Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
A. 40m^6 -4=4(10m^6-1) is not true.
B. 32m^4 +12m^3 =4m^3(8m +3) is not true.
Answer:
C. 15m^3-6m=3m(5m^2 -6m) is true.
D. 6m^2+18m=6m^2(1+3m) is true.
Step-by-step explanation:
Suppose a tank of water is a cylinder. The tank has a diameter of 14 inches and is filled
to a height of 9 inches. A fish tank decoration is placed in the tank and the water rises
by 2 inches with the decoration being completely covered by water. Find the volume of
the decoration to the nearest tenth of a cubic inch.
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
what is volume ?The quantity of space that an object or substance occupies is measured by its volume. Usually, it is expressed in cubic measures like cubic metres, cubic feet, or cubic inches. By multiplying an object's length, width, and height, or by applying a formula unique to the shape of the object, one can determine the volume of the object.
given
The cylinder's radius is equal to half of its diameter, or 14/2, or 7 inches. The new water level is 9 + 2 = 11 inches because the initial water level was 9 inches and the decoration raised the water level by 2 inches.
The decoration's volume is equivalent to the volume of water it removed from the area.
We can determine the volume of the ornamentation by using the following formula: V = r2h.
V = (72/2), which equals 98 cubic inches.
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
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Complete the following activity by identifying the location of the muscles, bones, and sensory organs.
Part One
1. Label each of the following body parts on the two pictures below: muscles, bones, and sensory
organs.
2. In the space provided, describe the function of each body part you labeled.
Name: Date:
Lesson 13.04: Building Muscles
Lesson Assessment: Building Muscles
Muscles:
Bones:
Sensory organs:
Muscles:
Part Two
In the space provided, describe how the bones, muscles, and sensory organs all work together.
I can give you with a general explanation of the functions of muscles, bones, and sensitive organs, as well as how they work together.
Muscles are responsible for movement and give the force needed to move bones. They're attached to bones via tendons and work in dyads or groups to produce coordinated movement. Muscles are also responsible for maintaining posture and generating heat.
Bones give a rigid frame for the body, cover internal organs, and serve as attachment points for muscles. They also store minerals similar as calcium and produce blood cells in the bone gist.
sensitive organs, similar as the eyes, cognizance, nose, and skin, descry and respond to stimulants in the terrain. They transmit information to the brain, which processes the information and generates an applicable response.
All three body corridor work together in the musculoskeletal system to produce movement, maintain posture, and respond to external stimulants. Muscles attach to bones and work together to produce coordinated movement. sensitive organs descry stimulants in the terrain and transmit information to the brain, which coordinates muscle movement and generates a response. Bones give the rigid frame and attachment points for muscles, as well as cover internal organs.
The general form of the equation of a circle is x2 y2 8x 22y 37 = 0. the equation of this circle in standard form is (x )2 (y )2 = . the center of the circle is at the point ( , ).
The centre οf the circle is (-4, -11).
What is a circle's general equatiοn?We knοw that the general equatiοn fοr a circle is (x - h)² + (y - k)² = r² with (h, k) representing the centre and r representing the radius. Sο multiply bοth sides by 21 tο get the cοnstant term οn the right side οf the equatiοn. Then, fοr the y terms, cοmplete the square.
Tο write a circle equatiοn in standard fοrm, we must cοmplete the square fοr bοth x and y.
Tο begin, cοnsider the fοllοwing equatiοn: x²+ y² + 8x + 22y + 37 = 0.
Let's separate the terms with x frοm the terms with y:
[tex](x^2 + 8x) + (y^2 + 22y) + 37 = 0[/tex]
We add (8/2)² = 16 tο bοth sides tο cοmplete the square fοr x: (x²+ 8x + 16) + (y² + 22y) + 37 = 16
Simplifying the left side οf the equatiοn and cοmbining cοnstants οn the right:
[tex](x + 4)^2 + (y^2 + 22y + 121) = 16 - 37 - 121\s(x + 4)^2 + (y + 11)^2 = 50[/tex]
The equatiοn can nοw be written in standard fοrm:
[tex](x + 4)^2/50 + (y + 11)^2/50 = 1[/tex]
The circle's centre is (-4, -11).
As a result, the standard fοrm οf the circle's equatiοn is (x + 4)²/50 + (y + 11)²/50 = 1, and the circle's centre is (-4, -11).
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The graph of f(t) = 7•2^t shows the value of a rare coin in year t. What is the meaning of the y-intercept?
Answer:
When it was purchased (year 0) the coin was worth $7
Step-by-step explanation:
we have
[tex]f(t) = 7(2)^t[/tex]
This is a exponential function of the form
[tex]y=a(b)^x[/tex]
where
a is the initial value
b is the base
In this problem we have
[tex]a=\$7[/tex]
[tex]b=2[/tex]
[tex]b=1+r[/tex]
so
[tex]2=1+r[/tex]
[tex]r=1[/tex]
[tex]r=100\%[/tex]
The y-intercept is the value of the function when the value of x is equal to zero
In this problem
The y-intercept is the value of a rare coin when the year t is equal to zero
[tex]f(0)=7(2)^0[/tex]
[tex]f(0)=\$7[/tex]
therefore
The meaning of y-intercept is
When it was purchased (year 0) the coin was worth $7
Answer:
Value of the coin when it was first released
-------------------------------
The y-intercept is the value of f(0).
Substitute t = 0 and find the y-intercept:
f(0) = 7 · 2⁰ = 7 · 1 = 7This is representing the value of the coin when it was released.
The expression tan(0) cos(0) simplifies to sin(0) . Prove it
Help asap please
Solve equation for x
216=6^4x+5
Answer: x=211/1296
Step-by-step explanation:
A manufacturer of paper used for packaging requires a minimum strength of 1400 g/cm2. To check on the quality of the paper, a random sample of 10 pieces of paper is selected each hour from the previous hour’s production and a strength measurement is recorded for each. The standard deviation of the strength measurements, computed by pooling the sum of squares of deviations of many samples, is known to equal 140 g/cm2, and the strength measurements are normally
distributed.
a) What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?
b) If the mean of the population of strength measurements is 1450 g/cm2, what is the
approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400?
The sample mean is 1450g/cm², the standard deviation is 44.3 g/cm² and the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2 is 0.8708
What is the approximate sampling distribution of the sample mean of n = 10 test pieces of paper?a) The sampling distribution of the sample mean of n = 10 test pieces of paper is approximately normal with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size:
mean of sample mean = mean of population = 1450 g/cm²
standard deviation of sample mean = standard deviation of population / square root of sample size
= 140 g/cm2 / √(10)
= 44.3 g/cm²
Therefore, the sampling distribution of the sample mean is approximately normal with mean 1450 g/cm2 and standard deviation 44.3 g/cm2.
b) To find the probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm2, we need to standardize the sample mean using the sampling distribution calculated in part (a):
z = (x - mean of sample mean) / standard deviation of sample mean
= (1400 - 1450) / 44.3
= -1.13
Using a standard normal distribution table or calculator, we can find the probability that z is less than -1.13 and subtract that probability from 1 to find the probability that z is greater than -1.13:
P(z > -1.13) = 1 - P(z < -1.13)
= 1 - 0.1292
= 0.8708
Therefore, the approximate probability that, for a random sample of n = 10 test pieces of paper, x is greater than 1400 g/cm² is 0.8708.
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a committee of 7 members is to be chosen from 6 artists, 4 singers and 5 writers. in how many ways can this be done if in the committee there must be at least one member from each group and at least 3 artists ?
There are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.
Here, we have to solve this problem, we can use the concept of combinations, which involves counting the ways to choose a specific number of items from a larger set without regard to the order of selection.
Given the conditions that at least one member must be chosen from each group (artists, singers, writers) and there must be at least 3 artists, we can break down the problem into cases.
Case 1: Choosing 1 artist, 1 singer, and 5 members from the remaining groups (writers).
Case 2: Choosing 2 artists, 1 singer, and 4 members from the remaining groups (writers).
Case 3: Choosing 3 artists, 1 singer, and 3 members from the remaining groups (writers).
For each case, we will calculate the number of ways to choose members and then sum up the results from all three cases to get the total number of ways.
Let's calculate the number of ways for each case:
Case 1:
Number of ways to choose 1 artist: 6C1 (6 ways)
Number of ways to choose 1 singer: 4C1 (4 ways)
Number of ways to choose 5 writers: 5C5 (1 way)
Total ways for case 1: 6C1 * 4C1 * 5C5 = 6 * 4 * 1 = 24
Case 2:
Number of ways to choose 2 artists: 6C2 (15 ways)
Number of ways to choose 1 singer: 4C1 (4 ways)
Number of ways to choose 4 writers: 5C4 (5 ways)
Total ways for case 2: 6C2 * 4C1 * 5C4 = 15 * 4 * 5 = 300
Case 3:
Number of ways to choose 3 artists: 6C3 (20 ways)
Number of ways to choose 1 singer: 4C1 (4 ways)
Number of ways to choose 3 writers: 5C3 (10 ways)
Total ways for case 3: 6C3 * 4C1 * 5C3 = 20 * 4 * 10 = 800
Now, add up the total ways from all three cases:
Total ways = 24 + 300 + 800 = 1124
So, there are 1124 ways to choose a committee of 7 members with at least one member from each group and at least 3 artists.
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A triangle has an area of 42 cm. The height of the triangle is 14 centimeters. What is the length of the base of the triangle?
How do I solve this?
Answer:
X+4
Step-by-step explanation:
Area = l *b
x^2 + 13x + 36 = (X+9) * b
x^2 + 9x + 4x + 36 = (X+9) * b
X(X+9) + 4(X+9) = (X+9) * b
(X+4) (X+9) = (X+9) * b
b = (X+4)
What is an equation of the line that passes through the point (5,1) and is parallel to
the line x +y = 9?
The line x + y = 9 is y = -x + 6 is keeps through the point (5,1).
To find the equation of the line that passes through the point (5,1) and is parallel to the line x + y = 9, we need to first find the slope of the line x + y = 9.
Rearranging the equation in slope-intercept form, we get y = -x + 9
The slope of this line is -1, since the coefficient of x is -1.
Since the line we want to find is parallel to this line, it will have the same slope of -1.
Using the point-slope form of a line, the equation of the line passing through the point (5,1) and with a slope of -1 is: y - 1 = -1(x - 5)
Simplifying and rearranging the equation, we get:
y - 1 = -x + 5
y = -x + 6
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Can anyone solve this ???
The result (recurrent value), A = sum j=1 to 89 ln(j), is true for every n. This is the desired result.
How do you depict a relationship of recurrence?As in T(n) = T(n/2) + n, T(0) = T(1) = 1, a recurrence or recurrence relation specifies an infinite sequence by explaining how to calculate the nth element of the sequence given the values of smaller members.
We can start by proving the base case in order to demonstrate the first portion through recurrence. Let n = 1. Next, we have:
Being true, ln(a1) = ln(a1). If n = k, let's suppose the formula is accurate:
Sum j=1 to k ln = ln(prod j=1 to k aj) (aj)
Prod j=1 to k aj * ak+1 = ln(prod j=1 to k+1 aj)
(Using the logarithmic scale) = ln(prod j=1 to k aj) + ln(ak+1)
Using the inductive hypothesis, the property ln(ab) = ln(a) + ln(b)) = sum j=1 to k ln(aj) + ln(ak+1) = sum j=1 to k+1 ln (aj)
(b), we can use the just-proven formula:
A = ln(1, 2,...) + ln + ln (89)
= ln(j=1 to 89) prod
sum j=1 to 89 ln = ln(prod j=1 to 89 j) (j).
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use the slicing method to find the volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles.
The volume of the solid whose base is the region inside the circle with radius 3 if the cross sections taken parallel to one of the diameters are equilateral triangles is 81/2*\sqrt3 by using the slicing method.
To find the volume of the solid whose base is the region inside the circle with radius 3, we need to integrate the area of the cross sections taken parallel to one of the diameters, which are equilateral triangles.
Let's consider a cross section of the solid taken at a distance x from the center of the circle.
Since the cross section is an equilateral triangle, all its sides have the same length.
Let this length be y. Since the triangle is equilateral, its height can be found using the Pythagorean theorem as follows:
[tex]height = \sqrt{(y^2 - (y/2)^2)} = \sqrt{(3/4y^2)}= \sqrt{3/2y}[/tex]
Therefore, the area of the cross section at a distance x from the center of the circle is:
[tex]A(x) = (1/2)y\sqrt{3/2y} = \sqrt{3/4y^2}[/tex]
Now, we need to integrate this area over the range of x from -3 to 3 (since the circle has radius 3):
[tex]V = \int\ [-3,3]\sqrt{3/4*y^2} dx[/tex]
To find the limits of integration for y, we need to consider the equation of the circle:
[tex]x^2 + y^2= 3^2[/tex]
Solving for y, we get:
[tex]y =\pm\sqrt{(3^2 - x^2)}=\pm\sqrt{(9^2 - x^2)}[/tex]
Since we want the cross sections to be equilateral triangles, we know that y is equal to the height of an equilateral triangle with side length equal to the diameter of the circle, which is 2*3 = 6. Therefore, we can write:
[tex]y = 3*\sqrt{3}[/tex]
Substituting this into the integral, we get:
[tex]V = \int\ [-3,3] \sqrt{3/4*(3\sqrt3)^2} dx[/tex]
[tex]= \int\ [-3,3] 27/4*\sqrt{3} dx[/tex]
Integrating, we get:
[tex]V = [27/4\sqrt{3x}]*[-3,3][/tex]
[tex]= 81/2*\sqrt{3}[/tex]
Therefore, the volume of the solid is [tex]81/2*\sqrt3[/tex]cubic units
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x cos y = 1, (2, pi/3), Find the derivative.
The derivative of the implicit function x · cos y = 1 at point (2, π / 3) is equal to y' = √3 / 6.
How to find the derivative of a function by implicit differentiation
In this problem we find the case of a implicit function of the form f(x, y), whose derivative must be found. This can be done by implicite differentiation, whose procedure is shown:
Derive the function by derivative rules.Clear y' within the resulting expression. Substitute x and y.Step 1 - Derive the expression by derivative rules:
cos y - x · sin y · y' = 0
Step 2 - Clear y' within the expression:
y' = cos y / (x · sin y)
Step 3 - Clear x and y in the resulting expression:
y' = cos (π / 3) / [2 · sin (π / 3)]
y' = 1 / [2 · tan (π / 3)]
y' = √3 / 6
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a class has a ratio of boys to girls of 3:4 for each statement below
The correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.
Explain about the ratio of the number?Irrespective whatever how a ratio is expressed, it is crucial to reduce it to the fewest whole numbers, just like with any fraction. To accomplish this, divide the integers by their largest common factor after discovering it.
Ratios can also be expressed as a fraction because they are straightforward division problems. Some folks prefer to use merely words to express ratios.
Class contains a ratio of boys to girls of 3: 4.
So, Boys / Girl = 3 / 4
Total students = boys + girls.
Total students = 3 + 4 = 7
So,
Girl / Total = 4/7
Thus, the correct statement explain for the given ratio of boys to girls of 3:4 is - this fraction of girls in the class is found to be 4/7.
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The complete question is-
A class has a ratio of boys to girls 3:4.
Select correct option:
a) The fraction of boys in the class is 3/4
b) The fraction of girls in the class is 4/7
c) The number of boys in the class is 6
d) The number of pupils in the class is 12
Give the coordinates for the translation of Rhombus ABCD with vertices A(-3,-2), B(0, 3),
C(5, 6), and D(2, 1).
Given the rule (x, y) = (x+2, y-6)
The new position of Rhombus ABCD after the translation can be described as follows: point A is now at (-1,-8), point B is at (2,-3), point C is at (7,0), and point D is at (4,-5).
To translate Rhombus ABCD using the rule (x, y) = (x+2, y-6), we add 2 to the x-coordinate and subtract 6 from the y-coordinate for each vertex.
Thus, the new vertices for the translated rhombus are:
A' = (-3+2, -2-6) = (-1, -8)
B' = (0+2, 3-6) = (2, -3)
C' = (5+2, 6-6) = (7, 0)
D' = (2+2, 1-6) = (4, -5)
Therefore, the coordinates for the translated Rhombus ABCD are A'(-1,-8), B'(2,-3), C'(7,0), and D'(4,-5).
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Gill opened an account at a different bank. The banks rate of interest was 6%. After one year the bank paid Gill interest. The amount in her account was now $2306
Answer:
Step-by-step explanation:
To solve this problem, we can use the formula for calculating simple interest:
I = P * r * t
where:
I = interest earned
P = principal (initial amount of money)
r = rate of interest
t = time (in years)
We can rearrange the formula to solve for the principal:
P = I / (r * t)
In this case, we know that Gill earned $2306 in interest after one year at a rate of 6%. So:
I = $2306
r = 0.06
t = 1 year
Substituting these values into the formula, we get:
P = $2306 / (0.06 * 1)
P = $38,433.33
Therefore, the initial amount of money that Gill deposited into her account was $38,433.33.
refer to exercise 7.11. suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample. if a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p (g1 ≤ ( y - u ) ≤ g2 ) = 90
Confidence interval = (y ± t∗s/√n)g1 = y - t*s/√ng2 = y + t*s/√n Substituting the values, g1 = 26.22 - 1.860*(0.11)/√9 = 25.84g2 = 26.22 + 1.860*(0.11)/√9 = 26.59Therefore, the statistics g1 and g2 that will satisfy the required inequality are 25.84 and 26.59 respectively.
The formula for finding the confidence interval is as follows: n − 1, where t is the value of the t-distribution corresponding to the specified confidence level and the sample size minus one.
As per the given exercise 7.11, suppose that in the forest fertilization problem the population standard deviation of basal areas is not known and must be estimated from the sample.
If a random sample of n = 9 basal areas is to be measured, find two statistics g1 and g2 such that p(g1 ≤ (y - u) ≤ g2) = 90
To find the statistics g1 and g2 that will satisfy the required inequality
the following formula can be used: Confidence interval = [tex](y ± t∗s/√n)[/tex]
From the formula, we can see that the confidence interval depends on the values of y, s, t and n.
The value of y is the sample mean
the value of s is the sample standard deviation
And the value of n is the sample size.
The value of t depends on the confidence level desired and the degrees of freedom for the t-distribution. In this case, the confidence level is 90%, which means that we want to find the value of t that will give us a total area of 0.90 under the t-distribution curve with 8 degrees of freedom .Using the t-table, the value of t can be found to be 1.860, where the value for 90% and 8 degrees of freedom is 1.860.t = 1.860Now, we need to calculate the value of s, which is the sample standard deviation.
Since we do not have any information about the population standard deviation, we will use the sample standard deviation as an estimate of the population standard deviations = σ/√nσ = s*√nσ = 0.11*√9σ = 0.33Substituting the values in the confidence interval formula
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10. Write the equation that is represented by the data in the table below.
Time (years)
0
1
2
3
4
5
No. of cars
5
10
20
40
80
160
How many years would it take to over 10,000 cars?
19. Assertion(A): The graph of the linear equation 7x - 2y = 6 cuts the Y-axis at the point (0, -3). Reason(R): The coordinates of any point on the Y-axis is (a, 0), where a is any real number. pls help
get the answer
Answer:
Pretty sure its C
Step-by-step explanation:
To cut through y axis, x axis is always 0, So it would be (0, a) where a is any real number, not (a,0) as is given in reason.
16^(3x-1) = 32. pls help
Answer:x=33/4096=0.008
Step-by-step explanation: 1.1 16 = 24
(16)3 = (24)3 = 212
Equation at the end of step
1
:
((212 • x) - 1) - 32 = 0
STEP
2
:
Equation at the end of step 2
4096x - 33 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve : 4096x-33 = 0
Add 33 to both sides of the equation :
4096x = 33
Divide both sides of the equation by 4096:
x = 33/4096 = 0.008
The island of Martinique has received $32,000
for hurricane relief efforts. The island’s goal is to
fundraise at least y dollars for aid by the end of
the month. They receive donations of $4500
each day. Write an inequality that represents this
situation, where x is the number of days.
An inequality representing the amount that the island of Martinique can received for hurricane relief efforts, where x is the number of days is y ≤ 32,000 + 4,500x.
What is inequality?Inequality is an algebraic statement that two or more mathematical expressions are unequal.
Inequalities can be represented as:
Greater than (>)Less than (<)Greater than or equal to (≥)Less than or equal to (≤)Not equal to (≠).The total amount received by the island = $32,000
The daily receipt of donations = $4,500
Let the number of days = x
Let the funds raised for aid = y
Inequality:y ≤ 32,000 + 4,500x
Thus, the inequality for the funds that the island can fundraise for hurricane relief aid by the end of the month is y ≤ 32,000 + 4,500x.
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The standard deviation of the weights of elephants is known to be approximately 15 pounds. We wish to construct a 95% confidence interval for the mean weight of newborn elephant calves. Fifty newborn elephants are weighed. The sample mean is 244 pounds. The sample standard deviation is 11 pounds Construct a 95% confidence interval for the population mean weight of newborn elephants. State the confidence interval (Round your answers to two decimal places.) Sketch the graph. (Round your answers to two decimal places.) CL - 0.95 X Calculate the error bound (Round your answer to two decimal places)
The error bound for the 95% confidence interval is (1.96 x Standard Deviation/√n), which in this case is (1.96 x 11/√50) = 2.56. This means that the true mean weight of newborn elephant calves lies within +/-2.56 pounds of the interval range.
The 95% confidence interval for the population mean weight of newborn elephants can be calculated using the sample mean of 244 pounds and the sample standard deviation of 11 pounds. The confidence interval is calculated using the following formula:
Confidence Interval = (Mean - (1.96 x Standard Deviation/√n)), (Mean + (1.96 x Standard Deviation/√n))
Where n is the sample size.
Therefore, the 95% confidence interval for the population mean weight of newborn elephants is (231.14, 256.86).
This can also be represented in a graph. The graph would have the x-axis representing the confidence interval, with a range from 231.14 to 256.86, and the y-axis representing the probability, which would be 0.95.
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I don’t know helppp
Me
[tex]f(x) = -2(x - 0.5)^2 + 6[/tex] is the equation of the quadratic function that passes through the points (-1, 14), (0, 8), (1, 6), and (2, 8).
What is quadratic function?
f(x) = ax2 + bx + c, where a, b, and c are numbers with a not equal to zero, is a quadratic function.
To find the equation of the quadratic function that passes through the points (-1, 14), (0, 8), (1, 6), and (2, 8), we can use the vertex form of the quadratic function, which is:
[tex]f(x) = a(x - h)^2 + k[/tex]
[tex]f(1) = a(1 - h)^2 + k\\\\6 = a(1 - h)^2 + k[/tex]
We can use a second point to find a relationship between h and k. Let's use the point (0, 8):
[tex]f(0) = a(0 - h)^2 + k\\\\8 = a(-h)^2 + k\\\\6 - 8 = a(1 - h)^2 + k - (a(-h)^2 + k)\\\\-2 = a(1 - h)^2 - a(h)^2\\\\-2 = a(1 - 2h + h^2) - a(h^2)\\\\-2 = a - 2ah + ah^2 - ah^2\\\\-2 = a - 2ah\\\\a = -2/(2h - 1)[/tex]
Let's use the second equation:
[tex]8 = a(-h)^2 + k\\\\8 = (-2/(2h - 1))(h^2) + k\\\\8(2h - 1) = -2h^2 + k(2h - 1)\\\\16h - 8 = -2h^2 + k(2h - 1)\\\\-2h^2 + 16h - 8 = k(2h - 1)\\\\k = (-2h^2 + 16h - 8)/(2h - 1)[/tex]
Now we can substitute this value of h into our expressions for a and k to get:
[tex]a = -2/(2(0.5) - 1) = -2\\\\k = (-2(0.5)^2 + 16(0.5) - 8)/(2(0.5) - 1) = 6[/tex]
So the equation of the quadratic function is:
[tex]f(x) = -2(x - 0.5)^2 + 6[/tex]
Therefore, [tex]f(x) = -2(x - 0.5)^2 + 6[/tex] is the equation of the quadratic function that passes through the points (-1, 14), (0, 8), (1, 6), and (2, 8).
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A cylindrical tin filled with oil has a diameter of 12cm and a height of 14cm. The oil is then poured in rectangular tin 16cm long and 11cm wide. What is the depth of the oil in the tin
The volume of cylindrical tin is 1584 [tex]cm^3[/tex]. The depth of the oil in the tin is 9cm.
[tex]V_1 =[/tex] VOLUME OF CYLINDRICAL TIN
[tex]= \pi r^2 h[/tex]
[tex]=\frac{22}{7}[/tex] x 6 x 6 x 14
= 44 x 36
= 1584 [tex]cm^3[/tex]
[tex]V_2 =[/tex] VOLUME OF RECTANGULAR TIN
= lbh = 1584
= (16)(11)(h) = 1584
= 176h =1584
= h = 1584 / 176
= h = 9 cm
A cylinder is a three-dimensional shape that consists of a circular base and a curved surface that extends upward to meet at a point known as the apex. The volume of a cylinder is the amount of space occupied by the shape and is given by the formula V = πr²h, Once we have calculated the area of the circular base, we can multiply it by the height of the cylinder to get the volume.
To calculate the volume of a cylinder, we need to know its dimensions, which are the radius and height. The radius is the distance from the center of the circular base to the edge, while the height is the distance between the two circular bases.
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The question may have one or more than one option correct
[tex]\displaystyle\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx[/tex]
The correct option is/are
A) 22/7 - π
B) 2/105
C) 0
D) 71/15 - 3π/2
Answer:
To solve the integral, we can use partial fractions and then integrate each term separately. The integrand can be written as:
[tex]\dfrac{x^4(1-x)^4}{1+x^2} = \dfrac{x^4(1-x)^4}{(x+i)(x-i)}[/tex]
Using partial fractions, we can write:
[tex]\dfrac{x^4(1-x)^4}{(x+i)(x-i)} = \dfrac{Ax+B}{x+i} + \dfrac{Cx+D}{x-i}[/tex]
Multiplying both sides by (x+i)(x-i), we get:
[tex]x^4(1-x)^4 = (Ax+B)(x-i) + (Cx+D)(x+i)[/tex]
Substituting x=i, we get:
[tex]i^4(1-i)^4 = (Ai+B)(i-i) + (Ci+D)(i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ci + 2B[/tex]
Substituting x=-i, we get:
tex^4(1+i)^4 = (Ci+D)(-i-i) + (Ai+B)(-i+i)[/tex]
Simplifying, we get:
[tex]16 = 2Ai + 2D[/tex]
Substituting x=0, we get:
[tex]0 = Bi + Di[/tex]
Substituting x=1, we get:
[tex]0 = A+B+C+D[/tex]
Solving these equations simultaneously, we get:
A = -22/7 + π
B = 0
C = 22/7 - π
D = -2/5
Therefore, the integral can be written as:
[tex]\int_0^1 \dfrac{x^4(1-x)^4}{1+x^2}dx = \int_0^1 \left[\dfrac{-22/7+\pi}{x+i} + \dfrac{22/7-\pi}{x-i} - \dfrac{2/5}{1+x^2}\right]dx[/tex]
Integrating each term separately, we get:
[tex]\int_0^1 \dfrac{-22/7+\pi}{x+i}dx = [-22/7+\pi]\ln(x+i) \bigg|_0^1 = [\pi-22/7]\ln\left(\dfrac{1+i}{i}\right)[/tex]
[tex]\int_0^1 \dfrac{22/7-\pi}{x-i}dx = [22/7-\pi]\ln(x-i) \bigg|_0^1 = [22/7-\pi]\ln\left(\dfrac{1-i}{-i}\right)[/tex]
[tex]\int_0^1 \dfrac{-2/5}{1+x^2}dx = -\frac{2}{5}\tan^{-1}(x)\bigg|_0^1 = -\frac{2}{5}\tan^{-1}(1) + \frac{2}{5}\tan^{-1}(0) = -\frac{2}{5}\tan^{-1}(1)[/tex]
Therefore, the correct options are:
A) [tex]\pi-\frac{22}{7}[/tex]
B) [tex]\frac{2}{105}[/tex]
C) 0
D) [tex]\frac{71}{15}-\frac{3\pi}{2}[/tex]
company that ships glass for a glass manufacturer claimed that its shipping boxes are constructed so that no more than 8 percent of the boxes arrive with broken glass. The glass manufacturer believed the actual percent is greater than 8 percent. The manufacturer selected a random sample of boxes and recorded the proportion of boxes that arrived with broken glass. The manufacturer tested the hypotheses H, :p = 0.08 versus H, :p > 0.08 at the significance level of a = 0.01. The test yielded a p-value of 0.001. Assuming all conditions for inference were met, which of the following is the correct conclusion?А. The p-value is greater than a, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.B. The p-value is greater than a, and the null hypothesis is rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.C. The p-value is greater than a, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.D. The p-value is less than a, and the null hypothesis is rejected. There is convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.E The p-value is less than a, and the null hypothesis is not rejected. There is not convincing evidence that the proportion of all boxes that contain broken glass is greater than 0.08.
The conclusion which is correct about given situation is D) The p-value (0.001) is less than the significance level (0.01), which means we reject the null hypothesis that the proportion of boxes with broken glass is equal to or less than 8%.
We have convincing evidence to suggest that the actual proportion of boxes with broken glass is greater than 8%. Therefore, we can conclude that the glass manufacturer's belief is supported by the sample data.
This conclusion is based on the fact that the p-value is less than the significance level, indicating that the observed data is unlikely to have occurred by chance alone assuming the null hypothesis is true.
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Eddie est discutiendo con Tana sobre las probabilidades de los distintos resultados al lanzar tres monedas. Decide lanzar una moneda de un centavo, una de cinco centavos y una de die centavos. ¿ Cuál es la probabilidad de que las tres monedas salgan cruz?
The probability of getting tails in the three coins would be 0.125 or 12.5%.
How to calculate the probability?To calculate the probability of an event happening, first, we need to identify the rate of the desired outcome versus the total possible outcomes. Moreover, to determine the total probability of two or more events happening we need to calculate the probability of each event and then multiply the results.
Probability of getting tails in any of the three coins:
1 / 2 = 0.5
Total probabilityy:
0.5 x 0.5 x 0.5 = 0.125 or 12.5%
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Ted is five times as old as Rosie was when Ted was Rosie's age. When Rosie
reaches Ted's current age, the sum of their ages will be 72. Find Ted's current age.
Answer:
45 yo
Step-by-step explanation:
Let's start by defining some variables to represent the ages of Ted and Rosie:
- Let's call Ted's current age "T"
- Let's call Rosie's current age "R"
From the problem statement, we know that:
- Ted is five times as old as Rosie was when Ted was Rosie's age. Written as an equation, this becomes:
T = 5(R - (T - R))
Simplifying this equation, we get:
T = 5(R - T + R)
T = 10R - 5T
- When Rosie reaches Ted's current age, the sum of their ages will be 72. Written as an equation, this becomes:
R + T = 72 - T
We now have two equations with two variables. We can use substitution to solve for T.
Substitute the second equation into the first equation to eliminate R:
T = 10R - 5T
T = 10(72 - T) - 5T
T = 720 - 15T
16T = 720
T = 45
Therefore, Ted's current age is 45.
The difference between two numbers is eight.
if the smaller number is n to the third power
what is the greater number?
The greater number is [tex]$n^3+8$[/tex]
Let x be the greater number and y be the smaller number. We know that x-y=8.
We are also given that the smaller number is n³.
So we can set up the equation:
x = y + 8
x = n³ + 8
Therefore, the greater number is [tex]$n^3+8$[/tex].
The greater number is given as n³ + 8. If the smaller number we get is represented by the n³, then by adding 8 to that value gives the greater number. The difference between the two numbers is always going to be 8, regardless of the value of n.
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