The height for a tree in a local park, Y, is normally
distributed with mean a of 161 cm and standard deviation of 10 cm.
(maintain two digits following decimal).
i) Find the z-score of Y = 185 cm.
ii

Answer:T=(X*520N)+650

Step-by-step explanation:

Answer:

-24x²

Step-by-step explanation:

remove the parentheses, multiply the numbers, apply exponent rule and add the numbers

The values of x and y which are the missing terms of the given triangle have their values as; x = ⁵/₂ and y = ⁹/₄

From the given triangle, we can see that the transverse line intersects both side lengths at their midpoints. Thus, we can say that;

3x - 4 = x + 1   ------(1)

⁴/₃y + 2 = 4y - 4   ------(2)

Let us solve equation 1 by rearranging to get;

3x - x = 1 + 4

2x = 5

x = ⁵/₂

Similarly, we can say that for equation 2;

4y - ⁴/₃y =  2 + 4

4y - ⁴/₃y = 6

Multiply through by 3 to get;

12y - 4y = 18

8y = 18

y = 18/8

y = ⁹/₄

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Answer: x>6

Step-by-step explanation:

Answer:

x > 6

Step-by-step explanation:

distribute: 3x + 12 -5x + 5 < 5

combine like terms: -2x + 17 < 5

subtract 17:  -2x < -12

divide -2 from both sides: -2x/-2 < -12/-2

switch signs x > 6

The uniform model assumes equal probabilities for all values within a given range when there is no reason to believe that any X-values are more likely than others.

In statistics, the uniform model assumes that all values within a given range have an equal probability of occurring. This means that there is no preference or bias towards any specific value within the range. The uniform distribution is often represented by a rectangular shape, where the probability of any particular value occurring is constant.

The uniform model is typically used when there is no reason to believe that any X-values are more likely than others. This means that there is no prior information or evidence indicating that certain values are more probable or occur more frequently than others. In other words, there is no specific distribution or pattern in the data that suggests any particular value is more likely to occur.

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The equation of the line through the points (0, 9) and (3, 0) is y = -3x + 9.

To find the equation of a line passing through two given points, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is one of the points on the line and m is the slope of the line.

First, we calculate the slope (m) using the formula: m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Substituting the values (0, 9) and (3, 0), we get m = (0 - 9)/(3 - 0) = -9/3 = -3.

Next, we choose one of the points, let's say (0, 9), and substitute its coordinates into the point-slope form: y - 9 = -3(x - 0).

Simplifying the equation, we get y - 9 = -3x, or rearranging it, y = -3x + 9.

Therefore, the equation of the line passing through the points (0, 9) and (3, 0) is y = -3x + 9.

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Step-by-step explanation:

\( f(x) = - 3 {x}^{2} + 9x - 2\)

A) f(-2) + f(1) = -32 + 4 = -28

B) f(-2) - f(1) = -32 - 4 = -36

According to Pythagorean theorem, the length of BE is 2√(61) units.

To solve this problem, we need to use the Pythagorean Theorem, which tells us that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, we can see that triangle ABE is a right triangle, with AB as the hypotenuse and BE and AE as the other two sides. Therefore, we can use the Pythagorean Theorem to find the length of BE.

To do this, we first need to find the length of AE. Since triangle ADE is a right triangle with a hypotenuse of length 4 and one leg of length 2, we can use the Pythagorean Theorem to find the length of the other leg, which is AE. Specifically, we have:

AE² + 2² = 4² AE² + 4 = 16 AE² = 12 AE = √(12) = 2√(3)

Now we can use the Pythagorean Theorem again to find the length of BE. Specifically, we have:

BE² + (2√(3))² = AB² BE² + 12 = (2AB)²

[since AB = AC = CD = DE = 4]

BE² + 12 = 16² BE² + 12 = 256 BE² = 244 BE = √(244) = 2√(61)

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If alternating current circuit is i=5 cos t + 5 sin t , the peak current for this circuit is 5√2 amperes.

The current in an alternating current circuit is given by the formula i=5 cos t + 5 sin t. Here, i represents the current in amperes, and t represents time in seconds.

The peak current for this circuit refers to the maximum current that occurs in the circuit. To find the peak current, we need to find the maximum value of the expression 5 cos t + 5 sin t.

The maximum value of the expression 5 cos t + 5 sin t can be found by using the fact that the maximum value of sin t + cos t is √2.

Using the Pythagorean theorem, we can find that the hypotenuse has length √2.

Therefore, the maximum value of 5 cos t + 5 sin t occurs when sin t = cos t = 1/√2.

Substituting these values into the expression, we get:

5 cos t + 5 sin t = 5(1/√2) + 5(1/√2) = 5√2

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Null and alternative hypothesis are statements about the sample statistics.

The null hypothesis of both a test typically forecasts no effect or no association between variables, even while the alternative hypothesis expresses their research's prediction of an effect or relationship.

Because Student's t distribution will be less leptokurtic as both degrees of freedom increase, the likelihood of extreme values decreases. Gradually, the distribution resembles a standard normal distribution.

The two primary forms of probability distributions are discrete probability distributions and continuous probability distributions. Each category includes a variety of probability distribution types.

The average relative frequency over all potential trials is known as probability.

For instance, the probability of a coin falling on heads is such that if you flip a coin an infinite number of times, it will land on heads 50% of the time.

Hence we can say that the Null and alternative hypothesis are statements about the sample statistics.

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Answer: 468.75

is ya answer

i think

sorry if im wrong

Answer:

468.75

Step-by-step explanation:

First we need to add 25% to 500.00 which is 625.

Next we need to subtract 25% from 625.

Now we have 468.75.

The selling price of the couch is $468.75.

Answer:

Step-by-step explanation:

-28

According to the given information, the solution is -1 5/9.

Division is a mathematical operation that involves splitting a quantity into equal parts or groups. It is the inverse operation of multiplication, and is used to find out how many times one quantity is contained within another quantity. In division, the dividend is the number being divided, the divisor is the number by which the dividend is divided, and the quotient is the result of the division.

We can convert the mixed number 4 1/2 to an improper fraction:

4 1/2 = 9/2

Then we can rewrite the division as multiplication by the reciprocal:

-7 ÷ 4 1/2 = -7 × 2/9

Now we can simplify by canceling out any common factors:

-7 × 2/9 = -14/9

Therefore, according to the given information, the solution is -1 5/9.

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Answer:

a) 14

b) green

c) fraction 6/14

percentage: 42.8% rounded: 40%

not sure about the decimal tho

Answer:

a) 14

b) green

c) 6/14

d)percent 42.8 %

round up 40 %

9514 1404 393

Answer:

  (b)  -36

Step-by-step explanation:

Synthetic division is often performed using a table of the kind shown in the attachment. The coefficients of f(x) are placed across the top, and the x-value to be evaluated is placed at the left. The rule for finding table entries is shown. (The first (left-most) number at the bottom is the leading coefficient of the polynomial.)

This table shows the remainder, which is f(-2), is -36.

__

The equation itself can be rewritten in "Horner form" to facilitate evaluation.

  f(x) = (((-x +2)x -1)x +4)x +8

In this form, substituting for x and doing the evaluation is easier for mental arithmetic. You will notice that the contents of parentheses at each level match the bottom line of the synthetic division table.

  f(-2) = (((-(-2) +2)(-2) -1)(-2) +4)(-2) +8

  = (((4)(-2) -1)(-2) +4)(-2) +8

  = ((-9)(-2) +4)(-2) +8

  = (22)(-2) +8

  = -36

  f(-2) = -36 . . . . remainder from synthetic substitution

Answer:

A = 3.14 mm²

Step-by-step explanation:

The formula for the area of a circle of radius r is A = πr².  If your circle has diameter 2 mm, then the radius is half that, or 1 mm.  The area of the circle will then be A = (3.14)(1 mm)², or 3.14 mm².  

Note:  the spelling of π is 'pi,' not 'pie.'

Answer:

$1,715  to fing out use a cosbnj vndbjerm c

Answer: $1,668

Step-by-step explanation: 2.5% of 1560 is 36. 36*3 is 108. 1560+108 is 1668.

Answer:

\(\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.\)

Step-by-step explanation:

System of Equations

Let's call:

x = number of nickels in the student's pocket

y = number of dimes in the student's pocket

Each nickel has a value of $0.05, so x nickels have a value of 0.05x

Each dime has a value of $0.10, so y dimes have a value of 0.10y

The student has a total of 10 coins, thus:

\(x+y=10\)

The total value of the coins is $0.85, thus

\(0.05x+0.10y=0.85\)

The system of linear equations that represents this scenario is:

\(\left\{\begin{matrix}x+y=10\\ 0.05x+0.10y=0.85\end{matrix}\right.\)

The following values are as follows: a) Mean = 0.6, b) standard deviation = 0.073 and c) Probability is 0.0855

a) As the number of samples is large enough which is up to 30 then the mean of the average number of moths in 30 traps is given as 0.6, given from the central limit theorem.

b) The population deviation divided by the square root of the sample size gives the standard deviation value.

standard derivation = σ/ \(\sqrt{n}\) = 0.4 / \(\sqrt{30}\) = 0.4/ 5.477 = 0.073

c) The probability that an approximately normally distributed data with the standard deviation, σ, with a sample size of n is greater than a number, x, and a mean, μ, is given by

1 - P (X < x)= P (X > x)

= 1 - P(z< x- µ/ σ/\(\sqrt{n}\))

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that the average number of moths in 30 traps is greater than 0.7 is given by:

1 -P (X - 0.7) = P (X > 0.7)

= 1 - P(z < \(\frac{0.7-0.6}{0.073}\)) = 1 - P(z < 1.369)

= 1 - 0.91455 = 0.0855

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Answer:

x=-5

Step-by-step explanation:

6x+3=5x-8 subtract 5x from both sides

x+3=-8x subtract 3 from both sides

x=-5

Answer:

x = - 11

Step-by-step explanation:

6x + 3 = 5x − 8

Subtract 5x from both sides.

6x + 3 − 5x = −8

Combine 6x and −5x to get x.

x + 3 = −8

Subtract 3 from both sides.

x = −8 − 3

Subtract 3 from −8 to get −11.

x= −11

Answer:

The chemical element loses 4% of its weight everyday

Step-by-step explanation:

Here, we are interested in knowing the percentage weight loss of the chemical each day.

The key to answering this is looking at the expression inside the bracket.

We can express M(t) = 169•(0.96)^t as

M(t) = 169•(1-0.04)^t

So what this means is that we need to find the percentage value corresponding to 0.04 since it is a constant term here

Mathematically, 0.04 is same as 4/100, so we can clearly say that the constant percentage loss is 4%

Answer:

0.96

Step-by-step explanation:

The exponential function modeling the mass of the sample is of the form M(t)=A⋅Bt. Therefore, AAA determines the initial mass of the sample (when Clemence began studying it) and BBB determines the daily change in the mass of the sample.

The mass of the sample is multiplied by \it{0.96}0.960, point, 96 every day. Since 0.96<10.96<10, point, 96, is less than, 1, the mass of the sample shrinks by a factor of 0.960.960, point, 96 every day.

Every day, the mass of the sample shrinks by a factor of 0.960.960, point, 96.

Answer: C

Step-by-step explanation:

Since the inequalities for all 4 options are different, all you need to look at are the inequality signs.

For the line with a positive slope (bottom left to top right), the point it ends at is not filled in, so that point is not included meaning it is x > 1.

For the line with a negative slope (top left to bottom right), the point it ends at is filled in, so that point is included meaning it is x \(\leq\) 1.

C. is the only one that has these inequalities.

The statement "P(A or B) = P(A) + P(B)" is False.

The correct statement is "P(A or B) = P(A) + P(B) - P(A and B)," which is known as the general law of addition for probabilities. This law takes into account the possibility of events A and B overlapping or occurring together.

The general law of addition for probabilities states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities minus the probability of both events occurring simultaneously. This adjustment is necessary to avoid double-counting the probability of the intersection.

Let's consider a simple example. Suppose we have two events: A represents the probability of flipping a coin and getting heads, and B represents the probability of rolling a die and getting a 6. The probability of getting heads on a fair coin is 0.5 (P(A) = 0.5), and the probability of rolling a 6 on a fair die is 1/6 (P(B) = 1/6). If we assume that these events are independent, meaning the outcome of one does not affect the outcome of the other, then the probability of getting heads or rolling a 6 would be P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 1/6 - 0 = 7/12.

In summary, the general law of addition for probabilities states that when calculating the probability of two events occurring together or separately, we must account for the possibility of both events happening simultaneously by subtracting the probability of their intersection from the sum of their individual probabilities.

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Answer:

A. 2:1

Step-by-step explanation:

pretty sure larger numbers go first

Answer:

D)  1:2

Step-by-step explanation:

Two values simulated from a lognormal distribution with μ = 5 and σ = 1.5 using the polar method and the given uniform random numbers are approximately 9.388968 and 0.2408667, respectively.

To generate values from a lognormal distribution using the polar method, we need pairs of independent standard normal random variables. We can use the Box-Muller transformation to obtain these pairs.

Let's use the given uniform random numbers to generate two values from a lognormal distribution with μ = 5 and σ = 1.5:

Uniform random numbers: 0.942, 0.108, 0.217, 0.841

Step 1: Generate pairs of standard normal random variables using the Box-Muller transformation.

Pair 1:

U1 = sqrt(-2 * log(0.942)) * cos(2 * π * 0.108) = -0.4808067

U2 = sqrt(-2 * log(0.942)) * sin(2 * π * 0.108) = 1.0399945

Pair 2:

U3 = sqrt(-2 * log(0.217)) * cos(2 * π * 0.841) = -2.2493955

U4 = sqrt(-2 * log(0.217)) * sin(2 * π * 0.841) = -0.7851325

Step 2: Convert the standard normal random variables to lognormal random variables.

Value 1:

X1 = exp(μ + σ * U1) = exp(5 + 1.5 * (-0.4808067)) ≈ 9.388968

Value 2:

X2 = exp(μ + σ * U3) = exp(5 + 1.5 * (-2.2493955)) ≈ 0.2408667

Therefore, two values simulated from a lognormal distribution with μ = 5 and σ = 1.5 using the polar method and the given uniform random numbers are approximately 9.388968 and 0.2408667, respectively.

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Answer: -1, 1

Step-by-step explanation:

The other answer is valid.

keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the equation above

\(x-3y=9\implies -3y=-x+9\implies y=\cfrac{-x+9}{-3} \\\\\\ y=\cfrac{-x}{-3}+\cfrac{9}{-3}\implies y=\cfrac{1}{3}x-3\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}\)

so we're really looking for the equation of a likne whose slope is 1/3 and it passes through (-10 , 9)

\((\stackrel{x_1}{-10}~,~\stackrel{y_1}{9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{9}=\stackrel{m}{ \cfrac{1}{3}}(x-\stackrel{x_1}{(-10)}) \implies y -9= \cfrac{1}{3} (x +10) \\\\\\ y-9=\cfrac{1}{3}x+\cfrac{10}{3}\implies y=\cfrac{1}{3}x+\cfrac{10}{3}+9\implies {\Large \begin{array}{llll} y=\cfrac{1}{3}x+\cfrac{37}{3} \end{array}}\)

Hence, the nickles she have is \(14\) dimes and \(56\) nickels.

What is the simplification?

Simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving.

Here given that,

Suzanne has a collection of \(70\) nickels and dimes. The number of nickels is four times the number of dimes .

Let \(x\) be the number of dimes and let \(4x\) be the number of nickles.

So,

\(x+4x=70\\\\5x=70\\\\x=\frac{70}{5}\\\\x=14\)

and

\(4x=4(14)\\\\4x=56\)

Hence, the nickles she have is \(14\) dimes and \(56\) nickels.

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