for a different pizza dough recipe, the equation f=2.5w represents the number of cups of flour, f, that you need for w cups of water. what is the constant of proportionality? explain what it means in this context.

Final answer:

The incorrect statement is that the nucleus of an atom contains protons and electrons; actually, the nucleus contains protons and neutrons, with electrons orbiting around it.

Explanation:

The statement that does not correctly describe the structure of an atom is 'Inside the nucleus of an atom are protons and electrons'. This statement is incorrect because the nucleus of an atom actually contains protons and neutrons, not electrons. Electrons are negatively charged sub-atomic particles that orbit around the nucleus. The nucleus itself is a small, dense center that is positively charged due to the presence of protons, which are positively charged. Neutrons, which have no electric charge, are also found within the nucleus.

Further expanding on atomic structure, the nucleus is very tiny compared to the rest of the atom, which is mostly empty space. The electrons residing in this space are in perpetual motion, creating a cloud-like region around the nucleus. Despite their small mass compared to protons and neutrons, the number of electrons equals the number of protons in a neutral atom, balancing the charge.

Part A: Alligators: [tex]\(A(t) = 20 \times (1 + 0.25)^t\), Crocodiles: \(C(t) = 25 + 10t\).[/tex]

Part B: After 4 years: Alligators: ~38, Crocodiles: 65.

Part C: Alligators and crocodiles equal: Solve [tex]\(20 \times (1 + 0.25)^t = 25 + 10t\).[/tex]

Part A:

Let's define the functions to represent the number of alligators and crocodiles in the swamp over the years.

For alligators:

[tex]\[A(t) = A_0 \times (1 + r)^t\][/tex]

Where:

[tex]- \(A(t)\) is the number of alligators in the swamp after \(t\) years.\\- \(A_0\) is the initial number of alligators (20 in this case).\\- \(r\) is the growth rate per year (25% or 0.25).\\- \(t\) is the number of years.[/tex]

For crocodiles:

[tex]\[C(t) = C_0 + n \times t\][/tex]

Where:

[tex]- \(C(t)\) is the number of crocodiles in the swamp after \(t\) years.\\- \(C_0\) is the initial number of crocodiles (25 in this case).\\- \(n\) is the number of new crocodiles joining each year (10 in this case).\\- \(t\) is the number of years.[/tex]

Part B:

To find the number of alligators after 4 years, we use the formula:

[tex]\[A(4) = 20 \times (1 + 0.25)^4\][/tex]

To find the number of crocodiles after 4 years, we use the formula:

[tex]\[C(4) = 25 + 10 \times 4\][/tex]

Part C:

To find when the number of alligators and crocodiles are the same, we set [tex]\(A(t) = C(t)\) and solve for \(t\).[/tex]

[tex]\[20 \times (1 + 0.25)^t = 25 + 10 \times t\][/tex]

This equation can be solved numerically to find the value of \(t\) when the number of alligators and crocodiles are the same.

Answer:

Having a savings account can contribute to a person’s overall financial well-being. Which one of the following is NOT a benefit of maintaining a savings account?

a.

A savings account provides security in tough financial times

b.

With a savings account, you can invest when the opportunity presents itself

c.

Having a savings account gives individuals the ability to borrow money from members in the community

d.

A savings account allows an individual to fulfill life long dreams

Step-by-step explanation:

C) Having a savings account gives individuals the ability to borrow money from members in the community

length of AC = 10 * sin(30) = 5 cm

Length of CD = 5 /tan(25) = 10.7cm

 answer is C

Answer

Find out the what is the length of CD , AC .

To prove

By using the trignometric identity

[tex]sin B = \frac{Perpendicular}{Hypotenuse}[/tex]

As in ΔABC

∠ B = 30° , AB= 10 cm

put in the trignometric identity

[tex]sin 30^{\circ} = \frac{AC}{10}[/tex]

As

[tex]sin30^{\circ} =\frac{1}{2}[/tex]

[tex]\frac{1}{2} = \frac{AC}{10}[/tex]

[tex]AC = \frac{10}{2}[/tex]

AC = 5cm

Now in the ΔADC

[tex]tan D^{\circ} = \frac{Perpendicular}{Base}[/tex]

∠ D = 25° , AC = Perpendicular = 5 cm

[tex]tan 25^{\circ} = \frac{5}{CD}[/tex]

tan 25 ° =  0.46630765815 (approx)

[tex]CD = \frac{5}{0.46630765815}[/tex]

CD = 10 .7cm ( approx )

Option (C) is correct .

To determine the extent of how many times greater is the number of bacteria in petri dish A than petri dish B, we simply have to take the ratio of the two.

1.75 x 10^18 / 6.25 x 10^15 = 280

So the bacteria in petri dish A is 280 times larger.

In scientific notation:

2.8 x 10^2

Answer:

280 is the answer, I did the test.

Solution:

we have been asked to find that , how many times one number is to the other given numbers.

To do this we will divide the larger number by the smaller number and the resulting number will be the answer of the question.

Here the larger number is [tex]8.5\times10^8[/tex]

The smaller number is [tex]3.4\times 10^5[/tex]

Now lets divide as follows

[tex]\frac{8.5\times10^8}{3.4\times 10^5} =\frac{8.5}{3.4}\times 10^{8-5}\\ \\\frac{8.5\times10^8}{3.4\times 10^5} =2.5\times10^3=2500[/tex]

Hence the correct option is C.

Answer:

The average rate of change of a function f(x) in the first two seconds is 25.

Step-by-step explanation:

Given : Graph , X represent the time , function f(x).

To find : the average rate of change of a function f(x) in the first two seconds is____.

Solution : The rate of change of f(x) with respect to x is the slope of the line.

slope : [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].

In first two second  ( 0, 50 ) , ( 2, 100).

slope : [tex]\frac{100-50}{2-0}[/tex].

slope : [tex]\frac{50}{2 }[/tex].

the average rate of change of a function f(x) in the first two seconds is 25.

Therefore,The average rate of change of a function f(x) in the first two seconds is 25.

Answer:

i need the equation I know that the distance is 105 miles

Step-by-step explanation:

helppppp

Janet has to pay off $65 to reduce her balance to no more than $60.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that Janet has a balance of 125 on a credit card on her next statement she wants to reduce her balance to no more than 60.

The amount to be paid will be calculated as,

Amount = 125 - 60

Amount = $65

To know more about an expression follow

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For combined classes of Ms. Zombo's and Mr. Stolarski's, the number of boys and girls are determined based on their respective ratios and total number of students. The combined ratio of boys to girls is 29:18.

The question asks for the combined ratio of boys to girls in both Ms. Zombo's and Mr. Stolarski's classes. Firstly, identify the number of boys and girls in each class based on the given ratio and total students. In Ms.Zombo's class, the ratio of boys to girls is 33:22, and there are total 15 students. So, the number of boys is (33/(33+22))*15= 9 boys and 6 girls. Similarly, in Mr.Stolarski's class the ratio is 55:33, there are 32 students, so there are (55/(55+33))*32 =20 boys and 12 girls.

Next step is to combine the classes. The total number of boys from both classes is 9 (from Ms. Zombo's class) + 20 (from Mr.Stolarski's class) = 29 boys. The total number of girls is 6 (from Ms. Zombo's class) + 12 (from Mr.Stolarski's class) =18 girls.

Therefore, the combined ratio of boys to girls from both classes is 29:18.

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Answer:

40 Miles.

5 hrs.

----------

2

Answer:

The correct option is C) Both plans will work for achieving the goal.

Step-by-step explanation:

Consider the provided information.

Plan A: Save $450 over the next 8 weeks by working 9 hours per week at $7.20 per hour.

For next 8 weeks by working 9 hours per week at $7.20 per hour, you will earn:

[tex]8 \times 9 \times 7.20 = 518.40[/tex]

We need to save $450 which is less than $518.40. Thus, plan A will work.

Plan B: Save $450 over the next 6 weeks by working 15 hours per week at $6.50 per hour.

For next 6 weeks by working 15 hours per week at $6.50 per hour, you will earn:

[tex]6 \times 15 \times 6.50 = $585.00[/tex]

We need to save $450 which is less than $585.00. Thus, plan B will work.

Hence, the correct option is C) Both plans will work for achieving the goal.

Answer:

the correct answer is B.-2/3

$65 * 6 = $390 total monthly payments made

The downpayment made is $125, so the total balance at the end is:

balance = $513 – ($125 + $390)

balance = - $2

There is an excess of 2 dollars at the end.

Sheila's balance at the beginning of the seventh month will be approximately $393.95 after considering the deferred payment and applying the interest rate.

To determine the balance at the beginning of the seventh month, follow these steps:

So, Sheila’s balance at the beginning of the seventh month is approximately $393.95.