Answers
we have
\(\begin{gathered} x=4\cos t \\ \frac{x}{4}=\cos t \end{gathered}\)\(\begin{gathered} y=5\sin t \\ \frac{y}{5}=\sin t \end{gathered}\)squared both sides each equation
\(\begin{gathered} \frac{x^2}{4^2}=\cos ^2t \\ \\ \frac{y^2}{5^2}=\sin ^2t \end{gathered}\)Adds both equations
\(\frac{x^2}{16}+\frac{y^2}{25}=\cos ^2t+\sin ^2t\)Remember that
\(\cos ^2t+\sin ^2t=1\)so
\(\frac{x^2}{16}+\frac{y^2}{25}=1\)This is the equation of a vertical ellipse
see the figure below
The equation of a vertical ellipse with center at origin is equal to
\(\frac{x^2}{b^2}+\frac{y^2}{a^2}=1\)where
a=5
b=4
center (0,0)
Related Questions
Bonita deposited $1300 into a bank account that earned 5.75% simple interest each year. She earned $299 in interest before closing the account.
No money was deposited into or withdrawn from the account.
How many years was the money in the account?
Round your answer to the nearest whole year.
Enter your answer in the box.
Answers
Answer:
Your answer is 4 Years!
Answer: 4 Years
Step-by-step explanation: Just to confirm the other person it is 4 years!
It is good programming style to always use a for loop when the number of times to repeat the action is known. The following code uses a while loop that mimics what a for loop should do. Rewrite it using a for loop that accomplishes exactly the same thing.
myprod = 1;
i = 1;
while i <= 4
num = input('Enter a number: ');
myprod = myprod ⁎ num;
i = i + 1;
end
Answers
myprod = 1
num = input("Enter a number: ")
for i in range(1, 5):
myprod *= num
help brainliest will be given 8 only
Answers
b. 26 vehicles
c. 10 vehicles
d. About 27%
Answer:
a)37
b)10
c)0 beacuse if there 11 then they would be speeding and also if it wrond try 10
d)28.571428571429%Step-by-step explanation:
what does one and sixty-three hundredths look like?
Answers
Answer:
1.630
Step-by-step explanation:
HELP PLEASE AS SOON AS POSSIBLE WILL GIVE U BRAINLIST
Answers
Answer:
The table represents a nonlinear function because the rate is not constant.
Step-by-step explanation:
As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.
A certain virus infects one in every 300 people. A test used to detect the virus in a person is positive 85% of the time if the person has the virus and 5% of the time if the person does not have the virus, (This 5% result is called a false positive.) Let A be the event "the person is Infected" and B be the event "the person tests positive", a) Find the probability that a person has the virus given that they have tested positive, l.e. find P(AB). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(AIB)= % b) Find the probability that a person does not have the virus given that they test negative, I.e. find P(A'B'). Round your answer to the nearest tenth of a percent and do not include a percent sign. P(A'B') =
Answers
This question is solved using the conditional probability concept.
Using this concept, we find that:
a) P(AIB)= 5.3%b) P(A'|B') = 99.9%First, the concept is presented.
Conditional Probability
We use the conditional probability formula to solve this question. It is
\(P(A|B) = \frac{P(A \cap B)}{P(B)}\)
In which
P(A|B) is the probability of event A happening, given that B happened.
\(P(A \cap B)\) is the probability of both A and B happening.
P(B) is the probability of B happening.
----------------------------------------------------
Question a:
For relation with the formula presented above, I will change events A and B.
Event A: Person is infected.
Event B: Positive test.
Probability of a positive test:
85% = 0.85 out of 1/300 (person has the virus).5% = 0.05 out of 299/300(person does not have the virus)Thus:
\(P(B) = 0.85\frac{1}{300} + 0.05\frac{299}{300} = \frac{0.85\times1 + 0.05\times299}{300} = 0.0527\)
Probability of a positive test and the person is infected.
85% = 0.85 out of 1/300. Thus:
\(P(A \cap B) = \frac{0.85}{300} = 0.0028\)
Desired probability:
\(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.0028}{0.0527} = 0.053\)
0.053*100% = 5.3%, thus:
P(AIB)= 5.3%
---------------------
Question b:
Event A: Does not have the virus
Event B: Test negative.
Probability of a negative test:
100% - 85% = 15% = 0.15 out of 1/300 (person has the virus).100% - 5% = 95% = 0.95 out of 299/300(person does not have the virus)Thus:
\(P(B) = 0.15\frac{1}{300} + 0.95\frac{299}{300} = \frac{0.15\times1 + 0.95\times299}{300} = 0.9473\)
Probability of a negative test and the person is not infected.
0.95 out of 299/300
Thus:
\(P(A \cap B) = \frac{0.95\times299}{300} = 0.9468\)
Desired probability:
\(P(A|B) = \frac{P(A \cap B)}{P(B)} = \frac{0.9468}{0.9473} = 0.999\)
0.999*100% = 99.9%, so:
P(A'|B') = 99.9%
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It Quiz: Graphs and Measurement
Diana is making enough soup to feed 9 people. She plans to serve all of the soup to her guests in 6-ounce bowls.
In order to make enough soup, she needs to add a total of 4.75 cups of water. There are 8 ounces in a cup.
How many total ounces of water did Diana add to her soup? What is the total number of ounces of the other
ingredients in her soup? Explain how you found your answers.
Type your answer in the box below.
mentum
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Mar 10
11:
Answers
Answer:
1. 57/16 or 3.5625 ounces of water
8 : 4.75
1 : 19/32 -----> divide both by 8
19/32x6=57/16 = 3.56 ounces
2. 2.4375 ounces of other ingredients
6-3.5625=2.4375
Find the area of the figure. Round to the nearest tenth if necessary. 386.3m^2 194.3m^2 193.1m^2 201.9m^2
Answers
Add the top and bottom numbers together, divide that by 2 then multiply by the height.
15.3 + 19.5 = 34.8
34.8/2 = 17.4
17.4 x 11.1 = 193.14
Answer is 193.1 m^2
You are washing cars over the summer. It costs you $3 to wash each car and a one-time cost of $35 for some supplies to market your car wash. You plan to charge $10 per wash. Write an equation and solve to determine the amount of cars you need to break even.
Answers
The amount of cars you need to break even is 5.
To determine the number of cars you need to break even, we can set up an equation where the revenue equals the total cost.
Let's denote the number of cars as x.
Revenue = Number of cars × Price per wash
= x × $10
Total cost = Cost per car × Number of cars + One-time cost
= $3x + $35
To break even, the revenue should be equal to the total cost:
x × $10 = $3x + $35
Now, let's solve this equation to find the value of x:
10x = 3x + 35
Subtract 3x from both sides:
10x - 3x = 3x + 35 - 3x
7x = 35
Divide both sides by 7:
x = 35 / 7
x = 5
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Simplify this expression.
2+. 3. 5-
Answers
Answer: B, because when we factor in each term it all checks out
In ΔXYZ, y = 500 inches, � m∠Y=117° and � m∠Z=10°. Find the length of z, to the nearest inch.
Answers
The length of z in the triangle is 97 inches.
How to find the side of a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.
Therefore, let's find the side z of the triangle XYZ using sine law as follows:
a / sin A = b / sin B = c / sin C
Hence,
500 / sin 117 = z / sin 10
cross multiply
500 sin 10 = z sin 117
divide both sides by sin 117
z = 500 sin 10 / sin 117
z = 86.8240888335 / 0.89100652418
z = 97.4410774411
Therefore,
z = 97 inches
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6 * 10x^{-3}/8*10x^{-6}
Answers
The simplified form of the given expression, 6 × 10⁻³ / 8 × 10⁻⁶, is 3/4 × 10³
Simplifying an expressionFrom the question, we are to simplify the given expression
The given expression is
6 × 10⁻³ / 8 × 10⁻⁶
Simplifying the expression
6 × 10⁻³ / 8 × 10⁻⁶
This can be written as
6/8 × 10⁻³/10⁻⁶
Reduce the fraction
3/4 × 10⁻³/10⁻⁶
Apply the division law of indices
3/4 × 10⁻³ ⁻ ⁽⁻⁶⁾
3/4 × 10⁻³ ⁺ ⁶
3/4 × 10³
Hence, the value is 3/4 × 10³
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Answer the photo please
Answers
The correct answer is C: The plot will be translated 3 units to the right.
What is translation?Translation in mathematics is a transformation that moves a figure in a straight line in any direction. It is also known as a slide. In a translation, the object is moved the same distance in the same direction.
This is the case because when each student adds 3 cm to their measurement, all the values shift to the right by 3 cm. This means that the box plot will be translated 3 units to the right. The interquartile range, range, and median will all be affected by this shift, but the magnitude of their change depends on the original distribution of the data. The interquartile range, for example, will generally increase, but the exact amount of increase depends on the spread of the data. The range will increase by 3 units, but the median may or may not be greater than 10, depending on the original distribution of the data.
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Cedric applied the rule to figure WXYZ.
Figure W X Y Z is reflected across the line of reflection m to form W prime X prime Y prime Z prime. Figure W prime X prime Y prime Z prime is rotated 180 degrees about point P to form W double-prime X double-prime Y double-prime Z double-prime.
What mistakes did he make? Select two options.
He applied the reflection to the pre-image first.
He applied the rotation to the pre-image first.
He changed the size of the figure instead of just applying a rotation.
He used point P as the center of rotation.
He used an incorrect angle of rotation around point P
Answers
The mistakes that were made regarding the transformation are:
He applied the reflection to the pre-image first.He used an incorrect angle of rotation around point PHow to illustrate the information?It should be noted that a transformation simply means the changing of the position of an object
In this case, the transformation is incorrect as he applied the reflection to the pre-image first and used an incorrect angle of rotation around point P.
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JASON BASEBALL TEAM SCORES 6 RUNS EVERY 2 INNINGS. WHAT IS THE RATIO OF RUNS TO INNINGS.
Answers
Answer:
6:2
Step-by-step explanation:
simple math ... then u simplify and the answer is 3:1
Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
Answers
The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C
How to calculate the debt using the stack methodFrom the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.
The amount of 150 dollars would then be added to the debt that has the second highest rate.
Hence the amount of debt that would be paid off first would be the first debt based on the stack method.
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The electrical resistance varies directly as the square of the voltage (V
) and inversely as the electric power (P
). If the voltage is 20
volts and the electric power is 5
watts, then the electrical resistance is 80
ohms.
Answers
The electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.
The electrical resistance is the measure of the difficulty in passing electric current through a wire or an electrical component. It depends on various factors, such as the material, dimensions, and temperature of the wire.The given statement says that the electrical resistance varies directly as the square of the voltage and inversely as the electric power.
In mathematical terms, this relationship can be expressed as R ∝ V²/PR = kV²/P where R is the electrical resistance, V is the voltage, P is the electric power, and k is the constant of proportionality. The constant k depends on the material, dimensions, and temperature of the wire or component.
The given statement implies that the constant k is the same for the given wire or component, and it is not affected by the voltage or the power.To find the value of k, we can use the given values of V, P, and R.
According to the statement, if the voltage is 20 volts and the electric power is 5 watts, then the electrical resistance is 80 ohms. Therefore,R = kV²/PR = k(20²)/5R = 400k/5R = 80 ohms
Substituting the value of R in the equation, we get80 = 400k/5k = (80 x 5)/400k = 1. Therefore, the equation that relates the electrical resistance, voltage, and power isR = V²/PThe constant of proportionality k is 1 for the given wire or component.
Therefore, the electrical resistance varies directly as the square of the voltage and inversely as the electric power, and the equation that relates them isR ∝ V²/PR = kV²/PR = V²/P. This relationship can be used to calculate the electrical resistance of the wire or component for any given voltage and power.
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QUICK PLEASE. George invested $1000 for 4 years. If the investments earned 5.5% compounded weekly, how many compounding period would occur and what is the interest rate?
Answers
The number of compounding period is 52.
The interest rate is 0.11%.
What is the compounding period and interest rate?The compounding period is the number of times the investment would earn a compound interest in a year. Because interest is compounded weekly, the compounding period would be equivalent to the number of weeks in a year. This is 52.
Interest rate = yearly interest / compounding period
5.5 / 52 = 0.11%
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Can someone explain how to do this?
Answers
y + 1/3 = -5/6
Isolate y by adding -1/3 to both sides:
(y + 1/3) + (-1/3) = -5/6 + (-1/3)
Addition is associative, meaning we can regroup the sums on the left side:
y + (1/3 + (-1/3)) = -5/6 + (-1/3)
1/3 and -1/3 cancel, so we're left with
y = -5/6 + (-1/3)
Adding a negative number is the same as subtracting:
y = -5/6 - 1/3
To combine the fractions and simplify the right side, you first have to find a common denominator. 6 is a multiple of 3, since 6 = 2•3. So multiply the numerator and denominator of 1/3 by 2:
1/3 • 2/2 = 2/6
So we get
y = -5/6 - 2/6
and because the denominators are identical, we can combine the fractions to get
y = (-5 - 2)/6
Simplify the numerator to get y :
y = -7/6
A line Passes through the point (9,-3) and has a slope of 2/3
write an equation in point-slope form for this line.
Answers
Answer:
y + 3 = \(\frac{2}{3}\) ( x - 9 )
Step-by-step explanation:
( \(x_{1}\) , \(y_{1}\) )
y - \(y_{1}\) = \(\frac{2}{3}\) ( x - \(x_{1}\) )
y = mx + b
~~~~~~~~~~
( 9 , - 3 )
y - ( - 3 ) = \(\frac{2}{3}\) ( x - 9 )
y + 3 = \(\frac{2}{3}\) ( x - 9 )
Whats the volume of the solid?
A. 8
B 12
c 32
d. 64
I WONT BREATHE UNTIL U ANSWER ME
Answers
The volume of the solid will be equal to V=64 Cubic inches.
What is volume?The space occupied by any solid object in the three-dimension is called as the volume.
Here we have 8 cubes in the solid object each cube has the side equal to 2 inches.
So the volume of one cube will be:
V=a³=2³=8 cubic inches
Since total number of the cubes are 8 so total volume will be:
V=8x8=64 cubic inches
hence the total volume will be equal to 64 cubic inches`
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Joseph is tracking the progress of her plant's growth. Today the plant is 8 cm high. The plant grows 1.5 cm per day
What is the linear model that represents the height of the plant after d days.
Answers
Answer:
y = 1.5x(or d) + 8
Step-by-step explanation:
1.5 is the slope and 8 is the y intercept(the constant term)
1.
a. Find the lengths of the unlabeled sides.
Answers
Answer:
The first one-6.324 (This number actually goes on forever), The second one-10
Step-by-step explanation:
1- (6*6)+(2*2), 36+4, 40, 40 unsquared=6.324
2- (8*8)+(6*6), 64+36, 100, 100 unsquared=10
Write a sentence of the form “–––––––––––––– is a function of –––––––.”
Type your response in the space below.
Answers
"Distance traveled is a function of time." In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
Distance is a fundamental concept in physics and mathematics that measures the extent or length between two points.
It represents the amount of ground covered or space traveled. When we say that distance is a function of various factors, it means that different variables or parameters can influence the distance traveled.
In the context of motion or travel, the distance traveled is often dependent on the amount of time that has passed.
The sentence "Distance traveled is a function of time" expresses this relationship, indicating that the distance traveled can be determined or calculated based on the value of time.
Thus, it implies that as time changes, the corresponding distance traveled also changes, establishing a functional relationship between the two variables.
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Help please mathematical answer pleas and I need it fast
Answers
Answer:
I gave the answer right for this
Every hour, the radio station plays 16 commercials that are a total 13 minutes in length. If x represents a 30-second commercial and y is a 60-second commercial, how many of each type of commercial is played?
Enter the equations that represent the scenario into the graphing calculator to find how many of each type of commercial is played.
x + y = 16
0.5x + y = 13
In one hour, the radio station plays
commercials that are 30 seconds long.
In one hour, the radio station plays
commercials that are 60 seconds long.
Answers
Answer:
6 and 10
Step-by-step explanation:
edge 2021 pls give brainliest
Use the properties of exponents to simplify the expression: 2(x13)65⋅y23
Answers
Explication: use the commutative property to reorder the terms .
2(13x)65y•23
Then Remove the parentheses
So 2•13=26 65•23=1,495
Then 26•1,495=38,870
Then you take the x and the y and your answer is 38,870xy sense x is before y
Enter the number that belongs in the green box
Answers
The angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
To find the measure of the angle between the sides measuring 4 and 5 in an obtuse triangle with side lengths 4, 5, and 7, we can use the Law of Cosines. The Law of Cosines states that in a triangle with side lengths a, b, and c, and an angle opposite to side c, the following equation holds:
\(c^2 = a^2 + b^2 - 2ab*cos(C)\)
In this case, we have side lengths a = 4, b = 5, and c = 7. We want to find the angle C, which is opposite to side c. Substituting these values into the Law of Cosines, we get:
\(7^2 = 4^2 + 5^2\)- 2(4)(5)*cos(C)
49 = 16 + 25 - 40*cos(C)
49 = 41 - 40*cos(C)
40*cos(C) = 41 - 49
40*cos(C) = -8
cos(C) = -8/40
cos(C) = -0.2
To find the measure of angle C, we can take the inverse cosine (arccos) of -0.2:
C = arccos(-0.2)
Using a calculator, we find that C ≈ 101.54 degrees.
Therefore, the measure of the angle between the sides measuring 4 and 5 in the obtuse triangle is approximately 101.54 degrees.
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What’s the circumference of a 4 inch pie
Answers
Answer:
c=12.56
Step-by-step explanation:
The carnival fundraiser at Westville Elementary School raised $300 on Friday. On Saturday, the carnival will raise 480 percent of that amount. Which statements are true about the amount of money that the carnival will raise on Saturday? Check all that apply. The answer will be less than $300 because 100 is less than 480. The answer will be greater than $300 because 480 is greater than 100. (100)(3) = 300, so 480(3) is the amount of money that the carnival will raise on Saturday. 480 + 300 is the amount of money that the carnival raised on Saturday. The carnival raised $780 on Saturday. The carnival raised $1,440 on Saturday. answer pleaseeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee.
Answers
Answer:
(100)(3) = 300, so 480(3) is the amount of money that the carnival will raise on Saturday.
The carnival raised $1,440 on Saturday.
Step-by-step explanation:
Both of these statements are true.
The carnival will raise $1,440 on Saturday, which you can calculate by doing 300(4.8), which is 1440.
It can also be calculated by doing 480(3) because you get the same answer, 1440.
Answer: 100)(3) = 300, so 480(3) is the amount of money that the carnival will raise on Saturday.
The carnival raised $1,440 on Saturday.
Step-by-step explanation: