Answers
Answer:
46.9
Step-by-step explanation:
sin54=x/58
58sin54=46.922
Related Questions
Select the correct answer from each drop-down menu.
The decimal equivalent of the fraction 2/15 is ____. The number of digits that should be repeating are __.
For the first blank options, 0.13, 0.1313, 0.133133, 0.1333
For the second blank options, 3, 2, 1, 0
Answers
Answer: 1. 0.1333 2. 1
Step-by-step explanation:
Step 1: 2/15 is the same as 2 divided by 15 which is 1.33333333333333333333333333333333333333333333333333 and so on.
Step 2: Clearly, the only number that is repeating is the 3.
121x
10
6
4
909
-6-5-4-3-2-12- 2 3 4 5 6 x
J
-8-
-10
B
h
Which statement is true regarding the functions on the
graph?
Of(6) = g(3)
Of(3) = g(3)
Of(3) = g(6)
Of(6) = g(6)
Answers
Answer:
The Question is not Correct but answer is f 3 and g 3
An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1050 feet apart..
airplane passes over the line joining them, each observer takes a sighting of the angle
elevation to the plane, as indicated in the figure. If A = 40 degrees and B = 30°, how high is th
airplane?
Answers
The airplane is 359.12 feet high.
Given,
The distance between the observers = 1050 feet
When an aero plane crosses the line connecting them, each observer measures the plane's elevation angle.
Angle A = 40 degrees
Angle B = 30 degrees
We have to find the height of the airplane.
Here,
C = 180 - (40 + 30) = 110°
According to the sine rule :
Sin110 / 1050 = Sin40 / b = Sin 30 / a
1050 sin40 / sin 110 = b = 718.24 ft
1050 sin 30 / sin 110 = a = 558.69 ft
Sin 40 = h / 558.69
h = 558.69 × sin 40
h = 359.12 feet
That is,
The airplane is 359.12 feet high.
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A concession stand at the Tennis Center sells a hamburger/drink combination dinner for $7. The profit, y (in dollars), can be approximated by
y=-0.001x² +
2+3.2x-400 where x is the number of dinners prepared.
(a) Find the number of dinners that should be prepared to maximize profit.
(h) What is the maximum profit?
Answers
The number of dinners that should be prepared to maximize profit is 1200.
The maximum profit is $1040
We know that,
y = ax²+ bx + c
The expression has the greatest value at x = -b/2a
From the question, we have
y=-0.001x² +2.4x-400
x = -b/2a
= -2.4/2*(-0.001)
=1200
substituting the value we get
y=-0.001x² +2.4x-400
y=-0.001*1200² +2.4*1200-400
y=$1040
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
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On average, a banana will last 6 days from the time it is purchased in the store to the time it is too rotten to eat. Is the mean time to spoil less if the banana is hung from the ceiling? The data show results of an experiment with 15 bananas that are hung from the ceiling. Assume that that distribution of the population is normal.
6.3, 3.5, 5.6, 4.2, 4.4, 3.9, 4.5, 5.5, 7.1, 5.6, 6.6, 6.1, 6.3, 7.2, 4
What can be concluded at the the
α
= 0.01 level of significance level of significance?
For this study, we should use
t-test for a population mean
The null and alternative hypotheses would be:
H
0
:
?
Select an answer
H
1
:
?
Select an answer
The test statistic
?
=
(please show your answer to 3 decimal places.)
The p-value =
(Please show your answer to 4 decimal places.)
The p-value is
?
α
Based on this, we should
Select an answer
the null hypothesis.
Thus, the final conclusion is that ...
The data suggest that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is not significantly less than 6 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.
The data suggest the population mean is not significantly less than 6 at
α
= 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6.
The data suggest the populaton mean is significantly less than 6 at
α
= 0.01, so there is statistically significant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is less than 6.
Answers
Considering the situation described, it is found that:
A t-test for a population mean should be used.The null hypothesis is: [tex]H_0: \mu = 6[/tex]The alternative hypothesis is: [tex]H_1: \mu < 6[/tex]The test statistic is of: t = -1.94.The p-value is of: 0.0364.The conclusion is of: The data suggest the population mean is not significantly less than 6 at α = 0.01, so there is statistically insignificant evidence to conclude that the population mean time that it takes for bananas to spoil if they are hung from the ceiling is equal to 6.What are the hypothesis tested?At the null hypothesis, it is tested if the mean is of 6 minutes, that is:
[tex]H_0: \mu = 6[/tex]
At the alternative hypothesis, it is tested if the mean is less than 6, hence:
[tex]H_1: \mu < 6[/tex]
What is the test statistic?The test statistic is obtained as follows:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
The parameters of the equation are:
[tex]\overline{x}[/tex] is the sample mean.[tex]\mu[/tex] is the value tested at the null hypothesis.s is the standard deviation of the sample.n is the sample size.Using a calculator from the sample, the values of the parameters are:
[tex]\overline{x} = 5.39, \mu = 6, s = 1.22, n = 15[/tex]
Hence the test statistic is:
[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]
[tex]t = \frac{5.39 - 6}{\frac{1.22}{\sqrt{15}}}[/tex]
t = -1.94.
What is the p-value and the conclusion?The p-value is obtained with a t-distribution calculator, with a left-tailed test, as we are testing if the mean is less than a value, with t = -1.94 and 15 - 1 = 14 df, hence it is of 0.0364.
Since the p-value is greater than the significance level of 0.01, the null hypothesis is not rejected and there is not enough evidence that the mean is less than 6 days.
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50 percent of 25 percent of the number is 96. What is the number?
Answers
Answer: 48
Step-by-step explanation:
first you divide 25/2 and you get 12.5 and that is irrelevant but what is relevant is that you divide 96 by 2 and you get 48 thus giving you the answer to that question. :)
En la pecera de Simón hay 6 veces la cantidad de peces de colores que peces guppy. Hay un total de 21 peces en la pecera. ¿Cuántos peces de colores más que peces guppy hay?
Answers
Answer:god is good
Step-by-step explanation:if u put this 1 stars u hate god
if u give 5 stars u love god
Draw the image of AABC under the translation (x, y) → (x, y + 3).
Answers
NO LINKS!! Please help me with these sequences Part 2x
Answers
Answer:
4. 121,800
5. 591 3/32
6. 1/4
Step-by-step explanation:
4. Sum of arithmetic sequenceYou want the sum of the first 200 terms of the arithmetic sequence starting 12, 18, 24, ....
The sum of the first n terms of an arithmetic sequence is given by the formula ...
Sn = (2·a1 +d(n -1))(n/2)
where a1 is the first term and d is the common difference. Your sequence has first term 12 and common difference 18-12 = 6. The desired sum is ...
S200 = (2·12 +6(200 -1))/(200/2) = (24 +1194)(100) = 121,800
5. Sum of geometric sequenceYou want the sum of the first 8 terms of the geometric sequence starting 12, 18, 27, ....
The sum of the first n terms of a geometric sequence is given by the formula ...
Sn = a1·(r^n -1)/(r -1)
where a1 is the first term and r is the common ratio. Your sequence has first term 12 and common ratio 18/12 = 3/2. The desired sum is ...
S8 = 12·((3/2)^8 -1)/(3/2 -1) = 24·6305/256 = 591 3/32
6. Sum of geometric sequenceFor this sequence, a1 = 1/12 and r = 2/3. When the sum is infinite and |r| < 1, the sum formula becomes ...
S = a1/(1 -r)
The desired sum is ...
S = (1/12)/(1 -2/3) = (1/12)/(4/12) = 1/4
Answer:
[tex]\textsf{4.} \quad 121,800[/tex]
[tex]\textsf{5.} \quad \dfrac{18915}{32}=591.09375[/tex]
[tex]\textsf{6.} \quad \dfrac{1}{4}[/tex]
Step-by-step explanation:
Question 4[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of an arithmetic series}\\\\$S_n=\dfrac{1}{2}n[2a+(n-1)d]$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $d$ is the common difference.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given arithmetic sequence:
12, 18, 24, ...The first term of the given sequence is 12.
The common difference can be found by subtracting the first term from the second term:
[tex]\implies d=a_2-a_1=18-12=6[/tex]
Therefore:
a = 12d = 6To find the sum of the first 200 terms, substitute n = 200, a = 12 and d = 6 into the formula:
[tex]\begin{aligned}S_{200}&=\dfrac{1}{2}(200)[2(12)+(200-1)(6)]\\&=100[24+(199)(6)]\\&=100[24+1194]\\&=100[1218]\\&=121800\end{aligned}[/tex]
Question 5[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Sum of the first $n$ terms of a geometric series}\\\\$S_n=\dfrac{a(1-r^n)}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\ \phantom{ww}$\bullet$ $n$ is the position of the term.\\\end{minipage}}[/tex]
Given geometric sequence:
12, 18, 27, ...The first term of the given sequence is 12.
The common ratio can be found by dividing the second term by the first term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{18}{12}=1.5[/tex]
Therefore:
a = 12r = 1.5To find the sum of the first 8 terms, substitute n = 8, a = 12 and r = 1.5 into the formula:
[tex]\begin{aligned}\implies S_{8}&=\dfrac{12(1-1.5^8)}{1-1.5}\\\\&=\dfrac{12\left(1-\frac{6561}{256}\right)}{-0.5}\\\\&=\dfrac{12\left(-\frac{6305}{256}\right)}{-0.5}\\\\&=\dfrac{-\frac{18915}{64}}{-0.5}\\\\&=\dfrac{18915}{32}\\\\&=591.09375\end{aligned}[/tex]
Question 6[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
Given geometric sequence:
[tex]\dfrac{1}{12},\dfrac{1}{18},\dfrac{1}{27},...[/tex]The first term of the given sequence is ¹/₁₂.
The common ratio can be found by dividing the second term by the first term:
[tex]\implies r=\dfrac{a_2}{a_1}=\dfrac{\frac{1}{18}}{\frac{1}{12}}=\dfrac{2}{3}[/tex]
Therefore:
a = ¹/₁₂r = ²/₃To find the sum of the infinite geometric sequence, substitute a = ¹/₁₂ and r = ²/₃ into the formula:
[tex]\begin{aligned}\implies S_{\infty}&=\dfrac{\frac{1}{12}}{1-\frac{2}{3}}\\\\&=\dfrac{\frac{1}{12}}{\frac{1}{3}}\\\\&=\dfrac{1}{12} \times \dfrac{3}{1}\\\\&=\dfrac{3}{12}\\\\&=\dfrac{1}{4}\end{aligned}[/tex]
The display on a calculator screen is shown below.
What number does the calculator display represent?
OA. 0.0000012312
B. 0.0000001231
OC. 1,231,151
D. 123,115.1
1.231151 E-6
Answers
The number which is as represented on the calculator display is; Choice A; 0.000001231151
What number does the calculator display represent?It follows from the task content that the number which is represented on the calculator display is to be identified.
By checking, The display of the calculator is; 1.231151 E-⁶.
The number above can be represented as follows;
1.231151 × 10-⁶.
Since a negative exponent on the number ten indicates a shift leftwards, it follows that the number represented on the calculator display is;
0.000001231151.
Therefore, the correct number represented on the calculator display is; Choice A; 0.000001231151.
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The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5), and (6, 4). Find the length of the sides of the rectangle and its perimeter.
Answers
Answer: This is a 1 by 5 rectangle
perimeter = 12 units
========================================================
Work Shown:
Label the vertices A,B,C,D
A = (1, 4)
B = (1, 5)
C = (6, 5)
D = (6, 4)
The x coordinates of points A and B are the same (x = 1). The difference in y values of these points is 5-4 = 1 unit. This is the height of the rectangle. In other words, it's the length of segment AB.
Points B and C have the same y coordinate (y = 5). The difference in x value is 6-1 = 5 which is the horizontal length of the rectangle. This is the length of segment BC.
In short, this is a 1 by 5 rectangle. It's one unit tall and five units across.
--------
Perimeter = 2*(length+width)
Perimeter = 2*(5+1)
Perimeter = 2*6
Perimeter = 12 units
Or you can add up the four sides (1,5,1 and 5) to get the same result.
Add the rational expressions. Show all work.
5/(x+3)(x-4) + 7/(x+2)(x-4)
Answers
The given rational expression when added gives
[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]
How to add rational expression?Given:
[tex] \frac{5}{(x + 3)(x - 4)} + \frac{7}{(x + 2)(x - 4)} [/tex]
Find the lowest common multiple (LCM)=
[tex] \frac{5(x + 2) + 7(x + 3)}{(x + 3)(x - 4)(x + 2)} [/tex]
Open parenthesis=
[tex] \frac{5x + 10 + 7x + 21}{(x + 3)(x - 4)(x + 2)} [/tex]
Collect and add like terms=
[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]
So therefore, the addition of the rational expression is
[tex] \frac{12x + 31}{(x + 3)(x - 4)(x + 2)} [/tex]
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The Jellybean jar has a radius of 6.2 cm and a height of 18.3 cm. What would be a
reasonable upper limit for the number of jellybeans in the jar? Reminder: Cylinder's
Volume = pi'r^2*h.
1
100
10000
100000
Please help
Answers
The volume or the upper limit of the jellybean jar is 2,208.83cm³.
What do we mean by Volume?The space occupied within an object's borders in three dimensions is referred to as its volume.
It is sometimes referred to as the object's capacity.
Volume and mass are the two fundamental characteristics of matter.
Volume is only the amount of space that a thing occupies.
There are a few methods for determining an object's volume depending on its physical state.
So, the volume of the Jellybean jar:
Formula: πr²h
Now, insert values and calculate as follows:
πr²h
π(6.2)²18.3
π38.44(18.3)
π703.452
2,208.83
Therefore, the volume or the upper limit of the jellybean jar is 2,208.83cm³.
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ne
Problem 14:
From this diagram, select the
pair of lines that must be
parallel if 45 47. If there
is no pair of lines, select
"none."
Playback
2
7
4
3
(first taught in
lesson 24)
9
8
6
After you pick your answer press GO.
A. l || n
B. oll q
C. l | m
D. pllq
E. None
10
7
GO
l
Contro
Lecture
& Problem
Scratchpa
Wallpaper
Answers
From the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .
As given in the question,
Given pair of lines,
Condition given that two angles are congruent ,
∠5 ≅ ∠7
Angle 5 is congruent to vertical opposite angle and to make a pair of parallel line Opposite angle should be congruent to angle 7.
Opposite angle and Angle 7 are pair of corresponding angles.
Line l should be parallel to the line m to satisfied the condition of
∠5 ≅ ∠7.
Therefore, from the given pair of parallel lines , the lines which satisfies the condition of two angles to be congruent that is ∠5 ≅ ∠7 are l || m .
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A Mrs. Sharpe’s Starbucks card has a balance of $37.45 remaining. If each visit she spends$5.35, which equation represents the number of visits, v, she may make using the card?
Answers
Answer:
the equation is 37.45-5.35v=0
Step-by-step explanation:
37.45-5.35v=0
minus 37.45 to both sides
-5.35v=-37.45
divide -5.35 from both sides
v=7
after 7 days she will finish the card
Please select ONLY ONE of the two questions below to respond to. Choose the one you feel
you can answer the best! This portion of your test will be graded after you submit your exam.
Rubric / Requirements:
1) Make sure your response answers each part of the prompt and is written in at least 3 complete
sentences. (2 points)
2) Proof read your response to ensure you have used proper capitalization and spelling. (1 point)
3) Explain the WHY or HOW behind your ideas! Justify your stances using your knowledge from this unit.
(7 points)
4) Plagiarism in any form is not permitted. You risk a 0% on this section of the exam if you plagiarize.
5) You may use a speech to text tool for your response.
OPTION 1: Political Factions
In his Farewell Address in 1796, George Washington gave the following warnings about the dangers of political
parties:
"[Parties always] distract the public councils and (weaken] the public administration. It agitates the community with ill-
founded jealousies and false alarms, kindles the animosity of one party against another, [encourages) occasionally riot
and insurrection. It opens the door to foreign influence and corruption, which finds access to the government itself
through the channels of party passions..."
QUESTION: Why did George Washington caution against the formation of political parties?
What potential risks do political parties pose towards democracy? Do you think that the
country should have followed his advice?
Answers
Answer of the why did George Washington caution against the formation of political parties?
What potential risks do political parties pose towards democracy? Do you think that the country should have followed his advice are as follows :
(a) He believes that the government was undermined by differences between the political parties. Additionally, he argues that "the alternate domination" of one party over another and concurrent attempts to exact revenge on their rivals have resulted in terrible atrocities and "is itself a frightful despotism."
(b)The democratic theory's main tenet is that democracies force administrations to take citizens' preferences into account. Every contemporary democracy is organized by political parties, and some observers contend that parties are what makes democracies responsive. Others, however, contend that parties give extremists a platform and make governments less receptive to the needs of the populace. As newly established democracies around the world grapple with concerns of representation and governability, the discussion of parties and democracy assumes fresh prominence.
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Find x and y. I need it ASAP
Answers
Using the proportionality theorem, the values are:
x = 3
y = 2
How to Apply the Proportionality Theorem?The proportional theorem states that if two triangles are similar to each other, then their corresponding side lengths have the same ratios.
The triangles above are similar to each other, therefore, their corresponding sides will have lengths that are proportional or have the same ratios.
Therefore:
3/1.5 = 6/x
Cross multiple
3x = (1.5)(6)
3x = 9
3x/3 = 9/3
x = 3
Find y:
3/1.5 = 4/y
3y = (1.5)(4)
3y = 6
3y/3 = 6/3
y = 2
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Question 1
Given the demand function D(p) = √/100 - 2p
Find the Elasticity of Demand at a price of $6.
At this price we would say demand is
Inelastic
Unitary
Elastic
Based on this to increase revenue we should
Lower prices
Keep prices unchanged
Raise prices
Answers
Answer:
At this price, i would say the demand is: Unitary Inelastic Elastic Based on this, to increase revenue we should: Lower Prices Raise Prices Keep Prices
What is the graphing form of y = x2 - 12x + 7
Answers
The vertex of the equation y=x^2-12x+7 is (6,-29) and the graph is given below.
In the given question we have to find the graphing form of y=x^2-12x+7.
The given equation is y=x^2-12x+7.
To graph the given equation we firstly express that equation in the standard form of parabola.
y=a(x-h)^2+k
Add and subtract 36 in the given equation;
y=x^2-12x+36-36+7
y=x^2-2×6×x+(6)^2-29
y=(x-6)^2-29
The vertex of the given equation is (6,-29).
The graph of the given equation is given below:
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The answer please this is geometry, we’ve been trying to identify triangles by angles & sides
Answers
The measure of the required angle ∠VUT = 80 degrees
Given : A triangle with angle measures as :
∠RTU = 50°
exterior angle ∠UVR = 120°
To find : ∠VUT
In the given triangle we can use the exterior angle sum property
which states that the angle opposite to the inside of the triangle and the angle outside the triangle
The angle outside the triangle is 120 degrees
120 = ∠VUT + 50
thus on subtracting 50 both sides we will get
∠VUT = 120 - 50
∠VUT = 80 degrees
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Beth's family is on a road trip. After driving for a while, they stopped for gas, and then traveled 65 1/4 more miles before they decided to stop for lunch. After lunch, they tripled their distance traveled before stopping for the night. Their total distance traveled that day was 372 miles. How many miles had they traveled before their first stop for gas?
Enter your answer as a simplified mixed number in the box.
Answers
The distance travelled before their first gas stop is 76.68 miles.
What is a mixed fraction?A fraction consisting of a quotient and remainder is a mixed fraction. we can convert the mixed fraction to improper fraction by first dividing the numerator by denominator and then taking the quotient as whole number and remainder as the numerator of proper fraction keeping the denominator same.
Consider that the distance covered before their first stop for gas be 'x'
The Total distance travelled is 372 miles
WE have given that after stopping for gas they travelled 65 1/4 miles and then tripled their distance. The equation is;
x + 261/4 + 3x = 372
4x + 261/4 = 372
16x + 261 = 1488
16x = 1227
x = 76.68 miles
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Madison wanted to go to the mall, but first she attended her brother Zane's basketball
game. The basketball game lasted 135 minutes, or 15 minutes longer than double the
time Madison spent at the mall. How long was Madison at the mall?
Answers
Answer: 60 minutes
Step-by-step explanation:
x=time Madison spent at the mall
2x + 15 = 135
2x = 135-15
x = 120/2 = 60
A group of people are asked how many hours of television they watch each day to the nearest hour. Here are the results:
3 1 2 0 0 1 0 3 2 4
Which of the following is true about this data set?
Answers
Answer:
2 people watch tv 3 hours a day, 3 people watch tv 0 hours a day, 2 people watch tv 1 hour a day, 2 people watch tv 2 hours a day, and 1 person watches tv 4 hours a day
Step-by-step explanation:
hope it helped :)
Beth makes $10.25/hour and Bartley makes $11.50 an hour. If Beth worked for 23 hours and Bartley worked for 17 hours, what was their difference in the amount of money they each earned?
Answers
The difference in the amount of money earned by Beth and Bartley is $40.25.
Given that, Beth makes $10.25/hour and Bartley makes $11.50 an hour.
What is the unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
If Beth worked for 23 hours
Money earned by Beth is
10.25×23=$235.75
If Bartley worked for 17 hours
Money earned by Bartley is
11.50×17 =$195.5
So, difference of money = 235.75-195.5
= $40.25
Hence, the difference in the amount of money earned by Beth and Bartley is $40.25.
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help please! Trig question on homework this is the only one I can’t really figure out!
Answers
The measure of central angle is 45°
Here, arc length S = 5π/4
radius r = 5
We need to find central angle θ
Using the formula of arc length,
S = r * θ
5π/4 = 5 * θ
θ = π/4
θ = 45°
Therefore, the measure of central angle is 45°
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a. {(−5,4), (−4, −1), (−2,1), (0,4), (1,3)
What is the domain and range and it is a function
b. {(−3, −4), (−1,2), (0,0), (−3,5), (2,4)}
Domain:
Range:
Function?
Answers
The domain is {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}
The given relation is {(−5,4), (−4, −1), (−2,1), (0,4), (1,3)
We need to find its domain and range
Domain of the set is {-5, -4, -2, 0, 1}
Range of the set is {4, -1, 1, 4, 3}
If in an relation every input has an single output, it is said to be a function
Here, every element of the domain has a single element in range, so it is a function
The given relation is {(−3, −4), (−1,2), (0,0), (−3,5), (2,4)}
We need to find its domain and range
Domain of the set is {-3, -1, 0, -3, 2}
Range of the set is {-4, 2, 0, 5, 4}
If in an relation every input has an single output, it is said to be a function
Here, every element of the domain has a single element in range, so it is a function
Therefore, the domain is {-5, -4, -2, 0, 1} and range is {4, -1, 1, 4, 3}
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NO LINKS! Please help me with this problem #4l
Answers
Answer:
equation: (x -1)²/64 -(y -4)²/80 = 1foci: (-11, 4), (13, 4)Step-by-step explanation:
You want the steps to finding the equation of the hyperbola with center (1, 4), vertices (-7, 4) and (9, 4) and that includes the point (-11, -6).
Equation of a hyperbolaThe standard-form equation of a hyperbola with center (h, k) and semi-axes 'a' and 'b' is ...
[tex]\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1[/tex]
The "linear eccentricity" 'c' is the distance from the center to a focus, and satisfies the equation ...
c² = a² +b²
The vertices are (h±a, k) and the foci are (h±c, k).
ApplicationThe center of the hyperbola is given as (1, 4). The distance from the right vertex to the center is ...
a = 9-1 = 8
The equation thus far is ...
(x -1)/8² -(y -4)/b² = 1
The value of 'b' can be determined from the given point:
(-11 -1)²/8² -(-6 -4)²/b² = 1
9/4 -100/b² = 1
5/4 = 100/b²
b² = 100/(5/4) = 80
The linear eccentricity is ...
c² = a² +b²
c² = 64 +80 = 144
c = √144 = 12
The foci are (1±12, 4) = (-11, 4) and (13, 4).
The equation is ...
(x -1)²/64 -(y -4)²/80 = 1
Step summaryThe given information was used to find semi-major axis 'a'. Together with the given center value (h, k), and the given point, the equation was written and solved for b².The value of 'c' was found from a² and b², and used to find the locations of the foci.
Answer:
[tex]\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1[/tex]
Center = (1, 4)Vertices = (-7, 4) and (9, 4)Foci = (-11, 4) and (13, 4)Step-by-step explanation:
Standard equation of a horizontal hyperbola (opening left and right):
[tex]\boxed{\dfrac{(x-h)^2}{a^2}-\dfrac{(y-k)^2}{b^2}=1}[/tex]
where:
Center = (h, k)Vertices = (h±a, k)Co-vertices = (h, k±b)Foci = (h±c, k) where c² = a² + b²Given:
Center = (1, 4)Vertices = (-7, 4) and (9, 4)Point on the hyperbola = (-11, -6)Therefore:
h = 1k = 4Find the value of a using the x-values of the vertices:
[tex]\begin{aligned}\implies h-a &= -7\\1-a &= -7\\a &= 8\end{aligned}[/tex]
[tex]\begin{aligned}\implies h+a &= 9\\1+a &= 9\\a &= 8\end{aligned}[/tex]
Therefore, a = 8.
Substitute the values of h, k and a into the formula:
[tex]\implies \dfrac{(x-1)^2}{8^2}-\dfrac{(y-4)^2}{b^2}=1[/tex]
[tex]\implies \dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{b^2}=1[/tex]
Substitute the given point on the hyperbola (-11, -6) into the equation and solve for b²:
[tex]\implies \dfrac{(-11-1)^2}{64}-\dfrac{(-6-4)^2}{b^2}=1[/tex]
[tex]\implies \dfrac{(-12)^2}{64}-\dfrac{(-10)^2}{b^2}=1[/tex]
[tex]\implies \dfrac{144}{64}-\dfrac{100}{b^2}=1[/tex]
[tex]\implies \dfrac{144}{64}-1=\dfrac{100}{b^2}[/tex]
[tex]\implies \dfrac{144}{64}-\dfrac{64}{64}=\dfrac{100}{b^2}[/tex]
[tex]\implies \dfrac{80}{64}=\dfrac{100}{b^2}[/tex]
[tex]\implies \dfrac{5}{4}=\dfrac{100}{b^2}[/tex]
[tex]\implies b^2=\dfrac{4 \cdot 100}{5}[/tex]
[tex]\implies b^2=\dfrac{400}{5}[/tex]
[tex]\implies b^2=80[/tex]
Therefore, the equation of the hyperbola is:
[tex]\boxed{\dfrac{(x-1)^2}{64}-\dfrac{(y-4)^2}{80}=1}[/tex]
To find the foci, first find c where c² = a² + b²:
[tex]\implies c=\sqrt{a^2+b^2}[/tex]
[tex]\implies c=\sqrt{64+80}[/tex]
[tex]\implies c=\sqrt{144}[/tex]
[tex]\implies c=12[/tex]
Substitute the found value of c, along with the values of h and k into the foci formula:
[tex]\implies (h+c, k)=(1+12, 4)=(13,4)[/tex]
[tex]\implies (h-c,k)=(1-12,4)=(-11,4)[/tex]
Therefore, the foci are (-11, 4) and (13, 4).
Graph the equation using the point and the slope.
1
y-4=(x-2)
Use the graphing tool to graph the equation. Use the point contained in the equation when drawing
the line.
Answers
Answer:
slope: 1
y-intercept: (0,2)
the second point to plot: (1,3)
Step-by-step explanation:
Points to plot
(0,2),(1,3),(-2,0)
The Wilson family had 8 children. Assuming that the probability of a child being born a girl is 0.5, find the probability that the Wilson family had: at least 3 girls
how do I do this problem
Answers
The probability that the family had at least 3 girls is 0.6367
How to determine the probability that the family had at least 3 girls?
This is a binomial probability experiment. We are going to use the binomial distribution formula for determining the probability of x successes:
P(x = r) = nCr . p^r . q^n-r
Given: n= 8, probabibility of sucess (p) = 0.5, x≥3 (at least 3 girls)
The failures can be calculated using q = 1 - p = 1 - 0.5 = 0.5
P(x≥3) = 1 - P(x≤3) = 1 - ( P(x= 0) + P(x= 1) + P(x= 2) + P(x= 3) )
Using the formula:
P(x≥3) = 1 - ( (8C0 x 0.5⁰ x 0.5⁸⁻⁰) +(8C1 x 0.5¹ x 0.5⁸⁻¹) + (8C2 x 0.5² x 0.5⁸⁻²) + (8C3 x 0.5³ x 0.5⁸⁻³) )
= 1 - ( (1/256) + (1/32) + (7/64) + (7/32) )
= 0.6367
Therefore, the probability that the Wilson family had at least 3 girls is 0.6367
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What are the values of x, y, and z?
I need help with this please help me
Answers
Answer:
X - 111
Y - 104
Z - 76
Step-by-step explanation:
X - Just add 45 and 66
Y - 180 minus 76
Z - 119 minus 43