Math 1125 – Unit 1 ~ Gunkelman Practice for Section 1.5 The Basics of Graphing Prep Skills The table represents the Seven Summits (the highest peaks from each continent). Mountain Mt. Kilimanjaro Elbrus Aconcagua Denali Vinson Massif Mt. Kosciusko Mt. Everest Continent Africa Europe South America North America Antarctica Australia Asia Height (ft) 19,340 18,510 22,834 20,320 16,864 7,310 29,035 What is the difference between the heights of the highest mountain in Africa and the highest mountain in Antarctica?

Answer:

m = 20

Linear

Linear

Step-by-step explanation:

m is the slope and we can find the slope by using the equation \(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\).

(45-25)/(1-0) = 20/1 = 20

Since the slope is constant throughout the whole data point (increased by 20 when x is changed by 1), we know that this is linear.

Same with option 3.

Answer:

-(1+7x)-6(-7-x)=26

-1-7x+42+6x=26

-x+41=26

-x=26-41

-x=-15

x=15

hope it helps you!

Answer:

x=15

Step-by-step explanation:

-1 - 7x + 42 + 6x = 26

41 -7x + 6x = 26

41 - x =26

-x = 26 - 41

-x = -15

x = 15

Answer:

cashier

Step-by-step explanation:

the discount is $7.50

Answer:

Why is his name Jack? lol what about Aron or Liam...something hotter i mean he is a football player.

Step-by-step explanation:

Answer:

The correct answer is 4,672.18.

Step-by-step explanation:

To solve this problem, we must look at the number we are given and determine what numbers are in which places.  The 4 is in the thousands place, the 6 is in the hundreds place, the 7 is in the tens place, the 2 is in the ones place, the 1 is in the tenths place, the 8 is in the hundredths place, and the 3 is in the thousandths place.  

The question asks us to round to the nearest hundredth, so this means that the number in the hundredths place should be the final digit.  In the number given, the number 8 is in the hundredths place.  Since the following digit (3) is less than 5, we round down and keep the 8 in the hundredths place.  This makes our answer 4,672.18.

Hope this helps!

The volume of the cone which has slant length of 5 and a diameter of 4 is 12.56 cubic units.

Volume of solid is the amount of quantity, which is obtained by the solid or object in the 3 dimensional space.

The more the volume of a object is obtains the more space. The volume of the cone can be given as,

\(V=\dfrac{1}{3}\pi r^2h\)

Here, (r) is the radius of the base of the cone and (h) is the height of the cylinder.

The diameter of the cone is 4 units. Thus, the radius of the cone is,

\(r=\dfrac{4}{2}\\r=2\rm units\)

As the cone has a slant length of 5. Thus, the height of the cone is,

\(h=\sqrt{5^2-4^2}\\h=\sqrt{9}\\h=3 \rm units\)

Here, the height is 3 units and the radius 2 units long. Thus the volume of the cone is,

\(V=\dfrac{1}{3}\times3.14\times (2)^2\times3\\V=12.56\rm units^3\)

Hence, the volume of the cone which has slant length of 5 and a diameter of 4 is 12.56 cubic units.

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Answer and Step-by-step explanation:

The moment generating function (MGF) of a random variable X is a function that produces moments of X. For a uniformly distributed finite set {a, a+1, ..., b}, the MGF can be calculated as Mx(t) = (e^(at) + e^((a+1)t) + ... + e^(bt)) / (b-a+1). In this case, X is uniformly distributed on {4,5,6,7}, so the MGF of X is Mx(t) = (e^(4t) + e^(5t) + e^(6t) + e^(7t)) / 4.

The MGF of the sum of independent random variables X and Y is the product of their individual MGFs. Therefore, the MGF of X+Y can be calculated as MX+Y(t) = Mx(t) * My(t). Y is uniformly distributed on {18,19,20,...,26}, so its MGF can be calculated in a similar manner as Mx(t), resulting in My(t) = (e^(18t) + e^(19t) + ... + e^(26t)) / 9. Therefore, MX+Y(t) = ((e^(4t) + e^(5t) + e^(6t) + e^(7t)) / 4) * ((e^(18t) + e^(19t) + ... + e^(26t)) / 9).

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Answer:

1,5

Step-by-step explanation:

cuz it's part of the green

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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Answer:

(a)

Step-by-step explanation:

Note the expansion of (x - 5y)² is

(x - 5y)² = x² - 10xy + 25y² , that is

(x - 5y)² = x² + 25y² - 10xy ← substitute given values

(- 16)² = 416 - 10xy

256 = 416 - 10xy ( subtract 416 from both sides )

- 160 = - 10xy ( divide both sides by - 10 )

xy = 16 → (a)

Answer:

Isolate the variable by dividing each side by factors that don't contain the variable.

Inequality Form:

p>15

Interval Notation:

(15,∞)

:)

The response is: Median = 5 and Mean = 6. The mean is a more accurate way to assess central tendency.

Finding the data set's mean and median will be our first step.

The average of the set is all that the mean is, and it will be

Mean = 5+0+5+2+0+10+7+8+10+21+5+8+2+5+3+5 / 16 \s= 96/16 \s= 6

As a result, the median is 5

We must evaluate the skewness of each metric to determine which is the superior one.

1.51 is the skew value.

It is therefore positively biased.

Thus If the distribution is positively skewed, the mean will be higher than both the median and the mode. Consequently, the response is Mean = 6, Median = 5. The mean is a more accurate way to assess central tendency.

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The domain of  f(x , y) = √(y - x²) / (1 - x²) is

D ∈ [0, 1).

The limit of a function in mathematics is a key idea in calculus and analysis regarding the behavior of that function close to a specific input.

Informally, a function f gives each input x an output f(x). If f(x) approaches L as x approaches input p, we say that the function has a limit L at that location. More specifically, any input that is sufficiently close to p when f is applied forces the output value arbitrarily close to L.

The concept of limit is specifically used in the various definitions of continuity. Roughly speaking, a function is continuous if all of its limits agree with the values of the function. The term "limit" is also used in the definition of the mathematical term "derivative," which in one-variable calculus refers to the maximum value of the slope of secant lines on a function's graph.

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Answer:

Y= -2/5X

Step-by-step explanation:

the equation is y=mx + b

slope: -2/5x

y- intercept: 0

all you do is combined your slope and y-intercept together: Y= -2/5X , you dont need to add +0 because it gonna just still be the same as y= - 2/5x

Y= -2/5X or y= -2/5x + 0 is the same so it can be any of these 2 that you pick but the correct way is y= -2/5x

When both groups are shifted to a situation in which they earn an alternative reward after being trained to navigate a runway for food, the group that received three food pellets will continue to perform the task at a high level while the group that received one food pellet will experience difficulty.

It is known that rats have a natural preference for higher rewards. As a result, the group that received three pellets will be more motivated to complete the task since they have already tasted a higher reward. Therefore, they will continue to perform at a high level in the new environment.

On the other hand, the group that received only one pellet may find it challenging to adapt to the new situation since they are now receiving a lower reward. As a result, they may struggle to complete the task, and their performance may decrease.

In conclusion, the group that received three pellets will perform better than the group that received one pellet when both groups are shifted to a situation in which they earn an alternative reward. This is because the rats have a natural preference for higher rewards.

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Answer:

a) Braxton's initial investment is equals to (=) Pam's initial investment.

b)The interest on Braxton's account is less than (< ) the interest on Pam's

   account.  

Step-by-step explanation:

Given - Braxton has money in a savings account. The equation

            B = \(800(1 + 0.03)^{t}\) can be used to calculate the amount of money    

            in dollars, B, Braxton has in his account after t years since opening

             the account.  Pam also has money in a savings account. The  

            equation, P= \(800(1 + 0.04)^{t}\)  can be used to calculate the  amount of  

             money in dollars, P, Pam has in her account after t years since  

              opening the account.      

To find - a) Braxton's initial investment ..........Pam's initial investment.

                b) The interest on Braxton's account .....the interest on Pam's

                    account.

Proof -

As given, Broxton equation is -  

                 Pam equation is -    

Now,

a.)

For initial investment , Put t = 0

⇒B = \(800(1 + 0.03)^{0} = 800(1) = 800\)  

   P =  \(800(1 + 0.04)^{0} = 800(1) = 800\)  

We can see that for  t = 0

Initial investment of Braxton = Initial investment of Pam

⇒Braxton's Initial investment = Pam's initial investment.

b.)

For the interest,

As we have not given any time period for which the interest has to be find.  

So , let the time period , t = 5 years

Therefore,

B = \(800(1 + 0.03)^{5} = 800(1.03)^{5} = 800(1.159) = 927.42\)  

P = \(800(1 + 0.04)^{5} = 800(1.04)^{5} = 800(1.217) = 973.32\)

Now,

Interest on Braxton's account = 927.42 - 800 = 127.42 ≈ 127

Interest on Pam's account = 973.32 - 800 = 173.32 ≈ 173

∴ we get

The interest on Braxton's account is less than the interest on Pam's account.

Here we have a program written in C++ language. Each // symbol is a relative comment explaining the reason for each command line (and is not included during the program execution).

The Program:

#include <iostream>

//c++ build in library

using namespace std;

//main code body starts here

int main()

{

 //declare variable to store phone numbers,its area code, prefix and line    number.

long pnumber;   //declare long variable

int ac, prefix, lnumber;

 //declare integer variables, where ac: Area Code and lnumber is the Line Number

cout<<"Enter a 10-digit Phone Number: "<<endl;

 //cout command prints on screen the desired message

 cin>>pnumber;

 //cin command enables the user to interact with the programm and enter information manually

//main body to obtain the desired output starts below

 //each 'division' is used to allocate the correct value at the correct

 //since prefix is used to get the desired output of ( )    -

 ac = pnumber/10000000;

 prefix = (pnumber/10000)%1000;

 lnumber = pnumber%10000;

 //main body ends here

 cout<<"Based on your 10-digit number"<<endl;

 cout<<"below you have (AreaCode), Prefix, and - line number "<<endl;

 cout<<"("<<ac<<")"<<""<<prefix<<"-"<<lnumber<<endl;

 //Prints on screen the desired output of the long 10 digit Number

 return 0; //ends program

}

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

The Output Sample:

Enter a 10-digit Phone Number:

8019004673

Based on your 10-digit number

below you have (Area Code), Prefix, and - line number

(801) 900-4673

....Programm finished with exit code 0

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The System Effectiveness is approximately 0.763.

To calculate the System Effectiveness, we need to multiply the values of Operational Readiness, Design Adequacy, Availability, Maintainability, and Mission Reliability.

System Effectiveness = Operational Readiness * Design Adequacy * Availability * Maintainability * Mission Reliability

Plugging in the given values:

System Effectiveness = 0.89 * 0.95 * 0.98 * 0.93 * 0.99

System Effectiveness ≈ 0.763

Therefore, the System Effectiveness is approximately 0.763.

The correct answer is a. 0.763.

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Answer

Use the fact that 45 times 1/9 = 5. Them multiply by 8 to get the answer, 40.

Step-by-step explanation:

The measure of the angles C and D are 60° and 190° respectively.

A quadrilateral is a closed object in geometry that is created by connecting four points, any three of which are not collinear. There are 4 sides, 4 angles, and 4 vertices in a quadrilateral.

From the given information the measure of angle c will be,

= [90° - (1/2)m∠A].

= [90° - 30°].

= 60°.

And we know the sum of all the interior angles in a quadrilateral is 360°.

Therefore, The measure of ∠D = 360° - (60° + 50° + 60°).

m∠D = 360° - 170°.

m∠D = 190°.

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The general solution of the given differential equation dy/dx = sin(9x)y is y = Ce^(1-cos(9x))/9, where C is the constant of integration.

This solution is obtained by integrating the given equation with respect to x and applying the initial condition. The integration involves using the chain rule and integrating the trigonometric function sin(9x). The constant C accounts for the family of solutions that satisfy the given differential equation. The exponential term e^(1-cos(9x))/9 indicates the growth or decay of the solution as x varies. Overall, the solution provides a mathematical expression that describes the relationship between y and x in the given differential equation.

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Answer:

x = 2

Step-by-step explanation:

Answer:

so the answer for the question is 1/4

Answer:

16 brainlist pls

Step-by-step explanation:

The area of ​​the rectangle will grow at a rate of 100 square inches per second if the width of the rectangle is 10 inches.

let the width w  of the rectangle is 1 inch and the length of the rectangle is "2w" inches.

The area of ​​the rectangle is given by

A = length x width = (2w)(w) =\(2w^2\) square inches if the width of the rectangle is 10 inches

To find out how fast the area of ​​a rectangle is changing, we need to differentiate the area over time.

dA/dt =\(d/dt (2w^2)\) = 4w(dw/dt)

where dw/dt is the rate of change in width.

as the length of the rectangle is increasing at a rate of 5 inches/second.

d(2w)/dt = 5 inches/second

Simplifying the above formula to:

2(dw/dt) = 5 inches/second

dw/dt = 5/2 inch/second

If the rectangle is 10 inches wide, then:

w = 10 inches

dw/dt = 5/2 inch/second

Substitute these values ​​into the formula for dA/dt.

dA/dt = 4w(dw/dt) = 4(10)(5/2) = 100 square inches per second

therefore, if the width of the rectangle is 10 inches, the area of ​​the rectangle will grow at a rate of 100 square inches per second. 

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Answer:

Hello! answer: 65

Step-by-step explanation:

This is a supplementary angle meaning it will add up to 180 degrees therefore... 180 - 115 = 65 therefore x = 65 hope that helps!

Answer:

x=65°

Step-by-step explanation:

180°= x + 115°

x = 180 - 115

x = 65°