What is the 10th term of the geometric sequence a(n)=-3(2)^(x-1_())

Given:

The graph of an exponential function.

To find:

The exponential growth factor as x increases by 1 unit.

Solution:

From the given graph, it is clear that the exponential function passes through the points (1,1) and (3,9). So, the equation of the exponential must must be satisfy by these points.

The general exponential function is:

[tex]y=ab^x[/tex]                 ...(i)

Where, a is the initial value and b is the growth factor.

Putting [tex]x=1,y=1[/tex] in (i), we get

[tex]1=ab^1[/tex]                  ...(ii)

Putting [tex]x=3,y=9[/tex] in (i), we get

[tex]9=ab^3[/tex]                  ...(iii)

Divide (iii) by (ii).

[tex]\dfrac{9}{1}=\dfrac{ab^3}{ab}[/tex]

[tex]9=b^2[/tex]

[tex]3=b[/tex]

b is the the growth factor and the value of b is 3.

Therefore, the exponential growth factor is 3 as x increases by 1 unit.

Answer:

exponential growth factor is 3

Step-by-step explanation:

Answer:

∆ PQR is congruent to ∆ STU

This means --

P = S

Q = T

R = U

R = 80°

S = P = 70°

So in ∆PQR, we know R = 80° , P = 70° and Q = ?

Using angle sum property of triangle,

P+ Q + R = 180°

70° + 80° + Q = 180°

150° + Q = 180°

Q = 30°

Hope This Helps :D

Answer:

25

Step-by-step explanation:

x + 25 = 50

=> x = 50 - 25

=> x = 25

Answer:

x = 25

Step-by-step explanation:

x + 25 = 50

Solve for x;

Step 1 :- Move 25 to the right-hand side and change their sign.

Step 2 :- Subtract 25 from 50.

Answer:

3) 109.27

4) 58.80

5) 48.65

Step-by-step explanation:

First divide the cost by the number of units to get the individual cost of each item.

Then multiply by the new number of units.

For example:  78.05 ÷ 5 = 15.61 for each.

                       15.61 x 7 = 109.27

Answer:

27y^12

Step-by-step explanation:

you multiply the exponents together

in this case: 4×3=12

and then multiply the base number by 3 as well.

Answer:

10.54263764

Step-by-step explanation:

[tex]3300=2000e^{.0475t}\\\\1.65=e^{.0475t}\\\ln(1.65)=.0475t\\.500775288=.0475t\\t=10.54263764[/tex]

Answer:

It will take about 10.5 years for the investment to reach $3,300.

Step-by-step explanation:

Continuous compound is given by:

[tex]\displaystyle A=Pe^{rt}[/tex]

Where P is the principal, e is Euler's number, r is the rate, and t is the time (in this case in years).

Since our principal is $2,000 at a rate of 4.75% or 0.0475, our equation is:

[tex]\displaystyle A=2000e^{0.0475t}[/tex]

We want to find the number of years it will take for our investment to reach $3,300. So, substitute 3300 for A and solve for t:

[tex]3300=2000e^{0.0475t}[/tex]

Divide both sides by 2000:

[tex]\displaystyle e^{0.0475t}=\frac{33}{20}[/tex]

We can take the natural log of both sides:

[tex]\displaystyle 0.0475t=\ln\left(\frac{33}{20}\right)[/tex]

Therefore:

[tex]\displaystyle t=\frac{1}{0.0475}\ln\left(\frac{33}{20}\right)\approx 10.54\text{ years}[/tex]

It will take about 10.5 years for the investment to reach $3,300.

Answer:

[tex]volume=1/3 ~BH[/tex]

[tex]=1/3(16)^{2} \sqrt{17^{2} -8^{2} }[/tex]

[tex]=1/3\times256\times15[/tex]

[tex]=1280 ~ft^{3}[/tex]

------------------------

hope it helps...

have a great day!!

Answer:

[tex]( {4}^{3} \div {5}^{ - 2} {)}^{5} [/tex]

Step-by-step explanation:

[tex] {4}^{15} . {5}^{10} [/tex]

hope this will help you more

have a great day..

Step-by-step explanation:

[tex]( \frac{4 {}^{3} }{5 {}^{ - 2} } ) {}^{5 } \\ ( \frac{4 {}^{15} }{5 {}^{10} } ) \\ \frac{4 {}^{15} }{5 {}^{10} } [/tex]

Answer:

any number

Step-by-step explanation:

It is because all real numbers are solutions to this

Answer:

x = infinite solutions

Step-by-step explanation:

[tex]\frac{2}{3}(6x+ 3) = 4x + 2\\\\\frac{12}{3}x + \frac{2 \times 3}{3} = 4x + 2\\\\4x + 2 = 4x + 2 \\\\Which\ is \ true \ for \ all \ values \ of \ x.[/tex]

Explanation:

For regular tessellations, the types of polygons that we can use are

We can only pick one of those shapes.

Shapes like regular octagons or pentagons will not work on their own because there is gap or overlap if we tried to glue them together. Think of tiles on the floor. There cannot be any gap or overlap when forming a tessellation.

If you wanted to use octagons to tessellate the plane, then you'd need squares to fill in the gaps. At this point, it's not considered a regular tessellation.

Answer:

B.

Step-by-step explanation:

(working backwards to explain)

[tex]\sqrt{5g^5h^2} \\\\\\h\sqrt{5g^5}\\\\\\g^2h\sqrt{5g}[/tex]

Answer:

4/200 is the answer

Answer:

7

Step-by-step explanation:

Here we have the hypotonouse and an angle

we are looking for the side opposite to the angle

this means we should use SOH

sin(26)=(x/16)

16*sin(26)=x

x=7.01393

which is closest to 7

Given:

The exponential function is:

[tex]R(x)=(5.3)^x[/tex]

To find:

The domain of the given exponential function.

Solution:

We know that the general form of an exponential function is:

[tex]f(x)=ab^x[/tex]

Where, a is the initial value and b is growth/decay factor.

This function is defined for all real values of x, so the domain of these type of functions is the set of all real number.

We have,

[tex]R(x)=(5.3)^x[/tex]

Here, a is 1 and b is 5.3. This function is defined for all real values of x

Therefore, the domain of these type of functions is the set of all real number or it can be written as [tex](-\infty,\infty)[/tex].

Answer:

a) t²- 4x + 4

b) 9y² - 4z

c) 10290v

Step-by-step explanation:

a+b) use identity (ax+b)(ax+c) = ax² + (b+c)x + bc

c) a × bx = abx

Answer: hello there here is your answer:

17.5 feet

Step-by-step explanation:

Area of rectangle = Length x Width  

Length = Area/Width = 122.5 / 7 = 17.5 feet

hope this helps

have a god day bye

Answer:

a) A score of 65 is in the 79.67th percentile.

b) A score less than 70 is below the 95.25th percentile.

c) 20.33% of the scores are greater than 65.

d) 95.25% of scores are less than 70.

e) 45.25% of the scores are between 50 and 60.

Step-by-step explanation:

Normal Probability Distribution

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

The mean is 60 and the standard deviation is 6.

This means that [tex]\mu = 60, \sigma = 6[/tex]

a. what is the percentile rank of the score 65?

This is the p-value of Z when X = 65.

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

[tex]Z = \frac{65 - 60}{6}[/tex]

[tex]Z = 0.83[/tex]

[tex]Z = 0.83[/tex] has a p-value of 0.7967.

Thus: A score of 65 is in the 79.67th percentile.

b. what is the percentile of the score less than 70?

Below the p-value of Z when X = 70. So

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

[tex]Z = \frac{70 - 60}{6}[/tex]

[tex]Z = 1.67[/tex]

[tex]Z = 1.67[/tex] has a p-value of 0.9525.

Thus: A score less than 70 is below the 95.25th percentile.

c. what is percent of the scores is greater than 65?

The proportion is 1 subtracted by the p-value of Z when X = 65.

From item a, when X = 65, Z has a p-value of 0.7967

1 - 0.7967 = 0.2033

0.2033*100% = 20.33%

20.33% of the scores are greater than 65.

d. what percent of scores is less than 70?

The proportion is the p-value of Z when X = 70, which, from item b, is of 0.9525.

0.9525*100% = 95.25%

95.25% of scores are less than 70.

e. what percent of the score is between 50 and 60?

The proportion is the p-value of Z when X = 60 subtracted by the p-value of Z when X = 50.

X = 60

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

[tex]Z = \frac{60 - 60}{6}[/tex]

[tex]Z = 0[/tex]

[tex]Z = 0[/tex] has a p-value of 0.5.

X = 50

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

[tex]Z = \frac{50 - 60}{6}[/tex]

[tex]Z = -1.67[/tex]

[tex]Z = -1.67[/tex] has a p-value of 0.0475.

0.5 - 0.0475 = 0.4525

0.4525*100% = 45.25%

45.25% of the scores are between 50 and 60.

Answer:

hope it helps

Answer:

[tex]\frac{125}{999}[/tex]

Step-by-step explanation:

Process of Elimination,  the decimal is 0.125 repeating

[tex]\frac{1}{8}[/tex] as a decimal is 0.125

[tex]\frac{1}{4}[/tex] as a decimal is 0.25

(Those two should've been easy to eliminate)

[tex]\frac{125}{1000}[/tex] as a decimal is 0.125  (since there are three zeros in the denominator, you move the decimal three spots to the left.)

This leaves us with:

[tex]\frac{125}{999}[/tex] If you divide 125 ÷ 999 you get 0.125125125...

Hope this helps Stay safe:)

Answer:

15 x 150 = 2250

2250 + 1000 = 3250

you make $3250,00

Answer:

Step-by-step explanation:

The number is divisible by 4 if the number formed by the last two digits is divisible by 4.

Since we are looking for the largest possible option, lets try 2-digit numbers formed by the given digits.

The smallest 2-digit number that is divisible by 4 is 36

Then the largest number is:

Answer:

2.56 * 10^11 L

Step-by-step explanation:

1 body has 40 L

Thus, the amount in 6.4 billion would be;

40 * 6.4 * 10^9

= 256 * 10^9

= 2.56 * 10^2 * 10^9

= 2.56 * 10^11 L

Answer:

A

Step-by-step explanation:

Answer:

[tex] \frac{3}{8} \: hours[/tex]

Step-by-step explanation:

Additional time =

[tex] \frac{1}{2} - \frac{1}{8} \\ = \frac{4}{8} - \frac{1}{8} \\ = \frac{3}{8} [/tex]

Answer:

3/8 hours is the time to Finnish

Answer:

A number line with a closed circle on 25, with shading to the right.

Explanation:

A closed circle means "greater than or equal to" or "less than or equal to".

A open circle means "less than" or "greater than"

Therefore, since the question says: "who are at least 25 years old", a closed circle is the correct answer.

And says it says "at least 25 years old" it means that it shaded to the right, and that the circle is on the number 25.

Answer:

A number line with a closed circle on 25, with shading to the right.

Step-by-step explanation:

...

Answer:

30 mins

Step-by-step explanation:

speed = distance/ time

speed of car A

= 20/ 12 km/ min

= 5/ 3 km/ min

also, speed of car A = speed of car B

speed of car B = 5/ 3 km/ min = 50km / time taken (in mins)

[tex] \frac{5}{3} = \frac{50}{t} [/tex]

[tex]5t = 150[/tex]

[tex]t = 30[/tex]

=> t = 30 mins

Answer:

76°,60°

Step-by-step explanation:

sum of angles of a triangle=180

x+64+x+80+44=180

2x+188=180

2x=180-188=-8

x=-8/2=-4

so angles are -4+60=60°

and -4+80=76°

answer

71-17=54

82-28=54

93-39=54

60-06=54

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

Answer:

0.6944

Step-by-step explanation:

25/36 is 0.6944 in division

Answer:

[tex]gradient = - \frac{1}{3} \\ { \tt{equation \: is \: y = - \frac{1}{3}x + 3 }}[/tex]

Answer:

The equation of a perpendicular line to  

y =( -1/3 )x+b (b is a normal number)

Step-by-step explanation:

1.Use the slope-intercept form to find the slope.

Tap for more steps...

m = 3

2. the perpendicular line to y=3x+3

must have a slope that is the negative reciprocal of the original slope.

thus,

m perpendicular  =  −1/3