What is the total amount in an account that has had $35 per month added into it for 30 years and grew with an annual interest rate of 7%?
Find the area of sector AOB. Express your answer in terms of pi and rounded to the nearest tenth.
To find the area of sector AOB, use the formula A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, the area is approximately 0.139 m², rounded to the nearest tenth.
Explanation:To find the area of sector AOB, we need to use the formula for the area of a sector: A = (θ/360) * π * r^2, where θ is the angle of the sector in degrees and r is the radius. In this case, the angle θ is given as 1.11 and the radius is given as 4.5. Plugging these values into the formula, we get A ≈ (1.11/360) * π * (4.5)^2.
Using a calculator, we can calculate the value to be approximately 0.139 m². Rounding to the nearest tenth, the area of sector AOB is 0.1 m².
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The areas of the sectors of circles 5 and 6 to the nearest tenth are 197.8 cm² and 6.3 ft² respectively.
What are the areas of the sectors?The area of the sector of a circle can be expressed as:
Area = ( θ/360º ) × πr²
Where θ is the sector angle in degrees, R is the radius of the circle, and π is constant pi.
For question5)
Angle θ = 70 degrees
Radius r = 18 cm
Area =?
Area = ( θ/360º ) × πr²
Plug in the values:
Area = ( 70/360º ) × π × 18²
Area = 63π cm²
Area = 197.8 cm²
For question 6)
Angle θ = 180 degrees
Diameter d = 4ft
Radius r = 4/2 = 2ft
Area =?
Area = ( θ/360º ) × πr²
Plug in the values:
Area = ( 180/360º ) × π × 2²
Area = 2π ft²
Area = 6.3 ft²
Therefore, the area of the sector is 6.3 ft².
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The points A(12,7)A12,7, B(12,-3)B12,-3, C(-2,-3)C-2,-3, and D(-2,7)D-2,7 form rectangle ABCDABCD. Which point is halfway between AA and BB?
Noel reads 90 minutes a day for six days. Tyra reads 60 minutes for eight days. what is the diffrence , in minutes , between the total amount of time Noel read and the total amount Tyra read.
A. 30
B. 40
C.60
D. 80
The difference between the total reading times of Noel and Tyra is 60 minutes. Therefore, the correct option is option C.
The difference in minutes between the total time Noel read and Tyra read can be calculated by adding up the individual reading times for each and then finding the difference.
Calculate Noel's total reading time: 90 minutes/day * 6 days = 540 minutes.Calculate Tyra's total reading time: 60 minutes/day * 8 days = 480 minutes.Find the difference: 540 minutes (Noel) - 480 minutes (Tyra) = 60 minutes.You draw two cards from a standard deck of 52 cards without replacing the first one before drawing the second. find the probability that the first card is an ace and that the second card is an ace?
4 aces in a deck
52 cards
you have a 4/52 reduced to 1/13 probability of picking an ace.
without replacing it there would be 51 cards left and 3 aces
so second probability of picking an ace is 3/51 reduced to 1/17
the probability of doing both = 1/13 x 1/17 = 1/221
Answer:
conf
Step-by-step explanation:
A ship traveled for a total of 72 miles over the course of 6 hours. Heading south, the ship traveled at an average speed of 13 miles per hour, and heading east, it traveled at an average speed of 10 miles per hour. For how many hours was the ahi heading east?
Gabrielle's age is three times Mikhail's age. The sum of their ages is 44. What is Mikhail's age?
Suppose your average, after taking 4 quizzes, is 73(out of 100). What must your average be on the next 5 quizzes to increase your average to 88 out of 100?
x = average of next 5 quizzes
4 * 73 = first 4 quizzes
There will be a total of 4 +5 = 9 quizzes
Average of all quizzes = 88 = (4*73+5x)/9
9*88 = 9*(292 +5x)/9
792 = 292 + 5x
500 = 5x
X = 500/5 = 100
Next 5 quizzes need to average 100
find the solution x-4y=9 and x-y=-9
see picture for solution
If prices Increase at a monthly rate of 2.3%, by what percentage do they increase in a year?
Of the books in a library, 1/3 came from Robbie's collection and 15 came from Marta's. Of the rest, 15 were Elena's 1/5 were Winfield's, and 5 were purchased from the bookstore. How many book are there in the library?
The total number of books in the library are 75.
What is an equation?
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two expressions 3x + 5 and 14, which are separated by the 'equal' sign.
What will be the equation for given scenario?Let the total number of books in the library be x.
The equation formed by using given information will be [tex]\frac{x}{3} +15+15+\frac{x}{5}+ 5=x[/tex]
Collect the like terms,
[tex]\frac{x}{3} +35+\frac{x}{5}=x[/tex]
On solving the equation for x we get x=75.
Therefore, the total number of books in the library are 75.
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Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.
The dependent variable is the additional charge applied for each hour whereas the independent variable is the charge to be applied on the first hour
The dependent variable would be $1.45 for each additional hour. The cost depends on every hour so we can't really calculate it unless we have the hours given.
$3 is independent since it's only charged on the first hour. It doesn't depend on any other information.
Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.Which sentence best describes the independent and dependent variables in the following problem? The parking garage charges $3 for the first hour of parking and $1.45 for each additional hour.
Explain how you can use place value patterns to describe how 50 and 5000 compare
The histogram shows the duration, in minutes, of movies in theaters.
What relationship between the median and mean is shown by the histogram?
A) The mean is less than the median.
B) The median is less than the mean.
C) The mean is equal to the median.
D) The median and mean cannot be compared from a histogram.
At the frozen yogurt shop, a machine fills cups with 4 ounces of frozen yogurt before the customer adds the toppings. After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces. Which of the following graphs represents the acceptable weights for the frozen yogurt options?
Answer: Third graph represents the acceptable weights for the frozen yogurt options.
Step-by-step explanation:
Since we have given that
Number of ounces of frozen yogurt a machine fills cups with before the customer adds the toppings = 4
After the cups are filled, customers add as many toppings as they want without the total weight exceeding 7 ounces.
So, it means the weight should be lie between 4 ounces and 7 ounces.
So, it can be written as [4,7].
4≤ x ≤7, here, x is the weight of frozen yogurt.
So, third graph represents the acceptable weights for the frozen yogurt options.
what is 475% of 9.2?
Can anyone help me solve a trigonomic identity problem and also help me how to do it step by step?
it's ((cos theta) * (cot theta))/(1-sin theta) - 1 = csc theta
Find the area of the shaded region below. The units are in feet.
Use 3.14 for π. Round your answer to two decimal places.
A company uses a variable percentage markup of 35% .if the total cost of a product is $15,what is its selling price
The selling price of a product with a 35% markup on a cost of $15 is calculated by adding the markup amount of $5.25 to the cost, resulting in a selling price of $20.25.
Explanation:To calculate the selling price of a product using a variable percentage markup, you first need to determine the amount of markup by converting the percentage to a decimal and multiplying by the cost of the product. In this case, with a 35% markup on a product that costs $15, the calculation is as follows:
$15 × 0.35 = $5.25
This $5.25 represents the amount of markup on the product. To find the selling price, you simply add the markup to the cost:
$15 + $5.25 = $20.25
Therefore, the selling price of the product would be $20.25.
An apple farmer has planted 0.3 of his orchard with cherry trees. The orchard is 8.59 acres in size. How many acres are planted with cherry trees
How many solutions to 15x+11=8x
answer this plz
14 students are surveyed about the clothes they are wearing.
8 students are wearing a t-shirt.
2 students aren't wearing jeans or a t-shirt.
3 students are wearing jeans and a t-shirt.
How many students are wearing jeans, but not a t-shirt?
2
3
4
5
Answer:
its
Step-by-step explanation:
A home pregnancy test is not always accurate. suppose the probability that the test indicates that a woman is pregnant when she actually is not is 0.02, and the probability the test indicates that a woman is not pregnant when she really is, is 0.03. assume that the probability that a woman who takes the test is actually pregnant is 0.7. what is the probability that a woman is pregnant if the test yields a not pregnant result?
The probability of a woman being pregnant if a home pregnancy test yields a negative result can be calculated using conditional probabilities and Bayes' theorem. From the provided probabilities, we can substitute into Bayes' theorem to calculate this probability.
Explanation:The subject of this question is based on conditional probabilities. From the question we know that:
The probability of the test indicating a woman is pregnant when she's not (false positive) is 0.02 i.e., P(Positive|Not Pregnant) = 0.02 The probability of the test indicating a woman is not pregnant when she actually is (false negative) is 0.03 i.e., P(Negative|Pregnant) = 0.03 The probability that a woman who takes the test is actually pregnant is 0.7 i.e., P(Pregnant) = 0.7
From the above, we can find the probability of a woman being pregnant even though the test results are negative. To find this we need to use Bayes' theorem, which states:
P(A|B) = P(B|A) * P(A) / P(B)
So, to calculate the probability of a woman being pregnant given a negative test result P(Pregnant|Negative), we need the probability of getting a negative result when pregnant P(Negative|Pregnant), the probability of a woman actually being pregnant P(Pregnant), and the total probability of getting a negative test result P(Negative).
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Need help with this word problem
2/3 of a number is 32, what is the number?
Perform the operation and reduce the answer fully.
frac{1}{12}+\frac{5}{9}
for the function y=-2+5sin(pi/12)(x-2)), what is the minimum value
Answer:
-7
Step-by-step explanation:
We are given that a function
[tex]y=-2+5 sin(\frac{\pi}{12}(x-2))[/tex]
We have to find the minimum value of y.
We know that range of sin x is [-1,1].
[tex]-1\leq sin(\frac{\pi}{12}(x-2))\leq 1[/tex]
[tex]-5\leq 5sin(\frac{\pi}{12}(x-2))\leq 5[/tex]
[tex]-5-2\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 5-2[/tex]
[tex]-7\leq -2+5sin(\frac{\pi}{12}(x-2))\leq 3[/tex]
[tex]-7\leq y\leq 3[/tex]
Maximum value of y=3
Minimum value of y=-7
Hence, the minimum value of given function =-7
Suppose we select, without looking, one marbles from a bag containing 4 red marbles and 10 green marbles.what is the probability of selecting a green marbles? cours hero
Multiply and Dividing Rational Numbers
8/9 ÷ 2/3
7/8 × 1/4
3/4×1/6
A turkey was cooked at 300 f in the oven for 5 hours. the internal temperature rose from 35 f to 150 f. what was the average rise in temperature per hour