This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.
(a) To find a 99% confidence interval on the mean diameter, we can use the t-distribution with n-1 degrees of freedom since the population standard deviation is not known. The formula for the confidence interval is:
CI = x ± tα/2,s/√n
where x is the sample mean, s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.
Plugging in the values, we get:
CI = 1.0056 ± t0.005/2,0.0246/√9
= 1.0056 ± 0.025
= (0.9806, 1.0306)
Therefore, we can be 99% confident that the true mean diameter of the metal pieces produced by the machine is between 0.9806 and 1.0306 centimeters.
(b) To compute a 99% prediction interval on a measured diameter of a single metal piece taken from the machine, we can use the formula:
PI = x ± tα/2,s(1 + 1/n)√(1 + 1/n)
where x is the point estimate of the diameter (in this case, the sample mean), s is the sample standard deviation, n is the sample size, and tα/2 is the t-value with (n-1) degrees of freedom for the desired level of confidence α.
Plugging in the values, we get:
PI = 1.0056 ± t0.005/2,0.0246(1 + 1/9)√(1 + 1/9)
= 1.0056 ± 0.052
= (0.9536, 1.0576)
Therefore, we can be 99% confident that a single metal piece produced by the machine will have a diameter between 0.9536 and 1.0576 centimeters.
(c) To find the 99% tolerance limits that will contain 95% of the metal pieces produced by this machine, we can use the formula:
TL = x ± kσ
where x is the sample mean, σ is the population standard deviation (which is estimated by the sample standard deviation s), k is the number of standard deviations from the mean that will contain the desired percentage of the population (in this case, 95% or 1.96 standard deviations for a normal distribution).
Plugging in the values, we get:
TL = 1.0056 ± 1.96(0.0246)
= (0.9573, 1.0539)
Therefore, we can be 99% confident that 95% of the metal pieces produced by the machine will have diameters between 0.9573 and 1.0539 centimeters. This interval is wider than the confidence interval in part (a) and the prediction interval in part (b) because it is based on the entire population of metal pieces, not just a sample.
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SOLVE ASAP!!
On the same coordinate plane, mark all points (x, y) that satisfy each rule.
a) y= -3-x
b) y= x-3
c) y= 3x+2
d) y= 3x-2
e) y= -3x+2
(SHOW COORDINATE PLANE GRAPH)
(WILL AWARD BRAINLIEST)
The point that satisfies y = -3-x is (0,-3), the point that satisfies y = x-3 is (0,-3), the point that satisfies y = 3x+2 is (0,2), the point that satisfies y = 3x -2 is (0,-2), the point that satisfies y = -3x+2 is (0,2). The graph is shown below.
To find the points that satisfy the equation y = -3 - x, we can substitute different values of x and solve for y.
When x = 0, y = -3 - 0 = -3, so one point is (0, -3).
When x = 1, y = -3 - 1 = -4, so another point is (1, -4).
When x = -1, y = -3 - (-1) = -2, so another point is (-1, -2).
By repeating this process for different values of x, we can find more points that satisfy the equation.
To find the points that satisfy the equation y = x - 3, we can again substitute different values of x and solve for y.
When x = 0, y = 0 - 3 = -3, so one point is (0, -3).
When x = 1, y = 1 - 3 = -2, so another point is (1, -2).
When x = -1, y = -1 - 3 = -4, so another point is (-1, -4).
To find the points that satisfy the equation y = 3x + 2, we can once again substitute different values of x and solve for y.
When x = 0, y = 3(0) + 2 = 2, so one point is (0, 2).
When x = 1, y = 3(1) + 2 = 5, so another point is (1, 5).
When x = -1, y = 3(-1) + 2 = -1, so another point is (-1, -1).
To find the points that satisfy the equation y = 3x - 2, we can once again substitute different values of x and solve for y.
When x = 0, y = 3(0) - 2 = -2, so one point is (0, -2).
When x = 1, y = 3(1) - 2 = 1, so another point is (1, 1).
When x = -1, y = 3(-1) - 2 = -5, so another point is (-1, -5).
To find the points that satisfy the equation y = -3x + 2, we can once again substitute different values of x and solve for y.
When x = 0, y = -3(0) + 2 = 2, so one point is (0, 2).
When x = 1, y = -3(1) + 2 = -1, so another point is (1, -1).
When x = -1, y = -3(-1) + 2 = 5, so another point is (-1, 5).
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Graph the line with slope
3/4
passing through the point (-4,-1)
.
Answer: See attached.
Step-by-step explanation:
First, we will create an equation with the slope given.
y = [tex]\frac{3}{4}[/tex]x + b
Then, we will substitute this value in and solve for b (our y-intercept). Then we will graph the equation.
y = [tex]\frac{3}{4}[/tex]x + b
(-1) = [tex]\frac{3}{4}[/tex](-4) + b
-1 = -3 + b
b = 2
Our final equation:
y = [tex]\frac{3}{4}[/tex]x + 2
See attached for the graph. We will plot the point (0, 2) for our y-intercept and then move 3 units up for every four units right, according to the slope.
The ratio of union members to nonunion members working for a company is 4 to 7. If there are 108 union members working for the company, what is the total number of employees?
The total number of employees in the company is 297 if ratio of union members to nonunion members working for a company is 4 to 7
The given ratio of union members to nonunion members, which is 4 to 7. This means that for every 4 union members, there are 7 nonunion members.
We are also given that there are 108 union members working for the company.
The total number of employees in the company be "x".
Let us from a proportional equation
4/11 = 108/x
To solve for x, we can cross-multiply and simplify:
4x = 1188
x = 297
Therefore, the total number of employees in the company is 297.
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Please help me asap need to get it done MANY POINTS WILL BE GIVEN
Answer:
Step-by-step explanation:
1. The line of best fit must have an equal number of points above and below the line
2. The line of best fit could be used as a predictions showing a trend in data
Carlos does 138 jumping jacks during gym class. John only does 89. How many more jumping jacks did Carlos do than John?
Answer:
Carlos did 49 more jumping jacks than John.
Step-by-step explanation:
Carlos = 138
John = 89
138 - 89 = 49
1. The domain for f(x) and g(x) is the set of all real numbers.
Let f(x) = 2x²+x-3 and g(x) = x - 1.
Find f(x) · g(x).
a. 2x³-x²+4x-3
b. 2x³-4x²+3
c. 2x³-x²-4x+3
d. x² - 4x +3
The solution to the multiplication of both functions is:
2x³ - x² - 4x + 3
How to find the product of functions?To multiply a function by another function, multiply their outputs. For example, if f (x) = 2x and g(x) = x + 1, then fg(3) = f (3) × g(3) = 6 × 4 = 24. fg(x) = 2x(x + 1) = 2x² + x.
We are told that the domain for f(x) and g(x) is the set of all real numbers.
The functions are given as:
f(x) = 2x² + x - 3
g(x) = x - 1
Thus:
f(x) · g(x) = (2x² + x - 3) * (x - 1)
= 2x³ + x² - 3x - 2x² - x + 3
= 2x³ - x² - 4x + 3
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Pls help
The shape below contains a triangle and a semi circle.
Round your response to two decimal places.
What is the perimeter of the shape above?
What is the area of the shape above?
The perimeter of the shape above is 22.22 units
the area of the shape above is 26 square units
How to determine the valuesWe can see from the diagram shown, that the shape is made up of a semicircle below and a triangle above.
Now, the formula for calculating the area of a triangle is expressed as;
A = 1/2bh
Such that the parameters are;
A is the areab is the base h is the height of the triangleNow, substitute the values
Area = 1/2 × 7 ×6
Multiply the values
Area = 42/2
Area = 26 square units
The formula for perimeter of a triangle is;
Perimeter = (a + b + c)
Perimeter = 6 + 7 + 9. 22
Add the values
Perimeter = 22. 22 units
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What is the nature of the roots of each quadratic equation?
1. [tex]x^{2}[/tex] + 5x + 3 = 0
2. [tex]2x^{2}[/tex] - 2x + 1 = 0
x² + 5x + 3 = 0, the quadratic equation has two distinct real roots
2x² - 2x + 1 = 0, no real roots. Instead, it has two complex conjugate roots.
x² + 5x + 3 = 0
To determine the nature of the roots of this quadratic equation, we need to calculate the discriminant using the formula:
Discriminant = b² - 4ac
where a, b, and c are the coefficients of the quadratic equation ax^2 + bx + c = 0.
In this case, a = 1, b = 5, and c = 3.
Discriminant = (5)² - 4(1)(3)
= 25 - 12
= 13
Since the discriminant is positive and not a perfect square, the quadratic equation has two distinct real roots
Now 2x² - 2x + 1 = 0
a = 2, b = -2, and c = 1
Plugging these values into the discriminant formula, we get:
b² - 4ac = (-2)² - 4(2)(1) = 4 - 8 = -4
Since the discriminant is negative, the quadratic equation 2x² -2x+1=0 has no real roots.
Instead, it has two complex conjugate roots.
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Repartir de forma directamente proporcional 40 000 entre personas de 3,7,10 años a) 3 años = 8 000, 7 años = 12 000, 10 años = 10 000 b) 3 años = 6 000, 7 años = 14 000, 10 años = 20 000 c) 3 años = 4000, 7 años = 8 000, 10 años = 18 000 d) 3 años = 5 000, 7 años = 10 000, 10 años = 10 000
When distributed directly proportionally among the people, using age, the result would be b) 3 years = 6,000, 7 years = 14,000, 10 years = 20,000.
How to distribute the number ?First, find the total age of the people give :
= 10 + 7 + 3
= 20
To amount that would go to 10 as a directly proportional measure is:
= 10 / 20 x 40, 000
= 20, 000
The amount to 7 as a directly proportional value would be:
= 7 / 20 x 40, 000
= 14, 000
The amount to 3 would follow the same pattern :
= 3 / 20 x 40, 000
= 6, 000
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Need help dont know how to do this question
The unknown angle in the cyclic quadrilateral is as follows:
m∠DGF = 75 degrees
How to find the angle of a cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle.
The sum of angles in a cyclic quadrilateral is 360 degrees.
Therefore, let's the angle m∠DGF as follows:
The opposite angles of a cyclic quadrilateral have a total of 180°.
4x + 7 + 8x - 31 = 180
12x - 24 = 180
12x = 180 + 24
12x = 204
divide both sides by 12
x = 204 / 12
x = 17
Hence,
m∠DGF = 4x + 7 = 4(17) + 7 = 68 + 7 = 75 degrees
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Which figure has two more faces than a rectangular prism ?
The figure that has two more faces than a rectangular prism is a Square pyramid.
How many faces does it have ?There are precisely six faces that a rectangular prism contains, which consists of a pair of identical rectangles for its top and bottom planes as well as four lateral faces consisting of corresponding right-angled, congruent rectangles. Hence, a solid figure that has two more sides than the aforementioned rectangular prism could only have eight total faces without exception.
An example of such an entity is a square pyramid whose base constitutes of four equal-length sides with four corresponding triangular surfaces converging at one single vertex on the summit's tip. Within this context, it possesses five faces (one square and four isosceles triangles), thus exceeding by two faces compared to the former geometric model.
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Which linear equation shows a proportional relationship?
y = 2x
y equals one third times x plus 2
y equals negative two fifths times x minus 1
y = 1
A linear equation which shows a proportional relationship include the following: A. y = 2x.
What is a proportional relationship?In Mathematics and Geometry, a proportional relationship refers to a type of relationship that produces equivalent ratios and it can be modeled or represented by the following mathematical equation:
y = kx
Where:
y represents the x-variable.x represents the y-variable.k is the constant of proportionality.Next, we would determine the constant of proportionality (k) by using various data points as follows:
Constant of proportionality, k = y/x
Constant of proportionality, k = 2/1 = 4/2 = 6/3 = 8/4
Constant of proportionality, k = 2.
Therefore, the required linear equation is given by;
y = kx
y = 2x
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The velocity v of a meteorite approaching earth is givin by v=k/
The velocity of the meteorite is 4 km per sec.
Given that, a meteorite is approaching the earth and is 10000 km away from earth,
we need to find the velocity,
v = k / √d
v = 400 / √10000
v = 400 / 100
v = 4 km per sec.
Hence, the velocity of the meteorite is 4 km per sec.
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The velocity at a distance of 6,889 kilometers is 6.795 Km/ sec.
We have,
The velocity v of a meteorite approaching earth is V = k/√d.
The distance from center of Earth = 8836
and, Velocity = 6 Km/ s
So, using the formula for velocity
6 = k/√8836
6 = k/94
k= 564 Km
Now, velocity at 6689 Km
V = 564/ √6889
V =6.795 km/sec
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Prove that sinθ cosθ = cotθ is not a trigonometric identity by producing a counterexample.
Answer:
cmon man
Step-by-step explanation:
We want to show that sinθ cosθ = cotθ is not true for all values of θ. To do this, we just need to find one counterexample, i.e., one value of θ for which the equation is not true.
Recall that cotθ = cosθ/sinθ. So, the equation sinθ cosθ = cotθ can be rewritten as sinθ cosθ = cosθ/sinθ.
Multiplying both sides by sinθ, we get:
sin^2θ cosθ = cosθ
Dividing both sides by cosθ, we get:
sin^2θ = 1
Taking the square root of both sides, we get:
sinθ = ±1
So, we need to find a value of θ such that sinθ is equal to ±1. This occurs when θ = π/2 + kπ, where k is an integer.
Now, let's check whether sinθ cosθ = cotθ is true for this value of θ. We have:
sin(π/2 + kπ) = ±1
cos(π/2 + kπ) = 0
cot(π/2 + kπ) = undefined (since cos(π/2 + kπ) = 0)
Therefore, sinθ cosθ = cotθ is not true for θ = π/2 + kπ, and we have found a counterexample. This shows that sinθ cosθ = cotθ is not a trigonometric identity.
A middle school took all of its 6th-grade students on a field trip to see a play at a theater that has 3260 seats. The students filled 95% of the seats in the theater. How many 6th graders went on the trip?
There were 3097 6th-grade students who went on the field trip to see the play at the theater.
We have,
If 95% of the 3260 seats in the theater were filled by the 6th-grade students,
We can find the total number of students by multiplying the total number of seats by the fill percentage as a decimal:
Number of 6th graders = 3260 x 0.95
Number of 6th graders = 3097
Therefore,
There were 3097 6th-grade students who went on the field trip to see the play at the theater.
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The solid below is dilated by a scale factor of 4. Find the volume of the solid created
upon dilation. Answer in terms of TT.
Answer:
units³
3
Submit Answer
Step-by-step explanation:
the volume of a sphere is
4/3 × pi × r³
the original sphere had a radius of 3.
now, after a dilation of factor 4 the radius is 3×4 = 12.
the volume of that sphere is then
4/3 × pi × 12³ = 4/3 × pi × 1728 = 2304pi
35 POINTS ANSWER FOR BRAINLIST
Colbie solved the equation below by completing the square. Did she complete the square correctly? Explain why or why not? Correct the mistake(s) – if there are any.
Answer:
Colbie did not complete the square correctly.
Colbie failed to add the square of half the coefficient of the term in x to both sides of the equation. She only added 25 to the left side of the equation. She also factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.
Step-by-step explanation:
Given quadratic equation:
[tex]2x^2+20x-48=0[/tex]
As the leading coefficient is not one, to complete the square we must first divide both sides of the equation by the leading coefficient, 2:
[tex]\dfrac{2x^2+20x-48}{2}=\dfrac{0}{2}[/tex]
[tex]x^2+10x-24=0[/tex]
Now move the constant to the right side of the equation by adding 24 to both sides of the equation:
[tex]\begin{array}{rcr}x^2+10x-24&=&0\\\vphantom{\dfrac12}+24 & &+24\\\cline{1-3}\vphantom{\dfrac12}x^2+10x\phantom{-24.}&=&24\end{array}[/tex]
We need to make the left side of the equation a perfect square trinomial. To do this, add the square of half the coefficient of the term in x to both sides of the equation.
The coefficient of the term in x is 10. Therefore, the square of half of this is 25:
[tex]\left(\dfrac{10}{2}\right)^2=5^2=25[/tex]
This is the point at which Colbie made her first mistake. She didn't add the square of half the coefficient of the term in x to both sides of the equation - she only added it to the left side.
Add 25 to both sides of the equation:
[tex]x^2+10x+25=24+25[/tex]
[tex]x^2+10x+25=49[/tex]
To continue to solve the equation, factor the perfect square trinomial on the left side of the equation:
[tex](x+5)^2=49[/tex]
↑ Colbie made her second mistake here. She factored x² + 10x + 25 incorrectly by using a subtraction sign in the binomial rather than an addition sign.
Square root both sides:
[tex]\sqrt{(x+5)^2}=\sqrt{49}[/tex]
[tex]x+5=\pm7[/tex]
Subtract 5 from both sides:
[tex]x+5-5=-5\pm7[/tex]
[tex]x=-5\pm7[/tex]
Therefore, the solutions are:
[tex]x=-5+7=2[/tex]
[tex]x=-5-7=-12[/tex]
Scientists are studying the population of a rare species of primates, known as a Javan gibbons, on the Raja Ampat Islands
in Indonesia. They are studying the gibbons on three different islands, Batanta, Misool, and Salawati. The scientists studied
the population growth and recorded the data in the table.
2. What type of function is M(x)? Justify your answer and show calculations to support your conclusion.
The data presented shows the growth of the Javanese gibbon population on three different islands over time.
What informs the data?Data trends must be analyzed to determine the type of function that is modeling population growth. A common way to do this is to plot the data points and observe the shape of the curve. However, since the table only contains data, you can analyze trends by looking at the differences between consecutive terms.
To do this, we can calculate the first difference and the second difference in the population data.
The first difference:
- Swing: 40 - 30 = 10, 50 - 40 = 10, 60 - 50 = 10
Example: 60 - 50 = 10, 75 - 60 = 15, 90 - 75 = 15
- Salavati: 80 - 60 = 20, 100 - 80 = 20, 120 - 100 = 20
The second difference:
- Batanta: 10 - 10 = 0, 10 - 10 = 0
- Example: 15 - 10 = 5, 15 - 15 = 0
- Salavati: 20 - 20 = 0, 20 - 20 = 0
The first difference is constant for each island and shows a linear relationship between time and population growth. Also, the second difference is zero, indicating a constant rate of change.
Therefore, we can conclude that the population growth modeling function is a linear function that can be written as
M(x) = mx + b
where x is the time in years, m is the slope (population growth rate), and b is the y-intercept (initial population).
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Multiply 6c(8 − 3c).
Answer:-30c
Step-by-step explanation:
you subtract 8 from 3c which is -5c than multiply by 6 which is -30c
A coupon book has a coupon for 10% off a ticket at a theme park. A ticket usually costs $80. How much would a visitor save with the coupon?
Answer: the visitor would save $8 with the coupon.
Step-by-step explanation: 10% of $80 = 0.1 x $80 = $8
How do I solve this?
Answer:
Step-by-step explanation:
A = length x width = (2w + 5)(w) = 2w² + 5w
P = 2(2w + 5) + 2w = 6w + 10
To graph: sorry, Brainly doesn't have graphing tools so I'll just have to describe it
A: parabola, opens up, vertex at (-1.25, -3,124), crosses x axis at (-2.5, 0) and (0,0)
P: straight line, slants up, with a slope of 6, y-intercept of 10, crosses x axis at (-1.667, 0)
FYI, the 2 graphs intersect at 2 points: (-2, 2) and (2.5, 25)
Sebastian bought a 30-pack of mechanical pencils and plans to give the same number of pencils each to 6 friends. Which equation can he use to find p, the number of pencils each friend will receive?
[tex]p+6 = 30\\p-6 = 30\\6p = 30\\\frac{p}{6} = 30[/tex]
1.) [tex]6p=30[/tex]
2.) Sebastian bought a pack of 30 mechanical pencils and plans to give the same number of pencils each to 6 friends.
Let a varible such as p be the number of pencils given by him to each students.
Now we need to find p we need to divide 30 by 6, we get
[tex]p = \frac{30}{6}[/tex]
[tex]to[/tex]
[tex]6p = 30[/tex]
Thus, the equation can he use to find p, the number of pencils each friend will receive is: [tex]6p = 30[/tex]
Answer:
[tex]6p = 30[/tex]
Step-by-step explanation:
3dxnn have's the explanation.
Find the median of 61, 55, 56, 61, 57, 55, 54
Check the picture below.
Two concentric circles form a target. The radii of the two circles measure 8 cm and 2 cm. The inner circle is the bullseye of the target. A
point on the target is randomly selected.
What is the probability that the randomly selected point is in the bullseye?
?
—
?
The probability that the randomly selected point is in the bullseye = 15/16.
How do we determine the probability that the point randomly selected is in the bullseye?To calculate the probability that the randomly selected point is in the bullseye, we shall first evaluate the area of each of the circles:
The area of the larger circle (outer circle) with radius 8 cm is given:
A_outer = πr² = π(8)² = 64π
The area of the smaller circle (inner circle) with radius 2 cm is given:
A_inner = πr² = π(2)² = 4π
The area of the bullseye (the region between the two circles) = the difference between the areas of the two circles:
A_bullseye = A_outer - A_inner
= 64π - 4π = 60π
Therefore, the probability that a randomly selected point is in the bullseye:
P = A_bullseye / A_outer
= (60π) / (64π)
P = 15/16
x
Therefore, the probability that the randomly selected point is in the bullseye = 15/16.
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birth weights for a simple random sample of 195 boys were recorded. the mean weight calculated for this sample was 3.04 kilograms and the standard deviation was 0.71 kilograms. what is the best point estimate for the birth weight of boys and construct a 90% confidence interval estimate of the mean birth weight of boys
Based on the information, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.
How to calculate the valuestandard error will be:
= 0.71 / ✓(195) = 0.051 kilograms
Substituting these values into the formula, we will then get:
Confidence interval = 3.04 ± (1.645) × (0.051)
Confidence interval = 3.04 ± 0.084
Confidence interval = (2.956, 3.124)
Therefore, we are 90% confident that the true mean birth weight of boys is between 2.956 and 3.124 kilograms.
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A different sample box has a height that is twice as long as the original box described in Problem 1. What is the
volume of this sample box? How does the volume of this sample box compare to the volume of the sample box ins
Problem 1
The original sample box had a volume of 343 cubic cm, which is half the volume of the new sample box.
Since the height of the new sample box is twice as long as the original box, its height will be 2×7=14 cm.
The length and width remain the same at 7 cm.
The volume of the new sample box is given by the formula:
V = lwh
Substituting the values, we get:
V = (7)(7)(14) = 686 cubic cm
Therefore, the volume of the new sample box is 686 cubic cm.
Comparing the volumes of the two boxes, we see that the new sample box has a larger volume than the original sample box.
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PLEASE ANSWER
Triangle ABC with vertices at A(−3, −3), B(3, 3), C(0, 3) is dilated to create triangle A′B′C′ with vertices at A′(−1, −1), B′(1, 1), C′(0, 1). Determine the scale factor used.
1
one half
3
one third
Answer: B) 1/2
Step-by-step explanation: Hope this helps! :)
The answer is 1/3. I looked it up on gpt and also got a 100 on this quiz
Explain the J curve effect when domestic currency is appreciated?
The J curve impact is an financial wonder that happens when domestic currency increases in value in esteem relative to other monetary forms within the remote trade advertise. The J curve impact is named for the shape of the bend that's made when the adjust of exchange and the esteem of a country's currency are plotted against time.
What occur to the J curve effect when domestic currency is appreciated?Within the brief run, when a country's money increases in value, its sends out ended up more costly and imports ended up cheaper. This implies that the request for a country's sends out will diminish, whereas the request for imports will increase. As a result, the adjust of exchange will at first
compound, which implies that the nation will have a exchange shortfall.
Be that as it may, within the long run, the J curve impact predicts that the adjust of exchange will in the long run progress, and the exchange shortage will turn into a exchange overflow. This happens because the increment within the cost of sends out due to the appreciation of the currency will in the long run lead to a diminish within the amount of trades requested. At the same time, the diminish within the price of imports due to the appreciation of the money will in the long run lead to an increment within the amount of imports requested. Over time, these changes in request will cause a move within the adjust of exchange, coming about in a exchange excess.
In this manner, the Jcurve impact portrays the short-term weakening within the adjust of exchange that happens when a money increases in value, taken after by a long-term enhancement within the adjust of exchange. This impact is named after the shape of the bend that's shaped when the adjust of exchange and the esteem of a country's cash are plotted against time, which looks like a "J" shape.
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The graph below shows a company's profit tox), in dollars, depending on the price of erasers x, in dollars, sold by the company
300+10x)
270
240
210-
180
150
120
90
60
Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (4 points)
Part B: What is an approximate average rate of change of the graph from x-1 tox-4, and what does this rate represent? (3 points)
Part C: Describe the constraints of the domain. (3 points)
The x-intercepts represent a zero profit.
The maximum value of the graph represents the maximum profit.
How to explain the informationThe function increases up till the vertex and decreases after it.
This means that the profit increases as it reaches the peak at the vertex.
It decreases after the vertex up till it reaches zero.
On the left of the first zero and on the right of the second zero, the profits are negative.
An approximate average rate of change of the graph from x = 3 to x =5 represents the reduction in profit from 3 to 5
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Which statements are always true regarding the diagram? Select three options
The following statements are always true regarding the given diagram having angles: m<3+m<4+m<5=180, m<5+m<6=180, m<2+m<3=m<6.
Statement 2 is always true because the sum of the three angles in a triangle is always 180 degrees.
Statement 3 is always true because the sum of the angles on a straight line is 180 degrees.
Statement 4 is always true because angles 2, 3, and 6 are opposite angles, which means they are congruent.
Thus, statements 1 and 5 are not always true. The sum of angles 3, 4, and 5 could be greater or less than the measure of angle 5. The sum of angles 2, 3, and 5 could be greater or less than the measure of angle 3.
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