How do you find the expression for the nth term in an exponential sequence.
Example:-
1, 3, 7, 15

The solution is, the quadrilateral ABCD is a trapezium.

In geometry a quadrilateral is a four-sided polygon, having four edges and four corners. The word is derived from the Latin words quadri, a variant of four, and latus, meaning "side".

here, we have,

from the given figure we get,

the figure has four sides, which are not all equal, and, two of them are parallel to each other.

here we get,

angle A = angle C = 80

angle B = angle D = 100

and, two sides are parallel to each other.

Hence, The solution is, the quadrilateral ABCD is a trapezium.

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Answer:

The true statement on the profitability is c.

Step-by-step explanation:

The theoretical profitability of the swimming, P(swimming), is one-half, but the experimental probability is 23 over 50.

The theoretical probability of an occurrence indicates the propensity to occur. The theoretical probability of receiving heads is 1/2 since we know that flipping a coin has an equal chance of landing tails or heads. The frequency of an event actually occurring in an experiment is referred to as its experimental probability.

The theoretical probability of swimming is 1 / 2 because it is either heads or tails. However, the experimental probability of swimming is:

so,

= Number of swimmers / Total number of students

= 23 / 50

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The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40. The correct statement is option B.

The theoretical probability of an event is the probability calculated based on the assumption of equally likely outcomes, while the experimental probability is the probability determined from actual data or outcomes observed in an experiment.

In this case, there are 40 students, and each camper flips a coin to decide between swimming and hiking. The outcome frequency shows that 12 students chose swimming, and 28 students chose hiking.

Let's compare the theoretical and experimental probabilities of swimming:

The theoretical probability of swimming, P(swimming), is one-half (1/2), as there are two equally likely outcomes (heads or tails) when flipping a fair coin.

The experimental probability of swimming is the number of students who chose swimming (12) divided by the total number of students (40), which is 12/40.

Now, let's analyze the options:

A. The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 28 over 40.

The theoretical probability is correct (1/2), but the experimental probability is incorrect (it should be 12/40, not 28/40).

B. The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.

This statement correctly represents both the theoretical probability (1/2) and the experimental probability (12/40).

C. The theoretical probability of swimming, P(swimming), is 12 over 28, but the experimental probability is one half.

This statement has incorrect values for both the theoretical and experimental probabilities.

D. The theoretical probability of swimming, P(swimming), is 28 over 40, but the experimental probability is one half.

The theoretical probability mentioned here (28/40) is not correct. The theoretical probability of swimming is 1/2 (one-half), not 28/40.

The correct statement is option B:

The theoretical probability of swimming, P(swimming), is one half, but the experimental probability is 12 over 40.

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The arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

In mathematics, an expression or mathematical expression is a combination of terms both variables and constants. For example -

2x + 4y + 5z

4y + 2x

Given are the expressions as given in the questions.

{a} -

5 - 9 = - 4

{b} -

8 - 8 = 0

{c} -

- 1 + 12 = 11

{d} -

- 12 + 12 = 0

{e} -

- 2 + 4 + 3

5

{f} -

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

Therefore, the arithmetic expressions are solved and answered below -

5 - 9 = - 4

8 - 8 = 0

- 1 + 12 = 11

- 12 + 12 = 0

- 2 + 4 + 3 = 5

- 4 + 3 + 2 - 1 = - 2 + 2 = 0

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{Complete question -

Calculate the following:

a) 5-9

b) 8-8

c) -1 + 12

d) -12 + 12

e) -2 +4+3

f) -4-3+2-1}

The probability of getting three or fewer heads on four flips of a fair coin is 0.75.

The fair coin is flipped four times. The sample space can be found as follows,

There will be 4 trial and each trial can have two outcomes so the total number of outcomes is 2x2x2x2.

Total possible outcomes are 16.

Now, the number of favorable outcomes when there will be 3 or less heads will be 6 because there has to be 3 heads in four position and that too without repetition.

So, the probability of event is,

P = Total favorable event/Total possible events

P(of three or fewer heads on four flips of a fair coin) = 6/8

So, probability of three or fewer heads on four flips of a fair coin is 0.75.

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The relationship between a statistic and a parameter is the same as the relationship between , Option(A) a sample and a population

The Population is defied as an entire group of individuals that we are interested in studying, while a sample is a subset of that population that we actually observe and collect data from.

A Parameter is defined as a numerical characteristic of a population, such as its mean or variance, whereas a statistic is a numerical characteristic of a sample, such as its sample mean or sample standard deviation.

The relationship between a sample and a population is similar to the relationship between a statistic and a parameter because a sample is used to estimate  information about the population, and a statistic is used to estimate  information about a parameter.

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Answer:

2. x=16

4. x=18.75, y=11.2

Step-by-step explanation:

2. x/8=30/15 ⇒x=2x8=16

4. x/15=8/6.4 ⇒x=1.25x15=18.75

  y/14=6.4/8 ⇒y=0.8x14=11.2

The missing side lengths x = 16; y = 11.2 and x = 18.75

Similar figures (2)

Given that the triangles are similar, we make use of the following equivalent ratio

8 : 15 = x : 30

Multiply the first ratio by 2

So, we have

16 : 30 = x : 30

By comparison, we have

x = 16

Similar figures (4)

Given that the triangles are similar, we make use of the following equivalent fraction equation

y/6.4 = 14/8

So, we have

y = 6.4 * 14/8

Evaluate

y = 11.2

For x, we have

x/8 = 15/6.4

This gives

x = 8 * 15/6.4

So, we have

x = 18.75

Hence, the value of x is 18.75

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The distance of 2√65 miles Joselyn is from where she started.

The formula of the distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

Her initial position is the origin (0, 0), and she ran 2 miles north to reach (0, 2). Then, she ran 10 miles east to reach (10, 2). After that, she ran 4 miles north to reach (10, 6). Then, she ran 4 miles east to reach (14, 6). Finally, she ran 2 miles north to reach (14, 8).

To find the magnitude of Joselyn's displacement, we can use the Pythagorean theorem.  

We can consider the displacement from the starting point to Joselyn's final position as the hypotenuse of a right triangle, and the north-south and east-west displacements as the two shorter sides.

Thus, the displacement (d) can be calculated as:

d = √((14 - 0)² + (8 - 0)²)

d = √(14² + 8²)

d = √(196 + 64)

d = √(260)

d = 2√65

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The value of x in the given figure is 6.

Alternate angles are angles that occur on opposite sides of the transversal line and have the same size.

Given that, two lines are parallel, line U ║ line V, we need to find the value of x,

Using the concept of alternate interior angles between parallel lines,

Alternate angles between the parallel, line are equal,

Therefore,

16x-6 = 90

16x = 96

x = 6

Hence, the value of x in the given figure is 6.

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the mile-a-minute weed can grow up to 0.25 inches per hour.

A fraction is a mathematical expression that represents a part of a whole. It is written as a ratio of two numbers, the numerator and the denominator, separated by a horizontal line. The numerator represents the part of the whole that is being considered, while the denominator represents the whole.

Given by the question.

To convert 0.5 ft per day to inches per hour, we can use the following conversion factors:

1 ft = 12 inches (since there are 12 inches in a foot)

1 day = 24 hours (since there are 24 hours in a day)

So, to convert 0.5 ft per day to inches per hour, we can use the following steps: Convert feet to inches:

0.5 ft x 12 inches/ft = 6 inches

Convert days to hours:

1 day = 24 hours, so:

6 inches/24 hours = 0.25 inches per hour

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The number of miles driven is 150

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

Base fee = $15.99

Additional charge = $0.90

Using the above as a guide, we have the following:

Total charge = Base fee + Additional charge * Number of miles

Substitute the known values in the above equation, so, we have the following representation

15.99 + 0.9 * Number of miles = 150.99

Evaluate the like terms

0.9 * Number of miles = 135

Divide

Number of miles = 150

Hence, the Number of miles is 150

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Triangle JKL is congruent to triangle MLK based on angle - angle - side congruency theorem

A triangle is a polygon that has three sides and three angles. Types of triangles are equilateral, isosceles, scalene, right angled triangle. In an equilateral triangle, two sides are equal.

Two triangles are said to be congruent, if all angles and all sides are congruent to each other.

From the diagram:

∠KJL = ∠LMK (Given)

∠JKL = ∠MLK (Given)

KL ≡ KL

PS = QS (Definition of equilateral triangle)

ΔJKL ≅ ΔMLK (angle - angle - side congruency theorem)

Triangle JKL is congruent to triangle MLK

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Answer:

Step-by-step explanation:

i don't know

A) The scale factor is 2.

B) The measure of m<C is 67.17.

C) The measure of m<Z is 75.96

D) The length of AD is 4 unit.

A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.

Given:

A) The scale factor is

= CB/ XY

= 5/ 2.5

= 2 unit

B) We’re given the measurement of angle XYZ, which is also the measurement of angle y.

Since angles in similar triangle are equivalent, if y(67.17)=c, then c must be equal to 67.17.

C) The measure of angle Z is equivalent to 75.96

D) The length of AD

= 2 x WX

= 2 x 2

= 4 unit

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The range of the given piecewise function is -

-4 ≤ x ≤ 3.

A piecewise function is a function that is defined on a sequence of intervals. A common example is the absolute value function.

Given is the piecewise function as shown in the image.

Range is the set of values that exist for a specific value in the domain of the function. So, we can write the range as the set of {y} values for the function. From the graph, we can write the range as -

-4 ≤ x ≤ 3

Therefore, the range of the given piecewise function is -

-4 ≤ x ≤ 3.

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Answer:

A : 0.9 B: 45.2 C:0.006 D:3/500 E:25% F: 1/4

Step-by-step explanation:

The measure of angle ∠A will be 53.13.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.

The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

The two sides are perpendicular = 9.2 and the base is 7.2. The angle ∠A will be calculated as:-

tan(A) = P / B

A = tan⁻¹ ( 9.2 / 7.2 )

A = 53.13°

Therefore, the measure of angle ∠A will be 53.13.

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Given:-

To find:-

Answer :-

Here we will make use of trigonometric ratios . As we know that,

[tex]\sf \implies \cos\theta =\dfrac{base}{hypotenuse} \dots (1)\\[/tex]

And here,

So on substituting the respective values in (1) , we have;

[tex]\sf \implies \cos64^\circ =\dfrac{x}{42} \\[/tex]

And the value of

[tex]\sf \implies 0.438 = \dfrac{x}{42} \\[/tex]

[tex]\sf \implies x = 42 \times 0.438 \\[/tex]

[tex]\sf \implies x = 18.396 \\[/tex]

[tex]\sf \implies \underline{\underline{ x \approx 18.4 }} \\[/tex]

and we are done!

Arianne's monthly mortgage payment will be $536.82.

A mortgage payment is generally made up of components like principal, interest, taxes and insurance. The interest is the cost of borrowing money. The amount of interest one pay is determined by your interest rate and your loan balance.

To calculate Arianne's monthly mortgage payment, we can use the following formula: M = P [ i(1 + i)^n ] / [ (1 + i)^n – 1 ]

First, we need to calculate the monthly interest rate: i = APR / 12 = 5% / 12 = 0.004167

Next, we can substitute the values into the formula: The computation of our monthly payment goes as follows:

= $90,000 [ 0.004167(1 + 0.004167)^360 ] / [ (1 + 0.004167)^360 – 1 ]

= $536.82.

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Answer: $4.20

Step-by-step explanation:

The bag contains $4.20. We know that 18% of the coins are pennies and 36% are dimes. There are 50 coins total, so 18% of 50 is 9 pennies and 36% of 50 is 18 dimes. Since there are 2 more nickels than pennies, there must be 11 nickels. 9 pennies plus 11 nickels plus 18 dimes equals 38 coins. To calculate the total amount of money, we multiply 38 by the value of each type of coin: 9 pennies x $0.01 = $0.09, 11 nickels x $0.05 = $0.55, and 18 dimes x $0.10 = $1.80. Adding these together, we get $0.09 + $0.55 + $1.80 = $2.44. Therefore, the bag contains $4.20.

Answer: There are 9 pennies, 18 dimes, and 11 nickels and 12 quarters

so in total, the bag has $11.2

Step-by-step explanation:

18% of 50 = 9

36% of 50 = 18

Answer:

Step-by-step explanation:

a)C

b)D

c)B

d)A

ok so 5/10=0.5

and 5/50=0.1

and 5/100=0.05

and 5/20=0.25

For all the given sequence of transformations, Rectangles ABCD and WXYZ will be similar.

It is given that Rectangles ABCD and WXYZ are similar, but not congruent.

For all the transformations given represents the similar rectangles. Dilations, rotations, translations and reflections all lead to similar figures.

Therefore, for all the given sequence of transformations, Rectangles ABCD and WXYZ will be similar.

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Two lines that form a right angle at their point of intersection are perpendicular to each other.

The negative reciprocal is equal to the slope of the perpendicular lines. A transversal line is a line that is perpendicular to two parallel lines. Equal pairs of alternate angles and matching angles are created in the case of the transversal line.

When two lines intersect at a right angle, they are perpendicular to each other. The junction is referred to as the point of perpendicularity. The perpendicular lines form a 90-degree angle, and they can be used to create a coordinate system or used in geometric constructions. Such lines are called perpendicular lines.

Correct Question :

Two lines that form a right angle at their point of intersection are called what?

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The principal for Account A is $150, and we do not have enough information to find the principal for Account B. Account A earned the most interest the first month because it has a higher monthly interest rate.

The principal for Account A can be found using the formula for simple interest:

I = Prt, where I is the interest, P is the principal, r is the interest rate, and t is the time in years.

Rearranging the formula to solve for P, we get P = I / (rt).

For Account A, the interest is $9.45, the interest rate is 3.6%, or 0.036, and the time is 21 months, or 1.75 years.

Plugging these values into the formula, we get:

P = $9.45 / (0.036 × 1.75) = $150

So the principal for Account A is $150.

For Account B, we do not have enough information to find the principal. We know the interest rate, but we do not know the interest or the time.

To determine which account earned the most interest the first month, we can compare the monthly interest rates.

The monthly interest rate for Account A is 3.6% / 12 = 0.3%, and the monthly interest rate for Account B is 2.4% / 12 = 0.2%.

Since the monthly interest rate for Account A is higher, it earned the most interest the first month.

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Answer:

One equivalent ratio that compares the number of boys to the number of girls in Harold's class is 7:6. Another equivalent ratio is 14:12, and yet another equivalent ratio is 21:18. These ratios are equivalent because they represent the same relationship between the number of boys and girls, just with different scale.

Answer:

14:12

21:18

35:30

Step-by-step explanation:

An equivalent ratio is a ratio that represents the same comparison as another ratio, but with different values. To find equivalent ratios to compare boys to girls in Harold's class, we can multiply or divide both the numerator and denominator of the original ratio by the same value.

The original ratio of boys to girls is 7 boys to 6 girls, or 7:6. Here are three equivalent ratios:

14:12 (multiplying both the numerator and denominator by 2)

21:18 (multiplying both the numerator and denominator by 3)

35:30 (multiplying both the numerator and denominator by 5)

The common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.

To find the common factors of two numbers, we need to find the factors of each number and then identify the ones that they have in common. For example, if we want to find the common factors of 20 and 45, we first find the factors of 20 and 45:

The factors of 20 are: 1, 2, 4, 5, 10, 20

The factors of 45 are: 1, 3, 5, 9, 15, 45

The factor 1 is always a common factor of any two numbers, since every number is divisible by 1. The factor 5 is a common factor of 20 and 45 because both 20 and 45 are divisible by 5. It is important to note that the other factors of 20 and 45 are not common factors, since they are not shared by both numbers.

Therefore, the common factors of 20 and 45 are 1 and 5, since these are the only factors that both numbers share.

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The nth term of the sequence is a{n} = 35 + (-5)(n - 1) and the 100th term would be a{100} = - 460.

A sequence in which the difference of the consecutive terms remain constant is called a arithmetic sequence.

Given is the sequence as -

35, 30, 25, 20

We can write the nth term of the sequence as -

a{n} = a + (n - 1)d                                            ... { 1 }

a{n} = 35 + (-5)(n - 1)

For {n} = 100, we can write -

a{100} = 35 + (-5)(99)

a{100} = 35 - 495

a{100} = - 460

Therefore, the nth term of the sequence is a{n} = 35 + (-5)(n - 1) and the 100th term would be a{100} = - 460.

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The SI (International System of Units) unit of pressure is the pascal (Pa), which is defined as one newton per square meter (N/m²).

To convert megapascals (MPa) to pounds per square inch (psi), you can use the following conversion factor:

1 MPa = 145.0377377 psi,

To convert, simply multiply the number of megapascals by 145.0377377 to get the equivalent pressure in psi.

For example, if you want to convert 20 MPa to psi, you can use the conversion factor as follows:

20 MPa × 145.0377377 psi/MPa = 2900.75515 psi (rounded to two decimal places)

Therefore, 20 MPa is approximately equal to 2900.76 psi.

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The equations are solved and the old account balance for Account #4 is given by A = - $ 30

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Acc #    Old Acc Balance ($)      Trans Amount ($)      New Acc Balance($)

1                       352                                       -48                      304

2                      432                                      +80                      512

3                       75                                       -100                     -25

4                       -30                                        52                       12

5                      -10                                        -20                     -30

So , the old account balance for the account number 4 is -30

Hence , the equation is A = - $ 30

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Percent error in Keiko's estimate is 6.25%

Percent error is the difference between estimated value and the actual value in comparison to the actual value and is expressed as a percentage.

[tex]Percent error=\frac{|observed value -true value|}{true value}*100[/tex]

Students estimate the distance a toy car will role down a ramp.

The car rolls 80cm.

Keiko estimate for the distance the car will role is 85cm.

Percent error in Keiko's estimate is calculated by,

[tex]Percent error=\frac{|observed value -true value|}{true value}*100[/tex]

                     = [tex]\frac{|85-80}{80} *100[/tex]

                     =6.25%

Hence, percent error in Keiko's estimate is 6.25%

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There 2300 different combinations of 3 people could you choose.

The sequence of the results is irrelevant when calculating the overall outcomes of an event using combinations.

Given:

We have to select 3 people from 25 people.

n= 25, r=3

So, the number of different combination is

= C(n, r)

= n!/ r! (n-r)!

= 25! / 3! (25- 3)!

= 25! / 3! x 22!

= 25 x 24 x 23 /3 x 2

= 25 x 23 x 4

= 2300

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