On your last credit card statement, you had a previous balance of $567.18, payments of $120, a periodic rate of 1.56 percent, and new charges totaling $45.17. What is your new balance?

$288.29
$447.18
$499.33
$567.18​

Given:

The expression is:

[tex]2\log_5(5x^3)+\dfrac{1}{3}\log_5(x^2+6)[/tex]

To find:

The single logarithm expression for the given expression.

Solution:

We have,

[tex]2\log_5(5x^3)+\dfrac{1}{3}\log_5(x^2+6)[/tex]

Using properties of the logarithm, we get

[tex]=\log_5(5x^3)^2+\log_5(x^2+6)^{\frac{1}{3}}[/tex]           [tex][\because \log x^n=n\log x][/tex]

[tex]=\log_5(25x^6)+\log_5\sqrt[3]{x^2+6}[/tex]

[tex]=\log_5(25x^6)\sqrt[3]{x^2+6}[/tex]          [tex][\because \log a+\log b=\log (ab)][/tex]

Therefore, the correct option is B.

Given:

The insect population function is:

[tex]f(x)=10(2)^x[/tex]

Where x is the number of weeks.

To find:

The population after 4 weeks.

Solution:

The population of insect after x weeks is given by:

[tex]f(x)=10(2)^x[/tex]

We need to find the population after 4 weeks.

After substituting [tex]x=4[/tex], we get

[tex]f(4)=10(2)^4[/tex]

[tex]f(4)=10(16)[/tex]

[tex]f(4)=160[/tex]

The population after 4 weeks is 160. Therefore, the correct option is C.

Answer:

last option

Step-by-step explanation:

the middle term is the sum of 4k and 4k which is 8k

Answer:

First, let's find the area of the whole pizza:

Area of circle = pi x r^2

r = 16 / 2

r = 8

Area of pizza = pi x 8^2 = 64pi

Now 45 degrees is 1/8 of the whole pizza (it is one-eighth of 360 degrees), and so a slice is proportional to the fraction of the area:

64pi / 8 = 8pi

The area of each slice is then 8pi in.^2

Step-by-step explanation:

Answer:

Binary-yes

Independent-yes

Number of trials- No

Same probability-yes

Step-by-step explanation:

Answer:

Binary?

✔ Yes

Independent?

✔ Yes

Number of trials?

✔ No

Same probability?

✔ Yes

Step-by-step explanation:

Answer:

12.6cm

Step-by-step explanation:

12.6 cm²

Area formula: (A = πr²)

If the diameter is 4 cm.. then that would mean the radius is 2 cm because the radius is half of the diameter. So, we already know the radius.. we just have to find the circumference.

Circumference formula: (C = πd) or (C = 2πr)

Finding the circumference : 3.14 × 4 = 12.56 cm

So, we now have the radius and circumference.

Radius = 2 cm

Circumference = 12.56 cm

Finding the Area : 3.14 × 2 × 2 = 12.56 cm²

So, 12.56 rounded to the nearest tenth is 12.6 cm².

Hope this helped! :)

Answer:

6⁹

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

[tex]\displaystyle \frac{6^6}{6^{-3}}[/tex]

Step 2: Simplify

Answer:

The fourth angle = 60°

Step-by-step explanation:

the sum of the interior angles of a quadrilateral is 360°.

The fourth angle = 360° - 100° - 120° - 80° = 60°

Given:

The table of values of an exponential function.

To find:

The function for the given table of values.

Solution:

The general exponential function is:

[tex]y=ab^x[/tex]        ...(i)

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

From the given table it is clear that the function passes through the points (1,9) and (2,36). It means the function must be true for these two points.

[tex]9=ab^1[/tex]        ...(ii)

[tex]36=ab^2[/tex]       ...(iii)

On dividing (iii) by (ii), we get

[tex]\dfrac{36}{9}=\dfrac{ab^2}{ab}[/tex]  

[tex]4=b[/tex]  

Putting [tex]b=4[/tex] in (ii), we get

[tex]9=a(4)^1[/tex]

[tex]\dfrac{9}{4}=a[/tex]

Putting [tex]a=\dfrac{9}{4},b=4[/tex] in (i), we get

[tex]y=\dfrac{9}{4}(4)^x[/tex]

[tex]y=9(4)^{x-1}[/tex]

The function notation with variable n is:

[tex]f(n)=9(4)^{n-1}[/tex]

Therefore, the correct option is D.

Step-by-step explanation:

S = 300 x .20(x)

hope this helps

Answer: 5 times

Step-by-step explanation:

Your question isn't well written but let me rewrite it based on what I believe that you wrote.

Lauren studies for 3 1/3 hours. She took a break every 2/3 hour. How many breaks did she take?

To solve the question, we have to divide the number if hours used in studying by the interval used in taking a break. This will be:

= 3 1/3 ÷ 2/3

= 10/3 / 2/3

= 10/3 × 3/2

= 5

She took a break 5 times

Answer:

the first (c) is the answer:  ΔABC ≅ ΔPQR

Step-by-step explanation:

Answer:

C that was the answer to mine and it was right

Step-by-step explanation:

Answer:

[tex]A=225cm[/tex]

Step-by-step explanation:

From the question we are told that:

Sides of the square post

[tex]L=15cm[/tex]  

Generally the equation for Area of a square A is mathematically given by

[tex]A=L*B[/tex]

Where L=B

Therefore

[tex]A=15*15[/tex]

[tex]A=225cm[/tex]

Answer:

cos 30

Step-by-step explanation:

cos 30 + sin 60 / 1+ sin 30 + cos 60

= root3 / 2 + root3/2 / 1 + 1/2 + 1/2

= root 6/2 by 4/2

= root 6/4

= root 3/2

= cos 30

Answer:

cos 30

Step-by-step explanation:

2−1⋅22−12−2−1⋅22−12

Step-by-step explanation:

Answer:

sorry in a hurry

Step-by-step explanation:

A rocket gets launched straight up into space. What is a possible description

of the rate of change (slope)?

Answer:

1663

Step-by-step explanation:

Answer:

42 miles

Step-by-step explanation:

20 x 16.7 = 334 miles on a full tank of gas

he drove 292 miles so 334 - 292 = 42 miles left

Answer:

V = 4.22ft^3

Step-by-step explanation:

Length: 2.25ft

Width: 1.5ft

Height: 1.25ft

Length x Width x Height = V

2.25 x 1.5 x 1.25 = 4.22ft, since we're dealing with volume of a 3D space, the answer is 4.22ft^3!

Answer:

0.54

Step-by-step explanation:

An integer is a WHOLE number without any fractional parts. Integers can be negative as long as it's a whole number.

Answer: 250+75x

Step-by-step explanation: 250 is the flat charge on the phone, and he pays 75 dollars as a monthly rate. x represents the amount on months.

Answer:

I can help you on question 4, and the only 2 I saw was <ZAY and <WAZ. I hope I at least helped with that one.

Step-by-step explanation:

Answer:

¡Hola! Lo siento, pero no hablo español. ¡qué tengas un lindo día! También necesito puntos porque soy nuevo.

Step-by-step explanation:

Answer:

g= - 3x/x-2

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

I used a calculator. I put integral values of 3 and 1 and then entered the equation inside absolute value bars

The total distance traveled by the laser beam in the given time interval is required.

The total distance traveled by the laser in the given time interval is 4 feet.

The given equation is

[tex]v(t)=t^2-4[/tex]

The given time interval is from t = 1 to t = 3 seconds.

In order to find the distance traveled we need to integrate the equation with respect to time and between the given intervals.

[tex]0=t^2-4\\\Rightarrow t=\pm 2=+2[/tex]

The laser will change the direction at [tex]t=2[/tex]

[tex]\int_1^3 v(t)=\int_1^2t^2-4 dt+\int_2^3t^2-4 dt\\\Rightarrow \int_1^3 v(t)=\dfrac{t^3}{3}-4t|_1^2+\dfrac{t^3}{3}-4t|_2^3\\\Rightarrow \int_1^3 v(t)=\left|\dfrac{2^3}{3}-4\times 2-(\dfrac{1^3}{3}-4)+\dfrac{3^3}{3}\right|-\left|4\times 3-(\dfrac{2^3}{3}-4\times2)\right|\\\Rightarrow \int_1^3 v(t)=\dfrac{5}{3}+\dfrac{7}{3}\\\Rightarrow \int_1^3 v(t)=\dfrac{12}{3}\\\Rightarrow \int_1^3 v(t)=4\ \text{m}[/tex]

Since, here distance is asked the absolute value of each integral is used.

Learn more about equation of motion:

https://brainly.com/question/25951773

Answer: 1.574 × 10-3

Step-by-step explanation:

To convert 0.001574 into scientific notation, follow these steps:

Move the decimal 3 times to right in the number so that the resulting number, m = 1.574, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -3

Write in the scientific notation form, m × 10n

= 1.574 × 10-3

Answer:

0.001574 in scientific notation  is 1.574 × 10^-3

Step-by-step explanation:

All numbers in scientific notation or standard form are written in the form m × 10n, where m is a number between 1 and 10 ( 1 ≤ |m| < 10 ) and the exponent n is a positive or negative integer.

To convert 0.001574 into scientific notation, follow these steps:

Move the decimal 3 times to right in the number so that the resulting number, m = 1.574, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -3

Write in the scientific notation form, m × 10n

= 1.574 × 10^-3

Therefore, the decimal number 0.001574 written in scientific notation is 1.574 × 10^-3 and it has 4 significant figures.

Hope this helped!!!

Answer:

15/4

Step-by-step explanation: