. What else might be used for weights?c. Suppose you had invested $10,000 in mutual funds at the beginning of 2007 and diversified the investment by placing$2000 in Domestic Equity funds, $4000 in International Equity funds,$3000 in Specialty Stock funds, and $1000 in Hybrid funds. What is the expected return on the portfolio?
The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories.
a. The weighted average total return for the mutual funds covered by Morningstar is 9.20%.
This is calculated by taking the sum of the products of the total return and the number of funds for each of the four categories:
(4.65 * 9191) + (18.15 * 2621) + (11.36 * 1419) + (6.75 * 2900) / (9191 + 2621 + 1419 + 2900) = 9.20%
b. Yes, there is a difficulty associated with using the number of funds as the weights in computing the weighted average total return for Morningstar. This is because the number of mutual funds in each category can fluctuate over time, and thus, the weights used to calculate the average total return may not accurately reflect the true performance of the mutual funds.
An alternative to using the number of funds as weights would be to use the dollar amount invested in each type of mutual fund as the weight. This would give a more accurate representation of the performance of the mutual funds.
c. The expected return on the portfolio is 9.63%.
This is calculated by taking the sum of the products of the total return and the amount invested in each of the four categories:
(4.65 * 2000) + (18.15 * 4000) + (11.36 * 3000) + (6.75 * 1000) / (2000 + 4000 + 3000 + 1000) = 9.63%
The weighted average total return for the mutual funds covered by Morningstar is 9.20%, calculated by taking the sum of the products of the total return and the number of funds for each of the four categories. However, using the number of funds as weights may not accurately reflect the true performance of the mutual funds, and an alternative would be to use the dollar amount invested in each type of mutual fund as the weight. The expected return on the portfolio is 9.63%, calculated by taking the sum of the products of the total return and the amount invested in each of the four categories.
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a wooden deck of a house needs paint. the function C(n)=24n+5 represents the cost of painting the deck as a function of the number of cans of paint used.The function n(A)=A/6 represents the number of cans of paint needed as a function of area in square ft of the deck. Write a function for the cost of painting the deck as a function of the area in square ft of the deck.
Answer: C(n)=24n+5 =24
(A)=A/6 =0
Step-by-step explanation:
Harold's computer hard drive has 131.25 GB of free space, which is about 17.5% of the capacity of his hard drive. What is the capacity of the hard drive in GB?
The total capacity of Harold's computer hard drive is 750 GB.
What is the capacity of the hard drive in GB?Total free space on Harold's computer hard drive = 131.25 GB
Percentage of free space on Harold's computer hard drive = 17.5%
Let
Total capacity of the hard drive = x
17.5% of x = 131.25
17.5/100 × x = 131.25
0.175 × x = 131.25
0.175x = 131.25
divide both sides by 0.175
x = 131.25 / 0.175
x = 750 GB
Hence, Harold's computer hard drive has a total capacity of 750 GB
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TRUE/FALSE. like the edges of a filled-in area, the endpoints of a polygon do not need to conform to snap points.
False is the statement, "Polygon endpoints need not conform to snap points, like the boundaries of a filled-in region."
The surface's perimeter is defined by the edge of a filled-in area. An area is a two-dimensional space that any surface can cover. Typically, the edges of the space serve as the surface's boundary. To create a closed area or surface, the edges or the boundary must link.
Similar to end points, snap points are the ends of a polygon's sides. A closed figure can only be formed when these endpoints are connected. A closed polygon is one that has n sides.
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what is the length q and r
The correct order of bond lengths P, Q, and R in the above diagram is P > Q > R. The correct option is A.
What is the bond length?The bond length is the distance between the centers of two bound atoms. Consider the fact that a homonuclear diatomic molecule's bonded atoms are separated by half their element's atomic radius (sometimes referred to as the covalent or bonding atomic radius).
Less percentage of s character in a bond means the length of orbitals of the molecule is more, and also the bond length is more.
Therefore, the correct option is A. P > Q > R.
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The question is incomplete. Your most probably complete question is given below:
Which is the correct order of bond lengths P, Q, and R in the above diagram?
P > Q > R
R > Q > P
Q > P > R
Q > R > P
A scale on a hiking map shows that
3
33 inches represents
1.25
1.251, point, 25 miles.
What number of inches on the map represent
10
1010 actual miles?
If 3 inches on the map represents 1.25 miles, we can use that proportion to find how many inches represents 10 miles.
3 inches / 1.25 miles = x inches / 10 miles
We can cross multiply and divide to find x:
x = (3 inches * 10 miles) / 1.25 miles
x = 24 inches
So on the map, 24 inches represent 10 actual miles.
Select the correct population parameter, null hypothesis, and alternative hypothesis., A nationwide poll revealed that 28% of teens said they seldom or never argue with their parents. Ralph wonders if this result would be different at his large high school, so he surveys a random sample of 175 students at his school.
The results from Ralph's survey are not statistically different from the national results.
Population Parameter: The percentage of teens who seldom or never argue with their parents in Ralph's large high school.
Null Hypothesis (H0): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is equal to the nationwide percentage of 28%.
Alternative Hypothesis (H1): The percentage of teens who seldom or never argue with their parents in Ralph's large high school is not equal to the nationwide percentage of 28%.
H0: p = 0.28
H1: p ≠ 0.28
To calculate whether or not the results from Ralph's survey are significantly different from the national result, a one-sample z-test can be used. The z-score is calculated using the following formula: z = (x-µ)/(σ/√n). In this example, x is the sample proportion of teens who seldom or never argue with their parents (Ralph's survey), µ is the population proportion (the nationwide poll results of 28%), σ is the population standard deviation, and n is the sample size (175).
If the z-score is outside of the critical region, then it can be said that the results from Ralph's survey are statistically different from the national results. If the z-score is within the critical region, then it can be said that the results from Ralph's survey are not statistically different from the national results.
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find the exact value of each of the remaining trigonometric functions of . rationalize denominators when applicable. cot
A function of an angle is a trigonometric function. They are utilized to connect the triangle's angles and sides' lengths.
What is meant by trigonometric functions?A right-angled triangle's angle can be related to side length ratios using trigonometric functions, which are real functions in mathematics. They are extensively employed in all geosciences, including navigation, solid mechanics, celestial mechanics, geodesy, and many more.
A common angle in trigonometry has six different functions. Sine, cosine, tangent, cotangent, secant, and cosecant are their names, respectively, as well as their acronyms.
Given that sin theta = √3/√7
Opposite = √3
Hypotenuse = √7
Get the adjacent
Adj² = (√7)²-(√3)²
simplifying the above equation, we get
Adj² = 7-3
Adj² = 4
Adj = √4
Adj = 2
Cos theta = adj/hyp = 2/√7
csc theta = 1/sin theta = 1/(√3/√7) = √7/√3
sec theta = 1/cos theta = 1/(2/√7) = √7/2
tan theta = opp./adj = √3/2
cot theta = 1/tan theta = 1/(√3/2) = 2/√3
= 2√3/3
The complete question is:
Find the exact value of each of the remaining trigonometric functions of theta. Rationalize denominators when applicable.
sin theta [tex]$=\sqrt{\frac{3}{7}}$[/tex] given that theta is in quadrant I.
cos theta=
csc theta =
sec theta =
tan theta =
cot theta =
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Without changing the order of the numbers, write an expression that is equivalent to -3 - 6?
Answer:
-2
Step-by-step explanation:
y-4+3(x-3)=0
How do I find y=mx+b
Answer:
Step-by-step explanation:
The slope-intercept form is y=mx+b, where m is the slope and b is the y intercept. y=mx+b
y=4x3−3
Reorder terms.
y=4 3x−3
Find the values of m and b using the form y= mx+b. 4 3b=−3
The slope of the line is the value of
m
, and the y-intercept is the value of
b
.
Slope:
4
3
y-intercept:
(0,−3)
The slope of the line is -3.
Given equation,
⇒ y - 4 + 3(x-3) = 0
⇒ y = 4 - 3(x-3)
⇒ y = 4 - 3x + 3
⇒ y = -3x + 7
Equation of slope-intercept form: y = mx + b
We know the slope is the value multiplied by x,
so the slope of the line is -3.
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Write this ratio as a fraction in simplest form without any units. 5 weeks to 21 days
Answer:
5/3
Step-by-step explanation:
1 week = 7 days
5 weeks = 5 × 7 days = 35 days
5 weeks to 21 days =
= 35 days to 21 days
= 35/21
= 5/3
Complete the missing values in the solution to the equation.
[tex] \tt \: 4x + y = 10 ---- eqⁿ[/tex]
[tex] \: [/tex]
-6 is already given ,
[tex] \: [/tex]
so , put the value of y = -6 in the given eqⁿ ~
[tex] \: [/tex]
[tex] \tt \: 4x + y = 10[/tex]
[tex] \: [/tex]
[tex] \tt \: 4x + (-6) = 10[/tex]
[tex] \: [/tex]
[tex] \tt \: 4x = 10 + 6[/tex]
[tex] \: [/tex]
[tex] \tt \: 4x = 16[/tex]
[tex] \: [/tex]
[tex] \tt \:x = \cancel \frac{16}{4} [/tex]
[tex] \: [/tex]
[tex] \underline{\boxed { \red{\tt \large \: x = 4}} { \green✓}}[/tex]
[tex] \: [/tex]
missing value is 4!
hope it helps! :)
Harry is a computer programmer and he earns £14 per hour Monday to Friday. If he works on a Sunday, he earns 1.75 times the hourly rate.What is his hourly rate on a Sunday
Answer:
$24.50
Step-by-step explanation:
hourly rate on Sunday is 1.75 times his normal hourly rate, that is
1.75 × $14 = $24.50
hourly rate on a Sunday is $24.50
A company orders boxed lunches from a deli. Assume each boxed lunch is the same price. The proportional relationship between the number of boxed lunches ordered, b, and the total cost in dollars and cents, c, can be represented by the equation c=9.4bc=9.4b. What is the cost in dollars and cents per boxed lunch?
The cost in dollars and cents per boxed lunch will be $9.40.
How to illustrate the equation?It should be noted that an equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
Since the proportional relationship between the number of boxed lunches ordered, b, and the total cost in dollars and cents, c, can be represented by the equation c=9.4b
The cost will be:
= 9.4 × 1
= 9.40
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Find the point (x, y) on the unit circle that corresponds to the real number t. t = 7/4
The point on the unit circle that corresponds to the real number t = 7/4 is given as follows:
(-0.1782, 0.9840).
What is the unit circle?For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].
With parameter t, the coordinates of the point are given as follows:
(cos(t), sin(t)).
Hence the x-coordinate when t = 7/4 is given as follows:
cos(7/4) = -0.1782.
The y-coordinate when t = 7/4 is given as follows:
sin(7/4) = 0.9840.
Meaning that the coordinates are:
(-0.1782, 0.9840).
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Factorise all of the questions.
Please answer a b c and d and please give an explanation on how to work each question out! It would really help ! It’s very urgent ty
Answer:
a.x (x + 1)
b. 3x (1 - 3x)
c. 7x (x² - 5)
d. 4x² (x + 6).
The following frequency data shows the number of states, including the District of Columbia, that
favored each party in the presidential popular vote in 1976 and in 2012.
What percent voted Republican in 1976? What type of frequency is this?
In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.
1976: Republican: 43 states, District of Columbia; Democrat: 6 states
2012: Republican: 24 states, District of Columbia; Democrat: 26 states
In 1976, 43/49 (including the District of Columbia) states voted Republican, which is 87.76%. This is a relative frequency.
1. Calculating the total number of states and District of Columbia in 1976: 43 + 6 + 1 = 50.
2. Calculating the percentage of states voting Republican in 1976: 43/50 (including the District of Columbia) = 0.87 or 87.76%.
3. This is a relative frequency because it is expressed as a ratio or proportion of the total number of states.
In 1976, 87.76% of the states, including the District of Columbia, voted Republican, which is a relative frequency.
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An equilateral triangle has sides of length (3x+7). Find the perimeter of triangle.
The perimeter of the equilateral triangle which has sides of length (3x+7) is 9x+21.
What is equilateral triangle?A triangle's three sides and angles must be equal for it to be considered an equilateral triangle.
An equilateral triangle is also referred to as an equiangular triangle because it has angles that are each 60 degrees in length. Because its sides and angles are equal, the equilateral triangle is regarded as a regular polygon or triangle.
Depending on how many sides a triangle has, there are three different types. These triangles are equilateral, isosceles, and scalene.
In an equilateral triangles all sides are equal
so,
perimeter = 3x+7 + 3x+7 + 3x+7
perimeter = 9x+21
Thus, perimeter of the equilateral trinagle which has sides of lenght (3x+7) is 9x+21.
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Factor
Will mark the brainliest! thanks
By distributive property, the polynomial (3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v² is equivalent to polynomial (1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²).
How to use distributive property to factor a polynomial
In this problem we find a polynomial that must be simplified by means of algebra properties, especially by distributive property. First, write the entire polynomial:
(3 / 2) · u² · v⁴ - 2 · (1 / 2) · u³ · v⁵ + (1 / 2) · u⁴ · v²
Second, use distributive property to simplify the polynomial thrice:
(1 / 2) · (3 · u² · v⁴ - 2 · u³ · v⁵ + u⁴ · v²)
(1 / 2) · u² · (3 · v⁴ - 2 · u · v³ + u² · v²)
(1 / 2) · u² · v² · (3 · v² - 2 · u · v³ + u²)
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HELP PLEASE FAST!!!!!!!!
The value of x = 19 and the value of z = 70° in the figure given above.
How do you find the value of x and z?In algebra, the letter "x" is frequently used to denote an unknown value. It is referred to as a "variable" or occasionally a "unknown.
" x is a variable in x + 2 = 7, but we can figure out its value if we try! A variable can be any letter, name, or symbol; it doesn't have to be "x"; examples include "y" and "w." Z-scores are calculated using the formula z = (x-)/, where x represents the raw score, the population mean, and the population standard deviation.
The z-score is simply the raw score less the population mean, divided by the population standard deviation, as the calculation demonstrates. A raw score's position relative to its distance from the mean is described by the z-score.
Using The property Vertically opposite angles are equal
110° = 9x - 61
⇒ 9x = 110 +61
⇒ 9x = 171
⇒ x = 171/9
⇒ x = 19
As all angles equal 360°
110° + 110° + 2z = 360°
⇒ 2z = 360° - (110° + 110°)
⇒ 2z = 140
⇒ z = 140/2
⇒ z = 140/2
⇒ z = 70°
Thus, The value of x = 19 and the value of z = 70° in the figure given above.
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What is the value of X if the equation is -3(x-9)=x-5
Therefore , the solution of the given problem of equation comes out to be x value is 8.
Define equation.The equal letter (=) is used to signify equivalence between the statements in a mathematical formula. Using mathematical equation, which are declarations of reality, it is shown that many mathematical variables are equivalent. For instance, the equal sign in the equation y + 6 = 12 divides the values 12 or b + 6 into two halves. The number of words that each side of a symbol corresponds to can be measured. Typically, a symbol's meaning is at odds with itself.
Here,
Given:
equation : -3(x-9) = x-5
To find the value of x ,
=> -3(x-9) = x-5
=> -3x +27 = x -5
=> 4x = 27 +5
=> 4x = 32
=> x =32/4
=> x= 8
Therefore , the solution of the given problem of equation comes out to be x value is 8.
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let s represent the number of randomly selected adults in a community surveyed to find someone with a certain genetic trait. the random variable s follows a geometric distribution with mean 4.66. which of the following is a correct interpretation of the mean?
In repeated sampling from the S distribution, the mean of the values will be close to 4.66, which is the appropriate interpretation of the mean.
What is mean?The arithmetic mean, also known as the arithmetic average or simply the mean or average, is the sum of a set of numbers divided by the total number of numbers in the set. The collection frequently consists of a set of findings from a survey, experiment, or observational study. The average of a group of values is referred to as the mean in mathematics and statistics. There are several methods for calculating the mean, including simple arithmetic means (adding the numbers together and dividing the result by the number of observations), geometric means, and harmonic means.
Here,
The average of the values will be close to 4.66 in repeated sampling from the S distribution, which is the correct interpretation of the mean.
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b. Use the side lengths, 6 m x 9 m, to find different side lengths for a rectangle that has the
same area. Show your equations using parentheses. Then estimate to draw the rectangle
and label the side lengths.
The area of a rectangle is found by multiplying the length by the width. So the area of the original rectangle is (6 m) x (9 m) = 54 m^2.
What is the sides of rectangle?If we want to find different side lengths that have the same area, we can keep the area constant and manipulate the length and width.
One way to do this is to multiply the original length by a certain factor and multiply the original width by the reciprocal of that factor.
For example, if we multiply the length by 2 and the width by 1/2, the area will remain the same: (6 m) x 2 = 12 m and (9 m) x (1/2) = 4.5 m. The new rectangle's dimensions would be 12 m x 4.5 m.
Another way to find different side lengths that have the same area is to multiply the original length and width by the same factor.
For example, if we multiply both the length and width by 2, the area will remain the same: (6 m) x 2 = 12 m and (9 m) x 2 = 18 m. The new rectangle's dimensions would be 12 m x 18 m.
So, to draw the rectangle with different side lengths that have the same area, you can use any of the above method, and label the side lengths accordingly.
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Find the smallest integer n such that $$(x^2 + y^2 + z^2)^2 \leq n(x^4 + y^4 + z^4)$$ for all real numbers x, y, and z.
Using the expansion of inequality, The smallest integer , n is 3 .
What in math is an integer?
A full number (not a fraction) that can be positive, negative, or zero is called an integer (pronounced IN-tuh-jer).
Integers include things like -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers are examples of non-integer numbers.
we have given in question that , n is an integer such that ,
(x²+y²+z²)²≤n(x⁴+y4⁴+z⁴)
Let us consider, a=x², b=y², and c=z² which are all nonnegative i.e a,b,c >0 , n>3 but we find least value of n
So, the above inequality become,
(a+b+c)² ≤ n (a²+b²+c²) ----(*)
by expanding both side of above equation we get, a² + b²+ c² + 2(ab + bc + ac) ≤n( a²+b²+c²)
2(ab + bc + ac) ≤ (n- 1) (a²+b²+c²)
=> (ab+bc+ac) ≤ (n- 1)/2 (a²+ b²+c²)
=> (xy)²+ (yz)²+(xz)²≤ (n-1)/2(x⁴+y⁴+z⁴)
If we put n=3− ∈ where ∈ >0 and x=y=z then
3 ≤ 2 or 1/2 which is wrong . Hence, the smallest value of n is 3.
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The complete question is -
Find the smallest integer n such that (x2+y2+z2)2≤n(x4+y4+z4)
for all real numbers x,y, and z.
Solve for x round to the nearest tenth
The solved for x round to the nearest tenth is x≈ 14.
What is meant by round ?
A spherical item. a circuitous or repetitive course; rounds in the hospital.A large-scale outburst at a gathering from a crowd of people.A song that is sung by multiple groups, each of which begins singing at a separate moment.Making a number simpler while maintaining a value that is close to what it was is known as rounding. Although less accurate, the outcome is simpler to utilize.For instance, 73 equals 70 when rounded to the closest 10, since 70 is closer to 73 than 80 is.Rounding numbers maintains the value of the original number while also making them "easier" to use or comprehend.Remember Sine of an angle is = opposite side /hypotenuse
So let the hypotenuse be x :
sin(54°) = opposite side / x
sin(54°) = 12 / x
To solve for x, divide sin(54°) by 12:
x = 12 / sin(54°)
x≈14
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according to a recent study, 27% of american college students graduate with no student loan debt. suppose we obtain a random sample of 127 american college students and record whether or not they have student loan debt. Suppose we obtain a random sample of 121 American college students and record whether or not they have student loan debt. 1) What is the mean of the distribution of ? .25 2) What is the standard deviation of the distribution of p ? .0394 3) What is the probability that more than 26 of the students in the sample will have graduated with no student loan debt?
Answer: .9072 is the awnswer
You have 15,000 to deposit in an account. You want it to be worth 20,000 in 5 years. What's the lowest interest rate? Round to the nearest 0.5%
Answer:
The lowest interest rate you would need to earn in order to have 15,000 become 20,000 in 5 years is 6.5%. This is based on the compound interest formula, where you would need to multiply the original amount by the interest rate (15,000 x 0.065 = 975) and add that amount to the original amount to equal your desired total (15,000 + 975 = 20,000).
The distribution of the amount of money spent by students on textbooks in a semester is
approximately normal in shape with a mean of 399 and a standard deviation of 34.
According to the standard deviation rule, approximately 99.7% of the students spent between $ ___ and $ ___ on textbooks in a semester.
Approximately 99.7 % of the students spent between $ 271 and $ 407 on textbooks in a semester.
When data is normally distributedThen , according to the Empirical rule , approximately 99.7% of the data lies with in the 2 standard deviations from mean.
Given : The distribution of the amount of money spent by students on textbooks in a semester is approximately normal in shape with
Mean = 339 standard deviation = 34.
Then , by
Empirical rule , approximately 99.7 % of the students spent between Mean ± 2 (Standard deviation) on textbooks in a semester.
where , Mean ± 2 (Standard deviation) = 339 ± 2(34)
=(339-2(34) , 339+2(31))
=(271 , 407)
Hence , Approximately 99.7% of the students spent between $ 271 and $ 407 on textbooks in a semester.
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Isabella is an artist who normally purchases her spray fixative in 6 2/3 ounce cans. If the economy size contains 1 2/5 as much spray, how many ounces will it contain?
Using multiplication operation, the number of ounces of Isabella's spray fixative contained in the economy size is 9¹/₃ ounces.
What is multiplication operation?Multiplication operation is one of the four basic mathematical operations, including addition, division, and subtraction.
The multiplication operation involves the multiplicand multiplied by the multiplier, resulting in a product.
The multiplication operand is depicted using (x), (*), or (of).
The normal spray fixative purchased by Isabella = 6²/₃ = 6.667 ounces
The relative size of the economy can = 1²/₅ of 6²/₃ ounces
The number of ounces in the economy can = 9¹/₃ ounces (1²/₅ x 6²/₃)
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