Which of the following is the radical expression of a to the four ninths power ?
A. 4a9
B. 9a4
C. fourth root of a to the ninth power
D. ninth root of a to the fourth power

Solution-

Quadratic regression equation,

[tex]y =ax^2+bx+c[/tex]

taking x = input/independent variable = year - 2000

and y = output/dependent variable = share of the global GDP

To plot a quadratic equation for the data points, we need to calculate all the constants a,b and c , then putting all the values in the general equation we can get the best fit curve for the data set.

Using, the graphing calculator, we can calculate the values of a, b, and c. The values were found to be,

a = -0.0471

b = 2.6366

c = 12.1001

Putting all the values,

[tex]y =-0.0471x^2+2.6366x+12.1001[/tex]

This is the best fit quadratic function that models the share of the global GDP.

For calculating the share of GDP in the year 2027, we can put the value of x to get the value of y.

x = year-2000=2027-2000=27,

[tex]y=-0.0471(27)^2+2.6366(27)+12.1001=-0.0471(729)+2.6366(27)+12.1001=48.95[/tex]

∴ In the year 2027, the maximum share will be 48.95% of total GDP.

The detailed answer explains how to find the quadratic function that models the data and calculates the predicted share of the GDP in 2027 using the quadratic function.

Quadratic Function Model:

Using the given data points, we can find the quadratic function that best models the developing economies' share of global GDP. This can be achieved by fitting a quadratic equation to the data.

The quadratic function that best models the data is: y(x) = 0.7386x^2 - 28.4235x + 276.0976

Predicted Share of GDP in 2027:

To find the predicted share of the GDP in 2027, substitute x = 27 (since 2027 is 27 years after 2000) into the quadratic function.

By calculating, the predicted share of the GDP in 2027 is approximately 44.5233%.

the difference between a proper fraction and an improper fraction is an improper fraction is a fraction that is bigger then the denominator for example 3/4 is a fraction and 7/4 is an improper fraction

Explanation is provided in the image attached.

Biconditional means they can both be the hypothesis and the conclusion.

If a number is divisible by 2, then the number is even.  TRUE

If a number is even, then it is divisible by 2. TRUE

Since both statements are true, then it is a biconditional statement.

Answer: Biconditional

Answer: In  1 hour, 12720 more times rabbit's heart beat than a dog's rabbits heart beat

Step-by-step explanation:

Since we have given that

Rabbit's heart beat in 1 min 212 times more than dog's heart beat in 1 min.

So, in 1 hour , we get,

[tex]1\text{ hour }= 60\text{ minutes}\\so, heartbeat = 212\times 60=12720[/tex]

So, in  1 hour, 12720 more times rabbit's heart beat than a dog's rabbits heart beat .

To determine how many more times a rabbit's heart beats than a dog's in an hour, multiply the rabbit's beats per minute by 60 to get the hourly beat total, and do the same for the dog. Subtract the dog's total from the rabbit's to find the difference. Assuming a dog's heart rate of 70 beats per minute, a rabbit's heart beats 8,520 more times per hour than a dog's.

To calculate how many more times a rabbit's heart beats than a dog's in one hour, we first need to establish the number of beats per hour for both animals. Since the rabbit's heart beat is 212 times per minute, we multiply this number by 60 (the number of minutes in an hour) to find out the total heartbeats in one hour for a rabbit:

Rabbit heartbeats per hour = 212 beats per minute x 60 minutes = 12720 beats per hour.

Next, we need the same figure for the dog. Without the specific heart rate for the dog, we'll assume a generic heart rate for calculation purposes. For example, if a dog's heart beats 70 times per minute (a common rate for dogs), we multiply by 60:

Dog heartbeats per hour = 70 beats per minute x 60 minutes = 4200 beats per hour.

Now, to find out how many more times the rabbit's heart beats than the dog's, we subtract the dog's heartbeats per hour from the rabbit's:

Rabbit's additional heartbeats = 12720 beats per hour - 4200 beats per hour = 8520 more beats per hour.

Attempted - 414 shots,

Made - 174 shots,

then fraction of the shots the player made is

[tex]\dfrac{174}{414}.[/tex]

Simplify it

[tex]\dfrac{174}{414}=\dfrac{87}{207}.[/tex]

Answer: in simplest form the fraction is [tex]\dfrac{87}{207}.[/tex]

(1) Next likely step is

3x = 18   (adding +3 to both sides of the eq.)

(2) 3x -2 = 3x + 5

simplify:

3x-3x = 5+2

0 = 7

This is never true, no matter what value of x is. So there is no (or zero) solution.

The answer is "Zero"

Answer:

3x=18

Step-by-step explanation:

3x-3=15

+3     +3

3X=18

second one is: 3x-2=3x+5

+2     +2

3x=3x7

+3x +3x

6X=7

Let’s start out by what we already know. He used 2/5 of flour to make bread and he used 16 Ibs to make bread. This implies that the amount is (2/5)x=16.

2/5x=16

X= 5 x 16/2

X= 40

Since he used 16 Ibs of flour for bread, the rest are for the muffins, which is around 24 Ibs.

We know that each thing of muffins will use 2/3 Ibs of flour.

24/2/3

24/1/2/3

24/1 x 3/2 = 36

36 is the answer to your question. :)

Simplifying

8x + -10 = 62

Reorder the terms:

-10 + 8x = 62

Solving

-10 + 8x = 62

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '10' to each side of the equation.

-10 + 10 + 8x = 62 + 10

Combine like terms: -10 + 10 = 0

0 + 8x = 62 + 10

8x = 62 + 10

Combine like terms: 62 + 10 = 72

8x = 72

Divide each side by '8'.

x = 9

Simplifying

x = 9

Answer: h(___9___) = 62

Step-by-step explanation:

A very simple way to solve this specific problem is acknowledging the fact that the left hand side (L.H.S) is being multiplied by a factor of 10 to get the equation on the right hand side (R.H.S). So, if we multiply the denominator by 10, we'll get the answer, which would be 1 × 10 = 10 weeks.

Hope I could help! :)

Answer:0.06

Step-by-step explanation:

As the two events are independent

Therefore

[tex]P(AandB) =P(A)\times P(B) [/tex]

As it is given that [tex]P(A) = 0.3 [/tex] and [tex]P(B) = 0.20 [/tex]

Putting these value we get

[tex]P(AandB) =0.3\times0.2 = 0.06 [/tex]

[tex] P(AandB)= 0.06 [/tex] is the required answer

Answer:

0.06

Step-by-step explanation:

just got it right on edge

P = 2(L + W)

510 = 2(L + W) ...divide both sides by 2

510/2 = L + W

255 = L + W

3/5(255) = 765/5 = 153 cm <== length

2/5(255) = 510/5 = 102 cm <== width

Answer: [tex]2 \frac{7}{10}[/tex]

Step-by-step explanation: Using the place value chart we can see that 2.7 means two and seven-tenths which can be written as the mixed number

[tex]2 \frac{7}{10}[/tex].

On the right side, both terms contain g, so we can factor it out

T = g(r+vt)

Now, to get g by itself, divide by the things in parentheses

g= T/(r+vt)

To solve the equation T=gr+gvt for g, you can factor out g from the right side, obtaining T=g(r+vt). Then, dividing both sides by (r+vt) will isolate g, resulting in g = T/(r+vt).

To rearrange the equation T=gr+gvt to solve for g, you need to factor out g from the right side of the equation. Factoring out g, you obtain T=g(r+vt). Dividing by (r+vt) on both sides then gives you the equation for g: g = T/(r+vt).

Here are the steps in detail:

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(x/4) +6 = 14

Subtract 6 from each side:

x/4 = 8

Multiply each side by 4:

x = 32

The answer to 8(2 + 7) would be 72 so 16 + 56 = 72 as well which means the answer is D) 16 + 56.

Hello there!

The answer should be the last option D.

Explanation:

↓↓↓↓↓↓↓↓↓↓↓↓↓

First you had to calculate with parenthesis

(2+7)=9

8*9

Then multiply and divide from left to right

8*9=72

[tex]8*2=16[/tex]

[tex]8*7=56[/tex]

Answer⇒⇒⇒16+56

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

The only number between 590 and 610 that is divisible by 2, 3, 5, and 10 is 600.

The question asks for numbers between 590 and 610 that are divisible by 2, 3, 5, and 10. To solve the problem, we need to find the numbers that can be divided evenly (without remainder) by all of these numbers.

After calculating, we can see that the only number that fits all these conditions is 600.

The number 600 is divisible by 2, 3, 5, and 10 which means it can be divided by these numbers without leaving a remainder. For example, 600 divided by 2 equals  '300', 600 divided by 3 equals '200', 600 divided by 5 equals '120', and 600 divided by 10 equals '60'.

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multiply the 2/8 x 4/9 first

then add the 7/9

you'll get 6/9

simplify to get the answer: 2/3

[tex]\frac{7}{9} -\frac{2}{8} \times \frac{4}{9}[/tex]

Start by multiplying the fractions together. When multiplying fractions they don't need to have a common denominator, so multiply 2/8 and 4/9 from left to right.

[tex]\frac{2}{8} \times \frac{4}{9} = \frac{8}{72}[/tex]

Now your new problem looks like: 7/9 - 8/72. When subtracting fractions they have to have common denominators so multiply 7/9 by 8/8.

[tex]\frac{7}{9} \times \frac{8}{8}= \frac{56}{72}[/tex]

You can now subtract 56/72 and 8/72 to get your final answer.

[tex]\frac{56}{72} -\frac{8}{72} = \frac{48}{72}[/tex]

This fraction can be simplified by dividing both sides by 8 because the numerator and denominator of this fraction are multiples of 8 and can be divided evenly by 8.

[tex]\frac{48}{72} \div \frac{8}{8} = \frac{6}{9}[/tex]

6/9 can be simplified even further by dividing both sides by 3 because both 6 and 9 can be divided evenly by 3.

[tex]\frac{6}{9} \div \frac{3}{3} = \frac{2}{3}[/tex]

D) 2/3 is your final answer.

Hey there!!

This question is based on "direct variation".

Direct variation says :-

... y = kx ( Where k is the constant ).

Given :-

... y = 5 and x = -45

Now, we will have to find the constant

... 5 = -45k

... -5 / 45 = k

... 1 / 9 = k

Now, find the value y and x value given is -24.

... y = -24k

... y = -24 * 1/9

... y = -8 * 1/3

... y = -8/3

Hope my answer helps!!

Answer:

13.5 kgs.

Step-by-step explanation:

Here we have to find conversion factor of lbs into kg.

For this we use the given information.

Given that the weight of a dog is 20 lbs and also 9 kg.

Hence we have conversion factor as

20 lbs = 9 kg

Or 1 lb =9/20 = 0.45 kg.

Using this, we find the 30 lb converted into kg.

For 1 lb, equivalent kg = 0.45

Hence for 30 lbs equivalent kg= 30(0.45) = 13.5 kg.

The answer is A. This is because you can see Brian's and Kelsey's cars traveled 4 more centimeters every 2 seconds.

Answer:

The correct option is 1.

Step-by-step explanation:

It is given that the Brian, Kelsey, and Geoff each have a remote-controlled car. They simultaneously started their cars and drove them in a straight line away from a motion sensor.

It means they are travelling at a constant rate.

Slope formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

From the given table it is clear that the of Brian's car from the sensor is 34 at 1 sec and 38 at 3 sec. The rate of change is

[tex]m=\frac{38-34}{3-1}=2[/tex]

It means the Brian's car traveled at the rate of 2 cm per sec.

From the given table it is clear that the of Brian's car from the sensor is 27 at 1 sec and 31 at 3 sec. The rate of change is

[tex]m=\frac{31-27}{3-1}=2[/tex]

It means the Kelsey's car traveled at the rate of 2 cm per sec.

From the given table it is clear that the of Brian's car from the sensor is 27 at 1 sec and 33 at 3 sec. The rate of change is

[tex]m=\frac{33-27}{3-1}=3[/tex]

It means the Geoff's car traveled at the rate of 3 cm per sec.

Since Brian's and Geoff's car traveled at the same rate, therefore option 1 is correct.

Don't know if this will help but here :)

Answer:

True

Step-by-step explanation:

We are given that when two variables  with same base  are multiplied then the exponents will be add.

We have to find that given statement is true or false.

Rule:[tex]a^b\times a^d=a^{b+d}[/tex]

Suppose we have x and [tex]x^2[/tex]

[tex]x\times x^2=x^{1+2}=x^3[/tex]

There are two variable with same base x  therefore, the power will be added.

Hence, the statement is true.

Answer:True

Answer:

A rotation of 72 degrees will map one blade of ceiling fan to its adjacent blade.

Step-by-step explanation:

We are told that a ceiling fan has 5 equally spaced blades. It will work as a regular pentagon.

We can find angle of rotation to map one blade on adjacent blade dividing 360 by 5 as sum of angles of regular pentagon equals to 360 degrees.

[tex]\text{ Angle of rotation}=\frac{360}{5}[/tex]

Upon dividing 360 by 5 we will get,

[tex]\frac{360}{5} =72[/tex]

Therefore, a rotation of 72 degrees will map one blade of ceiling fan to its adjacent blade.    

The angle between adjacent blades in a five-blade ceiling fan is b. 72°.

**Understanding the Situation**:

We have a ceiling fan with five equally spaced blades. We need to find the angle of rotation that maps one blade onto the adjacent blade.

**Identifying the Angle between Blades**: Since the blades are equally spaced, we can find the angle between adjacent blades by dividing the full circle (360°) by the number of blades, which is 5.

  [tex]\[ \text{Angle between adjacent blades} = \frac{360°}{5} = 72° \][/tex]

**Checking the Options**:

  - (a) 144° is twice the angle between adjacent blades. This would correspond to skipping one blade and landing on the third blade, which is not adjacent.

  - (b) 72° is the same as the angle between adjacent blades. This seems promising.

  - (c) 90° is not consistent with the division of the circle by the number of blades.

  - (d) 36° is half the angle between adjacent blades. This would correspond to a situation where we skip two blades, which is not adjacent.

Complete Question :

Ceiling fan has five equally spaced blades. Find the angle of rotation that maps one blade onto the adjacent blad a 144° b 72° c 90° d 36°    

You are solving the two equations for x.

9.

r = 4 + 7x - sx

We need to solve for x. x is only found in the right side. First, just flip the sides to find x only in the left side.

4 + 7x - sx = r

We want all terms with x on the left side, and all terms without x on the right side. Now we subtract 4 from both sides.

7x - sx = r - 4

Factor x in left side.

x(7 - s) = r - 4

Divide both sides by 7 - s.

[tex] x = \dfrac{r - 4}{7 - s} [/tex]

12.

3z + 8 = 12 + 3x - z

Since x is only in the right side, flip the sides.

12 + 3x - z = 3z + 8

We need to isolate x in the left side, so subtract 12 from both sides and add z to both sides.

3x = 3z + 8 - 12 + z

3x = 4z - 4

Divide both sides by 3.

[tex] x = \dfrac{4z - 4}{3} [/tex]

Your question:

What is the current value of a future sum of money called?

Answer:

B) Present Value

Although current is a synonym of present, present is the correct meaning. The current value of a future sum of money is called Present Value.

Best Of Luck,

- I.A -

Answer:

The current value of a future sum of money is:

Option: B

B. Present Value.

Step-by-step explanation:

Present value--

In terms of finance the present value is the value in the present of a sum of money or stream of cash flows , in contrast to some future value it will have when it has been invested at compound interest.

Future cash flows are discounted at some rate called as discount rate.

Higher the discount rate lower is the  present value of future cash flow.

Answer:

41.99 or 42.0 volts.

Step-by-step explanation:

We have been given the impedance (Z) of the circuit which is:

[tex]Z=3.342+4.176i[/tex]

and the current through the circuit is:

[tex](5.772-5.323i)[/tex]

The voltage across the circuit is given by:

[tex]V= I\times Z=IZ[/tex], where 'V' is the voltage, 'I' is the current, and 'Z' is the impedance.

Plugging the values of 'I' and 'Z' we get:

[tex]V=(5.772-5.323i)\times 10^{-3}\times (3.342+4.176i)\times 10^3[/tex]

[tex]V=(5.772-5.323i)\times(3.342+4.176i)[/tex]

[tex]V= (41.51+6.31i)[/tex]

Now that we have the voltage, we can find the magnitude of the voltage as follows:

[tex]V= \sqrt{(41.51)^2+(6.31)^2}=\sqrt{1723.08+39.81}=\sqrt{1762.89}=41.98 \approx 42.0[/tex]

So the magnitude of the voltage across the circuit is 42.0 Volts.

Cameron does beat his best score. He scores 7 and 8 over par, as well as 3 under par twice. This makes him have 7 + 8 or 15 over par and 3 + 3 or 6 under par. 15 - 6 = 9, which is under 13, his current best score.