A gradeshcool class has nine boys and twelve girls. Any two boys will fight if they're next to each other. How many ways can the teacher line up the students so that no two boys stand next to each other

Answer:

x= 11

Step-by-step explanation:

\( \frac{2(x + 5)}{4} = 8\)

Simplifying the fraction:

\( \frac{x + 5}{2} = 8\)

Multiply both sides by 2:

x+ 5= 8(2)

x+ 5= 16

Subtract both sides by 5:

x= 16 -5

x= 11

The monthly phone cost (p) would be $25 in this example. Monthly phone cost p equals $15 plus the additional charge per minute (a) multiplied by the number of minutes used (m).

To calculate the monthly phone cost, multiply the additional charge per minute (a) by the number of minutes used (m). Then add $15 to the result.
The equation p = 15 + am represents the relationship between the monthly phone cost (p), the base fee ($15), the additional charge per minute (a), and the number of minutes used (m).

To calculate the monthly phone cost (p), you need to add the base fee of $15 to the additional charge per minute (a) multiplied by the number of minutes used (m). The equation p = 15 + am represents this relationship.

Step 1:

Multiply the additional charge per minute (a) by the number of minutes used (m). This gives you the cost of the additional minutes used.

Step 2:

Add the cost of the additional minutes to the base fee of $15. This will give you the total monthly phone cost (p).

For example, let's say the additional charge per minute (a) is $0.10 and the number of minutes used (m) is 100.

Step 1:

0.10 * 100 = $10 (cost of additional minutes)

Step 2:

$10 + $15 = $25 (total monthly phone cost)

Therefore, the monthly phone cost (p) would be $25 in this example.

Remember, the equation p = 15 + am can be used to calculate the monthly phone cost for different values of the additional charge per minute (a) and the number of minutes used (m).

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The monthly phone cost, p, would be $52.50 when the additional charge per minute, a, is $0.25 and the number of minutes used, m, is 150.

The monthly phone cost, p, is determined by a base fee of $15 per month plus an additional charge, a, per minute used, m.

This relationship can be represented by the equation p = 15 + am.

To calculate the monthly phone cost, you need to know the additional charge per minute and the number of minutes used.

Let's consider an example:

Suppose the additional charge per minute, a, is $0.25 and the number of minutes used, m, is 150.

Using the equation p = 15 + am, we can substitute the values:

p = 15 + (0.25 * 150)

Now, let's calculate:

p = 15 + 37.5

p = 52.5

Therefore, the monthly phone cost, p, would be $52.50 when the additional charge per minute, a, is $0.25 and the number of minutes used, m, is 150.

Keep in mind that the values of a and m can vary, so the monthly phone cost, p, will change accordingly.

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The apparent capacity of a glass vessel refers to its perceived size or volume based on external dimensions, while the actual capacity represents the true volume of the vessel, taking into account both interior and exterior dimensions.

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The integral is divergent because the Comparison Theorem can be used to compare it to a known divergent integral. By comparing the given integral to the integral of 1/x^2, which is known to diverge, we can conclude that the given integral also diverges.


To determine whether the given integral is convergent or divergent, we can use the Comparison Theorem. This theorem states that if f(x) ≤ g(x) for all x ≥ a, where f(x) and g(x) are nonnegative functions, then if the integral of g(x) from a to infinity is convergent, then the integral of f(x) from a to infinity is also convergent.

Conversely, if the integral of g(x) from a to infinity is divergent, then the integral of f(x) from a to infinity is also divergent. In this case, we want to compare the given integral ∫ [infinity]. 0 x (x^3 + 1) dx to a known divergent integral. Let's compare it to the integral of 1/x^2, which is known to diverge.

To compare the two integrals, we need to show that 1/x^2 ≤ x(x^3 + 1) for all x ≥ a. We can simplify this inequality to x^4 + x - 1 ≥ 0. By considering the graph of this function, we can see that it is true for all x ≥ 0. Therefore, we have established that 1/x^2 ≤ x(x^3 + 1) for all x ≥ 0.

Since the integral of 1/x^2 from 0 to infinity is divergent, according to the Comparison Theorem, the given integral ∫ [infinity]. 0 x (x^3 + 1) dx is also divergent.

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Given that the cost is $1.10 per pound, we can calculate the cost per servable pound by dividing the total cost ($1.10 * 4 pounds) by the servable weight (2 pounds). Therefore, the correct option is c. $2.20.

The original weight of the food item is 4 pounds, and the cost per pound is $1.10. Therefore, the total cost of the food item is 4 pounds * $1.10 = $4.40.

The servable weight of the food item is 2 pounds. To find the cost per servable pound, we divide the total cost ($4.40) by the servable weight (2 pounds):

Cost per servable pound = Total cost / Servable weight = $4.40 / 2 pounds = $2.20.

Hence, the cost per servable pound for this food item is $2.20. Therefore, the correct option is c. $2.20.

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Answer:m,m,

Step-by-step explanation:

Answer:

Zeros:

Step-by-step explanation:

Given quadratic polynomial:

\(x^2+x -20\)

The zeros of a function f(x) are the x-values that satisfy the equation f(x)=0.  

Therefore, to find the zeros of the given function, set it to zero and solve for x.

Factor the quadratic:

\(\implies x^2+x-20=0\)

\(\implies x^2+5x-4x-20=0\)

\(\implies x(x+5)-4(x+5)=0\)

\(\implies (x-4)(x+5)=0\)

\(\boxed{\begin{minipage}{8.4 cm}\underline{Zero Product Property}\\\\If $a \cdot b = 0$ then either $a = 0$ or $b = 0$ (or both).\\\end{minipage}}\)

Apply the Zero Product Property:

\(\implies x-4=0 \implies x=4\)

\(\implies x+5=0 \implies x=-5\)

Therefore, the zeros of the given quadratic polynomial are:

Answer:

124-v=175

124-175=v

v= -51

The expression that equals the area of the poster in square metres would be = 1 + 5 hundredths. That is option A.

A square is defined as a quadrilateral that has four equal sides and edges of angle 90°.

From the given image, the painted area and the five painted boxes of the unpainted area is a wall poster.

The total number of boxes = 100

The painted boxes that represent the wall poster = 5

The total area of the wall poster = 1 + 5/100.

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Hi!

I can help you with joy!

Answer:

thirty-four point seven five.

Hope it helps.

Do ask me if you have any query.

Answered by

~Sparkles~

Answer:

58

Step-by-step explanation:

60+72+55+80=267

267+58=325

325/5=65

Answer:

Think about it this way: The x axis goes from left to right, correct? So just try to visualize actually picking up the object and flipping it over that axis. So since one tip of the triangle is on the coordinate (1,1), after reflecting the shape that same tip would be on (1,-1). You understand?

Answer:  The function that models the distance they drive is

f(x) = 50x + 20 where x is the time in hours

reasonable domain:  0 ≤ x ≤ 3

Step-by-step explanation:

examples:

95 = 50(1.5) + 20 After driving another hour and a half, they will have driven a total of 95 miles.

120 = 50(2) + 20  This means that after 2 more hours they will reach their destination.

There is a little ambiguity in the question. The function could be written as if they are starting out.  f(x) = 50t  

20 = 50(.4)  At 50 mph it took .4 hours to go 20 miles.

120 = 5(2.4)  The whole trip took 2.4 hours.

Richard's net pay for the week, considering Social Security, Medicare, and FIT deductions, can be calculated by subtracting the total deductions from his gross earnings.

First, let's determine the amount deducted for Social Security. The Social Security rate is 6.2%, and the maximum earnings subject to this deduction are $118,500. Since Richard is $1,000 below the maximum level, the amount subject to Social Security deduction is $1,000. Therefore, the Social Security deduction is 6.2% of $1,000.

Next, we calculate the Medicare deduction. The Medicare rate is 1.45%, and it is applied to the entire earnings of $1,700.

To calculate the FIT deduction, we need additional information about Richard's taxable income, tax brackets, and exemptions. Without this information, we cannot provide an accurate calculation for the FIT deduction.

Finally, we subtract the total deductions (Social Security, Medicare, and FIT) from Richard's gross earnings of $1,700 to obtain his net pay for the week.

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Answer: 25%

Step-by-step explanation: the probability of drawing blue=5/20

divide 5 by 20= .25 then make .25 into a %:25% (you just move the decimal to the right twice)

Answer:

There are 192 employees in the company.

Step-by-step explanation:

Let x be the total number of employees

Use ratio and proportion

\(\frac{120}{x} =\frac{5}{8} \\5x = 120(8)\\5x = 960\\\frac{5x}{5} = \frac{960}{5} \\x = 192\)

x = 192

Answer: 5.22

Step-by-step explanation:

The apothem = 87 cm = 0.87 m.

Using the formula \(A=\frac{1}{2}ap\) to find the area of the base, where a is the apothem and p is the perimeter, we get \(A=\frac{1}{2}(0.87)(6)=2.61\)

So, using the formula \(V=Bh\), we get the volume to be \(2.61(2)=5.22 \text{ m}^{3}\)

Answer:

57 + 5x < 65

Step-by-step explanation:

57 + 5x < 65

5x < 8

x < 1.6

Answer:

14.285714285714 %

Step-by-step explanation:

suppose the weekly payment is of x dollars

Then

Previous payment : $(x/40) per hour

New payment : $(x/35) per hour

Then

The percentage increase in the hourly rate of pay is :

\(=\frac{\frac{x}{35} -\frac{x}{40} }{\frac{x}{40} } \times100\)

\(=\frac{\frac{5x}{1400} }{\frac{x}{40} } \times100\)

\(=\frac{5x}{1400} \times \frac{40}{x} \times100\)

\(=\frac{200}{1400} \times100\)

\(=\frac{1}{7} \times100\)

\(=14.285714285714\)

Answer:

144 degrees

Step-by-step explanation:

We can use the formula (n-2)(180), where n = number of sides, to find the sum of all the interior angles in the decagon. Since a decagon has 10 sides:

(n-2)(180) = ?

(10-2)(180) = ?

(8)(180) = 1440.

Now, to find one interior angle in the decagon, divide 1440 by the number sides in our polygon (10).

1,440/10 = 144

               = 144 degrees

The data provide convincing evidence of a difference in the average calorie intake of diners at this restaurant.

The data do not provide convincing evidence that the average GRE verbal reasoning score has changed since 2004.

1: Since 2008, chain restaurants in California have been required to display calorie counts of each menu item.

Prior to menus displaying calorie counts, the average calorie intake of diners at a restaurant was 1100 calories.

After calorie counts started to be displayed on menus, a nutritionist collected data on the number of calories consumed at this restaurant from a random sample of diners.

Do these data provide convincing evidence of a difference in the average calorie intake of diners at this restaurant:
The data provide convincing evidence of a difference in the average calorie intake of diners at this restaurant.

The average calorie intake of diners before calorie counts were displayed was 1100 calories, while after calorie counts were displayed, the average calorie intake was lower.

This indicates that the calorie counts may have helped reduce the calorie intake of diners.
2: Based on the performance of those who took the GRE exam between July 1, 2004, and June 30, 2007, the average verbal reasoning score was calculated to be 462.

In 2011, the average verbal score was slightly higher.

Do these data provide convincing evidence that the average GRE verbal reasoning score has changed since 2004:

The data do not provide convincing evidence that the average GRE verbal reasoning score has changed since 2004. The increase in the average verbal score from 2004 to 2011 is not significant enough to prove a change in the average verbal reasoning score.

Further analysis would be required to determine if there has been a significant change in the average score.

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Answer:

4. But if u meant like rounding it would be 123.5

Step-by-step explanation:

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

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The general solution of the differential equation
y''(t) = 28e^(4t)sin(6t) is y(t) = c1e^(4t)sin(6t) + c2e^(4t)cos(6t).

To find the general solution of the differential equation
y''(t) = 28e^(4t)sin(6t), we can solve the homogeneous equation y''(t) = 0 and then find a particular solution for the non-homogeneous equation.

The homogeneous equation is y''(t) = 0, which has the general solution y(t) = c1 + c2t, where c1 and c2 are arbitrary constants.

To find a particular solution for the non-homogeneous equation, we can use the method of undetermined coefficients. Since the non-homogeneous term is of the form e^(4t)sin(6t), we can assume a particular solution of the form y_p(t) = Ate^(4t)sin(6t) + Bte^(4t)cos(6t). After taking the first and second derivatives, we can substitute them back into the original equation and solve for the coefficients A and B.
We obtain A = -7/200 and B = 3/100.

Therefore, the general solution of the differential equation
y''(t) = 28e^(4t)sin(6t) is y(t) = c1e^(4t)sin(6t) + c2e^(4t)cos(6t) - (7/200)te^(4t)sin(6t) + (3/100)te^(4t)cos(6t), where c1 and c2 are arbitrary constants.

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the vector equation for the line segment from (3, -4, 4) to (7, 2, 3) is:

r = <3, -4, 4> + t<4, 6, -1>

We can find a vector equation for the line segment by first finding the direction vector of the line segment, and then using it to write the equation in vector form.

The direction vector of the line segment is the difference between the two endpoints:

d = <7, 2, 3> - <3, -4, 4> = <4, 6, -1>

To write the vector equation in terms of the parameter t, we can use the parametric form of the equation of a line:

r = r_0 + td

where r is the position vector of a point on the line, r_0 is the position vector of a known point on the line (in this case, (3, -4, 4)), t is a scalar parameter, and d is the direction vector we just found.

Substituting the values we know, we get:

r = <3, -4, 4> + t<4, 6, -1>

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The hypotheses for the test are H₀: σ₁² = σ₂² and H₁: σ₁² ≠ σ₂². This is a two-tailed test to assess if there is a difference in the standard deviations of sound levels between the areas designated as "casualty doors" and operating theaters. The claim being investigated is whether or not there is a difference in the standard deviations.

The hypotheses for the test are:

H₀: σ₁² = σ₂² (There is no difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

H₁: σ₁² ≠ σ₂² (There is a difference in the standard deviations of the sound levels between the areas designated as "casualty doors" and operating theaters.)

This hypothesis test is a two-tailed test because the alternative hypothesis is not specifying a direction of difference.

To substantiate the claim that there is a difference in the standard deviations, we will conduct a two-sample F-test at a significance level of 0.10, comparing the variances of the two groups.

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The general solution of the differential equation is: y = ±√(7/6 eˣ + C)

To find the general solution of the differential equation 12yy' - 7eˣ = 0, we can use separation of variables.

First, we can divide both sides by 12y to get y' = 7eˣ/12y.

Next, we can multiply both sides by y and dx to separate the variables:

ydy = 7eˣ/12 dx

Integrating both sides, we get:

y²/2 = (7/12) eˣ + C

where C is the constant of integration.

Solving for y, we get:

y = ±√(7/6 eˣ+ C)

Therefore, the general solution of the differential equation is:

y = ±√(7/6 eˣ + C)

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Answer:

idek

Step-by-step explanation:

The ratio of the length of a side of a square to its perimeter is **1:4**. Therefore, any ratio that is not equivalent to 1:4 is a wrong answer. For example, 2:8 is equivalent to 1:4, but 3:8 is not.

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| 2 cm        | 8 cm      | 2:8   |

| 3 cm        | 12 cm     | 3:12  |

| 4 cm        | 16 cm     | 4:16  |

| 5 cm        | 20 cm     | 5:20  |

Part A: Click the wrong answers.

The wrong answers are **3:12** and **5:20**, because they are not equivalent to 1:4.

Part B: Drag numbers into each box to produce the correct answers. Place the smaller number in the box on the left.

To produce the correct answers, we need to find two numbers that have a ratio of 1:4. For example, we can use 1 and 4, or 2 and 8, or 3 and 12, etc.

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| [ ] cm      | [ ] cm    | [ ]:[ ]|

| [ ] cm      | [ ] cm    | [ ]:[ ]|

One possible way to fill in the blanks is:

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| [1] cm      | [4] cm    | [1]:[4]|

| [2] cm      | [8] cm    | [2]:[8]|

Another possible way is:

| Side length | Perimeter | Ratio |

| ----------- | --------- | ----- |

| [3] cm      | [12] cm   | [3]:[12]|

| [4] cm      | [16] cm   | [4]:[16]|

There are other possible ways as well, as long as the ratio is equivalent to 1:4.