Answer:
[tex]a_{n}[/tex] = 6n - 5
Step-by-step explanation:
there is a common difference between consecutive terms in the sequence
7 - 1 = 13 - 7 = 19 - 13 = 6
this indicates the sequence is arithmetic with nth term
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
here a₁ = 1 and d = 6 , then
[tex]a_{n}[/tex] = 1 + 6(n - 1) = 1 + 6n - 6 = 6n - 5
0/1
12. Ashton picked 6 pounds of pecans. He used of the pecans in a soup recipe. Ashton then
splits the pecans that are left in pound bags. How many bags of pecans does he have?
Ashton has 4.5 bags of pecans. since you can't have half a bag, he might need to round up to 5 bags
What is Fraction?A fraction represents a part of a whole.
If Ashton used 1/4 of the pecans in a soup recipe, he has 3/4 of the pecans left.
To find out how many pounds of pecans he has left.
we can multiply the original amount of pecans by 3/4:
3/4 x 6 pounds = 4.5 pounds
So Ashton has 4.5 pounds of pecans left to split into bags.
If he splits the remaining pecans into 1-pound bags, then he has:
4.5 pounds ÷ 1 pound/bag = 4.5 bags
Therefore, Ashton has 4.5 bags of pecans. However, since you can't have half a bag, he might need to round up to 5 bags
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The complete question
Ashton picked 6 pounds of pecans. He used 1/3 of the pecans in a soup recipe. Ashton puts the pecans that are left in 1/4 pound bags. How many bags of pecans does he have
Please help me by finding the degree measure of angle x
We can say in this triangle by Pythagorean theorem A2 = B2 + C2 => AC = sqrt115 after answering the provided question.
What exactly is a triangle?Because it has three sides and three vertices, a triangle is a polygon. It is a fundamental geometric shape. Triangle ABC is the name given to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered. A triangle is a polygon because it has three sides and three corners. The triangle's corners are defined as the points at which the three sides meet. The sum of three triangle angles yields 180 degrees.
Pythagorean theorem applies here, in this triangle
[tex]A^2 = B^2 + C^2[/tex]
[tex]AC = \sqrt{14^2 - 9^2}[/tex]
[tex]AC = \sqrt{196 - 81}[/tex]
[tex]AC = \sqrt{115}[/tex]
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dave wants to buy a new collar for each of his 5 cats. the collars come in a choice of 9 different colors. step 1 of 2 : how many selections of collars for the 5 cats are possible if repetitions of colors are allowed?
If repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
If Dave can choose from 9 different colors for each of his 5 cats, then he has 9 choices for the first cat, 9 for the second cat, and so on. To find the total number of possible selections, we can multiply the number of choices for each cat together:
9 x 9 x 9 x 9 x 9 = 59,049
In this case, there are 9 ways to choose the collar color for the first cat. Since Dave can choose from the same 9 colors for each of the 5 cats, so he has 9 choices for each cat. Therefore, by the principle of counting, the total number of ways to choose collars for all 5 cats is:
Therefore, if repetitions of colors are allowed, there are 59,049 possible selections of collars for the 5 cats.
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pls help me i need now and if the answer is correct i give free BRAINLIEST HERE!!!!
THANK YOU
The measures of the angles formed by the cords and secant in the circle are found using circle theorems and presented as follows;
m∠1 = 47.5°[tex]m\widehat{BD}[/tex] = 110°m∠COD = 55°[tex]m\widehat{CD}[/tex] = 20°m∠AOC = 100°m∠APB = 25°m∠ADB = 25°[tex]m\widehat{CD}[/tex] = 90°[tex]m\widehat{AB}[/tex] = 70°[tex]m\widehat{CD}[/tex] = 100°What is a secant of a circle?A secant is a line that has two points of intersection on a circle.
The specified parameters are;
1. The measure of arc [tex]m\widehat{AB}[/tex] = 80°, and the measure of [tex]m\widehat{CD}[/tex] = 15°
Angle at the center of the circle = 2 × Angle at the circumference
Angle at the center of the circle = The arc angle of the circle
Therefore;
m∠DAC = 15°/2 = 7.5°
m∠ACO = 80°/2 = 40°
The external angle of a triangle theorem, indicates that we get;
m∠1 = 40° + 7.5° = 47.5°
m∠1 = 47.5°
2. m∠BOD = 100°, [tex]m\widehat{AC}[/tex] = 90°
The intersecting chords theorem indicates that we get;
m∠BOD = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; 100° = (1/2)×(90° + [tex]m\widehat{BD}[/tex])
[tex]m\widehat{BD}[/tex] = 2 × 100° - 90° = 110°
[tex]m\widehat{BD}[/tex] = 110°
3. [tex]m\widehat{AB}[/tex] = 90°, [tex]m\widehat{CD}[/tex] = 20°
Therefore; m∠ACO = 90°/2 = 45°
m∠DAC = 20°/2 = 10°
The external angle theorem indicates that we get;
m∠COD = 45° + 10° = 55°
m∠COD = 55°
4. m∠1 = 35°, [tex]m\widehat{AB}[/tex] = 50°, therefore;
m∠ACO = 50°/2 = 25°
m∠CAO = 35° - 25° = 10°
[tex]m\widehat{CD}[/tex] = 2 × m∠CAO
Therefore; [tex]m\widehat{CD}[/tex] = 2 × 10° = 20°
[tex]m\widehat{CD}[/tex] = 20°
5. m∠AOC = (1/2)×([tex]m\widehat{AC}[/tex] + [tex]m\widehat{BD}[/tex])
Therefore; m∠AOC = (1/2)×(90° + 110°) = 100°
m∠AOC = 100°
6. [tex]m\widehat{CD}[/tex] = 20° and [tex]m\widehat{AB}[/tex] = 70°
The external secant, tangent theorem, indicates that we get;
m∠APB = (1/2) × ([tex]m\widehat{AB}[/tex] - [tex]m\widehat{CD}[/tex])
m∠APB = (1/2) × (70° - 20°) = 25°
m∠APB = 25°
7. [tex]m\widehat{AB}[/tex] = 50°,
The angle at the center of a circle is twice the angle subtended at the circumference, therefore;
m∠ADB = 50°/2 = 25°
m∠ADB = 25°
8. m∠CAD = 45°
The angle formed by an arc at the center of a circle theorem, indicates that we get;
[tex]m\widehat{CD}[/tex] = 2 × m∠CAD
[tex]m\widehat{CD}[/tex] = 2 × 45° = 90°
[tex]m\widehat{CD}[/tex] = 90°
9. m∠ACB = 70°
m∠ACB is the angle subtended by the arc [tex]m\widehat{AB}[/tex] on the circumference
Therefore;
[tex]m\widehat{AB}[/tex] = 2 × m∠ACB
[tex]m\widehat{AB}[/tex] = 2 × 70° = 140°
[tex]m\widehat{AB}[/tex] = 70°
10. m∠AOB = 80°, [tex]m\widehat{AB}[/tex] = 60°
m∠(AOB) = (1/2) × ([tex]m\widehat{AB}[/tex] + [tex]m\widehat{CD}[/tex])
Therefore; m∠(AOB) = 80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
80° = (1/2) × (60 + [tex]m\widehat{CD}[/tex])
[tex]m\widehat{CD}[/tex] = 2 × 80° - 60° = 100°
[tex]m\widehat{CD}[/tex] = 100°
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Based on this graph, what is the solution to the system of equations?
Answers:
A. There are an infinite number of solutions.
B. There is no solution.
C. (1, 3)
D. (2, 3)
E. (3, 2)
The solution is Option E.
The solution to the system of equations is the point of intersection of line and the lines intersect at the point A ( 3 , 2 )
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , -4 )
Let the second point be Q ( 7 , 6 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope m = 10 / 10 = 1
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 6 = 1 ( x - 7 )
y - 6 = x - 7
y = x - 1 be equation (1)
Now , the point of intersection of lines is at ( 3 , 2 )
Substitute the value of x and y in the equation , we get
when x = 3 , y = 2
2 = 3 - 1
2 = 2
Hence , the solution to the equation is ( 3 , 2 )
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b³+b²+4b factorize this
Answer: b (b²+b+4)
Step-by-step explanation:
b²=bb
b³=b²b
=b²b+bb+4b
=b(b²+b+4)
There were 230,600 jobs available in the field of radiology in the year 2014. Each year, that number is expected to grow by 0.9%.
Write a function that gives the expected number j(t) of jobs in radiology t years from the year 2014.
Answer:
J(t) = 230,600(1.009)^t
Step-by-step explanation:
J(t) = 230,600(1 + 0.009)^t, or
J(t) = 230,600(1.009)^t If this is Wrong ill do. it again!!
if you assume all outcomes are equally likely, what is the probability of getting either two odd numbers or two even numbers?
The probability of getting two odd numbers or two even numbers is 50%, since there are an equal number of odd and even numbers.
There are 6 possible outcomes when rolling two dice:
(1,1), (1,2), (2,1), (2,2), (1,3), (3,1).
The probability of getting two odd numbers is
2/6, or 1/3.
The probability of getting two even numbers is also
2/6, or 1/3.
Therefore, the probability of getting either two odd numbers or two even numbers is 2/3.
The probability of getting two odd numbers or two even numbers is 50%. This is because there are an equal number of odd and even numbers, so each outcome is equally likely. This means that the probability of getting two odd numbers or two even numbers is the same as the probability of getting one odd number and one even number. In both cases, the probability is 50%, since each outcome is equally likely. Therefore, the probability of getting two odd numbers or two even numbers is 50% as there are an equal number of odd and even numbers. This is because all possible outcomes are equally likely, and there are an equal number of odd and even numbers, so the probability of getting either two odd numbers or two even numbers is the same.
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3, -24, 192, ... Find the 19th term:
Answer:
Step-by-step explanation:
a
n
=ar
n−1
a
3
=ar
2
=24...(1)
a
6
=ar
5
=192...(2)
dividing (2) by (1) we get
ar
2
ar
5
=
24
192
r
3
=8⇒r=2
From (1)
ar
2
=24
a=
2
2
24
=6
∴a
10
=(6)(2)
10−1
=3072
question 8
help me asap
The sector area of the sector defined by the minor arc CB is given as follows:
7.5 cm².
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
We have that the radius is half the diameter, hence it's measure is given as follows:
r = 3 cm.
The angle measure of arc CB is given as follows, considering that BD is half the circle = 180º.
CB + 84º = 180º.
CB = 96º.
An entire circle has an angle of 360º, hence the area of the sector is given as follows:
A = 96/360 x π x 3²
A = 7.5 cm².
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Which one of the following points lies on the line 3x=2x-1
The point (-1, 2) lies on the line 3x = 2x - 1.
The equation 3x = 2x - 1 can be simplified by subtracting 2x from both sides to get x = -1.
So the line passes through the point (-1, y) for any value of y.
To check which of the following points lie on the line, we can substitute the x and y coordinates of each point into the equation and see if it is true.
a) (0, -1)
3(0) = 2(0) - 1
0 = -1
This point does not lie on the line.
b) (-1, 2)
3(-1) = 2(-1) - 1
-3 = -3
This point does lie on the line.
c) (1, -4)
3(1) = 2(1) - 1
3 = 1
This point does not lie on the line.
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The equation 7(2W + 3) = 14W + 20 has no solutions. Change one term in the original equation to create a new equation with infinitely many solutions.
The equation with infinitely many solutions is given as follows:
7(2W + 3) = 14W + 21.
How to obtain the equation with infinitely many solutions?
The system of equations for this problem is defined as follows:
7(2W + 3) = 14W + 20.
Applying the distributive property to the left side, we will have that:
14W + 21 = 14W + 20.
The two lines have the same slope but different intercepts, hence the system contains zero solutions.
To contain an infinite number of solutions, they must have the same slope and the same intercept, then the equation is given as follows:
7(2W + 3) = 14W + 21.
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Step-by-step explanation:
=
[tex]7(2w + 3) = 14w \\ 14w + 21 = 14w \\ 14w - 14w = - 21 \\ 0 = - 21 \\ = - 21[/tex]
a radioactive substance decays exponentially. a scientist begins with 100 milligrams of a radioactive substance. after 29 hours, 50 mg of the substance remains. how many milligrams will remain after 38 hours?
After 38 hours, there will be 43.1 mg of the radioactive substance remaining.This means that the amount of a radioactive substance decreases exponentially over time
Radioactive decay follows an exponential decay curve. This means that the amount of a radioactive substance decreases exponentially over time. The equation for this is: [tex]A(t) = A0*e^(-λ*t\\[/tex])Where A(t) is the amount of substance at time t, A0 is the initial amount of substance, and λ is the decay constant. In this problem, A0 = 100 mg, t = 29 hours, and A(t) = 50 mg. We can use this to solve for λ:50 mg = 100 mg * [tex]e^(-λ*29)λ =[/tex] -0.027Now that we have the decay constant, we can calculate the amount of substance remaining after 38 hours:A(38) = 100 mg * [tex]e^(-0.027*38[/tex]).A(38) = 43.1 mg.Therefore, after 38 hours, there will be 43.1 mg of the radioactive substance remaining.
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Luis wants to buy a skateboard that usually sells for $79.86. All merchandise is discounted by 12%. What is the total cost of the skateboard if Luis has to pay a state sales tax of 8.25%. Round your intermediate calculations and answer to the nearest cent.
The total cost of the skateboard is $
The total cost of the skateboard is $76.07.
What is the total cost of the skateboard?The first step is to determine the price of the skateboard after the 12% discount. A discount reduces the price of an item.
Price after discount = price before discount x (1 - percent discount)
$79.86 x (1 - 12/100)
$79.86 x (1 - 0.12)
$79.86 x 0.88
= $70.28
Price after the sales tax = (1 + sales tax) x price after discount
= (1 + 8.25/100) x $70.28
(1 + 0.0825) x $70.28
1.0825 x $70.28 = $76.07
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s this true or false? fraction numerator n squared plus 2 n space plus 5 over denominator n end fraction space element of space capital omega (n squared )true
The given expression is a fraction in the form of[tex](n^2 + 2n + 5)/n[/tex], which is an element of the set Omega ([tex]n^2[/tex]). This expression is true.
The given expression is a fraction in the form[tex](n^2 + 2n + 5)/n[/tex], which belongs to the set Omega[tex](n^2).[/tex] This statement is valid, as the fraction is simply a simplified form of a polynomial, which is an element of the Omega set. The numerator of the fraction is [tex]n^2 + 2n + 5[/tex], which is a quadratic equation in n. The denominator is n, which is a linear equation in n. As the numerator and denominator are both polynomials of n, the fraction is an element of the Omega set. Therefore, the statement is true.
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Select the correct answer. A line t runs upward to the right through two parallel horizontal lines r and s, forming 8 angles numbered from 1 to 8. Given: Transversal t passes through parallel lines r and s. Prove: ∠3 ≅ ∠6 ∠4 ≅ ∠5 Statement Reason 1. r || s given 2. ∠3 ≅ ∠7 ∠4 ≅ ∠8 For parallel lines cut by a transversal, corresponding angles are congruent. 3. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠1 ≅ ∠8 and ∠2 ≅ ∠7 Reason: Congruent Supplements Theorem B. Statement: m∠3 + m∠4 = 180° and m∠7 + m∠8 = 180° Reason: Linear Pair Theorem C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Answer:
The correct answer is C. Statement: m∠3 + m∠5 = 180° and m∠4 + m∠6 = 180° Reason: definition of supplementary angles.
This statement uses the definition of supplementary angles, which states that two angles are supplementary if their measures add up to 180 degrees. Since ∠3 and ∠6 are corresponding angles, and ∠4 and ∠5 are also corresponding angles, their measures must add up to 180 degrees in order for the parallel lines to be cut by the transversal.
Answer:
Option, D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
Step-by-step explanation:
In this question that you have put:
7 ≅ ∠6 and ∠8 ≅ ∠5 Reason =
Vertical Angles Theorem ( Or in similar terms VAT )
Make sure that you remember the following:
vertical angles are the angles that are opposite each other when the two line " meet together "
Thus, your answer to your questions is.
D. Statement: ∠7 ≅ ∠6 and ∠8 ≅ ∠5 Reason: Vertical Angles Theorem
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Find the simplified product:^3sqrt2x^5 x ^3sqrt64x^9
The simplified product of the ^3sqrt2x^5 x ^3sqrt64x^9 is [tex]24\sqrt{2} x^{17}[/tex]
Simplifying an expression is just another way to say solving a math problem. When you simplify an expression, you're basically trying to write it in the simplest way possible. At the end, there shouldn't be any more adding, subtracting, multiplying, or dividing left to do.
For finding the simplified product we will first remove the squareroot possible and simplify the value in a simplest way as possible. In the given question, first we will simplifying [tex]\sqrt{64}[/tex] and after simplifying it we will then apply [tex]a^{n} . a^{m} = a^{n+m}[/tex], and lastly we will multiply the two numbers i.e., 3 and 8.
[tex]3\sqrt{2}x^5x^3\sqrt{64}x^9[/tex]
[tex]3\sqrt{2}x^5x^3\sqrt{8^{2} }x^9[/tex]
[tex]3.8\sqrt{2}x^{5+3+9}[/tex]
[tex]3.8\sqrt{2}x^{17}[/tex]
[tex]24\sqrt{2}x^{17}[/tex]
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Select the correct answer.
Consider this function.
f(x) = 6log₂x - 3
Over which interval is function f increasing at the greatest rate?
OA. [2, 6]
OB. [1/8, 1/2]
OC. [1, 2]
OD. [1/2,1]
The function f(x) = 6log₂x - 3 increasing at the greatest rate in the interval [1/8, 1/2].
What are maxima and minima?The maxima and minima of a function are the extreme values within the range; in other words, they are the maximum and minimum values of a function, respectively, at a given position.
Let the function be f(x) = 6log₂x - 3
For the interval x ∈ [2, 6]
f(x) ∈ [-0.678, 3]
For the interval x ∈ [1/8, 1/2]
f(x) ∈ [ -9.96, -5.32]
For the interval x ∈ [1, 2]
f(x) ∈ [-3, -0.67]
For the interval x∈ [1/2, 1]
f(x) ∈ [-5.32, -3]
The function increased most rapidly in the interval [1/8, 1/2], as can be seen from the function value and its interval values.
Therefore, the range [1/8, 1/2] is where the function f(x) = 6log₂x - 3 increases at the fastest pace.
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D. A car dealer purchased 40 new cars at
$6500 each. He sold 40% of them at
$8000 each and the rest at $9000 each.
What was his total profit?
40%=
5
2
5
2
⋅40=16 cars at 8000 each =128,000 in sales
40−16=
24 cars at 9000 each
=216,000 in sales
Total sales: 128,000+216,000=344,000
Total expense: 6500⋅40=260,000
Total profit: 344,000−260,000=84,000
Answer:
$84000
Step-by-step explanation:
40% of the cars would be 16 cars that are sold for $8000 each.
16×$8000=$128000
The remaining 60% of cars would be 24 cars to be sold at $9000 each.
24×$9000=$216000
The total profit = the sum - the amount he paid for all cars.
total profit = ($128000+$216000) - (40×$6500)
total profit = $344000 - $260000
total profit = $84000
The triangles are similar.
What is the value of x?
See the attachment for the problem to be answered.
Answer:
16
Step-by-step explanation:
20/5 = 12/3 = x/4
x/4 = 4
x = (4)(4) = 16
Answer:16
Step-by-step explanation:multiply 4 by 4
at the grocery store, caleb has narrowed down his selections to 5 vegetables, 8 fruits, 3 cheeses, and 7 whole grain breads. he wants to use the express lane, so he can only buy 20 items. in how many ways can he choose which 20 items to buy if he wants all 3 cheeses?
Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.
To choose 20 items at the grocery store, Caleb has narrowed down his selections to 5 vegetables, 8 fruits, 3 cheeses, and 7 whole grain breads. Since he wants all 3 cheeses, he only needs to choose 17 more items.
The number of ways he can choose these 17 items from the remaining vegetables, fruits, and breads is given by the combination: C(5+8+7, 17) = C(20, 17) = 1140.
This formula means that there are 20 items to choose from, and Caleb wants to choose 17. The order doesn't matter, so we use a combination.
Therefore, Caleb can choose which 20 items to buy in 1140 ways if he wants all 3 cheeses.
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Compare the experimental and theoretical probabilities of each outcome.
Getting two tails
Getting two heads
Getting one heads and one tails
The theoretical probability of getting two tails is 1/4 = 0.25 = 25%. The experimental probability of getting two tails will change for every experiment.
The theoretical probability of getting two heads is 1/4 = 0.25 = 25%.
The theoretical probability of getting one head and one tail is 2/4 = 0.50 = 50%.
What is experimental probability?
The proportion of outcomes where a specific event occurs to all trials, not in a hypothetical sample space but in a real experiment, is known as the empirical probability, relative frequency, or experimental probability of an event.
Given that two coins flip together. The outcomes of a coin is {H,T}.
The outcomes after flipping of two coins are
{HH, HT, TH, TT}
The total number of outcomes is 4.
The number of outcomes to get two tails is 1.
The probability of getting two tails is 1/4 = 0.25 = 25%.
The number of outcomes to get two heads is 1.
The probability of getting two heads is 1/4 = 0.25 = 25%.
The number of outcomes to get one head and one tail is 2
The probability of getting one head and one tail is 2/4 = 0.50 = 50%.
The theoretical probabilities will change for every experiment.
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Cleopatra and her brother, Ptolemy, each have cylindrical water clocks (so they drain uniformly), but their clocks have different heights and diameters. Cleopatra’s clock drains from full down to empty in 4 hours and Ptolemy’s does so in 5 hours. After two hours of draining, the water height in both clocks is the same. What fraction of the height of Cleopatra’s clock is the height of Ptolemy’s? After each has been draining for three hours, what fraction of the water height of Ptolemy’s clock is equal to the water height of Cleopatra’s?
The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is 2/5
What is the volume of a cylinder?A cylinder is a three-dimensional shape that consists of two parallel circular bases connected by a curved lateral surface. The volume of a cylinder is the amount of space contained within the cylinder. It can be calculated using the formula:
Volume of cylinder = πr^2h
Let's denote the height and radius of Cleopatra's water clock as h_c and r_c, respectively, and the height and radius of Ptolemy's water clock as h_p and r_p, respectively. Since both clocks drain uniformly, we can use the formula for the volume of a cylinder to relate the height and radius of each clock to the time it takes to drain:
Volume of Cleopatra's clock =[tex]\mathrm{ \pi r_c^2h_c}[/tex]
Volume of Ptolemy's clock = [tex]\mathrm{\pi r_p^2h_p}[/tex]
Since Cleopatra's clock drains in 4 hours, the rate of draining is (Volume of Cleopatra's clock) / (4 hours), and similarly for Ptolemy's clock. We are given that after 2 hours of draining, both clocks have the same water height. Therefore, we can set the two rates of draining equal to each other and solve for the ratio of heights:
(Volume of Cleopatra's clock) / (4 hours) = (Volume of Ptolemy's clock) / (5 hours)
[tex]\pi r_c^2h_c / 4 = \pi r_p^2h_p / 5[/tex]
[tex]h_c / h_p = (r_p / r_c)^2 \times (5 / 4)[/tex]
We are not given the values of the radii, but we can see that the ratio of heights depends only on the ratio of the radii squared. Therefore, we don't need to know the actual sizes of the clocks, only the ratio of their radii. Let's call this ratio x:
[tex]x^2 = (h_c / h_p) \times(4 / 5)[/tex]
After two hours of draining, the water height in both clocks is the same, so we can set the volume of water in each clock equal to each other:
[tex]\pi r_c^2(h_c - 2h_c/4) = \pi r_p^2(h_p - 2h_p/5)[/tex]
[tex]\pi r_c^2h_c/2 =\pi r_p^2h_p/5*3[/tex]
[tex]r_c^2h_c/2 = r_p^2h_p/15[/tex]
Now, we can solve for the ratio of water heights after each clock has been draining for three hours:
Water height in Cleopatra's clock after 3 hours = [tex]\mathrm{h_c - (3/4)h_c = (1/4)h_c}[/tex]
Water height in Ptolemy's clock after 3 hours = [tex]\mathrm{ h_p - (3/5)h_p = (2/5)h_p}[/tex]
([tex]h_p[/tex] / (2/5)[tex]h_p[/tex] ) = ((1/4)[tex]h_c / h_c[/tex])
([tex]h_p[/tex] / (2/5)) = 1/4
[tex]h_p[/tex] = 2/5 * 1/4
[tex]h_p[/tex] = 1/10
Therefore, the fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is:
[tex]h_p / h_c[/tex]= 1/10 / (1/4) = 2/5
And the fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been draining for three hours is:
[tex]h_c / (2/5)h_p[/tex] = (1/4) / (2/5)(1/10) = (1/4) / (1/20) = 5/4
Hence,
The fraction of the height of Cleopatra's clock that is the height of Ptolemy's clock is: 2/5
The fraction of the water height of Ptolemy's clock that is equal to the water height of Cleopatra's clock after each has been drained for three hours is: 5/4.
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Pleaseeee help needddd done asappppp
8 is (6x^2-7x-5)/(2x + 1)
Kashif and ali invested equal sum in two different banks at 9% and 10% interest compound annually. In 6 years how much will kashif can more than ali
If Kashif and Ali invested equal sums in the two different banks at 9 % and 10% , then in 6 years Ali will have $0.0945 more than Kashif .
We use the formula for compound interest, to calculate the amount that each person will have after 6 years ;
Amount after 6 years for Kashif is :
⇒ A = P(1 + r/n[tex])^{nt}[/tex]
where A = (amount after 6 years) ; P = (initial investment)
r = interest rate = 9% ; n = 1 ; t = time period (6 years) ;
So, A = P(1 + 0.09/1)⁶ ⇒ P(1.09)⁶ ;
Amount after 6 years for Ali is :
⇒ A = P(1 + 0.10/1)⁶ = P(1.10)⁶ ;
So , difference in the amounts that Kashif has compared to Ali after 6 years is ⇒ P(1.09)⁶ - P(1.10)⁶ ;
Simplifying this expression, we get:
⇒ P(1.09⁶ - 1.10⁶) ;
≈ -$0.0945 ;
Since the value is negative, it means that after 6 years, Ali will have more money than Kashif and difference between their amounts is approximately $0.0945 .
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Wanda did 145 random math problems from each math book in her library. Each math book
in the library has an equal number of problems.
Is this sample of the math problems in the library likely to be representative?
Answer:
According to Kepler's third law, what is the orbital period of this asteroid in terms of Earth years? A certain asteroid is approximately 50 AU from the Sun.
A ladder leans against the side of a house. The angle of elevation of the ladder is 68° when the bottom of the ladder is 7 ft from the
is the top of the ladder from the ground? Round your answer to the nearest tenth.
Check
68°
O
X
Save-
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T
Answer:
17.3 feet
Step-by-step explanation:
We can use the tangent function to evaluate the height of the building.
The definition of the tangent function is
[tex]\tan x=\frac{O}{A}[/tex]
Where
[tex]A[/tex] is the side adjacent to the angle
[tex]O[/tex] is the side opposite to the angle
In this example we are given values of the adjacent side and the angle.
Knowing that we can evaluate the side opposite to the angle.
Numerical Evaluation
We are given
[tex]x=68\\A=7[/tex]
Substituting these values into the equation for the tangent function yields[tex]\tan 68=\frac{O}{7}[/tex]
Lets solve for [tex]O[/tex].
Multiply both sides by [tex]7[/tex].
[tex]O=7*\tan 68[/tex]
Evaluate [tex]\tan 68[/tex].
[tex]O=7*2.47508685[/tex]
[tex]O=17.325608[/tex]
Rounding to the nearest tenth gives us
[tex]O=17.3[/tex]
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You are given the dollar value of a product in 2015 and the rate at which the value of the product is expected to change during the next 5 years. Write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 15 represent 2015. )
2015 Value Rate $260,000 $5600 decrease per year
The linear equation that gives the dollar value V of the product in terms of the year t is V = - $5600t + $344,000.
V(t) is a function of t that expresses the value in the year 2000+t.
We know that the decrease is $5600 per year.
So,
V(t) = -$5600t + c
where c is the constant.
V(15) = -$5600 (15) + c = $260,000 [t = 15]
Hence, we can say that -
c = $260,000 + $5600 (15)
c= $260,000 + $84,000
c= $344,000
Now we got the value of c. We can write the equation as follows -
V = - $5600t + $344,000
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6.RP.3d-2016 (#39) Fei Yen's dog eats 8 ounces of dog food each day. Fei Yen bought a 28-pound bag of dog
food. How many 8-ounce servings are in a 28-pound bag of dog food?
A 14
B 56
C 224
D 448
There are 56 servings in a 28 pound bag of dog food.
What is Unitary Method ?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.
For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.
12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.
As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.
This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.
Given:
Each day Fei yen's dog eat dog food = 8 ounces
Fei yen bought a 28 pound bag of dog food.
And we know that 1 pound = 16 ounces
Then ,the food in ounces
= 28 x 16
= 448 ounces
Now, the number of 8 ounces servings are in a 28 pound bag of dog food
= 448 / 8
= 56
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Can any one help with me please
Answer:
85
Step-by-step explanation:
The vertical line that y is on adds up to 180 so if we take 180 - the number we already know (95) we get 85