A population of paramecia, P, can be modeled using the exponential
function P(t) 3(2), where t is the number of days since the
population was first observed. Which domain is most appropriate
=
to use to determine the population over the course of the first two
weeks?

Answer:

x = 4

Step-by-step explanation:

[tex]5^{9x} =25^{4x+2}[/tex]

First you need to get a common base as your number.

[tex]5^{9x} =5^{2(4x+2)}[/tex]

The second number changed because 5 squared is 25. Changing it to this form gives us the same base number of 5. Now we use the distributive property in the exponent.

[tex]5^{9x} =5^{8x+4}[/tex]

Now we can use this statement:

[tex]A^{m} =A^{n}[/tex] if [tex]m=n[/tex]

Using this we solve:

9x = 8x+4

-8x  -8x

x = 4

Hope it helps!

Answer:

119 4/7

Step-by-step explanation:

Add up all the sides

Hi Student!

Looking at the picture that was provided, we see that the problem statement is asking for us to determine the perimeter of the shape is.  Perimeter is the outer layer of the shape which would include the lengths of all the sides that are exposed to the outside.

In this case, we are given 7 different values which represent each of the different sides of the shape which we need to add together to get the perimeter.

Create an expression

Using the expression above, all we need to do is combine all of the values which will give us the outline on our shape.  However, since some of the values have different denominators, we will first need to combine the whole numbers and then combine those with a common denominator and finally apply a common denominator to be able to add the rest.

Combine the whole numbers

Combine those with a common denominator

Covert to mixed fraction and simplify

Find common denominator and combine

Simplify the expression

Therefore, the final answer for the perimeter of the figure that was provided would be [tex]119\frac{4}{7}[/tex] units.

"In order to meet ADA requirements, a wheelchair ramp must have an angle of elevation of no more than" the angle of elevation  is mathematically given as

∅=3.434

Generally, the equation for the angle is mathematically given as

[tex]\theta=\frac{opp}{adj}\\\\Therefore\\\\tan\theta=\frac{1.5}{25}\\\\tan\theta=\frac{1.5}{25}\\\\\theta=tan^{-1}\frac{1.5}{25}\\\\[/tex]

∅=3.434

In conclusion, the angle of elevation

∅=3.434

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Answer:

2018 I believe.

Step-by-step explanation:

He'll be two times his age in 2032 which is 28 years old. Subtract 28 from 2032 and you get 2018.

Answer:

2018

Step-by-step explanation:

in 2032 he will be 28 years old because he is 2 times older than 14, 2032-14=2018, because 14 years have passed since he was 14

The probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090

The given parameters are:

p = 47%

Sample size, n =500

The standard deviation is calculated as:

[tex]\sigma = \sqrt{np(1 - p)[/tex]

So, we have:

[tex]\sigma = \sqrt{500 * 47\%(1 - 47\%)[/tex]

Evaluate

σ = 11.16

The number of adults with hypertension is calculated as:

x = 500 * 0.5 = 250

And the mean is:

μ = 500 * 0.47 = 235

Start by calculating the z-score

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z = \frac{250 - 235}{11.16}[/tex]

Evaluate

z = 1.34

The probability is then calculated as:

P(z >1.34) = ??

From z table of probabilities, we have:

P(z >1.34) =  0.090

Hence, the probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090

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A triangle is a three-edged polygon with three vertices. If the triangle is rotated 180° about the cross then it will be done as shown below.

A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to b

If the triangle is rotated 180° about the cross then it will be done as shown below. This is because the triangle is 2 units away from the cross(dot) therefore, after rotation it will be at the same distance from the point.

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The answer will be x squared over 4 plus y squared over 8 equals 1.

An ellipse is an oval shape geometry having two focuses and the curve is equidistant from the focus.

The general equation of the ellipse is given as;

(x²/a²) + (y²/b²) = 1

The coordinates of a foci are: (±c, 0) where;

c² = b² - a²

However, we know that equation of directrix is; x = ±a/e

Now, Directrix is given ±4

Thus, a/e = 4

a = 4e

We also know that c = ae from ellipse foci coordinates.

Thus, ae = 2

since ae = 2, then (4e)e = 2

4e² = 2

e² = 2/4

e = 1/2

Thus;

a = 4 × 1/2

a = 2

Since c² = b² - a²;

2² = b² - 2²

4 = b² - 4

b² = 8

From (x²/a²) + (y²/b²) = 1, we can put our values to get;

x²/4 + y²/8 = 1

Hence the answer will be x squared over 4 plus y squared over 8 equals 1.

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Answer:

35 is the least common denominator

Step-by-step explanation:

35 is the least (smallest) common (same) multiple of 5 and 7. We use the smallest number that both 5 and 7 go into, because its supposed to be easier to use smaller numbers.

4/5 becomes 28/35 and 5/7 becomes 25/35. And now that they have the same denominator, you could add or subtract them.

Answer:

A. median

explain i just aced the test rn

Answer:

Angle bisector

Step-by-step explanation:

The line AD bisects both sides of the triangle. Both angles are congruent to each other since both sides are congruent to each other.

Answer:

  65.9 ft

Step-by-step explanation:

The Law of Sines tells us the relationship between an angle and the opposite side. We are given the angle opposite the given side, but we need the angle opposite the side of interest.

__

The sum of angles in a triangle is 180°, so the measure of the angle at the balloon is ...

  angle C = 180° -75° -60° = 45°

Then the distance between Amaya and Rochelle (c) is ...

  c/sin(C) = r/sin(R)

  c = r×sin(C)/sin(R) = (90 ft)×sin(45°)/sin(75°)

  c ≈ 65.8846

Amaya and Rochelle are about 65.9 feet apart.

Answer:

45m

Step-by-step explanation:

4m+19m+14m+8m=45m

For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

A rectangle is transformed according to the rule 90º.

The rectangle has vertices located at r'(–4, 4), s'(–4, 1), p'(–3, 1), and q'(–3, 4).

Then the location of q will be

For 90 degrees coordinate will be swapped and the position of the coordinate is in the third quadrant. Then the location of point q will be at (–4, –3).

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Answer: 10.6

Step-by-step explanation:

[tex]\sin 62^{\circ}=\frac{x}{12}\\x=12 \sin 62^{\circ} \approx \boxed{10.6}[/tex]

The independent variable: number of pounds of fertilizer; and dependent variable: number of square feet of garden covered.

Let

Dependent variable are variables which takes its value based on other values in an equation.

Independent variable are variables which takes its value outside an equation.

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The exponential function of the table is y = 0.75(2)^x

From the table, we have the following points

(x,y) = (0,0.75) and (1,1.5)

An exponential function is represented as:

y = ab^x

At (0,0.75), we have:

0.75 = ab^0

a = 0.75

Substitute a = 0.75 in y = ab^x

y = 0.75b^x

At (1,1.5), we have:

1.5 = 0.75b^1

Evaluate

1.5 = 0.75b

Divide both sides by 0.75

b =2

Substitute b =2 in y = 0.75b^x

y = 0.75(2)^x

Hence, the exponential function is y = 0.75(2)^x

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Answer:

A. -0.8

Step-by-step explanation:

The closer its absolute value to 1, the stronger the relationship is.

A. |-0.8| = 0.8

B. |-0.6| = 0.6

C. |-0.5| = 0.5

D. |-0.7| = 0.7

0.8 is closest to 1, therefore representing the strongest correlation.

Hope this helped :)

If Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.

Note that, speed is distance traveled per unit time.

Mathematically, Speed = Distance ÷ time.

Hence, Distance = Speed × time

Given that;

Distance = Speed × time

Distance = 14km/hr × 0.25hr

Distance = 3.5km or (3.5×1000)m

Distance = 3.5km or 3500m

Therefore, if Kara rollerblades at given average speed, in 15 minutes, she will rollerblade a distance of 3.5kilometers or 3500meters.

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Answer:

2.5 cups is equal to 1 pound.

Step-by-step explanation:

___2.5__ cups rice is equivalent to 1 pound

Hope This Helped

Answer:

2.5 cups of rice

I hope this helps

B. The square root function is the quadratic function reflected across

the line y = x, with a limited domain.

graph y=x^2 and y=√x and y=x

graph is attached

gathmath

Answer:

y = 7x +2

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2 ) and (x₂, y₂ ) = (- 1, - 5 )

m = [tex]\frac{-5-2}{-1-0}[/tex] = [tex]\frac{-7}{-1}[/tex] = 7

the line crosses the y- axis at (0, 2 ) ⇒ c = 2

y = 7x + 2 ← equation of line

Answer:

My guess would be b or d

Step-by-step explanation:

Applying the inscribed angle theorem, the measure of arc AB that doesn't go through point C is: 100 degrees.

Based on the inscribed angle theorem, if ∅ is the inscribed angle measure, the measure of the central angle subtended by the same arc equals 2(∅).

m∠BAC = 40 degrees.

Central angle = 2(40) = 80 degrees [based on the inscribed angle theorem]

Corresponding arc BC = 80 degrees.

Arc AC through point B = 180 degrees [half circle]

Arc AB = 180 - arc BC = 180 - 80 = 100 degrees.

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The simplified value is shown below:

Exponent refers to the number of times a number is used in a multiplication. Power can be defined as a number being multiplied by itself a specific number of times.

First,

3²*4³*[tex]2^{-1}[/tex]/(3*4)²

=9*64/144*2

= 576/288

=2

Second,

(3*2)^4 *[tex]3^{-3}[/tex]/2³*3

=1296/8*81

=1296/648

=2

Third,

[tex]3^{-3} *2^{-3} *6^{3} /(4^{0} )^{2}[/tex]

= [tex]6^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]

= [tex]2^{3}* 3^{3} /(1 )^{2} *3^{3} *2^{3}[/tex]

=1

Fourth,

[tex]2^{4}* 3^{5} /(2*3)^{5}\\=2^{4}* 3^{5} /2^{5}*3^{5}[/tex]

= 1/2

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The given quadratic equation [tex]y = x^2 + 3x - 10[/tex] Hence, the correct option is D one real root.

Let the quadratic equation given be of the form ax^2 + bx + c = 0, then

The quantity [tex]b^2 - 4ac[/tex] is called its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

The given quadratic equation

[tex]y = x^2 + 3x - 10[/tex]

a = 1

b = 3

c = -10

The discriminant

[tex]b^2 - 4ac[/tex]

= 9 - 4(1)(-10)

= 9- 40

= - 31

Thus, Non-real and distinct roots if the discriminant is negative.

Hence, the correct option is D one real root.

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Answer: 50.5

Step-by-step explanation:

[tex]\frac{30}{22}=\frac{x}{37}\\x=(30/22)(37) \approx \boxed{50.5}[/tex]

Answer:

what subject of math? Anything to do with calc is a tough area but I can try.

Step-by-step explanation:

Answer:

In the first step, there is an issue when distributing the -3 to the terms inside of the parentheses. When multiplying the -3 to the -5, you would get an answer of +15, not -15.

The full correct process is:

(4m + 9) - 3(2m - 5) = 4m + 9 - 6m + 15

                                = 4m - 6m + 9 + 15

                                = -2m + 24