Erin spent $15.75 on ingredients for cookies she's making for the school bake sale. How many cookies must she sell at $0.60 apiece to make a profit?

Answer:

\(3 \times \frac{1}{3 } + \frac{1}{2} \times - 12( \frac{1}{3} ) = \frac{1}{3} \)

The association between the MIF-173 G>C polymorphism and prostate cancer in Southern Chinese population has been the subject of research in the field of surgical oncology.

MIF (Macrophage Migration Inhibitory Factor) is a cytokine that has been implicated in various physiological and pathological processes, including cancer development and progression.

The MIF-173 G>C polymorphism refers to a genetic variation at position 173 in the MIF gene, where a guanine (G) nucleotide can be replaced by a cytosine (C) nucleotide.

These studies aim to understand whether the presence of this genetic variant is associated with an increased risk of developing prostate cancer or has any impact on the progression or prognosis of the disease in this

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The expression \(\sqrt[3]{8^{x} }\) is equivalent to, \(8^{x/3}\), So Option C is correct

An expression is a sentence with at least two numbers or variables having mathematical operation. Math operations can be addition, subtraction, multiplication, division.

For example, 2x+3

Given that,

An expression,  \(\sqrt[3]{8^{x} }\)

equivalent expression = ?

⇒   \(\sqrt[3]{8^{x} }\)

⇒  \(\sqrt[3]\)cube root can be written as 1/3 power of 8

So, expression will convert like this,

⇒   \(8^{x/3}\)

Hence, the equivalent expression is  \(8^{x/3}\)

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Elena's speed on the circular running track is 0.12 miles per hour

From the question, we have the following parameters that can be used in our computation:

Distance = 14 miles

Time to cover this distance = 120 of an hour

The above parameters mean that

Distance = 14 miles

Time = 120 hours

Elena's speed on the circular running track is then calculated as

Speed = 14 miles/120 hours

Evaluate the quotient

Speed = 0.12 miles per hours

Hence, the speed is 0.12 miles per hour

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The probability that a person arriving to use the machine will find it idle is 1/3 or 0.3333. Option a is correct.

Use the concept of an M/M/1 queue to calculate the probability, which models a single-server queue with exponential interarrival times and exponential service times.

In this case, the interarrival time follows an exponential distribution with a rate parameter of λ = 5 persons per hour (or 1/12 persons per minute). The service time (copying time) also follows an exponential distribution with a rate parameter of μ = 1/8 persons per minute (since each person uses the machine for an average of 8 minutes).

In an M/M/1 queue, the probability that the system is idle (no person is being served) can be calculated as:

P_idle = ρ⁰ × (1 - ρ), where ρ is the traffic intensity, defined as the ratio of the arrival rate to the service rate. In this case, ρ = λ/μ.

Plugging in the values, we have:

ρ = (1/12) / (1/8) = 2/3

P_idle = (2/3)⁰ × (1 - 2/3) = 1/3

Therefore, the probability is 1/3 or approximately 0.3333.

Thus, option (A) is the correct answer.

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Answer:

120

Step-by-step explanation:

Answer: The function rule C = 9n + 45 represents the cost of the shirts that the Math Club is selling. The variable C represents the total cost of the order and the variable n represents the number of shirts.

The number 9 in the function represents the price per shirt, this is because as the number of shirts increases by 1, the total cost increases by 9. This tells us that the cost of each shirt is $9.

The number 45 in the function represents the initial set-up fee charged to design the shirts. This is because even if no shirts are ordered, there is still a cost of $45. This represents a fixed cost that the Math Club must pay to have the shirts designed.

Step-by-step explanation:

Answer:

y= \(\frac{3x}{4}\) + \(\frac{1}{4}\)

you first find the gradient of the line by picking out any two coordinates then u fill the values in the equation of a line

Answer:

31.4 in

Step-by-step explanation:

the formula for circumference is 2*\(\pi\)*radius. Since the diameter (which is the radius multiplied by 2) is labeled we can divide 10 by 2 to get the radius. 10/2 is 5. Since pi is an infinite number, we round it to 3.14. Then, plug in the numbers. The expression will be 2*3.14*5. 2* = 10 and 10 * 3.14 you can just move the decimal so the answer is 31.4.

Given equation:

By using middle term factirization we get,

So, the roots are real and same.

Thus, the equation have a repeated real rools.

Answer: Option (A)

Answer:

-125 is the answer!!!!!!!!!!!!!

Step-by-step explanation:

:)

The simplest factorial design contains 2 independent variables with 2 conditions. The answer is option B.

A factorial design is a study in which two or more independent variables are manipulated to see their impact on the dependent variable. The simplest factorial design contains two independent variables, each with two conditions, for a total of four conditions. This is referred to as a 2x2 factorial design. The factors analyzed in such a design are the primary factor: Factor A, which has two levels, is known as the primary factor or the rows, and the secondary factor: Factor B, which has two levels, is referred to as the secondary factor or the columns.

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Answer:

56.52 inches

Step-by-step explanation:

pi is the ratio of the circumference to the diameter so you can simply multiply the diameter by pi to get the circumference which is 3.14 * 18 = 56.52

Answer:

You could drive 2805 miles on 55 gallons of gas

The car's gas mileage is 51 miles per gallon

Step-by-step explanation:

First, find the gas mileage by dividing the given number of miles by the number of gallons:

510/10

= 51

The car's gas mileage is 51 miles.

Find how far you can drive on 55 gallons of gas by multiplying 51 by 55

51(55)

= 2805

So, you can drive 2805 miles.

The area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

a. To find the area to the right of z = -1 for the standard normal distribution, we need to calculate the cumulative probability using the standard normal distribution table or a statistical calculator.

From the standard normal distribution table, the area to the left of z = -1 is 0.1587. Since we want the area to the right of z = -1, we subtract the left area from 1:

Area to the right of z = -1 = 1 - 0.1587 = 0.8413

Therefore, the area to the right of z = -1 for the standard normal distribution is approximately 0.8413.

b. To answer this question, we would need additional information about the mean and standard deviation of the annual salaries for first-year college graduates. Without this information, we cannot calculate specific probabilities or make any statistical inferences.

If we are provided with the mean (μ) and standard deviation (σ) of the annual salaries for first-year college graduates, we could use the properties of the normal distribution to calculate probabilities or make statistical conclusions. Please provide the necessary information, and I would be happy to assist you further.

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Answer: 7

Step-by-step explanation:

7+4+(3)^2-5(3)+2=

11+9-15+2=

20-15+2=7

\(\huge\text{Hey there!}\)

\(\mathsf{7 + 4 + f^2 - 5f + 2}\)

\(\mathsf{= 7 + 4 + 3^2 - 5(3) + 2}\)

\(\mathsf{= 7 + 4 + 9 - 15 + 2}\)

\(\mathsf{= 11 + 9 - 15 + 2}\)

\(\mathsf{= 20 - 15 + 2}\)

\(\mathsf{= 5 + 2}\)

\(\mathsf{= 7}\)

\(\huge\textbf{Therefore, your answer should be: }\)

\(\huge\boxed{\mathsf{7}}\huge\checkmark\)

\(\huge\text{Good luck on your assignment \& enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

The probability of having 7 boys in a family with 7 children is 1 out of 128, as there is only one favorable outcome out of 128 total possible outcomes.

To find the probability, we need to calculate n(E) and n(S).

In this case, event E represents the scenario where all 7 children are boys. The sample space S consists of all possible permutations of boys and girls for the 7 children, which is 2^7 = 128.

This is because each child has 2 possibilities (boy or girl), and we multiply these possibilities for all 7 children.

Since event E includes only one specific outcome (all boys), n(E) is equal to 1. Therefore, both n(E) and n(S) are 1 and 128, respectively. The probability of having 7 boys is given by n(E)/n(S) = 1/128.

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Answer:

200/3n

Step-by-step explanation:

It is a strangely worded question but you are dividing the paper in 3's n times so 3n will be part of the answer and you are dividing 200. So, the answer is 200/3n.

Answer:

Kindly check explanation

Step-by-step explanation:

Sale before fundraiser = 32

Sale on the day of fundraiser = c

Cost of each carnation sold = 0.25

(Cost * sale before fundraiser) + cost * sale on day of fundraiser

(0.25 * 32) + 0.25 * c

8 + 0.25c

Or

Total carnation sold * cost per carnation

(sale before fundraiser + sale on day of fundraiser) * cost per carnation

(32 + c) * 0.25

Yes, these facts make a prima facie case of trespass since Durfee's shoe, thrown from her side of the line, landed on Plunkett's property. This suggests that an unauthorized entry or interference with Plunkett's property has occurred.

Based on the given facts, there is a prima facie case of trespass. Durfee threw a shoe at the cat from her side of the property line, indicating an intentional act directed towards the cat, which was located on the fence between the properties. The fact that the shoe fell on Plunkett's property implies that the shoe crossed onto Plunkett's territory without permission. This intrusion onto Plunkett's property without lawful authority constitutes a prima facie case of trespass, suggesting a potential violation of property rights.

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Equivalent expressions are expressions with equal values

The decimal equivalent to 120% is 1.20

The percentage is given as:

n = 120%

Express as fraction

\(n = \frac{120}{100}\)

Divide

n =1.20

Hence, the decimal equivalent to 120% is 1.20

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Answer:

The answers are B and D

The investment problem is modeled by an initial value problem (IVP) where the rate of change of the investment is determined by the initial investment, monthly deposits, and the interest rate.

a) The investment problem can be modeled by an initial value problem where the rate of change of the investment, y(t), is given by the initial investment, monthly deposits, and the interest rate. The IVP can be written as:

dy/dt = 0.09y + 200, y(0) = 500.

b) To solve the IVP, we can use an integrating factor to rewrite the equation in the form dy/dt + P(t)y = Q(t), where P(t) = 0.09 and Q(t) = 200. Solving this linear first-order differential equation, we obtain the solution for y(t).

c) To find the value of the investment after 2 years, we substitute t = 2 into the obtained solution for y(t) and calculate the corresponding value.

d) After 2 years, the monthly deposit increases to $300. To find the value of the investment a year later, we substitute t = 3 into the solution and calculate the value accordingly.

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Answer:

63 m^2 would be your answer

Step-by-step explanation:

finding the area is preety easy

look at pic

The ratio of the capacities of the two similar cups found using the Volume of cylinder is: 2/3.

A cylinder's volume refers to the amount of interior room it has to hold a given quantity of material. In simplest language, the capacity of such a cylinder to hold an object is its volume. You can store any one of the three forms of matter—solid, liquid, or gas—within the confines of a cylinder.

A cylinder's volume refers to the amount of interior room it has to hold a given quantity of material. To put it another way, a cylinder's volume is how much it can hold.

As the two cups are similar, their radii will be same say 'r'.

Let the height of cup1 be h1 and cup 2 be h2.

Then,

h₁/h₂ = 2/3

h₂  = 1.5 h₁

ratio of their capacities:

Volume of cup1 / volume of cup 2

V1 / V2 = πr²h₁ / πr²h₂

Cancelling the same values:

V1 / V2 = h₁ / h₂

V1 / V2 = h₁ / 1.5 h₁

h₁ will get cancelled.

V1 /V2 = 2/3

Thus, the ratio of capacities of the two similar cups found using the Volume of cylinder is: 2/3.

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Answer:

\(Blue = \frac{8}{9}\)

Step-by-step explanation:

Given

\(Yellow = 1ft^2\)

\(Blue = 8z^{-1\)

Required

Evaluate Blue when z = 9

To do this, we simply substitute 9 for z in \(Blue = 8z^{-1\)

\(Blue = 8 * 9^{-1\)

Convert indices to fraction

\(Blue = 8 * \frac{1}{9}\)

\(Blue = \frac{8}{9}\)

Hence, the blue section has an area of \(\frac{8}{9}ft^2\)

Answer:

The null hypothesis describes the population parameters represented by the sample data if the predicted relationship does not exist.

Step-by-step explanation:

1. If a > 1, the range is (0, +∞).

2. If 0 < a < 1, the range is (0, +∞), but the function approaches 0 as x approaches infinity.

The range of the exponential function f(x) = ax, where a > 0 and a ≠ 1, depends on the sign of the coefficient a.

If a > 1, then the range of the function is (0, +∞), meaning it takes on all positive values and approaches infinity as x increases.

If 0 < a < 1, then the range of the function is (0, +∞), but the function approaches 0 as x approaches infinity. In other words, the function takes on positive values but becomes arbitrarily close to 0 as x increases.

In summary:

1.If a > 1, the range is (0, +∞).

2.If 0 < a < 1, the range is (0, +∞), but the function approaches 0 as x approaches infinity.

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Answer:

No.

In a right triangle one of the angles is right angle i.e 90° and, therefore, sum of other two angles will always be equal to 90°, which means the other two angles will be acute angles