In the year 2000, there were 200,000 cell phone subscribers in a city in new york. the number of subscribers increased by 60 percent per year after 2000. which equation can be used to model the number of subscribers, y, in the city t years after 2000?

The complete proofs are:

Proof 1

Proof 2

Proof 1

Lines a & b and c and d are given as parallel lines.

So, we have

a || b; c || d ⇒ Given

From the question, we have:

∠5 is supplementary to ∠4

So, we have

∠5 + ∠4 = 180

This is so because supplementary angles add up to 180

Corresponding angles are equal.

So, we have:

∠2 = ∠4

By the substituting ∠2 for ∠4 in ∠5 + ∠4 = 180, we have

∠5 + ∠2 = 180

Hence, angles ∠5 and ∠2 are supplementary angles

Proof 2

Line BD bisects angle ABC; lines AD & BC and AB & CD are given as parallel lines.

So, we have

BD bisects ∠ABC; AD || BC; AB || CD ⇒ Given

From the question, we have:

∠3 ≅ ∠4 ⇒ Definition of congruent angles

∠1 ≅ ∠3 ⇒ Definition of corresponding angles

Substitute ∠1 ≅ ∠3 in ∠3 ≅ ∠4

∠1 ≅ ∠4

Hence, the angles 1 and 4 are congruent

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Answer:

6

Step-by-step explanation:

Given an isosceles triangle the two sides opposite of congruent angles are equal to eachother, so you can create an equation setting the two sides equal to eachother and solve for x.

[tex]x+4=3x-8\\x=3x-12\\-2x=-12\\x=6[/tex]

The length of AC is simply x, therefore 6

Answer:

Bottom left

Step-by-step explanation:

Since the slope has to be positive it can't be the ones on the right side since both of them are negative. And the bottom left one is rising 3 and running 4. (formula = rise/run). See image.

Answer:

the answer is 1,2,4,5 and 7.

Answer: The answer is A,B,D,E,G

Step-by-step explanation: just trust me and enjoy your write answers. Have a nice day.

Answer:

B

Step-by-step explanation:

because i said so

The power output is  = 5W

Correct option is B.

Power is the quantity of energy that is transferred or transformed in a certain length of time. The unit of power is the watt, which in the International System of Units is equivalent to one joule per second.. Power may also be referred to as activity in earlier writings. The scalar property of power

Power is characterized as the rate at which a thing performs labor.

P = W/T ..... (1)

Work is calculated as the product of force applied to an item and the distance that object has traveled.

W = F.s

When we plug this value into the equation above, we get:

P = (F. s)/t

where,

power = P =?W

F = 10N Force Exercised

s = Displacement = 400cm = 4m  (1 meter = 100 centimeters).

t = Time required = 8s

Using the values in the equation above, we obtain

P = (10 x 4)/8

P = 5W

Hence, the correct option is Option b.

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I understand that the question you are looking for is :

Den pushes a desk 400 cm across the floor. He exerts a force of 10 N for 8 s to move the desk.

What is his power output? (Power: P = W/t)

a. 1.25 W

b. 5 W

c. 40 W

d.500 W

The height of the triangle is 11.3 in. The correct option is C. 11.3 in

From the question, we are to determine the height of the given triangle

The height of the given triangle is x in.

Now, we will determine the value of x

In the diagram, we can observe that the height divides the triangle into two equal halves

Thus,

By the Pythagorean theorem, we can write that

12² = x² + 4²

144 = x² + 16

144 - 16 = x²

∴ x² = 144 - 16

x² = 128

x = √128

x = 11.3

Hence, the height of the triangle is 11.3 in. The correct option is C. 11.3 in

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Answer: C, 93m^2

Step-by-step explanation:

first step is to find the surface area of the base. it's 3x3, so that would be 9m^2. the sides of the rectangular prism are 5x3, so one side is 15m^2. there are 4, so 15x4=60m^2. now for the top, which is a triangular prism. each side has a height of 4 and a base of 3. the area of a triangle is 1/2bh, so 1/2(3)(4), which is 6. 4 of these makes 24 m^2. add up all of final numbers to get 9+60+24. this comes to 93m^2, or C.

Answer:

90ft

Step-by-step explanation:

43,560ft² = L × l

43,560ft² = 484ft × l

43,560ft² ÷ 484ft = l

l = 90ft

The probability that the sum of the two numbers Malik picks is less than 5, given that the first number is odd and less than 5 is 0.0494.

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

Probability of an event P(E) = Number of favourable outcomes/Total number of outcomes.

Calculation for the given condition;

Either 1 or 3 must be present if a given integer is odd and smaller than 5.

The likelihood that it was picked from a set of nine numbers is (2/9).

The probability that the first integer is 1 is 50/50.

If it is and their combined number is less to 5, the second number will either be 1, 2, or 3.

The likelihood that it was picked out of the nine numbers is (3/9).

Additionally, there is a 50/50 probability that the first digit will be 3.

A second number is 1 if it is and the sum would be less than 5.

It was selected with a 1 in 9 chance of being one of the other 8 numbers.

The total probability is;

= (2/9)  times  [ (0.5 x 3/9)  +  (0.5 x 1/9) ]

= (2/9)  times  [ (1.5/9)  +  (0.5/9) ]

= (2/9)  times  [ 2/9 ]  =  4/81

= 0.0494

Therefore,  the probability that the sum of the two numbers malik picks is less than 5 is 0.0494.

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Answer:

See image

Step-by-step explanation:

Plato

The matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

In this question,

The angle is -π/3 = -60°

Clockwise rotations are denoted by negative numbers.

Matrix for counter-clockwise direction for an angle α is

[tex]\left[\begin{array}{cc}cos\alpha &-sin\alpha \\-sin\alpha &cos\alpha \end{array}\right][/tex]

Then, matrix for clockwise direction for an angle α

Put α = -α in the above matrix,

⇒ [tex]\left[\begin{array}{cc}cos(-\alpha) &-sin(-\alpha) \\-sin(-\alpha) &cos(-\alpha) \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}cos\alpha &sin\alpha \\sin\alpha &cos\alpha \end{array}\right][/tex]

Now substitute α = 60°

Then matrix becomes,

⇒ [tex]\left[\begin{array}{cc}cos60 &sin60 \\sin60 &cos60 \end{array}\right][/tex]

⇒ [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex]

Hence we can conclude that the matrix for the linear transformation for which rotates every vector in r2 is [tex]\left[\begin{array}{cc}\frac{1}{2} &\frac{\sqrt{3} }{2} \\ \frac{\sqrt{3} }{2} &\frac{1}{2} \end{array}\right][/tex].

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Answer:

Step-by-step explanation:

easy

y=3x-2

-3x+y=-2

-3x=-2-y

x=2/3+1/3y

Answer: $200

Step-by-step explanation:

       We will find 66⅔% of $300 to see how much Jay received. A percent divided by 100 becomes a decimal.

               66⅔% / 100 ≈ 0.667

               0.667 * $300 = $200

Answer:

Rs.11,111.11 (2 d.p.)

Step-by-step explanation:

The original price of the mobile is 100% of the price.

Therefore, the price of the mobile after a discount of 10% is 90% of the original price.

Let x be the original price.

If the price of the mobile after the discount is Rs.10000 then:

⇒ 90% of x = Rs.10000

⇒ 0.9x = 10000

⇒ x = 10000 ÷ 0.9

⇒ x = 11111.11  (2 d.p.)

M.P. =Rs 11111.1111

Answer:

Solution Given:

Selling price (S.P.) = Rs 10,000.

Discount =10%

Marked Price (M.P.)=?

we have

M.P. = S.P. + discount% of M.P.

keeping M.P. on same side

M.P. - discount% of M.P=S.P.

substituting value

M.P. - 10% of M.P.= Rs 10,000

taking common M.P.

M.P.(1-10%)=Rs. 10,000

we know that %=1/100

M.P.(1-10/100)=Rs 10,000

(9/10)M.P.= Rs 10,000

M.P.= Rs 10,000*10/9

M.P.=Rs11111.1111

The unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

Unit rate is the rate of a quantity in terms of another quantity per unit.

Unit rate(books per hour) = Number of books / Number of hours

= 1/4 ÷ 1/3

= 1/4 × 3/1

= (1×3) / (4×1)

= 3/4 books per hour

Therefore, the unit rate of 1/4 book 1/3 hour in books per hour is 3/4 books per hour.

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Step-by-step explanation:

....................

Answer:

a = 9

Step-by-step explanation:

[tex]\sqrt{2a-14} = 2[/tex]

2a - 14 = 4

2a = 18

a = 9

Answer:

The answer to this question is a = 9.

Step-by-step explanation:

To solve this problem, we need isolate the variable "a" on one side of the equation. Our first step must be to remove the square root. To do this, we should perform the inverse operation, which is squaring both sides.

√2a - 14 = 2

(√(2a - 14))² = 2²

2a - 14 = 4

Next, we should add 14 to both sides of the equation to get the variable term by itself.

2a - 14 + 14 = 4 + 14

2a = 18

Finally, we should divide both sides of the equation by 2 to remove the coefficient from the variable term.

a = 9

Therefore, the correct answer is a = 9.

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Answer:   9

Step-by-step explanation:

assuming that each box is 1 square inch then, you would get 9 square inches.

0,5 go down three to get 0,2

0,2 go left three to get -3,2

-3,2 go up three to get -3,5

-3,5 go right three to get 0,5

so you end up with a 3-by-3 box

Answer:

51.617

Step-by-step explanation:

tythe answer is 51.617 hope it helps

Explanation: The thousandths place is 51.6172 (Underlined is the thousandths) and since 2 is closest to zero we get an answer of 51.617.

Answer: 51.617

:)

The linear function of best fit for the information on the graph is:

f(x) = 200x + 100.

A linear function is modeled by:

y = mx + b

In which:

The function on the graph goes through points (3,700) and (4,900), that is, when x changes by 1, y changes by 200, which means that the slope is of 200 and the function is:

f(x) = 200x + b.

When x = 3, f(x) = 700, hence we use it to find b.

700 = 200(3) + b

b = 100.

Hence the function is:

f(x) = 200x + 100.

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Answer:

22, 23

Step-by-step explanation:

4x + 3(x + 1) = 157

4x + 3x + 3 = 157

7x + 3 = 157

7x = 154

x = 22

Answer:

So, having "hold-out" data allows you to have a nonpartisan set of data (so to speak) for you to refer to later, once you have made use of the "train" and "test" sets. That way you can make a fair assessment as to the difference between the new and old ('hold-out") sets.

Or if you need to repeat the experiment or model again - then you can refer to the "hold out data"

The rate of change for the function on the table is; 15 grapes eaten per minute.

It follows from the complete question that the table given indicates that;

On this note, it is conclusive that the rate of change of the function represented by the table is; 15 grapes eaten per minute.

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Applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

Trigonometric ratios are defined as the values of all trigonometric functions based on the right-angled triangle's side ratio. The trigonometric ratios of any acute angle in a right-angled triangle are the ratios of its sides to that angle.

Reference angle (∅) = 60

Adjacent = 4√3

Opposite = ?

tan 60 = opp/adj

tan 60 = Opp/4√3

√3 = opp/4√3

Opposite = √3 × 4√3

Opposite = 12

Reference angle (∅) = 60

Adjacent = 4√3

Hypotenuse = ?

cos 60 = adj/hyp

cos 60 = 4√3/hyp

hyp = 4√3/cos 60

hyp = 4√3/1/2

hyp = 4√3 × 2

hyp = 8√3

Therefore, applying the trigonometry ratios, the missing lengths for right triangle ABC are: 12 and 8√3.

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Using the normal distribution, it is found that:

a. A male sailor whose waist is 34.1 inches is at the 87.5th percentile.

b. 5.7% of male sailors requires custom uniform pants.

The z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The mean and the standard deviation are given, respectively, by:

[tex]\mu = 32.6, \sigma = 1.3[/tex]

For item a, the percentile is the p-value of Z when X = 34.1, hence:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

Z = (34.1 - 32.6)/1.3

Z = 1.15

Z = 1.15 has a p-value of 0.875.

Hence 87.5th percentile.

For item b, the proportion who does not require an special order is the p-value of Z when X = 36 subtracted by the p-value of Z when X = 30, hence:

X = 36:

Z = (36 - 32.6)/1.3

Z = 2.62

Z = 2.62 has a p-value of 0.996.

X = 30:

Z = (30 - 32.6)/1.3

Z = -2

Z = -2 has a p-value of 0.023.

0.996 - 0.023 = 0.943.

Hence the proportion who requires an special order is:

1 - 0.943 = 0.057.

5.7% of male sailors requires custom uniform pants.

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Answer:

54

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

2 x 3 x 3 x 5 x 5 x 5 x 5

Step-by-step explanation:

see picture

Answer:

[tex]x = 3.5[/tex]

[tex]y\approx1.666666667[/tex]

Step-by-step explanation:

To solve simultaneous equations, at least one of our variables must have the same coefficient. We can easily multiply the first equation by 4 to get 12y on both sides, so let's do that:

[tex]8x + 12y = 8[/tex]

No let's subtract the second equation from the first equation to get the third equation:

[tex]2x = 7[/tex]

Solve:

[tex]x = 3.5[/tex]

Now, we can substitute this value into one of the original equations - let's use the second one:

[tex]21 + 12y = 1[/tex]

Solve:

[tex]12y = - 20[/tex]

[tex]y = - \frac{ - 20}{12} = \frac{ - 10}{6} = - \frac{5}{3} \approx - 1.66666666667[/tex]

The vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).

The vertex of a parabola exists as the point at the intersection of the parabola and its line of symmetry. The vertex of the parabola exists as the minimum point on the graph for a positive right-handed parabola.

Given the equation of parabola exists [tex]$x^{2}=8 y$[/tex].

[tex]$\mathrm{y}=x^{2} / 8[/tex]

General vertex form for any given parabola exists [tex]$\mathrm{y}=\mathrm{a}(x-a)^{2}+\mathrm{b}$[/tex]

where (a, b) exists the coordinates of the vertex.

For this function it exists [tex]$\mathrm{y}=1 / 8(x-0)^{2}+0$[/tex]

The vertex of the given parabola exists at (0, 0).

Therefore, the vertex of the given parabola [tex]$x^{2}=8 \mathrm{y}$[/tex] exists (0, 0).

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