In ΔPQR, the length of QR is approximately 4.1 feet to the nearest tenth of a foot.
In ΔPQR, given that ∠R=90°, ∠P=26°, and PQ=8.5 feet, you want to find the length of QR to the nearest tenth of a foot.
Step 1: Since ∠R is a right angle (90°), we can use trigonometric ratios to find QR. First, let's find ∠Q. We know that the sum of angles in a triangle is 180°, so ∠Q = 180° - (∠P + ∠R) = 180° - (26° + 90°) = 64°.
Step 2: Now that we have all the angles, we can use the sine formula to find QR. We'll use the sine of ∠P (26°) and the given side PQ (8.5 feet) as our reference. The sine formula is:
QR = (PQ * sin(∠P)) / sin(∠Q)
Step 3: Plug in the known values:
QR = (8.5 * sin(26°)) / sin(64°)
Step 4: Calculate the sine values and the division:
QR = (8.5 * 0.4384) / 0.8988 ≈ 4.1326
Step 5: Round the answer to the nearest tenth of a foot:
QR ≈ 4.1 feet
In ΔPQR, the length of QR is approximately 4.1 feet to the nearest tenth of a foot.
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A bus arrives every 10 minutes at a bus stop. It is assumed that the waiting time for a particular individual is a random variable with a continuous uniform distribution.
a) What is the probability that the individual waits more than 7 minutes?
b) What is the probability that the individual waits between 2 and 7 minutes?A continuous random variable X distributed uniformly over the interval (a,b) has the following probability density function (PDF):fX(x)=1/0.The cumulative distribution function (CDF) of X is given by:FX(x)=P(X≤x)=00.
In the following question, among the various parts to solve- a) the probability that the individual waits more than 7 minutes is 0.3. b)the probability that the individual waits between 2 and 7 minutes is 0.5.
a) The probability that an individual will wait more than 7 minutes can be found as follows:
Given that the waiting time of an individual is a continuous uniform distribution and that a bus arrives at the bus stop every 10 minutes.Since the waiting time is a continuous uniform distribution, the probability density function (PDF) can be given as:fX(x) = 1/(b-a)where a = 0 and b = 10.
Hence the PDF of the waiting time can be given as:fX(x) = 1/10The probability that an individual waits more than 7 minutes can be obtained using the complementary probability. This is given by:P(X > 7) = 1 - P(X ≤ 7)The probability that X ≤ 7 can be obtained using the cumulative distribution function (CDF), which is given as:FX(x) = P(X ≤ x) = ∫fX(t) dtwhere x ∈ [a,b].In this case, the CDF of the waiting time is given as:FX(x) = ∫0x fX(t) dt= ∫07 1/10 dt + ∫710 1/10 dt= [t/10]7 + [t/10]10= 7/10Using this, the probability that an individual waits more than 7 minutes is:P(X > 7) = 1 - P(X ≤ 7)= 1 - 7/10= 3/10= 0.3So, the probability that the individual waits more than 7 minutes is 0.3.
b) The probability that the individual waits between 2 and 7 minutes can be calculated as follows:P(2 < X < 7) = P(X < 7) - P(X < 2)Since the waiting time is a continuous uniform distribution, the PDF can be given as:fX(x) = 1/10Using the CDF of X, we can obtain:P(X < 7) = FX(7) = (7 - 0)/10 = 0.7P(X < 2) = FX(2) = (2 - 0)/10 = 0.2Therefore, P(2 < X < 7) = 0.7 - 0.2 = 0.5So, the probability that the individual waits between 2 and 7 minutes is 0.5.
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How many more minutes can mate car travel per gallon of gas then jenna's car
Mate's car can travel approximately 5 more minutes per gallon of gas compared to Jenna's car.
To determine how many more minutes Mate's car can travel per gallon of gas compared to Jenna's car, we would need additional information about the fuel efficiency or miles per gallon (MPG) for each car.
Fuel efficiency is typically measured in terms of miles per gallon, indicating the number of miles a car can travel on a gallon of gas.
To calculate the difference in travel time, we would also need to know the average speed at which the cars are traveling.
Once we have the MPG values for Mate's car and Jenna's car, we can calculate the difference in travel time per gallon of gas by considering their respective fuel efficiencies and average speeds.
If Mate's car has a fuel efficiency of 30 MPG and Jenna's car has a fuel efficiency of 25 MPG, we can calculate the difference in travel time by comparing the distances they can travel on a gallon of gas.
Let's assume both cars are traveling at an average speed of 60 miles per hour.
For Mate's car:
Travel time = Distance / Speed
= (30 miles / 1 gallon) / 60 miles per hour
= 0.5 hours or 30 minutes.
For Jenna's car:
Travel time = Distance / Speed
= (25 miles / 1 gallon) / 60 miles per hour
= 0.4167 hours or approximately 25 minutes.
Without specific information about the MPG values and average speeds of the cars, it is not possible to provide an accurate answer regarding the difference in travel time per gallon of gas between Mate's car and Jenna's car.
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What percent is 444 out of 20278
Answer:
2.189565045862511
Step-by-step explanation:
Answer:
2.19 %
Step-by-step explanation:
Used a calculator (Answer is rounded to the nearest hundredths place.)
4(1/2+3/4)+(-2)
I need help
Answer:
3
Step-by-step explanation:
4(1/2+3/4)+(-2) Distribute.
2+3+(-2) Simplify.
2+3-2
5-2
3
Hope this helps!! Have an amazing day (。・∀・)ノ゙
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
The additional information required to prove that ΔXYZ and ΔFEG are congruent is ∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE. So option 1 and 5 are correct.
Here in the figure it is given that ∠F and ∠X are congruent. To prove the triangle is congruent we have to prove that either two sides including the angles are congruent or another angle and included side is congruent.
When ∠Z ≅ ∠G and XZ ≅ FG, two angles and included sides are congruent, so triangles are congruent.
∠Z ≅ ∠G and ∠Y ≅ ∠E , we can not apply ASA, since three angles are mentioned
XZ ≅ FG and ZY ≅ GE , Two sides are given, ASA cannot be applied, we need two angles
XY ≅ EF and ZY ≅ FG, is not possible.
∠Z ≅ ∠G and XY ≅ FE, one corresponding side and two angles are equal, so ΔXYZ ≅ ΔFEG according to ASA.
So, the correct answer is option 1 and option 5.
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The complete question is as follows and image is given below
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and ∠Y ≅ ∠E
XZ ≅ FG and ZY ≅ GE
XY ≅ EF and ZY ≅ FG
∠Z ≅ ∠G and XY ≅ FE
Answer:
1 and 5 are correct
Step-by-step explanation:
which graph is linear
Answer:
C
The third one
Hunters with dogs walked through the forest. If you count their legs, it will be 78, and if their heads, then 24. How many hunters were there and how many dogs did they have?
From the given data of hunters and do we find out there are 9 hunters and 15 dogs.
Let's assume that there were "h" hunters and "d" dogs.
Each hunter has two legs, and each dog has four legs, so the total number of legs can be expressed as:
2h + 4d = 78
We can simplify this equation by dividing both sides by 2:
h + 2d = 39
We also know that there were 24 heads in total, which includes the hunters and the dogs:
h + d = 24
We can now solve these two equations simultaneously to find the values of h and d.
First, we can solve for h in terms of d from the second equation:
h = 24 - d
We can substitute this expression for h in the first equation:
(24 - d) + 2d = 39
Simplifying and solving for d:
d = 15
Now that we know there were 15 dogs, we can substitute this value back into one of the equations to find the number of hunters:
h + d = 24
h + 15 = 24
h = 9
Therefore, there were 9 hunters and 15 dogs.
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What does the variable r represent in the equation 10r+4=8
Answer:
The value of variable r in the equation \(10r+4=8\) is \(\mathbf{r=0.4}\)
Step-by-step explanation:
We need to find the value of variable r in the equation \(10r+4=8\)
Step 1: Write the equation
\(10r+4=8\)
Step 2: Subtract 4 on both sides
\(10r+4-4=8-4\\10r=4\)
Step 3: Divide both sides by 4
\(\frac{10r}{10}=\frac{4}{10}\\r=0.4\)
So, The value of variable r in the equation \(10r+4=8\) is \(\mathbf{r=0.4}\)
You are traveling long distance for the first time in your new car. If the polynomial 90d² + 30d
represents the miles traveled and you have traveled for 15d hours, find the average speed in the
simplest form.
8d miles per hour
O 6d² + 2d miles per hour
6d+ 2 miles per hour
O6d² + 2 miles per hour
Therefore, the average speed in the simplest form is 6d² + 2d miles per hour.
What is expression?In mathematics, an expression is a combination of symbols and values that can be evaluated to obtain a result. Expressions can contain variables, constants, operators, and functions, which can be combined using arithmetic or algebraic operations to form more complex expressions. Examples of expressions include 2 + 3, x + 5, and sin(θ) + cos(θ).
Here,
The given polynomial 90d² + 30d represents the miles traveled. We can find the average speed by dividing the distance traveled by the time taken. Since we have traveled for 15d hours, the total distance traveled is (90d² + 30d) miles. Thus, the average speed is:
=(90d² + 30d) miles / (15d) hours
= 6d² + 2d miles per hour
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Zoe went out to her garden and cut 19 roses from the first rose bush, 28 roses from the second rose bush, 37 roses from the third rose bush, and 46 roses from the fourth rose bush. What kind of sequence is this?
Based on the given scenario, the kind of sequence explained is an arithmetic sequence
SequenceFirst bush = 19 rosesSecond bush = 28 rosesThird bush = 37 rosesFourth bush = 46First term, a = 19
Second term, a + d
28 = 19 + d
28 - 19 = d
9 = d
Common difference, d = 9Third term, a + 2d
= 19 + 2(9)
= 19 + 18
= 37
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4 to the 5 power + 12 to the 2 power
Answer:
The answer is 1168
Step-by-step explanation:
(4^5)+(12^2)=1168
Answer:
1168
Step-by-step explanation:
4^5 is 1024
12^2 is 144.
1024+144=1168
. jane has developed a new happiness questionnaire. to demonstrate its scientific merit, she uses it to measure happiness in 10 couples who have just started dating. she asks each participant to complete a happiness questionnaire. she waits a year, then attempts to re-contact each of the couples to ask them to complete the questionnaire again. jane then calculates the pearson r correlation coefficient between happiness levels at the outset of her study and one year later. what scientific standard is jane evaluating?
The scientific standard which jane evaluates based on the condition above is falsifiability.
It may appear that Jane is attempting to measure test-retest reliability, that is, a correlation between the first scores and those a year later. But without control over variables that could affect the second scores, there is there is hardly a strong argument for the reliability of her test. Moreover, some of the couples may not be together after a year has passed.
What is falsifiabilityFalsifiability or refutability is the probability that a statement can be falsified or proven false through observation or physical testing. Something that can be falsified does not mean that it is wrong, but it means that if the statement is wrong, then the error can be shown.
The claim that "it is not true that humans live forever" cannot be falsified because it is impossible to prove wrong. In theory, one would have to observe a human living forever to falsify that claim. On the other hand, "all humans live forever" is falsifiable because the death of a single human being can disprove the statement false (excluding metaphysical statements about the soul, which cannot be falsified).
Falsifiability, especially testability, is an important notion in science and philosophy of science. This thought was popularized by Karl Popper. Popper stated that a hypothesis, proposition, or theory is scientific if it can be falsified. Falsifiability is an important (but not sufficient) criterion for scientific ideas. He also stated that statements that cannot be falsified are unscientific.
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increase the number 22.5 by 0.4 of it
Answer:
Step-by-step explanation:
22.9
The following information should be taken into consideration to answer this item: If the scores of 400 subjects in a psychological scale have been distributed normally with the mean score of 100 and standard deviation of 15: The Z score that equivalent to the raw score 92.5 is.... A.+ 0.5 B. -1.25 C.-0.5 D.-0.25
The Z score that is equivalent to the raw score 92.5 is B. -1.25.
A Z score represents the number of standard deviations a raw score is from the mean in a normal distribution. To calculate the Z score, we use the formula: Z = (X - μ) / σ, where X is the raw score, μ is the mean, and σ is the standard deviation.
Given that the mean score is 100 and the standard deviation is 15, we can calculate the Z score for the raw score 92.5 as follows:
Z = (92.5 - 100) / 15
Z = -7.5 / 15
Z = -0.5
Therefore, the Z score that is equivalent to the raw score 92.5 is -0.5.
The Z score is a useful measure in statistics that allows us to standardize and compare data points across different distributions. It helps us understand the relative position of a data point within a distribution and determine how unusual or typical that data point is compared to others. By calculating the Z score, we can easily determine the percentage of data points that fall below or above a particular value in a normal distribution, which aids in making statistical inferences and drawing conclusions.
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Given f(x)=2x+1 and g(x)=3x−5, find the following: a. (f∘g)(x) b. (g∘g)(x) c. (f∘f)(x) d. (g∘f)(x)
The compositions between f(x) and g(x) are:
a. (f∘g)(x) = 6x - 9
b. (g∘g)(x) = 9x - 20
c. (f∘f)(x) = 4x + 3
d. (g∘f)(x) = 6x - 2
How to find the compositions between the functions?To get a composition of the form:
(g∘f)(x)
We just need to evaluate function g(x) in f(x), so we have:
(g∘f)(x) = g(f(x))
Here we have the functions:
f(x) = 2x + 1
g(x) = 3x - 5
a. (f∘g)(x)
To find (f∘g)(x), we first evaluate g(x) and then substitute it into f(x).
g(x) = 3x - 5
Substituting g(x) into f(x):
(f∘g)(x) = f(g(x))
= f(3x - 5)
= 2(3x - 5) + 1
= 6x - 10 + 1
= 6x - 9
Therefore, (f∘g)(x) = 6x - 9.
b. (g∘g)(x)
To find (g∘g)(x), we evaluate g(x) and substitute it into g(x) itself.
g(x) = 3x - 5
Substituting g(x) into g(x):
(g∘g)(x) = g(g(x))
= g(3x - 5)
= 3(3x - 5) - 5
= 9x - 15 - 5
= 9x - 20
Therefore, (g∘g)(x) = 9x - 20.
c. (f∘f)(x)
To find (f∘f)(x), we evaluate f(x) and substitute it into f(x) itself.
f(x) = 2x + 1
Substituting f(x) into f(x):
(f∘f)(x) = f(f(x))
= f(2x + 1)
= 2(2x + 1) + 1
= 4x + 2 + 1
= 4x + 3
Therefore, (f∘f)(x) = 4x + 3.
d. (g∘f)(x)
To find (g∘f)(x), we evaluate f(x) and substitute it into g(x).
f(x) = 2x + 1
Substituting f(x) into g(x):
(g∘f)(x) = g(f(x))
= g(2x + 1)
= 3(2x + 1) - 5
= 6x + 3 - 5
= 6x - 2
Therefore, (g∘f)(x) = 6x - 2.
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Please help me with this equation
Answer:21.46 is her profit
Step-by-step explanation:
Which decimal is equivalent to \dfrac{26}{9} 9 26 start fraction, 26, divided by, 9, end fraction? Choose 1 answer: Choose 1 answer: (Choice A) A 2.82.82, point, 8 (Choice B) B 2.\overline{8}2. 8 2, point, start overline, 8, end overline (Choice C) C 2.8892.8892, point, 889 (Choice D) D 2.92.9
Answer: C. 2.889 .
Step-by-step explanation:
To find : A decimal expression equivalent to \(\dfrac{26}{9}\) .
When we divide 26 by 9 , we get 2.88888888889 which is approximately equal to 2.889 [Round off to the nearest thousandth place]
Hence, the decimal is equivalent to\(\dfrac{26}{9}\) is 2.889.
Hence, the correct option is C. 2.889 .
Answer:
2.8 with the _ above the 8 dont listen to that other guy/girl
Consider the following differential equation to be solved by the method of undetermined coefficients. y" + 6y = -294x2e6x Find the complementary function for the differential equation. ye(X) = Find the particular solution for the differential equation. Yp(x) = Find the general solution for the differential equation. y(x) =
The complementary function for the differential equation is ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\). The particular solution for the differential equation is \(Yp(x) = -7e^(^6^x^)\). The general solution for the differential equation is y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) -\(7e^(^6^x^)\).
To find the complementary function for the given differential equation, we assume a solution of the form \(ye(x) = e^(^r^x^)\), where r is a constant to be determined. Plugging this into the differential equation, we get:
\(r^2e^(^r^x^) + 6e^(^r^x^) = 0\)
Factoring out \(e^(^r^x^)\), we obtain:
\(e^(^r^x^)(r^2 + 6) = 0\)
For a nontrivial solution, the term in the parentheses must equal zero:
\(r^2 + 6 = 0\)
Solving this quadratic equation gives us r = ±√(-6) = ±i√6. Hence, the complementary function is of the form:
ye(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\)
Next, we need to find the particular solution Yp(x) for the differential equation. The particular solution is assumed to have a similar form to the forcing term \(-294x^2^e^(^6^x^).\)
Since this term is a polynomial multiplied by an exponential function, we assume a particular solution of the form:
\(Yp(x) = (A + Bx + Cx^2)e^(^6^x^)\)
Differentiating this expression twice and substituting it into the differential equation, we find:
12C + 12C + 6(A + Bx + Cx^2) = \(-294x^2^e^(^6^x^)\)
Simplifying and equating coefficients of like terms, we get:
12C = 0 (from the constant term)
12C + 6A = 0 (from the linear term)
6A + 6B = 0 (from the quadratic term)
Solving this system of equations, we find A = -7, B = 0, and C = 0. Therefore, the particular solution is:
\(Yp(x) = -7e^(^6^x^)\)
Finally, the general solution for the differential equation is given by the sum of the complementary function and the particular solution:
y(x) = ye(x) + Yp(x)
y(x) = \(c1e^(^i^\sqrt6x)\) + \(c2e^(^-^i^\sqrt6x)\) - \(7e^(^6^x^)\)
This is the general solution to the given differential equation.
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Let X 1
,…,X n
be i.i.d. random variables from a distribution with pdf f(x;θ)={ θ
1
,
0
if −θ≤x≤0 and 0<θ<[infinity],
otherwise.
(a) Write down the likelihood function. (b) Find the maximum likelihood estimator of θ. Justify your answer. (c) Show that the maximum likelihood estimator of θ is a consistent estimator.
Therefore:P(θ < M) = 1andP(θn = -min(X₁,X₂,...,Xₙ) > M) → 0 as n → ∞This implies that θn converges to θ in probability as n → ∞, and thus the maximum likelihood estimator is consistent.
a) The likelihood function is:L(θ|x₁, x₂, ..., xₙ) = f(x₁;θ) · f(x₂;θ) · ... · f(xₙ;θ) = { θ 1, 0if −θ≤x₁≤0 and 0<θ<[infinity], otherwise } · { θ 1, 0if −θ≤x₂≤0 and 0<θ<[infinity], otherwise } · ... · { θ 1, 0if −θ≤xₙ≤0 and 0<θ<[infinity], otherwise } = θ ⁿ · Πi=1 ⁿI(-θ≤Xi≤0)where I() denotes the indicator function.
b) Let us first write the likelihood function as a function of the θ only: L(θ|x₁, x₂, ..., xₙ) = θ ⁿ · Πi=1 ⁿI(-θ≤Xi≤0)Let us differentiate this function with respect to θ and try to solve for when the derivative is zero:
∂L/∂θ = nθ ⁿ⁻¹ · Πi=1 ⁿI(-θ≤Xi≤0) · (-1) = 0, thus θ ⁿ⁻¹ · Πi=1 ⁿI(-θ≤Xi≤0) = 0.Since the likelihood function is non-negative, we know that the maximum must occur at one of the boundary values of θ, that is at θ = max(-x₁,-x₂,...,-xₙ) = -min(x₁,x₂,...,xₙ).
c) To show that the maximum likelihood estimator of θ is a consistent estimator, we need to show that it converges in probability to the true value of θ. Let us define the estimator for θ as: θn = -min(X₁,X₂,...,Xₙ)Then we need to show that: P(|θn - θ| > ε) → 0 as n → ∞ for any ε > 0.
As n → ∞, the smallest value X(i) will converge to 0 in probability due to the law of large numbers, so we get:P(|θn + min(X₁,X₂,...,Xₙ)| > ε) → 0 as n → ∞
However, since θ < infinity, we know that the support of the distribution will eventually include all values greater than some M > 0. Therefore:P(θ < M) = 1andP(θn = -min(X₁,X₂,...,Xₙ) > M) → 0 as n → ∞This implies that θn converges to θ in probability as n → ∞, and thus the maximum likelihood estimator is consistent.
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which of the following random variables is geometric? the number of 5s when rolling a die 35 times the number of spades dealt from a shuffled deck of 52 cards in a seven-card hand the number of heads when a coin is tossed 10 times the number of digits in a randomly selected row until a 9 is found the number of 8s in a row of 20 random digits
A geometric random variable is the number of 5s when rolling a die 35 times. (option 1)
This is due to the fact that rolling a 5 on any given roll has a probability of 1/6, and the number of 5s can be determined by counting the number of successes (rolling a 5) prior to the first failure (not rolling a 5).
If you roll a number other than 5, the expected number of unsuccessful iterations is 1/2pq, where p is the probability of success (1/6) and q is the probability of failure (5/6). Additionally, this can be expressed as (1-p)/p. Therefore, when rolling a die 35 times, the expected number of 5s is 35, or (1-1/6)/(1/6).
We can use the formula for the expected value of a geometric random variable, E[X] = (1-p)/p, where p is the probability of success, to demonstrate this mathematically. p is 1/6 in this case.
E[X] = (1-1/6)/(1/6) = 35 can be obtained by substituting this number into the formula. This indicates that 35 is the anticipated number of 5s after rolling a die 35 times.
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Complete Question:
which of the following random variables is geometric?
the number of 5s when rolling a die 35 times the number of spades dealt from a shuffled deck of 52 cards in a seven-card hand the number of heads when a coin is tossed 10 times the number of digits in a randomly selected row until a 9 is found the number of 8s in a row of 20 random digitsAdela has 24 bracelets. She makes 3 more
each day.
Isaiah has 10 bracelets. He makes
5 more each day.
The equations represent
the number of bracelets y each person has after x days.
Adela: y = 3x + 24
Isaiah: y = 5x + 10
Use elimination to solve the system of equations.
What does the solution mean in the situation?
The solution of the system of equations is; (7, 45).
The solution in this situation means that after 7 days, Adela and Isaiah would each have 45 bracelets.
What is the solution of the system of equations?It follows from the task content that the solution to the system of equations is to be determined and interpreted accordingly.
Since the given equations are;
Adela: y = 3x + 24Isaiah: y = 5x + 10By elimination, we must subtract Isaiah's equation from Adela's so that we have;
(y - y) = (3x - 5x) + (24 - 10)
0 = -2x + 14
2x = 14; x = 7.
Consequently, y = 3 (7) + 24
y = 21 + 24; y = 45.
Consequently, the solution to the system of equations as given in the task content is; (7, 45).
This means that after 7 days, Adela and Isaiah would both have; 45 bracelets.
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PLEASE ANWSER ASAP
Below, a two-way table is given
for student activities.
Sports Drama Work Total
7
3
13
2
5
5
Sophomore 20
Junior
20
Senior
25
Total
Find the probability the student is a sophomore,
given that they are in work.
P(sophomore | work) = P(sophomore and work) = [? ]%
P(work)
Round to the nearest whole percent.
The probability of P(sophomore | work) is 0.30.
Given that:
Sports Drama Work Total
Sophomore 20 7 3 30
Junior 20 13 2 35
Senior 25 5 5 35
Total 65 25 10 100
The probability is given as,
P = (Favorable event) / (Total event)
The probability of P(sophomore | work) is calculated as,
P = (3/100) / (10/100)
P = 3 / 10
P = 0.30
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Giving brainliest!
The expression on the left side of an equation is shown below.
3 (x + 1) + 9 = box
If the equation has no solution, which expression can be written in the box on the other side of the equation?
Group of answer choices
3 (x + 4)
2 (x + 6) + x
4(x – 3) – x
3 (x + 1) + 9 x
If the equation has no solution, the expressions that can be written in the box on the other side of the equation are A. 3(x + 4) and B. 2(x + 6) + x.
What is an equation?An equation represents a mathematical statement showing that two or more expressions share equality in value.
Equations show the equal or equivalent relationship between two mathematical expressions.
We depict equations using the equation symbol (=).
Given equation:
3 (x + 1) + 9 = box
= 3x + 3 + 9
= 3x + 12
A. 3(x + 4)
= 3x + 12
B. 2(x + 6) + x
= 2x + 12 + x
= 3x + 12
C. 4(x – 3) – x
= 4x - 12 - x
= 3x - 12
D. 3(x + 1) + 9x
= 3x + 3 + 9x
= 12x + 3
Thus, Options A and B can be written in the box on the other side of equation 3 (x + 1) + 9 = box, unlike Options C and D.
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Answer:
I think the answer is C if im wrong i am so srry
Step-by-step explanation:
How fast is 60 miles in km?
60 miles is equal to 96.56 kilometers.
To convert miles to kilometers, you can use the conversion factor of 1 mile = 1.60934 kilometers. To convert 60 miles to kilometers, you would multiply 60 by 1.60934.
60 miles * 1.60934 kilometers/mile = 96.56 kilometers
Another way to think about it is that 1 mile is about 1.6 kilometers, so 60 miles is about 60 x 1.6 = 96 kilometers
It's important to remember that when measuring distance, the Units of measurement must be consistent. For units of example, if you are measuring the distance between two cities, it would not make sense to use miles for one city and kilometers for the other.
In short, 60 miles is equivalent to 96.56 kilometers, which is a standard unit of measurement used in most of the world.
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Steve earns $8 per hour. his older brother earns $2 more per hour than Steve. what is the ratio of the money Steve earns in an hour to the money his brother earns is an hour.
A bag contains 25 marbles (5 red ones, 8 ue ones and 12 yellow ones.) When a marble is picked at a random one at a time from the bag and not put back into the bag, what is the chance of picking a yellow one twice in a row?
Answer:
The chance of picking a yellow marble twice in a row without replacement is 0.22
Step-by-step explanation:
The given number of marbles in the bag = 25 marbles
The number of red marbles in the bag = 5 red marbles
The number of blue marbles in the bag = 8 blue marbles
The number of yellow marbles in the bag = 12 yellow marbles
The chance of picking a yellow marble = 12/25
The chance of picking another yellow when the first one is not replaced = 11/24
Therefore, the chance of picking a yellow marble twice in a row = 12/25 × 11/24 = 1/25 × 11/2 = 11/50
Therefore;
The chance of picking a yellow marble twice in a row without replacement = 11/50 = 0.22
El resultado de \(2^{40}+2^{39}+2^{36}\) es divisible por i) 8 ii) 10 iii) 100
Explanation:
We can factor out 8 like so
2^40 + 2^39 + 2^36 = 2^3*2^37 + 2^3*2^36 + 2^3*2^33
2^40 + 2^39 + 2^36 = 2^3*(2^37 + 2^36 + 2^33)
2^40 + 2^39 + 2^36 = 8*(2^37 + 2^36 + 2^33)
Showing that 8 is a factor of 2^40 + 2^39 + 2^36
In other words, 2^40 + 2^39 + 2^36 is divisible by 8
13 m height
10 m
Find the exact volume of the cylinder.
-))
A)
6570 m3
B)
13071 m3
C)
260 m3
D)
32571 m3
Answer:
C) 260 m3
Step-by-step explanation:
Simplify the expression.
3²-4(2+3)
3-2 (3²-2)
11
Answer:
Step-by-step explanation:
3²-4(2+3) can be simplified as follows:
3²-4(2+3) = 9 - 4(5) (using the order of operations to first evaluate the expression inside the parentheses)
= 9 - 20
= -11
So, 3²-4(2+3) simplifies to -11.
However, the expression 3-2 (3²-2) can be further simplified using the order of operations:
3-2 (3²-2) = 3 - 2(9-2)
= 3 - 2(7)
= 3 - 14
= -11
So, the simplified expression is -11 in both cases.
The expression can be simplified as 1.
If we take a look at the expression
\(\frac{3^{2}-4(2+3)}{3-2(3^{2}-2) }=?\)We can simplify by applying the mathematical operation rule BODMAS and first simplify and calculate the contents inside the brackets hence the expression can be solved as :
\(\frac{3^{2}-4(5)}{3-2(9-2)} \\\)
\(\frac{3^{2}-4(5) }{3-2(7)}\)
\(\frac{3^{2}-20 }{3-14}\)
\(\frac{9-20}{3-14}\)
\(\frac{-11}{-11}\)
1
Thus, on simplification, the expression comes out to be 1.
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Discuss the existence and uniqueness of a solution to the differential equation 3+ 2)y"y-y-tant that satisfies the initial conditions y(3)- Yo.y(8)-Y, where Yo and Y1 are real constants. Select the correct choice below and fill in any answer boxes to complete your choice A. A solution is guaranteed on the interval___< t < because its contains the point T0 =___ and the function p(t)= ___ q(t)___ and gt ___ are equal on the interval B. A solution is guaranteed on the interval___< t < because its contains the point T0 =___ and the function p(t)= ___ q(t)___ and gt ___ are simultaneously countionous on the interval C. A solution is guaranteed only at the pouint T0 =___ and the function p(t)= ___ q(t)___ and gt ___ are simultaneously defined at the point
The solution to the differential equation that satisfies the initial conditions y(3) = y0 and y(8) = y1 is:
y(t) = (2/3)t - (1/3)cos(t) + (1/3)sin(t) + y1 + (1/3)sin(3) - (2
The given differential equation is:
3y''+2y'y-y-tan(t)=0
To check the existence and uniqueness of a solution, we need to verify if the function p(t) and q(t) satisfy the conditions of the Existence and Uniqueness Theorem.
The Existence and Uniqueness Theorem states that if the functions p(t) and q(t) are continuous on an interval containing a point t0 and if p(t) is not equal to zero at t0, then there exists a unique solution to the differential equation y'' + p(t) y' + q(t) y = g(t) that satisfies the initial conditions y(t0) = y0 and y'(t0) = y1.
Comparing the given differential equation with the standard form of the Existence and Uniqueness Theorem, we get:
p(t) = 2y(t)
q(t) = -t - tan(t)
g(t) = 0
To find the interval of existence, we need to check the continuity of p(t) and q(t) and also the value of p(t) at t0.
Here, p(t) is continuous everywhere and q(t) is continuous on the interval (3, 8). To check the value of p(t) at t0, we need to find y(t) that satisfies the initial conditions y(3) = y0 and y(8) = y1.
Let's assume that y(t) = A(t) + B(t), where A(t) satisfies y(3) = y0 and A'(3) = 0 and B(t) satisfies y(8) = y1 and B'(8) = 0.
Solving the differential equation for A(t), we get:
A(t) = c1 cos(sqrt(3)(t-3)) + c2 sin(sqrt(3)(t-3)) + (2/3)t - (1/3)cos(t) + (1/3)sin(t) + (1/3)sin(3)
Using the initial conditions y(3) = y0 and A'(3) = 0, we get:
A(t) = (2/3)t - (1/3)cos(t) + (1/3)sin(t) + (1/3)sin(3) - (2/3)cos(3) - y0
Solving the differential equation for B(t), we get:
B(t) = c3 cos(sqrt(3)(t-8)) + c4 sin(sqrt(3)(t-8)) + (2/3)t - (1/3)cos(t) + (1/3)sin(t) - (1/3)sin(3)
Using the initial conditions y(8) = y1 and B'(8) = 0, we get:
B(t) = (2/3)t - (1/3)cos(t) + (1/3)sin(t) - (1/3)sin(3) + (2/3)cos(3) + y1
Therefore, the solution to the differential equation that satisfies the initial conditions y(3) = y0 and y(8) = y1 is:
y(t) = (2/3)t - (1/3)cos(t) + (1/3)sin(t) + y1 + (1/3)sin(3) - (2)
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