7x(92+7) = (7x92)+(7x_)

The probability of A and B occurring simultaneously (P(A ∩ B)) is c. 0.00.

In this scenario, A and B are stated to be mutually exclusive events. Mutually exclusive events are events that cannot occur at the same time. This means that if event A happens, event B cannot happen, and vice versa.

Given that P(A) = 0.4 and P(B) = 0.5, we can deduce that the probability of A occurring is 0.4 and the probability of B occurring is 0.5. Since A and B are mutually exclusive, their intersection (A ∩ B) would be an empty set, meaning no outcomes can be shared between the two events. Therefore, the probability of A and B occurring simultaneously, P(A ∩ B), would be 0.

To further clarify, let's consider an example: Suppose event A represents flipping a coin and getting heads, and event B represents flipping the same coin and getting tails. Since getting heads and getting tails are mutually exclusive outcomes, the intersection of events A and B would be empty. Therefore, the probability of getting both heads and tails in the same coin flip is 0.

In this case, since events A and B are mutually exclusive, the probability of their intersection, P(A ∩ B), is 0.

Therefore, the correct answer is: c. 0.00

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Answer:

y=5x

Step-by-step explanation:

JK is perpendicular to a line that has a slope

What is Slope?

The ratio of how much y grows as x grows by a certain amount is known as a line's slope. The slope of a line indicates how steep it is, or how much y rises as x rises. Anywhere along the line, the slope remains constant (the same).

Two lines, L1 and L2, with slopes m1 and m2 are perpendicular if

m1 x m2 = -1.

In our case m1 = 1

1 x m2 = -1

m2 = -2

so the slope of the perpendicular line is -2.

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

As x increases, the line with a slope of -2 increases. Line JK is the only line displayed that fits this. Line AB cannot be the solution because it is "falling" as x grows.

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Answer:

8.6 ft

Step-by-step explanation:

I'm sure this is a problem where you use pythagorean theorem so since the person walks 7ft and climbs 5ft, you can form a right triangle.

So just do \(\sqrt{7^2+5^2}\) and you get \(\sqrt{74}\) which rounds to 8.6

The graphical representation that will be most appreciated for the data would be box plot, because the median can easily be determined from the large set of data. That is option A.

The box plot is a type of graphical representation of data that gIves more than one detail about the data set such as;

Box plots allow you to compare multiple data sets better than others dues to the above listed features that it has.

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The new probability of finding oil is 0.31 + 0.50 = 0.81.

a) The probability of finding oil is 0.50 + 0.20 = 0.70.

b) After 200 feet of drilling, the firm took a soil test. The probabilities of finding the particular type of soil identified by the test are: P(soil | high-quality oil) = 0.20, P(soil | medium-quality oil) = 0.80 and P(soil | no oil) = 0.20.

Using Bayes' theorem, the revised probabilities can be calculated as follows:

P(A1∩S)= P(A1).P(S|A1) = 0.50 * 0.20 = 0.10

P(A2∩S)= P(A2).P(S|A2) = 0.20 * 0.80 = 0.16

P(A3∩S)= P(A3).P(S|A3) = 0.30 * 0.20 = 0.06

P(S)=P(A1∩S)+P(A2∩S)+P(A3∩S) = 0.10 + 0.16 + 0.06 = 0.32

Then, the revised probabilities can be calculated as follows:

P(A1|S)= P(A1∩S) / P(S) = 0.10 / 0.32 = 0.31

P(A2|S)= P(A2∩S) / P(S) = 0.16 / 0.32 = 0.50

P(A3|S)= P(A3∩S) / P(S) = 0.06 / 0.32 = 0.19

Hence, the firm should interpret the soil test as follows: the revised probability of finding high-quality oil is 0.31, the revised probability of finding medium-quality oil is 0.50, and the revised probability of finding no oil is 0.19. The new probability of finding oil is 0.31 + 0.50 = 0.81.

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Saan po yung divisor?

Kailangan ko po

The values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

Thales's Theorem or Basic Proportionality Theorem states that if a line is drawn parallel to one side of a triangle intersecting the other two sides in distinct points, then the other two sides are divided in the same ratio.

Given are three figures of triangles,

Figure 1)

5/x+5 = 8/10

50 = 40+8x

x = 5/4

y = 7/7+y = 8/10

70 = 56 +8y

y = 4/7

Figure 2)

12/12+y = 18/18+6

12/12+y = 18/24

48 = 36 +3y

y = 4

12/4 = x/5

x = 15

Figure 3)

y/4 = 1.5/3

y = 2

x/6 = 1.5/3

x = 3

Hence, the values of x and y for fig. 1) is 5/4 and 4/7, for fig. 2) x = 15, y = 4 and for fig. 3) x = 3 and y = 2

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The payback period of the project is 2 years.

The payback period is a financial metric used to evaluate the time it takes for an investment to recoup its initial cost. It measures the length of time required for the cash inflows from the investment to equal or surpass the initial investment amount. In this case, the initial investment is $35,000, and the cash flows are $10,000 in year 1, $20,000 in year 2, and $10,000 in year 3. To calculate the payback period, we need to determine in which year the cumulative cash inflows will equal or exceed the initial investment.

By adding the cash flows year by year, we can see that at the end of year 1, the cumulative cash inflow is $10,000. By the end of year 2, the cumulative cash inflow becomes $30,000 ($10,000 from year 1 + $20,000 from year 2). Finally, at the end of year 3, the cumulative cash inflow reaches $40,000 ($10,000 from year 3).

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The formula for the final velocity,\(v_{f}\) , in terms of initial velocity, vi, acceleration, a, and time, t is given by \(V_{f}=at+V_{i}\)

A =\((V_{f}-V_{i} )/t\)  You can put \(1\) under A and then cross multiply.

\(at =V_{f} -V_{i}\)

Get \(V_{f}\)  by adding  \(V_{i}\) in both sides of the equation.

\(at+V_{i} =V_{f}\)

                                                OR

The final speed \(V_{f}\) in terms of other parameters is given by the relation \(V_{f}\)\(=at+V_{i}\)

How to calculate the acceleration of an object?

Mathematically, acceleration is calculated using this formula:

\(a=(V_{f}-V_{i} )/t\)

Where:

Making \(V_{f}\) the subject of the formula, we have:

\(at =V_{f} -V_{i}\)

\(V_{f} =V_{i} +at\)

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The statement that accurately describes the amplitude of a trigonometric function is "the amplitude is twice the height of the function from the x-axis to its highest point."So, the correct option is c.

The amplitude is twice the height of the function from the x-axis to its highest point.What is an amplitude of a function?The amplitude is defined as the difference between the highest and lowest point on a curve.
In the case of a trigonometric function, the amplitude is the distance between the center line and the maximum point (or minimum point) on the curve. The center line is the mean value of the curve or the horizontal line that passes through the center of the curve.

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The value of 'a' that makes the given system a dependent system is 4.

To make the given system a dependent system, we need to find the value of 'a' that makes both equations equivalent or proportional.

Let's begin by rearranging the first equation so that it is in the standard form y = (2/3)x.

Now, let's substitute this expression for y in the second equation and simplify:

6y - a - 4x = 0

6(2/3)x - a - 4x = 0

4x - a = 0

We can see that if we choose 'a' to be equal to 4, then both equations will be equivalent. In other words, the system will become a dependent system with infinitely many solutions.

To see why, let's substitute 'a' as 4:

6y - 4 - 4x = 0

6y - 4x = 4

Now, if we compare this equation to the first one we wrote, y = (2/3)x, we can see that they are equivalent. Thus, any solution that satisfies the first equation will also satisfy the second equation, and vice versa. This means that we have infinitely many solutions to the system.

In conclusion, the value of 'a' that makes the given system a dependent system is 4.

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The proof of the congruent sides RU and TS is given below.

What is congruent triangles?

In any orientation, two triangles are said to be congruent if their three sides and three angles are equal.

Therefore, if two triangles have the same number of sides on each side, they are said to be congruent. Additionally, we can determine that they are congruent if we have a side, an angle between the sides, and then another side that is congruent, in that order: side, angle, side.

Let the given figure is a rectangle RSTU.

Since the all four angles of rectangle are of 90 degree.

So, each angle of rectangle RSTU is 90 degree.

Let, US divides the angle RUT and angle RST and form two new triangles, ΔSRU and ΔSTU.

Both the triangles having same measure of angles and sides.

⇒  ΔSRU ≅ ΔSTU

As the triangles are congruent so their sides are congruent.

Hence, RU is congruent to TS.

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The critical points of the function are (0, 0) and (3/4, -9/4), To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point

To find the critical points of the function f(x, y) = 8x^3 + y^2 + 6xy, we need to find the values of (x, y) where the partial derivatives with respect to x and y are equal to zero.

Taking the partial derivative with respect to x, we have:

∂f/∂x = 24x^2 + 6y = 0.

Taking the partial derivative with respect to y, we have:

∂f/∂y = 2y + 6x = 0.

Solving these two equations simultaneously, we get:

24x^2 + 6y = 0,

2y + 6x = 0.

From the second equation, we can solve for y in terms of x:

Y = -3x.

Substituting this into the first equation:

24x^2 + 6(-3x) = 0,

24x^2 – 18x = 0,

6x(4x – 3) = 0.

Therefore, we have two possibilities for x:

1. x = 0,

2. 4x – 3 = 0, which gives x = ¾.

Substituting these values back into y = -3x, we get the corresponding y-values:

1. x = 0 ⇒ y = 0,

2. x = ¾ ⇒ y = -9/4.

Hence, the critical points of the function are (0, 0) and (3/4, -9/4).

To classify the critical points, we need to examine the second partial derivatives of f(x, y) at each point. However, since the original function does not provide any information about the second partial derivatives, further analysis is required to classify the critical points.

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Answer:

4 : 1 or 4 times

Step-by-step explanation:

V of sphere is

V = 4/3 π r³

then we can compare both of them dirextly

Vs : Vhs

4/3 π r³ : ½ (4/3 π (2r)³)

4/3 π r³ : ½ * 4/3 π 8r³

1 : ½ * 8

1 : 4

Vhs : Vs = 4 : 1

so the volume of hemisphere is 4 times bigger than the sphere.

Answer:

It is greater than the volume of the sphere.

Step-by-step explanation:

imagine math :D

Answer:

51

Step-by-step explanation:

Answer:

A = 1

B = 5

Step-by-step explanation:

The angle between the stick and the base of the box is 77. 9 degrees

To determine the angle between the stick and the base, we have to know the trigonometric identities.

These identities are;

From the information given, we have;

sin A = FB/AB

Given that;

GB = 14.5cm

AB = 18. 6cm

substitute for the length of the sides, we have;

sin A = 14.5/18. 6

Divide the values, we have;

sin A = 0. 7796

Find the inverse sine

A = 77. 9 degrees

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Answer:60-30 I guess

Step-by-step explanation:n60-30=30

Answer:

z^2 = y^2 + 6^2........equation 1

x^2 = y^2 + 24^2.....equation 2

30^2 = z^2 + x^2.......equation 3

put equation 1 and 2 in 3

30^2 = (y^2 +6^2) + (y^2 + 24^2)

900 = y^2 + 36 + y^2 + 576

900 = 2y^2 + 612

2y^2 = 900 - 612 = 288

divide both side by 2

y^2 = 144

find the square root of both sides

y = 12

recall

z^2 = y^2 + 6^2

z^2 = 144 + 36

z^2 = 180

z = 13.42

recall

x^2 = y^2 + 24^2

x^2 = 144 + 576

x^2 = 720

x = 26.83

Step-by-step explanation:

you get your 3 equations from the diagram above which as 3 triangles in it using pythagoras theorem

The values are:

x = 26.83

y = 12

z = 13.42

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

z² = y² + 6²........(1)

x² = y² + 24².....(2)

30² = z² + x²......(3)

Now, put the value from equation (1) and (2) in equation (3)

30² = ( y² + 6²)  + (y² + 24²)

900 = y² + 36 + y² + 576

900 = 2y² + 612

2y²  = 900 - 612

2y² = 288

y²  = 144

y= √144

y = 12

So, z² = y² + 6²

z² = 144 + 36

z² = 180

z = 13.42

and, x² = y² + 24²

x² = 144 + 576

x² = 720

x = 26.83

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Answer:

Hello, I solved it out for you and I did an example.

Step-by-step explanation:

a) Does not give an equivalent ratio

b) Does not give an equivalent ratio

c) Does not give  an equivalent ratio

d) Gives an equivalent ratio

An equivalent ratio is a ratio that is equal in value to a given ratio, but may have a different form. Two ratios are equivalent if they have the same relationship between the terms, even if the numbers are different.

In this case, we have the ratio 8/20. The process of addition or subtraction can not be able to give us the equivalent ratio that we are looking for but the multiplication  would do that. Recall that the original fraction is 8/20 so;

a) 10/22 = 5/11

b) 6/18 = 3/9

c) 4/10 = 2/5

d) 16/40 = 8/20

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Answer:

Just guessing here but would the bottom be 4,8,12,16,20 maybe since it is going by 4 then you do the same for the top since it is going by 3

Step-by-step explanation:

Answers:

Input the numbers only in each box. So that means you won't type in a comma.

The least common denominator is  12

=======================================================

Explanation:

Your teacher wants you to list the multiples of each denominator.

The values in bold are what will go in the boxes in those first two rows.

The least common denominator is 12 because it is the smallest thing found in common in the two lists above. In other words, 12 is the LCM (least common multiple) of 3 and 4. Note how 3*4 = 12. This works because 3 and 4 do not have any common factors between them other than 1.

The LCD (least common denominator) is the LCM of the denominators. The LCD is useful for when you want to add or subtract fractions. The denominators must be the same for you be able to add or subtract them.

The length of the deep end is 12 feet of the swimming pool.

Given: Area of the swimming pool is 210 square feet

Width of the pool = 10 feet

The length of the shallow end is 9 feet and the length of the deep end is d.

To find the value of d.

Let's solve the problem.    

The area of the swimming pool is 210

The width is 10

The deep end length is d

The shallow end length is 9

The total length of the swimming pool = The length of the deep end + The length of the shallow end

=> d + 9

Therefore, the total length of the swimming pool is d + 9

The surface of the swimming pool is rectangular, so

The area of rectangle = width × length

Therefore,

area of swimming pool = width of the pool × length of the swimming pool

=> 210 = 10 × (9 + d)

or 10 × (9 + d) = 210

Dividing both sides by 10:

10 × (9 + d) / 10 = 210 / 10

9 + d = 21

Subtracting 9 on both sides:

9 + d - 9 = 21 - 9

d = 12

Therefore the length of the deep end is 12 feet

Hence the length of the deep end is 12 feet of the swimming pool.

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The length of the deep end of the swimming pool is 12 feet.

We are given that:

The Area of the swimming pool = 210 square feet

width of the swimming pool = 10 feet

Length of shallow end = 9 feet

Let the length of the deep end be d.

Total length of the swimming pool = length of deep end + length of shallow end =  d + 9

Area of swimming pool = width × length

Substituting the values, we get that:

210 = 10 × (9 + d)

9 + d = 21

d = 12

Therefore the length of the deep end of the swimming pool is 12 feet.

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Answer:

15$

Step-by-step explanation:

Answer:

$15

Step-by-step explanation:

75.00(0.20) = $15

The expression is equivalent to 4 − 3(x + 2) + 2(3 − 2x) will be 4 − 7x. Then the correct option is A.

Given that:

Expression, 4 − 3(x + 2) + 2(3 − 2x)

The equivalent is the expression that is in different forms but is equal to the same value.

Simplify the expression, then we have

4 − 3(x + 2) + 2(3 − 2x)

4 − 3x − 6 + 6 − 4x

4 − 7x

Thus, the correct option is A.

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The missing options are given below.

4 − 7x

4 + 7x

7 − 4x

7 + 4x

It took 19 minutes for each to read 115 pages.

What is Algebraic expression ?

Algebraic expression can be defined as the combination of variables , constants and exponents.

Let x be the number of minutes

And y be the number of pages.

y = 96 + x  --equation1 (for danielle )

y=39+4x --equation2 (for lorenzo)

By substituting equation 1 in equation 2.

we get,

96+x = 39 + 4x

96-39+x = 39-39+4x

57+x = 4x

4x-x = 57

3x = 57

x = 57/3

x = 19 .

Substitute x = 19 in equation 1 we get y = 96 + 19 and y=115

in equation 2 we get , y = 39 + 4*19

y = 39+76

y = 115

Hence , it took 19 minutes for each to read 115 pages.

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