Answers
Answer:
[tex] x=\sqrt{10} [/tex]
[tex] y = \sqrt {14} [/tex]
[tex] z = \sqrt {35} [/tex]
Step-by-step explanation:
By geometric mean theorem:
[tex] x=\sqrt{2\times 5} [/tex]
[tex] x=\sqrt{10} [/tex]
By Pythagoras Theorem:
[tex] y^2 = x^2 + 2^2 [/tex]
[tex] y^2 = (\sqrt{10}) ^2 + 2^2 [/tex]
[tex] y^2 = 10 + 4 [/tex]
[tex] y^2 = 14 [/tex]
[tex] y = \sqrt {14} [/tex]
Again by Pythagoras Theorem:
[tex] z^2 = x^2 + 5^2 [/tex]
[tex] z^2 = (\sqrt{10}) ^2 + 5^2 [/tex]
[tex] z^2 = 10 + 25 [/tex]
[tex] z^2 = 35 [/tex]
[tex] z = \sqrt {35} [/tex]
Related Questions
A triangular prism of length 20 cm with a triangular base of side 8 cm and height 4 cm. Calculate the volume in litres.
Answers
The volume of a triangular prism with a base 8 cm and height of 4 cm, length of 20 cm = 0.32 liters.
To calculate the volume of a triangular prism, you multiply the area of the base triangle by the length of the prism. Given that the base triangle has a side length of 8 cm and a height of 4 cm, its area can be calculated as (1/2) * base * height = (1/2) * 8 cm * 4 cm = 16 cm².
Multiplying this by the length of the prism, which is 20 cm, we get the volume:
Volume = Base Area * Length = 16 cm² * 20 cm = 320 cm³.
To convert this volume to liters, we know that 1 liter is equal to 1000 cm³. Therefore, we can divide the volume in cm³ by 1000 to obtain the volume in liters:
Volume in liters = 320 cm³ / 1000 = 0.32 liters.
So, the volume of the triangular prism is 0.32 liters.
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Evaluate the expression for the given value.
2w+2l, when w=7, l=5
Answers
Answer:
2w+2l.
2(7)+2(5).
14+10.
24.
x/3 less than or equal to 7
Answers
Answer:
x ≤ 21
Step-by-step explanation:
x/3 ≤ 7
x ≤ 21
Answer:
x ≤ 21
Step-by-step explanation:
With this problem, we have to solve for x, and to do that, we isolate the variable.
To do this, let’s get rid of the /3 from the x by multiplying both sides by 3
now we get x ≤ 7 times 3
finall, we get x≤21
please help i’ll give brainliest
Answers
Answer:
An animal that eats dead animals or plants.
Step-by-step explanation:
Its lowkey the defintion lol
Four years ago. Sherman bought 150 shares of Boca-Cola stock for $15 a share. He received a dividend of $0.30 per share each year. If the stock price has increased to $50 per share, what would be his total return?
Answers
Sherman's total return on his investment in Boca-Cola stock is $5,430.
The formula for the total return on an investment is as follows:
total return = capital gain + dividend yield
Initially, Sherman bought 150 shares of Boca-Cola stock for $15 a share.
Therefore, the initial investment (also known as the initial cost) is:
$15 x 150 = $2,250
Four years later, the stock price of Boca-Cola is $50 per share.
The capital gain is calculated as follows:
capital gain = final share price - initial share price
capital gain = $50 - $15
capital gain = $35
Therefore, the capital gain on Sherman's 150 shares is:
$35 x 150 = $5,250
Next, we need to calculate the total amount of dividends that Sherman received over the 4 years. The dividend per share is $0.30. Therefore, the total amount of dividends received is:
total dividends = dividend per share x number of shares x number of years
Sherman received dividends for 4 years, so:
total dividends = $0.30 x 150 x 4
total dividends = $180
The dividend yield is calculated as follows:
dividend yield = total dividends / initial cost
dividend yield = $180 / $2,250
dividend yield = 0.08 or 8%
Finally, we can calculate the total return:
total return = capital gain + dividend yield
total return = $5,250 + $180
total return = $5,430
Therefore, Sherman's total return on his investment in Boca-Cola stock is $5,430.
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A tub contained 80 gallons
of water. The water drained from
the tub at a rate of 5 gallons every 4
minutes. At this rate, how many
minutes did it take
for all the water to
drain from the tub?
Answers
Answer:
its 64 because 4x16= 64
Step-by-step explanation:
Prove these are logically equivalent p->q, !q->!p ¬q→¬p,
p→q
Answers
From the truth table, we can see that p->q and ¬p∨q have the same truth values for all possible combinations of truth values for p and q. Therefore, we can conclude that p->q is logically equivalent to ¬p∨q. In summary, we can see that p->q is logically equivalent to both !q->!p and ¬p∨q.
To prove the logical equivalence of the given statements, we can show that they have the same truth values in all possible cases. We'll use a truth table to demonstrate this.
p | q | p->q | !q | !p | !q->!p | p->q = !q->!p
-------------------------------------------------
T | T | T | F | F | T | T
T | F | F | T | F | F | F
F | T | T | F | T | T | T
F | F | T | T | T | T | T
From the truth table, we can see that for all possible combinations of truth values for p and q, the statements p->q and !q->!p have the same truth values. Therefore, we can conclude that p->q is logically equivalent to !q->!p.
Now let's consider the second statement, p->q. We can rewrite it as ¬p∨q using the logical equivalence of implication.
The truth table for p->q and ¬p∨q is as follows:
p | q | p->q | ¬p | ¬p∨q
-----------------------------
T | T | T | F | T
T | F | F | F | F
F | T | T | T | T
F | F | T | T | T
From the truth table, we can see that p->q and ¬p∨q have the same truth values for all possible combinations of truth values for p and q. Therefore, we can conclude that p->q is logically equivalent to ¬p∨q.
In summary, we have shown that p->q is logically equivalent to both !q->!p and ¬p∨q.
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Use convolution notation with and set up the integral to write the final answer of the following initial value ODE. There is no need to evaluate the integral. x" - 8x' + 12x = f(t) with f(t)
Answers
The integral representation of the solution to the initial value ordinary differential equation (ODE) x'' - 8x' + 12x = f(t) with f(t) is given by x(t) = x₀ * δ(t) + x₁ * δ'(t) + ∫[a,b] G(t - τ) * f(τ) dτ.
The given ODE is a linear homogeneous second-order ODE with constant coefficients. To find the integral representation of the solution, we introduce the Dirac delta function, δ(t), and its derivative, δ'(t), as the basis for the particular solution.
To set up the integral representation for the solution of the initial value ODE x'' - 8x' + 12x = f(t), we first define the Green's function G(t - τ). The Green's function satisfies the homogeneous equation with the right-hand side equal to zero:
G''(t - τ) - 8G'(t - τ) + 12G(t - τ) = 0.
Next, we set up the integral representation as follows:
x(t) = x₀ * δ(t) + x₁ * δ'(t) + ∫[a,b] G(t - τ) * f(τ) dτ,
The integral represents the convolution of the forcing function f(τ) with the Green's function G(t - τ).
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Use Laplace transform to solve the following partial differential equation with prescribed boundary and initial data: Uz(x, t) + 2xut(x, t) = 2x, u(x,0) = 1, u(0,t) = 1, where x ER and t > 0. Show the details of your work.
Answers
The given partial differential equation is given by; Uz(x, t) + 2xut(x, t) = 2x
The Laplace transform of Uz(x, t) + 2xut(x, t) is given as follows; L[Uz(x,t)] + 2x L[ut(x,t)] = L[2x]sU(x,s) - u(x,0) + 2x[sU(x,s)-u(x,0)] = 2x/sU(x,s) + 2x/s^2 - 1(2x/s)U(x,s) = 2x/s^2 - 1 + sU(x, s)U(x, s) = [2x/s^2 - 1]/[2x/s - s]U(x, s) = s(2x/s^2 - 1)/(2x - s^2) = s/(2x - s^2) - 1/(2(s^2 - 2x))
By using the inverse Laplace transform, we have; u(x, t) = [1/s] * e^(s^2t/2x) - (1/2)sinh(t sqrt(2x)) / sqrt(2x)
Thus, the solution to the given partial differential equation is given as follows; u(x, t) = [1/s] * e^(s^2t/2x) - (1/2)sinh(t sqrt(2x)) / sqrt(2x)Where, u(x,0) = 1 and u(0,t) = 1.
The integral transform known as the Laplace transform is particularly useful for solving ordinary differential equations that are linear. It finds extremely wide applications in var-ious areas of physical science, electrical designing, control engi-neering, optics, math and sign handling.
The mathematician and astronomer Pierre-Simon, marquis de Laplace, gave the Laplace transform its name because he used a similar transform in his work on probability theory.
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Find sin(a) in the triangle.
Choose 1 answer:
Answers
Answer:
sin B sorryonlearning(PLEASE HELP ME ASAP)
Write down a number that has a value less than |4.7|
Answers
Answer:
4.6
Step-by-step explanation:
3.. litteraly anything less than that
Answer:
0
Step-by-step explanation:
|4.7| = 4.7
Any number less than a positive 4.7 is less than |4.7|.
It costs $1.16 to buy four-fifths a pound of apples. How much would it cost to
buy 8 pounds?
Answers
Answer:
11.60
Step-by-step explanation:
If the cost of 4/5th a pound of apples is $1.16, and we need to find the cost of that of 8 pounds, then you start by finding how many 4/5ths of a pound are in 8 pounds. 8 dividided by 0.8 (the decimal form of 4/5) is 10. Taking that 10, you would multiply the original cost of $1.16, which would bring you to the total of $11.60.
how do u turn 3 into a fraction?
Answers
Answer:
[tex]\frac{3}{1}[/tex]
Step-by-step explanation:
Put a 1 under it.
so the answer is 3/1
PLEASE HELPP ME!!!!
It would be greatly appreciated :)
Answers
Answer:
The slope of the line is 2/3
Answer: 1.5
Step-by-step explanation:
I plugged it in STAT, but you can do rise over run, or use the formula, y2-y2/x2-x1
The Martins’ van can hold up to 8 passengers. Debbie writes the inequality p < 8, where p is the number of passengers that can fit in the van. Select the choice that provides the best explanation for Debbie’s error and the correct answer in this case. Debbie should have used 8p because 8 passengers can fit in the van. The correct inequality is 8p < 1. Debbie should have switched the inequality symbol to greater than. The correct inequality is p > 8. Debbie should have included 8 as a possible choice. The correct inequality is p < 9. Debbie should have used the not equals sign to compare the two sides of the inequality. The correct answer is p ≠ 8.
Answers
Answer:
Debbie should have included 8 as a possible choice. The correct inequality is p < 9.
Step-by-step explanation:
Given
Passengers = Up to 8
Required
Determine why [tex]p < 8[/tex] is incorrect and make corrections
The inequality [tex]p < 8[/tex] means that the van can hold less than 8 passengers.
To make correction, the digit 8 has to be included in the inequality.
This can be written as:
[tex]p <9[/tex] or[tex]p \le 8[/tex]
Base on the given options, option (c) best answered the question.
A simple random sample of size n = 49 is obtained from a population that is skewed right with µ = 81 and σ = 14. (a) Describe the sampling distribution of x. (b) What is P (x>84.9)? (c) What is P (x≤76.7)? (d) What is P (78.1
Answers
The sampling distribution of x is N (µx = µ = 81, σx = 2.00).The probability of x > 84.9 is:P(x > 84.9) = P(z > 1.75) = 0.0401.The probability of 78.1 < x < 81 is:P(78.1 < x < 81) = P(-0.95 < z < 0) = 0.3289.
a)Sampling distribution of x
The sampling distribution of x is the probability distribution of all the possible sample means that can be drawn from a population under the same sampling method.
It represents the relative frequency of different values of x (sample mean) that can be obtained when samples of size n are taken from the population.
The sampling distribution of x is approximately normal when the sample size is sufficiently large, i.e. n ≥ 30. In this case, n = 49, which is sufficiently large to assume normality of sampling distribution of x.
The mean of the sampling distribution of x is µx = µ = 81, and the standard deviation is: σx = σ / √n = 14 / √49 = 2.00.
Hence, the sampling distribution of x is N (µx = µ = 81, σx = 2.00).
b)P(x > 84.9)
The z-score is:z = (x - µx) / σx = (84.9 - 81) / 2.00 = 1.75.
Using the standard normal distribution table, the probability of z > 1.75 is 0.0401.
Hence, the probability of x > 84.9 is:P(x > 84.9) = P(z > 1.75) = 0.0401
c)P(x ≤ 76.7)
The z-score is:z = (x - µx) / σx = (76.7 - 81) / 2.00 = -2.15
Using the standard normal distribution table, the probability of z ≤ -2.15 is 0.0150.
Hence, the probability of x ≤ 76.7 is:P(x ≤ 76.7) = P(z ≤ -2.15) = 0.0150d)P(78.1 < x < 81)
The z-score for x = 78.1 is:z1 = (x1 - µx) / σx = (78.1 - 81) / 2.00 = -0.95
The z-score for x = 81 is:z2 = (x2 - µx) / σx = (81 - 81) / 2.00 = 0
Using the standard normal distribution table, the probability of z1 < z < z2 is:P(z1 < z < z2) = P(-0.95 < z < 0) = P(z < 0) - P(z < -0.95) = 0.5000 - 0.1711 = 0.3289.
Hence, the probability of 78.1 < x < 81 is:P(78.1 < x < 81) = P(-0.95 < z < 0) = 0.3289.
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If the volume of the following cone is 640 feet³, what is the
length of the radius? Use 3.14 for and round the answer to
the nearest hundredth.
h=12 feet
The radius is
7
feet.
Answers
The length of the radius of the cone is approximately [tex]6.74[/tex] feet.
To find the length of the radius of the cone, we can use the formula for the volume of a cone:
[tex]\[\text{{Volume}} = \frac{1}{3} \pi r^2 h\][/tex]
The concept used to find the length of the radius is the formula for the volume of a cone.
Given that the volume is [tex]640[/tex] ft³ and the height (h) is [tex]12[/tex] ft, we can substitute these values into the formula:
[tex]\[640 = \frac{1}{3} \times 3.14 \times r^2 \times 12\][/tex]
Simplifying the equation:
[tex]\[\frac{640}{12 \times \frac{1}{3} \times 3.14} = r^2\]\[r^2 = \frac{640}{12 \times \frac{1}{3} \times 3.14}\]\[r^2 \approx 45.45\][/tex]
Taking the square root of both sides, we find:
[tex]\[r \approx \sqrt{45.45} \approx 6.74\][/tex]
Rounding the answer to the nearest hundredth, the length of the radius is approximately [tex]6.74[/tex] feet.
In conclusion, the length of the radius of the given cone, with a volume of [tex]640[/tex] ft³ and a height of [tex]12[/tex] feet, is approximately [tex]6.74[/tex] feet (rounded to the nearest hundredth).
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Please help me and no links
Answers
Answer:
Sam's is nonsense and Kim's is sense
Step-by-step explanation:
why? because 1/3 and 1/6 are not equivalent. and 1/3 is greater. so therfore Kim's makes sense
Much help is needed________
Answers
Answer:
it is 14
Step-by-step explanation:
Answer:
C) 14
Step-by-step explanation:
Volume of a Sphere:
V = 4/3πr³
V = 4/3(3.14)1.5³
V = 4/3(3.14)3.375
V = 14.13
14.13 ≈ 14
Element X is a radioactive isotope such that every 28 years, its mass decreases by
half. Given that the initial mass of a sample of Element X is 70 grams, how long
would it be until the mass of the sample reached 38 grams, to the nearest tenth of a
year?
Answers
Answer:
21
Step-by-step explanation:
Help!!! answer quickly pls
Answers
Most likely (3,0)
If it’s reflected across the y axis, then it should be the opposite of (-3,0)
Find the sample variance and standard deviation. 17, 10, 4, 8, 11 D Choose the correct answer below. Fill in the answer box to complete your choice. (Type an integer or a decimal. Round to one decimal
Answers
The sample variance is 10 and the standard deviation is 3.2.
How to find the sample variance and standard deviation?Given data: 17, 10, 4, 8, 11
The sample size, n = 5
Mean (m) = ∑x / n
m = (17 + 10 + 4 +8 + 11)/5
m = 50/5
m = 10
x x-m (x- m)²
17 17-10 = 7 49
10 10-10 = 0 0
4 4-10 = -6 36
8 8 - 10 = -2 4
11 11 - 10 = 1 1
90
∑(x- m)² = 90
Sample variance, s² = ∑(x-x)² /(n-1)
Sample variance, s² = 90/(10 - 1)
= 90/9
= 10
Standard deviation (S) = √variance
Standard deviation (S) = √10 = 3.2
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1. does a rectangle have opposite sides parallel
2. does a parallelogram have opposite sides parallel
3. does a trapezoid have opposite sides parallel
4. does a rhombus have opposite sides parallel
Answers
Answer:
yes I guess a rectangle has opposite sides parallel parallelogram has opposite sides parallel a trapezium has opposite sides parallel a rhombus has opposite sides parallel if I'm wrong please connect me right away thank you.
Answer:
1.Yes, 2 pairs
2.Yes, 2 pairs
3.Yes, 1 pair
4.Yes, 2 pairs
Step-by-step explanation:
1.Each pair of co-interior angles are supplementary, because two right angles add to a straight angle, so the opposite sides of a rectangle are parallel. This means that a rectangle is a parallelogram, so: Its opposite sides are equal and parallel. Its diagonals bisect each other.
2.A parallelogram is a four sided figure where the opposite sides are parallel.
3.A trapezoid is a quadrilateral with one pair of opposite sides parallel. It can have right angles (a right trapezoid), and it can have congruent sides (isosceles), but those are not required.
4.Every rhombus has two diagonals connecting pairs of opposite vertices, and two pairs of parallel sides.
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Answers
Answer:
y= 3
x= -2
Step-by-step explanation:
..,............
Please help with B ......
Answers
Answer:
17
Step-by-step explanation:
This means all students above 20, so 9 + 5 + 3 = 17
Answer:
17
pls mark brainliest
In the coordinate plane, what is the distance
between (-3, 5) and (-3,-8)?
Answers
Answer:
3
Step-by-step explanation:
Plug the coordinates into the distance formula to find that they are 3 units apart
Answer:
13 units
Step-by-step explanation:
sqrt (x2 - x1)^2 + (y2 - y1)^2
sqrt (-3 - (-3))^2 + (-8 -5)^2
sqrt (0)^2 + (-13)^2
sqrt 169
13
f(x) = x2. What is g(x)?
Help me please
Answers
Answer:
Answer is B
Step-by-step explanation:
Answer:
The answer is B
Step-by-step explanation:
The answer is B
what are the solutions tolog3x log3(x2 2) = 1 2log3x?x = –2x = –1x = 1x = 2there is no true solution.
Answers
To determine the solutions x⁵ + 2x³ = 3, you can use numerical methods or approximation techniques to estimate the values of x that satisfy the equation.
Let's solve the equation step by step to find the solutions.
Starting with the given equation:
log₃(x) + log₃(x² + 2) = 1 - 2log₃(x)
Now, let's simplify the equation using logarithmic properties. The sum of logarithms is equal to the logarithm of the product, and the difference of logarithms is equal to the logarithm of the quotient:
log₃(x(x² + 2)) = 1 - log₃(x²)
Next, we can simplify further by using the properties of exponents. The logarithmic equation can be rewritten in exponential form as:
([tex]3^{(log3(x(x^{2} +2)))} = 3^{(1-log3((x^{2}))}[/tex]
The base of the logarithm and the exponent cancel each other out, resulting in:
x(x² + 2) = [tex]3^{(1-log3(x^{2}))}[/tex]
Now, let's simplify the right-hand side by applying the power rule of logarithms:
x(x² + 2) = 3 / [tex]3^{(log3(x^{2} ))}[/tex]
Since [tex]3^{(log3(x^{2} ))}[/tex] is equal to x² by the definition of logarithms, the equation becomes:
x(x² + 2) = 3 / x²
Expanding the left-hand side:
x³ + 2x = 3 / x²
Multiplying through by x² to eliminate the fraction:
x⁵ + 2x³ = 3
This is a quadratic equation, which does not have a general algebraic solution that can be expressed in terms of radicals. Therefore, it is challenging to find the exact solutions analytically.
To determine the solutions, you can use numerical methods or approximation techniques to estimate the values of x that satisfy the equation.
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Using a standard deck of 52 cards, what is the probability that a
randomly dealt 5-card hand contains 2 kings and 3 cards that aren't
kings?
Answers
The probability that a randomly dealt 5-card hand contains 2 kings and 3 cards that aren't
kings is approximately 0.0399 or 3.99%.
To find the probability of randomly dealing a 5-card hand containing 2 kings and 3 cards that aren't kings, we need to calculate the number of favorable outcomes and divide it by the total number of possible outcomes.
The number of ways to choose 2 kings from the 4 available kings is given by the combination formula:
C(4, 2) = 4! / (2! * (4-2)!) = 6
Similarly, the number of ways to choose 3 non-king cards from the remaining 48 cards (52 cards total - 4 kings) is:
C(48, 3) = 48! / (3! * (48-3)!) = 17,296
Therefore, the number of favorable outcomes (hands with 2 kings and 3 non-king cards) is:
6 * 17,296 = 103,776
The total number of possible 5-card hands that can be dealt from a standard deck of 52 cards is:
C(52, 5) = 52! / (5! * (52-5)!) = 2,598,960
So, the probability of randomly dealing a 5-card hand containing 2 kings and 3 cards that aren't kings is:
P(2 kings and 3 non-kings) = favorable outcomes / total outcomes = 103,776 / 2,598,960 ≈ 0.0399
Therefore, the probability is approximately 0.0399 or 3.99%.
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the bakers at a bakery can make 160 bagels in 4 hours. how many bagels can they bake in 6 hours? what is the rate per hour
Answers
Answer: they can make 240 bagels in 6 hours and the rate per hour is 40
Step-by-step explanation: