How can the logarithmic expression be written?
Select True or False for each statement.

The value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.

An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.

It is given that, the given equation of is, y = 500×2ˣ

We have to find the value of y when x = - 3.

y = 500×2ˣ

y=500×2⁻³

y=62.5

Thus, the value of y when the value of x is -3 for the equation,y = 500×2ˣ will be y=62.5.

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Answer:162

Step-by-step explanation:

1.5 ft = 18 inches

so

9 * 18 = 162

In 6 years, the couple will have $32,916.38 in the account.

Answer:

Your answer is A) [tex]y=-\frac{3}{2}x-4[/tex]

Step-by-step explanation:

This is because the slope of a perpendicular line is a negative reciprocal in relation to the original line. In this example, [tex]\frac{2}{3}[/tex] is flipped to [tex]-\frac{3}{2}[/tex]

Answer:

Step-by-step explanation:

The value of x is 6 degree that makes m || n.

What is parallel lines?

Parallel lines are coplanar, straight lines in geometry that don't cross at any point. When two planes in the same three-dimensional space are parallel, they never cross. Curves that maintain a set minimum distance from one another and do not touch or intersect are said to be parallel curves.

(8) Given: m || n

We have to find the value of x that makes m || n.

The lines m and n are divides by the line l of angle 90 degree.

⇒ 16x - 6 = 90

Add 6 on both sides,

16x - 6 = 90 + 6

16x = 96

Divide both sides by 16

16x/16 = 96/16

x = 6

Hence, the value of x is 6 degree that makes m || n.

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Answer:3/2

Step-by-step explanation: so you have the number of cups of Chex Mix in the bag is 3x = 3*9 = 27 cups and the number of cups of chocolate chips is 2x = 2*9 = 18 cups. Indeed, we see that 27 + 18 = 45 and 27/18 = 3/2 as required.

With a 95 percent confidence interval, the proportion of people who favor the tax plan is 0.546 ,0.755

The value of n is the random sample n = 80

we have x as the number of people surveyed, = 52 respondents

Then p = x / n

p = 52 / 80

p = 0.65

From the z critical table, 95% confidence level = 1.96

we would have to use the confidence interval formula. This is given as:

[tex]p +- Z * \sqrt{\frac{p*(1-p)}{n} }[/tex]

we have to put in the values

[tex]0.65 +- 1.96 * \sqrt{\frac{0.65*(1-0.65)}{80} }[/tex]

0.65 ± 1.96 * 0.053326822

0.65 - 0.10452 , 0.65 + 0.10452

0.546 ,0.755

Therefore the proportion of persons that are in favor of this tax has been calculated as 0.546 ,0.755

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Answer: 6%

Step-by-step explanation:

R=100×480/2000×4

R=6%

Answer:

R

=

6

%

Step-by-step explanation:

The formula for Simple Interest is

S

I

=

P

R

T

100

Change the subject to be R.

R

=

100

×

S

I

P

T

Once that is done, we just need to substitute the values.

R

=

100

×

480

2000

×

4

R

=

6

%

The equation in slope-intercept form to find the height is y = 0.75x + 5 and the number of years it will take the tree to reach 20 feet is 24

The given parameters in the question are

Growth = 9 inches per year

Length of the tree after 4 years = 5 feet

Convert inches to feet

So, we have

Growth = 0.75 feet per year

A linear equation of this scenario is represented as

Length = Growth * Number of years + Initial length

So, we have

y = Growth * x + Initial length

This gives

5 = 0.75 * 4 + Initial length

Evaluate

Initial length = 2

So, the equation is

y = 0.75x + 2

This means that

y = 20

Recall that

y = 0.75x + 2

So, we have

0.75x + 2 = 20

Evaluate

0.75x = 18

Divide by 0.75

x = 24

Hence, the number of years is 24

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Using the formula of volume of a sphere, Ashely's company made 195 balls

The volume of sphere is the measure of space that can be occupied by a sphere. If we draw a circle on a sheet of paper, take a circular disc, paste a string along its diameter and rotate it along the string. This gives us the shape of a sphere.

The formula of volume of a sphere is given as

v = 4/3πr³

r = radius = 4.5in

volume of each spherical ball = 4/3π(4.5)³

volume of sphere = 381.7in³

The number of balls she made from 74325 in³ can be found by dividing it by 381.7in³

Number of balls = 194.7≅195 balls

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The system of equation is consistent and independent because it has one unique solution.

If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent.

Therefore, let's solve the equation,

y = -3x + 12

y = -6x + 2

Using substitution,

-6x + 2 = -3x + 12

-6x + 3x  = 12 - 2

-3x = 10

x = - 10 / 3

y = -6(-10 / 3) + 2

y = 60 / 3 + 2

y = 20 + 2

y = 2

Therefore, the system of equation is consistent and independent.

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11/24 many minutes did it take for the winner of the race to finish.

A fraction represents a part of a whole.

Given,

Kyla finished a 100 meter race in one and three-eighths minutes.

Kylas time is [tex]1\frac{3}{8}[/tex] minutes.

Convert mixed fraction to improper fraction.

11/8 minutes.

The winner of the raced finished in one-third of Kyla's time.

Which means 1/3 of 11/8

1/3×11/8

11/24

Hence, 11/24 many minutes did it take for the winner of the race to finish.

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The value of the unknown variable x in the given sequence is; 14

The formula for sum of an arithmetic sequence is;

Sₙ =ⁿ/₂(2a + (n − 1)d)

where;

a is first term

d is common difference

n is position of term

We are given the sequence as;

(x + 1) + (x + 4) + (x + 7) +...+ (x + 40) = 442

The common difference is;

x + 4 - (x + 1)

= 3

Now, to get the number of terms, we will say that the function follows the pattern;

aₙ = (x + 1) + 3n

Thus;

(x + 1) + 3n = x + 40

3n = 39

n = 13

Thus, there are n = 13 terms

Sₙ = ¹³/₂(2(x + 1) + (14 − 1)3) = 442

6.5(2x + 40) = 442

2x + 40 = 442/6.5

2x = 68 - 40

x = 28/2

x = 14

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Answer: 50

Step-by-step explanation:

10+15+6+4+6+11= 50

Edit=

We can see that the length of one side is 10, and the width of one is 15. For the other side of the width, we can subtract 4 from 15 to get 11. For the other length, we can subtract 6 from 10 to get four. We also have to add in the 6 and 4 because they are parts of the border. (10+15+11+4+6+4)

The polynomial f(x) of degree 5 that has the following zeros is

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4).

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents. In many branches of mathematics and science, polynomials are used. For instance, they are used to define polynomial functions, which show up in settings ranging from basic chemistry and physics to economics and social science. They are also used in calculus and numerical analysis to approximate other functions. Polynomial equations are used to form these functions.

The function's zeros are expressed as follows:

f(x) = (x-a)(x-b)..... where the a, b  are the zeros

f(x) = (x-(-2)) (x-3) (x -7)(x-0) ( x-4)

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)

Therefore, the polynomial f(x) of degree 5 that has the following zeros is

f(x) = (x+2) (x-3) (x-7)(x-0) (x-4)

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Montraie can make 2 cups of smoothies with the yogurt

From the question, we have the following parameters that can be used in our computation:

Cups of yogurt = 1 1/2

Each smoothie = 3/4 yogurt

Assume there exist a proportional relationship between the cups and the yogurt

The number of smoothies in the yogurt can be calculated using the following equation

Smoothies = (1 1/2)/(3/4)

Evaluate the quotient

Smoothies = 2

Hence, the cups is 2 yogurt

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The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰.

Index (indices) in Maths is the power or exponent which is raised to a number or a variable.

The mathematics of power or exponent of any number is called indices.

For example 5³ = 5²5 here we break 5³ into 5² and 5 so it is called the law of indices.

Another example could be 7² = 7³/7 here we divide to obtain power 2.

As per the given,

36 x¹⁵y²⁰/ 12 x³y⁵ = [(36/12) (x¹⁵y²⁰)/(x³y⁵)]

36 x¹⁵y²⁰/ 12 x³y⁵ = 3x¹⁵y²⁰ × x⁻³y⁻⁵z⁰

Hence "The negative and zero exponents of the given exponents will be 3 x¹⁵y²⁰ × x⁻³y⁻⁵z⁰".

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Answer:

.62 each

Step-by-step explanation:

Door:80( actual height) 44( height on set)

Table 28( actual height) 15.4 ( height on set)

Stool 18 ( actual height) 9.9 ( height on set)

Step-by-step explanation:

Times the actual height inches by 0.55 and you get your height on set.

The maximum number of hours that he can hire the cleaning service would be 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Consider that the number of hours for which the total cost would be the same be x

The first inequality is;

$15x > $75

Now equate equations

$15x - $75 = 0

15x = 75

x = 5

Hence, the maximum number of hours that he can hire the cleaning service would be 5.

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Answer:

Step-by-step explanation:

Start with y intercept (Where the line crosses the y-axis)

You place the first dot on (0,2)

Negative slope goes down

For the second dot, you go down one and move two to the right

Answer:

x = .5, - 1.5

Step-by-step explanation:

4x^2 + 4x =3

To solve for x, we can complete the square.

4 ( x^2 + x) = 3

x^2 + x = 3/4

Take the coefficient of x, divide by 2, and square.

(1/2)^2

Then add to each side.

x^2 + x + 1/4= 3/4 +1/4

(x+1/2) ^2 = 1

Take the square root of each side.

x+1/2 = ±1

x = ±1 -1/2

x = 1-1/2  or -1-1/2

x = 1/2, -3/2

x = .5, - 1.5

Answer:

x = 1/2   or   -3/2

Step-by-step explanation:

Rewrite in Standard Form:

4x²+4x=3 ==>  4x²+4x-3=0

Identify:  a=4   b=4   c= -3

Quadratic Formula:

[tex]x=\frac{-b+\sqrt{b^2-4ac}}{2a} or \frac{-b-\sqrt{b^2-4ac}}{2a}\\ \\=\frac{-4+\sqrt{4^2-4(4)(-3)}}{2(4)} or \frac{-4-\sqrt{4^2-4(4)(-3)}}{2(4)}\\\\=\frac{-4+\sqrt{16+48}}{8} or \frac{-4-\sqrt{16+48}}{8}\\\\=\frac{-4+\sqrt{64}}{8} or \frac{-4-\sqrt{64}}{8}\\\\=\frac{-4+8}{8} or \frac{-4-8}{8}\\\\=\frac{4}{8} or \frac{-12}{8}\\\\=\frac{1}{2} or -\frac{3}{2}[/tex]

Answer:4

Step-by-step explanation:

16/4=4

The scale factor of the dilation is, 1/4.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

We have to given that;

The trapezoid I'J'K'L' is a dilation of the trapezoid IJKL.

Here, The length of IJ = 16

And, The length of I'J' = 4

Hence, The scale factor of the dilation is,

⇒ I'J' / IJ = 4 / 16

               = 1/4

Thus, The scale factor of the dilation is, 1/4.

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The time  did Stanley run, swim, and bike yesterday if the total distance he covered was 64 miles is 1.5 hrs, 1 hrs, 3 hrs. The distance is 13.5 miles, 2.5 miles , 48 miles.

Let t represent the  time he ran

Let t -.5 represent  time he swam

Let 2t represent the  biking time

Hence,

9t + 2.5(t-.5) + 16(2t) = 64

9t + 2.5t - 1.25 + 32t = 64

Collect like terms

43.5t = 64 + 1.25

Divide both side by 43.5t

t = 65.25/43.5

t = 1.5 hrs (Time he ran)

So,

Time he swam

t -.5 where t is 1.5 hrs

1.5-.5 = 1 hr (Time he swam)

Biking time

2t where t is 1.5 hrs

2(1.5) = 3 hrs (biking time)

Distance of each

1.5(9) = 13.5 miles  (running)

1(2.5) = 2.5 miles   (swimming)

3(16) = 48 miles  (biking)

Total distance = 13.5 miles + 2.5 miles + 48 miles

Total distance = 64 miles

Therefore the time  is 1.5 hrs, 1 hrs, 3 hrs and the distance is 13.5 miles, 2.5 miles , 48 miles.

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Answer:

Step-by-step explanation:

the answer is a 28.27

Answer:

a) 28.27

Step-by-step explanation:

Formula we use,

→ πr²

Now the required area will be,

→ 3.14 × 3²

→ 3.14 × 9

→ 28.27 in²

Hence, the area is 28.27 in².

Answer:

700 months

Step-by-step explanation:

Answer:

80

Step-by-step explanation:

120 divided by 3 (for per half hr) is 40 and if you add 2 of the half hrs together (40+40) its 80