What is the recursive formula for the geometric sequence with this explicit
formula?

a^n=9(-1/3)^(n-1)

If P(a)=0.5 and P(b) =0.45, then P(a ∩ b) is 0.225.

Independent events are events such that the occurrence of one event won't affect the other.

Therefore,

P(a) × P(b) = P(a ∩ b)

Hence,

P(a) = 0.5

P(b) = 0.45

Therefore,

P(a ∩ b) = 0.5 × 0.45

P(a ∩ b) = 0.225

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Using similar triangles, it is found that the height of the taller pole is of 9.6m.

Similar triangles are triangles that have the same angles, and whose side lengths are proportional.

The hypotenuse of the smaller triangle is given as follows:

h² = 6² + 8² -> h = 10.

Hence the proportional relationship is:

[tex]\frac{10}{16} = \frac{6}{h}[/tex]

Applying cross multiplication:

10h = 96

h = 9.6m.

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The next step Juan will take is to multiply the second fraction by (x-2)/(x-2).

Given that Juan needs to rewrite this difference as one expression (3x/(x²-7x+10))-(2x/(3x-15)) and factor the denominator as (3x/(x-2)(x-5))-(2x/3(x-5)).

An algebraic expression in mathematics is an expression composed of variables and constants and algebraic operations (addition, subtraction, etc.). Expressions are made up of concepts.

The given expression is (3x/(x²-7x+10))-(2x/(3x-15))

Firstly, we will factored the denominator as

(3x/(x-2)(x-5))-(2x/3(x-5)).

Now, we will multiply and divide the second fraction by (x-2), we get

(3x/(x-2)(x-5))-((2x(x-2))/3(x-5)(x-2)).

Hence, the next step when subtracting these expressions (3x/(x-2)(x-5))-(2x/3(x-5)) is multiply the second fraction by (x-2)/(x-2).

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Step-by-step explanation:

The picture is the full explanation for this question answer.

18.19 is the solution for the given improper function.

The term "operation" in mathematics refers to the process of computing a value utilizing operands and a math operator. For the specified operands or integers, the math operator's symbol has predetermined rules that must be followed. In mathematics, there are five basic operations: addition, subtraction, multiplication, division, and modular forms.

To add 8 11/12 and 9 5/18, we need to first find a common denominator. The smallest number that both 12 and 18 divide evenly is 36.

Converting 8 11/12 to an improper fraction:

8 11/12 = (8 × 12 + 11) / 12 = 107/12

Converting 9 5/18 to an improper fraction:

9 5/18 = (9 × 18 + 5) / 18 = 167/18

Now that we have a common denominator of 36, we can add the two fractions:

107/12 + 167/18 = (107 × 3) / (12 × 3) + (167 × 2) / (18 × 2)

= 321/36 + 334/36 = 655/36

So 8 11/12 + 9 5/18 = 655/36 or approximately 18.19.

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Answer: 80 square units

Step-by-step explanation:

[tex]A=(8)(10)=80[/tex]

Answer:

2/50=1/25

Step-by-step explanation:

2 aces are removed hence 2 aces are left out of 50 cards

A data value is considered significantly low or significantly high  if its​ z-score is less than -2 or greater than 2.

What does it mean if z-score is 2?

What does a standard deviation of 2 mean?

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The correct question is -

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

The area of the logo is 136. 14 cm²

First, let's find the area of the semicircle

Area of semicircle = 1/2(πr²)

radius = 8/2 = 4cm

Substitute into the formula

Area of semicircle = [tex]\frac{1}{2} * 3. 142 * 4 * 4[/tex] = 25. 135 cm²

Now, let's find area of trapezium

Area of trapezium = [tex]\frac{a + b}{2} * h[/tex]

Area =  [tex]\frac{12 + 10. 2}{2} * 10[/tex]

Area = [tex]11. 1 * 10[/tex]

Area = 111 cm²

Area of logo = Area of trapezium + area of semicircle

Area of logo = 111 +  25. 135

Area of logo = 136. 14 cm²

Thus, the area of the logo is 136. 14 cm²

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The cost of the Baseball is $5.

Lets take football cost as "x"

And taking baseball cost as "y"

According to given conditions,

2y + 3x = 67

x= 3y + 4

Lets put the values of x in equation (1):

2y + 3 (3y+4) = 67

=> 2y + 9y + 12 = 67

=> 11y = 55

y = 5

x = 3(5) + 4

x = 19

Hence the cost of the Baseball is $5.

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The three consecutive integers are 5, 6, and 7.

What are consecutive integers?

Whole numbers that follow one another without a gap are known as consecutive integers. A few examples of consecutive integers are 15, 16, and 17, 1,2 and 3, and so on.

Finding the Consecutive Integers

Let the three consecutive integers be a, a + 1, and a + 2.

These three consecutive integers are to be such that two times the first integer when added to three times the second integer minus the third integer, it is equal to 21.

⇒ 2a + 3(a+1) - (a+2) = 21

2a + 3a + 3 - a -2 = 21

5a - a + 3 - 2 = 21

4a + 1 = 21

4a = 20

a = 20/4

a = 5

∴ a+1 = 5+1

a+1 = 6

And, a+2 = 5 + 2

a +2 =7

Hence, the three consecutive integers come out to be 5, 6, and 7

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The equations which gave the same solution as; 2.3p – 10.1 = 6.5p – 4 – 0.01p are;

It follows from the answer choices that the equation; 2.3p – 10.1 = 6.49p – 4 is equivalent to the given equation as the algebraic sum of p variables is evaluated on the right hand side.

The second equation; 230p – 1010 = 650p – 400 – p also is equivalent to the given equation, when multiplied through by 100.

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Answer:

B & C

Step-by-step explanation:

edge 2023

Answer: the answer is 661.55

Step-by-step explanation:

interest formula: F = Pe^(rt)

The theorem that would be included in the proof is: CPCTC theorem.

CPCTC stands for, "corresponding parts of the congruent triangles are congruent". The theorem states that, if two triangles can be proven to be congruent, then all the corresponding parts of the two triangles are equal to each other.

To prove that DB ≅ FC, given regular triangle DAF in the image attached below, we would have the following statements followed by their reasons in the bracket:

1. angle D ≅ angle F [given]

2. angle DBE ≅ angle ECF [given]

3. side DE ≅ side EF [given]

4. ΔDBE ≅ ΔECF [by the AAS congruence theorem]

5. DB ≅ FC [by the CPCTC theorem]

With the given proof, we can state that side DB is congruent to side FC.

Therefore, to prove that DB ≅ FC, the theorem that would be included in the proof is: CPCTC theorem.

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The new statement will be:

Nuclear energy is known to be one that produce a lot of radioactive waste and this tends to pose a threat to  human health and the environment.

Hence, The new statement will be:

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The Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0

According to the question,

1.0  1.5  2.5  2.0

a = 1.0

r = 1.5/1 = 1.5

r = 2.5/1.5 = 1.6667

r = 2/2.5 = 0.8

common ratio is different, so given sequence is not geometric sequence.

Hence,  the Lena has no common ratio for the sequence 1.0 1.5 2.5 2.0.

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The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

An equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

x/3 - 3/4 = 5/12

Hence:

x/3 = 5/12 + 3/4

x/3 = 7/6

x = 7/2

The solution to the expression x/3 - 3/4 = 5/12 is given as x = 7/2

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Answer:

1025.76

Step-by-step explanation:

Formula for a right rectangular pyramid is (l*w*h)/3

The length and width are both 18.7, so we can plug that in. The height is 8.8.

It becomes:

(18.7*18.7*8.8)/3, which equals the answer above.

Answer: I believe its 50 because you would have to see 3 x what equals 150

Step-by-step explanation:

The time taken to her to bag 150 bags is 50 minutes.

Grocery Items are any of the items listed that are offered only for off-premises consumption are as follows:-

(1) packaged or fresh fish, meat, or poultry.

(2) packaged or fresh plants or vegetables.

(3) packaged or fresh dairy goods (other than ice cream, frozen yogurt, or other confection/dessert items).

According to the given question, Three grocery bags are packed every minute. So, the time taken to 150 bag the time taken is computed as follows:-

Time Taken =  Total number of bags/Number of bags per minute

                   =  150 / 3

                   =  50 minutes

Therefore, it can be concluded that the time taken for her to bag 150 bags is 50 minutes.

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Based on definition of unit circle and angle properties on Cartesian plane, we find the following results: A: π/5, B: 3π/7, C: 4π/3.

Units circles are commonly used to understand angles and trigonometric functions in a simple way. Vectors in a unit circle are ordered pairs of polar form: (x, y) = (cos θ, sin θ).

To solve this problem, we must take these tips into account:

Then, we have the following results: A: π/5, B: 3π/7, C: 4π/3.

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The total surface area of the trapezoidal prism is 180m². Option C

The formula for the total surface area of a trapezoidal prism is;

Total surface area = h (b + d) + l (a + b + c + d)

Where

b and d are parallel sides = 3, 9

h is the distance = 8

l is the length of the trapezoidal prism. = 12

Substitute into the formula

Total surface area = [tex]8(3 + 6) + 12(3 + 6)[/tex]

Total surface area = 72 + 108

Total surface area = 180 m²

Thus, the total surface area of the trapezoidal prism is 180m². Option C

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Using linear functions, the cost will be the same, of $70, when there are 5 students.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the functions are:

The costs are the same when:

45 + 5x = 35 + 7x

2x = 10

x = 5.

The cost is:

y = 45 + 5 x 5 = $70.

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The equation that will produce the given graph is; 6x² + 6y² = 144

The standard equation of a circle can be expressed as:

(x + a)² + (y - b)² = r²

where;

(a, b) is the center of the circle

r is the radius of the circle.

From the diagram, we can see that the radius of the circle is between 4 and 5.  Thus, the correct equation must have a radius between these values.

From the option, we can see that the only equation that will have a radius between 4 and 5 is;

6x² + 6y² = 144

Divide through by 6 to get;

x² + y² = 24

x² + y² = √24

Thus r = √24 which is greater than 5

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The value of m based on the given equation -7 + 4m + 10 = 15 - 2m is 2

-7 + 4m + 10 = 15 - 2m

4m + 2m = 15 + 7 - 10

6m = 12

m = 12/6

m = 2

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Answer:

A little less than 320

Step-by-step explanation:

Round the miles to 168 and 150

Add together 168 + 150 = 318

Answer: a. a little less than 320

Answer:

C

Step-by-step explanation:

Please refer to the attached photo for step by step solutions.

Note: Square roots and squares will always cancel out each other.

Answer:

180

Step-by-step explanation:

Solution 1: Any straight line is 180 degrees.

Solution 2: Angle WX=Angle YZW+ Angle YZX

Angle YZW=Angle YZX=90

Angle YZW+ Angle YZX=90+90=180

So Angle WX=180

Answer:

Step-by-step explanation:

You can find WX if you know some special properties of special triangles:

1. A 45-45-90 triangle (a triangle with angle measures of 45°, 45°, and 90°) will have a 1:1:√2 ratio (the legs of the triangle are the same length and the hypotenuse is the length of any leg times √2)

2. A 30-60-90 triangle (a triangle with angle measures of 30°, 60°, and 90°) will have a 1:√3:2 ratio (the hypotenuse is twice the measure of the shorter leg, and the longer leg is √3 times the length of the shorter leg)

For reference, a leg is a side on a right triangle that isn't the hypotenuse.

In this picture, the first type of triangle is on the right, and the second type is on the left.

The shorter leg on the left triangle has a length of 10, and WZ is the longer leg. The longer leg is √3 times the shorter one, so WZ = 10√3

Both legs of a 45-45-90 triangle have the same measure, so ZX is 10.

Since WX is made up of WZ and ZX, it's length is the sum of both lengths.

[tex]{\rm WX} = 10\sqrt{3}+10[/tex]

[tex]{\rm WX} \approx 27.321[/tex]

Answer:

Step-by-step explanation:

The visualization of "4.298" on the number line is attached below.

Suppose we're measuring something whose values are numeric.

For each value of that thing we observe, we plot a dot above that value in the number line.

Thus, the total number of dots in the dot plot tells us the total number of observations of the values of that thing we did.

Thus, suppose if we observed the value 'x', then we will make a dot above 'x'. If there is already a dot over 'x', then we will make a new dot over that dot.

We know that 4.298 is greater than 4 but less than 5.

The visualization of "4.298" on the number line is attached below.

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The width that Mason should set his compass when constructing segment FG is: A. The distance from B to E.

FG should be congruent to segment BE. Based on this Mason should set his compass to the width of segment BE when Mason is constructing segment FG.

Hence, the width that Mason should set his compass when constructing segment FG is the distance from B to E which is option is A.

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Answer:

b to e

Step-by-step explanation:

plato

The dimension of the box should be 1.7×1.7×3.58 in inches, applying minimization of surface area.

Dimensions to Minimize the Surface Area of the Box

It is given that the box is square based with an open top.

⇒ The box has one square and 4 rectangles

Thus, the total surface area of the box is given as,

S= a²+ab+ab+ab+ab  

S= a²+4ab ______________ (1)

Here, a is the side of the squared base and length of the rectangular sides of the box, b is the breath of the rectangular sides of the box.

This equation is later used for minimization of the surface area.

Also, the volume, V = a²b

It is also given that volume of the box is 184 in³.

⇒ 184 = a²b _____________ (2)

Forming a One-Variable Equation

From equation (2), b=184/a²

Now, substitute this value of b in equation (1) to get,

S = a² + 4a(184/a²)

S = a² + 4(184/a)

S = a² + 736/a

Minimization of Surface Area to find the Dimension

We require a dimension that will minimize the surface area of the box. Hence, applying minimization surface area, dS/da = 0

dS/da = 2a -736/a²

0 = 2a -736/a²

⇒ 0 = 2a³- 736

2a³ = 736

a³ = 736/2

a³ = 368

a = ∛368

a= 7.17 in

∵V = a²b

184 = (7.17)²b

b = 184/7.17²

b = 184/51.4089

b = 3.58 in

Therefore, 1.7×1.7×3.58 in inches is the required dimension for the box, using minimization of surface area..

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