What is 497,349 plus 529,853

Answer:

6/8 = 12/18

Step-by-step explanation:

hope this helps :D

Given that sample standard deviation is zero. This indicates that the variance of sample is also zero as square of sample standard deviation is sample Variance. Variance is average of the squared deviations from mean. As shown in below formula

Since Variance = 0 , we substitute in formula and we get the sum of squares of deviations of all data points from mean should be zero. This is only possible if and only if all the data points in the data distribution are same as mean of the data distribution. In the case the variance and standard deviation will be zero.

Variance = Summation n to i = 1 \(\frac{(X_{1-X} )^2}{n-1}\)

        0 = Summation n to i = 1\(\frac{(X_{1-X} )^2}{n-1}\)

                Summation n to i \({(X_{1-X} )^2\) = 0

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Observe each pairs

#1

(82,4)

#2

(93,3)

#3

(61,6)

#4.

(22,?)

Answer:

• let the upper row be y and lower row be x

• Considering (4, 82):

\({ \rm{x :y = 4 :82 }} \\ \\ { \rm{ \frac{x}{y} = \frac{4}{82} }} \\ \\{ \boxed { \rm{ \: x = \frac{4y}{82} \: }}}\)

• when y is 22:

\({ \rm{x = \frac{(4 \times 22)}{82} }} \\ \\ { \rm{x \approx1}}\)

Answer: It'd be 1

Step-by-step explanation:

female workers:2250

% female workers:?

First, find the percentage of workers who aren't men since we are told the number of workers who aren't men

100-55=45

Therefore 45% of workers aren't men

Let the total number of workers =x

Now form an equation for the problem

\(x \times \frac{45}{100} = 2250\)

\(x = 2250 \div \frac{45}{100} \)

\(x = 5000\)

Therefore, there are 5000 workers in total

Answer: 388872

Step-by-step explanation: take 396000 divide it by 98.2%

The probability that the second ball drawn is a purple ball  is (e) 0.5833

From the question, we have the following parameters that can be used in our computation:

Green balls = 10

Purple balls = 14

This means that the total number of balls is

Total = 10 + 14

Evaluate the equation

So, we have

Total = 24

From the question, we understand that the ball is replaced

So, the probability that the second ball is purple ie

P(second purple) = purple/total

This gives

P(second purple) = 14/24

Evaluate

P(second purple) = 0.5833

Hence, the probability is (e) 0.5833

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The centroid of the octant of the solid sphere is located at the point (3r/8, 3r/8, 3r/8).

The centroid of a solid of constant density is defined as the point at which the entire mass of the object is considered to be concentrated.

For an octant of a solid sphere, we can imagine a sphere with radius r, and cut it into eight equal parts by three mutually perpendicular planes passing through the center of the sphere. An octant is one of these eight parts, consisting of one-eighth of the volume of the sphere.

Since the solid has constant density, we can assume that the mass is distributed evenly throughout the volume. The centroid of the octant will be located at the center of mass of this octant.

To find the coordinates of the centroid of the octant, we can use spherical coordinates. Let the radius of sphere be r, and let theta range from 0 to pi/2 and phi range from 0 to pi/2, so that we are considering only the octant in the positive x, y, and z directions.

The coordinates of the centroid will be (x_c, y_c, z_c), where

x_c = (3/(4pir^3)) * ∫∫∫ x dV

y_c = (3/(4pir^3)) * ∫∫∫ y dV

z_c = (3/(4pir^3)) * ∫∫∫ z dV

where the integrals are taken over the volume of the octant.

Using spherical coordinates, we can express x, y, and z in terms of r, theta, and phi, and we can express dV in terms of r, theta, and phi as well. After integrating over theta and phi, we get:

x_c = y_c = z_c = 3r/8

Therefore, the centroid is at the point (3r/8, 3r/8, 3r/8).

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Answer:

only the first answer option is correct.

Step-by-step explanation:

|-x - 4| = 8 has 2 solutions :

x = 4, x = -12 as |-8| = |8| = 8

this is correct.

3.4×|0.5x - 42.1| = -20.6 has no solution.

the left side is always a positive number for sure (product of a positive number and an absolute value, which is always a positive number). that can never be equal to a negative number.

|½x - 3/4| = 0 has exactly 1 solution.

x = 6/4

|2x - 10| = -20 has no solutions.

as in the second answer option, an absolute value is always a positive number and cannot be equal to a negative number.

|0.5x - 0.75| + 4.6 = 0.25 has no solutions.

as this is the same as

|0.5x - 0.75| = -4.35

as before, an absolute value is always positive and cannot be equal to a negative number.

|⅛x - 1| = 5 has exactly 2 solutions.

x = 48, x = -32 as |-5| = |5| = 5

Answer:

Part A: the cross section is a rectangle.

Part B: it’s a parallelogram.

Step-by-step explanation:

Part A explanation: The cross section is a rectangle. The cross section of any right prism parallel to its base is congruent to the base. Figure 2 shows the cross section of a right rectangular prism perpendicular to its base. The cross section is a rectangle.

Part B explanation: When a rectangular prism is cut diagonally to its base, the cross-section is a parallelogram.

Answer:

The answer to your problem is,

Step-by-step explanation:

A rectangle prism has a rectangular base and uniform in height

The shapes formed are:

Part A :

When the rectangular prism is cut so that it is perpendicular to the rectangular base, the the shape formed would be a rectangular base, then the shape formed would be a rectangular prism shape.

Part B :

When the rectangular prism is cut across the opposite diagonals, then the shape formed would be a triangular prism.

Thus the answer to your problem is,

The sides of ΔFED does AB in ΔABC correspond to:

AB --> EF  = (53°)

BC --> DE =  (37°)

AC --> DF=  (90°)

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

From the figure:

We have the following information:

ΔABC is similar to ΔFED.

WE have to find the which side in ΔFED does AB in ΔABC correspond to?

Now, According to the question:

ΔABC is similar to ΔFED.

So,

AB --> EF  = (53°)

BC --> DE =  (37°)

AC --> DF=  (90°)

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Answer:

13.24 ft

Step-by-step explanation:

To solve this problem you must apply the proccedure shown below:

1. You have:

Sinα=opposite/hypotenuse

α=62°

opposite=x

hypotenuse=15 ft

2. When you substitute the values into  Sinα=opposite/hypotenuse, you obtain:

Sinα=opposite/hypotenuse

Sin(62°)=x/15

3. You must clear "x", as below:

x=(15)(Sin(62°))

x=13.24 ft

The answer is. 13.24 ft

The range of the number of benefits is 38.8 million to 41.2 million

The given parameters are

Number of students, n = 30 million

Margin of error, E = 3%

The range of the number of benefits is then calculated as

Range = Number of students * (1 ± Margin of Error)

This gives

Range = n * (1 ± E)

So, we have

Range = 40 million * (1 ± 3%)

Expand the expression in the bracket

Range = 40 million * (1 - 3%, 1 + 3%)

Evaluate the sum and the differences

So, we have

Range = 40 million * (0.97, 1.03)

Evaluate the products

So, we have

Range = (38.8 million, 41.2 million)

Hence, the range of the number of benefits is 38.8 million to 41.2 million

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Complete question

The graph shows the results of a survey that asked 4300 students ages 7 to 18 what they thought would be the most important benefit of air travel in the future. There are about 40 million students in the United States. If the margin of error is \pm3\%±3%, what is the range of the number of students ages 7 to 18 who would likely say that "finding new resources for Earth" is the most important benefits

Linear regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables. It aims to find a linear equation that best fits the observed data points, allowing for the prediction of the dependent variable based on the independent variables.

In more detail, linear regression assumes a linear relationship between the dependent variable and the independent variables. The method estimates the parameters of the linear equation by minimizing the sum of the squared differences between the observed data points and the predicted values. This is typically done using a technique called ordinary least squares (OLS) regression. The resulting linear equation can be used to make predictions or infer the impact of the independent variables on the dependent variable.

Linear regression is widely used in various fields, including economics, finance, social sciences, and machine learning. It provides a simple and interpretable way to analyze and understand the relationship between variables. However, it is important to note that linear regression assumes certain assumptions about the data, such as linearity, independence of errors, and homoscedasticity. Violations of these assumptions can affect the accuracy and reliability of the regression model.

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Answer:

A

Step-by-step explanation:

on the left of the equation, (6^4)^-5 = 6^-20

the right side you add the exponents so it would be (-7-3) =-10

so it would be 6^-10, which is greater than 6^-20

To estimate the variable lubrication cost per machine hour using the least-squares regression method, we need to find the equation of the regression line that best fits the given data.

The equation will be in the form of y = mx + b, where y represents the lubrication cost and x represents the machine hours.

By using the least-squares regression method, we can find the values of m and b that minimize the sum of the squared differences between the actual lubrication costs and the predicted lubrication costs based on the machine hours.

Once the regression line equation is determined, we can substitute the value of machine hours (x) to find the estimated lubrication cost per machine hour (y). The closest value to this estimate will be the answer to the question.

To obtain the closest estimate, the complete dataset is required to perform the regression analysis and calculate the regression line equation.

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In a binary search, we start by dividing the list in half and checking whether the target item (in this case, Apple) is in the first or second half.

Since the list is already sorted alphabetically, we can start by dividing the list in half at the middle, which is Lemon.

The first fruit searched would be Lemon since it is the first item checked in the binary search process.

Then, we would check the second half of the list (from Orange to Plum), which includes the target item Apple. Therefore, the second fruit searched would be Apple itself.

When using binary search on the sorted fruits list, the first fruit searched would be the middle element, which is Lemon.

If Apple is not found, the search continues in the left half. The second fruit searched would be the middle element of the remaining left half, which is Berry.

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Answer:

x < -7

Step-by-step explanation:

The circle is open meaning -7 is not included in the answer

Answer:

-1

Step-by-step explanation:

(2 + -3)^3

2 + -3 = -1

(-1)^3

-1

But since (a-1) and (a+1) are both divisible by 2^n-1, one of them must be divisible by 2^n, which means that k or l must be even. This is a contradiction, which means that (l-k) cannot be equal to 2. Therefore, we have shown that 3 is a quadratic nonresidue for all mersenne primes p > 3.

A quadratic nonresidue is a number that is not a quadratic residue. The quadratic residue means a number which can be expressed as x^2 mod n for some integer value of x, and n is a positive integer. For all mersenne primes p > 3, we need to show that 3 is a quadratic nonresidue, using a proof by contradiction. We assume that 3 is a quadratic residue, which means that there exists an integer a such that a^2 mod p

= 3. Now we can write the mersenne prime as p

=2^n-1 for some positive integer n. Therefore, a^2 mod (2^n-1)

= 3.Using Fermat’s Little Theorem, we can write:a^(2^n-2) mod (2^n-1)

= 1We can write 2^n-1 as (a-1)(a+1). So, a^(2^n-2) mod (a-1)(a+1)

= 1.Now, since p is a prime number, a and 2^n-1 must be co-prime to each other. Thus, (a-1) and (a+1) must be divisible by 2^n-1. Hence, we can write (a-1)

= k(2^n-1) and (a+1)

= l(2^n-1) for some integers k and l.Now we can write 2

= (a+1) - (a-1)

= l(2^n-1) - k(2^n-1)

= (l-k)(2^n-1)Since 2^n-1 is an odd number, 2 must be divisible by (l-k), which means that (l-k) must be either 1 or 2. If (l-k) = 1, then a+1

= l(2^n-1) and a-1

= k(2^n-1)

= (l-1)(2^n-1). Therefore, we have a

= l(2^n-1)-1 and a

= (l-1)(2^n-1)+1. This gives us 2^n-2

= l+k, which means that l+k is even. But since (a-1) and (a+1) are both divisible by 2^n-1, one of them must be divisible by 2^n, which means that l or k must be even. This is a contradiction, which means that (l-k) cannot be equal to 1.If (l-k)

= 2, then a+1

= 2k(2^n-1) and a-1

= (k-1)(2^n-1). Therefore, we have a

= 2k(2^n-1)-1 and a

= (k-1)(2^n-1)+1. This gives us 2^(n-1)-1

= k+l, which means that k+l is odd. But since (a-1) and (a+1) are both divisible by 2^n-1, one of them must be divisible by 2^n, which means that k or l must be even. This is a contradiction, which means that (l-k) cannot be equal to 2. Therefore, we have shown that 3 is a quadratic nonresidue for all mersenne primes p > 3.

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Answer:

54

Step-by-step explanation:

deltamath gave me the answer

The length of w is 54 cm.

One of the six mathematical functions used to express the side ratios of right triangles, the trigonometric function includes the sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc). The figure shows these six trigonometric functions in respect to a right triangle. Surveying, engineering, and navigation issues where one of a right triangle's acute angles and the length of a side are known but the lengths of the other sides need to be determined can be solved with ease using trigonometry.

As per the given data:

x = 41 cm

v = 17 cm

∠W = 134°

To find the length of w:

From the cosine law:  \(cos(W) = \frac{x^2 + v^2 - w^2}{2xv}\)

\(w = \sqrt{x^2 + v^2 - 2xvcos(W)}\\w = \sqrt{(41)^2 + (17)^2 - 2(41)(17)cos(W)}\\w = \sqrt{1681 + 289 + 968.35} = \sqrt{2938.35}\\w = 54 \:cm\)

Hence, the length of w is 54 cm.

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Step-by-step explanation:

y = kx, where k is a real constant.

When x = 12, y = 60.

=> (60) = (12)k, k = 5.

Therefore when x = 20,

y = kx = (5)(20) = 100.

The solution to the initial value problem is \(y(t) = e^{(-t)} + 4e^{(-5t)} + 24e^t.\)

As per the question given,  

To solve the initial value problem using Laplace transformation, we need to apply the Laplace transform to both sides of the equation and use the initial conditions to solve for the unknown constants.

Taking the Laplace transform of the equation, we get:

\(L{y''} + 6L{y'} + 5L{y} = 24L\)\(e^{t}\)

Using the properties of Laplace transform, we can simplify this to:

\(s^2\) \(Y(s) - sy(0) - y'(0) + 6sY(s) - 6y(0) + 5Y(s) = 24/(s-1)\)

Substituting the initial conditions, we get:

\(s^2Y(s) - 2s - 6 + 6sY(s) - 12 + 5Y(s) = 24/(s-1)\)

Simplifying further, we get:

\((s^2 + 6s + 5)Y(s) = 24/(s-1) + 2s + 6\)

\(Y(s) = [24/(s-1) + 2s + 6] / (s^2 + 6s + 5)\)

To find the inverse Laplace transform of Y(s), we need to factor the denominator and use partial fractions:

\(Y(s) = [24/(s-1) + 2s + 6] / [(s+1)(s+5)]\)

\(Y(s) = [A/(s+1) + B/(s+5)] + [24/(s-1)]\)

Multiplying both sides by (s+1)(s+5)(s-1), we get:

\(24 = A(s+5)(s-1) + B(s+1)(s-1) + 24(s+1)(s+5)\)

Substituting s = -1, we get:

24 = 6B

B = 4

Substituting s = -5, we get:

24 = 24A

A = 1

Therefore, the partial fraction decomposition is

\(Y(s) = [1/(s+1) + 4/(s+5)] + [24/(s-1)]\)

Taking the inverse Laplace transform of each term, we get:

\(y(t) = e^{(-t)} + 4e^{(-5t)} + 24e^t\)

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Answer:

x = 47

Step-by-step explanation:

Because the lines are parallel, we know that some angles are the same, see the images attached. That means that A and B in the image are the same angles. So we know that angle A totals to 78 degrees. And the angle outside the triangle is 35. So the angle inside the triangle is

78 - 35 = 43.

The interior angles of a triangle add up to 180. We know that one angle is 43 and another angle is 90 because of the indicating square angle marker. That means that

43 + 90 + x = 180.

Then we can simplify the equation:

133 + x = 180⇒

x = 180 - 133⇒

x = 47

To find f'(1) using the definition of the derivative, we need to evaluate the limit as x approaches 1 of the expression (f(x) - f(1))/(x - 1).

Substituting f(x) = 3x + 2/x, we have (3x + 2/x - (3(1) + 2/(1)))/(x - 1).

Simplifying the expression, we get (3x + 2/x - 5)/(x - 1).

Taking the limit as x approaches 1, we obtain (3(1) + 2/(1) - 5)/(1 - 1).

This simplifies to (3 + 2 - 5)/(1 - 1), which is equal to 0/0.

To evaluate this indeterminate form, we can apply L'Hôpital's rule by taking the derivative of the numerator and denominator. However, in this case, the limit does not exist because the numerator and denominator do not approach a finite value.

To find the equation of the tangent line to the graph of y = 3x + 2/x at the point (1, 5), we can use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.

The slope of the tangent line can be found by taking the derivative of the function f(x) = 3x + 2/x and evaluating it at x = 1. However, as we determined earlier, the derivative does not exist at x = 1. Therefore, we cannot directly find the equation of the tangent line using the derivative.

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So values are

The rule is

Explicit formula

Equation here is

Answer:

\(f(x)=4^x\) grows at a faster rate than the given quadratic function.

Step-by-step explanation:

Given table:

\(\large \begin{array}{| c | c |}\cline{1-2} x & y \\\cline{1-2} 0 & 0 \\\cline{1-2} 1 & 3 \\\cline{1-2} 2 & 12 \\\cline{1-2} 3 & 27 \\\cline{1-2}\end{array}\)

First Differences in y-values:

\(0 \overset{+3}{\longrightarrow} 3 \overset{+9}{\longrightarrow} 12 \overset{+15}{\longrightarrow} 27\)

Second Differences in y-values:

\(3 \overset{+6}{\longrightarrow} 9 \overset{+6}{\longrightarrow} 15\)

As the second differences are the same, the function is quadratic.

The coefficient of \(x^2\) is always half of the second difference.

Therefore, the quadratic function is:

\(f(x)=3x^2\)

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

\(\dfrac{f(b)-f(a)}{b-a}\)

Therefore, the average rate of change for \(f(x)=3x^2\) over the interval
0 ≤ x ≤ 3 is:

\(\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{27-0}{3-0}=9\)

An exponential function that grows at a faster rate than \(f(x)=3x^2\) over the interval 0 ≤ x ≤ 3  is \(f(x)=4^x\)

\(\large \begin{array}{| c | c | c | c | c |}\cline{1-5} x & 0 & 1 & 2 & 3 \\\cline{1-5} f(x)=4^x & 1 & 4 & 16 & 64\\\cline{1-5} \end{array}\)

\(\textsf{Average rate of change}=\dfrac{f(3)-f(0)}{3-0}=\dfrac{64-1}{3-0}=21\)

As 21 > 9, \(f(x)=4^x\) grows at a faster rate than \(f(x)=3x^2\) over the interval 0 ≤ x ≤ 3.

Answer:

Look below.

Step-by-step explanation:

For further reference I suggest looking at Khan academy videos of this.

A. log8 5/9

B. log9 4

C. log6 2^3

Answer: Hmm

Step-by-step explanation:

Answer: The measure of angle FHG = 42 degrees. This is the same as the arc length.

The measure of angle FEG = 21 degrees. This is half the value of the arc length.

Step-by-step explanation:

If a circle has center M and arc KL is 126 degrees then ∠KJL is 126 degrees and ∠KJL is 63 degrees

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

Central angle is same as intercepted arc.

∠KJL = m(arc KL0

∠KJL =126 degrees

Inscribed angle  is equal to half of the intercepted arc.

To find inscribed angle , we divide the intercepted arc by 2.

∠KJL = 1/2(arc KL)

=1/2(126)

=63 degrees

Hence, if a circle has center M and arc KL is 126 degrees then ∠KJL is 126 degrees and ∠KJL is 63 degrees

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Answer:

Solution,

Let the age of sister be X

Let the age of boy be 2x

Now,

Five years ago,

\(3(x - 5) = 2x - 5 \\ or \: 3x - 15 = 2x - 5 \\ or \: 3x - 2x = - 5 + 15 \\ x = 10\)

Again,

Replacing value,

\(age \: of \: boy = 2x \\ \: \: \: \: \: \: \: \: \: \: \: \: \: = 2 \times 10 \\ \: \: \: \: \: \: \: \: \: \: \: = 20\)

hope this helps..

Good luck on your assignment..