x/3/4 = 100
what does x equal

The minimum number of students that must be in the professor's class in order to guarantee that at least 2 answer sheets are identical is 1025.

In order to answer this question, we need to use the Pigeonhole Principle, which states that if there are n pigeonholes and more than n objects, then at least one pigeonhole must contain more than one object.
In this case, the "pigeonholes" are the different possible combinations of answers for the 5 questions, and the "objects" are the students in the class.

Since there are 4 possible responses for each question, there are 4^5 = 1024 possible combinations of answers.
Now, suppose there are only 1023 students in the class.

Each student can choose one of the 1024 possible combinations of answers, and since there are more students than combinations, at least one combination must be chosen by two or more students.

Here are 5 questions, the total number of different answer sheets is 4^5 = 1024.

This represents the "pigeonholes." 3.

To guarantee that at least two answer sheets are identical, we need 1024 + 1 = 1025 students. This represents the "pigeons.

" According to the Pigeonhole Principle, if there are n pigeonholes and n+1 pigeons, at least one pigeonhole must contain at least two pigeons.

In this case, having 1025 students (pigeons) ensures that at least two students have identical answer sheets (pigeonholes).
But we want to guarantee that at least 2 answer sheets are identical.

This means we need to have one more student than the number of possible combinations, so that there is no way for each combination to be chosen by a different student.

Therefore, the minimum number of students required in the professor's class is 1024 + 1 = 1025.
So if there are 1025 or more students in the class, we can be sure that at least two answer sheets must be identical.

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Answer:

Step-by-step explanation:

To solve the system of equations by combining the equations, we can use the method of elimination:

x + 2y = -14 (equation 1)

-4x - y = 28 (equation 2)

We can eliminate y by multiplying equation 1 by 4 and adding it to equation 2:

4x + 8y = -56 (4 * equation 1)

-4x - y = 28 (equation 2)

7y = -28

Solving for y, we get:

y = -4

Substituting this value into equation 1, we get:

x + 2(-4) = -14

Solving for x, we get:

x - 8 = -14

x = -6

Therefore, the solution to the system of equations is x = -6 and y = -4.

Answer:

Let x = cube root of 400

Using a calculator x = 7.368 to 3 decimal places

So: 7 < x < 8

Hello there!

If a line has a slope of 3 and a y-intercept of 4, its equation looks like this:

\(y=3x+4\)

Hope this helps you! Mark Brainliest, please! :)

~Just a joyful teen

\(SilentNature\)

Answer:

y = 3x + 4

Step-by-step explanation:

Answer:

x        1            2             6            12         25

f(x)     22        34           82          154       310

f(3)= 46 means that in the third month, the online magazine provider will charge a total of $46.00

Step-by-step explanation:

For finding the missing f(x) values:

Plug in the x-values that are given into the original equation: f(x)= 12x + 10

ex: f(1)= 12(1) + 10 => 22

For finding the missing x value, set the original equation to the given f(x) value

ex: 34 = 12x + 10 => 2

Answer: There are 600 four-digit numbers divisible by 15.

Step-by-step explanation:

1005, 1020, 1035, 1050, 1065, 1080, 1095, 1110, 1125, 1140, 1155, 1170, 1185, 1200, 1215, 1230, 1245, 1260, 1275, 1290, 1305, 1320, 1335, 1350, 1365, 1380, 1395, 1410, 1425, 1440, 1455, 1470, 1485, 1500, 1515, 1530, 1545, 1560, 1575, 1590, 1605, 1620, 1635, 1650, 1665, 1680, 1695, 1710, 1725, 1740, 1755, 1770, 1785, 1800, 1815, 1830, 1845, 1860, 1875, 1890, 1905, 1920, 1935, 1950, 1965, 1980, 1995, 2010, 2025, 2040, 2055, 2070, 2085, 2100, 2115, 2130, 2145, 2160, 2175, 2190, 2205, 2220, 2235, 2250, 2265, 2280, 2295, 2310, 2325, 2340, 2355, 2370, 2385, 2400, 2415, 2430, 2445, 2460, 2475, 2490, 2505, 2520, 2535, 2550, 2565, 2580, 2595, 2610, 2625, 2640, 2655, 2670, 2685, 2700, 2715, 2730, 2745, 2760, 2775, 2790, 2805, 2820, 2835, 2850, 2865, 2880, 2895, 2910, 2925, 2940, 2955, 2970, 2985, 3000, 3015, 3030, 3045, 3060, 3075, 3090, 3105, 3120, 3135, 3150, 3165, 3180, 3195, 3210, 3225, 3240, 3255, 3270, 3285, 3300, 3315, 3330, 3345, 3360, 3375, 3390, 3405, 3420, 3435, 3450, 3465, 3480, 3495, 3510, 3525, 3540, 3555, 3570, 3585, 3600, 3615, 3630, 3645, 3660, 3675, 3690, 3705, 3720, 3735, 3750, 3765, 3780, 3795, 3810, 3825, 3840, 3855, 3870, 3885, 3900, 3915, 3930, 3945, 3960, 3975, 3990, 4005, 4020, 4035, 4050, 4065, 4080, 4095, 4110, 4125, 4140, 4155, 4170, 4185, 4200, 4215, 4230, 4245, 4260, 4275, 4290, 4305, 4320, 4335, 4350, 4365, 4380, 4395, 4410, 4425, 4440, 4455, 4470, 4485, 4500, 4515, 4530, 4545, 4560, 4575, 4590, 4605, 4620, 4635, 4650, 4665, 4680, 4695, 4710, 4725, 4740, 4755, 4770, 4785, 4800, 4815, 4830, 4845, 4860, 4875, 4890, 4905, 4920, 4935, 4950, 4965, 4980, 4995, 5010, 5025, 5040, 5055, 5070, 5085, 5100, 5115, 5130, 5145, 5160, 5175, 5190, 5205, 5220, 5235, 5250, 5265, 5280, 5295, 5310, 5325, 5340, 5355, 5370, 5385, 5400, 5415, 5430, 5445, 5460, 5475, 5490, 5505, 5520, 5535, 5550, 5565, 5580, 5595, 5610, 5625, 5640, 5655, 5670, 5685, 5700, 5715, 5730, 5745, 5760, 5775, 5790, 5805, 5820, 5835, 5850, 5865, 5880, 5895, 5910, 5925, 5940, 5955, 5970, 5985, 6000, 6015, 6030, 6045, 6060, 6075, 6090, 6105, 6120, 6135, 6150, 6165, 6180, 6195, 6210, 6225, 6240, 6255, 6270, 6285, 6300, 6315, 6330, 6345, 6360, 6375, 6390, 6405, 6420, 6435, 6450, 6465, 6480, 6495, 6510, 6525, 6540, 6555, 6570, 6585, 6600, 6615, 6630, 6645, 6660, 6675, 6690, 6705, 6720, 6735, 6750, 6765, 6780, 6795, 6810, 6825, 6840, 6855, 6870, 6885, 6900, 6915, 6930, 6945, 6960, 6975, 6990, 7005, 7020, 7035, 7050, 7065, 7080, 7095, 7110, 7125, 7140, 7155, 7170, 7185, 7200, 7215, 7230, 7245, 7260, 7275, 7290, 7305, 7320, 7335, 7350, 7365, 7380, 7395, 7410, 7425, 7440, 7455, 7470, 7485, 7500, 7515, 7530, 7545, 7560, 7575, 7590, 7605, 7620, 7635, 7650, 7665, 7680, 7695, 7710, 7725, 7740, 7755, 7770, 7785, 7800, 7815, 7830, 7845, 7860, 7875, 7890, 7905, 7920, 7935, 7950, 7965, 7980, 7995, 8010, 8025, 8040, 8055, 8070, 8085, 8100, 8115, 8130, 8145, 8160, 8175, 8190, 8205, 8220, 8235, 8250, 8265, 8280, 8295, 8310, 8325, 8340, 8355, 8370, 8385, 8400, 8415, 8430, 8445, 8460, 8475, 8490, 8505, 8520, 8535, 8550, 8565, 8580, 8595, 8610, 8625, 8640, 8655, 8670, 8685, 8700, 8715, 8730, 8745, 8760, 8775, 8790, 8805, 8820, 8835, 8850, 8865, 8880, 8895, 8910, 8925, 8940, 8955, 8970, 8985, 9000, 9015, 9030, 9045, 9060, 9075, 9090, 9105, 9120, 9135, 9150, 9165, 9180, 9195, 9210, 9225, 9240, 9255, 9270, 9285, 9300, 9315, 9330, 9345, 9360, 9375, 9390, 9405, 9420, 9435, 9450, 9465, 9480, 9495, 9510, 9525, 9540, 9555, 9570, 9585, 9600, 9615, 9630, 9645, 9660, 9675, 9690, 9705, 9720, 9735, 9750, 9765, 9780, 9795, 9810, 9825, 9840, 9855, 9870, 9885, 9900, 9915, 9930, 9945, 9960, 9975, 9990

There is a total of 600 four-digit numbers which are divisible by 15 and this can be determined by using the arithmetic progression.

Given :

Four-digit numbers are divisible by 15 and have 15 as the two middle digits.

Arithmetic progression can be used to determine the total number of four-digit numbers which are divisible by 15.

So by simply calculating in mind, it can be easily found out that the first four-digit number which is divisible by 15 is 1005 and similarly the last four-digit number divisible by 15 is 9990.

The \(\rm T_{n}\) term formula in the arithmetic progression is given by:

\(\rm T_n = a + (n-1)d\)    ----- (1)

where 'a' is the first term, 'd' is the difference between two consecutive numbers, \(\rm T_{n}\) is the last term in the progression, and 'n' is the total number of terms.

According to the given data the value of 'a' is 1005, the value of the last term \(\rm T_{n}\) is 9990 and the difference 'd' is 15.

Put the values of a, d, and \(\rm T_{n}\) in the equation (1).

\(9990=1005+(n-1)15\)

8985 = (n - 1)15

599 = n - 1

n = 600

Therefore, there is a total of 600 four-digit numbers which are divisible by 15.

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Angles are the space between intersecting lines, and they are measured in degrees or radians

The measure of angle ABC is y + x

The given parameters are:

ABD=y,

DBC=x,

EFH=y,

EFG=x

PQS = SQR = x

To determine the measure of angle ABC, we make use of angle ABD and angle DBC

Note that angle ABD and angle DBC have common vertices at points B and D

So, we have:

ABC = ABD + DBC

Substitute known values

ABC = y + x

Hence, the measure of angle ABC is y + x

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The critical numbers of the function h(p) = (p - 1) / (p^2 - 5) are "dne" (does not exist).

To find the derivative of h(p), we can apply the quotient rule. Taking the derivative, we have:

h'(p) = \([(p^2 - 5)(1) - (p - 1)(2p)] / (p^2 - 5)^2\)

Simplifying this expression, we get:

h'(p) = \((p^2 - 5 - 2p^2 + 2p) / (p^2 - 5)^2\)

= \((-p^2 + 2p - 5) / (p^2 - 5)^2\)

To find the critical numbers, we set h'(p) equal to zero and solve for p:

\(-p^2 + 2p - 5 = 0\)

However, this quadratic equation does not factor easily. We can use the quadratic formula to find the solutions:

p = (-2 ± √\((2^2 - 4(-1)(-5))) / (-1)\)

p = (-2 ± √(4 - 20)) / (-1)

p = (-2 ± √(-16)) / (-1)

Since the discriminant is negative, the equation has no real solutions. Therefore, the critical numbers of the function h(p) = (p - 1) / (\(p^2\) - 5) are "dne" (does not exist).

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Answer:

1. You can solve this problem by applying the Tangent Secant Theorem. Then, you have:

YX²=(YZ)(YV)

YX=√(YZ)(YV)

YZ=9+19

YV=9

2. When you substitute the values of YZ and YV into YX=√(YZ)(YV), you obtain:

YX=√(YZ)(YV)

YX=√(9+19)(9)

YX=√(28)(9)

YX=√252

YX=15.87

What is the length of YX?

The answer is: The lenght of YX is 15.87

Answer:

230 people

Step-by-step explanation:

55,200 divided by 240

Answer:

64

Step-by-step explanation:

the pattern is multiplying by 2 every day. if thursday there is 8 then friday there is (8X2) 16, saturday there is (16X2) 32, and sunday there is (32X2) 64.

Answer:

the correct answer is

Step-by-step explanation:

hope this helps u!!

The mean and the standard deviations values are calculated to be

Mean = 22; Standard deviation = 8.32

Information from the question include

The East Bay traps produce a mean of 12 pounds of lobsters per day with a standard deviation of 7 pounds.

The West Bay traps produce a mean of 10 pounds of lobsters a day with a standard deviation of 4.5 pounds.

the sum of the mean for the total weight of the lobsters is calculated by simple addition

= 12 + 10

= 22 pounds of lobsters per day

The standard deviation is not by simple addition it is solved as follows

= √(7² + 4.5²)

= 8.32 pounds

Therefore the mean and the standard deviation are 22 and 8.32 respectively

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be more specificlike what are the options

Answer:

904.88

Step-by-step explanation:

8.5% of 833.99 is 70.88915

70.88915 + 833.99 = 904.87915

904.87915 rounded to the closest cent is 904.88

Stay safe! <3

Answer:

The fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.

Step-by-step explanation:

Consider that the total take-home pay each month Jerry receives is, $x.

It is provided that:

The remaining amount can be computed by subtracting the amount spent from the total amount.

Compute the amount Jerry has spent so far:

Amount Spent = Car Payment + Food

                         \(=\frac{1}{6}x+\frac{1}{4}x\\\\=[\frac{1}{6}+\frac{1}{4}]x\\\\=[\frac{2+3}{12}]x\\\\=\frac{5}{12}x\)

Compute the remaining amount as follows:

Remaining Amount = Total Amount - Amount Spent

                                \(=x-\frac{5}{12}x\\\\=[1-\frac{5}{12}]x\\\\=[\frac{12-5}{12}]x\\\\=\frac{7}{12}x\)

Thus, the fraction of Jerry's take-home pay that is left after paying for these two items is 7/12.

Answer:

Yes! The sides 5,3 and 7 can create a triangle!

Step-by-step explanation:

It follows the rule:

a + b > c

a + c > b

c + b > a

The constant of proportionality is, 12

Yes, The graph of equation is a straight line.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Mark is planning a birthday party at the local skating rink.

And, The table shows the rates that are charged for parties at the skating rink.

Let two points on table are (5, 60) and (10, 120)

Now, The equation of line is,

⇒ y - 60 = (120 - 60) / (10 - 5) (x - 5)

⇒ y - 60 = 60/5 (x - 5)

⇒ y - 60 = 12(x - 5)

⇒ y - 60 = 12x - 60

⇒ y = 12x

Thus, The number of guests proportional to the cost.

And, Constant of proportionality = 12

And, The graph of y = 12x is a straight line.

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Complete question is shown in figure.

Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

Given that,

A fair coin is tossed 29 times.

We have to find what is the probability that at most 27 heads occur.

We know that,

A fair coin is tossed 29 times.

n=29

Probability of heads p=1/2

q= 1-p

q=1-1/2=1/2

We get

P (X=x) = ⁿCₓ qⁿ⁻ˣ pˣ

Now, the probability that at most 27 heads occurs is

P(X<27)

=1-[P(X=28)+ P(X=29)]

=1-[²⁹C₂₈(1/2)²⁹⁻²⁸(1/2)²⁸- ²⁹C₂₉(1/2)²⁹⁻²⁹(1/2)²⁹]

=1-[²⁹C₂₈(1/2)²⁹- ²⁹C₂₉(1/2)²⁹]

=1-[28+1](1/2)²⁹

=1-29×0.00000000186

=0.999999945

Therefore, Option- D is correct that is the probability that at most 27 heads occur is 0.99999994.

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Answer:

5.14 minutes

Step-by-step explanation:

4 pages / 7 minutes = 0.57 minutes per page

0.57 minutes/pg * 9 pages = 5.14 minutes

Answer:

he sum of a number and 16 is equal to 45. 2. The product of 6 and m is 216. 3. The difference of 100 and x is 57. 4. The quotient of z and 10 is 32. X+16= 45.

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

45 divided by 3 is 15 and if you multiply that by 2 you get 30. 32 - 2 is 30

Answer:

where is the table ? I can't answer

The flexible budget would reflect monthly operating income of $23,000 and $68,500 for 20,000 bottles of spray and 34,000 bottles of spray, respectively. The correct option is A.

The flexible budget is a tool that helps businesses to forecast their costs and revenues under different levels of activity. In this case, the flexible budget for Summer Nights bug spray is based on the following assumptions:

The selling price of each bottle of bug spray is $0.50.

The variable cost of each bottle of bug spray is $3.25.

The fixed cost is $42,000 for volumes up to 40,000 bottles of spray, and $60,000 for volumes above 40,000 bottles of spray.

The operating income for 20,000 bottles of spray is calculated as follows:

Revenue = 20,000 * $0.50 = $10,000

Variable costs = 20,000 * $3.25 = $65,000

Fixed costs = $42,000

Operating income = $10,000 - $65,000 - $42,000 = $23,000

The operating income for 34,000 bottles of spray is calculated as follows:

Revenue = 34,000 * $0.50 = $17,000

Variable costs = 34,000 * $3.25 = $110,500

Fixed costs = $60,000

Operating income = $17,000 - $110,500 - $60,000 = $68,500

Therefore, the flexible budget would reflect monthly operating income of $23,000 and $68,500 for 20,000 bottles of spray and 34,000 bottles of spray, respectively.

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a. The volume of water flowing out of the pipe every second can be calculated using the formula:

Volume per second = Area of the pipe * Speed of water

First, we need to calculate the area of the pipe. The diameter of the pipe is 8 inches, so the radius (r) is half of that, which is 4 inches (r = 4 inches).

Area of the pipe = π * r^2

Area of the pipe = π * (4 inches)^2

Area of the pipe ≈ 50.27 square inches

The speed of the water is given as 2 feet per second. We need to convert it to inches:

Speed of water = 2 feet/second * 12 inches/foot

Speed of water = 24 inches/second

Now, we can calculate the volume per second:

Volume per second = Area of the pipe * Speed of water

Volume per second = 50.27 square inches * 24 inches/second

Volume per second ≈ 1,206.48 cubic inches/second (rounded to two decimal places)

b. To find the height of the water in the tank after 5 minutes, calculate the volume of water that has flowed into the tank during that time.

Volume per minute = Volume per second * 60 seconds/minute

Volume per minute ≈ 1,206.48 cubic inches/second * 60 seconds/minute

Volume per minute ≈ 72,388.8 cubic inches/minute (rounded to one decimal place)

Divide the total volume of water by the cross-sectional area of the tank.

Cross-sectional area of the tank = π * (radius of tank)^2

Radius of the tank = 15 feet / 2 * 12 inches/foot = 90 inches

Cross-sectional area of the tank = π * (90 inches)^2

Cross-sectional area of the tank ≈ 25,465.84 square inches

Height of water in the tank after 5 minutes = Volume per minute / Cross-sectional area of the tank

Height of water in the tank after 5 minutes ≈ 72,388.8 cubic inches/minute / 25,465.84 square inches ≈ 2.84 inches (rounded to two decimal places)

c. To calculate the time required to fill 75% of the tank, we first need to find the total volume of the tank.

Volume of the tank = π * (radius of tank)^2 * height of tank

Volume of the tank = π * (90 inches)^2 * 6 feet * 12 inches/foot

Volume of the tank ≈ 2,034,711.57 cubic inches (rounded to two decimal places)

To find the time required to fill 75% of the tank, we multiply the total volume by 0.75 and divide it by the volume per minute.

Time to fill 75% of the tank = (0.75 * Volume of the tank) / Volume per minute

Time to fill 75% of the tank ≈ (0.75 * 2,034,711.57 cubic inches) / 72,388.8 cubic inches/minute ≈ 21.06 minutes

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The equation of a line that passes through the points (-4, 47) and (2, -16) is 21x + 2y - 10 = 0.

The standard form of a line is ax + by + c = 0. If the line passes through the points (x1, y1) and (x2, y2), the equation of the line is evaluated by

y - y1 = [(y2 - y1)/(x2- x1)] · (x - x1)

The given points are (-4, 47) and (2, -16).

The equation of the line that passes through these points is

y - 47 = (-16 - 47)/(2 + 4) × (x + 4)

⇒ y - 47 = -63/6 × (x + 4)

⇒ 6(y - 47) = -63(x + 4)

⇒ 6y - 282 = -63x - 252

⇒ 63x + 6y = 282 - 252 = 30

⇒ 21x + 2y = 10

Therefore, the required standard form of the line that passes through the given points is 21x + 2y - 10 = 0.

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Answer:

I think its geometric

Step-by-step explanation: it muiltiplying by 5

Answer:

Geometric.

It fits all the criteria to be a geometric sequence, not an arithmetic sequence.

Answer:

6c^6

Step-by-step explanation:

ASSUMING you meant 15 * sqrt(0.16c^12)

the parentheses are important, and without them, I can't tell what exactly you mean is square-rooted and what is not

Answer: 6c^6

Step-by-step explanation: