Answer:
Ali will cover 1,080m altogether.
Step-by-step explanation
If the field is 80m by 100m and there are 2 sides of each of those measurements to make a whole round around the field, then one round would be (80m x 2) + (100m x 2) = 360. Since Ali wants to do three laps around the field, then you multiply 360 x 3 to get 1080m total.
Given the function: f(x) = 2| x−1 | − 3
• Fully explain the three transformations required to produce this function from the
parent function.
• Find at least 3 points on the function and show ALL of your work explaining how you
found the y-values. Use these three points to graph the function given.
To produce the function f(x) = 2| x−1 | − 3 from the parent function f(x) = |x|, three transformations are required.
Horizontal shift: The function is shifted horizontally by 1 unit to the right. This is done by subtracting 1 from the input value of the function. The transformation is f(x) → f(x − 1).
Vertical stretch: The function is vertically stretched by a factor of 2. This is done by multiplying the output value of the function by 2. The transformation is f(x) → 2f(x − 1).
Vertical shift: The function is vertically shifted down by 3 units. This is done by subtracting 3 from the output value of the function. The transformation is f(x) → 2f(x − 1) − 3.
To find points on the function, we can substitute different values of x into the function and calculate the corresponding y-values. For example:
When x = 0: f(0) = 2|0 − 1| − 3 = -5
When x = 1: f(1) = 2|1 − 1| − 3 = -3
When x = 2: f(2) = 2|2 − 1| − 3 = -1
Using these points, we can plot the graph of the function f(x) = 2| x−1 | − 3. The graph is a V-shaped curve with the vertex at (1,-3), opening upwards. The points we found above can be plotted on the graph as (-1,-5), (1,-3), and (2,-1).
For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1
(a) Option A, if its value is a large positive number, statistic A x2 provides strong evidence for the alternative hypothesis.
(b) Option B, the null hypothesis that gender is not related to personal goals and the alternative hypothesis that gender is related to personal goals.
(c) Option B, the variables considered in the chi-square test for the evaluation of contingency table B are categorical variables.
(a) If the x2 statistic is a large positive number, it provides strong evidence for the alternative hypothesis. The x2 statistic is used in hypothesis testing to determine if there is a significant difference between observed and expected frequencies. Large positive values indicate that the observed frequency is significantly different from the expected frequency, supporting the alternative hypothesis.
(b) The hypotheses tested in the chi-square test for the contingency table are the null hypothesis that gender is not related to personal goals and the alternative hypothesis that gender is related to personal goals. personal goals. This test determines whether there is a significant relationship between two categorical variables.
(c) The variables considered in the chi-square test used to evaluate the contingency table are categorical variables. These variables cannot be assumed to be mean or normally distributed. The chi-square test is used to analyze the relationship between two or more categorical variables, where each variable has a discrete set of categories.
Complete Question:
For each problem, select the best response (a) A x2 statistic provides strong evidence in favor of the alternative hypothesis if its value is A. a large positive number. OB. exactly 1.96 c. a large negative number. D. close to o E. close to 1. (b) A study was performed to examine the personal goals of children in elementary school. A random sample of students was selected and the sample was given a questionnaire regarding achieving personal goals. They were asked what they would most like to do at school: make good grades, be good at sports, or be popular. Each student's sex (boy or girl) was also recorded. If a contingency table for the data is evaluated with a chi-squared test, what are the hypotheses being tested? A. The null hypothesis that boys are more likely than girls to desire good grades vs. the alternative that girls are more likely than boys to desire good grades. OB. The null hypothesis that sex and personal goals are not related vs. the alternative hypothesis that sex and personal goals are related. C. The null hypothesis that there is no relationship between personal goals and sex vs. the alternative hypothesis that there is a positive, linear relationship. OD. The null hypothesis that the mean personal goal is the same for boys and girls vs. the alternative hypothesis is that the means differ. O E. None of the above. (C) The variables considered in a chi-squared test used to evaluate a contingency table A. are normally distributed. B. are categorical. C. can be averaged. OD. have small standard deviations. E. have rounding errors.
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Help me please I'm struggling
In this case, x and y are both 27 degrees.
If I'm understanding you correctly, we have a semicircle with a triangle DEF engraved on it.
Vertex D has a 90 degree angle.
You are informed that angles D = 27 degrees, E = y degrees, and F = x degrees. You need to locate x and y.
Angle D is 90 degrees because triangle DEF is encircled by a semicircle.
Angles E and F therefore sum up to 90 degrees. Also, we are aware that angle D = 27° 2.
Angles E and F are so equal at 63 degrees and 27 degrees, respectively.
Describe a semicircle?Half of a circle is a semicircle. It is a 2D shape that results from splitting a circle into two equal pieces. . A protractor, a circle folded in half, and other everyday objects are some instances of semicircles.
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The diameter of a circle is 5 ft. Find its area in terms of pi
Answer:
[tex]6.25\pi \: {ft}^{2} [/tex]
Step-by-step explanation:
Given:
d = 5 ft
Find: a (area) - ?
First, we have to find the radius (r) of the circle, which is half diameter:
r = 0,5 × d
r = 0,5 × 5 = 2,5 ft
Now we can find the area of the circle (a):
[tex]a = \pi \times {r}^{2} = \pi \times ( {2.5})^{2} = 6.25\pi \: {ft}^{2} [/tex]
Answer: The area of the circle is 19.625
Step-by-step explanation:
The formula for area of a circle is
[tex]A = \pi r^2[/tex]
We know that the diameter is 5 ft. The radius is half of the diameter, so we take 1/2 * 5 = 2.5
So the radius is 2.5
Now we will fill in the numbers for the formula
[tex]A = 3.14 * (2.5)^2[/tex]
or (3.14)(2.5)(2.5)
When we multiply all of the numbers, the area of the circle is 19.625
Use tangents to solve the problem
The value of AD of the triangle using trigonometric ratios is: 18.7
How to use trigonometric ratios?The sum of angles in a triangle is 180 degrees. Thus:
∠ABC = 180 - (41 + 35)
∠ABC = 104°
Using sine rule, we have:
AB/sin 35 = AC/sin 104
AB = (42 * sin 35)/(sin 104)
AB = 42 * 0.5911
AB = 24.826
Now, using trigonometric ratio:
AD/AB = cos 41
AD = 24.826 * 0.7547
AD = 18.7
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What is a higher theoretical probability?
Event 1: Rolling two 3's in a row using a six sided dice
Event 2: Drawing two red suited face-cards in a row from a deck of cards?
Group of answer choices
Event 1
Event 2
Both are equally likley
Answer:
Event 1 and Event 2 have different probabilities, and it is not possible to determine which one is higher without additional information.
Event 1 involves rolling a six-sided dice, which has six possible outcomes, each with an equal probability of 1/6. The probability of rolling a 3 on a single roll is 1/6. Therefore, the probability of rolling two 3's in a row is (1/6) x (1/6) = 1/36.
Event 2 involves drawing from a deck of 52 cards, which includes 26 red cards (13 of which are face cards). The probability of drawing a red suited face-card on the first draw is 26/52 x 4/13 = 2/13, since there are 26 red cards out of 52 total cards, and 4 face-cards out of 13 cards of each suit. On the second draw, there will be one less card in the deck, so the probability of drawing another red suited face-card will be 25/51 x 3/12 = 5/204. The probability of drawing two red suited face-cards in a row is therefore (2/13) x (5/204) = 5/663.
Comparing the two events, we see that the probability of Event 1 is higher than that of Event 2. Therefore, rolling two 3's in a row using a six sided dice is the event with the higher theoretical probability.
(Please could you kindly mark my answer as brainliest you could also follow me so that you could easily reach out to me for any other questions)
Which of the following is equivalent to the expression below? (x+y+2) (y+1)
Answer:
D is correct.
Step-by-step explanation:
[tex](x + y + 2)(y + 1)[/tex]
[tex] xy + x + {y}^{2} + y + 2y + 2[/tex]
[tex] {y}^{2} + xy + x + 3y + 2[/tex]
So D is the correct answer.
On a recent trip to Six Flags, Logan kept track of how much money he had remaining after. paying to go on rides. Some of his data is shown in the table. What is the rate of change of Logan's money remaining per ride paid for? Six Flags Money Remaining ($) Number of Rides Paid For 10 15 20 50 9 30 20 10
So, the rate of change of Logan's money remaining per ride paid for varies between -1/15 and -1/3, depending on the two rides that we choose to calculate the slope.
What is slope?In mathematics, slope refers to the steepness of a line or a curve. More specifically, it is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or curve.
The slope of a straight line can be found by dividing the change in the y-coordinates (vertical change) by the change in the x-coordinates (horizontal change) between any two points on the line. This is often represented by the symbol "m".
by the question.
To find the rate of change of Logan's money remaining per ride paid for, we need to calculate the slope of the line that represents the relationship between the number of rides paid for and the money remaining.
We can start by plotting the data points on a coordinate plane, where the x-axis represents the number of rides paid for and the y-axis represents the money remains.
(15, 10) (30, 9)
(20, 20) (50, 10)
We can see that the two points (15, 10) and (30, 9) represent the two rides where Logan had $10 and $9 remaining, respectively, and (20, 20) and (50, 10) represent the two rides where Logan had $20 and $10 remaining, respectively.
To calculate the slope of the line that passes through these points, we can use the formula:
[tex]slope = (y_2 - y_1) / (x_2 - x_1)[/tex]
where (x1, y1) and (x2, y2) are the coordinates of the two points.
Using the points (15, 10) and (30, 9), we get:
[tex]slope = (9 - 10) / (30 - 15) = -1/15[/tex]
Using the points (20, 20) and (50, 10), we get:
[tex]slope = (10 - 20) / (50 - 20) = -1/3[/tex]
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Which series of transformations shows that trapezoid E’F’G’H is similar to trapezoid EFGH? Assume all dilations are centered at the origin
The answer is option D: Reflect trapezoid EFGH across side HG, translate it three units up and four units to the right, and dilate it by a scale factor of 1/2.
Describe Scale Factor?In mathematics, a scale factor is a ratio that describes how the size or dimensions of an object change when it is scaled up or down. It is the ratio of the size or measurement of an original object to the size or measurement of a new object that has been scaled by a certain factor.
For example, if the length of an object is multiplied by a scale factor of 2, the new object will be twice as long as the original object. Similarly, if the area of an object is multiplied by a scale factor of 3, the new object will have three times the area of the original object.
To show that trapezoid E’F’G’H is similar to trapezoid EFGH, we need to apply a sequence of transformations that preserves shape and size.
First, we notice that trapezoid EFGH can be transformed into trapezoid E’F’G’H by a dilation centered at the origin with a scale factor of 1/4, followed by a translation 3 units to the right and 4 units up. So, we need to find the transformation that maps EFGH onto E’F’G’H.
Option B reflects trapezoid EFGH across side EF, translates it 5 units up and 8 units to the right, and dilates it by a scale factor of 1/2. This transformation does not preserve shape and size, so it cannot be the correct option.
Option A reflects trapezoid EFGH across side HG, translates it 8 units up and 5 units to the right, and dilates it by a scale factor of 2. This transformation does not preserve shape and size either, so it cannot be the correct option.
Option C reflects trapezoid EFGH across side EF, translates it 4 units up and 3 units to the right, and dilates it by a scale factor of 2. This transformation does not preserve shape and size, so it cannot be the correct option.
Option D reflects trapezoid EFGH across side HG, translates it 3 units up and 4 units to the right, and dilates it by a scale factor of 1/2. This transformation preserves shape and size, so it is the correct option.
Therefore, the answer is option D: Reflect trapezoid EFGH across side HG, translate it three units up and four units to the right, and dilate it by a scale factor of 1/2.
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Mark the false statement from the graph below:
a. Vertex is (4,4).
b. The vertex is a Maximum Point.
c. Axis of symmetry is y=4.
d. X-intercepts are (2,0) and (6,0).
The statement that is NOT true is (C) The axis of symmetry is y = 4.
i tried doing this but i still get it wrong... it says to find the exact value of x. an explanation please?
Using some trigonometric relations we can see that x = 6.72
How to find the value of x?Here we know that the larger triangle is completely defined, then we can find the angle at X using a trigonometric relation:
Sin(a) = opposite cathetus/hypotenuse
Sin(a) = 7/25
Using the inverse sine function:
a = Asin(7/25) = 16.26°
Now, notice that angle at X is also an angle of the triangle whose x is a side, then we can use the relation:
sin(16.26°) = opposite cathetus/hypotenuse.
This time:
opposite cathetus = x
hypotenuse = 24
Replacing that:
sin(16.26°) = x/24
x = 24*sin(16.26°) = 6.72
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I got sick last week and missed the lessons for this math, can anybody please help me with question 27?
The answer of the given question is (a) an additional 4 tiles are needed to surround the new perimeter. (b) No, Percy's expression for the number of tiles is not equivalent to 4(s + 1).
What is Expression?An expression in mathematics is a combination of numbers, variables, and operations that represents a quantity or a value. Expressions can be simple or complex, and they can be used to represent anything from a single number to a complex algebraic equation. These expressions represent a sum of two numbers, a product of a number and a variable, a difference of a number and a constant, and the square root of a number, respectively.
a. Percy's table shows the number of tiles needed to surround a square pool with sides of length 1, 2, 3, 4, and 5 feet. He has calculated that for a pool with a side length of s feet, the number of tiles needed is given by the equation N = 8 + 4(s-1). From his table, he sees that as the side length of the pool increases by 1 foot, the number of border tiles needed increases by 4. This makes sense since each side of the pool gains 1 foot in length, so an additional 4 tiles are needed to surround the new perimeter.
b. No, Percy's expression for the number of tiles is not equivalent to 4(s + 1). Percy's equation is N = 8 + 4(s-1), which simplifies to N = 4s + 4. Stella's equation is 4(s + 1), which also simplifies to 4s + 4. Therefore, two expressions are equivalent, and they both give number of tiles needed to surround square pool with sides of length s feet.
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The back-to-back stem-and-leaf plot shows the test scores for two classes taught by the same teacher. Compare the samples using measures of center and variation. Are the test scores significantly greater for one class than the other?
A) The median and mean for Class A are higher than those for Class B. They have equal IQRs of 70.
The median and mean for Class A are higher than those for Class B. They have equal IQRs of 70.
B) The median and mean for Class A are lower than those for Class B. They have equal IQRs of 15.
The median and mean for Class A are lower than those for Class B. They have equal IQRs of 15.
C) The median and mean for Class A are same for Class B. They have equal IQRs of 70.
The median and mean for Class A are same for Class B. They have equal IQRs of 70.
D) The median and mean for Class A are higher than those for Class B. They have equal IQRs of 15.
Please show work, I’m really struggling with this one.
Looking at the back to back stem and leaf plot for the test scores, we can tell that D) The median and mean for Class A are higher than those for Class B. They have equal IQRs of 15.
How to compare the back to back stem and leaf plots ?The mean of Class A can be found to be :
= ( 70 + 70 + 75 + 75 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90 + 90 + 95 + 95 + 95 + 95 + 95 + 95 + 100 + 100 + 100 ) / 22
= 92
The mean of Class B would be :
= ( 70 + 70 + 70 + 75 + 75 + 75 + 75 + 75 + 80+ 80 + 80 + 80 + 80 + 85 + 85 + 85 + 85 + 90 + 90+ 90 + 95 + 95 + 100 ) / 23
= 82
The mean of Class A is therefore larger than Class B. The IQR cannot be up to 70 given that the lowest value of 70 and the highest is 100 so the correct option is option D.
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A bag contains 8 whit balls, 5 green balls, 7 blue
balls, and 10 black balls. If a single ball is
picked at random from the bag, what is the probability
that the ball is either a black or a white ball?
I need help I got 3/5 but the choice on my paper show 2/15 1/11 9/32 5/18
Answer: [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
There is a total of 8 + 5 + 7 + 10 = 30 balls. There is 8 + 10 = 18 black or white balls. 18 / 30 simplifies to [tex]\frac{3}{5}[/tex].
assuming that the laptop replacement times have a mean of 3.9 years and a standard deviation of 0.4 years, find the probability that 34 randomly selec
The probability that the 39 randomly-selected laptops have a mean "replacement-time" as 3.8 years or less is equal to 0.1058.
The distribution of the sample mean follows a normal distribution with mean (μ) = 3.9 years and standard deviation = σ/√n = 0.5/√39 years, where n = 39 is the sample size.
We want to find the probability that the sample mean replacement time is less than or equal to 3.8 years, which is written as : P(x' ≤ 3.8).
By using the z-score formula, we convert this to a standard normal distribution:
⇒ z = (x' - μ)/(σ/√n) = (3.8 - 3.9)/(0.5/√39) = -1.249,
Using a standard normal distribution table, the probability that a standard normal variable is less than or equal to -1.249,is approximately 0.1058,
Therefore, the required probability is approximately 0.1058.
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The given question is incomplete, the complete question is
Assuming that the laptop replacement times have a mean of 3.9 years and a standard deviation of 0.5 years, find the probability that 39 randomly selected laptops will have a mean replacement time of 3.8 years or less.
The table shows the probability a pupil chosen at random studies Italian, French, Russian or German. Subject Italian French Russian German
Probability
Declan select a pupil from the list at random 100 times. Work out an estimate for the total number of times Declan will select a pupil that studies French
When Declan selects a pupil from the list at random 100 times, the estimation on the total number of times Declan selects a pupil who studies French is equal to 20 (times).
We have a table present above which shows the probability a pupil chosen at random studies Italian, French, Russian or German. Now, Declan randomly select a pupil from the list at 100 times. We have to estimate for the total number of times Declan will select a pupil that studies French. From the table, the probability to select a pupil who studies French = 0.2
So, Total number of times Declan will select a pupil that studies French
= 0.2 × 100
= 20 times
Hence, required estimation on total number of times is 20.
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Complete question:
The above table shows the probability a pupil chosen at random studies Italian, French, Russian or German.
Subject Italian French Russian German
Probability
Declan select a pupil from the list at random 100 times. Work out an estimate for the total number of times Declan will select a pupil that studies French
Erin and her friends went to a movie on Thursday afternoon. It took 50 minutes to drive to the theater. They arrived at the theater 50 minutes before the movie started. Once it started, the movie lasted for 1 hour and 30 minutes and ended at 4:30 P.M. What time did Erin and her friends leave for the movies?
Answer: 12:30 P.M.
Step-by-step explanation:
50 + 50 + 50 + 90 minutes = 240 minutes
240 divided by 60 = 4
4 hours before 4:30 P.M. = 12:30 P.M.
Answer should be 12:30 P.M.
Answer:
They left the house at 1:20 P.M.
Step-by-step explanation:
The movie was an 1 1/2 so 4:30 - 1:30 = 3:00
Thy got there 50 minutes before so 3:00 - 0:50 = 2:10
It took them 50 minutes to get there so 2:10 - 0:50 = 1:20
Therefore they left the house at 1:20 P.M.
slope intersect anyone know how to solve grapgh????????
Answer:
y=-2x+6
I determined this by first calculating the slope which turned out to be -2, and then i solved using slope intercept formula y=mx+b. Slope is -2 because i input the 2 points 0,6 and 3,0 into slope formula
Step-by-step explanation:
Brainliest maybe ? :)
Which of the following are roots of the polynomial function?
The roots f the following polynomial function F(x) = x3 - x2 - 5x - 3 are (A) -1 and (B) 3.
What is a polynomial function?In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
For instance, the polynomial 2x+5 has an exponent of 1.
f(x) = anxn + anxn+1 +... + a2x2 + a1x + a0 is the formula for a polynomial. The greatest power of x in an expression is the polynomial's degree.
Polynomials of degrees 0, 1, 2, 3, and 4 are constant (non-zero) polynomials, linear polynomials, quadratics, cubics, and quartics, respectively.
So, there is only one true, positive root, according to Descartes' rule of signs. On the list, 3 is the only real number that is positive.
When dividing x3-x2-5x-3 by (x-3), we may use synthetic division to get the quotient and discover that it is x2+2x+1, which we know as (x+1)2.
As a result, 3 is a root and -1 is a root with multiplicity 2.
A and B are the options that need to be checked.
Therefore, the roots f the following polynomial function F(x) = x3 - x2 - 5x - 3 are (A) -1 and (B) 3.
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Complete question:
Which of the following are the roots of the polynomial function? Check all that apply.
F(x) = x3 - x2 - 5x - 3
14. Use Appropriate Tools Select and use
one of the following tools to find the
area of the rectangle: circular counters,
square-inch tiles, or rulers.
1 in.
2 in.
15.
In order to find the area of the given rectangle, we can use square-inch tiles or rulers. the area of the rectangle is 30 square inches. The length of the rectangle is 15 inches, width is 2 inches then area of 30 square inches.
Using square-inch tiles:
We can cover the rectangle with square-inch tiles and count the total number of tiles to find the area. Each tile represents one square inch, and the area of the rectangle is equal to the number of tiles covering it. We can start by covering one side of the rectangle with tiles, and then count the number of tiles used. The length of the rectangle is 15 inches, so we need to use 15 tiles to cover one side. We can then cover the other side with the same number of tiles, which gives us a total of 30 tiles. Therefore, the area of the rectangle is 30 square inches.
Using a ruler:
We can measure the length and width of the rectangle using a ruler and then multiply the two measurements to find the area. The length of the rectangle is 15 inches, and the width is 2 inches. Multiplying these values gives us an area of 30 square inches.
Using circular counters:
Circular counters are not an appropriate tool to find the area of a rectangle because they are circular in shape and cannot cover the entire surface of the rectangle.
In conclusion, to find the area of a rectangle, we can use appropriate tools such as square-inch tiles or rulers. These tools allow us to accurately measure the length and width of the rectangle and calculate the area by counting or multiplying the measurements.
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Eight shirts and six pairs of pants cost $726. Nine shirts and seven pairs of pants cost $831. Write a system of equations for the problem , using x as the cost of a shirt and y as the cost of a pair of pants.
Answer:
Step-by-step explanation:
8x + 6y = 726
9x + 7y = 831
56x + 42y = 5082
-54x - 42y = -4986
2x = 95
x = 47.50 Shirt
47.50(8) + 6y = 726
380 + 6y = 726
6y = 346
y = 57.67 pants
Price decreased by 20% a suit £180 now for £150 is this claim correct give reason for answer
The claim that the price of a suit decreased by 20% from £180 to £150 is incorrect. The actual decrease in price is about 16.7%.
The claim that the price of a suit decreased by 20% is incorrect.
A 20% decrease in price would mean that the new price is equal to 80% of the original price. So, if we take 80% of £180, we get:
0.8 x £180 = £144
Therefore, if the price of the suit decreased by 20%, the new price should be £144, not £150.
This means that the claim is incorrect and the price of the suit actually decreased by about 16.7% (i.e. (£180 - £150) / £180 x 100%).
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i need help finding x and y for this equation i will give brainliest
Answer:
Step-by-step explanation:
y = x² -10x + 16
y = (x - 8) (x - 2)
solve each when y = 0
x - 8 = 0
x - 8 + 8 = 0 +8
x = 8
and
x - 2 = 0
x - 2 + 2 = 0 +2
x = 2
SO solutions are (8, 0) and (2, 0)
Create a proportion from each set of numbers ONLY use 4 numbers from each set:
1) 66, 99, 8, 11, 6, 88
2) 45, 14, 25, 35, 19, 10
3) 5, 48, 12, 18, 1, 4
4) 9, 45, 13, 75, 25, 5
5) 72, 9, 84, 12, 6, 54
The proportions from the sets of numbers are 66/11 = 6/1, 35/14 = 25/10, 48/12 = 4/1, 45/9 = 25/5 and 72/12 = 6/1
Creating Proportions from Sets of NumbersTo create a proportion from each set of numbers, we must select 4 numbers from each set and express them as a fraction in the form of a/b = c/d.
Here are the proportions for each set:
66/11 = 6/135/14 = 25/1048/12 = 4/145/9 = 25/572/12 = 6/1Note: To create a proportion, we must select numbers that are related to each other in some way, such as the sides of a shape or the parts of a ratio.
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Write the equation of a line passing through the points (2,4) and (6,16).
1. y = 1/3 x + 14
2. y = 3x - 2
3. y = 3x + 2
4. y = 1/3 x + 13/3
The equation of a line passing through the points (2,4) and (6,16) is
2) y=3x-2.
What is equation?
When the slope of the line being studied is known, and the provided point is also the y intercept, the slope intercept formula, y = mx + b, is utilised (0, b). It provides both a slope and an intercept, which is why the form is known as the slope-intercept form.
Here the given two points are [tex](x_1,y_1)=(2,4)[/tex] and [tex](x_2,y_2)=(6,16)[/tex] .
Now using slope formula then,
=> slope m= [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{16-4}{6-2} =\frac{12}{4} = 3[/tex]
Now using equation formula then [tex]y-y_1=m(x-x_1)[/tex]
=> y-4=3(x-2)
=> y-4 = 3x-6
=> y = 3x-6+4
=> y = 3x-2
Hence the equation is 2) y = 3x-2.
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an apartment complex rents an average of 2.3 new units per week. if the number of apartments rented each week has a poisson distribution, then the probability of renting exactly three apartments in a week is
The probability of renting exactly three apartments in a week using poisson distribution is 0.2107.
A Poisson distribution is a probability distribution that is used to evaluate how many times a particular event is likely to occur during a certain period of time.
The formula for calculating the probability of an event in a poisson distribution is as follows:
where e = 2.71828 (Euler's constant), x = the number of occurrences, μ = the expected value/average number of occurrences.In the given problem, the average number of new apartments rented per week is 2.3. Therefore,μ = 2.3Using the formula for Poisson distribution, we get:
P(3) = e^−2.3 * 2.3^3 / 3!
P(3) = 0.2107Therefore, the probability of renting exactly three apartments in a week is 0.2107.
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A right triangle has a base of 6 centimeters and the height is
9 centimeters. What is the area of this triangle?
Answer:
27 cm^2
Step-by-step explanation:
Area of a triangle is B * H / 2
6 * 9 / 2 = 27
point b is located at (4 -16). where is b after a dilation with a scale factor of 3/4?
Answer:
Step-by-step explanation:
b is now located at (3,-12)
The city wants to build a bike path around a rectangular park. The bike path will surround the park and have the same width all the way around. The park is 300 feet by 200 feet (as shown in the picture).
Write an expression for the dimensions of the combined park and bike path in terms of x below:
The expression for the dimensions of the combined park and bike path in terms of x is length= 200+2x ft and width = 300+ 2x ft.
What is expression?
Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. Unknown variables, integers, and arithmetic operators are the components of an algebraic expression. There are no symbols for equality or inequality in it.
Here the given rectangle park length is 200ft and width is 300 ft.
Now in the given diagram , path for bike is expended in both sides of the park.
Length of bike path = x + x = 2x
Width of bike path = x + x = 2x
Then combined dimensions for park and bike path is,
=> length = length of park+ length of path
=> length = 200+2x ft
=> width = width of park + width of bike path
=> width = 300+ 2x ft.
Hence the expression for the dimensions of the combined park and bike path in terms of x is length= 200+2x ft and width = 300+ 2x ft.
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the table shows the pipe material for a municipal water supply system, by type of pipe (submains are typically under sidewalks and connect mains to individual properties). pipe material pipe type asbestos cement (ac) galvanized iron (gi) polyvinyl chloride (pvc) total submain 411 1189 844 2444 main 4051 0 1248 5299 trunk 903 0 0 903 total 5365 1189 2092 8646 what is the probability a randomly selected pipe is: a. made of pvc? b. a trunk? c. a main made of galvanized iron (gi)? d. a submain made of asbestos cement (ac)? 2. consider the pipe data in problem
a. The probability that a randomly selected pipe is made of PVC is approximately 0.242 or 24.2%.
b. The probability that randomly selected pipe is a trunk is 0.104
c. The probability that randomly selected pipe is a main made of galvanized iron (gi) is 0
d. The probability that randomly selected pipe is a submain made of asbestos cement is 0.168
What is probability?
The chance of an event can be calculated using the probability formula by simply dividing the favorable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favorable number of outcomes can never exceed the total number of outcomes.
a. The total number of pipes is 8646, and the number of pipes made of PVC is 2092. The probability of a randomly selected pipe being made of PVC is:
P(PVC) = 2092/8646 ≈ 0.242
b. The total number of pipes is 8646, and the number of trunk pipes is 903. The probability of a randomly selected pipe being a trunk is:
P(trunk) = 903/8646 ≈ 0.104
c. The total number of main pipes is 5299, and the number of main pipes made of galvanized iron (GI) is 0 (according to the table). Therefore, the probability of a randomly selected main pipe being made of GI is:
P(GI|main) = 0/5299 = 0
Note that the vertical bar "|" means "given" or "conditioned on".
d. The total number of submain pipes is 2444, and the number of submain pipes made of asbestos cement (AC) is 411. Therefore, the probability of a randomly selected submain pipe being made of AC is:
P(AC|submain) = 411/2444 ≈ 0.168
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