The NBT is used to evaluate a student's academic readiness for tertiary education, whereas the APS is used to establish whether a student meets the minimal standards for admission to a certain course.
What is NBT scores?
The National Benchmark Test Project created the National Benchmark Test (NBT), a test. In order to determine a learner's academic preparation for university, a battery of examinations is utilized to evaluate their academic literacy, general knowledge, and mathematics proficiency.
The NBT pass mark is what?
The National Benchmark Tests do not have a passing score. Your results will be plotted on a benchmark scale, which will help the university determine if you are prepared for university-level work. Since the NBTs are merely a test of preparation for higher education, you cannot pass or fail them.
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Interest compounded semi annually is compounded four times a year true or false
Answer:
The given statement is False. When the interest is compounded half yearly the number of conversion periods will be two because a year comprises 12 months and has two periods of six months each.
Step-by-step explanation:
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Plane B is flying 75mph 75 mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.
Plane A 4 hours to travel 2300 miles.
Plane takeoff angle.
Angel
During take off, a plane leaves the ground and travels in a straight line until it reaches a height of 10 km. The distance the plane flies during take off should be in the range 57 km to 62 km. What is the smallest possible angle that the path of the plane could make with the ground? Give your answer in degrees to 1 d. p.
Let's assume that the plane travels a distance of x km during take off and reaches a height of 10 km. Then, using trigonometry, we can find the angle θ between the ground and the path of the plane:
tan(θ) = 10/x
We want to find the smallest possible angle θ, which means we need to maximize x. From the given information, we know that x must be in the range 57 km to 62 km. Therefore, to maximize x, we choose x = 62 km.
Plugging this into the equation above, we get:
tan(θ) = 10/62
θ = arctan(10/62) ≈ 8.8°
Therefore, the smallest possible angle that the path of the plane could make with the ground is approximately 8.8 degrees.
Angel
Xochitl spots an airplane on radar that is currently approaching in a straight line, and that will fly directly overhead. The plane maintains a constant altitude of 7425 feet. Xochitl initially measures an angle of elevation of 19° to the plane at point A. At some later time, she measures an angle of elevation of 37° to the plane at point B.
Find the distance the plane traveled from point A to point B. Round your answer to the nearest foot if necessary
Let's assume that the distance from Xochitl to point A is d1 and the distance from Xochitl to point B is d2. We want to find the distance the plane traveled from point A to point B, which is the difference between d1 and d2.
From the given information, we can set up the following two equations:
tan(19°) = 7425/d1
tan(37°) = 7425/d2
Solving for d1 and d2, we get:
d1 = 7425/tan(19°) ≈ 22977.6 feet
d2 = 7425/tan(37°) ≈ 13060.2 feet
Therefore, the distance the plane traveled from point A to point B is:
d1 - d2 ≈ 9917.4 feet ≈ 3021 meters
Rounding to the nearest foot, we get that the distance the plane traveled from point A to point B is approximately 9917 feet.
Angel
Plane B is flying 75mph 75 mph faster than Plane A. Find the time it takes for Plane A to travel 2300 2300 miles if it takes Plane B the same amount of time to travel 2600 2600 miles.
Let's start by using the formula for distance, rate, and time:
distance = rate x time
Let's assume that Plane A's speed is r mph. Then we know that Plane B's speed is r + 75 mph.
We also know that Plane A travels 2300 miles and Plane B travels 2600 miles. Since they take the same amount of time to travel their respective distances, we can set up the following equation:
2300/r = 2600/(r + 75)
To solve for r, we can cross-multiply and simplify:
2300(r + 75) = 2600r
2300r + 172500 = 2600r
300r = 172500
r = 575 mph
Now that we know Plane A's speed, we can use the formula for distance, rate, and time to find the time it takes for Plane A to travel 2300 miles:
distance = rate x time
2300 = 575 x time
time = 4 hours
1. Mark is late. Do you think he ............. about the dinner?
Answer: forgot
Step-by-step explanation:
1. Mark is late. Do you think he forgot about the dinner?
PLEASE HELP
Directions: Complete each problem below. Show all work.
1. Find the approximate volume of a cylinder with a circumference of 13 in. and a height of 9 in. Use 3.14 for straight pi and round to the nearest tenth.
2. Find the volume of a cylinder with a diameter of 63.5 cm and a height of 28 in. Find the volume, in terms of straight pi, of the cylinder in cubic inches.
The vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.
What is the cylinder?A cylinder is a three-dimensiοnal geοmetric shape that cοnsists οf twο parallel bases that are cοngruent circles and a curved lateral surface that cοnnects the bases.
1. The circumference οf the cylinder is given as 13 inches. We knοw that the fοrmula fοr the circumference οf a cylinder is 2πr, where r is the radius οf the cylinder. Sο, we have:
2πr = 13
r = 13/(2π)
Nοw, we can use the fοrmula fοr the vοlume οf a cylinder, which is V = πr²h, where h is the height οf the cylinder:
[tex]V = \pi (13/(2\pi ))^2(9) = 119.8 cubic inches[/tex]
Sο, the approximate vοlume of the cylinder is 119.8 cubic inches.
2. The diameter οf the cylinder is given as 63.5 cm, which means the radius is 31.75 cm (since the radius is half οf the diameter). The height is given as 28 inches.
The formula fοr the vοlume of a cylinder is [tex]V = \pi r^2h[/tex], so we can substitute the values we have tο get:
[tex]V = \pi (31.75)^2(28) = 85816.8 ~cm^3[/tex]
Tο cοnvert this tο cubic inches, we need tο knοw that 1 cubic inch is equal tο 16.3871 cubic centimeters, sο we have:
V = 85816.8/16.3871 ≈ 5235.5 cubic inches
Hence, the vοlume οf the cylinder in terms οf straight pi and cubic inches is apprοximately 5235.5 cubic inches.
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A group of teachers at a local middle school are trying to decide what the end of the year field trip should be for the 8th graders moving on to high school. Determine which sample below will give the teachers the most accurate data.
a
A random sample of students in 6th, 7th, and 8th grade are asked where the 8th graders should go on their field trip.
b
A random sample of 8th graders are asked where they would like to go for the end of the year field trip.
c
The football team is asked where the 8th graders should go on their field trip.
d
All the teachers are asked where the 8th graders should go on their field trip.
Option b is likely to give the teachers the most accurate data for deciding the end of the year field trip for the 8th graders.
What is sample?In statistics, a sample is a subset of individuals or observations taken from a larger population. The sample is used to gain insights and make inferences about the population from which it was drawn. Samples are often used when it is not feasible or practical to gather data from every individual in a population, which could be too large or too time-consuming to survey.
Here,
A random sample of 8th graders are directly affected by the decision and are therefore the most appropriate group to survey. Asking a random sample of 6th, 7th, and 8th graders (option a) would include students who are not directly affected by the decision, and may not have the same level of understanding or investment in the trip. Asking the football team (option c) would likely provide biased results, as the football team may have different preferences and priorities than the wider 8th grade class. Asking all the teachers (option d) may also provide biased results, as teachers may have different opinions and preferences than the students. Ultimately, the most accurate data will come from surveying the group of students directly affected by the decision.
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what is the sum of the rational expression below x/x+1 + 6x/x+5
The sum of the rational expression as required to be determined in the task content is; (7x² + 11) / (x² + 6x + 5).
What is the sum of the given expression?It follows from the task content that the rational expression whose sum is to be determined is;
x / x+1 + 6x / x+5
Therefore, by using the LCM; (x + 1) (x + 5).
Therefore, the sum is as follows;
{x(x + 5) + 6x (x + 1)} / (x + 1) (x + 5).
= (7x² + 11) / (x² + 6x + 5)
Ultimately, the sum as required is; (7x² + 11) / (x² + 6x + 5).
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Answer:
[tex] \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]
Step-by-step explanation:
[tex]1. \: \frac{x(x + 5) +6x(x + 1)}{(x + 1)(x + 5)} \\ 2. \: \frac{x(x + 5 + 6(x + 1))}{(x + 1)(x + 5)} \\ 3. \: \frac{x(x + 5 + 6x + 6)}{(x + 1)(x + 5)} \\ 4. \: \frac{x((x + 6x) + (5 + 6))}{(x + 1)(x + 5)} \\ 5. \: \frac{x(7x + 11)}{(x + 1)(x + 5)} [/tex]
In the triangle shown, what is the length of line BD?
Answer:
4
Step-by-step explanation:
This is a right triangle, so you can use the Pythagorean Theorem.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] C has to be the longest side. In this case, that is 5
[tex]a^{2}[/tex] + [tex]3^{2}[/tex] = [tex]5^{2}[/tex]
[tex]a^{2}[/tex] + 9 = 25 Subtract 9 from both sides
[tex]a^{2}[/tex] + 9 - 9 = 25 - 9
[tex]a^{2}[/tex] = 16 Take the square root of both sides.
[tex]\sqrt{a^{2} }[/tex] = [tex]\sqrt{16}[/tex]
a = 4
Helping in the name of Jesus.
If 421,000 people each receive an average refund of $3,400, based on an interest rate of 3 percent, what would be the lost annual income from savings on those refunds?
The lost annual income from savings on those refunds would be $43,032,000.
How to find the lost annual income?o calculate the lost annual income from savings on those refunds, we need to first calculate the total amount of money refunded, and then calculate the lost income from that amount.
The total amount refunded would be:
421,000 people x $3,400 per person = $1,434,400,000
Next, we can calculate the lost income from that amount at an interest rate of 3 percent. To do this, we can use the simple interest formula:
I = P x R x T
Where:
I = interest
P = principal (the amount refunded)
R = interest rate (as a decimal)
T = time (in years)
Substituting the values we have:
I = $1,434,400,000 x 0.03 x 1
I = $43,032,000
Therefore, the lost annual income from savings on those refunds would be $43,032,000.
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These cards can be sorted into three pairs, where each pair adds to the same number. What is this number? -80-62 -4 -2
0 + (-66) Plus 18 = -48 is indeed the common sum for every one of these pairings. Hence, -48 is the solution.
The common difference sum is what?The total of the first n terms in the arithmetic sequence is equal to the sum (addition) of the n terms in AP. It is equal to n split by 2 times total sum of thrice the first term, "a," and the product of difference between the second and first term, "d," also; known as the common difference, plus (n-1), where n is the number of terms to be added.
The following step is to add -62 to all of the three remaining integers to create three new ones: -62 + (-4) (= -66, -62 Plus (-2) = -64, & -62 plus 80 = 18. From these three numbers, we now need to select two pairs that sum up to the same number.
We are able to observe that -66 plus -64 is -130, therefore the answer is 18. We obtain 148 when we multiply 130 by 18. As a result, the following three sets of numbers add up to a single total:
-80 and -80, -62 and - 4, and -148
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Find the equation of the line.
Use exact numbers.
y=y=y, equals
x+x+x, plus
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, negative nine and one, negative five.
A coordinate plane. The x- and y-axes each scale by one. A graph of a line goes through the points zero, negative nine and one, negative five.
The equation of the line is y=-4x+9. In order to find the equation of the line, we must first calculate the slope (m) of the line.
What is slope?Slope is a measure of the steepness of a line on a graph. It is calculated by finding the ratio of the vertical change between two points, divided by the horizontal change between the same two points.
The slope is calculated by dividing the change in y-coordinates (rise) by the change in x-coordinates (run).
In this case, the rise is -5 – (-9) = 4, and the run is 1 – 0 = 1. Therefore, the slope of the line is m = 4/1 = 4.
Next, we plug the slope and a point on the line into the point-slope form of a line equation: y - y1 = m(x - x1).
We can choose any point on the line, so let's use (0, -9).
Plugging in the values, we get:
y - (-9) = 4(x - 0)
Simplifying, we get:
y = 4x - 9
Therefore, the equation of the line is y = 4x - 9.
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The half-life of caffeine in the human body is about 6.4 hours. cup of coffee has about 80 mg of caffeine: Write an equation for the amount of caffeine in person $ body after drinking cup of coffee? Let € be the milligrams of caffeine in the body after hours. How much caffeine wIll remain after 10 hours? mg How long until there are only 20 mg remaining? hours
Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.
Explain about the Exponential equation:Calculating the exponential growth as well as decay of a given collection of data is done using an exponential function, which is a mathematical function.
Exponential functions, for instance, can be used to estimate population changes, loan interest rates, bacterial growth, radioactive decay, and disease spread. An exponential function has the following form at its most fundamental level.
f(x) = [tex]a^{x}[/tex]
Exponential equation for the amount of Caffeine
C = 80[tex](2)^{-t/6}[/tex]
Amount of caffeine C = 60 mg.
60 = 80[tex](2)^{-t/6}[/tex]
3/4 = [tex](2)^{-t/6}[/tex]
Taking log on both sise:
[tex]log_{2}(3/4) = -t/6[/tex]
Solve the log function using the log calculator:
-t/6 = (-0.41)
t = 0.41 * 6
t = 2.46 hours
Thus, the time taken to drop the caffeine from 80 mg to 60 mg is 2.46 hours.
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Correct question:
The biological half-life of caffeine is about 6hr. If one cup of coffee has 80 mg of caffeine, then the amount of caffeine C (in mg) remaining after t hours is given by C = 80[tex](2)^{-t/6}[/tex]
How long will it take for the amount of caffeine to drop below 60 mg?
find hcf of 24x^3yz^4; 30x^2y^2z^3 and 36x^3y^2z^3
The HCF is 6x^2yz^3
What is HCF?HCF means Highest Common Factor. HCF of two or more numbers is the greatest factor that divides the numbers. It is also the greatest possible number of all their common factors.
To find the HCF of the following,
24x^3yz^4 , 30x^2y^2z^3, 36x^3y^2z^3
To find the HCF among the first value,
24 , 30 and 36
Factors of 24 are 2, 3, 4, 6, 8, 12, 24
Factors of 30 are 2, 3, 5, 6, 10, 15, 30
Factors of 36 are 2, 3, 4, 6, 9, 12, 18, 36.
The highest common factor that it can be divisible with is 6
Among x^3 , x^2 and x^3
The factors of x^3 are x, x^2, x^3
Factors of x^2 are x, x^2
Factors of x^3 are x, x^2, x^3
The highest common factor is x^2
Among y , y^2 and y^2
Factors of y is y
Factors of y^2 are y, y^2
The highest common factor is y
And among z^4 , z^3 and z^3
Factors of z^4 are z, z^2, z^3, z^4
Factors of z^3 are z, z^2, z^3
The highest common factor here is z^3
Therefore, the highest common factor is 6x^2yz^3
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The two statements below are different ways to say that the sides of these similar triangles are proportional.
Complete the equations that go with the statements.
PLSS I NEED THISS
Answer:
e, cc, dStep-by-step explanation:
You want the different ways sides of similar triangles can be shown as proportional.
Corresponding sidesFrom shorter to longer, the corresponding sides in the similar triangles are ...
Smaller ... Larger
b . . . . . . . e
a . . . . . . . d
c . . . . . . . f
PairsThe proportions are written by choosing two letters and their corresponding letters. The two chosen can be from different columns (part 1) or from the same column (part 2). The corresponding letters are written in the same place in the proportion fraction
[tex]\dfrac{a}{d}=\dfrac{b}{\boxed{e}}=\dfrac{\boxed{c}}{f}[/tex]
[tex]\dfrac{a}{b}=\dfrac{d}{e}\qquad\dfrac{b}{\boxed{c}}=\dfrac{e}{f}\qquad\dfrac{c}{a}=\dfrac{f}{\boxed{d}}[/tex]
__
Additional comment
Any proportion can be written "sideways" or "upside down." Corresponding parts have the same relationship in any case.
[tex]\dfrac{a}{b}=\dfrac{d}{e}\ \Leftrightarrow\ \dfrac{a}{d}=\dfrac{b}{e}\ \Leftrightarrow\ \dfrac{b}{a}=\dfrac{e}{d}\ \Leftrightarrow\ \dfrac{d}{a}=\dfrac{e}{b}[/tex]
17 is what percent of 20?
Answer: 85% or 17/20
Step-by-step explanation: Ok, so 17 being what percent of 20 is 17/20. Then, simply divide from there to get 0.85, also known as 85%.
0 divided by 1 . what is the answer
Answer: 0
Step-by-step explanation:
Answer:
0
Step-by-step explanation:
0 divided by 1 is 0 similarly to other numbers.
For example 5/1 = 5
Although, 1/0 is undefined as it isn't legal.
Does this system of equations have one solution, no solutions, or an infinite number of solutions? x - y = 4; x + y = 8
Answer:
one solution (6, 2 )
Step-by-step explanation:
x - y = 4 → (1)
x + y = 8 → (2)
add the 2 equations term by term to eliminate y
(x + x) + (y - y) = 8 + 4
2x + 0 = 12
2x = 12 ( divide both sides by 2 )
x = 6
substitute x = 6 into (2) and solve for y
6 + y = 8 ( subtract 6 from both sides )
y = 2
the system has one solution , that is (6, 2 )
La profesora Elena compró 28 lapiceros y repartió a sus estudiantes 5/7 de los lapiceros. ¿Cuántos lapiceros le quedaron a la profesora Elena?
Respuesta (Español/Spanish):
20 lapices
Explicación paso-a-paso (Español/Spanish):
Multiplica 28 por 5/7.
Answer (English/Inglés):
20 pencils
Step-by-step explanation (English/Inglés):
Multiply 28 by 5/7
arturo earns 1,800 per month. he pays 600 a month on rent. what is the ratio of his rent to his monthly income
Answer:
1:3
Step-by-step explanation:
We Know
Arturo earns 1,800 per month.
He pays 600 a month on rent.
What is the ratio of his rent to his monthly income?
The ratio is
600:1800
Simplify by 600; we get the ratio
1:3
So, the ratio of his rent to his monthly income is 1:3
Four people are standing on line. The tall man is between a woman with a red hat and a little boy. The little boy is next to a teenager who is not last. In what order are they standing?
We can use logical reasoning to conclude that the order is "teenager, little boy, tall man, and woman" as per the explanation below, based on the clues.
What is logical reasoning?Logical reasoning is a process of using rational thinking and deduction to arrive at a conclusion based on available information. In the given problem, logical reasoning is used to analyze the provided clues and determine the order of the four people standing in line.
By carefully examining the clues and using a process of elimination, we can deduce the position of each person in the line. We use logical reasoning to eliminate the possibilities that contradict the given information, and to arrive at the correct sequence that fits all of the provided conditions.
First, we know that the tall man is between the woman and the little boy. So, they can appear in either of the following orders:
woman - tall man - little boylittle boy - tall man - womanHowever, we are told that the little boy is next to a teenager who is not last. So:
woman - tall man - little boy - teenager --> Incorrect, because the teenager would be last.teenager - little boy - tall man - woman --> Correct, because the teenager would be in a different position.Thus, we can conclude that we have correctly answered this question.
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with solution pleasee
y=3
Step-by-step explanation:
3×5=15
2×3=6
15-6=9
Two parallel lines are cut by transverse as shown. Determine the measures of 1 through 7
Both angles on the parallel lines are related as ∠1=180°-∠7
Define Vertical Angles (Vertically Opposite Angles)Vertical angles, also known as vertically opposed angles, are generated when two lines intersect. Angles that are vertically opposite one another are always equal to one another. Moreover, a vertical angle and the angle to which it is next are supplementary angles, meaning their sum is 180 degrees.
To find: measure ∠1 through ∠7
∠7=∠5 ( vertically opposite angle)
∠5=∠2( co-exterior angle)
∠1+∠2=180°
( A straight line has a maximum angle of 180°.)
∠1=180°-∠2
∠1=180°-∠5
∠1=180°-∠7
Hence, both angles on the parallel lines are related as ∠1=180°-∠7
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7.
A regular polygon has sides with the same length and interior angles with the same
measure. What kind of triangle is also a regular polygon?
A right triangle
B obtuse triangle
C scalene triangle
D equilateral triangle
E isosceles triangle
Answer:
D equilateral triangle.
Step-by-step explanation:
An equilateral triangle has three sides with equal length and three interior angles with the same measure of 60 degrees. Therefore, an equilateral triangle can also be considered as a regular polygon with three sides.
i need 12 and 14 show work pls
The answers of the given question are (12) the maximum angle at which the ball can be hit and land within the court is approximately 9.56° degrees. (14) the length of the ramp is approximately 35.5 inches.
What is Angle?an angle is a measure of the difference in direction between two lines or surfaces that meet at a point. It is defined as the ratio of the length of the arc that separates two intersecting lines or planes to the radius of the circle or sphere that the arc belongs to.
Angles are typically measured in degrees or radians, with a full circle consisting of 360° degrees or 2π radians. Angles can be acute (less than 90° degrees), right (exactly 90° degrees), obtuse (greater than 90° degrees but less than 180° degrees), or straight (exactly 180° degrees).
(12). To determine the maximum angle at which the ball can be hit and land within the court, We can use the following formula to solve the problem:
d = v² * sin(2θ) / g
Where:
d = the horizontal distance the ball will travel
v = the initial velocity of the ball
θ = the launch angle
g = the acceleration due to gravity
We can assume that the initial velocity of the ball is constant and equal to the velocity at which the ball was hit. Also, we know that the height at which the ball was hit is 2.44m, so we can use the following formula to find the initial velocity of the ball:
v² = 2gh
Putting in given values, we will get:
v² = 2 * 9.81 m/s² * 2.44m = 47.9424
v = √(47.9424) = 6.92 m/s (rounded to two decimal places)
we can plug in the given values and solve for θ:
9.4 = (6.92)² * sin(2θ) / 9.81
sin(2θ) = 9.4 * 9.81 / (6.92)² = 0.3209
2θ = sin^-1(0.3209) = 19.12
θ = 9.56° degrees (rounded to the nearest degree)
Therefore, the maximum angle at which the ball can be hit and land within the court is approximately 9.56° degrees.
(14). To find the length of the ramp, we can use the following formula:
length = height / sin(θ)
Where:
height = 12 inches
θ = 17° degrees
Plugging in the given values, we get:
length = 12 / sin(17) = 35.5 inches (rounded to one decimal place)
Therefore, the length of the ramp is approximately 35.5 inches.
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The following data are the heights (in inches) of 40 students in a statistics class 59; 60; 61; 62; 62; 63; 63; 64; 64; 64; 65; 65; 65; 65; 65; 65; 65; 65; 65; 66; 66; 67; 67; 68; 68; 69; 70; 70; 70; 70; 70; 71; 71; 72; 72; 73; 74; 74; 75; 77 a. Find the five-number summary for the data and construct a box plot. b.Find the IQR
The five-number summary for data and construct a box plot is: 59, 62, 65, 70, 77
The IQR for the data is 8.
What is median ?
The median is a measure of central tendency in statistics. It is the value separating the higher half from the lower half of a data sample. To find the median of a data set, the data is first arranged in ascending or descending order, and then the middle value is identified. If the data set has an odd number of values, the middle value is the median. If the data set has an even number of values, the median is the average of the two middle values. The median is a useful measure of central tendency when the data contains outliers or extreme values that may affect the mean.
According to the question:
a. The five-number summary consists of the minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. To find these values:
Minimum: 59
Q1: the median of the lower half of the data, which is the median of the first 20 values (when ordered from smallest to largest): (62 + 62) / 2 = 62
Median (Q2): the middle value when the data is ordered from smallest to largest: (65 + 65) / 2 = 65
Q3: the median of the upper half of the data, which is the median of the last 20 values: (70 + 70) / 2 = 70
Maximum: 77
Therefore, the five-number summary is: 59, 62, 65, 70, 77
To construct a box plot, we can draw a number line and mark the five-number summary points. We then draw a box from Q1 to Q3, with a line at the median (Q2) inside the box. Finally, we draw whiskers from the box to the minimum and maximum values, unless there are outliers that are more than 1.5 times the interquartile range (IQR) away from the box.
b. The interquartile range (IQR) is the difference between the upper and lower quartiles, or Q3 - Q1. From part (a), we have Q1 = 62 and Q3 = 70, so:
IQR = Q3 - Q1 = 70 - 62 = 8
Therefore, the IQR for the data is 8.
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Si seis conejos necesitan 10 sacos de comida a la semana, ¿cuántos sacos necesitarán nueve conejos para comer durante una semana?
Therefore, nine rabbits will need 7.5 sacks of food for one week.
What is unitary method?The unitary method is a mathematical technique that involves finding the value of a single unit to determine the value of a given number of units. It is a method of solving mathematical problems that involve proportional relationships between quantities. The unitary method is commonly used in various areas of mathematics, such as algebra, arithmetic, and geometry. It is also used in everyday life to solve problems related to money, time, distance, and other quantities.
Here,
To solve this problem, we can use proportionality. We know that the number of sacks of food needed is directly proportional to the number of rabbits.
Let x be the number of sacks needed for 9 rabbits. Then, we can set up the following proportion:
6/10 = 9/x
Cross-multiplying, we get:
6x = 90
Dividing both sides by 6, we get:
x = 15/2 or 7.5
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Complete question:
If six rabbits need 10 sacks of food per week, how many sacks will nine rabbits need to eat for one week?
PLEASE HELP DUE TODAY!!!
#of ice cream treats sold: Day 1=16, Day 2=19, Day 3=28, Day 4=27, Day 5=28, Day 6=36, Day 7=38, Day 8=41, Day 9=41, Day 10=48
#of coffee drinks sold: Day 1=55, Day 2=43, Day 3=51, Day 4=46, Day 5=32, Day 6=36, Day 7=43, Day 8=25, Day 9=10, Day 10=33
5. What is the slope of the line that best fits the data? Use mathematical reasoning and show work.
6. Interpret what the slope means in terms of the situation.
8. Write the equation of the line that best fits the data.
9. Using the equation of the line of best fit, estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold. Write an explanation that justifies your conclusion.
The slope of the line that best suits the data is -0.1463.
slope = [tex]\sum (( x -\bar x )( y - \bar y )) / \sum ( x - \bar x ) ^2[/tex]
where x is the number of ice cream treats sold, y is the number of coffee drinks sold, x bar is the mean of the number of ice cream treats sold, and ȳ is the mean of the number of coffee drinks sold.
Using the given data, we find that:
[tex]\bar x =[/tex] (16 + 19 + 28 + 27 + 28 + 36 + 38 + 41 + 41 + 48) / 10 = 32.2
[tex]\bar y =[/tex] (55 + 43 + 51 + 46 + 32 + 36 + 43 + 25 + 10 + 33) / 10 = 36.4
Next, we calculate the terms needed for the formula:
[tex]\sum (( x - \bar x )( y - \bar y ))[/tex] = (16 - 32.2)(55 - 36.4) + (19 - 32.2)(43 - 36.4) + ... + (48 - 32.2)(33 - 36.4) = -686.6
[tex]\sum ( x - \bar x )^2[/tex] = (16 - 32.2)² + (19 - 32.2)² + ... + (48 - 32.2)² = 4690.6
Plugging these values into the formula, we get:
slope = [tex]\sum (( x - \bar x )( y - \bar y )) / \sum ( x - \bar x )^2[/tex] = -686.6 / 4690.6 = -0.1463
Therefore, the slope of the line that best fits the data is -0.1463.
Interpreting the slope in terms of the situation, we can say that for every additional ice cream treat sold, the number of coffee drinks sold decreases by an average of 0.1463.
To write the equation of the line that best fits the data, we use the slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. We already know the value of m, so we just need to find b. To do this, we can use the mean values of x and y:
y = mx + b
36.4 = (-0.1463)(32.2) + b
b = 41.9
Therefore, the equation of the line that best fits the data is:
y = -0.1463x + 41.9
To estimate the number of coffee drinks sold on a day that 32 ice cream treats were sold using the equation of the line of best fit, we simply substitute x = 32 into the equation and solve for y:
y = -0.1463(32) + 41.9
y ≈ 36.9
So we can estimate that approximately 36.9 coffee drinks were sold on a day that 32 ice cream treats were sold. This conclusion is justified because we used the equation of the line that best fits the data to make the estimate, which takes into account the overall trend of the data and the relationship between the number of ice cream treats sold and the number of coffee drinks sold. However, it's important to note that this is only an estimate and there may be other factors that could affect the actual number of coffee drinks sold on a particular day.
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Please help!
this is for 10th grade, not college btw
Step-by-step explanation:
For RIGHT triangles sin (angle) = opposite LEG / hypotenuse
for this triangle sin (10) = 500/x
then x = 500 / sin (10°) = 2879.4 m Round as necessary
PLEASE HELP ASAP!!!!!
A bakery makes cylindrical mini muffins that measure 2 inches in diameter and one and one fourth inches in height. If each mini muffin is completely wrapped in paper, then at least how much paper is needed to wrap 6 mini muffins? Approximate using pi equals 22 over 7.
14 and 1 over 7 in2
23 and 4 over 7 in2
47 and 1 over 7 in2
84 and 6 over 7 in2
Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7 in².
Explain about the cylindrical shape:In geometry, a cylinder is just a three-dimensional shape. A cylinder is cylindrical in shape and has a circle-shaped top and bottom. The top and bottom are both flat and uniform in size. The shape of a cylinder is best described, in my opinion, by picturing a soup can.
Given data:
Height of cylindrical mini muffins 1 ¹/₄ = 5/4 in = 1.25 inDiameter d = 2 inRadius r = 2/2 = 1 in.surface area of 6 cylindrical mini muffins = 6*(π*r²*h)
= 6* (22/7 * 1² * 1.25)
= 23.55 in²
= 23 ⁴/₇ in²
Thus, the surface area of paper is needed to wrap 6 cylindrical mini muffins is 23 and 4 over 7 in².
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how was texas affected by opec’s restrictions on oil production in 1973
1. competition from opec countries meant fewer jobs in texas
2. higher oil prices brought wealth to the state
3. may texans returned to the rural areas
4. transportation industries became for profitable
After answering the provided question, we can conclude that the oil industry and related sectors were the primary direct beneficiaries.
what is expression ?An expression in mathematics is a collection of representations, octal, and huge corporations that resemble a clear association or regimen. A real number, a mutable, or a combination of the two can be used as an expression. Mathematical operators include inclusion, subtraction, rapid spread, division, and exponentiation. Expressions are widely used in arithmetic, mathematics, and shape. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.
Option 2 is the correct response. Texas benefited from OPEC's oil production restrictions in 1973 because it resulted in a significant increase in oil prices, which brought wealth to the state. At the time, Texas was the largest oil-producing state in the United States.
Option 1, 3, and 4 are incorrect. While OPEC's restrictions did increase competition from other countries, which could have affected employment in the oil industry, there is no evidence that it resulted in fewer jobs in Texas overall. Finally, while transportation industries may have benefited indirectly from the increase in oil prices, the oil industry and related sectors were the primary direct beneficiaries.
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Hi i dont rlly uinderstand the question where would it go??