Which expression is equivalent

The equation is y = 250(0.89)^x and the decay rate is 11%.

The initial value will be:

= 250(0.89)^x

= 250(0.89^0)

= 250

The decay rate will be:

= 1 - 0.89

= 0.11

= 11%

In conclusion, the equation is y = 250(0.89)^x and the decay rate is 11%.

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Answer:

y - 1 = -2(x + 2)  

Step-by-step explanation:

The general structure of an equation in point-slope form is:

y - y₁ = m(x - x₁)

In this form, "x" and "y" stand for the values of one point and "x₁" and "y₁" stand for the values of another point. The variable "m" represents the value of the slope. You have been given the values of one point and the slope. When you plug them into the general form, you get this answer:

Point: (-2, 1)

m = -2

y - y₁ = m(x - x₁)                    <----- Point-slope form

y - y₁ = -2(x - x₁)                    <----- Plug -2 in "m"

y - 1 = -2(x - (-2))                   <----- Plug in values from point

y - 1 = -2(x + 2)                    <----- Simplify

The value of the expression will be 2. Then the correct option is B.

The complete question is given below.

The value that approaches the output for the given input value. Limits are a very important tool in calculus.

The expression is given below.

[tex]\rightarrow \displaystyle \lim_{x \to 0}\dfrac{\cos x \ \tan 2x}{x}[/tex]

Then the value of the expression will be

Applying L'hospital rule, then we have

[tex]\rightarrow \displaystyle \lim_{x \to 0}\dfrac{\dfrac{d}{dx} \cos x \ \tan 2x}{\dfrac{d}{dx}x}\\\\\\\\\rightarrow \displaystyle \lim_{x \to 0}\dfrac{2 \cos x \sec^2 2x - \sin x \ \tan 2x}{1}\\[/tex]

Put the limit, then we have

⇒ 2 × cos 0 × sec² (2 × 0) – sin 0 × tan (2 × 0)

⇒ 2 × 1 × 1 – 0

⇒ 2

Then the correct option is B.

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Answer:

60

Step-by-step explanation:

Total degree of triangle interior angles is 180

So x+2x+3x=180

6x=180

x=30

Measurement of angle C is 2x which is 60 degree

Answer:

D. None of the above.

Step-by-step explanation:

Supplementary angles must add up to 180 degrees.

Complementary angles must add up to 90 degrees.

Vertical angles are opposite of each other.

Hope this helps!

If not, I am sorry.

The important similarity between the uniform and normal probability distributions is that the mean and the median of both distributions are equal

In a normal probability distribution, we have:

Mean = Median

In a uniform probability distribution, we have:

Mean = Median

This means that:

In both distributions, the mean and the median are equal

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The number of red car altogether is 34

The number of blue cars altogether is 36

The  number of silver car altogether 70

The car manufacturer has parked some cars in 2 car parks .

The first car park has 60 cars.

In the ratio 1 :2:3

Therefore,

red car = 1 / 6 × 60 = 10 cars

blue car = 2 / 6 × 60 = 20 cars

Silver car = 60 - 30 = 30 cars

The second car park has 80 cars.

The ratio are

In the ratio 3:2 5

Therefore,

red cars = 3 / 10 ×80 = 24

blue cars = 2 / 10 × 80 = 16

silver cars = 5 / 10 × 80 = 40

Therefore,

The number of red car altogether is 24 + 10 = 34 red car

The number of blue cars altogether is 20 + 16 = 36 blue cars

The  number of silver car altogether is 30 + 40 = 70 silver cars

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The chance of not throwing the ball to a receiver on either throw is 0.0375, or 3.75 per cent.

Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

This is event A when he misses the first throw. P(A) = 25%, or 0.25 Because event B takes place only after event A. When he misses on the second throw, event B occurs. P(B/A) = 15% or 0.15

P(A[tex]\cap[/tex]B) = P(A) P(B/A) P(A[tex]\cap[/tex]B)

P(A[tex]\cap[/tex]B) = (0.25)x(0.15) P(ANB)

P(A[tex]\cap[/tex]B) = 0.0375

Therefore the chance of not throwing the ball to a receiver on either throw is 0.0375, or 3.75 per cent.

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An equation is formed when two equal expressions. The value of k that makes the equation true is 4.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The value of k that will make the equation true is,

[tex]5a^2b^3(6a^kb)=30a^6b^4\\\\30\ a^{(2+k)}\ b^{(3+1)} = 30\ a^6\ b^4\\\\30\ a^{(2+k)} \ b^4 = 30\ a^6\ b^4\\\\a^{(2+k)} =a^6\\\\2+k = 6 \\\\ k = 4[/tex]

Hence, The value of k that makes the equation true is 4.

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The steps are shown below: -5<x<1

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

Given:

|x +2 | <-3

If we take the module is positive,

x+2 -2 < -3-2

x < -5

If we take the module is negative,

-( x+2)  < -3

-x -2 < -3

-x -2 +2 < -3 +2

-x< -1

x>1

Combining the inequalities,

-5<x<1

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[tex]\\ \rm\Rrightarrow log_5512[/tex]

[tex]\\ \rm\Rrightarrow log_52^9[/tex]

[tex]\\ \rm\Rrightarrow 9log_52[/tex]

[tex]\\ \rm\Rrightarrow 9\dfrac{log2}{log5}[/tex]

[tex]\\ \rm\Rrightarrow 3.876[/tex]

If your question is something different let me know by which I can change my answer

Answer:

3.876  (3 d.p.)

Step-by-step explanation:

Given:

Please note:  The question gives two values of log base 10 which should be used to help find the value of [tex]\log_5512[/tex]

Log Law:  Change of Base

[tex]\log_ba=\dfrac{\log_xa}{\log_xb}[/tex]

Change the given expression to log base 10:

[tex]\implies \log_5512=\dfrac{\log_{10}512}{\log_{10}5}[/tex]

Replace 512 with 2⁹, and 5 with 10/2:

[tex]\implies \dfrac{\log_{10}{2^9}}{\log_{10}\frac{10}{2}}[/tex]

[tex]\textsf{Apply the Power Log law}: \quad \log_ax^n=n\log_ax[/tex]

[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}\frac{10}{2}}[/tex]

[tex]\textsf{Apply the Log Quotient law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]

[tex]\implies \dfrac{9\log_{10}{2}}{\log_{10}10-\log_{10}2}[/tex]

[tex]\textsf{Apply log law}: \quad \log_aa=1[/tex]

[tex]\implies \dfrac{9\log_{10}{2}}{1-\log_{10}2}[/tex]

Given:

Substitute this into the expression and simplify:

[tex]\implies \dfrac{9(0.3010)}{1-0.3010}[/tex]

[tex]\implies \dfrac{2.709}{0.699}[/tex]

[tex]\implies 3.876\:(\sf 3\: d.p.)[/tex]

Answer:

2

Step-by-step explanation:

When a function and its inverse are composed, the output is equal the input.

Answer:

c =2.5

Step-by-step explanation

1.5×1.5=2.25

2×2=4

4+2.25=6.25

√6.25=2.5

c=2.5

Answer:

  (b)  8.9 m

Step-by-step explanation:

The mirror ensures that angle 1 is congruent to angle 2, so the triangles in the diagram are similar. The ratios of height to mirror distance are proportional.

__

The height of the object is proportional to its distance from the mirror, so we have ...

  (tree height)/(tree-to-mirror) = (person height)/(person-to-mirror)

  (tree height)/(2.5 m) = (1.78 m)/(0.5 m)

Multiplying this proportion by 2.5 m, we find ...

  tree height = (2.5 m)(1.78/0.5) = 8.9 m

The height of the palm tree is 8.9 meters.

The coordinates of the point that is 4/5 of the way from T to S is (2,10)

The given parameters are:

T = (6,-2)

S = (1,13)

Location = 4/5

The location 4/5 means

Ratio, m : n = 4 : 1

The coordinate is then calculated as:

[tex](x,y) = \frac{1}{m +n} * (mx_2 + nx_1,my_2 + ny_1)[/tex]

This gives

[tex](x,y) = \frac{1}{4 +1} * (4 * 1 + 1 * 6 , 4 * 13 + 1 * -2)[/tex]

Evaluate

[tex](x,y) = \frac{1}{5} * (10 , 50)[/tex]

This gives

(x,y) =  (2,10)

Hence, the coordinates of the point that is 4/5 of the way from T to S is (2,10)

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Answer:

7 and 8

Step-by-step explanation:

49 - 1 = 48. (1)

48 - 3 = 45. (2)

45 - 5 = 40. (3)

40 - 7 = 33. (4)

33 - 9 = 24. (5)

24 - 11 = 13. (6)

13 - 13 = 0. (7) The answer is 7

64 - 1 = 63. (1)

63 - 3 = 60. (2)

60 - 5 = 55. (3)

55 - 7 = 48. (4)

48 - 9 = 39. (5)

39 - 11 = 28. (6)

28 - 13 = 15. (7)

15 - 15 = 0. (8) the answer is 8

Answer:

Step-by-step explanation:

      In this, the given number is subtracted by consecutive odd numbers (1,3,5,7,9.....)  till we fer zero at the end. Count the number of steps performed and this number will be square root of the given number.

a) 49

√49 = 7

b)  64

√64 = 8

Answer:

D

Step-by-step explanation:

interior angles = 180

180-72

2534+?  but its not that clear cant understand it

The number of  students like physics more than mathematics is 15 , Option B is the correct answer.

A mathematical way of expressing quantity of a substance is called a Number.

Number of students in a school who like mathematics = 20

Number of students in a school who like physics = 35

number of students in a school who like only physics is 20

number of students who like only Mathematics is 5

the number of  students like physics more than mathematics is 20-5 = 15

Therefore Option B is the correct answer.

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The percentage increase is 22.72%

The given parameters are:

Initial = 440 coins

Final = 540 coins

The percentage increase is calculated as:

%Increase = (Final - Initial)/Initial * 100%

So, we have:

%Increase = (540 - 440)/440 * 100%

Evaluate the difference

%Increase = 100/440 * 100%

Evaluate the quotient

%Increase = 0.2272 * 100%

Evaluate the product

%Increase = 22.72%

Hence, the percentage increase is 22.72%

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Step-by-step explanation:

If a variables varies jointly, we can just divide it by the other variables in relation to it.

For example, since p variables jointly as q and square of r, then

[tex] \frac{p}{q {r}^{2} } = k[/tex]

where k is a constant

First, let find k. Substitute p= 200

q= 2, and r=3.

[tex] \frac{200}{2(3) {}^{2} } = k[/tex]

[tex] \frac{200}{18} = k[/tex]

[tex] \frac{100}{9} = k[/tex]

Now, since we know our constant, let find p.

[tex] \frac{p}{q {r}^{2} } = \frac{100}{9} [/tex]

Q is 5, and r is 2.

[tex] \frac{p}{5( {2}^{2}) } = \frac{100}{9} [/tex]

[tex] \frac{p}{20} = \frac{100}{9} [/tex]

[tex]p = \frac{2000}{9} [/tex]

[tex]a\cdot b=(7)(4)+(3)(-1)=25\\\\|a|=\sqrt{7^{2}+3^{2}}=\sqrt{58}\\\\|b|=\sqrt{4^{2}+(-1)^{2}}=\sqrt{17}\\\\\cos \theta=\frac{25}{\sqrt{58}\sqrt{17}}\\\\\theta=\cos^{-1} \left(\frac{25}{\sqrt{58}\sqrt{17}} \right) \approx 37.235^{\circ}[/tex]

Answer:

Step-by-step explanation:

Comment

If two secants intersect outside a circle (as these two do) then the angle at which they meet is 1/2 the difference between the intersected arcs. Put much simpler <DCF = 1/2 (arc EG - arc DF)

Givens

Arc EG = 127

Arc DF = 49

Solution

<DCF = 1/2(127 - 49)

<DCF = 1/2(78)

<DCF = 39

The graphed that represents the new function with the same slope and y-intercept is: graph Y.

Slope = rise/run along a line.

Y-intercept is the y-value of the point on the y-axis that the line intercepts.

Slope of the function given = rise/run = 2/1 = 2

2 multiplied by 1/2 = 2/2 = 1.

Y-intercept of the given function is: 1

1 increased by 3 units is: 1 + 3 = 4

The slope of graph Y = rise/run = 2/2/ = 1

The y-intercept is also 4

Therefore, the answer is: Graph Y

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Answer:

D. 531[tex]in^{2}[/tex]

Step-by-step explanation:

I suppose these are rectangles and not triangles.

Area of Rectangle = Length x Breadth

Area of Large Rectangle = 21 x 18

= 378[tex]in^{2}[/tex]

Area of Small Rectangle = 17 x 9

= 153[tex]in^{2}[/tex]

Total Area = Area of Large Rectangle + Area of Small Rectangle

= 378 + 153

= 531[tex]in^{2}[/tex]

The difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

The given polynomials are [tex](1.3t^{3}+0.4t^{2} -24t )[/tex] and [tex]0.6t^{2} +8-18t[/tex].

We need to find the additive inverse of the polynomial being subtracted.

In mathematics, the additive inverse of a number a is the number that, when added to a yields zero. This number is also known as the opposite, sign change, and negation.

Now, [tex](1.3t^{3}+0.4t^{2} -24t )-(0.6t^{2} +8-18t)[/tex]

[tex]=1.3t^{3}+0.4t^{2}-0.6t^{2}-24t+18t-8[/tex]

[tex]=1.3t^{3}-0.2t^{2}-6t-8[/tex]

The additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

Therefore, the difference of the polynomials is [tex]1.3t^{3}-0.2t^{2}-6t-8[/tex] and the additive inverse of the polynomial being subtracted is [tex]-0.6t^{2} +8+18t[/tex].

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Step-by-step explanation:

as we see in the sequence, each term is twice of the previous term.

we mark the Nth as a(N), then:

a(N)=2a(N-1)

Answer:

[tex]a_{n}[/tex] = 5[tex](2)^{n-1}[/tex]

Step-by-step explanation:

there is a common ratio between consecutive terms , that is

10 ÷ 5 = 20 ÷ 10 = 40 ÷ 20 = 80 ÷ 40 = 2

this indicates the sequence is geometric with explicit formula

[tex]a_{n}[/tex] = a₁[tex](r)^{n-1}[/tex]

where a₁ is the first term and r the common ratio

here a₁ = 5 and r = 2 , then

[tex]a_{n}[/tex] = 5 [tex](2)^{n-1}[/tex]

Answer:

[tex]5^{\circ}[/tex]

Step-by-step explanation:

[tex]~~~~~~~\tan \theta = \cot 85^{\circ}\\\\\implies \tan \theta = \tan\left(90^{\circ} - 85^{\circ} \right)\\\\\implies \tan \theta = \tan 5^{\circ}\\\\\implies \theta = 5^{\circ}[/tex]

14926.74417

Step-by-step explanation:

Based on the given conditions, formulate:

150000 ((2.4% +1)4-1)

Evaluate the equation/expression: 14926 14926.74417 get the result:14926.74417 Answer: 14926.74417

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