Bug S Bug S and Bug F is fast. Both bugs start at 0 on a number line and move in the positive direction. The bugs leave 0 at the same time and move at constant speeds. Four seconds later, F is at 12 and S is at 8. When will F and S be 100 units apart?

The equation for the function is D(x) = 65 - 0.8x. Where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

What is a linear function?

A linear function is a mathematical function that has a constant rate of change or slope between the independent variable (x) and the dependent variable (y). It is a function that can be graphically represented as a straight line.

We can use a linear function to approximate the depth of the water in the reservoir x months after the start of the study, since the depth is dropping at a constant rate of 0.8 meters per month. Let D(x) be the depth of the water in meters x months after the start of the study. Then we have:

D(x) = 65 - 0.8x

where 65 is the initial depth of the water and 0.8x is the amount by which the depth drops after x months.

Therefore, the equation for the function is D(x) = 65 - 0.8x.

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The volume of the solid is approximately 0.558 cubic units.

To find the volume of the solid, we need to integrate the area of the semi-circles along the a-axis.

We know that the diameter of each semi-circle is the distance between the functions f(x) and g(x), which is:

d(a) = f(a) - g(a) = ln(a) + 1 - (a-1) = ln(a) - a + 2

The radius of each semi-circle is half of the diameter, which is:

r(a) = (ln(a) - a + 2) / 2

The area of each semi-circle is π times the square of its radius, which is:

[tex]A(a) = πr(a)^2 = π/4 (ln(a) - a + 2)^2[/tex]

To find the volume of the solid, we integrate the area of each semi-circle along the a-axis, from a = e to a = 2:

V = ∫[e,2] A(a) da

V = ∫[e,2] π/4 [tex](ln(a) - a + 2)^2 da[/tex]

V ≈ 0.558 (rounded to the nearest thousandth)

Therefore, the volume of the solid is approximately 0.558 cubic units.

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Answer: 2.5 dm

Step-by-step explanation:

Divide 25.0 by 10

= 2.5

Answer:

162, 147 etc.

Step-by-step explanation:

we have to find

[tex]N = k^2 \cdot p[/tex]

we can iterate k = 1 to 10 to check all possible solutions,

[tex]N = 9^2 \cdot 2[/tex]

[tex]N = 7^2 \cdot 3[/tex]

N = 162, 147 etc.

Hopefully this answer helped you!!

Answer:

The formula for compound interest is given by:

A = P(1 + r/n)^(nt)

Where:

A = the amount of money accumulated after n years

P = the principal (initial investment)

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case, P = $2,500, r = 0.05 (since 5% = 0.05), n = 2 (since interest is compounded semiannually), and t = 15. Substituting these values into the formula, we get:

A = 2500(1 + 0.05/2)^(2*15)

A ≈ $5,551.33

Therefore, Lyla's investment will be worth approximately $5,551.33 after 15 years if interest is compounded semiannually.

The answer is x = 5±√61/2, I really hope this helps (:

1) y = -3x and y = -3x + 2: inconsistent system of equations.

2) y = x - 5 and -2x + 2y = - 10: consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15 : consistent and independent.

The given equation are:

The graph for each system of equations is plotted.

1) y = -3x and y = -3x + 2

From the graph 1 it is shown that the lines for the each equation form the parallel lines.

Thus, system of equations are inconsistent.

2) y = x - 5 and -2x + 2y = - 10

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

3) 2x - 5y = 10 and 3x + y = 15

From the graph 2 it is shown that the lines for the each equation form the coincident lines.

Thus, system of equations are consistent and independent.

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Answer:

The excluded value in the domain is x = 2 because the denominator of the rational function becomes zero at this value of x, which results in division by zero.

At x = 2, there is a vertical asymptote, which means that the graph of the function approaches positive or negative infinity as x approaches 2 from either side.

(x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.

Functiοn can be define in which it relates an input tο οutput.

If the graph οf a pοlynοmial functiοn P(x) has x-intercepts at x = -4, x = 0, and x = 5, then we knοw that the factοrs οf P(x) are (x + 4), x, and (x - 5). This is because a pοlynοmial has x-intercepts where the value οf P(x) is equal tο zerο, and this οccurs when each factοr is equal tο zerο.

Therefοre, we can cοnclude that (x + 4) and (x - 5) are factοrs οf the pοlynοmial P(x), but x is nοt necessarily a factοr. This is because x is a linear factοr with a zerο intercept, but it cοuld be cancelled οut by anοther factοr in the pοlynοmial.

Thus, the cοrrect statement is:

(x + 5) is nοt necessarily a factοr οf the pοlynοmial.

(x-4) is a factοr οf the pοlynοmial.

The degree οf the pοlynοmial is 3 οr greater since the pοlynοmial has three x-intercepts. Hοwever, we cannοt determine the exact degree οf the pοlynοmial withοut additiοnal infοrmatiοn.

Therefοre, (x + 5) is nοt necessarily a factοr οf the pοlynοmial, (x-4) is a factοr οf the pοlynοmial are cοrrect statement.

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Answer:

1.986 x 10 to the tenth power

Step-by-step explanation:

Slope is zero and the y-intercept is (0,-5)

What is slope ?

In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.

In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.

The formula for calculating slope is:

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

where (x1, y1) and (x2, y2) are two points on the line.

According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Comparing the equation Y = -5 to y = mx + b, we can see that:

The slope, m, is 0, since there is no x-term in the equation.

The y-intercept, b, is -5, since that is the constant value in the equation.

Therefore, the correct answer is:

B. Slope is zero and the y-intercept is (0,-5)


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The average ticket cost for each concert is given as follows:

The ticket costs are obtained by a system of equations, for which the variables are given as follows:

It cost a total of $1707 to purchase six tickets for concert A and six tickets for concert B, hence:

6a + 6b = 1707

a + b = 284.5.

Three tickets for concert B cost a total of $687, hence the cost for concert B is of:

3b = 687

b = 287/3

b = $95.67.

Replacing into the first equation, the cost for concert A is given as follows;

a = 284.5 - 95.67

a = $188.83.

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the pressure at a depth of 66 ft is 197,580 Pa, and the volume of the tank at this depth is 0.000505 L.

To find the pressure at a depth of 66 ft in a liquid, we can use the formula:

pressure = density x gravity x depth

Assuming the liquid in the tank is water, the density is 1000 kg/m³, and gravity is 9.81 m/s².

First, we need to convert 66 ft to meters:

66 ft x 0.3048 m/ft = 20.1168 m

Then, we can find the pressure at this depth:

pressure = 1000 kg/m³ x 9.81 m/s² x 20.1168 m = 197,580 Pa

To find the volume of the tank at this depth, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at a constant temperature:

P₁V₁ = P₂V₂

where P₁ and V₁ are the initial pressure and volume (1 atm and 10 L, respectively), and P₂ and V₂ are the final pressure and volume.

We can rearrange this equation to solve for V₂:

V₂ = (P₁ x V₁) / P₂

Substituting the values, we get:

V₂ = (1 atm x 10 L) / (197,580 Pa / 1 atm) = 0.000505 L

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By adding fractions that represent each of the amounts of cupcakes, we can see that you need 9 cupcakes for you and your friends.

Her we know that you want 3 halves of a cupcake for yourself, 8 halves for your friend, and 7 halves for your other friend.

So we just need to add all of these fractions, to do so, we need to solve the follwing opeartion:

3*(1/2) + 8*(1/2) + 7*(1/2)

3/2 + 8/2 + 7/2

All of these have the same denominator so we can directly add them up:

3/2 + 8/2 + 7/2 = (3 + 8 + 7)/2

(3 + 8 + 7)/2 = 18/2

18/2 = 9

You need 9 cupcakes for you and your friends.

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Complete question:

"I want 3 halves of a cupcake for myself, 8 halves for my friend, and 7 halves for our other friend. How many halves we need in total?"

Step-by-step explanation:

Area of the trapezoid = height x average of bases

                 area = 4 x (8+13)/2) = 42 in^2

Area of triangle  = 1/2 base * height   = 1/2 (13-8) * 4 = 10 in^2

Answer:

Experimental Procedure:

Materials:

Piece of wood

Electronic balance

Bunsen burner

Heat-resistant mat

Stopwatch or timer

Safety goggles

Lab coat

Safety Precautions:

Wear safety goggles and a lab coat to protect your eyes and clothing from any sparks or flames.

Place the heat-resistant mat under the Bunsen burner to prevent any accidental fires.

Use the Bunsen burner only under adult supervision.

Be cautious when handling hot objects, and allow them to cool before touching.

Procedure:

Measure the initial mass of the piece of wood using an electronic balance, and record it in a table.

Light the Bunsen burner, and place the piece of wood over the flame using tongs. Ensure that the wood is fully engulfed in the flame.

Use a stopwatch or timer to time how long the wood burns for (in this case, 15 minutes).

After 15 minutes, turn off the Bunsen burner and remove the piece of wood from the flame using tongs.

Allow the wood to cool, and then measure its final mass using the electronic balance, and record it in the table.

Calculate the difference between the initial and final mass of the wood, and record it in the table.

Repeat steps 1-6 three times to obtain three sets of data.

Calculate the average mass of the burned wood and compare it to the initial mass of the unburned wood to determine if the student's prediction was correct.

Conclusion:

If the average mass of the burned wood is less than the initial mass of the unburned wood, the student's prediction was correct, and he can conclude that the wood underwent a chemical change when it was burned. If the average mass is greater than or equal to the initial mass, the prediction was incorrect, and the student may need to revise his hypothesis or experimental design.

To subtract 6/7 from 2 1/4, we need to find a common denominator. The least common multiple of 7 and 4 is 28, so we can convert 2 1/4 to 9/4 and 6/7 to 24/28. Then we can subtract:

9/4 - 24/28

= 63/28 - 24/28

= 39/28

Therefore, 2 1/4 - 6/7 = 39/28.

To solve for the blank in 2 5/12 - blank = 2/3, we can start by converting 2 5/12 to an improper fraction:

2 5/12 = (2*12 + 5)/12 = 29/12

Then we can subtract 2/3 from both sides:

2 5/12 - 2/3 = blank

To subtract these fractions, we need to find a common denominator. The least common multiple of 3 and 12 is 12, so we can convert 2/3 to 8/12. Then we can subtract:

29/12 - 8/12

= 21/12

= 7/4

Therefore, the blank in 2 5/12 - blank = 2/3 is 7/4.

To subtract 5 3/8 from 7 1/12, we need to find a common denominator. The least common multiple of 8 and 12 is 24, so we can convert both mixed numbers to improper fractions:

7 1/12 = (712 + 1)/12 = 85/12

5 3/8 = (58 + 3)/8 = 43/8

Then we can subtract:

85/12 - 43/8

= 85/12 - (433)/(83)

= 85/12 - 129/24

= 5/24

Therefore, 7 1/12 - 5 3/8 = 5/24.

To solve for the blank in blank + 7/10 = 2 9/20, we can start by converting 2 9/20 to an improper fraction:

2 9/20 = (2*20 + 9)/20 = 49/20

Then we can subtract 7/10 from both sides:

blank + 7/10 - 7/10 = 49/20 - 7/10

Simplifying the right side:

49/20 - 7/10 = (492)/(202) - (74)/(104) = 98/40 - 28/40 = 70/40 = 7/4

Therefore, blank + 7/10 - 7/10 = 7/4, and solving for blank:

blank = 7/4

Therefore, the blank in blank + 7/10 = 2 9/20 is 7/4.

Answer:

0.00005

Step-by-step explanation:

you move 5 decimal places left starting from 7 and right it as a decimal.

Ans=0.00007

Step-by-step explanation:

the perimeter of a rectangle is

2×length + 2×width

in our case

length = width + 3

and

2×length + 2×width = 30

using the first equation in the second :

2×(width + 3) + 2×width = 30

width + 3 + width = 15

2×width + 3 = 15

2×width = 12

width = 12/2 = 6 ft

length = width + 3 = 6 + 3 = 9 ft

Answer:

32.67 square meters

Step-by-step explanation:

finding the area of the shaded region.

area of sector = (θ/360°) x πr²

where "θ" is the central angle of the sector in degrees, "r" is the radius of the sector, and π is a mathematical constant approximately equal to 3.14.

Substituting the given values into the formula, we get:

area of sector = (60°/360°) x π(14m)²

area of sector = (1/6) x 3.14 x 196m²

area of sector = 32.67m² (rounded to two decimal places)

Therefore, the area of the section is 32.67 square meters

The journal could use a one-tailed hypothesis test with a significance level (α) of 0.05 to determine whether there is a significant difference between the proportion of women and men.

In statistics, the p-value is a measure of the evidence against the null hypothesis. It is the probability of observing a test statistic as extreme as, or more extreme than, the one calculated from the sample data, assuming that the null hypothesis is true. In other words, the p-value is the probability of obtaining the observed results, or more extreme results, if the null hypothesis were true.

Given by the question.

To test the claim that women perceive the gender equality problem to be much more compared to men, the journal could test the following hypothesis:

Hypothesis: The proportion of women who perceive gender equality to be a major problem in the workplace (W) is significantly greater than the proportion of men who perceive gender equality to be a major problem in the workplace (M).

H0: W = M (there is no significant difference in perception of gender equality between men and women)

Ha: W > M (women perceive gender equality to be a major problem more than men do)

who perceive gender equality to be a major problem in the workplace. They could calculate the p-value and compare it to α. If the p-value is less than α, they would reject the null hypothesis and conclude that the proportion of women who perceive gender equality to be a major problem in the workplace is significantly greater than the proportion of men who perceive it to be a major problem.

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Answer:

  1759 square meters

Step-by-step explanation:

You want the surface area of a cuboid with a half-cylinder top.

The lateral area of the figure is the product of the length of the mailbox (0.45 m) and the perimeter of the end. The perimeter of the end is the sum of the lengths of the straight sides and half the circumference of a circle with diameter 0.3 m.

  P = 0.3 + 2·0.4 + π/2(0.3) = 1.571 . . . . . meters

  LA = Ph = (1.571 m)(0.45 m) = 0.70695 m²

The end area is twice the area of the rectangular portion of the end, plus the area of a circle 0.3 m in diameter.

 EA = (0.3 m)(0.4 m) + 3.14(0.3/2 m)² = 0.31065 m²

The total area of 1 mailbox is ...

  LA +EA = 0.70695 m² +0.31065 m² = 1.0176 m²

Then the area of 1728 mailboxes is ...

  1728 × 1.0176 m² ≈ 1758.4 m² ≈ 1759 m²

About 1759 square meters of aluminum will be needed for the 1728 mailboxes.

__

Additional comment

This presumes there is no waste in cutting the semicircular shape from the supplied aluminum.

Answer:

x is first angle

y is second angle

and z is third angle

Step-by-step explanation:

This question is solved by a system of equations. We have that:x is the first angle.y is the second angle.z is the third angle.Doing this, we get that:The first angle measures 30º.The second angle measures 67º.The third angle measures 83º.The sum of the measures of the angles of a triangle is 180. This means that The sum of the measures of the second and third angles is five times the measure of the first angle.This means that:From this, the first angle can be found:The measure of the first angle is of 30º.The third angle is 16 more than the second.This means that:Since We get that the second angle is:The second angle measures 67º.For the third angle:The third angle measures 83º.

Answer:

A.=False

B.=True

C.=False

D.=True

Step-by-step explanation:

The original ration is 2 gallons of water for 4 players.

Each player requires 1/2 gallon of water.

To get the amount of water needed multiply 1/2 by the amount of players.

1*(1/2) does not equal 1

2*(1/2) equals 1

10*(1/2) does not equal 4

30*(1/2) equals 15

The product of the expressions are;

Step 1: (x + 2)(x + 3) and 3(x + 3)/4(x + 5)

Step 3: 4(x + 3) × 3(x + 3)/4(x + 5)

Step 4: 3/x + 5

It is important to note that algebraic expressions are described as expressions that are composed of variables, terms, coefficients, constants and factors.

From the information given, we have the fraction;

4x + 8/x² + 5x + 6 × 3x + 9/4x + 20

To determine the product, let us reduce the expressions to their lowest forms, we have;

4x + 8 = 4(x + 2)

x² + 5x + 6 = (x + 2)(x + 3)

3x + 9 = 3(x +3)

4x + 20 = 4(x + 5)

Substitute the expressions

4(x + 2)/(x + 2)(x + 3)  × 3(x +3)/4(x + 5)

divide the common terms

4(x + 3) × 3(x + 3)/4(x + 5)

Divide further, we have.

3/x + 5

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The ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:

1/3.

The perimeter of a triangle is the total length of its three sides. To find the perimeter of a triangle, you need to add up the lengths of all three sides.

The ratio between the side lengths of triangle ABC and triangle XYZ is given as follows:

5/15 = 1/3.

The perimeter of a triangle is measured in units, as area the side lengths, hence they have the same ratio, and thus the ratio between the perimeter of triangle ABC and the perimeter of triangle XYZ is given as follows:

1/3.

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Answer: 49,000

48805 is greater than 48500, so it rounds to 49,000

Answer:

112

Step-by-step explanation:

According to the circle graph, the mystery books make up 20% of all books sold. So, we can calculate the number of mystery books sold as follows:

Number of mystery books = 20% of 560

= (20/100) x 560

= 112

Therefore, the number of mystery books sold at the book fair was 112.

Answer:

7/8 - 2/3 = 5/8 pint of water left in the bottle.

The gradient of the line is 5, and the y-intercept of the line is 15.

The given equation is in the form of y = mx + c, where m is the gradient (slope) of the line and c is the y-intercept of a straight line represented in 2D plane.

Rearranging the given equation, we get:

y - 6 = 5x + 9

Adding 6 to both sides, we get:

y = 5x + 15

Now we can see that the equation is in the required form of y = mx + c. The gradient (slope) of the line is 5, which is the coefficient of x in the equation. The y-intercept is 15, which is the constant term in the equation.

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