please help and show work​

The value of x from the given figure is 12 units.

Two triangles are similar if the angles are the same size or the corresponding sides are in the same ratio. Either of these conditions will prove two triangles are similar.

From the given figure,

Consider ΔPQR and ΔPQS,

∠P=∠P (Reflex property)

PQ=PQ (Reflex property)

∠PQR=∠PSQ=90°

By AA similarity, ΔPQR ~ ΔPQS

So, PQ/PR = PS/PQ

x/45 = 25/x

x²=45×25

x=15√5 units

Therefore, the value of x from the given figure is 15√5 units.

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Answer:

For number 2: 8/165

Step-by-step explanation:

The total number of coins = 11 ( 3 + 4 + 4 = 11).

The probability of picking a nickel first = 3/11 ( 4 nickels out of 11 total).

The probability of picking a dime second = 4/10 = 2/5 ( 3 dimes out of 10 coins left).

The probability of picking the third coin as a quarter = 4/9 ( 3 quarters out of 9 coins left).

I don't know the other problem, sorry.

Answer:

2)  8/165

3) 4/15

Step-by-step explanation:

2) P(N,D,Q) = 3/11 x 4/10 x 4/9

3) P(M,D) = 4/10 x 6/9

Answer:

87.95479

Step-by-step explanation:

10.3% of 853.93 km

Expand 10.3÷100 by multiplying both numerator and denominator by 10.

\( \small \sf \frac{10.3 \times 10}{100 \times 10} = 853.93 \\ \)

\( \small \sf \frac{103}{1000} = 853.93 \\ \)

convert decimal number 853.93 to fraction 85394÷100

\(\small \sf \frac{103}{1000} = \frac{85393}{100} \\\)

Multiplying 103÷1000 and 85393÷100 by numerator times numerator and denominator times denominator.

\(\small \sf \frac{103 \times 8539 3}{1000 \times 100} \\\)

Do the multiplication in the fraction

\(\small \sf \frac{8795479}{100000} \\ \)

Divide we get

87.95479

Another way to solve it

10.3% 853.93

we know that ; % = whole no. ÷ 100

then,

10.3 ÷ 100 × 853.93

Divide the numbers

0.103 × 853.93

multiply the numbers

87.95479

The student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

The gathered data is arranged in tables based οn frequency distributiοn. The infοrmatiοn cοuld cοnsist οf test results, lοcal weather infοrmatiοn, vοlleyball match results, student grades, etc. Data must be presented meaningfully fοr understanding after data gathering. A frequency distributiοn graph is a different apprοach tο displaying data that has been represented graphically.

Tο find the z-scοre οf the student whο scοred 428, we can use the fοrmula:

z = (x - μ) / σ

where x is the student's scοre, μ is the mean οf the distributiοn (400 in this case), and σ is the standard deviatiοn οf the distributiοn (60 in this case).

Plugging in the values, we get:

z = (428 - 400) / 60 = 0.467

Since the z-scοre οf the student is less than 0.524, which is the z-scοre cοrrespοnding tο the tοp 30% οf the distributiοn, we can cοnclude that the student did nοt scοre in the tοp 30%.

Therefοre, the student will nοt be admitted tο the schοοl based οn the admissiοn criteria οf scοring in the tοp 30%.

Hence, the student whο scοred 428 will nοt be admitted tο the schοοl because their scοre did nοt fall in the tοp 30% οf the distributiοn.

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The per capita birth rate of the given population of manned wolves 246 with number of birth as 83 is equals to 0.34  births per individual per year.

Number of births = 83

Initial population = 246

Time period = 1 year

Number of deaths = 42

The per capita birth rate is calculated as the number of births per individual in the population.

Typically expressed as a rate per unit time.

Per capita birth rate as follows,

Per capita birth rate

= (Number of births / Initial population) × (Time period / 1 year)

Substituting these values into the formula, we get,

Per capita birth rate

= (83 / 246) × (1 / 1)

= 0.3374

Rounding this to the hundredths place, we get,

Per capita birth rate = 0.34

Therefore, the per capita birth rate for this population of maned wolves is 0.34 births per individual per year.

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The expectation of Y is given by:

E[Y] = aVar(X) + (aE[X]^2 + bE[X] + c)

To derive the expectation of Y, we have:

E[Y] = E[ax^2 + bX + c]

Using the linearity of expectation, we can write:

E[Y] = E[ax^2] + E[bX] + E[c]

We know that E[c] = c, since the expected value of a constant is the constant itself. Also, E[bX] = bE[X], since b is a constant and can be taken outside the expectation operator. Therefore, we have:

E[Y] = aE[x^2] + bE[X] + c

To find E[x^2], we can use the fact that:

E[g(x)] = ∑ g(x) p(x)

Therefore, we have:

E[x^2] = ∑ x^2 p(x)

Since we don't know the specific distribution of X, we cannot calculate this directly. However, we can use a different formula for the variance of X, which is:

Var(X) = E[X^2] - E[X]^2

Rearranging this, we get:

E[X^2] = Var(X) + E[X]^2

Therefore, we can substitute this into our expression for E[Y], giving:

E[Y] = a(Var(X) + E[X]^2) + bE[X] + c

Simplifying this expression, we get:

E[Y] = aVar(X) + (aE[X]^2 + bE[X] + c)

Therefore, the expectation of Y is given by:

E[Y] = aVar(X) + (aE[X]^2 + bE[X] + c)

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a).The probability that a single student randomly chosen from all those taking the test scores 559 or higher is 0.4279. b).mean = 553.8, standard deviation =  5.6. c).  z-score =  0.929. d). The probability that the mean score of these students is 559 or higher is 0.8228. are the answers

The scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ = 553.8 and standard deviation σ = 28.

(a) Probability that a single student randomly chosen from all those taking the test scores 559 or higher: For this we need to calculate z-score and find the corresponding probability using a normal distribution table.

z = (559 - 553.8)/28

z  = 0.186

P(Z > 0.186) = 1 - P(Z ≤ 0.186)

From the standard normal distribution table, the corresponding value for

0.186 is 0.5721

P(Z > 0.186) = 1 - 0.5721

P(Z > 0.186) = 0.4279

The probability that a single student randomly chosen from all those taking the test scores 559 or higher is 0.4279.

(b) The mean and standard deviation of the sample mean score of 25 students:

The mean of the sampling distribution for x is:µx = µ = 553.8

The standard deviation of the sampling distribution for x is:

σx = σ/√n= 28/√25

σx = 5.6

(c) The z-score that corresponds to the mean score x of 559 is:

z = (x - µx)/σx

z = (559 - 553.8)/5.6

z = 0.929

(d) Probability that the mean score of these students is 559 or higher:

P(x > 559) = P(Z > 0.929)

From the standard normal distribution table, the corresponding value for 0.929 is

0.1772P(Z > 0.929) = 1 - 0.1772 = 0.8228

The probability that the mean score of these students is 559 or higher is 0.8228.

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In order to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need 3 call options.

To completely delta hedge your holdings of 480 shares of ABC company, you would need to calculate the number of call options required based on the delta of the option. The delta represents the change in the option price relative to the change in the underlying stock price. In this case, since the delta is given as 0.6, it means that for every $1 increase in the stock price, the option price will increase by $0.6.

To calculate the number of call options needed for delta hedging, you can use the following formula:

Number of call options = (Delta * Number of shares) / 100

Plugging in the given values, we have:

Number of call options = (0.6 * 480) / 100

Number of call options = 2.88

Since you cannot have a fractional number of options, you would need to round up to the nearest whole number. Therefore, you would need 3 call options to hedge your 480 shares of ABC company.

In summary, to completely delta hedge 480 shares of ABC company with an option delta of 0.6, you would need to acquire 3 call options.

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The number we're looking for is 7.

Let's call the number we're looking for "x". According to the problem, the square of the number is 42 more than the number itself. In equation form, this can be written as:

\(x^2\) = x + 42

To solve for x, we want to get all the terms on one side of the equation. We can start by subtracting x + 42 from both sides:

\(x^2\) - x - 42 = 0

Now we have a quadratic equation. We can solve it by factoring or by using the quadratic formula. Let's use factoring. We want to find two numbers that multiply to -42 and add up to -1 (since the coefficient of x is -1). One possible pair of numbers is -7 and 6, since -7 × 6 = -42 and -7 + 6 = -1. So we can rewrite the equation as:

(x - 7)(x + 6) = 0

This tells us that either x - 7 = 0 or x + 6 = 0. Solving for x in each case, we get:x = 7 or x = -6

We're looking for a positive number, so the solution is x = 7. Therefore, the number we're looking for is 7.

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The inverse of a conditional statement is the result of negating both the hypothesis and conclusion of the conditional statement. For example, the inverse of P → Q is ~P → ~Q.

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The detail from “The Gold Coin” that best supports the inference that Juan is beginning to enjoy reconnecting with people is when he helps the old woman carry her basket of fruit.

Juan is a thief, and he has been for many years. He has no friends, and he doesn't care about anyone but himself. But when he sees the old woman struggling with her groceries, he stops and helps her.

This act of kindness shows that Juan is beginning to change. He is starting to care about other people, and he is starting to understand that there is more to life than just stealing. This is a significant development in Juan's character, and it suggests that he is on the road to redemption.

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Answer: x = 2 & y = 0

Step-by-step explanation:*

Rewrite equations:

−x+4y=−2;−2x+5y=−4

Step: Solve−x+4y=−2for x:

−x+4y=−2

−x+4y+−4y=−2+−4y(Add -4y to both sides)

−x=−4y−2

−x

−1

=

−4y−2

−1

(Divide both sides by -1)

x=4y+2

Step: Substitute 4y+2 for x in −2x+5y=−4:

−2x+5y=−4

−2(4y+2)+5y=−4

−3y−4=−4(Simplify both sides of the equation)

−3y−4+4=−4+4(Add 4 to both sides)

−3y=0

−3y

−3

=

0

−3

(Divide both sides by -3)

y = 0

Step: Substitute 0 for y in x=4y+2:

x=4y+2

x=(4)(0)+2

x = 2 (Simplify both sides of the equation)

*I used MathPapa algebra calculator to solve this and get this explanation.

I hope this helps!

Answer:

(6/13,−8/13)

Step-by-step explanation:

Pls, choose me as brainliest!

Answer:

that's what you get on multiply ing the given matrices

Answer: ( 28, 43)

Step-by-step explanation: I took the test.

[ 2 -6 ] [ 5 ] = [ (2)(5) + (-6)(-3) ]   =  [ 28 ]

[ 8  -1 ] [ -3]    [ (8)(5) + (-1)(-3)  ]       [ 43 ]

Thus the answer is (28, 43)

Answer:

WHAT DO YOU NEED HELP WITH PERSON

Step-by-step explanation:

Answer:

x + y = 12

Step-by-step explanation:

We are given the following system of equations:

2x + 2y =24

x = 3y

We want to find the value of x + y.

We first need to find the values of x and y, which we will do by solving the system.

We can solve this system by substitution.

We know that x = 3y, so we can substitute 3y as x in 2x+2y=24.

This gives us:

2(3y) + 2y = 24

Multiply.

6y + 2y = 24

Add the terms together.

8y = 24

Divide both sides by 8.

y = 3

We found the y value, now let's find the value of x.

The second equation is x=3y, so if we plug the value of y in there, we can find the value of x.

Substitute 3 as y.

x = 3(3) = 9

The value of x is 9.

So, to find x+y, we substitute the values we found.

x + y = 3 + 9 = 12

Using the Normal Z-distribution and the values from the Z-table, We can calculate that 12.5% can be expected to score between 70 and 90 according to the value of mean and standard deviation provided.

As opposed to methods for gathering statistical data, mathematical statistics is the application of probability theory, a subfield of mathematics, to statistics. Because it integrates math ideas to create an analysis of a data set that may be used to comprehend a relationship in the data, statistics has earned a reputation for being an extremely challenging course, especially when studied in college.

A unique type of normal distribution with a mean of 0 and a standard deviation of 1 is known as the standard normal distribution, or z-distribution. By transforming the values of any normal distribution into z scores, it is possible to standardize it. Z scores provide the number of standard deviations from the mean that each value falls within.

mean =100

standard deviation =60

\(70 \leq x \leq 90\)

\(70-100 \leq x-100 \leq 90-100\)

\(-0.5 \leq Z \leq -0.167\)

P = 0.125(From Z-Table)

Required percentage  = 12.5%

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Answer:

It is 2 which represents 20,000

Answer:

\( \sqrt{x + 2} \)

If you horizontally shift the square root parent function f(x)=√x left two units the equation of the new function is: g(x) = √(x + 2).

A horizontal shift is a function transformation that shifts a graph to the left or right without changing its shape.

If we want to shift the square root parent function f(x) = √x two units to the left, we must replace the argument x with (x + 2), because a positive value of x + 2 gives us the same x value two units to the left.

So the equation of the new function is:

g(x) = √(x + 2)

This new function is the square root function shifted two units to the left. For any given input value of x, we add 2 to it before taking the square root. This causes the graph to shift horizontally to the left by two units.

Thus, g(x) = √(x + 2) will be the new function.

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a. The mean will not change. When considering the effect of sample size on the mean of the sampling distribution,

it's important to understand the concept of the Central Limit Theorem (CLT) and the properties of sampling distributions.

The Central Limit Theorem states that for a large enough sample size, the sampling distribution of the sample mean will be approximately normally distributed, regardless of the shape of the population distribution. Additionally, the mean of the sampling distribution will be equal to the population mean.

As the sample size increases, the sampling distribution becomes more representative of the population distribution, and the variability of the sample means decreases. However, the mean of the sampling distribution remains the same as the population mean.

This is an important property of the Central Limit Theorem. It means that increasing the sample size does not change the mean of the sampling distribution. The mean of the sampling distribution is solely determined by the population mean, not the sample size.

To put it simply, the mean of the sampling distribution represents the average of all possible sample means that could be obtained from a population. It is not influenced by the sample size but rather reflects the underlying population parameter.

Therefore, when the sample size increases, the mean of the sampling distribution will not change. It will remain the same as the population mean.

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The series ∑[(k² + 2)/(k³ - 7)] diverges using the limit comparison test and the series ∑(1/k) is a well-known harmonic series.

To determine the convergence of the series ∑[(k² + 2)/(k³ - 7)], we can use the limit comparison test. Let's compare it with the series ∑(1/k).

First, we need to find the limit of the ratio of the terms of the two series as k approaches infinity:

lim(k→∞) [(k² + 2)/(k³ - 7)] / (1/k)

Simplifying the expression, we get:

lim(k→∞) [(k² + 2)/(k³ - 7)] × (k/1)

Taking the limit as k approaches infinity, we have:

lim(k→∞) [(k² + 2)/(k³ - 7)] × (k/1) = 1

Since the limit is a finite positive value (1), we can conclude that the given series ∑[(k² + 2)/(k³ - 7)] and the series ∑(1/k) have the same convergence behavior.

The series ∑(1/k) is a well-known harmonic series, which diverges. Therefore, by the limit comparison test, the given series ∑[(k² + 2)/(k³ - 7)] also diverges.

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The question is -

Use the limit comparison test to determine whether the series converges. k² + 2/ k³ - 7

Solution

We need to find the mean, median and mode.

Since mean > median

The graph is right-skewed.

Answer:

3.75

Step-by-step explanation:

r²+9²=(6+r) ²

r²+81 = 36+12r + r²

81=36+12r

=> 12r = 45

r = 45/12 = 3.75

(a) The number of students applying to graduate schools: DISCRETE (b) The temperature in any given location: CONTINUOUS (c) The number of errors found on a student's research paper: DISCRETE (d) The distance traveled by a city bus each day: CONTINUOUS DATA SET.

(a) The number of students applying to graduate schools: DISCRETE

The number of students applying to graduate schools is a discrete data set because it consists of whole numbers or distinct values. It cannot take on fractional or continuous values.

(b) The temperature in any given location: CONTINUOUS

The temperature in any given location is a continuous data set because it can take on any value within a range. Temperature can have decimal values and can vary continuously, making it a continuous variable.

(c) The number of errors found on a student's research paper: DISCRETE

The number of errors found on a student's research paper is a discrete data set because it consists of whole numbers. The count of errors cannot have fractional values or exist between distinct values.

(d) The distance traveled by a city bus each day: CONTINUOUS

The distance traveled by a city bus each day is a continuous data set because it can take on any value within a range. Distance can have decimal values and can vary continuously, allowing for a continuous measurement.

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Answer:

x ≥ -7

Hope this helps : )

Step-by-step explanation:

The number line is showing a closed dot which means that the number the dot is on is a solution to the equation too. Since the arrow is pointing to the right (positive/greater numbers), then the sign is greater than and equal to.

Chase and Simon (1973) conducted a study on the memory of chess novices and experts for positions of chess pieces on a chessboard. They found that although experts generally have a better memory for chess positions than novices, novices performed equally or even better than experts when asked to recall random arrangements of chess pieces on the chessboard, even if the arrangements couldn't occur in a real game of chess.

One possible explanation for this phenomenon is that experts rely heavily on their knowledge of typical chess positions and patterns to remember the positions of the pieces. However, when the pieces are arranged randomly, these patterns are disrupted, and experts may struggle to apply their existing knowledge effectively. On the other hand, novices may not have developed strong patterns or strategies yet, so they approach the task with a more flexible mindset and are less affected by the random arrangement. They may use more general memory strategies, such as chunking or grouping the pieces together, which can be useful for recalling random arrangements.
In summary, novices may perform as well as experts when the pieces are arranged randomly because they rely less on established patterns and can use more general memory strategies to recall the positions.

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It is given that P = principal, R = rate of interest and T = time

Formula to find compound interest is:

A = P(1 + R/100)^T

where A = amount received after n years

P = principal amount invested

R = rate of interest

T = time for which the amount is invested

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest.

It is thought that Italy in the 17th century is where the concept of "interest on interest" or compound interest first appeared. It will accelerate the growth of a total more quickly than simple interest, which is solely calculated on the principal sum.

Money multiplies more quickly thanks to compounding, and the more compounding periods there are, the higher the compound interest will be.

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Answer: q=0.3p-2

Well everytime P goes up by one then Q goes up by positive 0.3

The stationing of BC1, EC1, BC, and EC2 can be determined by adding the respective distances to the station of Point A.

To determine the station of BC1, EC1, BC, and EC2, we need to understand the concept of stations in road centerline alignment. In road design and construction, stations are used to measure distances along the centerline of the road. The station of a point refers to its distance from a reference point, typically the starting point of the road.

Given that the station of Point A is 3+ def ghi, we can assume that the stationing system used is based on chainage, where the main stations are represented by whole numbers and the sub-stations are represented by decimals or fractions.

Let's break down the given distances:

The distance from Point A to Pls is 222.841.

The distance from Point Ply to Ply is 345.036.

The distance from Point Pl2 to b is 214.761.

Based on the given information, we can determine the stations as follows:

Station of Point A: 3+ def ghi (given).

Station of BC1: Station of Point A + Distance from Point A to Pls = 3+ def ghi + 222.841.

Station of EC1: Station of BC1 + Distance from Point Ply to Ply = (3+ def ghi + 222.841) + 345.036.

Station of BC: Station of EC1 + Distance from Point Pl2 to b = ((3+ def ghi + 222.841) + 345.036) + 214.761.

Station of EC2: Station of BC + Distance from Point Pl2 to b = ((3+ def ghi + 222.841) + 345.036 + 214.761) + 214.761.

The above equations represent the stationing along the road centerline from Point A to BC1, EC1, BC, and EC2, respectively. By substituting the given station of Point A and the distances into the equations, we can calculate the stations of BC1, EC1, BC, and EC2.

Please note that the specific numerical values for def, ghi, and the distances are not provided in the question, so the actual station values cannot be determined without those values. However, you can substitute the known values into the equations to calculate the stations once you have the complete information.

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Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

To determine the equivalent nominal interest rate compounded monthly for a given nominal interest rate compounded quarterly, we can use the formula for nominal interest rate conversion.

The formula is:

r = (1 + i/n)^n - 1

Where:

r is the nominal interest rate compounded annually (we're looking for this),

i is the nominal interest rate compounded quarterly (2.50% in this case),

n is the number of compounding periods per year (4 for quarterly compounding).

Plugging in the values, we have:

r = (1 + 0.025/4)^4 - 1

Calculating this expression, we find:

r ≈ 0.025335

Rounding this to two decimal places, the equivalent nominal interest rate compounded monthly is approximately 2.53%.

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Answer:Yes

Step-by-step explanation:

Carmela:3/4/3=1/4 per mile

Hari:1/2/2=1/4 per mile