annie, ben and claire are training for mathcounts. on january $1$st, they each started to solve a large packet of problems that their coach gave them. each of them worked at a constant rate. annie solved six problems each day and finished four days after ben did. claire solved three more problems each day than ben did and finished two days before he did. how many problems were in the packet their coach gave them?

Answer:

2) -3x+10

4) -4x+10+x

Step-by-step explanation:

Use the distributive property to get rid of the parentheses.

(2 × -2x) + (2 × 5) + x

-4x + 10 +x is correct, but the x's can be combined.

(-4x + x) + 10 = -3x + 10

Answer:

Rs.11000

Step-by-step explanation:

9900*110/100

Rs.11000

Note:110 is = when a 10% lose is there

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Answer:

CP = 11000

Step-by-step explanation:

Given,

SP = 9900

Loss% = 10

-----------------------------------------------

Let the CP be y,

\( \bold{ cp = \frac{(sp \times 100)}{(100 - loss\%)} }\)

\(⇒ \bold{y = \frac{(9900 \times 100)}{(100 - 10)} }\)

\( ⇒\bold{cp = \frac{9900 \times 100}{90} }\)

\(⇒ \bold{cp = 11000}\)

[Hence, the cost price of the dining table is Rs 11000.]

To answer this question, simply plug in the values that represent the variables into the respective equations.

If z=5 and y =3, then 12z - 3y can be written as:

(12 × 5) - (3 × 3)

(60) - (9)

= 51

If z = 5, then the expression 4z -z can be written as:

(4 × 5) - 5

20-5

= 15

51 and 15 are your answers

The amount of land the railroad companies received for each mile of track they laid varied depending on the specific circumstances and agreements.

However, a common benchmark used during the construction of railroads in the United States was the granting of land through the Homestead Act of 1862. Under this act, railroad companies were granted approximately 6,400 acres (10 square miles) of land for every mile of track laid. This land was typically located alongside the tracks and served as an incentive for the companies to expand and develop the rail network across the country.

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Answer:

-17

Step-by-step explanation:

(5x2+3x-5) - (2x2+8)

(10+3x-5) - (2x2+8)

(10-15) - (2x2+8)

-5 - (4+8)

-5 - 12

-17

Answer:

El CO, como el cianuro y el óxido nítrico (NO), inhibe la respiración mitocondrial al unirse al hemo ferroso a3 en el sitio activo de la COX, lo que detiene de manera efectiva la fosforilación oxidativa (16–21).

Step-by-step explanation:

The solution to the given differential equation is \(y(x) = -x^4/25 + x^2/15 - (3/25)e^(-3x) + (1/2)x^4cos(x) + (1/2)x^2sin(x) + C1e^(-3x) + C2\), where C1 and C2 are arbitrary constants.

To solve the given differential equation using the method of undetermined coefficients, we assume a particular solution of the form \(y_p = A(x^4 + Bx^2e^(-3x) + Csin(x))\), where A, B, and C are undetermined coefficients.

Step 1:

Differentiating y_p with respect to x, we obtain \(y_p' = 4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x).\)

Taking the second derivative, we have \(y_p" = 12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x).\)

Step 2:

Substituting y_p, y_p', and y_p" into the given differential equation, we get:

\((12Ax^2 + 2B(e^(-3x) - 3xe^(-3x)) + 2Bx(-3e^(-3x) + 9xe^(-3x)) - Csin(x)) + 5(4Ax^3 + 2Bx(e^(-3x) - 3xe^(-3x)) + Ccos(x)) = 2x^4 + x^2e^(-3x) + sin(x).\)

Simplifying the equation and grouping the like terms, we have:

\((12A + 20Ax^3) + (-6B + 10Bx)e^(-3x) + (-15Bx^2 + 9Bx^3) + (12A + 10C)cos(x) + (-C + 2Bx)sin(x) = 2x^4 + x^2e^(-3x) + sin(x).\)

Comparing the coefficients of the terms on both sides, we can determine the values of A, B, and C. Equating the coefficients of each term, we obtain:

\(12A + 20Ax^3 = 2x^4,\)

\(-6B + 10Bx = x^2e^(-3x),\)

\(-15Bx^2 + 9Bx^3 = 0,\)

12A + 10C = 0,

-C + 2Bx = sin(x).

Solving these equations, we find A = -1/25, B = 1/15, and C = 0.

Therefore, the particular solution is \(y_p = (-1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

To obtain the general solution, we add the particular solution y_p to the complementary function y_c, where y_c is the solution of the homogeneous equation y" + 5y' = 0. The general solution is given by y(x) = y_c + y_p.

The complementary function can be found by solving the homogeneous equation:

y" + 5y' = 0.

The characteristic equation associated with the homogeneous equation is r^2 + 5r = 0. Solving this quadratic equation

, we find two distinct roots: r = 0 and r = -5.

Therefore, the complementary function is \(y_c = C1e^(-5x) + C2\), where C1 and C2 are arbitrary constants.

Finally, the general solution to the given differential equation is:

\(y(x) = C1e^(-5x) + C2 - (1/25)x^4 + (1/15)x^2e^(-3x) + (1/2)x^2sin(x).\)

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Therefore, the slope of the line passing through the points (0,5) and (2,0) is -5/2.

In mathematics, slope refers to the measure of steepness of a line. It is the ratio of the change in y (vertical change) over the change in x (horizontal change) between any two points on the line. The slope of a line is represented by the letter "m" and can be calculated using the slope formula: m = (y2 - y1) / (x2 - x1) where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

Here,

To find the slope of a line, we use the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line.

Using the given coordinates, we have:

x1 = 0, y1 = 5

x2 = 2, y2 = 0

slope = (0 - 5) / (2 - 0)

slope = -5/2

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The correct answer is (D) Because the population mean of 118 mph does not fall within the confidence interval around the new mean, we can conclude that the program had an impact. In fact, we can conclude that the program seemed to increase the average speed of women’s serves.

Because the population mean of 118 mph does not fall within the confidence interval around the new mean, we can conclude that the program had an impact. In fact, we can conclude that the program seemed to increase the average speed of women’s serves.

The confidence interval around the group mean of 123 mph suggests that the true population mean lies somewhere within a certain range. Since the lower limit of this range is above the population mean of 118 mph, we can infer that the program had a positive impact on the participants' average serve speed.

This suggests that the program was successful in improving the participants' skills and abilities in tennis, resulting in faster serves.

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Answer:

b

Step-by-step explanation:

no

Answer:

The answer is B. the Pythagorean theorem

Step-by-step explanation:

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1. One mean 2. One proportion 3. Proportions from dependent samples 4. Two independent means 5. Means from dependent samples 6. Proportions from dependent samples

1. You want to estimate the typical salary for women working in the nursing field.
  Answer: One mean
2. You want to estimate the proportion of nurses that quit after working for only one year.
  Answer: One proportion
3. You want to estimate the difference in the number of men and women that quit the nursing field after only one year.
  Answer: Two independent means
4. You want to estimate the difference in the salaries of men and women working in the nursing field.
  Answer: Two independent means
5. The same one hundred people were asked in 2000 and in 2006 how much they had spent on medical bills. Has there been an increase in medical cost?
  Answer: Means from dependent samples
6. The same one hundred people were asked in the year 2000 and again in the year 2006 if they trusted their local hospitals. Has there been a change in people's trust?
  Answer: Proportions from dependent samples

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Answer: The linear model does not describe the data well because most of the points are located above the line.

Step-By-Step Explanation: The scatterplot shows the data points, and it also shows the linear model that Henry drew.

Answer:

the length of each of its edge is 3

Step-by-step explanation:

v=a^3

a=v^1/3=27^1/3=3

Answer:y=-5x-2

Step-by-step explanation:

This will have a negative slope since the line goes from left to right. Use rise over run to find the slope of -5 and look at the y axis where it intersects to get -2

Have a great day!

Answer:

prices of food and games and tickets

Answer:

(2, 1)

Step-by-step explanation:

\(\frac{X1+X2}{2} , \frac{Y1 + Y2}{2}\)

Answer:

The radius of the circle is 5.1, and the diameter of the circle is 10.2

Step-by-step explanation:

In the shown circle, the point from the center to the edge is 5.1, so that is the radius. Then, the diameter of a circle is twice its radius, so we have:

5.1 * 2 = 10.2

So the diameter of the circle is 10.2.

The radius of the circle is 5.1, and the diameter of the circle is 10.2.

Hope this helped!

To prove that the group g is cyclic, we analyze the possible values of the order |g|. We consider the cases for each possible value and demonstrate that in all cases, g is either cyclic or leads to a contradiction.

For |g| = 1, 2, 3, 5, or 7, the groups of these orders are always cyclic.

If |g| = 4, 6, 8, 9, 10, 12, or 15, we show that g cannot have the required subgroups. Assuming g is not cyclic, we find an element x of order 2 and additional elements y, z, w, etc., also of order 2. This contradicts the given conditions since g would be isomorphic to Z₂ × Z₂ or have more than one subgroup of order 3 or 5.

For composite orders |g| = pq, where p and q are prime, we generalize the analysis. By Cauchy's theorem, g has elements of order p and q, and since there is only one subgroup of each order, they are cyclic. We show that the intersection of these subgroups cannot have an order of pq, leading to a contradiction. Hence, g is cyclic.

Therefore, in all cases, g is proved to be cyclic. QED.

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Answer:

24.59 m/s

Step-by-step explanation:

Average speed(m/s) = distance travelled(m) / time taken(s)

Distance = 220 miles

220 miles = 354,056 meters

Time taken = 4 hours

4 hours = 14,400 seconds

Average speed = distance travelled / time taken

= 354,056 / 14,400

= 24.59 meter/seconds

= 24.59 m/s

Answer:

Step-by-step explanation:

2x+4y=48

5x+2y=64

Adult ticket: $10    Child ticket: $7

For 2 adults and 3 children with the given price per ticket, the family having brought $40 as a budget, their budget would not be high enough as the total would come to be $41. They'd be a dollar short.

The probability of winning at least one award is 1 - 0.2373 = 0.7627 or 76.27%.

If the probability of winning an MTV music award after being nominated is 25%, the probability of not winning is 75%. Thus, the probability of not winning any of the five awards is (0.75)^5 = 0.2373.

As for how many awards Ariana Grande should expect to win, we can use the expected value formula: E(x) = n * p, where n is the number of trials (in this case, 5) and p is the probability of success (0.25). Therefore, E(x) = 5 * 0.25 = 1.25. So, Ariana Grande can expect to win about 1 award.

Finally, to calculate the standard deviation associated with this probability, we can use the formula: σ = sqrt(n * p * (1-p)). Plugging in the values, we get σ = sqrt(5 * 0.25 * 0.75) = 0.866. Therefore, the standard deviation associated with this probability is approximately 0.866.

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The one-sample z-statistic for evaluating the hypothesis that unvaccinated people get COVID-19 is not 0.03 is -85.7. This statistic tested the hypothesis that unvaccinated people do not get COVID-19 at 0.03%.

In order to compute the one-sample z-statistic, we must first do a comparison between the observed proportion of COVID-19 instances in the placebo group and the expected proportion of 0.03. (p - p0) / [(p0(1-p0)) / n is the formula for the one-sample z-statistic. In this formula, p represents the actual proportion, p0 represents the predicted proportion, and n represents the sample size.

The observed proportion of COVID-19 instances among those who received the placebo is 162/18325 less than 0.0088. According to the received wisdom, the proportion that should be anticipated is 0.03. The total number of people sampled is 18325. After entering these numbers into the formula, we receive the following results:

z = (0.0088 - 0.03) / √[(0.03(1-0.03)) / 18325] ≈ (-0.0212) / √[(0.0291) / 18325] ≈ -85.7

As a result, the value of the z-statistic for just one sample is about -85.7. This demonstrates that the observed proportion of COVID-19 cases in the unvaccinated population is significantly different from the expected proportion of COVID-19 cases in that population.

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The surface with the given vector equation r(s, t) = s sin(4t), s^2, s cos(4t) is a parametric representation of a surface in three-dimensional space. It is a part of the parameterized family of surfaces known as the "spherical helicoid."

The spherical helicoid is formed by taking a circular helix and rotating it around its central axis.

In this case, the circular helix is generated by the function r(t) = (sin(4t), t, cos(4t)), where t represents the height of the helix.

The parameter s in the given equation scales the size of the helix.

The surface described by r(s, t) = s sin(4t), s^2, s cos(4t) exhibits a spiral-like shape that expands or contracts depending on the value of s.

The sinusoidal functions sin(4t) and cos(4t) determine the oscillations and curvature of the surface along the helical path.

The parameter s determines the scaling factor of the surface, affecting its size and spacing between the helices. Overall, the surface represents a family of helical structures with varying sizes and curvatures.

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Answer:

Everything but paralelograms i believe.

Step-by-step explanation:

The distance between your house and school is 4.1 miles.

According to the given question.

Point c represents your house.

Point d represents post office which is directly west to the point c i.e from house.

And point e represents school which is west of the post office.

Also, it is given that the distance between house and post office, cd is 1.7 miles.

And the distance between the post office and school,de is 2.4 miles.

Now, if we see the attached figure we can say that

cd + de = ce

⇒ 1.7miles  + 2.4miles  = 4.1 miles

Hence, the distance between your house and school is 4.1 miles.

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