(a) The optimal order quantity is 20 units.
(b) The order frequency is 8.75 times per year (12 months / 20 units per order).
(c) The annual holding cost is $13.13 and the annual setup cost is $12.86, so the total annual holding and setup cost is $26.99.
(d) The new economic order quantity is 28 units. (e) The order frequency is 6.25 times per year (12 months / 28 units per order). (f) The annual holding cost is $17.15 and the annual setup cost is $7.50, so the total annual holding and setup cost is $24.65.
(g) The results show that the new economic order quantity is higher and the annual holding and setup cost is lower due to the reduction in ordering cost. This means that it is more cost-effective to order a larger quantity of towels at a lower cost per order.
(h) To determine whether the soft goods department should take advantage of the discount, we need to calculate the total cost of purchasing 350 towels at the discounted price versus purchasing 175 towels at the regular price.
At the discounted price of $2.00 per towel, the total cost of purchasing 350 towels is:
Total cost = 350 × $2.00 = $700
At the regular price of $2.50 per towel, the total cost of purchasing 175 towels is:
Total cost = 175 × $2.50 = $437.50
Therefore, it is more cost-effective to purchase 175 towels at the regular price rather than 350 towels at the discounted price.
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As gamers progress through a video game, they earn a higher rank. In an online gaming network, gamers can see what fraction of the way they
are to the next rank. The line plot displays the fraction of the way to the next rank for all the gamers in the network. What fraction of gamers
have bof the way to go to the next rank?
Gamers Progress to Next Rank
Number
of
Gamers
Fraction of Progress to Next Level
A
A.
c.)
Question isn't well formatted, a picture if the question is attached below.
Answer:
1 / 4
Step-by-step explanation:
From the plot, each dot represent a gamer ; therefore, the total number of gamers will be counting all the dots ;
Total number of gamers = 24
Fraction of gamers that have 7 / 8 of the way to go ;
This means that they have 7/8 of the way left to proceed to next level ;
The fraction is : 1 - 7/8 = 1 /8
This means the number of of people whose progress are on 1/8 ; this is 6
Hence, fraction of gamers that have 7/8 of the way to go :
6 / 24 = 1 / 4
fully Factorise 7m^2 + 13m
Answer:
\(m(7m + 13)\)
Step-by-step explanation:
\(7m {}^{2} + 13m \\ m(7m + 13)\)
(a) If log4x=5, then x= (b) If log6x=8, then x=
(a)If log₄x = 5, the base is 4 and the logarithm is 5 , then x = 1024. (b) If log₆x = 8 the base is 6 and the logarithm is 8 then x = 1679616.
(a) In the equation log₄x = 5, the base is 4 and the logarithm is 5. To solve for x, we need to rewrite the equation in exponential form. In exponential form, 4 raised to the power of 5 is equal to x. Therefore, x = 4^5 = 1024.
(b) In the equation log₆x = 8, the base is 6 and the logarithm is 8. Rewriting the equation in exponential form, 6 raised to the power of 8 is equal to x. Hence, x = 6^8 = 1679616.
In both cases, we used the property of logarithms that states: if logₐx = y, then a raised to the power of y equals x. By applying this property, we can convert the logarithmic equations into exponential form and find the values of x.
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12. Triangle ABC has vertices A(-4, 0), B(-4, 5) and C(1, 5) along line AC. Which are the
coordinates of another slope triangle along the same line?
A. D(-2,-2), E(-2, 1) F(-1,0)
B₁6
B. D(-3, 0), E(-3, 1) F(-2, 1)
C. D(-5, -1), E(-5, 0) F(-4, -1)
D. D(-6, -2), E(-6, -1) F(-5, -1)
Please help will mark brainliest
Considering the given triangle ABC that has vertices A(-4, 0), B(-4, 5) and C(1, 5). The option that has same slope with similar interval is B. D(-3, 0), E(-3, 1) F(-2, 1)
What is slope?Slope refers to the gradient and is the ratio of the difference in the ordinate to the difference in the abscissa of in a given coordinate plane.
How to calculate slopeThe given information from the question include
A(-4, 0), B(-4, 5) and C(1, 5)
The slope of the given triangle is calculated as follows
slope = ( 0 - 5 ) / ( -4 - 1 )
slope = -5 / -5
slope = 1
The domain of the line is -4 ≤ x ≤ 1
The range of the line is 0 ≤ y ≤ 5
options C and D values do not satisfy the domain and range conditions
Options B and A satisfies the the domain and range conditions however the slope of option B is what is equal to the slope of the sloping part of the given triangle and hence the correct option.
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Suppose the probability of someone being female and voting for candidate a is 30%. What is the notation for this probability?
If the probability of someone being female and voting for a candidate is 30% , then the notation for this probability is , P(Female and Voting for A) = 0.30 , the correct answer is (c) .
This notation represents the joint probability of two events: being female and voting for candidate A. It means the probability that a randomly selected person is both female and voted for candidate A is 0.30.
In Option (a) P(Female | Voting for A) = 0.30 represents the conditional probability of being female given that the person voted for candidate A. It means the probability that a person who voted for candidate A is female is 0.30.
In Option (b) P(Voting for A | Female) = 0.30 represents conditional probability of voting for candidate A given that the person is female.
It means the probability that a female person voted for candidate A is 0.30.
Therefore , the correct option is (c) P(Female and Voting for A) = 0.30 .
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The given question is incomplete , the complete question is
Suppose the probability of someone being female and voting for candidate a is 30%. What is the notation for this probability?
(a) P(Female | Voting for A) = 0.30
(b) P(Voting for A | Female) = 0.30
(c) P(Female and Voting for A) = 0.30
The spill covered 11,000 square miles of ocean. The oil spread out in a circular pattern and the radius increased by 0.10mph. Use pi = 3.14 At this rate how many hours did it take for the oil to cover the area?
Answer:
3.14 times 0.10. comes out to be 31.4 .
Step-by-step explanation:
PLEASE HELP VERY URGENT
Suppose you know the following facts about angle ABC and angle DEF: (1) both triangles have sides of length a and b (2) For angle ABC, a^2 + b^2 = c^2 (3) For angle DEF, angle F is a right triangle. Use the list of expressions below to find the value of c in angle ABC and the length of the hypotenuse of angle DEF.
The value of c in angle ABC is _______ and the length of the hypotenuse of angle DEF is ________.
A. square root of a^2 + b^2
B. a^2 + b^2
C. b^2 - a^2
D. square root of a^2 - b^2
E. a^2 - b^2
F. square root of b^2 - a^2
(if u have trouble reading the text look at the attached photo for the question)
Answer:
√(a² + b²) is the answer as
Step-by-step explanation:
both ABC AND DEF are right triangles...
So Pythagoras theorem will work here
Given DC is tangent to circle N at point C, which statements are true?
- m∠DCN < m∠BAN
- BE is tangent to Circle N at point A.
- NB ≈ 6.1
Given DC is tangent to circle N at point C: m∠DCN < m∠BAN and BE is tangent to Circle N at point A, is True
(1) From the diagram, we can see that angles ∠DCN and ∠BAN are vertical angles, so they are equal in measure. Since DC is tangent to Circle N at point C, we know that m∠DCN is a right angle. Therefore, m∠DCN = 90° and m∠BAN = 90° - m∠DCN. Since m∠DCN is positive, we have m∠BAN < 90°, which implies that m∠DCN < m∠BAN. So, statement (1) is true.
(2) Since DC is tangent to Circle N at point C, we know that angle ∠CBE is a right angle, and hence BE is perpendicular to CE. Also, we know that CE is the radius of Circle N, so it is perpendicular to NB. Therefore, BE is tangent to Circle N at point A. So, statement (2) is true.
(3) The length of NB cannot be determined from the given information. We only know that CE = 6, but we do not know the radius of Circle N or the position of point B along the circle. Therefore, we cannot determine the length of NB. So, statement (3) cannot be determined.
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Complete question:
Given DC is tangent to circle N at point C, which statements are true?
- m∠DCN < m∠BAN
- BE is tangent to Circle N at point A.
- NB ≈ 6.1
Mr. Taylor and Mrs. Miller’s classes have been having a fundraising competition. they’ve both kept track of how much money they’ve raised in dollars versus the time in days. while mr. taylor’s class chose to graph their data, mrs. millers class chose to present it in a table. both classes have found that their fundraising over time has been proportional, where the daily increase in money raised is consistent. please explain why you chose this answer i will mark you brainliest
How do I prove that (x^2 +2xy + y^2) = (x + y) is true
Answer:
Use the given functions to set up and simplify
.
x=−y+1
x=−y
Step-by-step explanation:
Answer:
see explanation
Step-by-step explanation:
Your question should be
Prove that x² + 2xy + y² = (x + y)²
So
(x + y)² = (x + y)(x + y)
Each term in the second factor is multiplied by each term in the first factor, that is
x(x + y) + y(x + y) ← distribute parenthesis
= x² + xy + xy + y² ← collect like terms
= x² + 2xy + y²
Then
x² + 2xy + y² = (x + y)²
Select the expressions that are equivalent to 6(x + 7).
(7 + x) 6
6x + 42
(x + 7)6
42x + 6
Answer:
\(6x + 42\)
Step-by-step explanation:
Apply the distributive property:
\(6x + 6 \times 7\)
Multiply 6 by 7
\(6x + 42\)
Select ALL expressions that are equivalent to 8w + (w + 4) + 5w
a. 6w + (9w)
b. 8w + 6w + 5w
c. 9w + 4 + 5w
d. 13w + (w + 4)
e. 18w
Answer:
c is correct
Step-by-step explanation:
8w +(w+4) +5w
9w+4+5w
Solve each equation. Check your answers.
ln (t-1)²=3
t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.
What is Logarithm?The opposite of exponentiation is the logarithm.This indicates that the exponent to which a fixed number, base b, must be raised in order to obtain a specific number x, is represented by the logarithm of that number.A number's natural logarithm is its logarithm to the base of the transcendental and irrational number e, which is roughly equivalent to 2.718281828459.Now,
In ln ( t -1 )² = 3, by property of logarithm ( \(log_b(a)^m=m(log_b(a))\)),
=> 2 ( ln (t -1) ) = 3
=> ln (t - 1) = \(\frac{3}{2}\)
=> t - 1 = \(e^\frac{3}{2}\)
=> t = \(e^\frac{3}{2}\) + 1 = 4.48 + 1 = 5.48
Hence, t = 5.48 in ln (t - 1)² = 3, by properties of logarithm.
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S, P, T.
S, P, Y.
TP,x
TxY
Answer:
S , P , T
Step-by-step explanation:
collinear points are points that lie on the same line.
S , P , T lie on the same line and are therefore collinear
Answer:
SPT
Step-by-step explanation:
You also have XPY but that isn't a choice in your list. SPT goes in a straight line making it collinear
Calculators cost $40 each at Tech Central. How many calculators can Mrs.Robinson buy for her class with $1,000 if the tax on each calculator is 0.30? Write an equation.
Answer:
24
Step-by-step explanation:
TRUST
As the balloon inflates at 20 cubic inches per second, the diameter and radius are changing. let's focus on the moment when the radius is 12 inches. share your answer with correct units.
At the moment when the radius is 12 inches, the balloon is inflating at a rate of 20 cubic inches per second.
To determine the rate at which the radius is changing, we can use the formula for the volume of a sphere, which is given by \(V = \left(\frac{4}{3}\right)\pi r^3\), where V is the volume and r is the radius.
Taking the derivative of both sides with respect to time t, we get \(\frac{dV}{dt} = 4\pi r^2\left(\frac{dr}{dt}\right)\), where \(\frac{dV}{dt}\) represents the rate of change of volume with respect to time and \(\frac{dr}{dt}\) represents the rate of change of radius with respect to time.
Given that \(\frac{dV}{dt} = 20\) cubic inches per second, we can substitute this value into the equation and solve for \(\frac{dr}{dt}\) when r = 12 inches:
\(20 = 4\pi (12)^2 \left(\frac{dr}{dt}\right)\)
Simplifying the equation:
\(20 = 576\pi \left(\frac{dr}{dt}\right)\)
Dividing both sides by 576π:
\(\left(\frac{dr}{dt}\right) = \frac{20}{576\pi}\)
Therefore, the rate at which the radius is changing when the radius is 12 inches is approximately \(\frac{20}{576\pi}\) inches per second.
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How many solutions are there in the given equation?
y = 2x² + 6x + 4
Step-by-step explanation:
Use the quadratic formula
=
−
±
2
−
4
√
2
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
2
2
+
6
+
4
=
0
2x^{2}+6x+4=0
2x2+6x+4=0
=
2
a={\color{#c92786}{2}}
a=2
=
6
b={\color{#e8710a}{6}}
b=6
=
4
c={\color{#129eaf}{4}}
c=4
=
−
6
±
6
2
−
4
⋅
2
⋅
4
√
2
⋅
2
x=\frac{-{\color{#e8710a}{6}} \pm \sqrt{{\color{#e8710a}{6}}^{2}-4 \cdot {\color{#c92786}{2}} \cdot {\color{#129eaf}{4}}}}{2 \cdot {\color{#c92786}{2}}}
x=2⋅2−6±62−4⋅2⋅4
brainliest and follow and thanks
how many separate hypothesis tests does a two-factor analysis of variance with 2 levels of factor a and 3 levels of factor b involve?
A two-factor analysis of variance with 2 levels of factor A and 3 levels of factor B involves six separate hypothesis tests.
If the null hypothesis is correct, the F statistic will be low because the between-treatment variation (numerator) won't be greater than the residual or error variation (denominator). The F statistic will be high if the null hypothesis is untrue.
The residual variance, also known as the error variance, is the denominator of the F-ratio in a repeated-measures ANOVA and quantifies the amount of variance that would be predicted if neither a systematic treatment effect nor a personal characteristic were to influence the variability of the scores.
Hence we get the required answer.
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the area under the entire probability density curve is equal to ____
The probability density function is defined as the derivative of the cumulative distribution function. It represents the relative likelihood of a continuous random variable taking on a specific value. The total area under the probability density curve is always equal to 1.
For a continuous random variable X, the probability density function f(x) satisfies the following properties:
1. Non-negativity: f(x) ≥ 0 for all x.
2. Integrates to 1: The integral of the probability density function over the entire range of X is equal to 1:
∫[−∞, ∞] f(x) dx = 1
This integral represents the total area under the probability density curve, which must be equal to 1.
To calculate the probability of X falling within a certain interval [a, b], we can use the probability density function as follows:
P(a ≤ X ≤ b) = ∫[a, b] f(x) dx
This integral gives the probability that X takes on a value between a and b.
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1) 2 + x = 22 3) -6 + p = -18 5) -29 = -20 + n 7) -5 + r = -23 9) 11 = x + 13 11) 101 = n +55 2) -15 = -18 + n 4) -18 + v = -9 6) -19 = n - 13 8) -12 = k +5 10) 11 = -1 + x 12) x - 36 = -68
Answer:
1)x=20
3)p=−12
5)n=−9
7)r=−18
9)x=−2
11)n=46
2)n = 3
4)v=9
6)n=−6
8)k=−17
10)x=12
12)x=−32
Step-by-step explanation:
Let's solve your equation step-by-step.
1) 2+x=22
Step 1: Simplify both sides of the equation.
x+2=22
Step 2: Subtract 2 from both sides.
x+2−2=22−2
x=20
3) −6+p=−18
Step 1: Simplify both sides of the equation.
p−6=−18
Step 2: Add 6 to both sides.
p−6+6=−18+6
p=−12
5) −29=−20+n
Step 1: Simplify both sides of the equation.
−29=n−20
Step 2: Flip the equation.
n−20=−29
Step 3: Add 20 to both sides.
n−20+20=−29+20
n=−9
7) −5+r=−23
Step 1: Simplify both sides of the equation.
r−5=−23
Step 2: Add 5 to both sides.
r−5+5=−23+5
r=−18
9) 11=x+13
Step 1: Flip the equation.
x+13=11
Step 2: Subtract 13 from both sides.
x+13−13=11−13
x=−2
11) 101=n+55
Step 1: Flip the equation.
n+55=101
Step 2: Subtract 55 from both sides.
n+55−55=101−55
n=46
2) −15=−18+n
Step 1: Simplify both sides of the equation.
−15=n−18
Step 2: Flip the equation.
n−18=−15
Step 3: Add 18 to both sides.
n−18+18=−15+18
n=3
4) −18+v=−9
Step 1: Simplify both sides of the equation.
v−18=−9
Step 2: Add 18 to both sides.
v−18+18=−9+18
v=9
6) −19=n−13
Step 1: Flip the equation.
n−13=−19
Step 2: Add 13 to both sides.
n−13+13=−19+13
n=−6
8) −12=k+5
Step 1: Flip the equation.
k+5=−12
Step 2: Subtract 5 from both sides.
k+5−5=−12−5
k=−17
10) 11=−1+x
Step 1: Simplify both sides of the equation.
11=x−1
Step 2: Flip the equation.
x−1=11
Step 3: Add 1 to both sides.
x−1+1=11+1
x=12
12) x−36=−68
Step 1: Add 36 to both sides.
x−36+36=−68+36
x=−32
Please help I will give brainliest
Answer:
1. ∠YZX = 37°
2. ∠YXZ = 53°
3. XZ = 30 meters
Step-by-step explanation:
1. To solve for an unknown angle, we need to utilize the inverse of a trigonometric function.
⭐What are the inverses of the trigonometric functions?
\(sin^-1 (opposite/hypotenuse)\)\(cos^-1 (adjacent/hypotenuse)\)\(tan^-1(opposite/adjacent)\)To know which inverse of the trigonometric functions we use, we have to see the type of side lengths we are given (opposite, adjacent, or hypotenuse)
We are given side length XY, which is opposite of ∠YZX, and we are given side length YZ, which is adjacent to ∠YZX. Therefore, we will use \(tan^-1 (opposite/adjacent) =\)
Substitute the values we are given into the function:
\(tan^-1 (18/24) =\)
Compute this equation using a scientific calculator. I recommend using the Desmos Scientific Calculator:
\(= 37\)
∴ ∠YZX = 37°
2. We already know 2 angles (∠YZX = 37°, and ∠ZYX = 90°) Therefore, to find ∠YXZ, we have to utilize the triangle sum theorem.
⭐ What is the triangle sum theorem?
\(angle_1 + angle_2 +angle_3 = 180\)The sum of all angles in a triangle is 180°Substitute the angles we know already (∠YZX and ∠ZYX), and solve for ∠YXZ.
\(< YZX + < ZYX + < YXZ = 180\)
\(37 + 90 + YXZ = 180\)
\(127 + YXZ = 180\)
\(< YXZ = 53\)
∴ ∠YXZ = 53°
3. We already know 2 side lengths (ZY = 24 meters, and XY = 18). Therefore, to find XZ, we have to utilize the Pythagoras' theorem.
⭐ What is the Pythagoras' theorem?
\((C)^2 = (A)^2 + (B)^2\)C is the hypotenuse of the triangle, A is a leg of the triangle, and B is another leg of the trianglePythagoras' theorem can only be used on right trianglesSubstitute the values of the side lengths into the formula:
\((XZ)^2 = (XY)^2 + (ZY)^2\)
\((XZ)^2 = 18^2 + 24^2\)
Solve for XZ:
\((XZ)^2 = 324 + 576\)
\((XZ)^2 = 900\)
\(\sqrt{(XZ)^2} = \sqrt{900}\)
\(XZ = 30\)
∴ XZ = 30 meters
If a firm uses x units of input in process A, it produces 32x3/2 units of output. In the alternative process B, the same input produces 4x3 units of output. For what levels of input does process A produce more than process B?
Answer:
The outcomes produced by A would be greater than B. A further explanation is provided below.
Step-by-step explanation:
Given:
In process A,
Produced units = \(32x^{1.5}\)
In process B,
Produced units = \(4x^3\)
If the outcomes are equivalent then,
⇒ \(32x^{1.5}=4x^3\)
⇒ \(x^{1.5} = 8\)
By taking log both sides, we get
⇒ \(log \ 8= 1.5 \ log \ x\)
⇒ \(x=3.99\)
An antique vase was worth $185 when you inherited it from your grandma in
2007. In 2017, the vase is worth $325. Write and solve an equation to find how
much the vase should be worth in 2025
Answer:yes but that to is gonna get the same answer F(x) =1/2x+1/2
f-1(x) = [ ? ]x + [ ]
Step-by-step explanation:
Answer:
456,8
Step-by-step explanation:
325 / 185 / 10 * 8 * 325
The sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚. Work out the size of each of the eight interior angles.
The eight interior angle based on the information given will be 728°.
How to calculate the angle?From the information, the sizes of seven of the exterior angles of an octagon are 42˚, 110˚, 13˚, 67˚, 55˚, 11˚ and 53˚ and.we.wany to eork out the size of each of the eight interior angles
In this case, it should be noted the octagon has with sides. This will be Illustrated as:
= (n - 2) × 180
= (8 - 2) × 180
= 1080
The eight interior angle will be:
= 1080 - (42 + 110 + 13 + 67 + 55 + 11 + 54)
= 1080 - 352
= 728
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Question 11 of 30
What is the amplitude in the graph of y = 3sin(2x − 1) + 5?
-
Ο A. 1
B. 5
C. 2
D. 3
SUBMIT
3 is the amplitude, -4 is the minimum value, and 2 is the highest value.
What is amplitude?A function's amplitude is the distance that the graph of the function moves above and below its midline. The value of the amplitude when graphing a sine function is comparable to the value of the sine coefficient.the height difference between a periodic function's center line and peak (or trough).As an alternative, we might multiply the height from highest to lowest points by 2.the greatest deviation from equilibrium of a point on a vibrating body or wave in terms of displacement or distance traveled.
acc to our question-
Sin x is changed to sin 2x to modify the function's period from 2 πThe amplitude varies from 1 to 3, with a minimum value of -3 and a maximum value of 3, when sin 2x is substituted with 3 sin 2x.Then we translate 1 unit down by changing 3 sin 2x to 3 sin 2x - 1. Currently, the amplitude is 3, the period is, the minimum value is, the greatest value is, and the value in between is 2.Hence,3 is the amplitude, -4 is the minimum value, and 2 is the highest value
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A small company has a fleet of 6 pickup trucks and 5 delivery vans. A larger company has the same ratio of pickup trucks to delivery vans. If the larger company has 90 pickup trucks, how many delivery vans does it have?
Answer: 75 delivery vans
Step-by-step explanation:
The ratios are the same.
The small company has a ratio of 6 pickups : 5 delivery vans.
Assume the larger company's delivery vans are x.
Using direct proportion:
6 : 5
90 : x
Cross multiply:
6x = 450
x = 450 / 6
x = 75 delivery vans
Which of the numbers below correctly represents (-1)17?
Answer:
Step-by-step explanation:
https://answer.ya.guru/questions/6481809-which-number-line-correctly-represents-the-irrational-numbers.html
Answer:
i dont know because you didnt give number but is one -17 is so its that
Step-by-step explanation:
Plz, answer this question plz!
Answer:d
d
Step-by-step explanation:
Answer: C. 2/3
Step-by-step explanation:
Take the number of times the coin was flipped on heads (12)
and the total number of times the coin was flipped (18)
make it a fraction
12/18
reduce the fraction by dividing both numbers by 6
2/3
In the figure, a∥b and m∠3 = 34°.
What is the m∠7?
Enter your answer in the box. |__|
Therefore, In the figure, a∥b angle m∠7 = 34° .
What is angle ?An angle is a figure in Euclidean geometry made up of two rays that share a vertex, or common terminus, and are referred to as the sides of the angle. Angles of two rays lie in the plane containing the rays. Angles can also result from the intersection of two planes. Dihedral angles are the name given to them.
Here,
Given that a and b are parallel lines,
∠3 and ∠7 are corresponding angles and congruent
m∠3 = 34°
thus ,m∠7 =m∠3 = 34°
so, m∠7 = 34°
Therefore, In the figure, a∥b m∠7 = 34° .
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A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance Bo 81 Price 82 Rides where Attendance is the daily attendance (in 1,000s) , Price is the gate price (in S), and Rides is the number of rides at the amusement park: The researcher would like to construct interval estimates for Attendance when Price and Rides equal S85 and 30,respectively: The researcher estimates modified model where Attendance is the response variable and the explanatory variables are now defined as Price Price 85 and Rides Rides 30. A portion of the regression results is shown in the accompanying table: Regression Statistics Multiple 96 R Square 0 . 92 Adjusted Square Standard Error 9 . 75 Observations Standard Error 4.06 0.28 0.36 Coefficients 34 . 41 -1.20 3.62 t-stat 8 . 48 -4.23 10.15 P-value 4.33E-09 0.0002 1.04E-10 Lower 95$8 26 . 08 -1.79 2.89 Upper 958 42.74 ~0.62 4.35 Intercept Pricet Rides* According to the modified model, which of the following is 959 prediction interval for Attendance when Price and Rides equal $85 and 30, respectively? (Note that t0. 025,27 2 . 052.)'
the 95% prediction interval for Attendance when Price and Rides equal $85 and 30, respectively, is [21.03, 61.99].
To construct the prediction interval for Attendance when Price and Rides equal $85 and 30, respectively, we'll use the coefficient estimates and standard errors provided in the regression results.
The modified model is given by:
Attendance = 34.41 + (-1.20 * Price) + (3.62 * Rides)
First, calculate the prediction for Attendance:
Attendance = 34.41 + (-1.20 * 85) + (3.62 * 30) = 34.41 - 102 + 108.6 = 41.01
Next, we'll calculate the prediction interval using the standard error:
Standard Error = 9.75
The critical value for a 95% prediction interval with 27 degrees of freedom is t0.025,27 = 2.052.
Prediction Interval = Prediction ± (Critical Value * Standard Error)
Prediction Interval = 41.01 ± (2.052 * 9.75) = 41.01 ± 19.98
Lower Bound = 41.01 - 19.98 = 21.03
Upper Bound = 41.01 + 19.98 = 61.99
Therefore, the 95% prediction interval for Attendance when Price and Rides equal $85 and 30, respectively, is [21.03, 61.99].
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