Lauren was given a gift card for a coffee shop. Each morning, Lauren uses the card to buy one cup of coffee. The original amount of money on the gift card was $10 each cup of coffee costs $2. Make a table of values and then write an equation in terms of x, representing the amount money remaining on the card after buying x cups of coffee.

The first three terms of a sequence are given, so the 35th term is: [tex]a_n = 69[/tex]

A grouping of numbers in a specific order is known as a sequence. On the other hand, a series is described as the accumulation of a sequence's constituent parts. A sequence is a list of elements that has been arranged in a certain way.

An ordered list of numbers is a sequence. The three dots indicate that the established pattern should go forward. A phrase is used to describe each number in the series. The first word in the order 1, 3, 5, 7, 9,... is 1, the second is 3, the third is 5, and so on.

The first three terms are : 205, 201, 197, .......

The general term through the pattern is:

[tex]a_n = - 4n+209[/tex]

or, [tex]a_n = - 4(35)+209[/tex]    

here, n = 35

or, [tex]a_n = 69[/tex]

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The object's height was 300 ft above sea level when it was launched.

What is a quadratic equation?

An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as a[tex]x^{2}[/tex] + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term.

Given, the height of the object can be modeled by the function

           h(t)=-16t^2+100 t+300

Height of object when it was launched

At the time of launched, t=0

h = -16(0)^2 + 100(0) + 300 = 300 ft above sea level

Hence, the object's height was 300 ft above sea level when it was launched.

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Triangles are congruent, then there is no additional angles/sides should we mark in each triangle.

What is congruent triangles?

If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.

Since reflexive angles means is an angle that is more than 180 degrees and less than 360 degrees.

And the reflexive sides means the reflexive property of congruence states that any shape is congruent to itself.

Vertical angles are angles opposite each other where two lines cross.

But to check the congruence of two triangles we only have the angles and sides of the two triangles are same.

So, there is no additional angles/sides should we mark in each triangle.

Hence, triangles are congruent, then there is no additional angles/sides should we mark in each triangle.

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Answer:

He worked 26 hours at the vegetable farm and 4 hours at the paddy field.

Step-by-step explanation:

Let us take the working hour at a vegetable farm be x and at paddy field be y

He worked for both jobs for a total of 30 hours.

So,

x + y = 30 ...(1)

He earns Rs 200/- per hour from vegetable farm and Rs 250/- per hour from paddy field, total of Rs 6900.

So,

200x + 250y = 6900

2x + 5y = 138 ...(2)

From equation 1 we get,

x = 30 - y

Put the value of x = 30 - y in equation 2 we get,

2x + 5y = 138

2(30 - y) + 5y = 138

60 - 2y + 5y = 138

60 + 3y = 138

3y = 138 - 60

3y = 78

y = 26

Now, put the value of y in equation 1 we get,

x + y = 30

x + 26 = 30

x + 26 - 26 = 30 - 26

x = 4

Thus, He worked 26 hours at the vegetable farm and 4 hours at the paddy field.

The exact value for sin (∅) is √15/4 if  cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

In mathematics, the trigonometric functions—also known as circle, angle, or goniometric functions—are real functions that connect the angle of a right-angled triangle to the ratios of its two side lengths.  As some of the most basic periodic functions, they are frequently employed in Fourier analysis to examine periodic phenomena.

The sine, cosine, and tangent are the trigonometric functions that are most commonly utilized in contemporary mathematics. The cotangent, secant, and their less common reciprocals, the cosecant, are each of their reciprocals.

Given, cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

cos²∅+sin²∅=1

sin²∅=1-cos²∅

sin²∅=(1-(-1/4)²)

sin²∅=1-(1/16)

sin²∅=15/16

sin∅=√15/4

Therefore, the exact value for sin (∅) is √15/4 if  cos (∅)=-1/4 and ∅ is in the 3rd quadrant.

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The equation for total amount to be paid represented as y and pounds of potatoes represented as x will be y = 0.64x

Ax + By + C = 0 can be used to express a linear equation in two variables, where x and y are the two variables, and each has a degree of one.

Ex. -2x+3y=8

Total weight of potatoes in pounds Dontrell bought= x

Let total amount Dontrell he pays= $ y

It is given 5.5 pounds are bought by paying $3.52

5.5 pounds = $3.52

1 pound = $ 3.52/5.5

1pound=$0.64(Using Unitary method)

Dontrell buy x pounds potatoes and he pays $y

Therefore,

y=0.64x

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The total number of toys in the bag is 20

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

Frisbees = 5

Proportion of these Frisbees = 25%

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

Number of Frisbees = Total number of Frisbees * The proportion of these Frisbees

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

Total number of Frisbees * 25% = 5

Divide both sides by 25%

Total number of Frisbees = 20

Hence, the total is 20

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Answer:

3.17×10^3

Step-by-step explanation:

Hope it helps!

8x-20

Step-by-step explanation:

12x-18-4x-2

8x-20

Throughout a hypothesis test, the alternative hypothesis is assumed to be true.

Answer :-FALSE

What is hypothesis test ?

in hypothesis test we compare p-value with level of significance and conclude our null hypothesis is true or not true.

p-value decided null hypothesis is true or not true.

p-value <= level of significance then null hypothesis is true.

We do not say alternative hypothesis is assumed to be true.

Therefore Correct Options

FALASE

No matter what the conclusion of a hypothesis test is, neither the null or alternative hypothesis has been proven to be true.

Answer :- TRUE.

Because,

Yes, no matter what was the conclusion of hypothesis test.

We set always our claim in alternative hypothesis and conclude about the null hypothesis.

We check null hypothesis is true or do not true.

That's reason Correct Options TRUE.

When drawing a conclusion to a hypothesis test, compare the calculated p-value to the calculated test statistic.  

Answer :- FALSE

Because,

We Calculate the test statistic.

Using this test Statistic we calculate p-value

We compare p-value with level of significance and conclude it.

That's reason statement is false. We do to compare p-value and test statistic.

As a p-value approaches 0 it is more likely the hypothesis test conclusion will be "reject the null hypothesis.".

Answer :- TRUE

Because,

p-value is the probability that test hypothesis is accepted or rejected.

We compare always p-value with level of significance.

p-value < 0.05

We reject the null hypothesis.

In given problem p-value = 0

That is we reject the null hypothesis.

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of the hurricane. We get this from the given algebraic expression.

An expression is formed by variables, constants, and algebraic operations. Since the operation among them is an algebraic or arithmetic operation, it is said to be an algebraic expression.

It is given that the algebraic expression that relates the barometric pressure and the eye of the hurricane as

f(x) = 0.48 ln(x+2) + 27

Here x is the distance in miles from the eye of the hurricane.

f(x) is the pressure of the mercury in a barometer in inches

So, the required distance from the eye of the hurricane when the pressure of 28 inches of mercury in the meter is

(Here f(x) = 28)

f(x) = 0.48 ln(x+2) + 27

⇒ 28 = 0.48 ln(x+2) + 27

⇒ 0.48 ln(x+2) = 28 - 27

⇒ ln (x+2) = 1/0.48

⇒ ln(x+2) = 2.0833

Applying exponential base "e" on both sides, we get

(x+2) = [tex]e^{2.0833}[/tex]

⇒ x + 2 = 8.0309

⇒ x = 8.0309 - 2 = 6.0309

When the result is rounded to the nearest whole number, we get x = 6 miles.

Thus, for the pressure of 28 inches of mercury, the eye of the hurricane is 6 miles far from the barometer.

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The jumper is in free fall for 7.07 s if the parachute is opens at 1000 ft

The jumper is in free fall for 7.29 s if the parachute is opens at 950 ft

The reasonable domain for the function h is

0 ≤ t ≤ 10

The reasonable range for the function h is

0 ≤ h ≤ 1800

The duration of free fall is calculated using the given function

h = -16t² + 1800

the parachute is opens at 1000 ft

h = -16t² + 1800

1000 = -16t² + 1800

16t² = 1800 - 1000

16t² = 800

t² = 800 / 16

t² = 50

t = √50

t = 7.07 s

the time at this situation is 7.07s

the parachute is opens at 950 ft

h = -16t² + 1800

950 = -16t² + 1800

16t² = 1800 - 950

16t² = 850

t² = 850 / 16

t² = 53.125

t = √53.125

t = 7.2887 s

the time at this situation is 7.29s

reasonable domain

minimum t = 0

for maximum t, h = -16t² + 1800 = 0

16t² = 1800

t = 10.61

0 ≤ t ≤ 10

the reasonable domain is 0 ≤ t ≤ 10

reasonable range

h = -16t² + 1800

at t = 0, h = 1800

at t = 10.606, h = 0

0 ≤ h ≤ 1800

the reasonable range is 0 ≤ h ≤ 1800

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Solution:

60

Step-by-step explanation:

60 is divisible by 2 -> 60 / 2 = 30

60 is divisible by 3 -> 60 / 3 = 20

60 is divisible by 5 -> 60 / 5 = 12

Answer: 60

Step-by-step explanation:

60 has all prime factors of 2,3 and 5. :)

The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output is true.

Deep learning is part of machine learning methods and is based on artificial neural networks with representation learning. It is a machine learning technique that teaches computers to carry out operations that comes naturally to humans: learn by example. Deep learning is a key technology behind driverless cars, enabling them to recognize a stop sign, or to distinguish a pedestrian from a lamppost. Deep learning networks learn by identifying intricate data structures in the data they experience. By developing computational models that are composed of multiple processing layers, the networks can create multiple levels of abstraction to represent the data. A layer is the highest-level building block in deep learning. A layer is a container that usually receives weighted input, transforms it with a set of functions through data processing and passes these values as output to the next layer.

Note: The question is incomplete. The complete question probably is: The layers, in deep learning, represent the data processing that occurs in order to achieve the correct output. select one: true false.

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The constant of proportionality for the relationship is 70.

From the given graph (2, 140), (4, 280), (6, 420), (8, 560) and (10, 700).

Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value times the other. That constant is known as the "constant of proportionality".

From the graph we can see it is direct proportion.

Here, y∝x

⇒ y=kx

⇒ k=y/x

⇒ k=140/2

⇒ k=70

Hence, the constant of proportionality for the relationship is 70.

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Answer:

[tex]a=4, b=-8, c=-12[/tex]

Step-by-step explanation:

Compare the given equation with the general form [tex]y=ax^2 + bx+c[/tex].

We can determine the stream's current velocity by solving a set of equations, which gives us S is 2 mi/h.

The total speed of a motorboat traveling downstream is equal to the speed of the boat in still water plus the speed of the stream, whereas the total speed of a motorboat traveling upstream is equal to the speed of the stream minus one.

Therefore, the speed upstream is: (14 mi/h - S)

The speed downstream is (14 mph + S), where S is the stream's current flow rate.

We can construct the equations below after we know that it takes 15 minutes longer to walk 12 miles downstream:

14 mph plus speed (S) times the time (T minus 15 minutes) equals 12 miles.

In order to solve this, one of the variables in one of the equations needs to be isolated. I'll isolate T in the first equation:

T = (12 miles)/(14 miles per hour Plus S)

By substituting it in the other equation, we will obtain the following value: (14 mi/h - S)*((12 mi)/(14 mi/h + S) - 15 min) = 12 mi.

Taking only the favorable outcome, we obtain:

S = (24 - 25)/(-0.5) = 2 mph

2 mi/hr is the stream's current velocity.

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(X=60,Y=47,Z=73),  the measures of the three angles.

When two rays are linked at their ends, they create an angle in geometry. The sides or arms of the angle are what are known as these rays.

When two lines meet at a point, an angle is created.

An "angle" is the measurement of the "opening" between these two rays. It is symbolized by the character.

The circularity or rotation of an angle is often measured in degrees and radians.

Angles are a common occurrence in daily life.

Angles are used by engineers and architects to create highways, structures, and sports venues.

According to our question

x+y+z=180

The second and third angles' combined measurements equal twice the first angle's combined measurement, therefore

y+z−2x+y+z=2=0

Third angle has 26 more degrees than second angle, therefore

z−y+z=y+26=26

As a result, we obtain the equation system.

x+y+z=180−2x+y+z=0−y+z=26

(1)(2)(3)

By removing y and z, use equations (1) and (2) to determine x. To get rid of y and z, multiply equation (2) by one before adding it to equation (1).

x+y+z2x−y−z3xx=180=0=180=60(4)

To get rid of z, use equations (1) and 3). To get rid of z, multiply equation (3) by 1 and then add it to equation (1).

x+y+zy−zx+2y=180=−26=154(5)

To determine, substitute x=60 into equation (5).

x+2y(60)+2y2yy=154=154=94=47

In order to find, we can now change x=60 and y=47 in equation (1).

x+y+z(60)+(47)+zz+107z=180=180=180=73

Therefore, there is a solution.

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The difference between 3894256 and 756533 by rounding each number to the nearest thousand is 3138000

The first number = 3894256

The second number = 756533

To find the difference between the numbers we have to use the subtraction

Difference between 3894256 and 756533 = 3894256 - 756533

Subtract the numbers

= 3137723

Rounding of a number is write the numbers to the nearest place values like tens, hundreds and thousand etc.

Here, the number is 3137723 and we have to round the number to nearest thousand

Round to nearest thousand = 3137000

Therefore, the result nearest to the thousand is 3138000

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(a) 794g of the initial sample will be left in the sample after 25 years. (b) Time taken to decay to half of its original amount is 3.39 years.

Isotopes(200g) are atoms that have the same number of protons in their nucleus, but a different number of neutrons. This means that they have the same atomic number, but a different atomic mass. Because of this, isotopes have different physical and chemical properties. Isotopes can be stable, meaning that they do not undergo radioactive decay, or they can be unstable, meaning that they will undergo radioactive decay over time.

(a) Substituting 25 for t in the expression, we get:

[tex]A(25) = 200e^{0.0541 \times 25}[/tex]

         [tex]= 200e^{1.3525}[/tex]

Thus, after 25 years, there will be

[tex]200e^{1.3525} = 2003.97[/tex]

794 g of the initial sample left in the sample.

(b) We want to find t such that

[tex]A(t) = 200e^{0.0541}[/tex]                                          

       = 100.

Solving for t, we get:

[tex]= 200e^{0.0541} \times t=100[/tex]

Dividing both sides by 200 and applying the natural logarithm to both sides, we get:

0.0541 × t = ln(0.5)

Therefore,

[tex]t = \frac{ln(0.5)}{0.0541}[/tex]

  = 3.39 years.

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Answer:

The theoretical probability of rolling a two with one standard die is 1/6. This can be written as a decimal by dividing 1 by 6, which is approximately 0.167. As a percentage, this is approximately 16.7%. Here are all three forms:As a fraction: 1/6As a decimal: 0.167As a percentage: 16.7%

Step-by-step explanation:

Answer:

Step-by-step explanation:

12=666

0.26 is  probability that a graduating senior receives two or three job offers.

What is probability in math?

Calculating or estimating how likely or "possible" something is to occur is the subject of probability. Words like "certain," "impossible," or "probable" can be used to express the likelihood of an event occurring.              

                                             Probabilities in mathematics are always represented as fractions, decimals, or percentages with values ranging from 0 to 1.

P(2 or 3 jobs)=P(2 jobs)+P(3 jobs)-P(2 jobs and 3 jobs)=P(2 jobs) + P(3 jobs) since a student can not have 2 jobs as well as three jobs at a time.

So,

P(2 or 3 jobs)=0.15+0.11 = 0.26

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The final amount of the money according to compound interest model is $ 5342.80.

Herein we find a case of a money deposited that increases its amount in time by compound interest, that is, the amount increases continuously in time. The compound interest model is described below:

C' = C · (1 + r / 100)ⁿ

Where:

If we know that C = 4232, r = 6 and n = 4, then the final amount of the money is:

C' = 4232 · (1 + 6 / 100)⁴

C' = 5232.802

The final amount is $ 5342.80.

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The option A is correct

In other words, the amount of heat entering the system must be greater than the amount of mechanical effort leaving the system.

Recall the first law of thermodynamics' ideas in order to comprehend this.

dQ = dU + dW

Assuming perfect conditions. There is no heat loss outside. No matter how much heat we give the gas dQ , some of it will be utilised to boost the gas's internal energy while the rest will be used to produce work. This must be less than dQ in turn.

Because of this extremely fundamental characteristic of all engines, none of them can operate at 100% efficiency. Even the "Carnot engine," the most ideal engine, is not entirely efficient.

The option A is correct

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The area of the triangle below 8 yards

What is triangle?

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

Triangles are three-sided shapes. The many kinds of triangles go by various names. The size of the angles and the length of the sides determine the type of triangle (corners). Equilateral, isosceles, and scalene triangles are the three varieties of triangles based on the length of the sides.7-15=8

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The answer is 0.1657

Solution:

Given: [tex]\frac{1}{2*6}[/tex]+[tex]\frac{1}{4*8}[/tex]+ .. . . . . . . . +[tex]\frac{1}{20*24}[/tex]

∴ [tex]\frac{1}{12}[/tex] + [tex]\frac{1}{32}[/tex] + [tex]\frac{1}{60}[/tex] + [tex]\frac{1}{96}[/tex] + . . . . . .  + [tex]\frac{1}{480}[/tex]

∴ [tex]\frac{40}{480}[/tex] + [tex]\frac{15}{480}[/tex] + [tex]\frac{8}{480}[/tex] + . . . . . . +[tex]\frac{1}{480}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)

∴[tex]\frac{79.54}{480}[/tex]

= 0.1657

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After carefully calculating the sequence we have come to find that The answer of the given equation is 0.1657

What is a sequence?

A sequence is an ordered collection of enumerated objects in mathematics where repetitions are permitted. It has members, just like a set (also called elements, or terms). The length of the sequence refers to the total (possibly infinite) number of elements.

Contrary to a set, the same elements may appear more than once at various points in a sequence, and in contrast to a set, the order is important. The formal definition of a sequence is a function from natural numbers (the positions of the sequence's elements) to the elements at each position. A function from any index set is what is meant by an indexed family, which is a generalisation of the idea of a sequence.

[tex]\frac{1}{2\times6} + \frac{1}{4\times8} + \frac{1}{6\times10}.....\frac{1}{20\times24}[/tex] --------- (multiplying the numerator with quotient of 480/denominators)= 0.1657

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The equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45  × d, so option B is correct.

Equations are statements in mathematics that have two algebraic expressions on either side of the equals (=) sign. It shows that the expressions printed on the left and right sides have an equal relationship.

Given:

The distance travelled = 315 miles,

The distance on the map =  7 inches,

Calculate the equation represents the actual miles traveled,

Actual distance = The distance traveled / The distance on the map × The distance on the map

m = 315 / 7 × d

m = 45  × d

Therefore, the equation representing the actual miles traveled, m, relative to the distance shown on the map, d is m = 45  × d.

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top I think he or she is right

The length of the AB in the given right triangle is √3/6

Given that, a right triangle with the base measure 6 units and an acute angle 30°,

We need to find the measure of side AB,

So, we will use the concept of trigonometric ratios,

Tan 30° = AB / AC

Tan 30° = AB / 6

1 / √3 = AB / 6

AB = √3/6

Hence the length of the AB in the given right triangle is √3/6

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