Please Help!! Find the sum. In your final answer, include your calculations.

−3.45 + 5.1

Answer:

\(x(7-4x)\)

Step-by-step explanation:

You can factor the expression \(7x - 4x^2\) by factoring out an x value.

You will get:

\(x(7-4x)\).

There is nothing else you can factor out of the equation.

This statement is always valid for every non-negative integer n, therefore it holds true for n=150 as well.

The statement to be proved by induction is that "for every non-negative integer n, (5 − 5n) is a multiple of 5.

Basis Step ,Let's start with the first step, which is the basis step.

This step necessitates that we verify that the statement is correct for n = 0.

It is seen that (5 − 5 × 0) = 5, which is indeed a multiple of 5.

Therefore, the statement is true for n = 0.

Inductive Step The second stage is the inductive step.

This necessitates the assumption that the statement is true for n = k, and then proving that the statement is also true for n = k + 1.

In this case, we must assume that (5 − 5k) is a multiple of 5, and then prove that (5 − 5(k + 1)) is also a multiple of 5.

This is done as follows:(5 − 5(k + 1))= (5 − 5k − 5) = [(5 − 5k) − 5]

We already know that (5 − 5k) is a multiple of 5 because we are assuming the statement to be true for n = k.

Because we know that (5 − 5k) is a multiple of 5, it is safe to say that [(5 − 5k) − 5] is also a multiple of 5 since a multiple of 5 minus 5 will result in a multiple of 5.

This completes the induction step and the proof of the statement for all non-negative integers n is complete.

Conclusion: We've shown that the statement "for every non-negative integer n, (5 − 5n) is a multiple of 5" holds true by induction. This statement is always valid for every non-negative integer n, therefore it holds true for n=150 as well.

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Answer:

Step-by-step explanation:

6*[4-(42-63)]=

6*[4-(-21)]=

6*[4+21]=

6*25=150.

6*[4-9÷3]=

6*[4-27]=

6*(-23)=-138.

6*[4-3]=

6*1=6.

Answer:

I would say 3cm

Step-by-step explanation:

sorry if it's wrong but I sure it's right

Answer:

9:45 AM

Step-by-step explanation:

To get to work in the morning, Amanda cycles for 10 miles at the rate of 12 mph.

Time (hours) = Distance/speed

Hence, the time she spends cycling = 10mile/12 mph

= 0.8333333333 hour

Converting to minutes:

1 hour = 60 minutes

0.8333333333 hour =

0.8333333333 hours × 60 minutes/1 hour

= 50 minutes.

Hence, she spends 50 minutes cycling

She makes a 10 minutes stop for a cup of coffee, and then rides a bus for 15 minutes. The speed of the bus is 45 mph.

The total number of minutes she spends to get to work is calculated as:

(50 + 10 + 15)minutes

= 75 minutes.

It takes Amanda 75 minutes to get to work.

At what time will Amanda get to work if she leaves home at 8:30 AM?

= 8:30AM + 75 minutes

= 8:30 AM + 1 hour 15 minutes

= 9:45 AM

Answer:

The magnitude is sqrt((-4)^2 + (-9)^2) = 9.85. The angle is atan(-9/-4) = 180 deg + 66 deg = 246 deg = -114 deg.

Step-by-step explanation:

hope it help

Answer:

9.85

Step-by-step explanation:

|v|= √9²+(-4)²

=√81+16

=√97

|v|= 9.85

Answer: x>15

X/3 + 2 > 7

Subtract +2 from both sides to remove it from the left hand side of the >

X/3 > 5

Multiply both sides by 3 to remove the /3 from the left hand side of the > to fully get x on its own

X > 15

Answer:

220%,2.2,√5,2.25

Step-by-step explanation:

220%=2.2

√5=2.23

Answer:

d = 3.6 miles

Step-by-step explanation:

It is given that,

A Labor Day parade travels 2 miles north and then it marches 3 miles due east. We need to find how far will the parade travel to return to its original starting point?

It means we need to find the shortest path i.e. displacement.

So,

\(d=\sqrt{2^2+3^2}\\\\d=3.6\ \text{miles}\)

Hence, the parade will travel 3.6 miles to return to its original position.

Answer:it’s a I was stuck to

Step-by-step explanation:

Answer:

(- 5, 4 )

Step-by-step explanation:

under a reflection in the line y = x

a point (x, y ) → (y, x ) , then

G (4, - 5 ) → G' (- 5, 4 )

The coordinates of the image of vertex G are (-5, 4)

When reflecting a figure in a line or in a point, the image is congruent to the pre image. A reflection maps every point of a figure to an image across a fixed line. The fixed line is called the line of reflection.

here, we have,

Let us revise some cases of reflection

If the point (x, y) reflected across the x-axis , then its image is (x, -y)

If the point (x, y) reflected across the y-axis , then its image is (-x, y)

If the point (x, y) reflected across the line y = x , then its image is (y, x)

If the point (x, y) reflected across the line y = -x , then its image is (-y, -x)

From the given figure

∵ The line of the reflection is y = x

→ That means we will switch the coordinates of the point to find its image

∵ The coordinates of vertex G are (4, -5)

∴ The x-coordinate = 4 and the y-coordinate = -5

→ Switch the two coordinates

∴ The coordinates of its image G' are (-5, 4)

∴ The coordinates of the image of vertex G are (-5, 4)

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A scatter plot between a categorical independent variable and a dependent variable will consist of distinct data points or markers representing different categories along with their corresponding values on the dependent variable.

A scatter plot is typically used to visualize the relationship between two continuous variables. However, when one of the variables is categorical, the scatter plot can still be used to provide a visual representation of the relationship.

In this case, the scatter plot would display the values of the dependent variable on the y-axis, while the categorical independent variable would be represented on the x-axis. Each data point or marker on the plot corresponds to a specific category of the independent variable, and its position on the y-axis represents the value of the dependent variable associated with that category.

Since the independent variable is categorical, the data points on the scatter plot will not be connected by a continuous line or trend. Instead, they will be scattered across the x-axis, potentially forming distinct clusters or groupings based on the different categories.

By examining the distribution of data points and their positions along the dependent variable axis, one can gain insights into the relationship between the categorical independent variable and the dependent variable.

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Answer:

5/

Step-by-step explanation:

Answer:

5/8

Step-by-step explanation: The equation is: 3/8 + 1/4 but these are unlike fractions. Lets make them like fractions.

To make them like fractions you have to find the common denominator.

Common denominator: 8

Like fraction problem: 3/8 + 2/8 =...

5/8!

Using law of sine and triangle rule, the value of n is 443 inches

The law of sines establishes the relationship between the sides and angles of an oblique triangle(non-right triangle). Law of sines and law of cosines in trigonometry are important rules used for "solving a triangle". According to the sine rule, the ratios of the side lengths of a triangle to the sine of their respective opposite angles are equal.

The law of sines relates the ratios of side lengths of triangles to their respective opposite angles. This ratio remains equal for all three sides and opposite angles. We can therefore apply the sine rule to find the missing angle or side of any triangle using the requisite known data.

The formula is given as

a / sin A = b / sin B = c / sin C

In this triangle NOP, we can find the value of angle P

∠N +  ∠O  +  ∠P = 180

57 + 55 +  ∠P = 180  : Sum of angles in a triangle is equal 180 degrees

∠P= 180 - 112

∠P = 68

Using law of sine

p / sin P = n / sin N

490 / sin68 = n / sin57

n = [(490 * sin 57) / sin 68]

n = 443 inches

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Answer:

55 or 56

Step-by-step explanation:

I add 27 until I got to 486. I end up at 54 hours it not 57 so it is between 55 and 56 hours

The probability mass function of X( -3, -1, 1 ,3)  is P(X) 1/8 3/8 3/8 1/8.

A fair coin is flipped 3 times and the random variable X is defined as follows:

   X = 3 times the number of heads - 2 times the number of tails

To find the probability mass function of X, we can list all the possible outcomes and calculate their probabilities.

The Possible outcomes are as shown:

   3 heads (X = 3)

   2 heads, 1 tail (X = 1)

   1 head, 2 tails (X = -1)

   3 tails (X = -3)

And the Probabilities are:

   P(X = 3) = 1/8

   P(X = 1) = 3/8

   P(X = -1) = 3/8

   P(X = -3) = 1/8

Therefore, the probability mass function of X is:

X( -3, -1, 1 ,3)  is  P(X) 1/8 3/8 3/8 1/8

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The number of units produced increases from 2 to 452 as the number of factory workers increases from 0 to 90, which gives;

Part A:

Part B:

Part C:

Part A:

The correlation is the relationship between variables based on statistical data.

From the given table, the difference between consecutive terms of the x and y-values are constant, therefore as the x-values increases, the corresponding y-value increases.

Change in x-values, ∆x = 10 - 0 = 20 - 10 = 30 - 20 = 10

Change in y-values, ∆y = 52 - 2 = 102 - 52 = 152 - 102 = 50

Therefore;

Part B:

Given that the rate of change of the x-values is constant, and the rate of change of the y-values is a constant, the function relating the x and y-values is a linear function, which can be found as follows;

Slope of the equation, m = ∆y/∆x

Which gives;

m = 50/10 = 5

y - 2 = 5•(x - 0)

The function that best fits the data is therefore;

Part C:

The slope of the function is the coefficient of the variable x in the equation, y = m•x + c

The y-intercept of the function is the value of the constant term, c, in the equation, y = m•x + c

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The contents of array a will be modified such that the first and third rows will contain the values from the second row of the initial array.

After executing the given statements, the contents of array a will be modified. The first statement swaps the elements in the first and third rows of the array, while the second statement assigns the values from the second row to the first row.

The final contents of array a will depend on the initial values of the array. Let's break down the statements and their effects on array a:

1. a([3 1], :) = a([1 3], :):

This statement swaps the elements in the first and third rows of array a. The notation [3 1] represents the row indices to be swapped, and [1 3] represents the order of the new row indices.

Therefore, after executing this statement, the first row of array a will be swapped with the third row.

2. a([1 3], :) = a([2 2], :):

This statement assigns the values from the second row of array a to both the first and third rows. The notation [1 3] represents the row indices to be modified, and [2 2] represents the source row index.

Therefore, after executing this statement, the first and third rows of array a will contain the values from the second row.

The final contents of array a will depend on the initial values of the array. If we consider the initial array as:

a = [1 2 3; 4 5 6; 7 8 9]

After executing the given statements, the contents of array a will be:

a = [4 5 6; 4 5 6; 7 8 9]

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The time taken by a student to finish a statistics exam can be modeled using the following cumulative distribution function: F(x) = 1 - e^-0.9, x > 0

Suppose that the time taken for a student to finish the exam is constant from student to student.

Then the mean number (to the nearest whole number) of students who will finish the exam in less than 1 hour for 12 students randomly selected is 7

.Step-by-step explanation:

The cumulative distribution function is given by, F(x) = 1 - e^-0.9, x > 0

Now, let X be the time taken by a student to finish the statistics exam

Then, X ~ Exp (0.9 )

We know that the cumulative distribution function (CDF) of the exponential distribution with parameter λ is given by,F(x) = P(X ≤ x) = 1 - e^(-λx) , x > 0Here, λ = 0.9.

Therefore, the CDF of X is given by,F(x) = P(X ≤ x) = 1 - e^(-0.9x) , x > 0

The probability that a student finishes the exam in less than 1 hour is, P(X ≤ 1) = F(1) = 1 - e^(-0.9) ≈ 0.5271

This means that out of 12 students randomly selected,

The expected number of students who finish the exam in less than 1 hour is,μ = np= 12 × 0.5271≈ 6.3252

Hence, the mean number (to the nearest whole number) of students who will finish the exam in less than 1 hour for 12 students randomly selected is 7.

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Answer:

80inches

Step-by-step explanation:

17+17=34

23+23=46

34+46=80

Answer:

43

Step-by-step explanation:

the true values of each number is 26 and 17 so adding them gives you 26+17

The expected value for a student to spend on lunch each day from the survey of 50 students is $5.18.

The expected value for a student to spend on lunch each day is derived from the survey of 50 students. This value is calculated by taking the total number of dollars spent by all of the surveyed students and dividing it by the total number of students surveyed. In this particular survey, the total number of dollars spent was $247, and the total number of students surveyed was 50. Dividing $247 by 50 gives us a value of $4.94. This value is then rounded up to the nearest cent to give us the expected value of $5.18. This expected value is the average amount of money that a student can expect to spend on lunch each day from the survey. It is important to note that this value is an estimate, as individual student spending habits may vary greatly.

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============================

Work Shown:

Expand out the left hand side

(x-k)(x-5)

x(x-5)-k(x-5)

x^2-5x-kx+5k

Note that the constant term here is 5k. Yes k seems like a variable, but it's actually a constant. Once we know k, we can replace it to get a fixed number. In this case, k = 4 since 5k = 5*4 = 20 to have it match with the 20 at the end of x^2-9x+20

For the x terms, we have -5x-kx = -5x-4x = -9x which matches with the middle term of x^2-9x+20

Therefore,

(x-k)(x-5) = x^2-9x+20

updates to

(x-4)(x-5) = x^2-9x+20

The -4 and -5 multiply to 20, and they also add to -9. This helps confirm we have the right k value.

The correct option is (c) "none of these".Because the  the solution to the system of linear equations is (x, y) = (4/3, 5).

The given system of linear equations is:

y = 2 + 3........(1)

y = 3x + 1.......(2)

By putting equation (1) into equation (2):

y = 3x + 1

3x + 1 = 2 + 3

3x + 1 = 5

3x = 5-1

3x = 4

By Dividing both sides of the equation by 3:

x = 4/3

By putting this value of x into equation (2):

y = 3(4/3) + 1

y = 4 + 1

y = 5

Therefore, the solution to the system of linear equations is

(x, y) = (4/3, 5).

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Answer:

y=1/2x-4

Step-by-step explanation:

After Composite the given function  If \(f(x) = x^2\) and \(g(x) = x^2-7x+12\), \(g(f(x))\) is \(x^{4}\) - 7\(x^{2}\) + 12

What is a function?

A functiοn in mathematics is a cοnnectiοn between twο sets οf elements, the dοmain and the range, where each element in the dοmain is related tο a particular element in the range. An οutput value that cοrrespοnds tο an input value is prοduced by a set οf rules knοwn as a functiοn.

To find g(f(x)), we need to first compute f(x), which is \(x^{2}\). Then we plug that value into g(x) in place of x.

So, g(f(x)) = g(\(x^{2}\))

Now, we need to compute g(\(x^{2}\)).

g(\(x^{2}\)) is given by:

g(\(x^{2}\)) = \((x^2)^{2}\) - 7(\(x^{2}\)) + 12

Simplifying this expression, we get:

g(\(x^{2}\)) = \(x^{4}\) - 7\(x^{2}\) + 12

So the final answer is option C: \(x^{4}\)-7\(x^{2}\)+12.

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Answer:

=x

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

1-1=X-X

Answer:

(m - 10) and (m - 2)

Step-by-step explanation:

Given

m² - 12m + 20

Consider the factors of the constant term (+ 20) which sum to give the coefficient of the m- term (- 12)

the factors are - 10 and - 2, since

- 10 × - 2 = + 20 and - 10 - 2 = - 12, thus

m² - 12m + 20 = (m - 10)(m - 2)