If θ is an angle in standard position and its terminal side passes through the point (2,7), find the exact value of tan ⁡ � tanθ in simplest radical form.

Viola has covered a horizontal distance of 199.7 meters when driving 200 meters up a hill that makes an angle of 3 degrees with the horizontal.

Viola drives 200 meters up a hill that makes an angle of 3 degrees with the horizontal. To find the horizontal distance she covered, we can use the cosine formula:

Cos(θ) = adjacent/hypotenuse

In this case, the adjacent side is the horizontal distance we are trying to find, the hypotenuse is the distance she drove (200 meters), and the angle is 3 degrees. Plugging in these values, we get:

Cos(3º) = adjacent/200

Rearranging the equation to solve for the adjacent side, we get:

adjacent = 200*cos(3)

Using a calculator, we find that cos(3) is approximately 0.9986. Multiplying this by 200 gives us:

adjacent = 199.72

Therefore, the horizontal distance that Viola covered is approximately 199.72 meters.

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Answer:

  -5(g -3h +5)

Step-by-step explanation:

You want the factored form of -5g +15h -25.

The coefficient of g inside parentheses is 1, so the coefficient of g in the given expression (-5) must be the factor outside parentheses. You can divide the expression by this value to find the desired numbers:

  [tex]-5g+15h-25=-5\left(\dfrac{-5g+15h-25}{-5}\right)=-5\left(\dfrac{-5}{-5}g+\dfrac{15}{-5}h+\dfrac{-25}{-5}\right)\\\\=\boxed{-5(g-3h+5)}[/tex]

The rectangle with the given properties is added as an attachment

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

We start by calculating the side lengths using

Perimeter = 2 * (Length + Width)

So, we have

2 * (Length + Width) = 28

Divide by 2

Length + Width = 14

Because the y-axis is a line of symmetry, then it means that the rectangle is divided into equal segments by the y-axis

Here, we can assume that

Length = Width (this is so because a square is a type of rectangle)

So, we have

Length = Width = 7

The above computations also mean that the vertices are equidistant from the axes and the origin

So, we have

Vertices = (3.5, 3.5), (3.5, -3.5), (-3.5, 3.5) and (-3.5, -3.5)

See attachment for the rectangle

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Answer:

WX = 18

Step-by-step explanation:

given Δ V'W'X'  is [tex]\frac{2}{3}[/tex] of Δ VWX , then the sides of Δ VWX are [tex]\frac{3}{2}[/tex] of Δ V'W'X'

WX = [tex]\frac{3}{2}[/tex] × W'X' = [tex]\frac{3}{2}[/tex] × 12 = 3 × 6 = 18

To find out how much flour Ricky needs, we first need to find 1 1/2 times the amount of flour in the original recipe.

2 3/3 cups of flour is the same as 8/3 cups of flour.

To find 1 1/2 times the amount of flour in the original recipe, we can multiply 8/3 by 1 1/2:

8/3 x 3/2 = 24/6 + 4/6 = 28/6

So 1 1/2 times the amount of flour in the original recipe is 28/6 cups of flour.

To find out how much flour Ricky needs, we can multiply this amount by 1 1/2:

28/6 x 3/2 = 84/12 + 18/12 = 102/12

So Ricky needs 102/12 cups of flour, which simplifies to 8 1/2 cups of flour.

2.16% probability that the man would have done at least this well if he had no ESP.

As we know that for each coin toss, there are only two possible outcomes. Either he predicts the correct outcome, or he does not. Therefore, the tosses are independent. So, we can use the binomial probability distribution:

Binomial probability distribution says that, the binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X=x) = Cₙ, ₓ.pˣ.(1-p) ⁿ⁻ˣ

here, Cₙ, ₓ is the number of different combinations of the x objects from a set of n elements, which is given by the following formula:

Cₙ, ₓ = n/x(n-x)

here, p is the probability of X happening, therefore,

fair coin: Equally as likely to be heads or tails, so p = 0.5

number of times coin is flipped = 22

n = 22

now for the probability that he would have done at least this well if he had no ESP:

P(X>16) = P(X=16) + P(X=17) + P(X=18) + P(X=19) + P(X=20) + P(X=21) + P(X=22)

In which;

P(X = 16) = 0.0143; P(X = 17) = 0.0053; P(X = 18) = 0.0016; P(X = 19) = 0.0004; P(X = 20) = 0.0001

for the other values we know that they are close to 0, hence,

P(X>16) = P(X=16) + P(X=17) + P(X=18) + P(X=19) + P(X=20) + P(X=21) + P(X=22) = 0.0216

So we know that 2.16% probability that he would have done at least this well if he had no ESP

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Answer:

B

Step-by-step explanation:

Rate of change states

[tex] \frac{y2 - y1}{x2 - x1} [/tex]

They are asking from day 2 to day 5, making 2 and 5 our x1 and x2.

On the table, the number below 2 is 0.75. The number below 5 is 2.5. We can use these as y1 and y2.

Now we can plug it in

[tex] \frac{2.5 - 0.75}{5 - 2} = \frac{1.75}{3} = .58 = 0.6[/tex]

0.6 because it asks for approximate

Answer:

2

Step-by-step explanation:

2.13 (m + 2) = 8.52

m + 2 = 8.52/2.13

m + 2 = 4

m = 4 - 2

m = 2

The plane travels 2500 miles in 5 hours. The solution has been obtained by using unitary method.

What is the unitary method?

Using the unitary technique, the value of each individual unit is first calculated, and then the value of the necessary number of units is determined.

We are given that an airplane travels 125 miles in 1/4 hour. It travels the same number of miles each hour.

Using unitary method,

The miles traveled in 1 hour = 125 * 4 = 500 miles

So, the miles traveled in 5 hours = 500 * 5 = 2500 miles

Hence, the plane travels 2500 miles in 5 hours.

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Question:  An airplane travels 125 miles in 1/4 hour. It travels the same number of miles each hour. How many miles does the plane travel in 5 hours?

The values are 45, 4.5, 0.45, and 0.045.

Numbers are representations of quantity or quality.

We have many types of numbers such as,

- Decimal numbers

- Real numbers

- Rational numbers

- Irrational numbers

- Complex numbers

- Even numbers

- Odd numbers

- Whole numbers

We have,

We need to multiply the numbers without using a calculator.

The steps to multiply two decimal numbers without using a calculator.

Step 1:

Ignore the decimal points and multiply the two numbers as if they were whole numbers.

Step 2:

Count the total number of digits to the right of the decimal points in both numbers.

Step 3:

Add the number of digits from step 2, and place the decimal point in the product so that it has that many digits to the right.

Now,

3 x 15 =45

0.3 x 15 = 4.5

3 x 0.015 = 0.045

0.03 x 15 = 0.45

3 x 1.5 = 4.5

3 x 0.15 = 0.45

0.3 x 1.5 = 0.45

0.3 x 0.15 = 0.045

Thus,

The values are 45, 4.5, 0.45, and 0.045.

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The complete question.

Multiply the two decimal numbers without using a calculator,

3 x 15

0.3 x 15

3 x 0.015

0.03 x 15

3 x 1.5

3 x 0.15

0.3 x 1.5

0.3 x 0.15

The equivalent to the expression 3², which equals 9.

An exponent is a mathematical operation that involves raising a number to a certain power. In this case, you are curious about what 3 to the 2 power means. Let's explore this concept further.

When we write 3 to the 2 power, it means that we are multiplying 3 by itself two times. This can also be written as 3 raised to the power of 2, which is represented by the notation 3².

To illustrate this concept, let's use an example. Consider the expression 3². This means that we need to multiply 3 by itself twice, as indicated by the exponent of 2. In other words:

3² = 3 x 3 = 9

So, 3 to the 2 power is equal to 9. Another way to think about this is to imagine a square with sides of length 3. The area of this square would be 3 x 3, or 9.

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The requried first term of the sequence is $6.32.

Arithmetic progression is the series of numbers that have common differences between adjacent values

Here,
The amount of money Sally spends on breakfast each week forms an arithmetic sequence.

Let's use the formula for the sum of an arithmetic sequence to find the first term of the sequence. We know that Sally has already spent $31.64, which means that she has made 31.64/4.52 = 7 visits to the breakfast place. So the sum of the first 7 terms of the sequence is:

S₇ = 7/2 * (a₁ + a₇)

We know that a₇ = $4.52, so we can plug this into the formula and simplify

S₇ = 7/2 * (a₁ + 4.52)

a₁ = $6.32

Similarly, all the outcomes can be evaluated,
By the end of the year, Sally will have spent $891.36 on breakfast.

Therefore, the first term of the sequence is $6.32.

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The height difference in the dispenser before and after the use of the dispenser is found to be 8cm.

The shape of the dispenser is 5652 cubic centimeters and it is full of the liquid soap. The radius of the dispenser is given to be 7.5 centimeter.

Now, after using, the dispenser is left with 4239 cubic centimeters.

Now, we know the volume of the cylinder is given to be,

V = πR²H

R is radius and H is the height.

When the dispenser is full,

5652 = 3.14(7.5)²H

H = 32 cm.

Now, after the use let us say that the height is h,

4239 = 3.14(7.5)²h

h = 24cm.

Now, the height difference is H-h.

= 32-24

= 8 cm.

So, the height difference is 8 cm in the dispenser.

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The solution of the Chinese Remainder Theorem can be calculated by using the formula: [tex]{\displaystyle x=\sum _{i=1}^{k}a_{i}M_{i}N_{i}.}[/tex]

According to the Chinese remainder theorem, if one knows the remainders of the Euclidean division of an integer n by multiple numbers, one may uniquely calculate the remainder of the division of n by the product of these integers, provided that the divisors are pairwise coprime (no two divisors share a common factor other than 1).

For example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, we may calculate the remainder of n divided by 105 (the product of 3, 5, and 7) without knowing the value of n. This tells us that if n is a natural number less than 105, then the only possible value of n is 23.

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Answer:2

Step-by-step explanation:

Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

The cylindrical, which is frequently a lobed solid, comprises one of the most simple curvature geometric forms. In simple geometry, it is known as a prism with a circle as its basis. The term "cylinders" is also used to refer to an infinitely curved surface in a number of modern domains of topology and geometries. A "cylinder" is a two half object made up of curved surfaces with circle tops and bases. A cylinder is a two half solid figure with two bases that are both similar circles connected at its height, which is controlled by the separation of the legs from the center. Cans of iced drinks and the wicks from toilet paper are example of cylinders.

given

r = d/2 = 40/2 = 20 cm

v = pi *r*r*h

100 = 3.14 * 20*20 *h

100 = 1256*h

h = 0.08 cm

strong box = surface area of cuboid = 45 * 90

= 4050 cm2

surface area of water heater = A=2πrh+2πr2=2·π·20·0.08+2·π·202

≈2523.3

Yes, the room heater will fit into the robust box, which is 45 cm in width and 90 cm in height.

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The probability of the sum of the faces that the 2 dice are thrown simultaneously can be found by using the formula for the probability of independent events, which is P(A) * P(B).

The probability of the sum of the faces when 2 dice are thrown simultaneously depends on the specific sum you are looking for. You can use the formula P(A) * P(B) and the number of possible outcomes for each sum to find the probability.

First, let's determine the probability of each event. The probability of rolling a specific number on a single die is 1/6, since there are 6 possible outcomes. Therefore, the probability of rolling a specific number on both dice is (1/6) * (1/6) = 1/36.

Next, we need to determine the number of possible outcomes for the sum of the faces. There are 11 possible sums (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12), each with a different number of possible outcomes. For example, there is only one way to roll a 2 (1 + 1), but there are six ways to roll a 7 (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1).

Finally, we can use the formula to find the probability of each sum. For example, the probability of rolling a 7 is (6/36) = 1/6. The probability of rolling a 2 is (1/36).

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Yes, the tangent constraint can be applied between a line and an arc in many CAD (Computer-Aided Design) software programs.

In CAD, a tangent constraint is a geometric constraint that forces two entities (lines, arcs, circles, etc.) to share a common tangent at their point of contact. When you apply a tangent constraint between a line and an arc, the software will ensure that the line and the arc are always tangent to each other at their point of intersection.

This constraint is useful for designing mechanical components, such as gears or cams, where you need to ensure that the contact between two parts is smooth and continuous. It is also commonly used in architecture, where a building's curved surfaces may need to be tangent to adjacent straight lines or walls.

In short, the tangent constraint can be applied between a line and an arc, and it is a useful tool in many different fields of design.

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The simple interest Samuel will have to pay will be 60 Rs.

What exactly is simple interest?

Simple Interest is a simple way for computing interest on a loan or principle amount. Simple interest is a concept that is employed in numerous industries, including banking, finance, and automobiles. When you make a loan payment, the monthly interest is deducted first, followed by the principle amount.

The simple interest formula is as follows:

SI=P*R*T/100

SI stands for simple interest.

P stands for principal.

R is the interest rate (in percentage)

T denotes the length of time (in years)

The following formula is used to compute the total amount:

Amount (A) = Principal (P) x Simple Interest (SI)

Now,

As given principle=1000

rate=12%

time=6 months=1/2 years,

Then interest in 6 months will be = 1000*12*1/2*100

=10*12/2

=10*6

=60

Hence,

           The simple interest Samuel will have to pay will be 60 Rs.

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Answer:

required perimeter is 12.57mm

Using distributive property, the expression 55x+5 can be written as 5(11x+1).

Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.

Expression           Property         Equivalent expression

3(2+x)                 Distributive                  6+3x

2+(3+4)              Associative                  (2+3)+4

24x+18y             Distributive                 8(3x+y)

4x+5x                Commutative              5x+4x

5+2+3               Commutative               3+2+5

(5x.3y).2           Associative                  5x.(3y.2)

12-3x                Distributive                   3(4-x)

6+3                  Commutative                 3+6

(2x.3y).5z         Associative                  2x(3y.5z)

4(5-2y)             Distributive                   20-8y

y+0                  Identity                             y

a.b                  Commutative                   b.a

3x.1                  Identity                            3x

(a+b)+c           Associative                   a+(b+c)

55x+5            Distributive                   5(11x+1)

8(y-2)             Distributive                    8y-16

2x+5y             Commutative                5y+2x

Therefore, using distributive property, the expression 55x+5 can be written as 5(11x+1).

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A loaded lion valuation calculator is a tool to estimate the value of a high-growth startup based on financial metrics.

The stacked lion valuation mini-computer is a device used to gauge the worth of a new business in light of its monetary and functional exhibition. The expression "stacked lion" alludes to a startup that has raised huge measures of subsidizing and is supposed to fill quickly from here on out. The number cruncher considers a few variables, including the organization's income, development rate, net revenue, and industry valuation products, to decide an expected endeavor esteem (EV) and value esteem (EV short obligation). The adding machine may likewise calculate the organization's subsidizing history, supervisory crew, and serious scene. This valuation can be utilized by startup pioneers, financial backers, and different partners to decide the organization's worth and arrange speculation bargains. While the stacked lion valuation mini-computer can give a helpful gauge, it is critical to remember that startup valuations are innately dubious and may vacillate in light of changing economic situations and different variables.

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No, not all isosceles triangles are always similar. Two triangles are considered similar if their corresponding angles are congruent and their corresponding sides are in proportion. While all equilateral triangles are also isosceles triangles, not all isosceles triangles have congruent angles and proportional sides.

Any triangle with any two sides that have the same length is known as an isosceles triangle. An isosceles triangle has two equal-sized angles that are opposite from one other and have equal sides. Triangles are three-sided polygons in geometry that can be divided into three groups based on their sides, such as:

For example, consider an isosceles triangle with base angles of 70 degrees and a third angle of 40 degrees, and another isosceles triangle with base angles of 80 degrees and a third angle of 20 degrees. These triangles have different angles and are therefore not similar, even though they are both isosceles triangles.

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Answer: 49 napkins

Step-by-step explanation:

7 every 5

35/5=7

7*7

49

Answer: 25 napkin

Based on the given conditions, formulate: 35 x 5 divided by 7

35 x 5= 175/7= 25

the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).

The initial value problem given is: dy/dt = 5y, y(0) = y0

The solution to this differential equation is: y(t) = y0 × e⁽⁵t⁾

To find the value(s) of y0 for which the solution has a vertical asymptote at t = 4, we need to set t = 4 and solve for y0 such that the solution becomes infinite.

y(4) = y0 × e⁽⁵ˣ⁴⁾ = y0 × e²⁰

For the solution to have a vertical asymptote at t = 4, y0 × e²⁰ must be infinite. This means that y0 must be equal to 0.

Next, we need to determine the time interval of existence C<4 for the solution. The solution is continuous and differentiable for all values of t, so the time interval of existence is the entire real line, (-∞, ∞). Therefore, for the initial value problem dy/dt = 5y, y(0) = y0, the solution has a vertical asymptote at t = 4 only when y0 = 0, and the time interval of existence is the entire real line, (-∞, ∞).

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Answer:

d!!

Step-by-step explanation:

Answer:

Step-by-step explanation:

5, 4, 3, 7, 6, 10, 9, 13, 12, 16, 15

Answer:

Step-by-step explanation:

the population will be 2 678

If the triangles ΔABC≅ΔDEF then the congruent to side BA is ED.

The dimensions of the sides and angles of two or more triangles determine whether they are congruent. A triangle's size and shape are determined by its three sides and three angles, respectively. If pairs of corresponding sides and corresponding angles are equal, two triangles are said to be congruent. They are the exact same size and form. Triangles can satisfy a wide variety of congruence requirements.

From the ΔABC ≅ ΔDEF we observe that the corresponding segment to BA in triangle DEF is ED.

Hence, if the triangles ΔABC≅ΔDEF then the congruent to side BA is ED.

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Using the recursive formula we will see that:

f(2) = 5

Here we have a sequence such that we know that:

f(0) = 2

And the recursive formula is:

f(n + 1) = -2*f(n) + 3

So, first let's find f(1), to get that we use n = 0.

f(1) = -2*f(0) + 3

    = -2*2 + 3 = -4 + 3 = -1

And the next term is:

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

     = -2*-1 + 3

    = 2 + 3 = 5

Then the correct option is the third one.

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