The factory can make 744 quarts of ice cream per day.
To find out how many quarts of ice cream could be made in 48 hours, we can use the principle of proportionality. Since the factory makes 310 quarts of ice cream in 10 hours, we can set up a proportion:
310 quarts / 10 hours = x quarts / 48 hours
To solve for x, we can cross multiply:
310 quarts * 48 hours = 10 hours * x quarts
x = (310 quarts * 48 hours) / 10 hours = 1480 quarts
So the factory could make 1480 quarts of ice cream in 48 hours.
To find the rate per day, we need to divide the number of quarts made per hour by the number of hours in a day. Since there are 24 hours in a day, we can calculate the rate per day as:
rate per day = (310 quarts / 10 hours) * 24 hours = (31 quarts/hour) * 24 hours = 744 quarts/day
So the factory can make 744 quarts of ice cream per day.
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Find the missing term in the arithmetic sequence −14, _, _, 46
Estimate how many times larger 1.9 • 10^-8 is than 4.2 • 10^-13
Answer:
Step-by-step explanation:
a.[tex]1.9[/tex]·[tex]10^{-8}[/tex]=190000·[tex]10^{-13}[/tex]
b.so 190000÷4.2=4523
c.finally, about 4523 times
What is the difference of the polynomials 5x 3 4x 2 )-( 6x 2 2x 9?
The Solving we get the difference of the given polynomials [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] as [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .
What is a Polynomial ?
The polynomial is defined as the expression that is composed of variables, constants and exponents, which are combined by using mathematical operations such as addition, subtraction, multiplication and division .
Based on number of terms present in polynomial , they can be classified as monomial, binomial, and trinomial .
For Example : [tex]3x^{2} +4x[/tex] .
The polynomial is given as : [tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex] ;
On simplifying the above given polynomial ,
we get ,
= [tex]5x^{3} + 4x^{2} - 6x^{2} + 2x + 9[/tex]
On subtracting the like terms together in above equation ,
we get ;
= [tex]5x^{3} - 2x^{2} + 2x + 9[/tex]
Therefore , the difference of the polynomials is (d) [tex]5x^{3} - 2x^{2} + 2x + 9[/tex] .
The given question is incomplete , the complete question is
What is the difference of the polynomials?
[tex](5x^{3} + 4x^{2} ) - (6x^{2} - 2x - 9)[/tex]
A. –x³ + 6x² + 9
B. –x³ + 2x² – 9
C. 5x³ – 2x² – 2x – 9
D. 5x³ – 2x² + 2x + 9
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Angles A and B are complementary. If sin A = 4x + 10 and cos B = 2x + 16, what is the value of x?
The value of x is 10.66
What is complementary angles?
Complementary angles is when the sum of two angles is equal to 90 degrees. for example, 30 degrees and 60 degrees are complementary angles.
If the sum of two angles is 90 degrees then we say that they are complementary. Thus, the complement of an angle is obtained by subtracting it from 90. for example the complement of 40° is 90° - 40° = 50°
So we have Sin A and Cos B
4x + 10+ 2x + 16= 90
Collect like terms
6x+ 26= 90
6x= 90-26
6x= 64
x= 64/6
x= 10.66
Therefore, the value of x is 10.66
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What is the slope of a logarithmic graph?
The slope of a logarithmic graph depends on the type of logarithm used.
For a logarithmic function in the form y = log(b,x) where b is the base of the logarithm, the slope of the graph is undefined for x=0 and for x<0 because logarithmic functions are not defined in those cases.
For a natural logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.
For a common logarithm, the slope is negative infinity at x=0 and positive for x > 0. As x increases, the slope becomes closer to zero.
It's important to note that logarithmic functions are not linear functions, and therefore they do not have a constant slope, the slope of a logarithmic graph will change throughout the graph.
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Please help ASAP!
Solve the inequities:
k^2-7k+12. 25>0
2. 25y^2-3y+1<0
It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression
Solve the inequities:
k^2-7k+12. 25>0
2. 25y^2-3y+1<0
Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
It is not possible to mix ‘greater than’ and ‘less than’ inequality signs in the same expression
So Whenever you find two conclusions which are false Just check for these two symbols . In Most of the case where two conclusions are false and these two signs are not there respectively than that statement, you can call it as Neither Nor.
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The times taken by 25 people to complete a puzzle are shown. Draw a frequency polygon for data.
To create a frequency polygon calculate the midpoint, locate the midpoints and connect them with lines.
What is a frequency polygon?A frequency polygon is a form of graph that shows how frequently a particular variable—in this case, the amount of time it takes for people to finish a puzzle—occurs.
So, we must determine the midpoint or average of the range for each category.
0 < t < 10 = 5
10 < t < 20 = 15
20 < t < 30 = 25
30 < t < 40 = 35
2. Add a point where the data of the axis Y and X form an intersection.
3. Connect the points.
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What is the sum of all the positive two-digit integers where one of the digits is three times the other
The sum of all the positive two-digit integers where one of the digits is three times the other is 630.
To arrive at this result, the numbers can be broken down into two groups. The first group consists of numbers with 3 as the first digit, and the second group consists of numbers with 3 as the second digit.
For the first group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9. This gives a sum of 3+6+9+12+15+18+21+24+27 = 135.
For the second group, the sum is calculated by multiplying the 3 by all the numbers from 1 to 9 and then reversing the digits. This gives a sum of 30+60+90+12+51+81+21+42+72 = 495.
The total sum of all the positive two-digit integers where one of the digits is three times the other is 135+495 = 630.
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The function f is defined by f(x) = mx + b, where m and b are constants. If f(0) = 18 and f(1) = 20, what is the
value of m?
A mathematical constant is a key number whose value is fixed by an unambiguous definition, often referred to by a symbol.
What are 3 examples of a constant?A few more constant examples are :
The number of days in a week represents a constant.
In the expression 5x + 10, the constant term is 10.In 2a, 2 is a constant.In -7mn, -7 is a constant.In 3x, 3 is constant.A fixed value. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. Example: in "x + 5 = 9", 5 and 9 are constants.There are four major constants that appear within mathematical calculations. These math constants are used in a whole variety of equations and formulae and are repeatedly seen in a variety of areas.The easiest way we can find a constant term in math is to look first for stand-alone numbers, and then for coefficients and variables that can be solved for. A variable cannot be solved for and return only one value if it has an exponent, such as x^2.A function is called no constant if it takes more than one value (if there is more than one element in its range).Substitute:
m*o+b=18
m+b=20
Apply Zero Property of Multiplication:
b=18
m+b=20
Substitute into one of the equations:m+18=20
Rearrange unknown terms to the left side of the equation:m=20-18
Calculate the sum or difference:m=2
The solution of the system is:
b=18
m=2
The answer is b=18 m=2
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At a certain university, the average attendance at basketball games has been 2,925. This year the attendance for the first 15 games has been 2,515 with a standard deviation of 585. The athletic director claims that the attendance is the same as last year. If what are the critical values for this two-tailed t test
The absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.
population mean assumed to be 2925
sample mean = 2515
standard deviation of sample = 585.
sample size = 15
t-score is indicated because the standard deviation is taken from the sample rather than from the population.
t-score = (x - m) / s
x is the raw score
m is the raw mean of the population
s = standard deviation of sample/sqrt (sample size) = 585/sqrt(15) = 151.6217 rounded to 4 decimal places.
degrees of freedom = 15 minus 1 = 14.
t-score = (2515 - 2925)/151.6217 = -2.7123 rounded to 4 decimal places.
you need to know the confidence level.
at a 95% confidence level, the two-tailed critical t-score with 14 degrees of freedom = plus or minus 1.7613 rounded to 4 decimal places.
since the absolute value of the test t-score is less than the absolute value of the critical t-score, there is not enough evidence to say that the population mean has changed.
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Mr. Starnes and his wife have 6 grandchildren: Connor, Declan, Lucas, Piper, Sedona, and Zayne. They have 2 extra tickets to a holiday show, and will randomly select which 2 grandkids get to see the show with them.
a. Give a probability model for this chance process.
b. Find the probability that at least one of the two girls (Piper and Sedona) get to go to the show.
Probability that one of the girls (Piper as well as Sedona) will be able to attend the performance is one in five.
Explain the term Probability?Any probability is a mathematical representation of the likelihood or chance that a specific event will take place. All these proportions ranging from 0 to 1 and percentages varying from 0% through 100% can be used to describe probabilities.For the stated question-
There are 6 grandkids.There are two girls.Out of the six grandchildren, two are to be chosen.
There are 6C2 different ways to choose 2 out of 6 grandchildren.
6C2 = 6! / (6 - 2)!*2!
6C2 = 15
There are 15 different ways to choose two grandchildren out of six.There are 2C1 different ways to choose 1 of the 2 girls.
2C1 = 2
There are two different ways to choose one of the two girls.
Number of methods for choosing both girls = 2C2
Number of methods for choosing both girls equals one.
Probability of choosing 1 of the 2 grandchildren is 1/15.
The likelihood of choosing both girls is 2/15.
Probability that one of the females (Piper and Sedona) will be able to attend the performance is:
= 1/15 + 2/15.
= 3/15.
Thus, Probability that atleast one of girls (Piper as well as Sedona) will be able to attend the performance is one in five.
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Every tread of a staircase is 8 in. deep, and every riser is 6 in. high. How would you find the angle the staircase makes with the floor? Explain.
Answer:
36.9°
Step-by-step explanation:
You want to know the pitch angle of a staircase with a riser height of 6 inches and a tread depth of 8 inches.
TangentThe tangent of an angle is the ratio of the side opposite to the side adjacent:
Tan = Opposite/Adjacent
ApplicationThe tangent of the staircase angle to the floor will be the ratio of the riser height to the tread depth:
tan(α) = (6 in)/(8 in) = 3/4
The angle is found using the inverse tangent function.
α = arctan(3/4) ≈ 36.9°
__
Additional comment
You need to be a little bit careful here. Different authors define "tread depth" differently. For the purpose of this question, it must be defined as the horizontal distance between corresponding points on adjacent treads, as shown in the attached illustration.
Some authors define tread depth as the distance from the nosing to the riser. If that definition is used, the "run" of the step will be the tread depth less the nosing depth. The pitch angle will be the arctangent of the ratio of riser height to "run".
The tread depth of 8 inches is a little too narrow to be in compliance with some building codes. A more usual minimum is about 10 inches with a riser height of 7 1/2 inches.
Answer:
0.75 tangent 0.75
Step-by-step explanation:
Find the x-intercept and y-intercept
from the following linear equation:
X + 4y = -56
x - intercept ()
y - intercept ()
Answer:
x-intercept: (-56, 0)
y-intercept: (0, -14)
Step-by-step explanation:
The x-intercept is the point at which the line crosses the x-axis, so when y=0. To find the x-intercept, substitute y=0 into the given equation:
[tex]\begin{aligned}y=0\implies x+4(0)&=-56\\x+0&=-56\\x&=-56\end{aligned}[/tex]
Therefore, the x-intercept of the given linear equation is:
(-56, 0)The y-intercept is the point at which the line crosses the y-axis, so when x=0. To find the y-intercept, substitute x=0 into the given equation:
[tex]\begin{aligned}x=0\implies 0+4y&=-56\\4y&=-56\\y&=\dfrac{-56}{4}\\y&=-14\end{aligned}[/tex]
Therefore, the y-intercept of the given linear equation is:
(0, -14)Ericka was solving an exponential equation, and upon finishing, she realized her answer was incorrect when she substituted -5 back into her original equation. Identify Ericka’s mistake.
Ericka’s mistake is in ''Step 2.''
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Ericka was solving an exponential equation, and upon finishing, she realized her answer was incorrect when she substituted -5 back into her original equation.
Now,
Since, Ericka was solving an exponential equation.
Clearly, The equation is,
⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴
Step 1;
⇒ 5 ⁹ˣ⁺⁶ = 25³ˣ ⁻ ²⁴
⇒ 5 ⁹ˣ⁺⁶ = 5 ² ⁽³ˣ ⁻ ²⁴⁾
Step 2;
⇒ 9x + 6 = 2 (3x - 24)
So, Ericka’s mistake is in Step 2.
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Jackson picked apples for his family. He picked a total of 6 pounds. He took 2
3
4
pounds to his aunt and 1
7
8
pounds to his mother. How many pounds of apples were left to give to his grandmother? Use the numbers and symbols to write an equation that represents the problem, then solve the equation. Symbols may be used more than once or not at all.
2
3
4
1
7
8
6 y + =
PLEASE HELPPPPPPPP
"17/8" pounds of apples were left to give to his grandmother.
Since we have given that
The quantity of apples he picked is given by 6.1/2⇒13/2 pounds.
The quantity of apples he picked for his aunt is given by 2.3/4⇒11/4 pounds.
The quantity of apples he picked for his mother is given by 1.5/8⇒13/8 pounds.
So, the total quantity left for his grandmother is given by
first we have to add the quality of apples he picked for his aunt and the number of apples he picked for his mother.
After subtracting from what he picked.
⇒13/2-(11/4+13/8)
⇒13/2-(22+13/8)
⇒13/2-(35/8)
⇒52-35/8
⇒17/8
Hence, 17/8 pounds are left for his grandmother.
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how do i do this question
The slope of the line is given by the equation slope m = 3/2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , let the first point be P = P ( 0 , 1 )
Let the second point be Q = Q ( 2 , 4 )
Now , the slope of the line between the two points is
Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 4 - 1 ) / ( 2 - 0 )
On simplifying the equation , we get
Slope m = ( 3 / 2 )
Therefore , the value of m is 3/2
Hence , the slope of the line is 3/2
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At the opening session of the United States Supreme Court, each justice shakes hands with all the others. There are nine justices that sit on the Supreme Court. How many handshakes do they make during the opening session
According to probability, total number of handshakes will be 36.
How many handshakes are possible?Handshakes equal n * (n - 1)/2. This is the case because a handshake between two people is not counted twice and each of the n people can shake hands with n - 1 people (they wouldn't shake their own hand). Any number of people can be calculated using this formula.
The first person will need to shake eight (8) people's hands. Only seven (7) hands will need to be shook by the second person because the first handshake will not be repeated. Due to the same factors as mentioned above, only six (6) people will require a handshake from the third person. This continues until the final person has no one left to shake hands with because everyone has already done so.
The formula to calculate how many handshakes were exchanged is n = 8 + 7 + 6 +... + 1 = 36.
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3x -y=-2y solve for y pls help me
Answer:
-x
Step-by-step explanation:
3x - y = -2y
add y to both sides
3x = -3y
divide both sides by -3
-x = y
How many minutes will a bus take to cover 5 km travelling at 9 km/h?
Answer:
the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.
Step-by-step explanation:
To find out how many minutes it will take for a bus to cover 5km at a speed of 9km/h, we need to use the formula:
time = distance / speed
In this case, the distance is 5 km, and the speed is 9 km/h. To convert the speed to km/min we can divide 9 by 60.
9 km/h = 0.15 km/min (by dividing 9 by 60)
Now we can substitute the distance and speed into the formula:
time = 5 km / 0.15 km/min = 33.33 min
So, the bus will take approximately 33.33 minutes to cover 5km at a speed of 9 km/h.
It's important to note that in this problem km/h is the speed and the distance is given in km, so you need to convert it to km/min in order to find the time. Also the time you get will be in minutes.
Using a number line, find both the intersection and the union of the following
intervals:
(-∞,2) and [0,∞)
The answer choice which represents a number line for the intersection of the given intervals is; (-∞, 2).
The answer choice which represents a number line for the union of the given intervals is; (-∞, ∞).
What is the number line representation of the intersection and union of the given intervals?It follows from the task content that the number line which represents the intersection and union of both intervals given is to be determined.
Since the given intervals are; (-∞, 2) and [0,∞).
It follows that the intersection of both intervals is the interval; (-∞, 2).
Also, the interval which represents the union of both intervals is; (-∞, ∞).
Hence, the image which represents both scenarios is attached.
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In a market survey, 100 traders sell fruits. 40 sell apples, 46 oranges, 50 mangoes, 14 apples and oranges, 15 apples and mangoes and 10 sell all three fruits each of the 100 traders sell at least one of the three fruits. (A) how many traders sell only one fruit. (B) how many traders sell only two fruits.
a) The number of traders who sell only one fruit is given as follows: 88.
b) The number of traders who sell only two fruits is given as follows: 9.
How to obtain the amounts?The amounts are obtained using Venn sets in the context of this problem.
The sets are given as follows:
Set A: sells apples.Set B: sells oranges.Set C: sells mangoes.10 sell all three fruits, hence:
A ∩ B ∩ C = 10.
15 vendors sell apples and mangoes, hence:
(A ∩ C) + (A ∩ B ∩ C) = 15
(A ∩ C) = 5.
14 vendors sell apples and oranges, hence:
(A ∩ B) + (A ∩ B ∩ C) = 14
(A ∩ B) = 4.
Hence the number who sell two of them is of:
(A ∩ B) + (A ∩ C) = 4 + 5 = 9.
50 vendors sell mangoes, hence:
C + (A ∩ C) + (A ∩ B ∩ C) = 50
C = 35.
46 vendors sell oranges, hence:
B + (A ∩ B) + (A ∩ B ∩ C) = 46
B = 32.
40 vendors sell apples, hence:
A + (A ∩ B) + (A ∩ C) + (A ∩ B ∩ C) = 40.
A + 9 + 10 = 40
A = 21.
Hence the number of vendors who sell only one fruit is given as follows:
A + B + C = 21 + 32 + 35 = 88.
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What is the answer to g=6x for x
Answer:
The answer is x=g/6
Step-by-step explanation:
When solving an equation like this, you want to move x over to the left of =, which leaves g, and 6. now always remeber that the next variable, g for instance, will be the one divided by the factor, 6
What is quadrant 3 on a graph?
The lower left-hand corner of the graph is the third quadrant.
It contains the negative values of both x and y.
Quadrant
The axes of a two-dimensional Cartesian system divide the plane into four infinite regions called quadrants, each bounded by two half-axes.
Cartesian system
A Cartesian coordinate system in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in the same unit of length.
coordinates
Coordinates are numbers which determine the position of a point or a shape in a particular space.
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How do you draw a logarithmic graph?
Choose the range of values for the x-axis and the y-axis , Plot the points on the graph, using the logarithmic formula , Connect the points with a smooth curve and Label the axes and add any other details you want to include.
1. Choose the range of values for the x-axis and the y-axis. Select the minimum and maximum values for both the x-axis and the y-axis.
2. Plot the points on the graph, using the logarithmic formula. Use the formula log(x) = y to calculate the points that should be plotted on the graph. For example, if the x-axis range is from 1 to 10, and the y-axis range is from 0 to 10, then the first point would be (1,0).
3. Connect the points with a smooth curve. Once all the points have been plotted, use a ruler or a graphing calculator to connect them with a smooth curve.
4. Label the axes and add any other details you want to include. Use a ruler or a graphing calculator to label the axes and add any other details you want to include, such as a title, a legend, or a grid.
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frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week
A. when will they weigh the same, and how much will they weigh
B. Explain clearly
If frank weighs 160 lbs gains 2 lbs a week, john weighs 208 lbs and loses 3 lbs a week.
a. When they will weigh the same is 9.6 dieting days and the amount is 179.2lbs.
b. Based on the calculation both of them has the same amount of weight.
How to find the amount of weight?a. Weight
Let d represent the number of dieting days for this happen.
Since Frank gains 2 lb a day or a total of 2d lbs and John loses 3 lb a day for a total of 3d lbs
So,
John's weight = Frank's weight
Hence,
208 - 3d = 160 + 2d
Combine like terms
208 - 160 = 2d + 3d
48 = 5d
Divide both side by 5d
d = 48/5
d = 9.6 dieting days
The amount the weigh
Using John equation
Weigh = 208 - 3(9.6)
Weigh = 208 - 28.8
Weigh = 179.2 lbs
b. The amount they both weigh is the same as John weigh 179.2ilb and Frank as weigh the same.
Using Frank's equation
Weigh = 160 + 2(9.6)
Weigh = 160 + 19.2
Weigh = 179.2 lbs
Therefore when they will weigh the same is 9.6 dieting days and the amount is 179.2lbs.
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Translate the triangle.
The enter the new coordinates.
A (-2,4)
C
(-3,2)
B
(1,1)
<-4, -1 >
A'(-6, [?])
B'([ ], [ ])
C'([], [])
Therefore , the solution of the given problem of triangle comes out to be A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).
Explain the triangle.The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.
Here,
The image A'B'C' is formed by our transformation rule, (+3,y-2)
So:
1. Describe the updated coordinates for points A', B', and C'?
In order to locate these new positions, we have:
A' (-23, 2-2) => A'(1, 0) (1, 0)
B' => (-23, 4-2) => B'(1, 2) (1, 2)
C'=> (0+3,0-2) => C'(3,-2) (3,-2)
2. Explain the qualities that would emerge if the respective vertices were linked together by lines.
We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.
The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.
Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.
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Write and solve an equation to find the value of x.
Answer:
x = 60°
Step-by-step explanation:
opposite angle = congruentso
120 = 2x
x = 120 : 2
x = 60
check
120 = 2 x 60
120 = 120
the answer is good-1=1/3v
show work
∨=
⇄
Answer:
v = 1/-3
Step-by-step explanation:
cross multiply
-3v = 1
then:
divide through by the coefficient of v which is -3
-3v/-3 = 1/-3
[tex]-1=\dfrac{1}{3} v[/tex]
Flip:
[tex]\dfrac{1}{3} v=-1[/tex]
Multiply both sides by 3:
[tex]3\times(\dfrac{1}{3} v)=3\times(-1)[/tex]
[tex]\fbox{v = -3}[/tex]
Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is l. Use function notation.
what does P(11) represent in this situation? What is its value?
For a roll of paper with dimensions 3 feet cut to any desire length,
a) The value of perimeter when cut to 2.5 feet is 11 feet.
b) The complete table with filled perimeter column is present above . The function notation for perimeter is , P =2(L+ W)
c) P(11) , represents the length of paper cut to 11 feet in this situation. It's value i.e., P(11) = 28 feet .
Perimeter is defined as the sum of all boundary length of any geometry. We have a roll of paper with dimensions 3 feet ( i.e, width) is cut to any length. From, it we conclude that that paper is like quadrilateral shape but not square.
a) when the paper cut in a length of 2.5 feet , so, length (L) = 2.5 feet
The perimeter of quadilateral ( rectangle in this case ) is 2(L+W) so, perimeter
= 2( 2.5 + 3)
= 11.0 feet
b) Now, we have to complete "perimeter coulmn ," in the table and side lengths are provided.
Width (w) = 3 feet
length (l) = 1 feet
perimeter = 2(4) = 8
similarly, side lengths (ft.) perimeter ( ft.)
2.5 11
1 8
2 10
11 28
L 2( L + W)
The functional notation for perimeter is
P = 2(L+W) .
c) P(11) represents the length of paper in feet when the paper is cut at a length of 11 feet . It's value is 28 feet . So, the value of P(11) is 28 feet.
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Complete question:
A roll of paper that is 3 feet wide can be cut to any length.
a. If we cut a length of 2.5 feet, what is the perimeter of the paper?
b. Complete the table with the perimeter for each given side length. Then, write a rule for a function, P, that gives the perimeter of the paper in feet when the side length in feet is L, use a function notation.
c) what does P(11) represent in this situation? What is its value?
Suppose the average score on a national test is 600,with a standard deviation of 50. If each score is increased by 10, what are the new mean and standard deviation
On solving the provided question we can say that the new Mean = 610 mean .
What is mean?
A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean). is 50.
What is mean?
A dataset's mean is the sum of all values divided by the total number of values, often known as the arithmetic mean (as opposed to the geometric mean).
The mean score is calculated by dividing the total number of tests taken by all of the scores. The mean will therefore rise if you give each test a higher mark. The standard deviation is calculated as the square root of the product of the power of two of all test results, multiplied by the number of tests, and then subtracted from the mean.
Each score you raise by 10 will result in a 10 change in the mean. But as there will be no change in the distance between each score and the mean, the standard deviations will also not change.
Mean = 600
Average deviation is 50.
Scores went up by 10
Mean = 610
Average deviation is 50.
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