Total degree of freedom should be known to determine the critical values for an independent sample t test.
The largest number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the number of items in the data sample.
An independent t-test must be performed, and the following is required: a single categorical variable with two levels and groups that is independent. a single ongoing dependent variable.
For instance, the number of degrees of freedom to be employed in computations would be n - 1 if the sample size on a chi-square test was 'n'. to figure out the degrees of freedom for an N=9 sample size. 9 less 1 equals 8 (df=9-1=8).
Hence we get the required answer.
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Systems of Equation Task
Answer:
Priya: S=20w+50
Vanessa: S=25w+20
6 weeks
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Part aDefine the variables:
Let w be the number of weeks.Let S be the total savings (in dollars).Given that Priya starts with $50 in her bank account, the y-intercept of the linear equation modelling her savings will be 50.
If she then deposits $20 each week for 12 weeks, the slope will be 20.
Therefore, the linear equation that models Priya's savings is:
[tex]S=20w+50[/tex]Given that Vanessa starts with $20 in her bank account, the y-intercept of the linear equation modelling her savings will be 20.
If she then deposits $25 each week for 12 weeks, the slope will be 25.
Therefore, the linear equation that models Vanessa's savings is:
[tex]S=25w+20[/tex]Part bCreate a table for each linear equation from part a.
Priya Vanessa
[tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&70 \\\cline{1-2} 2& 90\\\cline{1-2} 3&110 \\\cline{1-2} 4&130 \\\cline{1-2} 5& 150\\\cline{1-2} 6&170 \\\cline{1-2} 7&190 \\\cline{1-2} 8&210 \\\cline{1-2} 9&230 \\\cline{1-2} 10&250 \\\cline{1-2} 11& 270\\\cline{1-2} 12& 290\\\cline{1-2} \end{aligned}[/tex] [tex]\begin{array}{|c|c|}\cline{1-2} w & S \\\cline{1-2} 1&45 \\\cline{1-2} 2& 70\\\cline{1-2} 3& 95\\\cline{1-2} 4& 120\\\cline{1-2} 5& 145\\\cline{1-2} 6& 170\\\cline{1-2} 7& 195\\\cline{1-2} 8& 220\\\cline{1-2} 9& 245\\\cline{1-2} 10& 270\\\cline{1-2} 11& 295\\\cline{1-2} 12&320 \\\cline{1-2} \end{aligned}[/tex]
Create a graph for each linear equation (see attachment).
Part cThe week in which Priya and Vanessa will have the same amount of savings is the week where the S-values in the tables are the same, and the point of intersection of the graphed lines.
Therefore, from inspection of the tables and graphs from part b, Priya and Vanessa will have the same amount of savings in week 6.
find a scalar equation of the plane that contains the point (1,2,3) and contains the line represented by the vector equation r(t)
The scalar equation of the plane that contains given points and lines can be written as: (-4)(x-1) + 4(y-2) + (-10)(z-3) = 0.
What is equation of plane?
A given point p(x, y, z) that is located on the plane and a normal vector n define the equation of a plane. A plane's vector and scalar components can be used to formulate the equation for the plane.
The parametric form of line equation,
[tex]p = p_0 + t. \vec v[/tex]
On comparing with the given equation in question, we can say that,
p = {x, y, z}, p₀ = {0, 6, 1,}, vec(v) = {3, -2, -2}
The scalar equation can be given by,
[tex][ \vec \omega, p - p_1] = 0[/tex]
Here, p₁ = {1, 2, 3} and ω is perpendicular to v and to the segment p₁ - p₀ So,
[tex]\vec \omega = \vec v \times (p_1 - p_0) = ( 3, -2, -2 ) \times (1, -4, -2)[/tex]
then,
[tex]\vec \omega = (-4, 4, -10)[/tex]
Therefore, the scalar equation can be written as:
(-4)(x-1) + 4(y-2) + (-10)(z-3) = 0
It can also be written as:
26 - 4x + 4y - 10z = 0
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Complete Question
Find a scalar equation of the plane that contains the point (1,2,3) and contains the line represented by the vector equation r(t) = [3t, 6 - 2t, 1 -2t] ?
Which is the graph of y = [x] -2?
nora invests $800 that pays simple interest at a rate of 6% per annum. what is her total annual interest on this investment?
Please solve with steps
Answer:
To calculate Nora's total annual interest on her $800 investment, we can use the following formula:
Interest = Principal x Rate x Time
In this case, the principal is $800, the rate is 6% per annum, and the time is 1 year. Plugging these values into the formula, we get:
Interest = $800 x 0.06 x 1
To convert the 6% rate to a decimal, we divide 6 by 100. This gives us 0.06. We then multiply the principal by the rate and the time to get the total annual interest. So the total annual interest on Nora's $800 investment is:
Interest = $800 x 0.06 x 1 = $48
Therefore, Nora will earn a total of $48 in interest on her $800 investment over the course of one year at a rate of 6% per annum.
Step-by-step explanation:
2(6-x)=3 help help help help
Answer:
x = 4.5
Step-by-step explanation:
2(6 - x) = 3 12 - 2x = 3 -2x = -9x = 4.5conduct the appropriate hypothesis test and compute the p-value. sunshine air has determined that their no-show rate for passengers booked on a flight is 6%. the airline has recently increased the cost of its travel insurance and and suspects the no-show rate for passengers will decrease. a random sample of 380 reservations resulted in 18 no-shows. at the 0.10 significance level, is there strong enough sample evidence to suggest that the no-show rate in less than 6%?
The p-value is 0.15 which is greater than the significance value 0.10 so null hypothesis cannot be rejected at 10% significance level , we do not have enough evidences to state that no- show rate is less than 6%.
As given in the question,
Null hypothesis : No show rate for passengers booked on given flight is 6%
Alternative hypothesis: No show rate for passengers booked on given flight is less than the 6%
P = 6%
= 0.06
1 - P = 1 - 0.06
= 0.94
random sample size 'n' = 380
no shows = 18
Sample proportion 'p' = 18/ 380
= 0.047
Now , z test statistic value :
z = (p - P)/ √P (1- P)/n
= (0.047 - 0.06)/√0.06( 0.94)/380
= -0.013 /0.012
= -1.083
p-value = 0.2788 ( using table)
0.2788 > 0.10
p-value is greater than significance value 0.10
Do not reject null hypothesis at 10% level of significance.
Therefore, as p-value is greater than significance value do not have enough evidences to state that no- show rate is less than 6%.
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4.) a radio station tower was built in two sections. from a point 87 feet from the base of the tower, the angle of elevation of the top of the first section is 25°, and the angle of elevation of the top of the second section is 400. to the nearest foot, what is the height of the top section of the tower? (lt. 3.7
The height of the top section of the tower is 32 feet.
The radio station tower is built in two sections. The tower is 87 feet from the viewing point. The angle of elevation of the bottom section is 25 degrees. The angle of elevation from the top of tower (both sections) is 40 degrees. Let the height of the bottom section be y and height of the bottom and top section be z.
Considering a right-angled triangle, tangent formula states that:
Tan ɵ = opposite side/ adjacent side where ɵ is the angle of elevation.
Hence, when ɵ = 25, opposite side = y, and adjacent side = 87
Tan 25 = y/ 87
y = 40.57 feet
Hence, when ɵ = 40, opposite side = z, and adjacent side = 87
Tan 40 = z/87
y = 73 feet
Let the height of the top section of the tower be x.
Hence, x = 73 - 40.57 = 32.4 ≈ 32 feet
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(6+3) to the power of 2 + (10-15 divide by 3 )
The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.
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.
The expression is given below.
⇒ (6 + 3)² + [10 - (15/3)]
Simplify the expression, then we have
⇒ (6 + 3)² + [10 - (15/3)]
⇒ (9)² + [10 - 5]
⇒ 81 + 5
⇒ 86
The value of the numerical expression (6 + 3)² + [10 - (15/3)] will be 86.
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how many eight digit numbers contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes? leading 0s are allowed.
0.0405 is the number that contain the digit 2 once, the digit 3 twice, the digit 4 thrice, and more 5s than threes, leading 0s are allowed.
According to collect from the data
Let us assume that the data as followed by
How many eight digit numbers contain the digit 2 exactly once, the digit 3 exactly twice, the digit 4 exactly thrice and more 5s than threes.
Let many eight digit numbers contain the digit 2 once, the digit 3 twice the digit 4 thrice and more 5s than threes.
2,3,3,4,4,4
now then:
= 8!/2!3!3!4!4!4!
= 8.7.6.5.4!/2×6×6×24×24×4!
= 35/864
Now 0.405 then the eight digit number contains the digit 2 once the digit 3 .
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Which action by x develops the theme of the struggle between self-identity and perception by others?.
The action by X that develops the theme of the struggle between self-identity and perception by others is: He wears special clothing to show people that he has superpowers.
Self-identity: It defines the combining of the various roles individuals fulfill throughout their lives. It also tells about awareness and beliefs about the self as an object or being.
The second is people are viewed that the individual as internalized roles, also called role identity.
Today, our identities encompass memories, experiences, relationships, and values, these components, help to create our identities and the sense of ourselves.
There are some aspects that will contribute to the development of different types of identities. They are race/ethnicity, gender, age, and class.
Social identity can be represented in terms of three factors:
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Is 250% of 44 less than 100, greater than 100 but less than 150, or greater than 150? Explain your reasonine.
The required value is evaluated as 110. The correct option is (B).
How to find percent value of a number?The percent value can be found by multiplying the given number with the percent divide by 100.
For example, 10% of 20 is 20 × 10/100 = 2.
The given expression for percentage is found as follows,
250% of 44
= 250/100 × 44
= 2.5 × 44
= 110
It can be written as 100 < 110 < 150.
Hence, the value of the given expression is 110 which is greater than 100 but less than 150 as 110 lies between the two numbers.
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horace horsecollar is interested in the opinion of vacationers at disney world. he creates a short survey and administers it to every 1000th person to enter the park, starting with the 364th person. what method did horace use to select his sample?
The method used by Horace to select his sample is Systematic Sampling.
A form of probability sampling technique called systematic sampling selects sample members from a broader population using a predetermined, periodic interval in addition to a random beginning point. The population size is divided by the intended sample size to arrive at this range, which is known as the sampling interval.
Horace desires to select every 1000th person to enter the park, starting with the 364th person. So he selects the 364th person, 1364th person, 2364th person, and so on. This is a perfect situation for Systematic Sampling.
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A rectangular sheet of material has a width that is 6 cm less than its length. The area of the sheet of material is 72 cm². What must be the width of the rectangular sheet?
O 6 cm
O 8 cm
O 12 cm
O 16 cm
Answer:
width = 6 cm
Step-by-step explanation:
Area = width x length
let x = length
width = x - 6
A = 72 cm² = x(x-6) = x² - 2x
rewrite the equation:
x² - 2x - 72 = 0
solve for x by factoring or the quadratic equation:
(x-12)(x+6) = 0
x = 12, -6
therefore x = length = 12
Width = 12 - 6 = 6
abc has vertices A (0,0) B (3,3) C (-3,3) classify the triangle by its sides
The triangle is isosceles as the two side AB = AC are equal in a triangle ABC has vertices A (0,0), B (3,3), and C (-3,3).
What is the triangle?One of the fundamental shapes in geometry is represented by the symbol Δ and consists of three connected vertices.
Given:
ABC has vertices A (0,0), B (3,3), and C (-3,3),
Calculate the distance of the side as shown below,
[tex]AB = \sqrt{(3-0)^2 + (3 - 0)^2}[/tex]
AB = [tex]\sqrt{9 + 9}[/tex]
AB = √18
AB = 3√2
Similarly, calculate BC and AC,
[tex]AC = \sqrt{(-3-0)^2 + (3 - 0)^2}[/tex]AC = [tex]\sqrt{9 + 9}[/tex]
AC = √18
AC = 3√2
[tex]BC = \sqrt{(-3-3)^2 + (3 - 3)^2}[/tex]
[tex]BC = \sqrt{36 +0}[/tex]
BC = 6
Here, two sides AB = AC of a triangle are equal, so it is an isosceles triangle.
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a rectangle is bounded by the -axis and the semicircle (see figure). what length and width should the rectangle have so that its area is a maximum?
Length and width should the rectangle have so that its area is a maximum are 4.242 and 2.121 respectively.
From the question, we have
Area = A = xy
A = xsqr(9-x^2)
Taking the derivative and set = 0
A' = (x/sqr(9-x^2)(-2x) + sqr(9-x^2) = 0
A' = -x^2 + 9 -x^2 = 0
-2x^2 =-9
x^2 = 9/2
x = 3/sqr2 = (3/2)sqr2 = 4.242
y = sqr(9-x^2) = sqr(9-9/2) = 3sqr2/2 = 2.121
Dimensions of the rectangle are 4.242 and 2.121 respectively
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
Complete question:
A rectangle is bounded by the x-axis and the semicircle y = radical 9 − x^2 (see figure). What length and width should the rectangle have so that its area is a maximum?
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The table below shows the number of students gaining certificates for outstanding achievements:
What is the modal number of certificates?
6
4
2
5
3
Examining the table showing number of students gaining certificates for outstanding achievements the modal number is 4
What is modal number in math?The most frequent number, or the one that appears the most frequently.
In a frequency table the frequency shows the number of times a the data measured appears
Looking at the table the number that has most frequency is 4. This means that the people that collected 4 certificates are more than any other set of people.
The next is two which have a frequency of two while the least the people that collected 6 certificates. they have a frequency of 2 which means they are only tow people
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are 4:1 and 8:3 eqivalent ratios?
Answer:
No
Step-by-step explanation:
if you divide 8:3 you get 4:1.5 which is not equivalent. In order for them to be equivalent it would need to be 4:1 and 8:2
Answer: No
Step-by-step explanation:
Let's start with what we know. Ratios can also be written as fractions:
4/1 and 8/3
These fractions do not simplify to the same thing, therefore they are not equal.
2.
How many solutions does the following equation have?
8.5m +8 = 8.5m
infinitely many solutions
O exactly one solution
Ono solutions
O exactly two solutions
The given equation has no solution. Option B is correct.
As mentioned, the solution of the equation 8.5m +8 = 8.5m is to be determined.
What are equations?The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.
Here,
Given expression,
8.5m + 8 = 8.5m
Now,
8.5m - 8.5m = 8
0 ≠ 8
Thus, the given equation has no solution. Option B is correct.
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what is the slope of this line
Answer:
y = 300x + 100
Step-by-step explanation:
y = mx + c
the line intersects the y axis at 100, so c = 100
m = difference between y-coordinates / difference between x-coordinates
m = (400-100)/(1-0) = 300/1 = 300
y = 300x + 100
make this in to an Inequality You have some money (m) and you want to bye snacks but your mom told you to also bye a pizza that cost $8. So on snacks you can spend.(s) s
Answer:
To turn the given statement into an inequality, we can write it in the form "m - s >= 8", which means that the amount of money you have (m) minus the amount you spend on snacks (s) must be greater than or equal to 8. This inequality represents the constraint that your mom has placed on your spending, requiring you to spend at least $8 on the pizza. In mathematical notation, the inequality would be written as:
m - s >= 8
This inequality states that the amount of money you have, minus the amount you spend on snacks, must be greater than or equal to 8 in order for you to be able to buy the pizza.
Step-by-step explanation:
Logarithms and natural logarithms are fundamentally different math structures and rely on totally different sets of properties to worth with.
True or False
Fill in as much information as you can in the sketch tool using the following information:
JH is perpendicular to JE and HI is perpendicular to IE. Additionally, JH is congruent to HI.
Write an explanation (using proof type language) OR use the table to create a two-colum proof to as to why JE is congruent to IE
The side JE is equal to side IE because all the sides of the square are congruent.
What is a square?It is a polygon with four sides. The total interior angle is 360 degrees. In a square, all the sides of the square are equal and each angle is 90 degrees. Its diagonals are all the same length and intersect in the center.
JH is opposite to JE and Hello is opposite to IE. Also, JH is congruent with HE.
Let 'm' be the side of the square.
HI = JE (Congruent)
HJ = IE (Congruent)
∠H = ∠J = ∠I = ∠E = 90°
Then the shape that is defined will be a square.
The side JE is equal to side IE because all the sides of the square are congruent.
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Which is a graph of the following?
The graph of the function f(x) = [x² if x ≤ 2] [x + 4 if x > 2]
How to determine the graph of the function?From the question, we have the following parameters that can be used in our computation:
f(x) = [x² if x ≤ 2] [x + 4 if x > 2]
The above function is a piecewise function, and it can be split as follows:
f(x) = [x² if x ≤ 2]
f(x) = [x + 4 if x > 2]
The domain x ≤ 2 in f(x) = [x² if x ≤ 2] means that:
The x values stop at 2 (i.e. 2 inclusive)
The domain x > 2 in f(x) = [x + 4 if x > 2] means that:
The x values starts at a value greater than 2 (i.e. 2 exclusive)
This is represented by the graph (d) with the open and closed circles
Hence, the graph is graph d
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A man of height 1.8 m observes the angle of elevation of the top of a building of height 107 m from the roof of a house and it is found to be 30°. If the distance between the house and the building is 25√3 m, find the height of the house..
Answer:
sorry
Step-by-step explanation:
idrk
The height of the house is approximately 29.43 meters.
What is the right triangle?A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.
We can use the tangent function to solve this problem.
The tangent of an angle is equal to the opposite side (the height of the house) divided by the adjacent side (the distance between the house and the building). In this case, the angle is 30 degrees and the opposite side is the height of the house, so we can write the following equation:
tan(30°) = height of house / 25√3
We can use a calculator or look up the value of tangent 30° to find that tangent 30 is approximately 0.577. Therefore, the equation becomes:
0.577 = height of house / 25√3
Multiplying both sides of the equation by 25√3 gives us:
height of house = 0.577 × 25√3
Plugging in the values and simplifying, we get:
height of house = 29.43 m
Therefore, the house's height is approximately 29.43 meters.
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What is the point-slope form of the line with slope − 14 that passes through the point − 2 9 )?
y - 9 = -14(x + 2) is the point-slope form of the line with slope − 14 that passes through the point − 2 9 )
Given a line with slope -14 that passes through the point (-2, 9).
To determine the point-slope form of the line, we need to use the formula y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the values into the formula, we get:
y - 9 = -14(x + 2)
Therefore, the point-slope form of the line is y - 9 = -14(x + 2).
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Given: triangle ABC is congruent to triangle ADC
Prove: AC bisects angle BAD and AC bisects angle BCD
Please help and thanks if you do
AC bisects angle BAD and AC bisects angle BCD is proved using CPCT rule.
What is the congruence theorem?Triangle congruence theorem or triangle congruence criteria help in proving if a triangle is congruent or not. The word congruent means exactly equal in shape and size no matter if we turn it, flip it or rotate it.
Given that, ΔABC≅ΔADC.
We know that, corresponding parts of congruent triangle are equal.
So, ∠BAC=∠DAC (∵CPCT)
∠BCA=∠DCA (∵CPCT)
∠BAD=∠BAC+∠DAC
⇒ ∠BAD=2∠BAC
⇒ ∠BAC=∠BAD/2
So, AC bisects ∠BAD
∠BCD=∠BCA+∠DCA
⇒ ∠BCD=2∠BCA
⇒ ∠BCD/2=∠BCA
So, AC bisects ∠BCD
Hence, proved AC bisects ∠BAD and AC bisects ∠BCD.
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How do you find the equation of a line with 2 lines?
By entering the values of m and b into the slope-intercept form of a line (y = mx + b), you may obtain the equation for the line.
Given,
Equation of a line;
A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
We have to find the equation of a line with 2 points;
Here,
Using the slope formula, determine the slope.Slope, m = (y₂ - y₁) / (x₂ - x₁)
To find the y-intercept, use the slope and one of the points (b).The x and y of your equation y = mx + b can be replaced by one of your points, and the m can be replaced by the slope you just calculated. The only variable remaining is b in such case. To solve for b, use the same methods you would to solve for a variable.
Therefore,
You can obtain the equation for a line by entering the values of m and b into the slope-intercept form of a line (y = mx + b).
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The sporting equipment has been sorted into baseballs and bats. The number of baseballs is four less than three times the number of bats. The equipment is 80% baseballs. Choose the equation that best represents this scenario.
The equation that best represents this scenario is x/(3x-4) =20/80. So, the correct option is B.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the number of bats be x.
The number of baseballs is four less than three times the number of bats.
The, the number of baseballs are 3x-4
The equipment is 80% baseballs. Then, the equipment is 20% bats.
So, the ratio from number of bats to number of baseballs is
x/(3x-4) =20%/80%
⇒ x/(3x-4) =20/80
Therefore, the option B is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
The sporting equipment has been sorted into baseballs and bats. The number of baseballs is four less than three times the number of bats. The equipment is 80% baseballs. Choose the equation that best represents this scenario
x/(3x-4) =80/20
x/(3x-4) =20/80
x/(3x-4) =80/100
x/(3x-4) =20/100
A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes. Each small box can hold 20 books and each large box can hold 45 books. There were twice as many large boxes sent as small boxes, which altogether can hold 440 books. Write a system of equations that could be used to determine the number of small boxes sent and the number of large boxes sent. Define the variables that you use to write the system.
The equations that could be used to determine the number of small boxes sent and the number of large boxes sent is 85b = 440.
What is the system of equations that could be used to determine the number of small boxes sent and the number of large boxes?From the information, each small box can hold 20 books and each large box can hold 45 books.
There was also twice as many large boxes sent as small boxes, which altogether can hold 440 books.
This will be:
2(20b) + 45b = 440
where b = number of books
40b + 45b = 440
85b = 440
The equation is 85b = 440
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We want to support a thin hoop by a horizontal nail and have the hoop make one complete small-angle oscillation each 2. 0 s.
Given that the hoop makes one complete oscillation in 2s, this implies that the period of oscillation is 2s
Then,
T = 2s
Let the Mass of the thin hoop be M
Let the Radius of the hoop be R
The moment of inertial of a hoop is
I = MR²
The period of a physical pendulum of small amplitude is given by
T = 2π √(I / Mgd)
Where,
T is the period in seconds
I is the moment of inertia in kgm²
M is the mass of the hoop
g is the acceleration due to gravity
g = 9.8m/s²
d is the distance from the rotational axis to the center of gravity
Therefore, d = R
Then, applying the formula
T = 2π √ (I / MgR)
So, we know that
I = MR²
Then,
T = 2π √( MR² / MgR)
T = 2π √(R/g)
Make R the subject of the formula
Square both sides
T² = 4π²(R/g)
T²g = 4π²R
Then, R = T²g / 4 π²
Since g = 9.8m/s² and T= 2s
R = 2² × 9.8 / 4π²
R = 0.993m
Then, the radius of the hoop is 0.993m
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