138 130 135 140 120 125 120 130 130 144 143 140 130 150 The mean (x) for the following ungrouped data distribution to its right is: a. 1.24 b. 2.01 c. 2:18 a.m. 2.45 The arithmetic mean of the sample is: a. 130 b. 132.5 c133.93 d. 9.0423

Answer:

A

Step-by-step explanation:

3.5 + p = 7.5

Subtract from 3.5 from both sides.

p = 7.5 - 3.5

Simplify

p = 4

A is the number line that has the correct answer.

Answer:

52.6 degrees

Step-by-step explanation:

tan^-1(72/55)

Angle of elevation is equals to 52°7'(approximately).

" Angle of elevation is the angle between the horizontal plane and  line of sight from the point of observation."

Formula used

In a right angled triangle,

tanθ = ( opposite side) / adjacent side)

According to the question,

As shown in diagram

Height of the building (AB) = 72m

Distance between base of the building and point of observation

(BC)= 55m

Angle of elevation = θ

Substitute the value in the formula we have,

 tanθ = AB / BC

          = 72 / 55

⇒ θ = tan⁻¹ (72 /55)

      = tan ⁻¹(1.3091)

      = 52° 7' (approximately)

Hence, angle of elevation is equals to 52°7'(approximately).

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a. To calculate the expected value of how much money you’ll get if you bet $10 on number 12 in Roulette, we can use the formula: Expected Value = (Probability of Winning * Amount Won) - (Probability of Losing * Amount Lost)

In this case, the probability of winning is 1/38, and the amount won is $350. The probability of losing is 37/38, and the amount lost is $10. Substituting these values into the formula, we get: Expected Value = (1/38 * $350) - (37/38 * $10)
Expected Value = $9.21 Therefore, the expected value of how much money you’ll get if you bet $10 on number 12 in Roulette is $9.21. b. Based on the expected value from part a, it is not a good idea to play Roulette over and over again. The reason is that the expected value is positive but small. This means that on average, you will win $9.21 for every $10 you bet, but the variance in the game can cause you to lose money in the long run.
For example, if you play 100 rounds of Roulette with a $10 bet on number 12 each time, you would expect to win $921 on average. However, there is a significant chance that you could lose money over these 100 rounds. The more you play, the greater the likelihood of experiencing a losing streak that would offset your winnings.

Therefore, while playing Roulette can be fun and exciting, it is not a sustainable way to make money. The small expected value means that over time, the casino will always come out ahead.

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Answer:

20.25inches

Step-by-step explanation:

Using the Pythagorean theorem,

h^2=7^2 +19^2

h^2=410

h=sqr 410=20.25inches

Answer:

-2

Step-by-step explanation:

The constant has only a number and no variable

-2 +6c +3c

-2 is the constant

6 is a coefficient for the variable term

3 is a coefficient for the variable term

-2

How

\(\\ \sf\longmapsto -2+6c+3c\)

\(\\ \sf\longmapsto -2+(6+3)c\)

\(\\ \sf\longmapsto -2+9c\)

\(\\ \sf\longmapsto 9c-2\)

Answer:

type 2 in the first box,

13/4 in the second box, and

-9/8 in the third one

Step-by-step explanation:Notice that you are asked to write the following quadratic expression in vertex form, so you need to find the "x" value of the vertex, and then the "y" value of the vertex:

\(x_{vertex}= -b/2a\)

Which in our case is: -13/4

and the value of the y for the vertex is obtained using the functional expression when x equals -13/4:

\(f(-13/4)= -9/8\)

Then your expression for this quadratic should be:

\(f(x)=2\,(x+\frac{13}{4} )^2+(-\frac{9}{8})\)

Then type 2 in the first box, 13/4 in the second box, and -9/8 in the third one

The degree 3 Taylor polynomial for the function f(x) = (x+5)sin(5x) at x=0 . The degree 3 Taylor polynomial for f(x) at x=0 is \(P(x) = 0 + 25x + (5/2)x^2 + (f"'(0)/3!)x^3.\)

To  find the degree 3 Taylor polynomial for f(x) at x=0, we need to calculate the function and its derivatives.

First, let's find f(0). Plugging x=0 into the function f(x) = (x+5)sin(5x), we have f(0) = (0+5)sin(5(0)) = 0.

Next, we find f'(x) by taking the derivative of f(x) with respect to x. Using the product rule and the chain rule, we get f'(x) = (1)(sin(5x)) + (x+5)(5cos(5x)) = sin(5x) + 5(x+5)cos(5x).

Evaluating f'(x) at x=0 gives us f'(0) = sin(0) + 5(0+5)cos(0) = 0 + 5(5)(1) = 25.

Taking the second derivative, f"(x), we differentiate f'(x) with respect to x, which yields f"(x) = 5cos(5x) + 5(x+5)(-5sin(5x)).  

Evaluating f"(x) at x=0 gives f"(0) = 5cos(0) + 5(0+5)(-5sin(0)) = 5 + 5(5)(0) = 5.

Now that we have the necessary values, we can construct the Taylor polynomial. The general form of a degree 3 Taylor polynomial is P(x) = f(0) + f'(0)x + (f"(0)/2!)x^2 + (f"'(0)/3!)x^3.

Substituting the values we calculated, the degree 3 Taylor polynomial for f(x) at x=0 is  the degree 3 Taylor polynomial for f(x) at x=0 is \(P(x) = 0 + 25x + (5/2)x^2 + (f"'(0)/3!)x^3.\)  

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To prove that the gcd operator is associative on Z+ (the set of positive integers), we need to show that for any positive integers a, b, and c, the equation gcd(a, gcd(b, c)) = gcd(gcd(a, b), c) holds true.

Let's start by considering the left-hand side (LHS) of the equation:

LHS: gcd(a, gcd(b, c))

Using the definition of gcd, we know that gcd(b, c) divides both b and c, and any common divisor of b and c must also divide gcd(b, c). Therefore, gcd(a, gcd(b, c)) must divide a and gcd(b, c).

Now, let's consider the right-hand side (RHS) of the equation:

RHS: gcd(gcd(a, b), c)

Again, using the definition of gcd, we know that gcd(a, b) divides both a and b, and any common divisor of a and b must also divide gcd(a, b). Therefore, gcd(gcd(a, b), c) must divide gcd(a, b) and c.

To prove the associativity of the gcd operator, we need to show that both sides of the equation have the same divisors.

Let d be any positive integer that divides both gcd(a, gcd(b, c)) and gcd(gcd(a, b), c). We need to show that d divides both a and c.

Since d divides gcd(a, gcd(b, c)), it must divide a and gcd(b, c).

Similarly, since d divides gcd(gcd(a, b), c), it must divide gcd(a, b) and c.

Combining these two facts, we can conclude that d must divide a, b, and c.

Therefore, any positive integer that divides both sides of the equation must divide a, b, and c.

Hence, we have proved that gcd(a, gcd(b, c)) = gcd(gcd(a, b), c) for all positive integers a, b, and c.

This shows that the gcd operator is associative on Z+.

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Let's solve the equation.

4 (2m -6) - 3p - 2m + 8

= 8m - 24 - 3p - 2m + 8 (We simplified 4 (2m -6))

= 6m - 16 - 3p (We added the 8 to the 24)

= 6m - 3p - 16 (We organized the variables together so it matches an answer.)

The answer is A!

Answer: hii

Step-by-step explanation:

How to solve your problem:

4 (2m -6) - 3p - 2m + 8

Simplify.

Distribute.

4 (2m -6) - 3p - 2m + 8

8m - 24 - 3p - 2m + 8

Add the numbers:

8m - 24 - 3p - 2m + 8

8m - 16 - 3p - 2m

Combine like terms:

8m - 16 - 3p - 2m

6m - 16 - 3p

Rearrange terms:

6m - 16 - 3p

6m - 3p - 16

Solution:

6m - 3p -16

Hopefully this helps you ~

- Matthew

Answer:

No

Step-by-step explanation:

4/9 divided by 5/7 is equal to 4/9 * 7/5 = 28/45. We can see that 63/20 is not equivalent to 28/45 as 28/45 is less than one and 63/20 is greater than one.

The given differential equation y x²y² = x² is a nonlinear and not separable differential equation, which corresponds to option (D).

A linear differential equation can be written in the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x. In this equation, the term x²y² makes it nonlinear.

A separable differential equation can be written in the form g(y)dy = f(x)dx, where g(y) and f(x) are functions of y and x, respectively. However, in the given equation, we cannot separate the variables y and x to obtain such a form.

To solve this particular differential equation, one approach is to rewrite it in a more manageable form. Let's rearrange the terms:

x² = y/(x²y²)

Now, we can multiply both sides by (x²y²) to eliminate the denominator:

x²(x²y²) = y

This equation is still nonlinear but can be used to find a particular solution for y given a specific initial condition.

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Reason:

GCF = greatest common factor

LCM = lowest common multiple

GCF of 6 and 8 = 2

LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24

We can list out the multiples of each to confirm this

If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.

The smallest height that their towers could be 24 cm.

The lowest of two or more natural numbers' common multiples is referred to as the Lowest Common Multiple (LCM). The least Common Multiple and Least Common Divisor are other names for it (LCD). For instance, 12 is the least frequent multiple of 4 and 6.

GCF = greatest common factor

LCM = lowest common multiple

GCF of 6 and 8 = 2

LCM of 6 and 8 = (6*8)/GCF = (6*8)/2 = 48/2 = 24

We can list out the multiples of each to confirm this

multiples of 6 are 6, 12, 18, 24, 30, ...

multiples of 8 are: 8, 16, 24, 32, ...

If Mason's tower is 24 cm tall, then he uses 24/6 = 4 blocks; while Daisy will use 24/8 = 3 blocks for her tower of the same height.

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Answer:

             48.56 m

Step-by-step explanation:

1 cm = 0.01 m

Or, if you want to change from cm to m. simply divide the cm by 100.

Thus,

             4856 cm ÷ 100 = 48.56 m

Move all terms not containing the variable from the center section of the inequality.

The formula expressing the radius of the circle, r (in cm), in terms of the number of seconds, t, since the circle started shrinking is r = r₀ - kt, where r₀ is the initial radius and k is the rate at which the circle is shrinking.

The formula r = r₀ - kt represents the relationship between the radius of the circle and the time elapsed since it started shrinking. Here's an explanation of the variables:

r represents the radius of the circle at any given time t.r₀ represents the initial radius of the circle when it started shrinking .k represents the rate at which the circle is shrinking, indicating how much the radius decreases per unit of time.t represents the number of seconds that have elapsed since the circle started shrinking.

By subtracting kt from the initial radius r₀, we can determine the current radius of the circle at any given time t. The term kt represents the amount by which the radius decreases over time, based on the rate of shrinkage defined by the value of k.

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The feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

To determine whether the feasible set for each system of constraints is convex, we need to analyze the constraints individually and examine their intersection.

a) (x1)² + (x2)² > 9

This constraint represents points outside the circle with a radius of √9 = 3. The feasible set includes all points outside this circle.

b) x1 + x2 ≤ 10

This constraint represents points that lie on or below the line x1 + x2 = 10. The feasible set includes all points on or below this line.

c) x1, x2 > 0

This constraint represents points in the positive quadrant, where both x1 and x2 are greater than zero.

Now, let's analyze the intersection of these constraints:

Considering the first two constraints (a and b), we can see that the feasible set consists of all points outside the circle (constraint a) and below or on the line x1 + x2 = 10 (constraint b).

To determine whether the feasible set is convex, we need to check if any two points within the set create a line segment that lies entirely within the set.

If we consider the points (5, 5) and (3, 7), both points satisfy the individual constraints (a) and (b). However, the line segment connecting these two points, which is the line segment between (5, 5) and (3, 7), exits the feasible set since it passes through the circle (constraint a) and above the line x1 + x2 = 10 (constraint b).

Therefore, the feasible set for this system of constraints is not convex, and the points (5, 5) and (3, 7) violate the convexity definition.

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No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

The probability formula defines the likelihood of the happening of an event. It is the ratio of favorable outcomes to the total favorable outcomes.

We have the information:

P(A)= 0.48  

P(B) = 0.42

P(A∩B) = 0.38

To find out if watching a movie and buying a popcorn are independent,

The formula is used:

P(A|B) = P(A∩B)/P(A)

Plug all the values in above formula:

P(A|B) = 0.38/0.48 = 0.79166

P(A|B) = 0.79

From the deductions above;

Hence, the answer is

No, because P(A|B) = 0.79 and the P(A) = 0.48 they are not equal.

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For complete question, to see the attachment

If 24 percent of the snack mix is pretzel, we simply need to multiply the total number of ounces by 0.24.

0.24 x 32 = 7.68

7.68 ounces of the snack mix will be pretzels.

Answer:

answer is D.

you multiply 32 x .24 = 7.68oz

Step-by-step explanation:

the way you solve this question

32 x .24%= 7.68 oz

make sure you place your decimal place to spaces to your left!

hope this helps!

Answer:

C is answer

Step-by-step explanation:

As per the addition formula, the value of the trigonometric function is -0.809.

In statistics, function is defined as a relationship between inputs where each input is related to exactly one output.

Here we have to find the value of the trigonometric function cos(13/15)cos(-/5)-sin(13/15)sin(-/5)  by using the addition and subtraction formula.

Here we have the following trigonometric function:

=> cos(13/15)cos(-/5)-sin(13/15)sin(-/5)

Now, we have to use the trigonometric addition formula,

=> Cos (A+B) = Cos A Cos B - Sin A Sin B

To solve the given function,

Here let us rewrite the given function based on the addition formula, then we get,

=> Cos ( 13π/15 + (-π/5) )

=> Cos( 12π/5)

=> Cos(144°)

=> -0.809

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Step-by-step explanation:

63k -10.5k square 2-5 and you have you answer

Answer:

C or D cause A B doesnt make sence its d

Step-by-step explanation:

-2.05 is the critical value for the left-tailed test .

What is critical z value?

The -1.96 and +1.96 standard deviations are the essential z-score values when adopting a 95 percent confidence level.

                               With a 95 percent confidence level, the uncorrected p-value is equal to 0.05.The critical value for a two-sided test is Z 1-/2, while for a one-sided test, it is Z 1.

                      You reject the null hypothesis if the absolute Z-value is higher than the crucial value. If not, you have not successfully ruled out the null hypothesis.

Given that,

α = 0.02.

left tailed test

Zα = 0.02 = -2.05

critical value = -2.05

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Answer:

(0,4) and (-4,0)

Step-by-step explanation:

Answer:

BM = 30 cm, DL = 42 cm

Step-by-step explanation:

The area of the parallelogram = 1470 cm², AB = 35 cm,  AD = 49 cm, DL and BM are the heights on sides AB and AD.

area of the parallelogram = base × height = AD × height of AD = AD × BM

⇒ 1470 cm² = 49 cm × BM

BM = 1470 cm² / 49 cm = 30 cm

BM = 30 cm

Also:

area of the parallelogram = base × height = AB × height of AB = AB × DL

⇒ 1470 cm² = 35 cm × DL

DL = 1470 cm² / 35 cm = 42 cm

DL = 42 cm

Answer:

B

Step-by-step explanation:

Edge 2021.

After 100 years:

Replace t by 100:

A (t) = 523 (1/2)^t/30

A (100) = 523 (1/2)^100/30 = 523 (1/2) ^10/3 = 51.88 =52 grams

The initial amount of the sample is 523

Answer:

x=2 and y=10

Step-by-step explanation:

Answer:

x = 2 and y = 10

Step-by-step explanation: