In what ways do you think presidents today are more powerful than they were in the past?

Final answer:

The probability of randomly choosing a girl or a freshman from the class is 0.916 or 91.6%. This is calculated by considering the total number of girls and freshmen in the class, while avoiding double-counting freshman girls in the calculation.

Explanation:

To calculate the probability that a randomly chosen student from the class is either a girl or a freshman, we need to consider the total number of students in the class, as well as the number of girls and the number of freshmen. The class consists of 15 boys and 21 girls, totaling 36 students. Out of these, 12 boys are freshmen and 15 girls are freshmen, but we must avoid double-counting the girls who are also freshmen.

First, we calculate the total number of freshmen: 12 boys + 15 girls = 27 freshmen. Next, we calculate the probability of picking a girl: 21 girls / 36 total students = 0.583 (to three decimal places). We then calculate the probability of picking a freshman: 27 freshmen / 36 total students = 0.750. However, since the freshmen include both boys and girls, we must subtract the probability of picking a freshman girl to avoid double-counting: 15 girls who are freshmen / 36 total students = 0.417.

Finally, we add the probability of picking a girl and the probability of picking a freshman, and subtract the probability of picking a freshman girl to obtain the inclusive probability: 0.583 (girl) + 0.750 (freshman) - 0.417 (freshman girl) = 0.916.

Therefore, the probability that a randomly chosen student is either a girl or a freshman is 0.916, or 91.6%.

The volume of the glass shell of the jar is 0.0136 ft³ and its weight is 2.24 lbs. The weight and volume of the water it will displace amounts to 2.24 lbs and 0.036 ft³ respectively. Consequently, the jar will sink approximately 2.2 inches into the water.

To begin, the volume of the glass shell of the jar will first need to be established. Given that the thickness of the glass is 3/16 inches, the outer radius of the jar is 3 inches + 3/16 inches = 3.1875 inches. To get the volume, utilise the formula for the volume of a cylinder, which is πr²h. Thus, with measurements converted to feet for the calculations (1 inch = 0.08333 foot), we have an external volume of π(0.265625 ft)² * 0.5 ft = 0.1118 ft³ and an internal volume of π(0.25 ft)² * 0.5 ft = 0.0982 ft³. Hence, the volume of glass is 0.1118 ft³ - 0.0982 ft³ = 0.0136 ft³

Next, the weight of the jar is determined by the formula mass = volume * density, so mass = 0.0136 ft³ * 165 lb/ft³ = 2.24 lbs.

To ascertain the weight of water the jar will displace, we consider the principle of buoyancy, which suggests that an object will displace a volume of fluid with a weight equal to its own weight. Thus, the weight of the water displaced is 2.24 lbs.

Then, the volume of this water is found with the formula volume = weight/density -> volume = 2.24 lbs / 62.5 lb/ft³ = 0.036 ft³.

Lastly, considering the jar will sink until the weight of the water being moved equals the weight of the jar. The volume of the water displaced equates to the submerged volume of the jar. Its depth in feet is then the volume divided by the cross-sectional area of the jar (internal radius), so the distance the jar sinks is roughly 0.036 ft³ / π(0.25 ft)²  = 0.18 ft -> convert to inches = 2.2 inches.

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Final answer:

Molly can purchase a maximum of 15 school lunches per month with a budget of $30, considering each lunch costs $1.95.

Explanation:

The question asks how many school lunches Molly can buy if each lunch costs $1.95 and she wants to spend no more than $30 each month. To find out how many lunches Molly can buy, we divide her monthly budget by the cost of one lunch.

So, we perform the calculation: $30 ÷ $1.95 ≈ 15.38. Since Molly cannot buy a fraction of a lunch, we round down to the nearest whole number, which means Molly can buy 15 lunches at most in a month without exceeding her budget.

Answer:

[tex]-3x^5y^2+4x^3y+10x^2[/tex]

Step-by-step explanation:

A polynomial in two variables is in standard form if its monomial from left to right are arrangerd in descending order. We say that a monomial [tex]x^ay^b[/tex] is greater than a monomial [tex]x^{a^{\prime}}y^{b^{\prime}}[/tex] if [tex]a+b > a^{\prime} + b^{\prime}[/tex] or [tex]a+b=a^{\prime}+b^{\prime} \quad \text{and} \quad (a,b)>(a^{\prime},b^{\prime}})[/tex] in the alphabetical order.

For example

[tex]x^2y>xy \quad \text{since} \quad 2+1>1+1 \\\\x^2y>xy^2 \quad \text{since} \quad 2+1=1+2 \quad \text{and} \quad 2>1[/tex]

The polynomial [tex]-3x^5y^2+4x^3y+10x^2[/tex] is in standard form, since [tex]x^5y^2 > x^3y >x^2[/tex]. On the other hand, the polynomial [tex]-8xy^2+4x^4y^2+3x^3[/tex] is not in standard form since [tex]x^4y^2>xy^2.[/tex]

The value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.

It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x

where a is a constant and a>1

It is given that:

The dollar value v(t) of a certain car model that is t years old is given by the exponential function.

[tex]\rm V(t)=24,500(0.95^t)[/tex]

The initial value plug t = 0 in the above function:

V(0) = $24500

Plug t = 13 years in the above exponential function

[tex]\rm V(13)=24,500(0.95^1^3)[/tex]

After calculating, we get:

V(13) = 12576.88

V(13) = 12576.9 dollars

Thus, the value after 13 years will be 12576.9 dollars if the dollar value v(t) of a certain car model that is t years old is represented by the exponential function.

Learn more about the exponential function here:

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Answer: both of u are wrong its one unit shift up one unit shift down

The correct answer is (x - 6)2 = 94

Answer:

A for me

Step-by-step explanation:

The smaller number is 82 and the larger number is 158.

Given that, the sum of two numbers is 240.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the smaller number be x.

The larger number is 6 less than twice the smaller.

Larger number = 2x - 6

Now, the sum of two numbers is 240.

So, x+2x-6 = 240

⇒ 3x - 6 =240

⇒ 3x = 246

⇒ x = 82

Larger number = 240 - 82

= 158

Therefore, the smaller number is 82 and the larger number is 158.

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