Determine whether quantities vary directly or inversely and find the constant of variation.
A teacher grades 25 students essays in 4 hours. Assuming he grades at the same speed, how long will it take him to grade 35 essays?

To find similarity ratio a:b

We take the sides and make a proportion

[tex]\frac{height \ of \ smaller \ cone}{height \ of \ larger \ cone} = \frac{radius \ of \ smaller \ cone}{radius \ of \ larger \ cone}[/tex]

[tex]\frac{9}{15} = \frac{6}{10}[/tex]

[tex]\frac{3}{5} = \frac{3}{5}[/tex]

So the ratio a:b is 3:5

Answer:

Step-by-step explanation:

No time because the wall is already built

Data that is collected can be either categorical or numerical data.Categorical variables represent types of data which may be divided into groups.

December is the twelfth and last month of the year .The word December is a  categorical discrete data which is also known as qualitative, because it is a name instead of a number.Among the options given December is a month of a year.

The month of the year is December is a categorical data .

Arithmetic is the answer

Answer:

 286 possible outcomes.

Step-by-step explanation:

We have been given total 13 identical marbles

We need to select 10 out of 13

We will use combination:

[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]

here,n=13 and r=10 on substituting the values in the formula we get:

[tex]^13C_{10}=\frac{13!}{10!(13-10)!}[/tex]

[tex]^13C_{10}=\frac{13\cdot 12\cdot 11\cdot10!}{10!\cdot 3!}[/tex]

[tex]\Rightarrow ^13C_{10}=\frac{13\cdot12\cdot11}{3\cdot2\cdot1}[/tex]

[tex]\Rightarrow 286[/tex]

So, there are 286 possible outcomes.

Possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].

Further explanation:

The formula of combination can be expressed as,

[tex]\boxed{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex]

Given:

A bag contains [tex]13[/tex] identical marbles.

Calculation:

Suzy randomly picks [tex]10[/tex] marbles from a bag of [tex]13[/tex] identical marble.

The number of possible outcomes that she can select [tex]10[/tex] marbles can be obtained as,

[tex]{\text{Possible}}\,{\text{outcomes}} = {\,^{13}}{C_{10}}[/tex]

Substitute [tex]13[/tex] for [tex]n[/tex] and [tex]10[/tex] for [tex]r[/tex] in equation [tex]{^n{C_r} = \frac{{n!}}{{r!\left( {n - r} \right)!}}}[/tex] to obtain the possible outcomes that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles.

[tex]\begin{aligned}{\text{Possible}}\,{\text{outcomes}}&= {\,^{13}}{C_{10}} \\ &= \frac{{13!}}{{10!\left( {13 - 10} \right)!}} \\ &= \frac{{13!}}{{10!\left( {3!} \right)}} \\ &= \frac{{13 \times 12 \times 11 \times 10!}}{{10!\, \times 3 \times 2 \times 1}} \\ &= 286\\\end{aligned}[/tex]

Hence, possible number of outcome that she can select [tex]10[/tex] marbles from [tex]13[/tex] identical marbles are [tex]\boxed{286}[/tex].

Learn more:

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2. Learn more about range and domain of the function https://brainly.com/question/3412497

3. Learn more about profit and loss https://brainly.com/question/2479097

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Combination

Keywords: Suzy, picks, marbles, 13 identical marbles, 10 marbles, possible, outcomes, select, combination, randomly picks, a bag contains 13 marbles.

To find the possible integer lengths for diagonal AC in quadrilateral ABCD, the Triangle Inequality Theorem is used. Possible integer values for AC are constrained between the sum and the difference of the lengths of the sides forming triangles ABC and CDA, resulting in potential lengths of 4, 5, 6, and 7.

The question pertains to finding all possible integer values for the diagonal AC of a quadrilateral ABCD given the lengths of the sides. To determine the possible lengths of AC, we need to inspect the properties of triangles that could form within the quadrilateral upon drawing this diagonal. The quadrilateral could possibly be a rectangle, a square, or a parallelogram, but without further information, we assume it is an irregular quadrilateral.

By using the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side, we can determine possible values for AC. Since ABCD is a quadrilateral with sides AB = 3, BC = 6, CD = 4, and DA = 4, diagonal AC can create two triangles, ABC and CDA. For triangle ABC, the sum of sides AB and BC is 9, so AC must be less than 9. Similarly, for triangle CDA, the sum of sides CD and DA is 8, so AC must be less than 8. Therefore, the maximum value for AC is 7. However, AC must also be greater than the difference of the sides, 3 for triangle ABC and 0 for triangle CDA. This leaves us with possible integer values of 4, 5, 6, and 7 for AC.

This linear programming problem can be solved by graphing the given inequalities to determine the feasible region. If this region is empty, there are no solutions. If the function is unbounded in this region, the maximal value can be infinitely large.

To solve this linear programming problem, we first need to identify its feasible region which is defined by its constraints. The constraints of this problem are as follows:

By graphing these inequalities we can identify the feasible region as the intersection of these inequalities. If the feasible region is empty, it means that there is no solution that satisfies all the constraints. If the objective function p = x - 2y is unbounded, it means that the maximum value of p can be infinitely large within this feasible region. By investigating both these situations, we should be able to determine whether an optimal solution exists or not.

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Answer:

40

Step-by-step explanation:

So she has 12 cucumbers to make 3 jars of pickles.

She uses 4 cucumbers to make each jar. (Based on the equation 12➗3 =4)

Shawtyyyy better be using those pickles on burgers and not eating it raw.

So she has 10 jars right? Right, and you know she used 4 pickles per jar, so

we can get the answer by the equation of 10 x 4 = 40

Have a great day shawtayyyyyy!

Answer:

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct

Step-by-step explanation:

[tex]\frac{(x-7)(x+1)}{(x+1)(x-5)}[/tex]

In an rational expression , if we have same factors at the top and bottom  then we cancel it out

In our given rational expression we have x+1  at the top and  bottom

so we cancel out x+1

After cancelling out x+1, we are left with

[tex]\frac{(x-7)}{(x-5)}[/tex]

option D is correct

The range of the function (eˣ)/(eˣ+c) is the closed interval [0,1].

The range of the function f(x) = (eˣ)/(eˣ+c) can be determined by analyzing the behavior of the function as x approaches positive and negative infinity. When x tends to positive infinity, the term eˣ grows much faster than c, so the denominator approaches infinity. Therefore, the function approaches 1 as x tends to infinity.

Similarly, when x tends to negative infinity, the term eˣ approaches 0 much faster than c, so the denominator becomes negligible. As a result, the function approaches 0 when x tends to negative infinity.

Since the function approaches 0 at negative infinity and approaches 1 at positive infinity, the range of the function is the closed interval [0,1].

Answer:

A. 12 square units.

Step-by-step explanation:

We have been given graph of a triangle and we are asked to find the area of our given triangle.

Since we know that area of a triangle is half the product of height of triangle and base of the triangle.

[tex]\text{Area of triangle}=\frac{1}{2}*\text{Base*Height}[/tex]

We can see that MN is base of our triangle and LM is height of triangle, so let us find lengths of MN and LM using distance formula.

[tex]\text{Distance}=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\text{Distance between point M and N}=\sqrt{(3--1)^2+(-4--4)^2}[/tex]

[tex]\text{Distance between point M and N}=\sqrt{(3+1)^2+(-4+4)^2}[/tex]

[tex]\text{Distance between point M and N}=\sqrt{(4)^2+(0)^2}[/tex]

[tex]\text{Distance between point M and N}=4[/tex]

[tex]\text{Distance between point L and M}=\sqrt{(-1--1)^2+(-4-2)^2}[/tex]  

[tex]\text{Distance between point L and M}=\sqrt{(-1+1)^2+(-6)^2}[/tex]  

[tex]\text{Distance between point L and M}=\sqrt{0+36}[/tex]  

[tex]\text{Distance between point L and M}=6[/tex]  

Now let us substitute our side lengths is area formula.

[tex]\text{Area of triangle LMN}=\frac{1}{2}*4*6[/tex]

[tex]\text{Area of triangle LMN}=2*6[/tex]

[tex]\text{Area of triangle LMN}=12[/tex]

Therefore, area of triangle LMN is 12 square units and option A is the correct choice.

A person needing a car for a few weeks while visiting family out of state would most likely choose A. Car rental for its short-term flexibility and convenience.

Car rental is the ideal choice for short-term car needs while visiting family out of state.

It offers flexibility in terms of duration, allowing individuals to rent vehicles for specific periods, such as a few weeks, without the commitment of ownership or long-term contracts.

With a wide range of vehicle options and rental locations available, car rental services provide convenience and accessibility.

Additionally, rental agreements typically include insurance coverage and roadside assistance, offering peace of mind to travelers during their stay.

Overall, car rental meets the temporary transportation needs of visitors efficiently and effectively.

Complete Question:

A person needing a car for a few weeks while visiting family out of state would most likely choose which of the following?

A. Car rental

B. Car share

C. Carpool

D. Car lease

Answer:

A. Jenny's initial height above the surface of the water

Step-by-step explanation:

Given : The expression below represents Jenny's vertical height, in feet, above the surface of the water after x seconds. [tex]-16x^2 +12x+10.[/tex]

To Find: Which statement best describes the term 10?

Solution:

[tex]h(x)=-16x^2 +12x+10.[/tex]

Substitute x = 0 i.e.time = 0 seconds

[tex]h(x)=-16x^2 +12x+10.[/tex]

[tex]h(0)=-16(0)^2 +12(0)+10.[/tex]

[tex]h(0)=10[/tex]

so, at time 0 the height was 10

So, 10 is the initial height.

Thus Option A is correct.

A. 10 is Jenny's initial height above the surface of the water.

Answer:

The answer is C

Step-by-step explanation:

Boy likes mayonnaise:  

12

(12 + 18 + 5)

=  

12 /35

= 0.3429 ≈ 34%

Girl likes mayonnaise:  

14

(14 + 13 + 15)

=  

14 /42

= 0.3333 ≈ 33%

thus,

boys (34 of 100) > girls (33 of 100)