Twenty, which is 4 more than half, of the students in Bryan’s homeroom have tickets to attend the school’s musical. Choose Yes or No to tell whether each of the following equations can be used to find the number of students in Bryan’s homeroom.

Answer:

The answer is D on edge 2020.

Step-by-step explanation:

Answer:

[tex]3\frac{4}{5}[/tex] pounds of food

Step-by-step explanation:

We have been given that Rodney bought a 25-pound bag of dog food. His dog ate [tex]10\frac{2}{5}[/tex] pounds of the food in the first month and [tex]10\frac{4}{5}[/tex] pounds in the second month.  

Let us find the amount of dog-food eaten by dog in two months.

[tex]\text{Dog-food eaten in 2 months}=10\frac{2}{5}+10\frac{4}{5}[/tex]

[tex]\text{Dog-food eaten in 2 months}=\frac{52}{5}+\frac{54}{5}[/tex]

[tex]\text{Dog-food eaten in 2 months}=\frac{52+54}{5}[/tex]

[tex]\text{Dog-food eaten in 2 months}=\frac{106}{5}[/tex]

Now we will subtract amount of food eaten by dog from the amount of food initially to find the remaining amount of dog food.

[tex]\text{Remaining amount of dog-food}=25-\frac{106}{5}[/tex]

[tex]\text{Remaining amount of dog-food}=\frac{5*25}{5}-\frac{106}{5}[/tex]

[tex]\text{Remaining amount of dog-food}=\frac{125}{5}-\frac{106}{5}[/tex]

[tex]\text{Remaining amount of dog food}=\frac{125-106}{5}[/tex]

[tex]\text{Remaining amount of dog food}=\frac{19}{5}[/tex]

[tex]\text{Remaining amount of dog food}=3\frac{4}{5}[/tex]

Therefore, [tex]3\frac{4}{5}[/tex] pounds of food was remaining in the bag at the end of the two months.

The general formula to describe the variation: M varies jointly with the cube root of the difference B and b is [tex]M=k \sqrt[3]{(B-b)}[/tex]

What is joint variation?

When two (or more) other variables are held constant, joint variation occurs when one variable directly fluctuates as each of the other variables.

Given that;

M varies jointly with the cube root of the difference B and b

The difference of  B and b (B-b)

let K be the the constant of proportionality

cube root of the difference B and b, [tex]\sqrt[3]{(B-b)}[/tex]

Then we have [tex]M=k \sqrt[3]{(B-b)}[/tex]

[tex]\[ M = k \cdot \sqrt[3]{B - b} \][/tex]

In the given context, the formula [tex]\( M = k \cdot \sqrt[3]{B - b} \)[/tex] represents a joint variation between the variable M, the cube root of the difference between B and b, and a constant of proportionality (k).

Joint variation occurs when a variable is directly proportional to the product of two or more other variables, each raised to a specific power.

Breaking down the formula, [tex]\( \sqrt[3]{B - b} \)[/tex] signifies the cube root of the difference between B and b. This reflects the relationship where M is jointly influenced by both the magnitude and sign of the difference between B and b.

The constant of proportionality (k) is introduced to account for the specific numerical relationship between M and the cube root of the difference.

For a practical example, consider a scenario where M represents the volume of a gas, B is the initial pressure, and b is the final pressure. The formula captures how the volume varies jointly with the cube root of the pressure difference.

As the pressure difference increases, the cube root of the difference influences the volume of the gas, and the constant of proportionality ensures the appropriate scaling of this relationship.

The joint variation formula provides a concise representation of the complex relationship between the variables involved.

Answer:

The factor form of given expression is 3(x+8) so the required number is 3.

Step-by-step explanation:

The given expression is

[tex]3x+24[/tex]

Write the factors of each term.

[tex]3x+24=3\times x+3\times 8[/tex]

In both terms, 3 is a common factor.

Take out the common factor 3.

[tex]3x+24=3(x+8)[/tex]

The factor form of given expression is 3(x+8). The factor (x+8) is given, therefore the required number is 3.

Answer:

Option D - $5370.30

Step-by-step explanation:

Given : If the APY of a savings account is 5.3%, and if the principal in the savings account is $5100 for an entire year.

To find : What will be the balance of the savings account after all the interest is paid for the year?          

Solution :

First we find the interest he paid.

The interest formula is [tex]I=P\times R\times T[/tex]

Where, P is the principal P=$5100

R is the rate of interest R=5.3%=0.053

T is the time T=1 year

Substituting the values,

[tex]I=5100\times 0.053\times 1[/tex]              

[tex]I=\$270.3[/tex]                  

The balance of the saving account is the sum of interest paid and principal value.

Amount = Interest +Principal

Amount = $270.3 +$5100          

Amount = $5370.3

Therefore, Option D is correct.      

Final answer:

An example of a real-world situation with an additive relationship between two quantities is the distance traveled by a car and the time it takes. The equation that models this relationship is Distance = Time x Speed.

Explanation:

An example of a real-world situation with an additive relationship between two quantities is the distance traveled by a car and the time it takes. Let's say that the car travels at a constant speed of 60 miles per hour. We can create a table with three pairs of values:

Time (hours), Distance (miles)

1                              60,

2                            120,

3                             180

In this case, the equation that models the relationship between the time and distance is Distance = Time x Speed. Since the car travels at a constant speed of 60 miles per hour, the equation can be simplified to Distance = 60 x Time.

Let x be the number.

Twelve times the number x  is 12·x=12x.

The number 12x increased by four is 12x+4. This result is no more than twenty-three, then

12x+4≤23.

Answer: 12x+4≤23.

Final answer:

There are 252 different starting lineups possible if positions are not assigned, and 30,240 starting lineups are possible if positions are assigned.

Explanation:

For part A of the question, where positions are not assigned, we can calculate the number of different starting lineup combinations by using the combination formula. Since we are choosing 5 players out of 10 without regard to order, we use:

C(n, k) = n! / (k!(n-k)!)

Where n is the total number of players to choose from, and k is the number of players we want to choose. Therefore, we have:

C(10, 5) = 10! / (5! (10-5)!) = 252

There are 252 different starting lineups possible if positions are not assigned.

For part B, where positions are assigned, we use the permutation formula because the order in which we select the players matters. This formula is:

P(n, k) = n! / (n-k)!

Since the order in which the players are chosen matters, we have:

P(10, 5) = 10! / (10-5)! = 30,240

There are 30,240 different starting lineups possible with positions assigned.

Answer:

$192 is over in his check-register.

Step-by-step explanation:

Ferdinand wrote a check to pay his monthly cable bill = $96.00

He accidentally recorded it as a credit in his check register rather than as a debit.

When he receives his bank statement he found his bank statement balance is less than his check register, he should compare it  by debiting twice of the cable bill from balance of his check register.

96 × 2 = $192

Ferdinand would compare his check register to his monthly bank statement by subtracting $192 form his balance of check register.

The formula to find circumference of circle is given by

[tex] C =2\pi r [/tex]

Where r is radius of circle and pi =3.14

We are given Circumference here as 361π

Plugging the value in the formula :

[tex] 361\pi =2\pi r [/tex]

r=361/2 = 180.5

radius of circle is 180.5.

We know that Diameter is double of radius.

So diameter = 2*180.5 = 361

Answer: Diameter of circle is 361.

Based on the graph of f(x), the value of f '(3) is approximately 3.

Based on the graph of f(x) below, the value of f '(3) is approximately 3.

graph of f(x) with a tangent line drawn at x=3 and the slope of the tangent line labeled as 3.

To estimate the value of f '(3), we can approximate the slope of the tangent line to the graph at x=3. The slope of the tangent line represents the instantaneous rate of change of the function at that point, which is equal to the derivative of the function at that point.

To approximate the slope of the tangent line, we can choose two points on the line and use the rise-over-run formula. In this case, we can choose the points (2,2) and (4,4), which are two points on the tangent line that are close to x=3. The slope of the tangent line is then:

(4-2)/(4-2) = 2/2 = 1

Therefore, we can estimate that the value of f '(3) is approximately 1.

Note that this is just an estimate, since we are approximating the slope of the tangent line. If we were to calculate the exact derivative of f(x) at x=3, we might get a slightly different answer. However, this estimate is close enough for most practical purposes.

Final answer:

The experienced roofer and the beginning roofer together can complete the job in approximately 15.6 hours, which is found by adding their work rates and taking the reciprocal of the sum.

Explanation:

To find how long it takes for both an experienced and a beginning roofer to roof a house together, we need to sum their work rates and then find the reciprocal of that sum. We'll start by considering the work rates of both the experienced and the beginning roofer. The experienced roofer can roof a house in 26 hours, which means the roofer completes 1/26 of the job per hour. The beginning roofer completes the job in 39 hours, which is 1/39 of the job per hour.

Now, we can calculate their combined work rate:
1/26 + 1/39 = (39 + 26) / (26 * 39) = 65 / 1014 = 1/15.6

These two roofers together complete 1/15.6 of the job per hour. To find out how long it will take them to complete the job together, we take the reciprocal of this rate:
1 / (1/15.6) = 15.6 hours.

Therefore, it would take the experienced and beginning roofer combined around 15.6 hours to roof the house together.