Answers
The equation of the polynomial using finite difference is y = 18x^3 - 126x^2 + 269x - 163 and other solutions are shown below
Finding the equation of the polynomialTo find the equation of the polynomial table using finite difference, we need to calculate the differences.
The differences are obtained by subtracting each value of y from the next value of y and this is repeated for the differences
So, we have
x 1 2 3 4 5
y -2 15 -4 49 282
1st 17 -19 53 233
2nd -36 72 180
3rd 108 108
Since the third differences are all the same, this indicates that the original data can be represented by a cubic polynomial.
We can use the formula for a cubic polynomial:
y = ax^3 + bx^2 + cx + d
Using the table of values, we have:
a + b + c + d = -2
8a + 4b + 2c + d = 15
27a + 9b + 3c + d = -4
64a + 16b + 4c + d = 49
Using a graphing calculator, we have
a = 18, b = -126, c = 269 and d = -163
So, we have
y = 18x^3 - 126x^2 + 269x - 163
Equations of the cubic polynomialWe can use the formula for a cubic polynomial:
y = a(x - x1)(x - x2)(x - x3)
Using the ordered pairs, we have:
y = a(x + 3)(x + 1)(x - 2)
At (0, -12), we have
a(0 + 3)(0 + 1)(0 - 2) = -12
a = 2
So, we have
y = 2(x + 3)(x + 1)(x - 2)
Expand
y = 2x^3 + 4x^2 - 10x - 12
Equations of the cubic polynomialWe can use the formula for a cubic polynomial:
y = a(x - x1)(x - x2)(x - x3)
Using the ordered pairs, we have:
y = a(x + 10)(x + 5)(x - 4)
At (-8, -2), we have
a(-8 + 10)(-8 + 5)(-8 - 4) = -2
a = -1/36
So, we have
y = -1/36(x + 10)(x + 5)(x - 4)
Expand
[tex]y = -\frac{x^3}{36}-\frac{11x^2}{36}+\frac{10x}{36}+\frac{200}{36}[/tex]
The number of solutions in g(x)We have
g(x) = -9x^5 + 3x^4 + x^2 - 7
g(x) is a polynomial function of odd degree (5), so it will have at least one real root.
Also, the leading coefficient is negative;
So, g(x) has at least one root in the interval (-∞, ∞).
Since g(0) = -7 < 0 and g(1) = -12 < 0, and g(x) is continuous, there exists a root of g(x) in the interval (0, 1).
Similarly, since g(-1) = 6 > 0 and g(-2) = 333 > 0, there exists a root of g(x) in the interval (-2, -1).
Since g(x) is a polynomial of odd degree, it cannot have an even number of real roots.
Therefore, g(x) has exactly one real root.
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Related Questions
In the accompanying diagram, tangent PA and secant PBC are drawn to circle O from point P. If the measure of arc AC = 90° and the measure of arc AB = 26°, what is the m/P? plsss helps
Answers
The measure of angle P in the accompanying diagram is 0.072, when the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees. This is determined by using the formula for the measure of a central angle: M/P = (arc measure)/(360°).
What is angle?Angle is a measure of the amount of turn between two straight lines or planes that have a common point or line of intersection. It is usually measured in degrees, radians, or gradians. An angle can be measured in different ways, such as the angle between two lines, the angle between two planes, or the angle between two points. Angles are important in mathematics, engineering, and physics as they help describe the shape and size of objects.
Since the measure of arc AC is 90 degrees and the measure of arc AB is 26 degrees, we can use the formula for the measure of a central angle:
M/P = (arc measure)/(360°)
Therefore, the measure of angle P is:
M/P = (26°)/(360°) = 0.072
Therefore, the measure of angle P is 0.072.
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a student takes a true-false test that has 14 questions and guesses randomly at each answer. let x be the number of questions answered correctly. find p(5) group of answer choices 0.0001 0.0611 0.1833 0.1222
Answers
The probability to answer 5 questions correctly from 14 true or false questions is 0.1222
The given situation represents a binomial experiment, where there are only two possible outcomes for each trial: success (answering correctly) and failure (answering incorrectly). To find the probability of a particular number of successes, we use the binomial probability formula:
P(x)= nCx × p^x × q^(n-x)
Where, n is the total number of trials, p is the probability of success on each trial, q is the probability of failure on each trial (1-p), and x is the number of successes desired.
n = 14 (total number of questions)
p = 1/2 (probability of answering correctly when guessing randomly), and q = 1/2 (probability of answering incorrectly when guessing randomly).
To find P(5), we substitute these values in the formula
P(5) = 14C5 * (1/2)^5 * (1/2)^9= 2002 * (1/32) * (1/512)= 2002 / 16384≈ 0.1222
Therefore, the answer is option D, 0.1222.
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An online retailer receives 5% of the cost of all sales made on their website. How much does the retailer make on a sale of $80?
Answers
The online retailer will make $4 on a sale of $80. This is calculated by multiplying the cost of the sale ($80) by the retailer's percentage (5%).
The first step in calculating the retailer's profit is to identify the cost of the sale. In this case, the cost of the sale is $80.
The next step is to identify the percentage of the cost that the retailer will receive. In this case, the retailer will receive 5% of the cost of the sale.
The third step is to calculate the retailer's profit. This can be done by multiplying the cost of the sale ($80) by the retailer's percentage (5%). This calculation results in $4, which is the retailer's profit for this sale. Hence, the online retailer will make $4 on a sale of $80.
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Male and female students were surveyed about dancing and playing sports. They had the following preferences:
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.25 0.27 0.52
Female students 0.17 0.31 0.48
Column totals 0.42 0.58 1
Which of the following is a two-way conditional relative frequency table for gender?
Do you prefer dancing or playing sports?
Playing sports Dancing
Male students 0.60 0.47
Female students 0.40 0.53
Column totals 1 1
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 0.48 0.52 1
Female students 0.35 0.65 1
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 25% 27% 52%
Female students 17% 31% 48%
Column totals 42% 58% 100%
Do you prefer dancing or playing sports?
Playing sports Dancing Row totals
Male students 50 54 104
Female students 34 62 96
Column totals 84 116 200
Answers
The option that shows a two-way conditional frequency table is option B as shown in the image attached.
What is a two-way conditional frequency table?A two-way conditional frequency table is a type of table that shows the frequency determined by two variables. In this case, the variables are:
Gender.Preferred activity.Moreover, this table uses numbers from 0 to 1 to express frequency rather than percentages or numbers of people.
Which option is correct?The correct option is option B because it meets the following requirements:
It displays the two variables: gender and preferred activities.It uses frequency values such as 0.48 rather than percentages or the number of people, which would be incorrect.The row totals are displayed in a third column than in a new row.Which of the following are true statements about a 30-60-90 triangle?
Check all that apply.
A. The hypotenuse is 3 times as long as the longer leg.
B. The hypotenuse is twice as long as the longer leg.
C. The longer leg is twice as long as the shorter leg.
D. The longer leg is 3 times as long as the shorter leg.
E. The hypotenuse is twice as long as the shorter leg.
F. The hypotenuse is 3 times as long as the shorter leg.
Answers
Answer:
D. The longer leg is √3 times as long as the shorter leg.E. The hypotenuse is twice as long as the shorter leg.Step-by-step explanation:
You want to know which of the listed statements is true of a 30°-60°-90° triangle.
Side lengthsThe ratios of side lengths in a 30°-60°-90° triangle are 1 : √3 : 2.
This makes the following statements true:
D. The longer leg is √3 times as long as the shorter leg.E. The hypotenuse is twice as long as the shorter leg.Please help me answer the following question :)
Answers
Answer:
y = x - 1
Step-by-step explanation:
to determine the equation of the line we require to find the slope of the line and its y- intercept, where it crosses the y- axis.
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (1, 0) ← 2 points on the line
m = [tex]\frac{0-(-1)}{1-0}[/tex] = [tex]\frac{0+1}{1}[/tex] = [tex]\frac{1}{1}[/tex] = 1
the line crosses the y- axis at (0, - 1 ) ⇒ c = - 1
y = x - 1
Question 8 of 15
If a sample of 226 runners is taken from a population of 340 runners, the
population mean, u, is the mean of how many runners' times?
OA. 226
O B. 340
OC. Neither 226 nor 340
Answers
Therefore, the population mean, u, is the mean of 340 runners' times, regardless of the sample size. The correct answer is (B) 340.
What is mean?In mathematics and statistics, the mean is a measure of central tendency of a set of numerical data, which represents the average value of the data. It is commonly known as the arithmetic mean and is calculated by adding up all the values in the data set and then dividing by the number of values.
Here,
The population mean, u, is the mean of the times for all 340 runners in the population. If a sample of 226 runners is taken from the population, then the mean of the sample will be an estimate of the population mean. However, the population mean itself is not affected by the size of the sample.
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After giving 1/3 of his money to his wife and 1/4 of it to his mother, Jake still had $600 left. How much money did he give to his mother?
Answers
Let's start by setting up an equation to represent the problem.
Let's say Jake started with x amount of money.
After giving 1/3 to his wife, he has 2/3 left: (2/3)x
After giving 1/4 of that amount to his mother, he has $600 left: (1/4)(2/3)x = $600
We can solve for x by isolating it:
(1/4)(2/3)x = $600
Multiplying both sides by 12/2 gives:
(2/3)x = $3600
Dividing both sides by 2/3 gives:
x = $5400
So Jake started with $5400.
To find out how much he gave to his mother, we can take 1/4 of 2/3 of $5400:
(1/4)(2/3)($5400) = $900
So he gave his mother $900.
Step-by-step explanation:
x = original amount of money
the problem description tells us he gives 1/3 of his money to his wife and 1/4 of his money to his mother. and then he had still $600 left.
x - (1/3)x - (1/4)x = 600
so let's bring every fractional term to .../12.
12x/12 - (4/4)×(1/3)x - (3/3)×(1/4)x = 600
12x/12 - 4x/12 - 3x/12 = 600
5x/12 = 600
5x = 600×12
x = 600×12/5 = 120×12 = $1440
he gave to his mother
(1/4) × 1440 = $360
can yall pretty pls help me!!!!!!!!!!!!!!!
Answers
41
−
15
=
26
41
-
15
=
26
.
answer: 26
Find all polar coordinates of point P where P = (9 , -pi/5)
Answers
the polar coordinates of P are: (r, θ) = ([tex]\sqrt{(81 +\pi ^{2} /25)}[/tex], -0.3586 + 2πk) for all integers k. There are an infinite number of polar coordinates for P, corresponding to different values of k.
To express the point P = (9, -π/5) in polar coordinates, we need to find its distance from the origin and the angle it makes with the positive x-axis.
The distance from the origin to P can be found using the formula:
r = [tex]\sqrt{(x^2 + y^2)}[/tex]
where x and y are the Cartesian coordinates of the point. Substituting the values for P, we get:
r = [tex]\sqrt{9^2}[/tex]
The angle θ that P makes with the positive x-axis can be found using the formula:
θ = atan(y/x)
where atan is the arctangent function. Substituting the values for P, we get:
θ = atan((-π/5)/9) ≈ -0.3586 radians
Note that the angle is negative because the point is in the fourth quadrant.
Therefore, the polar coordinates of P are:
(r, θ) = ([tex]\sqrt{(81 +\pi ^{2} /25)}[/tex], -0.3586 + 2πk) for all integers k.
There are an infinite number of polar coordinates for P, corresponding to different values of k.
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a gift has the dimensions shown .what is the volume of the gift box? the length is 14 1/4 the width is 9 1/4 and the height is 1 7/8 write your answer as a mixed number in simplest form
Answers
To find the volume of the gift box, we need to multiply the length, width, and height together.First, let's convert all the dimensions to improper fractions:
Length: 14 1/4 = 57/4,
Width: 9 1/4 = 37/4,
Height: 1 7/8 = 15/8
Now we can multiply them together:
57/4 * 37/4 * 15/8 = 31,635/128
To write this as a mixed number in simplest form, we need to divide the numerator by the denominator and express the result as a mixed number:
31,635/128 = 247 with remainder of 19
So, the volume of the gift box is 247 19/128
7-31.
During a given week, the museum had attendance as shown in the table at right. Z-31 HW
eTool (CPM) Homework Help
a. Numerically summarize the center and spread of attendance by finding the median and
interquartile range (IQR).
b. The museum management needs to tell the staff members their work schedules a week in
advance. The museum wants to have approximately one staff member for every 150 visitors.
How many staff members should be scheduled to work each week? Explain your reasoning.
c. Why is a scatterplot not an appropriate display of this data?
Answers
a. The median attendance is 796, and the IQR is 229. b. the museum should schedule 37 staff members. c. A scatterplot is not an appropriate display of this data because it is not continuous data, but rather discrete data.
Describe interquartile range?The interquartile range (IQR) is a statistical measure that represents the spread or variability of a dataset. It is the difference between the first quartile (Q1) and the third quartile (Q3) of a dataset.
To find the interquartile range, the dataset is first arranged in order from smallest to largest. The median of the dataset is then found, and the data is split into two halves: the lower half, which contains all the data points less than or equal to the median, and the upper half, which contains all the data points greater than or equal to the median.
a. To find the median and interquartile range (IQR), we first need to arrange the attendance numbers in order from lowest to highest:
400, 593, 680, 731, 861, 870, 940
The median is the middle number, or the average of the two middle numbers. In this case, the median is:
Median = (731 + 861) / 2 = 796
To find the IQR, we need to find the first quartile (Q1) and the third quartile (Q3). Q1 is the median of the lower half of the data, and Q3 is the median of the upper half of the data. To find Q1, we take the median of the numbers below the median:
400, 593, 680, 731
Q1 = (593 + 680) / 2 = 636.5
To find Q3, we take the median of the numbers above the median:
861, 870, 940
Q3 = (870 + 861) / 2 = 865.5
The IQR is the difference between Q3 and Q1:
IQR = Q3 - Q1 = 865.5 - 636.5 = 229
Therefore, the median attendance is 796, and the IQR is 229.
b. To find the number of staff members needed each week, we divide the total attendance by 150:
(870 + 940 + 731 + 400 + 861 + 680 + 593) / 150 ≈ 36.54
Rounding up to the nearest whole number, we get 37 staff members. Therefore, the museum should schedule 37 staff members to work each week to meet their goal of having approximately one staff member for every 150 visitors.
c. A scatterplot is not an appropriate display of this data because it is not continuous data, but rather discrete data. Attendance is measured in whole numbers of visitors, and there are only 7 data points in this set. A scatterplot is typically used to display continuous data, where there are many data points and each data point can take on any value within a certain range. Instead, a bar chart or a histogram would be a more appropriate display for this data set.
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The complete question is:
During a given week, the museum had attendance as shown in the table at right. a. Numerically summarize the center and spread of attendance by finding the median and interquartile range (IQR). b. The museum management needs to tell the staff members their work schedules a week in advance. The museum wants to have approximately one staff member for every 150 visitors. How many staff members should be scheduled to work each week? Explain your reasoning. c. Why is a scatterplot not an appropriate display of this data?
Day Attendance
1 870
2 940
3 731
4 400
5 861
6 680
7 593
ΔGHJ ~ ΔKLM . The measure of ∠L is 75° and the measure of ∠G is 45°. What is the measure of ∠M?
Answers
Step-by-step explanation:
K = G = 45°
L = H = 75 °
M = J = 180° - 45 - 75 = 60° ( because three angles sum to 180 degrees)
A pet store sells puppies and kittens in the ratio 5:4.
If their sales of puppies and kittens combined came to 36, how many puppies did they sell?
Answers
Let us consider the ratio to be x
So, as per the question's statement, we can write it as;
[tex]5x+4x=36[/tex]
[tex]\implies 9x=36[/tex]
We will divide 9 on both the sides, we get;
[tex]\implies x=\dfrac{36}{9} =4[/tex]
So, for getting the number of puppy sold we have to multiply it with 5, we get:
[tex]5x=5\times4=20[/tex]
They have sold 20 puppies.
Hence, the answer is [tex]20[/tex] puppies.
How do you calculate a ratio?Divide data A by data B to find your ratio. In the example above, 5/10 = 0.5. Multiply by 100 if you want a percentage. If you want your ratio as a percentage, multiply the answer by 100.
How to simplify a ratio?Ratios can be fully simplified just like fractions. To simplify a ratio, divide all of the numbers in the ratio by the same number until they cannot be divided any more.
a researcher selects a sample and administers a treatment to the individuals in the sample. if the sample is used for a hypothesis test, what does the null hypothesis say about the treatment?
Answers
The null-hypothesis (H₀) in a two-tailed hypothesis test states that there is no significant difference between the treatment group and the control group, the correct option is (c)The treatment has no effect on scores.
The "Null-Hypothesis" assumes that any difference between the treatment group and control group is due to chance, and that treatment has no real effect on the outcome variable being measured.
The "Alternative-Hypothesis" (H₁) says that the treatment does have an effect on scores, but it does not specify whether the effect is positive or negative.
The null hypothesis is typically assumed to be true until there is sufficient evidence to reject it in favor of the alternative hypothesis.
Therefore, the correct option is (c).
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The given question is incomplete, the complete question is
A researcher selects a sample and administers a treatment to the individuals in the sample. If the sample is used for a two-tailed hypothesis test, what does the null hypothesis (H₀) say about the treatment?
(a) The treatment increases scores.
(b) The treatment causes a change in scores.
(c) The treatment has no effect on scores.
(d) The treatment adds a constant to each score.
(e) The treatment decreases scores.
Please show working out
Answers
Perimeter of quadrilateral: P = 20 m and Total area = 18 sq. m.
Explain about the quadrilaterals:Quadrilaterals have the following two qualities:
A closed quadrilateral should have four sides.A quadrilateral's internal angles add up to 360°.Using Pythagorean theorem in two given right triangles for finding the missing sides.
In triangle PQR
PR² = QR² + QP²
PR² = 8² + 1²
PR² = 64 + 1
PR = √65
Now,
In triangle PRS
PR² = PS² + RS²
PS² = PR² - RS²
PS² = 65 - 16
PS = 7
Perimeter of quadrilaterals:
P = sum of all exterior sides
P = 8 + 1 + 4 + 7
P = 20 m
Total area = area of triangle PQR + area of triangle PRS
Total area = 1/2 *QR*PQ + 1/2 * PS *SR
Total area = 1/2*8*1 + 1/2*7*4
Total area = 18 sq. m
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Un florero con forma cilíndrica tiene un diámetro interior de 12cm y su altura es de 25cm. Queremos llenarlo hasta los 2/3 de su capacidad. ¿Cuántos litros de agua necesitamos?
Answers
We need 3 liters of water to fill the cylinder up to 2/3 of its capacity.
The formula for the volume of a cylinder is V=π r2 h, where V is the volume, π is pi, r is the radius and h is the height. The radius of the cylinder is half of the diameter, so the radius of this cylinder is 6 cm, and the height is 25 cm. Applying the formula, the volume of the cylinder is V=π[tex]*6^2*25[/tex]
=4500π cm3.
To fill it up to 2/3 of its capacity, we need 3000π cm3 of water. To convert this to liters, we need to divide by 1000, so the answer is 3000π/1000=3 liters of water.
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A seed sprouted and grew
2
3
of a foot in 3 months. What was its rate of growth?
Simplify your answer and write it as a proper fraction, mixed number, or whole number.
feet per month
Answers
After calculation, we know that rate of growth of the seed is 2/9 feet in 1 month which is in proper fraction.
What is the rate of growth?Take the current number and subtract it from the prior value to determine the growth rate.
The growth rate is then expressed as a percentage by multiplying the difference by the previous number and dividing by 100.
The three types of growth identified by the Harrod-Domar model are warranted growth, real growth, and the natural rate of growth.
The economy cannot continue to develop at this rate indefinitely or without experiencing a downturn, which is known as the warranted growth rate.
The annual increase in a country's real GDP rate is known as actual growth.
So, we know that the seed grows:
2/3 foot in 3 months
Then, the rate of growth in 1 month was:
= 2/3 ÷ 3
= 2/3 ÷ 3/1
= 2/3 * 1/3
= 2/9 foot
Therefore, after calculation, we know that rate of growth of the seed is 2/9 feet in 1 month which is in proper fraction.
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The given point P is located on the unit circle. P[24/25, 7/25}
Answers
Answer:
Yes
Step-by-step explanation:
Unit circle is the circle whose center is at origin (0, 0) and radius r = 1 unit.
equation of this circle is,
[tex]x^2 + y^2 = 1[/tex]
point P(24/25, 7/25) lies on the above curve (substitute and check).
therefore point P lies on unit circle.
Hopefully this answer have helped you!
For numbers 5 - 6, fill in the boxes for the area method, and then put a check mark next to the correct answer.
(5 points per question: 1 point for each blank and 1 point for the correct answer). 5. Fill in the blanks within the area model for (4a - 2b)(12a + 6b) and then put a check next to the answer after simplifying (combining like terms).
4a
Answers
Answer: 12a + 6b
-2b
-8ab
Check: 48a^2 - 24b^2
Step-by-step explanation:
divide polynomials by a binomial (x² + 2x ÷ 1) ÷ (x + 1)
Answers
[tex]X+1-\frac{2}{x+1}[/tex]
Step-by-step explanation:
when we use the way like this because the 2 was left by it own at the end so we need to do like this, by we cannot divide it by x
steps for long division :Long division can also be used to divide decimal numbers into equal groups. It follows the same steps as that of long division, namely, – divide, multiply, subtract, bring down and repeat or find the remainder.
8x+3y=-7 7x+2y=-3 solve by using elimination
Answers
Using elimination, the solution to the system of linear equations is x = -16/29 and y = -75/87.
What is a linear equation, exactly?
A linear equation is a mathematical equation that describes a straight line in a two-dimensional space. It is an algebraic equation that can be written in the form y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept.
Now,
To solve the system of equations 8x + 3y = -7 and 7x + 2y = -3 using elimination, we need to eliminate one of the variables by adding or subtracting the two equations.
One way to do this is to multiply the second equation by a suitable constant so that the coefficient of one of the variables is the negative of the corresponding coefficient in the first equation. In this case, if we multiply the second equation by 3, we can eliminate y by adding the resulting equation to the first equation:
8x + 3y = -7
(3)(7x + 2y = -3) -> 21x + 6y = -9
Adding the two equations, we get:
29x + 0y = -16
Simplifying, we get:
x = -16/29
Now, we can substitute this value of x into either of the original equations to solve for y. Let's use the first equation:
8x + 3y = -7
Substituting x = -16/29, we get:
8(-16/29) + 3y = -7
Simplifying, we get:
-128/29 + 3y = -7
Multiplying both sides by 29, we get:
-128 + 87y = -203
Solving for y, we get:
y = -75/87
Therefore, the solution to the system of equations is x = -16/29 and y = -75/87.
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what is the range of the function y= 2x + 3 when the domain is {-3, -1, 1}?
Answers
Answer:
Step-by-step explanation:
domain = x
range = y
when the domain is -1
y = 2(-1) - 3
y = -2 - 3
y = -5
range is -5
When the domain is 0
y = 2(0) - 3
y = 0 - 3
y = -3
range is -3
when the domain is 5
y = 2(5) - 3
y = 10 - 3
y = 7
range is 7
The range is { -5, -3, 7 }
the city council has 6 men and 3 women. if we randomly choose two of them to co-chair a committee, what is the probability these chairpersons are the same gender? select the correct fractional response. hint: consider there is no replacement of an individual who is already selected.
Answers
The probability that the two chairpersons chosen are of the same gender is 9/36.
Probability is a branch of mathematics that deals with the study of random events and their outcomes. It involves quantifying the likelihood of an event or outcome by assigning a numerical value between 0 and 1.
A probability of 0 means that the event is impossible, while a probability of 1 means that the event is certain.
Probabilities between 0 and 1 indicate the likelihood of the event occurring, with higher probabilities indicating a greater likelihood.
This can be calculated by looking at the number of possibilities when selecting two members from a group of nine (6 men, 3 women):
Total possibilities = 9C2 = 9!/(2!*7!) = 9*8/2 = 36
Ways of selecting two of the same gender = 6C2 + 3C2 = 6*5/2 + 3*2/2 = 15
Therefore, the probability of selecting two of the same gender is 15/36, which reduces to 9/36.
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I and m are in direct proportion.
The equation of proportionality is = = 9m.
If m increases from 4 to 7, how much will
increase by?
If your answer is a decimal, give it to 1 d.p.
Answers
Since I and m are in direct proportion, we can write:
I = km
where k is the constant of proportionality.
From the given equation of proportionality, we have:
I/m = 9
Multiplying both sides by m, we get:
I = 9m
So, the constant of proportionality is k = 9.
If m increases from 4 to 7, then we can find the increase in I as follows:
ΔI = I2 - I1
where I1 is the initial value of I when m = 4, and I2 is the final value of I when m = 7.
From the equation of proportionality, we have:
I1 = km1 = 9(4) = 36
I2 = km2 = 9(7) = 63
Therefore, the increase in I is:
ΔI = I2 - I1 = 63 - 36 = 27
So, if m increases from 4 to 7, then I increases by 27.
Three people Sagar, Basanta and Krishna are walking on the two edges of a straight road of 6 m width. Their position on a fixed time is found to be S(4, 6), B(6,-2) and K(4, 2). Find the equation of Basanta's walking route.
Answers
The equation of Basanta's walking route is: y = -2x + 10
How to find the equation of Basanta's walking routeWe can find the equation of Basanta's walking route by using the slope-intercept form of a linear equation:
y = mx + b
where m is the slope of the line and
b is the y-intercept.
To find the slope of Basanta's walking route, we can use the coordinates of two points on the line, namely B(6, -2) and K(4, 2):
slope = (y2 - y1) / (x2 - x1)
= (2 - (-2)) / (4 - 6)
= 4 / (-2)
= -2
To find the y-intercept, we can use the coordinates of one of the points on the line, for example, B(6, -2):
y = mx + b
-2 = (-2)(6) + b
-2 = -12 + b
b = 10
Therefore, the equation of Basanta's walking route is: y = -2x + 10
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how many gallons of pure acid should be added to 480 gallons of 22% acid solution to produce a solution that is 36%?
Answers
To produce 36% solution, 50 gallons of pure acid should be added to 480 gallons of 22% acid solution.
To solve the problem find out how many gallons of acid are there in the 22% solution
480*0.22= 105.6
Let the amount of pure acid required to produce 36% solution be x gallons.
So, the total amount of acid in the new solution will be
480 + x.
Write the equation for concentration:
(Total acid in the new solution)/ (Total volume of new solution) = 36/100
Using the above equation, we get;
[105.6+x]/[480+x] = 36/100
Cross multiply and simplify, we get;
3600 + 100x = 423.6 + 36x63.6x
= 3176.4x
= 3176.4/63.6x
x = 50
Therefore, the amount of pure acid required to produce 36% solution is 50 gallons.
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I need help, please say the right answers!
A. Define variables and write an equation to represent the relationship between the quantities.
B. How far would the biker travel in 20 minutes?
C. If the biker traveled 48 miles, how many minutes did he bike? Round to the nearest tenth.
Answers
A. The equation d = s * t shows relationship between the quantities.
B. They would cover a distance of 10 miles in 20 minutes.
C. Rounded to the nearest tenth, the biker would bike for 96.0 minutes.
What is distance?
Distance is the measure of the physical space between two objects or points. It is a scalar quantity that is usually measured in units such as meters, kilometers, miles, etc. In physics, distance is considered to be a fundamental concept and is often used in conjunction with time to calculate other physical quantities, such as speed and acceleration.
a. We can define the following variables:
t: time in minutes
d: distance traveled by the biker in miles
s: speed of the biker in miles per minute
Using these variables, we can write the equation d = s * t to represent the relationship between them.
b. If the biker rides for 20 minutes, we can use the equation d = s * t to find the distance traveled. Assuming the biker's speed is 0.5 miles per minute, we get:
d = 0.5 * 20 = 10 miles
Therefore, the biker would travel 10 miles in 20 minutes.
c. If the biker traveled 48 miles, we can use the equation t = d / s to find the time taken, where s is again assumed to be 0.5 miles per minute:
t = 48 / 0.5 = 96 minutes
Rounded to the nearest tenth, the biker would have ridden for 96.0 minutes to cover 48 miles.
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Factor please!
2x² + x - 21
Answers
Answer: (x-3)(2x+7)
Step-by-step explanation:
Answer:
(2x + 7 )(x - 3)
Step-by-step explanation:
You can find the original expression by using the box method on the factors.
What is the value of x in the equation ½ x- Zy = 30, when y = 152
Answers
1/2 x = Zy + 30
Substituting y = 152, we get:
1/2 x = Z(152) + 30
Multiplying both sides by 2, we get:
x = 2Z(152) + 60
So the value of x depends on the value of Z.