Answer:
steps below
Step-by-step explanation:
7. sin⁴α+2sin²α cos²α + cos⁴α
==> = (sin²α + cos²α)²
==> = 1
12. sec⁶A - tan⁶A = (sec²a-tan²A)(sec⁴A+sec²A tan²A+tan⁴A)
==> = ((1-sin²A)/cos²A) ( (sec⁴A-2sec²A tan²A+tan⁴A) + 3(sec²A tan²A))
==> = (cos²A/cos²A) ((sec²a-tan²A) + 3(sec²A tan²A))
==> = 1* (1 + 3(sec²A tan²A))
==> = 1 + 3(sec²A tan²A)
14. (1-tanθ) / (1+tanθ) = ((cotθ - 1)/cotθ) / ((cotθ + 1)/cotθ)
==> = (cotθ - 1) / (cotθ + 1)
Aaron has two summer jobs. During the week he works in the grocery store, and on the weekend he works at a nursery. He gets paid $20 per hour to work at the grocery store and $21 per hour to work at the nursery. How much does he earn if he works 13 hours at the grocery store and 9 hours at the nursery? How much does he earn if he works gg hours at the grocery store and n hours at the nursery?
Total pay, 13 hours at the grocery store and 9 hours at the nursery:
Total pay, g hours at the grocery store and n hours at the nursery:
If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,
Part a
He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery
Part b
He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery
The payment at the grocery store per hour = $20
The payment at the nursery per hour = $21
Part a
Number of hours he works at the grocery store = 13 hours
Number of hours he works at nursery = 9 hours
Total pay = 13×20 + 9×21
= 260 + 189
= $449
Part b
Number of hours he works at the grocery store = g hours
Number of hours he works at nursery = n hours
Total pay = 20g + 21n
Hence, If he gets paid $20 per hour to work at the grocery store and $2 per hour to work at nursery,
Part a
He will earn $449 if he works 13 hours at the grocery store and 9 hours at the nursery
Part b
He will earn 20g + 21n, if he works g hours at the grocery store and n hours at the nursery
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Multiple Choice. When calculating a z score for a distribution of means, we refer to the z score as a: (3 points) A) Standard score B) Standardized score C) z statistic D) Central limit theorem For questions 5-7, match the term with the symbol or expression on the right. ( 5 points each) 5. Theoretical mean of the sampling distribution of the mean a. M d. σ
M
6. Standard error of the mean b. S
M
2
e.
N
S
7. Sample Mean c. μ
M
f. μ 8. Assume that the average time to run a marathon in the population is 278 minutes with a standard deviation of 63 minutes. Use this information to answer the questions in number 7 . a. In the theoretical normal population, what percent of raw running times are greater than or equal to 260 AND less than or equal to 300 ? (20 points)
Answer: 1. The answer of sampling distribution is B) Standardized score.2. The matches are as follows: 5.
Theoretical mean of the sampling distribution of the mean - c. μ6.
Standard error of the mean - b. S2 /7.
Sample Mean - a. M8.
For the given question, the average time to run a marathon in the population is 278 minutes with a standard deviation of 63 minutes. We are to find the percentage of raw running times that are greater than or equal to 260 AND less than or equal to 300. We can use the formula for z-score given below:
z= x-μ/σ
z1= 260-278/63 = -0.29
z2= 300-278/63 = 0.35
Now we can find the probability for z-score -0.29 and 0.35 using the z-table. We will take the difference of the two probabilities to get the probability for the range -0.29 to 0.35.
z1= 0.3859
z2= 0.3632
P (0.35 > z > -0.29) = 0.3859 - 0.3632 = 0.0227
Converting this into percentage we get:
0.0227 x 100 = 2.27 %
Therefore, the percent of raw running times greater than or equal to 260 AND less than or equal to 300 is 2.27%.
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Examine the balanced equation for the reaction between lead(I) nitrate and sodium chloride.
Pb(NO3)2 + 2NaCl → 2NaNO3 + PbCl2
If 10.0 g of sodium chloride react with excess lead(II) nitrate, what mass of lead(II) chloride will be produced?
0 20.8 g
O 23.8 g
O 47.68
O 95.28
Find the distance between the points (-10, 2) and (-1, -10).
Write your answer as a whole number or a fully simplified radical expression. Do not round.
units
Let f(x) =4x-1 and g(x)=2^x+3. Find (f-g) (5)
Answer:
\(-16\)
Step-by-step explanation:
\(f(5)=4(5)-1=19 \\ \\ g(5)=2^5+3=35 \\ \\ (f-g)(5)=f(5)-g(5)=19-35=-16\)
5) Build mathematical model of the transportation problem: Entry elements of table are costs. Destination B2 B3 B4 28 A1 27 27 32 A2 15 21 20 A3 16 22 18 b 26 8 Source 3 BI 14 10 21 323324 12 13
This problem is an example of a balanced transportation problem since the total supply of goods is equal to the total demand.
The transportation problem is a well-known linear programming problem in which commodities are shipped from sources to destinations at the minimum possible cost. The initial step in formulating a mathematical model for the transportation problem is to identify the sources, destinations, and the quantities transported.
The objective of the transportation problem is to minimize the total cost of transporting the goods. The mathematical model of the transportation problem is:
Let there be m sources (i = 1, 2, …, m) and n destinations (j = 1, 2, …, n). Let xij be the amount of goods transported from the i-th source to the j-th destination. cij represents the cost of transporting the goods from the i-th source to the j-th destination.
The transportation problem can then be formulated as follows:
Minimize Z = ∑∑cijxij
Subject to the constraints:
∑xij = si, i = 1, 2, …, m
∑xij = dj, j = 1, 2, …, n
xij ≥ 0
where si and dj are the supply and demand of goods at the i-th source and the j-th destination respectively.
Using the given table, we can formulate the transportation problem as follows:
Let A1, A2, and A3 be the sources, and B2, B3, and B4 be the destinations. Let xij be the amount of goods transported from the i-th source to the j-th destination. cij represents the cost of transporting the goods from the i-th source to the j-th destination.
Minimize Z = 27x11 + 27x12 + 32x13 + 15x21 + 21x22 + 20x23 + 16x31 + 22x32 + 18x33
Subject to the constraints:
x11 + x12 + x13 = 3
x21 + x22 + x23 = 14
x31 + x32 + x33 = 10
x11 + x21 + x31 = 21
x12 + x22 + x32 = 32
x13 + x23 + x33 = 26
xij ≥ 0
In this way, we can construct a mathematical model of the transportation problem using the given table. The model can be solved using the simplex method to obtain the optimal solution.
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EFU ~ VWU. Find the length of UF. (photo included)
The length of UF is 15.
Given, EFU ~ VWU As per the similarity condition: EF/UW = EU/VW
Let UF = x and VW = y.
Then EU = x + 9 and UW = y + 7
Substituting the values of UF, VW, EU and UW in the above similarity condition, we get;
x/(y+7) = (x+9)/y
Cross multiplying, we get:
y(x+9) = x(y+7)
y x + 9y = x y + 7x
y x - x y = 7x - 9y
(y-x) = 7x - 9y
Let UF = x and VW = y
y - x = 7x - 9y 10y = 8x y = 4/5 x
Substituting the value of y in the equation y - x = 7x - 9y we get;4/5 x - x = 7x - 9(4/5 x) On solving, we get;
x = 15 Therefore, UF = x = 15
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A bag contains 12 red marbles, 14 blue marbles, and 18 white marbles. A student randomly chooses one marble, then randomly chooses a second marble without replacement. Which statement is true?
Answer:
Step-by-step explanation:
It’s dependent because the person doesn’t put the marble back so therefore it has a big affect on the rest of the marbles
n traveling across flat land you notice a mountain directly in front of you. Its angle of elevation (to the peak) is 3.5 degrees. After you drove 13 miles closer, the angle of elevation is 9 degrees. What is the approximate height of the mountain?
The height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.
Given,
In the question:
Its angle of elevation (to the peak) is 3.5 degrees.
After you drove 13 miles closer, the angle of elevation is 9 degrees.
To find the approximate height of the mountain.
What is trigonometry?
Trigonometry is a branch of mathematics that deals with the relationship between the sides and angles of a right-angle triangle.
Now, According to the question:
It is given that:
In traveling across flat land you notice a mountain directly in front of you.
Applying tan ratio:
tan3.5 = h/(15+x)
Here h is the height of the mountain and x is the distance between the base of the mountain and to the second position of the car.
h = (15 + x) tan3.5
h = x tan9
(15 + x) tan3.5 = x tan9
x = 9.44
h = 9.44 tan9
h = 1.49 miles
Hence, the height of the mountain is 1.49 miles if in traveling across flat land you notice a mountain directly in front of you.
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Sheridan, Inc has 10200 shares of 5%,€100 par value, cumulative preference shares and 21800 ordinary shares with a $1 par value outstanding at December 31, 2020. There were no dividends declared in 2018 . The board of directors declares and pays a €91800 dividend in 2019 and in 2020 . What is the amount of dividends received by the ordinary shareholders in 2020 ? €51000 €0 ϵ30600 €91800
The amount of dividends received by the ordinary shareholders in 2020 is €0.
In the given information, it is mentioned that Sheridan, Inc has 10,200 shares of 5%, €100 par value, cumulative preference shares and 21,800 ordinary shares with a $1 par value outstanding. It is also stated that a dividend of €91,800 was declared and paid in both 2019 and 2020. However, the question specifically asks for the amount of dividends received by the ordinary shareholders in 2020.
Based on the information provided, the dividends declared and paid are likely to be allocated to the cumulative preference shares rather than the ordinary shares. Cumulative preference shares have a higher priority for dividend payments compared to ordinary shares. Since there were no dividends declared in 2018 and a fixed amount of €91,800 was paid in both 2019 and 2020, it can be inferred that the entire dividend amount is allocated to the cumulative preference shares.
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Rectangle BBB is shown below. Nadia drew a scaled version of Rectangle BBB using a scale factor of \dfrac15
5
1
start fraction, 1, divided by, 5, end fraction and labeled it Rectangle CCC.
Answer:
2
Step-by-step explanation:
5 / 1/5 and 10 / 1/5
Answer:
The answer is 2
Step-by-step explanation:
Triangle DEF with vertices D(-6, -1), E(-3, -2), and F(-5, -7):
(a) Reflection: in the x-axis
(b) Rotation: 180°
The reflection of triangle DEF in the x-axis will have vertices D'(-6, 1), E'(-3, 2), and F'(-5, 7). The rotation of triangle DEF by 180° will have vertices D'(6, 1), E'(3, 2), and F'(5, 7).
To reflect triangle DEF in the x-axis, we need to reflect each point in the triangle across the x-axis. The x-axis is a horizontal line that passes through the origin, and any point above it needs to be reflected below it. In this case, the reflection of point D(-6, -1) would be D'(-6, 1), as the y-coordinate changes from -1 to 1. Similarly, the reflection of point E(-3, -2) would be E'(-3, 2), and the reflection of point F(-5, -7) would be F'(-5, 7). Thus, the reflection of triangle DEF in the x-axis would have vertices D'(-6, 1), E'(-3, 2), and F'(-5, 7).
To rotate triangle DEF by 180°, we need to rotate each point in the triangle by 180° about the origin. In this case, the rotation of point D(-6, -1) by 180° would be D'(6, 1), as the x-coordinate changes from -6 to 6 and the y-coordinate changes from -1 to 1. Similarly, the rotation of point E(-3, -2) would be E'(3, 2), and the rotation of point F(-5, -7) would be F'(5, 7). Thus, the rotation of triangle DEF by 180° would have vertices D'(6, 1), E'(3, 2), and F'(5, 7).
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what is 12 ÷ 1 1/5 ?
Answer:
10
Step-by-step explanation:
12 ÷ 1 1/5
Change to an improper fraction
12 ÷ ( 5*1+1)/5
12 ÷ 6/5
Copy dot flip
12 * 5/6
12/6 * 5
2*5
10
Answer:
10
Step-by-step explanation:
12 ÷ 1 1/5
Change into an improper fraction.
12 ÷ 6/5
Reciprocal and it becomes multiplication.
12 × 5/6
60/6
= 10
use the trapezoidal rule, the midpoint rule, and simpson's rule to approximate the given integral with the specified value of n. (round your answers to six decimal places.) 3 0 1 10 y5 dy, n
Therefore, the degree of the resulting polynomial is m + n when two polynomials of degree m and n are multiplied together.
What is polynomial?
A polynomial is a mathematical expression consisting of variables and coefficients, which involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. Polynomials can have one or more variables and can be of different degrees, which is the highest power of the variable in the polynomial.
Here,
When two polynomials are multiplied, the degree of the resulting polynomial is the sum of the degrees of the original polynomials. In other words, if the degree of the first polynomial is m and the degree of the second polynomial is n, then the degree of their product is m + n.
This can be understood by looking at the product of two terms in each polynomial. Each term in the first polynomial will multiply each term in the second polynomial, so the degree of the resulting term will be the sum of the degrees of the two terms. Since each term in each polynomial has a degree equal to the degree of the polynomial itself, the degree of the resulting term will be the sum of the degrees of the two polynomials, which is m + n.
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x2 +15-8x entre 3-x ayuda pliz
Can you help me solve this!
Hello!
surface area
= 2(6*2) + 2(4*2) + 4*6
= 2*12 + 2*8 + 24
= 24 + 16 + 24
= 64 square inches
Determine the type of angles.
Determine which lines, if any, are parallel.
Name the transversal.
1. Angles 2 and 6 are linear angles. 2. One name is transversal A
3. None are parallel for <2 + <6 = 180°
What are Linear Pair Angles?Linear pair angles are a pair of adjacent angles formed when two lines intersect. These two angles together form a straight line or a 180-degree angle.
In other words, when two lines intersect, the adjacent angles on either side of the intersection form a linear pair. Linear pair angles are also known as supplementary angles, which means that their sum is equal to 180 degrees.
Therefore, we have:
1. Angles 2 and 6 are linear angles because they lie on a straight line.
2. They lie on transversal A.
3. No pair of lines needs to be parallel for <2 + <6 = 180 degrees. The answer is none.
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select the slope of the line that joins the pair of points. a. (9, 10) and (7, 2) 1 of 5. 4 b. (-8, -11) and (-1, -5) 2 of 5. select choice c. (5, -6) and (2, 3) 3 of 5. select choice d. (6, 3) and (5, -1) 4 of 5. select choice e. (4, 7) and (6, 2) 5 of 5. select choice
The required slopes are:
(a) slope = 4
(b) slope = 6/7
(c) slope = -3
(d) slope = 4
(e) slope = -5/2
We know that,
When a line passing through (x₁, y₁) and (x₂, y₂)
Then the slope of the line be,
slope (m) = (y₂ - y₁) / (x₂ - x₁)
Using this formula, calculate the slope for each given points
a. (9, 10) and (7, 2)
⇒ slope (m) = (2 - 10) / (7 - 9)
= -8/-2 = 4
So, the slope is 4.
b. (-8, -11) and (-1, -5)
⇒ slope (m) = (-5 - (-11)) / (-1 - (-8))
= 6/7
So, the slope is 6/7.
c. (5, -6) and (2, 3)
⇒ slope (m) = (3 - (-6)) / (2 - 5)
= 9/-3
= -3
So, the slope is -3.
d. (6, 3) and (5, -1)
⇒ slope (m) = (-1 - 3) / (5 - 6)
= -4/-1
= 4
So, the slope is 4.
e. (4, 7) and (6, 2)
⇒ slope (m) = (2 - 7) / (6 - 4)
= -5/2
So, the slope is -5/2.
Therefore, the slope of the line that joins (-8, -11) and (-1, -5) is 6/7.
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A stack of paper is 2 feet tall One package of paper is 2/5 of a foot How many packages of paper are in the stack?
O 1 package
O 2 packages
O 5 packages
10 packages
(3) Find absolute max and mun for \( f(x)=(y-2) x^{2}-y^{2}+5 \) on Triangle with rectices \( (0,0),(1,1) \) and \( (-1,1) \)
The absolute maximum value is 5 \((attained at \((0,0)\))\), and the absolute minimum value is 1 \((attained at (0,2)(0,2)).\)
To find the absolute maximum and minimum values of the function \(\(f(x) =\)\((y-2)x^2 - y^2 + 5\)\)on the triangle with vertices \(\((0,0)\), \((1,1)\), and \((-1,1)\),\)we need to evaluate the function at the critical points and the boundary points of the triangle.
The vertices of the triangle are \((0,0)\), \((1,1)\), and \((-1,1)\). Let's evaluate the function at these points:
1. \(\((0,0)\):\)
\(\(f(0) = (0-2) \cdot 0^2 - 0^2 + 5 = -2 \cdot 0 - 0 + 5 = 5\).\)
2.\(\((1,1)\):\)
\\((f(1) = (1-2) \cdot 1^2 - 1^2 + 5 = -1 \cdot 1 - 1 + 5 = 3\).\)
3.\(\((-1,1)\):\)
\(\(f(-1) = (1-2) \cdot (-1)^2 - 1^2 + 5 = -1 \cdot 1 - 1 + 5 = 3\).\)
Now, let's consider the critical points of the function. To find the critical points, we need to find where the gradient of the function is zero or undefined. Since the function is defined in terms of both \(x\) and \(y\), we will find the partial derivatives with respect to \(x\) and \(y\) and set them equal to zero.
\(\(f_x = 2x(y-2)\)\)
\(\(f_y = x^2 - 2y\)\)
Setting \(\(f_x = 0\) and \(f_y = 0\),\)we have:
\(\(2x(y-2) = 0\)\)
\(\(x^2 - 2y = 0\)\)
From the first equation, we have two possibilities:
1. \(\(2x = 0\) (implies \(x = 0\))\)
2. \(\(y - 2 = 0\) (implies \(y = 2\))\)
From the second equation, we have:
\(\(x^2 - 2y = 0\)\)
\(\(x^2 = 2y\)\)
\(\(y = \frac{x^2}{2}\)\)
Combining the conditions, we have two critical points:
1.\(\((0,2)\)2. \(\left(\pm \sqrt{2}, \frac{(\pm \sqrt{2})^2}{2}\right) = \left(\pm \sqrt{2}, 1\right)\)\)
Now, we need to evaluate the function at these critical points:
1.\(\((0,2)\): \(f(0,2) = (2-2) \cdot 0^2 - 2^2 + 5 = -4 + 5 = 1\).\)
2\(. \(\left(\pm \sqrt{2}, 1\right)\):\)
\(\(f\left(\sqrt{2}, 1\right) = (1-2) \cdot \left(\sqrt{2}\right)^2 - 1^2 + 5 = -1 \cdot\)\(2 - 1 + 5 = 2\).\)
\(\(f\left(-\sqrt{2}, 1\right) = (1-2) \cdot \left(-\sqrt{2}\right)^2 - 1^2 + 5 = -1 \cdot 2 - 1 + 5\)
\(= 2\).\)
Now, we compare the values obtained at the vertices, critical points, and boundary points to determine the absolute maximum and minimum values.
The values we obtained are:
\(\(f(0,0) = 5\)\)
\(\(f(1,1) = 3\)\)
\(\(f(-1,1) = 3\)\)
\(\(f(0,2) = 1\)\)
\(\(f(\sqrt{2}, 1) = 2\)\)
\(\(f(-\sqrt{2}, 1) = 2\)\)
Therefore, the absolute maximum value is 5 \((attained at \((0,0)\)),\) and the absolute minimum value is 1 \((attained at \((0,2)\)).\)
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I can use your help please
Answer:
he needs to play 24 games of basketball
Roderigo has just finished paying back his $8,575 unsubsidized Stafford loan, which he took out to fund his four-year degree. The loan had a duration of ten years and an interest rate of 7. 1%, compounded monthly. Roderigo will allow interest capitalization. If Roderigo made monthly payments to pay off his loan, how much interest did he pay in total? Round all dollar values to the nearest cent. A. $4,547. 02 b. $3,426. 20 c. $7,353. 80 d. $5,436. 20 Please select the best answer from the choices provided A B C D.
Roderigo will pay $7353.80 in interest.
Interest capitalization means the interest earned is added to the principle amount so first we will use compound interest formula.
What is the formula for compound interest?\(Amount=p(1+\frac{r}{n} )^{nt}\)
p = 8575
r = 7.1% or 0.071
n = 12
t = 4
Putting the values in formula we get
\(Amount=8575(1+\frac{0.071}{12} )^{12(4)}\)
\(Amount=8575(1+\frac{0.071}{12} )^{48}\)
Solving this we get;
Amount = $11381.94
For the next part we have EMI formula as,
\(EMI=\frac{pr(1+r)^{n} }{(1+r)^{n-1}}\)
p = 11381.94
\(r=\frac{7.1}{\frac{12}{100} }=0.005917\)
\(n=(12)(10)\\n=120\)
\(EMI=\frac{11381.94(0.005979)(1+0.005979)^{120} }{(1+0.005979)^{120}-1}\)
EMI = $132.74
Now total payments made in 120 months (10 years) =
\(132.74(120)=15928.80\) dollars
interest paid =
\(15928.80-8575=7353.80\) dollars
Hence, Roderigo will pay $7353.80
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In a direct variation, y = 12 when x = 3. Write a direct variation equation
that shows the relationship between x and y.
O y = 12x
O y = 4x
O y = 3x
O y = 2x
helpppp
Answer:
fourth one
Step-by-step explanation:
please help this is my last equation on my assignment and its due at 5... -1.2x = 12
Which statements about the diagram are correct? Check all that apply.
BD = 9 in.
AB = 36 in.
DC = 6 StartRoot 3 EndRoot in.
AC = 12 StartRoot 3 EndRoot in.
BC = 18 StartRoot 3 EndRoot in.
Answer:
(C)DC = 6 StartRoot 3 EndRoot in.
(D)AC = 12 StartRoot 3 EndRoot in.
Step-by-step explanation:
What is the slope of the line that contains the points (2, -8) and (-4, 4)?
O2
112
id
2
O-2
Answer:
-2
Step-by-step explanation:
Δy =4- (-8) =12
Δx = -4 -2 = -6
12/(-6) =-2
HELP!!!! PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer: red hot= $4
gummies=$9
Step-by-step explanation:
3r+1g=21
-(3r+3g=39)
3r+1g=21
-3r-3g=-39
-2g=-18
g=9
3r+1(9)=21
3r=12
r=4
Q4. If 8= {rabbit, cat, dog, emu, turtle, mouse, aardvark) and H= (rabbit, emu, mouse) and J= {cat, dog}: list the members of H' b list the members of J' c list the members of H'UJ' what is HOR d e find (H')' what is HUH'?
This box plot represents the marks gained by students in an exam. Nobody gained exactly 30, 48 or 70 marks. 120 students gained less than 70 marks. How many students gained more than 48 marks?
Therefore , the solution of the given problem of scatter plot comes out
to be 2 regions contain 2 x 40 (or 80) students.
Definition of a scatter plotSeveral dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).
Here,
A box plot separates a data set into four areas, each identified by five lines. The lowest line displays the result, while the highest line displays the result. 25% of the data points are distributed across each region, and the median score is indicated by the middle line.
In this box plot, for instance, there are lines at 10, 30, 48, 70, and 100. The fact that no student received a score exactly equal to 30, 48, or 70 allows us to deduce the following:
Because the middle two sections represent the interquartile range (IQR), which comprises the middle 50% of the data, they are frequently "boxed" together.
We are informed that 120 students received test scores below 70. Additionally, since there are three regions with scores below 70 and each region has a 25% weighting, 3 x 25% (or 75% of the students) had scores below 70.
In other words, 75% of 120 students.
If there are 120 students total throughout the three regions, then each
region has 40 pupils, or one-third of the total.
The box plot indicates that there are two areas, and since each region has 40 students, there are 80 students total in the two regions.
As a result, two zones with two sets of 40 students each make up the solution to the scatter plot problem.
Therefore , the solution of the given problem of scatter plot comes out
to be 2 regions contain 2 x 40 (or 80) students.
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An open top box is to be made from a rectangular cardboard that is 15 in by 25 in by cutting out
squares from each corner and turning the sides up.
Round off your answers to three decimal places.
inches
What is the height of the box that will maximize the volume?
What is the maximum volume?
cubic inches
Answer:
10 and
40
Step-by-step explanation:
Answer:
10,40
Step-by-step explanation:
hehehehehehehehehehe