In a group of 150 people, 39 of them wear glasses. What is the probability of randomly selecting a person who does not wear glasses?

A. 111/150
B. 39/111
C. 111/189
D. 189/150
E. 39/150

we know that

The sum of the internal angles in the triangle must be  degrees

see the attached figure with letters to better understand the problem

Step

Find the measure of the angle x

In the triangle ABC

solve for x

therefore

the answer Part a)  is

the measure of angle x is

Step

Find the measure of the angle z

we know that

--------> by supplementary angles

substitute the value of x

therefore

the answer Part b)  is

the measure of angle z is

Step

Find the measure of the angle y

In the triangle ACD

solve for y

therefore

the answer Part c)  is

the measure of angle y is

Continuous variables must lie between a clearly defined interval that is true.

Continuous variables could take any value that is limited within a specified range. These variables are not limited to certain values only as can have both positive and negative values. They can usually cover a continuous set of values.

Unlike discrete variables, continuous variables are often associated with measurements and observations that can be further subdivided. For example; temperature, length, and weight. This concept of continuity states that there exists an infinite number of intermediate values. This property makes continuous variables best suitable for statistical analysis.

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The remaining keys are hashed and placed in the table using linear probing until all keys are placed.

The hash table that results from using the hash function h(k) = k mod 13 to hash the keys 2, 7, 4, 41, 15, 32, 25, 11, and 30, assuming collisions are handled by linear probing:
Index       Key
0      
1      
2             2
3             4
4             30
5             41
6             15
7             7
8             25
9             11
10    
11    
12            32
To fill in the table, we apply the hash function to each key and then check whether that index is already occupied.

If it is, we move to the next index and continue until we find an empty spot. In this case, we start with the key 2, which hashes to index 2.

This index is empty, so we insert the key there.

Next, we hash the key 7, which also goes to index 2.

Since that spot is already occupied, we move to the next index (3) and find that it's empty, so we insert 7 there.

We continue in this way for each key, resolving collisions by linear probing.
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Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

Answer: i don't really know how you want me to solve it

Use the formula x =−b/2a (b over 2a)

(1 second

to find the maximum and minimum.

6t^(2 )+ 12t + 30

which should give you this answer

6(t2+2t+5)

what i did was factor 6 out of 6t^(2 )+ 12t + 30

Answer: 1 second

Step-by-step explanation:

There are two ways to solve this:

1. Graph it. You will see an inverted parabola with time (in seconds) on the x axis and height (in feet) on the y axis. The top of the parabola is point (1, 36) which means at 1 second the ball will be at 36 feet. Since the balcony is at 30 feet, the ball only goes up 6 feet before it changes direction toward the ground.

2. Take the first derivative and set it equal to zero. The first derivative will give us the slope, or rate of change, of the parabola for any point t (on the x-axis). The rate of change when the ball reaches its maximum height will be zero, when it goes from a positive value (going up) to a negative value (going down).

-6t^2 + 12t + 30

First derivative = h'(t) = -12t + 12

Set h'(t) to zero: 0 = -12t + 12

t = 1 second

Either way works. Put 1 second into the original equation and it will return 36 feet. That's 36 feet aboove ground. 6 feet above the balcony from which it is thrown. You can throw better then that, I assume.

The corresponding CDF is:F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6.

The value of the constant A can be obtained by using the normalization condition that the integral of the PDF function over the entire possible range of X must be equal to 1. So, we can write the following integral to solve for

A:(∫f(x) dx) from 0 to π/2=∫A sin(x) dx= A [-cos(x)] evaluated at π/2 and 0= -A(cos(π/2) - cos(0))= A (1 - 0) =1. Therefore, the value of the constant A is 1. b. The CDF of the given random variable X is given as follows:

F(x)=∫f(x)dx from 0 to x, for 0 < x < π/2=∫sin(x) dx from 0 to x= [-cos(x)] evaluated at x and 0= -cos(x) - (-cos(0))= 1 - cos(x) for 0 < x < π/2=1 for x ≥ π/2. So, the corresponding CDF is as follows:

F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X can be obtained using the following formula:

E(X) = ∫xf(x)dx from 0 to π/2=∫x sin(x) dx from 0 to π/2= [-x cos(x)] evaluated at π/2 and 0 - ∫-cos(x) dx from 0 to π/2= -0 + cos(0) - ([-cos(x)] evaluated at π/2 and 0)= 0 + 1 - (-1)= 2. So, the expected value of the given random variable X is 2.

d. The variance of the given random variable X can be obtained using the following formula:

Var(X) = E(X²) - [E(X)]²=∫x² f(x)dx from 0 to π/2 - [E(X)]²=∫x² sin(x)dx from 0 to π/2 - (2)²= [-x² cos(x)] evaluated at π/2 and 0 + ∫2x cos(x)dx from 0 to π/2 - 4= -0 + π²/4 - 4 + (2 sin(x) + 2x cos(x)) evaluated at π/2 and 0= π²/4 - 2 - 4 + 2 + 2π= π²/4 + 2π - 6. So, the variance of the given random variable X is π²/4 + 2π - 6

Hence, the answer is: a. The value of the constant A is 1.b. The corresponding CDF is : F(x) = 1 - cos(x) for 0 < x < π/2F(x) = 1 for x ≥ π/2c. The expected value or mean of the given random variable X is 2. d. The variance of the given random variable X is π²/4 + 2π - 6

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Answer:

The solution to the recurrence relation is given by an = 2^(n+1) - 1.

Step-by-step explanation:

(a) To solve the recurrence relation an = an-2 + 4, with initial conditions a1 = 3 and a2 = 5, we'll consider two cases: one for when n is even and one for when n is odd.

For n even:

Substituting n = 2k (where k is a positive integer) into the recurrence relation, we get:

a2k = a2k-2 + 4

Now let's write out a few terms to observe the pattern:

a2 = a0 + 4

a4 = a2 + 4

a6 = a4 + 4

...

We notice that a2k = a0 + 4k for even values of k.

Using the initial condition a2 = 5, we can find a0:

a2 = a0 + 4(1)

5 = a0 + 4

a0 = 1

Therefore, for even values of n, the solution is given by an = 1 + 4k.

For n odd:

Substituting n = 2k + 1 (where k is a non-negative integer) into the recurrence relation, we get:

a2k+1 = a2k-1 + 4

Again, let's write out a few terms to observe the pattern:

a3 = a1 + 4

a5 = a3 + 4

a7 = a5 + 4

...

We see that a2k+1 = a1 + 4k for odd values of k.

Using the initial condition a1 = 3, we find:

a3 = a1 + 4(1)

a3 = 3 + 4

a3 = 7

Therefore, for odd values of n, the solution is given by an = 3 + 4k.

(b) To solve the recurrence relation an = 2an-1 + 1, with initial condition a1 = 1, we'll find a general expression for an.

Let's write out a few terms to observe the pattern:

a2 = 2a1 + 1

a3 = 2a2 + 1

a4 = 2a3 + 1

...

We can see that each term is one more than twice the previous term.

By substituting repeatedly, we can express an in terms of a1:

an = 2(2(2(...2(a1) + 1)...)) + 1

= 2^n * a1 + (2^n - 1)

Using the initial condition a1 = 1, we have:

an = 2^n * 1 + (2^n - 1)

= 2^n + 2^n - 1

= 2 * 2^n - 1

Therefore, the solution to the recurrence relation is given by an = 2^(n+1) - 1.

The area of the trapezoid that is given in the image below is calculated as: 62 square centimeters.

A trapezoid, like the one given in the image above, is a four-sided flat shape with one pair of parallel sides, and the parallel sides are called bases, while the other two sides are called legs. The area of trapezoid is given as:

A = 1/2 * (sum of the bases) * height

Given the following:

sum of bases = 10.4 + 7.9 + 6.5 = 24.8 cm

Height of trapezoid = 5 cm

Plug in the values:

Area of trapezoid (A) = 1/2 * 24.8 * 5

Area of trapezoid (A) = 62 square centimeters.

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The Surface area are shown below.

The total area of an object's external facing surfaces is its surface area. The base, top, and lateral surfaces (sides) of the object's surface are added together to get the object's overall surface area.

Given:

1. The height of the cone shape, h = 84 inches

radius = 8 inches

The cost per cubic inch is $2.25.

The cost of nickel for the sculpture is given by

= 2.25 x 1/3πr²h

= 2.25 x 1/3 x 3.14 x 8 x 8 x 84

= $12660.48.

2. The measure of sides are

A = 12

B = 10

C= 5

D= 13

So, the Lateral Surface Area

= ( 12 + 13 + 5) x 10

= 30 x 10

= 300 cm²

and, the total surface Area

= Area of two triangles + Area of rectangle

= 2 x 1/2 x 5 x 12 + 300

= 60+ 300

= 360 cm²

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Answer:

60cm and 100cm

Step-by-step explanation:

12 parts in total

240/12 is 20

each part is 20

3x20 is 60 and 5x20 is 100

Answer:

Mean =          15.83 hours

Median =  17 hours

Step-by-step explanation:

The first step to follow when dealing with data distributions is to arrange the data in either an ascending or descending order.

Once this is done, we have the responses as

responses: 9. 14, 16, 18, 19, 19

The mean of the distribution can be obtained by dividing the total sum of the values, by the number of respondents.

this is \(9 +14 + 19 + 18 + 16 + 14 + 19/ 6= 95/6 = 15.83\)

The mean of the distribution is 15.83 hours

The median is obtained by picking out the middle number of the distribution.  However, our distribution is even, and hence has two middle numbers. To solve this , we simply add the two numbers and divide by 2

= (16 + 18 )/2 = 34/2 = 17

Answer:

(a) The average television hours for the six students in the previous week    was 15.83 Hours.

(b) The median number of hours would be 17 Hours

Step-by-step explanation:

Mean

The mean of a group of numbers is the average of the numbers. The mean can be gotten with the expression in equation 1.

Mean = Σx / n ...............1

Where Σx is the sum of the numbers

n is the number of values

Substituting our values into equation 1 we have;

Mean = (19+9+18+ 16+14+19) ÷ 6

Mean = 95 ÷ 6

= 15.83 Hours

Therefore the average television hours for the six students in the previous week were 15.83 Hours.

The median of a group of numbers is the middle term of the numbers when arranged in ascending or descending order.

Given the television hours of the six students, we have;

19, 9, 18, 16, 14, 19

We arrange the numbers in ascending order from the smallest to the biggest;

9, 14, 16, 18, 19, 19

Since the number of value is even the median would be obtained by finding the mean of the two middle terms.

From our arranged data, 9, 14, 16, 18, 19, 19

the two middle numbers are 16, 18

Therefore the mean would be

(16+18) /2

=34/2

= 17 hours

Thus the median number of hours would be 17 Hours

Regular hexagon ABCDEF is inscribed in a circle with center H, the image of segment BC after 120 degree clockwise rotation about point H is the segment joining the points B' and C', which has endpoints (-0.5r\(\sqrt{3\), -0.5r) and (-0.5r, -0.5r).

Since the hexagon is inscribed in a circle with center H, we can conclude that H is also the center of the circle passing through vertices B, C, and D. Therefore, the circle passing through B, C, and D is also a 120 degree clockwise rotation of the circle passing through A, B, and C.

To find the image of segment BC after a 120 degree clockwise rotation about point H, we need to find the coordinates of B and C relative to H, and then apply a 120 degree rotation matrix to these coordinates.

Let the radius of the circle be r, and let the coordinates of H be (0,0). Then the coordinates of B and C are:

B: (r cos(60), r sin(60))

C: (r cos(0), r sin(0)) = (r, 0)

To apply a 120 degree clockwise rotation matrix, we can use the following matrix:

[ cos(-120) -sin(-120) ]

[ sin(-120) cos(-120) ]

Simplifying, we get:

[ cos(120) sin(120) ]

[ -sin(120) cos(120) ]

Applying this matrix to the coordinates of B and C, we get:

B': [ cos(120) sin(120) ][ r cos(60) ] = [ -0.5r \(\sqrt{3}\)]

[ -sin(120) cos(120) ][ r sin(60) ] [ -0.5r ]

C': [ cos(120) sin(120) ][ r ] = [ -0.5r ]

[ -sin(120) cos(120) ][ 0 ] [ -0.5r ]

Therefore, the image of segment BC after a 120 degree clockwise rotation about point H is the segment joining points B' and C', which has endpoints (-0.5r\(\sqrt{3}\), -0.5r) and (-0.5r, -0.5r), respectively.

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The absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

An absolute value function of vertex (h,k) is defined as follows:

y = a|x - h| + k.

In which a is the leading coefficient.

The coordinates of the vertex for this problem are given as follows:

(1, -2).

As the slope of the line is of 1, the leading coefficient is given as follows:

a = 1.

Hence the absolute value function for this problem is given as follows:

g(x) = |x - 1| - 2.

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The only real solutions to the system of equations are (x, y, z) = (k, k, k) and (x, y, z) = (k, -k, -k) for any real number k.

x² - y = z²

y² - z = x²

z² - x = y²

We can start by adding the first and second equations, third and first equations, and second and third equations to get:

x² + y² - z = x² - y + y² - z = z² - x + x² - y²

By rearranging terms, we get:

y² - y = z² - z

x² - x = y² - y

z² - z = x² - x

We can factor out (y - 1) from the first equation to get:

(y - 1)(y + 1) = (z - 1)(z + 1)

Similarly, we can factor out (x - 1) from the second equation and (z - 1) from the third equation to get:

(y - 1) = (x - 1)(y + 1)

(x - 1) = (z - 1)(x + 1)

(z - 1) = (y - 1)(z + 1)

we get:

(x-1)(y+1)(z+1) = (y-1)(z-1)(x+1)

If any of the factors on either side is equal to zero, then either x, y, or z equals 1 and one of the original equations will be violated. Therefore, we can assume that none of the factors are equal to zero and divide both sides by (x-1)(y-1)(z-1) to get:

(x+1)/(x-1) = (y+1)/(y-1) = (z+1)/(z-1)

This means that the three terms are equal and we can equate any two terms to get:

x + 1 = y + 1, or x + 1 = z + 1

Simplifying, we get:

x = y, or x = z

y = z, or z = y

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The statement "the coefficient of determination measures the variation in the dependent variable that is explained by the regression model" is true because coefficient of determination, or R-squared, measures the proportion of variance in the dependent variable that is explained by the independent variables in a regression model.

The coefficient of determination, or R-squared, is a statistical measure that evaluates the goodness of fit of a regression model. It quantifies the amount of variance in the dependent variable that can be explained by the independent variables in the model. R-squared ranges from 0 to 1, where a value of 0 means that none of the variation in the dependent variable is explained by the model, while a value of 1 indicates that all the variation is explained.

Therefore, R-squared is useful in assessing the predictive power of a model, and higher values are generally preferred. However, it is important to note that R-squared alone does not guarantee a good model, and other factors such as model assumptions and outliers should also be considered.

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Since the equation are the same no matter the arrangement, the value of -4y+x for the given equation to be true is 6.

Linear equation are equations that has a leading degree of 1.

Given the linear equation below:

x-4y=6

This expression can also be expressed as:

-4y + x = 6

Since according to the commutative law, x-4y = -4y+x, hence the value of -4y+x for the given equation to be true is 6.

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Lines have a larger m value, that is, m > 1 have steeper slope and lines having an m value between 0 and 1, usually in the form of a fraction have a flatter slope .

Slope is the rate of change in the dependent variable with respect to the independent variable.

For an equation of line of the type - y= mx +c , the slope is given by the m value.

Now, if the value of m > 1 like m=1,2,3, ... , the lines have a steeper slope and have a steep nature.

Similarly, if the value of m < 1 i.e. 0 < m < 1 like m=1/2,2/3, ... fractional values,  the lines have a flatter slope and do not have a steep nature.

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Minimum: 4, Q1: 22, Median: 31, Q3: 50, Maximum: 62. Interquartile Range (IQR): 28.

The interquartile range (IQR) is calculated as the difference between the third quartile (Q3) and the first quartile (Q1), which in this case is 50 - 22 = 28.

To find the minimum, we identify the smallest value in the data set, which is 4. The first quartile (Q1) represents the median of the lower half of the data. To determine Q1, we arrange the data in ascending order and find the value that divides the lower half. In this case, Q1 is 22. The median is the middle value of the data set, which is 31. Q3 represents the median of the upper half of the data, so we find the value that divides the upper half, which is 50. Finally, the maximum is the largest value in the data set, which is 62. The interquartile range is calculated as the difference between Q3 and Q1, giving us a value of 28.

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Answer:

110000=p(1+0.019)^168

23.62p=110000

p=4660

credit: sqdancefan

Answer:

84330

Step-by-step explanation:

The compound interest formula gives the value of an investment.

 A = P(1 +r/n)^(nt)

where principal P is invested at annual rate r compounded n times per year for t years. Using your given values, we can solve for P.

 110,000 = P(1 +0.019/12)^(12·14)

 P = 110,000/(1 +0.019/12)^(12·14) ≈ 110,000/1.00158333...^168

 P ≈ 110,000/1.30446

 P ≈ 84326.04 ≈ 84,330 . . . . dollars

Answer: the answer the D. 3

Answer:

Step-by-step explanation:

Answer: C

Step-by-step explanation:

The red graph is the result of reflecting the graph of y=f(x) across the x-axis and then translating 1 unit to the right.

Answer:

Number of moles = 41.67 (Approx)

Number of carbon atom = 250.97 x 10²³ (Approx)

Step-by-step explanation:

Given:

Amount of carbon = 500 g

Find:

Number of moles

Number of carbon atom

Computation:

Number of moles = 500 / Atomic number of weight

Number of moles = 500 / 12

Number of moles = 41.67 (Approx)

Number of carbon atom = Number of moles x Avogadro number

Number of carbon atom = 41.67 x 6.023 x 10²³

Number of carbon atom = 250.97 x 10²³ (Approx)

Answer:

4,-4 I think

Step-by-step explanation:

My brain is off right now so might be wrong

The inequality that represents the the possible numbers of x pairs of socks you can buy when you buy 2 pairs of sneakers, using a system of equations, is of:

y ≤ 7.

A system of equations is a set of equations involving multiple variables that are related, and then operations are made to solve these equations and identify the numeric value of each variable in the context of the problem from which the system was built.

For this problem, the variables are given as follows:

You have a $250 card to use at a sporting goods store. Each pair of sneakers is worth $80 and a pair of socks costs $12, hence the inequality regarding the total spending is:

80x + 12y ≤ 250.

When two pairs of sneakers are bought, we have that:

x = 2.

Hence the inequality regarding how many pairs of socks can be bought is:

80(2) + 12y ≤ 250.

160 + 12y ≤ 250.

12y ≤ 90

y ≤ 90/12

y ≤ 7. (rounded down, as you can buy 7 pairs of socks but not 8).

The cost of a pair of socks is of $12.

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After 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.

To find the concentration of sugar in the tank after 12 minutes, we need to consider the amount of sugar and water added during that time period.

The tank initially contains 100 gallons of water with 5 pounds of sugar mixed in. Over the course of 12 minutes, the tap pours in 10 gallons per minute of water and 1 pound per minute of sugar.

After 12 minutes, the total amount of water added is 10 gallons/minute * 12 minutes = 120 gallons. The total amount of sugar added is 1 pound/minute * 12 minutes = 12 pounds.

Therefore, the final volume of water in the tank is 100 gallons (initial) + 120 gallons (added) = 220 gallons.

To find the concentration of sugar in the tank after 12 minutes, we divide the total amount of sugar (5 pounds initial + 12 pounds added) by the final volume of water (220 gallons):

Concentration of sugar = (Total amount of sugar) / (Final volume of water)

= (5 pounds + 12 pounds) / 220 gallons

= 17 pounds / 220 gallons

Simplifying the expression, we get:

Concentration of sugar = 0.0773 pounds/gallon

Therefore, after 12 minutes, the concentration of sugar in the tank is approximately 0.0773 pounds per gallon.

It's important to note that in this scenario, we assume perfect mixing of the sugar and water in the tank. Also, the concentration of sugar may vary over time as more water and sugar are added.

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Answer:

b is the answer

Step-by-step explanation:

Answer:

the answer is B

Step-by-step explanation:

The inequality is given by the equation x + 96 ≤ 149

An inequality is an expression that shows the non equal comparison of two or more numbers and variables.

Let x represent the number of passengers that can be added to the plane.  Since the plane can take 149 passengers, hence:

x + 96 ≤ 149

The inequality is given by the equation x + 96 ≤ 149

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