Using the digits 1 to 9 to fill in the boxes only once, write the largest and smallest absolute value. Then find the decimal equivalent.

EX|3 X 104- 6 X 102|

=|30000-600|=|29, 400|= 29,400. This represents the decimal equivalent. is this the largest or smallest?

Once you find the largest possible answer, find the smallest answer you can make with the unused digits

The difference is: [tex]500 = (25 \times f) + (100 \times c)[/tex]

To write the inequality describing the total calorie count, we need to consider the calorie count of the french fries and chicken wings and ensure that it is less than 500 calories.

Let's start by defining the variables:

Let f be the number of french fries.

Let c be the number of chicken wings.

Next, we can determine the total calorie count for the french fries and chicken wings:

The number of calories per french fry is 25.

The number of calories per chicken wing is 100.

To calculate the total calorie count, we multiply the number of french fries by the calorie count per french fry and the number of chicken wings by the calorie count per chicken wing. Then, we sum the two values:

Total calorie count = [tex](25 \times f) + (100 \times c)[/tex]

We want this total to be less than 500 calories, so we can write the inequality as:

[tex](25 \times f) + (100 \times c) < 500[/tex]

This inequality ensures that the sum of the calories from the french fries and chicken wings is less than 500.

By varying the values of f and c within the constraints of the inequality, Ashley can ensure that the total calorie count for the lunch remains within her desired limit.

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The area of the composite figure is

Area of the semi circle + Area of the rectangle.

Formula for the area of a circle is

π x r²

= 3.14 x (2)²

= 3.14 x 4

≈ 12.57

Formula for the area of the rectangle is

L x B

= 4 x 11

= 44m²

Since the area of the semi circle = Area of circle /2

⇒ (πr²)/2

= 12.57/2

= 6.29

Hence are of the composite shape is

6.29 + 44

≈  50.29m²

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Full Question:

See attached image.

Answer:

Restrictions:

x ≠ -1/5; x ≠ 1

Answer:

[tex] \dfrac{5x - 9}{x - 1} [/tex]

Step-by-step explanation:

[tex] \dfrac{25x^2 - 40x - 9}{5x^2 - 4x - 1} = [/tex]

[tex] = \dfrac{25x^2 - 45x + 5x - 9}{5x^2 - 5x + x - 1} [/tex]

[tex] = \dfrac{5x(5x - 9) + 1(5x - 9)}{5x(x - 1) + 1(x - 1)} [/tex]

[tex] = \dfrac{(5x + 1)(5x - 9)}{(5x + 1)(x - 1)} [/tex]

[tex] = \dfrac{5x - 9}{x - 1} [/tex]

5x + 1 = 0

x = -1/5

x - 1 = 0

x = 1

Restrictions:

x ≠ -1/5; x ≠ 1

Answer:

[tex] \dfrac{5x - 9}{x - 1} [/tex]

The HCF of 560 and 729 is 1.

To find the HCF of 560 and 729, we use the Euclidean algorithm as follows;HCF of 560 and 729:Step 1: Divide the larger number by the smaller number, then find the remainder.729 ÷ 560 = 169 remainder 169Step 2: Divide the smaller number (i.e., 560) by the remainder (i.e., 169).560 ÷ 169 = 3 remainder 53.

Step 3: Divide the remainder from step 1 (i.e., 169) by the remainder from step 2 (i.e., 53).169 ÷ 53 = 3 remainder 10Step 4: Divide the remainder from step 2 (i.e., 53) by the remainder from step 3 (i.e., 10).53 ÷ 10 = 5 remainder 3Step 5: Divide the remainder from step 3 (i.e., 10) by the remainder from step 4 (i.e., 3).10 ÷ 3 = 3 remainder 1.

Step 6: Divide the remainder from step 4 (i.e., 3) by the remainder from step 5 (i.e., 1).3 ÷ 1 = 3 remainder 0The HCF of 560 and 729 is the last non-zero remainder, which is 1.

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The length of the fence must be 618cm

The volume that it can hold is 1,909,620 cm³

First, the fence is just equal to the circumference of the cylinder, remember that the circumfernce of a circle of diameter D is:

C = П*D

Here we use П = 3, then:

C = П*206cm

C = 3*206cm = 618cm

Now the volume, for a cylinder of diameter D and height H, the volume is:

V = П*(D/2)²*H

Replacing the values that we know we will get:

V = 3*(206cm/2)²*60cm = 1,909,620 cm³

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In the  word problem above, 0 small pizzas, 1 medium pizza, and 5 large pizzas were delivered to the college.

Let  S = number of small pizzas delivered

Let M = number of medium pizzas delivered

Let L = number of large pizzas delivered

We'll start by solving equation 1 for one variable and substituting it into the other equations.

S + M + L = 12

We can rewrite this equation as -

S = 12 - M - L

Now, substitute this value of S in equations 2 and 3 -

4S + 10M + 15L = 109

4(12 - M - L) + 10M + 15L = 109

48 - 4M - 4L + 10M + 15L = 109

6M + 11L = 61

2S + 4M + 13L = 81

2(12 - M - L) + 4M + 13L = 81

24 - 2M - 2L + 4M + 13L = 81

2M + 11L = 57

Now we have a system of two equations with two variables -

6M + 11L = 61 ...(4)

2M + 11L = 57 ...(5)

Subtract  equation   (5)from equation (4) -

(6M +   11L) - (2M +11L) = 61 - 57

4M = 4

M = 1

Substitute the value of M into equation (5) -

2(1) + 11L = 57

2 + 11L = 57

11L = 55

L = 5

Now substitute the values of M and L into equation (1) -

S + 1 + 5 = 12

S + 6 = 12

S = 6 - 6

S = 0

Therefore, the solution is -

S = 0 (no small pizzas)

M = 1 (1 medium pizza)

L = 5 (5 large pizzas)

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Full Question:

Although part of your question is missing, you might be referring to this full question:

a pizza shop delivered 12 pepperoni pizzas to a college on the first night of final exams. the total cost of the pizzas was $109. a small pizza costs $4 and contains 2 ounces of pepperoni. a medium pizza costs $10 and contains 4 ounces of pepperoni. a large pizza cost $15 and contains 13 ounces of pepperoni. the owner of the pizza shop used 5 pounds 1 ounces of pepperoni in making the 12 pizzas. how many pizzas of each size were delivered to the college?

Answer:

2/5 = g/80

5g = 160, so g = 32 grams of gold

Answer:1.9975

Step-by-step explanation:

The computation of the linear approximation of the given function is shown below:

L(x) = 2 - 1 ÷ 4(x)

As we are looking for √3.9

So here

x = 0.1

So

= 4 - 0.1

= 3.9

Now

L(0.1) = f(3.9) = 2 - (0.1 ÷ 4)

= 1.975

now

substitute the x = 0.01

Then

L(0.01) = f(3.99) = 2 - (0.01 ÷ 4)

= 1.9975

We simply applied the above equations

The linear approximation of √653 is approximately 24.8163.

To find the linear approximation to a function at a given point, we can use the formula:

L(x) = f(a) + f'(a)(x - a)

where L(x) is the linear approximation, f(a) is the value of the function at point a, f'(a) is the derivative of the function at point a, and (x - a) represents the difference between the given point x and the approximation point a.

In this case, we are given f(x) = √3 and we want to approximate √653 using the linear approximation. Let's find the linear approximation first.

Taking the derivative of f(x) = √3, we get:

f'(x) = 1 / (2√3)

Now, let's evaluate the linear approximation at a = 64:

L(x) = √3 + (1 / (2√3))(x - 64)

Substituting x = 653 into the linear approximation equation:

L(653) = √3 + (1 / (2√3))(653 - 64)

L(653) ≈ √3 + (1 / (2√3))(589)

L(653) ≈ √3 + (1 / (2√3))(589)

Calculating this approximation, we get:

L(653) ≈ √3 + (1 / (2√3))(589) ≈ 24.8163

Therefore, the linear approximation of √653 is approximately 24.8163, rounded to 4 decimal places.

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1) Number of participants whose headache remained is: 62

2) The probability of randomly selecting an individual whose headache remained is: 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933

From the table, we have the parameters as:

Number of participants that took medicine and headache went away = 120

Number of participants that took placebo and headache went away = 68

Number of participants that took and headache remained = 18

Number of participants that took placebo and headache remained = 44

1) Number of participants whose headache remained = 18 + 44 = 62

2) The probability of randomly selecting an individual whose headache remained is:

62/(62 + 120 + 68)

= 62/150

= 0.4133

3) The probability of randomly selecting an individual whose headache remained and took a placebo is:

44/150 = 0.2933

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To determine the original worth of the shares, we can use the concept of profit as a percentage of the original value. Since the profit is 25% of the original value, we can set up the following equation:

Profit = Original Value x Percentage

1328 = Original Value x 0.25

To solve for the Original Value, we can divide both sides of the equation by 0.25:

Original Value = 1328 / 0.25

Original Value = 5312

Therefore, the shares were worth $5312 when she originally purchased them.

It will take approximately 6.8 hours for the population to reach 250,000.

To solve this problem, we can use the concept of exponential growth. Let's denote the population size at time t as P(t).

Given that the culture grows at a rate proportional to its size, we can write the following differential equation:

dP(t)/dt = k * P(t),

where k is the proportionality constant.

We also know that after 1.5 hours, the population has increased to 875. Therefore, we have the following information:

P(0) = 50 (initial population size),

P(1.5) = 875.

To find the value of k, we can substitute the values into the differential equation:

875 = 50 * e^(1.5k).

Simplifying the equation, we get:

e^(1.5k) = 17.5.

Taking the natural logarithm of both sides, we have:

1.5k = ln(17.5).

Solving for k, we find:

k ≈ 0.6733.

Now, to find the time it takes for the population to reach 250,000, we can substitute the values into the exponential growth equation:

250,000 = 50 * e^(0.6733t).

Dividing both sides by 50 and taking the natural logarithm, we get:

ln(5,000) = 0.6733t.

Solving for t, we find:

t ≈ 6.84 hours.

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The electrostatic force between the two charges is 5,977.68 N.

The electrostatic force between the two charges separated by the given distance is calculated by applying Coulomb's law.

F = kq₁q₂ / r²

where;

The electrostatic force between the two charges is calculated as follows;

F = (9 x 10⁹ x 16.9 x 10⁻⁶ x 60.7 x 10⁻⁶ ) / ( 0.0393 )

F = 5,977.68 N

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Answer:

Assume that the formula is true for the (k + 1) term

Step-by-step explanation:

Proof by mathematical induction is a method of proving that a statement is true for all natural numbers.

The proof has three steps:

In the step "Assume that the formula is true for the (k + 1) term", we are assuming that the statement is true for some value of n, say k.

We then use this assumption to prove that the statement is also true for the next value of n, k + 1.

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o find the percent of those who passed the first test and also passed the second test, we can use the concept of conditional probability.

Given that 32% of the class passed both tests, and 70% of the class passed the first test, we want to determine the percentage of those who passed the first test and also passed the second test.

We can set up the calculation as follows:

Percentage = (Number of students who passed both tests) / (Number of students who passed the first test)

Since 32% of the class passed both tests and 70% of the class passed the first test, we can substitute these values into the equation:

Percentage = (0.32) / (0.70)

Calculating this division, we find:

Percentage ≈ 0.4571

Converting this to a percentage, we get approximately 45.71%.

Therefore, the correct answer is:

D. About 46% (rounded to the nearest percent).

The question is about percentages and the correct answer is that approximately 46% of the students who passed the first test also passed the second one.

The student's question is about the concept of percentages, a basic concept in Mathematics. The problem mentioned is about calculating the percentage of students who passed both tests out of those who passed the first one.

Given that 32% of the entire class passed both tests and that 70% of the class passed the first test, to find the percentage of students who passed the first test and also the second one, one can use the following steps:

Using these steps, you would find out that approximately 46% of the students who passed the first test also passed the second one. Therefore, D. About 46% is the correct answer.

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The sample variance of the given set of data is 7.2. The correct answer is 7.2.

To find the sample variance of the given set of data, follow these steps:

1. Calculate the mean of the data set:

  Mean (μ) = (5 + 6 + 11 + 11 + 9 + 6) / 6 = 48 / 6 = 8

2. Calculate the difference between each data point and the mean, and square each difference:

[tex](5 - 8)^2 = 9 \\ (6 - 8)^2 = 4 \\ (11 - 8)^2 = 9 \\ (11 - 8)^2 = 9 \\ (9 - 8)^2 = 1[/tex]

  [tex](6 - 8)^2 = 4[/tex]

3. Calculate the sum of all the squared differences:

  9 + 4 + 9 + 9 + 1 + 4 = 36

4. Calculate the sample variance:

  Variance [tex](s^2)[/tex] = sum of squared differences / (n - 1)

                 = 36 / (6 - 1)

                 = 36 / 5

                 = 7.2

Therefore, the provided set of data has a sample variance of 7.2. The right response is 7.2.

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The correct answer would be "None of these" since none of the provided options indicate a basic solution.

The solution with a pH of 2 is considered to have basic character. The pH scale measures the acidity or alkalinity of a solution, ranging from 0 to 14. A pH value below 7 indicates acidity, while a pH above 7 indicates alkalinity. Thus, a pH of 2 is highly acidic and not basic.

On the other hand, the pOH scale is the inverse of the pH scale and measures the concentration of hydroxide ions (OH-) in a solution. A higher pOH value indicates a higher concentration of hydroxide ions and a more basic solution. Therefore, a pOH of 13 or 4 would suggest a basic solution.

Considering the given answer choices, neither pOH = 13 nor pOH = 4 is considered to have basic character.

It's important to note that the pOH scale is less commonly used in everyday situations compared to the pH scale when discussing the acidity or basicity of a solution. So, the correct answer is none of these.

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Answer:

To apply the fourth-order Runge-Kutta method, we can use the following steps:

Given:

Initial condition: y = 1 when x = 0

Step size: h = 0.1

We want to find the approximate value of y when x = 1/5.

The fourth-order Runge-Kutta method involves the following steps:

Set up the following equations:

k1 = hf(x, y)

k2 = hf(x + h/2, y + k1/2)

k3 = hf(x + h/2, y + k2/2)

k4 = hf(x + h, y + k3)

Update the values:

y = y + (k1 + 2k2 + 2k3 + k4)/6

x = x + h

Repeat steps 1 and 2 until the desired x-value is reached.

Let's apply these steps to find the approximate value of y when x = 1/5:

Step 1:

x = 0, y = 1

h = 0.1

k1 = 0.1 * f(x, y) = 0.1 * f(0, 1)

k2 = 0.1 * f(x + h/2, y + k1/2) = 0.1 * f(0 + 0.1/2, 1 + k1/2)

k3 = 0.1 * f(x + h/2, y + k2/2) = 0.1 * f(0 + 0.1/2, 1 + k2/2)

k4 = 0.1 * f(x + h, y + k3) = 0.1 * f(0 + 0.1, 1 + k3)

Step 2:

y = y + (k1 + 2k2 + 2k3 + k4)/6

x = x + h

Repeat steps 1 and 2 until x = 1/5.

Performing these calculations step by step will yield the approximate value of y when x = 1/5 using the fourth-order Runge-Kutta method.

Step-by-step explanation:

Answer:

a) Range = 15

b) Median = 39.5

Step-by-step explanation:

Here, we are given a list of numbers and asked to find the range and median.

In a data set, range is the difference between the highest and lowest numbers. On the other hand, the median is the middle number when the data is in ascending order (from lowest to highest). When there are two middle numbers, add the numbers and divide by two to find the median of the data set.

Given data set: 51, 38, 48, 36, 39, 40, 39, 47

Step 1: List the data in ascending order.

36, 38, 39, 39, 40, 47, 48, 51

Step 2: Find the range (highest - lowest).

36, 38, 39, 39, 40, 47, 48, 51

51 - 36 = 15

Step 3: Find the median (middle number).

36, 38, 39, 39, 40, 47, 48, 51

(39 + 40)/2 = 79/2 = 39.5

Range:

15

Median:

39.5 (79/2 in fraction form)

Explanation:

When looking for the range, just remember that it is the difference between the largest number and the smallest one. In other words:

[tex]\textsf{Range = Largest Number - Smallest Number}[/tex]

The largest number is 51, an the smallest one is 36. So the range is:

Range = 51 - 36

           = 15

To find the median, we'll first list the numbers from least to greatest:

36, 38, 39, 39, 40, 47,48, 51

Since we have 8 numbers in the list, we find the mean of the two numbers in the middle, i.e., 39 and 40:

39 + 40

79 / 2

39.5

Hence, these are the answers.

Answer:

x = 4√2

Step-by-step explanation:

Identifying the triangle in the diagram:

45-45-90 triangle rules:

Finding x:

Since the hypotenuse is 8 units long and, we can find x by setting 8 equal to x√2:

(8 =  x√2) / √2

8/√2 = x

Rationalize the denominator to simplify:

(8/√2) * (√2/√2)

8√2 / 2

4√2

Thus, x = 4√2

The solution to the equation cos(6x) = sin(3x - 9) from the given options is x = -10. Option C.

To solve the equation cos(6x) = sin(3x - 9) according to the given options, we can substitute each option into the equation and check if it satisfies the equation.

A. x = 10:

cos(6 * 10) = sin(3 * 10 - 9)

cos(60) = sin(21)

However, cos(60) does not equal sin(21), so x = 10 is not a solution.

B. x = 11:

cos(6 * 11) = sin(3 * 11 - 9)

cos(66) = sin(24)

Again, cos(66) does not equal sin(24), so x = 11 is not a solution.

C. x = -10:

cos(6 * -10) = sin(3 * -10 - 9)

cos(-60) = sin(-39)

Interestingly, cos(-60) does equal sin(-39). Therefore, x = -10 satisfies the equation cos(6x) = sin(3x - 9). Thus, C. x = -10 is a solution.

D. x = 12:

cos(6 * 12) = sin(3 * 12 - 9)

cos(72) = sin(27)

Once again, cos(72) does not equal sin(27), so x = 12 is not a solution.

In summary, the solution to the equation cos(6x) = sin(3x - 9) from the given options is x = -10, which corresponds to option C.

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Answer: Its B (11)

Step-by-step explanation:

I did the test

The domain refers to the set of possible input values for a function. In the given question, the character's path in a video game is described using different inequalities. To find the domain, we need to identify the valid values for the variable x that satisfy all the given conditions.

From the first inequality, -6 ≤ x ≤ 4, we see that x can take any value between -6 and 4, inclusive.

Moving to the second inequality, -6 ≤ x ≤ 4, x ≠ -6, 2, we can see that x cannot be equal to -6 or 2, but it can still take any other value between -6 and 4.

Finally, in the third inequality, -12 ≤ x ≤ 10, x ≠ -6, 6, we find that x cannot be equal to -6 or 6, but it can still take any other value between -12 and 10.

Therefore, the domain of the character's path in the video game is the set of values for x that satisfy all the given conditions, which is -12 ≤ x ≤ 4, x ≠ -6, 2, 6.

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We have:

[tex]$\frac{600\text{ cc}}{45\text{ seconds}} = \frac{2000\text{cc}}{x \text{ seconds}}[/tex]

Cross multiplying, we get:

[tex]$600x = 90000$[/tex]

We divide both sides by 600 and get:

[tex]$\frac{600x}{600} = \frac{90000}{600}$[/tex]

[tex]$x=\boxed{150}$[/tex]

It takes 150 seconds (2 minutes and 30 seconds) for the sprayer to disperse 2000 cc of herbicide. Hope this helps!

Answer:

[tex]\frac{5}{6}[/tex] of the shelves of prescriptions have been picked up.

Step-by-step explanation:

First, let's write out the problem they want us to solve.

[tex]\frac{3}{6} +\frac{2}{6}[/tex]

Since the denominators are the same, we know our answer will have the same denominator, 6, and a numerator of whatever the two numerators, 3 and 2, totals.'

[tex]\frac{3}{6} +\frac{2}{6}=\frac{3+2}{6} =\frac{5}{6}[/tex]

Since 5 can't go into 6, we know the fraction can't be simplified. So, [tex]\frac{5}{6}[/tex] of the shelves of prescriptions have been picked up.

If this answer helped you, please leave a thanks!

Have a GREAT day!!!

Answer:

(x-4)²/16 + y²/4 = 1

Step-by-step explanation:

To find the equation of the ellipse, we need to determine the length of the major axis. Since the minor axis has length 4, and the vertex is at (4,-4), the distance from the center to the vertex is 4. Therefore, the major axis has length 8. Thus, the equation of the ellipse is

(x-4)²/16 + y²/4 = 1.

The relationship described by the equation 4y = 2x is proportional.

The relationship in the equation 4y = 2x is proportional. By simplifying the equation, we got that y = (1/2)x, which shows that y is directly proportional to x. In a proportional relationship, the ratio of y to x always remains constant.

In this scenerio, the constant of proportionality is 1/2. As x increases or decreases, y also increases or decreases by half of x.

So, the relationship between y and x in this equation is proportional, indicating that changes in x will result in corresponding proportional changes in y.

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The question is:-

Is the relationship described by the equation 4y = 2x proportional or non-proportional?

The percentage of residents aged 25 or older with Associate degrees, Bachelor,s degrees, and either graduate or professional degrees is 31%.

Given: Let the total number of residents aged 25 and older with associate degrees, bachelor,s degrees, and either graduate or professional degrees be "x" and the total number of residents of Indiana’s aged 25 and older be "y".

Therefore,

x= 326036 + 623200 + 348807

x=1298043 &

y=4,229,138

Percentage = (x/y)*100

Percentage = (1298043/4229138)*100

Percentage = 30.6% = 31%

So, the percentage of residents aged 25 or older with Associate degrees, Bachelor,s degrees, and either graduate or professional degrees is 31% (rounded to the nearest whole number).

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Answer:

Width = 7.3 feet

Step-by-step explanation:

Step 1:  Find the scale of the drawing:

Step 2:  Convert feet to inches:

Step 3:  Simplify the fraction:

Thus, the simplified fraction is 23/5952.

Step 4:  Find the actual width of the room:

Step 5:  Simplify the fraction:

Step 6:  Convert inches to feet:

Step 7:  Round to the nearest tenth of a foot:

Rounding to the nearest tenth of a foot, we get **7.3 ft**.

Thus, the actual width of the room is about 7.3 ft.