In an test with 30 students, 1 student has made 13 mistakes and
all other students have made fewer mistakes.
Prove that at least 3 students have made the same number of
mistakes.

Answer:

55

Step-by-step explanation:

Answer:

55/100

Step-by-step explanation:

The derivative dz/dt can be found using the chain rule. By differentiating each term with respect to t and applying the chain rule, we can calculate dz/dt as follows:

\(dz/dt = 2sin(t)cos(t) + 4e^tcos(t) + 4e^tsin(t) + 4e^t + 4sin(t)e^t.\)

By applying the chain rule, we can find dz/dt as follows: differentiate z with respect to x, then multiply it by dx/dt, and finally differentiate z with respect to y and multiply it by dy/dt.

The function z = x² + y² + xy can be rewritten as z = (sin(t))² + (4e^t)² + (sin(t))\((4e^t)\).

To find dz/dt, we need to find the partial derivatives of z with respect to x and y and multiply them by dx/dt and dy/dt, respectively.

The partial derivative of z with respect to x is (2x + y), and the partial derivative of z with respect to y is (2y + x).

Next, we differentiate x = sin(t) with respect to t, giving us dx/dt = cos(t).

Similarly, differentiating\(y = 4e^t\) with respect to t yields \(dy/dt = 4e^t.\)

Now we can apply the chain rule:

dz/dt = (2x + y) * dx/dt + (2y + x) * dy/dt

Substituting the expressions for x, y, dx/dt, and dy/dt:

\(dz/dt = (2sin(t) + 4e^t) * cos(t) + (2(4e^t) + sin(t)) * (4e^t)\)

Simplifying this expression will yield the final result.

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Answer:

c

Step-by-step explanation:

An interest rate expressed as 0.472 in decimal form is equivalent to 47.2% when expressed as a percentage.

To convert a decimal to a percentage, you need to multiply it by 100. In this case, the decimal 0.472 can be converted to a percentage by multiplying it by 100, resulting in 47.2%. The decimal representation signifies that the interest rate is 0.472 times the principal amount, whereas the percentage representation indicates that the interest rate is 47.2% of the principal amount.

When expressing interest rates, percentages are commonly used to provide a clearer understanding to individuals. Percentages make it easier to compare interest rates and determine the impact they will have on loans, investments, or savings.

The conversion between decimal and percentage forms is straightforward: move the decimal point two places to the right (equivalent to multiplying by 100) to convert from decimal to percentage, or move the decimal point two places to the left (equivalent to dividing by 100) to convert from percentage to decimal. In this case, the decimal interest rate of 0.472 becomes 47.2% when expressed as a percentage.

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Answer:

GH = 2√10

Step-by-step explanation:

Use the distance formula

d= √(x2-x1)²+(y2-y1)², where (x1= 0, y1=3) and (x2= -2, y2= -3)

d= √(-2-0)²+(-3-3)²

d= √4 +36

d= √40

d= 2√10

Answer:

  190

Step-by-step explanation:

The even digits and 5 cannot be in the units place of any 2-digit prime. That means the sum must be ...

  (2 +4 +5 +6)×10 +(1 +3 +7 +9) = 170 +20 = 190

__

There are several ways the set of primes can be created. A couple are ...

  {23, 41, 59, 67} or {29, 47, 53, 61}

Answer: 190

Step-by-step explanation: i just did Aops

If a bungee jumper free falls for 6 seconds, the bungee jumper falls 576 feet.

We are given that the amount of time it takes for a bungee jumper to free fall is given by the function t = √(d/16), where d represents the distance that the object falls in feet. We are also told that the bungee jumper free falls for 6 seconds.

To find the distance that the bungee jumper falls, we can plug in the value of t = 6 into the equation t = √(d/16) and solve for d.

t = √(d/16)

6 = √(d/16)

Square both sides to eliminate the square root:

36 = d/16

Multiply both sides by 16 to isolate d:

d = 36 x 16

d = 576 feet

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Complete question is:

The amount of time in seconds, t, it takes for a bungee jumper to free fall is given by the function t = √(d/16)  where d represents the distance that the object falls, in feet. if a bungee jumper free falls for 6 seconds, how far does the jumper fall?

4 Wrong Answers

\(Correct = 11*4=44\)

\(Incorrect = Correct - 40 = 4\)

The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.

The population proportion who participated in voting is given as 63% of all registered voters.

This means that out of every 100 registered voters, 63 participated in voting.

In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.

Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .

Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).

Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.

It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.

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Answer:so you have to get x by itself so minus 1 to both sides that would equals x=-6 thats your answer but if it was 2x=-6 then you wound divide until you get x by itself hope this helps but the answer is

x=-6

Step-by-step explanation:

Answer:

I got you!

So x is basically a placeholder for a number.  We don't know what that number is, so we just put the letter x so we can make an equation. x can also be shown as a ? or any symbol as long as it consitant throughout the whole equation. for x+1=-5, we are trying to find what number when added to 1 equals -5. Or.... 1+?=-5. We can subtract 1 from each side of the equation to get ?=-6. Or in this case, X=-6!

A right triangle is made up of two legs and one hypotenuse. The two legs meet at a 90° angle, and the hypotenuse is the right triangle's longest side and the side opposite the right angle.

Therefore,

M = 30°, O = 60°, Q = 90°. Because this is a right angle triangle with angle 90°

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Answer

The armadillo and Glyptodon descended from a common ancestor.

Step-by-step explanation:

The graph of g(x) is obtained by transformations of functions translating the graph of f(x) downward by 3 units, and the point (0, -3) is on the graph of g(x).

To transform the graph of f(x) = 3x to represent the function g(x) = 3x - 3, we need to perform a translation.

To translate the graph of f(x), we shift it vertically downward by 3 units. This means that each point on the graph of f(x) will be moved downward by 3 units to obtain the corresponding point on the graph of g(x).

The point (0, 0) on the graph of f(x) will be translated to (0, -3) on the graph of g(x), as it moves down by 3 units.

Therefore, the graph of g(x) is obtained by transformations of functions translating the graph of f(x) downward by 3 units, and the point (0, -3) is on the graph of g(x).

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Answer:

The intrest rate is 8% and after 7 years she will have made 149.90 in total intrest.

To compute the surface area of revolution about the -x- axis over the interval [0,1] for y=−3, we can use the formula:

SA = 2π ∫[a,b] y√(1+(dy/dx)²) dx

where a=0, b=1, and dy/dx is the derivative of y with respect to x. In this case, y=−3, so dy/dx=0.

Plugging in these values, we get:

SA = 2π ∫[0,1] -3√(1+0²) dx
SA = -6π ∫[0,1] dx
SA = -6π[x]₀¹
SA = -6π(1-0)

SA = -6π

Since surface area cannot be negative, we take the absolute value of the result, which gives us:
SA = 6π

Therefore, the surface area of revolution about the -x- axis over the interval [0,1] for y=−3 is 6π.

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a)0.1587 (or 15.87%)

b)0.6827 (or 68.27%)

c)0.0228 (or 2.28%)

1. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height less than 63 inches is 0.1587 (or 15.87%).

2. Using the Normal Distribution formula with a mean (μ) of 64 inches and standard deviation (σ) of 10 inches, the probability of randomly selecting a female college student with a height between 61 and 69 inches is 0.6827 (or 68.27%).

3. Using the Central Limit Theorem, the probability of finding an average of greater than 65 inches with a sample of 35 female college students is 0.0228 (or 2.28%).

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Answer: False

Step-by-step explanation:

4 x 106 = 424

Answer: false

Step-by-step explanation: I'm not even going to explain it just multiply 4 x 106

False - A test statistic with a larger absolute value is less likely by chance alone with a T distribution.

False - When comparing a T distribution to a Z distribution, a test statistic with a larger absolute value is less likely by chance alone with a T distribution.

The T distribution has heavier tails compared to the Z distribution, meaning it has more probability in the tails and less in the center. As a result, extreme values or larger absolute values of the test statistic are less likely to occur by chance alone in a T distribution compared to a Z distribution.

The T distribution is typically used when dealing with smaller sample sizes and when the population standard deviation is unknown and estimated from the sample. In such cases, the T distribution accounts for the added uncertainty associated with smaller sample sizes, resulting in a more conservative approach when evaluating the likelihood of extreme test statistics.

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Answer:

if the question is what is the are of the circle without the rectangle inside it, then we could solve it easily using the Mathematical formula for A Circle's area which is

\(\pi {r}^{2} \)

since a radius is half a diameter, and the diameter is 8cm, the radius becomes 4 cm

Step-by-step explanation:

π×4^2

3.14×16

50.24

If the function gives a line with a slope of 1.55 and the monthly cost for 17 HCF is $47.51, The monthly cost for 21 HCF is:   $53.71.

Let make use of slope-intercept form, y = mx + b.

Since the  slope is 1.55. And since 17 HCF costs $47.51, we the point on the line  is (17, $47.51)

Now let plug   the data above into our equation

$47.51= 1.55 (17) + b

Multiply

$47.51 = 26.35+ b

Subtract 26.35 form both sides

21.16 = b

So,  

y= mx + b

y = 1.55x + 21.16

Now let find the monthly cost where x = 21

y= 1.55 (21) +  21.16

Simplify

y = 32.55 + 21.16

y = $53.71

Therefore 21 HCF would cost the amount of  $53.71

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The features of the relation are given as follows:

1. Independent variable: number of weeks.

2. Dependent variable: money saved.

3. Yes, the relationship is linear.

4. The slope is of 40.

5. The domain is: {0, 1, 2, 3, 4, 5, 6, 7}.

6. The range is: {50, 90, 130, 170, 210, 250, 290, 330}.

7. The y-intercept is of $50.

8. The table has no x-intercept.

The output variable is a function of the input, hence the output is the dependent variable and the input is the independent variable.

The input and the output in this problem are given as follows:

In a linear relation, the rate of change of the output relative to the input is constant, and is called slope.

In the context of this problem, the money saved has a constant increase of $40 each week, hence:

The domain is the set containing the input values of the function, hence the number of weeks, as follows:

{0, 1, 2, 3, 4, 5, 6, 7}.

The range is the set containing the output values of the function, hence the money saved, as follows:

{50, 90, 130, 170, 210, 250, 290, 330}.

The y-intercept is the value of y when x = 0, hence, from the table, it is of:

y = 50.

The x-intercept is the value of x when y = 0. From the given table, y never assumes a value of 0, hence the function has no x-intercept.

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It is not of exponential order for h(t) = et2. F is of exponential order and has order. F is piecewise continuous. No function's Laplace transform is possible. g(t) = eat, where t [0,.

Non-exponential form:

To represent a scientifically notated number as a non-exponential quantity: • Remove the exponential component of the number by moving the decimal point the same number of places as the exponent's value. The decimal is moved to the right by the same number if the exponent is positive.

Here are a few instances of functions other than exponential ones. y = 3 1 x as a result. n = 0 3 p as a result. Because y = ( 4) x. Since b = 1, y = 6 0 x.

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Thus, the test for homogeneity follows the same procedures as the test for independence because the assumptions for performing the chi-square test for independence and chi-square test for homogeneity are the same.

The procedures for the chi-square test of homogeneity are the same as for the chi-square test of independence. The data is different for both tests. Tests of independence are used to determine whether there is a significant relationship between two categorical variables from the same population. One population is segmented based on the value of two variables. So there will be a column variable and a row variable.

The chi-square test of homogeneity of proportions can be used to compare population proportions from two or more independent samples, determining whether the frequency counts are distributed identically among different populations.

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Step-by-step explanation:

there is to be a stage 15m wide and 3m deep with a curved seating area as shown

Determine the area of the seating area?

Answer:

Comparison Group

Step-by-step explanation:

Answered this question for another person on Brainly :)

Answer:

Randomized control and experimental groups

When P is true, and Q is false, the proposition P ⊃ Q is false. Therefore, the answer is TFTT. The correct answer is option d. TFTT.

The given truth table for the compound proposition P ⊃ Q is: P Q P⊃QT T T T T F FT F T T F

The conditional P ⊃ Q implies that whenever the antecedent P is true, then the consequent Q is true as well.

This implies that the only time the conditional P ⊃ Q is false is when the antecedent is true, but the consequent is false.

Since we see in the truth table that when P is true, and Q is true, the proposition P ⊃ Q is also true.

However, when P is true, and Q is false, the proposition P ⊃ Q is false. Therefore, the answer is TFTT.

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The type of distribution which is utilized for the nominal data is option  b. Binomial distribution.

The appropriate distribution for nominal data is a binomial distribution.

The binomial distribution is used when the data consists of two possible outcomes.

The two outcomes such as success or failure, heads or tails, or pass or fail.

In nominal data, the categories do not have any inherent order.

And there is no numerical value associated with each category.

The binomial distribution gives the probability of obtaining a certain number of successes in a fixed number of independent trials.

The required probability of success is the same for each trial.

Therefore, option b.  binomial distribution is considered as more appropriate distribution for the nominal data.

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