Last year, the number of students at RSM increased by 100%. This year, the number of students increased by 150%. What percent of the number of students now equals the number of students two years ago?.

The number of students at the mariemont middle school in whole number is 360 students.

Exponents refers to the power to which a number, symbol or expression is to be raised.

Number of students at the mariemont middle school = 2³ × 3² × 5

= (2 × 2 × 2) × (3 × 3) × 5

= 8 × 9 × 5

= 360 students

In conclusion, there are 360 total number of students in mariemont middle school.

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(a) Fermat's Little Theorem states that for any prime number p and any integer a not divisible by p, a^(p-1) ≡ 1 (mod p).

Euler's totient function, denoted by φ(n), is the number of positive integers less than or equal to n that are relatively prime ton. For example, φ(10) = 4, since there are four numbers (1, 3, 7, and 9) that are relatively prime to 10.

Euler's Theorem states that for any integer a and any positive integer n relatively prime to a, a^φ(n) ≡ 1 (mod n).

(b) To simplify an expression using these theorems, we first check if the modulus n is a prime number or not. If it is a prime, we can use Fermat's Little Theorem to simplify the expression. For example, if we want to simplify 2^100 (mod 7), we can use Fermat's Little Theorem as follows:

2^6 ≡ 1 (mod 7)

Therefore, 2^100 ≡ (2^6) ^16 * 2^4 ≡ 1^16 * 16 ≡ 2 (mod 7)

If the modulus n is not a prime number, we can use Euler's Totient Function to simplify the expression. For example, if we want to simplify 3^100 (mod 10), we can use Euler's Totient Function as follows:

φ(10) = φ(2*5) = φ(2) * φ(5) = 1 * 4 = 4

Therefore, 3^4 ≡ 1 (mod 10)

Therefore, 3^100 ≡ (3^4) ^25 ≡ 1^25 ≡ 1 (mod 10)

Thus, we have simplified 3^100 (mod 10) to 1.

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Answer:

First, we can factor out 5x²y²z from each term:

15x²y³z+25x³y²z+35x²y²z² = 5x²y²z(3y+5xz+7z)

So the fully factorized expression is:

5x²y²z(3y+5xz+7z)

Answer:

Step-by-step explanation:

How do location and population density affect ways of life in Central Africa? Tropical forests have low population densities since they are not fertile areas. More densely populated areas are countries in which the capital city is an economic, political, and cul- tural hub.

(a) Is this an observational study or an experiment?

ans=Observational study – no treatment was imposed

(b) What are the explanatory and response variables?

ans=explanatory – time spent in child care from birth to age 4 response – adult rating of children’s behavior

d) Does this study show that child care causes children to be more aggressive? Explain.

No. Observational studies cannot show cause-and-effect

Researchers=someone whose job is to study a subject carefully, especially in order to discover new information or understand the subject better: She is a leading researcher in the field.

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Answer:

a = 4

Step-by-step explanation:

Parallel lines have the same slope.

y + 2x + 3 = 0 in the slope intercept form of the line is

y = -2x  - 3 .  I can see from this form that the slope is -2.  Use the point given (3, -4) and the slope -2 to write the new equation in the slope intercept form.  We need to find b.

y = -4  from the point given (3, -4)

x = 3  from the point given(3,-4)

m  = -2   from the other equation

y = mx + b

-4 = (-2)3 + b

-4 = -12 + b  Ad 12 to both sides

-4 + 12 = -12 + 12 + b

8 =b

Equation of the new line

y = mx + b

y = -2x + 8

ton find a, substitute -2 for x

y = -2(2) + 8

y = -4 + 8

y = 4

a = 4

The length of q is 5.4 cm, to the nearest 10th of a centimeter. In order to find the length of q, we can use the law of sines.

The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is the same for all sides and angles of the triangle.

In this case, we have:

q/sin 62° = s/sin 114°

Rearranging the equation and solving for q, we get:

q = (s*sin 114°)/sin 62°

Plugging in the given values, we get:

q = (3.1*sin 114°)/sin 62°

= 3.1*1.53/0.876

= 5.41 cm

Rounding this off to the nearest 10th of a centimeter, we get q = 5.4 cm.

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To the closest tenth of a centimeter, the length of q is 5.4 cm. We can use the rule of sines to calculate the length of q.

The law of sines is commonly used to find a triangle's elusive side or angle. If exact triangle measurement combinations are provided, this law can be used. ASA Given two angles as well as an included side, the goal is to determine the unknown side.

According to the rule of sines, the ratio of a triangle side's length to the sine of its opposing angle is identical for all triangle sides and angles.

In this instance, we have:

q/sin 62° = s/sin 114°

When we rearrange the equation and solve for q, we get:

q = (s*sin 114°)/sin 62°

With the provided values, we get:

q = (3.1*sin 114°)/sin 62°

= 3.1*1.53/0.876

= 5.41 cm

If we round this to the closest tenth of a centimeter, we get q = 5.4 cm.

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Refer to the image below,

The missing side, which is the hypotenuse, is approximately 12.2 units when rounded to the nearest tenth (one decimal spot).

To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Let's denote the length of the hypotenuse as "c". According to the Pythagorean theorem, we have:

\(c^2 = 7^2 + 10^2\)

Simplifying the equation:

\(c^2 = 49 + 100\)

\(c^2 = 149\)

To find the length of the hypotenuse, we take the square root of both sides:

c = √149

Calculating the square root of 149, we find that it is approximately 12.2.

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Answer:

(-2, -2)

Step-by-step explanation:

You have to find the lowest point of the graph.  That would be 2 to the left of the origin and 2 down.  Note that the scale on the graph differs for the x- and y-axis.

Most likely, the weights of the rabbits in this sample follow a normal distribution.

Based on the central limit theorem, when sample size is large enough (usually considered to be 30 or greater), the distribution of sample means tends to follow a normal distribution regardless of the shape of the population distribution. Since the sample size of 42 is greater than 30, it is likely that the weights of the rabbits in this sample follow a normal distribution. Additionally, since we know the mean weight and standard deviation of weights for the sample, we can calculate the z-score for any weight and determine the likelihood of it occurring within the sample.

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To determine which coefficients are significantly nonzero at the 0.01 significance level in isye 6414, we need to look at the p-values. If the p-value is less than 0.01, then the coefficient is considered significantly nonzero.

To find which coefficients are significantly nonzero at the 0.01 significance level in isye 6414, you will need to refer to the p-values. The p-value represents the probability of observing the coefficient's value if the null hypothesis is true. A p-value less than the chosen significance level (0.01 in this case) indicates that the coefficient is significantly nonzero.

First, obtain the regression output for isye 6414. This will include the estimated coefficients and their corresponding p-values. Next, compare each p-value to the significance level of 0.01. If a p-value is less than 0.01, then the coefficient is considered significantly nonzero.

For example, if the p-value for a coefficient is 0.005, it is less than 0.01, so the coefficient is significantly nonzero at the 0.01 significance level. Conversely, if the p-value is 0.02, it is greater than 0.01, so the coefficient is not significantly nonzero.

Repeat this process for all coefficients in isye 6414 to identify which ones are significantly nonzero at the 0.01 significance level.

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Question is : Which coefficients are significantly nonzero at the 0.01 significance level in the context of ISYE 6414 since p-value of the regression analysis?

We know at centroid medians bisect each other in the ratio 2:1.

\(\\ \sf\longmapsto TY=2x\)

\(\\ \sf\longmapsto 2x=30\)

\(\\ \sf\longmapsto x=\dfrac{30}{2}\)

\(\\ \sf\longmapsto x=15\)

Answer:

A

Step-by-step explanation:

On the median TW the distance from the vertex to the centroid is twice the distance from the centroid to the midpoint , then

YW = \(\frac{1}{2}\) × TY = \(\frac{1}{2}\) × 30 = 15

Answer:

60%

Step-by-step explanation:

Answer:

60%

Step-by-step explanation:

9/15=.6

.6 as a percent is 60%

Let R be a ring. Let f and g be two elements in R[x] with fg=0 and g≠0. Does there exist c∈R\{0} with cg=0?In order to solve this problem, we will employ an indirect proof or a proof by contradiction.

Let's assume that there doesn't exist any nonzero element c∈R such that cg=0.

Let's assume that f and g are elements of R[x] such that fg=0.

This means that there exist polynomials a and b in R[x] such that f=ag and g=bh.

As we have taken g≠0, we can assume that b has nonzero coefficients and hence has a nonzero constant coefficient.

Suppose that c is the leading coefficient of b, which is nonzero.

Then cb is the leading term of the product fg, as (ab)(bh)=a(b²)h². Since fg=0, the leading term of fg is zero.

This means that the coefficient of the leading term of cb must be zero, since it's the only term of fg that can cancel it out.

But this is a contradiction, since we've assumed that c is nonzero.

Therefore, our assumption that there doesn't exist any nonzero element c∈R such that cg=0 is incorrect.

There must exist such an element.

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Answer:

a. 1/12 (hope it help)

Step-by-step explanation:

5sec/60sec=1/12

Answer:

g(1) = - 0.2

Step-by-step explanation:

To evaluate g(1), substitute x = 1 into g(x) , that is

g(1) = \(\frac{1^2-3}{10}\) = \(\frac{1-3}{10}\) = \(\frac{-2}{10}\) = - 0.2

The expression 8* is equivalent to both 32 and 32².Expression 8* is an algebraic expression that can be expanded to 8*1 = 8. Thus, 8* is equivalent to 8.

An algebraic expression is a combination of terms, variables and operators that when simplified, evaluates to a numerical value. It is usually written in the form of equations and inequalities, where the terms represent numbers and variables represent unknown values.

When multiplied by 1, 8* is equivalent to 32. This is because 8*1 = 8 and 32*1 = 32. So, 8* = 32.

Expression 8* is also equivalent to 32². This is because 8*1 = 8 and 32² is 8 multiplied by itself. So 8* = 32².

The expressions A. (²/²), B. 8.8x+1, and F. 8-8-1 are not equivalent to 8*.

Expression A. (²/²) is not equivalent to 8*. This is because (²/²) is an undefined expression, while 8* is a defined expression.

Expression B. 8.8x+1 is not equivalent to 8*. This is because 8.8x+1 is an algebraic expression that includes the variable x, while 8* does not include any variables.

Expression F. 8-8-1 is not equivalent to 8*. This is because 8-8-1 is a subtraction expression, while 8* is a multiplication expression.

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Answer:

The answer is 41/7 or 5 6/7

Step-by-step explanation:

Answer:

Step-by-step explanation:

if we have 137 students, and out of this number 7 were in cars

137-7=130 students in buses

there are 5 buses

130/5=26

26 students in each bus

Answer:

67667.7

Step-by-step explanation:

let the number= Y

the question simply means that 0.15 percent of Y which give 10.5

so, let find Y:

0.15% of Y 10.15

0.15/100×y = 10.15

0.0015y= 10.15

divide bothsides by 0.0015

0.0015y/0.0015= 10.15/0.0015

y=6766.66

y= 6766.7 approximately

Answer:

m∠JKM = 63°

m∠MKL = 27°

Step-by-step explanation:

Since ∠JKL is a right angle. This means that by summing up both m∠JKM and m∠MKL will result in the same as ∠JKL figure. Thus, m∠JKM + m∠MKL = m∠JKL which is 90° by a right angle definition.

\(\displaystyle{\left(12x+3\right)+\left(6x-3\right) = 90}\)

Solve the equation for x:

\(\displaystyle{12x+3+6x-3 = 90}\\\\\displaystyle{18x=90}\\\\\displaystyle{x=5}\)

We know that x = 5. Next, we are going to substitute x = 5 in m∠JKM and m∠MKL. Thus,

m∠JKM = 12(5) + 3 = 60 - 3 = 63°

m∠MKL = 6(5) - 3 = 30 - 3 = 27°

Answer:

15 mph

Step-by-step explanation:

You need to find how much each side of the table is changing each time and change that into a fraction. In this example, the change in time is .5 hours. Repeat with the other side to get 12.5 miles. Next you change it into a fraction with the distance over the time to get 12.5/.5. Type this into the calculator to get the answer which is 15 mph.

The answer is D. R2, also known as the coefficient of determination, shows the percentage of the total variation in the dependent variable, Y, that is explained by the explanatory variable.

Of the four answer choices provided, only one is true of R2. Answer D is the correct statement regarding R2. It indicates that R2 shows the percentage of the total variation in the dependent variable, Y, that is explained by the explanatory variable. This statement is commonly used to evaluate the strength of a linear relationship between two variables. It is important to note that a high R2 value does not necessarily mean that the explanatory variable causes the dependent variable, but it does suggest a strong correlation between the two. This answer is provided in one paragraph consisting of three sentences.

In other words, R2 measures the proportion of the variance in the dependent variable that can be predicted from the independent variable(s). A higher R2 value indicates a better fit of the data, while a lower value suggests that the model may not explain much of the variation in the dependent variable.

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Answer:

answer is 1st one

Step-by-step explanation:

because I think so it is the additive inverse

When it takes 6 hours to travel and 8.7 hours to return home, there is a 45% increase in travel time.

A percentage is a number or ratio expressed as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" are also used, the percent sign, "%," is frequently used to indicate it. A percentage is a number without dimensions and without a standard measurement. In essence, percentages are fractions with a 100 as the denominator. We place the percent symbol (%) next to the number to indicate that the number is a percentage. For instance, you would have received a 75% grade if you answered 75 out of 100 questions correctly on a test (75/100).

Here,

Time take to arrive at vacation destination=6 hours

Time take to arrive at home=8.7 hours

percent increase=(8.7-6)/6*100

=45%

The percent increase in the time taken to come back to home is 45% when they took 6 hours to reach and 8.7 hours to comeback.

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Complete question:

It took the Phillips family 6 hours to drive to their vacation destination. Due to traffic, it took them 8 hours and 42 minutes to drive home. Percentage for Increase or Decrease!!

To construct a 98 percent confidence interval for the difference in proportions, we need to calculate the sample proportions and the standard error of the difference. First, let p1 be the proportion of cell phone users with a headset who missed their exit, and p2 be the proportion of those talking to a passenger who missed their exit.

Step 1: Identify the proportions.
- Proportion of cell phone users with a headset who missed their exit (p1): 15/24
- Proportion of cell phone users talking to a passenger who missed their exit (p2): 6/24

Step 2: Calculate the difference in proportions (p1 - p2).
- (15/24) - (6/24) = 9/24 = 0.375

Step 3: Calculate the standard error (SE) for the difference in proportions.
- SE = √[(p1 * (1 - p1) / n1) + (p2 * (1 - p2) / n2)]
- SE = √[((15/24) * (1 - 15/24) / 24) + ((6/24) * (1 - 6/24) / 24)] = √(0.01042) = 0.102

Step 4: Find the critical value (z-score) for a 98% confidence interval.
- Using a z-table or calculator, the z-score for a 98% confidence interval is approximately 2.33.

Step 5: Calculate the margin of error (ME).
- ME = z-score * SE
- ME = 2.33 * 0.102 ≈ 0.238

Step 6: Construct the 98% confidence interval.
- Lower limit: (p1 - p2) - ME = 0.375 - 0.238 ≈ 0.137
- Upper limit: (p1 - p2) + ME = 0.375 + 0.238 ≈ 0.613

The 98% confidence interval for the difference in proportions is approximately (0.137, 0.613). This means we can be 98% confident that the true difference in the proportion of cell phone users with a headset who missed their exit and those talking to a passenger who missed their exit falls within this interval.

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The largest interval I on which the solution is defined.

\(y(x)=\left(\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2}\right)^{2}\)

This is further explained below.

Generally, the equation for is  mathematically given as

\(\frac{d y}{d x}=\sqrt{y}\)

Separating variables and integrating

\(\begin{aligned}&\Rightarrow \int \frac{d y}{\sqrt{y}}=\int d x \\&\Rightarrow 2 \sqrt{y}=x+c \\&\text { Put } y\left(x_{0}\right)=y_{0} \\&\Rightarrow 2 \sqrt{y_{0}}=x_{0}+c \\&\Rightarrow c=2 \sqrt{y_{0}}-x_{0}(2) \\&\text { Put }(2) \text { in } \\&\Rightarrow 2 \sqrt{y}=x+2 \sqrt{y_{0}}-x_{0} \\&\Rightarrow \sqrt{y}=\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2} \\&\Rightarrow y(x)=\left(\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2}\right)^{2} \end{aligned}\)

In conclusion, the largest interval I on which the solution is defined.

\(y(x)=\left(\frac{x}{2}+\sqrt{y_{0}}-\frac{x_{0}}{2}\right)^{2}\)

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Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box

To determine the amount of wrapping paper used by Josue for the cube-shaped gift box, we need to calculate the surface area of the cube.

The net of the gift box consists of six squares, each representing a face of the cube. The dimensions provided in the figure show that each side of the squares is 5 cm.

Since a cube has six faces, we need to calculate the total surface area by multiplying the area of one square face by six.

The formula to find the area of a square is side length squared, so we can calculate the area of one square face as 5 cm * 5 cm = 25 cm².

Now, to find the total surface area, we multiply the area of one face by six: 25 cm² * 6 = 150 cm².

Therefore, Josue used 150 square centimeters of wrapping paper to cover the cube-shaped gift box.

It's worth noting that this calculation assumes that there is no overlap or excess wrapping paper used while wrapping the gift box. Additionally, we have assumed that the dimensions provided are accurate and refer to the side length of the squares in the net.

Overall, the amount of wrapping paper used can vary based on the wrapping technique employed and any additional decorations or folds added to the gift box.

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The correct set of possible results would be (0, 1, 0, 0), (1, 2, 1, 0) and (1, 2, 0, 1).

Your approach seems to be correct, but there seems to be a minor mistake in your final list of possible solutions. Let's go through the steps to clarify.

Given the initial conditions z=t=0, you obtained a partial solution (0,1,0,0).

Next, you solved the homogeneous equations for z=1 and t=0, which resulted in a solution (1,1,1,0).

Similarly, solving the homogeneous equations for z=0 and t=1 gives another solution (1,1,0,1).

To find the general solution, you combine the partial solution with the solutions obtained in the previous step, using parameters a and b.

(0,1,0,0) + a(1,1,1,0) + b(1,1,0,1)

Expanding this expression, you get:

(0+a+b, 1+a+b, 0+a, 0+b)

Simplifying, you obtain the following set of solutions:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Therefore, the correct set of possible results would be:

(0, 1, 0, 0)

(1, 2, 1, 0)

(1, 2, 0, 1)

Note that (0, 1, 1, 1) is not a valid solution in this case, as it does not satisfy the initial condition z = 0.

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Money paid by Park Jimin = $125

We need to find the tip , so,

→ 15% of the amount paid

→ $ 125 (15/100)

→ $ 18.75

Hence, the tip is of $ 18.75

Answer:

Jiminie paid 18.75

Step-by-step explanation: