Find two positive numbers whose square have a sum of 34 and difference of 16

There are 51,121,423 different committees that can be formed from 12 teachers and 32 students if the committee consists of both teachers and students.

To find the number of different committees that can be formed from 12 teachers and 32 students if the committee consists of both teachers and students, we need to use the combination formula. We can choose k members from a group of n members by using the formula:

n choose k = n! / (k! * (n-k)!)

In this case, we want to choose a committee that consists of both teachers and students, so we need to choose at least one teacher and at least one student. We can do this by choosing 1, 2, 3, ..., 11, or 12 teachers, and then choosing the remaining members of the committee from the students.

Let's start with choosing 1 teacher. There are 12 choices for the teacher, and we need to choose the remaining members of the committee from the 32 students. We can choose k students from a group of 32 students using the combination formula:

32 choose k = 32! / (k! * (32-k)!)

So the total number of committees that can be formed with 1 teacher and k students is:

12 * 32 choose k

To find the total number of committees that can be formed with at least one teacher and at least one student, we need to sum up the number of committees for each possible number of teachers:

total = 12 * (32 choose 1) + 12 * (32 choose 2) + ... + 12 * (32 choose 31) + 12 * (32 choose 32)

This is a bit cumbersome to calculate, but fortunately there is a shortcut: we can use the complement rule to find the number of committees that do not include any teachers, and then subtract this from the total number of committees. The number of committees that do not include any teachers is simply the number of committees that can be formed from the 32 students:

32 choose k = 32! / (k! * (32-k)!)

So the total number of committees that can be formed with at least one teacher and at least one student is:

total = 12 * (32 choose 1) + 12 * (32 choose 2) + ... + 12 * (32 choose 31) + 12 * (32 choose 32)
     = 12 * (2^32 - 1) - 32 choose 0
     = 12 * (2^32 - 1) - 1
     = 51,121,423

Therefore, there are 51,121,423 different committees that can be formed from 12 teachers and 32 students if the committee consists of both teachers and students.

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Answer:

answer would be -2/5

Step-by-step explanation:

i think thats what you mean i hope this helps

Answer: t= -1/3

Step-by-step explanation:

Multiply both sides of the equation by 15

-12t+6=10

Move constant to the right-hand side and change its sign

-12t=10-6

Subtract the numbers

-12t=4

Divide both sides of the equation by -12

t=-1/3

Alternative form:

t=-0.3333333333333333

Answer:

D

Step-by-step explanation:

when x=1, y should = 2

2(1)=2

so y=2x is correct

if ΔEFG, e = 75 cm, m∠G=141° and m∠E=16° then length of g is 171.24 cm

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

Given that ΔEFG, e = 75 cm, m∠G=141° and m∠E=16°

We need to find the length of g.

Because two angles are given, F = 180 – (141 +16 )

m∠F=180-157F=23

Now let us apply the sine rule

SinE/e=SinF/g

Sin16/75=sin23/g

g=171.24 cm

Hence, if ΔEFG, e = 75 cm, mm∠G=141° and mm∠E=16° then length of g is 171.24 cm

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Answer: 3/5

Step-by-step explanation:

my geometry teacher told me lolol

If a categorical independent variable contains 4 categories, then four dummy variables will be needed to uniquely represent these categories. a. 1 b. 2 c. 3 d. 4

How many dummy variables are needed to represent the categorical variable?

We need 1 less dummy variable than outcomes for the categorical variable.

categorical variable has 2 outcomes

So, we need 2-1 = 1 dummy variable.

Note: If our categorical variable had 5 outcomes, we would need 5-1 = 4 dummy variables.

b. Write the multiple regression equation relating the dependent variable to the independent variables.

Note: Depending your your professor, this can be written one of the following ways...

yhat = a + b1 x1 + bx2

yhat = b0 + b1 x1 + b2 x2

yhat = beta0hat + beta1hat x1 + betahat2 x2

where x1 is the ratio variable

and x2 is the dummy variable

c. Interpret the meaning of the coefficients in the regression equation.

b0 = the predicted value of y when x1 and x2 both equal 0.

b1 = the change in y when x1 increases by 1 unit holding x2 constant.

b2 = the predicted difference in y between the two possible outcomes of the categorical variable holding x1 constant

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Answer:

Mary ran the farthest

Step-by-step explanation:

Look at Diagram :)

As the Diagram shows, Mary ran the farthest!

Hope this Helps!

Answer:

u get 59.08 divide by 52 multiply by 100% u get da answer

Answer:

Becky is 7 years old.

Step-by-step explanation:

Let b - Becky's age

Equation - 3b = 21

Divide both size by 3 to isolate the variable.

21/3 is 7.

If Johnny is 21 years old he is three times as old as Becky then age of Becky is 7 years.

Two or more expressions with an Equal sign is called as Equation.

Given that Johnny is 21 years old

Johnny is three times as old as Becky.

We have to find the age of Becky.

Let x be the age of Becky.

As Johnny is three times as old as Becky.

We can write the equation as below

21=3x

Divide both sides by 3

7=x

Hence, if Johnny is 21 years old he is three times as old as Becky then age of Becky is 7 years.

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Answer:

math science and lot and etc

The volume of the solid is 9 cubic units, which is determined by the base in the first quadrant bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. As the cross sections perpendicular to the x-axis are squares, the volume can be calculated.

The volume of the solid can be calculated by finding the area of the base and then multiplying it by the height of the solid. The base of the solid is in the first quadrant and is bounded by the y-axis, the graph of y = x-1, the horizontal line y = 3, and the vertical line x = 1. This region forms a trapezoid, with an area of 6. As the cross sections perpendicular to the x-axis are squares, the height of the solid is 3 units. Thus, the volume of the solid is 6 multiplied by 3, which gives us a total volume of 9 cubic units. To calculate the volume, it is important to identify the base of the solid and the shape of the cross sections perpendicular to the x-axis. This will allow us to calculate the area of the base, and multiply it by the height of the solid to determine the total volume.

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Answer: -5/3

Step-by-step explanation:

Answer: m = -4/3

Step-by-step explanation:

If you're given two different coordinates, and you want to find the slope, the general rule is that you subtract the first coordinates from the first. The formula for these kinds of problems is \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\) .

The present value of the sequence of annual payments of Rs 25000 each, the first being made at the end of the 5th year and the last being paid at the end of the 12th year, if money is worth 6% is Rs. 158620.39.

1: We can use the formula to calculate the present value of the annuity:

P = A x [1 - (1+i)^-n] / i

Where

P = Present Value

A = Annuity

i = Interest Raten = Number of payments

2: Calculate the present value of each payment using the formula:

P1 = 25000 / (1.06)⁵

P2 = 25000 / (1.06)⁶

P3 = 25000 / (1.06)⁷

P4 = 25000 / (1.06)⁸

P5 = 25000 / (1.06)⁹

P6 = 25000 / (1.06)¹⁰

P7 = 25000 / (1.06)¹¹

P8 = 25000 / (1.06)¹²

3: Substitute the values into the formula to find the present value:

P = P1 + P2 + P3 + P4 + P5 + P6 + P7 + P8

P = (25000 / (1.06)⁵) + (25000 / (1.06)⁶) + (25000 / (1.06)⁷) + (25000 / (1.06)⁸) + (25000 / (1.06)⁹) + (25000 / (1.06)¹⁰) + (25000 / (1.06)¹¹) + (25000 / (1.06)¹²)

P = 158620.39

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In a simple regression model, the unexplained variation in the response variable is determined by summing the squares of errors. This method, known as residual sum of squares (RSS), quantifies the discrepancy between the observed values and the predicted values by the regression model.

In a simple regression model, the goal is to find a line that best fits the relationship between a single predictor variable (X) and a response variable (Y). However, due to various factors and sources of variability, the observed values of the response variable may not perfectly align with the predicted values based on the regression line.

The errors, or residuals, are the differences between the observed values and the predicted values. To quantify the unexplained variation, the errors are squared to eliminate negative values and emphasize larger deviations. These squared errors are then summed up, resulting in the residual sum of squares (RSS).

By calculating the RSS, one can assess the amount of unexplained variation or "error" in the regression model. A smaller RSS indicates that the model provides a better fit to the data, as it suggests less unexplained variation. On the other hand, a larger RSS implies a less accurate fit, with more unexplained variation in the model.

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The equation x = z represents a line in three-dimensional space that passes through the origin and has a slope of 1.

The equation x = z represents a line in three-dimensional space. In this case, the line is a diagonal line that extends infinitely in both the positive and negative directions. It passes through the origin (0, 0, 0) and has a slope of 1.

To understand this visually, imagine a coordinate system with x, y, and z axes. The line x = z can be represented by points such as (1, 0, 1), (-2, 0, -2), (3, 0, 3), and so on. These points all lie on the line where the x and z coordinates are equal.

You can also think of this equation as saying that the x-coordinate of a point is always equal to its z-coordinate. So if you have a point like (2, 0, 2), the x and z coordinates are equal, satisfying the equation x = z.

In terms of the region represented by this equation, it's a straight line that extends infinitely in both the positive and negative directions in the x-z plane. All points on this line have the property that their x and z coordinates are equal.

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The equation x = z represents a line in a three-dimensional coordinate system.

The equation x = z represents a line in a three-dimensional coordinate system. In this equation, the x-coordinate is always equal to the z-coordinate. This means that for any point on the line, the x-coordinate and the z-coordinate have the same value.

To understand this visually, imagine a three-dimensional coordinate system with x, y, and z axes. When x = z, it means that the points on the line have the same x and z values, while the y-coordinate can take any value. This line extends infinitely in both the positive and negative directions along the x and z axes.

For example, if we take the point (1, 2, 1) on this line, we can see that the x-coordinate (1) is equal to the z-coordinate (1). Similarly, if we take the point (-2, 5, -2), the x-coordinate (-2) is equal to the z-coordinate (-2).

In conclusion, the equation x = z represents a line in a three-dimensional coordinate system where the x-coordinate is always equal to the z-coordinate.

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Answer:

C

Step-by-step explanation:

The answer is w = 15.

-2w = -30 Divide -2 from both sides of the equation.

-2w ÷ -2 = -30 ÷ -2

w = 15

Answer:

The central angle, θ = (θ × 2π)/360°

Step-by-step explanation:

The diagram of the circle isn't provided, hence, the numerical value of the central angle, θ, isn't known.

But I'll be providing how to generally convert angles in degrees to their radian equivalent.

First of, for this conversion, we need to know that

360° = 2π radians

Then

θ = (θ × 2π)/360°

Hope this Helps!!!

Answer:

2.5

Step-by-step explanation:

khan academy

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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Answer:

circumference = π2r = (3.14)(2)(21) = 131.88 miles

Step-by-step explanation:

Answer:

131.9

Step-by-step explanation:

\(3.14 \times 21 \times 2\)

Answer:

Step-by-step explanation:

3m + 5 > 2(m - 7)

3m + 5 > 2m - 14

3m - 2m > -14 - 5

m > -19

Answer:

a₇ =  2.375

Step-by-step explanation:

There is a common ratio r between consecutive terms, that is

r = \(\frac{-76}{152}\) = \(\frac{38}{-76}\) = \(\frac{-19}{38}\) = - \(\frac{1}{2}\)

This indicates the sequence is geometric with nth term

\(a_{n}\) = a₁ \((r)^{n-1}\)

where a₁ is the first term and r the common ratio

Here a₁ = 152 and r = - \(\frac{1}{2}\) , then

\(a_{n}\) = 152 \((-\frac{1}{2}) ^{n-1}\) , so

a₇ = 152 \((-\frac{1}{2}) ^{6}\) = 152 × \(\frac{1}{64}\) = 2.375

Answer:

Solution given:

first term [a]=152

second term[b]=-76

common ratio[r]=\( \frac{-76}{152}\)=-1/2

now

for nth term ,we have

nth term =a \( {r}^{n -1} \)

now

7th term==152\( {-1/2}^{7 - 1} \)

=152×1/64=19/8

The maximum depth under water at which the shell of a chambered nautilus can withstand the pressure is 2589 feet (rounded to the nearest foot).

To determine the maximum depth at which the shell of a chambered nautilus can withstand the pressure, we need to calculate the total pressure the shell can endure and then convert it to depth. The total pressure consists of atmospheric pressure and hydrostatic pressure per foot of depth underwater.

The atmospheric pressure is 14.7 psi, and the hydrostatic pressure per foot of depth is 0.45 psi. We can set up the equation:

Total Pressure = Atmospheric Pressure + Hydrostatic Pressure * Depth

We know that the maximum pressure the shell can withstand is 1180 psi. By substituting the given values into the equation, we can solve for the depth. Rearranging the equation, we have:

1180 psi = 14.7 psi + 0.45 psi/ft x  Depth

Simplifying the equation, we get:

0.45 psi/ft x Depth = 1180 psi - 14.7 psi

By subtracting the atmospheric pressure from the total pressure, we find:

0.45 psi/ft x Depth = 1165.3 psi

Finally, by dividing both sides of the equation by 0.45 psi/ft, we can determine the depth to the nearest foot at which the shell can withstand the pressure. The calculated depth is approximately 2589 feet. Therefore, the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure is 2589 feet (rounded to the nearest foot).

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Answer: The answer is 2589 feet .

Step-by-step explanation: Quite simple it is 2589 feet .

Answer:

Step-by-step explanation:

The answer is D

The probability that Joe  will take no more than 7 tries to pass it is calculated as 0.7712.

Given: Every time Joe takes the fourth statistics quiz, he has a 19% chance of passing.

Mean = μ = 1/p = 1/(19/100) = 100/19 ≈ 5.26

Variance = σ² = (1-p)/p² = \(\frac{1-(19/100)}{19/100}^{2}\) 8100/361 ≈ 22.4376

Standard Deviation = σ = \(\sqrt{ \frac{1-p}{p^2} }\) = \(\sqrt{ \frac{1-(19/100)}{(19/100)^2} }\) = 90/19 ≈ 4.736

P(X = 7) = 0.05366

P(X<7) = 0.7175

P(X≤7) = 0.7712

Therefore, the probability that Joe  will take no more than 7 tries to pass it is 0.7712.

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Answer:

x=67

Step-by-step explanation:

subtract 90 because those are right angles from 23 and you get 67

Answer:

16 tons

Step-by-step explanation:

i hope this helps! have a wonderful rest of ur day :)

and if its not too much to ask will you mark me as brainliest pls, im trying to rank up this month and i only need 3 more, if not then its ok! ty and let me know if theres anything else you need!!

Answer:

16 tons

Step-by-step explanation:

I think it is 16 tons

sorry for answering so late lol i dont even remember how I got here

Answer:

the answer should be negative one and one-fourth, negative one -half

Step-by-step explanation:

hope this helps