Each side of a square is increasing at a rate of 7 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 16 cm2

To get the average rate of change between two points of a function, we use the formula:

In this case, we have:

Let's calculate p(4) and p(-7):

Now let's complete the calculation for the average:

So, the answer is 10.

1. The probability that exactly 12 students drive to school is 0.169.

2.The probability that more than 15 students drive to school is 0.027.

3. The probability that no more than 10 students drive to school is 0.004.

4. The mean and standard deviation of the sample are 13.6 and 2.4, respectively.

5. The percentage falling within 1 standard deviation of the mean is approximately 68%, which satisfies the empirical rule for normal distributions.

This problem involves the binomial distribution, since each student either drives to school (success) or does not (failure), and the probability of success is given as 0.68 for each student.

(1) The probability that exactly 12 students drive to school is given by the binomial probability mass function:

P(X = 12) \(= (20 choose 12) * (0.68)^12 * (1 - 0.68)^(20 - 12) = 0.169\)

(2) The probability that more than 15 students drive to school is given by the complement of the probability that at most 15 students drive to school:

P(X > 15) = 1 - P(X <= 15) = 1 - sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i)}\) for i = 0 to 15.

This is approximately 0.027.

(3) The probability that no more than 10 students drive to school is given by the cumulative distribution function:

P(X <= 10) = sum[(20 choose i) * \((0.68)^i * (1 - 0.68)^{20 - i}\) for i = 0 to 10. This is approximately 0.004.

(4) The mean of the binomial distribution is given by the formula np, where n is the sample size and p is the probability of success.

Thus, the mean is 200.68 = 13.6.

The standard deviation of the binomial distribution is given by the formula sqrt(np(1-p)), which is approximately 2.4.

(5) The percentage falling within one standard deviation of the mean is approximately 68% by the empirical rule, which is the same as the percentage of students who drive to school in the university.

However, the empirical rule applies to normal distributions, and the binomial distribution is not exactly normal.

Nonetheless, for large sample sizes, the binomial distribution can be approximated by a normal distribution using the central limit theorem, which would make the empirical rule applicable.

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Answer:

-7.1

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

4,12

1,3

4/12=4

12/3=4

The point (1,3) is mapped to the point by a dilation with the origin as the center. The dilation's scale factor is 4.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.

Finding the dilation's centre point is the first step in determining the scale factor. Next, we measure the distances between the centre point and various points on the preimage and the image. The ratio of these distances gives us the scale factor, as Math Bits Notebook accurately states.

The basic formula to find the scale factor of a dilated figure is: Scale factor is equal to the difference between the dimensions of the old and new shapes.

= 4,12

= 1,3

= 4/12 =4

= 12/3 =4

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The statement "P(A or B) = P(A) + P(B)" is False.

The correct statement is "P(A or B) = P(A) + P(B) - P(A and B)," which is known as the general law of addition for probabilities. This law takes into account the possibility of events A and B overlapping or occurring together.

The general law of addition for probabilities states that the probability of either event A or event B occurring is equal to the sum of their individual probabilities minus the probability of both events occurring simultaneously. This adjustment is necessary to avoid double-counting the probability of the intersection.

Let's consider a simple example. Suppose we have two events: A represents the probability of flipping a coin and getting heads, and B represents the probability of rolling a die and getting a 6. The probability of getting heads on a fair coin is 0.5 (P(A) = 0.5), and the probability of rolling a 6 on a fair die is 1/6 (P(B) = 1/6). If we assume that these events are independent, meaning the outcome of one does not affect the outcome of the other, then the probability of getting heads or rolling a 6 would be P(A or B) = P(A) + P(B) - P(A and B) = 0.5 + 1/6 - 0 = 7/12.

In summary, the general law of addition for probabilities states that when calculating the probability of two events occurring together or separately, we must account for the possibility of both events happening simultaneously by subtracting the probability of their intersection from the sum of their individual probabilities.

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Answer:34359738368

Step-by-step explanation: 2 to the 35th power is basically 2 x 2 35 times. You can solve it on a caculator by typing in 2 and pushing the button that allows you to enter 35 (which is the exponent, or the little number) The button will usually have an x with a little y at the top right corner

Given that,

Principal amount, P = 2000 dollars

Rate of interest, r = 6.75% = 0.0675

Final amount, A = 2900 dollars

The formula to find the final amount in a compound interest is,

A = P (1 + \(\frac{r}{n}\) )^ (nt)

n = number of times interest compounded in a year = 12 (Since compounded monthly.

Substituting the given values,

\(2900 = 2000 \huge \text[1 + \huge \text(\dfrac{0.0675}{12} \huge \text)\huge \text]^{(12t)}\)

\(2900 = 2000 (1.005625)^{(12t)\)

\(2900 = 2000 (1.069628)^t\)

\((1.069628)^t = 1.45\)

Taking logarithms on both sides,

\(\text{t} =\dfrac{\text{log}(1.45)}{\text{log}(1.069628)}\)

\(\boxed{\bold{t = 5.52 \thickapprox 5.5}}\)

Hence the time that the person must keep the money is 5.5 years.

Answer:

26-x

Step-by-step explanation:

If he started with 26 learners he lost x. Imagine x was a value of 5. To get the learners left you will have to subtract the numbers he lost from 26

(12x+5y)/3z

substitute in values

(12(12) + 5(6)) / 3(3)

simplify

(144 + 30) / 9

add

174 / 9

factor out a 3

58 / 3

Hope this helps :)

If you need any more explanation, feel free to ask.  If this really helps, consider marking brainliest.

- Jeron

Six pairs of congruent angles are:

To name six pairs of congruent angles:

Given: BCDE ≅ RSTU

Then,

Now, connect diagonals BD and RT.

So,

Therefore,  six pairs of congruent angles are:

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Answer:

your answer is -5-4-3-2-11

Step-by-step explanation:

this is because -5-4-3-2-11=-26, and that is the lowest term there

Answer:

(C) 7.5 units.

Step-by-step explanation:

If an empty can weighs 3 units each, there are 12 cans. The cans by themselves would weigh 3 * 12 = 36 units. Since the total weights of the syrup in cans is 492 units, the 5 liters of syrup (without the cans) would weigh about 492 - 36 = 456 units.

12 of 5 liters of syrup, we can say there are 12 * 5 = 60 liters of syrup. So, to find the weight of 1 liter of syrup, we just need to do 456 / 60 = 7.6. That is approximately 7.5 units.

So, the weight of 1 liter of syrup alone (without a can) is most nearly (C) 7.5 units.

Hope this helps!

L.C.M of 27, 12 and 36 is 108

L.C.M of 25 and 6 is 200

L.C.M of 14 and 12 is 84

L.C.M of 9, 8 and 7 is 504

L.C.M of 22 and 4 is 44

L.C.M of 32, 24 and 18 is 288

This the the smallest number that a certain group of numbers can divide without remainder.

Analysis:

The product of 27, 12 and 36 is 11664, which can only be divided by 108.

Therefore 108 is the L.C.M of the numbers.

The product of 25 and 8 is 200 which is only divisible by 200.

The product of 14 and 12 is `168 which is divisible by 84.

The product of 9, 8 and 7 is 504, which is divisible by 504

The product of 22 and 4 is 88 which is only divisible 44

The product of 32, 24 and 18 is 13824 which is only divisible by 288.

In conclusion, The L.C.M of the numbers are 108, 200, 84, 504, 44, 288 respectively.

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Answer:

\(3g + 40\) and g= 60

Step-by-step explanation:

hope this helps have a good rest of your night :) ❤

Answer:

C.$946.90

Step-by-step explanation:

S.I = 850×1.9×6÷100= $946.90

Answer:

I=prt

I=850×0.019×6

I=96.90

Step-by-step explanation:

Answer:

system of function:

f(x)=.5x+6

f(x)=x^2; x > 2

Step-by-step explanation:

there's a screenshot attached. Explanation: I'm using desmos and just type the functions like what the screenshot did to graph the piecewise function made by two functions

Step-by-step explanation:

hjh e e l c ma'am ww ww I can get a few

Answer:

between 10 and 12

Step-by-step explanation:

Given the measure of angles:

m∠B = 70°

m∠C = 60°

m∠A = 50°

Following this information, since the side lengths are directly proportional to the angle measure they see:

Angle B is the largest angle. Therefore, side AC is the longest side of the triangle since it is opposite of the largest angle.

Angle C is the smallest angle, so the side AB is the shortest side.

Therefore, side BC must be between 10 and 12 inches.

To construct a 90% confidence interval for the population proportion of all iPhones that obtain over 94 apps, we first need to calculate the sample proportion: p = 21/34 = 0.618.

Next, we need to determine the standard error of the proportion: SE = √(p(1-p)/n) = √(0.618(1-0.618)/34) = 0.097
Using a z-score of 1.645 (corresponding to a 90% confidence level), we can calculate the margin of error:
ME = z*SE = 1.645*0.097 = 0.160.

Finally, we can construct the confidence interval: p ± ME = 0.618 ± 0.160 = (0.458, 0.778)
Therefore, we can be 90% confident that the true proportion of all iPhones that obtain over 94 apps is between 0.458 and 0.778.

To construct a 90% confidence interval for the population proportion of all iPhones that obtain over 94 apps, we will use the following formula: CI = p ± z * √(p(1-p)/n), Here, p is the sample proportion, z is the z-score for the given confidence level, and n is the sample size.

First, we calculate the sample proportion (p): p = (Number of iPhones with over 94 apps) / (Total number of iPhones in the sample) = 21/34 ≈ 0.6176, For a 90% confidence interval, the z-score (z) is given as 1.645 (since z0.05 = 1.645).
Now, we can plug the values into the formula:

CI = 0.6176 ± 1.645 * √(0.6176 * (1 - 0.6176) / 34)
CI = 0.6176 ± 1.645 * √(0.2361 / 34)
CI = 0.6176 ± 1.645 * 0.0790
CI = 0.6176 ± 0.1301

Thus, the 90% confidence interval for the population proportion of all iPhones that obtain over 94 apps is approximately (0.4875, 0.7477).

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The city's population was changing by approximately 170.088 thousand persons/year between 2029 and 2037.

The population of a city can be modeled by P(t) = 170.088 thousand persons, where t is the number of years after 2000. To find out how rapidly the city's population was changing between 2029 and 2037, we need to calculate the difference in population between these two years and divide it by the number of years.

First, we need to find the population in 2029 and 2037. We can do this by plugging in the values of t into the equation:

P(29) = 170.088 * 29 = 4932.552 thousand persons

P(37) = 170.088 * 37 = 6293.256 thousand persons

Next, we need to find the difference in population between these two years:

P(37) - P(29) = 6293.256 - 4932.552 = 1360.704 thousand persons

Finally, we need to divide this difference by the number of years to find the rate of change:

1360.704 / (37 - 29) = 170.088 thousand persons/year

Therefore, the city's population was changing by approximately 170.088 thousand persons/year between 2029 and 2037.

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The length of the line segment B'C' is 3 units.

We can see that from the given graph that,

The coordinates of the points are:

B = (-2, 6)

C = (-2, 3)

If we translate the points 5 units to the right then the changed coordinates will be -

B' = (-2 + 5, 6) = (3, 6)

C' = (-2 + 5, 3) = (3, 3)

So the length of the B'C' is given by,

B'C' = √((3 - 3)² + (6 - 3)²) = √(0² + 3²) = √(0 + 9) = √9 = 3 units.

Hence the length of the line segment B'C' is 3 units.

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a. This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).

b. This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).

c. This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).

a. The mathematical relationship or model that shows ending inventory as a function of beginning inventory, production, and demand can be represented as:

sj = sj-1 + xj - dj

This equation states that the ending inventory for period j (sj) is equal to the beginning inventory from the previous period (sj-1) plus the production quantity in period j (xj), minus the demand in period j (dj).

b. If the production capacity for period j is given by Cj, the constraint that should be added is:

xj ≤ Cj

This constraint ensures that the production quantity in period j (xj) does not exceed the production capacity for that period (Cj).

c. If inventory requirements for period j mandate an ending inventory of at least Ij, the constraint that should be added is:

sj ≥ Ij

This constraint ensures that the ending inventory for period j (sj) is greater than or equal to the required inventory level for that period (Ij).

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Answer:

x = 138

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = B+ C

x = 68+ 70

x =138

Answer:

138 degrees

Step-by-step explanation:

A triangle is made up of 180 degrees, it lists 2 values already, 68&70. when added that equals 138.

So 180-138 is 42 degrees, which would be the last angle within the triangle.

Since a line is also 180 degrees, its 180-42, which makes x 138 degrees

Answer:

Step-by-step explanation:

Your question is incomplete.  Are you rounding to the nearest 100?  nearest 100,000?

4725806 to the nearest thousand is 4725800.

4725806 to the nearest unit is 4725806.

                 to the nerest ten is 4725810.

The radius of circle for the given length of rod is found as 1.65 ft

Perimeter of circle = 2 π r

In which,

When the length of the rod is bent to form the circle.

Length of rod = Perimeter of circle

10.38 = 2 π r

r = 10.38 /  2 π

r = 1.65

Thus, the radius of the circle for the given length of rod is found as 1.65 ft.

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Answer:

31 Minutes

Step-by-step explanation:

4.78 = 0.15 + 0.58

0.15m = 4.78 - 0.58

m = 4.78 - 0.58 divided by 0.15 = 28 minutes

So in total we have 28 + 3 = 31 minutes

Answer:

Ok, so to find the volume of a sphere, the volume is 4/3 (3.14 which is pie) times the radius cubed so r^3

so the radius of this sphere is 2 because 4-2=2

Step-by-step explanation:

so now we do 4/3 times 3.14 times 2^3 power=

now first we multiply 4/3 times 2 to the 3rd power bc we dont need to multiply pie (3.14) your answer would be 10.66667 so its 10.66667 pie (3.14) so round 10.66667 it would just be 10.7 because the 7 round up the 6 to a 7. Hope this helps!