In the figure, m∠2 = 70. Find the measure of each angle.

Answer:

Option (B)

Step-by-step explanation:

Group of 'n' friends is going to drive together.

Expected expenditure on gasoline and parking = $(15 + 20) = $35

Expected expenditure for lunch, tickets for museum and dinner

= (8 + 11 + 12) × n

= 31n

Expression representing total expenditure = 35 + 31n

This expression shows the expected expenditure on each friend = $31

Plus an extra expense on gasoline and parking = $35          

Therefore, Option (B) is the correct option.

The residual value when x = 4 is 6.72 if the line of best fit to be y = 2.78x – 4.4

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

Given the function:

y = 2.78x - 4.4

When x = 4:

y = 2.78(4) - 4.4 = 6.72

The residual value when x = 4 is 6.72 if the line of best fit to be y = 2.78x – 4.4

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Answer:

0.58

Step-by-step explanation:

on edge

Answer:

if i didnt get anything mixed up it would be A. dependent

Step-by-step explanation:

When the outcome affects the second outcome, which is what we called dependent events. Dependent events: Two events are dependent when the outcome of the first event influences the outcome of the second event.

Any function whose graph is NOT a line is said to be nonlinear. It has the equation f(x) = ax + b. With the exception of the form f(x) = ax + b, its equation can take any form. Any two points on the curve have the same slope.

To ascertain whether a table of values is a linear function, follow these steps:

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Answer:

Option D.

Step-by-step explanation:

We have the function:

f(x) = -a*(x + b)^(1/2)

Where:

a > 0

b > 0

Now, as a is positive and we have the coefficient "-a", we will have that the function is always negative.

Why? because (x + b)^(1/2) is always positive.

then: -a*(x + b)^(1/2) is always negative.

We also should see that the domain is not the set of all real numbers, because if:

x + b < 0, then we have the square root of a negative number, and we know that this is a complex number.

The only option that meets these two conditions is option D.

Answer

C

Step-by-step explanation:

Got it mf wrong

Answer:

k=8.125

Step-by-step explanation:

just divide 13 by 1.6

(1) Compute the following sums:

(a) P150

i=1 2

(b) P50

n=1 n

(c) P60

n=10 n

(d) P25

n=1 3n2

(e) P55

i=1 (i + 2)

(f) P500

k=100 k

(g) P50

k=2 (k2 − 2k + 1)

(h) P20

m=10 m3

Solution: For the solutions to these, we will use the following results, which have been

established by Gauss’s formula, and the notation shown below for convenience:

S0(n) = Xn

i=1

1 = n S1(n) = Xn

i=1

i = n(n + 1)

2

S2(n) = Xn

i=1

i

2 = n(n + 1)(2n + 1)

6

S3(n) = Xn

i=1

i

3 =

n(n + 1)

2

2

(a) P150

i=1 2=2P150

i=1 1 = 2(150) = 300

(b) P50

n=1 n = (50)(50+1)

2 = 1275

(c) P60

n=10 n = P60

n=1 n − P9

n=1 n = (60)(61)

2 − (9)(10)

2 = 1785

(d) P25

n=1 3n2 = 3P25

n=1 = 3(25)(26)(51)

6 = 5525

(e) P55

i=1 (i + 2) = P55

i=1 i + P55

i=1 2 = (55)(56)

2 + 2(55) = 1650.

(f) P500

k=100 k = P500

k=1 k − P99

k=1 k = (500)(501)

2 − (99)(100)

2 = 120300

(g) P50

k=2 (k2 − 2k + 1) = P50

k=2 k2 − 2

P50

k=2 k + P50

k=2 1

= (P50

k=1 k2 − 1) − 2(P50

k=1 k − 1) + (P50

k=1 1 − 1)

= ( (50)(51)(101)

6 − 1) − 2( (50)(51)

2 − 1) + (1(55) − 1) = 40430

(h) P20

m=10 m3 = P20

m=1 m3 − P9

m=1 m3 = [ (20)(21)

2 ]

2 − [

(9)(10)

2 ]

2 = 46125

(2) A clock at London’s Heathrow airport chimes every half hour. At the beginning of the

n’th hour, the clock chimes n times. (For example, at 8:00 am the clock chimes 8 times,

at 2:00 pm the clock chimes fourteen times, and at midnight the clock chimes 24 times.)

The clock also chimes once at half-past every hour. Determine how many times in total

the clock chimes in one full day. Use sigma notation to write the form of the series before

finding its sum.

Solution: ¡¡ There is no solution for this problem. ¿¿

Answer:

$4.50

Step-by-step explanation:

what you do is divide $22.50 by 5 pounds

The number of students the teacher bought for is 27.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cost of a yogurt cup = $2.

Cost of a textbook = $13

Cost for one students = 2 + 13 = $15

Total cost = $405

The number of students.

= Total cost / Cost of one student

= 405 / 15

= 27

Thus,

The number of students is 27.

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Answer:

Its Monday and Tuesday

Step-by-step explanation:

Answer:

Monday and Tuesday

Step-by-step explanation:

"Days colder than -1.75 F."

Note that in negative numbers the greater negative number contains a lesser value:

Tuesday: -1.9 F < -1.75 F

Monday: -2.5 F < -1.75 F

The probability that it was a fight of marine A is 0.5789

Given data:

Arfine Ahas 49% of all scheduled flights, airline B has 27 sud airline C has the remaining 24%.

Their on-4ime-rakes are 85%,60%, and 37% respectively.

A flight just left on-time

We need to find the probability that it was a fight of marine A, Probability = ?

Let A, B, and C be the events of selecting airlines A, B, and C, respectively.

P(A) = 49/100,

P(B) = 27/100,

P(C) = 24/100.

P(on-time|A) = 85/100,

P(on-time|B) = 60/100,

P(on-time|C) = 37/100.

The probability that the flight is on time is given as P(on-time).

P(on-time) = P(A) * P(on-time|A) + P(B) * P(on-time|B) + P(C) * P(on-time|C)

= (49/100) * (85/100) + (27/100) * (60/100) + (24/100) * (37/100)

= 0.718

The probability that it was a fight of marine A is given as:

P(A|on-time) = (P(A) * P(on-time|A)) / P(on-time)

= (49/100) * (85/100) / 0.718

= 0.5789

Therefore, the probability that it was a fight of marine A is 0.5789 (approximately).

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The sum of the interior angles for a pentagon is 540°

Sum of Interior Angles of a Pentagon :

The interior angles of a pentagon sum up to 540 degrees.. Regardless of how regular or irregular the pentagon is, this is true. By dividing the whole amount by 5, we can calculate the size of each internal angle in the case of regular pentagons. To determine the measure of a missing angle in the situation of irregular pentagons, we must first know the measurements of other angles.

Any pentagon's internal angles add up to 540° in the same way. This holds true regardless of how regular or irregular the pentagon is. By using the polygon angle sum formula, the following sum is obtained:

(n-2)180(n−2)×180°

where n represents the polygon's number of sides. We have n = 5 in the case of a pentagon. Consequently, utilizing the formula:

=(n-2)180=(n−2) ×180°

= (5-2) 180= (5−2) ×180°

= (3) 180= (3) ×180°

= 540=540°

Consequently, a pentagon's interior angles add up to 540 degrees.

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Answer:

0

3

Step-by-step explanation:

Check the picture below.

Answer:

D

Step-by-step explanation:

D on edg

According to the mapping diagram, the above is a function since there are no two values in set B where there is only one value in Set A mapped to them.

Mapping diagram:

A mapping diagram has two parallel columns. First column refers the domain of a function f , and the next column for its range. The lines or arrows are drawn from domain to range, to represent the relation between any two elements.

Given,

Here we have the two sets Set A and Set B.

And we need to fill  in the blanks below in order to justify whether or not the mapping shown represents a function.

We know that, a function has a very unique attribute of having one output attributed to each input.

Here the Set A is the domain while set B denotes the range.

And in each value in the domain would have exactly one value in the range which would be different for each value in the domain.

Therefore, this mapping diagram illustrates a 1 input to 1 output relationship, so it is a function.

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P(A) is the likelihood that a six-sided die will produce an even number when rolled (2, 4, or 6).

P(B) is the likelihood that a six-sided dice will land on four.

P(A) = 3/6 = 1/2

P(B) = 1/6

The probability of rolling an even number followed by a four, or P(C), equals P(A) * P(B) = 1/2*1/6 = 1/12 = 0.083 since events A and B are independent of one another.

With a six-sided die, there is a roughly 0.83*100 or 8.3% probability of rolling an even number (2, 4, or 6), followed by a four.

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Yes, Jerome's prediction is true that customers will draw a 10% discount coupon one-sixth of the time.

The possibility of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

Yes, Jeremore is correct.

It is given that a box has

Number of 10% discount coupons = 5

Number of 15% discount coupons = 8

Number of 20% discount coupons = 7

Number of 25% discount coupons = 6

Number of 40% discount coupons = 4.

The total coupons in the box = 5+8+7+6+4 = 30.

So, the probability that the customer will get a 10% coupon is

Number of 10% coupons/ Total coupons = 5/30= 1/6.

So, Jerome's prediction is true that customers will draw a 10% discount coupon one-sixth of the time.

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To prove that two angles in two triangles are congruent, you must use the Angle-Angle Postulate (AA).  The Angle-Angle Postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are congruent.

Therefore, to prove that two angles in two triangles are congruent, you must first show that the two angles have the same measure. This can be done by using the Angle Addition Postulate or by using subtracting the measure of one angle from the measure of the other.

Three vertices and three sides make up a triangle, which is a polygon. The triangle's angles are created when the three sides are joined end to end at a point. The three angles of the triangle sum up to 180 degrees.

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In order to find the values of x and y, let's compare both values of x given:

So we have that x = -14 and y = -5.

The function f(x)=\(x^2\)-2x+3 after putting x=1 then f(1)=2.

What is function?

An association between each element of a non-empty set A and at least one element of a different non-empty set B is called a function. In mathematics, a function is defined as a relation f between a set A (the function's domain) and a set B (its co-domain). f = (a,b)| for all values of a A and b B. Every element of set A must have exactly one image in set B for a relation to be considered a function. A relation from a non-empty set B is called a function if it has the property that no two separate ordered pairs in f have the same first element.  

Here the given function is ,

=> f(x)=\(x^2\)-2x+3

Now put x= 1 then

=> f(1) = \(1^2\)-2(1)+3

=>f(1) = 1-2+3

=> f(1) = 2

Hence the value of f(1)=2.

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Option A is the correct answer. The expression is (x+3)(x+7).

The given equation is x²+10x+21

we have to find the roots of the equation

x²+10x+21 =0

x²+3x+7x+21

x(x+3)+7(x+3)

(x+3),(x+7)

Now, we need to remember to factorize the given expression, x²+10x+21, and have to choose two numbers when you add them you get "10" and when you multiply them you get "21".

These numbers are:

7 and 3

Because:

7+3=10

7*3=21

Therefore, you get that the factorization of the expression  is the following:

(x+3)(x+7)

We can conclude that this factorization matches the first option.

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Given statement solution is :-Time cannot be negative in this context, we discard the solution t = -1,  the book will hit the ground after approximately 2.5 seconds.

To find the time when the book hits the ground, we need to determine when the height (h) becomes zero. We can set up the equation and solve for t.

The equation given is:

h = -\(16t^2 + 24t + 40\)

Setting h = 0, we have:

0 = \(-16t^2 + 24t + 40\)

Now we can solve this quadratic equation. There are a few methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula. In this case, we'll use the quadratic formula:

t = \((-b ± √(b^2 - 4ac)) / (2a)\)

For our equation, a = -16, b = 24, and c = 40. Plugging these values into the quadratic formula, we get:

t = \((-24 ± √(24^2 - 4*(-16)40)) / (2(-16))\)

t = \((-24 ± √(576 + 2560)) / (-32)\)

t = (-24 ± √3136) / (-32)

t = (-24 ± 56) / (-32)

Now we have two possible solutions:

t = (-24 + 56) / (-32) = 32 / (-32) = -1

t = (-24 - 56) / (-32) = -80 / (-32) = 2.5

Since time cannot be negative in this context, we discard the solution t = -1. Therefore, the book will hit the ground after approximately 2.5 seconds.

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Answer:

$53.60

Step-by-step explanation:

We are not given the angle of B but we can still construct ∠P. Here are the steps.

1) Draw a straight line - this has been completed.

2) Place your compass on point X and extend the compass and draw and arc cutting Line XY at point C.

3) Now take the compass and manually measure on the compas the distance between the two line segments on angle B.

4) without adjusting the compass on point C and draw an arc cutting the arc ealier created.

5) now place your ruler on point x and draw a Straightline from there throught the intersection z.

Now ∠P ≅ ∠B

See the attached.

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Based on the given dimensions of 28 by 50, Sara has enough material to build a birdhouse.

The dimensions provided, 28 by 50, represent the length and width of the material Sara has. To determine if it's enough to build a birdhouse, we need to consider the required dimensions for a birdhouse. The specific design and size of a birdhouse can vary, but generally, a birdhouse consists of a base, walls, a roof, and possibly additional features such as perches or entry holes.

Using the available material, Sara can cut out the required components of the birdhouse from the 28 by 50 piece. The exact dimensions of the required pieces will depend on the specific design she intends to create. By carefully planning and utilizing the available material efficiently, it is highly likely that Sara will have enough to construct a birdhouse. It is important for Sara to measure and mark the dimensions of each component accurately and consider any additional waste or margin of error during the cutting and assembly process.

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Sara wants to build the birdhouse shown. She bought a 25-inch by 46-inch sheet of plywood. Does Sara have enough wood to make the birdhouse? Explain.

Answer:

\(\begin{cases}a_1=1\\a_{n+1}=2 a_n\end{cases}\)

Step-by-step explanation:

A recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence.

The first three terms of the sequence are:

Therefore, as each term of the sequence is twice the previous term it is a geometric sequence.

When writing a recursive rule, remember to include the definition of the first term of the sequence.

Therefore, the recursive formula for the given situation is:

\(\begin{cases}a_1=1\\a_{n+1}=2 a_n\end{cases}\)

-----------------------------------------------------------------------------------------------

Additional information

The "a" signifies "term".  So a₁ is the first term, a₂ is the second term ... aₙ is the nth term.  Therefore, aₙ₊₁ is the next term.

"u" is regularly used instead of "a", but as "a" is used as the first term when writing explicit formulas, it is more preferable.

As a recursive formula for a sequence allows you to find the nth term of the sequence provided you know the value of the previous term in the sequence, to find the 6th term for example, we would need to calculate the previous terms first:

\(\implies a_1=1\)

\(\implies a_2=2 \cdot a_1=2 \cdot 1=2\)

\(\implies a_3=2 \cdot a_2=2 \cdot 2=4\)

\(\implies a_4=2 \cdot a_3=2 \cdot 4=8\)

\(\implies a_5=2 \cdot a_4=2 \cdot 8=16\)

\(\implies a_6=2 \cdot a_5=2 \cdot 16=32\)

Note:  It is more preferable to find an explicit formula for the nth term of a sequence since with an explicit formula we do not need to calculate the previous term(s).

The explicit formula for this sequence of this question is:

\(a_n=2^{n-1}\)

Therefore, to find the 6th term using the explicit formula, simply substitute n = 6 into the formula:

\(\implies a_6=2^{6-1}=2^5=32\)

As you can see, it yields the same result as the recursive formula but without the need to calculate the preceding terms.

Answer:

3/5

Step-by-step explanation:

6/10 => 3/5

in decimal form its 0.6

Answer:

6÷1000=0,6

Step-by-step explanation:

6÷1000=0,006

0,6/100=

0,6%

the Correct answer is 0,6

The expression is constant for b = -7.5, and the constant is 49.5.

A mathematical expression is a phrase that contains at least two terms or numbers and one action. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given that, The expression 3(5x - 1) + b(2x - 7) is constant

It means the expression doesn't consist of a variable. So, we need to find the 'b' such that the variable 'x' need to be eliminated.

The co-efficient of the 'x' should be '0'.

3(5x - 1) + b(2x - 7)

= 15x - 3 + 2bx - 7b

= (15 + 2b)x - 3 - 7b

Now, 15 + 2b = 0

2b = -15

b = -7.5

On substituting the value of 'b' in the expression,

= -3 - 7 * (-7.5)

= 52.5 - 3

= 49.5

Therefore, The expression is constant for b = -7.5, and the constant is 49.5

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There are many ways of doing it, but here is mine.

Step-by-step explanation:

x = 6, y = 16

So now you multiply six by four and you will get twenty four plus sixteen, if you add them then you will get forty.

The term that best matches the description provided is "object."

An object is a unit of data that represents an abstraction or a real-world entity, such as a person, place, or thing. In object-oriented programming, objects are instances of classes and contain attributes (data) and methods (functions) that define their behavior. Therefore, among the options given, "object" is the correct choice.

what is functions?

In mathematics and computer science, a function is a relationship between a set of inputs (called the domain) and a set of outputs (called the range) such that each input is associated with exactly one output. Functions are used to describe and model various phenomena and processes.

A function typically takes one or more input values, performs a specific operation or transformation on them, and produces an output value. The input values are often referred to as arguments or parameters, and the output value is the result of applying the function to the given inputs.

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