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The regular-size granola bar is 1 1/3 inches longer than the snack-size granola bar.

The regular-size granola bar has a volume of 4 cubic inches, while the snack-size bar has a volume of 3 cubic inches.

Since both bars have the same width and height, we can use the formula for the volume of a rectangular prism to find the length of each bar:

Regular-size bar: V = lwh = 4 cubic inches, w = 1 inch, h = 3/4 inch

l = V/wh = 4/(1 × 3/4) = 16/3 inches

Snack-size bar: V = lwh = 3 cubic inches, w = 1 inch, h = 3/4 inch

l = V/wh = 3/(1 × 3/4) = 4 inches

Therefore, the regular-size granola bar is (16/3 - 4) = 4/3 inches longer than the snack-size granola bar.

This can also be written as the mixed number 1 1/3 inches.

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Answer: 79

Step-by-step explanation:

63+65+73+×/4=79

multiply by 4 on both sides

201+x=280

subtract 201 from both sides

x= 79

If the population in the year 2007 is 111.3 million, then the population in the year 2044 will be 148.37 million.

In order to find the population in the year 2044, we use the population growth formula; which is : P = P₀ × (1 + r)ⁿ;

where P = future population, P₀ = initial population, r = annual growth rate, and n = number of years;

Substituting the values,

We get;

⇒ P = (111.3 million) × (1 + 0.0078)²⁰⁴⁴⁻²⁰⁰⁷;

Simplifying this expression,

We get;

⇒ P = (111.3 million) × (1.0078)³⁷;

⇒ P ≈ 148.37 million;

Therefore, the population in the year 2044 is estimated to be approximately 148.37 million.

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Answer:

Step-by-step explanation:

$314.50

The exponential function that model this situation is [tex]A(t) = 2500(1 + 0.035)^t.[/tex]

The account will have $5000 in 20 years.

Let A be the amount in the account after t years.

Then, we can model this situation with the function A(t) = 2500(1 + 0.035)^t with the use of compound intererst formula which is [tex]P = A*(1+r)^t[/tex]

To find when the account will have $5000, we can set A(t) = 5000 and solve:

5000 = 2500(1 + 0.035)^t

2 = (1.035)^t

Taking the natural logarithm:

ln(2) = t ln(1.035)

t = ln(2)/ln(1.035)

t = 20.148791684

t = 20 years.

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Answer:

1)  21 years

2) 26 years

Step-by-step explanation:

To model the account balance of Vanessa's account at t years, we can use an exponential function in the form:

[tex]\large\boxed{A(t) = A_0(1 + r)^t}[/tex]

where:

Given Vanessa invested $2500 into the account and it will increase in value by 3.5% each year:

Substitute these values into the formula to create an equation for A in terms of t:

[tex]A(t) = 2500(1 + 0.035)^t[/tex]

[tex]A(t) = 2500(1.035)^t[/tex]

To find when the account balance will be $5000, set A(t) equal to $5000 and solve for t:

[tex]A(t)=5000[/tex]

[tex]2500(1.035)^t=5000[/tex]

[tex](1.035)^t=\dfrac{5000}{2500}[/tex]

[tex](1.035)^t=2[/tex]

[tex]\ln (1.035)^t=\ln 2[/tex]

[tex]t \ln 1.035=\ln 2[/tex]

[tex]t=\dfrac{\ln 2}{ \ln 1.035}[/tex]

[tex]t=20.1487916...[/tex]

[tex]t=20.15\; \sf years\;(2\;d.p.)[/tex]

Therefore, it will take approximately 20.15 years for Vanessa's account to reach a value of $5000.

Since the interest rate is an annual rate of 3.5%, it means that the interest is applied once per year, at the end of the year. Therefore, we need to round up the number of years to the next whole number.

So Vanessa's account will have $5,000 after 21 years.

Note: After 20 years, the account balance will be $4,974.47. After 21 years, the account balance will be $5,148.58.

[tex]\hrulefill[/tex]

To model the increase in movie ticket prices over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the initial price of the ticket was $4.22 and the price has increased by 3.1% each year:

Substitute these values into the formula to create an equation for P in terms of t:

[tex]P(t) = 4.22(1 + 0.031)^t[/tex]

[tex]P(t) = 4.22(1.031)^t[/tex]

To find how many years until tickets cost $9.33, we can set P(t) equal to $9.33 and solve for t:

[tex]P(t)=9.33[/tex]

[tex]4.22(1.031)^t=9.33[/tex]

[tex](1.031)^t=\dfrac{9.33}{4.22}[/tex]

[tex]\ln (1.031)^t=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t \ln (1.031)=\ln \left(\dfrac{9.33}{4.22}\right)[/tex]

[tex]t =\dfrac{\ln \left(\dfrac{9.33}{4.22}\right)}{\ln (1.031)}[/tex]

[tex]t=25.9882262...[/tex]

Therefore, it will take approximately 26 years for movie ticket prices to reach $9.33, assuming the annual growth rate remains constant at 3.1%.

Step-by-step explanation:

3. Let P(t) be the number of people infected by the virus at time t (in days). We can model the situation with the following exponential function:

P(t) = 400 * 1.25^t

Here, 400 represents the initial number of infected people, and 1.25 represents the growth factor, since the virus is spreading to 25% more people each day.

To find the number of people infected after t days, we can substitute t = (log(3000) - log(400)) / log(1.25) into the equation:

P(t) = 400 * 1.25^t

P(t) = 400 * 1.25^((log(3000) - log(400)) / log(1.25))

P(t) ≈ 2,343

Therefore, approximately 2,343 people are infected when the total number of infections reaches 3000.

4. Let P(t) be the population of the town at time t (in years). We can model the situation with the following exponential function:

P(t) = 10,800 * 0.975^t

Here, 10,800 represents the initial population in 2002, and 0.975 represents the decay factor, since the population is decreasing at a rate of 2.5% each year.

To find when the population reaches half the 2002 value, we can set P(t) = 5,400 and solve for t:

5,400 = 10,800 * 0.975^t

0.5 = 0.975^t

log(0.5) = t * log(0.975)

t ≈ 28.2

Therefore, the population will reach half the 2002 value in approximately 28.2 years, which corresponds to the year 2030.

Answer:

3) 9.03 days

4)  27.38 years

Step-by-step explanation:

To model the spread of the virus over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 + r)^t}[/tex]

where:

Given the virus has infected 400 people in the town and is spreading to 25% more people each day:

Substitute these values into the formula to create a function for P in terms of t:

[tex]P(t) = 400(1 + 0.25)^t[/tex]

[tex]P(t) = 400(1.25)^t[/tex]

To find how many days it will take for 3000 people to be infected, set P(t) equal to 3000 and solve for t:

[tex]\begin{aligned}P(t)&=3000\\\implies 400(1.25)^t&=3000\\(1.25)^t&=7.5 \\\ln (1.25)^t&=\ln(7.5)\\t \ln (1.25)&=\ln(7.5)\\t &=\dfrac{\ln(7.5)}{\ln (1.25)}\\t&=9.02962693...\end{aligned}[/tex]

Therefore, it will take approximately 9.03 days for the virus to infect 3000 people, assuming the daily growth rate remains constant at 25%.

Note: After 9 days, 2980 people would be infected. After 10 days, 3725 people would be infected.

[tex]\hrulefill[/tex]

To model the population of the town over time, we can use an exponential function in the form:

[tex]\large\boxed{P(t) = P_0(1 - r)^t}[/tex]

where:

Given the initial population was 10,800 and the population has decreased at a rate of 2.5% each year:

Substitute these values into the formula to create a function for P in terms of t:

[tex]P(t) = 10800(1 -0.025)^t[/tex]

[tex]P(t) = 10800(0.975)^t[/tex]

To find how many days it will take for the population to halve, set P(t) equal to 5400 and solve for t:

[tex]\begin{aligned}P(t)&=5400\\\implies 10800(0.975)^t&=5400\\(0.975)^t&=0.5 \\\ln (0.975)^t&=\ln(0.5)\\t \ln (0.975)&=\ln(0.5)\\t &=\dfrac{\ln(0.5)}{\ln (0.975)}\\t&=27.3778512...\end{aligned}[/tex]

Therefore, it will take approximately 27.38 years for the population to reach half the 2002 value, assuming the annual decay rate remains constant at 2.5%.

The volume of water that the pool can hold is  150.72 cubic centimeters.

Remember that the volume of a cylinder of radius R and height H is:

V = pi*R²*H

Where pi = 3.14

For the pool we know that the height is H = 3ft, and the diameter is 8ft, then the radius is R = 8ft/2 = 4ft

Replacing that in the volume formula we will get:

V = 3.14*(4cm)²*3cm

V = 150.72 cubic centimeters.

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The height of rectangular prism B is 5 yards.

Let's first find the volume of rectangular prism B:

The volume of the solid figure = Volume of prism A + Volume of prism B

180 = 75 + length × width × height of prism B

105 = length × width × height of prism B

We know that the length of prism B is 7 yards and the width is 3 yards,

Substitute those values:

105 = 7 × 3 × height of prism B

105 = 21 × height of prism B

height of prism B = 105/21

height of prism B = 5

Therefore, the height of rectangular prism B is 5 yards.

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Step-by-step explanation:

It has

two sides 8x12

two sides 12x4

two sides 4x8           total 352 in^2

There are no solutions to the system of inequalities Option (d)

Inequalities are a fundamental concept in mathematics and are commonly used in solving problems that involve ranges of values.

A system of two inequalities is a set of two inequalities that are considered together. In this case, the system of inequalities is

y > 3x + 1

y < 3x - 3

The inequality y > 3x + 1 represents a line on the coordinate plane with a slope of 3 and a y-intercept of 1. The inequality y < 3x - 3 represents another line on the coordinate plane with a slope of 3 and a y-intercept of -3. We can draw these lines on the coordinate plane and shade the regions that satisfy each inequality.

The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

We can start by analyzing the inequality y > 3x + 1. This inequality represents the region above the line with a slope of 3 and a y-intercept of 1. Therefore, any point that is above this line satisfies this inequality.

Next, we analyze the inequality y < 3x - 3. This inequality represents the region below the line with a slope of 3 and a y-intercept of -3. Therefore, any point that is below this line satisfies this inequality.

To determine which values satisfy both inequalities, we need to find the region that satisfies both inequalities. This region is the intersection of the regions that satisfy each inequality.

When we analyze the regions that satisfy each inequality, we see that there is no region that satisfies both inequalities. Therefore, there are no values that satisfy the system of inequalities shown.

There are no solutions to the system of inequalities y > 3x + 1 and y < 3x - 3 by analyzing the regions that satisfy each inequality on a coordinate plane. The lack of a solution is determined by the fact that there is no region that satisfies both inequalities.

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Complete Question :

Which is true about the solution to the system of inequalities shown?

y > 3x + 1

y < 3x – 3

On a coordinate plane, 2 solid straight lines are shown. The first line has a positive slope and goes through (negative 2, negative 5) and (0, 1). Everything to the left of the line is shaded. The second line has a positive slope and goes through (0, negative 3) and (1, 0). Everything to the right of the line is shaded.

Options:

a)Only values that satisfy y > 3x + 1 are solutions.

b)Only values that satisfy y < 3x – 3 are solutions.

c)Values that satisfy either y > 3x + 1 or y < 3x – 3 are solutions.

d)There are no solutions.

Answer:

D

Step-by-step explanation:

The question that Diondra would ask that does not allow for variability is A. Which movie did her best friend like the most?

The other three questions ("How many awards did each movie win?", "What is the total dollar amount that each movie made from ticket sales?", and "How many weeks did each movie play in the theater?") all offer metrics by which a movie's popularity could be measured, and those measurements could vary from movie to movie.

However, the question about her best friend's favorite movie depends solely on the opinion of one individual, not a variable measure, and therefore doesn't allow for variability.

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a) The area of the entire trapezoidal rear window =  882 sq.in.

b) The fractional part of a complete circle is cleared on the rear window by the 18-inch wiper = 5/12

c) The area of the part of the rear window that is cleared by the wiper = 424.12 sq. in.

d) The percent of the area of the entire rear window is cleared by the wiper =  48.09%

We know that the formula for the area of trapezoid,

A = ((a + b) / 2) × h

Here, a = 36 in., b = 48 in. and height of the trapezoid h=21 in

Using above formula, the area of the entire trapezoidal rear window would be,

A = ((36 + 48) / 2) × 21

A = 882 sq.in.

Here, the 18-inch rear window wiper clears a 150° sector of a circle on the rear window.

We know that the measure of entire circle = 360°

So, the fractional part of a complete circle is cleared on the rear window by the 18-inch wiper would be,

150° / 360° = 5/12

Now we need to find the area of the part of the rear window that is cleared by the wiper.

We know that the formula for the area of sector of a circle is:

A = (θ/360) × πr²

Here, the central angle θ = 150° and radius r = 18 in.

A = (θ/360) × πr²

A = (150/360) × π × 18²

A = 424.12 sq. in.

Now we need to find the percent of the area of the entire rear window is cleared by the wiper.

P = [(area of the part of the rear window cleared by the wiper) / (area of the entire trapezoidal rear window)] × 100

P = (424.12 / 882) × 100

P = 48.09%

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The calculated value of the unit rate of the situation is (c) $12 per hour

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

$60.00 in 5 hours

This means that

Time = 5 hours

Total costs = $60.00

using the above as a guide, we have the following:

Unit rate = Total costs / time

substitute the known values in the above equation, so, we have the following representation

Unit rate = 60.00/5

Evaluate

Unit rate = 12

Hence, the unit rate of the situation is (c) $12 per hour

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If a top travels 8 centimeters each time it is spun and it is spun 7 times, the total distance it travels is 56 centimeters.

The total distance is determined by multiplication of the distance traveled per spin and the number of spins.

Multiplication involves the multiplicand, the multiplier, and the product.

The traveling distance per spun = 8 centimeters

The number of spinning of the top = 7 times

The total distance = 56 centimeters (8 x 7)

Thus, using multiplication, the total distance the top travels after the 7th spin is 56 centimeters.

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As far as a 5/1 ARM is concerned, note that the "1" refers to how often the rate can be adjusted after the initial fixed-rate period ends.

A 5/1 ARM is an adjustable rate mortgage loan (ARM) that has a fixed interest rate for the first five years. Following that, the 5/1 ARM transitions to an adjustable interest rate for the remainder of its term. The terms "variable" and "adjustable" are frequently used synonymously.

If you want a low monthly payment and don't expect to stay in your house for long, a 5/1 adjustable-rate mortgage (ARM) loan may be worth considering. For the first five years, rates on 5/1 ARMs are typically lower than rates on 30-year fixed-rate mortgages.

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The type of model that best fits the situation of a $500 raise in salary each year is a linear model.

In a linear model, the dependent variable changes a constant amount for constant increments of the independent variable.

In the given case, the dependent variable is the salary and the independent variable is the year.

You may build a table to show that for increments of 1 year the increments of the salary is $500:

Year         Salary        Change in year         Change in salary

2010           A                           -                                       -

2011           A + 500     2011 - 2010 = 1          A + 500 - 500 = 500

2012          A + 1,000   2012 - 2011 = 1          A + 1,000 - (A + 500) = 500

So, you can see that every year the salary increases the same amount ($500).

In general, a linear model is represented by the general equation y = mx + b, where x is the change of y per unit change of x, and b is the initial value (y-intercept).              

In this case, m = $500 and b is the starting salary: y = 500x + b.

The parabola y = x² scaled vertically by a factor of 1/10 gives y = x²/10

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

The parabola y = x² is scaled vertically by a factor of 1/10

The rule of this transformation is

Image = (x, ay)

Where

a = 1/10

So, we have

y = 1/10 * x²

Evaluate

y = x²/10

Hence, the image of the function is y = x²/10

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The total volume of the air space of spherical ball is A = 12.265625 inches³

Given data ,

Since each tennis ball has a diameter of 2.5 inches, the radius of each ball is 1.25 inches.

The air space around the balls can be thought of as a cylinder with a height equal to the diameter of one ball and a radius equal to the radius of one ball.

The height of the cylinder is 2.5 inches, and the radius is 1.25 inches.

The formula for the volume of a cylinder is:

V = πr²h

V = ( 3.14 ) ( 1.25 )² ( 7.5 )

V = 36.796875 inches³

where V is the volume, r is the radius, and h is the height.

So, the volume of the one ball is:

V₁ = ( 4/3 )π(1.25)³

V₁ = 8.177083 inches³

The total volume of three balls is = volume of 3 spherical balls

V₂ = 3V₁ = 3(8.177083) ≈ 24.53125 cubic inches

Therefore, the total volume of the air space around the three tennis balls is approximately A = 36.796875 inches³ - 24.53125 inches³

A = 12.265625 inches³

Hence , the volume of air space is A = 12.265625 inches³

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Answer:

In a geometric sequence, each term is found by multiplying the previous term by a constant value called the common ratio (r).

In this case, the first term (a₁) is 2, and the common ratio (r) can be found by dividing any term by its preceding term. Let's calculate it:

r = 6 / 2 = 3

Now, to find the 15th term (a₅₊₁₋₅), we can use the formula:

aₙ = a₁ * r^(n-1)

Substituting the values, we have:

a₁ = 2

r = 3

n = 15

a₁₅ = 2 * 3^(15-1)

Calculating the exponent first:

3^(15-1) = 3^14 = 4782969

Now, substituting this value back into the formula:

a₁₅ = 2 * 4782969

a₁₅ = 9565938

Therefore, the 15th term of the geometric sequence 2, 6, 18, ... is 9565938.

Step-by-step explanation:

Answer:

-10

Step-by-step explanation:

The required y-intercept of the line y = 4x - 10 is -10.

What is the intercept in the equation?

In the equation, the intercept is the value of the linear function where either of the variables is zero.

Here,

The equation y = 4x - 10 is in slope-intercept form, where the coefficient of x is the slope of the line, and the constant term is the y-intercept.

So, the y-intercept of the line y = 4x - 10 is -10. This means that the line intersects the y-axis at the point (0,-10). When x is 0, the value of y is -10, which is the y-intercept.

Thus, the required y-intercept of the line y = 4x - 10 is -10.

Answer:

24 cakes.

Step-by-step explanation:

6 cups of oil divided by 1/4 cup oil per cake = 24 cakes

6/(1/4) = 24

or 6/(0.25) = 24

She can make 24 cakes with 6 cups of oil.

Donna can expect her total monthly housing expenses to be approximately $842.71 for the first month after purchasing the house, assuming no tax benefits or amortization on the loan.

To calculate Donna's monthly housing expenses, we first need to determine the total amount of the mortgage. Since she puts down $25,000 on a $125,000 house, she will need to take out a mortgage for $100,000.

Next, we can calculate the annual cost of owning the house beyond the 5% cost of mortgage interest, which is given as 4.09% of the value of the house. So, 4.09% of $125,000 is:

0.0409 x $125,000 = $5,112.50

This means that Donna can expect to pay approximately $5,112.50 per year in additional expenses associated with owning the house.

To calculate the monthly cost, we simply divide this by 12:

$5,112.50 / 12 = $426.04

So, Donna can expect to pay approximately $426.04 per month in additional expenses associated with owning the house.

Adding the cost of the mortgage interest, we can calculate her total monthly housing expenses as follows:

Total monthly housing expenses = Mortgage interest + Additional annual costs / 12

Mortgage interest = 5% of $100,000 = $5,000 per year or $416.67 per month

Total monthly housing expenses = $416.67 + ($5,112.50 / 12) = $416.67 + $426.04 = $842.71

Hence, Donna can expect her total monthly housing expenses to be approximately $842.71

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The three equivalent equations are 2 + x = 5, x + 1 = 4 and -5 + x = -2. So, correct options are A, B and E.

Two equations are considered equivalent if they have the same solution set. In other words, if we solve both equations, we should get the same value for the variable.

To determine which of the given equations are equivalent, we need to solve them for x and see if they have the same solution.

Let's start with the first equation:

2 + x = 5

Subtract 2 from both sides:

x = 3

Now let's move on to the second equation:

x + 1 = 4

Subtract 1 from both sides:

x = 3

Notice that we got the same value of x for both equations, so they are equivalent.

Next, let's look at the third equation:

9 + x = 6

Subtract 9 from both sides:

x = -3

Since this value of x is different from the previous two equations, we can conclude that it is not equivalent to them.

Now, let's move on to the fourth equation:

x + (-4) = 7

Add 4 to both sides:

x = 11

This value of x is also different from the first two equations, so it is not equivalent to them.

Finally, let's look at the fifth equation:

-5 + x = -2

Add 5 to both sides:

x = 3

Notice that we got the same value of x as the first two equations, so this equation is also equivalent to them.

So, correct options are A, B and E.

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Complete question is:

Which of the following equations are equivalent? Select three options.

2 + x = 5

x + 1 = 4

9 + x = 6

x + (- 4) = 7

- 5 + x = - 2

Answer:

The answer is 33°

Yes you are correct

Step-by-step explanation:

angles on a straight line equal 180°

57+90+x=180

x+147=180

x=180-147

x=33°

Hi, I can't tell if there's a little square drawn in red to indicate that there's a right angle in the middle. There's some squiggly lines and so it's kind of hard to tell.

I am going to assume that there is. Let me know if there isn't.

The sum of these 3 angles would be 180 degrees.

As an equation, 57 + 90 + x = 180

Solve for x.

147 + x = 180

x = 33 degrees.

So this would be correct ASSUMING that there's a little red square drawn indicating that there's a right angle.

Answer:

just start scamming

Step-by-step explanation:

The surface area of the prism is 248.88 cm²

The area occupied by a three-dimensional object by its outer surface is called the surface area.

The surface area of a prism is expressed as;

SA = 2B + ph

where h is the height of the prism, B is the base area of the prism and P is the perimeter of the base.

Base area = 61.94 cm²

height = 5cm

perimeter = 5 × 5 = 25cm

SA = 2 × 61.94 + 25 × 5

SA = 123.88+ 125

SA = 248.88 cm²

Therefore the surface area of the prism is 258.88 cm²

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The probability of getting Blue then Green while spinning the wheel is

3 / 32

Probability is a branch of mathematics that helps us to understand the likelihood of an event occurring. It is represented by a number between 0 and 1, where 0 means the event is impossible and 1 means the event is certain. Probability can be used to make predictions and informed decisions in real-world situations.

From the given figure we can find out the following information

The probability of getting Blue While spinning the wheel = 3/8

The probability of getting Green While spinning the Wheel = 2 / 8

The probability of getting Blue then Green while spinning the wheel

= 3/8 * 2/8

= 6/64

= 3/32

Therefore, probability of getting Blue then Green while spinning the wheel is 3 / 32

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