The cost of each Caribbean wedding is $15,000 and the cost of each backyard swimming pool wedding is $5,000.
To solve the word problem involving Underwater Weddings Inc., we can let the cost of a Caribbean wedding be x dollars. Since a backyard swimming pool wedding costs $10,000 less, its cost would be x - 10,000 dollars.
The problem states that there were 5 pool weddings and 2 Caribbean weddings, and the total income was $55,000. This gives us the equation:
5(x - 10,000) + 2x = 55,000
Now, we solve for x:
5x - 50,000 + 2x = 55,000
7x = 55,000 + 50,000
7x = 105,000
x = 105,000 / 7
x = 15,000
Caribbean weddings cost $15,000 each.
Therefore, backyard swimming pool weddings cost $15,000 - $10,000 = $5,000 each.
What is a variable? a. A variable is an unknown number or value represented by a letter c. A variable represents a change in value b. A variable always represents the total amount d. A variable is always represented by the letter x Please select the best answer from the choices provided A B C D
ANSWER
a. A variable is an unknown number or value represented by a letter
EXPLANATION
In mathematics, we use letters to represent an unknown quantity or number.
For instance, we can use the letter , t, to represent time taken to cover a given distance.
We can use the letter , s, to represent displacement or distance covered by an object.
The letters that we use to represent the unknown values or numbers are called variables.
The correct answer is A.
A variable is a characteristic that can change in value across different instances. It can be represented by any letter and can be numerical or categorical. In mathematical contexts, it often represents an unknown value in an equation.
Explanation:A variable, which can be represented by any letter, and not just 'x', is a characteristic that can vary in value across different instances. It could refer to different types of measurables such as a numerical variable like 'x' representing the number of points earned by a student or a categorical variable like 'y' representing someone's party affiliation. Variables in mathematical contexts are often used in equations to represent unknown values.
For example, if 'x' represents the number of children in a family, each different integer value of 'x'(0, 1, 2, 3, etc) specifies a unique family structure. Therefore, option A : 'A variable is an unknown number or value represented by a letter' is the correct choice.
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Solve for x.
x/7 = -3
x = -21
explanation: a trick i used was just do -3 times 7 and get my answer -21. if you are unsure if the answer is right just check your work with a calculator. -21 divided by 7 is -3 so -21 is the value of x. please mark brainliest !!
The rule for a pattern is add 6. The first term is 5. Write the first five terms in a pattern
An automatic car wash uses 5/8 gallon of soap on each car that is washed.Yesterday,the ,car wash used a total of 30 gallons of soap.How many cars washed yesterday?
Answer:
48
Step-by-step explanation:
divide 30 by 5/8
Answer: 48 cars washed yesterday.
Step-by-step explanation:
Given : An automatic car wash uses [tex]\dfrac{5}{8}[/tex] gallon of soap on each car that is washed.
Yesterday,the ,car wash used a total of 30 gallons of soap.
Then, the number of car washed yesterday is given by :-
[tex]30\div\dfrac{5}{8}\\\\=30\times\dfrac{8}{5}=48[/tex]
Hence, 48 cars washed yesterday.
Which of the following represents a geometric series (remember what a series is as opposed to a sequence)?
3 + 9 + 15 + ...
3 + 9 + 27 + ...
3, 9, 27, ...
3, 9, 15, ...
The first answer is correct
Answer:
3 + 9 + 27 + ...
Step-by-step explanation:
3 + 9 + 15 + ... is not a geometric series because it has no common ratio.
[tex]\frac{15}{9}\ne \frac{9}{3}[/tex]
3 + 9 + 27 + ... is a geometric series because there is a common ratio;
[tex]r=\frac{27}{9}=\frac{9}{3}=3[/tex]
3, 9, 27, ... is a geometric sequence and not a series. The sum of all the terms in a geometric sequence forms a geometric series.
3, 9, 15, ... is a not a geometric series.
Instead of 1/4 an hour ellen spent 1/3 of an hour to meet each applicant how much more time did she spend meeting all applicants
Answer:
5 more minutes (total of 20 minutes per applicant)
Step-by-step explanation:
Divide an hour by 1/3 (60/3 = 20 minutes)
Divide an hour by 1/4 (60/4= 15 minutes)
By spending 1/3 of an hour (20 minutes) instead of 1/4 of an hour (15 minutes), she spent 5 more minutes meeting all applicants.
Find the probabilities of the events described and arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability of occurrence.
the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles
the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples
the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens
the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls
Answer: The probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.
i.e. 0.2<0.42<0.7<0.87
Step-by-step explanation:
Since we have given that
1) the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles
Probability would be [tex]\dfrac{\text{Red Marble}}{Total\ marble}}=\dfrac{5}{12}=0.42[/tex]
2) the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples
Probability would be [tex]\dfrac{Peach}{Total}=\dfrac{7}{10}=0.7[/tex]
3) the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens
Probability would be [tex]\dfrac{Green}{Total}=\dfrac{4}{20}=\dfrac{1}{5}=0.2[/tex]
4) the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls
Probability would be [tex]\dfrac{Golf\ ball}{Total}=\dfrac{13}{15}=0.87[/tex]
We need to arrange them in order from the event with the lowest probability of occurrence to the event with the highest probability occurrence:
So, 0.2<0.42<0.7<0.87
Hence, it becomes
the probability of picking a green token from a box containing 10 red, 6 blue, and 4 green tokens < the probability of picking a red marble from a bag containing 5 green, 3 red, and 4 blue marbles < the probability of picking a peach from a basket of fruit containing 7 peaches and 3 apples < the probability of picking a golf ball from a box containing 2 tennis balls and 13 golf balls.
Jen started her homework at 3:45 and she worked for 2 hours and 37 minutes, What time did she finish her homework?
A family has two cars. During one particular week, the first car consumed 40 gallons of gas and the second consumed 35 gallons of gas. The two cars drove a combined total of 2125 miles, and the sum of their fuel efficiencies was 55 miles per gallon. What were the fuel efficiencies of each of the cars that week?
Answer:
Car 1 : 40 gallons
Car 2 : 15 gallons
Step-by-step explanation:
F = Car 1 Fuel Efficiency
S = Car 2 Fuel Efficiency
F + S = 55
40F + 35S = 2125
Using the first equation...
S = 55 - F
Then substitute into the second equation.
40F + 35(55 - F) = 2125
Simplify
40F + 1925 - 35F = 2125
5F + 1925 = 2125
5F = 200
F = 40
Then plug it back into S = 55 - F
S = 15
Plug it back into F + S = 55 to check.
Hope this helps.
Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.
Let car 1 fuel efficiency = x
Let car 2 fuel efficiency = y.
Based on the information given,
x+ y = 55 ...... i
40x + 35y = 2125 ...... ii
Therefore, y = 55 - x ..... iii
Put equation iii into ii
40x + 35(55 - x) = 2125
40x + 1925 - 35x = 2125
Collect like terms
40x - 35x = 2125 - 1925
5x = 200
x = 200/5
x = 40
Since x + y = 55.
y = 55 - 40 = 15
Therefore, Car 1 fuel efficiency is 40 gallons and car 2 fuel efficiency is 15 gallons.
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Plsss Urgent !! A container at the petting zoo holds 8138.88 cubic centimeters of grain. Visitors can fill paper cones with grain from the container. The cones have a radius of 4 centimeters and a height of 9 centimeters. How many times can you fill a cone with the grain that is stored in the container? Use 3.14 to approximate the value of Pi.
Answer:
54 times you can fill a cone with the grain that is stored in the container
Step-by-step explanation:
step 1
Find the volume of the paper cone
The volume of the cone is
[tex]V=\frac{1}{3}\pi r^{2} h[/tex]
we have
[tex]r=4\ cm[/tex]
[tex]h=9\ cm[/tex]
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{1}{3}(3.14)(4)^{2} (9)=150.72\ cm^{3}[/tex]
step 2
Divide the total volume of the container by the volume of one paper cone
[tex]\frac{8,138.88}{150.72}=54[/tex]
Answer:
Its 54
Step-by-step explanation:
Plz help!
The graph of f(x)=sin(x) is transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.
What is the equation of the new function g(x) ?
Enter your answer in the box.
g(x)= ____
Answer:
g(x) = 2sin(x) + 3
Step-by-step explanation:
f(x) = sin(x)
transformed into a new function, g(x) , by stretching it vertically by a factor of 4 and shifting it 3 units to the right.
so
g(x) = 2sin(x) + 3
The mean number of words per minute (WPM) read by sixth graders is 81 with a standard deviation of 17 WPM. If 130 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 77.21 WPM? Round your answer to four decimal places.
Answer:
The probability that the sample mean would be greater than 77.21 WPM = 0.9945
Step-by-step explanation:
Mean number of Words per Minute = u = 81
Standard Deviation = s = 17
sample size = n = 130
Target value = x = 77.21
we can find the probability by converting x to z-score.
The formula for z-score = [tex]\frac{x-u}{\frac{s}{\sqrt{n} } }[/tex]
using given values, z-score = [tex]\frac{77.21-81}{\frac{17}{\sqrt{130} } }[/tex]
=> -2.54
using the z table, we can find the find the probability of -2.54, that is 0.9945.
Therefore, the probability that the sample mean would be greater than 77.21 WPM = 0.9945
The probability that the sample mean would be greater than 77.21 WPM is approximately [tex]\(0.9945\)[/tex] (rounded to four decimal places).
To find the probability that the sample mean is greater than 77.21 WPM, we need to use the Central Limit Theorem.
Here's the step-by-step process:
1. Identify the given information:
Population mean [tex](\(\mu\))[/tex]: 81 WPM
Population standard deviation [tex](\(\sigma\))[/tex]: 17 WPM
Sample size [tex](\(n\))[/tex]: 130
Sample mean [tex](\(\bar{x}\))[/tex]: 77.21 WPM
2. Calculate the standard error of the mean (SEM):
[tex]\[ \text{SEM} = \frac{\sigma}{\sqrt{n}} = \frac{17}{\sqrt{130}} \approx \frac{17}{11.4018} \approx 1.4910 \][/tex]
3. Find the Z-score for the sample mean:
[tex]\[ Z = \frac{\bar{x} - \mu}{\text{SEM}} = \frac{77.21 - 81}{1.4910} \approx \frac{-3.79}{1.4910} \approx -2.543 \][/tex]
4. Use the Z-score to find the probability:
We look up the Z-score of -2.543 in the standard normal distribution table.
[tex]\[ P(Z < -2.543) \approx 0.0055 \][/tex]
This is the probability that the sample mean is less than 77.21 WPM. Since we need the probability that the sample mean is greater than 77.21 WPM, we subtract this value from 1.
[tex]\[ P(\bar{x} > 77.21) = 1 - P(Z < -2.543) = 1 - 0.0055 = 0.9945 \][/tex]
Un the morning a farm worker packed 4 pints of strawberries every 5 minutes in the afternoon she packed 3 pints of strawberries ev ery 4 minutes what was the diference between her morning and afternoon packing rates in pints per hour
Answer:
In the morning, the packing rates per hour was 45. In the afternoon, the packing rates per hour was 40. The difference is 5.
CALCULUS HELP NEEDED PLEASE!!!!
1.) Find the area or the region bounded by the curves y = x^3 and y = 9x.
a. 0
b. 10.13
c. 40.50
d. 20.25
2.)The region in the first quadrant bounded by the x-axis, the line x = π, and the curve y = sin(sin(x)) is rotated about the x-axis. What is the volume of the generated solid?
a. 1.219
b. 3.830
c. 1.786
d. 5.612
1. The given curves intersect one another three times:
[tex]x^3=9x\implies x(x^2-9)=0\implies x=0,\pm3[/tex]
The area of the bounded region is
[tex]\displaystyle\int_{-3}^3|x^3-9x|\,\mathrm dx[/tex]
[tex]x^3-9x[/tex] is odd, but the absolute value makes it even. More formally,
[tex]|(-x)^3-9(-x)|=|-x^3+9x|=|x^3-9x|[/tex]
which means the integral is equivalent to
[tex]\displaystyle2\int_0^3|x^3-9x|\,\mathrm dx[/tex]
For [tex]0\le x\le 3[/tex], the definition of absolute value tells us that
[tex]|x^3-9x|=9x-x^3[/tex]
so the integral evaluates to
[tex]\displaystyle2\int_0^3(9x-x^3)\,\mathrm dx=\left(9x^2-\frac{x^4}2\right)\bigg|_{x=0}^{x=3}=\frac{81}2=40.5[/tex]
2. Using the disk method, the volume is given by the integral
[tex]\displaystyle\pi\int_0^\pi\sin^2(\sin x)\,\mathrm dx[/tex]
Use a calculator to get the result 1.219.
What is the simplified form of x plus 3 over x squared minus x minus 12 ⋅ x minus 4 over x squared minus 8x plus 16 ?
Answer:
[tex]\dfrac{1}{x^2-8x+16}[/tex]
Step-by-step explanation:
The expression, written in full, looks like this:
[tex]\dfrac{x+3}{x^2-x-12}\cdot\dfrac{x-4}{x^2-8x+16}[/tex]
To simplify this expression, it would help us out a lot if we could factor the expressions in the denominators. Let's handle [tex]x^2-x-12[/tex] first:
[tex]x^2-x-12=\\=x^2-4x+3x-12\\=x(x-4)+3(x-4)\\=(x-4)(x+3)[/tex]
Next, we can factor [tex]x^2-8x+16[/tex]:
[tex]x^2-8x+16=\\=x^2-4x-4x+16\\=x(x-4)-4(x-4)\\=(x-4)(x-4)\\=(x-4)^2[/tex]
Substituting these back into our original expression, we get
[tex]\dfrac{x+3}{(x-4)(x+3)}\cdot\dfrac{x-4}{(x-4)^2}[/tex]
On the left, we can cancel an (x+3) in the numerator and denominator, and on the right, we can cancel an (x-4), simplifying the expression to
[tex]\dfrac{1}{x-4}\cdot\dfrac{1}{x-4}[/tex]
Multiplying the two together gives us the fraction
[tex]\dfrac{1\cdot1}{(x-4)\cdot(x-4)}=\dfrac{1}{(x-4)^2}[/tex]
Since [tex](x-4)^2=x^2-8x+16[/tex], we can rewrite this fraction in simplified form as
[tex]\dfrac{1}{x^2-8x+16}[/tex]
Triangle with a height of 25 feet and base of 12 feet. What is the area of the triangle?
Answer:
150 ft
Step-by-step explanation:
triangle area formula= (b*h)/2
25 time 12 is 300. divide 300 by 2 and get 150.
Answer:
A = 150 ft^2
Step-by-step explanation:
The area of a triangle is found by using
A = 1/2 b*h where b is the base and h is the height
A = 1/2 (12)*25
A = 6*25
A = 150 ft^2
To the nearest hundredth, what is the value of x?
Question 2 options:
36.08
41.51
47.81
72.88
➷ cos41 = x/55
x = cos41 x 55
x = 41.50902
The correct option would be 41.51
✽➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
↬ ʜᴀɴɴᴀʜ ♡
Answer:
41.51
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos41° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{55}[/tex]
Multiply both sides by 55
55 × cos41° = x
⇒ x = 41.51 ( to the nearest hundredth )
Anita earns 60 points every time she shops at a grocery store. She needs a total of 2,580 points to receive a free prize. So far, she has earned 480 points. How many more times will Anita have to shop at the grocery store in order to earn the additional points she needs for a free prize?
Answer:
35 times
Step-by-step explanation:
The points Anita has remaining for a prize is 2580 - 480 = 2100 points
Since each time she earns 60 points, to get 2100 points, she needs to go:
[tex]\frac{2100}{60}=35[/tex] times
She needs to go 35 times
Answer:
35 times
Step-by-step explanation:
Which expression is equivalent to 10k+17–7j-18-11k
A. -8jk-1
B. -7j-k-1
C. -7j+k+1
D. -8j-k
Answer:
B
Step-by-step explanation:
An equivalent expression is an expression which is equal to 10k + 17 - 7j - 18 - 11k. You can expand or simplify an expression to make an equivalent expression. Combine like terms to form a new equivalent expression. Like terms are terms which have the same base or variable.
10k + 17 - 7j - 18 - 11k
10k -11k + 17 - 18 - 7j Move to group like terms together.
-k - 1 - 7j
This is the same solution as B written in a different order.
Answer:
BBBBBBBBBBBBBBBBBBBBBBB
Step-by-step explanation:)
If there are 42 boys and 56 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
The simplest direct ratio of boys to girls in the room is 3:4, which means for every 3 boys, there are 4 girls. This is determined by finding the greatest common divisor of the two quantities. Other possible ratios such as 6:8, 9:12, 12:16, and 15:20 are multiples of this base ratio.
Explanation:The question is asking for us to form all the possible ratios of boys to girls in the given situation. We are given that there are 42 boys and 56 girls. The simplest ratio of boys to girls can be determined by finding the greatest common divisor (GCD) of both numbers and then dividing both numbers by it. The GCD of 42 and 56 is 14, so if we divide both numbers by the GCD, we get the ratio of 3:4. This implies that for every 3 boys, there are 4 girls. However, other possible ratios could use multiple of these numbers. Therefore, the possible ratios of boys to girls in this scenario also include 6:8, 9:12, 12:16, 15:20, and so on.
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10=16(x-2)^2+10
show work
Answer:
x=2
Step-by-step explanation:
10=16(x-2)^2+10
Subtract 10 from each side
10-10=16(x-2)^2+10-10
0 =16(x-2)^2
Divide by 16
0/16 = 16/16 (x-2)^2
0 = (x-2)^2
Take the square root of each side
sqrt(0) = sqrt( (x-2)^2)
0 = x-2
Add 2 to each side
0+2 = x-2+2
2 =x
[tex]Cancel \ 10 \ on \ both \ sides.\\\\0 = 16(x - 2)^2\\\\\\Divide \ both \ sides \ by \ 16.\\0 = (x - 2)\\\\\\Now take the square root of both sides.\\\\0 = x - 2\\\\\\Add 2 to both sides.\\\\2 = x\\\\Switch sides.\\\\\fbox{x = 2}[/tex]
Leo bought a fish tank that is 37 inches wide, 24 inches long, and 15 inches high. One gallon of water fills 230.4 cubic inches of space. How many gallos of water, to the nearest tenth, will fill the fish tank?
Answer:
57.82 gallons will be needed to fill the tank
Step-by-step explanation:
Final answer:
Leo's fish tank can hold approximately 57.8 gallons of water to the nearest tenth, calculated by finding the volume of the tank in cubic inches and then converting that to gallons using the conversion factor.
Explanation:
To calculate how many gallons of water can fill the fish tank to the nearest tenth, we need to find the volume of the tank in cubic inches and then convert that to gallons using the given conversion factor.
Step 1: Calculate the volume of the tank in cubic inches
The volume of the tank (V) is given by the formula V = length × width × height.
V = 24 in. (length) × 37 in. (width) × 15 in. (height) = 13,320 cubic inches.
Step 2: Convert cubic inches to gallons
Using the conversion factor 1 gallon = 230.4 cubic inches:
Number of gallons = Volume in cubic inches ÷ Conversion factor
Number of gallons = 13,320 in³ ÷ 230.4 in³/gal ≈ 57.8 gallons
Therefore, Leo's fish tank can hold approximately 57.8 gallons of water when filled to the top.
public relations is part of business and administrative support true or false
Answer: true :))
Step-by-step explanation:
Public relations is part of business and administrative support as it helps manage a business's image and relationship with the public. Meanwhile, bureaucracy plays a role in not only enforcing policies but also in policy formation.
Explanation:Public relations is indeed a part of business and administrative support. Businesses use public relations to manage and protect their image and relationship with the public. It's a key component to business administration as it helps businesses improve their brand awareness, manage crises, and strengthen relationships with stakeholders.
The question about bureaucracy is a separate query and in this context, the statement is false. Bureaucracy is not only involved in enforcing policies to ensure people comply, but it is also involved in the process of policy formation. Through different departments and offices, information is gathered, policy proposals are developed and recommendations are made to decision-makers.
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Look at the function f(x)=x^2-2. Which of the following describes the domain and range of the function and its inverse?
Answer:
A
Step-by-step explanation:
The function is a quadratic whose graph is a parabola. All parabolas have no limitations on their domain. This means the domain of the function is all real numbers.
This parabola has a minimum value since its leading coefficient is positive. Its vertex is at (0,-2). This means its range is all values greater than -2 or y ≥ -2.
An inverse of a function is its reflection across the y=x line. This results in (x,y) in the function becoming (y,x) in its inverse. The domain of the function becomes the range of the inverse and the range of the function becomes the domain of the inverse. Inverse has x ≥ -2 as its domain and all real numbers for its range.
Answer:
A.
Step-by-step explanation:
I just got 100% on the quiz.
What is the length of side BC of the triangle? Enter your answer in the box. units Triangle A B C with horizontal side B C. Vertex A lies above side B C. Angle B and angle C are marked congruent. The length of side A C is labeled as 2 x plus 7. The length of side A B is labeled as 4 x minus 7. The length of side B C is labeled as 4 x.
Answer:
The length of BC = 28 units
Step-by-step explanation:
* In triangle ABC
∵ Angles B and C are congruent
∴ m∠B = m∠C
* In any triangle if two angles are equal in measure, then the triangle is isosceles means the two sides which opposite to the congruent angles are equal in length
∴ AB = AC
∵ AB = 4x - 7
∵ AC = 2x + 7
∴ 4x - 7 = 2x + 7 ⇒ collect like terms
∴ 4x - 2x = 7 + 7
∴ 2x = 14 ⇒ divide both sides by 2
∴ x = 14 ÷ 2 = 7
* Now we can find the length of BC
∵ The length of BC = 4x ⇒ substitute the value of x
∴ The length of BC = 4 × 7 = 28 units
To find the length of side BC of the triangle, you can use the fact that angle B and angle C are congruent. Set up an inequality using the lengths of side AB and side AC, and solve for x. Substitute x with an appropriate value to find the length of side BC.
Explanation:To find the length of side BC of the triangle, we can use the fact that angle B and angle C are congruent. Let's represent the length of side AB as 4x - 7 and the length of side AC as 2x + 7. Since the sum of the lengths of the two smaller sides of a triangle must be larger than the length of the largest side, we can set up an inequality: 4x - 7 + 2x + 7 > 4x. Simplifying this inequality, we get 6x > 0, which tells us that x must be greater than 0.
Since side BC is labeled as 4x, we can substitute x with any positive value greater than 0. For example, if we let x = 1, then side BC would have a length of 4(1) = 4 units.
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Identify the graph of x^2-8y=0 for theta=90º and write and equation of the translated or rotated graph in general form.
Answer:
The answer is parabola; (y')² - 8x' = 0 ⇒ answer (b)
Step-by-step explanation:
* At first lets talk about the general form of the conic equation
- Ax² + Bxy + Cy² + Dx + Ey + F = 0
∵ B² - 4AC < 0 , if a conic exists, it will be either a circle or an ellipse.
∵ B² - 4AC = 0 , if a conic exists, it will be a parabola.
∵ B² - 4AC > 0 , if a conic exists, it will be a hyperbola.
* Now we will study our equation:
* x² - 8y = 0
∵ A = 1 , B = 0 , C =
∴ B² - 4AC = (0)² - 4(1)(0) = 0
∵ B² - 4AC = 0
∴ it will be a parabola.
∵ Ф = 90°
* The point (x , Y) will be (x' , y')
∵ x = x'cosФ - y'sinФ and y = x'sinФ + y'cosФ
∵ cos(90) = 0 and sin(90) = 1
∴ x = -y' and y = x'
* lets substitute x and y in the first equation
∴ (-y')² - 8(x') = 0
∴ (y')² - 8x' = 0
* We notice that the x' took the place of y and y' took the place of x
∴ The parabola rotated around the origin by 90°
∴ The equation of the parabola is (y')² - 8x' = 0
* The answer is parabola, with angle of rotation 90°
* The equation is (y')² - 8x' = 0
* Look to the graph
- The blue is x² - 8y = 0
- The green is (y')² - 8x' = 0
Answer:
the correct answer is D)
parabola
Find the equation of the line that is parallel to the line x + 5y = 10 and passes through the point (1, 3).
Answer:
see explanation
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange x + 5y = 10 into this form
Subtract x from both sides
5y = - x + 10 ( divide all terms by 5 )
y = - [tex]\frac{1}{5}[/tex] x +2 ← in slope- intercept form
with slope m = - [tex]\frac{1}{5}[/tex]
• Parallel lines have equal slopes, hence
y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (1, 3) into the partial equation
3 = - [tex]\frac{1}{5}[/tex] + c ⇒ c = [tex]\frac{16}{5}[/tex]
y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{16}{5}[/tex] ← equation of parallel line
Answer:
A) y = − 1 /5 x + 16/ 5
Step-by-step explanation:
Write an equivalent exponential equation for the following three problems.
Answer with step-by-step explanation:
We are given three different expressions and we are to write an equivalent exponential equation for them.
We know that the standard form of a logarithmic expression is given by:
[tex]y = log_a ( x )[/tex] which is equivalent to the exponential form [tex]x = a ^ y[/tex].
1. [tex] log _ {10} (0.1) = -1 [/tex] ---> [tex]10^{-1}=0.1[/tex]
2. [tex] log _ {3} 9 = 2 [/tex] ---> [tex]3^2=9[/tex]
3. [tex] log _ 5 ( \frac { 1 } { \sqrt { 5 } } ) = -\frac { 1 } { 2 } [/tex] ---> [tex]5^{-\frac{1}{2} }=\frac{1}{\sqrt{5} }[/tex]
Consider two events such that P(A)=1/4, P(B)=2/5, and P(A∩B)=1/10. Are events A and B independent events?
Yes, they are independent because P(A)×P(B)=P(A∩B)
No, they are dependent because P(A)×P(B)=P(A∩B)
No, they are dependent because P(A)×P(B)≠P(A∩B)
Yes, they are independent because P(A)×P(B)≠P(A∩B)
Events A and B are independent events because the product of their probabilities (P(A)P(B)) equals the probability of the intersection of both events (P(A∩B)).
To determine if events A and B are independent events, we need to check if the product of their probabilities equals the probability of their intersection. According to the formula for independent events:
P(A AND B) = P(A)P(B)
Given:
P(A) = 1/4
P(B) = 2/5
P(A∩B) = 1/10
Let's calculate the product of P(A) and P(B):
P(A)P(B) = (1/4) × (2/5) = 1/10
Since P(A∩B) also equals 1/10, which is the same as the product of P(A) and P(B), it is therefore true that:
P(A AND B) = P(A)P(B)
This implies that events A and B are indeed independent because their combined probability equals the product of their probabilities.
One surface of a wheel on a toy wagon has an area of 36 square inches. What is the circumference of the wheel?
Answer:
I'm pretty sure the answer is 21.26
I hope thats right if not sorry mark me brainliest
The circumference of the wheel is 21.26 inch
What is circumference?The circumference of a circle refers to the measure of its boundary. If we open a circle and measure the boundary just like we measure a straight line, we get the circumference of the circle in terms of units of length like centimeters, meters, or kilometers.
Now let us learn about the elements that make up circumference. These are the three most important elements of a circle.
Center: The center of the circle is a point that is at a fixed distance from any other point from the circumference.Diameter: The diameter is the distance across the circle through the center, it is a line that meets the circumference at both ends and it needs to pass through the center.Radius: The radius of a circle is the distance from the center of a circle to any point on the circumference of the circle.Given:
Area of wheel= 36
πr² = 36
r²= 36/ 3.14
r = 3.385
Now,
Circumference of the wheel is
=2πr
=2*3.14*.3.385
=21.264 inches
Learn more about circumference of circle here:
https://brainly.com/question/4268218
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