10 points!!
Please help! Show explanation.

The probability that either event will occur to the nearest hundredth would be = 0.9

To calculate the probability of the given events, the sample space should be generated and followed by the probability of each sample space generated.

That is;

P(A) = 14/18 = 0.78

P(B) = 10/18 = 0.56

P(A and B) = 0.78×0.56 = 0.4368

Therefore ;

P(A or B)= 0.78+0.56-0.4368

= 1.34- 0.4368

= 0.9

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The histogram is solved and the data is bimodal, with a maximum range of 24. This means that the tide was frequently between 6 to 10 or 16 and 20 feet.

Given data ,

Let the number of observations of each interval is:

1 to 5: 2 observations.

6 to 10: 5 observations.

11 to 15: 2 observations.

16 to 20: 6 observations.

21 to 25: 1 observations.

Let the maximum range be represented as M

And , there are two similarly high bins for the histogram , hence the distribution can be said to be bimodal, with maximum range given as follows

M = 25 - 5

M = 21 - 1

M = 20

Hence , the histogram is solved

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Answer:

w=0,

w=-7

Step-by-step explanation:

Answer:

Step 3: Divide both sides of the equation in Step 2 by a to get x² + (b/a)x = -c/a.

Answer: 2,556 seats

Step-by-step explanation

18 x 142 =2,556 seats

4.5 radians when rounded off to the nearest tenth approximates a degree angle of 257.83.

To turn an angle from radians into degrees, is achieved relying on the following established formula:

Angle in Degrees = Angle in Radians * (180 / π)

where

π (pi) is approximately equal to 3.14159.

For conversion of 4.5 radians we have  

Angle in Degrees = Angle in Radians * (180 / π)

substituting to the above formula

Angle in Degrees = 4.5 * (180 / π)

use a calculator to get the value of pi:

Angle in Degrees = 4.5 * (180 / π)

Angle in Degrees ≈ 257.821 (rounded two decimal places)

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Answer:28

Step-by-step explanation:

•C= 2(3.14 x r)

•C= 2(3.14 x4.5)

•C=2(14.13)

•C=28.26

The 95% confidence interval for the mean is [3.23, 8.76].

The confidence of interval of the mean is calculated as follows;

Confidence interval = σ ± (t-value  x   μ)

where;

The standard error is calculated as follows:

μ = std / √n

μ = 5 / √15

μ = 1.29

Based on this value we will check the distrbution table, for the t-value of 95% confidence;

=  2.145.

Confidence interval = σ ± (t-value  x   μ)

= 6 ± (2.145 x 1.29)

= [3.23, 8.76]

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The requried equivalent fraction for the equivalent fraction to 3 3/4 and 1 2/3, is 45/12, and 20/12.

To find a common denominator for 4 and 3, we can multiply them together to get 12.

So, we can convert 3 3/4 as:

3 3/4 = 12/4 + 3/4 = 15/4

Similarly, we can convert 1 2/3 as:

1 2/3 = 5/3

Therefore, the equivalent fractions for 3 3/4 and 1 2/3 using a common denominator of 12 are:

15/4 = 45/12 and 5/3 = 20/12

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Answer:

37/24

Step-by-step explanation:

You have to find the common denominator.

Step-by-step explanation:

A linear function is a function where we have a constant rate of change.

The equation of a linear function is

[tex]y = mx + b[/tex]

where m is the slope (change in y/change in x)

and b is the y intercept.

Note: Sometimes our variables will different names, but

Slope is just change in dependent variable/change in independent variable.

A linear function has a constant slope throughout.

In this problem,

t is the independent variable

W is the dependent variable

So our point will. be

(t,W)

where t is number of weeks after planted

and W is weight

So the slope would be

Change in W/Change in t.

We know at 3 weeks, the pumpkin weighed 141

So this point is

(3,141)

We know 7 weeks, later, the pumpkin weighed 372 so

(10,372)

A. The weight the pumpkin gain each week is our slope so

[tex] \frac{372 - 141}{7} [/tex]

[tex] \frac{231}{7} = 33[/tex]

So the pumpkin gained 33 pounds each week.

Part 2: Is in slope intercept form,

and we know the slope,33,

[tex]w = 33t + b[/tex]

We don't know what b is.

Let plug in a coordinate pair, and solve for b.

Let's use (3,141)

[tex]141 = 33(3) + b[/tex]

[tex]141 = 99 + b[/tex]

[tex]42 = b[/tex]

So our equation is

[tex]w = 33t + 42[/tex]

Hope this helps

The weight that the pumpkin gained per week can be found to be 33 pounds.

The equation to show the relationship between pumpkin weight and elapsed time is W = 33 t + 42

The weight gained by the pumpkin per week can be found by the formula :

= (Weight gained after 7 more weeks - Weight after 3 weeks ) / 7 weeks

= ( 372 - 141 ) / 4

= 33 pounds

This means the original weight of the pumpkin was:
= 141 - ( 33 x 3 weeks )
= 42 pounds

The equation to show the relationship between pumpkin growth and weeks is therefore:

W = Growth per week x Number of weeks + original weight

W = 33 x + 42

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After 200 years, there will be 47.43 pounds left of the material.

We know that we start with 68 pounds, and after 40 years there are 63.3 pounds left, so we have an exponential decay:

63.3 = 68*(b)^40

Where b defines how it decays, we can solve that equation for b to get:

(63.3/68)^(1/40) = b

0.9982 = b

Then the decay is:

f(x) = 68*(0.9982)^x

The amount left after 200 years will be:

f(200) = 68*(0.9982)^200 = 47.43

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Answer:

1,2, and 4

Step-by-step explanation:

vertical angles theorem, which says that the vertical angles that are formed when two lines intersect are congruent.

The segments AB and CD on item 1 are classified as follows:

Perpendicular.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

The slope of segment AB is given as follows:

m = (3 - 13)/(0 - (-2))

m = -10/2

m = -5.

The slope of segment CB is given as follows:

m = (3 - 0)/(10 - (-5))

m = 3/15

m = 1/5.

The multiplication of these slopes is given as follows:

-5 x 1/5 = -1.

As the multiplication of the slopes is of -1, the segments are perpendicular.

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if A C B, then A n B = A U B is always true

The statement "if A C B, then A n B = A U B" can be rephrased as "if A is a subset of B, then the intersection of A and B is equal to the union of A and B".

Every element of A is also an element of B. Therefore, the intersection of A and B contains all the elements of A.

On the other hand, the union of A and B contains all the elements of A and all the elements of B. Since A is a subset of B, all the elements of A are already included in B, so the union of A and B is just equal to B.

Therefore, we have:

A n B = A (since all the elements of A are in both A and B)

A U B = B (since A is a subset of B)

So A n B = A U B = B, which means that the original statement "if A C B, then A n B = A U B" is true

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A linear equation is an equation in which each term has at max one degree. The table that represents a linear function is Table 1. Thus, the correct option is A.

We have,

A linear equation is an equation in which each term has at max one degree. Linear equation in variable x and y can be written in the form y = mx + c

Linear equation with two variables, when graphed on a cartesian plane with axes of those variables, give a straight line.

For the table to represent a linear function, the function must have a constant slope between any two points.

For the first table, the slope between the first two points is,

m = (7-3)/(2-1) = 4

The slope between the last two points is,

m = (15-11)/(4-3)

Hence, the table that represents a linear function is Table 1. Thus, the correct option is A.

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Answer: If y varies inversely as x, then:

y = k/x

where k is a constant of proportionality. To find k, we can use the initial condition that y = 6 when x = 8:

6 = k/8

Solving for k, we get:

k = 48

Now we can use this value of k to find y when x = 2:

y = 48/2 = 24

Step-by-step explanation:

I'm not 100 percent sure so please only rate after you see if it's right.

ANSWER: $1090

STEP 1:

The volume of one brick is given by multiplying its length, width, and height:

V = (7 1/4) in x 3 in x (2 1/4) in

V = (29/4) in x 3 in x (9/4) in

V = 2187/16 cubic inches

STEP 2:

The cost of one brick is given by multiplying the volume by the cost per cubic inch:

C = (2187/16 cubic inches) x $0.05/in^3

C = $1.09/brick

STEP 3: To find the cost of 1000 bricks, we simply multiply the cost of one brick by 1000:

Cost of 1000 bricks = 1000 x $1.09/brick

Cost of 1000 bricks = $1090

Therefore, the cost of 1000 bricks is $1090, rounded to the nearest cent.

Answer:

144ft^3

Step-by-step explanation:

To start, we have your formula: [tex]V=\frac{1}{2} (bh) (l)[/tex]
b = base length of the triangle.
h = height of the triangle.
l = length of the prism

Fill in for each of those values:
[tex]V = \frac{1}{2} (6x6)(8)[/tex]

[tex]V=\frac{1}{2} (36)(8)[/tex]

[tex]V=(18)(8)[/tex]

[tex]V=144[/tex]

Your answer, because it is a 3D shape, should be cubed, so:
[tex]V=144ft^{3}[/tex]

The recursive formula is 5/6

You should know that a recursive formula is an equation used to describe a sequence in which terms are defined using one or more previous terms along with an initial condition.

The given parameters are

aₓ = a(n-1) + 2

Where aₓ = 2aₓ₋1

= 2*5(₃₋₁) = 5(3-1) + 2

= 10₂ = 10 + 2

Taking the log of both sides

Log₂10 - Log12 = 0

Dividing by 10 we have

10/12 = 5/6

therefore the recursive formula is  5/6

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y = -x + 7

Slope-intercept form can give us valuable information about a graph.

Point-Slope Form

There are multiple ways to solve this problem; I am simply showing the way I use most often.

We can plug the known information into point-slope form and then simplify the equation into slope-intercept form. Point-slope is written as:

In this equation, y₁ and x₁ are the y and x values we are given and m is the slope. So, plug in the information.

Then, simplify the right side by distributing the -1.

Next, add 4 to both sides.

The equation in slope-intercept form is y = -x + 7.

Slope-intercept Form

Slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. So, our equation, y = -x + 7, shows that the slope is -1 and the y-intercept is 7. Using this information, we can compare the line to other linear functions or graph the line if needed.

Answer:

y = -x + 7 is your correct answer

Step-by-step explanation:

The ratio of science teachers to math teachers is 1:5.

The ratio of science teachers to math teachers can be found by dividing the number of science teachers by the number of math teachers.

The ratio of science teachers to math teachers = (Number of science teachers) / (Number of math teachers)

Here, the number of science teachers is 9 and the number of math teachers is 45.

The ratio of science teachers to math teachers = 9 / 45

Simplifying this ratio by dividing both the numerator and denominator by 9, we get:

The ratio of science teachers to math teachers = 1 / 5

Therefore, the ratio of science teachers to math teachers is 1:5.

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The number of children ticket sold is 90 while the number of adult ticket sold is 200.

Math land theatre charges $5.00 for children's tickets and $9.00 for adult tickets. One night the theatre sold 290 tickets and took in $2250.

Therefore, let's find the number of each type of ticket sold as follows:

Hence,

Let

Therefore, using equation,

c + a = 290

5c + 9a = 2250

Multiply equation(i) by 5

5c + 5a = 1450

5c + 9a = 2250

subtract the equation

4a = 800

divide both sides by 4

a = 800 / 4

a = 200

Therefore, let's find c

c = 290 - 200

c = 90

Hence,

number of children's ticket = 90

number of adult tickets = 200

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The numeric value of the function f(x) at x = 5 is given as follows:

f(5) = 74.75.

The second derivative of the function f(x) is given as follows:

f''(x) = 2x + 6sin(x).

Integrating the second derivative, the first derivative of the function is given as follows:

f'(x) = x² - 6cos(x) + K.

When x = 0, y' = 2, hence the constant K is given as follows:

2 = -6 + K

K = 8.

Hence:

f'(x) = x² - 6cos(x) + 8.

Integrating the first derivative, the function is given as follows:

f(x) = x³/3 - 6sin(x) + 8x + K.

When x = 0, y = 4, hence the constant K is given as follows:

K = 4.

Then:

f(x) = x³/3 - 6sin(x) + 8x + 4.

The numeric value at x = 5 is given as follows:

f(5) = 5³/5 - 6sin(5) + 8(5) + 4

f(5) = 74.75.

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Answer:

By using the formula down below you can find the area of a trapezoid

A = [tex]\frac{a+b}{2}[/tex]h

↑ Area

A = Base

B = Base

H = Height

Example.

A = 12

B = 4

H = 2

First “ A “ + “ B “ =

12 + 4 = 16

16 / 2 = 8

8 x “ h “

8 x 2 = 16

Answer is 16

Thus the answer is, above

So if you look that up then it will show you how to find the area of a trapizoid

Answer:

The silver will cost $1908.5125 to make one solid sphere

Step-by-step explanation:

The formula for the volume of a sphere is:

V = (4/3)πr^3

where r is the radius of the sphere.

Substituting the given value for the radius:

V = (4/3)π(4.5 cm)^3

= (4/3)(3.14)(91.125 cm^3)

= 381.7025 cm^3

The cost of the silver can be calculated by multiplying the volume by the cost per cm^3:

Cost = 381.7025 cm^3 × $5.00/cm^3

= $1908.5125

The area under the curve (since the function of the parabolic expression is y = x - x²) is 1/6 square units.

A parabolic function has an expression represented as f(x) = ax² + bx + c, which allows solving for x using either the factorization method or applying the quadratic formula. By zeroing out this expression, it becomes possible to determine its roots as with any quadratic equation.

In the case of the above function:

To find the area under the curve, above the x-axis, we need to integrate the parabolic expression from 0-1

that is:

∫[0,1](x-x²)dx

This is evaluated using the power rule

∫[0,1](x-x²)dx = [1/2x² - 1/3x³) fro x= 0 to x = 1

inserting the limits of the integration, we have:
[1/2 (1) ² - 1/3 ( 1) ³] - [1/2 (0)² - 1/3 (0) ³]

Simplified, and we have :

Area  = 1/2 - 1/3

Thus, Area under the curve = 1/6

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The values of x, y and z in the given simultaneous equation is:

x = 4

y = 6

z = -3

The 3 simultaneous equations are given as:

x + 7y - z = 49

2x - 5y + 2z = -28

x - 6y=-32

Rearranging the first equation  gives:

x = 49 - 7y + z

2x - 5y + 2z = -28

x - 6y = -32

Substitute 49 - 7y + z into equations 2 and 3 to get:

2(49 - 7y + z) - 5y + 2z = -28

49 - 7y + z - 6y = -32

Convert the equation in terms of u and solving simultaneously gives:

y = 6 and z = -3

Thus:

x = 49 - 7(6) + (-3)

x = 4

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