8-1 1/5
(Simplify your answer. Type a whole number, fraction, or a mixed number.)
orrect:

Given:

f(x) is an exponential function.

[tex]f(2.5)=26[/tex]

[tex]f(6.5)=81[/tex]

To find:

The value of f(12), to the nearest hundredth.

Solution:

The general exponential function is

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

For, x=2.5,

[tex]f(2.5)=ab^{2.5}[/tex]

[tex]26=ab^{2.5}[/tex]          ...(i)

For, x=6.5,

[tex]f(6.5)=ab^{6.5}[/tex]

[tex]81=ab^{6.5}[/tex]          ...(ii)

Divide (ii) by (i).

[tex]\dfrac{81}{26}=\dfrac{ab^{6.5}}{ab^{2.5}}[/tex]

[tex]\dfrac{81}{26}=b^4[/tex]

Taking 4th root on both sides, we get

[tex]\sqrt[4]{\dfrac{81}{26}}=b[/tex]

[tex]b\approx 1.32855[/tex]

Putting b=1.32855 in (i), we get

[tex]26=a(1.32855)^{2.5}[/tex]

[tex]26=a(2.03444)[/tex]

[tex]\dfrac{26}{2.03444}=a[/tex]

[tex]a\approx 12.7799[/tex]

Now, the required function is

[tex]f(x)=12.7799(1.32855)^x[/tex]

Putting x=12, we get

[tex]f(12)=12.7799(1.32855)^{12}[/tex]

[tex]f(12)=386.4224[/tex]

[tex]f(12)\approx 386.422[/tex]

Therefore, the value of f(12) is 386.422.

Answer:

x > -18

Step-by-step explanation:

If x was -18, -18/3 is -6 and -6-6 is -12. So, x must be greater than -18.

Answer:

x>-18

Step-by-step explanation:

Inequality answers are same as algebra but we use < or > for more than or less than and with line under for equal to.

x/3 -6 >-12

x/3 > -12 +6

x/3 > -6

x>-6 x 3

x> -18

Answer:

Step-by-step explanation:

Let the number be x.

3x - 6 = 2x

x - 6 = 0

x = 6

Answer: 1.91339285714

Step-by-step explanation:

Answer:

1/4 (1 - 3 x)

Step-by-step explanation:

Answer:

4,2

Step-by-step explanation:

Answer:

It is 4, 2

Step-by-step explanation:

Trust me

Answer:

54 houses has been sold this year

Step-by-step explanation:

So 6/7 OF the houses sold

63 houses in total

So you just multiply

63*6/7=54

Answer:

so, it's 3.75 to 3

Step-by-step explanation:

15 quarters is 3 dollars and 3 quarters

Answer: 15

Step-by-step explanation:  

                  260

Simplify  ———

                   17  

Final result :

   260            

 ——— = 15

     17            

Answer:

he can get 1224 gummy bears

Step-by-step explanation:

i 324 need 22432 po1n72

Answer:

4c + 6a < = 120 ...4(20) + 6(6) = 116 <== correct

4c + 4a < = 100....4(20) + 4(6) = 104 <== incorrect

first answer choice

Answer:

No, because the bike order does not meet the restrictions of 4c + 6a ≤ 120 and 4c + 4a ≤ 100

Step-by-step explanation:

IS THE CORRECT ANSWER!!!!

Step-by-step explanation:

The expanded form of 9.635 is given by :

[tex]9.635 =9+\dfrac{6}{10}+\dfrac{3}{100}+\dfrac{5}{1000}[/tex]

or

[tex]9.635 =9+0.6+0.03+0.005[/tex]

We can write it using the powers of ten.

[tex]9.635 =9.635 \times 10^0[/tex]

10⁰ is equal to 1.

Hence, this is the required solution.

Answer:

1/10

Step-by-step explanation:

Try it if I’m right pls brainleist

Answer:

2/0.8

Step-by-step explanation:

i divided

Answer:

the ratio of the first measurement to the second measurement is 11 / 18 or 11 : 18

Step-by-step explanation:

Given that;

diameter measurement of ball A = 33 mm

diameter measurement of ball B = 5.4 cm

Now, we convert the unit of measurement of ball B from centimeter to millimeter

we know that 1 cm = 10 mm

so 5.4 cm = x mm

x mm = 5.4 × 10 = 54 mm

therefore, diameter measurement of ball B is 54 mm.

Now, the ratio of the first measurement to the second measurement will be;

⇒ 33 / 54

we simplify the fraction

⇒ 11 / 18 or 11 : 18

Therefore, the ratio of the first measurement to the second measurement is 11 / 18 or 11 : 18

Answer:

Option A

:)))))))))))))))))))))))

Answer:

d the its simpel

Step-by-step explanation:

Answer:

A) No solution.

B) -2, 1, 2

C) 2, 1, - 2

D) Infinite number of solutions

Step-by-step explanation:

A) 2x + 5y - z = -2

3x - 2y + z = 4

-x + 7y - 2z = 2

Let's add eq(1) and eq(2) to eliminate z.

2x + 3x + 5y - 2y - z + z = -2 + 4

5x + 3y = 2 - - - (eq 4)

Let's multiply eq(2) by 2 and add to eq(3) to eliminate z.

6x - x - 4y + 7y + 2z - 2z = 8 + 2

5x + 3y = 6 - - -(eq 5)

Subtracting eq(4) from eq(5) gives;

0 = 4

This is inconsistent and thus the system of equation has no solution.

B) 4x + 5y + 3z = 3

-3x + 4y - z = 8

5x + 3y + 2z = -3

Multiply eq 2 by 3 and add to eq 1 to eliminate z;

4x - 9x + 5y + 12y + 3z - 3z = 3 + 24

-5x + 17y = 27 - - - (eq 4)

Multiply eq 2 by 2 and add to eq 3 to eliminate z;

5x - 6x + 3y + 8y + 2z - 2z = -3 + 16

-x + 11y = 13 - - - (eq 5)

Multiply eq (5) by -5 and add to eq 4 to get;

17y - 55y = 27 - 65

-38y = - 38

y = 1

Putting 1 for y in eq 5 gives; x = -2

Putting x = - 2 and y = 1 in eq 1 gives;

z = 2

C) 4x - 3y + 2z = 1

-2x + 3y - 2z = 3

2x - 3y + 3z = -5

Solving this equation simultaneously via a calculator gives;

x = 2, y = 1, z = - 2

D) 2x + 3y - z = -2

x - 9y + 2z = 8

-x - 12y + 3z = 10

Add eq(2) to eq (3) to get;

-21y + 5z = 18 - - - (eq 4)

Multiply eq 2 by 2 and add to eq 3 to get;

-30y + 7z = 26 - - - (eq 5)

From eq 4, z = (18 + 21y)/5

Put this in eq 5 to get;

-30y + 7(18 + 21y)/5 = 26

-30y + 126/5 + 147y/5 = 26

Solving this leads to infinite number of solutions

Answer:

Hi how are you doing today

This question is incomplete, the complete question is;

A household item uses 321 watts of electricity. This item is used for 27 hours each week. How much CO2 will be produced each week from this item?  (assume 1.37 pounds of CO2 is produced per KWH of electricity used)

Answer: 11.87 lbs of CO2 will be produced each week from this item

Step-by-step explanation:

Given that;

Average wattage Wattage of the item = 321 watts

Time used = 27 hours each week

CO2 produced each week = ?

so;

Total electricity consume = 321 × 27 = 8667 watt = 8.667 kWh

given that; 1.37 pounds of CO2 is produced per KWH of electricity used

hence; CO2 generated by our item will be;

⇒ 8.667 kWh × 1.37

= 11.87 lbs

Therefore,  11.87 lbs of CO2 will be produced each week from this item

Answer:

159 text messages

Step-by-step explanation:

Given that:

Predicted average = 2042

Number of months = 6

Number of texts for each of last 5 months :

Let number of text that must be sent in the sixth month = x

Predicted Average = (sum of texts / Number of months)

2042 = (2800 + 2481 + 2105 + 1975 + 2732 + x) / 6

2042 = (12093 + x) / 6

Cross multiply :

6 * 2042 = 12093 + x

12252 = 12093 + x

x = 12252 - 12093

x = 159

Answer:

-85

Step-by-step explanation:

Answer:

Therefore, the possible lengths (in whole inches) for the third side is

9 inches < x < 45 inches

Step-by-step explanation:

For the above question, we have a rule, the sum of the length of any two sides of the triangle must be greater than the length of the third side.

Hence:

She has two sides of length 18 inches and 27 inches

Let the third side = x

Hence:

a) 18 + 27 > x

45 > x

b) 18 + x > 27

x > 27 - 18

x > 9

Therefore, the possible lengths (in whole inches) for the third side is

9 inches < x < 45 inches

Answer:

0.12

Step-by-step explanation:

Probability is defined as the number of possible outcomes divided by the total outcome.

Given that 15% of the students drive to school and of  the students that drive to school, 80% are seniors then the probability a randomly selected  student drives to school and is a senior P(D&S)

= 15% * 80%

= 15/100 * 80/100

= 0.12

The 4th option

This question is based on the concept of probability. Therefore the correct option is (D), that is 0.12 is the probability a randomly selected  student drives to school and is a senior.

Given:

At a large high school, 15% of the students drive to school. Of the students that drive to school, 80% are seniors.

We have to calculated the probability a randomly selected  student drives to school and is a senior.

By the definition of probability,

Probability is  branch of mathematics, and it is defined as the number of possible outcomes divided by the total outcome.

Given that, 15% of the students drive to school and of  the students that drive to school, 80% are seniors.

Hence, the probability a randomly selected student drives to school and is a senior is ,

[tex]=\dfrac{15}{100} \times \dfrac{80}{100}\\\\= 0.15 \times 0.8\\\\= 0.12[/tex]

Therefore, the correct option is (D), that is 0.12 is the probability a randomly selected  student drives to school and is a senior.

For more details, prefer this link:

https://brainly.com/question/11234923

Answer:

0.5

Step-by-step explanation:

In 1 ounce there are 5 piece of Candy.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

There are 75 pieces of candy in a 15 oz bag.

So, Per ounce the amount of candy

= 75/ 15

= 5

Hence, In 1 ounce there are 5 piece of Candy.

Learn more about unitary Method here:

https://brainly.com/question/22056199

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