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The experimental probability that more than 10 spins are needed to land on each letter at least once is 75%

Experimental probability is a type of probability that is based on actual observations or experiments.

In experimental probability, the probability of an event occurring is calculated by conducting experiments and observing the outcomes. The probability of the event is then calculated by dividing the number of times the event occurred by the total number of trials or experiments.

In this case, experimental probability = number of times the event occurred / total number of trials

Experimental probability = 0.1 + 0.35 + 0.3 / 1

= 0.75 / 1

= 75%

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The actual distance from the movie theater to the school is given as follows:

A. 15 miles.

The actual distance from the movie theater to the school is obtained applying the proportions in the context of the problem.

On the map, the grocery store is 2 inches away from the library. The actual distance is 1.5 miles, hence the scale factor is of:

2 inches = 1.5 miles

1 inch = 0.75 miles.

The same map shows that the movie theater is 20 inches from the school, hence the actual distance is given as follows:

20 x 0.75 = 15 miles.

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The correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

To prove that [tex]BC^2 = AB^2 + AC^2[/tex], we can use the triangle similarity and the Pythagorean theorem. Here's a step-by-step explanation:

Given triangle ABC with right angle at A and segment AD perpendicular to segment BC.

By triangle similarity, triangle ABD is similar to triangle ABC. This is because angle A is common, and angle BDA is a right angle (as AD is perpendicular to BC).

Using the proportionality of similar triangles, we can write the following ratio:

[tex]$\frac{AB}{BC} = \frac{AD}{AB}$[/tex]

Cross-multiplying, we get:

[tex]$AB^2 = BC \cdot AD$[/tex]

Similarly, using triangle similarity, triangle ACD is also similar to triangle ABC. This gives us:

[tex]$\frac{AC}{BC} = \frac{AD}{AC}$[/tex]

Cross-multiplying, we have:

[tex]$AC^2 = BC \cdot AD$[/tex]

Now, we can substitute the derived expressions into the original equation:

[tex]$BC^2 = AB^2 + AC^2$\\$BC^2 = (BC \cdot AD) + (BC \cdot AD)$\\$BC^2 = 2 \cdot BC \cdot AD$[/tex]

It was made possible by cross-product property.

Therefore, the correct step to prove that [tex]BC^2 = AB^2 + AC^2[/tex] is:

By the cross product property, [tex]AC^2 = BC \cdot AD[/tex].

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The length of the ladder that is leaning on the building would be = 24ft. That is option B.

To determine the length of the ladder, the sine rule needs to be obeyed. That is

= a/sinA = b/sinB

Where;

a = 8.2 ft

A = 180-( 70+90

= 180- 160

= 20°

b = X

B = 90°

That is;

8.2/sin20° = b/sin90°

Make b the subject of formula;

b = 8.2×1/0.342020

= 23.9

= 24 ft

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For positive acute angles A and B, if it is known that SinA= 11/61 and tan B=4/3, cos(A-B) = 224/305.

We can use the trigonometric identity cos(A-B) = cosA cosB + sinA sinB to find the value of cos(A-B).

First, we need to find the value of cosA and sinB:

Since sinA = opposite/hypotenuse, we can draw a right triangle with opposite side 11 and hypotenuse 61, and use the Pythagorean theorem to find the adjacent side:

cosA = adjacent/hypotenuse = √(61² - 11²)/61 = 60/61

Since tanB = opposite/adjacent, we can draw another right triangle with opposite side 4 and adjacent side 3, and use the Pythagorean theorem to find the hypotenuse:

hypotenuse = √(4² + 3²) = 5

sinB = opposite/hypotenuse = 4/5

Now we can substitute these values into the formula:

cos(A-B) = cosA cosB + sinA sinB

= (60/61)(3/5) + (11/61)(4/5)

= 180/305 + 44/305

= 224/305

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The equation of the Damari's investment is B(x) = 30000 * 1.03ˣ

Damari's investment

Given that

Initial value, a = 30000

B(3) = 32306.72

The function is calculated as

B(x) = a * bˣ

Using B(3), we have

30000 * b³ = 32306.72

So, we have

b³ = 1.077

Take the cube root of both sides

b = 1.03

So, we have

B(x) = 30000 * 1.03ˣ

So, the function is B(x) = 30000 * 1.03ˣ

The boat of Sky's family

Here, we have

Initial value = 6000

Rate of depreciation = 6%

So, the function is

f(x) = 6000 * (1 - 6%)ˣ

So, we have

f(x) = 6000 * (0.94)ˣ

In 2024, we have

x = 2024 - 2021

x = 3

So, we have

f(3) = 6000 * (0.94)³

Evaluate

f(3) = 4983.50

This value is less than the offered value of $5000

This means that Sky's family should take the offer

The rule of the function

Here, we have the graph

From the graph, we have

Initial value, a = 8

Rate, b = 4.8/8

So, we have

Rate, b = 0.6

So, the function is

f(x) = 8 * 0.6ˣ

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An equation that satisfies all three pairs of a and b values listed in the table include the following: C. 3a - b = 10.

In order to determine an equation that satisfies all three pairs of a and b values listed in the table, we would substitute each of the numerical values corresponding to each variable into the given equations and then evaluate as follows;

a - 3b = 10

0 - 3(-10) = 30 (False).

3a + b = 10

3(0) - 10 = -10 (False).

3a - b = 10

3(0) - (-10)

0 + 10 = 10 (True).

3a - b = 10

3(1) - (-7)

3 + 7 = 10 (True).

3a - b = 10

3(2) - (-4)

6 + 4 = 10 (True)

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Complete Question:

Which equation satisfies all three pairs of a and b values listed in the table?

a b

0 -10

1 -7

2 -4

The equation is?

A.) a-3b=10

B.) 3a+b=10

C.) 3a-b=10

D.) a+3b=10

It will take Brenda 50 minutes to type 750 words at a rate of 15 words per minute.

To solve this problem, we can use the formula:

time = amount of work / rate

In this case, the amount of work is typing 750 words, and the rate is 15 words per minute. Substituting these values into the formula, we get:

time = 750 / 15 = 50 minutes

This calculation assumes that Brenda types at a constant rate of 15 words per minute. If her typing speed varies, the time it takes her to type 750 words may be different.

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The total height of the flyer at any time after deploying the wingsuit would be;

y = -3x + 200 + (-4.9t² + 420),

Now, Based on the given information, we can use the two functions to determine the height of the wingsuit flyer at a particular time.

During the freefall, the height of the flyer can be calculated using the function

y = -4.9x² + 420.

Let's say the flyer falls freely for t seconds before deploying the wingsuit.

Therefore, the height at the moment of deploying the wingsuit would be,

y = -4.9t² + 420.

After deploying the wingsuit, the height of the flyer is given by the function

y = -3x + 200.

We can combine these two functions to get the total height of the flyer at any given time after deploying the wingsuit.

So, the total height of the flyer at any time after deploying the wingsuit would be;

y = -3x + 200 + (-4.9t² + 420),

where x is the time after deploying the wingsuit and t is the time of freefall before deploying the wingsuit.

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a. The first term of the arithmetic sequence is 12.

b. The value of n for which the nth term is -33 is 16.

c. The common difference of the arithmetic sequence is -3.

a. The first term, u1, can be found by substituting n=1 into the given formula for the nth term:

u1 = 15 - 3(1) = 12

b. To find the value of n for which the nth term is -33, we set the formula for the nth term equal to -33 and solve for n:

un = 15 - 3n = -33

Adding 3n to both sides, we get:

15 = -33 + 3n

Adding 33 to both sides, we get:

48 = 3n

Dividing both sides by 3, we get:

n = 16

c. The common difference, d, is the difference between any two consecutive terms of the sequence. To find d, we can subtract any two consecutive terms, such as u2 and u1:

u2 = 15 - 3(2) = 9

u1 = 15 - 3(1) = 12

d = u2 - u1 = 9 - 12 = -3

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Using the cosine ratio, the value of the marked side in the image given below is approximately: y = 167.7.

The cosine ratio is defined as the ratio of the length of the hypotenuse of the right triangle over the length of the side that is adjacent to the reference angle. It is given as:

cos ∅ = length of hypotenuse/length of adjacent side.

From the image attached below, we have the following:

Reference angle (∅) = 37°

length of hypotenuse = 210

length of adjacent side = y

Plug in the values:

cos 37 = y/210

210 * cos 37 = y

y = 167.7

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Answer:

60 ft^2

Step-by-step explanation:

To get the total volume we will need to multiply all the lengths. This means we will have to do 4 x 3x 5.

4 x 3 x 5 = 15x 4 = 60

Answer:

60 ft³

Step-by-step explanation:

V = 4 ft × 3 ft × 5 ft

V = 12 ft² × 5 ft

V = 60 ft³

Answer:

  (-2, 10)

Step-by-step explanation:

You want the point that would be a solution to the inequalities ...

It can be useful to graph the inequalities, or develop a mental picture of what the graph would look like. Both boundary line slopes are fairly steep, and the lines cross in the third quadrant. The V-shaped space above that intersection  is the solution space.

The attachment shows the point (-2, 10) is a solution.

From the shape and location of the solution space, we can eliminate the choices ...

  (-8, 2) — too close to the x-axis in the far left part of the 2nd quadrant

  (10, -3) — no part of the 4th quadrant is in the solution space

It can work nicely to rewrite the inequalities as a comparison to zero.

  5x -2y +4 ≤ 0 . . . . . the first inequality in general form

  point (-2, 10): 5(-2) -2(10) +4 = -10 -20 +4 = -26 ≤ 0 . . . a solution

  point (4, 9): 5(4) -2(9) +4 = 20 -18 +4 = 6 > 0 . . . . . . . not a solution

  4x +y +7 ≥ 0 . . . . . . the second inequality in general form

  point (-2, 10): 4(-2) +(10) +7 = -8 +10 +7 = 9 ≥ 0 . . . . . . a solution

  point (4, 9): don't need to test (already known not a solution)

Point (-2, 10) is a solution.

__

Additional comment

We chose the use of "general form" inequalities for evaluating answer choices because ...

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Answer:

To convert square millimeters to square centimeters, we need to divide the area in square millimeters by 100 (since there are 100 square millimeters in a square centimeter).

So, the area of the top of Katrina's laptop in square centimeters would be:

57,000 mm² ÷ 100 = 570 cm²

Therefore, the area of the top of Katrina's laptop in square centimeters is 570 cm².

Answer:

1)

7+9-15 = add 7 and 9, then subtract 15

2)

15-(7+9) = The sum of 7 and 9 subtracted from 15

3)

15-(7+9) =  subtract 7 from 15, then add 9

Step-by-step explanation:

Learn BODMAS. The order of how to do equations. A simple tutorial on yt should be sufficient

Answer:91.26ft squared

255 number of adults and 355 number of students bought ticket.

Here,  we have,

Let the number of adults bought tickets are x and the number of students that bought tickets is (x + 100).

Since it is given that 100 more students brought tickets than adults.

Now, each adult ticket costs $5 and each student's ticket costs $3.5 and the total collected value of tickets is $2517.5.

So, 5x + 3.5(x + 100) = 2517.5

⇒ 8.5x + 350 = 2517.5

⇒ 8.5x = 2167.5

⇒ x = 255

So, 255 number of adults and (255 + 100) = 355 number of students bought ticket. (Answer)

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The greatest common factor of two terms given as 21x⁴ and 49x³ is equal to  7x³.

To find the greatest common factor (GCF) of two terms, we need to find the highest factor that is common to both terms. In this case, we have 21x⁴ and 49x³.

To find the factors, we can break each term down into its prime factors:

21x⁴ = 3 * 7 * x * x * x * x

49x³ = 7 * 7 * x * x * x

The common factors are 7 and x³. To find the GCF, we multiply these common factors together:

GCF = 7  * x³

GCF = 7x³

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Answer:

he should have subtracted 17 from both sides of the equation

Step-by-step explanation:

x+ 17 = 22

subtract 17 from both sides

X + 17 = 22

-17 -17

x = 5

Step-by-step explanation:

40 :100        yellow to purple,  divide both sides by 20

2:5

Answer:

the ratio of yellow to purple is 40:100 that is 2:5 in the simplest form.

Step-by-step explanation:

Hope it helps.

The expression that equals D + 3C in standard form is 2w² + 8w - 25.

To find an expression that equals D + 3C in standard form, we first need to simplify D and C.

Starting with D = 2w² - w - 7, we can rearrange the terms to put it in standard form:

D = 2w² - w - 7

D = 2w² - 2w + w - 7

D = 2w(w - 1) + (w - 7)

Next, simplifying C = 3w - 6:

C = 3w - 6

Now, we can substitute these expressions into D + 3C:

D + 3C = (2w² - w - 7) + 3(3w - 6)

Expanding and simplifying:

D + 3C = 2w² - w - 7 + 9w - 18

D + 3C = 2w² + 8w - 25

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The Second Linearly Independent solution of the differential equation is:

y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)

When solving a second-order linear differential equation of the form

x²y'' - 42y = 0, it is important to find two linearly independent solutions to fully describe the general solution. The first solution is given as y₁=x⁷.

To find the second linearly independent solution, we can use the method of reduction of order.

Let y₂ = u(x)y₁(x), where u(x) is a function to be determined.

Then we have y₂' = u(x)y₁'(x) + u'(x)y₁(x) and y₂'' = u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x).

Substituting y₂ and its derivatives into the original differential equation, we have:

x²(u(x)y₁''(x) + 2u'(x)y₁'(x) + u''(x)y₁(x)) - 42u(x)y₁(x) = 0

Dividing by x²y₁(x), we get:

u''(x)/u(x) + 2/x[u'(x)/u(x)] - 42/x² = 0

Let v(x) = u'(x)/u(x), then v'(x) = u''(x)/u(x) - (u'(x))²/(u(x))². Substituting v(x) into the above equation, we have:

v'(x) + 2/xv(x) - 42/x² = 0

This is now a first-order linear differential equation that can be solved using an integrating factor. Letting mu(x) = x², we have:

(x²v(x))' = 42

Solving for v(x), we get:

v(x) = 21/x + C/x²

where C is an arbitrary constant. Substituting back to u(x), we get:

u(x) = Ax³ + Bx⁻⁻¹⁸

where A and B are constants. Therefore, the second linearly independent solution is

y₂ = (Ax³ + Bx⁻¹⁸)x⁷ = Ax¹⁰ + Bx⁻¹¹

Hence, the general solution of the differential equation is:

y = c₁x⁷ + c₂(Ax¹⁰ + Bx⁻¹¹)

where c₁ and c₂ are arbitrary constants

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Diego is correct as the number of groups result to 6/5 or 1 1/5.

We have to find the number of groups of 5/6 in 1.

So, we need to perform the division as

= 1/ (5/6)

= 1 x 6/5

= 6/5

= 1 1/5

Thus, Diego is correct as the number of groups result to 6/5 or 1 1/5.

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The calculated number of plants the flower bed can contain is 120

From the question, we have the following parameters that can be used in our computation:

Dimensions = 16 m by 9 m

So, the area of the flower bed is

Area = 16 * 9

Evaluate

Area =  144

Also, we have

Each plant requires a space of 1.2m x 1m?

This means that

Plant area = 1.2 * 1

Plant area = 1.2

So, we have

Plants = 144/1.2

Evaluate

Plants = 120

Hence, the number of plants is 120

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Answer:

Step-by-step explanation:

To calculate the number of plants that can be planted in the rectangular flower bed, we need to calculate the area of the flower bed and divide it by the space required for each plant.

The area of the flower bed is calculated by multiplying its length and breadth.

So, the area of the flower bed is 16m x 9m = 144 sq.m.

Each plant requires a space of 1.2m x 1m = 1.2 sq.m.

Therefore, the number of plants that can be planted in the flower bed is:

144 sq.m. ÷ 1.2 sq.m./plant = 120 plants.

So, you can plant 120 plants in the rectangular flower bed.

The function that represents the number of comic book as a function of the number of years, t is expressed as y = 30x or f(t) = 30t.

We can use the given data to create a linear equation of the form y = mx + b, where y represents the number of comic books and x represents the number of years.

To find the equation, we can use any two pairs of (x, y) values. Let's use the first and fourth years:

First year: (1, 30)

Fourth year: (4, 120)

The slope, m, of the line can be calculated using the formula:

m = change in y / change in x = (120 - 30) / (4 - 1)

m = 90 / 3

m = 30

The y-intercept, b, can be found by substituting one of the (x, y) values and the slope into the linear equation, y = mx + b:

30 = 30(1) + b

b = 0

Therefore, the equation that represents the number of comic books, y, as a function of the number of years, x, is:

y = 30x

or

f(t) = 30t [where t represents the number of years.]

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Answer: 5/13

Step-by-step explanation:

To solve this problem, we can use the formula for conditional probability:

P(A|B) = P(A and B) / P(B)

where P(A and B) is the probability of both events A and B happening, and P(B) is the probability of event B happening.

Let's first calculate the total number of people in the class:

Total number of people = 5 + 6 + 2 + 11 = 24

Now, let's calculate the probability of having a cat and a dog:

P(cat and dog) = 5 / 24

Next, let's calculate the probability of having a cat:

P(cat) = (5 + 6 + 2) / 24 = 13 / 24

Finally, let's calculate the probability of having no dog:

P(no dog) = (6 + 11) / 24 = 17 / 24

Using the formula for conditional probability, we can calculate the probability of having both a cat and a dog given that a person has a cat:

P(cat and dog | cat) = P(cat and dog) / P(cat) = (5 / 24) / (13 / 24) = 5 / 13

Therefore, the probability that a student chosen randomly from the class has a cat and a dog is 5/13.

The angle measure of LJK is 27 degrees

Following the triangle sum theorem, we have that the sum of the interior angles of a triangle is 180 degrees

Also, we need to know that the sum of angles on a straight line is 180, then, we have;

<JLK = 180 - <LKM = 180 - (8x - 19)

Then, substitute the value, we have that;

<JKL + < JLK + < KJL = 180

Then,

3x - 16 + (180 - (8x - 19)) + 2x + 15 = 180

expand the bracket, we have;

3x - 16 - 8x - 19 + 2x + 15 = 0

add the like terms

-3x + 18 = 0

collect the terms

-3x = -18

x = 6

Then, the angle LJK = 2x + 15 = 2(6) + 15 = 27 degrees

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Answer:

800 books

problem solving steps：

adults:60%

young people:5%

children=100%-60%-5%

=35%

35%=280 books

1%=280÷35

=8

100%=800

so,there are 800 books

The values of the constants m and c include the following:

m = -1.3

c = 7.1

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;

y = mx + c

Where:

Since the point P(-7, 2) is mapped onto P' (3, -11) by the reflection y = mx + c, we can write the following system of equations;

2 = -7m + c    ...equation 1.

-11 = 3m + c    ...equation 2.

By solving the system of equations simultaneously, we have:

2 = -7m - 3m - 11

11 + 2 = -10m

13 = -10m

m = -1.3

c = 7m + 2

c = 7(-1.3) + 2

c = -7.1

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Answer:  $130 money did Brenda and Hazel have all together before buying decorations and snacks.

Here, we have,

You want to know Brenda and Hazel's combined money when the ratio of their remaining balances is 1 : 4 after Brenda spent $58 and Hazel spent $37. They had the same amount to start with.

Setup

Let x represent the total amount the two women started with. Then x/2 is the amount each began with, and their fnal balance ratio is ...

 (x/2 -58) : (x/2 -37) = 1 : 4

Solution

Cross-multiplying gives ...

 4(x/2 -58) = (x/2 -37)

 2x -232 = x/2 -37 . . . . . . eliminate parentheses

 3/2x = 195 . . . . . . . . . . . . add 232-x/2

 x = (2/3)(195) = 130 . . . . . multiply by 2/3

Brenda and Hazel had $130 altogether before their purchases.

Alternate solution

The difference in their spending is $58 -37 = $21.

This is the same as the difference in their final balances.

That difference is 4-1 = 3 "ratio units", so each of those ratio units is $21/3 = $7.

Their ending total is 1+4 = 5 ratio units, or $35.

The total they started with is $58 +37 +35 = $130.

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complete question:

Brenda and Hazel decide to throw a surprise party for their friend, Aerica. Brenda and Hazel each go to the store with the same amount of money. Brenda spends $58 on decorations, and Hazel spends $37 on snacks. When they leave the store, the ratio of Brenda’s money to Hazel’s money is 1 : 4. How much money did Brenda and Hazel have all together before buying decorations and snacks?