suppose that limx→6f(x)=15 and limx→6g(x)=−1. find the following limits. a.limx→6[f(x)g(x)]

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

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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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5 yards are equal to 15 feet. The solution has been obtained by using the unit conversion.

What is unit conversion?

The same feature is expressed in a different unit of measurement by using a unit conversion. For example, you may represent time in minutes rather than hours or distance in feet rather than miles. It is usual for measures to be given in one set of units, like feet, but to be requested in another set, like chains.

We are given 5 yards which are to be converted into feet.

We know that 1 yard = 3 feet

So,

⇒5 yards = 5 * 3

⇒5 yards = 15 feet

Hence, 5 yards are equal to 15 feet.

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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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Answer:

4.7

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

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

Answer:

33 miles

Step-by-step explanation:

You will use the Pythagoras' theorem ([tex]a^2+b^2=c^2[/tex])

Laura to her parents house is 'a', Her parents house to her grandparents house is 'c'

[tex]a^2+b^2=c^2\\c^2-a^2=b^2\\65^2-56^2=b^2\\4225-3136=b^2\\1089=b^2\\b=\sqrt{1089} \\b=33[/tex]

Laura is 33 miles from her grandparents house

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:

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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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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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 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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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 stem-and-leaf plot of the given data is attached. The correct options regarding percentage distribution, the distribution skewness, and gaps within the data are A, E, and F.

A stem and leaf plot refers to a technique used to to present and organize quantitative data (discrete or continuous) in a graphical format. It is displayed as table where each data value is split into a "stem" (the first digit or digits) and a "leaf" (usually the last digit). A stem and leaf plot can be used to visualize the shape of a distribution. The stem and leaf plot of the given data regarding the percentage loss of wetlands in the lower states is attached.

Based on the plot, it can be seen that:

Note: The question is incomplete. The complete question probably is: Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the lower 48 states, the percentage loss of wetlands per state is given. i) Make a stem-and-leaf display of these data. (Use the tens digit as the stem and the ones digit as the leaf. Enter NONE in any unused answer blanks.) ii). How are the percentages distributed? Is the distribution skewed? Are there any gaps? (Select all that apply.) A) The percentages are concentrated from 20% to 60%. B) ii. The percentages are concentrated from 60% to 90%. C) There is a gap showing that none of the lower 48 states has lost from 60% to 69% of its wetlands. D) These data are strongly skewed left. E) These data are fairly symmetric, perhaps slightly skewed right. F) There is a gap showing that none of the lower 48 states has lost from 10% to 19% of its wetlands. G) There are no gaps in the data.

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Step-by-step explanation:

If Sandra works for 42 hours per week and her weekly wage is £389.76, her hourly wage can be calculated as follows:

£389.76 / 42 hours = £9.28 per hour

When she receives a pay increase of 35p per hour, her hourly wage becomes:

£9.28 + 0.35 = £9.63 per hour

Her new weekly wage can then be calculated as:

£9.63 per hour * 42 hours = £404.66

So Sandra's new weekly wage is £404.66 after receiving a pay increase of 35p per hour.

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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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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Based on the definition of the geometric mean, the value of x is: 64.

The geometric mean of two numbers is the square root of the product of the two numbers.

In other words, if x and y are two numbers, the geometric mean of x and y is represented as √(xy).

If 16 is the geometric mean between 4 and x, then we have the following relationship:

√(4x) = 16

Squaring both sides:

4x = 256

Dividing both sides by 4:

x = 64

So the value of x is 64.

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Answer: 3m + 21

Step-by-step explanation:

The transitive closure by arithmetic operations on the adjacency matrix is  Compute A⁰ + A¹ + ... + A⁽ⁿ⁻¹⁾ where + is standard addition (integers)

The transitive closure of a graph is the set of all possible paths from one vertex to another in the graph.

The best method to determine the transitive closure by arithmetic operations on the adjacency matrix is C.

Compute

=> A⁰ + A¹ + ... + A⁽ⁿ⁻¹⁾

where + is standard addition (integers).

The standard addition of integers is used because we are counting the number of paths between each vertex.

In this method, we start by computing A⁰, which is simply the adjacency matrix itself.

A¹ gives us the number of paths between each vertex that are one step long. A² gives us the number of paths between each vertex that are two steps long, and so on. We continue this process until we have computed

=> A⁽ⁿ⁻¹⁾

where n is the number of vertices in the graph.

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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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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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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 most convenient type of loan Jane should consider obtaining based on her situation is an FHA loan.

FHA stands for Federal Housing Administration loan. This type of loan different from other loans allows those wanting to buy a house to request the loan with a very low down payment (about 3%). This makes it more accessible to people with limited incomes or who have not saved a lot of money to buy a house.

This is the best option for Janet because due to the low requirements, she can request the loan.

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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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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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Rounded to the nearest whole number, we would expect about 68 customers to pay with a credit card next week.

A whole number is a positive integer that does not have a fractional or decimal part. Whole numbers are the numbers we use for counting and for representing quantities that are not fractions or decimals. The set of whole numbers includes 0, 1, 2, 3, 4, 5, 6, and so on, with no limit on how high the numbers can go. Whole numbers do not include negative numbers or numbers with fractional or decimal parts.

To estimate the number of customers who will pay with a credit card next week, we can use the proportion of customers who paid with a credit card last week.

The total number of customers who paid with cash or a debit card is 77 + 27 = 104.

So the proportion of customers who paid with a credit card is 21/(104+21) = 0.1688 (rounded to four decimal places).

To estimate the number of customers who will pay with a credit card next week, we can multiply the expected total number of customers by this proportion:

0.1688 x 400 = 67.52

Rounded to the nearest whole number, we would expect about 68 customers to pay with a credit card next week.

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Answer:

41

Step-by-step explanation:

x - 23 = 18  Add 23 to both sides

x - 23 + 23 = 18 +23

x = 41

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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