Answer:
16.39 square units.
Step-by-step explanation:
The parametric equations x = sin t and y = 3 cos t describe a curve in the xy-plane known as an ellipse.
To see this, we can use the Pythagorean identity for sine and cosine:
sin^2 t + cos^2 t = 1
Multiplying both sides by 9, we get:
9 sin^2 t + 9 cos^2 t = 9
Substituting x = sin t and y = 3 cos t, we get:
9 x^2 + y^2/3 = 9
This is the equation of an ellipse centered at the origin with semi-axes a = 3 and b = sqrt(3), where a is the length of the horizontal semi-axis and b is the length of the vertical semi-axis.
The area of an ellipse is given by the formula:
Area = pi * a * b
Substituting the values of a and b, we get:
Area = pi * 3 * sqrt(3) ≈ 16.39
Therefore, the area of the ellipse described by the parametric equations x = sin t and y = 3 cos t is approximately 16.39 square units.
Find the length of
hk
Answer:
4 1/2
Step-by-step explanation:
If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.
JH * HK = GH * HI
3 * (2x+1) = 2 ( x+5)
Distribute
6x+3 = 2x+10
Subtract 2x from each side.
6x-2x+3 = 2x-2x+10
4x+3 = 10
Subtract 3 from each side.
4x = 10-3
4x= 7
Divide by 4.
x = 7/4
Now find HK.
HK = 2x+1
= 2(7/4)+1
= 7/2+1
= 9/2
= 4 1/2
Movie tickets for you and some of your friends cost $7 each. You all also want to purchase one popcorn for each person, which costs $4. Write an algebraic expression to represent the total cost of tickets and popcorn for any number of people.
Halla el valor de (2+3) ² =
Identifica la base, el exponente y
resuelve: (-8) ² =
La siguiente fracción 3/5 expresado en porciento es:
5/a = 7/5 halla el valor de a:
El número mixto 20 0 a fracción impropia es igual a:
3
(2+3)²=25, base=2+3, exponente=2, (-8)²=64, 3/5 expressed as a percent is 60%, a=7, 20 0/3 = 60/3 = 20/1.
What is percentage?
Percentage is a way of expressing a fraction or decimal as a portion of 100. It is often used to describe proportions or rates in various fields, such as finance, economics, and statistics.
What is exponent?
An exponent is a mathematical operation that involves raising a number to a power. The exponent represents the number of times the base is multiplied by itself. For example, in 2^3, 2 is the base and 3 is the exponent, and it means 2 multiplied by itself three times, resulting in 8.
According to the given information:
(2+3)² = (5)² = 25. The base is (2+3), the exponent is 2, and the result is 25.(-8)² = 64. The base is -8, the exponent is 2, and the result is 64.To express 3/5 as a percentage, we multiply by 100: 3/5 x 100 = 60%. Therefore, 3/5 is equal to 60%.To solve 5/a = 7/5 for a, we cross-multiply to get 5 x 5 = 7a. Simplifying, we get 25 = 7a, so a = 25/7.To convert the mixed number 20 3/3 to an improper fraction, we first multiply the whole number (20) by the denominator of the fraction (3), which gives us 60. Then we add the numerator of the fraction (3) to get 63. So 20 3/3 as an improper fraction is 63/3, which simplifies to 21.To know more about percentage, exponent visit:
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What is the equation and solution?
Answer:
Step-by-step explanation:
x + 5 = 3x - 7
-2x = -12
x = 6
x + 5 = 6 + 5 = 11
3(6) - 7 = 18 - 7 = 11
Kelly’s bill at a restaurant came to $21.52. If she decides to leave a 18% tip, how much of a tip did she leave
Answer:
$3.87 for the 18% tip.
so can u help me guys
Thus, 715,000 = 7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.
Explain about the scientific notations:The number of times that decimal point must be moved to obtain a number between 1 and 10 is the exponent in scientific notation. The decimal point is shifted to the left in order to represent this number in scientific notation.
The main goal of scientific notation is to simplify computations using numbers that are abnormally large or small. With scientific notation, every digit counts because zeros are just no longer used to denote the decimal point.
Given expression:
715,000 __ 7.15 x 10⁵
LHS = 715,000
Take the RHS value :
= 7.15 x 10⁵
This, can be simplifies as:
= 7.15 x 100,000
Now multiply the two values,
= 715,000 (RHS values)
as, LHS = RHS
LHS = 715,000
715,000 (RHS values)
Thus, 715,000 = 7.15 x 10⁵, using the concept of scientific notations, both the values are found to be equal.
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Use the following chart of years and price for an unstated item to answer the following questions.
1970 1975 1980 1985 1990 1995 2000
$87.32 $119.99 $206.79 $264.16 $283.16 $351.94 $349.69
What was the relative change from 1995 to 2000? (Enter your answer as a percentage rounded to the nearest hundredths.)
The relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.
How to calculate the relative change?To calculate the relative change from 1995 to 2000, we need to find the difference between the prices in those two years, and then express that difference as a percentage of the price in 1995.
Price in 1995 = $351.94
Price in 2000 = $349.69
Difference = Price in 2000 - Price in 1995
Difference = $349.69 - $351.94
Difference = -$2.25
The negative sign indicates a decrease in price from 1995 to 2000.
Now, we can calculate the relative change as a percentage:
Relative change = (Difference / Price in 1995) * 100
Relative change = (-$2.25 / $351.94) * 100
Relative change = -0.6392 * 100
Relative change = -63.92%
Therefore, the relative change from 1995 to 2000 is -63.92%, indicating a decrease in price of approximately 63.92%.
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3. Anika is on the crew to set up rides for the state fair. The crew does most of the setup on the day that the fair
arrives at the fairground and then continues to work on finishing the setup for about a week to have the rides
ready to go in time for the opening of the fair. The scatter plot shows Anika's setup time on different days and
the linear model for the data.
Anika's Setup Times
The equation of the line representing the linear model of the data in slope-intercept form is; y = -1.25·x + 17.5
What is the slope-intercept form of the equation of a line?The slope-intercept form of the equation of a line is; y = m·x + c, where m is the slope and c y-intercept.
The possible question includes;
What is the equation for the line in slope intercept form;
The points on the line are; (2, 15), and (6, 10)
The slope is; (10 - 15)/(6 - 2) = -5/4
The equation of the line is therefore;
y - 15 = (-5/4)·(x - 2)
-5/4 = -1.25
y = -1.25·x + 5/2 + 15 = -1.25·x + 17.5
y = -1.25·x + 17.5
The equation of the line in slope-intercept form is; y = -1.25·x + 17.5Learn more on the slope-intercept form of the equation of a line: https://brainly.com/question/28584447
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Express the second quantity as a percentage of the first: (a) 10 kilograms, 105 grams (b) 8 meters, 1 kilometer
(a) As a percentage, 105 grams is 1.04% of 10 kilograms.
(b) As a percentage 1 kilometer is approximately 99.21% of 8 meters.
How to Express a Quantity as a Percentage of another?(a) To express the second quantity, 105 grams, as a percentage of the first quantity, 10 kilograms, we first need to convert both quantities to the same unit.
10 kilograms is equal to 10,000 grams (since 1 kilogram = 1000 grams), so:
10,000 grams + 105 grams = 10,105 grams
105 grams / 10,105 grams * 100% = 1.04%
Therefore, 105 grams is 1.04% of 10 kilograms.
(b) To express the second quantity, 1 kilometer, as a percentage of the first quantity, 8 meters, we first need to convert both quantities to the same unit.
1 kilometer is equal to 1000 meters (since 1 kilometer = 1000 meters), so:
8 meters + 1000 meters = 1008 meters
1000 meters / 1008 meters * 100% = 99.21%
Therefore, 1 kilometer is approximately 99.21% of 8 meters.
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The area model shows 2 1/4. What is 2×2 1/4?
Step-by-step explanation:
2 1/4 = 9/4
2 × 2 1/4 = 2 × 9/4 = 9/2
what does ∫abfxdx means physically?
Step-by-step explanation:
Physically, integrating f(x)dx means finding the a. area to the right of point b. b. area to the left of point a . area under the curve and bounded by the lines x= a and x = d. d. area above the curve and bounded by the lines x = a and x = c. b. b.
Answer:
Step-by-step explanation:
means finding the area under the curve from a to b area t0 the left of point area t0 the right of point area above the curve from a to b CelecGne The exact value of xe ' dx is most nearly (A 7.8036 B) 11.807 14.034 19.614 CelecGne
You need a 60% alcohol solution. On hand, you have a 130 mL of a 55% alcohol mixture. You also
have 70% alcohol mixture. How much of the 70% mixture will you need to add to obtain the desired
solution?
Therefore , the solution of the given problem of unitary method comes out to be 70% alcohol combination with 130 mL of the 55% alcohol mixture.
What is a unitary method?Use the tried-and-true fundamental method, the real variables, and any useful information you learn from the broad and specific questions to complete the assignment. Customers may be given another chance to taste expression the products in response. If these improvements don't happen, we'll lose out on significant expression advances in programming understanding.
Here,
Let x represent the required amount (in mL) of the 70% alcohol mixture.
The total amount of alcohol in the final mixture would be equal to the desired 60% alcohol solution since it would be the sum of the alcohol in the 55% alcohol mixture and the alcohol in the 70% alcohol mixture.
=> 0.55 * 130 + 0.70 * x = 0.60 * (130 + x)
=> 71.5 + 0.70x = 78 + 0.60x
=> 0.10x = 6.5
=> x = 65
Therefore, to create a 60% alcohol solution, you would need to combine 65 mL of the 70% alcohol combination with 130 mL of the 55% alcohol mixture.
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7(-6)+7(-1/8) answer
Answer:
[tex]\displaystyle -42 \;\frac{7}{8}[/tex]
Step-by-step explanation:
We will simplify this expression.
Given:
7(-6)+7(-1/8)
Multiply:
[tex]\displaystyle -42- \frac{7}{8}[/tex]
Subtract:
[tex]\displaystyle -42 \;\frac{7}{8}[/tex]
Brandon used an indoor rock-climbing wall seven times. His climbing times, in
minutes, are shown in this list.
35, 16, 17, 18, 13, 13, 14
Why is the median the most useful measure of central tendency for these
times?
A The median is not affected by an outlier.
B
The median is equal to the range of the data.
C The median is the time that occurs most often.
D The median is a larger.value than the mean of the data.
The median the most useful measure of central tendency for these
times: is A) The median is not affected by an outlier.
Why is the median the most useful measure?The median is the middle value in a set of data when the values are arranged in order. In this case, the median of Brandon's climbing times would be 16, because it is the fourth value when the times are arranged in order:
13, 13, 14, 16, 17, 18, 35
The median is the most useful measure of central tendency for these times because it is not affected by an outlier, which is a value that is much larger or smaller than the other values in the data set.
In this case, the value 35 is an outlier, because it is much larger than the other values. If we were to use the mean as the measure of central tendency, the outlier would greatly influence the result. However, the median is not influenced by outliers, and therefore provides a better representation of the typical climbing time for Brandon.
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Can anybody please help me
Fast
The value of y that makes the hanger balance is 3.
What is the value of y?
The value of y can be solved considering linear equation method.
A linear equation is an algebraic equation in which the highest power of the variable(s) is always 1. It represents a straight line when graphed on a Cartesian coordinate plane. A linear equation can have one or more variables.
To solve for y in the equation 5 + y = 8, you can follow these steps:
Step 1: Subtract 5 from both sides of the equation to isolate the term with y on one side.
5 + y - 5 = 8 - 5
This simplifies to:
y = 3
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f(x)=2x^4-16x^3-3x^2- 8x-2
The positive zero of f is approximately =?
Answer:
To find the positive zero of the function f(x) = 2x^4 - 16x^3 - 3x^2 - 8x - 2, we can use a numerical method such as the Newton-Raphson method or the bisection method.
Let's use the bisection method to approximate the positive zero of f(x).
First, we need to find an interval [a, b] that contains the positive zero of f(x). We can start by evaluating f(x) at some values of x to determine where the function changes sign.
For example, evaluating f(0) and f(1) gives:
f(0) = 2(0)^4 - 16(0)^3 - 3(0)^2 - 8(0) - 2 = -2
f(1) = 2(1)^4 - 16(1)^3 - 3(1)^2 - 8(1) - 2 = -27
Since f(0) is negative and f(1) is also negative, we know that the positive zero of f(x) must be in the interval (0, 1).
Next, we can use the bisection method to refine our estimate of the positive zero. We start by finding the midpoint of the interval [a, b]:
c = (a + b) / 2
If f(c) is positive, then the positive zero of f(x) must be in the interval [a, c]. If f(c) is negative, then the positive zero of f(x) must be in the interval [c, b]. We can then repeat the process, dividing the interval in half each time, until we get an interval that is small enough to give us the desired level of accuracy.
Using this process, we can find the positive zero of f(x) to be approximately 0.818, rounded to three decimal places.
Note that this is just an approximation, and the actual value of the positive zero may be slightly different. We can check our answer by plugging it into f(x) and verifying that the result is very close to zero.
100 Points! Algebra question. Write a quadratic equation in standard form with -1/2, 3/4 as its roots. Please show as much work as possible. Photo attached. Thank you!
It took a crew 1 h 30 min to row 5 km upstream and back again. If the rate of flow of the stream was 8 km/h, what was the rowing speed of the crew in still water? km/h
The rowing speed of the crew in still water is:
x = 12 km/h.
What is meant by speed?
Speed is a measure of how fast an object is moving. It is usually expressed in units of distance per unit of time, such as miles per hour or meters per second. Speed can be calculated using the formula speed = distance/time.
According to the given information
We can use the formula:
distance = rate × time
to set up two equations based on the information given.
When the crew rows upstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x - 8)
When the crew rows downstream for 5 km, the time it takes is:
time = distance/rate
time = 5 / (x + 8)
The total time for the round trip is 1 hour 30 minutes, or 1.5 hours:
total time = time upstream + time downstream
1.5 = 5/(x-8) + 5/(x+8)
To solve for x, we can start by multiplying both sides of the equation by (x - 8)(x + 8) to clear the denominators:
1.5(x - 8)(x + 8) = 5(x + 8) + 5(x - 8)
Expanding and simplifying, we get:
1.5x^2 - 72 = 10x
Bringing all the terms to one side of the equation, we get:
1.5x^2 - 10x - 72 = 0
We can factor this quadratic equation by first dividing both sides by 1.5:
x^2 - (10/1.5)x - 48 = 0
We can then factor this expression as:
(x - 12)(x + 4) = 0
This gives us two possible values of x: x = 12 and x = -4.
Since we are looking for a rowing speed (which is a positive quantity), we can discard the negative solution and conclude that the rowing speed of the crew in still water is:
x = 12 km/h.
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What percent of 60 is 63?
Answer:37.8
Step-by-step explanation:
Answer:
105%
Step-by-step explanation:
First, do 63 x 100 then do 60 x 10 then you get 630 and 600.
Put 630 over 600. 630 / 600 is 1.05, which is converted to 105%
What is the total payment required to pay off a promissory note issued for $500.00 at 8% ordinary interest and a 90-day term? A. $507.20 C. $508.00 B. $540.00 D. $510.00
The total payment required to pay off the promissory note debt of 90 days term is D. $510.00.
The promissory note issued is for $500.
The interest rate is 8%.
Furthermore, the time frame is 90 days.
So the total payment is
= $500 + ($500 × 8% × 90 days ÷ 360 days)
= $500 + ($500 × 8% × 1/4)
= $500 + 10
= $510
Promissory notes are sometimes known as an IOU, a loan arrangement, or simply a note. It is a legal lending contract in which the borrower pledges to return the lender a specific amount of money within a specific time frame.
This type of document is legally binding and imposes a legal duty to repay the loan. Mortgages, school loans, car loans, company loans, and personal loans between family and friends all use promissory notes.
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Zoe makes a total of $72.85 selling cookies and cupcakes at a bake sale. If she sells 17 cupckaes for $3.25 each, how many cookies does she sell at $1,60 each?
PLEASE SHOW WORK
and I have to pass it pls
Answer: 11 Cookies
Step-by-step explanation:
let C be cookies
17($3.25) + 1.60C = $72.85
$55.25 + 1.60C = $72.85
1.60C = $17.60
C=11
She sells 11 cookies
Answer:
11
Step-by-step explanation:
To be able solve, you need to do 17 x 3.25, which would give you 55.25. Then you need to subtract 72.85 by 55.25, which is 17.60. Now divide 17.60 by 1.60. This should give you 11. Therefore, she sold 11 cookies.
I AM SO SORRY IF THIS DIDN'T MAKE SENSE!
PLS HELP ASAP!!!!
Objective: find the possibility of meals you can order.
There are 480 possible meals that can be ordered from the given choices at the Mexican restaurant.
What is probability?It is a branch of mathematics that deals with quantifying uncertainty and randomness in various situations, such as games of chance, weather forecasting, and statistical analysis.
To find the number of possible meals that can be ordered, we need to multiply the number of choices in each category.
There are 4 choices for the first category (Burrito, Salad, Bowl, or Quesadilla).
There are 5 choices for the second category (Steak, Carnitas, Chicken, Barbacoa, or Sofritas).
There are 4 choices for the third category (White Rice, Brown Rice, Black Beans, or Pinto Beans).
There are 6 choices for the fourth category (Hard Tacos, Soft Tacos, Fajita Veggies, or any of the previous three with Salad, Rice, or Beans added).
Using the multiplication rule, we can find the total number of possible meals as:
4 x 5 x 4 x 6 = 480
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The US Department of Energy reported that 45% of homes were heated by natural gas. A random sample of 314 homes in Oregon found that 175 were heated by natural gas. Test the claim that proportion of homes in Oregon that were heated by natural gas is different than what was reported. Use a 5% significance level.
The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.
Hypothesis testingNull hypothesis: The proportion of homes in Oregon heated by natural gas is the same as the reported national average of 45%.
Alternative hypothesis: The proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.
We can use a two-tailed z-test to test this hypothesis.
The test statistic is calculated as:
z = (p - P) / √[P(1-P)/n]
where p is the sample proportion, P is the hypothesized population proportion (0.45), and n is the sample size.
Using the values given in the problem, we have:
p = 175/314 = 0.557
P = 0.45
n = 314
Plugging these values into the formula, we get:
z = (0.557 - 0.45) / √[0.45(1-0.45)/314] = 3.039
Using a standard normal distribution table, we find that the probability of getting a z-value of 3.039 or higher (in absolute value) is less than 0.005.
Since the significance level is 0.05, which is greater than the p-value, we can reject the null hypothesis and conclude that there is evidence to support the alternative hypothesis.
Therefore, the proportion of homes in Oregon heated by natural gas is different than the reported national average of 45%.
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need some help setting up and solving these equations
The quantity of ounce for each kind of food that will be used would be given as follows;
Food A= 2.18oz
How to calculate the quantity of ounce for each number of foods?For food A;
The calories in an Oz = 100 cal
Total calories in the whole food = 1100cal
The equivalent of cal that should be in 2400;
= X
That is;
100= 1100
X = 2400
Make X the subject of formula;
x= 100×2400/1100
X = 240000/1100
X = 218
if 1 Oz = 100 cal
X Oz = 218
X Oz = 218/100
= 2.18oz
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find the area of the triangle shown below
the area of the triangle shown is 14 square inches
How to determine the areaIt is important to note that the formula that is used for calculating the area of a triangle is expressed with the equation;
A = 1/2bh
Such that the given parameters of the equation are;
A is the area of the triangleb is the base of the triangleh is the height of the triangleFrom the information given, we have that;
b = 3 + h = 3 + 4 = 7 inches
h = 4 inches
Now, substitute the values, we get;
Area = 1/2 (7)(4)
multiply the value and expand the bracket
Area = 1/2(28)
divide the values
Area = 14 square inches
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The numbers 1/2,x,y,3/4 are in increasing order of size. The differences between successive numbers in this list are all the same. What is the value of y?
Cornelio’s backyard is enclosed by a fence and the house. A diagram of the backyard is shown below.
Answer:
5,500 ft²
Step-by-step explanation:
Easiest way is to find the area of the entire 100 x 80 square, then subtract the footprint of the house (50 x 50):
Backyard area = (100 x 80) - (50 x 50) = 8000 - 2500 = 5500 ft²
Assume that adults have IQ scores that are normally distributed with a
mean of μ = 100 and a standard deviation o= 15. Find the probability
that a randomly selected adult has an IQ between 85 and 115.
Click to view page 1 of the table. Click to view page 2 of the table.
...
The probability that a randomly selected adult has an IQ between 85
and 115 is.
(Type an integer or decimal rounded to four decimal places as needed.)
Assume that adults have IQ scores that are normally distributed with a
mean of μ = 100 and a standard deviation o= 15. the probability that a randomly selected adult has an IQ between 85 and 115 is 0.6826.
How to find the probability?Let Z represent the standard normal random variable
Z = (X - μ) / σ
where:
X = IQ score
μ= mean (100)
σ= standard deviation (15).
In order to determine the probability we have to find the area
P(85 < X < 115) = P[(85 - 100) / 15 < Z < (115 - 100) / 15]
= P(-1 < Z < 1)
= Φ(1) - Φ(-1)
Where;
Φ= Cumulative distribution function
Using a standard normal distribution table
Φ(1) = 0.8413
Φ(-1) = 0.1587
So,
P(85 < X < 115) =0.8413 - 0.1587
= 0.6826
Therefore the probability is 0.6826.
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PLEASE RESPOND FAST I NEED IT ANSWERED
The data set lists the ages of the cast members of a recent children’s play. Find the median age. {14, 11, 8, 12, 5, 3, 17, 10, 8, 11}
Answer:
Mean: 9.9
Median: 10.5
Step-by-step explanation:
A box is 11 inches high, 18 inches long and 8 inches wide. What is the longest poster you could fit in the box? Explain why you can only fit one maximum length poster in the box but you can fit multiple 21 inch posters in the same box
Answer: the longest poster that could fit in the box is approximately 22.56 inches long.
Step-by-step explanation: Utilizing the Pythagorean theorem, able to calculate the corner to corner as takes after:
diagonal^2 = 11^2 + 18^2 + 8^2
diagonal^2 = 121 + 324 + 64
diagonal^2 = 509
inclining = sqrt(509)
corner to corner ≈ 22.56 inches