Suppose we have 2 events, A and B, with P(A) = 0.50, P(B) =
0.60, and P(A ∩ B) = 0.40.
(a) Find P(A|B). Round the percent to 1 decimal place, like
12.3%.
(b) Find P(B|A). Round the percent to 0 deci

Shannon found a stack of 100 collectible fantasy horse cards in her desk that she had forgotten about. She randomly looked at 20 cards and got 8 centaur, 7 pegasus, and 5 unicorn cards.

Based on the data, estimate how many unicorn cards are in the stack.

Answer:

s=ut +atsq/2

120=4u+4sq

4u=104

u=26m/sec

Answer:

26 m/s

Step-by-step explanation:

Given

\(s = ut + \frac{1}{2} {at}^{2} \)

When a = 2 , s = 120 and t = 4

Then

\(120 = u \times 4 + \frac{1}{2} \times 2 \times {4}^{2} \\ 120 = 4u + 16 \\ 120 - 16 = 4u \\ 104 = 4u \\ u = \frac{104}{4} \\ u \: = 26

Hope it will help :)❤

Answer:

Top Right

Step-by-step explanation:

The greater than or equal to sign makes the line solid, and the greater than 2 makes the shading go to the right

the right option is B.) a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22

A linear function is a polynomial function whose degree is utmost zero or one. It is represented as a straight line in the graph.

The corresponding graph for the given data is a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points (1,25), (3,19), (4,16) and (7,7)

Time(in days)    -    Number of boxes

1                                  25

3                                  19

4                                   16

7                                    7

This forms a straight line.

By critically observing the graph and relationship between the time and number of boxes, we determine a function for the graph.

That is y=--3x+28

Putting x=0, we get

y=-3(0)+28=28

Putting x=2, we get

y=-3(2)+28

y=22

hence,. a coordinate plane with the x axis labeled time in days and the y axis labeled number of boxes, with a line that passes through the points 0 comma 28 and 2 comma 22

The diagram is attached below.

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The upper sum for f(x)=x2 over [−1,1] with n=4 in fraction form is 11/8

In this case, we want to find the upper sum for the function f(x) = x² over the interval [-1,1], using 4 rectangles. To do this, we need to divide the interval into 4 equal sub-intervals of length (1-(-1))/4 = 1/2. Then, we need to find the height of each rectangle, which corresponds to the maximum value of the function on that sub-interval.

The first sub-interval is [-1,-1/2], and the maximum value of f(x) on this interval is f(-1/2) = (-1/2)² = 1/4. Therefore, the height of the first rectangle is 1/4, and its width is 1/2. So the area of the first rectangle is (1/4)*(1/2) = 1/8.

We repeat this process for the other three sub-intervals, finding the maximum value of f(x) on each one and multiplying it by the width of the sub-interval. Then, we add up the areas of the four rectangles to get the upper sum.

The final answer, in fractional form, is:

1/8 + 1/4 + 1/2 + 3/4 = 11/8

So the upper sum for f(x) = x² over [-1,1] with n=4 is 11/8.

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Answer:

84 seconds

Step-by-step explanation:

Because if you divide all of that you would get that answer

The approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

Given,

Number of trials of the simulation were performed = 25

Number of set of simulated shots = 10

We have to find the approximate probability that a 47% shooter makes  5 or more shots in 10 attempts;

The dots in the 5 shot mark is 9, 6 shot mark is 2, and 7 shot mark is 1.

Now the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts can be calculated below:

P(x5) = (dots in 5 short mark + dots in 6 shot mark + dots in 7 short mark) / 25

= (9 + 2 + 1) / 25

 = 12 / 25

Therefore, the approximate probability that a 47% shooter makes 5 or more shots in 10 attempts is 12/25

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Answer:

324

Step-by-step explanation:

a

2

a

1

=

12

4

=

3

a

3

a

2

=

36

12

=

3

⇒

common ratio

=

r

=

3

and first term

=

a

1

=

4

no: of terms

=

n

=

9

Sum of geometric series is given by

S

u

m

=

a

1

(

1

−

r

n

)

1

−

r

⇒

S

u

m

=

4

(

1

−

3

9

)

1

−

3

=

4

(

1

−

19683

)

−

2

=

−

2

(

−

19682

)

=

324

The polar coordinates of the point (5, -3) are (r, θ) = (√34, 5.7028) to 3 decimal places

To convert the Cartesian coordinates (5, -3) to polar coordinates, we can use the formulas:

r = √(x^2 + y^2)

θ = tan^(-1)(y/x)

Substituting the given values, we get:

r = √(5^2 + (-3)^2) = √34

θ = tan^(-1)(-3/5) = -0.5404 + π (since the point is in the third quadrant)

However, we need to express θ in the range 0 ≤ θ < 2π, so we add 2π to θ:

θ = -0.5404 + π + 2π = 5.7028

Therefore, the polar coordinates of the point (5, -3) are (r, θ) = (√34, 5.7028) to 3 decimal places.

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Answer:

the 92nd term of the arithmetic sequence is 731 because the common difference between them is 8.

The given expression is a simplified algebraic equation: (1/2) * a^2 - 3b + 2c. It represents a combination of variables a, b, and c with their respective coefficients.

Utilizing symbols and operations, an algebraic equation illustrates the equivalence or inequivalence of two expressions. These generated expressions may hold variables that have varying values.

The premise centered around calculus is to arrive at a solution by acquiring the correct value(s) of these variable(s), ultimately fulfilling the outlined specification in the problem. Algebraic equations can range from uncomplicated linear problems to elaborate polynomials and trigonometric functions.

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The amount of time the tennis ball will be in the air after launch is √2 seconds.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

The height of the tennis ball is given by the function h = - 16t² + 36, where t represents time in seconds.

Now, The amount of time the tennis ball will be in the air can be determined by the time when it hits the ground and at that time height of the ball should be zero.

Therefore, The time in the air is,

0 = - 16t² + 36.

16t² = 36.

t² = 2.

t = + √2 seconds, as time can not be negative.

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The solution set of the inequality 8x + 2 > 34 is x > 4

The system of inequality is given as:

8x + 2 > 34

8x + 2 > 34

From the above system of inequality, we can see that the inequalities in the system are the same.

This means that:

8x + 2 > 34

Subtract 2 from both sides of the inequality

8x > 32

Divide both sides by 8

x > 4

Hence, the solution set of the inequality 8x + 2 > 34 is x > 4

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Answer:

I would measure a 45° angle from the ground to the building. Then I would back up until the angle aligns with both the ground and the top of the building. I would measure the distance between me and the building to get the height of the building. Since the triangle is a 45, 45, 90 triangle, the distance between me and the building would be the same as from the ground to the top of the building.

Step-by-step explanation:

Sorry I'm not drawing a sketch for this but I'll put it very simply with a 45, 45, 90 triangle because that's easiest.

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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The value of x  for The quadrilateral which is a trapezoid is if the top is 21 and the bottom is 27 is option 2 that is 5.

Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided form or figure that has a perimeter and covers a specific area. It is a 2D figure rather than a 3D one. The bases of the trapezoid are the sides that are parallel to one another. Legs or lateral sides refer to the non-parallel sides. The height is the separation between the parallel sides.

From the given diagram, the expression below is true:

2(5x - 1) = 21 + 27

Expand

10x - 2 = 48

10x = 48 + 2

10x = 50

Divide both sides by 10

10x.10 = 50/10

x = 5

Hence the value of x is 5

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Answer:

The expanded form of 1.2*10^9 is 1400000000

I'm not very sure what you mean but I have found two solutions.

Solution No.1:

1400000000 - 7000 = 1399993000

Solution No.2:

Let's say the variable is "x"

7000 * x = 1400000000

x = 200000

Hope this helped! :)

Answer:

-300

Step-by-step explanation:

Step 1:  Find the amount Elmer's funds decreased after purchasing the rabbits:

Let x represent Elmer's funds.

Since Elmer bought five rabbits for $10 each, he lost $10 5 times.

x - (10 * 5)

x - 50

Thus, Elmer lost (spent) $50 for the 5 rabbits.

Step 2:  Find the amount Elmer's funds decreased after purchasing the  cupboards:

Since Elmer bought four cupboards for $70 each, he lost $70 4 times:

x - (50 + (70 * 4))

x - (50 + 280)

x - 330

Thus, after purchasing the rabbits and cupboards, Elmer lost $330.

Step 3:  Find the amount Elmer's funds increased after finding the twenty-dollar bill:

Since Elmer found a twenty-dollar bill, he gained $20

x - (330 + 20)

x - 310

Step 4:  Find the amount Elmer's funds increased after returning one rabbit:

Since Elmer returned one rabbit, he gained $10:

x - (310 + 10)

x - 300

Thus, Elmer's funds changed totally by -$300.

Putting all the information together, we have:

x - 10 - 10 - 10 - 10 - 10 - 70 - 70 - 70 - 70 + 20 + 10

x - 50 - 280 + 30

x - 330 + 30

x - $300

Answer:

1. is ounces

2. you would use ounces

3. 3.5 x 16 = 56

4. .5, 1, 1.5, 2, 2.5

Answer:

p = -13/10

Step-by-step explanation:

2/3 -2p = 5 + 4/3p

first isolate p

-2p = 5 + 4/3p -2/3

-2p -4/3p = 5 -2/3

then you expand the whole numbers to be able to solve each side

-6/3p -4/3p = 15/3 -2/3

subtract

-10/3p = 13/3

now you isolate p again by dividing each side by -10/3p

p = 13/3 ÷ -10/3

you cant divide fractions, so flip one of them and multiply

p = 13/3 x - 3/10

p = 39/30

simplify and you get p = 13/10

Answer:

the answer is A

B, C, D is false

The true sentence is,

⇒ 8.565 < |-13.23|

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

All the expressions are,

A) 8.565 < |-13.23|

B) 7/8 < 0.78

C) 4/11 < - 4.11

D) 23.5 < 2 3/5

Now, From A;

A) 8.565 < |-13.23|

RHS;

|-13.23| = 13.23

Hence, It is true.

Thus, The true sentence is,

⇒ 8.565 < |-13.23|

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The 95% confidence interval for the population mean is (16.426, 26.574

To find the 95% confidence interval, we can use the formula:

Confidence interval = sample mean ± (z-score)*(population standard deviation/√n)

where the z-score for a 95% confidence level is 1.96.

Plugging in the values given in the question, we get:

Confidence interval = 21.5 ± (1.96)*(19.4/√49)

Simplifying this expression, we get:

Confidence interval = 21.5 ± 5.074

Therefore, the 95% confidence interval for the population mean is (16.426, 26.574) as an open-interval.

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Coefficient is 2.

It is worth noting that the term "coefficient" is not limited to algebraic expressions.

It is a term used in many areas of mathematics and science, such as in linear equations, trigonometric functions, and chemical reactions.

In each case, the coefficient refers to the numerical factor that is multiplied by a variable or a component in a formula or equation.

In the expression 9x + 2 + 8y, the coefficient of x is 9 and the coefficient of y is 8.

The coefficient is the numerical factor that is multiplied by a variable. In this case, x has a coefficient of 9 because it appears as 9x, which means x is being multiplied by 9.

Similarly, y has a coefficient of 8 because it appears as 8y, which means y is being multiplied by 8.

The constant term, which is a term without a variable, in this expression is 2.

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Answer: x = 4

Step-by-step explanation:

1/4(2(x - 1) +10)=x

1/4(2x - 2 + 10) = x

1/4(2x + 8) = x

1/2x + 2 = x

1/2x = 2

x = 4

Answer:

C.  2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units

Step-by-step explanation:

Answer:

The Answer is C.

Step-by-step explanation:

2 StartRoot 2 EndRoot + 2 StartRoot 5 EndRoot units

The correct equation is b) C2+2e−⇒2C2. This equation represents the reduction of carbon (C) where two electrons (2e-) are gained, resulting in the formation of two carbon atoms (2C). The arrow pointing to the right (⇒) indicates the direction of the reaction.

In chemical reactions, electrons can be gained or lost, leading to oxidation or reduction processes. The equation b) C2+2e−⇒2C2 represents a reduction reaction, where C2 (a diatomic carbon molecule) gains two electrons (2e-) to form two separate carbon atoms (2C).

The equation a) F2+2e=>2F1- represents the reduction of fluorine (F2) to form two negatively charged fluorine ions (F1-). This equation is incorrect because fluorine does not form positive ions.

The equation c) S+3e=S3- represents the reduction of sulfur (S) where three electrons (3e-) are gained, resulting in the formation of a negatively charged sulfur ion (S3-). This equation is incorrect because sulfur typically forms sulfide ions (S2-) rather than S3-.

The equation d)  P+2e−>P3-  represents the reduction of phosphorus (P) where two electrons (2e-) are gained, forming a negatively charged phosphide ion (P3-). This equation is incorrect because phosphorus typically forms phosphide ions with a charge of -3 (P3-) or -2 (P2-), not P3-.

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The equation of the circle is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

From the question, we are to determine the equation of the circle

The equation of circle is given by

(x - h)² + (y - k)² = r²

Where (h, k) is the center

and r is the radius

From the given information,

The two circles are concentric

∴ (h , k) = (4, 6)

But the other circle has a radius that is twice as large

∴ r = 2 × 2

r = 4

Thus,

The equation of the circle becomes

(x - 4)² + (y - 6)² = 4²

(x - 4)² + (y - 6)² = 16

Hence, the equation which represents a circle that is concentric with the circle shown but has a radius that is twice as large is (x - 4)² + (y - 6)² = 16. The correct option is the second option (x - 4)² + (y - 6)² = 16

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

\(\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

\(\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3\)

So, the next term is 3 times the preceding term, that is :

Therefore, the next term is 162