Answer:
Step-by-step explanation:
given that Joan is building a sandbox in the shape of a regular pentagon.
The perimeter of the pentagon is
[tex]35y^4 - 65x^3[/tex]inches.
Since regular pentagon we know that all sides are equal and there are totally five sides.
Perimeter of regular pentagon = 5*side
= 5a where a = length of side
Equate 5a to given perimeter to get
[tex]5a=35y^4 - 65x^3\\[/tex]
divide by 5
[tex]a=\frac{35y^4 - 65x^3}{5} \\=7y^4-13x^3[/tex]
Answer:
D. 7y^4 - 13x^3 inches
Evaluate:
(-3g^2)^0
Where g=0
Answer:
undefined or 1
Step-by-step explanation:
(-3g^2)^0
Where g=0. (given)
now,
[tex](-3g^2)^0 \\ ( - 3(0) {}^{2} ) {}^{0} \\
[/tex]
undefined or 1
[tex]\text{Solve by plugging in 0 to g}\\\\(-3\left(0\right)^2)^0\\\\\text{Solve:0}\\\\(-3\left(0\right)^2)^0\\\\(-3(0))^0\\\\(0)^0=1\\[/tex]
1. In a certain course, grades are based on three tests worth 100 points each, three quizzes worth 50 points each, and a final exam worth 200 points. A student has test grades of 91, 82, and 88, and quiz grades of 50, 42, and 42. What is the lowest percent the student can get on the final and still earn an A (90% or more of the total points) in the course
Answer:
95%
Step-by-step explanation:
Three tests worth 100 points each = 3 X 100 = 300 points
Three quizzes worth 50 points each = 3 X 50 =150 points
Final exam worth 200 points
Total Obtainable Points=300+150+200=650
Total of test grades obtained (91, 82, and 88)=91+82+88=261
Total of quiz grades (50, 42, and 42) obtained = 50+42+42=134
Let x be the exam score for the student to obtain 90%
Therefore:
[tex]\frac{261+134+x}{650} X 100 \geq 90\\\frac{100(395+x)}{650} \geq 90\\39500+100x \geq 90X650\\39500+100x \geq 58500\\100x \geq 58500-39500\\100x \geq19000\\x \geq190\\[/tex]
The lowest score a student can score is 190.
Expressed as a percentage of 200,
[tex]\frac{190}{200}X100=95[/tex] per cent
The student must score a minimum of 95% in order to make an A.
The odds against an event are 4:7. Find the probability that that event will occur
Answer:
3:7 or .4285
Step-by-step explanation:
the odds against are 4:7 so the odds with must be 7-4=3
which will be written in 3:7 form
An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?
Step-by-step explanation:
Given : An equation for the depreciation of a car is given by [tex]y = A(1-r)^t[/tex], where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%.
To find : Approximately how old is the car?
Solution :
The value of a car is half what it originally cost i.e. [tex]y=\frac{1}{2} A[/tex]
The rate of depreciation is 10% i.e. r=10%=0.1
Substitute in the equation, [tex]y = A(1-r)^t[/tex]
[tex]\frac{1}{2} A= A(1-0.1)^t[/tex]
[tex]\frac{1}{2}= (0.9)^t[/tex]
Taking log both side,
[tex]\log(\frac{1}{2})=t\log (0.9)[/tex]
[tex]t=\frac{\log(\frac{1}{2})}{\log (0.9)}[/tex]
[tex]t=6.57[/tex]
[tex]t\approx 6.6[/tex]
Therefore, the car is about 6.6 years old.
Answer:
The car is 6.5 years old
Step-by-step explanation:
An equation for the depreciation of a car is given by [tex]y = A(1 - r)^t[/tex]
y = current value of the car
A = original cost
r = rate of depreciation
t = time in years
The value of a car is half what it originally cost
So, [tex]y = \frac{A}{2}[/tex]
The rate of depreciation is 10% = 0.1 =r
Substitute the values in equation
[tex]\frac{A}{2} = A(1 - 0.1)^t[/tex]
[tex]\frac{1}{2} =(1 - 0.1)^t[/tex]
[tex]\frac{1}{2} =(0.9)^t[/tex]
[tex]0.5=0.9^t[/tex]
t=6.57
Hence The car is 6.5 years old
In a shipment of 2,000 beach balls 150 are defective the manufacturer generates a random sample to simulate 20 beach balls to inspect in the next shipment the integers 1 to 150 represent defective beach balls
The concluding part of the question as obtained from the textbook;
The number on the 20 beach balls that come up in the simulated sample:
42, 1701, 638, 397, 113, 1243, 912, 380, 769, 1312, 76, 547, 721, 56, 4, 1411, 1766, 677, 201, 1840
A) Based on this sample, how many
defective beach balls might the
manufacturer expect in the next
shipment?
B) What is the difference between the
number of defective beach balls in the
actual shipment and the number
predicted in the next shipment?
Answer:
A) 500 defective beach balls.
B) Difference between the
number of defective beach balls in the
actual shipment and the number
predicted in the next shipment = 350
Step-by-step explanation:
The beach balls are labelled 1 to 2000 with the 150 defective ones labelled 1 to 150.
Then a random sample of 20 beach balls is picked, and the numbers are presented as
42, 1701, 638, 397, 113, 1243, 912, 380, 769, 1312, 76, 547, 721, 56, 4, 1411, 1766, 677, 201, 1840
Note that only the defective beach balls have numbers 1 to 150.
A) The number of beach balls with numbers from 1 to 150 in the sample is 5 (numbers 42, 113, 76, 56, 4). This is the number of defective beach balls in the sample.
Probability of getting a defective ball in the next shipment = (5/20) = 0.25
If every shipment contains 2000 beach balls, then there will be (0.25 × 2000) defective beach balls in the next sample; 500 defective beach balls.
B) Number of defective beach balls in actual shipmemt = 150
Number of predicted defective beach balls in the next shipment = 500
difference = 500 - 150 = 350.
Hope this Helps!!!
Answer:
C.) 500
Step-by-step explanation:
In a shipment of 2,000 beach balls, 150 are defective. The manufacturer generates a random sample to simulate 20 beach balls to inspect in the next shipment. The integers 1 to 150 represent defective beach balls.
42 1701 638 397 113
1243 912 380 769 1312
76 547 721 56 4
1411 1766 677 201 1840
12. Based on this sample, how many defective beach balls might the manufacturer expect in the next shipment?
Group of answer choices
A.) 100
B.) 200
C.) 500
D.) 1000
Which of the following is true of qualitative research methods? Question 5 options: Qualitative researchers must be able to translate numerical data into meaningful narrative information. Qualitative researchers seek to fit their answers into predetermined categories rather than to understand research participants. Qualitative research is less superior for studying topics that involve complex psychological motivations. Qualitative researchers emphasize their samples are made up of representative rather than relevant consumers.
Complete Question:
Which of the following is true of qualitative research methods?
A. Qualitative data may be analyzed qualitatively or quantitatively.
B. Qualitative researchers must be able to translate numerical data into meaningful narrative information.
C. Qualitative researchers seek to fit their answers into predetermined categories rather than to understand research participants.
D. Qualitative research is less superior for studying topics that involve complex psychological motivations.
E. Qualitative researchers emphasize their samples are made up of representative rather than relevant consumers.
Answer:
A. Qualitative data may be analyzed qualitatively or quantitatively.
Step-by-step explanation:
Qualitative data research is a way or method to gather or collect non-numerical information either by observation or by asking crucial questions. It is a scientific method.
Qualitative data research involves the gathering accurate data and one of the way to do this is by carrying out surveys.
Qualitative data research determines WHY a particular action is carried out.
There are various methods of Qualitative data research. They are:
a. Direct Observation
b. In-depth interviews
c. Focus groups
d. Open end surveys
e. Oral History
f. Ethnographic observation
Qualitative data may be analysed qualitatively or quantitatively.
Qualitative research methods involve the collection and analysis of non-numerical data to understand subjective experiences and behaviors.
Explanation:Qualitative research methods involve the collection and analysis of non-numerical data to understand subjective experiences and behaviors. It emphasizes open-ended questions, in-depth interviews, and observations to gain insights into complex psychological motivations. Qualitative researchers do not seek to fit their answers into predetermined categories but rather aim to understand research participants and their experiences.
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Convert the following radian angle into degrees.
The degree of the radian angle 0.11 is [tex]6.3^{\circ}[/tex]
Explanation:
It is given that the radian angle is 0.11
We need to determine the degrees of the radian angle.
To convert the radian into degrees, let us multiply the radian with [tex]\left(\frac{180}{\pi}\right)[/tex]
Thus, we have,
[tex]0.11\times\left(\frac{180}{\pi}\right)=\frac{19.8}{\pi}[/tex]
It is given that [tex]\pi=3.14[/tex]
Substituting [tex]\pi=3.14[/tex] in the above expression, we have,
[tex]\frac{19.8}{3.14} =6.303...[/tex]
Rounding off to the nearest tenth, we have,
[tex]6.3^{\circ}[/tex]
Thus, the degree of the radian angle 0.11 is [tex]6.3^{\circ}[/tex]
A circular track is being built for students to use in P.E., at a nearby school. The distance from one side, straight through the center, to the opposite side, is 136 m. The circumference of the track is ? M. Round to the nearest 100th.
what's the inverse of y=ln(x+5) and what's the inverse of y=e^x +4
Step-by-step explanation:
To find the inverse of a function y = f(x), switch x and y, then solve for y.
y = ln(x + 5)
x = ln(y + 5)
eˣ = y + 5
y = eˣ − 5
y = eˣ + 4
x = eʸ + 4
x − 4 = eʸ
y = ln(x − 4)
Please help
Trig: Laws of Cosines.
In Δ ABC , side a =3, side b =15 and m < C= 108* . Find side ' c' to the nearest integer.
Answer: 16
Step-by-step explanation:
law of cosines says that c^2 = a^2 + b^2 -2abcosC
so c^2 = 3^2 +15^2 - 2*2*15*cos108
c^2 = 234 - (-27.8115294937 )
c^2 = 261.811529494
c = 16.18 rounds to 16
Answer:
16
Step-by-step explanation:
c² = a² + b² - 2(a)(b)cos(C)
c² = 3² + 15² - 2(3)(15)cos(108)
c² = 261.8115295
c = 16.18059114
Maria skates 40 feet due south in a skating rink. Then she skates 60 feet due east. Maria then skates diagonally across the ring back to where she started. What is the total distance, to the nearest foot, maria skates.
Answer:
172 ft
Step-by-step explanation:
Due south and due east form a 90-degree angle.
Her path is a right triangle. The 60 ft and 40 ft distances are the legs of the right triangle. We can use the Pythagorean theorem to find the hypotenuse. Then we add the lengths of the three sides to find the total distance she traveled which is the perimeter of the right triangle.
a^2 + b^2 = c^2
(40 ft)^2 + (60 ft)^2 = c^2
1600 ft^2 + 3600 ft^2 = c^2
c^2 = 5200 ft^2
c = 72 ft
perimeter = a + b + c = 40 ft + 60 ft + 72 ft = 172 ft
Answer: total distance is 172 feet
Step-by-step explanation:
The different directions along which Maria moved forms a right angle triangle.
The diagonal distance, h across the ring back to where she started represents the hypotenuse of the right angle triangle. The distances due south and east represents the opposite and adjacent sides of the right angle triangle.
To determine h, we would apply Pythagoras theorem which is expressed as
Hypotenuse² = opposite side² + adjacent side²
Therefore,
h² = 60² + 40²
h² = 5200
h = √5200
h = 72 feet
The total distance, to the nearest foot, maria skates is
72 + 60 + 40 = 172 feet
the base of the 37 foot ladder is 9 feet from the wall of a building. will the top of the ladder reach a window ledge 35 feet above the ground?
-I know its a yes but what is the math in it?
Answer:
The answer to your question is Yes.
Step-by-step explanation:
The math in this problem is that we need to use the Pythagorean theorem to solve it. Pythagorean theorem is part of trigonometry a branch of Maths.
Data
base = 9 ft
length = 37 ft
height = ?
Pythagorean theorem
c² = a² + b²
length = c
base = a
height = b
37² = 9² + b²
-Solve for b
b² = 37² - 9²
-Simplify
b² = 1369 - 81
b² = 1288
-Result
b = 35.88
-Conclusion
The ladder will reach a height higher than 35 ft.
Subscriptions to a fashion magazine have gone down by a consistent 5% each year. If the magazine currently has 25,000 subscribers, how many will there be in 6 years?
After 6 years the number of subscribers are 16500.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
Given that Subscriptions to a fashion magazine have gone down by a consistent 5% each year.
The magazine currently has 25,000 subscribers.
We need to find the number of subscribers after 6 years.
[tex]A=Pe^{rt}[/tex]
where r is rate of interest
t is the time
p is the initial subscribers
[tex]A=25000e^{0.05(6)}[/tex]
[tex]A=25000e^{0.3}[/tex]
A=25000(1.34)
A=33500
As it is going down so we need to subtract 33500-25000
8500
So from initial subscribers 8500 are left.
250000-8500
16500
Hence, after 6 years the number of subscribers are 16500.
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People start to leave the stadium at the end of a football game. The number of people, PPP, that are left in the stadium mmm minutes after the end of the game is given by the equation above. How many people were present when the game ended but before people started to leave? P=45,000−1,000m
Answer:
45,000
Step-by-step explanation:
If P=45,000−1,000m,
where P=The number of people left in the stadium m minutes after the end of the game
We want to determine how many people were present when the game ended but before people started to leave.
Note that immediately the game ended,
m=0
Therefore, the number of people left in the stadium
P=45000−(1000 X 0)
P=45000
There were 45,000 people.
ski-lift cables aren’t string at an angle 30 ° to the top of a 5000 ft mountain. How long are the cables?
Answer: the length of the cable is 10000 feet.
Step-by-step explanation:
A right angle triangle is formed. The length of the cable represents the hypotenuse of the right angle triangle. The height of the mountain represents the opposite side of the right angle triangle. To determine the length of the cable, L, we would apply the Sine trigonometric ratio.
Sin θ = opposite side/hypotenuse. Therefore,
Sin 30 = 5000/L
L = 5000/Sin 30 = 5000/0.5
L = 10000 ft
Is a chi-square goodness of fit test always applied to a one way table?
Answer:
Yes
Step-by-step explanation:
A chi-square test (y) examine whether it is good enough to fit, and associates a detected dispersal of Categorical data to the theorized dispersal shown in one-way table demonstrations distribution. If we get an empty hypothesis of the Chi test, it means no relationship exists between the categorial variables in the population, and they are not dependent on each other.
A farmer sold 20% of his chickens in the morning. He sold 240 chickens in the afternoon. He had 30% of his chickens left. How many chickens did the farmer have at first?
Answer:
The afrmer had 480 chickens at first
Step-by-step explanation:
We make an assumption here, that the initial number of chickens that the farmer has, is C.
Chickens sold by the farmer is (20% of C) + 240 chickens
Number of chickens left after selling in the morning and afternoon is 30% of C
So, the first number of chickens = Number of chickens sold + Number of chickens left
This gives us an equation that will be solved to obtain C.
C = ([tex]\frac{20}{100}[/tex] × C) + 240 chickens + ([tex]\frac{30}{100}[/tex] × C) = 0.2C + 240 chickens + 0.3C
C = 0.5C + 240 chickens
C - 0.5C = 240 chickens
0.5C = 240 chickens
C = [tex]\frac{240 chickens}{0.5}[/tex]
C = 480 Chickens
Answer: the answer is C = 480
Step-by-step explanation:
what is the value of x.
A. 17
B. 16
C. 16.5
D. 15
Answer:
Step-by-step explanation:
Because angle FGH and angle HGE are congruent, that angle bisector, namely GH, separates this largr triangle into one that shares sides in proportion to each other.
That means that [tex]\frac{x}{13.5} =\frac{68}{54}[/tex]
Cross multiply to get
54x = 918 and
x = 17
Choice A.
A rectangular prism has a length of 10ft, a height of 20ft, and a width of 6ft. What is its volume, in cubic ft?
Sawyer wants to fence in a rectangular spot for his garden. If he has 92 feet of fencing and works the length of the garden to be five feet less than twice it's width, what will be the area of the garden?
Answer: the area of the garden is 493 ft²
Step-by-step explanation:
Let L represent the length of the rectangular garden.
Let W represent the width of the rectangular garden.
The formula for determining the perimeter of a rectangle is expressed as
Perimeter = 2(L + W)
If he has 92 feet of fencing, it means that
2(L + W) = 92
Dividing through by 2, it becomes
L + W = 46 - - - - - - - - - - - -1
He wants the length of the garden to be five feet less than twice its width. This means that
L = 2W - 5
Substituting L = 2W - 5 into equation 1, it becomes
2W - 5 + W = 46
2W + W = 46 + 5
3W = 51
W = 51/3
W = 17 feet
L = 2W - 5 = 2 × 17 - 5
L = 29 feet
The area of the garden is
LW = 29 × 17 = 493 ft²
If x and y are positive integers and the mean of 4, 20, and x is equal to the mean of y and 16, what is the smallest possible value of x + y?
Answer:
5
Step-by-step explanation:
(4+20+x)/3 = (y+16)/2
2(24+x) = 3(y+16)
48 + 2x = 3y + 48
2x = 3y
Since x and y are positive integers, they can't be 0. To satisfy 2x = 3y
We'll have to use LCM of 2 and 3, which is 6 (or a multiple of 6)
For the least value, we use 6
To make both sides 6,
x = 3 and y = 2
Hence x + y = 5
Using the percentage-of-receivables method for recording bad debt expense, estimated uncollectible accounts are $43,000. If the balance of the Allowance for Doubtful Accounts is $4,600 balance before adjustment, what is the amount of bad debt expense for that period?
Step-by-step explanation:
Given that
Estimated uncolllectible account balance = $43,000
Balance of the allowance for doubtful accounts = $4,600
So the amount of bad debt expense is
Since it is not mentioned whether it is a credit or debit balance so we calculated by considering the both
If we considered the debit balance of allowance for doubtful debts so,
= $43,000 + $4,600
= $47,600
And, if credit balance, so
= $43,000 - $4,600
= $38,400
Solve 1/3 x = -4/5????
Answer:
x = −2.4
Step-by-step explanation:
Solve for x by simplifying both sides of the equation, then isolating the variable.
Exact Form: x = −12/5
Decimal Form: x = −2.4
Which of the following are ordered pairs for the equation y = 1/8x + 11?
(0,11) (8,12) (16,13)
(0,11) (7,13) (8,15)
(0,11) (5,12) (7,13)
(0,11) (6,12) (8,13)
Answer:
Again, A.
Step-by-step explanation:
Just graph the equation, but you can tell just by looking at it that (0,11) is the y-intercept meaning that it's one of the answer choices.
What is the y- value of the solution to the linear system below?
Answer: y = 6
y = -3x - 12
y = 3x + 24
Use elimination method to get 2y = 12 so y = 6.
Answer: the last option is the correct answer.
Step-by-step explanation:
The given system of equations is expressed as
y = - 3x - 12- - - - - - - - - - - - -1
y = 3x + 24- - - - - - - -- - - - - - -2
We would apply the method of elimination. Since x has the same coefficient and the sign is opposite, we would eliminate x by adding equation 1 to equation 2. It becomes
y + y = - 3x + 3x - 12 + 24
2y = 12
Dividing the left hand side and the right hand side of the equation by 2, it becomes
2y/2 = 12/2
y = 6
Trigonometry
Angle Sum and Difference, Double Angle and Half Angle Formulas
Find the exact value of:
Cos 20* cos 45* + sin 20* sin 45*
Answer:
cos(25)
Step-by-step explanation:
cosAcosB + sinAsinB = cos(A-B)
cos(20)cos(45) + sin(20)sin(45)
= cos(20-45) = cos(-25)
= cos(25) or 0.906
Brian is moving his 18 books. He has packed an equal number of books into each 5 empty boxes. How many books are in each box? How many books are left over?
Answer:
3 books per box, 3 left over.
Step-by-step explanation:
Brian has 18 books, and he is packing them into 5 boxes. 18 is only divisible by 1, 3, 9, and 18.
1 x 5 = 5 books = 13 left over. Still enough to pack more books.
3 x 5 = 15 books = 3 left over. This is the answer, but let's check the others as well.
9 x 5 = 45 books. He doesn't have that many! He can't put 9 books in each box because it would only take 2 boxes he's using all 5.
18 x 5 = 90 books. We can clearly see this isn't the answer. He would only be able to put all 18 books in 1 box but he wants to use all 5 boxes.
There are 3 books in each box with 3 left over.
Brian has 3 books in each of the 4 boxes, with 3 books remaining as leftovers after packing them equally.
Explanation:Brian is moving his 18 books and has packed an equal number of books into each of the 5 empty boxes. To find out how many books are in each box, we divide the total number of books by the number of boxes, which is = 18 books ÷ 5 boxes = 3 books per box with 3 books left over. Therefore, there will be 3 full boxes and one box with 3 leftover books.
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1. Consider the inequality 2x < 6(2).
a. Write the inequality to describe the possible values of x.
b. What could you do to both sides of the original inequality to determine your answer to part (a)?
We want
[tex]2x<6\cdot 2=12[/tex]
So, if we divide both sides by 2, we have
[tex]x<6[/tex]
So, we can accept all values for [tex]x[/tex], as long as they are less than 6 (excluded)
Answer:
a) 2x < 6(2)
x < 6
x can take any real value less than 6
b) divide both sides by 2;
Or multiply both sides by ½
2) Do MN and PQ bisect each other? If so, choose the proper formula to prove it. If not, explain the
reason.
Step-by-step explanation:
If the segments bisect each other, they will share the same midpoint.
Midpoint formula is:
(x, y) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Midpoint of MN is:
(x, y) = ((-5 + 5)/2, (6 + -2)/2)
(x, y) = (0, 2)
Midpoint of PQ is:
(x, y) = ((5 + -5)/2, (3 + 1)/2)
(x, y) = (0, 2)
So the segments do bisect each other.
The object below was made by placing a cone on top of a cylinder. The base of the cone is congruent to the base of the cylinder.1) What is the volume, in cubic centimeters, of the object? Explain how you found the volume of the (2) smaller shapes.2) Then explain how you found the volume of the total shape.**Do not just show your answer. Explain your steps and the numbers you used.**Did you use radius? Height? Diameter? Base? Pi (3.14)?
Answer:
Part 1) The volume of the object is [tex]32\pi\ cm^{3}[/tex] or [tex]100.48\ cm^{3}[/tex]
Part 2) see the procedure
Step-by-step explanation:
The picture of the question in the attached figure
Part 1) What is the volume, in cubic centimeters, of the object?
we know that
The volume of the object is equal to the volume of the cylinder plus the volume of the cone
Find the volume of the cone
The volume of the cone is equal to
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
[tex]h=3\ cm[/tex]
substitute the values
[tex]V=\frac{1}{3}\pi (2^{2})(3)=4\pi\ cm^{3}[/tex]
Find the volume of the cylinder
The volume of the cylinder is equal to
[tex]V=\pi r^{2} h[/tex]
we have
[tex]r=4/2=2\ cm[/tex] -----> the radius is half the diameter
[tex]h=(10-3)=7\ cm[/tex]
substitute the values
[tex]V=\pi (2^{2})(7)=28\pi\ cm^{3}[/tex]
Part 2) Then explain how you found the volume of the total shape
The volume of the total shape is equal to the volume of the cylinder plus the volume of the cone
[tex]4\pi\ cm^{3}+28\pi\ cm^{3}=32\pi\ cm^{3}[/tex] ------> exact value
Find the approximate value of the volume
assume
[tex]\pi=3.14[/tex]
[tex]32(3.14)=100.48\ cm^{3}[/tex]
Answer:
Step-by-step explanation: