Which factor of 24 can help you solve 24 divided by 4?

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 critical values t₀ for a two-sample t-test is ± 2.0.6

To find the critical values t₀ for a two-sample t-test to test the claim that the population means are equal (i.e., µ₁ = µ₂), we need to use the following formula:

t₀ = ± t_(α/2, df)

where t_(α/2, df) is the critical t-value with α/2 area in the right tail and df degrees of freedom.

The degrees of freedom are calculated as:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

n₁ = 14, n₂ = 12, X₁ = 6,X₂ = 7, s₁ = 2.5 and s₂ = 2.8

α = 0.05 (two-tailed)

First, we need to calculate the degrees of freedom:

df = (s₁²/n₁ + s₂²/n₂)² / [(s₁²/n₁)²/(n₁-1) + (s₂²/n₂)²/(n₂-1)]

= (2.5²/14 + 2.8²/12)² / [(2.5²/14)²/13 + (2.8²/12)²/11]

= 24.27

Since this is a two-tailed test with α = 0.05, we need to find the t-value with an area of 0.025 in each tail and df = 24.27.

From a t-distribution table, we find:

t_(0.025, 24.27) = 2.0639 (rounded to four decimal places)

Finally, we can calculate the critical values t₀:

t₀ = ± t_(α/2, df) = ± 2.0639

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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%.

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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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.