Suppose a normal distribution has a mean of 62 and a standard deviation of
4. What is the probability that a data value is between 55 and 63? Round your
answer to the nearest tenth of a percent.
O A. 55.9%
O B. 56.9%
O C. 53.9%
O D. 54.9%

256 is the lateral surface area.

What's the lateral surface area?  

Side indicates the side of  commodity. thus, lateral surface area is  set up by chancing  the  face area of the sides of the object.

                                 This is done by chancing  the border of the base and multiplying it by the height of any three- dimensional figure.

For the given situation,

The sides of the triangle are 5 cm, 6 cm, 5 cm.

The length of the prism = 16 cm

The formula for lateral surface area of triangular prism is

LSA = (perimeter)(length)

On substituting the above values,

 LSA = (5 + 6 + 5)(16)

        = (16)(16)

         = 256

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Answer: To find the relative frequency for each discount, we need to divide the number of customers who received each discount by the total number of customers.

Discount           Number of customers                          Relative Frequency

10%                    70                                                            0.35

25%                   99                                                            0.495

30%                   31                                                             0.155

To determine if it is appropriate for the manager to want approximately half of the customers to receive the 25% discount, we can calculate the relative frequency for the 25% discount and compare it to 0.5 (or 50%).

Relative frequency for 25% discount = 99/200 = 0.495

Since the relative frequency for the 25% discount is already very close to 0.5, it seems like an appropriate method to achieve the manager's goal. However, it's worth noting that this method may not be the most effective in terms of maximizing profits or customer satisfaction. It's always important for businesses to carefully consider their pricing strategies and discount policies.

Step-by-step explanation:

From the given information provided, the percent of yellow tint in the new mixture is 36.4%.

The total amount of yellow tint in the original mixture is:

0.30 × 50 liters = 15 liters

When 5 liters of yellow tint are added to the mixture, the total amount of yellow tint becomes:

15 + 5 = 20 liters

The total amount of new mixture is:

50 + 5 = 55 liters

To find the percentage of yellow tint in the new mixture, we divide the amount of yellow tint by the total amount of the mixture and multiply by 100:

(20/55) × 100 = 36.4%

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The eccentricity for r=5/2+1sin theta and  the equation of the directrix of r=26. 4/4+4. 4 cos theta is 0.5 and x=6

To find the eccentricity of the polar equation r = 5/2 + 1sin(θ), we first need to convert it to rectangular form:

r = 5/2 + 1sin(θ)

r = 5/2 + 1y/r

r^2 = (5/2)r + y

x^2 + y^2 = (5/2)r + y

x^2 + y^2 = (5/2)√(x^2 + y^2) + y

x^2 - (5/2)√(x^2 + y^2) + y^2 = 0

We can see that this is the equation of a conic section, specifically an ellipse, since the signs of the x^2 and y^2 terms are the same. The standard form of an ellipse centered at the origin is:

x^2/a^2 + y^2/b^2 = 1

Comparing this to our equation, we can see that a^2 = (5/2) and b^2 = 1. The eccentricity of an ellipse is given by:

e = √(1 - b^2/a^2)

Plugging in our values, we get:

e = √(1 - 1/(5/2))

e = √(3/5)

e ≈ 0.5

Therefore, the answer is (A) 0.5.

To find the equation of the directrix for the polar equation r = 26.4/4 + 4.4cos(θ), we first need to convert it to rectangular form:

r = 26.4/4 + 4.4cos(θ)

r = 6.6 + 4.4x/r

r^2 = 6.6r + 4.4x

x = (r^2 - 6.6r)/4.4

We can see that this is the equation of a parabola, since the highest degree of the variable r is 2. The standard form of a parabola with its focus at (0, p) is:

y = (1/4p)x^2

Comparing this to our equation, we can see that p = -6.6/4 = -1.65. The directrix of a parabola is a line perpendicular to the axis of symmetry and located at a distance of |p| from the focus. Since the axis of symmetry is the x-axis, the equation of the directrix is:

y = 1.65

However, since the question asks for the equation of the directrix in terms of x, we can rewrite this as:

x = 0

Therefore, the answer is (C) x = 6.

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The remainder when f(x)=-6x^23+x^11-x^6+2x is divided by x+1 is -7.

Explanation: In this question, we can solve the problem by using the Remainder Theorem. The remainder theorem states that when we divide a polynomial f(x) by x−a then we get a remainder equal to f(a). So, here we can take a=−1 and find the remainder of f(x).

Here is the given polynomial,

()=−6^23+^11−^6+2

We are asked to find the remainder when f(x) is divided by x+1. Using the remainder theorem, we can find the remainder of f(x) by evaluating f(−1).

(−1)=−6(−1)^23+(−1)^11−(−1)^6+2(−1)=6+1+1−2=6

Now, we have the remainder as 6. However, we need the remainder when f(x) is divided by x+1. The relationship between the remainder and the divisor of a polynomial is that when we divide a polynomial f(x) by x−a, we get a remainder of r(x) such that:

()=(−)()+()

where q(x) is the quotient of the division.

So, the question asks us to divide the polynomial f(x) by x+1 and get the remainder. Here is the long division of f(x) by x+1:

The remainder is −7. Therefore, the remainder when f(x) is divided by x+1 is -7.

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Answer: we can't see the images

Step-by-step explanation:

Answer:

Step-by-step explanation:

be can not see the pictures sir do better ni***

Answer:

x = 1 , y = 10

Step-by-step explanation:

Given : y = 8 + 2x

by substitution,

4x + 8 + 2x = 14
6x + 8 = 14
6x = 14 - 8
6x = 6
x = 6/6 = 1


y = 8 + 2x
y = 8 + 2(1)
y= 10

Proof :
if x = 1,

4 (1) + 8 +2 (1) = 14
4 + 8 + 2 = 14
14 = 14

if y = 10 and x = 1

4 ( 1) + 10 = 14
4 + 10 = 14
14 = 14



For both equations, LHS = RHS
Therefore Proved.


hope it helps!

Answer:

2 ounces per person

Step-by-step explanation:

Answer:

  115°

Step-by-step explanation:

You want the measure of angle S opposite angle (4x+5)° in an inscribed quadrilateral in which the other two angles are (5x-2)° and (7x+2)°.

The measure of an inscribed angle is half the measure of the arc it intercepts.

Two opposite angles in an inscribed quadrilateral intercept arcs that total the full circle.  Since the sum of double those angles is 360°, the sum of opposite angles of an inscribed quadrilateral is 180°—they are supplementary.

We can use this to find the value of x:

  (5x -2)° +(7x +2)° = 180°

  12x = 180 . . . . . . simplify

  x = 15 . . . . . . . divide by 12

Now, the angle opposite S can be found to be ...

  (4x +5)° = (4·15 +5)° = 65°

Angle S is the supplement of this:

  S = 180° -65°

  S = 115°

75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.

Actual experiments and sufficient documentation of the occurrence of occurrences serve as the foundation for experimental probability, sometimes referred to as empirical probability. A number of real experiments are carried out in order to ascertain the likelihood of any event. Random experiments are studies that don't have a predetermined outcome. The results of such tests are unpredictable. The chance of random experiments is calculated repeatedly. A trial is a repeating of an experiment that is performed a certain number of times.

Given that, mean of 3.5 minutes and a standard deviation of 1 minute.

Now, for 75% we have:

P(X > x) = 0.75

The z-score is given by:

0.75 = (X - μ) / σ

Substituting the formula we have:

0.75 = (X - 3.5) / 1

0.75 = X - 3.5

X = 0.75 + 3.5 = 4.25.

Hence, 75 % of the college students will take more than 4.25 minutes when trying to find a parking spot in the library parking lot.

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Answer: To find the equation that passes through (4, 8), we need to check which equation contains that point.

Line A has an equation of y = (2/5)x + (194/5). Plugging in x = 4, we get y = (2/5)(4) + (194/5) = 198/5, which is not equal to 8.

Line B has an equation of y = (-5/5)x + 30. Plugging in x = 4, we get y = (-5/5)(4) + 30 = 26, which is not equal to 8.

Line C has an equation of y = (13/13)x - 7. Plugging in x = 4, we get y = (13/13)(4) - 7 = -3, which is not equal to 8.

Line D has an equation of y = (-27/7)x + (491/7). Plugging in x = 4, we get y = (-27/7)(4) + (491/7) = 377/7, which is not equal to 8.

Therefore, none of the given equations has (4, 8) as its solution.

Step-by-step explanation:

Answer:

2.5 oz each

Step-by-step explanation:

2 boys and 2 girls

10 divided by 2 is 5, 5 is not an even number.
there would be 2 left after our calculation.
meaning that 2 in half's (hence .5)  is 4 so each child would get 2.5 oz of paint.

Hope this helps, thanks :)

Answer: 2 1/2

Step-by-step explanation:

Answer:  B

Step-by-step explanation:

Answer:

The length of line segment CD is 10.3 units (rounded to 2 decimal places).

Step-by-step explanation:

To find the length of line segment CD, we need to use the distance formula, which is:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

Here, (x1, y1) = (1, -5) and (x2, y2) = (6, 4).

So, substituting these values in the distance formula, we get:

Distance = √[(6 - 1)^2 + (4 - (-5))^2]

= √[5^2 + 9^2]

= √(25 + 81)

= √106

≈ 10.3 (rounded to 2 decimal places)

Therefore, the length of line segment CD is 10.3 units (rounded to 2 decimal places).

Hope this helps!

Answer:

x = 48

Step-by-step explanation:

given a line parallel to a side of a triangle and it intersects the other two sides, it divides those sides proportionally, that is

[tex]\frac{x}{18}[/tex] = [tex]\frac{56}{21}[/tex] ( cross- multiply )

21x = 18 × 56 = 1008 ( divide both sides by 21 )

x = 48

Angle between vector a and vector b is 0 degrees or 180 degrees.

What is vector?

A vector is a quantity that not only indicates magnitude but also indicates how an object is moving or where it is in relation to another point or item. Euclidean vector, geometric vector, and spatial vector are other names for it.

In mathematics, a vector's magnitude is defined as the length of a segment of a directed line, and the vector's direction is indicated by the angle at which the vector is inclined.

What is scalar quantity?

Physical quantities with merely magnitude and no direction are referred to as scalar quantities. These physical quantities can be explained just by their numerical value without any further guidance. These physical values can be added according to the basic algebraic rules, and in this case, only their magnitudes are added.

GIVEN:

If vector a is equal to k (scalar quantity)times vector b.

then vector a and vector b are parallel to each other.

The angle between two parallel vectors is 0 degrees or 180 degrees.

So, the angle between vector a and vector b is

0 degrees or 180 degrees.

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Answer:

1/2 of the pool is filled, and in the second situation, the entire pool is filled.

Step-by-step explanation:

Let's start by finding the hourly filling rate of each pump. The first pump can fill the pool in 4 hours, so its hourly rate is 1/4 of the pool. The second pump can fill the pool in 6 hours, so its hourly rate is 1/6 of the pool.

For the first situation, the first pump works for 2 hours, so it fills 2/4 or 1/2 of the pool. The second pump does not work in this situation, so it fills 0 of the pool. Therefore, the total amount of the pool filled is 1/2.

For the second situation, the first pump works for 2 hours and fills 1/2 of the pool. The second pump works for 3 hours and fills 3/6 or 1/2 of the pool. Therefore, the total amount of the pool filled is 1/2 + 1/2 = 1.

So, in the first situation, 1/2 of the pool is filled, and in the second situation, the entire pool is filled.

Answer:

429

Step-by-step explanation:

Answer: 104

Step-by-step explanation:

If .6 or 60% of the animals in the shelter are dogs, then we can multiply .6 by 260 to get how many are dogs.

.6 times 260 is 156.

260-156=104.

Answer:

[tex](250*50-102)+152[\tex]

The correct mean of the 50 observations is 249.96.

To find the correct mean, we need to adjust the value that was wrongly copied. The difference between 152 and 102 is 50, so the corrected total of the 50 observations would be:

Corrected total = (original total - 102) + 152

= [tex](250*50-102)+152[/tex]

= [tex]12498[/tex]

Therefore, the correct mean of the 50 observations is:

Correct mean = Corrected total / Number of observations

= [tex]12498 / 50[/tex]

= 249.96

Hence, the correct mean of the 50 observations is 249.96.

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A two-way relative frequency table, in general, is an effective instrument for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and conduct methodical hypothesis testing.

A tool used to display the connection between two sets of paired data is a two-way relative frequency table, which arranges the data in rows and columns. The frequency of each combination is indicated in the chart, which can also be used to determine its relative frequency, which is calculated as the frequency of the combination divided by the total number of observations.

The benefit of using a two-way relative frequency table to illustrate relationships between pairs of paired data is that it gives a more comprehensive image of the data and the interrelationships between the variables. More specifically, it enables us to:

Finding patterns and trends is simple thanks to the table's presentation of the data. We can see which combinations are more or less prevalent than others by examining the relative frequencies of each set of values, and we can spot patterns in the data that might not be obvious otherwise.

Calculate conditional probabilities: Conditional probabilities are the likelihoods of one event given the occurrence of another event, and they can be determined using the chart. We can determine the likelihood that a smoker is male or female and the likelihood that a non-smoker is male or female, for instance, if we have a two-way table illustrating the connection between gender and smoking status.

Testing hypothesis: The table can be used to evaluate theories about how the variables are related to one another. A chi-square test, for instance, can be used to determine whether gender and smoking status are significantly associated.

In general, a two-way relative frequency table is an effective tool for analysing paired data because it offers a succinct and clear summary of the relationship between the variables, enabling us to spot patterns and test theories in a methodical manner.

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Answer:

The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.

B is correct.

Step-by-step explanation:

Here we have two situation of system of models.

[tex]\text{The height (h) of a falling volleyball as function of time (t):h}(t)=14-16t^2[/tex]

[tex]\text{The height (h) of the hands of a player as function of time (t):h}(t)=7-24t-16t^2[/tex]

We need to find the height of ball above the ground at the instant the player begins jump.

At t=0, player begins jump.

We put t=0 into [tex]h(t)=7+24t-16t^2[/tex]

Height of player hand at t=0 , h=7 feet.

Now we will set t=0 for first model.  

[tex]h(0)=14-16\times0^2 \ = > 14[/tex]

Thus, The volleyball is 14 feet above the ground at the instant the pl;ayer begins her jump.

B is correct.

Answer: B

Step-by-step explanation:

EDGE 2023

Answer:

the answer to ur question is: 1218816

So, if we have the original coordinates of point G, we can swap the x and y values and negate the new y-value to find the coordinates of point G after a 90° counterclockwise rotation about the origin.

To perform a 90° counterclockwise rotation about the origin, we can use the following transformation:

x' = -y

y' = x

This means that the new x-coordinate (x') will be the negative of the original y-coordinate (y), and the new y-coordinate (y') will be the original x-coordinate (x).

If we have the coordinates of point G, we can apply this transformation to find the new coordinates after the rotation.

Let's say that the coordinates of point G are (x, y). Then, the new coordinates (x', y') after the rotation will be:

x' = -y

y' = x

So, the new coordinates will be (-y, x). Therefore, if we want to find the new coordinates after a 90° counterclockwise rotation, we just need to swap the x and y values and negate the new y-value. This gives us the following coordinates for point G after the rotation:

G' = (-y, x)

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If you spend a $5 per turn on a fair game to win $15 for each win and you lose the first round but win the next two rounds, then the net payoff is $15

Since you spend $5 per turn and play three rounds, your total cost is $5 x 3 = $15.

If you win a game, you receive $15, so winning two games will give you $15 x 2 = $30.

However, since you lost the first round, you only won two out of three rounds. Therefore, your net payoff is:

= $30 - $15

Subtract the numbers

= $15

Therefore, your net payoff is $15

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Therefore , the solution of the given problem of probability comes out to be the medium addition because it has the greatest expected utility (0.72).

The primary goal of the structures within a methodology expression known as criteria is to provide an indication of the probability that the assertion is true or that a specific event will occur. Any number between zero and one, at which 0 is frequently indicated as a possibility and 1 has frequently used to denote a level of confidence, can be used to represent chance. The chance that a specific event will occur is displayed in a probability diagram.

Here,

The following formula can be used to determine each option's anticipated financial value:

=> EMV of big addition =  (0.4 * $100,000) plus (0.6 * -$40,000) for a total of $16,000.

=>  EMV of the middle addition is

= (0.4 * $40,000) plus (0.6 * -$10,000) for a total of $14,000.

=>  EMV of a minor addition =  (0.4 * 10,000) plus (0.6 * 5,000), which equals $6,000

The large addition should be chosen by the physicians as it has the greatest expected financial value of $16,000.

dividing each outcome's usefulness value by its likelihood, then adding the results:

=> (0.4 * 1.0) + (0.6 * 0.0) = 0.4 is the EU of the big addition.

=> (0.4 * 0.9) + (0.6 * 0.6) = 0.72 is the EU of medium addition.

Smaller EU =  (0.4 * 0.5) +  (0.6 * 0.6) = 0.58

The doctors should choose the medium addition because it has the greatest expected utility (0.72), according to expected utility theory.

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The number of bald eagles in the state in the winter of 1999 is 273.909, where The number of bald eagles in a state during the winters from 1996 to 2002 can be modeled by the quartic function.

by the given information the equation is

[tex]f(x) = -3.439(x)^4 + 35.952(x)^3 - 99.139(x)^2 + 41.541(x) + 178.192[/tex]

where x = number of years since 1996

The given quartic function must be changed to x = 3 in order to determine the number of bald eagles in the state during the winter of 1999:

[tex]f(3) = -3.439(3)^4 + 35.952(3)^3 - 99.139(3)^2 + 41.541(3) + 178.192[/tex]

When we condense this expression, we get:

f(3) = -3.439(81) + 35.952(27) - 99.139(9) + 41.541(3) + 178.192

f(3) = -1107.759 + 970.104 - 892.251 + 124.623 + 178.192

f(3) = 273.909

Hence, in the winter of 1999, there were roughly 273.909 bald eagles in the state.

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