how many different rational numbers between $\dfrac{1}{1000}$ and $1000$ can be written either as a power of $2$ or as a power of $3$, where the exponent is a (possibly negative) integer?

[tex]a < 6\to \begin{cases} 0\\ 1\\ 2\\ 3\\ 4\\ 5 \end{cases}\hspace{5em}b < 6\to \begin{cases} 0\\ 1\\ 2\\ 3\\ 4\\ 5 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 2a-ab\implies a(2-b)[/tex]

now, in the expression above, if we set a = 0, we land on 0, if we set b = 2, we land on 0 again, and 0 is the least of all positive integers.

Answer:

12.41

Step-by-step explanation:

[tex]29 \times 0.40 = 11.6[/tex]

[tex]11.6 \times 0.07 = 0.812[/tex]

[tex]0.812 + 11.6 = 12.412[/tex]

The measure of the arc in degrees is 137.50°

An angle is said to have a measure of 1 radian if it is subtended at its center by an arc of lengths 1 unit in a unit circle. "rad" is the sign used to represent the radian unit of measurement.  

Here we have

An arc of a circle that measures 2.4 radians.  

We need to find the measure in degrees  

As we know 1 radian = 180°/π

2.4 radians = [ 180/π ] × 2.4 degrees  

= [57.324] × 2.4

= 137.57°  ( approx)    

Therefore,

The measure of the arc in degrees is 137.50°

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Answer: Let's denote the length of the candle on day 1 as L.

On day 2, the length of the candle is L/2, on day 3 it is L/2^2, on day 4 it is L/2^3 and on day 5 it is L/2^4.

So, on day 5, the length of the candle is L/2^4 = L/(222*2) = L/16.

Given that the length of the candle on day 1 is 18 inches, we have:

L = 18

And the length of the candle on day 5 is:

L/16 = 18/16 = 9/8

So, the length of the candle on day 5 is 9/8 inches.

Step-by-step explanation:

After 15 years, the area of the forest will be approximately 1523.4 km

A percentage is a unit used to express a portion of a whole number as a fraction of 100.

In this scenario, we are know that the area of a forest decreases by 6.25% each year. This means that each year, the area of the forest will decrease by

=> 6.25/100 times its original size.

To find the area of the forest after 15 years, we need to calculate the total decrease in area over 15 years. We can do this by multiplying the original area of the forest by the percentage decrease each year, and then repeating this calculation 15 times.

Starting with the original area of 2500km, we can calculate the first year's decrease by multiplying

=> 2500  x 100/6.25 = 157.5 km.

To find the area after the first year, we subtract

=> 2500 km - 157.5 = 2342.5 km.

We can repeat this calculation for the next 14 years to find the total decrease in area over 15 years. We can also use the calculator provided to simplify the calculation.

To do this, we enter 2500, then press the multiply button, enter 0.0625, then press the equal button, then press the subtract button, and finally enter the result from the previous calculation until we reach the final answer.

This means that the total decrease in area over 15 years was approximately

=> 1523.4 km,

which is equal to 61% of the original area of the forest

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The fraction that satisfies the problem is 20/24.

Equivalent fractions are fractions that have the same value, but different numerators and denominators.

If the fraction is equivalent to 5/6, then the numerator and denominator of the fraction is a multiple of 5 and 6, respectively.

Let x be the factor

fraction = 5x / 6x

If the sum of my numerator and my denominator is 44, then:

5x + 6x = 44

11x = 44

x = 4

fraction = 5x / 6x = 20/24

The final statement says that the sum of the digits in the denominator is 6.

2 + 4 = 6

Hence, the fraction is 20/24.

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The correct inequality which describes the problem is,

⇒ x - 4.3 < 6

A relation by which we can compare two or more mathematical expression is called an inequality.

Given that;

Chad's phone plan includes a certain amount of data each month.

And, he has used 4.3 gigabytes of data. He has less than 6 gigabytes of data left for the rest of the month.

Now, Let x represent how many gigabytes of data are included in Chad's phone plan each month.

Hence, The correct inequality which describes the problem is,

⇒ x - 4.3 < 6

⇒ x < 6 + 4.3

⇒ x < 10.3

Thus, The correct inequality which describes the problem is,

⇒ x - 4.3 < 6

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Work Shown:

c^5 x c

c^5 x c^1

c^(5+1)

c^6

The rule is to add the exponents when multiplying exponential expressions. The bases must be the same. The rule in symbolic form is a^b*a^c = a^(b+c)

The work needed to build the pyramid is calculated by multiplying the area of the base by the height and the density of the stone.

The work needed to build the pyramid can be calculated by using the formula Work = Area x Height x Density. The area of the base of the pyramid can be calculated by using the formula Area = Side^2, where Side is the length of the side of the square base. In this case, the side of the square base is 7740 ft. So, the area of the base is 7740^2 ft^2. The height of the pyramid is 860 ft (due to erosion, its current height is slightly less). The density of the stone is estimated at 168 lb/ft. So, the work needed to build the pyramid is calculated by multiplying the area of the base by the height and the density of the stone, like this: Work = 7740^2 ft^2 x 860 ft x 168 lb/ft = 9.76 x 10^9 lb-ft.

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Answer:

f(x) = x + 5

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (0, 5) ← 2 points on the line

m = [tex]\frac{5-0}{0-(-5)}[/tex] = [tex]\frac{5}{0+5}[/tex] = [tex]\frac{5}{5}[/tex] = 1

the line crosses the y- axis at (0, 5 ) ⇒ c = 5

y = x + 5 , or

f(x) = x + 5

Answer:

x+5

Step-by-step explanation:

Because I said so

The value of x is 10.

The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.

|AC|^2 = |AB|^2 + |BC|^2    

Given;

Base=6

Perpendicular=8

Now

x^2=6^2+8^2

X^2=36+64

X^2=100

x=10

Therefore, by pythagoras theorem the answer will be 10.

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Answer:

a) 16, b) 16

Step-by-step explanation:

1. Find f. Plug in 2 for x.

[tex]2^{2} +6(2)=16.[/tex]

2. Find g by performing the same action.

2-1=1.

3. Now that we have f and g, we can multiply them.

[tex](fg)(2)=16(1)=16.[/tex]

a) is 16.

4. b) is (gf)(2)=1(16), which is still 16.

b) is 16.

Answer:

4, -2, and -5.

Step-by-step explanation:

All the real solutions of f(x) = 0 are 4, -2, and -5.  We know y = f(x) and f(x) = 0.  So, we can conclude that y = 0.  When y = 0, it means there isn't a point that moves up or down the y axis (vertically).  The point would only move horizontally.  When looking at the points on the x-axis, we see 4, -2, and -5.  Those are on the x-axis and haven't moved vertically.  So, the coordinates for those points would be 4, 0, -2, 0, and -5, 0.  Remember, y = 0, and 4, -2, and -5 all have a zero in the y value.  Therefore, the answer is 4, -2, and -5.

The new mandated change is, grade 4N's physical education class will end at 2:23 PM.

Physical education for grade 4N typically lasts 30 minutes and begins at 1:43 PM and concludes at 2:13 PM (2:13 PM - 1:43 PM).

Let's assume that the newly required adjustment extends the end of the class by 10 minutes, making the time change (c) 10 minutes.

Adding the time modification to the existing end time will yield the new end time:

2:13 PM + 10 minutes = 2:23 PM

So, with the new mandated change, grade 4N's physical education class will end at 2:23 PM.

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The domain of the function here is {0 ≤ x ≤ 600}. The first option is the right answer.

The domain of a function is the set of all input values (or independent variables) for which the function is defined and produces a valid output (or dependent variable). It is the set of values that can be plugged into a function and yield a valid result.

The domain of this function in this context is {0 ≤ x ≤ 600}.

This is because x represents the number of t-shirts Henry sells and he has ordered 600 shirts. So, he can only sell a non-negative number of shirts (x ≥ 0) and a maximum of 600 shirts (x ≤ 600). Any values outside this range are not meaningful in this context, hence they are not part of the domain.

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10 packages are available, some of which contain only 3 and others 4 rookie cards. There are a maximum of 38 rookie cards in all.

In math, a linear equation one of that of the form y=mx+b. The slope is B, and the una is m. As y and x are variable, the previous statement is frequently referred to as a "system of equations with 2 variables." Bivariate linear equations are logistic equations with two or more variables. Formulas can be found in various locations, including 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. When such an equation has had the structure y=mx+b, where m represents the slope and b its y-intercept, it is known to as being linear. A model formula is said to be cubic if its solution seems to have the form y=mx+b, wherein m stands for the gradient and b for the y-intercept.

3x + 4y = 38

x + y = 12 ( Multiply by -3)

Hence

3x + 4y = 38

-3x - 3y = -36

Add

y = 2

In the case where y = 2

x = 12 - y

x = 12 - 2

x = 10,

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The volume of the ball is 267.95cm³ and the density of the ball is  0.335gcm⁻³

Density is a measure of the mass of an object per unit of volume. It is usually expressed in units of grams per cubic centimeter (g/cm3).

In this problem, the density of the ball is calculated as;

density = mass / volume

volume = volume of sphere

volume = 4/3πr³

volume = 4/3 * 3.14 * 4³

volume = 267.95cm³

The volume is 267.95cm³

The density of the ball = mass / volume

density = 90 / 267.95 = 0.335gcm⁻³

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The equation of line is y = -10x + 1500 , where the slope is m = -10

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = -10x + 1500   be equation (1)

where x is the number of minutes

and y is the altitude in feet

when x = 0

Substituting the value of x = 0 in the equation , we get

y = 1500 feet

when x = 5

Substituting the value of x = 5 in the equation , we get

y = -10 ( 5 ) + 1500

y = -50 + 1500

y = 1450 feet

when x = 8

Substituting the value of x = 8 in the equation , we get

y = -10 ( 8 ) + 1500

y = -80 + 1500

y = 1420 feet

when x = 10

Substituting the value of x = 10 in the equation , we get

y = -10 ( 10 ) + 1500

y = -100 + 1500

y = 1400 feet

when x = 30

Substituting the value of x = 30 in the equation , we get

y = -10 ( 30 ) + 1500

y = 300 + 1500

y = 1200 feet

So , the plane's altitude after 5 minutes would be 1450 feet and after 30 minutes, the plane's altitude would be 1200 feet

Now , the plane will reach the ground when y = 0

0 = -10x + 1500

10x = 1500

x = 150 minutes

Hence , the equation of line is y = -10x + 1500

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The confidence interval for the proportion of adults who approve of the candidate is given as follows:

(0.45, 0.51).

A confidence interval is obtained as the proportion estimate plus/minus the margin of error.

The parameters for this problem are given as follows:

Hence the bounds of the confidence interval are given as follows:

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Step-by-step explanation:

a probability is always the ratio

desired cases / totally possible cases

in our experiment the totally possible cases for pulling not a heart is 40.

7 + 11 + 9 + 13 = 40

in that experiment we see that out of these 40 pulls we got 9 hearts. and therefore 40 - 9 = 31 non-hearts.

so, the experimental probability for not pulling a heart is

31/40 = 0.775 = 77.5%

Answer:

yes 77.5%

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Let e represent the number of students with blue eyes. Then the number of students with blond hair is 2e. The total number of students is ...

 3 + e + 2e -6 = 30

We subtracted 6 because the expressions e and 2e cause the 6 students with both blond hair and blue eyes to be counted twice.

 3e = 33 . . . . add 3 and simplify

 e = 11

11 students have blue eyes.

Answer:

11

Step-by-step explanation:

11

venn daigram

The diameter of circle A is equal to line segment TB.

In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle refers to the set of all points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).

Based on the information provided about circle A, we can reasonably infer and logically deduce that its diameter is represented by line segment TB. Furthermore, the radius of circle A can be calculated as follows;

Diameter = radius + radius

Diameter = TA + AB

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The transformations of the triangle ABC to A'B'C' are (a) and (e)

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

ABC = (-6, 2), (-4, 6) and (-2, 2)

Rotate the triangle by 180 degrees

So, we have the following representation

Image 1 of ABC = (6, -2), (4, -6) and (2, -2)

Translate the triangle 1 units left

So, we have the following representation

A'B'C' = (5, -2), (3, -6) and (1, -2) ---- option (a)

Another possible sequence is as follows

Reflect the triangle across the x and y axes

So, we have the following representation

Image 1 of ABC = (6, -2), (4, -6) and (2, -2)

Translate the triangle 1 units left

So, we have the following representation

A'B'C' = (5, -2), (3, -6) and (1, -2) ---- option (e)

Hence, the transformations are (a) and (e)

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A local restaurant charges $15 for a jumbo cheese pizza and $1.35 for each additional topping.

the total cost, y, for x toppings on a jumbo pizza is represented  in slope-intercept form, by the equation y = $1.35x + $15

The slope-intercept equation for the total cost, y, for x toppings on a large cheese pizza is y = mx + b, where m is the slope and b is the y-intercept.

First, we must determine the slope (m). The slope shows the $1.35 cost of each subsequent topping. So, m = $1.35.

The y-intercept must then be determined (b). The y-intercept shows the large cheese pizza's starting cost of $15. So, b = $15.

When we plug these values into the equation, we get:

y = $1.35x + $15

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Kim was solving a problem using the six steps first she read the problem then she wrote down the facts and figures next she knew she had to find a relation between what’s given and what's asked for.

After that, she formulated a plan or strategy to solve the problem. Then, she carried out the plan and solved the problem. Finally, she checked her answer to see if it made sense and if it was reasonable.

These six steps are often used in problem-solving and are a useful way to approach a problem systematically. By following these steps, one can ensure that all the relevant information is taken into consideration, a plan is developed to solve the problem, and the solution is verified before presenting it as the final answer.

The six steps are:

1. Determining the problem statement.

2. Identifying the main causes of the problem.

3. Developing viable solutions relevant to the problem.

4. Selecting one solution among the options.

5. Applying the solution on the problem at hand.

6. Evaluating the effect of the solution on the problem.

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x equals 1 ± the square root of 5 end root

Answer:

  A  { y | y ∈ ℝ, y ≠ -4, -3 }

Step-by-step explanation:

You want to know the range of the function shown in the graph.

The range is the vertical extent of the graph, the set of possible function output values.

Here, the function approaches the horizontal asymptote y = -3, but never has that output value. The "hole" at (5, -4) means the function never has the output value -4, either.

The range is all real numbers (ℝ) except -4 and -3.

The perfect square trinomial is 4x² - 4x + 1. The correct answer would be an option (A).

Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.

The expression is given in option (A), as follows:

4x² - 4x + 1

(2x)² - 2 × 2x × 1 + 1²

Compare to the formula a² - 2 × a × b + b² = (a - b)², and we get

(2x - 1)²

Thus, this is a perfect square trinomial.

Hence, the correct answer would be an option (A).

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