An experiment involves rolling a six-sided die. Let event A = the event of rolling an even number, and event B = the event of rolling a number less than or equal to 3. Then P(A/B) =
A. 1/3
B. 3/6
C. 1/6

The first six terms of the given sequence are 0, 3, 8, 15, 24, 35

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given is a formula for a sequence aₙ = n²-1, we need to find the first six terms of the sequence,

Put n = 1 for first term,

a₁ = 1²-1

= 0

Put n = 2, for second term,

a₂ = 2²-1

= 3

Put n = 3, for third term,

a₃ = 3²-1

= 8

Put n = 4, for fourth term,

a₄ = 4²-1

= 15

Put n = 5, for fifth term,

a₅ = 5²-1

= 24

Put n = 6, for sixth term,

a₆ = 6²-1

= 35

Hence, the first six terms of the given sequence are 0, 3, 8, 15, 24, 35

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Answer: The probability of Hans winning and taking no more than three shots can be calculated using the principle of total probability and the law of total probability.

Let's call the event of Hans winning and taking no more than three shots "A". Then, the probability of event A can be broken down into several cases:

Case 1: Hans wins in one shot: P(A|Hans wins in one shot) = P(Hans wins in one shot) = 0.4.

Case 2: Hans wins in two shots: P(A|Hans wins in two shots) = P(Franz misses in the first shot) * P(Hans wins in the second shot) = (1 - 0.4) * 0.4 = 0.24.

Case 3: Hans wins in three shots: P(A|Hans wins in three shots) = P(Franz misses in the first two shots) * P(Hans wins in the third shot) = (1 - 0.4)^2 * 0.4 = 0.144.

Finally, the probability of event A can be calculated using the law of total probability as follows:

P(A) = P(A|Hans wins in one shot) + P(A|Hans wins in two shots) + P(A|Hans wins in three shots) = 0.4 + 0.24 + 0.144 = 0.784.

So, the probability of Hans winning the competition and taking no more than three shots is 0.784.

Step-by-step explanation:

The following values, when rounded to one significant figure in accordance with the stated statement, are 3*10⁴, 3, and 1*10⁴ m.

True figures are the number of digits that increase a value's accuracy, often a measurement. Starting with the first semi-digit, we count actual numbers. All the decimal places to the right of the next non-zero digit after the calculation are significant. The number 0.0079800, for instance, includes five significant digits. If a measurement includes the noughts to the side of the last non-zero digit, they are all significant.

As stated in the preceding sentence:

a). 25637 ≈  3*10⁴

b). 2.51 ≈ 3

c). 9877m ≈ 10000m = 1*10⁴m

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The correct conversion factors to indicate the number of feet in one mile is: 1 mi = 5280 ft.

To convert miles to feet, we must use the equality: 1 mi = 5280 ft.

Using the table of equalities, we can see that 1 mi = 5280 ft, so the correct conversion factor to indicate the number of feet in one mile is 1 mi = 5280 ft.

To convert miles to feet, we use the conversion factor of 1 mile being equal to 5280 feet. This means that for every 1 mile, there are 5280 feet. To convert a specific number of miles to feet, we multiply the number of miles by the conversion factor of 5280 feet/mile. For example, if we want to convert 2 miles to feet, we multiply 2 by 5280 to get 10560 feet. Hence, 2 miles is equal to 10560 feet. This conversion factor can be used to convert any number of miles to feet, as long as we use it consistently and accurately.

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The geometric relation between the vectors v and w are:

The vectors are in the same direction.

Now, According to the question:

Geometrical Interpretation of Scalar Product

From the scalar product formula, we have a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → ) , that is, the scalar product of vectors a and b is equal to the magnitude of vector a times the projection of a onto vector b.

Vectors describe movement with both direction and magnitude. They can be added or subtracted to produce resultant vectors. The scalar product can be used to find the angle between vectors.

Now, vw =-||v|| ||w||

a.b = |a| |b| cos θ = |a| proj→b(→a) proj b → ( a → )

vw =-||v|| ||w|| cos θ = |v| proj →w(→v) proj w → ( v → )

Hence, The vectors are in the same direction.

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Answer:

y = 2x

Step-by-step explanation:

We know

They earn $2 for each cup of lemonade they sell. So, the equation is

y = 2x

The value of the equation is -46, the correct option is A.

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

A mathematical equation is a statement with two equal sides and an equal sign in between. An equation is, for instance, 4 + 6 = 10. Both 4 + 6 and 10 can be seen on the left and right sides of the equal sign, respectively.

Given;

The equation; a+16=-30

Now,

a=-30-16

a=-46

Therefore, the answer of equation will be -46

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Answer: A: 120

Step-by-step explanation:

When adding all sides of a triangle it should always equal 180 degrees so by adding 30+30=60 after you do 180-60=120 or the proper way is 30+30+x=180

60+x=180

-60     -60

x=120

Answer:

4.7

Step-by-step explanation: anything over 5 you round up

The graph shows the discontinuity of the function at x = -1 and x = 1. Therefore, the values of x at which the function is not continuous are -1 and 1.

The graph shows that at x = -1 and x = 1, the graph has a sharp jump in the value of the function. This means that the function is not continuous at those points, and thus the values of x at which the function is not continuous are -1 and 1. The graph represents a mathematical function, and the concept of continuity is crucial in mathematical analysis. A function is considered continuous at a specific point if the value of the function at that point exists and the limit of the function as the input approaches that point is equal to the value of the function at that point. In this particular graph, the function experiences a sharp increase or decrease in its value at the points x = -1 and x = 1. This sudden change in the function's value indicates that the function is not continuous at these points, meaning that its value does not approach a single limiting value as the input approaches these points. Thus, the points -1 and 1 are the values of x at which the function is not continuous.

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The total surface area of the triangular pyramid is 170.4 inches².

The area of a three dimensional object on it's outer surface is called the surface area of the object.

A triangular pyramid has a triangular base and three triangular faces.

Given that, base of a triangular pyramid is an equilateral triangle. Each side of the base measures 12 in. The area of the base is 62.4 in².

Area of the base = 62.4 inches²

Slant height = 6 inches

Length of edge of each of the three triangular faces = 12 inches

Area of a triangular face = [tex]\frac{1}{2}[/tex] × 12 × 6 = 36 inches²

Area of three triangular faces = 3 × 36 inches² = 108 inches²

Total surface area = 108 inches² + 62.4 inches² = 170.4 inches²

Hence 170.4 inches² is the total surface area of the pyramid.

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At B: 11:35 Bart will arrive back at the Railway Station for the final time

Let's call the number of circuits Bart completes "n".

Each circuit takes 5 minutes to travel between each stop and 5 stops in total, so each circuit takes 5 * 5 = 25 minutes.

The bus waits 10 minutes at the Railway Station between each circuit, so the total time for each circuit is 25 + 10 = 35 minutes.

Bart will complete 4 circuits, so the total time he spends on the bus tomorrow is 4 * 35 minutes = 140 minutes.

The first departure of the day from the Railway Station is at 09:15, so after 140 minutes of travel, Bart will arrive back at the Railway Station at 09:15 + 140 minutes = 11:35.

Therefore, the answer is B) 11:35.

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A joule is one unit of energy, while a kilojoule is 1000 joules.

KJ x 1,000 = J.

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The horizontal distance jade she covered is approximately 2.0 km.

Let x be the horizontal distance,

Given,

Viola drives 2 kilometers up a hill that makes an angle of 9 with the horizontal.

Thus, the angle between the horizontal and the direction of his walking = 9°, and The angle between the horizontal and vertical = 90°

By making the diagram of the given situation,

The angle between vertical and the direction of his walking = 180°(9+90°)=180° - 99° = 81°

By the law of sine,

[tex]\frac{sin90}{2}=\frac{sin 81}{x}[/tex]

x*sin 90°=2*sin 81°

x= 1.97537668119 ≅ 2.0

Hence, the horizontal distance jade she covered is approximately 2.0 km.

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The equation of a line that has a slope of -1/3 and y-intercept at (0, 1) is y = -x/3 + 1.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

From the information provided above, we have the following slope and y-intercept on the line:

Therefore, the required equation of line is given by:

y = mx + c

y = (-1/3)x + 1

y = -x/3 + 1

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The inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)

An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of the function produces the output x. x. A function that has an inverse is called invertible, and the inverse is denoted by f⁻¹.

Given that, a set of ordered pairs defines a function.

{(-49,7), (-56,8), (-63,9), (-70,10)}

We need to find its inverse function,

Since, we know that,

The inverse of a function means that the input becomes the output of the function and the output becomes input.

When the function is given in the form of ordered pairs, the first element of each ordered pair represents the input and the second element represents the output.

Therefore,

The inverse will be:

{(7, -49), (8,-56), (9,-63), (10, -70)}

Hence, the inverse of the function defined by the ordered pairs are (7, -49), (8, -56), (9,-63), (10, 70)

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The correct statement regarding the linear function is given as follows:

a) The slope of the function is 85, and it represents the change in net profit per product sold.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

The function for this problem is given as follows:

P(x) = 125x - (40x + 1200).

In slope-intercept format, it is obtained as follows:

P(x) = 125x - 40x - 1200

P(x) = 85x - 1200.

Hence the slope is of 85, representing the rate of change, and option a is the correct option.

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At time t=0 the signal value is 10, then it decreases to 3, increases to 25, decreases to 4, increases to 30, decreases to 2 and then increases to 17.

At time t=0 the signal value is 10. This is the starting point for monitoring the signal every second. After one second, the signal value decreases to 3. After another second, the signal value increases to 25. After another second, the signal value decreases to 4. After another second, the signal value increases to 30. After another second, the signal value decreases to 2. Finally, after the last second, the signal value increases to 17. As the signal is monitored every second, it is possible to track its changes over time. This example signal had some fluctuation, with both increases and decreases in the value. It started at 10, decreased to 3, then increased to 25, decreased to 4, increased to 30, decreased to 2, and then increased to 17. This example shows how a signal can fluctuate over time, and how its value can change with each second that passes.

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Peter's gross semi-monthly earnings are P7,717.5 and each of his men's gross semi-monthly earnings are P6,150.

To calculate Peter's gross earnings,

We need to find the commission he earns on his own sales and the override commission he earns on his men's sales.

Peter's Commission on his own sales:

2.5% of P5,500 = P137.5

Peter's Override Commission on his men's sales:

0.5% of (number of men * P4,000) = 0.5% of (number of men * 4000)

Let's assume he has 4 men.

Then the total override commission would be:

0.5% * 4 * 4000 = P80

So Peter's gross semi-monthly earnings would be:

P5,500 + P137.5 + P80 + P2,000 = P7,717.5

To calculate the gross earnings of each of Peter's men, we need to find their basic semi-monthly salary, their commission on their own sales, and their transportation allowance.

Each man's basic semi-monthly salary: P4,000

Each man's Commission on their own sales will be:

3.75% * P4,000 = P150

So each man's gross semi-monthly earnings would be:

P4,000 + P150 + P2,000 = P6,150

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The probability that at most 8 of 9 students take the bus to school is approximately 0.9538.

To find the probability of at most 8 students taking the bus, we can use the cumulative distribution function (CDF) of the binomial distribution.

The CDF gives the probability of getting a certain number or fewer of successes in a fixed number of trials, where each trial has a fixed probability of success.

The CDF of a binomial distribution with parameters n (number of trials) = 9 and p (probability of success) = 0.75 is given by:

F(k) = Σ(i = 0 to k) (9 choose i) * (0.75)^i * (0.25)^(9-i)

where (9 choose i) is the binomial coefficient, which gives the number of ways to choose i successes from n trials.

Thus, to find the probability of at most 8 students taking the bus, we compute the CDF at k = 8:

F(8) = Σ(i = 0 to 8) (9 choose i) * (0.75)^i * (0.25)^(9-i)

Using a binomial calculator or programming language, we can find the value of F(8) which is approximately 0.9538.

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Note can be repeated, but all the note cannot be the same to form an ordered five-note musical logo.

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Conjecture about the relationship between tan(0) and tan(90 – 0) is tan(90-θ) is equal to cot θ.}. Tan(-) is equal to -tan, as is known. Therefore, eqn1 can be expressed as follows: -tan(90-), which results in -cot.

The equivalent of the given angle (90 degrees) in radians can also be used to indicate a tan angle of 90 degrees (1.57079 . . .) 90 degrees = 90° (180°/90°) rad = /2 or 1.5707... Given that the tangent function is periodic, we can write tan 90° as tan(90° + n 180°), where n Z.

tan(90-θ) is equal to cot θ.}

Tan(-θ) = -tanθ

-tan(90-θ) =  -cotθ.

-cotθ.

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The dependent variable is the number of games and the independent variable is the number of months.

We know that Quincy was given 3 video games for his new game system and every month he saves enough to get 2 more video games.

Then the two variables are the number of months and the number of games.

We know that he starts with 3 games and each month he adds 2 more, then we can write the relation:

y = 3 + 2*x

Where y is the number of games and x the number of months.

Then the independent variable is the number of months, and the dependent variable (which depends on the other one) is the number of games.

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The exact fractions. 2 x2−4 dx −2 = 10.6666

What is Fractions?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.

A fraction is used to denote a portion or component of a whole. It stands for the proportionate pieces of the whole. Numerator and denominator are the two components that make up a fraction. The numerator is the number at the top, and the denominator is the number at the bottom

[tex]\int\limits^2_2 {|x^{2} -4|} \, dx[/tex]

Eliminate absolutes

[tex]|x^{2} -4| : -2\leq x\leq 2[/tex]

without absolutes is

[tex]\int\limits^2_2 {x^{2} +4} \, dx \\\int\limits^2_2 {-x^{2} } \, dx +\int\limits^2_2 {4} \, dx \\[/tex]

=(-x³/3 )²₋₂ +4x )-₂²

=(-1/3 ) ( 8+8) +4(2+2)

= -16/3 +16

=32/3

= 10.6666

So the exact fraction is [tex]\int\limits^2_2 {|x^{2} -4|} \, dx[/tex]

=10.6666

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Answer: 3m + 21

Step-by-step explanation:

The investment in 2% rate of interest was $2800 and the investment in 3% rate of interest was $3200.

Let the amount invested in 2% interest rate be x. So, the remaining invested amount = (6000 - x). The simple interest will be calculated by the formula -

S.I. = P×R×T/100, where S.I. is simple interest, P is principal, R is rate of interest and T is time.

Also, the sum of interest in each is $152. So, finding the individual interest first.

SI = x × 2 × 1/100

SI = 2x/100

SI = (6000 - x) × 3 × 1/100

SI = (18000 - 3x)/100

Finding the value of x.

2x/100 + (18000 - 3x)/100 = 152

Multiplying the equation with 100

2x + 18000 - 3x = 15200

3x - 2x = 18000 - 15200

x = 2800

Investment in 3% rate = 6000 - 2800

Investment in 3% rate = $3200

Thus, the investment was $2800 and $3200.

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limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x). Since limx→6f(x) = 15 and limx→6g(x) = -1, then limx→6[f(x)g(x)] = 15 * (-1) = -15. This means that the limit of the product of the two functions is -15.

We can use the limit laws of product to solve this limit.

limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x)

= 15 * (-1)

= -15

To solve this limit, we can use the limit laws of product. By the limit laws of product, the limit of a product is equal to the product of two limits. Therefore, limx→6[f(x)g(x)] = limx→6f(x) * limx→6g(x). Since limx→6f(x) = 15 and limx→6g(x) = -1, then limx→6[f(x)g(x)] = 15 * (-1) = -15. This means that the limit of the product of the two functions is -15.

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The measure of the indicated angle in each triangle is ∠U=80° and ∠Q =93°

The measure of each triangle's specified angle.

Comprehensive explanation:

Calculate the indicated angle's measurement.

Given: The additional two triangle angles.

Solution:

We are aware that a triangle's three angles add up to 180 degrees.

So,

The measure of the indicated angle in each triangle.​

1st TRIANGLE

∠U+∠V+∠T =180°

∠U+63°37° =180°

∠U= 180°-100°

∠U=80°

2ND TRIANGLE

∠A+∠B+∠C=180°

46°+90°+∠C =180°

∠C=44°

The measure of the indicated angle in each triangle.​

3rd TRIANGLE

∠R+∠P+∠Q= 180°

36°+51°+∠Q =180°

∠Q =93°

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Answer:

C

Step-by-step explanation:

15mpg

$1.09/gallon

10.5 per day * 22 days = 231 miles

will need 231/15 gallons of gas = 15.4gallons

cost = 15.4*1.09 = $16.79