The sum of two numbers is 37 and the difference is 9. What are the numbers

Therefore , the solution is first angle = 63° and second angle = 27° for

complementary angle problem.

A pair of angles is considered to be complementary if their sum equals 90 degrees. Two angles are referred to as submissive if their sums total 180 degrees. Follow-up pain Utilizing fresh gruesome milk, as usual Prior to, before, ahead of The slopes of thirty and sixty degrees, for example, are supplementary. In contrast to a supplemental angle, which is two angles joined to create a 90 degree angle, a supplemental angle involves two angles joined to create a 180 degree angle.

Here,

Given :

Let us consider first angle be x

and second angle is less than 36°

=>  x - 36°

So , there are complementary angle there sum will be equal to 90°

=> x + x - 36°  = 90°

=>  2x =  90° + 36°

=> x = 126°/2

=> x =63°

First angle = 63°

and second angle = 63° - 36° = 27°

Therefore , the solution is first angle = 63° and second angle = 27° for

complementary angle  problem.

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Answer:

See below

Step-by-step explanation:

This is a system of equations. That means you are trying to find the point that makes both lines true at the same time.

To do this you have to solve for one variable at a time. Luckily, these equations already have one variable that will cancel. If you add 2x and -2x, you get 0. I'm going to line these up like a vertical math problem to show you how it works.

-2x + 3y = 12

2x +3y = 0                    Add together

-------------------

0x + 6y = 12                Simplify by removing the 0x

6y =12                        Divide both sides by 6 to solve for y

y = 2

Plug 2 in for y in one of the original equations.

2x + 3(2) = 0

2x + 6 = 0                   Subtract 6 from both sides

2x = -6                        Divide by 2 to solve for x

x = -3

The point that makes both lines true is (-3,2). This is where the lines intersect.

Answer:

7

Step-by-step explanation:

A square has 4 sides, all of equal length. We can simply find the square root of the area to find the length and width, or length of each side. So to find the length, you find the square root of the area.

\( \sqrt{49} = 7\)

To determine for which values of m the function o(x) = ez is a solution to the equation d'y 10- dy dx - 20y = 0, we need to substitute the function o(x) into the equation and solve for the constant m.

First, let's differentiate o(x) = ez with respect to x:

o'(x) = d/dx(ez) = z * d/dx(e^x) = z * e^x = zo(x)

Next, let's substitute o(x) and o'(x) into the given equation:

o'(x) - 10o(x) - 20o(x) = zo(x) - 10o(x) - 20o(x) = (z - 30) o(x) = 0

For the equation to hold true for all x, the coefficient of o(x), which is z - 30, must equal zero. Therefore, we have z - 30 = 0, which gives z = 30.

So, the function o(x) = ez is a solution to the equation for z = 30.

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★» -30, 10

★» Yes, I use ★» at the beginning of each sentence, it's my style.

Answer:Its c

Step-by-step explanation:

A concave hexagon with 2 pairs of congruent sides is a shape that has six sides and two pairs of sides that are of equal length, but the shape curves inward at one or more angles, creating a concave indentation.

A hexagon is a six-sided polygon, and when two pairs of its sides are congruent,

it means that four of its sides have the same length, if the shape curves inward at one or more angles,

it creates a concave hexagon, which means that the indentation on the shape is facing inward, rather than outward, a concave hexagon with 2 pairs of congruent sides is a six-sided polygon with four sides of equal length, but with a curvature that creates an inward indentation.

Hence, a concave hexagon with 2 pairs of congruent sides is a six-sided figure with an indentation and two sets of sides with equal lengths.

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The temperature after 1 minute is 5, the t-coordinate of the fixed point to be equal to 1 is f(t) = 2t + 3 and the corresponding y-value is 5.

In a two-dimensional coordinate system, such as the Cartesian coordinate system, each point is represented by an ordered pair (x,y) where x represents the horizontal position and y represents the vertical position.

The problem statement asks us to find the temperature after 1 minute, which means we need to find the y-coordinate of the point on the graph that corresponds to t=1. In other words, we need to evaluate the function f at t=1 to find the corresponding y-value.

If the function f(t) is given by f(t) = 2t + 3, then the point corresponding to t=1 would have coordinates (1, 5), since f(1) = 2(1) + 3 = 5. Therefore, the corresponding y-value would be 5, which represents the temperature after 1 minute.

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The probability that one microprocessor works is 0.8 and the probability that at least one microprocessor works is 0.99968.

a. The probability that one microprocessor works is 0.8, since 20% are defective. Assuming independence, the probability that all five work is:

P(all work) = (0.8)^5 = 0.32768

Therefore, the probability that all five microprocessors work is 0.32768.

b. The probability that at least one microprocessor works is equivalent to the complement of the probability that none of the microprocessors work. The probability that one microprocessor does not work is 0.2, and assuming independence, the probability that none of the five work is:

P(none work) = (0.2)^5 = 0.00032

Therefore, the probability that at least one microprocessor works is:

P(at least one works) = 1 - P(none work) = 1 - 0.00032 = 0.99968

Therefore, the probability that at least one microprocessor works is 0.99968.

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 If a symmetric matrix can be inverted into a diagonal matrix using another matrix, then it is diagonalizable. Accordingly, it may be said that there is a matrix P that can be inverted such that P-1 * A * P = D, where D is a diagonal matrix and A is the symmetric matrix. The diagonal entries of D are the appropriate eigenvalues, while the columns of P are the eigenvectors of A.

  The matrix P is the foundation of the vector space because its columns are linearly independent and it is invertible. The inner product of any two different eigenvectors is 0, as A's eigenvectors are orthogonal to one another due to its symmetry.

 We can divide each eigenvector by its norm to get an orthonormal basis from this collection of eigenvectors. As a result, a group of eigenvectors that are orthonormal to one another and serve as the vector space's orthonormal basis are produced.

  Therefore, A symmetric matrix is diagonalizable and has an orthonormal eigen basis  consisting of orthonormal eigenvectors, which can be obtained by dividing each eigenvector by its norm.

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The statement If a simple random sample is chosen with replacement, each individual has the same chance of selection on every draw is True.

If a simple random sample is chosen with replacement, it means that after each selection, the chosen individual is placed back into the population before the next selection is made. In this case, each individual in the population has the same chance of being selected for every draw.

The process of replacing the selected individual ensures that the selection probabilities remain constant throughout the sampling process. As a result, each individual has an equal probability of being chosen on each draw, making the statement true.

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Answer:

B, D

Step-by-step explanation:

A: I'm struggling because its telling us that the patients from two months ago but not last month.

B: Yes, there must be some patients lost more than 8lb for the calculation of average.

C: No, the average could be the middle number of two data, some patients may lost exactly 8lb but not absolutely.

D: Yes, like what's on choice B, there must be some patients lost more than 8lb to ensure the average data is equal to 8lb, unless everyone is losing 8lb exactly.

E: No, the data and the number of patients are not exactly the same, for example if two patients are losing 1lb and another patients is losing 22lb, the average is still 8lb.

F: Definitely not ture, we already found two choices correct.

Answer:

(B) 32.75 lb.

Step-by-step explanation:

We know that 1 pound (lb) is equal to 16 ounces (oz). Therefore, to convert 32 lb 12 oz to pounds, we need to first convert the 12 oz to pounds and then add it to 32 lb.

12 oz ÷ 16 oz/lb = 0.75 lb

So, 32 lb 12 oz is equal to:

32 lb + 0.75 lb = 32.75 lb

Therefore, the answer is (B) 32.75 lb.

(Reference to Chatgpts work)

Answer: If I understood correctly, the answer would be A, adults who buy any clothes. I'm not too sure though that would make sense.

Answer:

\(\sf Slope =\dfrac{1}{8}\)

Step-by-step explanation:

(0,2) ;  (8 ,3)

Slope:

\(\sf \boxed{Slope = \dfrac{y_2-y_1}{x_2-x_1}}\)

         \(\sf = \dfrac{3-2}{8-0}\\\\=\dfrac{1}{8}\)

The total number of reptile/fish pets written in scientific notation is 1.6*10^8

We know that there are estimates to be:

Notice that all these numbers writen in scientific notation, and we need to add them.

To add them, the exponent in the 10 must be equal in both numbers, so we can rewrite:

1.5*10^8 = 150*10^6

Now we can add these two to get:

150*10^6 + 9.5*10^6 = 159.6*10^6

Now to write this as scientific notation, we need to have only one digit on the left side of the decimal point, so we can rewrite this as:

159.6*10^6 = 1.596*10^8

Rounding this to two decimal places we will get:

1.596*10^8 = 1.6*10^8

So there are 1.6*10^8 pet fish and pet reptile in the US.

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Answer:

it depends on whether the outlier is a high outlier or a low outlier

Step-by-step explanation:

The mean of a data set is the average of the data set. So if I had the data set {5, 2, 10} the average would be (5+2+10)/3 = 5.667. Now if I added an outlier like 10,000 it would increase the mean significantly. It changes it significantly but I cannot say whether it increases or decreases it without knowing the value of the outlier, since if I had the outlier -10,000 that would decrease the mean, but I had the outlier 10,000 it would increase it. So it depends on whether the outlier is a high outlier or a low outlier

Answer:

the answer is d

Step-by-step explanation:

you multiply 35x8=240 then

you divide 240/40=7

The statement "An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated" is False.

Consistency is an important property of estimators in statistics. An estimator is consistent if its value approaches the true value of the parameter being estimated as the sample size increases.

In other words, if we repeatedly take samples from the population and compute the estimator, the values we obtain will be close to the true parameter value.

This is an essential characteristic of a good estimator, as it ensures that as more data is collected, the estimation error decreases.

However, as the sample size decreases, the value of the estimator is more likely to deviate from the true value of the parameter. The reason for this is that a small sample size may not be representative of the population, and as a result, the estimation error may increase.

As a consequence, the statement is false. In conclusion, consistency is a property that an estimator possesses when its value converges to the true value of the parameter as the sample size grows.

As the sample size decreases, the estimator may become less reliable, leading to an increase in the estimation error.

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The solution of the initial value problem Dy(t)/dt + 8y(t) = 1 + e-6t is option (c) y(t) = (1/8) - (1/8) * e^(-8t).

To solve the given initial value problem, we can use the method of integrating factors.

The given differential equation is:

\(dy(t)/dt + 8y(t) = 1 + e^(-6t)\)

First, we write the equation in the standard form:

\(dy(t)/dt + 8y(t) = 1 + e^(-6t)\)

The integrating factor (IF) is given by the exponential of the integral of the coefficient of y(t), which is 8 in this case:

IF = \(e^(∫8 dt)\)

=\(e^(8t)\)

Now, we multiply both sides of the differential equation by the integrating factor:

\(e^(8t) * dy(t)/dt + 8e^(8t) * y(t) = e^(8t) * (1 + e^(-6t))\)

Next, we can simplify the left side by applying the product rule of differentiation:

\((d/dt)(e^(8t) * y(t)) = e^(8t) * (1 + e^(-6t))\)

Integrating both sides with respect to t gives:

\(∫(d/dt)(e^(8t) * y(t)) dt = ∫e^(8t) * (1 + e^(-6t)) dt\)

Integrating the left side gives:

\(e^(8t) * y(t) = ∫e^(8t) dt\)

\(= (1/8) * e^(8t) + C1\)

For the right side, we can split the integral and solve each term separately:

\(∫e^(8t) * (1 + e^(-6t)) dt = ∫e^(8t) dt + ∫e^(2t) dt\)

\(= (1/8) * e^(8t) + (1/2) * e^(2t) + C2\)

Combining the results, we have:

\(e^(8t) * y(t) = (1/8) * e^(8t) + C1\)

\(y(t) = (1/8) + C1 * e^(-8t)\)

Now, we can apply the initial condition y(0) = 0 to find the value of C1:

0 = (1/8) + C1 * e^(-8 * 0)

0 = (1/8) + C1

Solving for C1, we get C1 = -1/8.

Substituting the value of C1 back into the equation, we have:

\(y(t) = (1/8) - (1/8) * e^(-8t)\)

Therefore, the solution to the initial value problem is:

\(y(t) = (1/8) - (1/8) * e^(-8t)\)

The correct answer is option (c) \(y(t) = (1/8) - (1/8) * e^(-8t).\)

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The number of years it will take for the value of the money in the account to reach $153,400 would be = 17 years.

Simple interest is defined as the amount of money that is received as an extra cash based on an investment made in an account.

The principal amount of money invested= $96,000

The rate of interest = 3.5%

The total interest on the principal amount = $153,400- $96,000 = $57,400

The time for this investment= ?

Using the formula for simple interest= p×T×R/100

57,400 = 96,000 ×T× 3.5 /100

Make T the subject of formula;

T = 57,400×100/96,000×3.5

T = 5740000/336000

T = 17 years (approximately)

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( p(B \mid A) \) is the probability of getting THH, which is 1/3.

To determine \( p(B \mid A) \), we need to consider the outcomes that satisfy event A (having at least two consecutive heads) and then determine how many of those outcomes also satisfy event B (the last flip is tails). Let's analyze the possible outcomes:

There are a total of 2^3 = 8 equally likely outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT.

Among these outcomes, the ones that satisfy event A (at least two consecutive heads) are: HHH, HHT, THH.

Out of these three outcomes, only one (THH) satisfies event B (the last flip is tails).

Therefore, \( p(B \mid A) \) is the probability of getting THH, which is 1/3.

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The given statement "The diagonal of a parallelogram does not create alternate interior angles" is false because alternate interior angles are formed when two parallel lines are intersected by a transversal, and they are located on opposite sides of the transversal and between the two parallel lines.

In a parallelogram, the opposite angles are congruent, meaning they have equal measures. When a diagonal is drawn in a parallelogram, it creates two pairs of congruent opposite angles, but these angles are not considered alternate interior angles.

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Answer:

68

Step-by-step explanation:

What you do in problems like this,For example on this question you would multiply 12 by 7 and then subtract what they took away which would be 68.

The scalar potential function is \(f = 7xyA^2zA^3+c\).

Given: F(x, y, z) = 7y²z³ i + 14xyz³ j + 21xy²z² k

F is a conservative field if curl F = 0, there exist a scalar potential function  such that F = ∇f.

curl f = \(\\i j k| \frac{a}{ax} \frac{a}{ay} \frac{a}{az} |\\7y^2z^3 14xyz^3 21xy^2z^2\)

\(= i[\frac{a}{ay}(21xy^2z^2)-\frac{a}{az}(14xyz^3) ] - j[\frac{a}{ax}(7y^2z^2)-\frac{a}{az}(7y^2z^3) ]+k[\frac{a}{ax}(14xyz^3)-\frac{a}{ay}(7y^2z^3) ]\)

= i(0) - j(0) + k(0)

= 0

Thus,curl F is conservative.

To find f such that F = gradf.

\(7yA^2zA^3i+14xyzA^3j+21xyA^2zA^2k = i(\frac{df}{dx} )+j(\frac{df}{dy} )+k(\frac{df}{dz} )\)

\(\frac{df}{dx} = 7yA^2zA^3\\\\\frac{df}{dx} = 14xyzA^3\\\\\frac{df}{dx} = 21xyA^2zA^2\)

Integrate the above terms with respect to x.

\(f = 7xyA^2zA^3+c_1\\\\f = 7xyA^2zA^3+c_2\\\\f = 7xyA^2zA^3+c_3\)

Hence the answer is, the scalar potential function is \(f = 7xyA^2zA^3+c\).

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The derivative of y with respect to x, y', is given by:

y' = (4^2x) * (e^(5x)) * (log(x) + (1/x))

To find y', we will use logarithmic differentiation. Let's break down the steps:

Step 1: Take the natural logarithm (ln) of both sides of the equation to simplify the expression.

ln(y) = ln(4^(2x) * e^(5x * log(x)))

Step 2: Apply logarithmic properties to simplify the expression further.

ln(y) = 2x * ln(4) + 5x * log(x)

Step 3: Differentiate both sides of the equation with respect to x.

(1/y) * y' = 2 * ln(4) + 5 * log(x) + 5x * (1/x)

Step 4: Solve for y' by multiplying both sides by y.

y' = y * (2 * ln(4) + 5 * log(x) + 5x * (1/x))

Step 5: Substitute y with its original expression.

y' = (4^2x) * (e^(5x)) * (log(x) + (1/x))

Using logarithmic differentiation, we found that the derivative of y with respect to x, y', is given by (4^2x) * (e^(5x)) * (log(x) + (1/x)). This method allows us to find the derivative of complex functions by taking the logarithm of both sides and then differentiating implicitly.

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Answer: X = 121

Step-by-step explanation:

Because 180 degrees is a flat line, you subtract 59 from 180 to get the remaining angle values

The connected sum operation does not have an inverse as it destroys information about the original spaces.

A simple intuitive reason for this is that if one connects two spaces, the operation doesn't have any way of determining which space is the "original" one, and which one is the "newly added" one.

The connected sum of two spaces X and Y is defined as follows: take a copy of X, a copy of Y, remove an open ball from each of them, and then glue the resulting two spaces together along the open balls' boundaries. This is denoted by $X \# Y$.The connected sum operation does not have an inverse, which can be rigorously proved as follows:

Similarly, $Z$ is orientable if and only if both $X$ and $Y$ are orientable.

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Answer:

Step-by-step explanation:

5 less than the product of a number squared and 8, translating the expression:

By using the concept of direct proportion, it can be calculated that

The equation which represents the given relationship is

\(p = \frac{2}{3}m\)

What is direct proportion?

Suppose there are two quantities. Proportionality indicates that if there is a change in the value of one quantity, the value of other quantity also changes but maintaining a constant ratio

Direct proportion

Two quantities are said to be in direct proportion if on increasing the value of one quantity, the value of other quantity also increases and vice versa.

For example cost of a commodity and quantity of a commodity are in direct proportion

The number of pages read, p, varies directly as the number of minutes spent reading, m.

So the equation is

p = km, where k is the constant of proportionality

After 15 minutes, Zoe had read 10 pages.

Putting m = 15 and p = 10

10 = k \(\times\) 15

k = \(\frac{10}{15}\)

k = \(\frac{2}{3}\)

So the equation which represents the given relationship is

\(p = \frac{2}{3}m\)

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