Answer:
Step-by-step explanation:
The values of the letters are: a = k / (648b), b = k / (1296c), c = k / (1296b) and 24c = k / (576a).
To determine the value of the letters in the given sequences, we need to first recall the formula for inverse proportionality, which states that the product of the terms in one sequence is equal to the constant value of the product of the terms in the other sequence. Mathematically, we can represent this as:
4 x 8 x a x 18 = k = 54 x b x 24 x c
Here, k is the constant of proportionality. To find the value of the letters, we can solve for them algebraically. First, we can simplify the equation by dividing both sides by 4 x 18 x 24:
a = k / (4 x 8 x 18 x 24 / 54 x b x c)
a = k / (6b c)
Next, we can substitute the given values of the sequence into the equation and simplify:
a = k / (6b c) = k / (648b)
Multiplying both sides by 648b, we get:
648b a = k
Similarly, we can solve for the values of the other letters as follows:
b = k / (54 x 24 x c) = k / (1296c)
24c = k / (4 x 8 x a x 18) = k / (576a)
c = k / (54 x b x 24) = k / (1296b)
Therefore, the values of the letters are:
a = k / (648b)
b = k / (1296c)
c = k / (1296b)
24c = k / (576a)
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solve this problem and I will give u brainlist.
From the calculation, you are 100 m away from the plateau.
What is the angle of elevation?The angle of elevation is the angle between a horizontal line of sight and a line of sight that is directed upwards, or the angle between the horizontal and the line of sight when an observer is looking upward.
We know that;
Angle of elevation = 35°
Height of the Plateau = 70 m
Thus;
Tan 35 =70/x
x = Your distance from the plateau.
x = 70/Tan 35
x = 100m
In trigonometry and geometry, the angle of elevation—which can be expressed in degrees, radians, or other angular units—is frequently employed to address issues with heights and distances.
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Can someone please help me ASAP? It’s due tomorrow
You work at Dave's Donut Shop. Dave has asked you to determine how much each box of a dozen donuts should cost. There are 12 donuts in one dozen. You determine that it costs $0.27 to make each donut. Each box costs $0.16 per square foot of cardboard. There are 144 square inches in 1 square foot.
Using mathematical operations, each box of a dozen donuts should cost $3.40.
What are the mathematical operations?The basic mathematical operations used to determine the cost of a dozen donuts include multiplication and addition.
Firstly, the total cost of 12 donuts is computed by multiplication, while the total cost of the donuts per box (including the cost of the box) is obtained by addition.
1 dozen = 12 donuts
The cost unit of a donut = $0.27
The total cost of donuts = $3.24 ($0.27 x 12)
The cost per square foot of cardboard = $0.16
The total cost of a dozen donuts and the box = $3.40 ($3.24 + $0.16)
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Hannah has an offer from a credit card issuer for 0% APR for the first 30 days
and 12. 22% APR afterwards, compounded daily. What effective interest rate
is Hannah being offered?
To find the effective interest rate that Hannah is being offered, we need to take into account the compounding period, which is daily in this case. The effective annual interest rate (EAR) can be calculated using the formula:
EAR = (1 + APR/n)^n - 1
where APR is the annual percentage rate, and n is the number of compounding periods per year.
For the first 30 days, Hannah is offered a 0% APR, so the EAR for this period is simply 0.
After 30 days, Hannah is offered a 12.22% APR compounded daily, which means that there are 365 compounding periods per year. Therefore, the EAR for this period can be calculated as follows:
EAR = (1 + 0.1222/365)^365 - 1
≈ 0.1267
So the effective interest rate that Hannah is being offered is approximately 12.67%.
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a consumer activist decides to test the authenticity of the claim. she follows the progress of 20 women who recently joined the weight-reduction program. she calculates the mean weight loss of these participants as 14.8 pounds with a standard deviation of 2.6 pounds. the test statistic for this hypothesis would be
The test statistic for the hypothesis about a consumer activist decides to test the authenticity of the claim is t = 1.38.
In a hypothesis test, a test statistic—a random variable—is computed from sample data. To decide whether to reject the null hypothesis, you can utilise test statistics. Your results are compared to what would be anticipated under the null hypothesis by the test statistic. The p-value is computed using the test statistic.
A test statistic gauges how closely a sample of data agrees with the null hypothesis. Its observed value fluctuates arbitrarily from one random sample to another. When choosing whether to reject the null hypothesis, a test statistic includes information about the data that is important to consider. The null distribution is the sample distribution of the test statistic for the null hypothesis.
Sample size, n = 20
Sample mean, x = 14.8 pounds
Sample standard deviation, s = 2.6
The null hypothesis is,
[tex]H_o[/tex]: μ ≤ 14
The alternative hypothesis is,
[tex]H_a[/tex] : μ > 14
t-test statistic is defined as:
[tex]t = \frac{x - \mu}{\frac{s}{\sqrt{n} } }[/tex]
[tex]= \frac{14.8 - 14}{\frac{2.6}{\sqrt{20} } }[/tex]
= [tex]\frac{0.8}{0.581}[/tex]
= 1.377
t = 1.38.
Therefore, the test statistic for the hypothesis is 1.38.
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Complete question"
An advertisement for a popular weight-loss clinic suggests that participants in its new diet program lose, on average, more than 14 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 20 women who recently joined the weight-reduction program. She calculates the mean weight loss of these participants as 14.8 pounds with a standard deviation of 2.6 pounds. The test statistic for this hypothesis would be Multiple Choice -1.38 1.38 1.70 -1.70 O O
Lines b and a are intersected by line f. At the intersection of lines f and b, the bottom left angle is angle 4 and the bottom right angle is angle 3. At the intersection of lines f and a, the uppercase right angle is angle 1 and the bottom left angle is angle 2.
Which set of equations is enough information to prove that lines a and b are parallel lines cut by transversal f?
Answer:
Step-by-step explanation:
To prove that lines a and b are parallel lines cut by transversal f, we need to show that the alternate interior angles are congruent. According to the given information, angle 2 and angle 3 are corresponding angles, and angle 1 and angle 4 are corresponding angles.
Therefore, the set of equations that is enough information to prove that lines a and b are parallel lines cut by transversal f is:
angle 2 = angle 3 (corresponding angles)
angle 1 = angle 4 (corresponding angles)
Matt knows 4 x 6 = 24. what other math fact does this help matt remember? circle the letter of the correct answer. sadie chose a 6 + 4 = 10 as the correct answer. how did she get that answer?
The math fact that 4 x 6 = 24 helps Matt remember that 6 x 4 = 24, and Sadie arrived at the answer 10 for 6 + 4 by incorrectly adding the numbers in reverse order.
Matt knows that 6 x 4 = 24. This helps him remember that 4 x 6 and 6 x 4 are both equal to 24.
The math fact that Matt can remember based on 4 x 6 = 24 is that multiplication is commutative. This means that the order of the numbers being multiplied doesn't affect the result. So, if 4 multiplied by 6 equals 24, it also implies that 6 multiplied by 4 would give the same result of 24.
Sadie arrived at the answer 10 for 6 + 4 by mistakenly swapping the order of the numbers and performing the addition incorrectly. The correct sum for 6 + 4 is indeed 10. Sadie's error demonstrates the importance of following the correct order of operations, where addition should be performed after ensuring the numbers are in the correct order.
As for Sadie's answer of 6 + 4 = 10, it is not directly related to the multiplication fact that Matt knows.
It is possible that Sadie used a different math fact or strategy to arrive at that answer.
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Pls answer this asap
Answer:
(C) Neither
Step-by-step explanation:
You want to know if the function values in the table represent an even function, and odd function, or neither.
SymmetryAn Even function is symmetrical about the y-axis:
f(-x) = f(x)
An Odd function is symmetrical about the origin:
f(-x) = -f(x)
ApplicationThe attached graph of the given points shows the function has no symmetry at all.
The table represents neither an even nor odd function.
Answer:
Neither
Step-by-step explanation:
In an even function, f(x) = f(-x).
Look at x = 2 and x = -2.
f(2) = -4; f(-2) = 2
Since f(2) ≠ f(-2), the function is not even.
In an odd function, f(x) = -f(-x).
Look at f(2) and f(-2).
f(2) = -4; f(-2) = 2
Since f(2) ≠ -f(-2), the function is not odd.
Answer: C Neither
In 2016, Dave bought a new car for $15,500. The current value of the car is $8,400. At what annual rate did the car depreciate in value? Express your answer as a percent (round to two digits between decimal and percent sign such as **. **%). Use the formula A(t)=P(1±r)t
To find the annual rate at which the car depreciated, we need to use the formula for exponential decay:
A(t) = P(1 - r)^t
where A(t) is the current value of the car after t years, P is the initial value of the car, and r is the annual rate of depreciation.
We know that P = $15,500 and A(t) = $8,400, so we can plug in these values to solve for r:
$8,400 = $15,500(1 - r)^t
Divide both sides by $15,500:
0.54 = (1 - r)^t
Take the logarithm of both sides:
log(0.54) = t*log(1 - r)
Solve for r:
log(0.54)/t = log(1 - r)
1 - r = 10^(log(0.54)/t)
r = 1 - 10^(log(0.54)/t)
Plugging in t = 7 (since the car has depreciated for 7 years), we get:
r = 1 - 10^(log(0.54)/7) ≈ 9.35%
Therefore, the car depreciated at an annual rate of approximately 9.35%.
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Select allá transformations that Will map a pentágon onto itself
There are several transformations that can be applied to a pentagon in order to map it onto itself. One such transformation is a rotation of 72 degrees, which can be performed by rotating the pentagon about its center point by 72 degrees clockwise. This will result in the pentagon appearing exactly as it did before the rotation, but in a different orientation.
Another transformation that will map a pentagon onto itself is a reflection along one of its symmetry lines. A pentagon has five symmetry lines, which are lines that divide the shape into two congruent halves. Reflecting the pentagon along any of these lines will result in the same shape being produced, but in a mirror image orientation.
Finally, a translation can also be used to map a pentagon onto itself. This involves moving the pentagon a certain distance in a particular direction, such as shifting it 2 units to the right or 3 units upwards. As long as the distance and direction of the translation are such that the pentagon ends up exactly where it started, it will be a valid transformation.
Overall, there are several transformations that can be applied to a pentagon in order to map it onto itself, including rotations, reflections, and translations.
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If c(t) = 53.2te^{- 0.26} measures the concentration, in ng/ml of a drug in a person's system thours after the drug is administered. a) What is the peak concentration of the drug? b) When does the drug reach peak concentration?
(a) To find the peak concentration of the drug, we need to find the maximum value of c(t). Since c(t) is an exponential function, its maximum value occurs at its maximum point, which is where its derivative is equal to zero. We can find this point by taking the derivative of c(t) and setting it equal to zero:c'(t) = 53.2e^{-0.26} - 13.832te^{-0.26} = 0Solving for t, we get t = 3.870 hours. Therefore, the peak concentration of the drug is c(3.870) = 109.2 ng/ml.(b) To find when the drug reaches peak concentration, we have already found that it occurs at t = 3.870 hours. Therefore, the drug reaches peak concentration 3.870 hours after it is administered.
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The peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.
To find the peak concentration of the drug and when it reaches that peak, we'll need to consider the given function c(t) = 53.2te^(-0.26t), where t is the time in hours.
a) To find the peak concentration, we need to determine the maximum value of c(t). We can do this by taking the first derivative of c(t) with respect to t and setting it equal to 0.
c'(t) = 53.2(-0.26)e^(-0.26t) + 53.2e^(-0.26t) = 0
Now, solve for t:
t ≈ 3.85 hours
b) Plug the value of t back into the c(t) function to find the peak concentration:
c(3.85) = 53.2(3.85)e^(-0.26(3.85)) ≈ 42.83 ng/ml
So, the peak concentration of the drug is approximately 42.83 ng/ml, and it occurs around 3.85 hours after the drug is administered.
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A segment with endpoints A (4, 2) and C (1,5) is partitioned by a point B such that AB and BC form a 1:3 ratio. Find B.
O (1, 2. 5)
O (2. 5, 3. 5)
O (3. 25, 2. 75)
O (3. 75, 4. 5)
The answer is (3.25, 2.75)
To find point B, we can use the fact that AB and BC form a 1:3 ratio. Let's start by finding the coordinates of point B.
First, we need to find the distance between A and C. We can use the distance formula for this:
[tex]d = \sqrt{ ((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where [tex](x1, y1) = (4, 2)[/tex] and [tex](x2, y2) = (1, 5)[/tex]
[tex]d = \sqrt{((1 - 4)^2 + (5 - 2)^2)} = \sqrt{(9 + 9)} = \sqrt{(18)}[/tex]
Next, we need to find the distance between A and B, which we'll call x, and the distance between B and C, which we'll call 3x (since AB and BC are in a 1:3 ratio).
Using the distance formula for AB:
[tex]x = \sqrt{\\((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where [tex](x1, y1) = (4, 2)[/tex] and [tex](x2, y2) = (Bx, By)[/tex]
[tex]x = \sqrt{((Bx - 4)^2 + (By - 2)^2)[/tex]
Using the distance formula for BC:
[tex]3x = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where [tex](x1, y1) = (1, 5)[/tex] and [tex](x2, y2) = (Bx, By)[/tex]
[tex]3x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]
Now we can set up an equation using the fact that AB and BC are in a 1:3 ratio:
[tex]x / 3x = 1 / 4[/tex]
Simplifying this equation, we get:
[tex]4x = 3(AB)[/tex]
[tex]4x = 3\sqrt{((Bx - 4)^2 + (By - 2)^2)[/tex]
And
[tex]9x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]
Now we have two equations and two unknowns (Bx and By). We can solve for Bx in the first equation and substitute into the second equation:
[tex]Bx = (3\sqrt{((Bx - 4)^2 + (By - 2)^2))} / 4[/tex]
[tex]9x = \sqrt{((Bx - 1)^2 + (By - 5)^2)[/tex]
[tex]81((Bx - 4)^2 + (By - 2)^2) / 16 = (Bx - 1)^2 + (By - 5)^2[/tex]
Expanding the squares and simplifying, we get:
[tex]81Bx^2 - 648Bx + 1245 = 16Bx^2 - 32Bx + 266[/tex]
[tex]65Bx^2 - 616Bx + 979 = 0[/tex]
Using the quadratic formula, we get:
[tex]Bx = (616 ± \sqrt{(616^2 - 4(65)(979)))} / (2(65))[/tex]
[tex]Bx = (616 ± \sqrt{(223456))} / 130[/tex]
[tex]Bx = 3.25[/tex] or [tex]Bx = 10.2[/tex]
We can eliminate the solution Bx ≈ 10.2 because it is outside the segment AC. Therefore, the solution is:
B = (3.25, 2.75)
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Find the value of b. Round your answer to the nearest hundredth.
Image may not
be drawn to scale.
The value of the tangent segment b is 20.15.
What is the value of side b?The secant-tangent power theorem, also known as the tangent-secant theorem, states that if a tangent and a secant are drawn from a common external point to a circle, then the product of the length of the secant segment and its external part is equal to the square of the length of the tangent segment.
It is expressed as:
( tangent segment )² = External part of the secant segment + Secant segment.
From the diagram:
Tangent segment = WX = b
External part of the secant segment = YX = 14
Secant segment = ZX = 15 + 14 = 29
Plug these values into the above formula and solve for b.
( tangent segment )² = External part of the secant segment + Secant segment.
b² = 14 × 29
b² = 406
b = √406
b = 20.15
Therefore, the value of b is 20.15.
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A, b & c form the vertices of a triangle.
∠cab = 90°,
∠abc = 65° and ac = 8.9.
calculate the length of bc rounded to 3 sf.
The length of BC rounded to 3 significant figures is 6.98.
Since ∠cab = 90°, we can use the Pythagorean Theorem to find the length of AB.
Let's call BC = x, then we have:
sin(65°) = AB/BC
AB = sin(65°) * BC
In right triangle ABC, we have:
AB^2 + BC^2 = AC^2
(sin(65°) * BC)^2 + BC^2 = 8.9^2
Solving for BC, we get:
BC = 8.9 / sqrt(sin^2(65°) + 1)
BC ≈ 6.98
Therefore, the length of BC rounded to 3 significant figures is 6.98.
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each of the following questions could be the basis for a statistical study. how would the collected data look different for each question? do you think they would lead to the same result or different results? what percentage of internet dates lead to marriage? what percentage of marriages begin with internet dates?
Answer:is 230
Step-by-step explanation:
230 i hoped i helped
Which expression is equivalent to the given expression? ( 10 c 6 d - 5 ) ( 2 c - 5 d 4 ) A. 20 c d B. 20 c d C. 20 c 30 d 20 D.
So the equivalent expression that matches one of the answer choices is option C, 100c/3d.
What is expression?In mathematics, an expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponentiation, and so on) that can be evaluated to produce a value. An expression can represent a single number or a more complex calculation, and it can be written using symbols, variables, and/or numbers.
Here,
To simplify the given expression, we need to multiply the two binomials using the distributive property:
(10c6d - 5)(2c - 5d/4)
= 10c * 2c + 10c * (-5d/4) - 5 * 2c - 5 * (-5d/4)
= 20c² - 25cd + 10c + 25/4 d
None of the answer choices match this expression exactly, but we can simplify it further. Factoring out a common factor of 5 from the last two terms, we get:
20c² - 25cd + 10c + 25/4 d
= 5(4c² - 5cd + 2c + 5/4
20c/3 * 5d/4
= 100c/3d
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14. If AB represents 50%, what is the length of a
line segment that is 100%?
Answer:
2*Ab Or AC
Step-by-step explanation:
No detail in question
After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4. 5% each year and he will earn $63,417 for his tenth year of work
Herbert will earn $63,417 for his tenth year of work which is calculated using compound interest formula.
After graduating from college, Herbert decided to join a new company. He agreed to a salary which will increase by 4.5% each year. This means that every year, Herbert's salary will increase by 4.5% of his previous year's salary. For example, if his salary in the first year is $50,000, his salary in the second year will be $52,250, and so on.
To find out Herbert's salary for his tenth year of work, we need to use compound interest formula. The formula is:
A = P(1 + r)ⁿ
Where:
A = Final amount (salary in the tenth year)
P = Initial amount (salary in the first year)
r = Annual interest rate (4.5%)
n = Number of years (10)
Substituting the values in the formula, we get:
A = $50,000(1 + 0.045)¹⁰
A = $63,417
Therefore, Herbert will earn $63,417 for his tenth year of work. It is important to note that the increase in salary is a result of compound interest, which means that the salary growth rate accelerates over time. This is a good incentive for Herbert to stay with the company and work hard.
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Solve for x and y.
15)
4+18y
10x
10x-6
16y+6
N
L
M
The value of x and y is 11 and 4 respectively
What is cyclic quadrilateral?A cyclic quadrilateral is a quadrilateral which has all its four vertices lying on a circle. It is also sometimes called inscribed quadrilateral.
A theorem in circle geometry states that the sum of opposite angles in a cyclic quadrilateral are supplementary. i.e they sum up to give 180.
10x + 16y+6 = 180
10x+16y = 174... eqn1
4+18y +10x-6 = 180
18y +10x = 182... eqn2
subtract equation 1 from 2
2y = 8
y = 8/2 = 4
Subtitle 4 for y in equation 1
10x+ 16(4)= 174
10x= 174-64
10x = 110
x= 110/10
x = 11
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Candace is flipping a coin a certain number of times. The theoretical probability of her flipping tails on all flips is 1/32. How many times is she flipping the coin?
Candace is flipping the coin 5 times.
What is probability?The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out.
The theoretical probability of flipping tails on any single flip of a fair coin is 1/2, since there are two equally likely outcomes (heads or tails) on each flip.
If Candace is flipping the coin a certain number of times and the theoretical probability of flipping tails on all flips is 1/32, we can set up the equation:
[tex](1/2)^n[/tex] = 1/32
where n is the number of times Candace is flipping the coin.
We can simplify this equation by taking the logarithm of both sides:
[tex]log((1/2)^n) = log(1/32)[/tex]
Using the property of logarithms that [tex]log(a^b) = b*log(a)[/tex], we can rewrite the left-hand side as:
n*log(1/2) = log(1/32)
We can simplify the logarithms using the fact that log(1/a) = -log(a), so:
n*(-log(2)) = -log(32)
Dividing both sides by -log(2), we get:
n = -log(32) / log(2)
Using a calculator, we find:
n ≈ 5
Therefore, Candace is flipping the coin 5 times.
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Question content area top
Part 1
Sandra
biked
700
meters
on Friday. On Saturday,
she
biked
4
kilometers. On Sunday,
she
biked
2
kilometers,
600
meters. How many
kilometers
did
Sandra
bike over the three days
Use the Lagrange Error Bound to give a bound on the error, E₄, when eˣ is ap- proximated by its fourth-degree (n = 4) Taylor polynomial about 0 for 0 ≤ x ≤ 0.9.
The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.
How to find the Lagrange error bound for the fourth-degree Taylor polynomial?To find the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0, we need to find the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].
Since the nth derivative of [tex]e^x[/tex] is [tex]e^x[/tex] for all n, the fifth derivative is also [tex]e^x[/tex]. To find the maximum value of[tex]e^x[/tex]on the interval [0, 0.9].
We evaluate [tex]e^x[/tex] at the endpoints and at the critical point x = 0.45, which is the midpoint of the interval:
[tex]e^0[/tex] = 1
[tex]e^0.9[/tex]≈ 2.4596
[tex]e^0.45[/tex] ≈ 1.5684
The maximum value of [tex]e^x[/tex] on the interval [0, 0.9] is approximately 2.4596.
The Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 is given by:
E₄(x) ≤ (M/5!)[tex]|x-0|^5[/tex]
where M is the maximum value of the fifth derivative of [tex]e^x[/tex] on the interval [0, 0.9].
So, we have:
E₄(x) ≤ (2.4596/5!) [tex]|x|^5[/tex] for 0 ≤ x ≤ 0.9
Substituting x = 0.9 into this inequality, we get:
E₄(0.9) ≤ (2.4596/5!)[tex](0.9)^5[/tex] ≈ 0.000129
Therefore, the Lagrange error bound for the fourth-degree Taylor polynomial of [tex]e^x[/tex] about 0 for 0 ≤ x ≤ 0.9 is approximately 0.000129.
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A sheet of dough has six identical circles cut from
it. Write an expression in factored form to represent the
approximate amount of dough that is remaining. Is
there enough dough for another circle
Approximate amount of dough that is remaining. Is (length - 2r)(width - 3r) - 6πr^2.
Without the size of the original sheet of dough or the size of the circles cut from it, it's not possible to give an exact expression. However, assuming that each circle has the same radius of 'r' and the original sheet of dough was a rectangle, we can write an expression in factored form for the remaining area of the dough:
Remaining area of dough = (Area of original rectangle) - 6(Area of circle)
= (length x width) - 6(πr^2)
= (length - 2r)(width - 3r) - 6πr^2
Whether there is enough dough for another circle would depend on the size of the circles and the original sheet of dough.
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A bag of M&Ms has 4 blue, 8 red, 6 orange, 12 green M&Ms of equal size. If one M&M is selected at random, what is the probability it is NOT red?
The probability of selecting an M&M that is not red is 11/15.To find the probability of selecting an M&M that is not red, we need to first find the total number of M&Ms in the bag,
It is the sum of the number of M&Ms of each color: 4 + 8 + 6 + 12 = 30.
Next, we need to find the number of M&Ms that are not red, which is the sum of the number of M&Ms of all other colors: 4 + 6 + 12 = 22.
Therefore, the probability of selecting an M&M that is not red is 22/30, which can be simplified by dividing both the numerator and the denominator by 2:
22/30 = 11/15
So the probability of selecting an M&M that is not red is 11/15.
In other words, there is an 11/15 chance that the selected M&M will be blue, orange, or green, and a 4/15 chance that it will be red.It is important to note that this assumes that each M&M is equally likely to be selected, and that the bag is well-mixed so that each M&M has an equal chance of being chosen.
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a) Calculate the scale factor from shape A to shape B.
b) Find the value of t.
Give each answer as an integer or as a fraction in its simplest form.
A
5 cm
15 cm
7cm
B
12 cm
4cm
t cm
The scale factor from A to B is 5 / 4.
The value of t in the diagram is 5.6 cm.
How to find scale factor?Scale factor is the ratio between corresponding measurements of an object and a representation of that object.
Therefore, let's find the scale factor from the shape A to the shape B as follows:
5 / 4 = 15 / 12
Therefore, the scale factor is 5 / 4.
Hence, let's find the value of t in the diagram as follows:
Therefore, using the proportionality,
7 / t = 5 / 4
cross multiply
28 = 5t
divide both sides by 5
t = 28 / 5
t = 5.6 cm
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Find The Area Of This Shape.
Answer:
34.65 mi²
Step-by-step explanation:
Area of parallelogramam = b · h
b = 6.3 mi
h = 5.5 mi
Let's solve
6.3 · 5.5 = 34.65 mi²
So, the area of the shape is 34.65 mi²
what is the radius of a basketball if the volume is 11488.2 cm? round your answer the the nearest whole number. use 3.14 as π .
Answer:
The radius of the basketball is 20 cm.
Step-by-step explanation:
The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius.
We are given that the volume of the basketball is 11488.2 cm, so we can set up the equation:
11488.2 = (4/3)πr^3Simplifying, we get:
(4/3)πr^3 = 11488.2Dividing both sides by (4/3)π, we get:
r^3 = 11488.2 / (4/3)πr^3 = 7239.79Taking the cube root of both sides, we get:
r ≈ 20Rounding to the nearest whole number, the radius of the basketball is 20 cm.
solve the initial value problem. f '(x) = 5 x2 − x2 5 , f(1) = 0
We can start by integrating both sides of the differential equation to obtain:
∫f '(x) dx = ∫([tex]5x^2 - x^2/5[/tex]) dx
f(x) = (5/3)[tex]x^3[/tex] - (1/15) [tex]x^5[/tex] + C
where C is the constant of integration.
To find the value of C, we can use the initial condition f(1) = 0:
f(1) = (5/3)[tex](1)^3[/tex] - (1/15) [tex](1)^5[/tex] + C = 0
Simplifying this equation gives:
C = (1/15) - (5/3)
C = -2/9
Therefore, the solution to the initial value problem f '(x) = 5[tex]x^2[/tex] − [tex]x^2[/tex]/5 , f(1) = 0 is:
f(x) = (5/3) [tex]x^3[/tex] - (1/15) [tex]x^5[/tex] - (2/9)
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Add one number to each column of the table so that it shows a function
To add one number to each column of the table and make it show a function, we need the specific table or information about the columns to provide a precise answer.
How to create a function?To transform the given table into a function, we need to add a column that represents the output values corresponding to each input value. A function relates each input value to a unique output value.
Here is an example of how the table could be modified to represent a function:
Input (x) Output (y)
1 3
2 5
3 7
4 9
In this modified table, the output values (y) are obtained by adding 2 to each input value (x). This ensures that each input value is associated with a unique output value, satisfying the definition of a function.
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Mariah is training for a sprint distance triathlon. She plans on cycling from her house to the library, shown on the grid with a scale in miles. If the cycling portion of the triathlon is 12 miles, will mariah have cycled at least 2/3 of that distance during her bike ride?
Mariah cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
What is a triathlon?A triathlon is described as an endurance multisport race consisting of swimming, cycling, and running over various distances.
The coordinates are given as follows:
Library (4,9).Mariah's House: (9, 2).Suppose that we have two points, and . The distance between them is given by:
distance = √(x2 - x1)² + (y2-y1)²
We substitute in the equation
Hence the distance between her house and the library is:
D = 8.6 miles.
She cycles a distance of 8.6 miles, which is more than 8 miles, hence more than 2/3 of the cycling portion of the triathlon.
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